The role of hydrological modelling uncertainties in climate change impact assessments of Irish river catchments

This study attempts to assess the uncertainty in the hydrological impacts of climate change using a multi-model approach combining multiple emission scenarios, GCMs and conceptual rainfall-runoff models to quantify uncertainty in future impacts at the catchment scale. The uncertainties associated with hydrological models have traditionally been given less attention in impact assessments until relatively recently. In order to examine the role of hydrological model uncertainty (parameter and structural uncertainty) in climate change impact studies a multi-model approach based on the Generalised Likelihood Uncertainty Estimation (GLUE) and Bayesian Model Averaging (BMA) methods is presented. Six sets of regionalised climate scenarios derived from three GCMs, two emission scenarios, and four conceptual hydrological models were used within the GLUE framework to define the uncertainty envelop for future estimates of stream flow, while the GLUE output is also post processed using BMA, where the probability density function from each model at any given time is modelled by a gamma distribution with heteroscedastic variance. The investigation on four Irish catchments shows that the role of hydrological model uncertainty is remarkably high and should therefore be routinely considered in impact studies. Although, the GLUE and BMA approaches used here differ fundamentally in their underlying philosophy and representation of error, both methods show comparable performance in terms of ensemble spread and predictive coverage. Moreover, the median prediction for future stream flow shows progressive increases of winter discharge and progressive decreases in summer discharge over the coming century.     

Importance of geological information for assessing drain flow in a Danish till landscape

There has, in recent years, been an increasing interest in developing nutrient load mitigation measures focussing on tile drains. To plan the location of such tile drain measures, it is important to know where in the landscape drain flow is generated and to understand the key factors governing drain flow dynamics. In the present study, we test two approaches to assess spatial patterns in drain flow generation and thereby assess the importance of including geological information. The approaches are the widely used topographical wetness index (TWI), based solely on elevation data, and hydrological models that include the subsurface geology. We set‐up an ensemble of 20 hydrological models based on 20 stochastically generated geological models to predict drain flow dynamics in the clay till Norsminde catchment in Denmark and test the results against TWI. We find that the hydrological models predict observed daily drain flow reasonably well. High drain flow volumes were found in stream valleys and in wetlands and lower drain flow volumes in the more hilly parts of the catchment. In spite of the apparent connection to the landscape, there was no statistically significant correlation between TWI and drain flow at grid scale (100 × 100 m). TWI was therefore not found to be a sufficient index on its own to assess where drain flow is generated, especially in the highlands of the catchment. The geology below 3 m was found to have a large impact on the drain flow, and correlations between sand percentage in the subsurface geology and drain flow volume were found to be statistically significant. Geological uncertainty therefore give rise to uncertainty on simulated drain flow, and this uncertainty was found to be high at the model grid scale but decreasing with increasing scale.     

A data assimilation approach to discharge estimation from space

River discharge is currently monitored by a diminishing network of gauges, which provide a spatially incomplete picture of global discharges. This study assimilated water level information derived from a fused satellite Synthetic Aperture Radar (SAR) image and digital terrain model (DTM) with simulations from a coupled hydrological and hydrodynamic model to estimate discharge in an un‐gauged basin scenario. Assimilating water level measurements led to a 79% reduction in ensemble discharge uncertainty over the coupled hydrological hydrodynamic model alone. Measurement bias was evident, but the method still provided a means of improving estimates of discharge for high flows. The study demonstrates the potential of currently available synthetic aperture radar imagery to reduce discharge uncertainty in un‐gauged basins when combined with model simulations in a data assimilation framework, where sufficient topographic data are available. The work is timely because in the near future the launch of satellite radar missions will lead to a significant increase in the volume of data available for space‐borne discharge estimation. Copyright © 2009 John Wiley & Sons, Ltd.     

Impacts of model initialization on an integrated surface water–groundwater model

Integrated hydrologic models characterize catchment responses by coupling the subsurface flow with land surface processes. One of the major areas of uncertainty in such models is the specification of the initial condition and its influence on subsequent simulations. A key challenge in model initialization is that it requires spatially distributed information on model states, groundwater levels and soil moisture, even when such data are not routinely available. Here, the impact of uncertainty in initial condition was explored across a 208 km² catchment in Denmark using the ParFlow.CLM model. The initialization impact was assessed under two meteorological conditions (wet vs dry) using five depth to water table and soil moisture distributions obtained from various equilibrium states (thermal, root zone, discharge, saturated and unsaturated zone equilibrium) during the model spin‐up. Each of these equilibrium states correspond to varying computation times to achieve stability in a particular aspect of the system state. Results identified particular sensitivity in modelled recharge and stream flow to the different initializations, but reduced sensitivity in modelled energy fluxes. Analysis also suggests that to simulate a year that is wetter than the spin‐up period, an initialization based on discharge equilibrium is adequate to capture the direction and magnitude of surface water–groundwater exchanges. For a drier or hydrologically similar year to the spin‐up period, an initialization based on groundwater equilibrium is required. Variability of monthly subsurface storage changes and discharge bias at the scale of a hydrological event show that the initialization impacts do not diminish as the simulations progress, highlighting the importance of robust and accurate initialization in capturing surface water–groundwater dynamics. Copyright © 2015 John Wiley & Sons, Ltd.     

Using internal catchment information to reduce the uncertainty of discharge and baseflow predictions

The semi-distributed hydrological model TOPMODEL was tested with data from the Can Vila research basin (Vallcebre) in order to verify its adequacy for simulating runoff and the relative contributions from saturated overland flow and groundwater flow. After a test of the overall performance of the model, only data from a wet period were selected for this work. The test was performed using the GLUE method. The model was conditioned on continuous discharge and water table records. Furthermore, point measurements of recession flow simultaneous with water table depth and the extent of saturated areas were used to condition the distributions of the more relevant parameters, using new or updated evaluation measures. A wide range of parameter sets provided acceptable results for flow simulation when the model was conditioned on flow data alone, and the uncertainty of prediction of the contribution from groundwater was extremely large. However, conditioning on water table records and the distribution of parameters obtained from point observations strongly reduced the uncertainty of predictions for both stream flow and groundwater contribution.     

A comparison of helicopter‐borne electromagnetic systems for hydrogeologic studies

The increased application of airborne electromagnetic surveys to hydrogeological studies is driving a demand for data that can consistently be inverted for accurate subsurface resistivity structure from the near surface to depths of several hundred metres. We present an evaluation of three commercial airborne electromagnetic systems over two test blocks in western Nebraska, USA. The selected test blocks are representative of shallow and deep alluvial aquifer systems with low groundwater salinity and an electrically conductive base of aquifer. The aquifer units show significant lithologic heterogeneity and include both modern and ancient river systems. We compared the various data sets to one another and inverted resistivity models to borehole lithology and to ground geophysical models. We find distinct differences among the airborne electromagnetic systems as regards the spatial resolution of models, the depth of investigation, and the ability to recover near‐surface resistivity variations. We further identify systematic biases in some data sets, which we attribute to incomplete or inexact calibration or compensation procedures.     

Slopes of an airborne electromagnetic resistivity model interpolated jointly with borehole data for 3D geological modelling

We investigate a novel way to introduce resistivity models deriving from airborne electromagnetic surveys into regional geological modelling. Standard geometrical geological modelling can be strengthened using geophysical data. Here, we propose to extract information contained in a resistivity model in the form of local slopes that constrain the modelling of geological interfaces. The proposed method is illustrated on an airborne electromagnetic survey conducted in the region of Courtenay in France. First, a resistivity contrast corresponding to the clay/chalk interface was interpreted confronting the electromagnetic soundings to boreholes. Slopes were then sampled on this geophysical model and jointly interpolated with the clay/chalk interface documented in boreholes using an implicit 3D potential‐field method. In order to evaluate this new joint geophysical–geological model, its accuracy was compared with that of both pure geological and pure geophysical models for various borehole configurations. The proposed joint modelling yields the most accurate clay/chalk interface whatever the number and location of boreholes taken into account for modelling and validation. Compared with standard geological modelling, the approach introduces in between boreholes geometrical information derived from geophysical results. Compared with conventional resistivity interpretation of the geophysical model, it reduces drift effects and honours the boreholes. The method therefore improves what is commonly obtained with geological or geophysical data separately, making it very attractive for robust 3D geological modelling of the subsurface.     

Hydrological modelling uncertainty analysis for different flow quantiles: a case study in two hydro-geographically different watersheds

This study focuses on analysis of hydrological model parameter uncertainty at varying sub-basin spatial scales. It was found that the variation in sub-basin spatial scale had little influence on the entire flow simulations. However, the different sub-basin spatial scales had a significant impact on the reproduction of the flow quantiles. The coarser sub-basin spatial scale provided a better coverage of most prediction uncertainty in observations. However, the finer sub-basin spatial scale produced the best single simulation output closer to the observations. In general, the optimal sub-basin spatial scales (ratio to the entire watershed size) in the two test watersheds were found to be in the ranges 14–19% and 2–4% for good simulation of high and low flows, respectively. It is therefore worthwhile to put more effort into reproducing different flow quantiles by investigating an appropriate sub-basin spatial scale.     

Regional‐scale mapping of groundwater discharge zones using thermal satellite imagery

Mapping groundwater discharge zones at broad spatial scales remains a challenge, particularly in data sparse regions. We applied a regional scale mapping approach based on thermal remote sensing to map discharge zones in a complex watershed with a broad diversity of geological materials, land cover and topographic variation situated within the Prairie Parkland of northern Alberta, Canada. We acquired winter thermal imagery from the USGS Landsat archive to demonstrate the utility of this data source for applications that can complement both scientific and management programs. We showed that the thermally determined potential discharge areas were corroborated with hydrological (spring locations) and chemical (conservative tracers of groundwater) data. This study demonstrates how thermal remote sensing can form part of a comprehensive mapping framework to investigate groundwater resources over broad spatial scales. Copyright © 2013 John Wiley & Sons, Ltd.     

Relative model score: a scoring rule for evaluating ensemble simulations with application to microbial soil respiration modeling

This paper defines a new scoring rule, namely relative model score (RMS), for evaluating ensemble simulations of environmental models. RMS implicitly incorporates the measures of ensemble mean accuracy, prediction interval precision, and prediction interval reliability for evaluating the overall model predictive performance. RMS is numerically evaluated from the probability density functions of ensemble simulations given by individual models or several models via model averaging. We demonstrate the advantages of using RMS through an example of soil respiration modeling. The example considers two alternative models with different fidelity, and for each model Bayesian inverse modeling is conducted using two different likelihood functions. This gives four single-model ensembles of model simulations. For each likelihood function, Bayesian model averaging is applied to the ensemble simulations of the two models, resulting in two multi-model prediction ensembles. Predictive performance for these ensembles is evaluated using various scoring rules. Results show that RMS outperforms the commonly used scoring rules of log-score, pseudo Bayes factor based on Bayesian model evidence (BME), and continuous ranked probability score (CRPS). RMS avoids the problem of rounding error specific to log-score. Being applicable to any likelihood functions, RMS has broader applicability than BME that is only applicable to the same likelihood function of multiple models. By directly considering the relative score of candidate models at each cross-validation datum, RMS results in more plausible model ranking than CRPS. Therefore, RMS is considered as a robust scoring rule for evaluating predictive performance of single-model and multi-model prediction ensembles.     

Constructing the Apparent Geological Model by Fusing Surface Resistivity Survey and Borehole Records

We constructed an apparent geological model with resistivity data from surface resistivity surveys. We developed a data fusion approach by integrating dense electrical resistivity measurements collected with Schlumberger arrays and wellbore logs. This approach includes an optimization algorithm and a geostatistic interpolation method. We first generated an apparent formation factor model from the surface resistivity measurements and groundwater resistivity records with an inverse distance method. We then converted the model into a geology model with the optimized judgment criteria from the algorithms relating the apparent formation factors to the borehole geology. We also employed a non-parametric bootstrap method to analyze the uncertainty of the predicted sediment types, and the predictive uncertainties of clay, gravel, and sand were less than 5%. Overall, our model is capable of capturing the spatial features of the sediment types. More importantly, this approach can be arranged in a self-updated sequence to enable adjustments to the model to accommodate newly collected core records or geophysical data. This approach yields a more detailed apparent geological model for use in future groundwater simulations, which is of benefit to multi-discipline studies.     

Spatial uncertainty in bias corrected climate change projections and hydrogeological impacts

The question of which climate model bias correction methods and spatial scales for correction are optimal for both projecting future hydrological changes as well as removing initial model bias has so far received little attention. For 11 climate models (CMs), or GCM/RCM – Global/Regional Climate Model pairing, this paper analyses the relationship between complexity and robustness of three distribution‐based scaling (DBS) bias correction methods applied to daily precipitation at various spatial scales. Hydrological simulations are forced by CM inputs to assess the spatial uncertainty of groundwater head and stream discharge given the various DBS methods. A unique metric is devised, which allows for comparison of spatial variability in climate model bias and projected change in precipitation. It is found that the spatial variability in climate model bias is larger than in the climate change signals. The magnitude of spatial bias seen in precipitation inputs does not necessarily correspond to the magnitude of biases seen in hydrological outputs. Variables that integrate basin responses over time and space are more sensitive to mean spatial biases and less so on extremes. Hydrological simulations forced by the least parameterized DBS approach show the highest error in mean and maximum groundwater heads; however, the most highly parameterised DBS approach shows less robustness in future periods compared with the reference period it was trained in. For hydrological impacts studies, choice of bias correction method should depend on the spatial scale at which hydrological impacts variables are required and whether CM initial bias is spatially uniform or spatially varying. Copyright © 2015 John Wiley & Sons, Ltd.     

Observational and predictive uncertainties for multiple variables in a spatially distributed hydrological model

In this study, uncertainty in model input data (precipitation) and parameters is propagated through a physically based, spatially distributed hydrological model based on the MIKE SHE code. Precipitation uncertainty is accounted for using an ensemble of daily rainfall fields that incorporate four different sources of uncertainty, whereas parameter uncertainty is considered using Latin hypercube sampling. Model predictive uncertainty is assessed for multiple simulated hydrological variables (discharge, groundwater head, evapotranspiration, and soil moisture). Utilizing an extensive set of observational data, effective observational uncertainties for each hydrological variable are assessed. Considering not only model predictive uncertainty but also effective observational uncertainty leads to a notable increase in the number of instances, for which model simulation and observations are in good agreement (e.g., 47% vs. 91% for discharge and 0% vs. 98% for soil moisture). Effective observational uncertainty is in several cases larger than model predictive uncertainty. We conclude that the use of precipitation uncertainty with a realistic spatio‐temporal correlation structure, analyses of multiple variables with different spatial support, and the consideration of observational uncertainty are crucial for adequately evaluating the performance of physically based, spatially distributed hydrological models.     

Constraining complex aquifer geometry with geophysics (2-D ERT and MRS measurements) for stochastic modelling of groundwater flow

Stochastic modelling is a useful way of simulating complex hard-rock aquifers as hydrological properties (permeability, porosity etc.) can be described using random variables with known statistics. However, very few studies have assessed the influence of topological uncertainty (i.e. the variability of thickness of conductive zones in the aquifer), probably because it is not easy to retrieve accurate statistics of the aquifer geometry, especially in hard rock context. In this paper, we assessed the potential of using geophysical surveys to describe the geometry of a hard rock-aquifer in a stochastic modelling framework.The study site was a small experimental watershed in South India, where the aquifer consisted of a clayey to loamy–sandy zone (regolith) underlain by a conductive fissured rock layer (protolith) and the unweathered gneiss (bedrock) at the bottom. The spatial variability of the thickness of the regolith and fissured layers was estimated by electrical resistivity tomography (ERT) profiles, which were performed along a few cross sections in the watershed. For stochastic analysis using Monte Carlo simulation, the generated random layer thickness was made conditional to the available data from the geophysics. In order to simulate steady state flow in the irregular domain with variable geometry, we used an isoparametric finite element method to discretize the flow equation over an unstructured grid with irregular hexahedral elements.The results indicated that the spatial variability of the layer thickness had a significant effect on reducing the simulated effective steady seepage flux and that using the conditional simulations reduced the uncertainty of the simulated seepage flux.As a conclusion, combining information on the aquifer geometry obtained from geophysical surveys with stochastic modelling is a promising methodology to improve the simulation of groundwater flow in complex hard-rock aquifers.     

A methodology for quantifying the value of spatial information for dynamic Earth problems

We develop a methodology for assessing the value of information (VOI) from spatial data for groundwater decisions. Two sources of uncertainty are the focus of this VOI methodology: the spatial heterogeneity (how it influences the hydrogeologic response of interest) and the reliability of geophysical data (how they provide information about the spatial heterogeneity). An existing groundwater situation motivates and in turn determines the scope of this research. The objectives of this work are to (1) represent the uncertainty of the dynamic hydrogeologic response due to spatial heterogeneity, (2) provide a quantitative measure for how well a particular information reveals this heterogeneity (the uncertainty of the information) and (3) use both of these to propose a VOI workflow for spatial decisions and spatial data. The uncertainty of the hydraulic response is calculated using many Earth models that are consistent with the a priori geologic information. The information uncertainty is achieved quantitatively through Monte Carlo integration and geostatistical simulation. Two VOI results are calculated which demonstrate that a higher VOI occurs when the geophysical attribute (the data) better discriminates between geological indicators. Although geophysical data can only indirectly measure static properties that may influence the dynamic response, this transferable methodology provides a framework to estimate the value of spatial data given a particular decision scenario.     

Probabilistic and ensemble simulation approaches for input uncertainty quantification of artificial neural network hydrological models

Artificial neural network (ANN) has been demonstrated to be a promising modelling tool for the improved prediction/forecasting of hydrological variables. However, the quantification of uncertainty in ANN is a major issue, as high uncertainty would hinder the reliable application of these models. While several sources have been ascribed, the quantification of input uncertainty in ANN has received little attention. The reason is that each measured input quantity is likely to vary uniquely, which prevents quantification of a reliable prediction uncertainty. In this paper, an optimization method, which integrates probabilistic and ensemble simulation approaches, is proposed for the quantification of input uncertainty of ANN models. The proposed approach is demonstrated through rainfall-runoff modelling for the Leaf River watershed, USA. The results suggest that ignoring explicit quantification of input uncertainty leads to under/over estimation of model prediction uncertainty. It also facilitates identification of appropriate model parameters for better characterizing the hydrological processes.     

Calibration of high-resolution geophysical data with tracer test measurements to improve hydrological predictions

Relationships between porosity and hydraulic conductivity tend to be strongly scale- and site-dependent and are thus very difficult to establish. As a result, hydraulic conductivity distributions inferred from geophysically derived porosity models must be calibrated using some measurement of aquifer response. This type of calibration is potentially very valuable as it may allow for transport predictions within the considered hydrological unit at locations where only geophysical measurements are available, thus reducing the number of well tests required and thereby the costs of management and remediation. Here, we explore this concept through a series of numerical experiments. Considering the case of porosity characterization in saturated heterogeneous aquifers using crosshole ground-penetrating radar and borehole porosity log data, we use tracer test measurements to calibrate a relationship between porosity and hydraulic conductivity that allows the best prediction of the observed hydrological behavior. To examine the validity and effectiveness of the obtained relationship, we examine its performance at alternate locations not used in the calibration procedure. Our results indicate that this methodology allows us to obtain remarkably reliable hydrological predictions throughout the considered hydrological unit based on the geophysical data only. This was also found to be the case when significant uncertainty was considered in the underlying relationship between porosity and hydraulic conductivity.     

Copula‐based uncertainty modelling: application to multisensor precipitation estimates

The multisensor precipitation estimates (MPE) data, available in hourly temporal and 4 km × 4 km spatial resolution, are produced by the National Weather Service and mosaicked as a national product known as Stage IV. The MPE products have a significant advantage over rain gauge measurements due to their ability to capture spatial variability of rainfall. However, the advantages are limited by complications related to the indirect nature of remotely sensed precipitation estimates. Previous studies confirm that efforts are required to determine the accuracy of MPE and their associated uncertainties for future use in hydrological and climate studies. So far, various approaches and extensive research have been undertaken to develop an uncertainty model. In this paper, an ensemble generator is presented for MPE products that can be used to evaluate the uncertainty of rainfall estimates. Two different elliptical copula families, namely, Gaussian and t‐copula are used for simulations. The results indicate that using t‐copula may have significant advantages over the well‐known Gaussian copula particularly with respect to extremes. Overall, the model in which t‐copula was used for simulation successfully generated rainfall ensembles with similar characteristics to those of the ground reference measurements. Copyright © 2010 John Wiley & Sons, Ltd.     

Internal catchment process simulation in a snow‐dominated basin: performance evaluation with spatiotemporally variable runoff generation and groundwater dynamics

Hydrologic models have increasingly been used in forest hydrology to overcome the limitations of paired watershed experiments, where vegetative recovery and natural variability obscure the inferences and conclusions that can be drawn from such studies. Models are also plagued by uncertainty, however, and parameter equifinality is a common concern. Physically‐based, spatially‐distributed hydrologic models must therefore be tested with high‐quality experimental data describing a multitude of concurrent internal catchment processes under a range of hydrologic regimes. This study takes a novel approach by not only examining the ability of a pre‐calibrated model to realistically simulate watershed outlet flows over a four year period, but a multitude of spatially‐extensive, internal catchment process observations not previously evaluated, including: continuous groundwater dynamics, instantaneous stream and road network flows, and accumulation and melt period spatial snow distributions. Many hydrologic model evaluations are only on the comparison of predicted and observed discharge at a catchment outlet and remain in the ‘infant stage’ in terms of model testing. This study, on the other hand, tests the internal spatial predictions of a distributed model with a range of field observations over a wide range of hydroclimatic conditions. Nash‐Sutcliffe model efficiency was improved over prior evaluations due to continuing efforts in improving the quality of meteorological data collection. Road and stream network flows were generally well simulated for a range of hydrologic conditions, and snowpack spatial distributions were well simulated for one of two years examined. The spatial variability of groundwater dynamics was effectively simulated, except at locations where strong stream–groundwater interactions exist. Model simulations overall were quite successful in realistically simulating the spatiotemporal variability of internal catchment processes in the watershed, but the premature onset of simulated snowmelt for one of the simulation years has prompted further work in model development. Copyright © 2011 John Wiley & Sons, Ltd.