3.3 Soil Moisture Data
Soil water availability in the root zone is a direct indicator of agricultural drought because it constitutes a governing factor of the state of vegetative growth through the availability of water for transpiration (Keyantash and Dracup, 2002). Measur-ing soil moisture content over the entire domain of Germany at a spatial resolution of 4 × 4 km, for example, is logistically and economically infeasible (Vereecken et al., 2008). LSMs or hydrologic models are therefore often employed to estimate this key variable over large spatial domains and longer periods (Andreadis and Lettenmaier, 2006; Sheffield and Wood, 2007; Wang et al., 2009; Mishra et al., 2010; Wang et al., 2011).
In this study, the mesoscale Hydrologic Model, mHM (Samaniego et al., 2010) was used to generate a large ensemble of daily soil moisture fields for the period from 1950 to 2010. A three layer soil scheme was used to model the soil moisture dynamics over the entire root zone depth (i.e. approximately up to 2 m below ground). The depth of the first two layers was fixed to 5 cm and 25 cm, whereas the depth of the last one was variable according to soil characteristics provided by the soil texture map. The spatial resolution of each grid was 4 × 4 km (level-1).
A short description of mHM and the generation of ensemble soil moisture fields are given below.
3.3.1 The mesoscale Hydrologic Model mHM
The mesoscale Hydrologic Model is a process-based water balance model (Samaniego et al., 2010) that has been developed over the last five years at the Helmholtz Cen-tre for Environmental Research - UFZ. This spatially explicit model does not differ significantly from existing large scale hydrologic models (e.g. the HBV and the VIC-3L model) on how dominant hydrologic processes at the meso- and macro-scales are conceptualized, but on how the effective parameters of the model are quantified at a selected modeling scale and on how the sub-grid variability of physiographic characteristics provided at level-0 is taken into account for the esti-mation of these effective parameters. These two fundamental differences constitute the core of the multiscale parameter regionalization technique (Samaniego et al., 2010) that is embedded into mHM. Extensive numerical experiments have shown that this technique is capable of coping with the large spatio-temporal variability of the input data and as a result, mHM is able to produce quite good perfor-mance at multiple spatial resolutions and locations other than those used during calibration (i.e. proxy basin and flux-matching tests).
Currently, mHM has been evaluated in more than one hundred basins in Ger-many ranging from 4 km2 to 47 000 km2 (Samaniego et al., 2010; Kumar et al., 2010, 2013b). This model is driven by disaggregated fields of daily forcings such
as precipitation, temperature, and potential evapotranspiration. It accounts for the following hydrological processes: canopy interception, snow accumulation and melting, evapotranspiration, infiltration, soil moisture dynamics in three layers, surface runoff, subsurface storage, discharge generation, percolation, baseflow, and flood routing within the river reaches. Readers may refer to Samaniego et al. (2010) for a detailed model description as well as its parametrization.
The morphological and physiographic data required for setting up mHM include a digital elevation model (50 × 50 m) acquired from the Federal Agency for Cartography and Geodesy, a vector soil map containing information on soil textural properties such as sand and clay contents of different soil horizons, and a vector map of hydro-geologic formations containing properties such as saturated hydraulic conductivity. Both vector maps at a scale of 1:1 000 000 were obtained from the Federal Institute for Geosciences and Natural Resources of Germany. Three Corine land cover seamless vector data (http://www.eea.europa.eu) for the years 1990, 2000, and 2006 were employed to account for the changes in states of land cover over the simulation time period (1950-2010). Land cover states, prior to the year 1990, were inferred from the Corine 1990 map. Monthly variability of the leaf area index was estimated for each land cover class with MODIS scenes from 2001 to 2009. These data are freely available from https://lpdaac.usgs.gov/get data.
For a detailed description on data processing and setting up mHM in several river basins, interested readers may refer to Samaniego et al. (2010); Kumar et al.
(2010). Previous data sets were re-sampled on a common spatial resolution of 100 × 100 m denoted as level-0. This level of information provides the sub-grid variability of all morphological and physiographic variables required to run the model at any coarser resolution denoted as level-1 (e.g. 4 km). The time series of discharge data across several gauging stations were acquired from the EURO-FRIEND program (http://ne-friend.bafg.de) and the Global Runoff Data Centre (http://www.bafg.de).
Gridded fields of daily average precipitation as well as maximum, minimum, and average air temperatures at 4×4 km spatial resolution (level-2) were estimated from their respective point measurement data from about 5600 rain gauges and 1120 meteorological stations, which are operated by the German Meteorological Service (DWD). Two interpolation techniques were used to derive the daily fields of precipitation, which are detailed in section 3.3.2. Gridded estimates for temper-ature fields were obtained with external drift kriging, wherein the terrain elevation was used as a drift variable. The daily fields of potential evapotranspiration were estimated with the Hargreaves and Samani method (Hargreaves and Samani, 1985) and were subsequently corrected to account for the spatial variability of the terrain aspect.
3.3. Soil Moisture Data
3.3.2 Ensemble Description and Experimental Design
Two major sources of parametric uncertainty were identified through sensitivity analysis. The most important one is related with the variability of the global cal-ibration parameters of mHM (i.e. space and time independent), and the second one is related with the parameters required for the rainfall interpolation method.
Consequently, the uncertainty tree was divided into two main branches, each one driven by two independent interpolation methods but both based on the same rainfall measurements. These two branches were denoted as DWD1 and DWD2.
Other meteorological variables such as daily, minimum, and maximum tempera-ture required in both branches were kept the same. This assumption was taken considering 1) that precipitation interpolation is one the most important source of error in the input data (Mo et al., 2012), and 2) that the areal coverage of snow-dominated areas in Germany is geographically limited.
The DWD1 branch was created with external drift kriging using terrain elevation as a drift and a combined variogram that comprised a nugget and an exponential part. The resolution of this product was 4 × 4 km, with daily time steps from 1950 to 2010. The best fit parameters (i.e. nugget, range, and sill) were found through a cross-validation procedure.
The DWD2 branch was obtained by re-sampling the original daily REGNIE prod-uct (Deutscher Wetterdienst (DWD), 2013) available at 1 × 1 km into a regular grid similar to that of the DWD1 data set. Thek-nearest’s neighbor technique and a standard geo-referencing algorithm were employed for this purpose. The DWD1 data was used to complete this set with daily fields from 1950 to 1959 since the REGNIE data set is only available from 1960 to 2010. The REGNIE data is based on multiple linear regression having elevation, geographic location, and aspect as predictors.
Within each branch, the propagation of the parameter uncertainty into the soil moisture simulations was evaluated by an ensemble of one hundred best parameter sets of mHM. The following procedure was implemented for their selection. First, in every major river basin depicted in Figure 3.1, the dynamically dimensioned search algorithm (Tolson and Shoemaker, 2007) was employed to find good sets of global parameters which exhibit an acceptable model efficiency [e.g. Nash-Sutclife-Efficiency of at least 0.75] during the evaluation period (for details refer to Kumar et al., 2010, 2013b). In the next step, all parameter sets found for a given basin were transferred to the remaining ones. Finally, only those sets exhibiting a model efficiency greater than or equal to 0.65 at recipient locations were retained as members of the best global parameter sets. This implies that these super sets of global parameters are able to reproduce water fluxes in all major river basins in Germany with an efficiency of at least 0.65. It may be noted that a single set of VIC-3L model parameters for a large domain in the midwestern United States was used in a study by Mishra et al. (2010) for assessing historical drought events. In
Ems Weser Elbe
Figure 3.1: Map of Germany indicating the main river basins used for this study.
Selected locations for uncertainty analysis of the soil moisture clima-tology are depicted with a dot.
contrast to that, in this study the ensemble of 200 model realizations was used for the subsequent analysis of historical drought events in Germany including both uncertainty branches.
In general, mHM requires at least five years of spin-up time to equilibrate. To min-imize the influence of initial conditions, all state variables (e.g. water content at a given soil layer) in each ensemble member were initialized with their climatologi-cal averages corresponding to the precise time of year at the initialization (Rodell et al., 2005). The climatological average was estimated as the long term mean of a given state variable within a seven-day window around the first of January. The DWD1 precipitation estimate was employed to estimate the long term mean. This procedure allowed to reduce the spin-up time to one year without inducing large bias due to inappropriate initial conditions. Thus, model simulations during the starting year 1950 were discarded from the following analysis.