The Coupled Hydrology–Human Activity Information (CHHAI) dataset: a global benchmark dataset for model comparison and evaluation

To What End: Resilience, Tradeoffs, and the Lessons of Katrina

The problems of identifying the most appropriate model structure for a given problem and quantifying the uncertainty in model structure remain outstanding research challenges for the discipline of hydrology. Progress on these problems requires understanding of the nature of differences between models. This paper presents a methodology to diagnose differences in hydrological model structures: the Framework for Understanding Structural Errors (FUSE). FUSE was used to construct 79 unique model structures by combining components of 4 existing hydrological models. These new models were used to simulate streamflow in two of the basins used in the Model Parameter Estimation Experiment (MOPEX): the Guadalupe River (Texas) and the French Broad River (North Carolina). Results show that the new models produced simulations of streamflow that were at least as good as the simulations produced by the models that participated in the MOPEX experiment. Our initial application of the FUSE method for the Guadalupe River exposed relationships between model structure and model performance, suggesting that the choice of model structure is just as important as the choice of model parameters. However, further work is needed to evaluate model simulations using multiple criteria to diagnose the relative importance of model structural differences in various climate regimes and to assess the amount of independent information in each of the models. This work will be crucial to both identifying the most appropriate model structure for a given problem and quantifying the uncertainty in model structure. To facilitate research on these problems, the FORTRAN‐90 source code for FUSE is available upon request from the lead author.

Data assimilation is predominantly used for state estimation, combining observational data with model predictions to produce an updated model state that most accurately approximates the true system state whilst keeping the model parameters fixed. This updated model state is then used to initiate the next model forecast. Even with perfect initial data, inaccurate model parameters will lead to the growth of prediction errors. To generate reliable forecasts, we need good estimates of both the current system state and the model parameters. This article presents research into data assimilation methods for morphodynamic model state and parameter estimation. First, we focus on state estimation and describe implementation of a three‐dimensional variational (3D‐Var) data assimilation scheme in a simple 2D morphodynamic model of Morecambe Bay, UK. The assimilation of observations of bathymetry derived from synthetic aperture radar (SAR) satellite imagery and a ship‐borne survey is shown to significantly improve the predictive capability of the model over a 2‐year run. Here, the model parameters are set by manual calibration; this is laborious and is found to produce different parameter values depending on the type and coverage of the validation dataset. The second part of this article considers the problem of model parameter estimation in more detail. We explain how, by employing the technique of state augmentation, it is possible to use data assimilation to estimate uncertain model parameters concurrently with the model state. This approach removes inefficiencies associated with manual calibration and enables more effective use of observational data. We outline the development of a novel hybrid sequential 3D‐Var data assimilation algorithm for joint state‐parameter estimation and demonstrate its efficacy using an idealised 1D sediment transport model. The results of this study are extremely positive and suggest that there is great potential for the use of data assimilation‐based state‐parameter estimation in coastal morphodynamic modelling. Copyright © 2012 Royal Meteorological Society

Current land surface models use increasingly complex descriptions of the processes that they represent. Increase in complexity is accompanied by an increase in the number of model parameters, many of which cannot be measured directly at large spatial scales. A Monte Carlo framework was used to evaluate the sensitivity and identifiability of ten parameters controlling surface and subsurface runoff generation in the Variable Infiltration Capacity model (VIC). Using the Monte Carlo Analysis Toolbox (MCAT), parameter sensitivities were studied for four U.S. watersheds along a hydroclimatic gradient, based on a 20‐year data set developed for the Model Parameter Estimation Experiment (MOPEX). Results showed that simulated streamflows are sensitive to three parameters when evaluated with different objective functions. Sensitivity of the infiltration parameter (b) and the drainage parameter (exp) were strongly related to the hydroclimatic gradient. The placement of vegetation roots played an important role in the sensitivity of model simulations to the thickness of the second soil layer (thick2). Overparameterization was found in the base flow formulation indicating that a simplified version could be implemented. Parameter sensitivity was more strongly dictated by climatic gradients than by changes in soil properties. Results showed how a complex model can be reduced to a more parsimonious form, leading to a more identifiable model with an increased chance of successful regionalization to ungauged basins. Although parameter sensitivities are strictly valid for VIC, this model is representative of a wider class of macroscale hydrological models. Consequently, the results and methodology will have applicability to other hydrological models.

Undirected graphical models such as Markov random fields or Boltzmann machines prove useful in many signal processing and machine learning tasks. However, parameter estimation in these models is difficult due to the intractable normalising constant in their probability density functions. One powerful technique for parameter estimation in such models is score matching. This technique makes use of an objective function which is independent of the normalising constant and constitutes locally consistent estimators for the parameters of such models. However, score matching is only applicable to fully-observed models. In this paper, we extend the applicability of score matching to models with latent variables. Our estimators are unbiased, based on Monte Carlo integration. Unbiased gradient estimators open the way to optimisation through stochastic approximation. We demonstrate the performance of our methodology on two synthetic problems.

The simulation of natural streamflow at ungauged basins is one of the fundamental challenges in hydrology community. The key to runoff simulation in ungauged basins is generally involved with a reliable parameter estimation in a rainfall-runoff model. However, the parameter estimation of the rainfall-runoff model is a complex issue due to an insufficient hydrologic data. This study aims to regionalize the parameters of a continuous rainfall-runoff model in conjunction with a Bayesian statistical technique to consider uncertainty more precisely associated with the parameters. First, this study employed Bayesian Markov Chain Monte Carlo scheme for the estimation of the Sacramento rainfall-runoff model. The Sacramento model is calibrated against observed daily runoff data, and finally, the posterior density function of the parameters is derived. Second, we applied a multiple linear regression model to the set of the parameters with watershed characteristics, to obtain a functional relationship between pairs of variables. The proposed model was also validated with gauged watersheds in accordance with the efficiency criteria such as the Nash-Sutcliffe efficiency, index of agreement and the coefficient of correlation.

A methodology is proposed to aid parameter estimation in fundamental models of pharmaceutical processes. This methodology addresses situations with insufficient data to reliably estimate all parameters, when the estimation is complicated by uncertain independent variables. The proposed method uses an augmented sensitivity matrix to rank the combined set of parameters and uncertain inputs from most estimable to least estimable. An updated mean‐squared‐error criterion is then used to determine the appropriate parameters and inputs that should be estimated, based on the ranked list. A model for one step in a batch pharmaceutical production process with an uncertain initial reactant concentration is used to illustrate the method, revealing that the initial reactant concentration in each batch should be estimated along with three out of six model parameters. Non‐estimable parameters are fixed at their initial values to prevent overfitting. The method will aid error‐in‐variables parameter estimation in many situations involving limited data.

In this study, the authors applied version 4 of the Community Land Model (CLM4) integrated with an uncertainty quantification (UQ) framework to 20 selected watersheds from the Model Parameter Estimation Experiment (MOPEX) spanning a wide range of climate and site conditions to investigate the sensitivity of runoff simulations to major hydrologic parameters and to assess the fidelity of CLM4, as the land component of the Community Earth System Model (CESM), in capturing realistic hydrological responses. They found that for runoff simulations, the most significant parameters are those related to the subsurface runoff parameterizations. Soil texture–related parameters and surface runoff parameters are of secondary significance. Moreover, climate and soil conditions play important roles in the parameter sensitivity. In general, water-limited hydrologic regime and finer soil texture result in stronger sensitivity of output variables, such as runoff and its surface and subsurface components, to the input parameters in CLM4. This study evaluated the parameter identifiability of hydrological parameters from streamflow observations at selected MOPEX basins and demonstrated the feasibility of parameter inversion/calibration for CLM4 to improve runoff simulations. The results suggest that in order to calibrate CLM4 hydrologic parameters, model reduction is needed to include only the identifiable parameters in the unknowns. With the reduced parameter set dimensionality, the inverse problem is less ill posed.

Despite offering spatially and temporally continuous measurements, the use of remotely sensed P and E in data‐scarce catchments is hindered by the lack of ground‐based measurements that enable comprehensive validation. This study proposes a novel validation framework that characterizes the combined error in the long‐term average estimates of remotely sensed P and E by making use of the Budyko hypothesis, specifically Fu's equation. A Root Mean Square Error (RMSE)‐based error metric that is capable of translating individual biases in P and E estimates onto the Budyko space is developed. A controlled sensitivity experiment using data from Model Parameter Estimation Experiment (MOPEX) catchments in the United States showed that the developed error metric is more sensitive to biases in P compared to biases in estimates of E. Validating the framework using combinations of different satellite‐based estimates of P and E revealed that the framework succeeds in arriving at the same conclusions as a traditional validation method with regards to the quality of P and E data sets. The framework offers a physically consistent, parametrically efficient basis for the selection of remotely sensed P and E data sets for hydrologic studies. Due to lack of consideration for catchment storage in the formulation of Fu's equation, the developed error metric is limited to long temporal time scales. As a result, the error metric is capable of characterizing the bias in P and E data sets and not the variance.

This paper studies how streamflow predictability varies with basin characteristics. We introduce an index of basin complexity that is based on a model of least statistical complexity that is needed to reliably predict daily streamflow of the basin. We then relate it with climate, vegetation and soil characteristics of the basin. Daily streamflow is modeled using k nearest neighbor model of lagged streamflow that predicts next time step streamflow based on the occurrences of similar streamflow events from the past. In order to calculate basin complexity, we identify difficult streamflow events of the basin and then use Vapnik‐Chervonenkis generalization theory, which trades off model performance with Vapnik‐Chervonenkis dimension (i.e., a measure of model complexity), to find a k nearest neighbor model of appropriate complexity for predicting a difficult streamflow event of the basin. The average of selected model complexities corresponding to difficult events is then defined as the basin's complexity. Basin complexity of 412 Model Parameter Estimation Experiment basins from continental United States are then related with its six basin characteristics. All the characteristics have been derived from the Model Parameter Estimation Experiment database to represent climate, vegetation and soil characteristics of the basins in a concise manner. Results find that more complex basins that are drier have less seasonal rainfall, vegetation with more storage capacity (i.e., smaller 5‐week Normalized Difference Vegetation Index gradient), and faster responsive soils. The results reaffirm prior observations that minimum complexity that is required to model a basin depends on its climate and landscape characteristics (e.g., complex models do not perform well in dry basins).

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 10 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 postprocessed forecasts have better correlation with observation after Cop‐BMA application.

Climate change impact assessment on hydropower generation using multi-model climate ensemble

Abstract. Recent work suggests that a coupled effective energy and mass transfer (EEMT) term, which includes the energy associated with effective precipitation and primary production, may serve as a robust prediction parameter of critical zone structure and function. However, the models used to estimate EEMT have been solely based on long-term climatological data with little validation using direct empirical measures of energy, water, and carbon balances. Here we compare catchment-scale EEMT estimates generated using two distinct approaches: (1) EEMT modeled using the established methodology based on estimates of monthly effective precipitation and net primary production derived from climatological data, and (2) empirical catchment-scale EEMT estimated using data from 86 catchments of the Model Parameter Estimation Experiment (MOPEX) and MOD17A3 annual net primary production (NPP) product derived from Moderate Resolution Imaging Spectroradiometer (MODIS). Results indicated positive and significant linear correspondence (R2 = 0.75; P < 0.001) between model and empirical measures with an average root mean square error (RMSE) of 4.86 MJ m−2 yr−1. Modeled EEMT values were consistently greater than empirical measures of EEMT. Empirical catchment estimates of the energy associated with effective precipitation (EPPT) were calculated using a mass balance approach that accounts for water losses to quick surface runoff not accounted for in the climatologically modeled EPPT. Similarly, local controls on primary production such as solar radiation and nutrient limitation were not explicitly included in the climatologically based estimates of energy associated with primary production (EBIO), whereas these were captured in the remotely sensed MODIS NPP data. These differences likely explain the greater estimate of modeled EEMT relative to the empirical measures. There was significant positive correlation between catchment aridity and the fraction of EEMT partitioned into EBIO (FBIO), with an increase in FBIO as a fraction of the total as aridity increases and percentage of catchment woody plant cover decreases. In summary, the data indicated strong correspondence between model and empirical measures of EEMT with limited bias that agree well with other empirical measures of catchment energy and water partitioning and plant cover.

There is no consensus on how changes in both temperature and precipitation will affect regional vegetation. We investigated controls on hydrologic partitioning at the catchment scale across many different ecoregions, and compared the resulting estimates of catchment wetting and vaporization (evapotranspiration) to remotely sensed indices of vegetation greenness. The fraction of catchment wetting vaporized by plants, known as the Horton index, is strongly related to the ratio of available energy to available water at the Earth's surface, the aridity index. Here we show that the Horton index is also a function of catchment mean slope and elevation, and is thus related to landscape characteristics that control how much and how long water is retained in a catchment. We compared the power of the components of the water and energy balance, as well as landscape characteristics, to predict Normalized Difference Vegetation Index (NDVI), a surrogate for vegetation productivity, at 312 Model Parameter Estimation Experiment (MOPEX) catchments across the United States. Statistical analysis revealed that the Horton index provides more precision in predicting maximum annual NDVI for all catchments than mean annual precipitation, potential evapotranspiration, or their ratio, the aridity index. Models of vegetation productivity should emphasize plant‐available water, rather than just precipitation, by incorporating the interaction of climate and landscape. Major findings related to the Horton index are: (1) it is a catchment signature that is relatively constant from year‐to‐year; (2) it is related to specific landscape characteristics; (3) it can be used to create catchment typologies; and (4) it is related to overall catchment greenness.

Error measures for fuzzy linear regression: Monte Carlo simulation approach