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The uncertainty in flood frequency relations can be decreased by adding reconstructed historic flood events to the data set of measured annual maximum discharges. This study shows that an artificial neural network trained with a 1‐D/2‐D coupled hydraulic model is capable of reconstructing river floods with multiple dike breaches and inundations of the hinterland with high accuracy. The benefit of an artificial neural network is that it reduces computational times. With this network, the maximum discharge of the 1809 flood event of the Rhine River and its 95% confidence interval was reconstructed. The study shows that the trained artificial neural network is capable of reproducing the behavior of the hydraulic model correctly. The maximum discharge during the flood event was predicted with high accuracy even though the underlying input data are, due to the fact that the event occurred more than 200 years ago, uncertain. The confidence interval of the prediction was reduced by 43% compared to earlier predictions that did not use hydraulic models.

Satellite estimates of inland water quality have the potential to vastly expand our ability to observe and monitor the dynamics of large water bodies. For almost 50 years, we have been able to remotely sense key water quality constituents like total suspended sediment, dissolved organic carbon, chlorophyll a, and Secchi disk depth. Nonetheless, remote sensing of water quality is poorly integrated into inland water sciences, in part due to a lack of publicly available training data and a perception that remote estimates are unreliable. Remote sensing models of water quality can be improved by training and validation on larger data sets of coincident field and satellite observations, here called matchups. To facilitate model development and deeper integration of remote sensing into inland water science, we have built AquaSat, the largest such matchup data set ever assembled. AquaSat contains more than 600,000 matchups, covering 1984–2019, of ground-based total suspended sediment, dissolved organic carbon, chlorophyll a, and SDDSecchi disk depth measurements paired with spectral reflectance from Landsat 5, 7, and 8 collected within ±1 day of each other. To build AquaSat, we developed open source tools in R and Python and applied them to existing public data sets covering the contiguous United States, including the Water Quality Portal, LAGOS-NE, and the Landsat archive. In addition to publishing the data set, we are also publishing our full code architecture to facilitate expanding and improving AquaSat. We anticipate that this work will help make remote sensing of inland water accessible to more hydrologists, ecologists, and limnologists while facilitating novel data-driven approaches to monitoring and understanding critical water resources at large spatiotemporal scales.

This data set accompanies the manuscript ‘Velocity Field Estimation on Density-Driven Solute Transport With a Convolutional Neural Network’. Concentration fields are stored as portable pixel maps (.ppm) and flow fields are stored in the Middlebury .flo file format (http://vision.middlebury.edu/flow/code/flow-code/README.txt).

Accurate estimation of terrestrial evapotranspiration (E) is critical to understand the world's energy and water cycles. MOD16 is the core algorithm of the widely used global E data set (the Moderate Resolution Imaging Spectroradiometer [MODIS] E product). However, it exhibits considerable uncertainties in some regions. Based on the data from 175 flux towers, we identified the key parameters of the MOD16 algorithm using the Sobol' sensitivity analysis method across biomes. The output of the MOD16 algorithm was sensitive to eight parameters. Among them, beta, which is treated as a constant (0.2 kPa) across biomes in the original MOD16 algorithm, was identified as the parameter to which the algorithm was most sensitive. We used the differential-evolution Markov chain method to obtain the proper posterior distributions for each key parameter across a range of biomes. The values of the key parameters for the different biomes were accurately estimated by differential-evolution Markov chain in comparison with data from the flux towers. We then evaluated the performances of the original MOD16 and the optimized MOD16 and compared them at multiple spatial scales (i.e., site, catchment, and global). We obtained relatively consistent and more reliable E simulations using the optimized MOD16 at all three scales. In the future, more attention should be paid to uncertainties in the algorithm's structure and its parameterizations of soil moisture constraint, canopy resistance, and energy partitioning.

Machine learning (ML) algorithms are being increasingly used in Earth and Environmental modeling studies owing to the ever-increasing availability of diverse data sets and computational resources as well as advancement in ML algorithms. Despite advances in their predictive accuracy, the usefulness of ML algorithms for inference remains elusive. In this study, we employ two popular ML algorithms, artificial neural networks and random forest, to analyze a large data set of flood events across Germany with the goals to analyze their predictive accuracy and their usability to provide insights to hydrologic system functioning. The results of the ML algorithms are contrasted against a parametric approach based on multiple linear regression. For analysis, we employ a model-agnostic framework named Permuted Feature Importance to derive the influence of models' predictors. This allows us to compare the results of different algorithms for the first time in the context of hydrology. Our main findings are that (1) the ML models achieve higher prediction accuracy than linear regression, (2) the results reflect basic hydrological principles, but (3) further inference is hindered by the heterogeneity of results across algorithms. Thus, we conclude that the problem of equifinality as known from classical hydrological modeling also exists for ML and severely hampers its potential for inference. To account for the observed problems, we propose that when employing ML for inference, this should be made by using multiple algorithms and multiple methods, of which the latter should be embedded in a cross-validation routine.

Hydrological model calibration combining Earth observations and in situ measurements is a promising solution to overcome the limitations of the traditional streamflow-only calibration. However, combining multiple data sources in model calibration requires a meaningful integration of the data sets, which should harness their most reliable contents to avoid accumulation of their uncertainties and mislead the parameter estimation procedure. This study analyzes the improvement of model parameter selection by using only the spatial patterns of satellite remote sensing data, thereby ignoring their absolute values. Although satellite products are characterized by uncertainties, their most reliable key feature is the representation of spatial patterns, which is a unique and relevant source of information for distributed hydrological models. We propose a novel multivariate calibration framework exploiting spatial patterns and simultaneously incorporating streamflow and three satellite products (i.e., Global Land Evaporation Amsterdam Model [GLEAM] evaporation, European Space Agency Climate Change Initiative [ESA CCI] soil moisture, and Gravity Recovery and Climate Experiment [GRACE] terrestrial water storage). The Moderate Resolution Imaging Spectroradiometer (MODIS) land surface temperature data set is used for model evaluation. A bias-insensitive and multicomponent spatial pattern matching metric is developed to formulate a multiobjective function. The proposed multivariate calibration framework is tested with the mesoscale Hydrologic Model (mHM) and applied to the poorly gauged Volta River basin located in a predominantly semiarid climate in West Africa. Results of the multivariate calibration show that the decrease in performance for streamflow (?7%) and terrestrial water storage (?6%) is counterbalanced with an increase in performance for soil moisture (+105%) and evaporation (+26%). These results demonstrate that there are benefits in using satellite data sets, when suitably integrated in a robust model parametrization scheme.

Image-based methodologies, such as large scale particle image velocimetry (LSPIV) and particle tracking velocimetry (PTV), have increased our ability to noninvasively conduct streamflow measurements by affording spatially distributed observations at high temporal resolution. However, progress in optical methodologies has not been paralleled by the implementation of image-based approaches in environmental monitoring practice. We attribute this fact to the sensitivity of LSPIV, by far the most frequently adopted algorithm, to visibility conditions and to the occurrence of visible surface features. In this work, we test both LSPIV and PTV on a data set of 12 videos captured in a natural stream wherein artificial floaters are homogeneously and continuously deployed. Further, we apply both algorithms to a video of a high flow event on the Tiber River, Rome, Italy. In our application, we propose a modified PTV approach that only takes into account realistic trajectories. Based on our findings, LSPIV largely underestimates surface velocities with respect to PTV in both favorable (12 videos in a natural stream) and adverse (high flow event in the Tiber River) conditions. On the other hand, PTV is in closer agreement than LSPIV with benchmark velocities in both experimental settings. In addition, the accuracy of PTV estimations can be directly related to the transit of physical objects in the field of view, thus providing tangible data for uncertainty evaluation.

To enable operational flood forecasting and drought monitoring, reliable and consistent methods for precipitation interpolation are needed. Such methods need to deal with the deficiencies of sparse operational real-time data compared to quality-controlled offline data sources used in historical analyses. In particular, often only a fraction of the measurement network reports in near real-time. For this purpose, we present an interpolation method, generalized REGNIE (genRE), which makes use of climatological monthly background grids derived from existing gridded precipitation climatology data sets. We show how genRE can be used to mimic and extend climatological precipitation data sets in near real-time using (sparse) real-time measurement networks in the Rhine basin upstream of the Netherlands (approximately 160,000 km2). In the process, we create a 1.2 × 1.2 km transnational gridded hourly precipitation data set for the Rhine basin. Precipitation gauge data are collected, spatially interpolated for the period 1996-2015 with genRE and inverse-distance squared weighting (IDW), and then evaluated on the yearly and daily time scale against the HYRAS and EOBS climatological data sets. Hourly fields are compared qualitatively with RADOLAN radar-based precipitation estimates. Two sources of uncertainty are evaluated: station density and the impact of different background grids (HYRAS versus EOBS). The results show that the genRE method successfully mimics climatological precipitation data sets (HYRAS/EOBS) over daily, monthly, and yearly time frames. We conclude that genRE is a good interpolation method of choice for real-time operational use. genRE has the largest added value over IDW for cases with a low real-time station density and a high-resolution background grid.

In this work we investigate methods for gaining greater insight from hydrological model runs conducted for uncertainty quantification and model differentiation. We frame the sensitivity analysis questions in terms of the main purposes of sensitivity analysis: parameter prioritization, trend identification and interaction quantification. For parameter prioritization, we consider variance-based sensitivity measures, sensitivity indices based on the L1-norm, the Kuiper metric and the sensitivity indices of the DELSA methods. For trend identification, we investigate insights derived from graphing the one-way ANOVA sensitivity functions, the recently introduced CUSUNORO plots and derivative scatterplots. For interaction quantification, we consider information delivered by variance-based sensitivity indices. We rely on the so-called given-data principle, in which results from a set of model runs are used to perform a defined set of analyses. One avoids using specific designs for each insight, thus controlling the computational burden. The methodology is applied to a hydrological model of a river in Belgium simulated using the well established Framework for Understanding Structural Errors (FUSE) on five alternative configurations. The findings show that the integration of the chosen methods provide insights unavailable in most other analyses.

A high-resolution gridded daily precipitation data set was combined with a landslide inventory containing over 2000 events in the period 1972–2012 to analyze rainfall thresholds which lead to landsliding in Switzerland. We colocated triggering rainfall to landslides, developed distributions of triggering and nontriggering rainfall event properties, and determined rainfall thresholds and intensity-duration ID curves and validated their performance. The best predictive performance was obtained by the intensity-duration ID threshold curve, followed by peak daily intensity Imax and mean event intensity Imean. Event duration by itself had very low predictive power. A single country-wide threshold of Imax = 28 mm/d was extended into space by regionalization based on surface erodibility and local climate (mean daily precipitation). It was found that wetter local climate and lower erodibility led to significantly higher rainfall thresholds required to trigger landslides. However, we showed that the improvement in model performance due to regionalization was marginal and much lower than what can be achieved by having a high-quality landslide database. Reference cases in which the landslide locations and timing were randomized and the landslide sample size was reduced showed the sensitivity of the Imax rainfall threshold model. Jack-knife and cross-validation experiments demonstrated that the model was robust. The results reported here highlight the potential of using rainfall ID threshold curves and rainfall threshold values for predicting the occurrence of landslides on a country or regional scale with possible applications in landslide warning systems, even with daily data.

Although rainfall estimation employing microwave links from cellular telecommunication networks is recognized as a new promising measurement technique, its potential for long-term large-scale operational rainfall monitoring remains to be demonstrated. This study contributes to this endeavor by deriving a continuous series of rainfall maps from a large 2.5 year microwave link data set of, on average, 3383 links (2044 link paths) covering Netherlands (∼3.5 × 104 km2), a midlatitude country (∼5°E, ∼52°N) with a temperate climate. Maps are extensively verified against an independent gauge-adjusted radar rainfall data set for different temporal (15 min, 1 h, 1 day, 1 month) and spatial (0.9, 74 km2) scales. The usefulness of different steps in the rainfall retrieval algorithm, i.e., a wet-dry classification method and a filter to remove outliers, is systematically assessed. A novel dew filter is developed to correct for dew-induced wet antenna attenuation, which, although a relative underestimation of 6% to 9% is found, generally yields good results. The microwave link rainfall estimation technique performs well for the summer months (June, July, August), even outperforming interpolation of automatic rain gauge data (with a density of ∼1 gauge per 1000 km2), but large deviations are found for the winter months (December, January, February). These deviations are generally expected to be related to frozen or melting precipitation. Hence, our results show the potential of commercial microwave links for long-term large-scale operational rainfall monitoring.

The correct interpretation of ensemble information obtained from the parallel implementation of multiple land surface models (LSMs) requires information concerning the LSM ensemble's mutual error covariance. Here we propose a technique for obtaining such information using an instrumental variable (IV) regression approach and comparisons against a long-term surface soil moisture data set acquired from satellite remote sensing. Application of the approach to multimodel ensemble soil moisture output from Phase 2 of the North American Land Data Assimilation System (NLDAS-2) and European Space Agency (ESA) Soil Moisture (SM) Essential Climate Variable (ECV) data set allows for the calculation of optimal weighting coefficients for individual members of the NLDAS-2 LSM ensemble and a biased-minimized estimate of uncertainty in a deterministic soil moisture analysis derived via optimal averaging. As such, it provides key information required to accurately condition soil moisture expectations using information gleaned from a multimodel LSM ensemble. However, existing continuity and rescaling concerns surrounding the generation of long-term, satellite-based soil moisture products must likely be resolved before the proposed approach can be applied with full confidence.

Hydrology is rich in methods that use information theory to evaluate monitoring networks. Yet in most existing studies, only the available data set as a whole is used, which neglects the intraannual variability of the hydrological system. In this paper, we demonstrate how this variability can be considered by extending monitoring evaluation to subsets of the available data. Therefore, we separately evaluated time windows of fixed length, which were shifted through the data set, and successively extended time windows. We used basic information theory measures and a greedy ranking algorithm based on the criterion of maximum information/minimum redundancy. The network investigated monitored surface and groundwater levels at quarter-hourly intervals and was located at an artificially drained lowland site in the Spreewald region in north-east Germany. The results revealed that some of the monitoring stations were of value permanently while others were needed only temporally. The prevailing meteorological conditions, particularly the amount of precipitation, affected the degree of similarity between the water levels measured. The hydrological system tended to act more individually during periods of no or little rainfall. The optimal monitoring setup, its stability, and the monitoring effort necessary were influenced by the meteorological forcing. Altogether, the methodology presented can help achieve a monitoring network design that has a more even performance or covers the conditions of interest (e.g., floods or droughts) best.

Bayesian model averaging (BMA) ranks the plausibility of alternative conceptual models according to Bayes' theorem. A prior belief about each model's adequacy is updated to a posterior model probability based on the skill to reproduce observed data and on the principle of parsimony. The posterior model probabilities are then used as model weights for model ranking, selection, or averaging. Despite the statistically rigorous BMA procedure, model weights can become uncertain quantities due to measurement noise in the calibration data set or due to uncertainty in model input. Uncertain weights may in turn compromise the reliability of BMA results. We present a new statistical concept to investigate this weighting uncertainty, and thus, to assess the significance of model weights and the confidence in model ranking. Our concept is to resample the uncertain input or output data and then to analyze the induced variability in model weights. In the special case of weighting uncertainty due to measurement noise in the calibration data set, we interpret statistics of Bayesian model evidence to assess the distance of a model's performance from the theoretical upper limit. To illustrate our suggested approach, we investigate the reliability of soil-plant model selection following up on a study by Wohling et al. (2015). Results show that the BMA routine should be equipped with our suggested upgrade to (1) reveal the significant but otherwise undetected impact of measurement noise on model ranking results and (2) to decide whether the considered set of models should be extended with better performing alternatives.

© 2015. American Geophysical Union. All Rights Reserved. Experimental design and data collection constitute two main steps of the iterative research cycle (aka the scientific method). To help evaluate competing hypotheses, it is critical to ensure that the experimental design is appropriate and maximizes information retrieval from the system of interest. Scientific hypothesis testing is implemented by comparing plausible model structures (conceptual discrimination) and sets of predictions (predictive discrimination). This research presents a new Discrimination-Inference (DI) methodology to identify prospective data sets highly suitable for either conceptual or predictive discrimination. The DI methodology uses preposterior estimation techniques to evaluate the expected change in the conceptual or predictive probabilities, as measured by the Kullback-Leibler divergence. We present two case studies with increasing complexity to illustrate implementation of the DI for maximizing information withdrawal from a system of interest. The case studies show that highly informative data sets for conceptual discrimination are in general those for which between-model (conceptual) uncertainty is large relative to the within-model (parameter) uncertainty, and the redundancy between individual measurements in the set is minimized. The optimal data set differs if predictive, rather than conceptual, discrimination is the experimental design objective. Our results show that DI analyses highlight measurements that can be used to address critical uncertainties related to the prediction of interest. Finally, we find that the optimal data set for predictive discrimination is sensitive to the predictive grouping definition in ways that are not immediately apparent from inspection of the model structure and parameter values.

A Bayesian model averaging (BMA) framework is presented to evaluate the worth of different observation types and experimental design options for (1) more confidence in model selection and (2) for increased predictive reliability. These two modeling tasks are handled separately because model selection aims at identifying the most appropriate model with respect to a given calibration data set, while predictive reliability aims at reducing uncertainty in model predictions through constraining the plausible range of both models and model parameters. For that purpose, we pursue an optimal design of measurement framework that is based on BMA and that considers uncertainty in parameters, measurements, and model structures. We apply this framework to select between four crop models (the vegetation components of CERES, SUCROS, GECROS, and SPASS), which are coupled to identical routines for simulating soil carbon and nitrogen turnover, soil heat and nitrogen transport, and soil water movement. An ensemble of parameter realizations was generated for each model using Monte-Carlo simulation. We assess each model's plausibility by determining its posterior weight, which signifies the probability to have generated a given experimental data set. Several BMA analyses were conducted for different data packages with measurements of soil moisture, evapotranspiration (ETa), and leaf area index (LAI). The posterior weights resulting from the different BMA runs were compared to the weight distribution of a reference run with all data types to investigate the utility of different data packages and monitoring design options in identifying the most appropriate model in the ensemble. We found that different (combinations of) data types support different models and none of the four crop models outperforms all others under all data scenarios. The best model discrimination was observed for those data where the competing models disagree the most. The data worth for reducing prediction uncertainty depends on the prediction to be made. LAI data have the highest utility for predicting ETa, while soil moisture data are better for predicting soil water drainage. Our study illustrates, that BMA provides an objective framework for data worth analysis with respect to both model discrimination and model calibration for a wide range of applications.

We use a machine learning approach to seek an accurate, physically sound predictor, to estimate the mean velocity for open-channel flow when submerged arrays of rigid cylinders (model vegetation) are present. A genetic programming routine is used to find a robust relationship between relevant properties of the model vegetation and flow parameters. We use published data from laboratory experiments covering a broad range of conditions to obtain an equation that matches the performance of other predictors from recent literature in terms of accuracy, while showing a less complex structure. We also investigate how different criteria for data selection, as well as the size of the data set used to train the algorithm, influences the accuracy of the resulting predictors. Our results show that a proper use of Machine-Learning techniques does not only provide empirical correlations, but can yield physically sound models as representative of the physical processes involved. We provide a clear, thorough example of the application of GP, its advantages and shortcomings, to encourage the use of data-driven techniques as part of the data analysis process, and to address common misconceptions of machine learning as simple correlation techniques or physically senseless statistical analysis.

The WFDEI meteorological forcing data set has been generated using the same methodology as the widely used WATCH Forcing Data (WFD) by making use of the ERA-Interim reanalysis data. We discuss the specifics of how changes in the reanalysis and processing have led to improvement over the WFD. We attribute improvements in precipitation and wind speed to the latest reanalysis basis data and improved downward shortwave fluxes to the changes in the aerosol corrections. Covering 1979–2012, the WFDEI will allow more thorough comparisons of hydrological and Earth System model outputs with hydrologically and phenologically relevant satellite products than using the WFD.

The sustainability of the confined aquifer system in the San Luis Valley, Colorado is of utmost importance to the valley's agricultural economy. There is a dearth of hydraulic head measurements in the confined aquifer to which the current groundwater flow model can be calibrated. Here we investigate the extent to which spatially and temporally dense measurements of deformation from Interferometric Synthetic Aperture Radar (InSAR) data can be used to fill in spatial and temporal gaps in the head data set by calibrating the InSAR data with head at the monitoring well locations. We conduct this calibration at 11 wells where we expect sufficient deformation for reliable InSAR measurement, given the accepted level of uncertainty (∼1 cm). In the San Luis Valley, crop growth degrades the quality of the InSAR signal, which means that the high-quality deformation data may not be collocated with the wells. We use kriging to estimate the deformation directly at the well locations. We find that the calibration is valid at three well locations where the seasonal magnitude of the deformation is much larger than the uncertainty of the InSAR measurement. At these well locations, we predict head prior to and within the temporal sampling window of the head measurements. We find that 59% of the InSAR-predicted hydraulic head values agree with the measured values, within the uncertainty of the data. Given our success in extending the hydraulic head data temporally, the next step in our research is to use InSAR data to interpolate spatially between head measurements.

International audience; Analyzing the behavior of heavy precipitation, high temperatures, and extremes of other environmental variables has become an important research topic both for hydrologists and climatologists. Extreme value theory provides a well‐developed mathematical foundation to statistically model excesses above a high threshold. Practitioners often assume that those excesses approximately follow a generalized Pareto distribution. To infer the two parameters of this distribution, a variety of estimations has been proposed and studied. Among them, maximum likelihood estimation offers an elegant way to include covariates, but imposing an explicit form on the parameters dependence. When analyzing large data sets, this procedure can be too slow and sometimes produce aberrant values due to optimization problems. To overcome these drawbacks, a method based on probability weighted moments and Kernel regression is proposed, tested, and applied to a Swiss daily precipitation data set. The method is implemented as a freely available R package

In natural lakes, where thermal stratification hinders complete mixing, the theoretical value T0 of the water renewal time provides a low-order approximation to the time T37 when 37% of the original water is still present within the lake; this time could be operatively regarded as the actual value of the water renewal time. In this paper, we present a simple nonparametric model to estimate the age distribution of water within stratified natural lakes, taking into account fundamental aspects of its mass exchange and thermal evolution. This distribution provides a straightforward way to compute T37. The model is presented as a system of ordinary differential equations along with a MATLAB script for its numerical solution, so that it can be easily applied to lakes where a minimum of limnological data are available, without the need of extensive meteorological data set and modeling expertise that an hydrodynamic model would require to the same purpose. The case of a deep oligomictic Italian prealpine lake (Lake Iseo) is considered: after a positive comparison with the results obtained using a 1-D lake hydrodynamic model, the reiterated application to the available time series allows to approximate the water age probability distribution. This distribution is used to compute the actual value of the water renewal time, that resulted T37 = 1.6T0.

We explore the bankfull width (Wbf) versus drainage area (Ada) relationship across a range of climatic and geologic environments and ask (1) is the relationship between ln(Wbf) and ln(Ada) best described by a linear function and (2) can a reliable relationship be developed for predicting Wbf with Ada as the only independent variable. The principal data set for this study was compiled from regional curve studies and other reports that represent 1018 sites (1 m ≤ Wbf ≤ 110 m and 0.50 km2 ≤ Ada ≤ 22,000 km2) in the continental United States. Two additional data sets were used for validation. After dividing the data into small, medium, and large-size basins which, respectfully, correspond to Ada

Regional flood frequency analysis aims to estimate flood risk at sites where little or no hydrological data are available. The index-flood model is one of the commonly employed models for this purpose. In this model, the predicted value depends on the growth curve and its regional parameters. The latter are estimated as weighted averages of the at-site parameters. Traditional approaches are mainly based on site record lengths or region size to define these weights. Hence, they are not representative of the hydrological similarity between sites within a region. In addition, they are not defined to reach optimality in terms of model performance. To overcome these limitations, the present paper aims to propose a new optimal iterative weighting scheme to the index-flood model. The proposed approach is based on a number of elements: a statistical depth function to introduce similarity between sites, a weight function to amplify and control the depth values, an iterative procedure to improve estimation accuracy, and an optimization algorithm to objectively automate the choice of the weight function. A data set from the Island of Sicily (Italy) is used to compare the proposed approach with traditional ones. On the basis of the L-moments and using cluster analysis techniques, the studied region is subdivided into three homogeneous subregions. The results indicate that the proposed approach performs significantly better than traditional ones both in terms of relative bias and relative root mean squares error. The proposed approach allows identification of cross correlation in the region and provides a significant performance improvement.

[1] Statistical models relating anthropogenic modifications of the watershed landscape to alterations in streamflow are often plagued by heterogeneity in background watershed conditions and coinciding trends in climate that can complicate the interpretation of clear statistical relationships. This study introduces the use of panel regression as a modeling approach that can better accommodate basin heterogeneity and identify more robust signals between anthropogenic impacts on the watershed landscape and hydrologic response. Panel regression techniques pool multidimensional data recorded across individuals (i.e., watersheds) and through time to better characterize within- and between-variability in the hydrologic data set. The separate attribution of variability to both time and space dimensions enables the method to better identify response characteristics that are generalizable across watersheds. This study introduces in detail two broad classes of panel regression models (the fixed effects and random effects models) that may be particularly useful in the context of identifying and quantifying the impact of human-induced landscape alterations on hydrologic response. The technique is presented in a case study relating watershed urbanization to changes in the annual runoff coefficient for 19 watersheds in the Northeast United States. Comparisons are made against more standard cross-sectional and time-based regression analyses. The results show that the estimated relationship between urbanization and the annual runoff coefficient in this region is highly dependent on the dimensions of data examined (space or time) and model structure selected, with the most sophisticated and appropriate model suggesting that no significant relationship can be detected.

[1] Data splitting is an important step in the artificial neural network (ANN) development process, whereby the available data are divided into training, testing, and validation subsets to ensure good generalization ability of the model. Considering that only one split of the data is typically used when developing ANN models, data splitting has a significant impact on model performance, depending on which data are allocated to the three subsets. Therefore, it is important to find a data splitting method that consistently results in predictive validation errors that are representative of the predictive errors obtained over the full range of the available data. This paper addresses this issue by introducing a benchmarking approach for comparing different data splitting methods in terms of (1) bias, which is the difference between the expected validation performance over the entire data set and that obtained using a particular data splitting method and (2) variability, which is the spread of the validation errors obtained by repeated implementation of that method. The utility of the proposed approach is assessed on a number of well-known data splitting methods in the context of four water resources ANN modelling problems. The results obtained indicate that the proposed approach for comparing data splitting methods is more representative than the previous approach where a value of zero is used as the predictive performance benchmark, as it can avoid the selection of an over-optimistic data splitting method that under-represents extreme data in the validation set.

[1] Hydraulic and hydrologic modeling has been moving to larger spatial scales with increased spatial resolution, and such models require a global database of river widths and depths to facilitate accurate river flow routing. Hydraulic geometry relationships have a long history in estimating river channel characteristics as a function of discharge. A simple near-global database of bankfull widths and depths (along with confidence intervals) was developed based on hydraulic geometry equations and the HydroSHEDS hydrography data set. The bankfull width estimates were evaluated with widths derived from Landsat imagery for reaches of nine major rivers, showing errors ranging from 8 to 62% (correlation of 0.88), although it was difficult to verify whether the satellite observations corresponded to bankfull conditions. Bankfull depth estimates were compared with in situ measurements at sites in the Ohio and Willamette rivers, producing a mean error of 24%. The uncertainties in the derivation approach and a number of caveats are identified, and ways to improve the database in the future are discussed. Despite these limitations, this is the first global database that can be used directly in hydraulic models or as a set of constraints in model calibration.

WATER RESOURCES RESEARCH, VOL. 49, 7144–7149, doi:10.1002/wrcr.20498, 2013 Extended contingency table: Performance metrics for satellite observations and climate model simulations A. AghaKouchak 1 and A. Mehran 1 Received 21 May 2013; revised 29 July 2013; accepted 19 August 2013; published 7 October 2013. [ 1 ] Validation of gridded satellite observations and climate model simulations are fundamental to future improvements in retrieval algorithms and model developments. Among the metrics, the contingency table, which includes a number of categorical indices, is extensively used in evaluation studies. While the categorical indices offer invaluable information, they do not provide any insight into the volume of the variable detected correctly/incorrectly. In this study, the contingency table categorical metrics are extended to volumetric indices for evaluation of gridded data. The suggested indices include (a) Volumetric Hit Index (VHI): volume of correctly detected simulations relative to the volume of the correctly detected simulations and missed observations; (b) Volumetric False Alarm Ratio (VFAR): volume of false simulations relative to the sum of simulations; (c) Volumetric Miss Index (VMI): volume of missed observations relative to the sum of missed observations and correctly detected simulations; and (d) the Volumetric Critical Success Index (VCSI). The latter provides an overall measure of volumetric performance including volumetric hits, false alarms, and misses. First, using two synthetic time series, the volumetric indices are evaluated against the contingency table categorical metrics. Then, the volumetric indices are used to evaluate a gridded data set at the continental scale. The results show that the volumetric indices provide additional information beyond the commonly used categorical metrics that can be useful in evaluating gridded data sets. Citation: AghaKouchak, A., and A. Mehran (2013), Extended contingency table: Performance metrics for satellite observations and climate model simulations, Water Resour. Res., 49, 7144–7149, doi:10.1002/wrcr.20498. Introduction [ 2 ] Remotely sensed radar and satellite observations and climate model simulations are subject to uncertainties and biases arising from physical and algorithmic aspects. Evalua- tion and uncertainty quantification of remotely sensed data and climate model simulations are fundamental to scientific advancements, algorithm/model developments, and integra- tion of data into applications. For this reason, numerous studies are devoted to evaluation of remote sensing data [e.g., Anagnostou et al., 1998; AghaKouchak et al., 2010a; Turk et al., 2008; Norouzi et al., 2011; Jackson et al., 2005; Pinker et al., 2009; Dorigo et al., 2010; AghaKouchak et al., 2010b; Mehran and AghaKouchak, 2013], and climate model simulations [e.g., Phillips and Gleckler, 2006; Jiang et al., 2012; Feddema et al., 2005; Liepert and Previdi, 2012] versus gridded ground-based observations. [ 3 ] Recently, several efforts are devoted to development of metrics and tools for validation of weather and climate Department of Civil and Environmental Engineering, University of California Irvine, Irvine, California, USA. Corresponding author: A. AghaKouchak, University of California Irvine, E4130 Engineering Gateway, Irvine, CA 92697-2175, USA. (amir.a@uci.edu) ©2013. American Geophysical Union. All Rights Reserved. 0043-1397/13/10.1002/wrcr.20498 models as well as satellite observations. Gleckler et al. [2008] suggested several performance metrics for validation of historical climate model simulations. Gilleland [2013] proposed the spatial prediction comparison test for evalua- tion of precipitation forecasts. AghaKouchak et al. [2011b] developed several indices for evaluation of high quantiles of satellite precipitation observations. Entekhabi et al. [2010] introduced a number of metrics for evaluation of remotely sensed soil moisture observations. Hossain and Huffman [2008] recommended a set of spatial, retrieval, and temporal error metrics for satellite data sets that can advance hydro- logic applications. Gebremichael [2010] outlined a frame- work for validating satellite data sets using ground-based observations. A number of geometrical and object-oriented metrics are also proposed for spatial validation and verifica- tion (e.g., Davis et al., 2009; AghaKouchak et al., 2011a; Brown et al., 2004]. [ 4 ] Among the metrics, the contingency table [Wilks, 2006] which includes a number of categorical indices is extensively used in evaluation studies [e.g., Behrangi et al., 2011; Haile et al., 2012; Hao et al., 2013; Gourley et al., 2012; Hirpa et al., 2010; Anagnostou et al., 2010]. The contingency table is used to analyze or validate the rela- tionship between two categorical variables and is the cate- gorical equivalent of the scatterplot. The contingency table metrics describe whether simulations or remote sensing observations (hereafter, SIM) hit or miss the reference observations (hereafter, OBS) and/or lead to false estimates

[1] Hydrodynamic modeling of lakes requires an extensive amount of data that must often be measured far from the shore and throughout the water column. Accordingly, long-term comprehensive data sets for lakes are relatively rare. Lake Iseo is a deep prealpine lake, which we have monitored since 1995 on a monthly basis, collecting high-resolution data since 2011. These measurements were complemented with additional time series from surrounding meteorological stations and a comprehensive data set has been gathered for the period 1995–2012. This can be used, among other things, to test the capabilities of models to investigate the dynamics of a deep lake.

Runoff prediction in ungauged catchments is a recurrent problem in hydrology. Conceptual models are usually calibrated by defining a feasible parameter range and then conditioning parameter sets on observed system responses, e.g., streamflow. In ungauged catchments, several studies condition models on regionalized response signatures, such as runoff ratio or base flow index, using a Bayesian procedure. In this technical note, the Model Parameter Estimation Experiment (MOPEX) data set is used to explore the impact on model performance of assumptions made about the prior distribution. In particular, the common assumption of uniform prior on parameters is shown to be unsuitable. This is because the uniform prior on parameters maps onto skewed response signature priors that can counteract the valuable information gained from the regionalization. To address this issue, we test a methodological development based on an initial transformation of the uniform prior on parameters into a prior that maps to a uniform response signature distribution. We demonstrate that this method contributes to improved estimation of the response signatures.

] This paper addresses the signatures of catchment geomorphology on base flow recessioncurves. Its relevance relates to the implied predictability of base flow features, which arecentral to catchment-scale transport processes and to ecohydrological function. Movingfrom the classical recession curve analysis method, originally applied in the Finger LakesRegion of New York, a large set of recession curves has been analyzed from Swissstreamflow data. For these catchments, digital elevation models have been preciselyanalyzed and a method aimed at the geomorphic origins of recession curves has beenapplied to the Swiss data set. The method links river network morphology, epitomized bytime-varying distribution of contributing channel sites, with the classic parameterization ofrecession events. This is done by assimilating two scaling exponents, and b

[1] A 11 year data set of spatially distributed snow water equivalent (SWE) was used to inform a quantitative, near-optimal sensor placement methodology for real-time SWE estimation in the American River basin of California. Rank-based clustering was compared with geographically based clustering (subbasin delineation) to determine the existence of stationary covariance structures within the overall SWE data set. The historical SWE data, at 500 × 500 m resolution, were split into 8 years of training and 3 years of validation data. Within each cluster, a quantitative sensor-placement algorithm, based on maximizing the metric of mutual information, was implemented and compared with random placement. Gaussian process models were then built from validation data points selected by the algorithm to evaluate the efficacy of each placement approach. Rank-based clusters remained stable interannually, suggesting that rankings of pixel-by-pixel SWE exhibit stationary features that can be exploited by a sensor-placement algorithm, yielding a 200 mm average root-mean-square error (RMSE) for 20 randomly selected sensing locations. This outperformed geographic and basin-wide placement approaches, which generated 460 and 290 mm RMSE, respectively. Mutual information-based sampling provided the best placement strategy, improving RMSE between 0 and 100 mm compared with random placements. Increasing the number of rank-based clusters consistently lowered average RMSE from 400 mm for 1 cluster to 175 mm for 8 clusters, for 20 total sensors placed. To optimize sensor placement, we recommend a strategy that couples rank-based clustering with mutual information-based sampling design.

[1] The paper introduces a logical extension to data-based mechanistic (DBM) modeling, which provides hypothetico-inductive (HI-DBM) bridge between conceptual models, derived in a hypothetico-deductive manner, and the DBM model identified inductively from the same time-series data. The approach is illustrated by a quite detailed example of HI-DBM analysis applied to the well-known Leaf River data set and the associated HyMOD conceptual model. The HI-DBM model significantly improves the explanation of the Leaf River data and enhances the performance of the original DBM model. However, on the basis of various diagnostic tests, including recursive time-variable and state-dependent parameter estimation, it is suggested that the model should be capable of further improvement, particularly as regards the conceptual effective rainfall mechanism, which is based on the probability distributed model hypothesis. In order to verify the efficacy of the HI-DBM analysis in a situation where the actual model generating the data is completely known, the analysis is also applied to a stochastic simulation model based on a modified HyMOD model.

[1] Predictions of daily flows in ungauged streams frequently rely on index gauges, where the timing of the daily flow at the index gauge is assumed to be similar to that in the ungauged stream. When some limited flow measurements are available at the ungauged sites, the strength of correlation between these flows and candidate index gauges can inform the selection of the index gauges. Here the use of the correlation of daily flows to select index gauges is systematically evaluated using a large flow data set from the Ohio River Valley, USA. Then, a novel method is introduced for predicting the strength with which daily flows at different gauges are correlated with daily flow at a completely ungauged site, using the physical characteristics of the ungauged site. The index gauges can then be selected based on these predicted correlations. The analysis indicates that this new method provides a means of identifying index sites that will yield a desired level of accuracy in flow predictions at ungauged locations. The ungauged sites at which sufficient index gauges are not available are also identified, and flow predictions are not calculated for these sites. Using this new method improves the overall accuracy of predicted flows, relative to existing methods.

This paper presents a data set that describes the spatial and temporal variability of soil moisture within the 6 ha Nerrigundah catchment, located in a temperate region of eastern Australia. The data set includes high-resolution elevation data; high- resolution (20 m) near-surface soil moisture maps; soil moisture profile measurements at 13 locations, with one being applicable for one-dimensional modeling; soil moisture measurements from four different measurement devices at a single location; soil temperature profile measurements; soil heat flux and supporting meteorological measurements, including data obtained with two pluviometers and four collecting rain gauges; surface roughness measurements; soil information for 19 locations, including field measurements of saturated hydraulic conductivity; and catchment runoff measurements. These data are available on the World Wide Web at http://www.civag.unimelb.edu.au/ jwalker/data/nerrigundah.

Fuzzy logic (FL) was applied to simulate latent heat fluxes of six coniferous forests. The goal was to test the application possibilities of fuzzy logic and to evaluate the information that could be derived from it. The data set consisted of five forests of the Euroflux project and a set of the Douglas fir Speulderbos, 1 year before and 1 year after a thinning. A set of models was compared to their performance and interpretability: a general FL model, FL models for the 2 years of the Speulderbos, and a forest growth model parameterized for Douglas fir. The performance of the FL models was close to optimal. The rules of the FL models made objective model comparison possible and showed a change in the sensitivity to vapor pressure deficit of the Speulderbos. Fuzzy logic proved to be a very promising method for top down modeling of forest gas exchange, systematic model evaluation, and model simplification.

Rainfall products derived from radar data often consume vast amounts of storage space and are time-consuming to analyze. Shipborne radar data collected during the Tropical Ocean Global Atmosphere (TOGA) Coupled Ocean-Atmosphere Response Experiment (COARE) provide an extensive data set to examine rainfall characteristics in the tropical Western Pacific Ocean. TOGA COARE shipborne radar-rainfall products have been organized into a database with efficient storage and access time characteristics. Software for reading and visually browsing the data has been developed and made available to provide users with a convenient method to study the data set.

This study compares published cartometric and photogrammetric digital elevation models (DEMs) of various grid spacings with a ground truth data set, obtained by ground survey, and studies the implications of these differences on key hydrologic statistics. Inferred catchment sizes and stream networks from published DEMs were found to be significantly different than those from the ground truth in most instances. Furthermore, the width functions and cumulative area relationships determined from the published DEMs were found to fall consistently outside the 90% confidence limits determined from the ground truth for more than 60% of the relationship, suggesting that these hydrologic properties are poorly estimated from published DEMs. However, the slope-area relationships determined from published DEMs were found to be less sensitive to catchment shape, size, and stream network, with the relationship falling outside the 90% confidence limits for less than 40% of the relationship for all catchments identified from the published DEMs. A published relationship linking the horizontal resolution with the vertical accuracy of the DEM was tested, predicting a horizontal resolution of about 10 m for the published DEMs tested.