[1] The requirements for hydrological models have increased considerably during the previous decades to cope with the resolution of extensive remotely sensed data sets and a number of demanding applications. Existing models exhibit deficiencies such as overparameterization, the lack of an effective technique to integrate the spatial heterogeneity of physiographic characteristics, and the nontransferability of parameters across scales and locations. A multiscale parameter regionalization (MPR) technique is proposed as a way to address these issues simultaneously. Using this technique, parameters at a coarser scale, in which the dominant hydrological processes are represented, are linked with their corresponding ones at a finer resolution in which input data sets are available. The linkage is done with upscaling operators such as the harmonic mean, among others. Parameters at the finer scale are regionalized through nonlinear transfer functions which link basin predictors with global parameters to be determined through calibration. MPR was compared with a standard regionalization (SR) method in which basin predictors instead of model parameters are first aggregated. Both methods were tested in a basin located in Germany using a distributed hydrologic model. Results indicate that MPR is superior to SR in many respects, especially if global parameters are transferred from coarser to finer scales. Furthermore, MPR, as opposed to SR, preserves the spatial variability of state variables and conserves the mass balance with respect to a control scale. Cross-validation tests indicate that the transferability of the global parameters to ungauged locations is possible.Citation: Samaniego, L., R. Kumar, and S. Attinger (2010), Multiscale parameter regionalization of a grid-based hydrologic model at the mesoscale, Water Resour. Res., 46, W05523,

Key Points A calibrated model does not guarantee cross‐scale and location transferability Calibration parameters of MPR exhibit quasi‐scale invariance, but HRU does not MPR also outperfromed HRU for parameter transferability across locations

We investigate the temporal behavior of transport coefficients in a model for transport of a solute through a spatially heterogeneous saturated aquifer. In the framework of a stochastic approach we derive explicit expressions for the temporal behavior of the center‐of‐mass velocity and the dispersion of the concentration distribution after a point‐like injection of solute at time t=0, using a second‐order perturbation expansion. The model takes into account local variations in the hydraulic conductivity (which, in turn, induce local fluctuations in the groundwater flow velocities) and in the chemical adsorption properties of the medium (which lead to a spatially varying local retardation factor). In the given perturbation theory approach the various heterogeneity‐induced contributions can be systematically traced back to fluctuations in these quantities and to cross correlations between them. We analyze two conceptually different definitions for the resulting dispersion coefficient: the “effective”dispersion coefficient which is derived from the average over the centered second moments of the spatial concentration distributions in every realization and the “ensemble” dispersion coefficient which follows from the second moment of the ensemble‐averaged concentration distribution. The first quantity characterizes the dispersion in a typical realization of the medium, whereas the second one describes the (formal) dispersion properties of the ensemble as a whole. We give explicit analytic expressions for both quantities as functions of time and show that for finite times their temporal behavior is remarkably different. The ensemble dispersion coefficient which is usually evaluated in the literature considerably overestimates the dispersion typically found in one given realization of the medium. From our explicit results we identify two relevant timescales separating regimes of qualitatively and quantitatively different temporal behavior: The shorter of the two scales is set by the advective transport of the solute cloud over one disorder correlation length, whereas the second, much larger one, is related to the dispersive spreading over the same distance. Only for times much larger than this second scale, do the effective and the ensemble dispersion coefficient become equivalent because of mixing caused by the local transversal dispersion. The formulae are applied to the Borden experiment data. It is concluded that the observed dispersion coefficient matches the effective dispersion coefficient at finite times proposed in this paper very well.

Accurately predicting regional-scale water fluxes and states remains a challenging task in contemporary hydrology. Coping with this grand challenge requires, among other things, a model that makes reliable predictions across scales, locations, and variables other than those used for parameter estimation. In this study, the mesoscale hydrologic model (mHM) parameterized with the multiscale regionalization technique is comprehensively tested across 400 European river basins. The model fluxes and states, constrained using the observed streamflow, are evaluated against gridded evapotranspiration, soil moisture, and total water storage anomalies, as well as local-scale eddy covariance observations. This multiscale verification is carried out in a seamless manner at the native resolutions of available datasets, varying from 0.5 to 100 km. Results of cross-validation tests show that mHM is able to capture the streamflow dynamics adequately well across a wide range of climate and physiographical characteristics. The model yields generally better results (with lower spread of model statistics) in basins with higher rain gauge density. Model performance for other fluxes and states is strongly driven by the degree of seasonality that each variable exhibits, with the best match being observed for evapotranspiration, followed by total water storage anomaly, and the least for soil moisture. Results show that constraining the model against streamflow only may be necessary but not sufficient to warrant the model fidelity for other complementary variables. The study emphasizes the need to account for other complementary datasets besides streamflow during parameter estimation to improve model skill with respect to “hidden” variables.

Abstract. The lack of comprehensive groundwater observations at regional and global scales has promoted the use of alternative proxies and indices to quantify and predict groundwater droughts. Among them, the Standardized Precipitation Index (SPI) is commonly used to characterize droughts in different compartments of the hydro-meteorological system. In this study, we explore the suitability of the SPI to characterize local-and regional-scale groundwater droughts using observations at more than 2000 groundwater wells in geologically different areas in Germany and the Netherlands. A multiscale evaluation of the SPI is performed using the station data and their corresponding 0.5 • gridded estimates to analyze the local and regional behavior of groundwater droughts, respectively. The standardized anomalies in the groundwater heads (SGI) were correlated against SPIs obtained using different accumulation periods. The accumulation periods to achieve maximum correlation exhibited high spatial variability (ranges 3-36 months) at both scales, leading to the conclusion that an a priori selection of the accumulation period (for computing the SPI) would result in inadequate characterization of groundwater droughts. The application of the uniform accumulation periods over the entire domain significantly reduced the correlation between the SPI and SGI (≈ 21-66 %), indicating the limited applicability of the SPI as a proxy for groundwater droughts even at long accumulation times. Furthermore, the low scores of the hit rate (0.3-0.6) and a high false alarm ratio (0.4-0.7) at the majority of the wells and grid cells demonstrated the low reliability of groundwater drought predictions using the SPI. The findings of this study highlight the pitfalls of using the SPI as a groundwater drought indicator at both local and regional scales, and stress the need for more groundwater observations and accounting for regional hydrogeological characteristics in groundwater drought monitoring.

Land surface models incorporate a large number of process descriptions, containing a multitude of parameters. These parameters are typically read from tabulated input files. Some of these parameters might be fixed numbers in the computer code though, which hinder model agility during calibration. Here we identified 139 hard‐coded parameters in the model code of the Noah land surface model with multiple process options (Noah‐MP). We performed a Sobol' global sensitivity analysis of Noah‐MP for a specific set of process options, which includes 42 out of the 71 standard parameters and 75 out of the 139 hard‐coded parameters. The sensitivities of the hydrologic output fluxes latent heat and total runoff as well as their component fluxes were evaluated at 12 catchments within the United States with very different hydrometeorological regimes. Noah‐MP's hydrologic output fluxes are sensitive to two thirds of its applicable standard parameters (i.e., Sobol' indexes above 1%). The most sensitive parameter is, however, a hard‐coded value in the formulation of soil surface resistance for direct evaporation, which proved to be oversensitive in other land surface models as well. Surface runoff is sensitive to almost all hard‐coded parameters of the snow processes and the meteorological inputs. These parameter sensitivities diminish in total runoff. Assessing these parameters in model calibration would require detailed snow observations or the calculation of hydrologic signatures of the runoff data. Latent heat and total runoff exhibit very similar sensitivities because of their tight coupling via the water balance. A calibration of Noah‐MP against either of these fluxes should therefore give comparable results. Moreover, these fluxes are sensitive to both plant and soil parameters. Calibrating, for example, only soil parameters hence limit the ability to derive realistic model parameters. It is thus recommended to include the most sensitive hard‐coded model parameters that were exposed in this study when calibrating Noah‐MP.

Abstract. Land surface and hydrologic models (LSMs/HMs) are used at diverse spatial resolutions ranging from catchment-scale (1-10 km) to global-scale (over 50 km) applications. Applying the same model structure at different spatial scales requires that the model estimates similar fluxes independent of the chosen resolution, i.e., fulfills a fluxmatching condition across scales. An analysis of state-of-theart LSMs and HMs reveals that most do not have consistent hydrologic parameter fields. Multiple experiments with the mHM, Noah-MP, PCR-GLOBWB, and WaterGAP models demonstrate the pitfalls of deficient parameterization practices currently used in most operational models, which are insufficient to satisfy the flux-matching condition. These examples demonstrate that J. Dooge's 1982 statement on the unsolved problem of parameterization in these models remains true. Based on a review of existing parameter regionalization techniques, we postulate that the multiscale parameter regionalization (MPR) technique offers a practical and robust method that provides consistent (seamless) parameter and flux fields across scales. Herein, we develop a general model protocol to describe how MPR can be applied to a particular model and present an example application using the PCR-GLOBWB model. Finally, we discuss potential advantages and limitations of MPR in obtaining the seamless prediction of hydrological fluxes and states across spatial scales.

Increased availability and quality of near real‐time observations provide the opportunity to improve understanding of predictive skills of hydrologic models. Recent studies have shown the limited capability of river discharge data alone to adequately constrain different components of distributed model parameterizations. In this study, the GRACE satellite‐based total water storage (TWS) anomaly is used to complement the discharge data with the aim to improve the fidelity of mesoscale hydrologic model (mHM) through multivariate parameter estimation. The study is conducted on 83 European basins covering a wide range of hydroclimatic regimes. The model parameterization complemented with the TWS anomalies leads to statistically significant improvements in (1) discharge simulations during low‐flow period, and (2) evapotranspiration estimates which are evaluated against independent data (FLUXNET). Overall, there is no significant deterioration in model performance for the discharge simulations when complemented by information from the TWS anomalies. However, considerable changes in the partitioning of precipitation into runoff components are noticed by in‐/exclusion of TWS during the parameter estimation. Introducing monthly averaged TWS data only improves the dynamics of streamflow on monthly or longer time scales, which mostly addresses the dynamical behavior of the base flow reservoir. A cross‐evaluation test carried out to assess the transferability of the calibrated parameters to other locations further confirms the benefit of complementary TWS data. In particular, the evapotranspiration estimates show more robust performance when TWS data are incorporated during the parameter estimation, in comparison with the benchmark model constrained against discharge only. This study highlights the value for incorporating multiple data sources during parameter estimation to improve the overall realism of hydrologic models and their applications over large domains.