Application of Copulas in Geostatistics

This paper demonstrates how empirical copulas can be used to describe and model spatial dependence structures of real-world environmental datasets in the purest form and how such a copula model can be employed as the underlying structure for interpolation and associated uncertainty estimates. Using copulas, the dependence of multivariate distributions is modelled by the joint cumulative distribution of the variables using uniform marginal distribution functions. The uniform marginal distributions are the effect of transforming the marginal distributions monotonically by using the ranks of the variables. Due to the uniform marginal distributions, copulas express the dependence structure of the variables independent of the variables’marginal distributions which means that copulas display interdependence between variables in its purest form. This property also means that marginal distributions of the original data have no influence on the spatial dependence structure and can not “cover up” parts of the spatial dependence structure. Additionally, differences in the degree of dependence between different quantiles of the variables are readily identified by the shape of the contours of an empirical copula density. Regarding the quantification of uncertainties, copulas offer a significant advantage: the full distribution function of the interpolated parameter at every interpolation point is available. The magnitude of uncertainty does not depend on the density of the observation network only, but also on the magnitude of the measurements as well as on the gradient of the magnitude of the measurements. That means for the same configuration of the observation network, interpolating two events with very similar marginal distribution, the confidence intervals look significantly different for both events.Claus P. Haslauer, Jing Li, and András Bárdoss

Efficient calibration of a distributed pde-based hydrological model using grid coarsening

Partial-differential-equation based integrated hydrological models are now regularly used at catchment scale. They rely on the shallow water equations for surface flow and on the Richards' equations for subsurface flow, allowing a spatially explicit representation of properties and states. However, these models usually come at high computational costs, which limit their accessibility to state-of-the-art methods of parameter estimation and uncertainty quantification, because these methods require a large number of model evaluations. In this study, we present an efficient model calibration strategy, based on a hierarchy of grid resolutions, each of them resolving the same zonation of subsurface and land-surface units. We first analyze which model outputs show the highest similarities between the original model and two differently coarsened grids. Then we calibrate the coarser models by comparing these similar outputs to the measurements. We finish the calibration using the fully resolved model, taking the result of the preliminary calibration as starting point. We apply the proposed approach to the well monitored Lerma catchment in North-East Spain, using the model HydroGeoSphere. The original model grid w ith 80,000 finite elements was complemented with two other model variants with approximately 16,000 and 10,000 elements, respectively. Comparing the model results for these different grids, we observe differences in peak discharge, evapotranspiration, and near-surface saturation. Hydraulic heads and low flow, however, are very similar for all tested parameter sets, which allows the use of these variables to calibrate our model. The calibration results are satisfactory and the duration of the calibration has been greatly decreased by using different model grid resolutions

Estimating climate-change effects on a Mediterranean catchment under various irrigation conditions

Study region: The Lerma catchment, a small (7.3km²) sub-catchment of the Ebro Basin in northern Spain. Study focus: The Lerma catchment underwent a monitored transition to irrigated agriculture, using water from outside the catchment, between 2006 and 2008. This transition has successfully been simulated using the partial-differential-equation-based model HydroGeoSphere, simulating coupled evapotranspiration, surface water, and groundwater flow in the catchment. We use the calibrated model to study how irrigation practices influence the response of the Lerma catchment to the climate change projected for northern Spain. We consider four different irrigation scenarios: no irrigation, present irrigation, climate-adapted irrigation with current crops, and adapted irrigation for crops requiring less water. The climate scenarios are based on four regional climate models and two downscaling methods. New hydrological insight: The simulated catchment responses to climate change show clear differences between the irrigation scenarios. In future climate, groundwater levels and base flows decrease more when irrigation is present than without irrigation, because groundwater levels and base flow in present climate are already at low levels without irrigation. In contrast, annual peak discharges increase more in non-irrigated cases than in irrigated cases. Irrigation increases water availability and an associated rise in potential evapotranspiration results in higher actual evapotranspiration during summer. In non-irrigated scenarios, by contrast, actual evapotranspiration in summer is controlled by precipitation and thus decreases in future climate

Using an integrated hydrological model to estimate the usefulness of meteorological drought indices in a changing climate

Droughts are serious natural hazards, especially in semi-arid regions. They are also difficult to characterize. Various summary metrics representing the dryness level, denoted drought indices, have been developed to quantify droughts. They typically lump meteorological variables and can thus directly be computed from the outputs of regional climate models in climate-change assessments. While it is generally accepted that drought risks in semi-arid climates will increase in the future, quantifying this increase using climate model outputs is a complex process that depends on the choice and the accuracy of the drought indices, among other factors. In this study, we compare seven meteorological drought indices that are commonly used to predict future droughts. Our goal is to assess the reliability of these indices to predict hydrological impacts of droughts under changing climatic conditions at the annual timescale. We simulate the hydrological responses of a small catchment in northern Spain to droughts in present and future climate, using an integrated hydrological model calibrated for different irrigation scenarios. We compute the correlation of meteorological drought indices with the simulated hydrological time series (discharge, groundwater levels, and water deficit) and compare changes in the relationships between hydrological variables and drought indices. While correlation coefficients linked with a specific drought index are similar for all tested land uses and climates, the relationship between drought indices and hydrological variables often differs between present and future climate. Drought indices based solely on precipitation often underestimate the hydrological impacts of future droughts, while drought indices that additionally include potential evapotranspiration sometimes overestimate the drought effects. In this study, the drought indices with the smallest bias were the rainfall anomaly index, the reconnaissance drought index, and the standardized precipitation evapotranspiration index. However, the efficiency of these drought indices depends on the hydrological variable of interest and the irrigation scenario. We conclude that meteorological drought indices are able to identify years with restricted water availability in present and future climate. However, these indices are not capable of estimating the severity of hydrological impacts of droughts in future climate. A well-calibrated hydrological model is necessary in this respect