Statistics for Spatial Data.

Decomposition of the mean squared error and NSE performance criteria: Implications for improving hydrological modelling

The Soil and Water Assessment Tool (SWAT) model is a continuation of nearly 30 years of modeling efforts conducted by the USDA Agricultural Research Service (ARS). SWAT has gained international acceptance as a robust interdisciplinary watershed modeling tool as evidenced by international SWAT conferences, hundreds of SWAT-related papers presented at numerous other scientific meetings, and dozens of articles published in peer-reviewed journals. The model has also been adopted as part of the U.S. Environmental Protection Agency (USEPA) Better Assessment Science Integrating Point and Nonpoint Sources (BASINS) software package and is being used by many U.S. federal and state agencies, including the USDA within the Conservation Effects Assessment Project (CEAP). At present, over 250 peer-reviewed published articles have been identified that report SWAT applications, reviews of SWAT components, or other research that includes SWAT. Many of these peer-reviewed articles are summarized here according to relevant application categories such as streamflow calibration and related hydrologic analyses, climate change impacts on hydrology, pollutant load assessments, comparisons with other models, and sensitivity analyses and calibration techniques. Strengths and weaknesses of the model are presented, and recommended research needs for SWAT are also provided.

/pdf/the-soil-and-water-assessment-tool-historical-development-4e4d97tdfq.pdf

The Soil and Water Assessment Tool: Historical Development, Applications, and Future Research Directions

The Soil and Water Assessment Tool (SWAT) model is a continuation of nearly 30 years of modeling efforts conducted by the U.S. Department of Agriculture (USDA), Agricultural Research Service. SWAT has gained international acceptance as a robust interdisciplinary watershed modeling tool, as evidenced by international SWAT conferences, hundreds of SWAT-related papers presented at numerous scientific meetings, and dozens of articles published in peer-reviewed journals. The model has also been adopted as part of the U.S. Environmental Protection Agency's BASINS (Better Assessment Science Integrating Point & Nonpoint Sources) software package and is being used by many U.S. federal and state agencies, including the USDA within the Conservation Effects Assessment Project. At present, over 250 peer-reviewed, published articles have been identified that report SWAT applications, reviews of SWAT components, or other research that includes SWAT. Many of these peer-reviewed articles are summarized here according to relevant application categories such as streamflow calibration and related hydrologic analyses, climate change impacts on hydrology, pollutant load assessments, comparisons with other models, and sensitivity analyses and calibration techniques. Strengths and weaknesses of the model are presented, and recommended research needs for SWAT are provided.

Soil and Water Assessment Tool: Historical Development, Applications, and Future Research Directions, The

How do movements in the distribution of income and wealth affect the macroeconomy? We analyze this question using a calibrated version of the stochastic growth model with partially uninsurable idiosyncratic risk and movements in aggregate productivity. Our main finding is that, in the stationary stochastic equilibrium, the behavior of the macroeconomic aggregates can be almost perfectly described using only the mean of the wealth distribution. This result is robust to substantial changes in both parameter values and model specification. Our benchmark model, whose only difference from the representative‐agent framework is the existence of uninsurable idiosyncratic risk, displays far less cross‐sectional dispersion and skewness in wealth than U.S. data. However, an extension that relies on a small amount of heterogeneity in thrift does succeed in replicating the key features of the wealth data. Furthermore, this extension features aggregate time series that depart significantly from permanent income behavior.

/pdf/income-and-wealth-heterogeneity-in-the-macroeconomy-1p1dd3prlk.pdf

Income and Wealth Heterogeneity in the Macroeconomy

[1] A new global optimization algorithm, dynamically dimensioned search (DDS), is introduced for automatic calibration of watershed simulation models. DDS is designed for calibration problems with many parameters, requires no algorithm parameter tuning, and automatically scales the search to find good solutions within the maximum number of user-specified function (or model) evaluations. As a result, DDS is ideally suited for computationally expensive optimization problems such as distributed watershed model calibration. DDS performance is compared to the shuffled complex evolution (SCE) algorithm for multiple optimization test functions as well as real and synthetic SWAT2000 model automatic calibration formulations. Algorithms are compared for optimization problems ranging from 6 to 30 dimensions, and each problem is solved in 1000 to 10,000 total function evaluations per optimization trial. Results are presented so that future modelers can assess algorithm performance at a computational scale relevant to their modeling case study. In all four of the computationally expensive real SWAT2000 calibration formulations considered here (14, 14, 26, and 30 calibration parameters), results show DDS to be more efficient and effective than SCE. In two cases, DDS requires only 15–20% of the number of model evaluations used by SCE in order to find equally good values of the objective function. Overall, the results also show that DDS rapidly converges to good calibration solutions and easily avoids poor local optima. The simplicity of the DDS algorithm allows for easy recoding and subsequent adoption into any watershed modeling application framework.

https://agupubs.onlinelibrary.wiley.com/doi/epdf/10.1029/2005WR004723

Dynamically dimensioned search algorithm for computationally efficient watershed model calibration

We introduce a new framework for the global optimization of computationally expensive multimodal functions when derivatives are unavailable. The proposed Stochastic Response Surface (SRS) Method iteratively utilizes a response surface model to approximate the expensive function and identifies a promising point for function evaluation from a set of randomly generated points, called candidate points. Assuming some mild technical conditions, SRS converges to the global minimum in a probabilistic sense. We also propose Metric SRS (MSRS), which is a special case of SRS where the function evaluation point in each iteration is chosen to be the best candidate point according to two criteria: the estimated function value obtained from the response surface model, and the minimum distance from previously evaluated points. We develop a global optimization version and a multistart local optimization version of MSRS. In the numerical experiments, we used a radial basis function (RBF) model for MSRS and the resulting algorithms, Global MSRBF and Multistart Local MSRBF, were compared to 6 alternative global optimization methods, including a multistart derivative-based local optimization method. Multiple trials of all algorithms were compared on 17 multimodal test problems and on a 12-dimensional groundwater bioremediation application involving partial differential equations. The results indicate that Multistart Local MSRBF is the best on most of the higher dimensional problems, including the groundwater problem. It is also at least as good as the other algorithms on most of the lower dimensional problems. Global MSRBF is competitive with the other alternatives on most of the lower dimensional test problems and also on the groundwater problem. These results suggest that MSRBF is a promising approach for the global optimization of expensive functions.

A Stochastic Radial Basis Function Method for the Global Optimization of Expensive Functions

As part of the construction of a simulation model to test an acid precipitation neutralization mechanism, the stream hydrograph was separated into its baseflow and event water components using stable environmental isotopes of water, a naturally occuring conservative tracer. Three snowmelt events and one storm event during the winter and spring of 1984 were studied at an instrumented watershed in the Hubbard Brook Experimental Forest, New Hampshire. Conditions for use of the isotopic tracer were not always met, however. During the latter part of the snowmelt and the storm, the isotopic content of the groundwater and event water were not distinguishable. Furthermore the isotopic content of the meltwater varied considerably over time, thereby reducing the precision of the hydrograph separation. Frequent sampling of the meltwater is mandatory to assess this variability. Because the concentration of major cations and anions were measured as well, chemical tracers could be compared to the isotopic tracer, when the isotopic hydrograph separation was reliable, to test whether the chemical tracer was conservative. Dissolved silica was found to act as a conservative tracer for this watershed.

A Comparison of Chemical and Isotopic Hydrograph Separation

We present a new strategy for the constrained global optimization of expensive black box functions using response surface models. A response surface model is simply a multivariate approximation of a continuous black box function which is used as a surrogate model for optimization in situations where function evaluations are computationally expensive. Prior global optimization methods that utilize response surface models were limited to box-constrained problems, but the new method can easily incorporate general nonlinear constraints. In the proposed method, which we refer to as the Constrained Optimization using Response Surfaces (CORS) Method, the next point for costly function evaluation is chosen to be the one that minimizes the current response surface model subject to the given constraints and to additional constraints that the point be of some distance from previously evaluated points. The distance requirement is allowed to cycle, starting from a high value (global search) and ending with a low value (local search). The purpose of the constraint is to drive the method towards unexplored regions of the domain and to prevent the premature convergence of the method to some point which may not even be a local minimizer of the black box function. The new method can be shown to converge to the global minimizer of any continuous function on a compact set regardless of the response surface model that is used. Finally, we considered two particular implementations of the CORS method which utilize a radial basis function model (CORS-RBF) and applied it on the box-constrained Dixon---Szego test functions and on a simple nonlinearly constrained test function. The results indicate that the CORS-RBF algorithms are competitive with existing global optimization algorithms for costly functions on the box-constrained test problems. The results also show that the CORS-RBF algorithms are better than other algorithms for constrained global optimization on the nonlinearly constrained test problem.

Constrained Global Optimization of Expensive Black Box Functions Using Radial Basis Functions

We present a new derivative-free algorithm, ORBIT, for unconstrained local optimization of computationally expensive functions. A trust-region framework using interpolating Radial Basis Function (RBF) models is employed. The RBF models considered often allow ORBIT to interpolate nonlinear functions using fewer function evaluations than the polynomial models considered by present techniques. Approximation guarantees are obtained by ensuring that a subset of the interpolation points is sufficiently poised for linear interpolation. The RBF property of conditional positive definiteness yields a natural method for adding additional points. We present numerical results on test problems to motivate the use of ORBIT when only a relatively small number of expensive function evaluations are available. Results on two very different application problems, calibration of a watershed model and optimization of a PDE-based bioremediation plan, are also encouraging and support ORBIT's effectiveness on blackbox functions for which no special mathematical structure is known or available.

http://www.optimization-online.org/DB_FILE/2008/05/1989.pdf

Christine A. Shoemaker

Papers

Dynamically dimensioned search algorithm for computationally efficient watershed model calibration

A Stochastic Radial Basis Function Method for the Global Optimization of Expensive Functions

A Comparison of Chemical and Isotopic Hydrograph Separation

Constrained Global Optimization of Expensive Black Box Functions Using Radial Basis Functions

ORBIT: Optimization by Radial Basis Function Interpolation in Trust-Regions