Water is a chemical compound that is fundamental to all forms of life on Earth.
It constitutes 60% of animal and 90% of plant biomass (Shuttleworth, 2012). It shapes the Earth in many aspects: for example, water forms landscapes due to erosion or weathering and is partly responsible for the Earth’s surface temperature, since water vapor is the most important greenhouse gas. In consequence, investi-gating the spatial and temporal distribution of water resources is of big interest for humanity.
Figure 1.1: Volumetric view on the Earth’s water resources. The big sphere repre-sents the volume of available water on, in, and above Earth (fresh and salt water) compared to the Earths volume. The middle-size sphere on its right side depicts the available liquid fresh water resources on Earth including groundwater, lakes, swamps, and rivers. The small-est sphere, located below the former, shows the volume of surface fresh water (lakes and rivers) compared to the Earth’s volume (source:
http://water.usgs.gov/edu/earthhowmuch.html).
Compared to the total volume of the Earth, all available water resources are small as shown in Figure 1.1. The 96.5% of the available water on Earth is allocated to oceans as non-potable salt water (Table 1.1). The remaining water could poten-tially be used as drinking water. The majority of it is stored as ice or snow in glaciers and ice caps. Only less than 1% of the Earth’s water remains accessible as liquid freshwater. It constitutes a volume of approximately 10.6 106 km3 and is stored in rivers, lakes and the subsurface water, i.e., soil moisture and groundwater.
Table 1.1: Main water reservoirs of the earth characterized by volume and turnover times (Shiklomanov, 1993; Shuttleworth, 2012).
Volume Percentage Approximate (106 km2) of total residence time
Ocean ∼1340 ∼96.5 1 000-10 000 years
Glaciers, ice, and permafrost ∼27 ∼1.8 10-1 000 years
Groundwater ∼23 ∼1.7 15 days - 10 000 years
Atmosphere ∼0.013 ∼0.001 ∼10 days
Lakes, swamps, marshes ∼0.187 ∼0.014 ∼10 days
Rivers ∼0.002 ∼0.0002 ∼15 days
Soil moisture ∼0.017 ∼0.001 ∼50 days
Although the volume of freshwater is marginal compared to total Earths water resources, it is the major resource of drinking water and plant available water.
Potable water would exhaust anytime soon, if it is not constantly renewed by the hydrologic cycle as shown in Figure 1.2 (Shuttleworth, 2012). Water evaporates from land and the ocean, drains as precipitation, and accumulates in rivers, lakes and subsurface reservoirs on land. Finally, it flows back to the ocean where it evaporates again. As Table 1.1 shows, surface water and atmospheric water vapor have fast turnover rates, whereas groundwater is replaced very slowly. Soil mois-ture, the main source of plant available water, is in between these temporal scales with an approximated turnover rate of 50 days.
Anomalies of water fluxes and states within the hydrologic cycle, either cause an excess or scarcity of water, i.e., floods and droughts. Precise knowledge on the spatio-temporal distribution of water within this cycle is essential in order to monitor and predict such hydrologic extremes.
Unfortunately, the states and fluxes of this cycle, e.g., soil moisture and evapotran-spiration, are unknown at many places of the world since they are not observed.
The vast majority of measured variables are meteorological observations, i.e., pre-cipitation and climate variables. Less than 10−10% of the area of Germany is covered by rain gauge area despite the fact that Germany has the highest sta-tion density worldwide. Besides meteorological observasta-tions, river runoff if often
tives of black box models are artificial neural network models (e.g., Tokar and Johnson, 1999; Dawson and Wilby, 2001; Tongal and Berndtsson, 2016) or autore-gressive moving average models (Box et al., 2008).
White box models are based on the main physical laws which are governing the hydrologic phenomena: the equations of mass, momentum and energy (Abbott and Refsgaard, 1996). The model domain is spatially and temporally discrete. Usually this discretization is based on finite elements or finite volumes. They are usually applied to gain process understanding. Disadvantages of these models are their high computational costs, their demand on a tremendous amount of data, their scale-dependency, and their overparameterization (Todini, 2007b; Beven, 2008, 2012). This makes it difficult to use them for operational purposes. For these reasons, physically based models are not yet as popular as process-based models in the hydrologic community. Examples for white box models are HYDRUS (ˇSimnek et al., 2008), ParFlow (Kollet and Maxwell, 2006) and MODFLOW (McDonald and Harbaugh, 1984).
The fundamental principle of process-based hydrologic (grey box) models is the fulfillment of the water balance, i.e. the conservation of mass. They are driven by meteorological forcings and output hydrologic responses of the catchment, e.g., river runoff or evapotranspiration (Beven, 2012). Usually a cascade of reservoirs characterizes these models. The reservoirs represent different states of the hy-drologic cycle such as interception, snow accumulation, soil water retention, and groundwater storage. They are connected by hydrologic fluxes such as snow melt-ing, evapotranspiration, percolation and runoff generation. Process-based mod-els are widely used in catchment hydrologic studies because of their reasonable computational costs and low data demand. Well known process-based models are HBV (Bergrstr¨om, 1976), Variable Infiltration Capacity (VIC) model (Liang et al., 1994), LISFLODD (De Roo et al., 2000), SAC-SMA (Burnash et al., 1973), and mHM (Kumar et al., 2013b; Samaniego et al., 2010) among others.
In hydrologic models, catchments are treated differently regarding their spatial representation. Three different kinds of model approaches exist: lumped, semi-distributed, and distributed hydrologic models. Lumped models treat the entire catchment as one homogenous unit in which the hydrologic inputs, processes and outputs are averaged in space. Semi-distributed models subdivide the model do-main into functional units. Distributed models work on defined, geometrical grids.
The advantage of distributed models is a high spatial resolution of the estimated hydrologic fluxes and states compared to the two other approaches (Beven, 1992;
Carpenter and Georgakakos, 2006; Kumar, 2010). This study is based on a spa-tially distributed model: the process-based hydrologic model mHM.
1.3. Uncertainty in Hydrologic Modeling
1.3 Uncertainty in Hydrologic Modeling
All of the aforementioned models underlie uncertainties in their hydrologic predic-tions. These uncertainties are attributed to four different sources: initial condi-tions, model structure, input data, and model parameters (Wagener and Gupta, 2005; Liu and Gupta, 2007; Beven, 2008).
Running a hydrologic model simulation without knowledge of the initial conditions, e.g., state of the soil moisture, will lead to biased model simulations. Hydrologic models need a certain amount of simulation time to adapt to the conditions within the catchment at the start of the simulation period if the initial conditions are unknown. A decent amount of observational data should be reserved for model spin-up to avoid initialization errors. Climatological values of the model states can be used for initialization, to minimize this spin-up time.
The model structural uncertainty depends on the decision for a particular model or modeling concept. This choice is usually based on subjective criteria, e.g., the modeler’s preference for a particular model (Wagener et al., 2003). Different models will produce different results at the same location because of the model design. Hydrologic models differ in the mathematical description of processes, the parameterization of these processes, and in the hydrologic processes that are considered within the model (Beven, 2012). A multi-model setup for the area under investigation can expose model structural uncertainties in hydrologic predictions.
The third source of uncertainty arises from the input data. Usually, hydrologic models are driven by spatially distributed fields of meteorological variables. Be-sides the measurement errors, the interpolation approach is another source of er-rors. Predictions of the future behavior of hydrologic systems depend on forecasts of global or regional climate models (Beven, 2008). These climate models underlie predictive uncertainties themselves which are propagated to the hydrologic model (e.g., Thober et al., 2015).
The fourth source of uncertainty is connected to the model parameters. All of the aforementioned models are mathematical abstractions of nature and usually depend on parameters which allow the model to adapt to local conditions of the watershed or grid cell (Kuczera and Mroczkowski, 1998). These parameters do not necessarily represent physical entities due to model conceptualization and a lack of observations of hydrologic processes on the relevant scale, e.g., mesoscale (Beven, 2012). Further, every hydrologic model, regardless of its spatial explic-itness (lumped or distributed), is to some degree the approximation of a het-erogeneous world (Wagener and Gupta, 2005). Consequently, the parameters of hydrologic models can be seen as effective parameters that are usually determined by calibration. A calibration is the backward estimation of the model parame-ters aiming to reproduce an observed response of the hydrologic system, e.g., river runoff at the catchment outlet.
Two different approaches of estimating model parameters can be differentiated:
the manual calibration and the automatic calibration (Gupta et al., 1999). The manual calibration needs to be conducted by an experienced hydrologist whose judgment of the model skill may be subjective. Automatic calibration routines, such as the Shuffled Complex Evolution (SCE) algorithm (Duan et al., 1992) or the Dynamically Dimensioned Search (DDS) algorithm (Tolson and Shoemaker, 2007), are searching for the best fit between the model and observations based on an objective criterion or objective function. The objective function quantifies the error of the model with respect to a particular observation. Typical error metrics in hydrologic modeling are the root mean square error or the Nash-Sutcliffe efficiency criterion (Nash and Sutcliffe, 1970). The parametric uncertainty is the inability to adequately locate a “best” parameter set (Wagener and Gupta, 2005).
Calibration can lead to multiple or equifinal parameter sets, which perform equally satisfactorily compared to observations (Beven and Freer, 2001).
Within this study, the effect of parameter uncertainties that arise from running in-dependent calibration runs for the hydrologic model mHM is analyzed. The herein used automatic calibration algorithm is the DDS algorithm, which is broadly ap-plied in hydrology. This algorithm converges faster to good calibration results compared to, e.g., the SCE algorithm (Tolson and Shoemaker, 2007). It termi-nates after a fixed number of iterations rather than after a convergence criterion.
The uncertainties of different hydrologic fluxes and states are analyzed regarding their spatio-temporal distribution, and are reviewed regarding their implications on soil moisture drought analyzes in Germany. An approach is presented to re-duce parameter uncertainties by calibrating the model against additional data, i.e., satellite retrieved land surface temperature.
1.4 Droughts
Droughts are natural phenomena that are caused by precipitation amounts below the expected or normal (Wilhite, 2005). They can occur in all climatic zones irre-spectively of the typical amount of rainfall in a region (Wilhite and Glantz, 1985).
They are creeping events, which can easily last several years and reach national to continental spatial coverage (Andreadis et al., 2005; Sheffield and Wood, 2011;
Sheffield et al., 2014).
Droughts are the second most severe natural disaster beside floods. They af-fected worldwide 2.2 billion people between 1950-2014 (Guha-Sapir et al., 2015).
Its consequences reach from economic losses, mass migrations, and famines to casualties, among others (Hodell et al., 1995; Field, 2000; Wilhite et al., 2007).
For example, in Germany the 2003 heat wave and drought event caused 7,000 fatalities (European Commission, 2007). On the European level death toll was estimated to exceed 70,000 (Robine et al., 2008). This severe drought event
im-1.4. Droughts pacted many socio-economic fields such as agriculture, forestry or inland navi-gation. The agro-economic loss in Germany was estimated to 1.5 billion EUR (COPA-COGECA, 2003). In entire Europe the agricultural sector had to cope with losses of 15 billion EUR.
According to the fifth assessment report of the International Panel on Climate Change (IPCC) ”there will be a marked increase in extremes in Europe, in par-ticular, in heat waves, droughts, and heavy precipitation events” (IPCC, 2012).
The European Commission reported that the frequency of droughts has already increased and will further increase (EEA, 2012a). Additionally, Trenberth et al.
(2014) discuss that anthropogenic factors of climate change will speed up the es-tablishment of droughts and increase drought intensities. This makes droughts an important field of research in Central Europe.
Figure 1.3: The four different types of drought and their sequence of occurrence.
(source: National Drought Mitigation Center, University of Nebraska-Lincoln, USA)
Since droughts have an impact on many parts of society, there is no generally accepted definition of droughts (Wilhite, 2005). Different disciplines, e.g., water resources management or agriculture, focus on different variables of the hydrologic cycle, e.g., river runoff or soil moisture, respectively. This led to the classifi-cation of droughts into four types: meteorological, agricultural, hydrologic, and socio-economic drought as shown in Figure 1.3 (Wilhite and Glantz, 1985; WMO, 2006). The meteorological drought is usually defined as a deficiency of precipita-tion amount in a defined period of time. The hydrologic drought is characterized
by exceptional low surface and subsurface water availability, such as reduced river runoff and low groundwater levels. A low availability of soil moisture, which is the major water resource for plants in most regions of the world, is termed agricul-tural drought. All of the aforementioned drought types can lead to a shortfall in water supply leading to monetary losses, which characterizes the socio-economic impacts.
A drought monitoring system which delivers timely information about onset, ex-tent and intensity, could help to reduce drought related fatalities and economic losses (Wilhite, 1993). Within this study, such a system is developed for Ger-many. It focuses on the analysis of soil moisture droughts, because of their high agro-economic relevance for Germany (e.g., Schindler et al., 2007; D¨oring et al., 2011).
1.5 Research Objectives
The main objective of this study is the development of an operational drought monitoring system for agricultural droughts in Germany. Therefore, spatially con-tinuous fields of soil moisture are derived with a hydrologic model, i.e., mHM.
Hydrologic models are uncertain in hydrologic predictions due to uncertainties in the parameter estimation process, amongst others. These uncertainties need to be considered if predicting drought characteristics, such as drought severity or du-ration. Further, the ability of spatially distributed fields of satellite derived land surface temperature is explored to reduce parameter uncertainties. Finally, the operational framework of the German Drought Monitor is presented.
Hydrologic modeling is usually conducted at the catchment scale. Catchment bor-ders have to be crossed when conducting predictions on the national domain. In consequence, the parameters of the hydrologic model need to be sufficient and sta-ble for application in distinct catchments. Additionally to the equifinality prosta-blem, transferring calibrated model parameters to remote locations will lead to uncer-tainties in the model simulation. A framework to determine such parameters is presented in Chapter 2 in order to address the following research objectives:
• Derive highly resolved and spatially consistent estimations of hydrologic states and fluxes, i.e., evapotranspiration, soil moisture, groundwater recharge, per grid cell generated runoff, for Germany between 1950 and 2010.
• Analyze the spatio-temporal distribution of parametric uncertainties of these variables.
A retrospective drought analysis from 1950 to 2010 is anticipated based on the soil moisture fields of these estimations. An algorithm for the estimation of a Soil Moisture Index (SMI) is developed and implemented for performing drought
1.5. Research Objectives analyzes. Based on the SMI, the following research objectives are addressed in Chapter 3:
• Reconstruction of agricultural drought conditions and identification of bench-mark events.
• Investigate the effect of parametric uncertainty on drought characteristics, such as duration, spatial extent, severity, and magnitude.
Chapter 4 will deal with the reduction of parametric uncertainties observed in the above-mentioned studies. Using satellite derived land surface temperature and a newly developed and implemented land surface temperature module for mHM, the following research objectives will be addressed:
• Reduction of parameter estimation uncertainties by calibrating a hydrologic model with spatial patterns of satellite derived land surface temperature.
• Assessment of the predictive skill of satellite land surface temperature re-garding river runoff.
Finally, the operationalization of a drought monitoring system for Germany is presented in Chapter 5. The research question addressed is:
• How to deliver timely information about agricultural droughts to the decision makers and the public to potentially mitigate negative impacts?
The last chapter summarizes and discusses the major findings of this work and provides an outlook for further improvements of the drought monitoring frame-work.
Chapter 2
A High-Resolution Dataset of Water Fluxes and States for Germany
Accounting for Parametric Uncertainty
This chapter is largely based on the manuscript:
Zink, M., Kumar, R., Cuntz, M., and Samaniego, L. (2016): A High-Resolution Dataset of Water Fluxes and States for Germany Accounting for Parametric Uncer-tainty, Hydrology and Earth Systen Sciences Discussions, doi:10.5194/hess-2016-443, in review.
2.1. Abstract
2.1 Abstract
Long term, high-resolution data of hydrologic fluxes and states are needed for many hydrological applications. Since long-term, large-scale observations of such variables are not feasible, hydrologic or land surface models are applied to derive them. This study aims to analyze and provide a high-resolution dataset of land surface variables over Germany, accounting for uncertainties caused by the estima-tion of equifinal model parameters. Furthermore, the spatiotemporal distribuestima-tion of uncertainties in various hydrological variables as well as the propagation of un-certainties through different model compartments is investigated. The mesoscale hydrological model (mHM) is employed to create an ensemble (100 members) of daily fields of evapotranspiration, groundwater recharge, generated discharge and soil moisture at a spatial resolution of 4 km in the period 1950-2010. The model is evaluated with observed runoff in 222 catchments, which have not been used for calibrating the model. In these catchments the mean and the standard deviation of the ensemble median N SE for daily discharge are 0.68 and 0.09, respectively.
The modeled evapotranspiration, which is evaluated with observations at eddy co-variance stations, exhibits a five times larger error in spring during the onset of the vegetation period compared to the other seasons. Our analysis indicates the low-est uncertainty for evapotranspiration, while the larglow-est uncertainty is observed for groundwater recharge. The uncertainty of the hydrologic variables varies through-out the course of a year with exception of evapotranspiration, which stays almost constant. The uncertainties in soil moisture and recharge are recognized to propa-gate to the modeled discharge. Our study emphasizes the role of accounting for the uncertainty due to equifinal parameter sets when reconstructing high-resolution, model-based datasets.
2.2 Introduction
Consistent, long-term data of meteorological and hydrological variables at high spatial resolution are needed for applications like i) impact assessment studies such as drought, flood or climate change analyzes (Sheffield and Wood, 2007;
Samaniego et al., 2013; Huang et al., 2010), ii) studies that need spatially and temporally continuous observation based data, e.g., for temporal disaggregation (Thober et al., 2014) or downscaling of climate model data (Wood et al., 2004), Ensemble Streamflow Prediction (Day, 1985), or reverse Ensemble Streamflow Pre-diction (Wood and Lettenmaier, 2008).
Continuous observations of hydrologic fluxes and states are economically and lo-gistically not feasible on regional to national scales (Vereecken et al., 2008). Soil moisture observations, for example, are scarcely conducted. Additionally, these measurements are usually only representative for a small control volume of a few
cm3. Evapotranspiration measurements at eddy covariance stations have a foot-print of ten to hundreds of meters, but are available at only 827 stations worldwide (http://fluxnet.ornl.gov, April 2016).
Alternatives are remote sensing or reanalysis data. These data are broadly avail-able, but do not consider the conservation of mass, i.e., the closure of the water balance. Apart from that reanalysis data have spatial resolutions of at most 1/4◦ (Dee et al., 2016). Continuous remote sensing products are not available due to their addiction to cloud free conditions (Mu et al., 2007; Liu et al., 2012). How-ever, hydrologic models driven by observational data are the prime alternative to derive consistent water fluxes and states on large spatial domains.
Observational driven datasets are estimate by Maurer et al. (2002); Zhu and Let-tenmaier (2007); Livneh et al. (2013); Zhang et al. (2014) on the national scale.
These data are based on the Variable Infiltration Capacity (VIC) model (Liang et al., 1994) having at most a spatial resolution of 1/16◦ and cover the United States, Mexico and China. Studies, like Nijssen et al. (2001); Fan and van den Dool (2004); Berg et al. (2005); Sheffield et al. (2006), are focusing on the global
These data are based on the Variable Infiltration Capacity (VIC) model (Liang et al., 1994) having at most a spatial resolution of 1/16◦ and cover the United States, Mexico and China. Studies, like Nijssen et al. (2001); Fan and van den Dool (2004); Berg et al. (2005); Sheffield et al. (2006), are focusing on the global