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Although high performance computers and advanced numerical methods have made the application of fully-integrated surface and subsurface flow and transport models such as HydroGeoSphere common place, run times for large complex basin models can still be on the order of days to weeks, thus, limiting the usefulness of traditional workhorse algorithms for uncertainty quantification (UQ) such as Latin Hypercube simulation (LHS) or Monte Carlo simulation (MCS), which generally require thousands of simulations to achieve an acceptable level of accuracy. In this paper we investigate non-intrusive polynomial chaos for uncertainty quantification, which in contrast to random sampling methods (e.g., LHS and MCS), represents a model response of interest as a weighted sum of polynomials over the random inputs. Once a chaos expansion has been constructed, approximating the mean, covariance, probability density function, cumulative distribution function, and other common statistics as well as local and global sensitivity measures is straightforward and computationally inexpensive, thus making PCE an attractive UQ method for hydrologic models with long run times. Our polynomial chaos implementation was validated through comparison with analytical solutions as well as solutions obtained via LHS for simple numerical problems. It was then used to quantify parametric uncertainty in a series of numerical problems with increasing complexity, including a two-dimensional fully-saturated, steady flow and transient transport problem with six uncertain parameters and one quantity of interest; a one-dimensional variably-saturated column test involving transient flow and transport, four uncertain parameters, and two quantities of interest at 101 spatial locations and five different times each (1010 total); and a three-dimensional fully-integrated surface and subsurface flow and transport problem for a small test catchment involving seven uncertain parameters and three quantities of interest at 241 different times each. Numerical experiments show that polynomial chaos is an effective and robust method for quantifying uncertainty in fully-integrated hydrologic simulations, which provides a rich set of features and is computationally efficient. Our approach has the potential for significant speedup over existing sampling based methods when the number of uncertain model parameters is modest ( ≤ 20). To our knowledge, this is the first implementation of the algorithm in a comprehensive, fully-integrated, physically-based three-dimensional hydrosystem model. [ABSTRACT FROM AUTHOR]

Hydrologic modeling requires the handling of a wide range of highly nonlinear processes from the scale of a hill slope to the continental scale, and thus the computational efficiency of the model becomes a critical issue for water resource management. This work is aimed at implementing and evaluating a flexible parallel computing framework for hydrologic simulations by applying OpenMP in the HydroGeoSphere (HGS) model. HGS is a 3D control-volume finite element model that solves the nonlinear coupled equations describing surface–subsurface water flow, solute migration and energy transport. The computing efficiency of HGS is improved by three parallel computing schemes: 1) parallelization of Jacobian matrix assembly, 2) multi-block node reordering for performing LU solve efficiently, and 3) parameter privatization for reducing memory access latency. Regarding to the accuracy and consistency of the simulation solutions obtained with parallel computing, differences in the solutions are entirely due to use of a finite linear solver iteration tolerance, which produces slightly different solutions which satisfy the convergence tolerance. The maximum difference in the head solution between the serial and parallel simulations is less than 10 −3 m, using typical convergence tolerances. Using the parallel schemes developed in this work, three key achievements can be summarized: (1) parallelization of a physically-based hydrologic simulator can be performed in a manner that allows the same code to be executed on various shared memory platforms with minimal maintenance; (2) a general, flexible and robust parallel iterative sparse-matrix solver can be implemented in a wide range of numerical models employing either structured or unstructured mesh; and (3) the methodology is flexible, especially for the efficient construction of the coefficient and Jacobian matrices, compared to other parallelized hydrologic models which use parallel library packages. [ABSTRACT FROM AUTHOR]

Summary This work presents an iterative, water balance based approach to estimate actual evapotranspiration (ET) with integrated surface/subsurface flow models. Traditionally, groundwater level fluctuation methods have been widely accepted and used for estimating ET and net groundwater recharge; however, in watersheds where interactions between surface and subsurface flow regimes are highly dynamic, the traditional method may be overly simplistic. Here, an innovative methodology is derived and demonstrated for using the water balance equation in conjunction with a fully-integrated surface and subsurface hydrologic model (HydroGeoSphere) in order to estimate ET at watershed and sub-watershed scales. The method invokes a simple and robust iterative numerical solution. For the proof of concept demonstrations, the method is used to estimate ET for a simple synthetic watershed and then for a real, highly-characterized 7000 km 2 watershed in Southern Ontario, Canada (Grand River Watershed). The results for the Grand River Watershed show that with three to five iterations, the solution converges to a result where there is less than 1% relative error in stream flow calibration at 16 stream gauging stations. The spatially-averaged ET estimated using the iterative method shows a high level of agreement ( R 2 = 0.99) with that from a benchmark case simulated with an ET model embedded directly in HydroGeoSphere. The new approach presented here is applicable to any watershed that is suited for integrated surface water/groundwater flow modelling and where spatially-averaged ET estimates are useful for calibrating modelled stream discharge. [ABSTRACT FROM AUTHOR]