Modeling Ungauged Tributaries using Geographical Information Systems (GIS) and System Dynamics Carlos A. Aragón1, Len A. Malczynski2 , Enrique R. Vivoni1, Vince C. Tidwell2, and Sarah Gonzales1.
Abstract While there are many instrumented basins throughout the world, the majority of watersheds that act as tributaries remain ungauged, in particular for semiarid areas. In this study, we will present results from the application of a semi-distributed watershed model in the Río Salado basin, New Mexico, USA. The model is formulated in Powersim Studio 2005, a system dynamics software package capable of representing physical process equations in a graphical manner. Geographical information systems (GIS) are used to both pre-process data into the model domain (e.g. hydrological response units) and to post-process spatial model results. For example, by processing data in ArcMap and ArcHydro, land-surface properties of a tributary can be used as input parameters for the model. The goal of this project is to combine current GIS tools with a dynamic watershed model to create maps depicting an estimate of the contributions of ungauged, semiarid tributaries, such as the Río Salado, to larger main-stem rivers.
Introduction Uninstrumented watersheds pose a problem to scientists around the world, in that the degree to which they contribute to the water balance of a region cannot be measured. Often this unaccounted for water is simply lumped in with other difficult to measure components of the water balance such as groundwater discharge. This may produce a balanced model of the system, however water policy decisions are often based on surface water and groundwater flow rates. In order for these decisions to be made correctly, there should be a proper allocation of water resources (Ward et al. 2006). The ungauged tributary model was created as part of a joint effort by the New Mexico Institute of Mining and Technology and Sandia National Laboratories to address this issue, and provide local governments with a tool to aid in the water allocation process. Part of a larger decision-support model, that includes economic, ecological, and water right factors, applied to the Middle Río Grande region in New Mexico, the ungauged tributary model presented here focuses on the production of runoff by uninstrumented watersheds. In order to test the accuracy of the model, it is first applied to the Río Salado, a fairly well instrumented watershed in central New Mexico. This allows model output to be compared to historical data in order to build confidence in the model performance. The larger system dynamics model is run on a monthly time step to reduce computational time, with the goal of near real time use in a decision-making setting with interested stakeholders (Ahmad et al. 2004; Nandalal et al. 2003). To account for the variability of precipitation within a month, an event based timing structure was
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implemented in the ungauged tributary model. This required that a great deal of the model development occur within the VB-script language, embedded in Powersim, a system dynamics software package. For the model development described here Powersim is the primary software package utilized. Powersim is dynamically linked to Microsoft EXCEL, in that it is able to transfer input and output directly to EXCEL while the model is running. Parameter values necessary for the model were calculated using ESRI GIS software packages, and then modified in EXCEL to be used by the Powersim model. After the model runs were completed, output stored in EXCEL was used to create maps in GIS, such as the percentage of total runoff contributed by each portion of the watershed (Figure 1).
Figure 1 – Flowchart describing how the software packages interact, with EXCEL acting as the link between GIS and the Powersim model. Methods The ungauged tributary model is formulated in Powersim Studio 2005, a system dynamics software package able to represent physical process equations in a graphical manner similar to a flowchart (Powersim, 2006). Powersim uses a combination of four basic symbols to depict an equation: constant, auxiliary, stock and link. Constants hold a single value or an array of values and can be used to toggle between values to examine sensitivity of parameters. Auxiliaries hold equations that combine constants, other auxiliaries, and flows from stocks. Auxiliaries also allow the use of VB-script to program more complex equations. In this model VB-script was used for the water balance loops, which required calculations to be run on a smaller timescale than the monthly one set for the model. Stocks act as buckets, holding information and increasing or decreasing storage amounts at each time-step based on the auxiliary controlled flows connected to it. Links, as their name implies, provide a pathway for information between the other three symbols, and control the direction that information moves. Comprised of multiple components that account for the physical processes that take place in a watershed, the ungauged tributary model attempts to determine the amount of runoff produced by a watershed given a rainfall event. Input of rainfall is first step in the water balance equation for a watershed. Due to the scarcity of rainfall data, perhaps the most important factor for runoff generation, models often create synthetic rainfall time series to use as forcing. The synthetic rainfall component adopted in this model is a stochastic rainfall scheme based on work by Rodriguez-Iturbe and Eagleson (1987) that starting from the mean values of precipitation intensity, storm duration, and inter-storm duration,
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for each month, generates new synthetic values for each storm event. The new synthetic value is the mean multiplied by the natural log of a randomly generated number between 0 and 1. The maximum and minimum temperatures for each storm event were calculated in the same manner. The next step in the water balance for a watershed is interception by the vegetation cover in the basin. The interception component of the Brook90 model was used because of its simplicity, which eased in implementation in Powersim. The interception rate is the fraction of total rainfall intercepted by leafs in the canopy based on the leaf area index or LAI (Federer, 1995). Rain that is not intercepted or falls through the canopy, as well as rain that falls on unvegetated portions of the watershed, reaches the soil and is relocated depending on the state of the hydrologic system at the time. The water balance at the land surface is modeled after the Three Layer Variable Infiltration Capacity (VIC-3) model created by Liang et al. (1994, 2001). The VIC-3 model divides a watershed into land cover units based on vegetation type and calculates runoff based on a three-soil-layer infiltration model (see Figure 2). The land surface was classified into hydrologic response units (HRUs), which are contiguous parcels of the land surface with unique soil and vegetation types (Arnold et al. 2005). Water that reaches an HRU infiltrates into the first 10 cm layer of the soil, which represents the topsoil.
Figure 2 – Schematic that represents the three-soil-layer infiltration model as applied to each HRU in the Rio Salado.
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As the soil layer fills, water drains to the lower layers, is evaporated directly from the soil, or is transpired by vegetation. Evapotranspiration from the first layer is fashioned after the Hargreaves Evapotranspiration (ET) model (Hargreaves 1975; Hargreaves et al. 1985; Hargreaves et al. 2003). The maximum monthly potential evapotranspiration is calculated based on the amount of incoming solar radiation and monthly air temperature values (max, min, mean) (Hargreaves 1975; Hargreaves et al. 1985; Hargreaves et al. 2003). After the first layer of soil reaches its holding capacity, any water added becomes runoff and is routed to the watershed outlet. All of the water produced by an HRU is routed directly to the outlet; the time required for a runoff pulse to reach the watershed outlet is determined by the Manning equation. Variables required in this calculation such as slope and distance to the outlet were obtained from the GIS processing of the HRUs. The temperature based precipitation allocation method of the Brook90 model was used to partition a portion of the precipitation as snowfall (Federer, 1995). Melting of the snow is based on the degree-day method developed by Martinec et al (1983). In order to acquire input parameters for the Powersim model, preprocessing was performed using the ArcHydro toolbar in ArcMap. The HRUs for the Rio Salado were created in ArcMap with the following steps, presented in a graphical manner in Figure 3: 1. Similar soil and vegetation types are combined into new classes by adding a new (soilclass/vegclass) column to the attribute table. 2. Adjacent identical classes are dissolved to limit the total number of HRUs created in the basin. 3. Intersecting the soils map and vegetation map creates an HRU map. 4. Each HRU is then exported to a unique coverage file so that the DEM and flow length grids can be clipped to determine routing parameters. 5. Characteristics for each HRU are stored in an EXCEL spreadsheet for use by Powersim model. The original soils map was created from the NM STATSGO Soil Classes data, while the vegetation map was created from the National Land Cover Data for NM. Both datasets can be located on the University of New Mexico’s RGIS database website at http://rgis.unm.edu/data_entry.cfm. The ungauged tributary model will be applied to the middle Río Grande sub-basin, which stretches from Ottowi bridge, in northern NM to Elephant Butte Reservoir in the south. The total river distance is about 320 km, and the total basin area is nearly 60,000 km2. The basin is comprised of more than 174 separate watersheds ranging in size from 8 km2 to 18,000 km2. The watersheds were derived using the ArcHydro processing tools in the following manner. First the sinks in the DEM are filled so that all flow will move to a basin outlet. Next the flow direction is determined for each cell and the flow accumulation or number of upstream cells is calculated. Using threshold value of 9 km2, a stream network is defined, which is used to determine the boundaries of the small catchments. In this way, the total number of tributaries flowing into the Río Grande was determined. This study focuses on the Río Salado, a semi arid ephemeral watershed
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located in central New Mexico. The Río Salado covers approximately 3,500 km2 and has an average annual rainfall of about 400 mm (Simcox, 1983; Vigerstøl, 2003).
Figure 3 – GIS processing to reclassify soil and vegetation maps, which combined produce an HRU map. Note in c) the flow paths to the basin outlet for three of the HRUs are shown.
The Río Salado was selected because of its location within the Middle Río Grande study area (Figure 4, upper left corner) and because of its semiarid nature (Caylor et al. 2005). Although the Río Salado does not contribute much flow to the Río Grande it does contribute a great deal of sediment (Simcox, 1983). The ability to predict future flow rates in the Río Salado may aid in predicting sediment loading as well. Another reason for selecting the Río Salado is the availability of rainfall and stream flow data. There is a stream gauge near the outlet to the Río Grande with hourly measurements from 1947 to 1984, as well as numerous rain gauges with records of varying lengths (Figure 4). This data will eventually be used to calibrate the model and assess its performance.
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Figure 4 – Rio Salado watershed location in the state of New Mexico. The colors on the watershed are 200 m elevation contours. Rain gauges are shown in yellow and the stream gauge near the outlet to the Río Grande is shown in red. Results Setting up the model for its initial run on the Río Salado required the collection of soil and vegetation parameters for each HRU and creation of a parameter database. Soil parameters in the model such as hydraulic conductivity and porosity were based on values from Clapp and Hornberger (1978). The necessary vegetation parameters came from tables found in two sources: LAI values (Federer, 1996) and other plant parameters such as interception capacity (Breuer et al. 2003). The mean monthly air temperature data, used to stochastically generate event temperatures, was derived from daily values collected at the Red Tank site for 2003. Red Tank is located within the Río Salado watershed just northwest of the outlet, in a juniper shrubland. Mean precipitation values used to generate storm events were set to simulate the scarcity of storms in semi-arid regions, mean precipitation = 5 mm/hr, mean storm duration = 1 hour, mean interstorm duration = 15 days. These values were selected to simulate convective summer storms for which the model was applied. The model was setup to run for a full year and the output shown in Figure 5 is from the month of June. While the model is applied to each HRU within the Río Salado separately, the time series shown are summations of hourly values for the entire basin. A total volume of just over 12.5 million cubic meters of water was applied over the month with single storms contributing as much as 1 million cubic meters of water in just three hours.
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This extremely large volume is due to rainfall being applied uniformly to an HRU for the entire duration of a storm. With such large volumes of rainfall, the high runoff volume of 7 million cubic meters is not surprising. These high volumes will be tested against historical observations during future calibrations. The ET ratio, a measure of the aridity of a region, is calculated from the model output shown in Figure 5 by dividing the precipitation volume by the volume of water lost to evapotranspiration (Budyko, 1974). Arid areas have a precipitation to potential evapotranspiration ratio equal to or greater than 0.05 and less than 0.20 (UNSD, 2004). The runoff ratio computed as runoff volume divided by precipitation volume is a measure of the efficiency of a watershed to produce runoff. For this simulation the ET ratio is 0.09 and the runoff ratio is 0.59, which shows that the simulated Río Salado is arid and capable of producing large runoff volumes.
Figure 5 – Time series of model output for a typical synthetic June. The light blue line at the top of the graph is the rainfall, the dark blue at the bottom is the runoff and the red continuous line is the ET. Figure 6 illustrates an example of spatial output from the model. It is important to note that the percentage of the total runoff contributed by each HRU shows that very few HRUs are responsible for the amount of runoff that reaches the river. In this simulation three HRUs contribute over 65 percent of the total runoff. The average response time for storms in this simulation is 16 hours, which is caused by the HRUs that produce runoff being located a great distance (60-100 km) from the basin outlet.
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Figure 6 – Spatial map of the percentage of the total runoff contributed by each HRU. Note that a majority of the runoff is produced by three HRUs, while the remainder of the watershed produces little to no runoff. Conclusions The output from the model is very encouraging because the watershed seems to respond realistically to the synthetic rainfall that is applied, when examining the timing and magnitude of the runoff pulses. Even though the model has yet to be calibrated, the results show reasonable behavior. In order for the calibration of the model to be successful and as accurate as possible, new parameter values that better represent the actual conditions in the Río Salado will need to be tested. In the case of the precipitation data this will be achieved by processing historical data from the rain gauges in the area. The problem of rain falling uniformly over an entire HRU must still be addressed and should reduce the total volume of precipitation that is applied to the model. Due to the random nature of the rainfall generator applied to each HRU, there will be a unique model simulation for every month, and different HRUs will contribute runoff to the ungauged tributary outlet. Once the model has been shown to accurately simulate the Río Salado, it will be tested in another instrumented basin such as the Río Puerco to see which parameter values are transferable and which will need to be calibrated to each watershed. Finally, it will be applied to the remaining watersheds in the Middle Rio Grande basin to estimate the ungauged additions to monthly flow in the river. Overall this is an important first step at determining the contribution of streamflow by ungauged tributaries to rivers in semi-arid regions. In the near future this model will become a useful tool in the realm of water policy decision-making. 8
Acknowledgments Sandia National Laboratories and New Mexico Institute of Mining and Technology, Department of Earth and Environmental Sciences provided the majority of funding for this research. NMAGEP provided additional research funding, and with the assistance of the New Mexico Tech Graduate Student Association provided travel funding to attend the ESRI International User Conference. Glen Jones and the New Mexico Bureau of Geology & Mineral Resources provided technical support and registration to the conference. References Ahmad S, and SP Simonovic, 2004, Spatial system dynamics: New approach for simulation of water resources systems, Journal of Computing in Civil Engineering 18 (4): 331-340 OCT Arnold JG, and N Fohrer, 2005, SWAT2000: Current capabilities and research opportunities in applied watershed modeling, Hydrological Processes 19 (3): 563-572 Sp. Iss. SI FEB 28 Breuer L, K Eckhardt, and HG Frede, 2003, Plant parameter values for models in temperate climates, Ecological Modeling169 (2-3): 237-293 NOV 15 Budyko, MI, 1974, Climate and Life, translated from Russian by D. H. Miller, Academic, San Diego, Calif. Caylor KK, S Manfreda, and I Rodriguez-Iturbe, 2005, On the coupled geomorphological and ecohydrological organization of river basins, Advances in Water Resources 28 (1): 69-86 JAN Clapp Rb, and GM Hornberger, 1978, Empirical equations for some soil hydraulicproperties, Water Resources Research 14 (4): 601-604 Federer, CA, 1995, BROOK90: A simulation model for evaporation, soil water, and sreamflow, version 3.1. Computer freeware and documentation. Durham, NH: U.S Forest Service Federer, CA, 1996, Intercomparison of methods for calculating potential evaporation in regional and global water balance models, Water Resources Research Vol. 32, NO 7, Pages 2315-2321 Hargreaves, G. H. ~1975, Moisture availability and crop production, Trans. ASAE, 18~5!, 980–984.
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Hargreaves GL, GH Hargreaves, and JP Riley, 1985, Irrigation Water Requirements for Senegal River Basin, Journal of Irrigation and Drainage Engineering-ASCE 111 (3): 265275 Hargreaves GH, and RG Allen, 2003, History and evaluation of Hargreaves evapotranspiration equation, Journal of Irrigation and Drainage Engineering-ASCE 129 (1): 53-63 JAN-FEB Liang, X, DP Lettenmaier, EF Wood, and SJ Burges, 1994, A simple hydrologically based model of land surface water and energy fluxes for general circulation models, Journal of Geophysical Research 99(D7), 14415–14428. Liang, X, and ZH Xie, 2001 A new surface runoff parameterization with subgrid-scale soil heterogeneity for land surface models, Advances in Water Resources 24(9/10), 1173–1193. Martinec, J, A Rango, and E Major, 1983, The Snowmelt-Runoff Model (SRM) User’s Manual, NASA Reference Publ. 1100, Washington, D.C., USA Nandalal, KDW, and SP Simonovic, 2003, Resolving conflicts in water sharing: A systemic approach, Water Resources Research 39(12), 1362, oi:10.1029/2003WR002172 Powersim, 2006, Powersim Software – The Business Simulation Company, http://www.powersim.com/ Rodriguez-Iturbe I, PS Eagleson, 1987 Mathematical- Models of rainstorm events in space and time, Water Resources Research 23 (1): 181-190 JAN Simcox, Alison C, 1983, The Río Salado at flood, New Mexico Geological Society Guidebood, 34th field conference, Socorro Region II UNSD, 2004, UNSD/UNEP Questionnaire 2004 on environment statistics http://unstats.un.org/UNSD/environment/q2004land.pdf Vigerstøl, Kari, 2003, Masters Thesis – Drought management in Mexico’s Río Bravo Basin, University of Washington Ward, FA, BH Hurd, T Rahmani, and N Gollehon, 2006 Economic impacts of federal policy responses to drought in the Rio Grande Basin, Water Resources Research 42, W03420, doi:10.1029/2005WR004427.
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Author Information Carlos A Aragon, Graduate Research Assistant, Department of Earth and Environmental Sciences, New Mexico Institute of Mining and Technology, 801 Leroy Pl. – MSEC 216, Socorro, NM 87801,US, 505-385-2351,
[email protected] Dr. Leonard A Malczynski, Geohydrology Department, Sandia National Laboratories, PO Box 5800, Albuquerque, NM 87185, US, 505-844-7219,
[email protected]
Dr. Enrique R Vivoni, Department of Earth and Environmental Sciences, New Mexico Institute of Mining and Technology, 801 Leroy Pl. – MSEC 244, Socorro, NM 87801, US, 505 835-5611,
[email protected] Dr Vincent C Tidwell, Geohydrology Department, Sandia National Laboratories, PO Box 5800, Albuquerque, NM 87185, US, 505 844-6025,
[email protected] Sarah Gonzales, Department of Earth and Environmental Sciences, New Mexico Institute of Mining and Technology, 801 Leroy PL – MSEC 216, Socorro, NM 87801, US, 505-835-5591,
[email protected]
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