Water balance estimation in high Alpine terrain by combining distributed modeling and a neural network approach ( Berchtesgaden Alps , Germany )

The water balance in high Alpine regions is often characterized by significant variation of meteorological variables in space and time, a complex hydrogeological situation and steep gradients. The system is even more complex when the rock composition is dominated by soluble limestone, because unknown underground flow conditions and flow directions lead to unknown storage quantities. Reliable distributed modeling cannot be implemented by traditional approaches due to unknown storage processes at local and catchment scale. We present an artificial neural network extension of a distributed hydrological model (WaSiM-ETH) that allows to account for subsurface water transfer in a karstic environment. The extension was developed for the Alpine catchment of the river “Berchtesgadener Ache” (Berchtesgaden Alps, Germany), which is characterized by extreme topography and calcareous rocks. The model assumes porous conditions and does not account for karstic environments, resulting in systematic mismatch of modeled and measured runoff in discharge curves at the outlet points of neighboring high alpine subbasins. Various precipitation interpolation methods did not allow to explain systematic mismatches, and unknown subsurface hydrological processes were concluded as the underlying reason. We introduce a new method that allows to describe the unknown subsurface boundary fluxes, and account for them in the hydrological model. This is achieved by an artificial neural network approach (ANN), where four input variables are taken to calculate the unknown subsurface storage conditions. This was first developed for the high Alpine subbasin K̈ onigsseer Ache to improve the monthly water balance. We explicitly derive the algebraic transfer function of an artificial neural net to calculate the missing boundary fluxes. The result of the ANN is then implemented in the groundwater module of the hydrological model as boundary flux, and considered during the consecutive model process. We tested several ANN setups in different time increments to investigate ANN performance and to examine resulting runoff dynamics of the hydrological model. The ANN with 5-day time increment showed best results in reproducing the observed water storage data (r2 = 0.6). The influx of the 20-day ANN showed best results in the hydrological model correction. The boundary influx in the subbasin improved the hydrological model, as performance increased from NSE = 0.48 to NSE = 0.57 for subbasin Königsseetal, from NSE = 0.22 to NSE = 0.49 for subbasin Berchtesgadener Ache, and from NSE = 0.56 to NSE = 0.66 for the whole catchment within the test period. This combined approach allows distributed quantification of water balance components including subsurface water transfer.


Introduction
Alpine catchments are very important albeit vulnerable landscapes. Most of the major European rivers have their headwaters in Alpine catchments, and their discharge is transported via river systems to lower-lying areas (EEA, 2007). The Alps are crucial for water accumulation and water supply (e.g. Viviroli and Weingartner, 2004). For 5 sustainable water management of water resources in alpine areas, it is imperative to understand the hydrological processes, their quantities and dynamics. Distributed hydrological modeling has become an important tool for describing the water balance in catchments (e.g. Goldscheider, 2011). However, those methods faces challenges in Alpine areas, on account of high altitudinal gradients, variation of meteorological parameters in time and scale, snow cover dynamics and unknown subsurface water fluxes and storages. The situation is even more complex, when the mountain ranges within a watershed consist of soluble limestone, dissected by small fractures and dominant flow paths up to caves and numerous spring locations, as is the case for this study area. The duality of karst, enfolding slow and fast infiltration, slow and fast groundwater 15 flow and unknown storage, leads to heterogeneous water flow in the unsaturated and saturated zone (Attkinson, 1977;Bakalowicz, 2005;Kiraly, 2003;Sauter et al., 2006;White, 2002White, , 2003. Many approaches at different temporal and spatial scales deal with the modeling of hydrological processes in karst aquifers (e.g. Teutsch and Sauter, 1991). Spring hydrograph, chemograph, and tracer breakthrough curve analysis focus 20 on small-scale effects of karst conduits to define the size and the characteristics of one individual spring aquifer (Birk et al., 2004;Einsiedl, 2005;Geyer et al., 2008;Bonacci, 2004;Hauns et al., 2001;Kovacs et al., 2001;Grasso and Jeannin, 2002;Maloszweski et al., 2005;Weiler et al., 2003). Other approaches concentrate on karst genesis or theoretical conduit flow (Sauter et al., 2006;Romanov et al., 2004;Ford, 2003). Dis- 25 tributive methods, such as "Single Continuum Porous Equivalent", "Double Continuum Porous Equivalent", "Discrete Single Fracture Sets" or "Discrete Multiple Fracture Set", "Hybrid Models" (Sauter et al., 2006) attempt to take into account the heterogeneity of 217 Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | karst aquifers within single conduits or parameter fields in a spatial continuum, however mainly concentrate on modeling water fluxes within the saturated zone. The duality of karst makes it tremendously difficult to find an adequate parameterization to successfully model groundwater flow in present distributed models, which principally assume porous conditions (Kiraly, 2003). In the past, many studies have applied dis-5 tributed groundwater models in karst environments (Scanlon et al., 2003;Caroll et al., 2008;Martinez Santos and Andreu, 2010;Worthington, 2003), or other conceptual approaches such as (Rimmer and Salingar, 2006). These approaches do not deal with the effects of a massif Alpine karst aquifer itself on the hydrology of a catchment or sub-catchment. Barthel (2011) recommends groundwater studies that focus on the 10 catchment scale. Kunstmann et al. (2006b) applied the distributed model WaSiM-ETH in alpine catchments. To the author's knowledge, so far, no attempt has been made to examine the complete water balance of an Alpine karstified watershed and its subcatchments by applying a distributed hydrological model to determine possible subsurface boundary fluxes. White and White (2003) describe groundwater basins as total 15 recharge areas including all surface stream catchments that drain into the conduit system of a spring. Overall, karst ground water basins from springs do not correlate with the boundaries of overlying surface water basins; they may also be linked by piracy or spillover routes. Conduits develop across surface water divides thereby transmitting water to or from other nearby surface water basins. Furthermore, groundwater basins 20 have one set of flow paths active during base flow conditions and quite a different set of flow paths during flood flow conditions (White and White, 2003). Our study area is characterized by hundreds of springs connected to fracture, conduit or cave systems with an unknown set of active or inactive flow paths. We assume, however, that water fluxes in an high Alpine 1000 m banked limestone aquifer with an inclined stratifica- 25 tion can lead to groundwater inflow, outflow or redistribution on an even larger scale than spring basins -at catchment scale, where subbasins cover valleys in mountainous regions, and that this affects river runoff within those subbasins and consecutive streams.
218 Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper |

Summary of the new approach
Within the study area, each of the three high Alpine head subcatchments is unique in subsurface hydrological systems (Kraller et al., 2011), and measured runoff differs significantly in between the valleys within the same time period. By applying the distributed model, we are able to show that high Alpine aquifers do have tremendous effect 5 on the hydrology of subbasins and that common approaches for distributed modeling (Richards, 2-D -Groundwater-Model, Darcy and continuity equation) of water balance perform insufficiently. By analyzing measured runoff, and model results for precipitation, evapotranspiration and runoff we found systematic data patterns in model mismatch, and, consequently mismatch in modeled and observed water storage in three 10 neighbouring subbasins "Klausbachtal", "Wimbach" and "Königsseetal" (Fig. 1). This under-and overestimation affects model results in consecutive subbasins within the model area and the model area outflow. Different precipitation interpolation approaches did not allow to correct for this mismatch. Therefore, we conclude that different storage conditions lead to under and overestimation of runoff, and thus we develop a method 15 to calculate missing water fluxes to enable flexible inflow and outflow at subbasin scale on a monthly time basis. We derive the analytical solution of the artificial neural net to calculate observed water storage which can be implemented in the distributed model as inflow or outflow in the saturated zone as continuous boundary flux (Fig. 2). The implemented flux is considered in the model run and affects modeled stream discharge 20 of consecutive subbasins. Not only does this method allow to describe water storage dynamics and resulting groundwater inflow and outflow in karstic terrains; it also allows to adapt distributed hydrological models to karst dominated watersheds.

Study area and former karst research results
The study site encompasses the watershed of the river Berchtesgadener Ache and is 25 situated in the Berchtesgaden Alps in the southeast of Germany in the Federal State of 219 Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Bavaria. The area covers 432 km 2 and is mostly German territory. Ten per cent, however, is Austrian national territory. Most of the area can be assigned to the Man and Biosphere Reserve Berchtesgaden, of which the core zone is Berchtesgaden National Park (IUCN Category II) with an area of 210 km 2 (Fig. 1). The climate in the area is cool-temperate and humid. Mean temperature is 4.5 • C. Precipitation has an altitude 5 -dependent gradient of 47 mm/100 m. Annual precipitation ranges from 1500 mm in the valleys to up to 2600 mm in higher elevated regions. Maximum precipitation is 250-350 mm in July in the high Alpine regions of the test site, albeit high uncertainties exist as only few stations are established in higher regions. The number of days with snow cover is more than 300 per year in peak regions. Dominant biotopes are 10 forest, limestone grasslands, rock and scree, mountain pines and lakes and glaciers. The Berchtesgaden Alps are situated in the northern limestone Alps and can be seen as a geomorphological unit. The nine associated mountain ranges to the watershed "Berchtesgadener Ache" are shaped in close proximity as plateaus and ridges. Three valleys stretching from south to north, separating four mountain massifs from each is covered by the Tiefjuvavikum which itself lies beneath the Hochjuvavikum. Alpine fold leads to a typical slope and inclined stratigraphy of the existing rock formations. The mountain massifs Hochkalter and Watzmann slope slightly in a northern direction (Fischer, 2005;Langenscheidt, 1994). The soluble limestone has been exposed to karstification processes since the Alpine lift, which took place in different phases. 25 Typical karst phenomena in the region are the presence of dolines, basins, dry stream beds, caves and karrens. The massif karst aquifer in the area is characterized by matrix, fractures and conduits. The epikarst and vadose zones are more dominant than the phreatic zone. Most of the spring discharge is a reaction to precipitation events.

220
Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | A spring horizon at the south shore of a lake which shows phreatic behaviour but reacts also to precitpitation events. There are no permanent sinking streams within the study area, but snowmelt and rain immediately infiltrate through swallow holes, especially on karst plateaus. Based on spring locations, the boundary between unsaturated and saturated zone is estimated at an altitude of 601 m a.s.l. and 1500 m a.s.l. maximum, 5 but mainly at 700-1000 m a.s.l. Consequently, the unsaturated zone can be up to 1000 m in thickness. The eight rivers within the watershed drain the area in a northerly direction. Based on nine river gauges available for the basin, it can be divided into nine subbasins (Fig. 1). Several tracer experiments, a spring database and geological conditions indicate a main groundwater flow direction from the south. Further-10 more, groundwater redistribution between subcatchments is also indicated between three neighbouring Alpine head sub-catchments streching from north to south (Kraller et al., 2011). These subbasins are located in a highly karstified area with a steep terrain.

Model set up
We applied the distributed model WaSiM-ETH (Schulla, 1997(Schulla, , 2007 in a horizontal resolution of 50 m and a temporal resolution of 1 h. The basin and borders of the subbasins were derived by the digital elevation model and the location of river gauges.

5
Eight gauges are located in Germany and one in Austria. The model uses physicallybased algorithms within its modular system. Precipitation interpolation was done using Inverse Distance Weighting and linear regression linearly combined (IDW weighted with 0.25). Interpolation of other meteorological input data was done by Inverse Distance Weighting. Infiltration is calculated after Peschke (1977), evapotranspiration af-10 ter Penman-Monteith (Penman, 1948;Monteith, 1975;Brutsaert, 1982), snow cover dynamics are calculated following Strasser (2008). Direct flow (surface runoff) is the sum of infiltration excess, saturation excess and a defined fraction of the snow melt. Vertical soil water fluxes within a defined number of soil layers and depth in the unsaturated zone are described by solving the Richards equation (Richards, 1931). Soil 15 parameterization is done according to Van Genuchten (1976). Interflow is calculated depending on suction, drainable water content and saturated hydraulic conductivity. The distributed model was applied with a 2-D groundwater model coupled to the unsaturated zone with a vertical boundary flux. The lower boundary of the unsaturated zone is the depth of the groundwater layer. Horizontal groundwater flow is calculated 20 by the flow equation derived from Darcy's law and the continuity equation. The saturated zone is located within the defined soil layers and depth, groundwater level is calculated corresponding to soil water content and previous storage conditions. The aquifer is assumed to be unconfined. Storage conditions within the unsaturated zone are initialized for each discretization layer with a water content corresponding to an 25 hydraulic equilibrium with the groundwater (fluxes are zero) and the groundwater table is assumed to be at a depth of 20 % of the soil column. In principle, the model environment is not able to account for karstic underground. A porous aquifer is assumed. It 222 Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | represents a substitutional porous media model whose parameters must be interpreted as effective parameters approximating the karstic environment on subcatchment scale (Kunstmann et al., 2006a). Next to numerous free model parameters, sensitive calibration parameters are the recession constant k rec for the saturated hydraulic conductivity and the interflow drainage density d r (Schulla, 1997(Schulla, , 2007. Discharge routing is done 5 with a kinematic wave approach, including a flow time table, retardation and translation. Due to fast infiltration and high evapotranspiration in bare karst area, we adapted parameters for evapotranspiration over rock surfaces leading to increased evapotranspiration for these areas. Furthermore, we also allowed for macropore -infiltration as it is implemented in the distributed model after Jansson and Karlberg (2001). Data for soil classification were derived from the existing soil database of the National Park authority and the concept soil map provided by the Bavarian Environment Agency. Land use classification was derived from Lotz (2006) and Corine Land Cover data. We classified 15 land use types and 20 soil types within the model area. Soil stratification was defined for 40 layers with a depth of 0.2 m to 4.0 m according the distributed porous ap- 15 proach. Information on the hydraulic saturated conductivity was derived from BGRSGD (2007). Best parameterization for aquifer thickness and the specific storage coeffcient were iteratively estimated. River courses were derived from the digital elevation model during preprocessing. The discharge data was provided by the Traunstein water management office and the Salzburg hydrographical service. Meteorological input data 20 was provided by 33 weather stations whereby 20 are automatic and 15 are mechanical stations (Table 1). The stations are equally distributed in altitude (604-1973 m a.s.l.) and space throughout the model area ( Fig. 4)

Analysis of precipitation interpolation methods
We found, there to be a mass problem within the distributed model, because it was not 25 able to reproduce measured runoff in the Alpine head catchments. Various interpolation methods to analyze whether precipitation input data was the cause for the deviation or not were investigated. The precipitation interpolation methods Inverse Distance 223 Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Weighting (IDW), Elevation Dependent Regression and a linear combination of IDW and Elevation Dependent Regression (weighting factor IDW: 0.25) were tested for the annual sum of precipitation in subbasin Königsseetal. Annual sums of interpolated precipitation were 1559 mm for IDW, 1704 mm for regression and 1643 mm for the linear combination of both methods (Table 2). IDW shows the lowest value because the 5 elevation dependency of the precipitation was not considered (1559 mm). Analyses of station data within the area however proved gradient dependency of precipitation amount. In high Alpine terrain, IDW was not considered appropriate for the application. Regression showed the highest value, because it did not reproduce station data (1704 mm). The combined method is giving a value between the two other methods, 10 because it takes into account elevation dependency and station data (1643 mm). We analyzed both methods for one station by comparing the overall mean from 2001-2010. The analysis revealed that REG + IDW could best reproduce the station data. Figure 5 shows modeled runoff resulting from the different interpolation methods. Runoff dynamics differ slightly, and no method resulted in improved model results. Therefore, 15 we conclude unknown storage processes to be the most likely cause for the model mismatch.

Outcomes distributed modeling -identification and quantification of boundary fluxes
In a first step, we analyzed annual sums and overall means of measured runoff 20 and modeled precipitation, evapotranspiration and runoff at the river gauges of the three high Alpine neighbouring head subbasins Klausbachtal (1), Wimbachtal (2) and Königsseetal (4) ( nual sums of modeled runoff, dependent on precipiation input. Mean annual modeled discharge was 1325 mm in subbasin Klausbachtal, 1280 mm in subbasin Wimbachtal and 1201 mm in subbasin Königsseetal. Consequently, a systematic over-and underestimation of discharge was found in these sub-catchments when comparing modeled to measured runoff (Fig. 6). Based on analyses of several precipitation interpolation approaches, we assume that different annual sums of measured runoff in subbasin Klausbachtal, Wimbachtal and Königsseetal to be the result of subsurface boundary fluxes that were not taken into account by the distributed model, leading to under and overestimation of measured runoff during model runs. Since it is the characteristic subsurface conditions and resulting water fluxes that influence the water balance in karst 15 aquifers, the monthly sums of water storage for subbasins Klausbachtal, Wimbachtal and Königsseetal were analyzed in model runs and reality to gain more information about the annual dynamics of the water storage. By substracting the runoff (Q) from the incoming effective precipitation (Eq. 1) storage reduction or buildup is expressed and is assumed to be positive in winter and summer (snow storage and soil storage) 20 and negative in spring and autumn (snow melt and soil storage decrease), leading to a systematic pattern throughout one year. Deviations from the assumed pattern for the observed water storage may give insights into groundwater inflow, outflow or redistribution at subbasin scale due to subsurface water fluxes. Monthly sums of modeled and observed water storage were analyzed (Eqs. 2 and 3).  Figure 7b shows the water storage derived from the measured runoff.

5
It shows negative peaks during summer for subbasins Klausbachtal and Königsseetal (Fig. 7b). There is more runoff than precipitation coming in, indicating groundwater inflow and explaining the amount of measured annual runoff. In subbasin Klausbachtal, there is less soil storage and snow melt, indicating groundwater outflow and explaining the annual lack of water. Table 4 shows the maximum, minimum and mean of monthly modeled and measured water storage. In subbasin Klausbachtal, mean of observed water storage is positive (15 mm), indicating water outflow from the subbasin. It is underestimated by the distributed model (−2 mm), because water outflow is not calculated and all incoming precipitation is routed to the stream. In subbasins Wimbachtal and Königsseetal, mean water storage is negative (−24 mm; −59 mm) indicating more 15 river runoff than incoming precipitation and consequently water inflow into the system. Figure 8 shows monthly sums for measured runoff and distributed model runoff for summer months of the years 2007 to 2011. Modeled runoff underestimates measured runoff. Figure 9 shows the annual dynamic of main water balance components for each hydrological year within the study period for subbasin Königssetal. Figure 9a,b shows 20 the sum of snowmelt and rain and snowmelt only. In November, snowmelt and rain are hydrological input into the system, from February to June snowmelt is dominant, and from June to October it is mainly rainfall that contributes to the water balance in the subbasin. The evapotranspiration (Fig. 9c) shows an annual dynamic with a peak in July. Figure 9d shows water storage derived from the modeled runoff by the distributed model. In winter months, storage is nearly zero, in spring values are negative due to snow melt, while in summer values are slightly positive due to soil water storage. Figure 9e shows the water storage derived from the measured runoff. In winter months, the storage is positive due to snow cover build-up. In May there is strong snow melt impact, leading to negative storage values. In summer months, storage remains negative, indicating water inflow through unknown subsurface processes. We assume that underground catchment sizes differ from surface catchment sizes as they are presumed for distributed modeling, and that this is the cause of deviating water storage quantities (Fig. 2).

4 Artificial neural net to calculate boundary fluxes and distributed model correction
Analysis of the mismatches indicate, that there are systematic subsurface boundary fluxes, which can be expressed as observed water storage. The distributed model needs to be adapted to the special hydrological systems in the high Alpine karst environment. We developed an Artificial Neural Network (ANN) as introduced by Herz et al. (1991) and Haykin (1999) to calculate the observed water storage (Fig. 2)

Artificial Neural Network (ANN)
We implemented a two layer feedforward Artificial Neural Network (ANN) with a sigmoid function in the hidden layer and a linear function in the output layer for the subbasins Klausbachtal, Wimbachtal and Königsseetal each (Fig. 10). The exogenous inputs are 25

227
Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | monthly means of temperature T m (t), relative humidity RH m (t) and monthly sums of snowmelt SN m (t) and rain P m (t), which is QS m (t) (Eq. 4) and gives the observed water storage S(t) (Eq. 5). Explanatory variables for the artificial neural net are outputs of the distributed model to ensure that the ANN is not based on any measured data. During the training process and input data testing, three input variables turned out to 5 perform best. Temperature T m (t) and air humidity RH m (t) as interpolated meteorological variables to capture seasonality and air moisture; Q Sm is the calculated input into the hydrological system. This study concentrates on monthly sums; therefore, no sliding window is needed. Selection of the number of hidden neurons was done by trial and error. Best results were obtainend with 20 neurons (n = 20) in the hidden layer. 10 The ANN was trained and validated with 65 months (m = 65) and tested for m = 44 (test data). The dataset for training and validation was split up into m = 56 (85 %) for training and m = 11 for validation (15 %). Net training to obtain the parameters a i to f i was done with the Levenberg-Marquardt algorithm for which the RMSE was chosen as the objective function to be minimized (Eq. 6). Table 5 shows the weights and biases 15 derived by the training process.
Net input and output were normalized from r min = −1 to r max = 1 and backtransformed 20 using the following equations (Eqs. 7 and 8) during pre-and postprocessing: 228 Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper |

Performance evaluation -ANN
We show monthly sums of observed water storage simulated with the ANN in subbasin Königsseetal for the test period of the neural net from March 2007 to October 2009 (m = 444). Correlation of the observed water storage simulated with the ANN and the observed water storage give r 2 = 0.48 (Fig. 11), whereby the NSE = 0.43 and 5 the RMSE = 0.27 (Table 6). Figure

Distributed model correction: implementation of boundary flux in the saturated zone
We used the monthly outcomes of the artificial neural network as a basis for the con-20 stant boundary flux into the distributed model (Fig. 2). The monthly sum of observed water storage simulated with the neural net was subtracted from the modeled water storage already calculated for the investigated period (Eq. 9). The difference was implemented as continuous boundary flux Q bound (t) in m s −1 per hour for each month in the saturated zone at selected sites at the border of subcatchments. Therefore, the This method is not a bias correction of modeled runoff at the outlet point, but an inflow within the groundwater model, which the model accounts for and which is considered 5 in the following modeling process. The inflow size can vary from one grid cell to the whole subbasin area. We implemented a boundary flux based on the results of the test period of the neural net from July to October for the years 2007 to 2009. The results are presented in Fig. 13. 10 Within the scope of this study, we could show the limitations of a distributed model in high alpine terrain with massive carbonate aquifers. We were able to quantify systematic model mismatch at subbasin scale and point out hydrological processes within these heterogeneous catchments that deviate from common model assumptions (Darcy Flow, Porous Media Conditions). To enable distributed modeling within 15 these catchments, which are the origin of lowland river runoff quantities and dynamics, we developed a method to describe and account for the missing water quantities. By the given station data and interpolation method, unrealistic precipitation assumptions are not the case and could be suspended as the underlying reason for the model mismatch. Therefore, we concluded an uneven observed water balance for the given 20 sub-catchments to be the cause, because of unknown subsurface boundary fluxes. Or, in other words, the real catchment size for river gauges differs from the size assumed by the distributed model due to underground fluxes. By assuming porous conditions, the model is unable to account for extreme differences in hydrological system at catchment scale resulting in consistent model mismatch. Figure 15 shows the results of the approach provides detailed information on the heterogeneous Alpine catchment. The annual sum of precipitation ranges from 1300 mm in the valleys to over 2100 mm in mountainous regions. Evapotranspiration is calculated from zero to over 1400 mm at extreme locations. Relative humidity ranges from 0.70 % to over 0.82 %. Mean annual temperature is from 10 • C in valleys to −2 • C at elevated regions. The massive karst 5 aquifer itself and, the location of all conduits and subsurface flow channels, remains a black box. However, based on tracer experiments and the spring locations we were able to synthesize that the main underground flow direction tends to be north, which corresponds with the results of the distributed model mismatch (Kraller et al., 2011). Since we are unable to quantify each underground flux in the study area, and especially the dynamics throughout a hydrological year, we chose a statistical method to capture unknown underground flow processes at catchment scale on a monthly basis. By developing the artificial neural net, we were able to reproduce monthly storage deviations. A two layer feedforward backpropagation network with a sigmoid function in the hidden layer and a linear function in the output layer with 20 neurons in the Performance of the distributed model improved with implementation of the constant boundary flux (Eq. 9). NSE increased from 0.34 to 0.57 and the RMSE decreased from 6.10 mm to 1.66 mm, which shows that after implementation of the boundary flux the distributed model was better at reproducing the measured runoff (Table 6). Figure 13 shows monthly sums of measured runoff, modeled runoff and  Figure 14 shows main components of the annual water balance of 2007 in subbasin Königsseetal before and after distributed model correction. As the inflow takes place in the saturated zone module, annual sums of precipitation (1604 mm), evapotranspiration (432 mm), effective precipitation (1181 mm) and observed water storage 5 (−618 mm) are equally calculated before and after the boundary influx. Observed water storage was negative in the annual balance, because subsurface water inflow takes place throughout subbasin borders (derived by the DEM). In the original model run, the modeled runoff (1094 mm) underestimated measured runoff. After implementing the boundary flux, modeled runoff is increased to 1487 mm. Originally, modeled water 10 storage was minimal (18 mm), because the distributed model calculates even annual water balances internally. By correcting the distributed model with the constant inflow on a monthly basis, annual modeled water storage resulted in −306 mm and better reproduction of observed water storage. At river gauge St. Leonhardt, which is the outlet of the whole catchment, modeled runoff also increases, showing improved dis- 15 tributed modeling for the overall study area. Figure 15 shows the mean groundwater level in the region in the year 2006-2007. Based on the assumed soil layers, which had to be in the given range of the distributed model, groundwater reaches the surface in valley regions, as steep gradients lead to increased flow in hill slopes. Soil moisture in the root zone ranges from zero to almost 100 %. Storage capacities are 20 reached within the saturated zone in the given soil layers, and water excess is given to the unsaturated zone. Figure 16 presents runoff components of modeled runoff in year 2007 before and after implementation of the boundary flux. In the original model run, interflow and baseflow were calculated almost equally, whereas direct flow is the main contributor to modeled runoff. After implementing the boundary flux, interflow 25 increased most, whereas baseflow and directflow remain almost unchanged. As the groundwater module and unsaturated zone module in the distributed model are coupled bidirectionally, baseflow is converted to interflow within model performance. ANN has been used previously in hydrological studies, but mainly to predict and calculate the discharge of a given river course or spring rather than deviating storage conditions. Our new method describes the ANN analytically, and enables to calculate unknown storage processes in complex hydrogeological environments on a monthly basis. With this method, the distributed model reproduces storage conditions more realistically in high Alpine karst terrain, which leads to a more realistic runoff at catchment scale.