An open problem that arises when using modern iterative linear solvers, such as the preconditioned conjugate gradient (PCG) method or Generalized Minimum RESidual method (GMRES) is how to choose the residual tolerance in the linear solver to be consistent with the tolerance on the solution error. This problem is especially acute for integrated groundwater models which are implicitly coupled to another model, such as surface water models, and resolve both multiple scales of flow and temporal interaction terms, giving rise to linear systems with variable scaling. This article uses the theory of 'forward error bound estimation' to show how rescaling the linear system affects the correspondence between the residual error in the preconditioned linear system and the solution error. Using examples of linear systems from models developed using the USGS GSFLOW package and the California State Department of Water Resources' Integrated Water Flow Model (IWFM), we observe that this error bound guides the choice of a practical measure for controlling the error in rescaled linear systems. It is found that forward error can be controlled in preconditioned GMRES by rescaling the linear system and normalizing the stopping tolerance. We implemented a preconditioned GMRES algorithm and benchmarked it against the Successive-Over-Relaxation (SOR) method. Improved error control reduces redundant iterations in the GMRES algorithm and results in overall simulation speedups as large as 7.7x. This research is expected to broadly impact groundwater modelers through the demonstration of a practical approach for setting the residual tolerance in line with the solution error tolerance.

Mountain regions in arid and semi-arid climates, such as California, are considered particularly sensitive to climate change because global warming is expected to alter snowpack storage and related surface water supply. It is therefore important to accurately capture snowmelt processes in watershed models for climate change impact assessment. In this study we use the Soil and Water Assessment Tool (SWAT) to estimate projected changes in snowpack and streamflow in four alpine tributaries to the agriculturally important but less studied southern Central Valley, California. Watershed responses are evaluated for four CMIP5 climate models (HadGEM_ES, CNRM-CM5, CanESM2 and MIROC5) and two emission scenarios (RCP 4.5 and RCP 8.5) for 2020-2099. SWAT models are calibrated following a dual-objective, lumped calibration approach with an automatic calibration against observed streamflow (stage 1) and a manual calibration against reconstructed Parallel Energy Balance (ParBal) snow water equivalent (SWE) data (stage 2). Results indicate that under a warming climate, peak streamflow is expected to increase 0.5-4 times in magnitude in the coming decades and to arrive 2-4 months earlier in the year because of earlier snowmelt. In the foreseeable future, snow cover will reduce gradually in the lower elevations and diminish at higher rates at higher elevation towards the end of the 21st century. Surface water supply is predicted to increase in the southern Central Valley under the evaluated scenarios but increased temporal variability (wetter wet seasons and drier dry seasons) will create new challenges for managing supply. The study further highlights that the use of remote sensing based, reconstructed SWE data could fill the current gap of limited in-situ SWE observations to improve the snow calibration of SWAT to better predict climate change impacts in semi-arid, snow-dominated watersheds.

Complete representation of rainfall–runoff responses in complex, large watersheds using a single-objective parameterization approach in watershed models is often unachievable. In this study we present a calibration approach for the SWAT+ model that independently fits model parameters for different flow segments of the hydrograph. The approach is demonstrated for the Feather River, California, USA, using daily streamflow from the Lake Oroville Reservoir outlet gage. Results show that when model parameters were independently fitted for different flow segments the KGE, NSE, PBIAS, and RSR values improved to 0.96, 0.99, −3.3, and 0.10, respectively, compared to 0.72, 0.66, −9.30, and 0.53, respectively, achieved under a multiobjective and full hydrograph (average hydrograph) calibration. The results highlight that when considering the average hydrograph and flow duration curves, a more balanced representation of both poorly and well-performing segments is achieved, emphasizing the importance of segment-specific parameterization and multi-objective evaluation for accurately representing different flow conditions.