Search

Search Results

• 1. [Article] Improving Robustness of Hydrologic Parameter Estimation by the Use of Moving Block Bootstrap Resampling

  Modeling of natural systems typically involves conceptualization and parameterization to simplify the representations of the underlying process. Objective methods for estimation of the model parameters ...

  Citation × Citation Citation Abstract Copy Title: Improving Robustness of Hydrologic Parameter Estimation by the Use of Moving Block Bootstrap Resampling Author: Moradkhani, Hamid, Ebtehaj, Mohammad, Gupta, Hoshin V. Year: 2010 Modeling of natural systems typically involves conceptualization and parameterization to simplify the representations of the underlying process. Objective methods for estimation of the model parameters then require optimization of a cost function, representing a measure of distance between the observations and the corresponding model predictions, typically by calibration in a static batch mode and/or via some dynamic recursive optimization approach. Recently, there has been a focus on the development of parameter estimation methods that appropriately account for different sources of uncertainty. In this context, we introduce an approach to sample the optimal parameter space that uses nonparametric block bootstrapping coupled with global optimization. We demonstrate the applicability of this procedure via a case study, in which we estimate the parameter uncertainty resulting from uncertainty in the forcing data and evaluate its impacts on the resulting streamflow simulations. Title: Improving Robustness of Hydrologic Parameter Estimation by the Use of Moving Block Bootstrap Resampling Author: Moradkhani, Hamid, Ebtehaj, Mohammad, Gupta, Hoshin V. Year: 2010 Modeling of natural systems typically involves conceptualization and parameterization to simplify the representations of the underlying process. Objective methods for estimation of the model parameters then require optimization of a cost function, representing a measure of distance between the observations and the corresponding model predictions, typically by calibration in a static batch mode and/or via some dynamic recursive optimization approach. Recently, there has been a focus on the development of parameter estimation methods that appropriately account for different sources of uncertainty. In this context, we introduce an approach to sample the optimal parameter space that uses nonparametric block bootstrapping coupled with global optimization. We demonstrate the applicability of this procedure via a case study, in which we estimate the parameter uncertainty resulting from uncertainty in the forcing data and evaluate its impacts on the resulting streamflow simulations. Close

• 2. [Article] Toward Reduction of Model Uncertainty: Integration of Bayesian Model Averaging and Data Assimilation

  Multimodeling in hydrologic forecasting has proved to improve upon the systematic bias and general limitations of a single model. This is typically done by establishing a new model as a linear combination ...

  Citation × Citation Citation Abstract Copy Title: Toward Reduction of Model Uncertainty: Integration of Bayesian Model Averaging and Data Assimilation Author: Parrish, Mark A., Moradkhani, Hamid, DeChant, Caleb Matthew Year: 2012 Multimodeling in hydrologic forecasting has proved to improve upon the systematic bias and general limitations of a single model. This is typically done by establishing a new model as a linear combination or a weighted average of several models with weights on the basis of individual model performance in previous time steps. The most commonly used multimodeling method, Bayesian model averaging (BMA), assumes a fixed probability distribution around individual models' forecast in establishing the prior and uses a calibration period to determine static weights for each individual model. More recent work has focused on a sequential Bayesian model selection technique with weights that are adjusted at each time step in an attempt to accentuate the dynamics of an individual model's performance with respect to the system's response. However, these approaches still assume a fixed distribution around the individual models' forecast. A new sequential Bayesian model-averaging technique is developed incorporating a sliding window of individual model performance around the forecast. Additionally, this new technique relaxes the fixed distribution assumption in establishing the prior utilizing a particle filter data assimilation method that reflects both the performance dynamics of the models' forecasts along with their uncertainty. A comparative analysis of the different BMA strategies is performed across different rates of change in the hydrograph. Results show that methods employing the particle filter show higher probabilistic skill in high ranges of volatility but are overconfident in medium and low ranges of volatility. Title: Toward Reduction of Model Uncertainty: Integration of Bayesian Model Averaging and Data Assimilation Author: Parrish, Mark A., Moradkhani, Hamid, DeChant, Caleb Matthew Year: 2012 Multimodeling in hydrologic forecasting has proved to improve upon the systematic bias and general limitations of a single model. This is typically done by establishing a new model as a linear combination or a weighted average of several models with weights on the basis of individual model performance in previous time steps. The most commonly used multimodeling method, Bayesian model averaging (BMA), assumes a fixed probability distribution around individual models' forecast in establishing the prior and uses a calibration period to determine static weights for each individual model. More recent work has focused on a sequential Bayesian model selection technique with weights that are adjusted at each time step in an attempt to accentuate the dynamics of an individual model's performance with respect to the system's response. However, these approaches still assume a fixed distribution around the individual models' forecast. A new sequential Bayesian model-averaging technique is developed incorporating a sliding window of individual model performance around the forecast. Additionally, this new technique relaxes the fixed distribution assumption in establishing the prior utilizing a particle filter data assimilation method that reflects both the performance dynamics of the models' forecasts along with their uncertainty. A comparative analysis of the different BMA strategies is performed across different rates of change in the hydrograph. Results show that methods employing the particle filter show higher probabilistic skill in high ranges of volatility but are overconfident in medium and low ranges of volatility. Close

• 3. [Article] Combined Assimilation of Streamflow and Satellite Soil Moisture with the Particle Filter and Geostatistical Modeling

  Assimilation of satellite soil moisture and streamflow data into a distributed hydrologic model has received increasing attention over the past few years. This study provides a detailed analysis of the ...

  Citation × Citation Citation Abstract Copy Title: Combined Assimilation of Streamflow and Satellite Soil Moisture with the Particle Filter and Geostatistical Modeling Author: Yan, Hongxiang, Moradkhani, Hamid Year: 2016 Assimilation of satellite soil moisture and streamflow data into a distributed hydrologic model has received increasing attention over the past few years. This study provides a detailed analysis of the joint and separate assimilation of streamflow and Advanced Scatterometer (ASCAT) surface soil moisture into a distributed Sacramento Soil Moisture Accounting (SAC-SMA) model, with the use of recently developed particle filter-Markov chain Monte Carlo (PF-MCMC) method. Performance is assessed over the Salt River Watershed in Arizona, which is one of the watersheds without anthropogenic effects in Model Parameter Estimation Experiment (MOPEX). A total of five data assimilation (DA) scenarios are designed and the effects of the locations of streamflow gauges and the ASCAT soil moisture on the predictions of soil moisture and streamflow are assessed. In addition, a geostatistical model is introduced to overcome the significantly biased satellite soil moisture and also discontinuity issue. The results indicate that: (1) solely assimilating outlet streamflow can lead to biased soil moisture estimation; (2) when the study area can only be partially covered by the satellite data, the geostatistical approach can estimate the soil moisture for those uncovered grid cells; (3) joint assimilation of streamflow and soil moisture from geostatistical modeling can further improve the surface soil moisture prediction. This study recommends that the geostatistical model is a helpful tool to aid the remote sensing technique and the hydrologic DA study. Title: Combined Assimilation of Streamflow and Satellite Soil Moisture with the Particle Filter and Geostatistical Modeling Author: Yan, Hongxiang, Moradkhani, Hamid Year: 2016 Assimilation of satellite soil moisture and streamflow data into a distributed hydrologic model has received increasing attention over the past few years. This study provides a detailed analysis of the joint and separate assimilation of streamflow and Advanced Scatterometer (ASCAT) surface soil moisture into a distributed Sacramento Soil Moisture Accounting (SAC-SMA) model, with the use of recently developed particle filter-Markov chain Monte Carlo (PF-MCMC) method. Performance is assessed over the Salt River Watershed in Arizona, which is one of the watersheds without anthropogenic effects in Model Parameter Estimation Experiment (MOPEX). A total of five data assimilation (DA) scenarios are designed and the effects of the locations of streamflow gauges and the ASCAT soil moisture on the predictions of soil moisture and streamflow are assessed. In addition, a geostatistical model is introduced to overcome the significantly biased satellite soil moisture and also discontinuity issue. The results indicate that: (1) solely assimilating outlet streamflow can lead to biased soil moisture estimation; (2) when the study area can only be partially covered by the satellite data, the geostatistical approach can estimate the soil moisture for those uncovered grid cells; (3) joint assimilation of streamflow and soil moisture from geostatistical modeling can further improve the surface soil moisture prediction. This study recommends that the geostatistical model is a helpful tool to aid the remote sensing technique and the hydrologic DA study. Close

• 4. [Article] Uncertainty Quantification of Satellite Precipitation Estimation and Monte Carlo Assessment of the Error Propagation into Hydrologic Response

  The aim of this paper is to foster the development of an end-to-end uncertainty analysis framework that can quantify satellite-based precipitation estimation error characteristics and to assess the influence ...

  Citation × Citation Citation Abstract Copy Title: Uncertainty Quantification of Satellite Precipitation Estimation and Monte Carlo Assessment of the Error Propagation into Hydrologic Response Author: Moradkhani, Hamid, Hong, Yang, Sorooshian, Soroosh Year: 2006 The aim of this paper is to foster the development of an end-to-end uncertainty analysis framework that can quantify satellite-based precipitation estimation error characteristics and to assess the influence of the error propagation into hydrological simulation. First, the error associated with the satellite-based precipitation estimates is assumed as a nonlinear function of rainfall space-time integration scale, rain intensity, and sampling frequency. Parameters of this function are determined by using high-resolution satellite-based precipitation estimates and gauge-corrected radar rainfall data over the southwestern United States. Parameter sensitivity analysis at 16 selected 5ø ? 5ø latitude-longitude grids shows about 12?16% of variance of each parameter with respect to its mean value. Afterward, the influence of precipitation estimation error on the uncertainty of hydrological response is further examined with Monte Carlo simulation. By this approach, 100 ensemble members of precipitation data are generated, as forcing input to a conceptual rainfall-runoff hydrologic model, and the resulting uncertainty in the streamflow prediction is quantified. Case studies are demonstrated over the Leaf River basin in Mississippi. Compared with conventional procedure, i.e., precipitation estimation error as fixed ratio of rain rates, the proposed framework provides more realistic quantification of precipitation estimation error and offers improved uncertainty assessment of the error propagation into hydrologic simulation. Further study shows that the radar rainfall-generated streamflow sequences are consistently contained by the uncertainty bound of satellite rainfall generated streamflow at the 95% confidence interval. Title: Uncertainty Quantification of Satellite Precipitation Estimation and Monte Carlo Assessment of the Error Propagation into Hydrologic Response Author: Moradkhani, Hamid, Hong, Yang, Sorooshian, Soroosh Year: 2006 The aim of this paper is to foster the development of an end-to-end uncertainty analysis framework that can quantify satellite-based precipitation estimation error characteristics and to assess the influence of the error propagation into hydrological simulation. First, the error associated with the satellite-based precipitation estimates is assumed as a nonlinear function of rainfall space-time integration scale, rain intensity, and sampling frequency. Parameters of this function are determined by using high-resolution satellite-based precipitation estimates and gauge-corrected radar rainfall data over the southwestern United States. Parameter sensitivity analysis at 16 selected 5ø ? 5ø latitude-longitude grids shows about 12?16% of variance of each parameter with respect to its mean value. Afterward, the influence of precipitation estimation error on the uncertainty of hydrological response is further examined with Monte Carlo simulation. By this approach, 100 ensemble members of precipitation data are generated, as forcing input to a conceptual rainfall-runoff hydrologic model, and the resulting uncertainty in the streamflow prediction is quantified. Case studies are demonstrated over the Leaf River basin in Mississippi. Compared with conventional procedure, i.e., precipitation estimation error as fixed ratio of rain rates, the proposed framework provides more realistic quantification of precipitation estimation error and offers improved uncertainty assessment of the error propagation into hydrologic simulation. Further study shows that the radar rainfall-generated streamflow sequences are consistently contained by the uncertainty bound of satellite rainfall generated streamflow at the 95% confidence interval. Close

• 5. [Article] Detecting Non-Stationary Hydrologic Model Parameters in a Paired Catchment

  Non-stationarity represents one of the major challenges facing hydrologists. There exists a need to develop modelling systems that are capable of accounting for potential catchment changes, in order to ...

  Citation × Citation Citation Abstract Copy Title: Detecting Non-Stationary Hydrologic Model Parameters in a Paired Catchment Author: Pathiraja, Sahani, Marshall, Lucy, Sharma, Ashish, Moradkhani, Hamid Year: 2016 Non-stationarity represents one of the major challenges facing hydrologists. There exists a need to develop modelling systems that are capable of accounting for potential catchment changes, in order to provide useful predictions for the future. Such changes may be due to climatic temporal variations or human induced changes to land cover. Extensive research has been undertaken on the impacts of land-use change on hydrologic behaviour, however, few studies have examined this issue in a predictive modelling context. In this paper, we investigate whether a time varying model parameter estimation framework that uses the principles of Data Assimilation can improve prediction for two pairs of experimental catchments in Western Australia. All catchments were initially forested, but after three years one catchment was fully cleared whilst another had only 50% of its area cleared. Their adjacent catchments remained unchanged as a control. Temporal variations in parameters were detected for both treated catchments, with no comparable variations for the control catchments. Improved streamflow prediction and representation of soil moisture dynamics were also seen for the time varying parameter case, compared to when a time invariant parameter set from the calibration period was used. While we use the above mentioned catchments to illustrate the usefulness of the approach, the methods are generic and equally applicable in other settings. This study serves as an important validation step to demonstrate the potential for time varying model structures to improve both predictions and modelling of changing catchments. Title: Detecting Non-Stationary Hydrologic Model Parameters in a Paired Catchment Author: Pathiraja, Sahani, Marshall, Lucy, Sharma, Ashish, Moradkhani, Hamid Year: 2016 Non-stationarity represents one of the major challenges facing hydrologists. There exists a need to develop modelling systems that are capable of accounting for potential catchment changes, in order to provide useful predictions for the future. Such changes may be due to climatic temporal variations or human induced changes to land cover. Extensive research has been undertaken on the impacts of land-use change on hydrologic behaviour, however, few studies have examined this issue in a predictive modelling context. In this paper, we investigate whether a time varying model parameter estimation framework that uses the principles of Data Assimilation can improve prediction for two pairs of experimental catchments in Western Australia. All catchments were initially forested, but after three years one catchment was fully cleared whilst another had only 50% of its area cleared. Their adjacent catchments remained unchanged as a control. Temporal variations in parameters were detected for both treated catchments, with no comparable variations for the control catchments. Improved streamflow prediction and representation of soil moisture dynamics were also seen for the time varying parameter case, compared to when a time invariant parameter set from the calibration period was used. While we use the above mentioned catchments to illustrate the usefulness of the approach, the methods are generic and equally applicable in other settings. This study serves as an important validation step to demonstrate the potential for time varying model structures to improve both predictions and modelling of changing catchments. Close

• 6. [Article] Time Varying Parameter Models for Catchments with Land Use Change: the Importance of Model Structure

  Rapid population and economic growth in South-East-Asia has been accompanied by extensive land use change with consequent impacts on catchment hydrology. Modelling methodologies capable of handling changing ...

  Citation × Citation Citation Abstract Copy Title: Time Varying Parameter Models for Catchments with Land Use Change: the Importance of Model Structure Author: Pathiraja, Sahani, Anghileri, Daniela, Burlando, Paolo, Sharma, Ashish, Marshall, Lucy, Moradkhani, Hamid Year: 2017 Rapid population and economic growth in South-East-Asia has been accompanied by extensive land use change with consequent impacts on catchment hydrology. Modelling methodologies capable of handling changing land use conditions are therefore becoming ever more important, and are receiving increasing attention from hydrologists. A recently developed Data Assimilation based framework that allows model parameters to vary through time in response to signals of change in observations is considered for a medium sized catchment (2880 km²) in Northern Vietnam experiencing substantial but gradual land cover change. We investigate the efficacy of the method as well as the importance of the chosen model structure in ensuring the success of time varying parameter methods. The framework was utilized with two conceptual models (HBV and HyMOD) that gave good quality streamflow predictions during pre-change conditions. Although both time varying parameter models gave improved streamflow predictions under changed conditions compared to the time invariant parameter model, persistent biases for low flows were apparent in the HyMOD case. It was found that HyMOD was not suited to representing the modified baseflow conditions, resulting in extreme and unrealistic time varying parameter estimates. This work shows that the chosen model can be critical for ensuring the time varying parameter framework successfully models streamflow under changed land cover conditions. It also serves as an effective tool for separating the influence of climatic and land use change in retrospective studies where the lack of a paired control catchment precludes such an assessment. Title: Time Varying Parameter Models for Catchments with Land Use Change: the Importance of Model Structure Author: Pathiraja, Sahani, Anghileri, Daniela, Burlando, Paolo, Sharma, Ashish, Marshall, Lucy, Moradkhani, Hamid Year: 2017 Rapid population and economic growth in South-East-Asia has been accompanied by extensive land use change with consequent impacts on catchment hydrology. Modelling methodologies capable of handling changing land use conditions are therefore becoming ever more important, and are receiving increasing attention from hydrologists. A recently developed Data Assimilation based framework that allows model parameters to vary through time in response to signals of change in observations is considered for a medium sized catchment (2880 km²) in Northern Vietnam experiencing substantial but gradual land cover change. We investigate the efficacy of the method as well as the importance of the chosen model structure in ensuring the success of time varying parameter methods. The framework was utilized with two conceptual models (HBV and HyMOD) that gave good quality streamflow predictions during pre-change conditions. Although both time varying parameter models gave improved streamflow predictions under changed conditions compared to the time invariant parameter model, persistent biases for low flows were apparent in the HyMOD case. It was found that HyMOD was not suited to representing the modified baseflow conditions, resulting in extreme and unrealistic time varying parameter estimates. This work shows that the chosen model can be critical for ensuring the time varying parameter framework successfully models streamflow under changed land cover conditions. It also serves as an effective tool for separating the influence of climatic and land use change in retrospective studies where the lack of a paired control catchment precludes such an assessment. Close

• 7. [Article] Daily Discharge Forecasting Using Least Square Support Vector Regression and Regression Tree

  Prediction of river flow is one of the main issues in the field of water resources management. Because of the complexity of the rainfall-runoff process, data-driven methods have gained increased importance. ...

  Citation × Citation Citation Abstract Copy Title: Daily Discharge Forecasting Using Least Square Support Vector Regression and Regression Tree Author: Sahraei, Shahram, Andalani, Saeed Zare, Zakermoshfegh, Mohammad, Sisakht, Babak Nikeghbal, Talebbeydokhti, Nasser, Moradkhani, Hamid Year: 2015 Prediction of river flow is one of the main issues in the field of water resources management. Because of the complexity of the rainfall-runoff process, data-driven methods have gained increased importance. In the current study, two newly developed models called Least Square Support Vector Regression (LSSVR) and Regression Tree (RT) are used. The LSSVR model is based on the constrained optimization method and applies structural risk minimization in order to yield a general optimized result. Also in the RT, data movement is based on laws discovered in the tree. Both models have been applied to the data in the Kashkan watershed. Variables include (a) recorded precipitation values in the Kashkan watershed stations, and (b) outlet discharge values of one and two previous days. Present discharge is considered as output of the two models. Following that, a sensitivity analysis has been carried out on the input features and less important features has been diminished so that both models have provided better prediction on the data. The final results of both models have been compared. It was found that the LSSVR model has better performance. Finally, the results present these models as a suitable models in river flow forecasting. Title: Daily Discharge Forecasting Using Least Square Support Vector Regression and Regression Tree Author: Sahraei, Shahram, Andalani, Saeed Zare, Zakermoshfegh, Mohammad, Sisakht, Babak Nikeghbal, Talebbeydokhti, Nasser, Moradkhani, Hamid Year: 2015 Prediction of river flow is one of the main issues in the field of water resources management. Because of the complexity of the rainfall-runoff process, data-driven methods have gained increased importance. In the current study, two newly developed models called Least Square Support Vector Regression (LSSVR) and Regression Tree (RT) are used. The LSSVR model is based on the constrained optimization method and applies structural risk minimization in order to yield a general optimized result. Also in the RT, data movement is based on laws discovered in the tree. Both models have been applied to the data in the Kashkan watershed. Variables include (a) recorded precipitation values in the Kashkan watershed stations, and (b) outlet discharge values of one and two previous days. Present discharge is considered as output of the two models. Following that, a sensitivity analysis has been carried out on the input features and less important features has been diminished so that both models have provided better prediction on the data. The final results of both models have been compared. It was found that the LSSVR model has better performance. Finally, the results present these models as a suitable models in river flow forecasting. Close

• 8. [Article] Improving Soil Moisture Profile Prediction With the Particle Filter-Markov Chain Monte Carlo Method

  Satellite soil moisture estimates have received increasing attention over the past decade. This paper examines the applicability of estimating soil moisture states and soil hydraulic parameters through ...

  Citation × Citation Citation Abstract Copy Title: Improving Soil Moisture Profile Prediction With the Particle Filter-Markov Chain Monte Carlo Method Author: Yan, Hongxiang, DeChant, Caleb Matthew, Moradkhani, Hamid Year: 2015 Satellite soil moisture estimates have received increasing attention over the past decade. This paper examines the applicability of estimating soil moisture states and soil hydraulic parameters through two particle filter (PF) methods: The PF with commonly used sampling importance resampling (PF-SIR) and the PF with recently developed Markov chain Monte Carlo sampling (PF-MCMC) methods. In a synthetic experiment, the potential of assimilating remotely sensed near-surface soil moisture measurements into a 1-D mechanistic soil water model (HYDRUS-1D) using both the PF-SIR and PF-MCMC algorithms is analyzed. The effects of satellite temporal resolution and accuracy, soil type, and ensemble size on the assimilation of soil moisture are analyzed. In a real data experiment, we first validate the Advanced Microwave Scanning Radiometer--Earth Observing System (AMSR-E) soil moisture products in the Oklahoma Little Washita Watershed. Aside from rescaling the remotely sensed soil moisture, a bias correction algorithm is implemented to correct the deep soil moisture estimate. Both the ascending and descending AMSR-E soil moisture data are assimilated into the HYDRUS-1D model. The synthetic assimilation results indicated that, whereas both updating schemes showed the ability to correct the soil moisture state and estimate hydraulic parameters, the PF-MCMC scheme is consistently more accurate than PR-SIR. For real data case, the quality of remotely sensed soil moisture impacts the benefits of their assimilation into the model. The PF-MCMC scheme brought marginal gains than the open-loop simulation in RMSE at both surface and root-zone soil layer, whereas the PF-SIR scheme degraded the open-loop simulation. Title: Improving Soil Moisture Profile Prediction With the Particle Filter-Markov Chain Monte Carlo Method Author: Yan, Hongxiang, DeChant, Caleb Matthew, Moradkhani, Hamid Year: 2015 Satellite soil moisture estimates have received increasing attention over the past decade. This paper examines the applicability of estimating soil moisture states and soil hydraulic parameters through two particle filter (PF) methods: The PF with commonly used sampling importance resampling (PF-SIR) and the PF with recently developed Markov chain Monte Carlo sampling (PF-MCMC) methods. In a synthetic experiment, the potential of assimilating remotely sensed near-surface soil moisture measurements into a 1-D mechanistic soil water model (HYDRUS-1D) using both the PF-SIR and PF-MCMC algorithms is analyzed. The effects of satellite temporal resolution and accuracy, soil type, and ensemble size on the assimilation of soil moisture are analyzed. In a real data experiment, we first validate the Advanced Microwave Scanning Radiometer--Earth Observing System (AMSR-E) soil moisture products in the Oklahoma Little Washita Watershed. Aside from rescaling the remotely sensed soil moisture, a bias correction algorithm is implemented to correct the deep soil moisture estimate. Both the ascending and descending AMSR-E soil moisture data are assimilated into the HYDRUS-1D model. The synthetic assimilation results indicated that, whereas both updating schemes showed the ability to correct the soil moisture state and estimate hydraulic parameters, the PF-MCMC scheme is consistently more accurate than PR-SIR. For real data case, the quality of remotely sensed soil moisture impacts the benefits of their assimilation into the model. The PF-MCMC scheme brought marginal gains than the open-loop simulation in RMSE at both surface and root-zone soil layer, whereas the PF-SIR scheme degraded the open-loop simulation. Close

• 9. [Article] Improved Bayesian Multi-Modeling: Integration of Copulas and Bayesian Model Averaging

  Bayesian Model Averaging (BMA) is a popular approach to combine hydrologic forecasts from individual models, and characterize the uncertainty induced by model structure. In the original form of BMA, the ...

  Citation × Citation Citation Abstract Copy Title: Improved Bayesian Multi-Modeling: Integration of Copulas and Bayesian Model Averaging Author: Madadgar, Shahrbanou, Moradkhani, Hamid Year: 2014 Bayesian Model Averaging (BMA) is a popular approach to combine hydrologic forecasts from individual models, and characterize the uncertainty induced by model structure. In the original form of BMA, the conditional probability density function (PDF) of each model is assumed to be a particular probability distribution (e.g. Gaussian, gamma, etc.). If the predictions of any hydrologic model do not follow certain distribution, a data transformation procedure is required prior to model averaging. Moreover, it is strongly recommended to apply BMA on unbiased forecasts, whereas it is sometimes difficult to effectively remove bias from the predictions of complex hydrologic models. To overcome these limitations, we develop an approach to integrate a group of multivariate functions, the so-called copula functions, into BMA. Here, we introduce a copula-embedded BMA (Cop-BMA) method that relaxes any assumption on the shape of conditional PDFs. Copula functions have a flexible structure and do not restrict the shape of posterior distributions. Furthermore, copulas are effective tools in removing bias from hydrologic forecasts. To compare the performance of BMA with Cop-BMA, they are applied to hydrologic forecasts from different rainfall-runoff and land-surface models. We consider the streamflow observation and simulations for ten river basins provided by the Model Parameter Estimation Experiment (MOPEX) project. Results demonstrate that the predictive distributions are more accurate and reliable, less biased, and more confident with small uncertainty after Cop-BMA application. It is also shown that the post-processed forecasts have better correlation with observation after Cop-BMA application. Title: Improved Bayesian Multi-Modeling: Integration of Copulas and Bayesian Model Averaging Author: Madadgar, Shahrbanou, Moradkhani, Hamid Year: 2014 Bayesian Model Averaging (BMA) is a popular approach to combine hydrologic forecasts from individual models, and characterize the uncertainty induced by model structure. In the original form of BMA, the conditional probability density function (PDF) of each model is assumed to be a particular probability distribution (e.g. Gaussian, gamma, etc.). If the predictions of any hydrologic model do not follow certain distribution, a data transformation procedure is required prior to model averaging. Moreover, it is strongly recommended to apply BMA on unbiased forecasts, whereas it is sometimes difficult to effectively remove bias from the predictions of complex hydrologic models. To overcome these limitations, we develop an approach to integrate a group of multivariate functions, the so-called copula functions, into BMA. Here, we introduce a copula-embedded BMA (Cop-BMA) method that relaxes any assumption on the shape of conditional PDFs. Copula functions have a flexible structure and do not restrict the shape of posterior distributions. Furthermore, copulas are effective tools in removing bias from hydrologic forecasts. To compare the performance of BMA with Cop-BMA, they are applied to hydrologic forecasts from different rainfall-runoff and land-surface models. We consider the streamflow observation and simulations for ten river basins provided by the Model Parameter Estimation Experiment (MOPEX) project. Results demonstrate that the predictive distributions are more accurate and reliable, less biased, and more confident with small uncertainty after Cop-BMA application. It is also shown that the post-processed forecasts have better correlation with observation after Cop-BMA application. Close

• 10. [Article] Statistical Comparisons of Watershed-Scale Response to Climate Change in Selected Basins across the United States

  In an earlier global climate-change study, air temperature and precipitation data for the entire twenty-first century simulated from five general circulation models were used as input to precalibrated ...

  Citation × Citation Citation Abstract Copy Title: Statistical Comparisons of Watershed-Scale Response to Climate Change in Selected Basins across the United States Author: Risley, John, Moradkhani, Hamid, Hay, Lauren, Markstrom, Steve Year: 2011 In an earlier global climate-change study, air temperature and precipitation data for the entire twenty-first century simulated from five general circulation models were used as input to precalibrated watershed models for 14 selected basins across the United States. Simulated daily streamflow and energy output from the watershed models were used to compute a range of statistics. With a side-by-side comparison of the statistical analyses for the 14 basins, regional climatic and hydrologic trends over the twenty-first century could be qualitatively identified. Low-flow statistics (95% exceedance, 7-day mean annual minimum, and summer mean monthly streamflow) decreased for almost all basins. Annual maximum daily streamflow also decreased in all the basins, except for all four basins in California and the Pacific Northwest. An analysis of the supply of available energy and water for the basins indicated that ratios of evaporation to precipitation and potential evapotranspiration to precipitation for most of the basins will increase. Probability density functions (PDFs) were developed to assess the uncertainty and multimodality in the impact of climate change on mean annual streamflow variability. Kolmogorov?Smirnov tests showed significant differences between the beginning and ending twenty-first-century PDFs for most of the basins, with the exception of four basins that are located in the western United States. Almost none of the basin PDFs were normally distributed, and two basins in the upper Midwest had PDFs that were extremely dispersed and skewed. Title: Statistical Comparisons of Watershed-Scale Response to Climate Change in Selected Basins across the United States Author: Risley, John, Moradkhani, Hamid, Hay, Lauren, Markstrom, Steve Year: 2011 In an earlier global climate-change study, air temperature and precipitation data for the entire twenty-first century simulated from five general circulation models were used as input to precalibrated watershed models for 14 selected basins across the United States. Simulated daily streamflow and energy output from the watershed models were used to compute a range of statistics. With a side-by-side comparison of the statistical analyses for the 14 basins, regional climatic and hydrologic trends over the twenty-first century could be qualitatively identified. Low-flow statistics (95% exceedance, 7-day mean annual minimum, and summer mean monthly streamflow) decreased for almost all basins. Annual maximum daily streamflow also decreased in all the basins, except for all four basins in California and the Pacific Northwest. An analysis of the supply of available energy and water for the basins indicated that ratios of evaporation to precipitation and potential evapotranspiration to precipitation for most of the basins will increase. Probability density functions (PDFs) were developed to assess the uncertainty and multimodality in the impact of climate change on mean annual streamflow variability. Kolmogorov?Smirnov tests showed significant differences between the beginning and ending twenty-first-century PDFs for most of the basins, with the exception of four basins that are located in the western United States. Almost none of the basin PDFs were normally distributed, and two basins in the upper Midwest had PDFs that were extremely dispersed and skewed. Close