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During the last decades, a number of methods have been developed for the estimation of hydrologic model parameters. One frequently used and relatively simple algorithm is the parameter estimation (PEST) method. A close examination of this algorithm shows that it is very similar to the Extended Kalman Filter (EKF). The differences between the methods are caused by the derivation of the algorithms: the EKF is derived through a minimization of the square difference between the true and the estimated model state, while PEST has been derived through a minimization of an objective function related to, but not equal to, the root mean square error between the model results and the observations. The objective of this paper is to analyze the performance of these two algorithms. A synthetic-data experiment has been developed for this purpose. It has been found that under high observation errors and/or temporally sparse observations the EKF can lead to a stable parameter estimation, while it is possible that under the same circumstances PEST does not yield a solution. Also, the choice of the initial guess for the parameter values can be an important issue in the application of PEST, while this is not so important for the EKF. The application of the Marquardt algorithm can lead to stable parameter estimates in case the PEST algorithm fails (meaning that nonphysical parameter values were obtained which lead to a premature abortion of the model simulations), but numerically the EKF is still superior. In order to solve this problem, a simple alternative to the Marquardt algorithm has been developed, which leads to a quicker convergence.

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... Different types of remotely sensed information have been integrated with TOPLATS trough data assimilation (DA) procedures for improving streamflow simulation (Pauwels et al., 2002Pauwels et al., , 2001), soil moisture simulation (Crow et al., 2001; Houser et al., 1998; Lucau-Danila et al., 2005) or latent heat fluxes estimation (Crow and Wood, 2003). TABLE 1The model's behavior and performance has also been explored, for instance, to evaluate its sensitivity to soil parameters (Loosvelt et al., 2014bLoosvelt et al., , 2011) or to analyze different calibration strategies (Goegebeur and Pauwels, 2007 ; Usuga and Pauwels, 2008; Pauwels et al., 2009). Table 1On this study, parameters selected for TOPLATS sensitivity analysis and calibration were chosen principally according to information extracted from these works. ...

... Calibration related researches (Table 1) were in some cases focused on obtaining optimal streamflow values at catchment outlet (Crow and Wood, 2002), while some others aimed to obtain accurate soil moisture simulations (Goegebeur and Pauwels, 2007). Pauwels et al. (2009) pointed out that the three most important soil parameters in the determination of the soil moisture content were the saturated hydraulic conductivity (K s ), the pore size distribution index (B), and the bubbling pressure (ψ c ). Bormann et al. (2007) proposed a calibration procedure based on first, reproducing the longterm water balance tuning vegetation parameters (stomatal resistances) and secondly, on optimizing the model efficiency by fitting the baseflow recession: adjusting baseflow at complete saturation (Q 0 ) and the hydraulic conductivity decay (f) parameters. ...

... For simplification and to allow catchment behavior comparison, only CON approach values are shown in this section. Parameter value ranges to be explored by the algorithm were defined according to references in previous TOPLATS works (Goegebeur and Pauwels, 2007; Loaiza Usuga and Pauwels, 2008; Peters-Lidard et al., 1997). K s , had its BP within 1e -4 and 1e -5 m/s for La Tejeria and Arga, but in Cidacos these values were higher (between 1e -3 and 1e -4 m/s) (Fig. 7). ...

Physically based hydrological models are complex tools that provide a complete description of the different processes occurring on a catchment. The TOPMODEL-based Land-Atmosphere Transfer Scheme (TOPLATS) simulates water and energy balances at different time steps, in both lumped and distributed modes. In order to gain insight on the behavior of TOPLATS and its applicability in different conditions a detailed evaluation needs to be carried out. This study aimed to develop a complete evaluation of TOPLATS including: 1) a detailed review of previous research works using this model; 2) a sensitivity analysis (SA) of the model with two contrasted methods (Morris and Sobol) of different complexity; 3) a 4-step calibration strategy based on a multi-start Powell optimization algorithm; and 4) an analysis of the influence of simulation time step (hourly vs. daily). The model was applied on three catchments of varying size (La Tejeria, Cidacos and Arga), located in Navarre (Northern Spain), and characterized by different levels of Mediterranean climate influence. Both Morris and Sobol methods showed very similar results that identified Brooks-Corey Pore Size distribution Index (B), Bubbling pressure (ψc) and Hydraulic conductivity decay (f) as the three overall most influential parameters in TOPLATS. After calibration and validation, adequate streamflow simulations were obtained in the two wettest catchments, but the driest (Cidacos) gave poor results in validation, due to the large climatic variability between calibration and validation periods. To overcome this issue, an alternative random and discontinuous method of cal/val period selection was implemented, improving model results.

... The methodology used to calibrate the model was developed by Goegebeur and Pauwels (2007). The methodology is based on the equations of the Extended Kalman Filter. ...

... The equations are applied recursively throughout an iteration process, based on which the methodology can be referred to as weight-adaptive recursive parameter estimation. Only a short description will be given here, for a full description we refer to Goegebeur and Pauwels (2007). ...

... The standard deviation of the observation noise was set to 0.05. Similar as in Goegebeur and Pauwels (2007), the offdiagonal values of Q k were set to zero, and the diagonal elements were set to the square of a predefined fraction of its corresponding parameter value. A sensitivity analysis indicated that when this fraction was equal to 0.025 a relatively low number (order of 10) iterations was necessary to obtain convergence in the parameter values. ...

A detailed understanding of the magnitude of the different components of the hydrologic cycle in Mediterranean mountainous catchments is important for a number of different reasons, such as reservoir management and land use planning. Since it is currently impossible to fully monitor a catchment continuously in a spatially distributed manner, the only way to obtain estimates of the different water and energy balance terms is the application of hydrologic models. These models rely on a large number of parameters, of which estimates are rarely available. The objective of this paper is to assess to which degree the overall performance of a hydrologic model can be improved through the estimation of model parameters using observed soil moisture values. In situ observations of soil moisture, surface runoff, infiltration, and soil temperature in the Ribera Salada catchment in the Southeastern Pyrenees are used for this purpose. Before calibration, the model yielded poor results for all these variables. The use of soil and TOPMODEL parameters estimated using one year of soil moisture observations improved the modeled soil moisture values throughout the study period. A strong improvement in the modeled surface runoff and infiltration was also obtained. The model has been found to adequately reproduce the observed soil temperature. As a summary, the results indicate that using one year of soil moisture observations to calibrate a hydrologic model in Mediterranean mountainous catchments may be sufficient, and that this parameter estimation can lead to a strong improvement in the overall model performance.

... To compare the performance of the WSCC and L-WSCC, two sets of simulations were implemented on hourly and daily scale. The PEST (parameter estimation) automatic calibration algorithm [80] was adopted for the calibration of the WSCC and other modules (evapotranspiration, runoff sources partition, and flow concentration) parameters based on Xinanjiang model. PEST is a model-independent nonlinear parameter estimation and uncertainty analysis program, which is a flexible and generic calibration tool [80]. ...

... The PEST (parameter estimation) automatic calibration algorithm [80] was adopted for the calibration of the WSCC and other modules (evapotranspiration, runoff sources partition, and flow concentration) parameters based on Xinanjiang model. PEST is a model-independent nonlinear parameter estimation and uncertainty analysis program, which is a flexible and generic calibration tool [80]. It has the advantages of fast optimization speed and good robustness [81], which can be used in any of these hydrologic models and has been widely applied [82,83]. ...

The spatial distribution of water storage capacity has always been the critical content of the study of saturation-excess runoff. Xin′anjiang model uses the water storage capacity curve (WSCC) to characterize the distribution of water storage capacity for runoff yield calculation. However, the mathematical and physical foundations of WSCC are unclear, which is impossible to simulate runoff generation with complex basins accurately. To fill this gap, we considered the dominant role of basin physical characteristics in water storage capacity and developed a new integrated approach to solve the spatial distribution of water storage capacity (L-WSCC) to account for the spatiotemporal dynamics of their impact on runoff generation. The main contribution of L-WSCC was to confer WSCC more physical meaning and the spatial distribution of water storage capacity was explicitly represented more accurately, so as to better express the runoff generation and provide a new approach for runoff yield calculation in non-data basin. L-WSCC was applied to Misai basin in China and promising results had been achieved, which verified the rationality of the method (the mean Nash–Sutcliffe efficiency (NSE):0.86 and 0.82 in daily and hourly scale, respectively). Compared with WSCC, the performance of L-WSCC was improved (mean NSE: 0.82 > 0.78, mean absolute value of flood peak error (PE): 12.74% < 21.66%). Moreover, the results of local sensitivity analyses demonstrated that land-use and land cover was the major driving factor of runoff yield (the change of mean absolute error (ΔMAE): 131.38%). This work was significant for understanding the mechanisms of runoff generation, which can be used for hydrological environmental management and land-use planning.

... 13 been used extensively in applications related to water resources (Govender and Everson, 2005;Goegebeur and Pauwels, 2007;Wang and Brubaker, 2015). Through this work, PEST-VIC interface is established for effective implementation of optimization algorithm to obtain "best" ...

... In the present work, the PEST model is executed with an objective function of minimizing the squared sum of errors (SSE) between model simulated streamflow (Q sim ) values and observed streamflow (Q obs ). Details pertaining to the concept of PEST model can be obtained from Doherty (2001) and Goegebeur and Pauwels (2007). ...

Assessing the impacts of Land Use (LU) and climate change on future streamflow projections is necessary for efficient management of water resources. However, model projections are burdened with significant uncertainty arising from various sources. Most of the previous studies have considered climate models and scenarios as major sources of uncertainty, but uncertainties introduced by land use change and hydrologic model assumptions are rarely investigated. In this paper an attempt is made to segregate the contribution from (i) general circulation models (GCMs), (ii) emission scenarios, (iii) land use scenarios, (iv) stationarity assumption of the hydrologic model, and (v) internal variability of the processes, to overall uncertainty in streamflow projections using analysis of variance (ANOVA) approach. Generally, most of the impact assessment studies are carried out with unchanging hydrologic model parameters in future. It is however necessary to address the nonstationarity in model parameters with changing land use and climate. In this paper, a regression based methodology is presented to obtain the hydrologic model parameters with changing land use and climate scenarios, in future. The Upper Ganga Basin (UGB) in India is used as a case study to demonstrate the methodology. The semi-distributed Variable Infiltration Capacity (VIC) model is set-up over the basin, under nonstationary conditions. Results indicate that model parameters vary with time, thereby invalidating the often-used assumption of model stationarity. The streamflow in UGB under nonstationary model condition is found to reduce in future. The flows are also found to be sensitive to changes in land use. Segregation results suggest that model stationarity assumption and GCMs along with their interactions with emission scenarios, act as dominant sources of uncertainty. This paper provides a generalized framework for hydrologists to examine stationarity assumption of models before considering them for future streamflow projections and segregate the contribution of various sources to the uncertainty.

... Bárdossy and Singh (2008) put forward the robust parameter estimation (ROPE) algorithm, which looks for parameter optimal space instead of a single optimal point. Parameter estimation (PEST) is another powerful tool to estimate model parameters (PEST 2005, Goegebeur andPauwels 2007). ...

... If a point is trapped by small pits and bumps on a relatively flat objective function surface, it is not very likely for it to jump out of the trap to reach the global optimum. For more details of the PEST method and procedure, refer to PEST (2005) and Goegebeur and Pauwels (2007). ...

The use of a physically-based hydrological model for streamflow forecasting is limited by the complexity in the model structure and the data requirements for model calibration. The calibration of such models is a difficult task, and running a complex model for a single simulation can take up to several days, depending on the simulation period and model complexity. The information contained in a time series is not uniformly distributed. Therefore, if we can find the critical events that are important for identification of model parameters, we can facilitate the calibration process. The aim of this study is to test the applicability of the Identification of Critical Events (ICE) algorithm for physically-based models and to test whether ICE algorithm-based calibration depends on any optimization algorithm. The ICE algorithm, which uses the data depth function, was used herein to identify the critical events from a time series. Low depth in multivariate data is an unusual combination and this concept was used to identify the critical events on which the model was then calibrated. The concept is demonstrated by applying the physically-based hydrological model WaSiM-ETH on the Rems catchment, Germany. The model was calibrated on the whole available data, and on critical events selected by the ICE algorithm. In both calibration cases, three different optimization algorithms, shuffled complex evolution (SCE-UA), parameter estimation (PEST) and robust parameter estimation (ROPE), were used. It was found that, for all the optimization algorithms, calibration using only critical events gave very similar performance to that using the whole time series. Hence, the ICE algorithm-based calibration is suitable for physically-based models; it does not depend much on the kind of optimization algorithm. These findings may be useful for calibrating physically-based models on much fewer data.
Editor D. Koutsoyiannis; Associate editor A. Montanari
Citation Singh, S.K., Liang, J.Y., and Bárdossy, A., 2012. Improving calibration strategy of physically-based model WaSiM-ETH using critical events. Hydrological Sciences Journal, 57 (8), 1487–1505.

... One frequently used and relatively simple algorithm is the Parameter ESTimation, PEST method (Doherty and Johnston, 2003). Many examples of the application of the PEST algorithm for the calibration of hydrologic models can be found in the literature (Al-Abed and Whiteley, 2002;Zyvoloski et al., 2003;Wang and Melesse, 2005;Liu et al., 2005;Bahremand andDe Smedt, 2006, 2008;Goegebeur and Pauwels, 2007;Nossent and Bauwens, 2007). ...

... Many examples of application of the PEST algorithm for the calibration of hydrologic models can be found in the literature, e.g. Al-Abed and Whiteley(2002),Doherty and Johnston (2003),Wang and Melesse (2005),Liu et al. (2005),Skahill and Doherty (2006),,Bahremand and De Smedt (2008),Goegebeur and Pauwels (2007),Gallagher and Doherty (2007),Skahill et al. (2009). ...

Hydrological models are developed to better understand hydrological processes by easing the characterization of the real world data. Distributed hydrological models are used and developed to model spatially distributed hydrological processes in an entire catchment. Dealing with spatial distribution of parameters makes such models capable of performing various water resource assessments based on current and future changes in catchments, as well as for flood prediction.
The WetSpa distributed hydrologic model is used to assess how well distributed models can reproduce streamflow, and generate meaningful hydrographs at interior locations or ungaged-basins. This is done by applying the WetSpa model to the second phase of the "Distributed Model Intercomparison Project", or DMIP2, organized by the National Oceanic and Atmospheric Administration (NOAA), National Weather Service-Office of Hydrologic Development (NWS-OHD), USA. Data from 17 United States Geological Survey streamflow gaging stations are used in this study. The model implementations are based on 30-m spatial resolution and 1 hour time-step for all basins. There are five parent basins with nested subbasins. Two types of simulations are performed, i.e. simulations with uncalibrated model parameters and simulations with optimized model parameters.
In order to estimate the model parameters, while reducing the model calibration effort, an automated calibration procedure is applied by incorporating a model-independent parameter estimator, PEST. The automated approach, with observed flow hydrographs at selected stations as calibration targets, gives the best set of parameters by adjusting the values until the discrepancies between observed and simulated hydrographs is reduced to a minimum in the weighted least squares sense. In this study, the PEST program served as an optimization algorithm to estimate the model parameters, sensitivity of the parameters and model prediction accuracy.
Results of the uncalibrated and calibrated model runs show that the model calibration improves the model performance significantly. Nevertheless, subbasins simulation results show that calibration of the model for the parent basin is no guarantee for good performance for the subbasins.
Therefore, to improve the model calibration, as it evidently improves model performance, a Box Cox transformation is used to transform flow discharges in order to stabilize the error variance and an autoregressive integrated moving average (ARIMA) time series model is fitted to the transformed residuals to transfer model errors into disturbances that are homogeneous and uncorrelated. Consequently, these disturbances are used as calibration target in the PEST program for calibrating the hydrological model. Calibration of the transformed model yields improved estimates of the model parameters with smaller confidence bounds. Hence, parameter uncertainty is reduced by applying the Box--Cox transformation and the ARIMA error model to transform the model residuals. Also, the sensitivity analysis of the WetSpa model to parameter shows that the model is most sensitive to the baseflow recession coefficient and correction factor for potential evaporation, implying that precise measured/calculated potential evapotranspiration (PET) data and baseflow recession constant estimates are needed as input to the model.
PEST nonlinear predictive uncertainty analysis is used to explore the uncertainty associated with key model predictions by maximizing or minimizing a particular model output. This analysis shows that the original WetSpa model, when calibrated with utmost care by removing heteroscedacity and autocorrelation of the residuals, still remains flawed with respect to predicting extreme flows. The reason for this is the inadequate model procedure to qualify runoff by means of a runoff coefficient. Hence, this part of the model is improved in order to use WetSpa as an effective and accurate model to predict flooding in a river basin.
Results of the WetSpa application to the basins and subbasins in the DMIP2 project show that the model structure for groundwater drainage is inadequate. In WetSpa, groundwater flow is modeled with a linear reservoir method on small subcatchment scale. PEST parameter sensitivity analysis shows that the baseflow recession constant is a highly sensitive model parameter. WetSpa model application results show that there is a lack of fit between basin and subbasins base flow recession coefficients, such that the model performance for the subbasins, particularly smaller subbasins, becomes inaccurate. This is comparatively solved by inclusion of a Boussinesq based equation to calculate baseflow recession coefficient at basin and subbasin level, causing the modified WetSpa model to be more accurate when simulation runs are performed for subbasins or ungaged basins.

... A large number of studies have concentrated on the calibration and validation of these models using soil moisture data. Recent examples of such studies are De Lannoy et al., (2006), Campo et al. (2006), Kampf & Burges (2007), Santanello Jr. et al. (2007, and Goegebeur & Pauwels (2007). However, the possibility of the use of these models to predict soil moisture regimes has up till now not been investigated. ...

... Table 3 lists these parameter values. Using the observations, the soil parameters were adjusted using the Extended Kalman Filter equations, as described in Goegebeur & Pauwels (2007). Observations of the infiltration, runoff rates, soil temperature, and soil moisture content during the remainder of the study period were then used for model validation. ...

Soil moisture regimes under different land uses were observed and modeled in a representative forest basin in the Catalunyan Pre-Pyrenees, more specifically in the Ribera Salada catchment (222.5 km2), from 1998 through 2005. The vegetation cover in the catchment consists of pasture, tillage and forest. A number of representative plots for each of these land cover types were intensely monitored during the study period. The annual precipitation fluctuates between 516 and 753 mm, while the soil moisture content oscillates between 14 and 26% in the middle and low lying areas of the basin, and between 21 and 48% in shady zones near the river bed, and in the higher parts of the basin. Soil moisture and rainfall are controlled in the first place by altitude, with the existence of two climatic types in the basin (sub-Mediterranean and sub-alpine), and further by the land use. A fully physical process-based hydrologic model (TOPLATS) was found to be able to simulate exactly the soil moisture regimes in the basin in the different combination of local abiotic and biotic factors. The TOPLATS-based results are more precise than the results obtained using another frequently used method, more specifically the Newhall Simulation Model (NSM), which has been developed to simulate soil moisture regimes. NSM was found to overestimate wet soil moisture regimes. The differences between the obtained results can be explained by the model structure. On the one hand, TOPLATS uses a full set of meteorological forcing data to apply a large number of coupled physical equations to simulate the interaction between the land surface and the atmosphere. These equations require a large number of parameters which can be obtained either by calibration or by in-situ measurements. On the other hand, the NSM uses only air temperature and precipitation to apply a number of regression-based threshold equations, requiring no site-specific parameters. While the NSM has certainly proven to be useful in conditions where computational power is limited, and if one is careful in the interpretation of its results, the conclusions from this paper indicate that more attention should be paid to the use of hydrologic models for the estimation of soil moisture regimes.

... [4] The objective of this paper is to demonstrate a calibration procedure for conceptual rainfall-runoff models, leading to parameter estimates which result in good model simulations under all boundary conditions. The work is based on Goegebeur and Pauwels [2007], in which the equations of the Extended Kalman Filter (EKF) were used for model calibration, and compared to the the results of the PEST algorithm. The Extended Kalman Filter has been used for model parameter estimation for a number of decades. ...

... [14] The rainfall-runoff model, explained in Figure 3, is used by Matgen et al. [2006] and is one of the models used by Goegebeur and Pauwels [2007]. The model uses observed precipitation (R tot (t)) and potential evapotranspiration (ETP(t)) as input, both in m 3 s À1 . ...

The determination of the parameters for hydrologic models has been the subject of a large number of studies during the last 3 decades. A multitude of methods have been developed for this purpose. Generally, the mismatch between the model simulations and the observations is lumped into an objective function, which is then is optimized by these methods. This can lead to parameter values that result in a good model performance under certain (e.g., low flow) conditions but not under other (e.g., high flow) conditions. The objective of this paper is to demonstrate a calibration algorithm which leads to a good model performance under all boundary conditions. This algorithm is referred to as Multistart Weight-Adaptive Recursive Parameter Estimation (MWARPE). For this purpose the equations of the Extended Kalman Filter (EKF) have been used recursively in a Monte-Carlo approach, strongly increasing the chance that a globally optimal parameter set is obtained instead of a local optimum. The method has been applied to a rainfall-runoff model for the Zwalm catchment in Belgium, using a 1-year, a 2-year, and a 3-year calibration period. The results have been compared to the Shuffled Complex Evolution (SCE)-UA method. A synthetic study revealed that for narrow parameter limits the SCE-UA algorithm outperformed MWARPE, while for broad parameter limits the opposite occurred. For the test case using in situ observed data, the SCE-UA method resulted in slightly lower RMSE values than MWARPE, but MWARPE performed better outside the calibration period. It has been found that MWARPE can bypass local optima in the determination of the final parameter set. Also, the best initial parameter sets (with the lowest RMSE) do not lead to the best final parameter values. To apply the method only four parameters need to be specified, more specifically the number of starting points, the number of iterations per starting point, one parameter used to initialize the model error covariance matrix, and the observation error. For this reason, the method could be a simple alternative to more complex methods if model parameters have to be determined when time and/or computational power are limited.

... In our study, the SRPCM was used to optimize the parameters of the BIOME-BGC model notwithstanding its effectiveness in parameter optimization has been verified only for hydrological models. The SRPCM can directly search the optimal parameter values on the parametric function surface, while other available parameter optimization methods including the PEST algorithm usually search optimal parameter values on the objective function surface (Goegebeur & Pauwels 2007). In SRPCM, the non-linear parametric calibration problem is transformed into a linear parametric calibration problem by use of a differential system response relation between model output variations and parameter value variations, thus avoiding the local optimal value problem. ...

The daily gross primary productivity (GPP) and evapotranspiration (ET) in the Xilingol grassland ecosystem of Inner Mongolia were simulated using the BioGeochemical Cycles (Biome-BGC) model for 2003–2019 and under future climate-change scenarios. The system was optimized using the System Response Parameter Calibration Method (SRPCM). The temporal variations of GPP, ET and water use efficiency (WUE) were investigated, and the impacts of precipitation and temperature were explored. Results showed that (i) the BIOME-BGC model performed better when optimized using the SRPCM than by applying the Model-Independent Parameter Estimation approach (PEST); (ii) GPP and ET at annual and seasonal scales showed an insignificant increasing trend; (iii) WUE at the annual scale and in growing seasons showed an insignificant increasing trend and a slight decreasing trend in non-growing seasons; (iv) annual GPP and ET were more sensitive to changes in precipitation than changes in temperature with WUE keeping relatively stable with years; (v) precipitation is a critically controlling factor for GPP and ET in growing seasons and for ET and WUE in non-growing seasons; and (vi) combined temperature and precipitation changes had greater impacts on GPP/ET/WUE than individual changes.
HIGHLIGHTS
The SRPCM was proposed for parameter optimization of the BIOME-BGC model.;
The variations of GPP, ET and WUE in 2003–2019 were explored on multiple time-scales.;
GPP, ET and WUE in growing seasons played a decisive role in annual GPP and ET.;
Daily WUE within 0–2 g/kg dominated in both non-/growing seasons during 2003–2019.;
The combined rise of temperature and precipitation has greater impacts on GPP/ET/WUE than only temperature or precipitation rise.;

... The parameter estimation (PEST) [45][46][47] hydrological parameter estimation model, which is model-independent parameter estimation software that undertakes the task of uncertainty analysis, is adopted to optimize the parameters of the SPHY model. The PEST was published in 1999 and experienced rapid development. ...

Quantitative analysis of changes in Lhasa River runoff components was significant to local water resources management. This study constructed the spatial processes in hydrology (SPHY) model in the Lhasa River Basin and optimized the model’s parameters using the hydrograph partitioning curves (HPC) method. The Lhasa River Basin’s precipitation and temperature were forecasted for 2020 to 2100 using the statistical downscaling model (SDSM) and two scenarios from the fifth generation of the Canadian earth system model (CanESM5) dataset, shared socioeconomic pathways 1-2.6 (SSP1-2.6) and shared socioeconomic pathways 2-4.5 (SSP2-4.5). This study analyzed the potential changes in Lhasa River runoff and components based on the future climate. The results showed that the Lhasa River runoff from 2010 to 2019 was composed of snowmelt runoff, glacier melt runoff, rainfall runoff, and baseflow, with the proportions of 15.57, 6.19, 49.98, and 28.26%, respectively. From 2020 to 2100, under the SSP1-2.6 scenario, the precipitation and average temperature increased by 0.76mm and 0.08 °C per decade. Under the SSP2-4.5 scenario, the increasing rate was 3.57 mm and 0.25 °C per decade. Due to the temperature increase, snowmelt and glacier melt runoff showed a decreasing trend. The decline rate of total runoff was 0.31 m3/s per year under the SSP1-2.6 scenario due to the decrease in baseflow. Under the SSP2-4.5 scenario, total runoff and rainfall runoff showed a clear increasing trend at an average rate of 1.13 and 1.16 m3/s per year, respectively, related to the significant increase in precipitation. These conclusions suggested that climate change significantly impacted the Lhasa River’s total runoff and runoff components.

... Fifteen flood events were chosen to calibrate the model parameters and six events to verify the model. Calibration and optimization of XAJ model parameters were based on the parameter estimation algorithm (PEST) with MATLAB environment [69]. Thirteen parameters related to evapotranspiration, runoff generation, runoff source partition and runoff routing ( Table 2) were calibrated. ...

The study of runoff under the influence of human activities is a research hot spot in the field of water science. Land-use change is one of the main forms of human activities and it is also the major driver of changes to the runoff process. As for the relationship between land use and the runoff process, runoff yield theories pointed out that the runoff yield capacity is spatially heterogeneous. The present work hypothesizes that the distribution of the runoff yield can be divided by land use, which is, areas with the same land-use type are similar in runoff yield, while areas of different land uses are significantly different. To prove it, we proposed a land-use-based framework for runoff yield calculations based on a conceptual rainfall–runoff model, the Xin’anjiang (XAJ) model. Based on the framework, the modified land-use-based Xin’anjiang (L-XAJ) model was constructed by replacing the yielding area (f/F) in the water storage capacity curve of the XAJ model with the area ratio of different land-use types (L/F; L is the area of specific land-use types, F is the whole basin area). The L-XAJ model was then applied to the typical cultivated–urban binary land-use-type basin (Taipingchi basin) to evaluate its performance. Results showed great success of the L-XAJ model, which demonstrated the area ratio of different land-use types can represent the corresponding yielding area in the XAJ model. The L-XAJ model enhanced the physical meaning of the runoff generation in the XAJ model and was expected to be used in the sustainable development of basin water resources.

... In our study, the SRPCM was tentatively used to optimize the parameters of the BIOME-BGC model parameter values on the objective function surface (Goegebeur et al., 2007). In SRPCM, the nonlinear parametric calibration problem is transformed into a linear parametric calibration problem by use of the 432 differential system response relation between model output variation and parameter variation, thus the 433 irrelevant local optimal value problem can be avoided by the SRPCM. ...

The daily gross primary productivity (GPP) and evapotranspiration (ET) in the Xilingol temperate grassland ecosystem of Inner Mongolia, China were simulated during 2003 to 2019 and under future climate change scenarios by the BioGeochemical Cycles (Biome-BGC) model, which was optimized by the system response parameter calibration method (SRPCM), the temporal variations of GPP, ET and WUE (GPP/ET) on multiple time scales were investigated, and the impacts of precipitation and temperature on them were explored. The results revealed: the BIOME-BGC model performed better optimized by SRPCM than by PEST; GPP and ET at annual and seasonal scales all showed an insignificant increasing trend; WUE at annual scale and in growing seasons all showed an insignificant increasing trend with it presenting a slight decrease trend in non-growing seasons; the intra-annual distributions of GPP, ET and WUE were very uneven with the highest GPP and ET appearing in July and the highest WUE in September; annual GPP and ET are more sensitive to the changes in precipitation than in temperature with WUE keeping relatively stable with years; precipitation is a critically controlling factor to GPP and ET in growing seasons and to ET and WUE in non-growing seasons; monthly precipitation exhibited greater influence on GPP, ET and WUE than monthly temperature with the previous month’s precipitation imposing bigger effects on GPP than the current month’s; the combined increase scenarios in temperature and precipitation impose greater impacts on GPP/ET/WUE than the ones only increasing in temperature or precipitation.

... The model calibration aimed to align the model's results with observed data by adjusting the model parameters, which was crucial for model application. The PEST (Parameter Estimation) automatic calibration algorithm is a flexible and generic calibration tool that can be used in any of these models and has been widely applied [92]. Hence, the PEST algorithm was linked to the coupled model in the MATLAB environment for model calibration and validation in our study. ...

As an ecological consequence of intensified anthropogenic activities, more frequent extreme rainfalls have resulted in significant increases in water levels and discharge in southwestern China. This phenomenon presents a significant challenge in flood risk and ecological management. Land use is one of the major factors significantly affecting the flooding process, and it is inextricably tied to the ecological risk of floods. Hence, flood risk estimates based on land use are essential for flood control and land use planning. In this study, a coupled hydrologic–hydraulic model was developed to analyze the relationship between flood ecological risk and land use in order to provide new insights into current flood risk management practices. Ten real flood events (of different magnitudes) in the Zhaojue river basin (650 km2) were chosen to evaluate the credibility and performance of the coupled model’s application. Promising results were obtained, with sufficient reliability for flood risk assessment purposes. The results of our flood risk analysis also indicated that the model effectively reproduced overland flow and competently accounted for flood evolution. This work is significant in the understanding of the mechanism of the flood process and its relationship with land use, and it can be used in decision support for the prevention and mitigation of flood disasters and for land use planning.

... The average areal rainfall was calculated with the Thiessen polygonal method [63]. The parameter estimation (PEST) automatic calibration algorithm was adopted to calibrate the model with a MATLAB environment [64]. This algorithm had the advantages of the inverse Hessian method and the steepest descent method, and can obtain the optimal parameter results through fewer model runs [65]. ...

Floods are one of the main natural disaster threats to the safety of people’s lives and property. Flood hazards intensify as the global risk of flooding increases. The control of flood disasters on the basin scale has always been an urgent problem to be solved that is firmly associated with the sustainable development of water resources. As important nonengineering measures for flood simulation and flood control, the hydrological and hydraulic models have been widely applied in recent decades. In our study, on the basis of sufficient remote-sensing and hydrological data, a hydrological (Xin’anjiang (XAJ)) and a two-dimensional hydraulic (2D) model were constructed to simulate flood events and provide support for basin flood management. In the Chengcun basin, the two models were applied, and the model parameters were calibrated by the parameter estimation (PEST) automatic calibration algorithm in combination with the measured data of 10 typical flood events from 1990 to 1996. Results show that the two models performed well in the Chengcun basin. The average Nash–Sutcliffe efficiency (NSE), percentage error of peak discharge (PE), and percentage error of flood volume (RE) were 0.79, 16.55%, and 18.27%, respectively, for the XAJ model, and those values were 0.76, 12.83%, and 11.03% for 2D model. These results indicate that the models had high accuracy, and hydrological and hydraulic models both had good application performance in the Chengcun basin. The study can a provide decision-making basis and theoretical support for flood simulation, and the formulation of flood control and disaster mitigation measures in the basin.

... The core step in satellite remote sensing is inverse modeling, which is used to calibrate selected model parameters. Calibration refers to adjusting the parameters in a model so that the behavior of the model is as close as possible to the behavior of the real system being simulated (Goegebeur and Pauwels 2007). The reflectance values obtained at water quality stations were extracted from atmospherically corrected satellite imagery for analysis. ...

Monitoring water at high spatial and temporal resolutions is important for maintaining water quality because the cost of pollution remediation is often higher than the cost of early prevention or intervention. In recent decades, the availability and affordability of satellite images have regularly increased, thus supporting higher-frequency and lower-cost alternative methods for monitoring water quality. The core step in satellite remote sensing detection is inverse modeling, which is used to calibrate model parameters and enhance the similarity between the model and the real system being simulated. The reflectance values measured at water quality stations are extracted from atmosphere-corrected satellite imagery for analysis. However, various external environmental, hydrological, and meteorological factors affect the evaluation results, and the results obtained with different parameters can vary. This literature review shows that nonpoint-source pollution caused by stormwater runoff can also be monitored using satellite imagery. To improve the accuracy of satellite-based water quality prediction, the temporal resolution of field measurements can be increased, thus better considering the influence of seasonality. Then, the atmospheric correction module can be improved by using available atmospheric water content products. Moreover, because water surface ripples affect reflectance, wind speed and direction should be considered when comparing water quality scenes.

... The model independent LM method based parameter estimation software PEST (Doherty, 2004(Doherty, , 2007a(Doherty, , 2007b, which quantifies model to measurement misfit in the weighted least squares sense, is now widely used to support hydrologic and environmental model calibration. In addition to its traditional groundwater model calibration application setting (Zyvoloski et al., 2003;Tonkin and Doherty, 2005;Moore and Doherty, 2006;Gallagher and Doherty, 2007a), it is now employed to calibrate ecological models (Rose et al., 2007), land surface models (Santanello Jr. et al., 2007) and models in other application areas including nonpoint source pollution (Baginska et al., 2003;Haydon and Deletic, 2007), surface hydrology (Doherty and Johnston, 2003;Gutiérrez-Magness and McCuen, 2005;Kunstmann et al., 2006;Skahill and Doherty, 2006;Doherty and Skahill, 2006;Gallagher and Doherty, 2007b;Goegebeur and Pauwels, 2007;Iskra and Droste, 2007;Kim et al., 2007;Maneta et al., 2007), and surface water quality (Rode et al., 2007). Skahill et al. (2011) focused on one drawback associated with LM-based model independent parameter estimation as implemented in PEST; viz., that it requires estimates, based on finite differences, of the derivatives of the objective function with respect to the model parameters. ...

The objective of this article is to demonstrate, by way of example(s), how to use our implementation of the MLSL method for model independent parameter estimation to calibrate a GSSHA hydrologic model. The purpose is not to present or focus on the theory which underlies the parameter estimation method, but rather to carefully describe how to use the ERDC software implementation of MLSL that accommodates the PEST model independent interface to calibrate a GSSHA hydrologic model. Given the computational expense associated with global optimization, we will initially consider variations of our MLSL implementation on a computationally efficient test problem in attempts to provide the interested reader with an intuitive sense of how the method works. (https://hdl.handle.net/11681/7374)

... This value is important for optimizing stability and was based on the mean of the literature values (Table 1). In systems containing high observation errors and/or sparse observations PEST may fail to yield a solution (Goegebeur and Pauwels, 2007). The condition number is an indication of the successful calculation of an optimal unique solution. ...

... It is convenient to simulate the salt water migration in the sand column. The parameter optimization is calculated with PEST (parameter estimate) code [19]. ...

Injecting freshwater and pumping salt water are effective methods to restore the salt water in a coastal area. Based on a one-dimensional vertical experiment, the variable density flow is simulated under the condition of different injection directions and injection rates of fresh water. A one-dimensional mathematical model of variable density flow and solute transport is established. The mathematical models are solved using the implicit difference method. Fortran code is developed to simulate and verify the vertical flow of variable density flow in different directions. Through both numerical simulation and experimental studies, it is found that the variable density fluid in the direction of reverse gravity is different from that in the direction of gravity. On this basis, the most effective desalination model of salt water is further discussed. It provides a theoretical and technical method for the restoration of salt water in the vertical injection of freshwater. In order to improve the remediation efficiency and reduce the cost in the engineering application, the suitable water injection rate should be ensured, considering the suitable construction time and zone of a study area.

... Automated calibration of selected model parameters is performed using the Parameter Estimation (PEST) software package (Doherty, 2004) that has often been used for similar purposes in land surface hydrology (e.g. Goegebeur and Pauwels, 2007;Immerzeel and Droogers, 2008;van der Velde et al., 2009). PEST can operate, by writing and reading model input and output files via supplied templates, as a shell around any model that can be run from a command line. ...

In this paper, the discrete electromagnetic model developed at the Tor Vergata University of Rome (hereafter, TV-DEM) is used to simulate both active and passive L-band signals using a single set of input parameters. The simulations are compared to Aquarius observations collected from a view angle of 28.7° over the Maqu study area located near the north-eastern edge of the Tibetan Plateau. The TV-DEM parameters litter biomass, litter moisture factor, plant moisture and standard deviation of height variations are calibrated for Aquarius observations collected during the 2012 and 2013 warm seasons. The calibrated parameters are used to reproduce the brightness temperature (Tb) and backscattering coefficient (σo) for the 2014 and 2015 warm season as an independent assessment.
The results show that the calibrated TV-DEM simulations capture Aquarius observations reasonably well with coefficients of determination (R²'s) varying from 0.75 to 0.86 for the Tb's and from 0.36 to 0.68 (−) for the σo's depending on the polarization and adopted matchup set (e.g. calibration or validation). The simulations, however, systematically overestimate the H polarized Aquarius observation and underestimate the V polarized observations. The calibrated TV-DEM is also utilized for soil moisture retrieval from three combinations of Aquarius data, including a set of both active and passive microwave observations. The obtained error metrics indicate that the soil moisture estimates from the active/passive data have the smallest bias (− 0.008 m³ m− 3) and the lowest unbiased root mean squared difference (0.021 m³ m− 3), while soil moisture retrieved using a calibrated τ (optical depth)-ω (single scattering albedo) model based algorithm provided the best R². These results warrant further investigation of the synergistic use of active/passive data for soil moisture retrieval as well as the use of complex physically radiative transfer model as part of well-established algorithms.

... The Kalman Filter explicitly propagates these errors in time, assuming a linear dynamic model. The 10 Extended Kalman Filter (EKF) re-estimates the Jacobian of the dynamic model at each new time step in order to address possible non-linearities in the evolution of the errors (Goegebeur and Pauwels, 2007). In systems where the error covariances are either difficult to define or the computational cost to propagate them is too great, the Ensemble Kalman Filter (EnKF) estimates the error covariance at each timestep using 15 the ensemble members (Weerts and El Serafy, 2006;Pauwels and De Lannoy, 2009). ...

The present study explores the application of a data assimilation (DA) procedure to correct the radar rainfall inputs of an event-based, distributed, parsimonious hydrological model. A simplified Kalman filter algorithm was built on top of a rainfall-runoff model in order to assimilate discharge observations at the catchment outlet. The study site is the 114 km<sup>2</sup> Lez Catchment near Montpellier, France. This catchment is subject to heavy orographic rainfall and characterized by a karstic geology, leading to flash flooding events. The hydrological model uses a derived version of the SCS method, combined with a Lag and Route transfer function. Because it depends on geographical features and cloud structures, the radar rainfall input to the model is particularily uncertain and results in significant errors in the simulated discharges. The DA analysis was applied to estimate a constant correction to each event hyetogram. The analysis was carried out for 19 events, in two different modes: re-analysis and pseudo-forecast. In both cases, it was shown that the reduction of the uncertainty in the rainfall data leads to a reduction of the error in the simulated discharge. The resulting correction of the radar rainfall data was then compared to the mean field bias (MFB), a corrective coefficient determined using ground rainfall measurements, which are more accurate than radar but have a decreased spatial resolution. It was shown that the radar rainfall corrected using DA leads to improved discharge simulations and Nash criteria compared to the MFB correction.

... The equations are applied recursively throughout an iteration process, based on which, the methodology can be referred to as weight-adaptive recursive parameter estimation. For a full description we refer to Goegebeur and Pauwels (2007). Model simulation with TOPLATS at each availability of observations from each site. ...

Current evapotranspiration in a typical Mediterranean catchment
has been assessed in the Ribera Salada catchment in the Spanish pre-Pyrenees, using
two equations, as an alternative to direct measurements. Evapotranspiration rates
from the soil column (including root water uptake) and evaporation rates from the
canopy interception were estimated. A soil-water balance model was also applied.
These approaches have been used to estimate the evapotranspiration rate for Mediterranean
vegetation, Quercus ilex, Pinus sylvestris, Pinus uncinata, pasture and tillage
in seven experimental plots. Observations of precipitation, infiltration, surface runoff,
soil moisture contents and deep soil percolation are used for this purpose. The calculated
evapotranspiration rates are coincident with the established values by other
authors on Mediterranean zones, which indicate that the estimation of the different parts of the overall plot scale evapotranspiration rates is a promising and relatively
cheap technique for applications in disciplines such as hydrology, ecology, and forest
management. Finally, the estimated evapotranspiration from the soil-water balance
model “TOPLATS” has been compared with assessed values. The model has
some uncertainties associated with the water flux into the soil, which entails either an
overestimation or underestimation of the evapotranspiration values. This response is
associated with soil moisture and canopy interception model formulation. A more detailed
characterization of the different hydrologic balance components could be used
for model improvement.

... The ensemble Kalman filter (EnKF) [Evensen, 2003] and the particle filter [Smith and Gelfand, 1992] are the most commonly used data assimilation techniques in hydrological modeling [Reichle et al., 2002;Chen and Zhang, 2006;Weerts and El Serafy, 2006;Camporese et al., 2009;Ng et al., 2009;Pauwels and De Lannoy, 2009;Hendricks Franssen et al., 2011;Pasetto et al., 2012;Ridler et al., 2014]. The ensemble framework used in these assimilation methods to compute the statistical quantities of interest allows EnKF and particle filters to be applied not only for updating model states but also for uncertainty estimation, model performance diagnostics, parameter estimation, and sensor failure analysis [Van Geer et al., 1991;Moradkhani et al., 2005;Goegebeur and Pauwels, 2007;Liu and Gupta, 2007;Hendricks Franssen and Kinzelbach, 2008;Sun et al., 2009;Trudel et al., 2014;Pasetto et al., 2015]. Advanced computational methods for hydrological modeling, including reduced order modeling and data assimilation, will be further discussed in section 3. Table 1 highlights important advances made in the development of physically based models [e.g., Narasimhan and Witherspoon, 1976;Celia et al., 1990;Gerke and van Genuchten, 1993], but also in areas that are highly relevant to hydrological modeling but that have evolved into major fields of their own: characterizing the highly nonlinear constitutive relations in unsaturated media [e.g., Mualem, 1976;Clapp and Hornberger, 1978]; parameter estimation and model calibration methods [e.g., Yeh, 1986;Gupta et al., 1998]; catchment and flow path delineation from topographic data [e.g., Band, 1986;Tarboton, 1997]; and stochastic Water Resources Research 10.1002/2015WR017780 hydrology [e.g., Gelhar and Axness, 1983;Gelhar et al., 1992]. ...

Integrated, process-based numerical models in hydrology are rapidly evolving, spurred by novel theories in mathematical physics, advances in computational methods, insights from laboratory and field experiments, and the need to better understand and predict the potential impacts of population, land use, and climate change on our water resources. At the catchment scale, these simulation models are commonly based on conservation principles for surface and subsurface water flow and solute transport (e.g., the Richards, shallow water, and advection-dispersion equations), and they require robust numerical techniques for their resolution. Traditional (and still open) challenges in developing reliable and efficient models are associated with heterogeneity and variability in parameters and state variables; nonlinearities and scale effects in process dynamics; and complex or poorly known boundary conditions and initial system states. As catchment modeling enters a highly interdisciplinary era, new challenges arise from the need to maintain physical and numerical consistency in the description of multiple processes that interact over a range of scales and across different compartments of an overall system. This paper first gives an historical overview (past 50 years) of some of the key developments in physically based hydrological modeling, emphasizing how the interplay between theory, experiments, and modeling has contributed to advancing the state of the art. The second part of the paper examines some outstanding problems in integrated catchment modeling from the perspective of recent developments in mathematical and computational science.

... PEST was used for automatic calibration. PEST is a modelindependent parameter estimation, so it can be applied to many other modeling environments (Doherty and Skahill 2006;Fienen et al. 2009;Goegebeur and Pauwels 2007;Kim et al. 2007). PEST recognizes the position of the model input file and the parameter set for calibration from a template file (e.g., .tpl). ...

Basin discretization effects in HSPF simulations were investigated to provide useful insights for hydrologists to determine the proper catchment size for basin scale modeling. The next generation radar (NEXRAD) rainfall estimates were incorporated into the HSPF modeling environment to generate streamflows at various catchments sizes ranging from 37 to 2,484 km(2). This research aims to identify how HSPF model performance can be improved by a marginal level of spatial discretization in rainfall-runoff modeling. Parameter estimation software was used for model calibration using data periods from 1998 to 2000. All simulations at different discretization levels above approximately 23% of the basin size resulted in good statistical values, with correlation coefficients of 0.82-0.87 and Nash-Sutcliffe efficiency coefficients of 0.61-0.73. However, the modeling performances of HSPF are limited when the catchment size reaches below 8.18% of the basin size, regardless of automatic calibration efforts. The result indicates that basin discretization at finer scales does not necessarily improve HSPF simulation results with NEXRAD inputs. (C) 2014 American Society of Civil Engineers.

... However, this weakness can be overcome using a methodology developed by Skahill and Doherty (2006), where GML calibration runs are initiated from different points in the parameter space so that the chance of finding the global minimum is improved as much as possible. Many examples of applying the PEST algorithm for calibration of hydrologic models can be found in the literature; e.g., Al-Abed and Whiteley (2002), Doherty and Johnston (2003), Wang and Melesse (2005), Liu et al. (2005), Skahill and Doherty (2006), Bahremand and De Smedt (2008), Goegebeur and Pauwels (2007), Gallagher and Doherty (2007), and Skahill et al. (2009). ...

Calibration of a distributed hydrologic model (WetSpa) for modeling river flows is performed using automatic parameter optimization. The main purpose of this research is to provide more confidence in the uncertainty analysis of the model parameters and predictions. A Box-Cox transformation and an autoregressive integrated moving average (ARIMA) time series model are used to transform the correlated and nonstationary model residuals to white noise disturbances, which can be minimized by ordinary least squares optimization. The WetSpa model is applied to the Illinois River basin, with a spatial resolution of 30 m and 1 h time step for a 10-year simulation period (1996–2006). The model is calibrated using river flow records (1996–2002) and validated using the remaining flow data (2002–2006). The results show that simple calibration of the model is inaccurate, as the residuals exhibit heteroscedasticity, which results in inaccurate estimates of the model parameters and large prediction uncertainty. The model calibration is improved when the calibration is combined with a Box-Cox transformation of the discharge and ARIMA modeling of the residuals, which considerably enhances the confidence of the model parameter estimates and of the model predictions.
Read More: http://ascelibrary.org/doi/abs/10.1061/(ASCE)HE.1943-5584.0001141

... The model independent LM method based parameter estimation software PEST (Doherty, 2004(Doherty, , 2007a, which quantifies model to measurement misfit in the weighted least squares sense, is now widely used to support hydrologic and environmental model calibration. In addition to its traditional groundwater model calibration application setting (Zyvoloskia et al. 2003;Tonkin and Doherty, 2005;Moore and Doherty, 2005;Gallagher and Doherty, 2007a), it is now employed to calibrate ecological models (Rose et al. 2007), land surface models (Santanello Jr. et al. 2007) and models in other application areas including nonpoint source pollution (Baginska et al. 2003;Haydon and Deletic, 2007), surface hydrology (Doherty and Johnston, 2003;Gutiérrez-Magness and McCuen, 2005;Kunstmann et al. 2006;Skahill and Doherty, 2006;Doherty and Skahill, 2006;Gallagher and Doherty, 2007b;Goegebeur and Pauwels, 2007;Iskra and Droste, 2007;Kim et al. 2007;Maneta et al. 2007), and surface water quality (Rode et al. 2007). ...

The objective of this technical note is to demonstrate, by way of example(s), how to use the Engineer Research and Development Center (ERDC) implementation of the Levenberg-Marquardt (LM) and Secant LM (SLM) method for model independent parameter estimation to calibrate a Gridded Surface Subsurface Hydrologic Analysis (GSSHA) hydrologic model. The purpose is not to present or focus on the theory which underlies the parameter estimation method(s), but rather to carefully describe how to use the ERDC software implementation of the secant LM method that accommodates the PEST model independent interface to calibrate a GSSHA hydrologic model. We will consider variations of our Secant LM (SLM) implementation in attempts to provide the interested reader with an intuitive sense of how the method works. We will also demonstrate how our LM/SLM implementation compares with its counterparts as implemented in the popular PEST software. (https://hdl.handle.net/11681/7371)

... Because state variables were considered unobservable in this previous study, accuracy was indirectly assessed by stream flow forecasting. Goegebeur and Pauwels (2007) compared the performance of extended Kalman filter with Parameter ESTimation (PEST) method that minimizes an objective function as briefly introduced above. The latter is different from the extended Kalman filter approach minimizing a square error with observation. ...

Aerodynamic roughness height (Zom) is a key parameter
required in several land surface hydrological models, since errors in
heat flux estimation are largely dependent on optimization of this
input. Despite its significance, it remains an uncertain parameter which
is not readily determined. This is mostly because of non-linear
relationship in Monin-Obukhov similarity (MOS) equations and uncertainty
of vertical characteristic of vegetation in a large scale. Previous
studies often determined aerodynamic roughness using a minimization of
cost function over MOS relationship or linear regression over it,
traditional wind profile method, or remotely sensed vegetation index.
However, these are complicated procedures that require a high accuracy
for several other related parameters embedded in serveral equations
including MOS. In order to simplify this procedure and reduce the number
of parameters in need, this study suggests a new approach to extract
aerodynamic roughness parameter from single or two heat flux
measurements analyzed via Ensemble Kalman Filter (EnKF) that affords
non-linearity. So far, to our knowledge, no previous study has applied
EnKF to aerodynamic roughness estimation, while the majority of data
assimilation study have paid attention to updates of other land surface
state variables such as soil moisture or land surface temperature. The
approach of this study was applied to grassland in semi-arid Tibetan
Plateau and maize on moderately wet condition in Italy. It was
demonstrated that aerodynamic roughness parameter can be inversely
tracked from heat flux EnKF final analysis. The aerodynamic roughness
height estimated in this approach was consistent with eddy covariance
method and literature value. Through a calibration of this parameter,
this adjusted the sensible heat previously overestimated and latent heat
flux previously underestimated by the original Surface Energy Balance
System (SEBS) model. It was considered that this improved heat flux
estimation especially during the summer Monsoon period, based upon a
comparison with precipitation and soil moisture field measurement. For
an advantage of this approach over other previous methodologies, this
approach is useful even when eddy covariance data are absent at a large
scale and is time-variant over vegetation growth, as well as is not
directly affected by saturation problem of remotely sensed vegetation
index.

... The Kalman Filter explicitly propagates these errors in time, assuming a linear dynamic model. The 10 Extended Kalman Filter (EKF) re-estimates the Jacobian of the dynamic model at each new time step in order to address possible non-linearities in the evolution of the errors (Goegebeur and Pauwels, 2007). In systems where the error covariances are either difficult to define or the computational cost to propagate them is too great, the Ensemble Kalman Filter (EnKF) estimates the error covariance at each timestep using 15 the ensemble members (Weerts and El Serafy, 2006;Pauwels and De Lannoy, 2009). ...

The present study explores the application of a data assimilation (DA) procedure to correct the radar rainfall inputs of an event-based, distributed, parsimonious hydrological model. A simplified Kalman filter algorithm was built on top of a rainfall-runoff model in order to assimilate discharge observations at the catchment outlet. The study site is the 114 km2 Lez Catchment near Montpellier, France. This catchment is subject to heavy orographic rainfall and characterized by a karstic geology, leading to flash flooding events. The hydrological model uses a derived version of the SCS method, combined with a Lag and Route transfer function. Because it depends on geographical features and cloud structures, the radar rainfall input to the model is particularily uncertain and results in significant errors in the simulated discharges. The DA analysis was applied to estimate a constant correction to each event hyetogram. The analysis was carried out for 19 events, in two different modes: re-analysis and pseudo-forecast. In both cases, it was shown that the reduction of the uncertainty in the rainfall data leads to a reduction of the error in the simulated discharge. The resulting correction of the radar rainfall data was then compared to the mean field bias (MFB), a corrective coefficient determined using ground rainfall measurements, which are more accurate than radar but have a decreased spatial resolution. It was shown that the radar rainfall corrected using DA leads to improved discharge simulations and Nash criteria compared to the MFB correction.

... From the analysis of field data, they demonstrated that the EKF can be applied to determine the aquifer parameters successfully. Goegebeur and Pauwels (2007) applied the EKF to a conceptual rainfall-runoff model with 10 parameters and demonstrated its robustness for parameter calibration, especially for problems with high observation errors, infrequent observations, and/or strongly erroneous initial parameters. Shamir et al. (2010) utilized ensemble EKF to link upstream watersheds and channels to main river channels and tributaries in a large regulated basin for flood forecasting. ...

Yeh and Chen (J Hydro 342(3–4):283-294, 2007) integrated a slug test solution for a well having a finite-thickness skin with the simulated annealing (SA) to determine the hydraulic parameters of the skin zone and formation zone. Some results obtained in positive-skin scenarios are however not accurate if compared with the target values of the parameters. This study first employs the sensitivity and correlation analyses to quantify the relationship between two normalized sensitivities and analyze the resulting errors in parameter estimates. It is found that the inaccuracy in parameter estimates can be attributed to following two problems: (1) the normalized sensitivities of the skin thickness and hydraulic conductivity are highly correlated and (2) the SA algorithm is very sensitive to round-off error in well-water-level (WWL) data. A parameter identification approach is thus developed based on the extended Kalman filter (EKF) coupled with the solution used by Yeh and Chen (J Hydro 342(3–4):283-294, 2007) to determine the parameters in six positive-skin scenarios where the parameters were not accurately determined before. We show that previous two problems can be overcome by the proposed approach because it is designed to account for uncertainties of measurements. Moreover, the EKF can save 99.8% and 99.9% computing time when compared with the results using the SA in analyzing 20 WWL data and 47 WWL data, respectively.

... The model independent Levenberg-Marquardt (LM) method based parameter estimation software PEST (Doherty, 2004(Doherty, , 2007a, which quantifies model-to-measurement misfit in the weighted least squares sense, is now widely used to support environmental model calibration. In addition to its traditional groundwater model calibration application setting (Zyvoloskia et al., 2003;Tonkin and Doherty, 2005;Moore and Doherty, 2006;Gallagher and Doherty, 2007a), it is now employed to calibrate ecological models (Rose et al., 2007;Gaucherel et al., 2008), land surface models (Santanello Jr. et al., 2007) and models in other application areas including nonpoint source pollution (Baginska et al., 2003;Haydon and Deletic, 2007), surface hydrology (Doherty and Johnston, 2003;Gutié rrez-Magness and McCuen, 2005;Kunstmann et al., 2006;Skahill and Doherty, 2006;Doherty and Skahill, 2006;Gallagher and Doherty, 2007b;Goegebeur and Pauwels, 2007;Iskra and Droste, 2007;Kim et al., 2007;Maneta et al., 2007), and surface water quality (Rode et al., 2007). ...

Our independent Levenberg-Marquardt (LM) implementation accommodates the PEST model independent and input control file protocol. First, to reduce the number of model calls needed to find a local minimum we use a combination of Broyden rank one updates (secant method) and central and forward finite differences to update the model sensitivity matrix at each optimization iteration. The exact combination of Broyden rank one updates and finite differences is easily specified by the user. While PEST Version 11 does include the ability to utilize Broyden updates, that implementation does not realize the complete efficiency gains that are possible. Second, we have added Multi Level Single Linkage (MLSL), a stochastic global optimization algorithm, to our PEST compatible model independent calibration software. MLSL uses the LM algorithm for local search and a minimum distance threshold to avoid repeated visits to the same local minima. The use of our MLSL implementation requires only a minor addition to a PEST input control file. Efficiencies that can be achieved for LM method based model independent calibration from a properly implemented secant version of the LM method will be demonstrated by examining the reduction in the total number of model calls for single HEC-HMS / watershed model inversion runs associated with the use of our independent LM implementation that accommodates the PEST model independent and input control file protocol. Using HEC-HMS / watershed models, we will also compare the efficiencies, in terms of the number of model calls required to achieve a given objective function value, of our implementations of Multistart, Trajectory Repulsion, and MLSL with that of Shuffled Complex Evolution (SCE) and Covariance Matrix Adaption Evolutionary Strategy (CMAES), as interfaced to PEST.

... One frequently used and relatively simple algorithm is the Parameter ESTimation, PEST method (Doherty and Johnston, 2003). Many examples of the application of the PEST algorithm for the calibration of hydrologic models can be found in the literature (Al-Abed and Whiteley, 2002;Zyvoloski et al., 2003;Wang and Melesse, 2005;Liu et al., 2005;De Smedt, 2006, 2007;Goegebeur and Pauwels, 2007;Nossent and Bauwens, 2007). ...

This paper describes the application of a spatially distributed hydrologic model (WetSpa) Water and Energy Transfer between Soil, Plants and Atmosphere, for the second phase of the Distributed Model Intercomparison Project (DMIP2) study. The model implementation is based on 30-m spatial resolution and 1 h time-step for all basins and interior watersheds involved in the DMIP study. Rainfall inputs are derived from Next Generation Radar (NEXRAD). The distributed model parameters are based on an extensive database of watershed characteristics available for the region, including digital maps of topography, soil type, and landuse. The model is calibrated and validated on part of the river flow records for each basin and applied to the smaller interior watersheds not used in calibration to assess the model performance in ungaged basins. The statistics improve significantly with calibration of the global model parameters but even for uncalibrated simulations, the WetSpa model reproduces flow rates of acceptable accuracy for most cases. To evaluate the model performance during calibration and validation periods, an Aggregated Measure (AM) is introduced that measures different aspects of the simulated hydrograph such as shape, size and volume. The statistics for the five calibration basins show that the model produces very good to excellent results for the calibration period. With the exception of Blue River basin, the overall model performance for the validation period remains good to very good, indicating that the model is able to simulate the relevant hydrologic processes in the basins accurately. The performance of the uncalibrated model for the subcatchments is more variable, but the hourly flow rates generally reproduced with reasonable accuracy indicating an encouraging performance of the model.

... The program is able to run a model as many times as needed while adjusting parameter values until the discrepancies between selected model outputs and a complementary set of field or laboratory measurements is reduced to a minimum in a weighted least-squares sense. Numerous examples of the application of the PEST algorithm for the calibration of hydrologic models can be found in the literature and PEST proves to be a time-saving tool compared to other model calibration techniques (Al-Abed and Whiteley, 2002;Baginska et al., 2003;Zyvoloski et al., 2003;Doherty and Johnston, 2003;Wang and Melesse, 2005;Liu et al., 2005;De Smedt, 2006, 2007;Goegebeur and Pauwels, 2007;Nossent and Bauwens, 2007). A few years ago, the United States Hydrology Laboratory (HL) (then the Hy-drologic Research Laboratory) of NWS began a major research effort called Distributed Model Intercomparison Project (DMIP) to address the question: how can the NWS best utilize the NEXRAD data to improve its river forecasts? ...

This paper describes the application of a spatially distributed hydrological model WetSpa (Water and Energy Transfer between Soil, Plants and Atmosphere) using radar-based rainfall data provide by the United States Hydrology Laboratory of NOAA's National Weather Service for a distributed model intercomparison project. The model is applied to the river basin above Tahlequah hydrometry station with 30-m spatial resolution and one hour time–step for a total simulation period of 6 years. Rainfall inputs are derived from radar. The distributed model parameters are based on an extensive database of watershed characteristics available for the region, including digital maps of DEM, soil type, and land use. The model is calibrated and validated on part of the river flow records. The simulated hydrograph shows a good correspondence with observation (Nash efficiency coeffiecient> 80%, indicating that the model is able to simulate the relevant hydrologic processes in the basin accurately.

... Use of these parameters reduces model-to-measurement misfit considerably; at best they supply missing system features that explain that misfit, while at worst they function as effective surrogates for those that do. A not dissimilar approach is followed by Young [2002], Thiemann et al. [2001], and Goegebeur and Pauwels [2007], who use recursive updating of hydrologic model parameters to accommodate the fact that the roles of these parameters change over time in order to compensate for inadequacies in a model's ability to respond to a succession of rainfall events. Lin and Beck [2007] demonstrate the use of an innovative recursive prediction error algorithm in inferring time variability of parameter estimates. ...

“Structural noise” is a term often used to describe model-to-measurement misfit that cannot be ascribed to measurement noise and therefore must be ascribed to the imperfect nature of a numerical model as a simulator of reality. As such, it is often the dominant contributor to model-to-measurement misfit. As the name “structural noise” implies, this type of misfit is often treated as an additive term to measurement noise when assessing model parameter and predictive uncertainty. This paper inquires into the nature of defect-induced model-to-measurement misfit and provides a conceptual basis for accommodating it. It is shown that inasmuch as defect-induced model-to-measurement misfit can be characterized as “noise,” this noise is likely to show a high degree of spatial and temporal correlation; furthermore, its covariance matrix may approach singularity. However, the deleterious impact of structural noise on the model calibration process may be mitigated in a variety of ways. These include adoption of a highly parameterized approach to model construction and calibration (including the strategic use of compensatory parameters where appropriate), processing of observations and their model-generated counterparts in ways that are able to filter out structural noise prior to fitting one to the other, and/or through implementation of a weighting strategy that gives prominence to observations that most resemble predictions required of a model.

... The methodology used to estimate the parameters has been explained in detail in [54]. Only a short description is given here. ...

It is widely recognized that synthetic aperture radar (SAR) data are a very valuable source of information for the modeling of the interactions between the land surface and the atmosphere. During the last couple of decades, most of the research on the use of SAR data in hydrologic applications has been focused on the retrieval of land and biogeophysical parameters (e.g., soil moisture contents). One relatively unexplored issue consists of the optimization of soil hydraulic model parameters, such as, for example, hydraulic conductivity values, through remote sensing. This is due to the fact that no direct relationships between the remote-sensing observations, more specifically radar backscatter values, and the parameter values can be derived. However, land surface models can provide these relationships. The objective of this paper is to retrieve a number of soil physical model parameters through a combination of remote sensing and land surface modeling. Spatially distributed and multitemporal SAR-based soil moisture maps are the basis of the study. The surface soil moisture values are used in a parameter estimation procedure based on the extended Kalman filter equations. In fact, the land surface model is, thus, used to determine the relationship between the soil physical parameters and the remote-sensing data. An analysis is then performed, relating the retrieved soil parameters to the soil texture data available over the study area. The results of the study show that there is a potential to retrieve soil physical model parameters through a combination of land surface modeling and remote sensing.

... There is on the other hand parameter estimation software that has been coupled with some specific models, for example the SUFI package for parameter estimation in the MACRO model (Roulier and Jarvis, 2003), parameter estimation algorithms that have been introduced into the WARM simulation environment (Acutis and Confalonieri, 2006) or parameter estimation for saturatedeunsaturated flow problems (Durner et al., 1999). There is also the PEST software that can be coupled to a wide range of complex models (Goegebeur and Pauwels, 2007). However, in these cases the range of goodness-of-fit criteria is very limited. ...

Parameter estimation for complex process models used in agronomy or the environmental sciences is important, because it is a major determinant of model predictive power, and difficult, because the models and associated data are complex. Statistics provides guidance for parameter estimation under various assumptions concerning model error, but it is hard to know which assumptions are most acceptable for these models. We therefore propose a collection of parameter estimation methods. All are based on weighted least squares, but different assumptions lead to different weights. The methods allow one to fit simultaneously several different response variables. One can assume that all errors are independent or on the contrary are correlated. One can assume that model error has expectation zero or not. A software package called OptimiSTICS has been developed, that allows one to implement all of the proposed methods with the STICS crop-soil model. The software can in addition treat the case where some parameters are genotype specific while others are common to all genotypes. The software can also automatically do several sequential stages of parameter estimation. An example is presented, which shows the information that can be obtained, and the conclusions drawn, from comparing the different estimation methods.

... The model independent Levenberg–Marquardt (LM) method based parameter estimation software PEST (Doherty, 2004Doherty, , 2007a,b), which quantifies model-to-measurement misfit in the weighted least squares sense, is now widely used to support environmental model calibration. In addition to its traditional groundwater model calibration application setting (Zyvoloskia et al., 2003; Tonkin and Doherty, 2005; Moore and Doherty, 2006; Gallagher and Doherty, 2007a), it is now employed to calibrate ecological models (Rose et al., 2007; Gaucherel et al., 2008), land surface models (Santanello Jr. et al., 2007) and models in other application areas including nonpoint source pollution (Baginska et al., 2003; Haydon and Deletic, 2007), surface hydrology (Doherty and Johnston, 2003 ; Gutié Magness and McCuen, 2005; Kunstmann et al., 2006; Skahill and Doherty, 2006; Doherty and Skahill, 2006; Gallagher and Doherty, 2007b; Goegebeur and Pauwels, 2007; Iskra and Droste, 2007; Kim et al., 2007; Maneta et al., 2007), and surface water quality (Rode et al., 2007). The primary focus of this article is to show how it is possible to efficiently overcome a couple of drawbacks associated with LMbased Model Independent Parameter Estimation as implemented in PEST. ...

This article describes some of the capabilities encapsulated within the Model Independent Calibration and Uncertainty Analysis Toolbox (MICUT), which was written to support the popular PEST model independent interface. We have implemented a secant version of the Levenberg–Marquardt (LM) method that requires far fewer model calls for local search than the PEST LM methodology. Efficiency studies on three distinct environmental model structures (HSPF, FASST, and GSSHA) show that we can find comparable local minima with 36–84% fewer model calls than a conventional model independent LM application. Using the secant LM method for local search, MICUT also supports global optimization through the use of a slightly modified version of a stochastic global search technique called Multi-Level Single Linkage [Rinnooy Kan, A.H.G., Timmer, G., 1987a. Stochastic global optimization methods, part I: clustering methods. Math. Program. 39, 27–56; Rinnooy Kan, A.H.G., Timmer, G., 1987b. Stochastic global optimization methods, part ii: multi level methods. Math. Program. 39, 57–78.]. Comparison studies with three environmental models suggest that the stochastic global optimization algorithm in MICUT is at least as, and sometimes more efficient and reliable than the global optimization algorithms available in PEST.

Aiming at the problems of low signal precision and uncertain sparsity in traditional structural damage identification methods, a structural damage identification method based on an extended Kalman filter and response reconstruction technology is proposed. Firstly, the extended Kalman filter is used for signal filtering analysis, and the standard deviation of the filtered signal is calculated to preliminarily analyze the damage location of the structure. Secondly, the Kalman filter is used for data fusion of the filtered signal, and the orthogonal matching pursuit algorithm of compressed sensing reconstruction is introduced to set the signal sparsity range and reconstruct the response. When the reconstructed signal meets the accuracy requirements of the Euclidean norm relative error, the standard deviations of the reconstructed signal are used to identify the damage location, and the damage degree of the structure is determined by the relationship between the signal standard deviation before and after the damage. The identification effect is verified by the damage location and degree of ASCE benchmark structure story and truss structure rod elements. The results show that the proposed method has certain reliability.

of the empirical wavelet transform (EWT), discrete wavelet transforms (DWT), extended Kalman filter (EKF), two
models of multilayer perceptrons (MLP), and group method of data handling (GMDH) neural networks. Two
synoptic stations of Tabriz (semi-arid climate) and Rasht (humid climate) covering data period (1987–2019)
were selected for forecasting. 70% of the data was used for model training and 30% for validation. Three
forecasting horizons (1, 3, and 6 months ahead SPEI) were investigated. Autocorrelation function and partial
autocorrelation function were used to determine the optimal inputs to the models. The outcomes of the present
study showed that in both stations, the combination of machine learning models with two types of wavelet
transforms (EWT and DWT) compared to the standalone models improved the performance of the forecasting
(correlation coefficient, R = 0.9980, root mean square error, RMSE = 0.0483 for Tabriz Station and R = 0.9988,
RMSE = 0.0521 for Rasht Station). A comparison of the EWT and DWT wavelets showed that the EWT had better
performance in all forecasting intervals. By raising the forecasting interval from one month to six months, EWT
performance was more evident than DWT performance. In 6-month forecasting horizon, the DWT had almost no
effect on model performance improvement. In both stations, the combination of the EWT and MLP-EKF model
had the best performance in forecasting SPEI drought index.

Weather Research and Forecasting (WRF) model was a tool for simulating daily air surface temperatures over northern Thailand. The model was forced by the Community Climate System Model Version 3 (CCSM3) during the baseline period (1990-1999) and the projected period (2016-2025) under the Intergovernmental Panel on Climate Change (IPCC) A1B scenario. Domain of study covers Indochina region with parent domain of 45 km and two nested domains of 15 km and 5 km, respectively. The daily minimum and maximum temperature simulations during baseline period were compared with station data provided by Thai Meteorological Department (TMD). Kalman filter method was applied to correct the systematic error of temperature simulations. Warming in minimum and maximum temperatures was found over northern Thailand which was less than global warming projection. The study indicated that the frequency of hot (cool) temperature extremes will increase (decrease) in the near future.

A software for automatic parameter estimation (PEST) was used to estimate 24 parameters in the root zone water quality model (RZWQM2) and analyze the sensitivity of each parameter by controlling the proportion of function values of simulation difference from various observation variables in the objective function, including soil moisture, soil nitrate, leaf area index and yield of crop. The results show that parameters of PHW, P1VW and PHM were the three most influential parameters to the overall simulation performance of the RZWQM2 model when the proportion of simulation difference for each observation variable was closest. In contrast to the trial and error method, RZWQM2 model after calibrated with PEST could accurately simulate the moisture and nitrogen transport in soil profile and crop growth in a rotation system of waxy mazy and winter wheat. This study could help estimate RZWQM2 parameters in different agricultural management practices and could also provide a reference for the application of PEST in other models for parameter optimization.

Accurate information about contaminant plume migration in the subsurface plays an important role in risk assessment and emergency response during site remediation. Rapid emergency response during severe soil contamination can help to reduce the extent of damage and the risk of groundwater contamination. The use of subsurface contaminant transport models, coupled with stochastic data assimilation schemes, can provide accurate prediction of contaminant transport to enhance the reliability of risk assessment in the area of environmental remediation. In this study, a two-dimensional deterministic model is used to simulate the advective and diffusive transport of benzene in the subsurface. A robust adaptive Kalman filter (AKF) is constructed as a stochastic data assimilation scheme to improve the prediction of the benzene contaminant plume. The AKF has been proposed to overcome the limitations of the conventional Kalman filter (KF) by reducing the uncertainties associated with the process and observation noise statistics. The impact of the adaptive filter on the KF performance is examined by comparing model predictions with a simulated true field, which is created by introducing random noise into an observation model. The results show that the KF data assimilation scheme can give a more accurate prediction of the benzene plume than the conventional numerical approach although its prediction accuracy is minimal in comparison to the AKF scheme. The KF scheme reduces the root-mean-square error (RMSE) of the plume estimate from 5.0 to 1.1-mg/L at the end of the 10-day simulation. Furthermore, by constructing the AKF data assimilation scheme, the prediction error of KF reduces from 1.1 to 0.9-mg/L, indicating 18% improvement in prediction accuracy. Also, the results of the sensitivity test suggest that filter stability and accuracy greatly depends on the window size, which must be specified to start the adaptive process.

The hydraulic model EPANET was applied and calibrated for the water distribution system (WDS) of La Sirena, Colombia. The Parameter ESTimator (PEST) was used for parameter optimization and sensitivity analysis. Observation data included levels at water storage tanks and pressures at monitoring nodes. Adjustable parameters were grouped into different classes according to two different scenarios identified as constrained and unconstrained. These scenarios were established to evaluate the effect of parameter space size and compensating errors over the calibration process. Results from the unconstrained scenario, where 723 adjustable parameters were declared, showed that considerable compensating errors are introduced into the optimization process if all parameters were open to adjustment. The constrained scenario on the other hand, represented a more properly discretized scheme as parameters were grouped into classes of similar characteristics and insensitive parameters were fixed. This had a profound impact on the parameter space as adjustable parameters were reduced to 24. The constrained solution, even when it is valid only for the system's normal operating conditions, clearly demonstrates that Parallel PEST (PPEST) has the potential to be used in the calibration of WDS models. Nevertheless, further investigation is needed to determine PPEST's performance in complex WDS models.

Prediction of a conservative solute transport in the subsurface is investigated by applying a Kalman filter (KF) that uses time-correlated-error and a KF that uses Gaussian error. The observation data generated from an analytical solution of a two-dimensional advection-dispersion equation with additive time-correlated random errors were used as the measurement equation for the KF with time-correlated measurement errors and the KF with white Gaussian errors. A measurement-differencing algorithm was adopted in deriving a discrete time varying KF with time-correlated measurement errors for predicting contaminant transport in the subsurface in the case of observations with time-correlated errors. Simulation results indicated an improved root mean square error (RMSE) profile of KF with time-correlated errors over KF with white Gaussian error. The KF with time-correlated-error reduced the error in the prediction by 11.4% when compared to the KF with white Gaussian error. The stability analysis of the two filters indicated that both filters were stable and convergent for the entire simulation duration. DOI: 10.1061/(ASCE)EE.1943-7870.0000524. (C) 2012 American Society of Civil Engineers.

Distributed hydrological models have become the main tool to study the hydrology natural law and solve the hydrology practice question. However, the definition of model parameter values limits their application. Manual calibration is time consuming and often tedious, and the automatic calibration method could be an innovative way of improving the traditional model fitting procedure. PEST is designed for easy linkage with other models and has been applied to many distributed hydrological model. Therefore, the PEST model is selected in this paper to link with the WATLAC model and calibrate the parameters, and compare the calibration results with manual results. The results show that the difference of two group parameter values is obvious. The PEST model can easily drive the WATLAC model and gain the optimal parameter values efficiently. The WATLAC model produces an overall good fit, the Ens values, except in 2001, are more than 0.83 and with an average of 0.93. But the relative runoff depth errors are larger slightly than manual results. The simulated stream flow hydrographs with PEST demonstrated a closer agreement with the observed hydrographs, while, the model simulation using manual calibration method behaved not very well and there was a tendency for the model to enlarge the peak flows.

The application of Soil-Vegetation-Atmosphere-Transfer (SVAT) scheme into the estimation of soil moisture profile in semi-arid regions is largely constrained by a scarcity of spatially distributed soil and hydraulic property information. Especially, on a large scale in very dry and sandy soils or other extreme conditions, it is difficult to accurately map soil and hydraulic properties with soil maps-based Pedo-Transfer Functions (PTFs), because PTFs are usually semi-empirically defined for specific sites. One strategy to overcome this limitation is to employ satellite data for a purpose of calibration. This paper provides an operational framework of inverting the SVAT soil hydraulic variables from the deterministic ensemble Kalman filter (DEnKF) analysis of Soil Moisture and Ocean Salinity (SMOS) surface soil moisture product. This inverse calibration was first verified with the Analyses Multidisciplinaires de la Mousson Africaine (AMMA) super site data representative of a single grid cell (0.25°) of satellite data. At this local scale, the results demonstrated that the mis-estimation problems of soil surface variable C1 and equilibrium soil moisture θgeq were successfully solved after calibration, demonstrating a better agreement with the field measurement of soil moisture profile than the SMOS product and un-calibrated SVAT scheme using soil maps-based PTFs. On the meso scale, the calibrated SVAT scheme using inverted surface variables appropriately captured a non-linear relationship between surface and root zone soil moisture by showing a typical soil moisture profile in dry climates, where dry surface soil moisture is spatially consistent with rainfall events, but wet root zone soil moisture shows low correlations with surface soil moisture distributions and rainfall events. In contrast, the un-calibrated SVAT scheme using soil maps-based PTFs significantly overestimated surface soil moisture and rainfall effect. This approach suggests several operational merits in that there is no need to heavily rely on empirically defined PTFs or recalibrate land surface parameters for different land surface conditions, and this can be applied even when parameter measurements are unavailable or highly uncertain.

Modeling the behavior of contaminants in a subsurface flow is important in predicting the fate of the pollutants, in risk assessment, and as a preliminary step of the mitigation process. A two-dimensional transport model with advection and dispersion is used as the deterministic model of a conservative contaminant transport in the subsurface. With the system model alone, it is very difficult to predict the true dynamic state of the pollutant. Therefore, observation data are needed to guide the deterministic system model to assimilate the true state of the contaminant. Extended Kalman Filter (EKF), which is essentially a first order approximation to an infinite dimensional problem, is used in this study to predict the contaminant plume transport. A traditional root mean square error (RMSE) of pollutant concentrations is used to examine the effectiveness of the EKF in contaminant transport modeling. The result shows that EKF can reduce 74 to 91% of prediction errors compared to the numerical method while working with the full set of observation data and using the analytical solution as the true solution. It can reduce 24 to 90% of prediction errors while working with only 2.25% observation-site data and a simulated random true field.

A study was carried out at Ribera Salada Catchment (NE Spain), affected by the abandonment of agriculture since 1950s, to determine the components of water budget under different land uses. The predominant land use is forestry (oak and pine), from forest to subalpine and sub-Mediterranean vegetation. Agriculture produces potatoes, alfalfa and cereals with a low level of nitrogen fertilization and high mountain grasslands with low level technology and low trampling. Field monitoring consisted of precipitation and evapotranspiration (ET) measurements, surface water collection with runoff boxes, continuous soil water measurement with capacitance probes, throughfall pluviometers and stem flow rings. This study presents the results of applying a weekly water balance in six stations over two years (2004-2005). The balance was established in two steps. The water balance was measured at each station. We applied the TOPLATS model a fully process-based hydrologic model, simulating all processes related to the hydrologic cycle. In the application, a large number of meteorological inputs are needed, and a relatively large number of soil physical, topographic, and land cover parameters need to be determined. For this study, TOPLATS has been calibrated using soil moisture data from one year, while the model validation has been performed across multiple years. The proposed balance is an acceptable reproduction of the field water behaviour during this period. The methodology used is appropriate for understanding the behaviour of the study basin. The results obtained indicated that the model accurately predicted the water budget of the watersheds measured in both years.

In support of the overall scientific objective of the Boreal Ecosystem-Atmosphere Study (BOREAS), which encompasses the improved understanding of the interactions between the boreal forest and the atmosphere, a process-based water and energy balance model is applied to observed forcing data, and the results are presented and discussed. Observed tower forcing and validation data are analyzed. A consistent diurnal pattern in the energy balance closure of the validation data is obtained. Simulations are performed for a number of BOREAS flux tower sites. The model successfully simulates the temporally averaged Bowen ratio and the evaporative part of precipitation over the different BOREAS flux tower sites during the 1994 and 1996 intensive field campaigns. At finer temporal scales a small phase shift in sensible heat flux and net radiation exists between the observed and model-derived quantities. The ground heat flux is found to be slightly larger than the observations during the course of the day. It is suggested that the sensitivity of the model to parameters such as the moss thickness, thermal conductivity, and heat capacity is responsible for these differences. The moss moisture content and the different components of the energy balance were very well matched for a continuous simulation during 1996. Overall, the accuracy performance of the model is equivalent to the accuracy of the input forcing data.

One of the governing scientific objectives of the Boreal Ecosystem–Atmosphere Study (BOREAS) is the development of methods for applying process models over large spatial scales using remote sensing and other integrative modeling techniques. This paper presents the first step in a modeling strategy that focuses on scaling a point model up to the BOREAS regional scale. The objective of this paper is to compare the effect of differences in spatial resolution of land cover data to land–atmosphere model results relative to the effect of differences in land cover sensors and classification schemes. The analysis suggests that the uncertainty in model results arises mainly from the uncertainty in the land cover classification and that the lack of spatial resolution has a lower effect. Overall, an uncertainty of approximately 15% in modeled energy and water balance fluxes and states has to be assigned because of the uncertainty in land cover classification.

The objective of this paper is to improve the performance of a hydrologic model through the assimilation of observed discharge. Since an observation of discharge at a certain time is always influenced by the catchment wetness conditions and meteorology in the past, the assimilation method will have to modify both the past and present soil wetness conditions. For this purpose, a bias-corrected retrospective ensemble Kalman filter has been used as the assimilation algorithm. The assimilation methodology takes into account bias in the forecast state variables for the calculation of the optimal estimates. A set of twin experiments has been developed, in which it is attempted to correct the model results obtained with erroneous initial conditions and strongly over-and underestimated precipitation data. The results suggest that the assimilation of observed discharge can correct for erroneous model initial conditions. When the precipitation used to force the model is underestimated, the assimilation of observed discharge can reduce the bias in the modeled turbulent fluxes by approximately 50%. This is due to a correction of the modeled soil moisture. In the case of an overestimation of the precipitation, an improvement in the modeled wetness conditions is also obtained after data assimilation, but this does not lead to a significant improvement in the modeled energy balance. The results in this paper indicate that there is potential to improve the estimation of hydrologic states and fluxes through the assimilation of observed discharge data.

From 32 CRR-catchment cases (combinations from four conceptual rainfall-runoff models (CRR) and eight catchments) calibrated with either two or three optimization methods, (1) the shuffle complex evolution method (SCE-UA), (2) the multiple start Simplex (MSX), and (3) the local Simplex, it seems that all three methods produced parameter sets of comparable, local-optimum quality. Even with comparable performance among the models, some parameter values derived by the three optimization methods for the same CRR-catchment cases are surprisingly different from each other. In addition, parameter sets of SCE-UA or MSX, which often produce marginally better results than the local Simplex at the calibration stage, could end up with worse results at the validation stage. Apparently, given the inherent limitations of calibration data, model inadequacies, and identifiability problems, it is impossible to achieve global convergence in the parameter search. However, other than those for dry catchments such as Ihimbu or Bird Creek, the parameter sets obtained are generally feasible. Both SCE-UA and the local Simplex are viable optimization tools, while MSX is inefficient computationally. SCE-UA can complete the parameter search in one run, while the local Simplex often requires multirun operations to get good results.

The 1999 Southern Great Plains Hydrology Experiment (SGP99) provides comprehensive datasets for evaluating microwave remote sensing of soil moisture algorithms that involve complex physical properties of soils and vegetation. The Land Surface Microwave Emission Model (LSMEM) is presented and used to retrieve soil moisture from brightness temperatures collected by the airborne Electronically Scanned Thinned Array Radiometer (ESTAR) L-band radiometer. Soil moisture maps for the SGP99 domain are retrieved using LSMEM, surface temperatures computed using the Variable Infiltration Capacity (VIC) land surface model, standard soil datasets, and vegetation parameters estimated through remote sensing. The retrieved soil moisture is validated using field-scale and area-averaged soil moisture collected as part of the SGP99 experiment, and had a rms range for the area-averaged soil moisture of 1.8%-2.8% volumetric soil moisture.

The successful application of a conceptual rainfall-runoff (CRR) model depends on how well it is calibrated. Despite the popularity of CRR models, reports in the literature indicate that it is typically difficult, if not impossible, to obtain unique optimal values for their parameters using automatic calibration methods. Unless the best set of parameters associated with a given calibration data set can be found, it is difficult to determine how sensitive the parameter estimates (and hence the model forecasts) are to factors such as input and output data error, model error, quantity and quality of data, objective function used, and so on. Results are presented that establish clearly the nature of the multiple optima problem for the research CRR model SIXPAR. These results suggest that the CRR model optimization problem is more difficult than had been previously thought and that currently used local search procedures have a very low probability of successfully finding the optimal parameter sets. Next, the performance of three existing global search procedures are evaluated on the model SIXPAR. Finally, a powerful new global optimization procedure is presented, entitled the shuffled complex evolution (SCE-UA) method, which was able to consistently locate the global optimum of the SIXPAR model, and appears to be capable of efficiently and effectively solving the CRR model optimization problem.

This paper describes the development of a process-based water and energy
balance model for use in high latitudes under both summertime and
wintertime conditions. The model is developed as a part of the Boreal
Ecosystem-Atmosphere Study (BOREAS). The model differs from its original
version in the representation of hydrological processes specific to
climatic and ecologic conditions in high latitudes: the impact of an
organic layer on the water and energy balance of the boreal forest; the
parameterization of frozen ground and snow accumulation and ablation;
and the effect of open water bodies on the calculation of the radiative
energy and water budget. The model can be run either in a fully
distributed or an aggregated statistical mode. The resulting macroscale
hydrological model can be used, off line, to study the energy and water
balance of the boreal forest and potentially can be used as a
land-atmosphere parameterization in atmospheric models.

1] Practical experience with the calibration of hydrologic models suggests that any single-objective function, no matter how carefully chosen, is often inadequate to properly measure all of the characteristics of the observed data deemed to be important. One strategy to circumvent this problem is to define several optimization criteria (objective functions) that measure different (complementary) aspects of the system behavior and to use multicriteria optimization to identify the set of nondominated, efficient, or Pareto optimal solutions. In this paper, we present an efficient and effective Markov Chain Monte Carlo sampler, entitled the Multiobjective Shuffled Complex Evolution Metropolis (MOSCEM) algorithm, which is capable of solving the multiobjective optimization problem for hydrologic models. MOSCEM is an improvement over the Shuffled Complex Evolution Metropolis (SCEM-UA) global optimization algorithm, using the concept of Pareto dominance (rather than direct single-objective function evaluation) to evolve the initial population of points toward a set of solutions stemming from a stable distribution (Pareto set). The efficacy of the MOSCEM-UA algorithm is compared with the original MOCOM-UA algorithm for three hydrologic modeling case studies of increasing complexity., Effective and efficient algorithm for multiobjective optimization of hydrologic models, Water Resour. Res., 39(8), 1214, doi:10.1029/2002WR001746, 2003.

Several contributions to the hydrological literature have brought into question the continued usefulness of the classical paradigm for hydrologic model calibration. With the growing popularity of sophisticated "physically based" watershed models (e.g., land-surface hydrology and hydrochemical models) the complexity of the calibration problem has been multiplied many fold. We disagree with the seemingly widespread conviction that the model calibration problem will simply disappear with the availability of more and better field measurements. This paper suggests that the emergence of a new and more powerful model calibration paradigm must include recognition of the inherent multiobjective nature of the problem and must explicitly recognize the role of model error. The results of our preliminary studies are presented. Through an illustrative case study we show that the multiobjective approach is not only practical and relatively simple to implement but can also provide useful information about the limitations of a model.

1] Markov Chain Monte Carlo (MCMC) methods have become increasingly popular for estimating the posterior probability distribution of parameters in hydrologic models. However, MCMC methods require the a priori definition of a proposal or sampling distribution, which determines the explorative capabilities and efficiency of the sampler and therefore the statistical properties of the Markov Chain and its rate of convergence. In this paper we present an MCMC sampler entitled the Shuffled Complex Evolution Metropolis algorithm (SCEM-UA), which is well suited to infer the posterior distribution of hydrologic model parameters. The SCEM-UA algorithm is a modified version of the original SCE-UA global optimization algorithm developed by Duan et al. [1992]. The SCEM-UA algorithm operates by merging the strengths of the Metropolis algorithm, controlled random search, competitive evolution, and complex shuffling in order to continuously update the proposal distribution and evolve the sampler to the posterior target distribution. Three case studies demonstrate that the adaptive capability of the SCEM-UA algorithm significantly reduces the number of model simulations needed to infer the posterior distribution of the parameters when compared with the traditional Metropolis-Hastings samplers.

A methodology for developing regional parameter estimation equations, designed for application to continental scale river basins, is described. The approach, which is applied to the two-layer Variable Infiltration Capacity (VIC-2L) land surface hydrologic model, uses a set of 34 unregulated calibration or “training” catchments (drainage areas 102–104 km2) distributed throughout the Arkansas–Red River basin of the south central U.S. For each of these catchments, parameters were determined by: a) prior estimation of two of the model parameters (saturated hydraulic conductivity and pore size distribution index) from the U.S. Soil Conservation Service State Soil Geographic Data Base (STATSGO) data base; and b) estimation of the remaining seven parameters via a search procedure that minimizes the sum of squares of differences between predicted and observed streamflow. The catchment parameters were then related to 11 ancillary distributed land surface characteristics extracted from STATSGO, and 17 variables derived from station meteorological data. The seven regression equations explained from 54 to 76% of the variance of the parameters. The most frequently occurring ancillary variables were the average permeability, saturated hydraulic conductivity, and SCS hydrologic Group B (typically soils with moderately high infiltration rates) fraction derived from STATSGO, and the average temperature and standard deviation of fall precipitation. The method was tested by comparing simulations using the regional (regression equation) parameters for six unregulated catchments not in the parameter estimation set. The model performance using the regional parameters was quite good for most of the calibration and validation catchments, which were humid and semi-humid. The model did not perform as well for the smaller number of arid to semi-arid catchments.

An important goal of spatially distributed hydrologic modeling is to provide estimates of streamflow (and river levels) at any point along the river system. To encourage collaborative research into appropriate levels of model complexity, the value of spatially distributed data, and methods suitable for model development and calibration, the US National Weather Service Hydrology Laboratory (NWSHL) is promoting the distributed modeling intercomparison project (DMIP). In particular, the project is interested in how spatially distributed estimates of precipitation provided by the next generation radar (NEXRAD) network, high resolution digital elevation models (DEM), soil, land-use and vegetation data can be integrated into an improved system for distributed hydrologic modeling that provides more accurate and informative flood forecasts.

Adverse socio-economic impacts of recent floods both in Europe and other continents emphasize the need for accurate flood forecasting capabilities towards improved flood risk management services. Flood forecasting models are often data-intensive. These model are inherited with (i) conceptual parameters that often cannot be assessed by field measurements, as in conceptual models; and/or (ii) empirical parameters that their direct measurements are either difficult e.g. roughness coefficient or costly, e.g. survey data. There is also a category of practical problems, where modelling is required but gauged data are not available. Models, other than purely theoretical ones e.g. Large Eddy Simulation models, need calibration and the problem is even more pronounced in the case of ungauged rivers. Optimal values of these parameters in a mathematical sense can be identified by a number of techniques as discussed and applied in this paper. New generations of satellites are now able to provide observation data that can be useful to implement these techniques. This paper presents the results of synthesised flood data emulating data obtained from remote sensing. A 1-dimensional, steady state flow in a channel of simple geometry is studied. The paper uses optimization methods and the extended Kalman filter to ascertain/improve the values of the parameters.

Based on 1-km land surface model geophysical predictions within the United States Southern Great Plains (Red-Arkansas River basin), an observing system simulation experiment (OSSE) is carried out to assess the impact of land surface heterogeneity, instrument error, and parameter uncertainty on soil moisture products derived from the National Aeronautics and Space Administration Hydrosphere State (Hydros) mission. Simulated retrieved soil moisture products are created using three distinct retrieval algorithms based on the characteristics of passive microwave measurements expected from Hydros. The accuracy of retrieval products is evaluated through comparisons with benchmark soil moisture fields obtained from direct aggregation of the original simulated soil moisture fields. The analysis provides a quantitative description of how land surface heterogeneity, instrument error, and inversion parameter uncertainty impacts propagate through the measurement and retrieval process to degrade the accuracy of Hydros soil moisture products. Results demonstrate that the discrete set of error sources captured by the OSSE induce root mean squared errors of between 2.0% and 4.5% volumetric in soil moisture retrievals within the basin. Algorithm robustness is also evaluated for the case of artificially enhanced vegetation water content (W) values within the basin. For large W(>3 kg·m<sup>-2</sup>), a distinct positive bias, attributable to the impact of sub- footprint-scale landcover heterogeneity, is identified in soil moisture retrievals. Prospects for the removal of this bias via a correction strategy for inland water and/or the implementation of an alternative aggregation strategy for surface vegetation and roughness parameters are discussed.

Owing to the nonlinearity of the rainfall-infiltration-runoff relationship, soil water content in the river basin represents a key environmental variable to be monitored for flood management purposes. In this study an attempt was made to sequentially assimilate into a simple lumped conceptual rainfall-runoff model an estimate of the soil saturation level. The estimate was obtained from: (a) field measurements of water table depth; and (b) backscattering of the radar signal emitted by active microwave sensors on board ERS-1. The assimilation scheme is based on an extended Kalman filter as both simulated and observed soil saturation states are prone to errors. The magnitude of the internal state updating thus depends on the ratio of errors on the observations and the model. The analysis of a series of ERS-1 SAR images showed that hydrologically relevant information could be retrieved from radar imagery by averaging the backscattering coefficient over clusters of pixels for which the sensitivity towards changing moisture conditions is significant. The assimilation procedure is performed on the experimental Alzette River basin (1175 km2). Improvements of model performance through data assimilation demonstrate the usefulness of field measurements and remote sensing observations in flood forecasting applications.

Physically based, two-dimensional, distributed parameter Hortonian hydrologic models are sensitive to a number of spatially varied parameters and inputs and are particularly sensitive to the initial soil moisture field. However, soil moisture data are generally unavailable for most catchments. Given an erroneous initial soil moisture field, single-event calibrations are easily achieved using different combinations of model parameters, including physically unrealistic values. Verification of single-event calibrations is very difficult for models of this type because of parameter estimation errors that arise from initial soil moisture field uncertainty. The purpose of this study is to determine if the likelihood of obtaining a verifiable calibration increases when a continuous flow record, consisting of multiple runoff producing events is used for model calibration. The physically based, two-dimensional, distributed, Hortonian hydrologic model CASC2D [Julien et al., 1995] is converted to a continuous formulation that simulates the temporal evolution of soil moisture between rainfall events. Calibration is performed using 6 weeks of record from the 21.3 km2 Goodwin Creek Experimental Watershed, located in northern Mississippi. Model parameters are assigned based on soil textures, land use/land cover maps, and a combination of both. The sensitivity of the new model formulation to parameter variation is evaluated. Calibration is performed using the shuffled complex evolution method [Duan et al., 1991]. Three different tests are conducted to evaluate model performance based on continuous calibration. Results show that calibration on a continuous basis significantly improves model performance for periods, or subcatchments, not used in calibration and the likelihood of obtaining realistic simulations of spatially varied catchment dynamics. The automated calibration reveals that the parameter assignment methodology used in this study results in overparameterization. Additional research is needed in spatially distributed hydrologic model parameter assignment methodologies for hydrologic forecasting.

The small-scale (10 to 100 m) and local-scale (100m to 10 km) effects of topography (elevation, slope, and aspect) and snow redistribution by wind on the evolution of the snowmelt are investigated. The chosen study area is the 142 km2 Upper Kuparuk River basin located on the North Slope of Alaska. Two land surface models (LSMs) designed for regional and global climate studies apply different techniques to resolve these additional processes and features and their effects on snowmelt. One model uses a distributed approach to simulate explicitly the effects of topography on snowmelt at a 131-m resolution across the entire Upper Kuparuk watershed. By contrast, the other LSM employs a simple parameterization to implicitly resolve the effects of wind-blown snow on the hydrology of the Upper Kuparuk basin. In both cases, the incorporation of these local- and small-scale features within the LSMs leads to significant heterogeneity in the 1997 end-of-winter spatial distribution of snow cover in the Upper Kuparuk watershed. It is shown that the consideration of subgrid-scale snow-cover heterogeneity over complex Arctic terrain provides a better representation of the end-of-winter snow water equivalent, an improved simulation of the timing and amount of water discharge of the Upper Kuparuk River, and an alteration of other surface energy and water budget components.

This paper presents the model development component of a body of research which addresses aggregation and scaling in multiscale hydrological modeling. Water and energy balance models are developed at the local and catchment scales and at the macroscale by aggregating a simple soil-vegetation-atmosphere transfer scheme (SVATS) across scales in a topographic framework. A spatially distributed approach is followed to aggregate the SVATS to the catchment scale. A statistical-dynamical approach is utilized to simplify the large-scale modeling problem and to aggregate the SVATS to the macroscale. The resulting macroscale hydrological model is proposed for use as a land surface parameterization in atmospheric models. It differs greatly from the current generation of land surface parameterizations owing to its simplified representation of vertical process physics and its statistical representation of horizontally heterogeneous runoff and energy balance processes. The spatially distributed model formulation is explored to understand the role of spatial variability in determining areal-average fluxes and the dynamics of hydrological processes. The simpler macroscale formulation is analyzed to determine how it represents these important dynamics, with implications for the parameterization of runoff and energy balance processes in atmospheric models.

The paper describes a simple physically based conceptual model of runoff production based on catchment topography and the spatial variablity of rainfall and soil properties. Both infiltration excess (Horton type) and saturation excess (Dunne type) runoff production mechanisms are considered. The effect of topography is modeled using the In (α/tan β)-topographic index method of Beven and Kirkby (1979). The effects of the spatial variability of soil properties and rainfall on areal average infiltration rates are handled using a quasi-analytical approach. The interaction between the two mechanisms of runoff production and the effect of a finite water table on the infiltration excess mechanism are explicitly considered. The model equations are cast in a dimensionless form to clarify the interrelationships involved in hydrological responses and to identify measures of similarity between different heterogeneous catchments. The dimensionless formulation has led to the identification of five similarity parameters and three dimensionless variables representing initial conditions and storm characteristics. Finally, a number of experiments were performed to study the sensitivity of the runoff production response to some of these similarity parameters.

Using high-resolution (1 km) hydrologic modeling of the 575 000-km2 Red-Arkansas River basin, the impact of spatially aggregating soil moisture imagery up to the footprint scale (32-64 km) of spaceborne microwave radiometers on regional-scale prediction of surface energy fluxes is examined. While errors in surface energy fluxes associated with the aggregation of soil moisture are potentially large (>50 W m-2), relatively simple representations of subfootprint-scale variability are capable of substantially reducing the impact of soil moisture aggregation on land surface model energy flux predictions. This suggests that even crude representations of subgrid soil moisture statistics obtained from statistical downscaling procedures can aid regional-scale surface energy flux prediction. One possible soil moisture downscaling procedure, based on an assumption of spatial scaling (i.e., a power-law relationship between statistical moments and scale), is demonstrated to improve TOPmodel-based Land-Atmosphere Transfer Scheme (TOPLATS) prediction of grid-scale surface energy fluxes derived from coarse-resolution soil moisture imagery.

Automatic methods for model calibration seek to take advantage of the speed and power of digital computers, while being objective and relatively easy to implement. However, they do not provide parameter estimates and hydrograph simulations that are considered acceptable by the hydrologists responsible for operational forecasting and have therefore not entered into widespread use. In contrast, the manual approach which has been developed and refined over the years to result in excellent model calibrations is complicated and highly labor-intensive, and the expertise acquired by one individual with a specific model is not easily transferred to another person (or model). In this paper, we propose a hybrid approach that combines the strengths of each. A multicriteria formulation is used to ``model'' the evaluation techniques and strategies used in manual calibration, and the resulting optimization problem is solved by means of a computerized algorithm. The new approach provides a stronger test of model performance than methods that use a single overall statistic to aggregate model errors over a large range of hydrologic behaviors. The power of the new approach is illustrated by means of a case study using the Sacramento Soil Moisture Accounting model.

In support of the eventual goal to integrate remotely sensed observations with coupled )and-atmosphere mode)s, a soil-vegetation-atmosphere transfer scheme is presented which can represent spatial)y variable water and energy balance processes on timesca)es of minutes to months. This scheme differs from previous schemes developed to address similar objectives in that it: (1) represents horizontal heterogeneity and transport in a TOPMODEL framework, and (2) maintains computational efficiency while representing the processes most important for our applications. The mode) is based on the original TOPMODEL-based )and surface-atmosphere scheme (Famiglictti and Wood, 1994a) with modifications to correct for deficiencies in the representation of ground heat flux, soil column geometry, soil evaporation, transpiration, and the effect of atmospheric stability on energy fluxes. These deficiencies were found to cause errors in the mode) predictions in quantities such as the sensible heat flux, to which the development of the atmospheric boundary layer is particularly sensitive. Application of the mode) to the entire First International Satellite Land Surface Climatology Project Field Experiment 1987 experimental period, focusing on Intensive Field Campaigns 3 and 4, shows that it successfully represents the essential processes of interest.

A recently proposed method for calibrating lumped rainfall-runoff models, called FDTFERUHDIT, is analysed and evaluated on synthetic data. Based on the Unit Hydrograph concept this method performs a simultaneous identification of the excess rainfall series and the transfer function or unit hydrograph through an alternating iterative procedure without presuming any runoff production model or applying any arbitrary baseflow removal. A general evaluation framework was built to allow for generation of realistic data both error-free and contaminated with controlled errors. The problems of the method's convergence and sensitivity to errors in the data and the model structure assumed are tackled. A rather exhaustive series of tests involve also evaluations of the effects of a priori choices of optimisation algorithms and their parameters, as well as assessments of sampling effects. Combinations of these factors are also tested. Finally, useful guidelines for practical use of the new identification approach are derived.

A derivation is presented for the effective atmospheric emissivity to predict downcoming long-wave radiation at ground level under a clear sky and for a nearly standard atmosphere. The results are in good agreement with those obtainable with empirical formulae based on water vapor pressure and temperature. However, the proposed formulation has the advantage that its simple functional form is based on physical grounds without the need for empirical parameters from radiation measurements. Also, in contrast to the empirical equations, it may be adjusted in a simple way to reflect changes in climatic and atmospheric conditions.

Relationships of soil water tension and hydraulic conductivity with soil water content are needed to quantify plant available water and to model the movement of water and solutes in and through soils. To provide the best estimates possible from previous analyses, a comprehensive search of the literature and data sources for hydraulic conductivity and related soil-water data was made in 1978. From this search, data for 1323 soils with about 5350 horizons from 32 states were assembled. -from Authors

Automatic optimization algorithms are used routinely to calibrate conceptual rainfall-runoff (CRR) models. The goal of calibration is to estimate a feasible and unique (global) set of parameter estimates that best fit the observed runoff data. Most if not all optimization algorithms have difficulty in locating the global optimum because of response surfaces that contain multiple local optima with regions of attraction of differing size, discontinuities, and long ridges and valleys. Extensive research has been undertaken to develop efficient and robust global optimization algorithms over the last 10 years. This study compares the performance of two probabilistic global optimization methods: the shuffled complex evolution algorithm SCE-UA, and the three-phase simulated annealing algorithm SA-SX. Both algorithms are used to calibrate two parameter sets of a modified version of Boughton's [1984] SFB model using data from two Australian catchments that have low and high runoff yields. For the reduced, well-identified parameter set the algorithms have a similar efficiency for the low-yielding catchment, but SCE-UA is almost twice as robust. Although the robustness of the algorithms is similar for the high-yielding catchment, SCE-UA is six times more efficient than SA-SX. When fitting the full parameter set the performance of SA-SX deteriorated markedly for both catchments. These results indicated that SCE-UA's use of multiple complexes and shuffling provided a more effective search of the parameter space than SA-SX's single simplex with stochastic step acceptance criterion, especially when the level of parameterization is increased. Examination of the response surface for the low-yielding catchment revealed some reasons why SCE-UA outperformed SA-SX and why probabilistic optimization algorithms can experience difficulty in locating the global optimum.

Snowmelt hydrology is a very important component for applying SWAT (Soil and Water Assessment Tool) in watersheds where the stream flows in spring are predominantly generated from melting snow. However, there is a lack of information about the performance of this component because most published studies were conducted in rainfall-runoff dominant watersheds. The objective of this study was to evaluate the performance of the SWAT model's snowmelt hydrology by simulating stream flows for the Wild Rice River watershed, located in northwestern Minnesota. Along with the three snowmelt-related parameters determined to be sensitive for the simulation (snowmelt temperature, maximum snowmelt factor, and snowpack temperature lag factor), eight additional parameters (surface runoff lag coefficient, Muskingum translation coefficients for normal and low flows, SCS curve number, threshold depth of water in the shallow aquifer required for return flow to occur, groundwater "revap" coefficient, threshold depth of water in the shallow aquifer for "revap" or percolation to the deep aquifer to occur, and soil evaporation compensation factor) were adjusted using the PEST (Parameter ESTimation) software. Subsequently, the PEST-determined values for these parameters were manually adjusted to further refine the model. In addition to two commonly used statistics (Nash-Sutcliffe coefficient, and coefficient of determination), a measure designated "performance virtue" was developed and used to evaluate the model. This evaluation indicated that for the study watershed, the SWAT model had a good performance on simulating the monthly, seasonal, and annual mean discharges and a satisfactory performance on predicting the daily discharges. When analyzed alone, the daily stream flows in spring, which were predominantly generated from melting snow, could be predicted with an acceptable accuracy, and the corresponding monthly and seasonal mean discharges could be simulated very well. Further, the model had an overall better performance for evaluation years with a larger snowpack than for those with a smaller snowpack, and tended to perform relatively better for one of the stations tested than for the other.

Increasing demand for timber products results in the expansion of commercial afforestation in South Africa. The conversion of indigenous seasonally dormant grassland to evergreen forests results in increased transpiration and ultimately a reduction in catchment runoff, creating a negative impact on the country's scarce water supplies. In order to assist managers in the decision-making processes it is important to be able to accurately assess and predict hydrological processes, and the impact that land use change will have on water resources. The Soil and Water Assessment Tool (SWAT) provides a means of performing these assessments. One of the key strengths of the SWAT model lies in its ability to model the relative impacts of changes in management practices, climate and vegetation on water quantity and quality.
The aim of this study was to determine if the SWAT model could reasonably simulate hydrological processes in daily time steps from two small South African catchments. To verify the SWAT model a grassland (C VIgrass) and Pinus patula afforested catchment (C IIpine) were selected from the Cathedral Peak hydrological research station in the KwaZulu Natal Drakensberg mountains. These catchments were chosen because of the availability of detailed hydrological records and suitable land use.
Observed and simulated streamflow for C VIgrass and C IIpine were compared. When model fits of observed and simulated streamflow for C VIgrass were acceptable, this parameter set was then used in the configuration of C IIpine. Results show that the model performs well for C VIgrass with reasonable agreement between modelled and observed data (R2 = 0·68). Comparisons for C IIpine show a total oversimulation of streamflow for the period 1950 to 1965, with deviations between observed and modelled data increasing from 1959 to 1965, due to the model not accounting for the increase in ET brought about by the maturing pine plantation. Copyright

Calibrating a comprehensive, multi-parameter conceptual hydrological model, such as the Hydrological Simulation Program Fortran model, is a major challenge. This paper describes calibration procedures for water-quantity parameters of the HSPF version 10·11 using the automatic-calibration parameter estimator model coupled with a geographical information system (GIS) approach for spatially averaged properties. The study area was the Grand River watershed, located in southern Ontario, Canada, between 79° 30′ and 80° 57′W longitude and 42° 51′ and 44° 31′N latitude. The drainage area is 6965 km2. Calibration efforts were directed to those model parameters that produced large changes in model response during sensitivity tests run prior to undertaking calibration. A GIS was used extensively in this study. It was first used in the watershed segmentation process. During calibration, the GIS data were used to establish realistic starting values for the surface and subsurface zone parameters LZSN, UZSN, COVER, and INFILT and physically reasonable ratios of these parameters among watersheds were preserved during calibration with the ratios based on the known properties of the subwatersheds determined using GIS. This calibration procedure produced very satisfactory results; the percentage difference between the simulated and the measured yearly discharge ranged between 4 to 16%, which is classified as good to very good calibration. The average simulated daily discharge for the watershed outlet at Brantford for the years 1981–85 was 67 m3 s−1 and the average measured discharge at Brantford was 70 m3 s−1. The coupling of a GIS with automatice calibration produced a realistic and accurate calibration for the HSPF model with much less effort and subjectivity than would be required for unassisted calibration. Copyright © 2002 John Wiley & Sons, Ltd.

The use of a fitted parameter watershed model to address water quantity and quality management issues requires that it be calibrated under a wide range of hydrologic conditions. However, rarely does model calibration result in a unique parameter set. Parameter nonuniqueness can lead to predictive nonuniqueness. The extent of model predictive uncertainty should be investigated if management decisions are to be based on model projections. Using models built for four neighboring watersheds in the Neuse River Basin of North Carolina, the application of the automated parameter optimization software PEST in conjunction with the Hydrologic Simulation Program Fortran (HSPF) is demonstrated. Parameter nonuniqueness is illustrated, and a method is presented for calculating many different sets of parameters, all of which acceptably calibrate a watershed model. A regularization methodology is discussed in which models for similar watersheds can be calibrated simultaneously. Using this method, parameter differences between watershed models can be minimized while maintaining fit between model outputs and field observations. In recognition of the fact that parameter nonuniqueness and predictive uncertainty are inherent to the modeling process, PEST's nonlinear predictive analysis functionality is then used to explore the extent of model predictive uncertainty.