Article

Improvement of the PEST parameter estimation algorithm through Extended Kalman Filtering

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Abstract

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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... El modelo TOPLATS ha sido utilizado en la estimación de la humedad en el suelo para diferentes usos del suelo. Este modelo fue calibrado con las ecuaciones del filtro Kalman extendido (EKF), que se derivan de la minimización del cuadrado de la diferencia entre los valores reales y los estimados (Goegebeur & Pauwels, 2007). Esta metodología interrelaciona correctamente los valores de lluvia, humedad en el suelo, escorrentía y infiltración, siendo los valores de humedad los mas ajustados a los valores reales. ...
... The TOPLATS model, when used to estimate soil moisture under different cover types, was calibrated with Extend Kalman filter (EKF) equations derived through a minimization of the square difference between the true and estimated model state (Goegebeur & Pauwels, 2007). This methodology interrelates correctly rainfall, soil moisture, runoff and infiltration. ...
... Chapter 3 consists in the calibration of the TOPLATS model using soil moisture simulated values, by means of Kalman equations (Goegebeur and Pauwels, 2007). ...
Article
RESUMEl principal objectiu daquesta investigació és estudiar la dinàmica hidrològica duna conca Mediterràniaafectada per canvis dús del sòl, mitjançant el monitoreig daquest i de laigua superficial. Aquestobjectiu sha treballat a partir mesuraments de components del balanç hídric pels diferents tipus decobertura i sòl, amb règims dhumitat i temperatura de transició.Aquest estudi sha realitzat a la conca de la Ribera Salada (Prepirineu meridional Català, al NEdEspanya), amb una extensió de 222.5 km2, i un interval altitudinal de 420 a 2385 m i predomini dependents entre 12 - 25 % i 25 - 50 %. El substrat consisteix en conglomerats calcaris massius, calcilutitesi llims. La precipitació es de 507 i 763 mm. Amb sòls poc profunds, calcaris i pedregosos, essentmajoritàriament Inceptisòls (Typic Calciusteps, Typic Haploustepts) i Entisòls (Typic Ustifluvents, TypicUdorthortents). A les zones més elevades de la conca, els sòls són més humits, degut a laugment de laprecipitació, on es produeixen processos de descarbonatació del sòl. Lús del sòl és majoritàriamentforestal, amb presència decosistemes de ribera, subalpins i vegetació submediterrània. Algunes àrees estroben amb cultius de patata, cereal i pastures. Una de les característiques més importants daquestaconca són els canvis dús del sòl que ha patit en els últims 50 anys degut a labandó dels masos i cultiustradicionals. Es seleccionaren vuit llocs de mostreig considerant les següents cobertes: Quercus ilex, boscde ribera, Pinus sylvestris, pastures, cultius (cereal-patata) i Pinus uncinata. A partir de lany 1997 fins el2005, shan anat monitorejant el contingut dhumitat del sòl, lescolament i els cabals. Des del 2004 shananat anotant dades de drenatge. Les variables meteorològiques es mesuren a lestació de Lladurs de laXAC (Xarxa Agrometeorològica de Catalunya).Els resultats obtenguts durant tres anys mostren una domini del règim dhumitat ústic (SSS, 2006), o xèricen aquells anys més secs. En la modelització de règims dhumitat i temperatura del sòl, sutilitzaren elsmodels de simulació NSM "Newhall simulation model" (Newhall, 1976) i JSM "Jarauta simulationmodel" (Jarauta 1989). NSM (Newhall,1976) tendeix a sobre estimar el règim dhumitat del sòl, peròJSM (Jarauta, 1989) simula correctament el règim dhumitat del sòl (SSS, 2006) de la conca, funcionantmillor en condicions intermitges dhumitat del sòl. Ambdós models simulen correctament el règim detemperatura dels sòls. Predomina un règim de temperatura mèsic-tèrmic, amb tendència a tèrmic els anyssecs. A petita escala la profunditat del sòl, pendent, pedregositat i una alta porositat del sòl són factoresque varien el règim dhumitat del sòl. La informació de sòl i clima, complementada mitjançant SIG, vapermetre lobtenció de mapes de règim dhumitat del sòl de la conca, a escala 1:50000, els qualspermeten establir mediante simució els règims dhumitat del sòl en diferents escenaris de canvismeteorològics.El model TOPLATS ha sigut utilitzat en lestimació de lhumitat del sòl en diferents usos del sòl. Aquestmodel fou calibrat amb les equacions del filtre Kalman estès (EKF), que deriven de la minimització delquadrat de la diferència entre els valors reals i els estimats (Goegebeur & Pauwels, 2007). Aquestametodologia interrelaciona correctament els valors de pluja, humitat del sòl, escolament i infiltració,essent els valors dhumitat els que més saproximen als reals. Els resultats mostren que aquest filtre ésuna eina útil per estimar el volum daigua del sòl emmagatzemada en conques a escala puntual,assegurant una aplicació correcta del model hidrològic.Per la modelització del comportament de lhumitat del sòl i diferents components del balanç hídricsutilitzà el modelo TOPLATS (Famiglietti & Wood, 1994). El model de simulació TOPLATS permitesimulà acceptablement el comportament de lhumitat del sòl. Els resultats de infiltració, escolament,intercepció, evapotranspiració de referència i temperatura del sòl són correctes. Les diferències existentsentre valors simulats i observats són: lhumitat del sòl no sobrepassa el 5%, la infiltració fluctua entre 4%i 15%, la diferència entre els valors reals i simulats devapotranspiració, depèn de lestació de lany,essent 1mm a lhivern i 2.7 mm a lestiu. La temperatura varia entre 0.01ºC i 3.5ºC. El model calibratprediu amb precisió el comportament de les diferents components del balanç hídric. Respecte als valorsmesurats daigua de drenatge correspon al 11-41 % de la pluja total.Respecte al balanç daigua en el sòl (ΔSW), els valors són negatius durant cert període de lany, arribant avalors crítics els mesos secs. La recuperació de humitat del sòl durant la resta de mesos succeeix demanera parcial. A la part mitja de la conca, alguns mesos els valors dhumitat del sòl sacosten acondicions de punt de marchites (ecosistema submediterrani). A la part alta de la conca el sòl conservahumitat (ecosistema subalpí). Els valors de cabal trobats corresponen a aportacions per escolament elcuals són molt baixos. La majoria de les sortides es deuen a evapotranspiració, intercepció, infiltració idrenatge (en ordre de importància).RESUMENEl principal objetivo de esta investigación es estudiar la dinámica hidrológica de una cuenca Mediterráneaafectada por los cambios de uso del suelo, mediante el monitoreo del suelo y el agua superficial. Dicho objetivose ha abordado a partir de la medición de componentes del balance hídrico para diferentes tipos de cobertura ysuelo, considerando regimenes de humedad y temperatura de transición.Este estudio se ha realizado en la cuenca de la Ribera Salada (Prepirineo meridional Catalán, NE España) de222.5 km2, con un intervalo altitudinal de 420 a 2385 m y predominio de pendientes entre 12 - 25 % y 25 - 50%. El sustrato consiste en conglomerados calcáreos masivos, calcilutitas y limos. La precipitación anual es de507 y 763 mm. Los suelos són poco profundos, calcáreos y pedregosos, siendo en su mayoría Inceptisols(Typic Calciusteps, Typic Haploustepts) y Entisols (Typic Ustifluvents, Typic Udorthortents). En las partesaltas de la cuenca los suelos son más húmedos, debido al aumento de la precipitación, allí ocurren procesos dedescarbonatación del suelo. Predomina el uso forestal, con ecosistemas de ribera, subalpinos y vegetaciónsubmediterránea. Algunas áreas se dedican al cultivo de patatas, cereal y pastos. Una de las características másimportantes de esta cuenca es los importantes cambios de uso del suelo sufridos en los últimos 50 años, debidoal abandono de las masías y cultivos tradicionales.Se seleccionaron ocho sitios de muestreo, considerando las siguientes coberturas: Quercus ilex, bosque deribera, Pinus sylvestris, pastos, cultivo (cereal-patata) y Pinus uncinata. A partir del año 1997 hasta 2005, sehan venido monitoreando el contenido de humedad del suelo, escorrentía y caudales. Desde 2004 se vienentomando datos drenaje. Las variables meteorológicas se miden la estación Lladurs perteneciente a la XAC(Xarxa Agrometeorológica de Cataluña).Los resultados obtenidos par un period de tres años muestran una predominancia del regimen de humedadústico (SSS, 2006), o xérico en los años más secos. Se utilizaron los modelos de simulación NSM "Newhallsimulation model" (Newhall, 1976) y JSM "Jarauta simulation model" (Jarauta 1989) en la modelización deregimenes de humedad y temperatura del suelo. NSM (Newhall,1976) tiende a sobre estimar el régimen dehumedad del suelo. Por contra, JSM (Jarauta, 1989) simula de forma correcta el régimen de humedad del suelo(SSS, 2006) presente en la cuenca, funcionando mejor bajo condiciones medias de humedad del suelo. Ambosmodelos simulan de forma correcta el régimen de temperatura de los suelos. Predomina un régimen detemperatura mésico-térmico, con tendencia a térmico para los años secos. A pequeña escala la profundidad delsuelo, pendiente, pedregosidad y alta porosidad del suelo son factores que hacen variar el régimen de humedaddel suelo. La información de suelo y clima, complementada mediante SIG, permitió obtener mapas de régimende humedad del suelo para la cuenca, a una escala 1:50000, los cuales permiten establecer mediante simulaciónlos regimenes de humedad en el suelo bajo diferentes escenarios de cambios meteorológicos.El modelo TOPLATS ha sido utilizado en la estimación de la humedad en el suelo para diferentes usos delsuelo. Este modelo fue calibrado con las ecuaciones del filtro Kalman extendido (EKF), que se derivan de laminimización del cuadrado de la diferencia entre los valores reales y los estimados (Goegebeur & Pauwels,2007). Esta metodología interrelaciona correctamente los valores de lluvia, humedad en el suelo, escorrentía yinfiltración, siendo los valores de humedad los mas ajustados a los valores reales. Los resultados muestran queeste filtro es una herramienta para estimar el volumen de agua en el suelo almacenada en las cuencas a escalapuntual, asegurando una aplicación correcta del modelo hidrológico.Para la modelización del comportamiento de la humedad del suelo y los diferentes componentes del balancehídrico se utilizó el modelo TOPLATS (Famiglietti & Wood, 1994). El modelo de simulación TOPLATSpermite simular aceptablemente el comportamiento de la humedad del suelo. Los resultados para infiltración,escorrentía, intercepción, evapotranspiración de referencia y temperatura del suelo son correctos. Lasdiferencias existentes entre valores simulados y observados son: la humedad del suelo no sobrepasa el 5%, lainfiltración fluctúa entre 4% y 15%, la diferencia entre los valores reales y simulados de evapotranspiración,depende de la estación del año, siendo 1mm en invierno y 2.7 mm en verano, la temperatura varia entre 0.01 ºCy 3.5ºC. El modelo calibrado predice con precisión el comportamiento de las diferentes componentes delbalance hídrico. Respecto a los valores medidos para agua de drenaje corresponde al 11-41 % de la lluvia total.Respecto al balance de agua en el suelo (ΔSW), los valores son negativos para un corto periodo del año,alcanzando valores críticos en meses secos. La recuperación de humedad del suelo para el resto de los mesesocurre de manera parcial. En la parte media de la cuenca, para algunos meses los valores de humedad del sueloson cercanos a condiciones de punto de marchites permanente (ecosistema submediterráneo). En la parte altade la cuenca el suelo conserva condiciones intermedias de humedad (ecosistema subalpino). Los valores decaudal encontrados corresponden a los aportes por escorrentía, los cuales son muy bajos. La mayor parte de lassalidas ocurren por evapotranspiración, intercepción, infiltración y drenaje (en orden de importancia).ABSTRACTThe main aim of this research is to study the hydrological dynamics of a Mediterranean mountain basinaffected by land use changes, by means of the monitoring of soil and surface water. This aim has beenreached by measuring and simulating hydric balance components of different soils and under differentvegetational types, considering water and temperature transition regimes.This research was done in Ribera Salada basin (Catalan Pre Pyrenees, NE Spain), with an area of 222.5km2, altitudes between 420 and 2385 m, with predominance slopes between 12 - 25 % and 25 - 50 %. Thesubstrate consists of massive calcareous conglomerates, calcilutites and limestones. Main annualprecipitation are 507 to 763 mm. Soils are shallow, calcareous and stony, being most of them Inceptisols(Typic Calciusteps, Typic Haploustepts) and Entisols (Typic Ustifluvents, Typic Udorthortents). In theupper and moister part of the basin soil decarbonatation takes place. Forest use is predominant, goingfrom brook forest environments to subalpine and submediterranean vegetation. Agricultural uses includemainly the growing of cereals, potatoes and pastures. One of the most important characteristics in thisbasin are the significant soil use changes in the last 50 years, due to the abandonment of farms andtraditional crops.Eight sites were studied, corresponding to soils under Quercus ilex, brook forest, Pinus sylvestris, pasture,crops (cereal-potatoes) and Pinus uncinata. From 1997 until 2005, soil moisture, run-off, water flow andinterception were monitored. From 2004 on, drainage data has been recorded. Meteorological variableswere measured by means of a complete Lladurs meteorological station, belonging to XAC (CatalanAgrometeorological Network).The obtained results to three years show the predominance of ustic moisture regime (SSS, 2006), or xericduring the driest years. The simulation models NSM "Newhall simulation model" (Newhall, 1976) andJSM "Jarauta simulation model" (Jarauta 1989) were used to represent soil moisture and temperatureregimes. NSM estimates a higher level of soil moisture regimes than observed. On the contrary, JSMsimulates correctly soil moisture regimes, working better under intermediate soil moisture conditions.Both models simulate correctly the soil temperature regimes, being mesic-thermic to thermic during thedriest years. At detailed scale (plot observation), soil depth, slope, stone amount and high soil porosity arefactors that affect the soil moisture regimes. Soil and climate information, implemented through a GIS,allowed us to obtain soil moisture regime maps of the basin at a 1:50000 scale, which are very useful tosimulate soil moisture regimes in different scenarios of meteorological changes.The TOPLATS model, when used to estimate soil moisture under different cover types, was calibratedwith Extend Kalman filter (EKF) equations derived through a minimization of the square differencebetween the true and estimated model state (Goegebeur & Pauwels, 2007). This methodology interrelatescorrectly rainfall, soil moisture, runoff and infiltration. Among them, the obtained soil moisture valuescorresponded the best to observed data. The results show that it is a useful tool to estimate soil watervolume stored in basins at a point scale, ensuring a correct application of this hydrological model.To model soil moisture behaviour and the different hydric balance components, the TOPLATS model(Famiglietti & Wood, 1994) was used. TOPLATS model simulates correctly the soil moisture behaviour.The differences between observed and simulated values are the following: soil moisture does not surpass5%; the infiltration fluctuates between 4% to 15%; in evapotraspiration depends on the season beingbetween 1 mm in winter to 2.7 mm in summer, soil temperature values difference fluctuates between0.01ºC and 3.5ºC.The calibrated model predicts precisely the behaviour of different hydric balancecomponents. The measured water drainage amount is 11-41 % of total rain.The observed and simulated soil water storage in the basin (ΔSW), has negative values during the driestmonths. Soil moisture recovery during the rest of the months is only partial. In the medium part of thebasin, occupied by submediterranean ecosystems, soil moisture values are closer to drought conditionsduring some months of the year. In the highest part of the basin (subalpine ecosystems) there areintermediate soil moisture conditions in dry periods. Most part of water outputs are due toevapotranspiration, interception, infiltration and drainage, in decreasing order of importance. Run-offvalues are very low.
... 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). ...
Article
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. ...
Article
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.
... 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). ...
Thesis
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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. ...
Article
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 . ...
Article
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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.
... 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). ...
Article
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.
... 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). ...
Article
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.
... 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. ...
Article
“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 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? ...
Article
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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.
... 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. ...
Technical Report
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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)
... The methodology used to estimate the parameters has been explained in detail in [54]. Only a short description is given here. ...
Article
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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. ...
Article
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, 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). ...
Article
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.
... 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. ...
Article
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.
... 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. ...
Article
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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 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). ...
Article
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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.
... 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. ...
Article
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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.
... This reduces the dimensionality Scatter plots of SSLE-estimated T and S using drawdown and incorrect boundary conditions and (B) scatter plots of x and y components of velocity for SSLE-estimated T and S using drawdown and incorrect boundary conditions. of the inverse problem without choosing a priori which parameters are more important or where pilot points should be located. Kalman filters are another class of candidate inversion algorithm; they are popular in control and systems engineering and have been applied hydrologic problems in different ways (Chen and Zhang 2006; Goegebeur and Pauwels 2007). They are more general than nonlinear least squares, since model and measurement noise can be incorporated directly into the inversion process, obviating the need for smoothing noisy data, but they do not have any means of incorporating the spatial correlation between the parameters into the estimation process, as SSLE does. ...
Article
While tomographic inversion has been successfully applied to laboratory- and field-scale tests, here we address the new issue of scale that arises when extending the method to a basin. Specifically, we apply the hydraulic tomography (HT) concept to jointly interpret four multiwell aquifer tests in a synthetic basin to illustrate the superiority of this approach to a more traditional Theis analysis of the same tests. Transmissivity and storativity are estimated for each element of a regional numerical model using the geostatistically based sequential successive linear estimator (SSLE) inverse solution method. We find that HT inversion is an effective strategy for incorporating data from potentially disparate aquifer tests into a basin-wide aquifer property estimate. The robustness of the SSLE algorithm is investigated by considering the effects of noisy observations, changing the variance of the true aquifer parameters, and supplying incorrect initial and boundary conditions to the inverse model. Ground water flow velocities and total confined storage are used as metrics to compare true and estimated parameter fields; they quantify the effectiveness of HT and SSLE compared to a Theis solution methodology. We discuss alternative software that can be used for implementing tomography inversion.
... 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). ...
Article
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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 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. ...
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... 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). ...
Technical Report
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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)
... 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. ...
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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.
... 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]. ...
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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.
... 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). ...
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... 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]. ...
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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.
... 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). ...
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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.
... 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). ...
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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.
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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.
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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.
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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.
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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.
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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.
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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.
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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.
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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.
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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.
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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
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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.
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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.
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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
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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.
Article
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.
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In this paper, we investigate the possibility to improve discharge predictions from a lumped hydrological model through assimilation of remotely sensed soil moisture values. Therefore, an algorithm to estimate surface soil moisture values through active microwave remote sensing is developed, bypassing the need to collect in situ ground parameters. The algorithm to estimate soil moisture by use of radar data combines a physically based and an empirical back-scatter model. This method estimates effective soil roughness parameters, and good estimates of surface soil moisture are provided for bare soils. These remotely sensed soil moisture values over bare soils are then assimilated into a hydrological model using the statistical correction method. The results suggest that it is possible to determine soil moisture values over bare soils from remote sensing observations without the need to collect ground truth data, and that there is potential to improve model-based discharge predictions through assimilation of these remotely sensed soil moisture values. Copyright © 2002 John Wiley & Sons, Ltd.
Article
The modelling package Annualized Agricultural Nonpoint Source Model (AnnAGNPS) was applied to the prediction of export of nitrogen and phosphorus from Currency Creek, a small experimental catchment within the Hawkesbury–Nepean drainage basin of the Sydney Region. The catchment is 255 ha in area and has experienced extensive soil erosion and losses of nutrients from intensive vegetable cultivation, irrigated dairy pasture and poultry farms. Simulations of nitrogen and phosphorus loads in the Currency Creek catchment were performed at various temporal scales and the degree of calibration was quantified by comparing the simulated data with the monitoring results. In addition, the model independent, nonlinear parameter estimation code PEST, was applied for sensitivity testing to determine and assess the relative importance of the key parameters of the model. Event flows were simulated satisfactorily with AnnAGNPS but only moderate accuracy was achieved for prediction of event-based nitrogen and phosphorus exports. The biggest deviations from the measured data were observed for daily simulations but trends in the generated nutrients matched observed data. Despite achieving good resemblance between measured and predicted phosphorus loads the model showed high level of sensitivity to assigned pH values for topsoil. Increase in pH by one unit resulted in up to 34% increase in model generated particulate phosphorus load.
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In this paper, we investigate to which degree information concerning the spatial patterns of remotely sensed soil moisture data are needed in order to improve discharge predictions from hydrological models. For this purpose, we use the TOPMODEL-based Land–Atmosphere Transfer Scheme (TOPLATS). The remotely sensed soil moisture values are determined using C-band backscatter data from the European Space Agency (ESA) European Remote Sensing (ERS) Satellites. A baseline run, without soil moisture assimilation, is established for both the distributed and lumped versions of the land–atmosphere scheme. The modeled discharge matches the observations slightly better for the distributed model than for the lumped model. The remotely sensed soil moisture data are assimilated into the distributed version of the model through the ‘nudging to individual observations’ method, and the ‘statistical correction assimilation’ method. The remotely sensed soil moisture data are also assimilated into the lumped version of the model through the ‘statistical correction assimilation’ method. The statistical correction assimilation method leads to similar, and improved, discharge predictions for both the distributed and lumped models. The nudging to individual observations method leads, for the distributed model, to only slightly better results than the statistical correction assimilation method. As a consequence, it is suggested that it is sufficient to assimilate the statistics (spatial mean and variance) of remotely sensed soil moisture data into lumped hydrological models when one wants to improve hydrological model-based discharge predictions.
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Three different automated methods for calibration of rainfall-runoff models are presented and compared. The methods represent various calibration strategies that utilise multiple objectives and allow user intervention on different levels and different stages in the calibration process. The methods have been applied for calibration of a test catchment and compared on validation data with respect to overall performance measures in terms of water balance error and general hydrograph shape, and simulation of high and low flow events. The results illustrate the problem of non-uniqueness in model calibration since none of the methods are superior with respect to all performance measures considered. In general, the different methods put emphasis on different response modes of the hydrograph. Calibration based on the use of generic search routines in combination with user-specified calibration priorities is seen to compare favourably with an expert system that is designed for the specific model being considered and requires user intervention during the entire calibration process.
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Accurate measurements of the turbulent exchanges of mass and energy at the land surface are necessary for a good understanding of the various components of the hydrological cycle. The two most commonly used methods to measure evapotranspiration rates are the Bowen ratio energy balance (BREB) and the Eddy correlation (EC) methods. These methods are applicable when a number of requirements, mostly with respect to terrain topography and homogeneous fetch extension, are fulfilled. On the other hand, meteorological variables can be used to calculate evapotranspiration rates. The two most frequently used methods for this purpose are the Penman-Monteith (PM) combination equation and the Priestley-Taylor (PT) approximation. The objective of this paper is to compare these different methods under non-ideal conditions, more specifically for a wet sloping grassland. The BREB-based and EC-based latent heat fluxes are intercompared, and a good agreement between the estimates from both methods is found. A comparison between the results of the PM and PT methods and the measured latent heat fluxes is then done. A strong annual cycle in the calculated values for the PT alfa factor (α), with a mean annual average value of 1.21 ± 0.79, has been observed. This annual cycle is related to the annual cycle of the humidity of the soil, which can be evaluated by either the soil moisture or the vapor deficit of the air. A strong annual cycle in the inverted surface resistances has also been observed. A relationship between the inverted surface resistances and α has been found, in which the highest values for α coincide with low surface resistances, and vice versa. The results indicate that the methods to measure and calculate latent heat fluxes are in a good agreement, and that imposing an annual cycle in the surface resistance and α leads to an improvement in the estimated evapotranspiration rates. The results suggest that it is possible to measure or model evapotranspiration rates in situations where the theoretical requirements (more specifically a non-sloping surface) are not met.
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In the last decade the increasing accessibility of computing means has made the application of spatially-distributed hydrological model an attractive perspective for both researchers and practitioner hydrologists. The availability of physically-based approaches does not generally overcome the need to calibrate at least a part of the model parameters and the complexity of distributed models, making the computations highly intensive, has often prevented an extensive analysis of calibration issues. The purpose of this study is an evaluation of a series of automatic calibration experiments (using the Shuffled Complex Evolution method) performed with a highly conceptualised, continuously simulating, distributed hydrologic model. The calibration and validation data consist of real precipitation and discharge observations referring to a mid-sized (1050 km2), highly vegetated watershed, located in the Apennine Mountains in Italy. Major flood events that occurred in the 1990–2000 decade are simulated with the parameters obtained by calibrating the rainfall-runoff model referring to different scenarios of historical data availability. A first set of experiments investigates the length of the calibration period required for an efficient parameterisation. The second analysis focuses on the influence on model calibration of the spatial resolution of the rainfall input and is carried out by varying the size and distribution of the raingauge network. A third aspect regards the analysis of the reliability of model parameters in simulating the discharge in ungauged river sections. The aim of the study is to provide the user with indications for appropriately selecting the historical data base to be used for model calibration. The results indicate how reducing the length of the calibration period under the extension of three months seems to deteriorate significantly the rainfall-runoff model performances. The model simulations are satisfactory also under the hypothesis of spatially uniform rainfall, provided that the mean areal rainfall intensity is estimated on the basis of a sufficiently extended number of raingauges, whereas there is a strong worsening with an excessive reduction of the raingauge network density. Finally, the distributed model has proven to be able to provide reliable simulations referring to ungauged internal river sections.
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The development of automated (computer-based) calibration methods has focused mainly on the selection of a single-objective measure of the distance between the model-simulated output and the data and the selection of an automatic optimization algorithm to search for the parameter values which minimize that distance. However, practical experience with model calibration suggests that no single-objective function is adequate to measure the ways in which the model fails to match the important characteristics of the observed data. Given that some of the latest hydrologic models simulate several of the watershed output fluxes (e.g. water, energy, chemical constituents, etc.), there is a need for effective and efficient multi-objective calibration procedures capable of exploiting all of the useful information about the physical system contained in the measurement data time series. The MOCOM-UA algorithm, an effective and efficient methodology for solving the multiple-objective global optimization problem, is presented in this paper. The method is an extension of the successful SCE-UA single-objective global optimization algorithm. The features and capabilities of MOCOM-UA are illustrated by means of a simple hydrologic model calibration study.
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An Ensemble Kalman filter (EnKF) is used to assimilate airborne measurements of 1.4 GHz surface brightness temperature (TB) acquired during the 1997 Southern Great Plains Hydrology Experiment (SGP97) into the TOPMODEL-based Land–Atmosphere Transfer Scheme (TOPLATS). In this way, the potential of using EnKF-assimilated remote measurements of TB to compensate land surface model predictions for errors arising from a climatological description of rainfall is assessed. The use of a real remotely sensed data source allows for a more complete examination of the challenges faced in implementing assimilation strategies than previous studies where observations were synthetically generated. Results demonstrate that the EnKF is an effective and computationally competitive strategy for the assimilation of remotely sensed TB measurements into land surface models. The EnKF is capable of extracting spatial and temporal trends in root-zone (40 cm) soil water content from TB measurements based solely on surface (5 cm) conditions. The accuracy of surface state and flux predictions made with the EnKF, ESTAR TB measurements, and climatological rainfall data within the Central Facility site during SGP97 are shown to be superior to predictions derived from open loop modeling driven by sparse temporal sampling of rainfall at frequencies consistent with expectations of future missions designed to measure rainfall from space (6–10 observations per day). Specific assimilation challenges posed by inadequacies in land surface model physics and spatial support contrasts between model predictions and sensor retrievals are discussed.
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Soil moisture satellite mission accuracy, repeat time and spatial resolution requirements are addressed through a numerical twin data assimilation study. Simulated soil moisture profile retrievals were made by assimilating near-surface soil moisture observations with various accuracy (0, 1, 2, 3, 4, 5 and 10%v/v standard deviation) repeat time (1, 2, 3, 5, 10, 15, 20 and 30 days), and spatial resolution (0.5, 6, 12 18, 30, 60 and 120 arc-min). This study found that near-surface soil moisture observation error must be less than the model forecast error required for a specific application when used as data assimilation input, else slight model forecast degradation may result. It also found that near-surface soil moisture observations must have an accuracy better than 5%v/v to positively impact soil moisture forecasts, and that daily near-surface soil moisture observations achieved the best soil moisture and evapotranspiration forecasts for the repeat times assessed, with 1–5 day repeat times having the greatest impact. Near-surface soil moisture observations with a spatial resolution finer than the land surface model resolution (∼30 arc-min) produced the best results, with spatial resolutions coarser than the model resolution yielding only a slight degradation. Observations at half the land surface model spatial resolution were found to be appropriate for our application. Moreover, it was found that satisfying the spatial resolution and accuracy requirements was much more important than repeat time.
Article
In 1960, R.E. Kalman published his famous paper describing a recursive solution to the discrete-data linear filtering problem. Since that time, due in large part to advances in digital computing, the Kalman filter has been the subject of extensive research and application, particularly in the area of autonomous or assisted navigation. The Kalman filter is a set of mathematical equations that provides an efficient computational (recursive) means to estimate the state of a process, in a way that minimizes the mean of the squared error. The filter is very powerful in several aspects: it supports estimations of past, present, and even future states, and it can do so even when the precise nature of the modeled system is unknown. The purpose of this paper is to provide a practical introduction to the discrete Kalman filter. This introduction includes a description and some discussion of the basic discrete Kalman filter, a derivation, description and some discussion of the extended Kalman filter, and a relatively simple (tangible) example with real numbers & results.