For an overview of USGS information products, including maps, imagery, and publications, visit ht... more For an overview of USGS information products, including maps, imagery, and publications, visit https://store.usgs.gov. Any use of trade, firm, or product names is for descriptive purposes only and does not imply endorsement by the U.S. Government. Although this information product, for the most part, is in the public domain, it also may contain copyrighted materials as noted in the text. Permission to reproduce copyrighted items must be secured from the copyright owner.
Flow exchange between surface and groundwater is of great importance be it for beneficial allocat... more Flow exchange between surface and groundwater is of great importance be it for beneficial allocation and use of water resources or for the proper exercise of water rights. In large-scale regional studies, most numerical models use coarse grid sizes, which make it difficult to provide an accurate depiction of the phenomenon. In particular, a somewhat arbitrary leakance coefficient in a third type (i.e., Cauchy, General Head) boundary condition is used to calculate the seepage discharge as a function of the difference of head in the river and in the aquifer, whose value is often found by calibration. A different approach is presented to analytically estimate that leakance coefficient. It is shown that a simple equivalence can be deduced from the analytical solution for the empirical coefficient, so that it provides the accuracy of the analytical solution while the model maintains a very coarse grid, treating the water-table aquifer as a single calculation layer. Relating the empirical leakance coefficient to the exact conductance, derived from physical principles, provides a physical basis for the leakance coefficient. Factors such as normalized wetted perimeter, degree of penetration of the river, presence of a clogging layer, and anisotropy can be included with little computational demand. In addition the river coefficient in models such as MODFLOW, for example, can be easily modified when grid size is changed without need for recalibration.
The occurrence of saltwater intrusion in a karstic, coastal aquifer is assessed in the context of... more The occurrence of saltwater intrusion in a karstic, coastal aquifer is assessed in the context of management issues. • Groundwater quality of freshwater springs, mainly impacted by seawater intrusion, is assessed. • The effects of different kinds of boundary conditions on groundwater flow are compared. • Different scenarios are simulated to assess the effects of natural forcing and human interactions.
Flow exchange between surface and ground water is of great importance be it for beneficial alloca... more Flow exchange between surface and ground water is of great importance be it for beneficial allocation and use of the water resources or for the proper exercise of water rights. That exchange can take place under a saturated or unsaturated flow regime. Which regimes occur depend on conditions in the vicinity of the interactive area. Withdrawals partially sustained by seepage may not bring about desaturation but greater amounts eventually will. The problem considered in this paper deals only with the steady-state case. It is meant as a first step toward a simple, yet accurate and physically based treatment of the transient situation. The primary purpose of the article is to provide simple criteria for determination of the initiation of desaturation in an aquifer originally in saturated hydraulic connection with a river or a recharge area. The extent of the unsaturated zone in the aquifer will increase with increasing withdrawals while at the same time the seepage rate from the river increases. However the seepage increase will stop once infiltration takes place strictly by gravity in the aquifer and is no longer opposed by the capillary rise from the water table below the riverbed. Following desaturation simple criteria are derived and simple analytical formulae provided to estimate the river seepage based on the position of the water table mound below the clogging layer and at some distance away from the river bank. They fully account for the unsaturated flow phenomena, including the existence of a drainage entry pressure. Two secondary objectives were to verify that (1) the assumption of uniform vertical flow through a clogging layer and that (2) the approximation of the water table mound below the seepage area as a flat surface were both reasonably legitimate. This approach will be especially advantageous for the implementation of the methodology in large-scale applications of integrated hydrologic models used for management.
Here we test model discrimination criteria through comparisons with cross-validation experiments.... more Here we test model discrimination criteria through comparisons with cross-validation experiments. Three common model discrimination criteria are considered [AICc, BIC, and KIC (as used, KIC is equivalent to MLBMA)] along with two other statistics [the calculated error variance and the weighted sum of squared residuals]. The study is conducted using the computer codes UCODE_2005 and MMA and a MODFLOW model of the Maggia Valley ground-water system in Southern Switzerland. The tests focus on prediction of eight heads and three flows midway along the valley where ecological consequences and, therefore, model precision are of great concern. Sixty-four alternative models were designed deterministically and differ in how the river, recharge, bedrock topography, and hydraulic conductivity are represented. Computationally frugal linear (local) sensitivity analysis statistics made it easy to obtain substantial insight into the many alternative models. For example, leverage statistics were use...
ABSTRACT Most surface flows to the 20-km-long Maggia Valley in Southern Switzerland are impounded... more ABSTRACT Most surface flows to the 20-km-long Maggia Valley in Southern Switzerland are impounded and the valley is being investigated to determine environmental flow requirements. The aim of the investigation is the devel-opment of a modelling framework that simulates the dynamics of the ground-water, hydrologic, and ecologic systems. Because of the multi-scale nature of the modelling framework, large-scale models are first developed to provide the boundary conditions for more detailed models of reaches that are of eco-logical importance. We describe here the initial (large-scale) groundwa-ter/surface water model and its calibration in relation to initial and boundary conditions. A MODFLOW-2000 model was constructed to simulate the inter-action of groundwater and surface water and was developed parsimoniously to avoid modelling artefacts and parameter inconsistencies. Model calibration includes two steady-state conditions, with and without recharge to the aquifer from the adjoining hillslopes. Parameters are defined to represent areal re-charge, hydraulic conductivity of the aquifer (up to 5 classes), and streambed hydraulic conductivity. Model performance was investigated following two system representation. The first representation assumed unknown flow input at the northern end of the groundwater domain and unknown lateral inflow. The second representation used simulations of the lateral flow obtained by means of a raster-based, physically oriented and continuous in time rainfall-runoff (R-R) model. Results based on these two representations are compared and discussed.
ABSTRACT Model discrimination techniques are used to evaluate alternative conceptual models. Thor... more ABSTRACT Model discrimination techniques are used to evaluate alternative conceptual models. Thorough consideration of alternative conceptual models is an important and often neglected step in the study of many natural systems, including groundwater systems. This means that many modelling efforts are less useful for system management than they could be because they exclude alternatives considered important by some stakeholders, which makes them vulnerable to criticism. Important steps include identifying reasonable alternative models and possibly using model averaging to improve predictions and measures of prediction uncertainty. Here we used the computer code MMA (Multi-Model Analysis) as a modelling tool to help: (1) model development, (2) make predictions, and (3) understand the physical processes most important to the system. We focus on the ability of a groundwater model constructed using MODFLOW to predict heads and flows in the Maggia Valley, Southern Switzerland, where connections between groundwater, surface water and ecology are of interest. Sixty-four alternative models were designed deterministically and differ in how the river, recharge, bedrock topography, and hydraulic conductivity are characterized. None of the models correctly represent heads and flows in the Northern and Southern part of the valley simultaneously. A cross-validation experiment was conducted to compare model discrimination results with the ability of the models to predict eight heads and three flows to the stream along three reaches midway along the valley where ecological consequences and, therefore, model accuracy are of great concern. Results suggest: (1) Model averaging appears to have improved prediction accuracy in the problem considered. (2) The most significant model improvements occurred with introduction of spatially distributed recharge and improved bedrock topography. (3) The simplest models poorly represented the system in the area of interest.
ABSTRACT Thorough consideration of alternative conceptual models is an important and often neglec... more ABSTRACT Thorough consideration of alternative conceptual models is an important and often neglected step in the study of many natural systems, including groundwater systems. This means that many modelling efforts are less useful for system management than they could be because they exclude alternatives considered important by some stakeholders, which makes them more vulnerable to criticism. Important steps include identifying reasonable alternative models and possibly using model discrimination criteria and associated model averaging to improve predictions and measures of prediction uncertainty. Here we use the computer code MMA (Multi-Model Analysis) to: (1) manage the model discrimination statistics produced by many alternative models, (2) mange predictions, and (3) calculate measures of prediction uncertainty. (1) to (3) also assist in understand the physical processes most important to model fit and predictions of interest. We focus on the ability of a groundwater model constructed using MODFLOW to predict heads and flows in the Maggia Valley, Southern Switzerland, where connections between groundwater, surface water and ecology are of interest. Sixty-four alternative models were designed deterministically and differ in how the river, recharge, bedrock topography, and hydraulic conductivity are characterized. None of the models correctly represent heads and flows in the Northern and Southern part of the valley simultaneously. A cross-validation experiment was conducted to compare model discrimination results with the ability of the models to predict eight heads and three flows to the stream along three reaches midway along the valley where ecological consequences and, therefore, model accuracy are of great concern. Results suggest: (1) Model averaging appears to have improved prediction accuracy in the problem considered. (2) The most significant model improvements occurred with introduction of spatially distributed recharge and improved bedrock topography. (3) The simplest models poorly represented the system in the area of interest.
ABSTRACT Methods for analyzing inverse modeling results can be separated into two categories: (1)... more ABSTRACT Methods for analyzing inverse modeling results can be separated into two categories: (1) linear methods, such as Cook's D, which are computationally frugal and do not require additional model runs, and (2) nonlinear methods, such as cross validation, which are computationally more expensive because they generally require additional model runs. Depending on the type of nonlinear analysis performed, the additional runs can be the difference between 10's of runs and 1000's of runs. For example, cross-validation studies require the model to be recalibrated (the regression repeated) for each observation or set of observations analyzed. This can be computationally prohibitive if many observations or sets of observations are investigated and/or the model has many estimated parameters. A tradeoff exists between linear and nonlinear methods, with linear methods being computationally efficient, but the results being questioned when models are nonlinear. The trade offs between computational efficiency and accuracy are investigated by comparing results from several linear measures of observation importance (for example, Cook's D, DFBETA's) to their nonlinear counterparts based on cross validation. Examples from ground water models of the Maggia Valley in southern Switzerland are used to make comparisons. The models include representation of the stream-aquifer interaction and range from simple to complex, with associated modified Beale's measure ranging from mildly nonlinear to highly nonlinear, respectively. These results demonstrate applicability and limitations of applying linear methods over a range of model complexity and linearity and can be used to better understand when the additional computation burden of nonlinear methods may be necessary.
ABSTRACT Hydrological models of surface-water flow and infiltration allow for a process-based rep... more ABSTRACT Hydrological models of surface-water flow and infiltration allow for a process-based representation of recharge to ground water models. Recharge is a fundamental and often difficult to quantify component of a groundwater system, in part because recharge and hydraulic conductivity changes tend to similarly affect hydraulic heads, the most common kind of observations in groundwater systems. Here the goal is to analyze the importance of using recharge derived from hydrologic processes for groundwater model development and furthermore the importance of a spatially distributed value of recharge. To achieve the goal we followed this procedure: 1) independently calibrate and test the groundwater and hydrological models (accomplished as described in Foglia et al., 2007GW, 2009WRR, in press WRR); 2) for the hydrological model, we present a new sensitivity analysis and calibration obtained with a set of observations that provides more detail at low flows, which was identified as important by Foglia et al. (2009); 3) couple the two models (here, one-way coupling transfers infiltration from the surface-water model to the groundwater model after multiplying by an estimated factor); 4) identify important parameters and observations using a sensitivity analysis conducted with linear statistics for this computationally demanding model; 5) use regression in an hypothesis testing framework to explore parameter and observation importance further and also explore resulting estimates and model fit. The analysis is carried out using s physically based models of groundwater flow (MOFLOW-2000) and surface hydrology (TOPKAPI) developed for the Maggia Valley in Southern Switzerland. Calibration and sensitivity analysis were performed using UCODE_2005. Sensitivity analysis is used to identify the most important observations for both the individual and coupled models. As expected, the observations belonging to the hydrological model play a more significant role in the coupled calibration. Results suggest the importance of distributed recharge and allow development of new strategies for its further evaluation in the groundwater model development and calibration.
Model adequacy is evaluated with alternative models rated using model selection criteria (AICc, B... more Model adequacy is evaluated with alternative models rated using model selection criteria (AICc, BIC, and KIC) and three other statistics. Model selection criteria are tested with cross-validation experiments and insights for using alternative models to evaluate model structural adequacy are provided. The study is conducted using the computer codes UCODE_2005 and MMA (MultiModel Analysis). One recharge alternative is simulated using the TOPKAPI hydrological model. The predictions evaluated include eight heads and three flows located where ecological consequences and model precision are of concern. Cross-validation is used to obtain measures of prediction accuracy. Sixty-four models were designed deterministically and differ in representation of river, recharge, bedrock topography, and hydraulic conductivity. Results include: (1) What may seem like inconsequential choices in model construction may be important to predictions. Analysis of predictions from alternative models is advised. (2) None of the model selection criteria consistently identified models with more accurate predictions. This is a disturbing result that suggests to reconsider the utility of model selection criteria, and/or the cross-validation measures used in this work to measure model accuracy. (3) KIC displayed poor performance for the present regression problems; theoretical considerations suggest that difficulties are associated with wide variations in the sensitivity term of KIC resulting from the models being nonlinear and the problems being ill-posed due to parameter correlations and insensitivity. The other criteria performed somewhat better, and similarly to each other. (4) Quantities with high leverage are more difficult to predict. The results are expected to be generally applicable to models of environmental systems.
We evaluate the utility of three interrelated means of using data to calibrate the fully distribu... more We evaluate the utility of three interrelated means of using data to calibrate the fully distributed rainfall-runoff model TOPKAPI as applied to the Maggia Valley drainage area in Switzerland. The use of error-based weighting of observation and prior information data, local sensitivity analysis, and single-objective function nonlinear regression provides quantitative evaluation of sensitivity of the 35 model parameters to the data, identification of data types most important to the calibration, and identification of correlations among parameters that contribute to nonuniqueness. Sensitivity analysis required only 71 model runs, and regression required about 50 model runs. The approach presented appears to be ideal for evaluation of models with long run times or as a preliminary step to more computationally demanding methods. The statistics used include composite scaled sensitivities, parameter correlation coefficients, leverage, Cook's D, and DFBETAS. Tests suggest predictive ability of the calibrated model typical of hydrologic models.
In this work, we provide suggestions for designing experiments where calibration of many models i... more In this work, we provide suggestions for designing experiments where calibration of many models is required and guidance for identifying problematic calibrations. Calibration of many conceptual models which have different representations of the physical processes in the system, as is done in cross-validation studies or multi-model analysis, often uses computationally frugal inversion techniques to achieve tractable execution times. However, because these frugal methods are usually local methods, and the inverse problem is almost always nonlinear, there is no guarantee that the optimal solution will be found. Furthermore, evaluation of each inverse model's performance to identify poor calibrations can be tedious. Results of this study show that if poorly calibrated models are included in the analysis, simulated predictions and measures of prediction uncertainty can be affected in unexpected ways. Guidelines are provided to help identify problematic regressions and correct them.
For an overview of USGS information products, including maps, imagery, and publications, visit ht... more For an overview of USGS information products, including maps, imagery, and publications, visit https://store.usgs.gov. Any use of trade, firm, or product names is for descriptive purposes only and does not imply endorsement by the U.S. Government. Although this information product, for the most part, is in the public domain, it also may contain copyrighted materials as noted in the text. Permission to reproduce copyrighted items must be secured from the copyright owner.
Flow exchange between surface and groundwater is of great importance be it for beneficial allocat... more Flow exchange between surface and groundwater is of great importance be it for beneficial allocation and use of water resources or for the proper exercise of water rights. In large-scale regional studies, most numerical models use coarse grid sizes, which make it difficult to provide an accurate depiction of the phenomenon. In particular, a somewhat arbitrary leakance coefficient in a third type (i.e., Cauchy, General Head) boundary condition is used to calculate the seepage discharge as a function of the difference of head in the river and in the aquifer, whose value is often found by calibration. A different approach is presented to analytically estimate that leakance coefficient. It is shown that a simple equivalence can be deduced from the analytical solution for the empirical coefficient, so that it provides the accuracy of the analytical solution while the model maintains a very coarse grid, treating the water-table aquifer as a single calculation layer. Relating the empirical leakance coefficient to the exact conductance, derived from physical principles, provides a physical basis for the leakance coefficient. Factors such as normalized wetted perimeter, degree of penetration of the river, presence of a clogging layer, and anisotropy can be included with little computational demand. In addition the river coefficient in models such as MODFLOW, for example, can be easily modified when grid size is changed without need for recalibration.
The occurrence of saltwater intrusion in a karstic, coastal aquifer is assessed in the context of... more The occurrence of saltwater intrusion in a karstic, coastal aquifer is assessed in the context of management issues. • Groundwater quality of freshwater springs, mainly impacted by seawater intrusion, is assessed. • The effects of different kinds of boundary conditions on groundwater flow are compared. • Different scenarios are simulated to assess the effects of natural forcing and human interactions.
Flow exchange between surface and ground water is of great importance be it for beneficial alloca... more Flow exchange between surface and ground water is of great importance be it for beneficial allocation and use of the water resources or for the proper exercise of water rights. That exchange can take place under a saturated or unsaturated flow regime. Which regimes occur depend on conditions in the vicinity of the interactive area. Withdrawals partially sustained by seepage may not bring about desaturation but greater amounts eventually will. The problem considered in this paper deals only with the steady-state case. It is meant as a first step toward a simple, yet accurate and physically based treatment of the transient situation. The primary purpose of the article is to provide simple criteria for determination of the initiation of desaturation in an aquifer originally in saturated hydraulic connection with a river or a recharge area. The extent of the unsaturated zone in the aquifer will increase with increasing withdrawals while at the same time the seepage rate from the river increases. However the seepage increase will stop once infiltration takes place strictly by gravity in the aquifer and is no longer opposed by the capillary rise from the water table below the riverbed. Following desaturation simple criteria are derived and simple analytical formulae provided to estimate the river seepage based on the position of the water table mound below the clogging layer and at some distance away from the river bank. They fully account for the unsaturated flow phenomena, including the existence of a drainage entry pressure. Two secondary objectives were to verify that (1) the assumption of uniform vertical flow through a clogging layer and that (2) the approximation of the water table mound below the seepage area as a flat surface were both reasonably legitimate. This approach will be especially advantageous for the implementation of the methodology in large-scale applications of integrated hydrologic models used for management.
Here we test model discrimination criteria through comparisons with cross-validation experiments.... more Here we test model discrimination criteria through comparisons with cross-validation experiments. Three common model discrimination criteria are considered [AICc, BIC, and KIC (as used, KIC is equivalent to MLBMA)] along with two other statistics [the calculated error variance and the weighted sum of squared residuals]. The study is conducted using the computer codes UCODE_2005 and MMA and a MODFLOW model of the Maggia Valley ground-water system in Southern Switzerland. The tests focus on prediction of eight heads and three flows midway along the valley where ecological consequences and, therefore, model precision are of great concern. Sixty-four alternative models were designed deterministically and differ in how the river, recharge, bedrock topography, and hydraulic conductivity are represented. Computationally frugal linear (local) sensitivity analysis statistics made it easy to obtain substantial insight into the many alternative models. For example, leverage statistics were use...
ABSTRACT Most surface flows to the 20-km-long Maggia Valley in Southern Switzerland are impounded... more ABSTRACT Most surface flows to the 20-km-long Maggia Valley in Southern Switzerland are impounded and the valley is being investigated to determine environmental flow requirements. The aim of the investigation is the devel-opment of a modelling framework that simulates the dynamics of the ground-water, hydrologic, and ecologic systems. Because of the multi-scale nature of the modelling framework, large-scale models are first developed to provide the boundary conditions for more detailed models of reaches that are of eco-logical importance. We describe here the initial (large-scale) groundwa-ter/surface water model and its calibration in relation to initial and boundary conditions. A MODFLOW-2000 model was constructed to simulate the inter-action of groundwater and surface water and was developed parsimoniously to avoid modelling artefacts and parameter inconsistencies. Model calibration includes two steady-state conditions, with and without recharge to the aquifer from the adjoining hillslopes. Parameters are defined to represent areal re-charge, hydraulic conductivity of the aquifer (up to 5 classes), and streambed hydraulic conductivity. Model performance was investigated following two system representation. The first representation assumed unknown flow input at the northern end of the groundwater domain and unknown lateral inflow. The second representation used simulations of the lateral flow obtained by means of a raster-based, physically oriented and continuous in time rainfall-runoff (R-R) model. Results based on these two representations are compared and discussed.
ABSTRACT Model discrimination techniques are used to evaluate alternative conceptual models. Thor... more ABSTRACT Model discrimination techniques are used to evaluate alternative conceptual models. Thorough consideration of alternative conceptual models is an important and often neglected step in the study of many natural systems, including groundwater systems. This means that many modelling efforts are less useful for system management than they could be because they exclude alternatives considered important by some stakeholders, which makes them vulnerable to criticism. Important steps include identifying reasonable alternative models and possibly using model averaging to improve predictions and measures of prediction uncertainty. Here we used the computer code MMA (Multi-Model Analysis) as a modelling tool to help: (1) model development, (2) make predictions, and (3) understand the physical processes most important to the system. We focus on the ability of a groundwater model constructed using MODFLOW to predict heads and flows in the Maggia Valley, Southern Switzerland, where connections between groundwater, surface water and ecology are of interest. Sixty-four alternative models were designed deterministically and differ in how the river, recharge, bedrock topography, and hydraulic conductivity are characterized. None of the models correctly represent heads and flows in the Northern and Southern part of the valley simultaneously. A cross-validation experiment was conducted to compare model discrimination results with the ability of the models to predict eight heads and three flows to the stream along three reaches midway along the valley where ecological consequences and, therefore, model accuracy are of great concern. Results suggest: (1) Model averaging appears to have improved prediction accuracy in the problem considered. (2) The most significant model improvements occurred with introduction of spatially distributed recharge and improved bedrock topography. (3) The simplest models poorly represented the system in the area of interest.
ABSTRACT Thorough consideration of alternative conceptual models is an important and often neglec... more ABSTRACT Thorough consideration of alternative conceptual models is an important and often neglected step in the study of many natural systems, including groundwater systems. This means that many modelling efforts are less useful for system management than they could be because they exclude alternatives considered important by some stakeholders, which makes them more vulnerable to criticism. Important steps include identifying reasonable alternative models and possibly using model discrimination criteria and associated model averaging to improve predictions and measures of prediction uncertainty. Here we use the computer code MMA (Multi-Model Analysis) to: (1) manage the model discrimination statistics produced by many alternative models, (2) mange predictions, and (3) calculate measures of prediction uncertainty. (1) to (3) also assist in understand the physical processes most important to model fit and predictions of interest. We focus on the ability of a groundwater model constructed using MODFLOW to predict heads and flows in the Maggia Valley, Southern Switzerland, where connections between groundwater, surface water and ecology are of interest. Sixty-four alternative models were designed deterministically and differ in how the river, recharge, bedrock topography, and hydraulic conductivity are characterized. None of the models correctly represent heads and flows in the Northern and Southern part of the valley simultaneously. A cross-validation experiment was conducted to compare model discrimination results with the ability of the models to predict eight heads and three flows to the stream along three reaches midway along the valley where ecological consequences and, therefore, model accuracy are of great concern. Results suggest: (1) Model averaging appears to have improved prediction accuracy in the problem considered. (2) The most significant model improvements occurred with introduction of spatially distributed recharge and improved bedrock topography. (3) The simplest models poorly represented the system in the area of interest.
ABSTRACT Methods for analyzing inverse modeling results can be separated into two categories: (1)... more ABSTRACT Methods for analyzing inverse modeling results can be separated into two categories: (1) linear methods, such as Cook's D, which are computationally frugal and do not require additional model runs, and (2) nonlinear methods, such as cross validation, which are computationally more expensive because they generally require additional model runs. Depending on the type of nonlinear analysis performed, the additional runs can be the difference between 10's of runs and 1000's of runs. For example, cross-validation studies require the model to be recalibrated (the regression repeated) for each observation or set of observations analyzed. This can be computationally prohibitive if many observations or sets of observations are investigated and/or the model has many estimated parameters. A tradeoff exists between linear and nonlinear methods, with linear methods being computationally efficient, but the results being questioned when models are nonlinear. The trade offs between computational efficiency and accuracy are investigated by comparing results from several linear measures of observation importance (for example, Cook's D, DFBETA's) to their nonlinear counterparts based on cross validation. Examples from ground water models of the Maggia Valley in southern Switzerland are used to make comparisons. The models include representation of the stream-aquifer interaction and range from simple to complex, with associated modified Beale's measure ranging from mildly nonlinear to highly nonlinear, respectively. These results demonstrate applicability and limitations of applying linear methods over a range of model complexity and linearity and can be used to better understand when the additional computation burden of nonlinear methods may be necessary.
ABSTRACT Hydrological models of surface-water flow and infiltration allow for a process-based rep... more ABSTRACT Hydrological models of surface-water flow and infiltration allow for a process-based representation of recharge to ground water models. Recharge is a fundamental and often difficult to quantify component of a groundwater system, in part because recharge and hydraulic conductivity changes tend to similarly affect hydraulic heads, the most common kind of observations in groundwater systems. Here the goal is to analyze the importance of using recharge derived from hydrologic processes for groundwater model development and furthermore the importance of a spatially distributed value of recharge. To achieve the goal we followed this procedure: 1) independently calibrate and test the groundwater and hydrological models (accomplished as described in Foglia et al., 2007GW, 2009WRR, in press WRR); 2) for the hydrological model, we present a new sensitivity analysis and calibration obtained with a set of observations that provides more detail at low flows, which was identified as important by Foglia et al. (2009); 3) couple the two models (here, one-way coupling transfers infiltration from the surface-water model to the groundwater model after multiplying by an estimated factor); 4) identify important parameters and observations using a sensitivity analysis conducted with linear statistics for this computationally demanding model; 5) use regression in an hypothesis testing framework to explore parameter and observation importance further and also explore resulting estimates and model fit. The analysis is carried out using s physically based models of groundwater flow (MOFLOW-2000) and surface hydrology (TOPKAPI) developed for the Maggia Valley in Southern Switzerland. Calibration and sensitivity analysis were performed using UCODE_2005. Sensitivity analysis is used to identify the most important observations for both the individual and coupled models. As expected, the observations belonging to the hydrological model play a more significant role in the coupled calibration. Results suggest the importance of distributed recharge and allow development of new strategies for its further evaluation in the groundwater model development and calibration.
Model adequacy is evaluated with alternative models rated using model selection criteria (AICc, B... more Model adequacy is evaluated with alternative models rated using model selection criteria (AICc, BIC, and KIC) and three other statistics. Model selection criteria are tested with cross-validation experiments and insights for using alternative models to evaluate model structural adequacy are provided. The study is conducted using the computer codes UCODE_2005 and MMA (MultiModel Analysis). One recharge alternative is simulated using the TOPKAPI hydrological model. The predictions evaluated include eight heads and three flows located where ecological consequences and model precision are of concern. Cross-validation is used to obtain measures of prediction accuracy. Sixty-four models were designed deterministically and differ in representation of river, recharge, bedrock topography, and hydraulic conductivity. Results include: (1) What may seem like inconsequential choices in model construction may be important to predictions. Analysis of predictions from alternative models is advised. (2) None of the model selection criteria consistently identified models with more accurate predictions. This is a disturbing result that suggests to reconsider the utility of model selection criteria, and/or the cross-validation measures used in this work to measure model accuracy. (3) KIC displayed poor performance for the present regression problems; theoretical considerations suggest that difficulties are associated with wide variations in the sensitivity term of KIC resulting from the models being nonlinear and the problems being ill-posed due to parameter correlations and insensitivity. The other criteria performed somewhat better, and similarly to each other. (4) Quantities with high leverage are more difficult to predict. The results are expected to be generally applicable to models of environmental systems.
We evaluate the utility of three interrelated means of using data to calibrate the fully distribu... more We evaluate the utility of three interrelated means of using data to calibrate the fully distributed rainfall-runoff model TOPKAPI as applied to the Maggia Valley drainage area in Switzerland. The use of error-based weighting of observation and prior information data, local sensitivity analysis, and single-objective function nonlinear regression provides quantitative evaluation of sensitivity of the 35 model parameters to the data, identification of data types most important to the calibration, and identification of correlations among parameters that contribute to nonuniqueness. Sensitivity analysis required only 71 model runs, and regression required about 50 model runs. The approach presented appears to be ideal for evaluation of models with long run times or as a preliminary step to more computationally demanding methods. The statistics used include composite scaled sensitivities, parameter correlation coefficients, leverage, Cook's D, and DFBETAS. Tests suggest predictive ability of the calibrated model typical of hydrologic models.
In this work, we provide suggestions for designing experiments where calibration of many models i... more In this work, we provide suggestions for designing experiments where calibration of many models is required and guidance for identifying problematic calibrations. Calibration of many conceptual models which have different representations of the physical processes in the system, as is done in cross-validation studies or multi-model analysis, often uses computationally frugal inversion techniques to achieve tractable execution times. However, because these frugal methods are usually local methods, and the inverse problem is almost always nonlinear, there is no guarantee that the optimal solution will be found. Furthermore, evaluation of each inverse model's performance to identify poor calibrations can be tedious. Results of this study show that if poorly calibrated models are included in the analysis, simulated predictions and measures of prediction uncertainty can be affected in unexpected ways. Guidelines are provided to help identify problematic regressions and correct them.
Uploads
Papers by Steffen Mehl