Shuffled Complex Evolution-University Of Arizona Research Articles

Constrained shuffled complex evolution algorithm and its application in the automatic calibration of Xinanjiang model

The Shuffled Complex Evolution—University of Arizona (SCE-UA) is a classical algorithm in the field of hydrology and water resources, but it cannot solve constrained optimization problems directly. Using penalty functions has been the preferred method to handle constraints, but the appropriate selection of penalty parameters and penalty functions can be challenging. To enhance the universality of the SCE-UA, we propose the Constrained Shuffled Complex Evolution Algorithm (CSCE) to conveniently and effectively solve inequality-constrained optimization problems. Its performance is compared with the SCE-UA using the adaptive penalty function (SCEA) on 14 test problems with inequality constraints. It is further compared with seven other algorithms on two test problems with low success rates. To demonstrate its effect in hydrologic model calibration, the CSCE is applied to the parameter optimization of the Xinanjiang (XAJ) model under synthetic data and observed data. The results indicate that the CSCE is more advantageous than the SCEA in terms of the success rate, stability, feasible rate, and convergence speed. It can guarantee the feasibility of the solution and avoid the problem of deep soil tension water capacity (WDM)<0 in the optimization process of the XAJ model. In the case of synthetic data, the CSCE can accurately find the theoretical optimal parameters of the XAJ model under the given constraints. In the case of observed data, the XAJ model optimized by the CSCE can effectively simulate the hourly rainfall-runoff events of the Hexi Basin and achieves mean Nash efficiency coefficients greater than 0.75 in the calibration period and the validation period.

Crop yield prediction using MODIS LAI, TIGGE weather forecasts and WOFOST model: A case study for winter wheat in Hebei, China during 2009–2013

Timely and reliable in-season forecasting of crop yield is crucial for regional and national agricultural management. To improve the winter wheat yield prediction accuracy at the regional scale, we developed a data assimilation scheme that assimilated the MODIS leaf area index (LAI) into the WOrld FOod STudies (WOFOST) model. The meteorological data of the WOFOST model include current weather data, 15-day THORPEX Interactive Grand Global Ensemble (TIGGE) forecast dataset and weather forecast data generated by TIGGE forecast and historical meteorological data (1979–2008) using the vectorial angle method. The WOFOST model was calibrated within 10 subregions of Hebei province based on field measured winter wheat growth data from each corresponding agrometeorological station to account for the spatial variability of crop and soil parameters to some extent, and the Savitzky-Golay (S-G) filtered MODIS LAI was then assimilated into the WOFOST model for regional winter wheat yield forecasting. We constructed a four-dimensional variational data assimilation (4DVar) cost function to account for the observations and model errors from Feb. 10th to Apr. 30th, and the Shuffled Complex Evolution-University of Arizona (SCE-UA) algorithm was used to minimize the cost function by reinitializing three WOFOST parameters. The winter wheat yield forecasting date was started from Apr. 30th, and the results showed that assimilating MODIS LAI into the WOFOST model substantially improved the accuracy of regional wheat yield predictions (R = 0.60, CCC = 0.53, RMSE = 619.73 kg/ha) compared with the unassimilated results (R = 0.35, CCC = 0.24, RMSE = 857.32 kg/ha), and the relative error (RE) between the averaged predicted yield and official statistics for most cities decreased after data assimilation. This demonstrated that assimilating MODIS LAI can optimize the simulation of LAI in the WOFOST model, thereby further reduce the uncertainty of yield forecasting. These promising results highlighted the potential of integrating remotely sensed data, crop model and weather forecasts for in-season prediction of crop yield at the regional scale.

Better revisiting chlorophyll content retrieval with varying senescent material and solar-induced chlorophyll fluorescence simulation on paddy rice during the entire growth stages

Solar-induced chlorophyll fluorescence at 760 nm (SIF) is a promising proxy of photosynthesis and can help improving plant stress monitoring. The Soil-Canopy Observation of Photochemistry and Energy fluxes (SCOPE) model combines radiative transfer and enzyme kinetics of photosynthesis and is widely used to interpret SIF at different temporal and spatial scales. In this study, growing season canopy hyperspectral reflectance between 400 nm and 900 nm was used to retrieve chlorophyll content (Cab) and leaf inclination (LIDFa) using radiative transfer models (RTMs) combined with the shuffled complex evolution-University of Arizona (SCE-UA) method. These parameters were then used to simulate diurnal and seasonal trends of SIF for paddy rice. The results showed that the accuracy of Cab retrieval was improved when the variation in senescent material (Cs) was considered, especially in the later growth stages. The SCOPE model was able to reliably interpret the diurnal cycle and seasonal trend of SIF with a correlation coefficient of 0.92 and RMSE of 0.12 w m−2 sr-1 um−1. Our results revealed that the SCOPE model provides a promising method for interpreting SIF variations but its accuracy should be evaluated in different growth stages. This will serve as a significant reference for detecting plant photosynthetic activity and physiological traits at different growth stages.

An integrated approach for non-revenue water reduction in water distribution networks based on field activities, optimisation, and GIS applications

This paper describes the development of an integrated approach for water pipe network calibration and lea quantification. The proposed approach provides a practical procedure that merges field measurements and mathematical modeling for leak quantification and network calibration. The use of Evolutionary Algorithms (EA) using both Genetic Algorithms (GA) and Shuffled Complex Evolution – University of Arizona (SCE-UA) to calculate the pinpointed leak outflows well as to identify any faulty meters. Also, by treating pinpointed physical leaks as junction points, the model, via EPAnet connection, calibrates the network and calculates their demands (which is equivalent to physical losses) and estimating pipes roughness factor (CHW) for better network calibration. Besides, throughout the process, the developed model uses GA and SCE-UA but departs from traditional use in using floating-point representations and introducing a new self-adaptive constraint handling function, which yields optimal results in fewer generations (model runs). Two pilot networks are selected, a well-known hypothetical network (Hanoi network) to present the general mathematical model, while a real network (Faisal city network) is used to test the integrated approach. The model integrates EPAnet for the required hydraulic modeling during the simulation and GIS for input data integration and output representation during the whole procedure. The results prove the approach's accuracy and efficiency.

Comparison of Regional Winter Wheat Mapping Results from Different Similarity Measurement Indicators of NDVI Time Series and Their Optimized Thresholds

Generally, there is an inconsistency between the total regional crop area that was obtained from remote sensing technology and the official statistical data on crop areas. When performing scale conversion and data aggregation of remote sensing-based crop mapping results from different administrative scales, it is difficult to obtain accurate crop planting area that match crop area statistics well at the corresponding administrative level. This problem affects the application of remote sensing-based crop mapping results. In order to solve the above problem, taking Fucheng County of Hebei Province in the Huanghuaihai Plain of China as the study area, based on the Sentinel-2 normalized difference vegetation index (NDVI) time series data covering the whole winter wheat growth period, the statistical data of the regional winter wheat planting area were regarded as reference for the winter wheat planting area extracted by remote sensing, and a new method for winter wheat mapping that is based on similarity measurement indicators and their threshold optimizations (WWM-SMITO) was proposed with the support of the shuffled complex evolution-University of Arizona (SCE-UA) global optimization algorithm. The accuracy of the regional winter wheat mapping results was verified, and accuracy comparisons with different similarity indicators were carried out. The results showed that the total area accuracy of the winter wheat area extraction by the proposed method reached over 99.99%, which achieved a consistency that was between the regional remote sensing-based winter wheat planting area and the statistical data on the winter wheat planting area. The crop recognition accuracy also reached a high level, which showed that the proposed method was effective and feasible. Moreover, in the accuracy comparison of crop mapping results based on six different similarity indicators, the winter wheat distribution that was extracted by root mean square error (RMSE) had the best recognition accuracy, and the overall accuracy and kappa coefficient were 94.5% and 0.8894, respectively. The overall accuracies of winter wheat that were extracted by similarity indicators, such as Euclidean distance (ED), Manhattan distance (MD), spectral angle mapping (SAM), and spectral correlation coefficient (SCC) were 94.1%, 93.9%, 93.3%, and 92.8%, respectively, and the kappa coefficients were 0.8815, 0.8776, 0.8657, and 0.8558, respectively. The accuracy of the winter wheat results extracted by the similarity indicator of dynamic time warping (DTW) was relatively low. The results of this paper could provide guidance and serve as a reference for the selection of similarity indicators in crop distribution extraction and for obtaining large-scale, long-term, and high-precision remote sensing-based information on a regional crop spatial distribution that is highly consistent with statistical crop area data.

Hydropower generation in future climate scenarios

Knowledge on the effects of climate change in a system can contribute to the better management of its water and energy resources. This study evaluates the consequences of alterations in the rainfall and temperature patterns for a hydroelectric plant. The methodology adopted consists of four steps. First, a hydrological model is developed for the chosen basin following a semi-distributed and conceptual approach. The hydrological model is calibrated utilizing the optimization algorithm Shuffled Complex Evolution - University of Arizona (SCE-UA) and then validated. Secondly, a hydropower model is developed for a hydroelectric plant of the chosen basin. The hydropower model is adjusted to the physical characteristics of the plant. Thirdly, future climate scenarios are extracted from the literature for the studied area. These scenarios include quantitative and seasonal climate variations, as well as different initial reservoir levels. Fourth, the hydrological-hydropower model is simulated for 52 scenarios and the impact of changes in the rainfall and temperature patterns for hydropower generation is evaluated. For each scenario, the water storage in the reservoir and energy produced by the plant are analyzed. The financial impact for extreme scenarios is presented. The methodology is applied to the Três Marias hydroelectric plant at the upper São Francisco river basin (Brazil) and it can be replicated to any other hydropower system. The results show that extreme positive values predicted for rainfall will likely not cause issues to the plant, considering a moderate rise in temperature. However, negative predictions for rainfall, regardless of changes in temperature, should be an alert to the authorities responsible for water and energy resources management.

Evaluation of regional estimates of winter wheat yield by assimilating three remotely sensed reflectance datasets into the coupled WOFOST–PROSAIL model

Abstract To estimate regional-scale winter wheat (Triticum aestivum) yield, we developed a data-assimilation scheme that assimilates remotely sensed reflectance into a coupled crop growth–radiative transfer model. We generated a time series of 8-day, 30-m-resolution synthetic Kalman Smoothed reflectance by combining MODIS surface reflectance products with Landsat surface reflectance using a KS algorithm. We evaluated the assimilation performance using datasets with different spatial and temporal scales (e.g., three dates for the 30-m Landsat reflectance, 8-day and 1-km MODIS surface reflectance, and 8-day and 30-m synthetic KS reflectance) into the coupled WOFOST–PROSAIL model. Then we constructed a four-dimensional variational data assimilation (4DVar) cost function to account for differences between the observed and simulated reflectance. We used the shuffled complex evolution–University of Arizona (SCE-UA) algorithm to minimize the 4DVar cost function and optimize important input parameters of the coupled model. The optimized parameters were used to drive WOFOST and estimate county-level winter wheat yield in a region of China. By assimilating the synthetic KS reflectance data, we achieved the most accurate yield estimates (R2 = 0.44, 0.39, and 0.30; RMSE = 598, 1288, and 595 kg/ha for 2009, 2013, and 2014, respectively), followed by Landsat reflectance (R2 = 0.21, 0.22, and 0.33; RMSE = 915, 1422, and 637 kg/ha for 2009, 2013, and 2014, respectively) and MODIS reflectance (R2 = 0.49, 0.05, and 0.22; RMSE = 1136, 1468, and 700 kg/ha for 2009, 2013, and 2014, respectively) at the county level. Thus, our method improves the reliability of regional-scale crop yield estimates.

Does the Complexity of Evapotranspiration and Hydrological Models Enhance Robustness?

In this study, five hydrological models of increasing complexity and 12 Potential Evapotranspiration (PET) estimation methods of different data requirements were applied in order to assess their effect on model performance, optimized parameters, and robustness. The models were applied over a set of 10 catchments that are located in South Korea. The Shuffled Complex Evolution-University of Arizona (SCE-UA) algorithm was implemented to calibrate the hydrological models for each PET input while considering similar objective functions. The hydrological models’ performance was satisfactory for each PET input in the calibration and validation periods for all of the tested catchments. The five hydrological models’ performance were found to be insensitive to the 12 PET inputs because of the SCE-UA algorithm’s efficiency in optimizing model parameters. However, the five hydrological models’ parameters in charge of transforming the PET to actual evapotranspiration were sensitive and significantly affected by the PET complexity. The values of the three statistical indicators also agreed with the computed model evaluation index values. Similarly, identical behavioral similarities and Dimensionless Bias were observed in all of the tested catchments. For the five hydrological models, lack of robustness and higher Dimensionless Bias were seen for high and low flow as well as for the Hamon PET input. The results indicated that the complexity of the hydrological models’ structure and the PET estimation methods did not necessarily enhance model performance and robustness. The model performance and robustness were found to be mainly dependent on extreme hydrological conditions, including high and low flow, rather than complexity; the simplest hydrological model and PET estimation method could perform better if reliable hydro-meteorological datasets are applied.

Modeling Pollutant Buildup and Washoff Parameters for SWMM Based on Land Use in a Semiarid Urban Watershed

SWMM (Storm Water Management Model) has been widely used in urban water resources management. Despite its popularity, no commonly accepted pollutant buildup and washoff parameters are available for urban areas in semi-arid or arid climate, which covers 30% of global land area and is sustaining fast growth. This study provides a method to determine these parameters using inverse modeling and apply it in a semi-arid Texan urban watershed. Because GIS land use data is not available for early 1980s, it was determined from aerial photography from 1984 to 2006, and GIS land use data from 2006. Calibration using Shuffled Complex Evolution – University of Arizona (SCEUA) was used for hydraulic parameters followed by pollutant parameters. Confidence intervals of pollutant parameters were calculated by GLD (Generalized Lambda Distribution). Buildup parameters are clustered in narrow numerical ranges, indicating that spatially uniform factors are responsible for pollutant buildup. Washoff parameters do not cluster and are distributed more evenly, indicating strong influence of local factors such as topography. The results also imply that the commonly used parameter values need major revision.

Radiometric Cross-Calibration of GF-4 PMS Sensor Based on Assimilation of Landsat-8 OLI Images

Earth observation data obtained from remote sensors must undergo radiometric calibration before use in quantitative applications. However, the large view angles of the panchromatic multispectral sensor (PMS) aboard the GF-4 satellite pose challenges for cross-calibration due to the effects of atmospheric radiation transfer and the bidirectional reflectance distribution function (BRDF). To address this problem, this paper introduces a novel cross-calibration method based on data assimilation considering cross-calibration as an optimal approximation problem. The GF-4 PMS was cross-calibrated with the well-calibrated Landsat-8 Operational Land Imager (OLI) as the reference sensor. In order to correct unequal bidirectional reflection effects, an adjustment factor for the BRDF was established, making complex models unnecessary. The proposed method employed the Shuffled Complex Evolution-University of Arizona (SCE-UA) algorithm to find the optimal calibration coefficients and BRDF adjustment factor through an iterative process. The validation results revealed a surface reflectance error of <5% for the new cross-calibration coefficients. The accuracy of calibration coefficients were significantly improved when compared to the officially published coefficients as well as those derived using conventional methods. The uncertainty produced by the proposed method was less than 7%, meeting the demands for future quantitative applications and research. This method is also applicable to other sensors with large view angles.

Application and recalibration of soil water retention pedotransfer functions in a tropical upstream catchment: case study in Bengawan Solo, Indonesia

Abstract Hydrological models often require input data on soil-water retention (SWR), but obtaining such data is laborious and costly so that SWR in many places remains unknown. To fill the gap, a prediction of SWR using a pedotransfer function (PTF) is one of the alternatives. This study aims to select the most suitable existing PTFs in order to predict SWR for the case of the upper Bengawan Solo (UBS) catchment on Java, Indonesia. Ten point PTFs and two continuous PTFs, which were developed from tropical soils elsewhere, have been applied directly and recalibrated based on a small soil sample set in UBS. Scatter plots and statistical indices of mean error (ME), root mean square error (RMSE), model efficiency (EF) and Pearson’s correlation (r) showed that recalibration using the Shuffled Complex Evolution-University of Arizona (SCE-UA) algorithm can help to improve the prediction of PTFs significantly compared to direct application of PTFs. This study is the first showing that improving SWR-PTFs by recalibration for a new catchment based on around 50 soil samples provides an effective parsimonious alternative to developing a SWR-PTF from specifically collected soil datasets, which typically needs around 100 soil samples or more.

Real-time updating of HEC-RAS model for streamflow forecasting using an optimization algorithm

ABSTRACT Real-time updating of channel flow routing models is essential for error reduction in hydrological forecasting. Recent updating techniques found in scientific literature, although very promising, are complex and often applied in models that demand much time and expert knowledge for their development, posing challenges for using in an operational context. Since powerful and well-known computational tools are currently available, which provide easy-to-use and less time-consuming platforms for preparation of hydrodynamic models, it becomes interesting to develop updating techniques adaptable to such tools, taking full advantage of previously calibrated models as well as the experience of the users. In this work, we present a real-time updating procedure for streamflow forecasting in HEC-RAS model, using the Shuffled Complex Evolution - University of Arizona (SCE-UA) optimization algorithm. The procedure consists in a simultaneous correction of boundary conditions and model parameters through: (i) generation of a lateral inflow, based on Soil Conservation Service (SCS) dimensionless unit hydrograph and; (ii) estimation of Manning roughness in the river channel. The algorithm works in an optimization window in order to minimize an objective function, given by the weighted sum of squared errors between simulated and observed flows where differences in later intervals (start of forecast) are more penalized. As a case study, the procedure was applied in a river reach between Salto Caxias dam and Hotel Cataratas stream gauge, located in the Lower Iguazu Basin. Results showed that, with a small population of candidate solutions in the optimization algorithm, it is possible to efficiently improve the model performance for streamflow forecasting and reduce negative effects caused by lag errors in simulation. An advantage of the developed procedure is the reduction of both excessive handling of external files and manual adjustments of HEC-RAS model, which is important when operational decisions must be taken in relatively short times.

Estimating winter wheat biomass by assimilating leaf area index derived from fusion of Landsat-8 and MODIS data

A sufficient number of satellite acquisitions in a growing season are essential for deriving agronomic indicators, such as green leaf area index (GLAI), to be assimilated into crop models for crop productivity estimation. However, for most high resolution orbital optical satellites, it is often difficult to obtain images frequently due to their long revisit cycles and unfavorable weather conditions. Data fusion algorithms, such as the Spatial and Temporal Adaptive Reflectance Fusion Model (STARFM) and the Enhanced STARFM (ESTARFM), have been developed to generate synthetic data with high spatial and temporal resolution to address this issue. In this study, we evaluated the approach of assimilating GLAI into the Simple Algorithm for Yield Estimation model (SAFY) for winter wheat biomass estimation. GLAI was estimated using the two-band Enhanced Vegetation Index (EVI2) derived from data acquired by the Operational Land Imager (OLI) onboard the Landsat-8 and a fusion dataset generated by blending the Moderate-Resolution Imaging Spectroradiometer (MODIS) data and the OLI data using the STARFM and ESTARFM models. The fusion dataset had the temporal resolution of the MODIS data and the spatial resolution of the OLI data. Key parameters of the SAFY model were optimised through assimilation of the estimated GLAI into the crop model using the Shuffled Complex Evolution-University of Arizona (SCE-UA) algorithm. A good agreement was achieved between the estimated and field measured biomass by assimilating the GLAI derived from the OLI data (GLAIL) alone (R2=0.77 and RMSE=231gm−2). Assimilation of GLAI derived from the fusion dataset (GLAIF) resulted in a R2 of 0.71 and RMSE of 193gm−2 while assimilating the combination of GLAIL and GLAIF led to further improvements (R2=0.76 and RMSE=176gm−2). Our results demonstrated the potential of using the fusion algorithms to improve crop growth monitoring and crop productivity estimation when the number of high resolution remote sensing data acquisitions is limited.

A data assimilation-based method for optimizing parameterization schemes in a land surface process model

Optimizingtheparameters of a land surface process model (LSPM) through data assimilation (DA) can not only improve and perfect theparameterization schemes in the LSPM through the physical mechanism, but also increase its regional adaptability and simulation capability. This has practical importance for improving simulation results and the climate-prediction capability of general circulation models (GCMs) and regional climate models (RCMs). This paper presents a DA-based method for optimizingtheparameterization schemes in LSPMs. We optimize the unsaturated-soil water flow (UnSWF) model as an example by developing a soil-moisture assimilation scheme based on the UnSWF model and the extended Kalman filter (EKF) algorithm, and then combining them with the Variable Infiltration Capacity (VIC) model. Using a month as the assimilation window, we used the Shuffled Complex Evolution-University of Arizona (SCE-UA) algorithm to minimize the objective function through simulated and assimilated soil moisture, achieved the best fit with the given objective function measurement, and optimized the parameters of the UnSWF model, including the saturated-soil hydraulic conductivity, moisture content, matrix potential, and the Clapp and Hornberger constant. The optimal values of the model parameters were obtained during the DA period (the year 1986), and then the optimized parameters were used to improve the UnSWF model. Finally, numerical simulation experiments were carried out from 1986 to 1993 to evaluate the simulation capability of the improved model and to explore and realize the DA-based method for optimizing the soil water parameterization scheme in LSPMs. The experimental results indicated that the optimized model parameters improved and perfected the model based on the physical mechanism, and increased its simulation capability; the optimized model parameters had good temporal portability and their adaptability was stronger, achieving the aim of improving the model. Therefore, this method is reasonable and feasible. This paper provides a good reference for DA-based optimization of the parameterization schemes in LSPMs.

New Multisite Cascading Calibration Approach for Hydrological Models: Case Study in the Red River Basin Using the VIC Model

AbstractA novel multisite cascading calibration (MSCC) approach using the shuffled complex evolution–University of Arizona (SCE-UA) optimization method, developed at the University of Arizona, was employed to calibrate the variable infiltration capacity (VIC) model in the Red River Basin. Model simulations were conducted at 35 nested gauging stations. Compared with simulated results using a priori parameters, single-site calibration can improve VIC model performance at specific calibration sites; however, improvement is still limited in upstream locations. The newly developed MSCC approach overcomes this limitation. Simulations using MSCC not only utilize all of the available streamflow observations but also better represent spatial heterogeneities in the model parameters. Results indicate that MSCC largely improves model performance by decreasing the number of stations with negative Nash-Sutcliffe coefficient of efficiency (NSCE) values from 69% (66%) for a priori parameters to 37% (34%) for single-site ...

Analysis of Constrained Optimization Problems by the SCE-UA with an Adaptive Penalty Function

AbstractEvolutionary algorithms are used to solve optimization problems in a wide range of fields and are considered to be global optimization algorithms. However, evolutionary algorithms are limited in that they cannot be used to solve optimization problems with constraints. Additional methods to implement constraints must be used with these algorithms when solving constrained optimization problems. The purpose of the study is to improve the Shuffled Complex Evolution-University of Arizona (SCE-UA) algorithm to include constraints. An adaptive penalty function that is easy to implement, free of parameter tuning, and guaranteed to find a solution for every problem at every run was used to impose constraints on the SCE-UA. The modified SCE-UA was validated by application to two constrained optimization problems. The algorithm was also applied to an automatic calibration of the storm water management model (SWMM), which is a hydrological model. An automatic calibration by unconstrained optimization (the ori...

Hydrological Model Calibration by Sequential Replacement of Weak Parameter Sets Using Depth Function

It is always a dream of hydrologists to model the mystery of complex hydrological processes in a precise way. If parameterized correctly, a simple hydrological model can represent nature very accurately. In this study, a simple and effective optimization algorithm, sequential replacement of weak parameters (SRWP), is introduced for automatic calibration of hydrological models. In the SRWP algorithm, a weak parameter set is sequentially replaced with another deeper and good parameter set. The SRWP algorithm is tested on several theoretical test functions, as well as with a hydrological model. The SRWP algorithm result is compared with the shuffled complex evolution-University of Arizona (SCE-UA) algorithm and the robust parameter estimation (ROPE) algorithm. The result shows that the SRWP algorithm easily overcomes the local minima and converges to the optimal parameter space. The SRWP algorithm does not converge to a single optima; instead, it gives a convex hull of an optimal space. An ensemble of results can be generated from the optimal space for prediction purpose. The ensemble spread will account for the parameter estimation uncertainty. The methodology was demonstrated using the hydrological model (HYMOD) conceptual model on upper Neckar catchments of southwest Germany. The results show that the parameters estimated by this stepwise calibration are robust and comparable to commonly-used optimization algorithms. SRWP can be an alternative to other optimization algorithms for model calibration.

Simulation of Groundwater Levels Using Tank Model with Consideration of Mixed Hydrological Structure in Kumamoto City

ABSTRACT Groundwater level is a major parameter in quantifying groundwater resource. Application of simple tools to simulate and predict groundwater levels is an important issue in groundwater hydrology. Tank model is a simple and useful conceptual hydrological model which is capable to simulate different system states without considering complex hydrological structure. The Shuffled Complex Evolution-University of Arizona (SCE-UA) algorithm is an efficient automatic calibration algorithm in searching the global optimum of objective function. This paper investigated the capability of mixed-tank model for consideration of mixed hydrological structure to simulate the groundwater level fluctuation with precipitation in four observation wells in Kumamoto City. The SCE-UA algorithm was introduced and modified to minimize the root-mean-square error (RMSE) between simulation and observation data for parameter calibration. The simulation accuracy was also assessed by Nash-Sutcliffe efficiency (NSE) coefficient. The results indicate that the mixed-tank model is highly effective for the simulation of groundwater levels showing different behaviors in their fluctuation situations.

유역유출 및 수질모의에 관한 SWMM의 자동 보정 모듈 개발

SWMM은 홍수유출 해석, 유역유출 연속모의, 수질모의가 가능한 모형으로서 전세계적으로 널리 사용되고 있는 모형이다. 하지만 유역유출 연속모의와 수질모의에는 다수의 불명확한 매개변수가 포함되어 있으므로 이는 SWMM의 사용에 제약이 되고 있다. 본 연구의 목적은 SWMM을 이용한 유역유출 연속모의와 수질모의의 정확도를 높이고 효율성을 향상시킬 수 있도록 자동 보정 모듈을 개발하는 것이다. SWMM의 자동 보정 모듈은 전역최적화 알고리즘인 집합체 혼합진화 알고리즘과 SWMM을 연계하고, SWMM 내 추정대상 매개변수의 선정 및 적절한 탐색 범위를 설정함으로써 개발되었다. 개발된 자동 보정 모듈의 적절성은 동향 수위관측소 유역에 대하여 구성된 유역유출 및 수질모의 모형의 보정 및 검증을 통해 검토되었다. 그 결과, 자동 보정 모듈을 통해 보정된 모형은 유역의 유출현상을 매우 잘 모사하였고, 수질의 경우에도 비교적 양호한 결과를 도출하였다. 개발된 자동 보정 모듈은 향후 유역유출 모의와 수질해석에 관한 다양한 연구와 설계 등에 활용될 수 있을 것이다. The SWMM (storm water management model) has been widely used in the world and is a watershed runoff simulation model used for a single event or a continuous simulation of runoff quantity and quality. However, there are many uncertain parameters in the watershed runoff continuous simulation module and the water quality module, which make it difficult to use the SWMM. The purpose of the study is to develop an automatic calibration module of the SWMM not only for watershed runoff continuous simulation, but also water quality simulation. The automatic calibration module was developed by linking the SWMM with the SCE-UA (shuffled complex evolution-University of Arizona) that is a global optimization algorithm. Estimation parameters of the SWMM were selected and search ranges of them were reasonably configured. The module was validated by calibration and verification of the watershed runoff continuous simulation model and the water quality model for the Donghyang Stage Station Basin. The calibration results for watershed runoff continuous simulation model were excellent and those for water quality simulation model were generally satisfactory. The module could be used in various studies and designs for watershed runoff and water quality analyses.

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.