Commission for Climatology (CCl) Expert Team on Climate Risk and ...... Warwick. -28.2061. 152.1003. 213. 17. 41529. Toowoomba Airport. -27.5425. 151.9134.
ADAPTATION OF WATER SENSITIVE URBAN DESIGN TO CLIMATE CHANGE
ASHIQ M. RASHEED
B.Sc (Civil Engineering, Honours)
A thesis submitted in fulfilment of the requirement of the degree of Doctor of Philosophy Science and Engineering Faculty Queensland University of Technology
2018
This thesis is dedicated to my beloved parents, Ayna & Abdul Rasheed for their unconditional love, support and encouragement throughout.
You raise me up, so I can stand on mountains You raise me up to walk on stormy seas I am strong when I am on your shoulders You raise me up to more than I can be - Brendan Graham -
Abstract Water Sensitive Urban Design (WSUD) is the stormwater management philosophy adopted in Australia to manage stormwater quality and quantity to minimise the impacts of urban developments on the surrounding environment. However, the treatment systems adopted in WSUD along with the stormwater quality estimation are typically designed considering static climate conditions. Changing climate in future scenarios including changes to rainfall patterns and characteristics of rainfall can reduce the effectiveness of such WSUD systems. However, there is not a robust methodology available to support the adaptation of WSUD to climate change. This is primarily due to lack of future climate data for frequent rainfall events at the small catchment scale. However, there is no appropriate methodology available for downscaling or generating such high-resolution rainfall data. In this research, methodologies were developed to generate high-resolution rainfall data for future climate change scenarios and impacts of climate change on the stormwater quality and quantities were assessed using the generated rainfall data. The research was undertaken taking southeast Queensland, Australia as the study area. Accordingly, a detailed analysis was carried out to test the rainfall homogeneity within the region so that representative meteorological stations can be selected. Long-term rainfall data sets were obtained for representative meteorological stations to facilitate the analysis. Two separate statistical downscaling models were developed to spatially and temporally downscale rainfall data from two GCMs, EC-EARTH and ACCESS 1.0 for two climate change scenarios, RCP 4.5 and RCP 8.5. The downscaled data were then used to assess the impacts of climate change on the stormwater quality and quantities. The impact assessment included at-site frequency analysis to generate Intensity-Frequency-Duration (IFD) curves and estimation of stormwater quality for the future climate change scenarios. The analysis undertaken to evaluate the degree of rainfall homogeneity suggested that the entire southeast Queensland can be treated as homogeneous region based on the characteristics of the continuous rainfall. However, based on individual rainfall characteristics such as antecedent dry-days, maximum rainfall intensities, total rainfall and duration of the rainfall events, there were two separate homogeneous regions identified, namely, Coastal-SEQ and Inland-SEQ. Thereby, Gold Coast Seaway station (40764) and Toowoomba Airport stations (41529) were selected to represent the Coastal-SEQ and Inland-SEQ respectively. A new spatial downscaling tool, ‘spdownscale’ was developed based on quantile-quantile bias correction approach. This tool was used to spatially downscale rainfall data for I
future climate change scenarios at the two representative meteorological stations for southeast Queensland. Overall, the models developed by the spdownscale for spatial downscaling performed well for both GCMs. Two statistical indexes, RMSE and the gradient of observation-simulation scatter plots were used for the validation purposes. The bias-corrected GCM outputs from both the GCMs were closely comparable to the observed data. A new temporal downscaling model was developed based on first-order homogeneous Markov model to translate the 3-hour rainfall time-series into 5-minute time-series. This model was used to temporally downscale the bias-corrected (spatially downscaled) rainfall data at the two representative meteorological stations for southeast Queensland. The model performance was assessed based on an independent historical rainfall dataset. Overall, the simulated rainfall was in agreement with the observed rainfall in terms of the probability distribution and the maximum rainfall intensities at both representative meteorological stations. IFD curves generated using at-site frequency analysis for future climate change scenarios. Overall, there was a significant increase in the IFDs for the future climate change scenarios compared to the present IFD provided by the Bureau of Meteorology (BoM). In general, smaller duration frequent rainfall and the longer duration infrequent rainfalls were expected to increase significantly in both climate change scenarios. On average, the IFDs for the Coastal-SEQ were expected to increase by 23-30% in the near future and 38-45% distant future. The IFDs for the Inland-SEQ were expected to increase by 5-15% in the near future and 37-38% in the distance future. Based on the estimated changes in the design rainfall, this research suggests an approach to estimate the design flow rates in the design of WSUD treatment system by introducing a climate change factor Cf into the Rational Method procedure. The values for the Cf for southeast Queensland is also presented and proposed to be incorporated into the city council guidelines for WSUD in order to adapt the impacts of climate change in the design of WSUD. A stormwater quality model was developed to estimate the Event Mean Concentration (EMC) of the Total Suspended Solids (TSS) generated from urban residential catchments for future climate change scenarios. The model was designed to automatically extract all independent rainfall events from a given rainfall time-series and simulate water quality parameters based on event-based rainfall characteristics. Overall, the pollutant export showed a varying pattern in the future climate change scenario. In Coastal-SEQ, the median pollutant export was expected to increase by 15% and 9% for RCP 4.5 (2026-2045) and RCP 4.5 (2081-2100), whereas, the median pollutant export was expected to decrease by 10% and 2% for RCP 8.5 (2026-2045) and RCP 8.5 (2081-2100).In Inland-SEQ, the median pollutant export was expected to decrease by 13%, 21% and 13% for RCP 4.5 (2026-2045), RCP 8.5 (2026-2045) and II
RCP 8.5 (2081-2100) respectively and a slight increase of 1% for RCP 4.5 (2081-2100). However, the rainfall runoff was estimated to increase significantly and thus resulting in significantly low pollutant concentrations in the future stormwater runoffs. The ensemble median of the EMC showed a decrease of 50%, 53%, 48% and 47% for RCP 4.5 (2026-2045), RCP 4.5 (2081-2100), RCP 8. 5 (2026-2045) and RCP 8.5 (2081-2100) climate change scenarios respectively in Coastal-SEQ and the ensemble median of the EMC showed a decrease of 38%, 48%, 44% and 43% for RCP 4.5 (2026-2045), RCP 4.5 (2081-2100), RCP 8.5 (2026-2045) and RCP 8.5 (2081-2100) climate change scenarios respectively in Inland-SEQ. Based on these results a set of new water quality parameters for future climate change scenarios were developed and proposed to be incorporated into the Model for Urban Stormwater Improvement Conceptualisation (MUSIC) guidelines of the southeast Queensland in order to adapt the impacts of climate change in the design of WSUD treatment systems.
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Keywords Water Sensitive Urban Design, pollutant process, stormwater quality, climate change, downscaling.
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List of publications Rasheed AM, Egodawatta P, Goonetilleke A and McGree J (2017), spdownscale: Spatial Downscaling
Using
Bias
Correction
Approach,
R
package
version
0.1.0.
https://CRAN.R-project.org/package=spdownscale
Rasheed AM, Egodawatta P, Goonetilleke A and McGree J (2017), ‘spdownscale’ A Spatial Downscaling Tool Based on Bias Correction Approach, 7th IWA-ASPIRE Conference 2017 & Water Malaysia Exhibition 2017.
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Statement of Authorship The work contained in this thesis has not been previously submitted to meet requirements for an award at this or any other higher education institution. To the best of my knowledge and belief, the thesis contains no material previously published or written by another person except where due reference is made.
QUT Verified Signature
Ashiq M. Rasheed November 2018
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Acknowledgements I wish to express my sincere gratitude to my principal supervisor Dr. Prasanna Egodawatta for his guidance, support and accomplished academic supervision. My appreciation is further extended to my associate supervisors Prof. Ashantha Goonetilleke and A/Prof. James McGree for their valuable expert advice and guidance during the candidature. I would like to express my appreciation to the High-Performance Computing and Advanced Research Computing Group of QUT, particularly to Mr. Abdul Sharif for the HPC training and support provided. I also greatly acknowledge the timely support received from the IT helpdesk team of QUT. I would like to acknowledge the support from Bureau of Meteorology, Australia for their support in the data collection for the research. A special thanks to Ms. Tamika Tihema for her support and advice. I am also grateful to the Program for Climate Model Diagnosis and Intercomparison (PCMDI) for providing CMIP5 GCM data for this research. A special thanks to Prof. Ashish Sharma for his support and feedbacks given to improve the research methodology. Finally, I like to express my gratitude to my siblings and friends for their encouragement and unconditional love.
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Table of Content Chapter 1 Introduction ..................................................................................... 1 1.1 Background ......................................................................................................... 1 1.2 Research problem ................................................................................................ 2 1.3 Aims and objectives ............................................................................................ 3 1.4 Justification for the research ............................................................................... 3 1.5 Description of the research .................................................................................. 4 1.6 Scope ................................................................................................................... 5 1.7 Outline of the thesis ............................................................................................ 6 Chapter 2 Water Sensitive Urban Design ........................................................... 7 2.1 Background ......................................................................................................... 7 2.2 The concept of Water Sensitive Urban Design.................................................... 8 2.2.1 Non-structural measures ............................................................................... 9 2.2.2 Structural Measures ....................................................................................10 2.3 WSUD treatment systems and their treatment and hydraulic design................13 2.3.1 Swale ...........................................................................................................13 2.3.2 Bioretention basin .......................................................................................14 2.3.3 Constructed wetlands ..................................................................................16 2.4 Stormwater pollutants........................................................................................19 2.4.1 Nutrients .....................................................................................................19 2.4.2 Organic Carbon ...........................................................................................20 2.4.3 Heavy Metals...............................................................................................20 2.4.4 Hydrocarbons ..............................................................................................20 2.4.5 Suspended Solids .........................................................................................21 2.5 Pollutant process ................................................................................................22 2.5.1 Pollutant build-up .......................................................................................22 2.5.2 Pollutant wash-off .......................................................................................24 XIII
2.6 Stormwater quality modelling ........................................................................... 27 2.6.1 Hydrological modelling ............................................................................... 27 2.6.2 Water quality modelling ............................................................................. 28 2.7 Conclusions........................................................................................................ 30 Chapter 3 Climate Change and Downscaling ................................................... 33 3.1 Background ....................................................................................................... 33 3.2 Climate change .................................................................................................. 34 3.3 Emission scenarios ............................................................................................. 35 3.4 Global Circulation Models................................................................................. 40 3.5 Downscaling ...................................................................................................... 45 3.5.1 Comparison of statistical and dynamic downscaling methods .................... 46 3.5.2 Statistical downscaling ............................................................................... 48 3.5.3 Components of a statistical downscaling scheme ........................................ 51 3.5.4 Statistical downscaling tools ....................................................................... 53 3.6. Uncertainties in climate change projections ..................................................... 54 3.7 Conclusions........................................................................................................ 56 Chapter 4 Research Design and Methods ......................................................... 59 4.1 Background ....................................................................................................... 59 4.2 Research design ................................................................................................. 60 4.2.1 Critical review of literature ........................................................................ 62 4.2.2 Selection of study area, study tools and analytical methods ...................... 62 4.2.3 Data collection............................................................................................ 62 4.2.4 Modelling and analysis ............................................................................... 63 4.3 Study tools ........................................................................................................ 65 4.3.1 Programming platform ............................................................................... 65 4.3.2 Climate data operators ............................................................................... 67 4.4 Analytical methods............................................................................................ 68 4.4.1 Homogeneous Analysis ............................................................................... 68 4.4.2 Spatial Downscaling ................................................................................... 74 XIV
4.4.3 Markov model .............................................................................................77 4.4.4 Rainfall frequency analysis ..........................................................................79 4.4.5 Stormwater quality modelling .....................................................................81 4.4.6 Classical univariate data analysis ................................................................84 4.5 Conclusions ........................................................................................................85 Chapter 5 Selection of Representative Meteorological Stations for Downscaling 87 5.1 Background ........................................................................................................87 5.2 Study area and data collection ...........................................................................88 5.2.1 Study area ...................................................................................................88 5.2.2 Data collection ............................................................................................89 5.3 Assessment of rainfall homogeneity in southeast Queensland ............................90 5.3.1 Continuous-rainfall approach ......................................................................91 5.3.2 Event-based rainfall approach .....................................................................92 5.4 Boundaries and representative meteorological station of the homogeneous regions ......................................................................................................................98 5.4.1 Rainfall homogeneous regions within southeast Queensland .......................98 5.4.2 Representative meteorological stations for southeast Queensland ............. 100 5.5 Conclusions ...................................................................................................... 101 Chapter 6 Spatial Downscaling of Rainfall Data Using Bias Correction Method .................................................................................................................... 103 6.1 Background ...................................................................................................... 103 6.2 Development of the spatial downscaling tool ................................................... 104 6.2.1 Downscaling method ................................................................................. 104 6.2.2 Architecture of the downscaling tool ......................................................... 105 6.2.3 Functions of spdownscale .......................................................................... 111 6.4 Spatial downscaling of rainfall data for southeast Queensland (SEQ) ............. 113 6.4.1 Spatial downscaling for Coastal-SEQ ........................................................ 113 6.4.2 Spatial downscaling for Inland-SEQ .......................................................... 119 6.4 Conclusions ...................................................................................................... 122 XV
Chapter 7 Temporal Downscaling of Rainfall Data Using First-order Markov Model ........................................................................................................... 123 7.1 Background ......................................................................................................123 7.2 First-order homogeneous Markov model ..........................................................124 7.2.2 Assumptions used in the model .................................................................124 7.2.3 Architecture of the model ..........................................................................125 7.3 Temporal downscaling for southeast Queensland .............................................127 7.3.1 Calibration .................................................................................................128 7.3.2 Validation ..................................................................................................128 7.3.3 Future rainfall generation ..........................................................................135 7.4 Conclusions.......................................................................................................135 Chapter 8 Design Rainfall for Future Climate Change Scenarios ..................... 137 8.1 Background ......................................................................................................137 8.2 Rainfall frequency analysis ...............................................................................138 8.2.1 IFD generation for the historical data .......................................................140 8.2.2 IFD generation for future climate change scenarios ..................................144 8.3 Adaptation of WSUD to changes in the future IFDs .......................................158 8.4 Conclusions.......................................................................................................161 Chapter 9 Impact of Climate Change on Pollutant Export and Stormwater Quality ......................................................................................................... 163 9.1 Background ......................................................................................................163 9.2 Model setup ......................................................................................................164 9.2.1 Catchment .................................................................................................166 9.3.1 Event separations ......................................................................................167 9.3.2 Pollutant process modelling .......................................................................167 9.3.3 Runoff modelling .......................................................................................169 9.3 Impacts of climate change on pollutant process ...............................................170 9.3.1 Changes in pollutant processes in the Coastal-SEQ ..................................171 9.3.2 Changes in pollutant process in the Inland-SEQ .......................................175 XVI
9.4 Impacts of climate change on water quality ..................................................... 179 9.4.1 Changes in stormwater quality in the Coastal-SEQ .................................. 179 9.4.2 Changes in stormwater quality in the Inland-SEQ.................................... 180 9.5 Water quality parameters for MUSIC modelling ............................................. 182 9.7 Conclusions ...................................................................................................... 187 Chapter 10 Conclusions and Recommendations .............................................. 189 10.1 Conclusions..................................................................................................... 189 10.1.1 Event-based rainfall homogeneity assessment for southeast Queensland . 190 10.1.2 Downscaling of rainfall data .................................................................... 191 10.1.3 Design rainfall for future climate change scenarios.................................. 192 10.1.4 Stormwater quality and quantity characteristics in the future climate change scenarios ............................................................................................................. 193 10.2 Recommendations........................................................................................... 195 References .................................................................................................... 197 Appendix A .................................................................................................. 223 Appendix B .................................................................................................. 225 B.1: Source code for ParaCal() function of spdownscale .................................... 225 B.2: Source code for ResVal() function of spdownscale ...................................... 227 B.3: Source code for downscale() function of spdownscale ................................. 232 Appendix C .................................................................................................. 235 C1: Example of First-order Markov process....................................................... 235 C2: Sample source code for temporal downscaling (station: 40476, GCM: ACCESS 1.0, RCP: RCP 4.5, period: 20206-2045) ............................................................ 237 Appendix D .................................................................................................. 245 Appendix E .................................................................................................. 253
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List of Figures Figure 2.1: Incorporation of BPPs and BMPs in WSUD (adapted and reproduced from Whelans et al. 1994; Mangangka, 2013)........................................................................ 9 Figure 2.2: Typical stormwater treatment systems, target pollutant size and hydraulic loading (Adapted and reproduced from Wong et al., 2000) .........................................12 Figure 2.3: Vegetated swales ........................................................................................14 Figure 2.4: Typical cross section of a bioretention system (Adapted and reproduced from BCC & MWB, 2006)....................................................................................................15 Figure 2.5: Typical section of a constructed wetland (Adapted and reproduced from VSC, 1999) ...................................................................................................................17 Figure 2.6: Conceptual chain of pollutant process (adapted and reproduced from Goonetilleke et al., 2014) .............................................................................................22 Figure 2.7: Pollutant build-up in different land uses (adapted from Sartor et al., 1974) .....................................................................................................................................23 Figure 2.8: Hypothetical representations of surface pollutant load over time (Adapted and reproduced from Vaze and Chiew, 2002) ..............................................................26 Figure 2.9: Hydrological process (adapted from O’Loughlin and Stacks, 2004) ...........28 Figure 3.1: (a) CO2 emission (b) cumulative CO2 emission for SRES storyline from 1990 to 2100 (adapted from IPCC (2000) and reproduced) .................................................37 Figure 3.2: (a) Radiative forcing (b) Corresponding CO2 emission pathways for RCPs (adapted and reproduced from van-Vuuren et al. (2011)) ...........................................39 Figure 3.3: Average (1986-2005) rainfall simulations from CMIP5 models for (a) summer and (b) winter (Adapted from CCIA (2015)). The regions are from the NRM cluster (see NRM cluster - see chapter 3, CCIA (2015)). ........................................................43 Figure 3.4: The average annual cycle of rainfall for Australia (Regions: AUS-Australia, EA- East Australia, NA- North Australia, R-Rangelands, SA – South Australia and SS- Southern Slopes) (Adapted from CCIA (2015)) ....................................................44 Figure 3.5: Component of statistical downscaling (Adapted from Diaz-Nieto and Wilby (2005) and Wilby et al. (2004)) ...................................................................................52 Figure 4.1: Steps of the research design .......................................................................61 XIX
Figure 4.2: Modelling and analysis .............................................................................. 64 Figure 4.3: Basic algorithm of a K-means cluster analysis .......................................... 70 Figure 4.4: Basic algorithm of an agglomerative hierarchical cluster analysis............. 71 Figure 4.5: Graphical definitions of cluster proximity ................................................. 72 Figure 4.6: Definition sketch for heterogeneity (Adapted from Hosking and Wallis (1997))......................................................................................................................... 73 Figure 4.7: Probability parameters for at-site frequency analysis ............................... 80 Figure 5.1: Southeast Queensland ............................................................................... 88 Figure 5.2: The locations of the selected meteorological stations ................................ 90 Figure 5.3: Dendrogram generated from the cluster analysis ...................................... 95 Figure 5.4: Geographical locations of the meteorological stations and their grouping 96 Figure 5.5: Scatterplots of the event-based rainfall characteristics (Red dots refer to the stations of Cluster 1, Black dots refer to the stations of - Cluster 2 and Green dots refer to the stations of Cluster 3) ........................................................................................ 97 Figure 5.6: Boundaries of Coastal-SEQ and Inland-SEQ rainfall homogeneous regions .................................................................................................................................... 99 Figure 6.1: Architecture of downscaling tool ..............................................................106 Figure 6.2: Developing the statistical model for bias correction. (a) Mapping zero rainfall; (b) The Polynomial relationship between the threshold values of the observed data and GCM data. Three points have been used for the curve – red dot is found using the calibration data and the black dots refer to the lowest (0) and the largest (1) possible values; (c) Mapping non-zero rainfall. ........................................................................109 Figure 6.3: Calibration parameters for EC-EARTH (Gold Coast Seaway) ................114 Figure 6.4: Calibration parameters for ACCESS 1.0 (Gold Coast Seaway) ...............115 Figure 6.5: Validation results for EC-EARTH (Gold Coast Seaway) ........................117 Figure 6.6: Validation results for ACCESS 1.0 (Gold Coast Seaway) .......................118 Figure 6.7: Calibration results for EC-EARTH (Toowoomba Airport) ......................120 Figure 6.8: Validation results for EC-EARTH (Toowoomba Airport) .......................121 Figure 7.1: Flow diagram of the model process ..........................................................126 Figure 7.2: Validation outputs of the cumulative probability distribution ................129 Figure 7.3: Temporal patterns for rainfall data over 3-hour periods ..........................132 XX
Figure 7.4: Validation outputs of maximum rainfall intensities. (a) Gold Coast Seaway station and (b) Toowoomba Airport station .............................................................. 133 Figure 7.5: Validation outputs of 3-hour total rainfall. (a) Gold Coast Seaway station and (b) Toowoomba Airport station .......................................................................... 134 Figure 8.1: IFD relationship curves for the Gold Coast Seaway station. The broken lines show the curves generated using the at-site frequency analysis and the solid lines are that from BoM ........................................................................................................... 142 Figure 8.2: IFD relationship curves for the Toowoomba Airport station. The broken lines show the curves generated using the at-site frequency analysis and the solid lines are that from BoM ..................................................................................................... 143 Figure 8.3: IFD curves for Gold Coast Seaway station (40764) for RCP 4.5 climate change scenario for the period 2026-2045. The broken-lines denote the values of realizations (10 for each ARI) and solid lines denote the mean of the realizations .... 145 Figure 8.4: IFD curves for Gold Coast Seaway station (40764) for RCP 4.5 climate change scenario for the period 2081-2100. The broken-lines denote the values of realizations (10 for each ARI) and solid lines denote the mean of the realizations .... 146 Figure 8.5: IFD curves for Gold Coast Seaway station (40764) for RCP 8.5 climate change scenario for the period 2026-2045. The broken-lines denote the values of realizations (10 for each ARI) and solid lines denote the mean of the realizations .... 147 Figure 8.6: IFD curves for Gold Coast Seaway station (40764) for RCP 8.5 climate change scenario for the period 2081-2100. The broken-lines denote the values of realizations (10 for each ARI) and solid lines denote the mean of the realizations .... 148 Figure 8.7: IFD curves for Toowoomba Airport (41529) for RCP 4.5 climate change scenario for the period 2026-2045. The broken-lines denote the values of realizations (10 for each ARI) and solid lines denote the mean of the realizations ............................. 149 Figure 8.8: IFD curves for Toowoomba Airport (41529) for RCP 4.5 climate change scenario for the period 2081-2100. The broken-lines denote the values of realizations (10 for each ARI) and solid lines denote the mean of the realizations ............................. 150 Figure 8.9: IFD curves for Toowoomba Airport (41529) for RCP 8.5 climate change scenario for the period 2026-2045. The broken-lines denote the values of realizations (10 for each ARI) and solid lines denote the mean of the realizations ............................. 151 Figure 8.10: IFD curves for Toowoomba Airport (41529) for RCP 8.5 climate change scenario for the period 2081-2100. The broken-lines denote the values of realizations (10 for each ARI) and solid lines denote the mean of the realizations ............................. 152 XXI
Figure 9.1: Processes associated with the stormwater quality model .........................165 Figure 9.2: Conceptual catchment .............................................................................166 Figure 9.3: Probability distribution of the pollutant exports (Coastal-SEQ) .............174 Figure 9.4: Probability distribution of the pollutant exports (Inland-SEQ)...............178 Figure 9.5: Water quality parameters ........................................................................182 Figure 9.6: EMC for future climate change scenarios for Coastal-SEQ. The dotted lines denote the actual distribution of the data and the solid lines donate the log-normal distribution fitted data (based on the mean and standard deviation)........................184 Figure 9.7: EMC for future climate change scenarios for Inland-SEQ. Note: The dotted lines denote the actual distribution of the data and the solid lines donate the log-normal distribution fitted data (based on the mean and standard deviation)........................185
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List of Tables Table 2.1: Models for pollutant build-up .....................................................................24 Table 2.2: Wash-off capacity factors for different rainfall intensities (Adapted from Egodawatta, 2007) .......................................................................................................25 Table 3.1: Main characteristics of the four SRES storylines (adapted and reproduced from IPCC (2000)) .......................................................................................................36 Table 3.2: List of GCM of CMIP5 and their resolutions (Adapted from IPCC (2014) and CCIA (2015)) ........................................................................................................41 Table 3.3: Strengths and weaknesses of statistical and dynamical downscaling (Adapted from Wilby and Dawson (2004), Ahmed et al. (2013), Schmidli et al. (2007), Jaw et al. (2015) and Mearns et al. (1999)) .................................................................................47 Table 4.1: Comparison of R and Matlab against the selection criteria ........................66 Table 4.2: Comparison of R and Matlab against the selection criteria ........................67 Table 4.3: Equations for capacity factors.....................................................................83 Table 4.4: Summary of the comparison of Mike Urban, MUSIC and XP-SWMM models with the selection criteria.............................................................................................83 Table 5.1: Dispersion indexes based on event-based rainfall approach for southeast Queensland...................................................................................................................93 Table 5.2: Data matrix for the cluster analysis............................................................94 Table 5.3: Dispersion indexes for Hosking and Wallis heterogeneity test for CoastalSEQ and Inland-SEQ ...................................................................................................98 Table 5.4: Local government bodies included in the identified homogeneous regions ..99 Table 6.1: Descriptions of the functions and datasets in spdownscale ....................... 111 Table 6.2: A summary of calibration and validation periods used for the downscaling ................................................................................................................................... 114 Table 7.1: A summary of calibration and validation periods used for the temporal downscaling ................................................................................................................ 128 Table 8.1: Return periods and the corresponding frequency factors for EV-I distribution ................................................................................................................................... 140 Table 8.2: IFDs generated using at-site frequency analysis for station 40764 ............ 141 XXIII
Table 8.3: IFDs generated using at-site frequency analysis for station 41529 ............141 Table 8.4: Change factors for IFDs for Coastal-SEQ for RCP 4.5 (2026-2045) .........154 Table 8.5: Change factors for IFDs for Coastal-SEQ for RCP 4.5 (2081-2100) .........154 Table 8.6: Change factors for IFDs for Coastal-SEQ for RCP 8.5 (2026-2045) .........154 Table 8.7: Change factors for IFDs for Coastal-SEQ for RCP 8.5 (2081-2100) .........155 Table 8.8: Change factors for IFDs for Inland-SEQ for RCP 4.5 (2026-2045) ...........155 Table 8.9: Change factors for IFDs for Inland-SEQ for RCP 4.5 (2081-2100) ...........155 Table 8.10: Change factors for IFDs for Inland-SEQ for RCP 8.5 (2026-2045) .........156 Table 8.11: Change factors for IFDs for Inland-SEQ for RCP 8.5 (2081-2100) .........156 Table 8.12: Comparison of the percentages increase in the IFDs suggested by this research and interim climate change guideline of the AR&R for SEQ.......................157 Table 8.13: summary of the treatment and hydraulic design aspects of WSUD systems (BCC & MBW (2006) and GCCC (2005)).................................................................159 Table 8.14: Proposed change factors for southeast Queensland (2026-2045)..............160 Table 8.15: Proposed change factors for southeast Queensland .................................162 Table 9.1: Equations for capacity factors ...................................................................169 Table 9.2: Pollutant build-up and pollutant wash-off (Gold Coast Seaway station) .171 Table 9.3: Estimated changes in antecedent dry-days for future climate change scenarios (Coastal-SEQ) ............................................................................................................172 Table 9.4: Estimated changes in maximum rainfall intensities for future climate change scenarios (Coastal-SEQ) .............................................................................................172 Table 9.5: Pollutant build-up and pollutant wash-off (41529) ...................................175 Table 9.6: Estimated changes in antecedent dry-days for future climate change scenarios (Inland-SEQ)..............................................................................................................176 Table 9.7: Estimated changes in maximum rainfall intensities for future climate change scenarios (Inland-SEQ) ..............................................................................................176 Table 9.8: Estimated changes in EMCs for future climate change scenarios (CoastalSEQ) ..........................................................................................................................179 Table 9.9: Pollutant exports and the effective rainfall for the present and future climate change scenarios for Coastal-SEQ ..............................................................................180
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Table 9.10: Estimated changes in EMCs for future climate change scenarios (InlandSEQ) .......................................................................................................................... 180 Table 9.11: Pollutant exports and the effective rainfall for the present and future climate change scenarios for Inland-SEQ................................................................................ 181 Table 9.12: Comparison of EMCs from this study and MUSIC guideline for SEQ .... 183 Table 9.13: Water quality parameters for MUSIC modelling .................................... 186 Table 9.14: Proposed water quality parameters for MUSIC modelling to incorporate climate change ........................................................................................................... 188 Table 10.1: Proposed change factors for southeast Queensland ................................. 193 Table 10.2: Proposed water quality parameters for MUSIC modelling to incorporate climate change ........................................................................................................... 195
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Abbreviations AEP
Annual Exceedance Probability
ANN
Artificial Neural Network
AR&R
Australian Rainfall & Runoff
ARI
Average Recurrence Interval
BCC
Brisbane City Council
BMP
Best Management Practice
BoM
Bureau of Meteorology
BPP
Best Planning Practice
CA
Cluster Analysis
CCIA
Climate Change in Australia
CDF
Cumulative Density Function
CDO
Climate Data Operators
CF
Capacity Factor
Cf
Change Factor
CMIP
Coupled Model Intercomparison Project
CRAN
Comprehensive R Archive Network
CSIRO
Commonwealth Scientific and Industrial Research Organisation
CV
Coefficient of Variation
EMC
Event Mean Concentration
EV-I
Extreme Value Type 1 Distribution
EV-III
Extreme Value Type 3 Distribution
GCM
Global Climate Models/ Global Circulation Models
GPL
General Public Licence
GUI
Graphical User Interface XXVII
HMM
Homogeneous Markov Model
IFD
Intensity-Frequency-Duration
IPCC
Intergovernmental Panel on Climate Change
KNN
K-Nearest Neighbours
kT
Frequency Factor
MUSIC
Model for Urban Stormwater Improvement Conceptualisation
NHMM
Non-Homogeneous Markov Model
NRM
National Resource Management
PCA
Principal Component Analysis
PDF
Probability Density Function
QQ
Quantile-Quantile
QUDM
Queensland Urban Drainage Manual
RCM
Regional Climate Model
RCP
Representative Concentration Path
RMSE
Root Mean Square Error
SD
Standard Deviation
SDM BoM
Statistical Downscaling Models, Bureau of Meteorology
SDSM
Statistical DownScaling Model
SEQ
South East Queensland
SEQHWP
South East Queensland Healthy Waterways Partnership
SRES
Special Report on Emission Scenarios
SS
Suspended Solids
SSE
Sum of Square Error
TP
Total Phosphorous
TPM
Transition Probability Matrix
TSS
Total Suspended Solids
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WGCM - WCRP
Working Group on Coupled Modelling, World Climate Research Programme
WSUD
Water Sensitive Urban Design
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XXX
Chapter 1 Introduction 1.1 Background Stormwater quality is a critical concern and leads to detrimental effects on human and environmental health. Various pollutants generated by urban anthropogenic activities are deposited on urban surfaces and get washed off during storm events. These pollutants can be transported to receiving waters leading to quality degradation. The impacts on receiving water quality degradation include elevated toxicity, algal blooms and excessive sedimentation. Thus, implementing stormwater pollution mitigation strategies to improve the quality of receiving waters has become increasingly important. Water Sensitive Urban Design (WSUD) is the stormwater management philosophy adopted in Australia. The fundamental concept of the philosophy is to manage stormwater quality and quantity to minimise the impacts of urban developments on the surrounding environment (Lloyd et al., 2002). WSUD concepts have been developed to provide technically effective, economical and less environmentally damaging solutions for stormwater management. However, there are barriers to widespread implementation of WSUD philosophy. In this regard, the long-term viability of implemented WSUD systems is perceived with a high level of importance (Lloyd et al., 2002). The primary concern is that the treatment systems adopted in WSUD approach are typically designed considering current climate conditions. This fact is stem from the use of historical rainfall data series in stormwater quality modelling, which is an integral component of WSUD adoption. Changing climate in future scenarios including changes to rainfall patterns and characteristics of dry periods can reduce the effectiveness of such WSUD systems (Beecham and Chowdhury, 2012). Climate change would have a significant impact on the future stormwater quality and quantity, and thus the functionality of WSUD systems. Researchers are in agreement that future climate in Australia will feature more intense rainfall events and longer dry days due to global warming (IPCC, 2014; Abbs et al., 2007; Hughes, 2003, Holper, 1
2012). On the other hand, some other studies have noted drying trends in some regions of Australia, suggesting an increased number of dry days and a decrease in total annual rainfall (Holper, 2012).
1.2 Research problem The design and implementation of the WSUD are typically based on static climate conditions. In the design process, future changes in the rainfall characteristics and dry periods due to climate change are not taken into account appropriately. This is primarily due to the lack of future rainfall data at very fine temporal and spatial resolutions. Although many downscaling studies have been undertaken in recent years, those studies were seldom extended to a complete climate change impact assessments nor meet the resolution requirement of the impact assessment models. Thus, most climate change impact assessments were based on simple scaling of daily climate data that is consistent with global projections. For example, Burge at al. (2012) estimated the impact of climate change in the annual pollutant export in Mornington Peninsula Shrine based on a simple scaling of local climate that was roughly consistent with global projection. Similarly, the AR&R (2015) suggested interim climate change factors to adjust the current Intensity-Frequency-Duration (IFD) values for future were based on the regional temperature projections for Australia. However, these approaches are inherently subjected to many assumptions and simplifications and thus do not provide an accurate and robust assessment at the local or small catchment scale studies (Wilby et al., 2004). On the other hand, the changes in the rainfall patterns and characteristics of dry days will have potential adverse impacts on stormwater quality. The increase in dry days may result in more pollutants accumulated (build-up) on urban catchment surfaces. The increase in rainfall intensity can wash-off a higher fraction of build-up pollutants from catchment surfaces. Such changes can result in completely different pollutant loads and concentrations from urban catchments, requiring improved stormwater treatment devices compared to their designed characteristics (Ball et al., 1998; Egodawatta et al., 2007; Sartor et al., 1974). On the other hand, changes in the stormwater quantities due to climate change would impact the hydraulic aspects of the design of WSUD due to the potential changes in the magnitude and the frequency of the rainfalls events. Thus, the WSUD treatment systems may not meet the desired objectives in the future. Therefore, it is important to assess the impacts of climate change on the stormwater quality and quantity for an effective design and implementation of WSUD for the future. However, a robust methodology to support the adaptation of WSUD to climate change does not exist. This is primarily due to lack of predicted future climate data for frequent rainfall events at the small catchment scale. Moreover, there is no appropriate 2
methodology available for downscaling or generating such fine-scale rainfall data. The available downscaling methods and tools typically target monthly and daily climate variable for larger regions (for example, SDSM (Wilby and Dawson, 2004) and BoMSDM (Timbal and McAvaney, 2001)). Such downscaling methods do not support the design and implementation needs of WSUD, which are informed by frequent rainfall events at small catchment scales. Therefore, developing methodologies and tools to downscale rainfall data at fine temporal and spatial resolution and assessing the impacts of climate change on stormwater quality and quantity using those high-resolution rainfall data are essential in order to make informed decisions on adapting WSUD to climate change.
1.3 Aims and objectives The aim of this study was to develop methodologies to generate catchment scale rainfall data for future climate change scenarios and use the generated data to assess the impacts of climate change on the stormwater quality and quantity. The primary objectives of the research were to, 1. Develop a new approach to identify frequent event-based rainfall homogeneous regions thereby facilitating the selection of representative meteorological stations for detailed analysis. 2. Develop a methodology to spatially downscale Global Circulation Model (GCM) rainfall outputs to match the observation at small catchment scales. 3. Develop methodologies to temporally downscale rainfall time-series to finer temporal resolutions so that they can be used in event-based impact assessment models. 4. Develop the Intensity-Frequency-Duration relationships (IFD) for future climate change scenarios. 5. Assess the impacts of climate change on stormwater runoff and quality for different climate change scenarios.
1.4 Justification for the research Climate change is one of the most alarming problems that the world is currently facing. The evidence of climate change around the world is significant. According to the Intergovernmental Panel on Climate Change (IPCC), it is very likely that the hot extremes, heat waves and heavy precipitation events will occur more frequently and thus will impact the natural and man-made systems (IPCC, 2007; CCIA, 2015). Therefore, a significant global attention has been given to climate change studies in the 3
last two decades. Studies have been conducted to address the potential causes of the climate changes and their impacts on various natural and man-made systems. Among them, the impacts of climate change on the water system are perceived with a high level of importance (IPCC, 2008). In this regard, the impacts of climate change on the WSUD are of significant interest in countries such as Australia. WSUD is the strategic approach adopted in Australia for urban planning and design to enable effective integration of water systems to eliminate the adverse impacts of urbanization. Although the use of WSUD concept in the urban design of Australia is vital, there is no national plan for adapting WSUD to climate change, which can lead to premature obsolescence of WSUD systems. This emphasises the importance of researches that aim to understand the potential impacts of climate change on the WSUD systems in order to formulate guidelines and policies to mitigate the adverse impacts of climate change. Therefore, this research has been conducted to advance current knowledge based on the impacts of climate change on WSUD. The advancement of knowledge primarily includes developing methodologies to generate high-resolution future rainfall data and simulate the stormwater quality and quantity for future climate change scenarios. The insights developed from this study intend to play a significant role in supporting the formulation and implementation of policies and guidelines for the adaptation of WSUD to climate change.
1.5 Description of the research The research was conducted in two phases. In Phase 1, downscaling models were developed to produce more accurate future rainfall data for different climate change scenarios. The downscaling included spatial downscaling and temporal downscaling. In Phase 2, the outputs of Phase 1 were used to assess the impacts of climate change on WSUD. The Phase 2 of the analysis consisted of an onsite frequency analysis to develop IFD relationships for future climate change scenarios and modelling of stormwater quality to assess the impact of climate change on the pollutant process, stormwater quality and quantity. In order to perform the Phase 1 of the research, selecting appropriate meteorological stations was critical. It was required to select meteorological stations with general rainfall characteristics equivalent to the study area while having a long period of records available to facilitate the downscaling. Therefore, a set of statistical tests (cluster analysis and Hosking and Wallis heterogeneity tests) were performed to identify homogeneous regions within the study area and to select meteorological stations to 4
represent those homogeneous regions. Thereby, any analysis using the representative meteorological station data were appropriately inferred to the homogeneous regions within the study area (Objective 1). New spatial downscaling software (as an R package) was developed to spatially downscale GCM outputs (rainfall data) based on quantile-quantile bias correction approach. The software was used to downscale rainfall data for future climate change scenarios at the selected representative meteorological stations (Objective 2). Then, a weather generating model was developed based on first-order homogeneous Markov model to temporally downscale the rainfall data. The outputs from the spatial downscaling (Objective 2) were then temporally downscaled using the developed model and thereby developing fine-scale rainfall time-series for different climate change scenarios (Objective 3). An at site frequency analysis was performed on the developed future rainfall data to assess the impacts of climate change on Intensity-Frequency-Duration (IFD) relationships. IFDs are considered as the primary portal to obtain design rainfall events for the design of WSUD treatment systems. The results are then appropriately inferred to be adapted in the WSUD treatment system design guidelines (Objective 4). An event-based stormwater quality model was developed to estimate the changes in the pollutant process (primarily, pollutant build-up and pollutant wash-off), stormwater quantity and quality for different climate change scenarios. Accordingly, a fundamental understating of the future stormwater quality and quantity scenarios was developed (Objective 5).
1.6 Scope The focus of this research was to develop detailed understating of the impact of climate change on the Water Sensitive Urban Design. With this focus, the study was confined to few dimensions. The primary scopes of the research are: •
The research was undertaken by taking southeast Queensland as a primary study area. This limits the direct use of the results of the impact assessment to other parts of the world. However, the tools developed for downscaling future rainfall data and methodologies including the models developed for the impact assessment were generic and applicable anywhere in the world.
•
The uncertainties associated with the climate change projections were not addressed in detail. However, a careful and thorough investigation of the selection of most suitable GCMs and use of all recommended climate change
5
scenarios (RCP 4.5 and RCP 8.5) provide confidence to the projections of this study. These decisions were supported by in-depth literature review. •
The future stormwater quantity and quality are functions of a range of parameters including changes to the urban form, catchment properties, available management strategies and rainfall characteristics of the region. Future variabilities of all these influential factors are well established and known before the design and implementation of WSUD except for the rainfall characteristics. Therefore, this research was primarily focused on understanding the future stormwater quantity and quality due to the future changes in rainfall characteristics.
•
The investigation of water quality was based only on the primary pollutant processes namely, build-up and wash-off and the research primarily focused on TSS generation from impervious urban residential catchments.
1.7 Outline of the thesis This thesis consists of ten chapters. Chapter 1 is the introduction to the research. Chapter 2 and Chapter 3 provide a critical review of the research literature that is relevant to this research. These chapters describe the background information related to the research and identify the knowledge gaps. Chapter 4 outlines the details of the research design and method. The study area, data collection and the selection of the meteorological stations for the study are discussed in Chapter 5. The analyses of the research are presented in Chapters 6, 7, 8 and 9. Chapter 6 is focused on the spatial downscaling, whereas Chapter 7 is focused on the temporal downscaling. The objectives of the chapters are to develop methodologies (models) to downscale rainfall data at finer spatial and temporal resolution and to develop rainfall time-series for the future climate change scenarios at the selected meteorological stations. Chapter 8 discusses the development of IFDs for future climate change scenarios and Chapter 9 discusses the impacts of climate change on pollutant processes and stormwater qualities. Chapter 10 presents the conclusions of the research and provides recommendations for future research. Finally, references used throughout the thesis are listed and Appendices A to E are attached to provide the additional information referred in the main text.
6
Chapter 2 Water Sensitive Urban Design 2.1 Background Urban catchments have a complicated water cycle involving potable water supply, wastewater disposal and stormwater drainage systems. Typically, these systems are designed and managed as independent systems (Lloyd et al., 2002). Domestic, commercial and industrial water demands are met by treated water harvested from catchments, which are located long away from the urban areas with demand. Wastewater generated from urban areas is conveyed to treatment plants, treated and discharged to the environment. Stormwater generated within urban areas is often conveyed through the drainage systems to reduce flooding. However, in recent days, increasing environmental awareness on water resources led governments and industries to consider more integrated and efficient ways of managing urban water cycle, while exploring opportunities to reuse, sustainable treatments and management (Wong, 2006; Gardiner and Hardy, 2005). This philosophical approach is known as the Water Sensitive Urban Design (WSUD) in Australia. WSUD primarily aims to minimise the hydrological and water quality impacts of urban developments, while integrating all three components of the urban water cycle in an efficient and environmentally friendly approach. Stormwater management is a subset of overall WSUD, which primarily focused on flood control, runoff management and stormwater quality improvements, and create opportunities to harvest and reuse stormwater for non-potable purposes (Lloyd et al., 2002). The primary focus of this study was on WSUD relating to stormwater management including stormwater quality, quantity and treatment options of WSUD. Therefore, comprehensive understanding of the current scientific knowledge on stormwater pollution and treatment, with a specific focus on WSUD treatment systems was critical for the successful completion of this research. For this, a critical review of the literature focusing on pollutant types; pollutant process; structural and nonstructural WSUD practices; WSUD treatment systems and their design; and stormwater quality modelling was undertaken and presented in this chapter. The literature review 7
was further extended to investigate the potential implication of climate change on WSUD and presented in detail in Chapter 3. In-depth literature review presented in this chapter helped to formulate the research objectives and to provide justification for methods adopted in this research. A detail discussion of research design and methods opted for this research is presented in Chapter 4. This chapter presents discussions on the concept of WSUD, WSUD structural treatment systems such as swale, bioretention basin and constructed wetland, pollutant processes and stormwater quality modelling. A special focus is given to the influential rainfall characteristics and models opted in estimating event-based stormwater qualities and quantities generated from small urban catchments.
2.2 The concept of Water Sensitive Urban Design Water Sensitive Urban Design (WSUD) is a philosophical approach of integrating the urban water cycle to minimize the environmental degradation and preserve the aesthetics of the water environment (Wong, 2006; Lloyd et al., 2002; Goonetilleke et al., 2014; VSC, 1999).
Accordingly, the objectives of WSUD includes protecting and
enhancing natural water systems in urban developments; integrating stormwater treatment into the landscape by incorporating multiple use corridors that maximise the recreational values of developments; protecting the quality of water draining from urban catchments; reducing runoff and peak flows from urban catchments by using local detention measures; minimising and disconnecting impervious surfaces; and adding value while reducing drainage infrastructure development costs (VSC, 1999). The objectives of the WSUD are achieved by practices that uphold the long-term success of a stormwater management scheme. The practices can be classified into two namely Best Planning Practices (BPPs) and Best Management Practices (BMPs) as illustrated in Figure 2.1. In a broader context, the BPPs and BMPs are applied in a stormwater management system to protect and enhance the receiving waters by mimicking the natural waterways and the associated processes. Both BPPs and BMPs in WSUD comprise structural and non-structural components to achieve the WSUD objectives including pollutant preventions, conveyance of stormwater, treatment, stormwater harvesting and reuse.
8
Technology
Design
Best Management Practice
Best Planning Practice
WATER SENSITIVE URBAN DESIGN
Efficient, sustainable and attractive solutions
Figure 2.1: Incorporation of BPPs and BMPs in WSUD (adapted and reproduced from Whelans et al. 1994; Mangangka, 2013) 2.2.1 Non-structural measures Non-structural WSUD measures are primarily pollution-prevention practices designed to eliminate or minimise pollutants entering stormwater runoff. They typically exist in the form of policies, guidelines, regulations, educational and enforcement programmes, primarily instrumented to change social and community behaviour (Taylor and Wong, 2002). Non-structural WSUD measures often complement the performance of structural WSUD measures, which are installed within urban stormwater drainage systems. The effectiveness of the non-structural practices in minimising the negative impacts of urban development is difficult to quantify and document. This can be primarily due to the fact that the non-structural measures do not involve permanent solutions. They can vary based on the geographical locations, social and economic factors. However, a number of researchers in Australia, New Zealand, United States and Germany have reported that there is an increasing trend in the use of not-structural WSUD measures such as educational and enforcement programmes (Sieker and Klein, 1998; Taylor et al., 2007; Taylor and Wong, 2002). They have also suggested that the use of combined nonstructural and structural stormwater management measures as solutions for stormwater management problems have extensive advantages compared to the use of structural systems alone. This implies that non-structural measures support and enhance the effectiveness of other structural measures of a stormwater management scheme.
9
Several authors have attempted to classify non-structural measures (for example, Brown, 1999; ASCE & US EPA, 2002; LSRC, 2001). Though the classifications vary, Cooperative Research Centre (CRC) for catchment hydrology identified five core categories of non-structural measures featured in the Australian context (Taylor and Wong, 2002). They are: 1. Town planning controls - Controls that promote WSUDs and BMPs in the construction of new residential developments including residential housing lots, roads, and for new commercial and industrial areas. 2. Strategic planning and institutional controls - Strategic stormwater management plans and secure funding mechanisms to support the implementations. 3. Pollution prevention procedures - Onsite non-structural measures including erosion and sediment control, waste management and infrastructural maintenance including street sweeping, routine cleaning of the stormwater drainage systems. 4. Education and participation programmes - Programmes that promote awareness through media campaigns, training programmes and stormwater drain stencilling programmes. 5. Regulatory controls - Enforcement of local regulations to control erosion and sediment on development sites and the use of regulatory implements. For example, using environmental licences to manage premises likely to contaminate stormwater. 2.2.2 Structural Measures Structural measures refer to the use of WSUD treatment systems that collect, convey and treat stormwater runoff before discharging to the receiving waters. The treatment processes in WSUD systems vary with the treatment measures. The primary treatment processes involved in WSUD treatment systems can be classified into three, namely, physical process, physicochemical process and biological process (Scholes et al., 2008; Goonetilleke et al., 2014). Physical process primarily involves settling and filtration. Settling refers to the removal of particulate matters by means of gravity (Ellis et al., 2004). Settling of particulate matter is highly dependent on the detention time and slow flow conditions of water and thus designed accordingly (Ellis et al., 2004). Settling is one of the primary mechanisms of particulate pollutant removal in sedimentation basins, retention basins and constructed wetlands (Greenway, 2010). Filtration refers to the removal of particulate 10
matter via physical sieving as the stormwater flows through a porous filtration media, typically layers of soil substrate (Ellis et al., 2004). Filtration is one of most prominent treatment mechanism in porous media such as porous paving, filtration basins and bioretention systems (Scholes et al., 2008). Physicochemical processes are often referred as supplementary in stormwater pollutant removal processes in WSUD treatment systems such as bioretention basins, sedimentation tanks and constructed wetlands (Ellis et al. 2004; Goonetilleke, 2014). Physicochemical processes enhance water quality by primarily treating fine particulates and dissolved pollutants, which are difficult to remove solely by physical processes. The physicochemical process facilitates pollutant to flock into large particles to facilitate settlement. The primary chemical process includes adsorption (the accumulation of pollutants at the interface between the solid surface and solution due to ion exchange) and flocculation (the separation of solids from the water column by the attachment of small particles and settling by means of gravity) (Scholes et al., 2008; Sharkey, 2006). Similar to the physicochemical process biological processes also complement the physical process by effective removal of dissolved pollutants (Taylor et al., 2005). Biological processes occurring within WSUD treatment systems include plant and algal uptake; microbial degradation; and nitrification and denitrification processes (Scholes et al., 2008; Hong et al., 2006; Hatts et al., 2008). Plant, algal and microbial uptake facilitate the removal of pollutants such as nitrogen, phosphorous and heavy metals from the stormwater (Hatts et al., 2007). In return, this satisfies the nutrient supply for the plants and micro-organisms in the WSUD systems. However, the plant and microbial uptakes are slow processes and require dense vegetation and long retention time (Scholes et al. 2008; Greenway, 2010). The nitrification and the denitrification processes take place due to the oxidation and reduction of nitrogen in presence of plants and microorganisms (Goonetilleke et al., 2014). The biological processes are dominant in WSUD systems such as constructed wetlands, bioretention basins and bioretention swales. The WSUD structural treatment systems can be broadly classified as primary level treatment systems, secondary level treatment systems and tertiary level treatment systems. Primary level treatment targets removal of litter, gross pollutants and coarse sediment. Common examples of primary level treatment systems are gross pollutant traps, trash racks, sediment traps and oil traps. Secondary level treatment aims to remove sediments, particulate matters and bacteria along with the partial removal of heavy metals and hydrocarbons. Common examples of secondary level treatment systems include vegetated buffer strips, grass swales, detention basins, bioretention basins, sedimentation basin, infiltration trenches and infiltration basins. Tertiary treatment level treatment involves the removal of fine sediments, nutrients, bacteria 11
and heavy metals. Wetlands and bioretention systems are common examples of tertiary level WSUD treatment systems (VSC, 1999). The selection of WSUD treatment systems is closely linked to the particle size range of targeted pollutants (Wong et al., 2000). Figure 2.2 illustrates the link between the particle size of the pollutants and treatment systems used. Accordingly, the treatment systems such as gross pollutant traps and sedimentation basins can operate under high hydraulic loading due to large size of targeted pollutants. As the target pollutants size reduces, required treatment processes change to include chemical and biological treatment, which essentially require considerably low hydraulic loading rate (Wong, 2006). Particle size grading
Gross solids >5000µm Coarsemedium sized particulates 125-5000µm Fine particulates 10-125µm
Treatment Measures
Gross pollutant trap
Hydraulic loading Q/Afacility 1000000 m/yr 100000 m/yr
Sedimentation basin (wet &dry) Grass swale & Filter strips
50000 m/yr 5000 m/yr Surface flow wetlands Infiltration systems Sub-surface flow wetland
Vary fine / Colloidal particulates 0.45-10µm Dissolved particles 1800GtC
B2 Medium- High 1450-1800GtC 1500
B1 Medium-Low 1100-1450GtC
1000
A1B A1T
Low 1
Update the new proximity matrix
Number of clusters
=1 END
Figure 4.4: Basic algorithm of an agglomerative hierarchical cluster analysis In agglomerative hierarchical clustering, the proximity among the clusters is defined by three different approaches namely; (a) simple link, (b) complete link; and (c) group average. Single link determines the Euclidean distance between the closest two objects of different clusters while complete links determine the Euclidean distance between the farthest two objects as shown in Figures 4.5(a) and 4.5(b) respectively. The group average determines the average pairwise Euclidean distance to measure the proximity of clusters as shown in Figure 4.5(c). 71
(a) Single link
(b) Complete link
(c) Group average
Figure 4.5: Graphical definitions of cluster proximity B Hosking Wallis Heterogeneity test The primary aim of this test is to estimate the degree of heterogeneity of a given group of meteorological stations and to evaluate whether the set of meteorological stations can be treated as homogeneous. This test primarily compares the variations in the Lmoments of the probability distribution of the observations at the meteorological stations. L-moments are parameters that describe the location, scale and the shape of probability distributions of a given dataset. Mean, standard deviation (SD), coefficient of variation (L-CV), coefficient of skewness (L-skewness) and coefficient of kurtosis (Lkurtosis) are the primary L-moment that describes a probability distribution. These Lmoments are often used to objectively assess the heterogeneity of a group of meteorological stations. Accordingly, in an ideal situation, every station in a homogeneous region should have the same L-moments. However, in practice, the Lmoments are different for every meteorological station due to differences in their 72
observations. Nevertheless, they can be reasonably treated as homogeneous if the differences in the L-moments of the meteorological stations are statistically insignificant (Hosking and Wallis, 2005). The Hosking and Wallis heterogeneity test estimates the degree of heterogeneity of a group of meteorological stations and assesses whether they can be treated reasonably as a homogeneous region. The test compares the between-station dispersion of L-moments for a group of stations with what would be expected for an artificially developed homogeneous region as presented in Figure 4.6. The artificial homogeneous region is developed by repeated simulations that generate synthetic rainfall data with the same record lengths of the actual meteorological stations based on the regional average Lmoments. Then, the dispersions in the L-moment of the actual and simulated
Observed data
L-CV
L-CV
meteorological stations are compared using an appropriate statistical index. Simulated data (Artificial homogeneous region)
L-skewness
L-skewness
Figure 4.6: Definition sketch for heterogeneity (Adapted from Hosking and Wallis (1997)) The regional weighted average of L-CV, 𝑡𝑡(𝑅𝑅) , L-skewness, 𝑡𝑡3 (𝑅𝑅) and L-kurtosis 𝑡𝑡4 (𝑅𝑅) in Hosking Wallis heterogeneity test are calculated using Equations 4.3, 4.4 and 4.5 respectively. (𝑅𝑅)
𝑡𝑡
𝑡𝑡3
(𝑅𝑅)
=
=
∑𝑁𝑁 𝑛𝑛 𝑡𝑡𝑗𝑗 𝑗𝑗=1 𝑗𝑗 ∑𝑁𝑁 𝑛𝑛 𝑗𝑗=1 𝑗𝑗 ∑𝑁𝑁 𝑛𝑛 𝑡𝑡 𝑗𝑗 𝑗𝑗=1 𝑗𝑗 3 ∑𝑁𝑁 𝑛𝑛 𝑗𝑗=1 𝑗𝑗
73
(4.3)
(4.4)
𝑡𝑡4
(𝑅𝑅)
=
∑𝑁𝑁 𝑛𝑛 𝑡𝑡 𝑗𝑗 𝑗𝑗=1 𝑗𝑗 4
(4.5)
𝑁𝑁
∑𝑗𝑗=1 𝑛𝑛𝑗𝑗
Where, N refers to the number of stations in the region and nj refers to the record length of station j. In order to measure the heterogeneity of the meteorological stations, Hosking Wallis heterogeneity test suggests three dispersion measures based on the L-CV; L-CV and Lskewness; and L-skewness and L-kurtosis as given in Equations 4.6, 4.7 and 4.8 respectively. ∑𝑛𝑛𝑗𝑗=1 𝑛𝑛𝑗𝑗 (𝑡𝑡(𝑗𝑗) − 𝑡𝑡𝑅𝑅 )2
𝑉𝑉1 = {
𝑉𝑉2 =
𝑛𝑛
∑𝑗𝑗=1 𝑛𝑛𝑗𝑗
}1/2
∑𝑛𝑛𝑗𝑗=1 𝑛𝑛𝑗𝑗 {(𝑡𝑡(𝑗𝑗) − 𝑡𝑡𝑅𝑅 )2 + �𝑡𝑡3 (𝑗𝑗) − 𝑡𝑡3 𝑅𝑅 �2 }1/2 𝑛𝑛
∑𝑗𝑗=1 𝑛𝑛𝑗𝑗
(4.6)
(4.7)
𝑛𝑛
𝑉𝑉3 =
∑𝑗𝑗=1 𝑛𝑛𝑗𝑗 {�𝑡𝑡3 (𝑗𝑗) − 𝑡𝑡3 𝑅𝑅 �2 + �𝑡𝑡4 (𝑗𝑗) − 𝑡𝑡4 𝑅𝑅 �2 }1/2 ∑𝑛𝑛𝑗𝑗=1 𝑛𝑛𝑗𝑗
(4.8)
These dispersion measures are then for an artificial homogeneous region. A four parameter kappa distribution is fitted to the regional average L-moment ratios (1, 𝑡𝑡(𝑅𝑅) , 𝑡𝑡3 (𝑅𝑅) and 𝑡𝑡4 (𝑅𝑅) ) to simulate 𝑁𝑁𝑠𝑠𝑠𝑠𝑠𝑠 realization of an artificial homogeneous region with N stations with the same record length of the actual meteorological stations. The mean 𝜇𝜇𝑣𝑣 and the standard deviation 𝜎𝜎𝑣𝑣 of the dispersion measures of the simulated
homogeneous region are calculated. Then, the dispersions of the actual and simulated homogeneous regions are compared using a statistical index H, as given in Equation 4.9. 𝐻𝐻𝑖𝑖 =
(𝑉𝑉𝑖𝑖 − µ𝑣𝑣 ) 𝜎𝜎𝑣𝑣
for 𝑖𝑖 = 1,2 and 3
(4.9)
Based on the Equation 4.9, three statistical indexes, H1, H2 and H3 are calculated based on the corresponding dispersion measures V1, V2 and V3. The region is declared acceptably homogeneous if H < 1, possibly heterogeneous if 1 ≤ H < 2 and definitely heterogeneous if H ≥ 2 (Hosking and Wallis, 1997 & 2005). 4.4.2 Spatial Downscaling As discussed in Chapter 3, the future rainfall data can be obtained from GCM outputs. However, the GCM outputs are inherently coarse in resolutions and unsuitable for local scale investigations (Abbs et al., 2007; Wilby and Dawson, 2004). Therefore, it was a 74
requirement of the Objective 2 of the research to develop methodologies to spatially downscale the GCM outputs to finer resolutions. Several authors have proposed methodologies to downscale GCM outputs to finer spatial resolutions (Wilby and Dawson, 2004; Timbal et al., 2009; Richardson, 1981, Hughes et al., 1999; Semenov and Barrow, 2002). Accordingly, the downscaling methods can be primarily classified as dynamic downscaling and statistical downscaling (NCAR, 2009). Dynamic downscaling involves embedding a higher resolution regional climate model (RCM) within the coarser resolution GCM. The RCM uses the GCM simulation outputs as boundary conditions around its domain to physically simulate the dynamics of the atmosphere within its finer grids (Leduc and Laprise, 2009; Walsh and Syktus, 2003). Statistical downscaling uses outputs from GCMs as predictors in developing relationships with local climate variables (predictands) or corrects the GCM outputs to match the observation by statistical means (Wilby et al., 1998 & 2008). As noted by Ahmed et al. (2013), Schmidli et al. (2007), and Jaw et al. (2015), statistical downscaling methods are less expensive, straightforward, computationally undemanding and capable of producing more accurate climate information than dynamic downscaling. A detail literature review has been undertaken on the selection of downscaling method and presented in Chapter 3. Based on this review, statistical downscaling was selected for this research. Commonly used statistical downscaling methods can be classified as regression methods (Kim et al, 1984; Goyal and Ojha, 2012), weather classification methods (Timbal and McAvaney, 2001), weather generating method (Wilks and Wilby 1999; Bordoy and Burlando, 2014), change factor methods (Diaz-Nieto and Wilby, 2005) and bias correction methods (Ines and Hansen, 2006; Sharma et al., 2007, Elshamy et al., 2009; Mishra and Herath 2015). Regression, weather classification and weather generation methods involve establishing statistical relationships between the coarse resolution climate variables (predictors) and fine resolution local climate variables (predictands) (Wilby et al., 1998 & 2008). The predictands are typically the observed climate variable such as temperature, rainfall and evaporation while the predictors are the climate data such as mean sea level pressure, surface minimum and maximum temperature, specific humidity and zonal and meridional wind components. In contrast, the change factor method involves adjusting the observed data by multiplying the ratio between future and present climates simulated by the GCM. Bias correction methods involve establishing a relationship to correct the GCM outputs to match observed data. Several statistical downscaling tools have been developed based on downscaling approaches as discussed above (For example, SDSM - based on regression and weather generation methods (Wilby and Dawson, 2013); BoM-SDM - based on weather 75
classification method (Timbal et al., 2009); and LARS-WS based on weather generation method (Semenov and Barrow, 2002)). However, there are many limitations in the existing downscaling tools. Many of the existing downscaling tools (that are based on the regression, weather classification and weather generation method) typically produce daily climate data which is not adequate for accurate analysis (for example SDSMWilby and Dawson, 2004). Some of the tools are research-specific and specifically developed to downscale targeted climate characteristics. Also, they are associated with GCMs from the CMIP 3 family with older emission scenarios (for example, SDM-BoM), while, more accurate and feasible emission scenarios are provided in the 5th assessment report of IPCC (IPCC, 2014). Moreover, most of the available downscaling tools are not available for public use and not easily accessible. Due to these reasons, it was required to develop a completely new spatial downscaling tool for this research. The bias correction approach was used to develop the spatial downscaling tool in this research. This is because the bias correction approach does not require predictor variables. The other downscaling approaches require different sets of predictor variables at the same temporal resolutions of the predictand to develop the downscaling relationships. Use of those methods is restricted due to the availability of GCM outputs as predictor variables only in daily and monthly temporal resolutions. This limits the use developing models to downscale rainfall of sub-daily temporal resolutions which is the core requirement of this research. Moreover, the bias correction approach is technically robust, straightforward and simple compared to other statistical downscaling methods. Bias can be defined as the systematic misrepresentation of the statistics of the simulation (Teutschbein and Seibert, 2012). The systematic misrepresentation is inherent to all models in general due to reasons such as limitations on resolutions, and simplification of processes and equations (Haerter et al., 2010; Ehret et al., 2012). These errors can be easily identifiable and corrected. This approach is generally referred as the bias correction. The quantile-quantile (Q-Q) mapping is a popular bias correction technique used in various recent climate change studies (Ines and Hansen 2006, Sharma et al., 2007, Elshamy et al., 2009; Mishra and Herath 2015). It maps the GCM outputs to the observed data based on their probability distributions. Cumulative Density Functions (CDF) are constructed separately for the GCM outputs and the observed data. Then, for a given quantile of the GCM output, the value corresponding to the same quantile in the observed data is mapped by assuming that the ratio between the observed rainfall and the GCM outputs is a constant as presented in Equation 4.10. 𝑥𝑥𝑜𝑜 = 𝑐𝑐 𝑥𝑥𝑠𝑠 76
(4.10)
Where, 𝑥𝑥𝑜𝑜 and 𝑥𝑥𝑠𝑠 refer to the observed rainfall and GCM rainfall output respectively and c is a constant. This equation can be rewritten as shown in Equation 4.11 to Equation 4.14. 𝑥𝑥𝑜𝑜,𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝 𝑥𝑥𝑜𝑜,𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓 = 𝑥𝑥𝑠𝑠,𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝 𝑥𝑥𝑠𝑠,𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓 𝑥𝑥𝑜𝑜,𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓 = 𝑥𝑥𝑜𝑜,𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓 =
(4.11)
𝑥𝑥𝑜𝑜,𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝 × 𝑥𝑥𝑠𝑠,𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓 𝑥𝑥𝑠𝑠,𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝
𝐹𝐹𝑜𝑜,𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝 −1 (𝑞𝑞) 𝐹𝐹𝑠𝑠,𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝
−1
(𝑞𝑞)
(4.12)
× 𝑥𝑥𝑠𝑠,𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓
(4.13)
Therefore, 𝑥𝑥𝑜𝑜,𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓 =
𝐹𝐹𝑜𝑜,𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝 −1 �𝐹𝐹𝑠𝑠,𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓 �𝑥𝑥𝑠𝑠,𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓 �� 𝐹𝐹𝑠𝑠,𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝 −1 �𝐹𝐹𝑠𝑠,𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓 �𝑥𝑥𝑠𝑠,𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓 ��
× 𝑥𝑥𝑠𝑠,𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓
(4.14)
Where, 𝐹𝐹 () and 𝐹𝐹 −1 () refer the cumulative density and its inverse functions respectively and subscripts o and s refer to the observed data and GCM outputs respectively. 4.4.3 Markov model It is a requirement to select suitable tools to achieve Objective 3 of developing temporal downscaling models. Temporal downscaling models are commonly developed based on different stochastic data generation techniques such as Artificial Neural Network (ANN), K-Nearest Neighbours (KNN) and Markov models. All the methods are dataintensive, require long sequences of data, and are sensitive to missing or erroneous data in the calibration set (Wilby et al., 2004). Among them, Markov models are more commonly used and proven in downscaling rainfall to finer temporal resolutions (Richardson, 1981, Hughes et al., 1999; Charles et al., 1999; Mehrotra and Sharma, 2006). Markov models are probabilistic models with a particular set of conditional assumptions. However, Artificial Neural Network and K-Nearest Neighbours do not link to any probabilistic conditions. In addition, KNN and ANN techniques are data-driven and therefore expected to perform poorly when working with a limited period of data in comparison to a Markov model. Therefore, Markov model was used to develop a temporal downscaling model in this research. Markov models are used to describe systems that follow a chain of linked events, where the occurrence of an event depends only on the previous states of the system (Wilks, 1999). Markov models can be classified into two classes, namely, Homogeneous Markov Model (HMM) and Non-Homogeneous Markov Model (NHMM). HMM assumes that the state of weather at a time is a dependent only on the state of the weather at the previous time, whereas NHMM assumption based on the fact that the state of weather at a time is a dependent not only on the state of the weather at the previous time but 77
also on the current values of some atmospheric variables (predictors). These variables are provided by different climate models simulations. The NHMM, therefore, perform well and more popularly used to temporally downscale rainfall (Hughes et al., 1999). However, use of NHMM for rainfall downscaling is limited only up to monthly or daily temporal resolutions due to the absence of GCM predictor variable at sub-daily temporal resolutions. However, this research required downscaling 3-hour rainfall time-series into 5-minute time-series and therefore NHMM is not a suitable method. Furthermore, there is no established approach to downscale such finer resolution climate data. In contrast, HMM does not require any predictor variable for temporal downscaling. Moreover, HMM is a straightforward and simple approach to weather generation. Therefore, HMM weather generating technique was used to develop a temporal downscaling model in this research. Accordingly, the temporal downscaling model was developed based on the following principles. 1. The first order dependency The model assumes that the occurrence of a rainfall event at any given time-step is only depended on the rainfall event of the previous time step. This can be mathematically expressed as given in Equation 4.15. 𝑃𝑃 (𝑥𝑥𝑡𝑡 |𝑥𝑥𝑡𝑡−1 , 𝑥𝑥𝑡𝑡−2 , … , 𝑥𝑥0 ) = 𝑃𝑃 (𝑥𝑥𝑡𝑡 |𝑥𝑥𝑡𝑡−1 )
(4.15)
Where, x=(x0,x1,x2,…,xt,…,xn) refers to the rainfall sequence; 𝑃𝑃 (𝐴𝐴|𝐵𝐵) refers to the probability of event A occurring given the previous event is B; xt refers to the rainfall at time t; and xt-1 refer to the rainfall at time t-1. 2. The transition probability remains constant with time Transition probability refers to the probability of a particular event (for example, 𝑠𝑠𝑗𝑗 ) occurring, given that a particular event (for example,𝑠𝑠𝑖𝑖 ) has occurred in previous time step. The transition probabilities for all possible transitions are determined based on a long historical rainfall records. These transition probabilities are assumed independent of time.
This can be mathematically
expressed as given in Equation 4.16 𝑃𝑃𝑃𝑃 �𝑥𝑥𝑡𝑡 = 𝑠𝑠𝑗𝑗 �𝑥𝑥𝑡𝑡−1 = 𝑠𝑠𝑖𝑖 � = 𝑃𝑃 �𝑥𝑥(𝑡𝑡+𝜏𝜏) = 𝑠𝑠𝑗𝑗 �𝑥𝑥(𝑡𝑡+𝜏𝜏)−1 = 𝑠𝑠𝑖𝑖 �
(4.16)
Where, S=(s1,s2,s3,…,si,…,sm) refers to the discrete weather states (all possible rainfall recordings of the station) and 𝑥𝑥 ∈ 𝑆𝑆.
3. Data generation
A Transition Probability Matrix (TPM) can be developed by considering all possible transitions based on a historical rainfall data. Then, the rainfall data can be generated using the TPM and a sequence of random numbers. For example, if 78
the current state of rainfall is xt-1=si (initial condition) and Ru be a random number between 0 and 1 and if,
Then the model determines,
𝑙𝑙−1
𝑙𝑙
𝑛𝑛=1
𝑛𝑛=1
� 𝑃𝑃𝑖𝑖𝑖𝑖 < 𝑅𝑅𝑢𝑢 ≤ � 𝑃𝑃𝑖𝑖𝑖𝑖 𝑥𝑥𝑡𝑡 = 𝑠𝑠𝑙𝑙
And, for the next event, xt-1=sl is considered as the current state and such the process continues. 4.4.4 Rainfall frequency analysis The hydraulic design of WSUD systems directly linked to the design rainfall (BCC & MBW. 2006). Therefore, it is important to estimate the changes in the design rainfalls for future climate change scenarios, forming the Objective 4 of this research. Hence, an at-site frequency analysis was conducted to generate Intensity-Frequency-Duration (IFD) curves for future climate scenarios. IFD relationships can be developed by performing a regional frequency analysis to a large number of stations in the region (for example, IFDs for Australia - AR&R, (2015)). This approach involves a collective use of the statistics of the recorded rainfall data at different meteorological stations to estimate the IFD relationship for a large region. Regional frequency analysis recognises that meteorological stations with rainfall records for a shorter period would considerably impose uncertainties and bias into the estimation of the IFDs, and therefore, those meteorological station data are used together with the neighbouring stations. Hence, regional frequency analysis is expected to produce more robust results and therefore popularly used in the development of the national IFD relationships (AR&R, 2015; Green et al., 2012; Madsen et al., 2009; Hosking and Wallis, 1997). However, regional frequency analysis essentially requires rainfall records at several meteorological stations. But, in this research, the future data was developed only for representative meteorological stations. Further, regional frequency analysis is a complex process that involves a number of challenging phases including comprehensive data screening, regionalising and estimation of the frequency distribution (Hosking and Wallis, 2005). Such complex analyses are beyond the scope of this research. In this research, a conventional at-site frequency analysis was undertaken for the selected representative meteorological stations. The percentage changes in the future IFDs developed at these stations were then inferred to the homogeneous regions represented by those stations.
79
The probability of an event exceeds xT, ∞
𝑃𝑃 (𝑥𝑥 ≥ 𝑥𝑥𝑇𝑇 ) = � 𝑓𝑓(𝑥𝑥)𝑑𝑑𝑑𝑑 𝑥𝑥𝑇𝑇
𝑓𝑓(𝑥𝑥) 𝑘𝑘𝑇𝑇 𝜎𝜎 0
𝜇𝜇
𝑥𝑥𝑇𝑇
Figure 4.7: Probability parameters for at-site frequency analysis The IFDs are developed based on the probability distributions of the annual series of maximum rainfall of a particular duration. Figure 4.7 illustrates the estimation of the magnitude of the rainfall for a given return period (expected time between the occurrences of such similar events or the frequency of the event) based on the probability distribution. Accordingly, the magnitude of the rainfall of a particular return period can be given by Equation 4.17. 𝑥𝑥𝑇𝑇 = 𝜇𝜇 + 𝑘𝑘𝑇𝑇 𝜎𝜎
(4.17)
Where, 𝑥𝑥𝑇𝑇 refers to the magnitude of the rainfall for a return period T and kT refers to frequency factor. Frequency factor only depends on the return period for a given probability distribution. Therefore, frequency factors can be determined based on return period of interest and the fitted probability distribution. Two primary probability distribution families, namely, Generalised Extreme Value (GEV) distribution, Pearson type distributions are used in rainfall frequency analysis. For example, Hajani and Rahman (2018) used GEV and Pearson type distribution (LP3) for design rainfall estimation and reported that both distribution performed were suitable for the design rainfall estimation. However, probability distributions from GEV family including Extreme Value type I (EV-I), also referred as the Gumbel distribution and extreme value type III (EV-III), also referred as Weibull distributions are the most commonly used probability distributions to fit the maximum rainfall events. EV-I is most suitable for modelling extreme rainfalls and maximum flowrates whereas EV-III is suitable for modelling minimum flows (Koutsoyiannis, 2004). Therefore, in this research, extreme value type I (EV-I) probability distribution is used to fit the annual series of the maximum rainfalls. The general form of the EV-I distribution is given by Equation 4.18. 80
𝑓𝑓(𝑥𝑥) =
−(𝑥𝑥−𝛼𝛼) 1 −(𝑥𝑥−𝛼𝛼) 𝑒𝑒 𝛽𝛽 𝑒𝑒−𝑒𝑒 𝛽𝛽 𝛽𝛽
(4.18)
Where, 𝛼𝛼 and 𝛽𝛽 are location and scale parameters respectively. 𝛼𝛼 and 𝛽𝛽 can be mathematically expressed by Equations 4.19 and 4.20 respectively. √ 𝛼𝛼 =
6𝜎𝜎 𝜋𝜋
𝛽𝛽 = 𝜇𝜇 − 0.5772𝛼𝛼
(4.19) (4.20)
Where, 𝜇𝜇 and 𝜎𝜎 refer to the mean and standard deviation of the distribution. The relationship between the frequency factor and return period for an EV-I distribution is given by Equation 4.21. √ 𝑘𝑘𝑇𝑇 = −
6 𝑇𝑇 �0.5772 + ln �ln � ��� 𝜋𝜋 𝑇𝑇 − 1
(4.21)
Where, 𝑘𝑘𝑇𝑇 and 𝑇𝑇 refer to the frequency factor and return period respectively. 4.4.5 Stormwater quality modelling Stormwater quality modelling can be strategically used in estimating the future stormwater quality and informed decision making of future stormwater pollution mitigation. The stormwater quality model replicates the urban stormwater by replicating the build-up, wash-off, rainfall and runoff properties by means of mathematical models. Therefore, stormwater quality modelling essentially consists of two major components, namely, pollutant process modelling and hydrologic and hydraulic modelling. A Pollutant process modelling Pollutant process modelling refers to the mathematical representation of the pollutant processes. The primary pollutant processes that constitute the stormwater quality are pollutant build-up and pollutants wash-off (Egodawatta, 2007). Therefore pollutant build-up and pollutant wash-off were considered in this research to estimate the pollutant generated and transported from urban catchments. Reliable estimation of pollutant generation primarily depends on the mathematical functions and the parameters used to estimate the pollutant build-up. Several authors have proposed different mathematical relationships to model the pollutant build-up process such as reciprocal; logarithmic; exponential and power functions (Sartor et al., 1974; Ball et al., 1998; Egodawatta, 2007; Liu, 2011). A comprehensive study conducted by Egodawatta (2007) in areas of Gold Coast, Queensland suggested that a power 81
function could better replicate the observed pollutant build-ups compared to other mathematical functions. This study was also consistent with a previous investigation by Ball et al. (1998). Hence in this research, a power equation is used to estimate the pollutant build-up as presented in Equation 4.22, 𝐵𝐵 = 𝑎𝑎𝐷𝐷𝑏𝑏
(4.22)
Where, B refers to build-up load on road surfaces (in g/m2); D refers to the antecedent dry-days; and a and b refer to the build-up coefficients. On the other hand, the most common mathematical function used to replicate the pollutant transport (wash-off) from the road surface is based on exponential functions. Different forms of exponential equations have been suggested by several researchers. Also, different rainfall and runoff parameters have been suggested as independent variables in the exponential equations proposed. For an example, Chiew et al. (1997) used runoff volume to estimate the wash-off whereas Sartor et al. (1974) used rainfall intensities to estimate the wash-off. However, Egodawatta (2007) concluded that the wash-off can be well replicated using the equation proposed by Sartor (1974) based on studies conducted in southeast Queensland and hence used in this research. The generic format of the equation suggested by Sartor (1974) is presented in Equation 4.23. 𝑊𝑊 = 𝑊𝑊𝑜𝑜 (1 − 𝑒𝑒−𝑘𝑘𝑘𝑘𝑘𝑘 )
(4.23)
Where, W refers to the weight of mobilised material after time t; Wo refers to the initial weight of the material on the surface; I refers to the rainfall intensity; and k refers to the wash-off co-efficient. Equation 4.23 suggests that the weight of material mobilised by a storm event is a simple function of the rainfall intensity, initial weight of the material and the surface characteristics of the catchment, assuming that any storm event would have the potential to wash-off all available pollutants on the surface. However, Egodawatta (2007) argued that the fraction of pollutant wash-off during a storm is always less than 1, suggesting a capacity factor, CF into the wash-off equation as given by Equation 4.24 and the capacity factors can be calculated using equations presented in Table 4.3. 𝑊𝑊 = 𝐶𝐶𝐹𝐹 (1 − 𝑒𝑒−𝑘𝑘𝑘𝑘𝑘𝑘 ) 𝑊𝑊𝑜𝑜
82
(4.24)
Table 4.3: Equations for capacity factors Intensity Range, I , (mm/hr)
Capacity Factor
5-40
0.01 𝐼𝐼 + 0.1
40-90
0.5
90-133
0.0098 𝐼𝐼 − 0.38
B Hydrological and hydraulic modelling Hydrologic and hydraulic models are often used to estimate the stormwater quantities generated from catchments to support the stormwater quality modelling (Zoppou, 2001). Hydrologic and hydraulic models supply essential runoff information to the water quality modelling to calculate the pollutant concentration resulting from catchments during storm events. In this research, in order to estimate the hydrological and hydraulic parameters, three commercially available and popularly used models namely, Mike URBAN, MUSIC and XP-SWIMM were evaluated based on the three criteria listed below, 1. Highly compatible with the adopted methodology of estimating stormwater quality. The model expected to estimate event-based Event Mean Concentrations (EMC) from a long period (20-years) of rainfall data. 2. Ability to manage large data. The research intended to simulate around 80 sets of 5-minute rainfall time-series for 20-year data (generated at two different stations, for two different GCMs, two different climate change scenarios, two different future timeframes and each of them having 10 realizations) 3. The capability of importing data in different file formats A comparison of the three models against the selection criteria is presented in Table 4.4. Table 4.4: Summary of the comparison of Mike Urban, MUSIC and XP-SWMM models with the selection criteria Models
Criteria 1
Criteria 2
Criteria 3
Mike URBAN
×
×
√
MUSIC
×
√
×
XP-SWMM
×
×
×
Note: √√ -very good; √ -good; and X - poor
83
Accordingly, none of the models was able to satisfy all the selection criteria. In particular, no model was compatible to estimate event-based EMCs for a long period of rainfall which is a primary requirement of the research. This is primarily because that the commercially available models are not capable of separating independent events for a rainfall time-series. Therefore, in this research, a new model was developed to simulate the hydrological and hydraulic to support the stormwater quality estimation. A detailed discussion on the development of the stormwater quality model for this research is presented in Chapter 9. 4.4.6 Classical univariate data analysis A Mean and Standard Deviation Mean and Standard Deviation (SD) are the commonly used statistics to describe characteristics of a univariate data set. The mean is primarily the most representative single value to describe the central tendency of a data set, whereas, SD describes the spread of data with respect to the mean. A smaller SD refers to the concentrated dataset and larger SD refers to a broadly distributed dataset (Hamburg, 1970). B Quantiles In statistics and probability theory, quantiles are cut-points dividing the range of a probability distribution into attached intervals or dividing the observations in a sample similarly. Typically, quartiles are the three cut points that will divide a dataset into four equal-sized groups. The cut-points are referred as Q1 (25% value), Q2 (median) and Q3 (75% value). C Root Mean Square Error (RMSE) Mathematical models were developed in different stages of this research. These equations required to be best fit the observed data of the validation periods. Therefore, it was critical to establish a statistics to define the goodness of fit. Among different statistics, RMSE is one of the most commonly applied techniques (Hamburg, 1970) and used appropriately in this research. RMSE is the measures of the average of the difference between the observation and the simulated values using the developed models. Smaller RSME refers to good simulation and large RMSE refers to poor simulation. The equation used to calculate Root Mean Square Error is given by Equation 4.25.
84
𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟 =
1 𝑛𝑛 ���𝑥𝑥𝑜𝑜,𝑖𝑖 − 𝑥𝑥𝑠𝑠,𝑖𝑖 �2 � 𝑛𝑛 𝑖𝑖=1
(4.25)
Where, 𝑥𝑥𝑜𝑜 and 𝑥𝑥𝑠𝑠 refer to the observed and the simulated data.
4.5 Conclusions This chapter provides a detailed discussion on the construct of the research methodology, selection of research tools and analytical methods to achieve the research objectives. The research methodology includes a comprehensive literature review; selection of study area, study tools and analytical methods; data collection; and modelling and analysis. A particular focus was given to the selection of study tools and analytical methods in this chapter. Based on a detailed review on the ability to perform various statistical analysis, availability and accessibility, managing large data and ability to develop new software, R has been selected as the programming platform for the research. On the other hand, different analytical methods have been selected to achieve the objectives of the research. Hosking Wallis heterogeneity test and cluster analysis were selected to identify homogeneous regions and select representative meteorological stations for the research thereby achieve Objective 1 of the research. A spatial downscaling model based on QQ bias correction method and a temporal downscaling model based on homogeneous Markov model were decided to be developed to generate future rainfall data at finer spatial and temporal resolutions in order to achieve Objective 2 and 3 of the research. An at-site frequency analysis was expected to be performed to develop IFDs for future climate change scenarios to achieve Objective 4. Finally, a stormwater quality model was expected to be developed to estimate the stormwater qualities for future climate change scenarios and thereby achieve the Objective 5 of the research.
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Chapter 5 Selection of Representative Meteorological Stations for Downscaling 5.1 Background Developing statistical downscaling models requires high quality observed rainfall data for long periods (Wilby and Dawson, 2004). Such observed rainfall data are typically obtained from meteorological stations. However, the discrepancy in recorded time steps and missing data in a given area can diminish the quality of data needed for downscaling studies. Moreover, when a region with multiple meteorological stations is concerned, all stations do not necessarily require to be considered in developing the downscaling models due to similarities in data sets. Performing downscaling based on data belonging to multiple meteorological stations is time-consuming. Therefore, selecting the appropriate meteorological stations for downscaling studies was a critical task. The scientific approach adopted in this research was to identify meteorological stations with similar rainfall characteristic by identifying rainfall homogeneous regions within the study area and thereby selecting representative meteorological stations. Analytical tools used for identification of homogeneous regions and selecting representative rainfall stations are presented in Section 4.4.1 in detail. Development of downscaling models was undertaken based on the observations at the representative meteorological stations and the future rainfall data generated at these stations were appropriately used for the respective homogeneous regions of the study area. Development of downscaling models and their technical attributes are presented in Chapter 6 and Chapter 7. This chapter first presents the details of the selected study area and methods and criteria adopted for data collection. Then, detail discussions are presented on the delineation of homogeneous regions within the study area and selection of representative meteorological stations for downscaling.
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5.2 Study area and data collection 5.2.1 Study area Based on the selection criteria established in Chapter 4, southeast Queensland (SEQ) was selected as the study area for this research. SEQ is a political, biogeographical and administrative region of the state of Queensland in Australia. SEQ comprises of 3.4 million people out of the state's population of 4.8 million, which is around 70% of the total population of Queensland (ABS, 2014). The area covered by SEQ varies, depending on the definition of the region, though it tends to include Queensland's three largest cities: the capital city Brisbane; the Gold Coast; Logan City and the Sunshine Coast (see Figure 5.1). SEQ covers 22,420 square kilometres and incorporates 11 local government areas, extending 240 kilometres from Noosa in the north to the Gold Coast and New South Wales border in the south, and 140 kilometres west to Toowoomba. SEQ consists of highly urban areas, especially along the coast with rapid urban developments; population growth; tourism and industrial development.
Figure 5.1: Southeast Queensland SEQ has a subtropical climate. SEQ experiences warm temperate summers with the average daily temperature varying between 200C and 280C. The winters are slightly cooler with the average daily temperature varying between 90C and 200C. While the seasonal rainfall pattern of SEQ is relatively consistent with wet summers and dry 88
winters, there is a considerable spatial variation in the average rainfall across the region. In average, the mean annual rainfall in SEQ varies between 800mm and 1700mm. SEQ consists of a widespread network of waterways, creeks, and rivers spread across the region. However, studies on the waterways of SEQ have shown that the waterways are highly polluted by the stormwater runoff originating from the urban areas of the region (WBD, 2010; BCC & MBM, 2006; Goonetilleke et al., 2005). To counter this, SEQ has adopted the holistic approach of Water Sensitive Urban Design in the planning and design of urban developments in order to eliminate the negative impacts of urbanisation on the natural waterways. As a result, SEQ has a broad implementation of the WSUD philosophy in its developments. SEQ is one of the most vulnerable regions in Australia to climate change due to its growing population and coastal location. The Intergovernmental Panel on Climate Change (IPCC, 2007) identified SEQ region as one of the ‘hot spots’ in Australia to be affected by climate change. The average annual temperature in SEQ has increased 0.4 °C (from 19.4 °C to 19.8 °C) between 1998 and 2007, showing a trend for further increase in the future (CCIA, 2015; Syktus et al., 2009). Studies have indicated an increase of up to 4°C in the average annual temperature by 2070 (Syktus et al., 2009; DEHP, 2016; CCIA, 2015). However, the influence of the climate change on the average annual rainfall is less clear (CCIA, 2015). 5.2.2 Data collection SEQ has extensive metrological station network with measurements taken in daily, 3hour, 30-minute and 1-minute (pluviography) formats. Among them, 17 meteorological stations were used for this research based on the availability of longer period of observation (at least for 5-years) in pluviographic format. The locations of the stations with their station number are presented in Figure 5.2, while additional information of the selected meteorological stations is presented in Table A1 in Appendix A. Rainfall events were extracted from the time-series of data from each of the meteorological stations and variables such as antecedent dry day period, maximum rainfall intensity, total rainfall depth and the rainfall duration of rainfall events were determined. The following criteria were considered in extracting individual rainfall characteristics. • An event was considered independent only if the consecutive event was separated by 3-hour antecedent dry duration. Otherwise, those events were treated as a single event.
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• An event that constitutes less than 1-mm total rainfall for a period greater than 1-hour was not considered as a storm event (but a drizzle) and not considered for the analysis. • The maximum rainfall intensities (in mm/hr) of the events were estimated by calculating the moving total of 1-hour rainfall throughout the storm duration. • Any event having data entries with poor quality was discarded for the analysis.
Figure 5.2: The locations of the selected meteorological stations
5.3 Assessment of rainfall homogeneity in southeast Queensland Among 17 meteorological stations identified, not all stations have substantially long recordings of high quality observed data, which is a prerequisite for developing statistical downscaling models. Furthermore, the observed data at these meteorological stations 90
may be similar in nature, and therefore, not all meteorological stations required to be considered in developing the downscaling models. Therefore, the strategy adopted in this research was to identify homogeneous rainfall regions within the study and selecting one meteorological station that has a high-quality observation for long period for each of the identified homogeneous regions as the representative meteorological station. By this way, development of downscaling models can be focused on the observations at the representative meteorological stations and the future rainfall data generated at these stations can be inferred to the entire rainfall homogeneous region. The delineation of homogeneous regions for SEQ was carried out based on two different approaches: 1. Based on the characteristics of the continuous rainfall data (continuous-rainfall approach); and 2. Based on the characteristics of the event-based rainfall data (event-based rainfall approach). 5.3.1 Continuous-rainfall approach In the continuous rainfall approach, the rainfall data series of the selected meteorological stations are tested for regional homogeneity purely based on the probabilistic characteristics of the rainfall recordings. The degrees of homogeneity of the stations are objectively determined using Hosking and Wallis heterogeneity test. Technical details of the Hosking and Wallis heterogeneity test are presented in Section 4.4.1 in Chapter 4. The Hosking and Wallis heterogeneity test estimates the degree of homogeneity of a group of meteorological stations based on the dispersion of L-moments among the given group of stations with what would be expected from an artificially developed homogeneous region (refer Section 4.1.1). In order to quantify the homogeneity of a selected region, the test uses three dispersion indexes, namely, H1, H2 and H3. The region is declared acceptably homogeneous if H1,H2, H3 < 1, possibly heterogeneous if 1 ≤ H1,2,3 < 2 and definitely heterogeneous if H1,2,3 ≥ 2 (Hosking and Wallis, 1997 & 2005). Further, Hosking and Wallis (2005) suggested that dispersion index H1 alone can be used to identify homogeneous regions as it has higher discriminatory power than other indexes. However, many studies use all three dispersion indexes or at least first two dispersion indexes to identify homogeneous regions (Mishra and Herath, 2015; Viglione, 2012). Therefore, in this research, the first two indexes, H1 and H2 have only been used to assess the degree of homogeneity of the region. The dispersion indexes were generated using an R package called ‘homtests’ (Viglione, 2012). Hosking and Wallis heterogeneity test was performed using ‘homtests’ package on the selected 17 meteorological stations. All stations consisted of high quality and 91
substantially complete rainfall data in a pluviographic format for the period between 2011 and 2015. Therefore, rainfall data from this period was used to test the homogeneity of the meteorological stations. The results suggested that the entire SEQ could be treated as homogeneous with H1 = 0.6483 and H2 =0.9142. 5.3.2
Event-based rainfall approach
Although the overall rainfall characteristics of the entire SEQ were homogeneous, the event-based rainfall characteristics of the region may be different. For example, an event with intense rainfall for a short period of time and an event with less intense rainfall for a longer period of time may result in similar overall (average) rainfall characteristics. However, these events can potentially produce completely different stormwater quality and quantity scenarios. Therefore, it was important to consider the homogeneity of meteorological stations based on event-based rainfall characteristic when selecting the representative meteorological stations for this research. In the context of WSUD, the event-based rainfall characteristics are perceived with more importance than the overall rainfall characteristics. Rainfall event characteristics such as antecedent dry days, rainfall intensities, total rainfall depth and rainfall durations are key characteristics of rainfall that are directly related to the stormwater quality and quantity. For example, pollutant build-up is primarily influenced by the antecedent dry days (Sartor et al., 1974; Ball et al., 1998; Egodawatta, 2007; Liu, 2011). In terms of pollutant wash-off, some researchers have identified the rainfall intensities (Sartor et al., 1974; Egodawatta, 2007) as the primary influence on stormwater quality, while others have indicated that the total rainfall depth (Chiew et al., 1997) is the primary influence. In addition, the total rainfall depth and the duration of rainfall events jointly provide indications to the quantities of stormwater generated from catchments (Zoppou, 2001; Egodawatta, 2007). Therefore, the homogeneity assessment required for this study needs consideration of event-based rainfall characteristics such as antecedent dry days, rainfall intensities, total rainfall depth and rainfall durations. Similar to the continuous-rainfall approach, Hosking and Wallis heterogeneity test was performed to objectively assess the degree of rainfall homogeneity of the selected 17 meteorological stations of SEQ based on the event-based rainfall characteristics. Rainfall events were extracted from the time-series of data from these meteorological stations for a period between 2011 and 2015 based on the criteria established in Section 5.2.2. Rainfall characteristics such as antecedent dry day period, maximum rainfall intensity, total rainfall depth and the rainfall duration of each event were determined and Hosking and Wallis heterogeneity tests were performed based on each rainfall characteristics separately. The results of the Hosking and Wallis heterogeneity test based on the eventbased rainfall characteristic are presented in Table 5.1. 92
Table 5.1: Dispersion indexes based on event-based rainfall approach for southeast Queensland 𝑯𝑯𝟏𝟏
𝑯𝑯𝟐𝟐
Remarks
3.37
1.16
Heterogeneous
1.95
0.59
Possibly heterogeneous
Total rainfall
0.81
0.32
Homogeneous
Duration
0.25
0.10
Homogeneous
Antecedent dry day periods Maximum rainfall intensity
Based on the first two dispersion indexes (H1 and H2,) antecedent dry day periods showed a higher level of heterogeneity compared to other event-based rainfall characteristics. The maximum rainfall was found to be potentially heterogeneous across SEQ. In contrast, the total rainfall and the rainfall duration were homogeneous across the SEQ. Overall these results suggest that the entire SEQ cannot be considered homogeneous
based
on the
event-based
rainfall
characteristics. Accordingly,
homogeneous regions suggested based on the continuous-rainfall approach may not necessarily be homogeneous based on individual rainfall characteristics. In addition, it was also noticeable that antecedent dry days and the maximum rainfall intensity showed heterogeneity among the meteorological stations while the total duration and the total rainfall of the events were homogeneous. Therefore, it can be concluded that antecedent dry day periods and maximum rainfall intensity have higher spatial variation and thus should be the deciding rainfall characteristics in delineations of the homogeneous regions. Accordingly, the next step was to identify all potential homogeneous regions inside SEQ and to assess the degree of homogeneity of identified potential homogeneous regions (using the Hosking and Wallis heterogeneity test). In order to identify the potential homogeneous regions, cluster analysis was performed based on the rainfall characteristics. A detailed discussion on the cluster analysis and the algorithm associated with different cluster analyses are presented in Section 4.4.1. Agglomerative hierarchical cluster analysis was performed using R package ‘stats’ (R Development Core Team, 2016). The parameters used for the analysis included 3rd quartile (Q3) values of antecedent dry day periods, maximum rainfall intensity, total rainfall and duration of the individual events of each station as given in Table 5.2. This was because the average or the median of the rainfall characteristics at the considered meteorological stations were expected to be similar in nature and therefore may not be grouped into 93
discrete clusters. In contrast, selecting a higher quantile value may result in too many unrealistic clusters. Therefore, the 3rd quartile values were used in this analysis. Table 5.2: Data matrix for the cluster analysis 3 rd quartile values – Q3 Maximum Total intensities rainfall (mm/h) (mm)
Serial number
Station number
Antecedent dry-days (days)
1
40004
6.4
7.1
12.0
5.3
2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17
40043 40082 40093 40211 40717 40764 40842 40861 40908 40913 40922 40958 40983 40988 41525 41529
5.4 8.4 6.0 5.9 3.8 5.0 6.0 4.3 3.3 6.1 9.8 6.1 7.1 4.2 7.9 8.2
6.7 7.6 6.0 6.8 6.4 7.0 6.6 8.2 5.9 7.4 8.2 7.3 7.6 6.2 6.6 7.8
13.4 14.4 13.5 11.6 12.3 12.4 12.1 13.8 10.4 13.2 12.4 12.6 12.8 11.9 14.1 13.2
6.1 5.9 5.9 4.8 5.7 6.0 5.4 7.2 5.3 5.8 6.2 5.3 5.3 6.5 5.9 5.7
94
Duration (h)
Figure 5.3 presents the dendrogram developed using the ‘stats’ package. The dendrogram illustrates the merging of similar meteorological stations forming clusters at different levels and successively merging into a single cluster. Based on Figure 5.3, it can be seen that there are three discrete branches of the dendrogram forming three clusters. Accordingly, Cluster 1 comprised of Stations 9, 7 and 11. Cluster 2 comprised of Stations 3, 12, 14, 16 and 17 and Cluster 3 comprised of Stations 1, 5, 6, 8, 10, 13
Distance
and 15.
6
5
4
3
16 10
9 2 12 3
1
6 15 7 11
0
14 17
2 4
5 8
1 13
Figure 5.3: Dendrogram generated from the cluster analysis The geographical locations of the meteorological stations of the clusters are presented in Figure 5.4. Figure 5.4 suggests that the meteorological stations of Cluster 1 and Cluster 2 were located in close proximity to the coast of the SEQ and the meteorological stations of Cluster 3 were located inland. However, Cluster 1 and Cluster 2 stations do not show clear geographical separation.
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Cluster 1 Cluster 2 Cluster 3
Figure 5.4: Geographical locations of the meteorological stations and their grouping Further, scatter plots were produced to examine of meteorological stations of the three clusters based on the considered rainfall characteristics and presented in Figure 5.5. It can be observed from Figure 5.5 that the meteorological stations of the Cluster 3 have a clear distinction between the meteorological stations of Cluster 1 and Cluster 2. In contrast, the meteorological station of Cluster 1 and Cluster 2 showed no clear separations. These results suggest that the Cluster 1 and Cluster 2 can be treated as single clusters representing the coastal SEQ while the Cluster 3 representing the inland SEQ. Accordingly, two potential homogeneous regions were identified within the study area, namely, Coastal-SEQ and Inland-SEQ. 96
14000 Inland
12000
12000 Inland
10000
10000
8000
Coast
8000 Coast
6000
6000
300
340
Antecedent dry-days (min)
Antecedent dry-days (min)
14000
0.6
420 380 Duration (min)
0.7
0.8
0.9
1.0
Intensity (mm/min)
14000
12000
Inland
10000
8000
6000 Coast 11
12
13
14
Total rainfall (mm)
Figure 5.5: Scatterplots of the event-based rainfall characteristics (Red dots refer to the stations of Cluster 1, Black dots refer to the stations of - Cluster 2 and Green dots refer to the stations of Cluster 3) 97
The results of the cluster analysis provided insight for selecting the potential homogeneous regions, and the rainfall homogeneousness were tested objectively for the selected groups. The degree of homogeneousness of the identified regions of CoastalSEQ and Inland-SEQ were evaluated by performing Hosking and Wallis heterogeneity tests using event-based rainfall characteristics. The summary of the result is presented in Table 5.3. As shown in Table 5.3, the dispersion indexes H1 and H2 were found less than one for all the rainfall characteristics for both Coastal-SEQ and Inland-SEQ. Therefore, Coastal-SEQ and Inland-SEQ were identified as two separate homogeneous regions within SEQ based on the event-based rainfall characteristics. Table 5.3: Dispersion indexes for Hosking and Wallis heterogeneity test for CoastalSEQ and Inland-SEQ Coastal-SEQ
Inland-SEQ
H1
-0.20
H2
1.18
H1
-0.35
0.06
0.78
0.97
-0.61
-0.65
Total rainfall
-0.55
0.65
-0.54
-0.10
Duration
0.26
0.32
-1.29
-1.00
Antecedent dry day periods Maximum rainfall intensity
H2
5.4 Boundaries and representative meteorological station of the homogeneous regions 5.4.1 Rainfall homogeneous regions within southeast Queensland Based on the Hosking and Wallis Heterogeneity test and cluster analysis presented in Section 5.3, two homogeneous regions, namely Coastal-SEQ and Inland-SEQ were identified within the study area based on event-based rainfall characteristics. The Coastal-SEQ includes the greater Brisbane regions, north Brisbane and south Brisbane areas whereas the Inland-SEQ includes the western regions. The boundaries for the two regions were determined by forming polylines along the perpendicular bisectors of two neighbouring stations from the two different regions. Then, these borderlines were smoothened and adjusted slightly to fit the nearest local government boundaries for consistency as presented in Figure 5.6. The local government bodies included in the identified homogeneous regions is presented in Table 5.4.
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Table 5.4: Local government bodies included in the identified homogeneous regions Region
Local government bodies Brisbane City Council, Gold Coast City Council, Logan City Council, Redland City Council, Moreton Bay Regional Council and Sunshine Coast Regional Council. Ipswich City Council, Scenic Rim Regional Council, Lockyer Regional Council and Somerset Regional Council
Coastal-SEQ
Inland-SEQ
Coastal-SEQ
Inland-SEQ
Figure 5.6: Boundaries of Coastal-SEQ and Inland-SEQ rainfall homogeneous regions
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The results are partially consistent with the adopted climate regions for SEQ in the WSUD conceptual design (BCC & MBW, 2006). However, BCC & MBW (2006) further separated coastal SEQ into three regions namely, North Coast, Greater Brisbane and South Coast. However, the partitioning was based on a subjective approach. Two climate characteristics, average number of rain days per year and mean annual rainfall were only considered in this approach. Even though the costal-SEQ has been identified as three separate homogeneous regions by BCC & MBW (2006), the entire Coastal-SEQ showed the similar average number of rain days per year and mean annual rainfall. On the other hand, based on the National Resource Management (NRM) homogeneous regions, the entire SEQ is considered as a single homogeneous region called East Coast which contradicts the results of this research. NRM regions defined largely correspond to the broad-scale climate and biophysical regions of Australia. However, climate change impacts and adaptation approach of Australia is broadly based on NRM regions (Dowdy et al., 2015, CCIA, 2015). For example, the interim climate change factors suggested by AR&R (2015) were based on the NRM regions, implying the changes in the temperatures and rainfall for the entire region is uniform. However, many climate change impact assessments such as WSUD are sensitive to changes in the local-scale rainfall. Therefore, the homogeneous regions identified based on event-based rainfall characteristics in this research are more appropriate for local-scale investigations. 5.4.2 Representative meteorological stations for southeast Queensland Meteorological stations within the identified homogeneous regions have similar rainfall characteristics such as antecedent dry day periods, rainfall intensities, total rainfall and rainfall durations. Based on this, it can be hypothesised that the future rainfall data generated (using downscaling models) based on the data from any of the stations can be inferred to the respective homogeneous regions. However, in order to develop downscaling models, suitable metrological stations within each homogeneous region should be selected as representative meteorological stations. In this regard, the criteria adopted for selection is primarily based on the availability of high quality and complete data sets for a long period of time. In addition to this selection criterion, stations used in previous studies relating to WSUD were given more preference and stations along the borderlines were given less preference in the selection of representative meteorological stations. Accordingly, for Coastal-SEQ, Gold Coast Seaway station (40764) was selected as the representative meteorological stations. Gold Coast Seaway station has rainfall recording in pluviographic format since 2000 with almost 100% completeness. Moreover, Gold Coast Seaway station has been used in several previous research studies including Ma (2016), Chowdhury (2018), Liu (2011) and Egodawatta (2007). For Inland-SEQ, 100
Toowoomba Airport station (41529) was selected as the representative meteorological station since the station has the longest period of the rainfall records in pluviographic format (since 2009 with around 100% completeness) compared to other meteorological station in Inland-SEQ. The rainfall data of the representative meteorological stations were used to develop downscaling models and the future data generated based on these downscaling models were inferred to the respective homogeneous regions. The procedures of developing downscaling models are presented in Chapter 6 and Chapter 7 in detail.
5.5 Conclusions The following conclusions were derived from the analysis of this chapter: • The entire southeast Queensland can be treated as a homogeneous region based on the
continuous-rainfall
approach.
However,
based
on
individual
rainfall
characteristics such as antecedent dry-days, maximum rainfall intensities, total rainfall and duration of the rainfall events, there were two separate homogeneous regions identified. This implies that although the characteristics of the continuous rainfall data between stations were statistically similar, the event-based characteristics have a significant difference among stations. • Antecedent dry-days and maximum rainfall intensities of the rainfall events have significant variation between the coastal and the inland areas of SEQ compared to the total rainfall and duration of the event. • Two homogeneous regions were identified based on the event-based rainfall characteristics and named as Coastal-SEQ and Inland-SEQ. Coastal-SEQ includes Brisbane City Council, Gold Coast City Council, Logan City Council, Redland City Council, Moreton Bay Regional Council and Sunshine Coast Regional Council areas and the Inland-SEQ includes Ipswich City Council, Scenic Rim Regional Council, Lockyer Regional Council and Somerset Regional Council areas. • Two representative meteorological stations Gold Coast Seaway station (40764) and Toowoomba Airport stations (41529) were selected to represent the Coastal-SEQ and Inland-SEQ respectively based on a set of selection criteria.
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Chapter 6 Spatial Downscaling of Rainfall Data Using Bias Correction Method 6.1 Background As noted in Chapter 3, statistical downscaling models are popularly used in many climate change impact assessments as they are less expensive, straightforward, computationally undemanding and capable of producing more accurate climate information than dynamic downscaling (Ahmed et al., 2013; Schmidli et al., 2007; Jaw et al., 2015). Several statistical downscaling tools have been suggested in the literature based on different downscaling methods (Timbal and McAvaney, 2001; Mehrotra and Sharma (2006); Wilks and Wilby 1999; Mishra and Herath, 2015). However, there are many limitations in the existing downscaling tools. The limitations include the ability to produce only daily climate data, which is not adequate for accurate impact assessment including the assessment of future stormwater quantities and qualities. Some of the tools are research-specific and developed only to downscale targeted climate characteristics. Moreover, some tools are associated with Global Circulation Models (GCM) from the CMIP 3 family with older emission scenarios and not available for public use. Therefore, a more robust spatial downscaling tool was developed in this research to eliminate the limitations in the existing downscaling tools. The tool was designed to develop Quantile-Quantile (Q-Q) bias correction models to downscale rainfall data from Global Circulation Models. The reason for the selection of Q-Q bias correction approach for this tool is presented in detail in Section 4.4.2. Further, the new spatial downscaling tool was used to produce Q-Q bias correction models to downscale 3-hour rainfall timeseries from two GCMs, namely, ACCESS 1.0 and EC-EARTH for southeast Queensland (SEQ). The models were developed based on the rainfall data from selected representative meteorological stations discussed in Chapter 5. The approach adopted for temporal downscaling of the bias-corrected data is explained in Chapter 7.
103
This chapter presents a detailed discussion on the development of the new downscaling tool including the downscaling method used in developing the tool, its architecture and the capabilities. The chapter also presents the characteristics of spatially downscaled rainfall data for SEQ.
6.2 Development of the spatial downscaling tool 6.2.1 Downscaling method As noted in Chapter 4, the bias correction method was selected for the development of the spatial downscaling tool. The primary reason for this selection is that the bias correction method does not require predictors, unlike other downscaling methods. Most of the other methods require reliable predictor variable from the GCMs at the same temporal resolutions of the predictands. However, GCMs, in general, do not produce predictor variables at the sub-daily temporal resolution (CMIP5, 2015). Therefore, statistical downscaling methods which require predictor variables (such as regression method, weather classification methods and weather generating methods) are not suitable for this research. In contrast, bias correction methods do not require predictor variables and therefore, more suitable for this research. In addition, the bias correction method is one of the most effective statistical downscaling methods gaining popularity among researchers working on climate change impact assessments (Mishra and Herath, 2015). In general, all GCMs are inherent to systematic misrepresentations during their simulation stage (Teutschbein and Seibert, 2012), due to limitations in scales and simplification of processes and equations (Haerter et al., 2010; Ehret et al., 2012). These misrepresentations in the GCM simulations can be easily identified and corrected. This identification and correction of misrepresentation in GCM data are referred to as the bias correction. Quantile-Quantile (Q-Q) bias correction is a popular bias correction method used in a range of recent climate change studies (Ines and Hansen, 2006; Sharma et al., 2007; Elshamy et al., 2009; Mishra and Herath 2015). The Q-Q bias correction method compares the probability distribution of the GCM data and the observed data and accordingly corrects the bias in the GCM data. A detailed discussion on the stepby-step procedure for the Q-Q bias correction approach used in the development of the new statistical downscaling tool is presented below.
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6.2.2 Architecture of the downscaling tool A step-by-step procedure adopted to develop a downscaling tool using the Q-Q bias correction method is discussed in this section. The discussion utilises the schematic provided in Figure 6.1. Step 1: Input data The tool was designed to operate with two types of input data, namely, observed data and GCM data. Both of these data sets are used for calibration and validation of the tool. A separate future data set obtained from GCMs for the required future climate scenario is also needed for this tool. Observed data used for calibration and validate is typically from a meteorological station, while the GCM data is from the Global Climate Model simulations for the same historical period as for the observed data. Both datasets used for calibration and validation required to be recorded at the same time steps. The data for the historical period was required to be further split into two sets for the use of calibration and the validation of the models as shown in Figure 6.1. Step 2: Determination of probability distribution parameters and construction of the cumulative density functions The tool was designed to determine the basic probability distribution parameters such as mean, standard deviation, shape factor and scale factors of the data sets in order to construct the cumulative density functions. The cumulative density functions are developed assuming a two-parameter gamma distribution. The two-parameter gamma distribution was adopted to model the rainfall data in this tool due to its common use in studies relating to rainfall data analysis (Mirsha and Herath, 2015; Hanson and Vogal, 2008; Sharma and Singh, 2010; Husak et al., 2007). Furthermore, the gamma distribution is invertible and readily available on the R platform. The general form of the cumulative density function of the two-parameter gamma distribution is shown in Equation 6.1. 𝑥𝑥
𝐹𝐹 (𝑥𝑥, 𝛼𝛼, 𝛽𝛽) = � 𝑓𝑓 � 0
−𝑥𝑥 1 𝛼𝛼−1 � 𝛽𝛽 � 𝑥𝑥 𝑒𝑒 � 𝑑𝑑𝑑𝑑 𝛽𝛽 𝛼𝛼 Г(𝛼𝛼)
(6.1)
Where, x represents the rainfall data (0 ≤ x = threshold) { crtd_mod_v[i]= xx_mod_v[i] * stats::qgamma(ff_mod_v [i],sh_obs_c,,sc_obs_c) /stats::qgamma(ff_mod_v [i],sh_mod_c,,sc_mod_c) } else{ crtd_mod_v[i]=0.0} # crtd_mod_v # turn on/off to view it ## display results of the validation/summary # plotting /generating gamma curves for validation # modelling data using gamma distribution (above thresold)_ Observation # selecting threshold to plot thresholds (here, I have used the threshold of same data) p=stats::ecdf(obs_v) threshold_obs_v= (round(p(0.0),3))*1000 # threshold_obs_v # turn on/off to view it # modeling obs_val f_obs_v=c(1) x_obs_v=c(1) # defining variables for (i in threshold_obs_v:999) f_obs_v[i-threshold_obs_v+1]=i/1000 for (i in 1:length(f_obs_v)) x_obs_v[i]=round((stats::qgamma(f_obs_v[i],sh_obs_v,,sc_obs_v)),1) # f_obs_v # turn on/off to view it # x_obs_v # turn on/off to view it p.plot= graphics::plot(x_obs_v,f_obs_v,xlim=c(0,50),type="l",col= "green") #x=x_obs_v x= obs_v p=stats::ecdf(x) graphics::lines(p,col="green") # turn on/off to display actual data # modelling data using gamma distribution (above thresold)_model # selecting threshold to plot thresholds (here, I have used the threshold of same data) p=stats::ecdf(mod_v) threshold_mod_v= round(p(0.0),3)*1000 # return the probabily at zero in 2 digit # threshold_mod_v 229
# turn on/off to view it f_mod_v=c(1) x_mod_v=c(1) # defining variables for (i in threshold_mod_v:999) f_mod_v[i-threshold_obs_v+1]=i/1000 for (i in 1:length(f_mod_v)) x_mod_v[i]=round((stats::qgamma(f_mod_v[i],sh_mod_v,,sc_mod_v)),1) #f_mod_v # turn on/off to view it #x_mod_v # turn on/off to view it graphics::lines(x_mod_v,f_mod_v,type="l",col= "red") #x=x_mod_v x= mod_v p=stats::ecdf(x) graphics::lines(p,col= "red") # fitting true values on to modeled curve, turn on/off to display actual data # Modeling corrected data using gamma distribution # selecting threshold to plot thresholds (here, I have used the threshold of same data) p=stats::ecdf(crtd_mod_v) threshold_crtd_mod_v= round(p(0.0),3)*1000 # return the probabily at zero in 2 digit # threshold_crtd_mod_v # turn on/off to view it #parameters m_crtd_mod_v= mean(crtd_mod_v) s_crtd_mod_v= stats::sd(crtd_mod_v) sh_crtd_mod_v= (m_crtd_mod_v/s_crtd_mod_v)^2 sc_crtd_mod_v= s_crtd_mod_v^2/m_crtd_mod_v f_crtd_mod_v=c(1) x_crtd_mod_v=c(1) # defining variables for (i in threshold_crtd_mod_v:999) f_crtd_mod_v[i-threshold_obs_v+1]=i/1000 for (i in 1:length(f_mod_v)) x_crtd_mod_v[i]=round((stats::qgamma(f_crtd_mod_v[i],sh_crtd_mod_v,, sc_crtd_mod_v)),1) # f_crtd_mod_v # turn on/off to view it # x_crtd_mod_v # turn on/off to view it graphics::lines(x_crtd_mod_v,f_crtd_mod_v,type="l",col= "blue") #x=x_crtd_mod_v,f_crtd x= crtd_mod_v p=stats::ecdf(x) graphics::lines(p,col="blue") # fitting true values on to modeled curve, turn on/off to display actual data #VALIDATION SUMMARY/RESULT ### creating th A matrix for validation index f=c(1) for (i in 1:1000) f[i]=(i-1)/1000 #f #crtd_mod_v #obs_v$pr #mod_v$pr xx_obs_v=c(1) xx_mod_v=c(1) xx_crtd_mod_v=c(1) for(i in 1:length(f)) { 230
xx_obs_v[i]=round((stats::qgamma(f[i], sh_obs_v,,sc_obs_v)),1) xx_mod_v[i]=round((stats::qgamma(f[i], sh_mod_v,,sc_mod_v)),1) xx_crtd_mod_v[i] =round((stats::qgamma(f[i], sh_crtd_mod_v,,sc_crtd_mod_v)),1)} f= matrix(f) xx_crtd_mod_v= matrix(xx_crtd_mod_v) xx_obs_v=matrix(xx_obs_v) xx_mod_v= matrix(xx_mod_v) A=cbind(f,xx_obs_v,xx_mod_v,xx_crtd_mod_v) #A ### RMSV rmsv_obs_vs_mod=c(1) rmsv_obs_vs_crmod=c(1) for (i in 1:length(xx_obs_v)) rmsv_obs_vs_mod[i]=((xx_mod_v[i]-xx_obs_v[i])^2)^.5 for (i in 1:length(xx_obs_v)) rmsv_obs_vs_crmod[i]=((xx_crtd_mod_v[i]-xx_obs_v[i])^2)^.5 rmsv1=mean(rmsv_obs_vs_mod) rmsv2=mean(rmsv_obs_vs_crmod) # rmsv1 # rmsv2 # has to be transformed into summmary ### gradient # plot (xx_obs_v,xx_crtd_mod_v,type = "l",col="blue") # lines(xx_obs_v,xx_obs_v,type = "l",col="green") # lines(xx_obs_v,xx_mod_v,type = "l",col="red") # turn on/off to view it graphics::plot (xx_obs_v,xx_obs_v,col="green") graphics::lines(xx_obs_v,xx_obs_v,type = "l",col="green") #lines (xx_obs_v,xx_crtd_mod_v,col="blue") fit1=stats::lm(xx_crtd_mod_v~xx_obs_v) graphics::abline(fit1, col="blue") #fit1 # turn on/off to view it # summary(fit1) # turn on/off to view it # lines (xx_obs_v,xx_mod_v) # turn on/off to view it fit2=stats::lm(xx_mod_v~xx_obs_v) graphics::abline(fit2,col="red") # fit2 # summary(fit2) # turn on/off to view it #coef(fit1) #coef(fit2) err=round((((threshold_obs_vthreshold_crtd_mod_v)^2)^.5)/threshold_obs_v*100,2) validation_output_list=list(percentage_error_in_the_thresholds =err,root_mean_squre_error_in_mod=rmsv1 ,root_mean_squre_error_in_crtdmod=rmsv2,gradient_of_obs_vs_mod_line= fit2$coefficients[2],gradient_of_obs_vs_crtdmod_line=fit1$coefficien ts[2]) print(validation_output_list) return(NULL) }
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B.3: Source code for downscale () function of spdownscale #' @title Spatial Downscaling #' @description Generating the future climate data (rainfall) #' @param obs_c vector of observational climate data (rainfall) used for calibrating the model #' @param mod_c vector of GCM/RCM rainfall data (rainfall) used for calibrating the model #' @param obs_v vector of observational climate data (rainfall) used for validating the model #' @param mod_v vector of GCM/RCM climate data (rainfall) used for validating the model #' @param mod_fut vector of GCM/RCM future climate data (rainfall) need to be downscaled #' @details #'1) Dry-days correction / Defining threshold values #' #' The relationship between the cumulative frequencies (thresholds) corresponding to the dry days of GCM/RCM data and that of the observational data is defined by a polynomial function given by; #' #'threshold_obs = (threshold_mod)^n #' #'n = ln(threshold_obs_c) / ln(threshold_mod_c) #' #' #'2) wet-days correction / Correcting the intensity of the GCM/RCM data #' #'Two parameter (shape and scale factors) gamma distribution function is used to model the frequency distributions of the rainfall data. The GCM/RCM rainfall above the threshold were corrected using unique correction factors for different cumulative frequencies. #' #'corrected_mod_fut = mod_fut * F-1(F.mod_fut, sh_obs_c,,sc_obs_c)/ F-1 (F.mod_fut,sh_mod_c,,sc_mod_c) #' #'where obs - observational data; mod - GCM/RCM data; n - constant; c - calibration; v - validation; fut - future data; sh - shape factor; sc- scale factor; F. - cumulative density function and F-1 inverse of cumulative density function #' @export #' @examples #' #subsetting dat_model #' mod_calibration=subset(data_model,(year==2003|year==2005|year==2007| year==2009|year==2011)) #' mod_validation= subset(data_model,(year==2004|year==2006|year==2008|year==2010|year= =2012)) #' #subsetting data_observation #' obs_calibration=subset(data_observation,(year==2003|year==2005|year= =2007|year==2009|year==2011)) #' obs_validation=subset(data_observation,(year==2004|year==2006|year== 2008|year==2010|year==2012)) #' #creating the input vectors #' obs_c=obs_calibration$pr 232
#' mod_c=mod_calibration$pr #' obs_v=obs_validation$pr #' mod_v=mod_validation$pr #' mod_fut= data_model_future$pr #' #' downscale(obs_c,mod_c,obs_v,mod_v,mod_fut) #' #' @return NULL downscale = function(obs_c,mod_c,obs_v,mod_v,mod_fut) { m_obs_c=mean(obs_c) m_mod_c=mean(mod_c) m_obs_v=mean(obs_v) m_mod_v=mean(mod_v) s_obs_c=stats::sd(obs_c) s_mod_c=stats::sd(mod_c) s_obs_v=stats::sd(obs_v) s_mod_v=stats::sd(mod_v) sh_obs_c=(m_obs_c/s_obs_c)^2 sh_mod_c=(m_mod_c/s_mod_c)^2 sh_obs_v=(m_obs_v/s_obs_v)^2 sh_mod_v=(m_mod_v/s_mod_v)^2 sc_obs_c=s_obs_c^2/m_obs_c sc_mod_c=s_mod_c^2/m_mod_c sc_obs_v=s_obs_v^2/m_obs_v sc_mod_v=s_mod_v^2/m_mod_v ### finding thresholds for calibration data (for both model and obsevartion) p=stats::ecdf(obs_c) thr_obs_c= p(0.0) # return the probabily at zero} threshold_obs_c= (round(p(0.0),3))*1000 # return the probabily at zero in 2 digit # for calibration_obs p=stats::ecdf(mod_c) thr_mod_c= p(0.0) threshold_mod_c= (round(p(0.0),3))*1000 # for calibration_mod p=stats::ecdf(obs_v) thr_obs_v= p(0.0) threshold_obs_v= (round(p(0.0),3))*1000 # for validation_obs p=stats::ecdf(mod_v) thr_mod_v= p(0.0) threshold_mod_v= (round(p(0.0),3))*1000 # for validation_mod n=log(thr_mod_c)/log(thr_obs_c) # FUTURE # parameters m_mod_fut= mean(mod_fut) s_mod_fut= stats::sd(mod_fut) sh_mod_fut= (m_mod_fut/s_mod_fut)^2 sc_mod_fut= s_mod_fut^2/m_mod_fut ### Bias correction xx_mod_fut=mod_fut ff_mod_fut=c(1) crtd_mod_fut=c(1) p=stats::ecdf(mod_fut) thr= p(0.0) threshold=thr^(1/n) # this is new from the convensional bias correction #threshold # turn on/off to view it 233
for (i in 1:length(xx_mod_fut)) ff_mod_fut[i]= stats::pgamma(xx_mod_fut[i],sh_mod_fut,,sc_mod_fut) #ff_mod_fut # turn on/off to view it for (i in 1:length(ff_mod_fut)) if (ff_mod_fut[i] >= threshold) { crtd_mod_fut[i]= xx_mod_fut[i] * stats::qgamma(ff_mod_fut[i],sh_obs_c,,sc_obs_c)/stats::qgamma(ff_mod _fut [i],sh_mod_c,,sc_mod_c) } else{ crtd_mod_fut[i]=0.0} crtd_mod_fut=round(crtd_mod_fut,1) # turn on/off to view it crtd_mod_fut=matrix(crtd_mod_fut) crtd_mod_fut
