Real-Time Updating of Rainfall Threshold Curves for ...

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Real-Time Updating of Rainfall Threshold Curves for Flood Forecasting Saeed Golian 1; Mohammad Reza Fallahi 2; Seyyed Mahmoudreza Behbahani 3; Soroosh Sharifi 4; and Ashish Sharma 5

Abstract: The rainfall threshold (RT) method is a nonstructural flood mitigation approach that is emerging as an effective flood forecasting tool. A critical RT value is the minimum cumulative rainfall depth necessary to cause critical water level or discharge at a cross section of a river. The major drawback of the RT approach is associated with the offline methods used for extracting critical RT values based on some fixed watershed characteristics and rainfall conditions. In this paper, a novel methodology is presented for real-time updating of RT curves for flood forecasting using a rainfall-runoff model and an artificial neural network. In this method, in addition to the rainfall depth, observed discharges are also used to update the rainfall threshold curves for real-time soil moisture and rainfall temporal and spatial patterns. The method was tested on the Walnut Gulch watershed with a 50-min time of concentration for selected historical rainfall events. It was shown that applying the proposed updating method can prevent the issuance of false warning, e.g., for the flood of August 2006, and in some cases increase the lead time of flood forecasting, e.g., 20-min increase in lead time for the flood of June 2008. Using data for 14 major historical rain events, it was shown that by applying the updating method, the hit rate is increased by an average of 28% and the false rate is decreased by an average of 51%. DOI: 10.1061/(ASCE)HE.1943-5584.0001049. © 2014 American Society of Civil Engineers. Author keywords: Artificial neural network; Flood forecasting; Rainfall threshold method; Updating.

Introduction Among all natural hazards, floods are the most frequent, destructive, and costly disasters. Between 1950 and 2000, floods were estimated to account for one-third of all economic losses, half of all deaths, and 70% of homelessness caused by extreme natural hazards (Scheuren et al. 2008). In 2011 alone, floods affected the lives of approximately 139.8 million people and were responsible for 20.4% of the total reported number of fatalities and 19.3% of total damages by natural disasters worldwide (Guha-Sapir et al. 2011). Recently published research on linking climate change to annual maximum floods indicate that the number of reported floods have increased by an average of 7.4% per year (Scheuren et al. 2008; Eshak et al. 2013). To mitigate the negative outcomes associated with flood events, several structural and nonstructural flood-mitigation approaches have been developed. Structural methods of flood control involve the construction of structures such as reservoirs, weirs, diversion 1

Assistant Professor, Civil Engineering Dept., Shahrood Univ. of Technology, 3619995161 Shahrood, Iran (corresponding author). E-mail: [email protected] 2 M.Sc. Graduate, Dept. of Irrigation and Drainage Engineering, Agricultural College of Aboureyhan, Univ. of Tehran, 3391653755 Tehran, Iran. 3 Associate Professor, Dept. of Irrigation and Drainage Engineering, Agricultural College of Aboureyhan, Univ. of Tehran, 3391653755 Tehran, Iran. 4 Lecturer, School of Civil Engineering, Univ. of Birmingham, Birmingham B15 2TT, U.K. 5 Professor, Univ. of New South Wales, Civil Engineering Building (H20), Level 3, Room CE307, Kensington Campus, Australia. Note. This manuscript was submitted on May 15, 2013; approved on June 19, 2014; published online on August 14, 2014. Discussion period open until January 14, 2015; separate discussions must be submitted for individual papers. This paper is part of the Journal of Hydrologic Engineering, © ASCE, ISSN 1084-0699/04014059(9)/$25.00. © ASCE

channels, and levees to prevent bank overflow. In contrast, nonstructural methods aim to reduce the harmful effects of flooding by implementing management concepts such as flood plain zoning, soil and water conservation programs, flood-proofing of individual objects, flood forecasting and warning systems, seasonal reservoir management strategies, flood insurance programs, and public information and education (Lyle 1998; Petry 2002). In addition to not being economically viable and environmentally friendly due to the known hydrologic and hydraulic uncertainties, structural methods are often operationally unreliable (Milly et al. 2002; Goubanova and Li 2007). On the other hand, nonstructural approaches have economical and environmental advantages, and hence are recommended for general implementation [United Nations Environment Programme (UNEP) 2002; Golian et al. 2010]. To achieve a successful and effective flood mitigation program, the best mix of all flood management options available, including both structural and nonstructural approaches, should be considered (Andjelkovic 2001). The aim of flood forecasting and warning systems is to provide in-time useful information for making crucial decisions such as issuing alerts or activating required protection measures (Martina et al. 2006) and mitigating a potential disaster. These systems have been installed and effectively used in the last half century in various parts of the world. The first advanced flood forecasting system, National Weather Service River Forecast System (NWSRSF), was developed by the National Oceanic and Atmospheric Administration (NOAA) and its recent version is used in 13 major watersheds of the United States (UNEP 2002). Denmark, Japan, and France are among the countries that have made substantial investments in the development and implementation of flood forecasting systems and models. These systems range from relatively simple techniques such as correlation of peak levels and flows between different sites to more sophisticated techniques such as rainfall-runoff models linked with hydrological channel routing models. As an evolving forecasting approach, the rainfall threshold (RT) method is commonly used for landslide and debris flow

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hazard forecasting (Neary and Swift 1987; Martelloni et al. 2012) and flood forecasting (Martina et al. 2006; Norbiato et al. 2008; Golian et al. 2010, 2011). A critical RT value is defined as the cumulative rainfall depth, which causes landslide at a particular region of the watershed or critical water level (or discharge) at a cross section of the river. In flood forecasting, a rainfall threshold curve is a plot of threshold values, all corresponding to the same specific discharge, versus time. When for an event the cumulative rainfall depth curve intersects a critical RT curve, the peak discharge at the target point is expected to be equal to or greater than the RT curve critical discharge, and a flood warning may be issued (Fig. 1). The RT method provides a useful concept that allows forecasters to quickly use local precipitation information and to update warnings without the need to run complex forecasting models. Also, by reducing the available information to an interpretable level, this method can be directly used by nontechnical users to make vital decisions (Golian et al. 2010). This approach can also be used as a reliable backup method in the event of the failure of the main flood warning system due to electricity black out or model instabilities (O’Connell 2005). Obtaining rainfall threshold values for dry, moderate, and wet initial soil moisture conditions and performing Bayesian statistical analysis on historic long-term time series of precipitation, Martina et al. (2006) concluded that rainfall thresholds are dependent on the initial soil moisture conditions. Amadio et al. (2003) developed a flood forecasting system by obtaining rainfall threshold values for the critical cross sections of the Arno River in Italy for different initial soil moisture conditions. Using the Hydrologic Engineering Center Hydrologic Modeling System (HEC-HMS), Montesarchio et al. (2009) developed a simple method for deriving rainfall threshold curves for different soil moisture conditions and different temporal distributions. Golian et al. (2010) considered the rainfall spatial distribution in derivation of rainfall threshold curves by applying a Monte Carlo method. Golian et al. (2011) also compared different methods for modeling rainfall spatial dependencies and concluded that the efficiency of flood forecasting methods can be increased by up to 25% compared with the spatially uniform rainfall scenario. The major drawback of the rainfall threshold method is associated with the offline methods used for extracting critical RT values based on some fixed watershed characteristics (e.g., loss parameters) and presumed initial rainfall conditions (i.e., temporal and spatial rainfall distribution). In real-time applications, however, these conditions vary from time to time and one location to another even throughout a single rain event. For instance, land cover usually changes in different seasons, and hence infiltration rates change with time. Moreover, extracting RT values for all possible temporal and spatial rainfall patterns is practically infeasible. The

Fig. 1. Rainfall threshold curve as a flood warning system © ASCE

inability to extract RT values for real-time rainfall conditions and watershed characteristics makes this method less accurate than rainfall-runoff approaches used for flood hazard assessment. In this paper, a novel methodology is presented for real-time updating of critical RT curves and enhanced flood warning decision making. In this approach, an artificial neural network (ANN) is employed for correcting the predictions of a rainfall-runoff model for real-time watershed characteristics and rainfall conditions. As a case study, the proposed methodology is applied for updating hypothetical critical RT curves for two flood events at the Walnut Gulch Experimental Watershed (WGEW) in Arizona. It is shown that updating RT curves using this approach can improve the accuracy of flood forecasting.

Artificial Neural Network ANN is a system that imitates the neural system of human brain for solving different types of problems. Mathematically, an ANN represents a class of ﬂexible nonlinear models that is capable of discovering hidden patterns from data without making prior assumptions about the underlying relationships (Zheng and Zhong 2011). A neural network consists of a number of interconnected layers of neurons (computational units), which convert an input vector into the output (Fig. 2). Adjacent layers are connected by links that govern the flow of information between neurons. Each neuron first applies weights to its inputs, then applies a function to the sum of weighted inputs, and finally passes the output on to the next layer. The weights are the most important factor in approximating the desired output and their values are adjusted in a process called training. In this process, first the network is initialized by assigning small random values to the network’s weights. Then the network is shown how it is expected to behave by presenting it with a number of examples, i.e., pairs of input and expected outputs. Training occurs through an algorithm called back-propagation (BP) (Rumelhart and McClelland 1986) in which the inputs of a training pair are presented to the network and an output is calculated. This output is then compared with the training pair output (expected output) and an error is calculated that is used for adjusting the weights of the network. This process is repeated for all the training pairs and the network’s output is improved at each step through the adjustments of the weights. Once the network is trained, its performance is validated using a set of unseen data. For an in-depth review of ANNs and their application, the reader is referred to Govindaraju and Rao (2000). Neural networks have been used extensively in hydrology (Maier and Dandy 2000) for solving a wide variety of problems including discharge forecasting (Brath et al. 2002), time series prediction (Zheng and Zhong 2011), and improvement of hydrological models in real-time applications (Anctil et al. 2003).

Fig. 2. Schematic diagram of a multilayer perceptron (MLP) artificial neural network 04014059-2

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Methodology The method proposed in this study for real-time updating of RT curves is based on updating the output of a calibrated rainfall-runoff model by estimating its prediction error for revised soil moisture and rainfall pattern conditions using an ANN. For this purpose, first a suitable rainfall-runoff model is selected and calibrated using historic recorded data. Generally, any event-based semidistributed or distributed rainfall-runoff model can be used for RT curve updating. The main criteria for selecting an appropriate hydrologic model are ease of use, required input data versus accessible data, spatial discretization scale, and history of past usage in the study area (Saghafian et al. 2013). Calibration is generally performed by comparing simulated and observed hydrographs for a number of historic rainfall events. Following this, a set of rainfall threshold curves is derived for different possible watershed conditions and spatial and temporal rainfall patterns, each corresponding to a different discharge at the target points (e.g., watershed outlets). This is achieved using an inverse modeling procedure in which the calibrated hydrologic model is run iteratively with different rainfall depths for a specific set of possible rainfall duration and initial soil moisture conditions (Golian et al. 2010). Due to the small size of the watershed, the rainfall spatial distribution was assumed to be uniform and Huff’s (1990) distribution was adopted as the temporal pattern of the rainfall. Fig. 3 schematically shows a number of RT curves for a target point of a watershed each corresponding to a different discharge. This figure also shows that at any time step during a rainfall, in addition to the observed discharge (Qo ) measured at the target point, a discharge value can also be obtained from the interpolation between two critical discharges corresponding to the two adjacent RT curves (QRT ), henceforth referred to as the interpolated discharge. The difference between these two discharges is considered as the observed error (eo ¼ Qo − QRT ). In the next step a multilayer perceptron (MLP) ANN is trained, i.e., the weights of each of its neurons are adjusted. Here, various time steps of a number of historical rainfall events and the corresponding calculated observed error values (eo ) were used for training the ANN. To update a critical RT curve for a real-time event, the time series of the event’s cumulative rainfall is considered. The following steps are then performed: 1. For t initial time steps, observed errors (eo ) are calculated using observed discharge values (Qo ) and adjacent RT curves.

2. For the next time step, calculated observed errors from the previous t time steps are fed into the trained ANN to predict the model’s error ½es ðt þ 1Þ. 3. Updated discharge ½QRTA ðt þ 1Þ is calculated by adding the predicted error ½es ðt þ 1Þ to the interpolated discharge ½QRT ðt þ 1Þ. 4. QRTA ðt þ 1Þ is compared with the critical discharge of the RT curve (Qc ) and a warning is issued if QRTA ðt þ 1Þ > Qc . 5. Steps 2 to 4 are repeated for the next time steps until the cumulative rainfall intersects the critical RT curve. 6. At this time step, the RT curve represents the real-time updated discharge (QRTA ), and hence its position should be updated. This is done by shifting the curve upwards or downwards by a rainfall adjustment depth equivalent to QRTA − QC , which is obtained by interpolating between the critical RT curve and adjacent RT curves. The selection of t depends on the time step length of recorded data and a suitable value for t can be found through trial and error. For a data set with a given time step, a value of t is considered suitable if using a larger value for it would produce similar updated RT curves, whereas considering a smaller number would produce significantly different error values. Fig. 4 illustrates the steps for calculating real-time discharges and Fig. 5 summarizes the entire real-time RT updating process. Performance Evaluation of the RT Curve Updating Method The performance of the proposed RT curve updating method can be evaluated for a number of rain events using a 2 × 2 contingency table (Montesarchio et al. 2009) (Table 1). This table presents the four possible situations that may occur for a given rain event. A hit is the situation when the updated discharge exceeds the discharge of the critical RT (QRTA > QC ) and a warning is issued. If a warning is not issued for this situation, it is regarded as a miss. When QRTA is less than QC and a warning is issued, there is a false alarm, but if correctly no warning is issued, there is a correct rejection. Performance evaluation is performed by calculating the hit rate and false alarm rate criteria, defined as follows: Hit rate ¼ of hits=ðof hits þ of missesÞ

ð1Þ

False rate ¼ of false alarms=ðof false alarms þ of correct rejectionsÞ

ð2Þ

The value of hit rate varies from 0 to 1, the latter value being desirable. Also the range of values for false rate goes from 0 to 1, the former value being desirable. To evaluate the performance of the method, the values of these performance criteria are compared before and after adopting the proposed updating method for an RT curve.

Fig. 3. Schematic illustration of RT curves and their use for calculating QRT © ASCE

Fig. 4. Obtaining error time series and updating RT curve discharge

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on the lower two-thirds and desert grasses on the upper one-third. The precipitation regime is dominated by the North American monsoon with approximately 60% of the annual total coming during July, August, and September with events that are localized shortduration, high-intensity convective thunderstorms. Almost all the runoff is generated by summer thunderstorm precipitation and runoff volumes and peak flow rates vary greatly with area and on an annual basis (Goodrich et al. 2008). A network of 88 weighing rain gauges arranged in a grid throughout the watershed is used to measure the precipitation. Various runoff measuring structures, including broad-crested V-notch weirs, H-flumes, and Santa Rita supercritical flow flumes, are used to measure runoff. Geographic information system (GIS) data layers are available for a number of the watershed’s characteristics including elevation, land use, slope, soil type, vegetation, and channel network, enabling systematic study and modeling of the watershed. Fig. 6 shows the elevation map of the WGEW watershed and the location of the selected target point (flume 1), which is located at the outlet of the watershed. For more information about the WGEW watershed, the reader is referred to Goodrich et al. (2008), Renard et al. (2008), Stone et al. (2008), and Heilman et al. (2008). Also, the data used in this study can be found on the USDA’s online database (2014a). To evaluate the proposed updating approach, 14 major historical flood events (Table 2) were selected and used for both training the ANN and evaluating the performance of the method. Rainfall data were obtained by averaging the data from all available rain gauges over the entire watershed.

Results

Fig. 5. Different stages of the proposed RT curve updating methodology; the shaded boxes represent the stages that are different from other RT studies

Table 1. Two by Two Contingency Table Used for Updating Performance Evaluation (Adapted from Montesarchio et al. 2009) Observation Intersection No intersection

Warning

No warning

Hit False alarm

Miss Correct rejection

Case Study To test the proposed methodology, the WGEW in southeast Arizona (31°43′N, 110°41′W) was chosen for its large number of rain gauges and flow measurement flumes and also availability of historic precipitation and discharge data needed for testing the methodology. The watershed has an area of 150 km2 and its elevation ranges from 1,220 to 1,950 m. WGEW is located between the Sonoran and Chihuahuan deserts and surrounds the city of Tombstone, Arizona, which has a semiarid climate, mean annual temperature at of 17.7°C, and mean annual precipitation of 312 mm. The watershed is mainly covered with desert shrubs © ASCE

In this study, the HEC-HMS model (USACE HEC 2000) was chosen as the hydrologic model for updating RT curves at the selected target point. Within the model, the Soil Conservation Service curve number (SCS-CN) (SCS 1971) and Clark unit hydrograph (Kull and Feldman 1998) methods were used to model infiltration losses and for transforming excess rainfall to runoff, respectively, and the Muskingum method was used for flood routing in reaches. Initial CN values were derived from relevant tables by overlaying land-use and soil hydrologic group maps (Maidment 1993). Model calibration was performed manually by trial and error on a subset of the data by visual comparison between simulated and observed hydrographs with more emphasis on arriving at a better fit between simulated and observed peak discharges (Golian et al. 2010). Manual calibration is the most widely used approach to calibrate hydrologic models based on closeness of some criteria, i.e., objective measures or visual comparison of the model outputs and observed data (Boyle et al. 2000; Blasone et al. 2007). In addition to visual comparison, two goodness-of-fit criteria, namely, coefficient of determination, R2 , and Nash-Sutcliffe efficiency index (NSE), were estimated for the calibration data set and also a subset of unseen events (validation data set) to help in selecting the final calibration parameter set. Fig. 7 illustrates the modeled versus observed hydrographs for selected events of the calibration and validation datasets. The HEC-HMS model parameters for WGEW’s subwatersheds are given in Table 3. In this table, Tc is time of concentration and R is the storage coefficient in Clark unit hydrograph method. Following the inverse modeling method, the calibrated HECHMS was used to extract hypothetical RT curves at the target point for critical discharges between 2 and 100 cm (Fig. 8). For this purpose, recorded rainfall depths at rain gauge stations were used to calculate a spatially averaged rainfall value over the watershed.

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Fig. 6. WGEW elevation map and location of the target point [data from USDA Agricultural Research Service (ARS) 2014b]

Table 2. Summary of the Selected Flood Events Date August 6, 2000 October 19, 2000 August 14, 2001 August 4, 2002 August 27, 2003 August 9, 2005 August 11, 2006 September 4, 2006 July 20, 2007 July 27, 2007 August 6, 2007 July 19, 2008 July 26, 20100 July 25, 2011

Peak discharge (cm)

Total precipitation (mm)

55.6 15.3 14.26 33.27 33.5 10.4 18.6 32.2 17 12.3 19.2 43.8 9.15 20.9

28.8 26.9 7.1 15.5 32.7 8.8 15.1 7.5 32.5 10.5 13.3 33.4 10.8 8.7

This assumption is in accordance with the small size of watershed (147 km2 , approximately). Also the Huff distribution (Huff 1990) was used for calculating the rainfall temporal distribution. In the next step, an MLP ANN model was employed for the prediction of error time series. Using extracted RT curves, the observed error (QRT ) was calculated for the time steps of a number of historic rainfall events. These data were then partitioned into three data sets: (1) training data set, which was used for training the ANN (fitting its internal parameters, i.e., weights); (2) validation data set used for obtaining the required number of hidden units and © ASCE

neurons; and (3) test data set, which was used for assessing the overall performance of the trained ANN. Here, a feedforward network with BP learning algorithm (Levenberg-Marquardt method) was employed to predict errors with linear and hyperbolic tangent sigmoid transfer functions as the transfer functions of the output and hidden layers, respectively. The effectiveness of the ANN was evaluated by comparing its predictions for all three data sets using the root-mean-squared error (RMSE) and coefficient of determination (R2 ) goodness-of-fit criteria (Table 4). Based on this analysis, a three-layer neural network with five neurons in the hidden layer was found to be suitable for the purpose. Two rainfall events during the summers of 2006 and 2008 were selected for updating hypothetical critical RT curves using the proposed methodology. These events were selected to illustrate two advantages of updating the RT curves, i.e., (1) preventing false alarm and increasing the accuracy of RT method (August 2006 flood event) and (2) increasing the lead time by applying the updating method on RT curves (June 2008 flood event). August 2006 Rainfall Event This event occurred on August 20, 2006, had a total average rainfall depth of 27 mm over a 6-h period, and produced a peak discharge of 19.52 cm at the target point. For this event, 20-cm discharge was assumed to be critical. The recorded data had a time step length of 1 min and through trial and error the suitable value of t was determined to be 9. Table 5 shows the data for the first nine time steps of

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Fig. 7. Modeled versus observed hydrographs for (a) calibration (September 1999); (b) validation (October 2007) events

Table 3. Parameters of HEC-HMS Model for WGEW’s Subwatersheds Subwatershed W1 W2 W3 W4 W5

Area

(km2 )

CN (I)

Tc (h)

R (h)

Time step

46 45 68 71 48

0.54 0.5 0.39 0.4 0.3

0.18 0.17 0.13 0.13 0.1

1 2 3 4 5 6 7 8 9

41.2 15.2 19 35.3 35.9

Fig. 8. RT curves extracted for critical discharges between 2 and 100 cm

Table 4. Performance of the Trained ANN on Training, Validation, and Testing Data Sets Performance index RMSE R2

Training

Validation

Test

All data combined

2.62 0.99

5.12 0.97

5.46 0.98

4.83 0.99

this event and the calculated errors used as inputs to the trained ANN for predicting the errors in the next time steps. In this table, each time step is equal to 1 min and so the indicated times are real times from the onset of the event. To demonstrate the real-time updating method, the cumulative rainfall time series of this event was used for updating three hypothetical RT curves at 2, 5, and 20 cm. © ASCE

Table 5. Difference between QRT and Observation Discharge (Qo ) Time (min)

PCum

Qo

QRT

eo ðtÞ

1 2 3 4 5 6 7 8 9

0 0.01 0.02 0.03 0.03 0.03 0.03 0.15 3.27

0 0 0.57 0.75 1.00 1.30 1.64 2.04 2.48

0 0 0.01 0.01 0.01 0.01 0.01 0.05 1.08

0 0 0.55 0.74 0.98 1.28 1.63 1.98 1.39

The cumulative rainfall curve of this event intersects the 2-cm RT curve after 143 min from the start of the rainfall. Hence, the calculated errors of nine previous time steps (from 133 to 142 min) were fed into the trained ANN and the value of estimated error for the 143th time step was obtained as 0.89 cm. This error was added to the QRT of 2 cm and the updated threshold discharge (QRTA ) was calculated as 2.89 cm. As a result of the updating, it was found that the RT curve at its original location corresponds to a 2.89-cm discharge, and therefore its position needs to be adjusted. Because the estimated error was positive, the RT curve was shifted downwards by a rainfall value equivalent to 0.89 cm [Fig. 9(a)]. Similarly, the cumulative rainfall curve intersects the 5-cm RT curve at the 173th time step, and following the same updating approach a QRTA of 3.79 cm was obtained. Hence, the RT curve was shifted upwards to its real-time position [Fig. 9(b)]. Because the cumulative rainfall curve intersects the 20-cm RT curve [Fig. 9(c)], assuming that 20 cm is the critical discharge at the outlet of the watershed, a warning should be issued. However, the maximum observed discharge for this event was recorded as 19.52 cm, and therefore this would be a false alarm. In other words, issuing a warning based on the offline 20-cm RT curve would cause a false alarm. But as is shown in Fig. 9(c), after updating the 20-cm RT curve, the cumulative rainfall does not intersect this RT line and there is no need for a flood warning to be issued. June 2008 Flood Event As another example, the June 2008 rain event was selected for testing the effect of updating RT curves on the accuracy of issuing flood warnings. This event happened on June 12, 2008, had a total rainfall depth of 26 mm over a 3.5-h period, and produced a peak

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Fig. 9. Updating (a) 2; (b) 5; (c) 20-cm RT curves for the August 2006 flood event

Table 6. Hit Rate and False Rate before and after Updating RT Curves for a Critical Discharge of 20 cm Performance criterion

Before updating

After updating

0.63 0.43

0.85 0.25

Hit rate False rate

Table 7. Hit Rate and False Rate before and after Updating RT Curves for Different Critical Discharges Critical discharge (m3 =s) 10

Fig. 10. Updating the 30-cm critical RT curve for the June 2008 flood event

15 25 30

discharge of 42 cm at the target point. For this event, a 30-cm discharge was assumed to be the critical. Fig. 10 shows the 30-cm RT curve before and after updating. It is observed that the cumulative rainfall curve intersects the original 30-cm RT curve at the 152nd time step. However, after updating, the 30-cm RT curve is shifted down and the cumulative rainfall curve intersects the updated 30-cm RT curve at the 132th time step. This means that using updating causes the lead time of flood forecasting to be increased by 20 min, which is considerable in comparison to the time of concentration of the watershed (approximately 50 min). Performance Evaluation To evaluate the proposed updating procedure using 14 major historical rain events (Table 2) and assuming a 20-cm critical discharge, the contingency table was generated once before and © ASCE

Performance criterion

Before updating

After updating

Hit rate False rate Hit rate False rate Hit rate False rate Hit rate False rate

0.63 0.51 0.58 0.48 0.71 0.58 0.58 0.52

0.81 0.18 0.79 0.27 0.83 0.31 0.73 0.22

once after updating all the RT curves, and subsequently the false rate and hit rate performance criteria were calculated (Table 6). It was observed that after updating the number of hit events increased from five to six events, while the number of false events decreased from three to one. As a result, the hit rate increased from 0.63 to 0.85 after updating (34% rise in the number of hits) and the value of the false rate criterion dropped from 0.43 to 0.25 (41% decrease in the amount of false alarms). These numbers indicate that updating the RT curves by the proposed method can significantly improve the accuracy of flood forecasting. To investigate the effectiveness of the proposed method for other critical discharges, simulations were repeated for 10-, 15-, 25-, and 30-cm critical discharges and the contingency table was produced (Table 7). As can be seen, for all investigated critical discharges

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updating the RT curves has caused the hit rate to improve by an average of 27% and the false rate to drop by an average of 53%.


Conclusions In this paper, a methodology was presented for real-time updating of rainfall threshold curves and improving the accuracy of flood forecasting. In the conventional rainfall threshold method, only observed rainfall depths are used for decision making, but in the proposed method observed discharges are also utilized. In this method, after calibrating a suitable rainfall-runoff model an inverse hydrological modeling approach is used to extract RT curves for critical discharges. Then, using the data of some historical rainfall events, an ANN is trained to estimate the prediction error of the rainfallrunoff model for real-time watershed and rainfall pattern conditions. The updated critical discharge at any time step during the event is calculated by adding the predicted error for that time step to the interpolated discharge from RT curves. The proposed method was tested on the Walnut Gulch Experimental Watershed for some hypothetical critical discharges and historic rain events. It was shown that applying the proposed updating method can prevent the issuance of false warning and in some cases increase the lead time of flood forecasting. Using the data of 14 major historical rain events and considering five critical discharges, on average, the hit rate increased from 63 to 85% and the false rate decreased from 43 to 25%. It was concluded that applying the updating approach and using real-time observed discharges can significantly improve the reliability of flood forecasting based on the rainfall threshold method. The proposed methodology can only be applied to gauged basins that are equipped with hydrometric gauges at target points. For improving the accuracy of the RT method for ungauged basins, other techniques should be sought and investigated. Furthermore, errors from the adopted hydrologic model and its calibration quality will affect the final result. The method should be further developed to include the uncertainties associated with different sources of uncertainty including model and parameter uncertainties. Further applications of ANN for updating RT curves, such as applying ANNs with different architectures for predicting the errors of more time steps ahead, could be the subject of future works.

Notation The following symbols are used in this paper: eo = observed error for any time step; es = simulated error from ANN for any time step; QRT = interpolated critical discharge from RT curves before updating; and QRTA = ipdated discharge.

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