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STREAMFLOW SIMULATING USING SRM by: Jennifer Nemitz Final Project for: FOR 520 – Snow Hydrology Fall 2002 TABLE OF CONTENTS 1.0 INTRODUCTION 1 1.1 The Snowmelt Runoff Model 1 1.2 Basin Description 3 2.0 METHODS 5 3.0 RESULTS AND DISCUSSION OF TRIAL VARIATIONS OF EACH MODEL PARAMETER 6 3.1 Optimization of the Critical Temperature 7 3.2 Optimization of the Lag Time to Gage 9 3.3 Optimization of the Degree-Day Factor 10 3.4 Optimization of the Runoff Coefficients 12 3.4.1 Snow Runoff Coefficient 12 3.4.2 Rain Runoff Coefficient 13 3.5 Optimization of the Rainfall Contributing Area 13 4.0 RESULTS AND DISCUSSION OF THE BEST FIT MODEL PARAMETERS 15 5.0 CONCLUSIONS ABOUT THE USEFULNESS OF SRM 17 6.0 REFERENCES 20 APPENDIX 21 1 1.0 INTRODUCTION The purpose of this exercise is to become familiar with the hydrologic simulation of streamflow from the seasonal melting of a snowpack for mountainous basins. The Snowmelt Runoff Model (SRM) was used to simulate streamflow for the Upper Yakima River Basin for the 1989 melt season. The runoff volume for the entire basin was calculated using SRM and compared to the measured runoff volume for a 5-month period running from late February 1989 until early June 1989. The importance of the critical mean daily air temperature, the lag time to gage, the degree-day melt factor, the snow runoff coefficient, the rain runoff coefficient, and the rainfall contributing area was demonstrated for the simulation of streamflow. Each parameter was varied individually above and below optimum values. The impact of variation of each parameter was shown both graphically and by computing correlation coefficients and mean runoff volume differences between computed and measured runoff. Based upon the individual parameter variations, a best-fit set of parameters was chosen to achieve a final runoff simulation. 1.1 The Snowmelt Runoff Model Martinec (1975) originally developed the Snowmelt Runoff Model (SRM) for small European basins. With the advent of satellite remote sensing technology for the aerial estimation of snow covered area, SRM has been applied to ever-larger basins. The model has been applied to over 80 basins of varying sized in 25 different countries (De Walle, 2002). The largest basin that SRM has been applied to is the Ganges River Basin at 2 917,000 km3 (Seidel et al., 2000). SRM was also tested and accepted by the World Meteorological Organization (WMO) in relation to runoff simulations (WMO, 1986) and to partially simulated conditions of real time runoff forecast (WMO, 1992). SRM computes the daily discharge for a basin by superimposing computed snowmelt and rainfall water production onto the calculated recession flow according to the following equation (De Walle, 2002): A ⋅10000 Q n +1 = [cSn ⋅ a n (Tn + ∆Tn )Sn + c Rn Pn ] (1 − k n +1 ) + Q n k n +1 (1) 86400 where: Q = average daily discharge c = runoff coefficient expression the losses as a ratio (runoff/precipitation), with cs referring to snowmelt and cr to rain a = degree-day factor T = number of degree-days ∆T = the adjustment by temperature lapse rate when extrapolating the temperature from the station to the average hypsometric elevation of the basin or zone S = ratio of the snow covered area to the total area P = precipitation contributing to runoff A = area of the basin or zone k = recession coefficient indicating the decline of discharge in a period without snowmelt or rainfall. n = sequence of days during the discharge computation period. The number of degree-days, the ratio of snow covered area to total area, and precipitation need to be measured daily. The temperature lapse rate, snow and rain runoff coefficients, critical temperature, recession coefficient, and lag times are basin specific and should be determined for each basin. If the elevation range of a basin is large, elevations zones should be used and Equation 1 is modified (De Walle, 2002). If elevation zones are used, the mean hypsometric elevation of each zone must be calculated by using an area- elevation curve. 3 1.2 Basin Description The basin of interest for this project is the Upper Yakima River Watershed in Washington (Figure 1, next page). The Upper Yakima Watershed was modeled for the 1989 melt season from late February until early June. The area of the basin is 2130 square miles with a range in elevation from 1200 feet to 6960 feet. The basin was broken down into 5 elevation zones: Zone A: 5700-6960 feet Zone B: 3000-5700 feet Zone C: 2400-3000 feet Zone D: 1800-2400 feet Zone E: 1200-1800 feet. The zonal hypsometric mean elevations were previously calculated in an unpublished thesis and are shown in Figure 2. All air temperature, precipitation, measured streamflow, and snow cover data and an initial set of model parameters were given for the five elevation zones. The recession constant for the basin was also know from the previously mentioned unpublished thesis. Figure 2. Zonal mean hypsometric mean elevations for the Upper Yakima Watershed. 4 Figure 1. Map of the Upper Yakima Watershed showing locations of the main streams, rivers and water bodies within the basin. 5 2.0 METHODS The computed runoff volume for the Upper Yakima Watershed was simulated and compared to the measured (actual) runoff volume for the watershed. The critical temperature, lag time to gage, degree-day factor, snow runoff coefficient, rain runoff coefficient, and rainfall contributing area were initially varied individually to find an optimal value and to visually see how the variation affected the simulated runoff. Parameters were varied both above and below the optimum value. For simplicity and to avoid over-fitting the model parameters, the parameters were kept constant over time and over the elevation zones. The volume difference (%) and the coefficient of determination (R2) were calculated to determine the optimal values. Based upon the optimization of the individual model parameters, an optimal combination of all six parameters was determined. Since the parameters may not vary independently of each other, the final optimal values for each parameter did not necessarily have to be the same as the optimal values determined for the independent individual tests. The individual optimal values were merely used as a starting point for the parameter combination optimization. As with the individual parameters, the combined parameters were initially kept constant over time and over the elevation zones. However, due to an over-prediction of runoff through the second half of March and a very large under-prediction of runoff in the first half of May, some of the parameters were varied with time to achieve the R2 values requested as a final product for the assignment. The model parameters were still held constant over elevation zone. 6 3.0 RESULTS AND DISCUSSION OF TRIAL VARIATIONS OF EACH MODEL PARAMETER The critical temperature, lag time to gage, degree-day factor, snow runoff coefficient, rain runoff coefficient, and rainfall contributing area were initially varied individually to find an optimal value. The starting set of parameters is graphed in Figure 3 and their values are presented in Table 1. Only one parameter at a time was varied with the rest of the parameters remaining at their starting values. Each parameter was varied both above and below the optimal value to determine how perturbations affect each parameter. The volume difference (%) and the coefficient of determination (R2) were calculated to determine the optimal values. In addition, a visual assessment on how each perturbation affected the matching of the timing and magnitude of the flow between the calculated and measured curves was performed. The snowmelt depletion and accumulative melts curves for each zone were also visually analyzed and discussed where significant changes occurred. All additional graphs for non-optimal tries are presented in the Appendix. Figure 3. Measured (red) vs. computed (green) runoff for initial parameter values. 7 Table 1 - Initial Model Parameters Snow Runoff Rain Runoff Rainfall Lag Time Degree Day Tcrit (Tc) Coefficient Coefficient Contributing (L) Factor (AN) (Cs) (Cr) Area (RCA) Value 1 6 0.100 0.200 0.200 1 3.1 Optimization of the Critical Temperature The critical temperature (Tc) is the temperature at which precipitation changes from rain into snow for a given hydrologic basin. The range for critical temperature generally varies from 0 to 2ºC. In our calculations, the critical temperature was used to determine if the measured precipitation for our basin fell as rain or snow. If the average daily temperature was above the critical temperature, the precipitation was assigned to be rainfall and the precipitation immediately contributes to runoff. If the average daily temperature was below the critical temperature the precipitation was assigned to be snowfall and is kept in storage by SRM until it is melted on subsequent warm days. Computed runoff curves were calculated using critical temperatures of 0, 1, 2, 3, 4, and 5˚C (Table 2). The optimal runoff curve was calculated using a critical temperature of 4˚C (Figure 4). Values of the critical temperature below the optimal value shifted the computed runoff curve upward resulting in an increasingly larger over-prediction of the computed runoff. Values of the critical temperature above the optimal value shifted the computed runoff curve downward resulting in an under-prediction of the computed runoff. As the critical temperature is raised, more of the precipitation is assigned as snow, which now must be melted before runoff can be assigned and the computed runoff curve 8 is shifted downward. As the critical temperature is lowered, more of the precipitation is assigned as rainfall and immediately contributes to runoff. The computed runoff curve would shift upwards. No significant changes were observed in the snowmelt depletion and accumulative melt curves. Table 2 - Statistical Parameters when Tcrit is Varied Tcrit = 0 Tcrit = 1 Tcrit = 2 Tcrit = 3 Tcrit = 4 Tcrit = 5 Volume -22.1663 -1.5908 1.4064 2.7005 4.4566 5.8712 Difference (%) Correlation -0.502 0.4698 0.5317 0.5588 0.5856 0.5837 Coefficient Figure 4. Measured (red) vs. computed (green) runoff for the optimal Tcrit = 4˚C. 9 3.2 Optimization of the Lag Time to Gage Lag times (L) for runoff / snowmelt to travel through the basin and flow through the gage are typically determined directly from the basin hydrographs from previous years. Generally, the larger the basin, the larger the lag time will be. However, since we do not have information concerning previous years’ hydrographs for our basin, an estimate can be made instead for basin size. Since our basin is greater than 5000 km2, a lag time of greater than 12 hours can be expected from the WMO intercomparison test (WMO, 1986). Computed runoff curves were calculated using critical lag times of 0, 6, 12, 18, and 24 hours (Table 3). The optimal runoff curve was calculated using a lag time of 18 hours (Figure 5). Values of the lag time below the optimal value shifted the computed runoff curve to the left. Values of the lag time above the optimal value shifted the computed runoff curve to the right. In both cases, the shifts caused computed and measured runoff peaks and valleys to fall out of sync. No significant changes were observed in the snowmelt depletion and accumulative melt curves. Table 3 – Statistical Parameters When Lag Time to Gage is Varied 0 hrs 6 hrs 12 hrs 18 hrs 24 hrs Volume -1.477 -1.5908 -1.223 -0.2861 -0.7994 Difference (%) Correlation 0.4491 0.4698 0.4849 0.4952 0.4926 Coefficient 10 Figure 5. Measured (red) vs. computed (green) for the optimal Lag Time = 18 hours. 3.3 Optimization of the Degree Day Factor The degree-day factor (AN) allows one to calculate how much melt is produced from a snowpack in a given day for a given hydrologic basin. In our calculation, the degree- day factor was used to determine the potential melt for each day. If the average daily temperature was above 0ºC, the potential melt was assigned a value of the degree-day factor times the average daily temperature. If the average daily temperature was below 0ºC, the potential melt was assigned a value of zero as no melt was assumed to occur. Computed runoff curves were calculated using degree-day factors of 0.050, 0.070, 0.100, 0.200 and 0.300 (Table 4). The optimal runoff curve was calculated using a degree-day factor of 0.090 (Figure 6). Values of the degree-day factor below the optimal value shifted the computed runoff curve downward resulting in an increasingly larger 11 under-prediction of the computed runoff due to the decreased melt prediction. Values of the degree-day factor above the optimal value shifted the computed runoff curve upward resulting in an increasingly larger over-prediction of the computed runoff due to the increased melt prediction. Doubling the degree-day factor more than doubled the total snowmelt depth (from 42 in. to 102 for zone E) on the snow depletion curve and the accumulated melt depth (from 27 in. to 66 in.) on the accumulated melt depth curve. Table 4 - Statistical Parameters the Degree-Day Factor is Varied 0.05 0.07 0.09 0.100 0.200 0.3 Volume 31.6742 18.3873 5.0753 -1.5908 -68.5315 -135.8446 Difference (%) Correlation 0.0685 0.369 0.4837 0.4698 -2.3915 -10.3928 Coefficient Figure 6. Measured (red) vs. computed (green) runoff for the optimal Degree-Day Factor = 0.090. 12 3.4 Optimization of the Runoff Coefficients The runoff coefficient accounts for the difference (loss) between the available water volume and the outflow volume from a basin. The runoff coefficient is necessary as water can be lost to infiltration, evaporation, sublimation, interception, evapotranspiration, snowfall gage catch efficiency, and lack of precipitation data in mountainous regions. Depending on the dominant process for the time of year, the runoff coefficient will differ. For example, losses would be expected to be largest late in the snowmelt season as evapotranspiration begins to take hold. There are separate runoff coefficients for rain (cR) and snow (cS). 3.4.1 Optimization of the Snow Runoff Coefficient Computed runoff curves were calculated using snow runoff coefficients 0.100, 0.200, and 0.300 (Table 5). The optimal runoff curve was calculated using a snow runoff coefficient of 0.200 (Figure 3). Values of the snow runoff coefficient below the optimal value shifted the computed runoff curve downward. Values of the snow runoff coefficient above the optimal value shifted the computed runoff curve upward. No significant changes were observed in the snowmelt depletion and accumulative melt curves. Table 5 - Statistical Parameters when cS is Varied 0.100 0.200 0.300 Volume Difference (%) 31.7762 -1.5908 -35.0464 Correlation Coefficient 0.0512 0.4698 -0.3357 13 3.4.2 Optimization of the Rain Runoff Coefficient Computed runoff curves were calculated using rain runoff coefficients 0.100, 0.200, and 0.300 (Table 6). The optimal runoff curve was calculated using a rain runoff coefficient of 0.200 (Figure 3). Values of the rain runoff coefficient below the optimal value shifted the computed runoff curve downward. Values of the rain runoff coefficient above the optimal value shifted the computed runoff curve upward. No significant changes were observed in the snowmelt depletion and accumulative melt curves. Table 6 - Statistical Parameters when cR is Varied 0.100 0.200 0.300 Volume Difference (%) 15.963 -1.5908 -19.4683 Correlation Coefficient 0.4052 0.4698 0.1035 3.5 Optimization of the Rainfall Contributing Area The rainfall contributing area (RCA) can be varied as only one of two cases. For the first case where RCA=0, the snowpack is not assumed to be ripe (snow temperature is below 0ºC). Rain that falls on the snowpack is assumed to be utilized to warm the snowpack and is not included as melt. In this case, only the rain that falls on snow-free areas is considered in the calculation. For the second case where RCA=1, the snowpack is assumed to be ripe (snow temperature equals 0ºC). The second case assumes that an amount of water equal to the rainfall input leaves the snowpack. Therefore, rain falling anywhere in the basin contributes to the calculation of runoff. 14 Computed runoff curves were calculated using rainfall contributing values of 0, 1, and a changeover partway through the year (Table 7). The optimal runoff curve was calculated using the mixed rainfall contributing area value with the value changing from 0 to 1 on 4/5/89 (Figure 7). Inspection of the temperature values across all 5 zones indicated that the majority of the daily temperatures were above freezing meaning that the snowpack would probably be ripe after 4/5/89. No significant changes were observed in the snowmelt depletion and accumulative melt curves. Table 7 - Statistical Parameters when RCA is Varied 0 1 Mix Volume Difference (%) 12.4559 -1.5908 5.493 Correlation Coefficient 0.5602 0.4698 0.6230 Figure 7. Measured (red) vs. computed (green) runoff for the optimal Mixed RCA. 15 4.0 RESULTS AND DISCUSSION OF BEST-FIT MODEL PARAMETERS Based upon the optimization of the individual model parameters, an optimal combination of all six parameters was determined. Since the parameters may not vary independently of each other, the final optimal values for each parameter did not necessarily have to be the same as the optimal values determined for the independent individual tests. The individual optimal values were merely used as a starting point for the parameter combination optimization. The process proceeded on a trial and error basis from the starting point of the individual parameter tests and proceeded until the suggested R2 values in the range of 0.7-0.8 were achieved. As with the individual parameters, the combined parameters were initially kept constant over time and over the elevation zones. However, due to an over-prediction of runoff through the second half of March and a very large under-prediction of runoff in the first half of May, some of the parameters were varied with time. The model parameters were always held constant over elevation zone. The final optimal combined computed runoff curve was calculated by first starting with the optimal RCA and an R2 value of 0.6230. The optimal RCA was selected as a starting point because it was the individual parameter that had the largest influence on raising the R2 value in the individual trials. Adding the individual optimal critical temperature increased the R2 value to 0.6314. However, the optimal degree-day factor lowered the R2 value and the initial value of AN = 0.100 turned out to produce the best R2 value when in conjunction with the other parameters. The optimal lag time lowered the R2 value and a new combined optimal value of L = 12 hours was used. The R2 value 16 for the new optimal lag rose to 0.6327. The snow runoff coefficient was held at the initial and optimal value. The majority of the temperatures in the basin were above the freezing temperature after 4/5/89, so the snow runoff coefficient shouldn’t be as important and the rainfall coefficient. Variation of the snow runoff coefficient before 4/5/89 did not increase the R2 value. The rain runoff coefficient turned out to be the parameter with the biggest influence on the R2 value in the combined parameter trials. A very large runoff spike occurred between 5/4/89 and 5/17/89 that was severely underestimated. For the remainder of the simulation, the runoff was mildly underestimated. The only parameter that whose variation affected this spike was the rain runoff coefficient. During the period from the beginning of the simulation until 5/3/89, the rain runoff coefficient was assigned a value of 0.200. From 5/4/89 to 5/17/89, the rain runoff coefficient was assigned a value of 0.600. From 5/18/89 until the end of the simulation, the rain runoff coefficient was assigned a value of 0.250. The dramatic increase necessary in the rain runoff coefficient does occur late in the melt season and perhaps could be the result of direct channel flow within the basin and opposed to generalized overland flow (De Walle, 2002). A summary of the best-fit model parameters is presented in Table 8. The best-fit computed runoff curve is presented in Figure 8. Table 8 – Best Fit Model Parameters Snow Runoff Rainfall Lag Time Degree Day Rain Runoff Tcrit (Tc) Coefficient Contributing (L) Factor (AN) Coefficient (Cr) (Cs) Area (RCA) Value 4 12 0.100 0.200 Varied (0.200-0.600) Mix 17 Figure 8. Measured (red) vs. computed (green) runoff for the best-fit model parameters. 5.0 CONCLUSIONS ABOUT THE USEFULNESS OF SRM SRM is a semi-distributed, deterministic model in which snowcover is broken down by elevation zone. Therefore, SRM predicts a single streamflow value from a given set of parameters. In general, distributed models can better predict the timing of events and better predict the results of unusual snowmelt events as compared to statistical models. SRM is at a disadvantage as it is one of the simpler distributed models as uses the degree- 18 day approach as opposed to the energy budget approach and does not account for such parameters as forest cover, cold content, slope/aspect effects, liquid routing, or interception. However, the simplicity of SRM may be an advantage as the other parameters are often very hard to quantify on a basin wide scale. In fact, the SRM outperforms many other more complex models both in terms of the R2 value and in the volume difference. On a more personal note stemming from my experiences with this project, the model output for SRM, as with any model, can be highly dependent upon the user. Since some of the parameters may be interconnected, a choice to start with the optimization of one parameter versus another may change the end result. For our example, if I chose to optimize the snow runoff coefficient before the rainfall contributing area, my end R2 value would be about the same, but I would have corrected the over-calculation in late March at the expense of other points on the curve. I chose to optimize the rainfall contributing area first simply because I could understand how that parameter worked. Common sense would indicate that the snow would become ripe if the average daily temperature was consistently well above freezing. The snow runoff coefficient is a parameter derived from previous knowledge of basin behavior. I only knew that I was changing a parameter to achieve a best fit, without understanding the other ramifications. The same could be said for the under-calculation in May and the rain runoff coefficient. Though my solution looks good and achieves the prescribed R2 values, I would not stake my career on it (not yet anyway, maybe in the future). 19 In summary, anyone could endlessly change parameters to achieve a best-fit curve without any knowledge of the concepts behind the fit such a snowmelt hydrology or the basin characteristics. A nice looking solution does not have to equate with a correct, applicable solution. However, if a user understands the concepts behind the model and can apply those concepts to the basin of interest, a model can become a very powerful tool. Any model is only as good as what goes into it, whether data or the knowledge and interpretation of the user. 20 6.0 REFERENCES De Walle, D. (2002) Class Notes. Martinec, J. (1975) Snowmelt-Runoff Model for stream flow forecasts. Nordic Hydrology 6(3), 145-154. Seidel, K., Martinec, J., and Baumgartner, M. F., (2000) Modeling runoff and impact of climate change in large Himalayan basins. Proceedings of International Conference on Integrated Water Resources Management for Sustainable Development, New Delhi, India, 1020-1028. WMO (1986) Intercomparison of Models of Snowmelt Runoff. Operational Hydrology Report 23, WMO, Geneva, Switzerland. WMO (1992) Simulated real-time intercomparison of hydrological models. Operational Hydrology Report 38, WMO, Geneva, Switzerland.