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Mechanistic water balance approach for reconstructing past streamflow using tree ring (proxy) records
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Long-term records of streamflow are important for water resources planning and management purposes. The extent of instrumental streamflow records is about 100 years at most which may not provide an adequate picture of past variability, thus affecting assessments of future trends and scenarios that use these data. Proxy reconstructions of streamflow can augment limited streamflow data and are often done using regression analysis of tree ring data from moisture sensitive trees with instrumental streamflow. Such reconstructions cannot account for watershed factors such as change in land cover or land use that do not directly affect tree growth but that may influence streamflow. In this research, seasonal water balance models were developed as a mechanistic approach to reconstruct streamflow with proxy inputs of precipitation and air temperature. Selection of the appropriate mechanistic model could allow examination of sources of uncertainty in the reconstructions as well as "what if" scenarios. We examined three models: the Thornthwaite model modified for use with seasonal input data and two adaptations of a simple water balance model with different approaches to account for snow accumulation and melt. The models were calibrated with Monte Carlo and shuffled complex evolution (SCE) approaches using Parameter-elevation Regressions on Independent Slopes Model (PRISM) seasonal temperatures and precipitation to reconstruct streamflow for the upper reaches of the West Walker River Basin at Coleville, CA. The simple water balance model with snow equations from the Water and Snow balance MODeling system (WASMOD) performed best, with R2 = 0.94, RMSE = 7.05 cm, and Nash-Sutcliffe efficiency = 0.94 using the Monte Carlo calibration approach. Better performance metrics were achieved for all models with the SCE calibration approach and some parameters were substantially different between the two calibration approaches. A sensitivity analysis indicated the Thornthwaite model had the most sensitive parameters, but none of the models were well-suited for directly modeling changes in evapotranspiration. The water balance models were also calibrated using the SCE approach with inputs from proxy reconstructions of precipitation and temperature. The simple water balance model with WASMOD snow component performed better than the other two models with R2 = 0.78, RMSE = 10.07 cm, and Nash-Sutcliffe efficiency = 0.78. The simple water balance model with WASMOD snow component consistently had better performance metrics than the other models with the proxy and PRISM inputs, fewer model parameters compared to the other two models, and parameters that were sensitive to allow simulation of "what if" scenarios. The simple water balance model with WASMOD snow component was used to reconstruct past streamflow with the proxy reconstruction of precipitation and temperatures for Water Year (WY) 1500-1980 for West Walker River basin. The reconstruction estimated some similar wet and dry episodes as other reconstructions and provided an estimate of snow remaining in the watershed at the end of each water year over the reconstructed time period.