Watershed Model Calibration Research Articles

Enhanced watershed model evaluation incorporating hydrologic signatures and consistency within efficient surrogate multi-objective optimization

This paper presents a new framework for calibrating computationally expensive watershed models with multi-objective optimization methods and hydrological consistency analysis. The analysis evaluates different algorithms' efficiencies for finding watershed model calibration solutions within a limited budget. Two surrogate multi-objective algorithms GOMORS and ParEGO are compared to five evolutionary algorithms without surrogates on two watershed models. We test the algorithms’ performance with two multi-objective formulations (i.e., threshold-based flow separation and decomposition of the Nash-Sutcliffe Efficiency (NSE)). Results indicate that the surrogate-based GOMORS is the most computationally efficient overall. We also propose a framework to select among the calibration solutions obtained from multi-objective optimization using different hydrologic signatures. GOMORS is assessed for its ability to identify hydrologically acceptable calibrations. The decomposition of NSE is the most effective calibration formulation in terms of hydraulic consistency analysis. In addition, hydrologic signatures could be used effectively to filter non-dominated solutions obtained from multi-objective optimization.

Rainfall distributional properties control hydrologic model parameter importance.

Study regionSemi-arid region of the Western United States of America in 16.6 km2 WS10 watershed using data from the highly instrumented Walnut Gulch Experimental Watershed managed by the USDA-Agricultural Research Services. Study focusHydrologic model parameters are generally designed to represent watershed physiographic properties. This study investigates the possible impact of climate forcing, particularly precipitation across a watershed, on model parameter identification – a topic that has historically received minimal attention. To address this gap, we conducted time-varying and time-aggregate sensitivity analysis of a physically based distributed hydrologic model on a heavily instrumented watershed under various observed and synthetic storm events to assess how the distributional properties of rainfall in space and time influence the importance model parameters. Particularly, we focused on a semi-arid watershed with an area larger than the typical convective storms in the region. New hydrologic insightResults show that there is a significant variation in parameter importance following rainfall spatial and temporal properties and that characterizing the relationship between parameter importance and rainfall properties is essential for identifying parameter values that adequately capture the watershed behaviors. We further showed that a power-law function linking parameter importance to precipitation properties can extrapolate results to other climate regimes. More analyses across different watersheds, climate forcing, and models are required to improve our understanding and strategies for parametrization and calibration of watershed models.

Calibration of Watershed Conceptual Models Using Local and Global ptimization

Many issues related to water resources require the solution of optimization problems. Optimization problems can be quite difficult such as the calibration of many conceptual watershed models. Conceptual watershed models are formulated using empirical relationships between hydrological variables observed in nature or field experiments .The success of automatic calibration depends mainly on the choice of optimization method. Most early attempts to calibrate watershed models have been based on local-search optimization methods. Local optimization methods are not designed to handle the presence of multiple regions of attraction, multi-local optima, insensitivities and parameter interdependencies, and other problems encountered in the calibration of watersheds models. It is therefore imperative that global optimization procedures that are capable of dealing with these various difficulties be employed. In this study, one local search optimization method and one global search method are used to calibrate the parameters a simple tenparameter rainfall-runoff model. The local search method is the well-known Rosenbrock's direct search method; the global search method is the newly developed Shuffled Complex Evolution (SCE) method . The results revealed that Shuffle Complex Evolution optimization method is more superior to Rosenbrok’s direct search method. The results confirmed the finding of many watershed modellers about the dependency of Rosenbrock’s method on the choice of initial search points. It further adds that Rosenbrock’s method is only effective when the initial search points are taken within 5 % or less from the true optimum parameter set. The results indicate that a proper choice of optimization methods can enhance the possibility of obtaining unique and conceptually realistic parameter estimate.

Scalable deep learning for watershed model calibration

Watershed models such as the Soil and Water Assessment Tool (SWAT) consist of high-dimensional physical and empirical parameters. These parameters often need to be estimated/calibrated through inverse modeling to produce reliable predictions on hydrological fluxes and states. Existing parameter estimation methods can be time consuming, inefficient, and computationally expensive for high-dimensional problems. In this paper, we present an accurate and robust method to calibrate the SWAT model (i.e., 20 parameters) using scalable deep learning (DL). We developed inverse models based on convolutional neural networks (CNN) to assimilate observed streamflow data and estimate the SWAT model parameters. Scalable hyperparameter tuning is performed using high-performance computing resources to identify the top 50 optimal neural network architectures. We used ensemble SWAT simulations to train, validate, and test the CNN models. We estimated the parameters of the SWAT model using observed streamflow data and assessed the impact of measurement errors on SWAT model calibration. We tested and validated the proposed scalable DL methodology on the American River Watershed, located in the Pacific Northwest-based Yakima River basin. Our results show that the CNN-based calibration is better than two popular parameter estimation methods (i.e., the generalized likelihood uncertainty estimation [GLUE] and the dynamically dimensioned search [DDS], which is a global optimization algorithm). For the set of parameters that are sensitive to the observations, our proposed method yields narrower ranges than the GLUE method but broader ranges than values produced using the DDS method within the sampling range even under high relative observational errors. The SWAT model calibration performance using the CNNs, GLUE, and DDS methods are compared using R2 and a set of efficiency metrics, including Nash-Sutcliffe, logarithmic Nash-Sutcliffe, Kling-Gupta, modified Kling-Gupta, and non-parametric Kling-Gupta scores, computed on the observed and simulated watershed responses. The best CNN-based calibrated set has scores of 0.71, 0.75, 0.85, 0.85, 0.86, and 0.91. The best DDS-based calibrated set has scores of 0.62, 0.69, 0.8, 0.77, 0.79, and 0.82. The best GLUE-based calibrated set has scores of 0.56, 0.58, 0.71, 0.7, 0.71, and 0.8. The scores above show that the CNN-based calibration leads to more accurate low and high streamflow predictions than the GLUE and DDS sets. Our research demonstrates that the proposed method has high potential to improve our current practice in calibrating large-scale integrated hydrologic models.

A flow-weighted approach to generate daily total phosphorus loads in streams based on seasonal loads

Phosphorus (P) is an essential nutrient for all forms of life but its over-enrichment can result in eutrophication of surface waters. For many watersheds around the world, some seasonal total P (TP) load datasets may exist but the continuous and multi-year daily TP concentrations and/or load datasets are not available due to the lacks of in situ P sensor measurement, time-consuming, and budget constraint. Traditionally, the seasonal TP loads are normally obtained with measuring daily TP concentrations for a couple of times within a season in a watershed, and then these daily TP concentrations along with their respective daily discharges are used to calculate the seasonal TP loads for the watershed. However, without the continuous and multi-year daily TP load dataset, development of total maximum daily load (TMDL) and calibration of watershed models for TP cannot be achieved. A flow-weighted method was developed (with detailed procedures) here to generate the daily TP loads based on the seasonal loads. The method was rigorously validated using the measured daily TP datasets from three different US Geological Survey gage stations. With very good statistical comparisons between the method predicted and field measured TP loads, we demonstrated that the flow-weighted method herein is a useful tool to disaggregate the seasonal TP loads into the daily TP loads when the measured daily TP data are not available while the TMDL development and model calibrations/validations are inevitable.

On the sensitivity of modelled groundwater recharge estimates to rain gauge network scale

Rainfall is often the largest component of the water budget and even a small uncertainty percentage may lead to challenges for accurately estimating groundwater recharge as a calculated residual within a water budget approach. Watersheds are a common scale for water budget assessment, and rainfall monitoring networks typically have widely spaced gauges that are frequently outside the watershed of interest. The effects of rainfall spatial variability and uncertainty on groundwater recharge estimates have received little attention and may influence water budget-derived recharge estimations. In the present study, the influence of spatial density in rainfall measurement on the numerical estimation of groundwater recharge was investigated through a series of modelling scenarios utilizing field data obtained from progressively denser rain gauge networks associated with a typical watershed in southern Ontario. The uncertainty of the recharge component of the water budget was used as a metric to aid interpretation of results. The scenarios employed networks composed of: 1) one nearby national weather station (within 3 km), 2) a regional network of six stations (within 30 km), and 3) a local network of six stations, five of which were within the selected watershed. A coupled and fully distributed hydrologic model (MIKE SHE) was used in the scenario analysis and applied to the Alder Creek watershed on the Waterloo Moraine near Kitchener-Waterloo, Ontario. Rainfall showed poor spatial correlation, even at the daily time scale. Average annual results over a three-year period showed that recharge rates varied up to 140 mm per year (~40% of previously estimated annual recharge) among scenarios, with differences between scenarios greater than the water budget uncertainty during one of the years. These findings suggest that the availability of local rainfall measurements has the potential to influence the calibration of transient watershed hydrogeological models.

Chaotic Dynamically Dimensioned Search Algorithm

Dynamically dimensioned search algorithm (DDS) has been proved to be an effective algorithm for solving optimization problems in actual applications, such as distributed watershed model calibration, reservoir operation, pump-and-treat problem, and Radiation Therapy (IMRT) beam angle optimization. However, it always traps in local optimal, especially for multimodal problems. To further improve the performance of DDS, this article proposes a novel chaotic dynamically dimensioned search algorithm (CDDS) by incorporating chaos theory into DDS. The improvement is performed by using three strategies: chaotic initialization, a new Gaussian mutation operator, and a chaotic search. The chaotic map generates an initial population to improve the quality of the initial solution. Chaotic initialization can enhance the exploration ability of DDS because of its intrinsic ergodic and stochastic property. A new Gaussian mutation operator is used to increase convergence speed and the exploitation ability. Meanwhile the chaotic search is utilized to jump out of the local optimal. The optimal CDDS among 13 CDDS variants is compared with other optimization algorithms on 20 classical benchmark test functions, 14 shifted rotated benchmark functions from CEC2005, and 30 benchmark functions from CEC2014 in terms of exploitation and exploration. We testify the applicability and effectiveness on a cascade reservoirs operation optimization problem in real world tasks. The experimental results and analyses demonstrate the superiority of the proposed algorithm in increasing the solution quality and accelerating the convergence.

Multi-site watershed model calibration for evaluating best management practice effectiveness in reducing fecal pollution

In this study, the Soil and Water Assessment Tool (SWAT) is coupled with the Bacteria Source Load Calculator (BSLC) to develop alternative scenarios of agricultural best management practice (BMP) implementation and septic system repair to achieve total maximum daily load (TMDL) targets for Escherichia coli (E. coli) in a small agricultural watershed located in Michigan, USA. Due to the uncertainty involved in bacterial source estimation from wildlife and failing septic systems in agricultural watersheds, we propose a method for estimating their respective bacteria loading during SWAT calibration, which was performed at eight sampling locations and validated at a ninth. BMP implementation scenarios were prioritized based on their ability to meet TMDL targets at the lowest cost using a spatially targeted subwatershed ranking identifying the greatest E. coli source contribution. BMP effectiveness is driven by E. coli source locations defined in the BSLC-SWAT linkage. The framework developed here, from linking BSLC to SWAT to ranking subwatersheds, was effective in meeting the TMDL targets and is readily transferable to other watersheds. Agricultural BMPs were unsuccessful in meeting TMDL targets, but the target can be met by repairing about 60 of 110 estimated failing septic tanks.

Impacts of incorporating dominant crop rotation patterns as primary land use change on hydrologic model performance

Abstract Crop rotation is a commonly used management practice in the central U.S. whereby different agricultural crops are grown on a farm field in successive years to help maintain the productive capacity of the soil. Understanding hydrologic responses to crop rotation is critical for developing appropriate crop rotation strategies for sustainable water resources management. These responses are not well understood due to limited availability of multi-year, crop-specific land use-land cover data. The study focuses on the Smoky Hill River watershed in west-central Kansas, a typical agro-ecosystem watershed in the Central Great Plains of the U.S. A multi-year land use dataset developed for the state of Kansas was used to identify 3-year crop rotation patterns in the watershed for three different periods (2006–08, 2008–10, 2010–12). Out of 276 unique rotations, 21 rotations were found to be dominant, with rotation patterns of grain sorghum-fallow-winter wheat (G-F-W), winter wheat-winter wheat-fallow (W-W-F), and continuous winter wheat (W-W-W) occupying more than 81% of the cropland in each rotation period. From 2006 to 2012, the coverage of grain sorghum increased by 26% and corn by 305%, while winter wheat decreased by 20%. Three 11-year simulation scenarios based on three 3-year crop rotation patterns were implemented in the SWAT model and separately calibrated for streamflow at two gauge sites. The SWAT model produced good calibration statistics for the periods corresponding to the applied crop rotations, while the statistics tended to decrease for other periods, with Nash-Sutcliffe Efficiency coefficient becoming unsatisfactory for periods of six to eight years outside of the calibration period. Applying a different number of dominant crop rotations to the SWAT model, it was found that the number can be reduced down to the five most dominant without significant loss in model performance. While the optimum number of crop rotations must be evaluated for each agricultural watershed, this finding provides valuable information for watershed model development and calibration, which can help to avoid issues of over-parameterization and equifinality.

Augmenting Watershed Model Calibration with Incorporation of Ancillary Data Sources and Qualitative Soft Data Sources

AbstractWatershed simulation models such as the Soil & Water Assessment Tool (SWAT) can be calibrated using “hard data” such as temporal streamflow observations; however, users may find upon examination of model outputs, that the calibrated models may not reflect actual watershed behavior. Thus, it is often advantageous to use “soft data” (i.e., qualitative knowledge such as expected denitrification rates that observed time series do not typically exist) to ensure that the calibrated model is representative of the real world. The primary objective of this study is to evaluate the efficacy of coupling SWAT‐Check (a post‐evaluation framework for SWAT outputs) and IPEAT‐SD (Integrated Parameter Estimation and Uncertainty Analysis Tool‐Soft & hard Data evaluation) to constrain the bounds of soft data during SWAT auto‐calibration. IPEAT‐SD integrates 59 soft data variables to ensure SWAT does not violate physical processes known to occur in watersheds. IPEAT‐SD was evaluated for two case studies where soft data such as denitrification rate, nitrate attributed from subsurface flow to total discharge ratio, and total sediment loading were used to conduct model calibration. Results indicated that SWAT model outputs may not satisfy reasonable soft data responses without providing pre‐defined bounds. IPEAT‐SD provides an efficient and rigorous framework for users to conduct future studies while considering both soft data and traditional hard information measures in watershed modeling.

Watershed model calibration to the base flow recession curve with and without evapotranspiration effects

AbstractCalibration of watershed models to the shape of the base flow recession curve is a way to capture the important relationship between groundwater discharge and subsurface water storage in a catchment. In some montane Mediterranean regions, such as the midelevation Providence Creek catchment in the southern Sierra Nevada of California (USA), nearly all base flow recession occurs after snowmelt, and during this time evapotranspiration (ET) usually exceeds base flow. We assess the accuracy to which watershed models can be calibrated to ET‐dominated base flow recession in Providence Creek, both in terms of fitting a discharge time‐series and realistically capturing the observed discharge‐storage relationship for the catchment. Model parameters estimated from calibrations to ET‐dominated recession are compared to parameters estimated from reference calibrations to base flow recession with ET‐effects removed (“potential recession”). We employ the Penn State Integrated Hydrologic Model (PIHM) for simulations of base flow and ET, and methods that are otherwise general in nature. In models calibrated to ET‐dominated recession, simulation errors in ET and the targeted relationship for recession (−dQ/dt versus Q) contribute substantially (up to 57% and 46%, respectively) to overestimates in the discharge‐storage differential, defined as d(lnQ)/dS, relative to that derived from water flux observations. These errors result in overestimates of deep‐subsurface hydraulic conductivity in models calibrated to ET‐dominated recession, by up to an order of magnitude, relative to reference calibrations to potential recession. These results illustrate a potential opportunity for improving model representation of discharge‐storage dynamics by calibrating to the shape of base flow recession after removing the complicating effects of ET.

Multiple-response Bayesian calibration of watershed water quality models with significant input and model structure errors

While watershed water quality (WWQ) models have been widely used to support water quality management, their profound modeling uncertainty remains an unaddressed issue. Data assimilation via Bayesian calibration is a promising solution to the uncertainty, but has been rarely practiced for WWQ modeling. This study applied multiple-response Bayesian calibration (MRBC) to SWAT, a classic WWQ model, using the nitrate pollution in the Newport Bay Watershed (southern California, USA) as the study case. How typical input and model structure errors would impact modeling uncertainty, parameter identification and management decision-making was systematically investigated through both synthetic and real-situation modeling cases. The main study findings include: (1) with an efficient sampling scheme, MRBC is applicable to WWQ modeling in characterizing its parametric and predictive uncertainties; (2) incorporating hydrology responses, which are less susceptible to input and model structure errors than water quality responses, can improve the Bayesian calibration results and benefit potential modeling-based management decisions; and (3) the value of MRBC to modeling-based decision-making essentially depends on pollution severity, management objective and decision maker's risk tolerance.

Watershed model calibration framework developed using an influence coefficient algorithm and a genetic algorithm and analysis of pollutant discharge characteristics and load reduction in a TMDL planning area

Manual calibration is common in rainfall-runoff model applications. However, rainfall-runoff models include several complicated parameters; thus, significant time and effort are required to manually calibrate the parameters individually and repeatedly. Automatic calibration has relative merit regarding time efficiency and objectivity but shortcomings regarding understanding indigenous processes in the basin. In this study, a watershed model calibration framework was developed using an influence coefficient algorithm and genetic algorithm (WMCIG) to automatically calibrate the distributed models. The optimization problem used to minimize the sum of squares of the normalized residuals of the observed and predicted values was solved using a genetic algorithm (GA). The final model parameters were determined from the iteration with the smallest sum of squares of the normalized residuals of all iterations. The WMCIG was applied to a Gomakwoncheon watershed located in an area that presents a total maximum daily load (TMDL) in Korea. The proportion of urbanized area in this watershed is low, and the diffuse pollution loads of nutrients such as phosphorus are greater than the point-source pollution loads because of the concentration of rainfall that occurs during the summer. The pollution discharges from the watershed were estimated for each land-use type, and the seasonal variations of the pollution loads were analyzed. Consecutive flow measurement gauges have not been installed in this area, and it is difficult to survey the flow and water quality in this area during the frequent heavy rainfall that occurs during the wet season. The Hydrological Simulation Program-Fortran (HSPF) model was used to calculate the runoff flow and water quality in this basin. Using the water quality results, a load duration curve was constructed for the basin, the exceedance frequency of the water quality standard was calculated for each hydrologic condition class, and the percent reduction required to achieve the water quality standard was estimated. The R2 value for the calibrated BOD5 was 0.60, which is a moderate result, and the R2 value for the TP was 0.86, which is a good result. The percent differences obtained for the calibrated BOD5 and TP were very good; therefore, the calibration results using WMCIG were satisfactory. From the load duration curve analysis, the WQS exceedance frequencies of the BOD5 under dry conditions and low-flow conditions were 75.7% and 65%, respectively, and the exceedance frequencies under moist and mid-range conditions were higher than under other conditions. The exceedance frequencies of the TP for the high-flow, moist and mid-range conditions were high and the exceedance rate for the high-flow condition was particularly high. Most of the data from the high-flow conditions exceeded the WQSs. Thus, nonpoint-source pollutants from storm-water runoff substantially affected the TP concentration in the Gomakwoncheon.

Hydro-environmental runoff projection under GCM scenario downscaled by Artificial Neural Network in the Namgang Dam watershed, Korea

Until recently, hydrological impacts and prediction caused by climate change have been popular issues. However, a basin-scale hydro-environmental study has begun to attract attention recently due to the difficulties in watershed model calibration and uncertainty propagation in the data relaying procedure from the GCM (General Circulation Model) process to watershed modeling process, which leads to unrealistic projections. In addition, reliable downscaling scheme is essential in utilizing the GCM model output for hydrological applications. The main objective of this study is to suggest a reliable ANN (Artificial Neural Network)-based GCM scenario and its application for hydro-environmental projection using a watershed model. In this report, the Namgang Dam watershed in the Nakdong river basin was selected as the case study. To examine the vulnerability of the Namgang dam watershed caused by climate change, the change in streamflow and pollutant material runoff due to climate change were predicted using the watershed model, SWAT (Soil Water Assessment Tool), based on the IPCC’s A1B GCM scenario, which is downscaled using the ANN and Nonstationary Quantile Mapping. The results of this study will be used for suggesting an effective counterplan from an engineering point of view, and developing an integrated water sources management system.

Computational Procedure for Evaluating Sampling Techniques on Watershed Model Calibration

A variety of computational techniques have been developed to efficiently and effectively draw realizations from the parameter space of watershed models for parameter estimation. However, to date, it has not been clearly understood how these techniques should be evaluated side by side. The main goal of this study is to develop and demonstrate a computational procedure for evaluating parameter sampling techniques. The analysis hinges on the evaluation of (1) efficiency in minimizing objective functions at the lowest required realizations; (2) effectiveness in drawing samples that adequately represent watershed characteristics based on automatic calibration results, and (3) effectiveness in enhancing the identifiability of the effective parameter space. The proposed procedure was applied to evaluate the performance of six commonly implemented sampling techniques for multisite, multiresponse parameter estimation of a river basin scale model in the Eagle Creek Watershed, Indiana, in the Midwestern United States. Results show that a particular technique surpassed all other methods in convergence speed and behavioral statistics. In addition, solutions derived using that technique were distributed closely in relatively small regions of the whole domain space, which enhanced the efficiency of the parameter search process.

Toward improved calibration of watershed models: Multisite multiobjective measures of information

This paper presents a computational framework for incorporation of disparate information from observed hydrologic responses at multiple locations into the calibration of watershed models. The framework consists of three components: 1) an a-priori characterization of system behavior; 2) a formal and statistically valid formulation of objective function(s) of model errors; and 3) an optimization engine to determine the Pareto-optimal front for the selected objectives. The proposed framework was applied for calibration of the Soil and Water Assessment Tool (SWAT) in the Eagle Creek Watershed, Indiana, USA using three single objective optimization methods [Shuffled Complex Evolution (SCE), Dynamically Dimensioned Search (DDS), and DiffeRential Evolution Adaptive Metropolis (DREAM)], and one multiobjective optimization method. Solutions were classified into behavioral and non-behavioral using percent bias and Nash–Sutcliffe model efficiency coefficient. The results showed that aggregation of streamflow and NOx (NO3-N + NO2-N) information measured at multiple locations within the watershed into a single measure of weighted errors resulted in faster convergence to a solution with a lower overall objective function value than using multiple measures of information. However, the DREAM method solution was the only one among the three single objective optimization methods considered in this study that satisfied the conditions defined for characterizing system behavior. In particular, aggregation of streamflow and NOx responses undermined finding “very good” behavioral solutions for NOx, primarily because of the significantly larger number of observations for streamflow. Aggregation of only NOx responses into a single measure expedited finding better solutions although aggregation of data from nested sites appeared to be inappropriate because of correlated errors. This study demonstrates the importance of hydrologic and water quality data availability at multiple locations, and also highlights the use of multiobjective approaches for proper calibration of watershed models that are used for pollutant source identification and watershed management.

Modification of the SCE-UA to Include Constraints by Embedding an Adaptive Penalty Function and Application: Application Approach

Evolutionary algorithms that are commonly used for automatic calibration of watershed runoff simulation models are unconstrained optimization algorithms. The watershed runoff phenomenon, however, is quite complex, so there are some limitations to the calibration of such models with a single-objective function. The purposes of this study are to improve the shuffled complex evolution-University of Arizona (SCE-UA) to include constraints and to develop an automatic calibration module of the SWMM (storm water management model). An adaptive penalty function was used to impose constraints on the SCE-UA. Two constraints are imposed to diminish errors of peak flow and peak time on a watershed runoff event simulation. We applied the new automatic calibration module to a watershed runoff event simulation for the Milyang Dam Basin in Korea. The automatic calibration results that included the constraints showed improvement in reducing errors of peak flow and peak flow occurrence time. The overall shapes of flood hydrographs were also more similar to observed hydrographs than those of automatic calibration results without the constraints.

홍수유출 모형 자동 보정의 벌칙함수를 이용한 기능 향상 연구

유역유출 모의 모형의 자동 보정에 주로 사용되는 진화계열의 알고리즘은 무제약 최적화 알고리즘이다. 이러한 진화계열 알고리즘에 제약조건을 반영하기 위해서는 제약조건을 다룰 수 있는 별도의 방법이 요구된다. 본 연구의 목적은 진화계열 알고리즘의 일종인 집합체 혼합진화 알고리즘에 벌칙함수를 적용하여 제약조건을 고려할 수 있도록 하는 것이다. 또한, 제약조건을 고려할 수 있는 집합체 혼합진화 알고리즘을 SWMM의 자동 보정 모듈에 적용하여 기존 자동 보정 모듈의 기능을 개선하는 것이다. 홍수유출 해석에서는 첨두유량과 관련된 지표가 중요하므로 첨두유량의 오차와 첨두유량 발생시간의 오차를 제어할 수 있는 제약조건을 구성하였다. 제약조건을 포함하여 구성된 자동 보정 모듈은 밀양댐 유역과 구로1 빗물펌프장 배수유역의 홍수유출 모의 모형에 대하여 적용되었다. 자동 보정의 결과는 제약조건의 포함 유무에 따른 결과를 비교하여제시되었다. 그 결과, 제약조건을 고려함에 따라 본래의 목적함수를 크게 위배하지 않으면서, 첨두유량과 첨두유량 발생시간의 오차가 크게 개선되었다. 또한, 검증을 통해서도 제약최적화를 통한 자동보정의 적절성이 검토되었다. 결론적으로 벌칙함수를 이용한 제약조건의 반영을 통해 자동 보정 모듈의 기능을 향상시킬 수 있었다. Evolutionary algorithms, which are frequently used in an automatic calibration of watershed runoff simulation models, are unconstrained optimization algorithms. An additional method is required to impose constraints on those algorithms. The purpose of the study is to modify the SCE-UA (shuffled complex evolution-University of Arizona) to impose constraints by a penalty function and to improve performance of the automatic calibration module of the SWMM (storm water management model) linked with the SCE-UA. As indicators related to peak flow are important in watershed runoff event simulation, error of peak flow and error of peak flow occurrence time are selected to set up constraints. The automatic calibration module including the constraints was applied to the Milyang Dam Basin and the Guro 1 Pumping Station Basin. The automatic calibration results were compared with the results calibrated by an automatic calibration without the constraints. Error of peak flow and error of peak flow occurrence time were greatly improved and the original objective function value is not highly violated in the automatic calibration including the constraints. The automatic calibration model with constraints was also verified, and the results was excellent. In conclusion, the performance of the automatic calibration module for watershed runoff event simulation was improved by application of the penalty function to impose constraints.

A quasi-multistart framework for global optimization of expensive functions using response surface models

We present the AQUARS (A QUAsi-multistart Response Surface) framework for finding the global minimum of a computationally expensive black-box function subject to bound constraints. In a traditional multistart approach, the local search method is blind to the trajectories of the previous local searches. Hence, the algorithm might find the same local minima even if the searches are initiated from points that are far apart. In contrast, AQUARS is a novel approach that locates the promising local minima of the objective function by performing local searches near the local minima of a response surface (RS) model of the objective function. It ignores neighborhoods of fully explored local minima of the RS model and it bounces between the best partially explored local minimum and the least explored local minimum of the RS model. We implement two AQUARS algorithms that use a radial basis function model and compare them with alternative global optimization methods on an 8-dimensional watershed model calibration problem and on 18 test problems. The alternatives include EGO, GLOBALm, MLMSRBF (Regis and Shoemaker in INFORMS J Comput 19(4):497---509, 2007), CGRBF-Restart (Regis and Shoemaker in J Global Optim 37(1):113---135 2007), and multi level single linkage (MLSL) coupled with two types of local solvers: SQP and Mesh Adaptive Direct Search (MADS) combined with kriging. The results show that the AQUARS methods generally use fewer function evaluations to identify the global minimum or to reach a target value compared to the alternatives. In particular, they are much better than EGO and MLSL coupled to MADS with kriging on the watershed calibration problem and on 15 of the test problems.

BASINS/HSPF: Model Use, Calibration, and Validation

This article presents recommendations by model developers and the authors about calibration and validation procedures for the Hydrological Simulation Program - Fortran (HSPF) as applied through BASINS. HSPF is a continuous simulation watershed model that simulates nonpoint-source runoff and pollutant loadings for a watershed and performs flow and water quality routing in stream reaches and well-mixed lakes and impoundments. HSPF can be used to estimate nonpoint-source loads from various land uses as well as fate and transport processes in streams and lakes. This article describes the ideal calibration and validation process for the full range of constituents modeled by HSPF, as well as the process for acceptable minimum calibration and validation of this model. The model information and guidance provided in this article may be used to help in determining the scope of the proposed ASABE Standard/Engineering Practice for model calibration and validation. Model calibration and validation are necessary and critical steps in any model application. For HSPF and most other watershed models, calibration is an iterative procedure of parameter evaluation and refinement, as a result of comparing simulated and observed values of interest. Model validation is in reality an extension of the calibration process. Its purpose is to ensure that the calibrated model properly assesses all the variables and conditions that can affect model results, and to demonstrate the ability to predict field observations for periods separate from the calibration effort. For HSPF calibration and validation, a “weight of evidence” approach is most widely used in practice when models are examined and judged for acceptance for assessment and regulatory purposes. This article explores the “weight of evidence” approach and the current practice of watershed model calibration and validation based on more than 30 years of experience with HSPF. Example applications are described and model results are shown to demonstrate the graphical and statistical procedures used to assess model performance. In addition, quantitative criteria for various statistical measures are discussed as a basis for evaluating model results and documenting the model application efforts.