Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | 0.57. This Sciences = Discussions Earth System Hydrology and , and 1 0.34 to NSE = , T. Marke 2,3 , S. Vogl 2,3 216 215 in discharge curves at the outlet points of neighboring ff , H. Kunstmann 0.48). The boundary influx in the sub-catchment improved 2 = 2 r ciently ( ffi 1 , M. Warscher 1 This discussion paper is/has been under review for the journal Hydrology and Earth System Sciences (HESS). Please refer to the corresponding final paper in HESS if available. Institute for Geography and Regional Science, Karl-Franzens University of Graz, Karlsruhe Institute of Technology (KIT), Institute for Meteorology and ClimateInstitute Change for Geography, University of Augsburg, Universitaetsstr. 10, cluding subsurface water transfer. tributed model. This is achieved bythree an input Artificial variables Neural are Network taken approach toWe (ANN), calculate explicitly where the derive unknown the subsurface storage algebraic conditions. transferthe function missing of boundary an fluxes. artificial Thewater neural result net of module to the of calculate ANN is theconsecutive then model distributed implemented process. in model the The ground- as ANNage was boundary data able su to flux, reproduce andthe the distributed considered observed model, water during as stor- performance the combined increased approach from allows NSE distributed quantification of water balance components in- modeled and measured runo high alpine sub-catchments. Variousto precipitation explain interpolation systematic methods did mismatches,were not and concluded allow unknown as subsurface theto describe hydrological underlying the processes reason. unknown subsurface boundary We fluxes, introduce and a account for new them method in the that dis- allows directions lead to unknownbe implemented storage by quantities. traditional approachesand Reliable due catchment distributed to scale. unknown We modeling present storagehydrological cannot an processes model artificial at (WaSiM-ETH) neural local that network extension allowsin of to a a karstic account distributed environment. for The subsurfaceriver extension water “Berchtesgadener was Ache” transfer developed (Berchtesgaden for the Alps,by Alpine Germany), extreme catchment which topography of is and the characterized calcareousand rocks. does The not model assumes account porous for conditions karstic environments, resulting in systematic mismatch of The water balance in highof Alpine meteorological regions variables is in space often andsteep characterized time, gradients. by a significant The complex system variation hydrogeological is situationinated even and more by complex soluble when limestone, the because rock composition unknown is underground dom- flow conditions and flow Abstract Hydrol. Earth Syst. Sci. Discuss.,www.hydrol-earth-syst-sci-discuss.net/9/215/2012/ 9, 215–259, 2012 doi:10.5194/hessd-9-215-2012 © Author(s) 2012. CC Attribution 3.0 License. Water balance estimation in highterrain Alpine by combining distributed modeling and a neural network approach (Berchtesgaden Alps, Germany) G. Kraller U. Strasser 1 Heinrichstr. 36, 80102 Graz, Austria (IMK-IFU), Kreuzeckbahnstr. 19, 824573 Garmisch-Partenkirchen, Germany 86159 Augsburg, Germany Received: 13 December 2011 – Accepted:Correspondence 19 to: December 2011 G. – Kraller Published: ([email protected]) 5 JanuaryPublished 2012 by Copernicus Publications on behalf of the European Geosciences Union. 5 25 15 20 10 Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | , , , ; 2006 ). For ). Dis- , Bonacci erent set ; ff 2004 2003 Caroll et al. Maloszweski , , ; ; 2008 , Ford 2003 ; 2002 Sauter et al. , ). Our study area is Teutsch and Sauter , ; ). The Alps are crucial 2004 2003 ), or other conceptual ap- , 2003 , , Geyer et al. 2007 ; , 2003 , Kiraly Scanlon et al. EEA 2005 ; , Viviroli and Weingartner ). These approaches do not deal with ) describe groundwater basins as total erent temporal and spatial scales deal 2005 within those subbasins and consecutive Grasso and Jeannin ff Romanov et al. , ; ff ; White and White 2006 ) applied the distributed model WaSiM-ETH Einsiedl Worthington 2003 ; ; 218 217 , ( cult to find an adequate parameterization to ). However, those methods faces challenges ). In the past, many studies have applied dis- 2001 ffi 2006 , , 2006b 2010 2004 ) attempt to take into account the heterogeneity of ( 2011 2003 , , Bakalowicz , , ; ). Other approaches concentrate on karst genesis or ) recommends groundwater studies that focus on the 2006 , ects river runo Kiraly ff 1977 2003 2011 , Kovacs et al. ( , Birk et al. Sauter et al. ; White and White Goldscheider Rimmer and Salingar 2001 ). Many approaches at di , Kunstmann et al. Sauter et al. ects of karst conduits to define the size and the characteristics of one Barthel Attkinson ff 2003 Weiler et al. , ; 2002 2005 ects of a massif Alpine karst aquifer itself on the hydrology of a catchment or Martinez Santos and Andreu Hauns et al. , ff , ; ). Spring hydrograph, chemograph, and tracer breakthrough curve analysis focus ; streams. water to or from otherhave nearby one surface set water of basins. flowof Furthermore, paths flow groundwater active paths basins during during basecharacterized flood flow by flow conditions hundreds conditions and of ( quitewith springs a an connected di unknown to set fracture, offluxes conduit active in or or an inactive cave flow high systems tion paths. Alpine can We 1000 lead assume, m to however, bankedthan that groundwater water spring limestone inflow, basins aquifer outflow – with orous at an redistribution regions, catchment inclined on and scale, that an stratifica- where this subbasins even cover larger a valleys scale in mountain- recharge areas including all surfacetem stream of catchments that a drain spring. intothe the Overall, boundaries conduit karst of sys- ground overlying water surfacespillover basins water routes. from basins; springs they Conduits do may also not develop be correlate across linked with surface by water piracy or divides thereby transmitting face boundary fluxes. in alpine catchments.to To the examine the author’s complete knowledge, watercatchments so by balance far, applying of no a an distributed attempt Alpine hydrological has model karstified to been watershed determine and made possible its subsur- sub- 2008 the e sub-catchment. catchment scale. tributed groundwater models in karst environments ( proaches such as ( ever mainly concentrate on modelingality water of fluxes karst within makessuccessfully the it saturated model zone. tremendously groundwater di flow Theassume in du- porous present conditions distributed ( models, which principally karst aquifers within single conduits or parameter fields in a spatial continuum, how- with the modeling of hydrological processes in karst aquifers (e.g. nant flow paths up to cavesarea. and The numerous duality spring of locations, karst, asflow enfolding is slow and the and case unknown fast for storage, infiltration, this slow leadssaturated study and to zone fast groundwater heterogeneous ( water flow in the unsaturated and “Hybrid Models” ( in Alpine areas,parameters on in account time of andfluxes high scale, and altitudinal snow storages. gradients, cover The variationwithin dynamics situation a of and watershed is consist unknown meteorological even of subsurface more soluble limestone, complex, water dissected when by the small fractures mountain and ranges domi- 1991 on small-scale e individual spring aquifer ( 2004 et al. theoretical conduit flow ( tributive methods, such as “SinglePorous Continuum Equivalent”, Porous “Discrete Equivalent”, Single “Double Fracture Continuum Sets” or “Discrete Multiple Fracture Set”, White sustainable water management ofunderstand water the resources hydrological in processes, alpine theirdrological areas, quantities modeling it and has dynamics. is becomein imperative Distributed to hy- catchments an (e.g. important tool for describing the water balance Alpine catchments are very importantEuropean albeit rivers vulnerable have landscapes. their Mosttransported of headwaters via the in river major Alpine systemsfor to catchments, water lower-lying and accumulation areas their and ( discharge water is supply (e.g. 1 Introduction 5 5 25 15 20 10 15 10 25 20 Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | ect ers ff ff di ). The ). This 2 ff 1 Man and ). The three 3 erent storage erent phases. ff ff ¨ onigsseetal” (Fig. ). The climate in the area is 1 ), and measured runo ects modeled stream discharge C. Precipitation has an altitude ◦ ff , and thus we develop a method , and model results for precipita- ff ff 2011 (Fig. , 2 erent precipitation interpolation approaches ff ). The soluble limestone has been exposed 220 219 Kraller et al. 1994 we found systematic data patterns in model mis- , and is mostly German territory. Ten per cent, how- , of which the core zone is Berchtesgaden National ff 2 ects model results in consecutive subbasins within the ff Langenscheidt ; ciently. By analyzing measured runo 2005 ffi , Fischer trix, fractures and conduits.the The phreatic epikarst zone. and Most vadose zones of are the more spring dominant discharge than is a reaction to precipitation events. to karstification processes sinceTypical karst the phenomena Alpine in the lift,beds, region which caves are and took the karrens. presence place of The in dolines, massif di basins, karst dry aquifer stream in the area is characterized by ma- main tectonic units in theis area are covered arranged by on the topfold of Tiefjuvavikum leads one which another: to itself The a lies baseThe typical Tirolikum beneath mountain slope the massifs and Hochjuvavikum. Hochkaltertion inclined ( and stratigraphy Alpine of Watzmann the slope existing slightly rock in formations. a northern direc- valleys stretching from southother are to representative for north, thelimestone area. separating and Dominant four rock Ramsau mountain formations are Dolomite,present. massifs Triassic but Dachstein from The Jurassic banked each and limestone700 m with Cretaceous of a Dolomite rock extends layer along series thickness an are of altitudinal gradient up also up to to 2100 1000 m m (Fig. covering 500– – dependent gradient ofthe 47 mm/100 valleys m. to Annual up250–350 precipitation mm to ranges in from 2600 July mm 1500ties in mm in exist the in higher as high only elevated Alpinewith few regions. regions stations snow of are cover Maximum the established isforest, test precipitation in more limestone site, higher is than grasslands, regions. albeit 300 rock highThe and The per Berchtesgaden uncertain- scree, number year Alps mountain of in are pines days peak situatedas and in regions. a lakes the geomorphological and northern Dominant unit. glaciers. limestone“Berchtesgadener biotopes Alps Ache” are The and are nine can shaped be associated in seen mountain close proximity ranges as to plateaus the and watershed ridges. Three Bavaria. The area coversever, 432 km is Austrian nationalBiosphere territory. Reserve Most Berchtesgaden of thePark area (IUCN can Category be II)cool-temperate assigned with and to an humid. the area of Mean 210 temperature km is 4.5 The study site encompasses thesituated in watershed the of Berchtesgaden the Alps river in the Berchtesgadener southeast Ache of and Germany is in the Federal State of as inflow or outflowimplemented in flux is the considered saturated in theof zone model consecutive as run subbasins. and continuous a boundary Notdynamics only flux and does resulting (Fig. groundwater this inflow method andto allow outflow adapt in to distributed karstic describe hydrological terrains; models water it to storage also karst allows dominated watersheds. 2 Study area and former karst research results did not allow to correctconditions for this lead mismatch. to Therefore, under weto and conclude calculate that overestimation missing di of water runo fluxeson to enable a flexible monthly inflow time and basis. outflowcalculate at We observed subbasin derive water scale the storage analytical which solution can of be the artificial implemented in neural net the to distributed model on the hydrology of(Richards, subbasins 2-D and – that Groundwater-Model, common Darcyperform and approaches insu continuity for equation) distributed of modeling watertion, balance evapotranspiration and runo match, and, consequently mismatchneighbouring in subbasins modeled “Klausbachtal”, and observed “Wimbach”under- water and and storage “K overestimation in three a model area and the model area outflow. Di Within the study area,in subsurface each hydrological of systems thesignificantly ( three in high between the Alpinetributed valleys head model, within we subcatchments are the able is same to show unique time that high period. Alpine aquifers By do have applying tremendous the e dis- Summary of the new approach 5 5 25 15 20 10 25 15 20 10 Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | ). Soil Kraller ) is the ff ) is filled 2 ) and very 1931 3 , ), snow cover ) in a horizontal 1982 , 2007 Richards , ), evapotranspiration af- ). Interflow is calculated 1997 1977 , 1976 ( Brutsaert ( ; ¨ onigssee (511 mio m ). Direct flow (surface runo 1975 Schulla , Peschke 2008 ( 221 222 ). ) is characterized by forests at lower altitudes Monteith 3 Van Genuchten 2 ; Strasser 1948 , ) is characterized by Lake K 2 Penman ). Several tracer experiments, a spring database and geolog- 1 ). These subbasins are located in a highly karstified area with a steep ter- 2011 , ¨ onigsseetal (163.54 km 3.1 Model set up We applied the distributed model WaSiM-ETH ( is assumed to be atment a is depth of not 20 able % of to the account soil for column. karstic In underground. principle, the A model environ- porous aquifer is assumed. It 3 Distributed modeling in high Alpine terrain saturated zone with azone vertical is boundary the flux. depthby of The the the lower groundwater flow boundary layer. equation ofurated Horizontal derived the zone groundwater from unsaturated is flow Darcy’s is locatedcalculated law calculated within corresponding and the to the defined soil continuityaquifer soil water equation. is layers content assumed and The and to depth,are be sat- previous unconfined. storage initialized groundwater conditions. level Storage for is conditions eachhydraulic The within equilibrium discretization the with layer unsaturated the with groundwater zone (fluxes a are zero) water and content the corresponding groundwater table to an sum of infiltration excess,Vertical saturation soil excess water and fluxes asaturated within defined zone a are fraction described defined of byparameterization number the solving is of snow the done soil melt. Richards according equation layersdepending to ( and on depth suction, inThe drainable the distributed water un- model content was and applied saturated with hydraulic a conductivity. 2-D groundwater model coupled to the un- basins were derived byEight the gauges are digital located elevation inbased model algorithms Germany within and and its one the modular inInverse system. location Austria. Precipitation Distance of interpolation The Weighting river was model done andwith gauges. uses using 0.25). physically- linear regression Interpolationtance of linearly Weighting. other combined meteorological Infiltration (IDW input ister weighted calculated data Penman-Monteith after was ( done bydynamics Inverse are Dis- calculated following resolution of 50 m and a temporal resolution of 1 h. The basin and borders of the sub- K steep gradients. Itwhile is to bounded the by southMeer”. mount it Geologically is Watzmann and surrounded and hydrologically, by the theseological a neighboring and Hagengebirge huge subbasins hydrological plateau, Alpine features show (Fig. unique karst ge- plateau, called “Steinernes and high Alpine plateau and ridgemountain karst Reiteralm at and higher mount altitudes. Hochkalter.with It Dolomite is Subbasin gravel bounded Wimbachtal deposits, by (35.69 forming the km arounded plateau porous by mounts aquifer Hochkalter with and a Watzmann,bonate depth which stratum. of are 300 In characterzied m. the by southern It a part, is huge it sur- car- is surrounded by dolomite mountains. Subbasin 1000 m in thickness. Thedirection. eight rivers within Based the on watershednine drain nine the subbasins area river (Fig. in gauges aical available northerly conditions for the indicate basin,more, a it groundwater main can redistribution groundwater be betweenthree flow divided neighbouring subcatchments direction Alpine into is from head sub-catchments alsoet the streching al. indicated south. from between north to Further-rain. south Subbasin ( Klausbachtal (42.79 km also to precitpitation events. Therearea, are but no permanent snowmelt sinking andon streams karst rain within plateaus. the immediately study Based infiltratesaturated on through zone spring is locations, swallow estimated the holes,but boundary at especially an between mainly unsaturated altitude at and of 700–1000 601 m m a.s.l. a.s.l. and 1500 m Consequently, a.s.l. the maximum, unsaturated zone can be up to A spring horizon at the south shore of a lake which shows phreatic behaviour but reacts 5 5 25 15 20 10 15 20 10 Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | ff 5 dy- cient ff ff BGRSGD ). Data for 2001 ( ranged from 996 mm ff at the river gauges of the ). Discharge routing is done ff 2007 , ered significantly in these subcatch- ff for the saturated hydraulic conductivity di Jansson and Karlberg 1997 ) and Corine Land Cover data. We clas- ff , erent interpolation methods. Runo ) rec ff 4 ¨ k onigsseetal. Annual sums of interpolated ). IDW shows the lowest value because the 2006 224 223 2 ( Schulla ( r in the Alpine head catchments. Various interpola- Lotz d IDW could best reproduce the station data. Figure ff + ). Annual sums of measured runo ). Next to numerous free model parameters, sensitive calibra- 3 resulting from the di ff 2006a , ). The stations are equally distributed in altitude (604–1973 m a.s.l.) 1 ce and the Salzburg hydrographical service. Meteorological input data ffi er slightly, and no method resulted in improved model results. Therefore, ff ). Best parameterization for aquifer thickness and the specific storage coe ective parameters approximating the karstic environment on subcatchment scale boundary fluxes ff ¨ ¨ onigsseetal (4) (Table onigsseetal. Annual sums of measured runo Kunstmann et al. 2007 ments. Precipitation ranged1621 from to 1607 1940 mm to in 2112 mm subbasin in Wimbachtal subbasin and Klausbachtal, from from 1511 to 1869 mm in subbasin of station data withinamount. the In area high howevertion. Alpine proved Regression terrain, gradient showed IDW dependency the was(1704 of highest mm). not precipitation value, considered The because combined appropriate itbecause method did for it not is the takes reproduce giving applica- into station aanalyzed account data both value elevation methods between dependency for one the and station twoThe by station comparing other analysis data the revealed methods, overall (1643 that mean mm). REG from 2001–2010. We In a firstand step, modeled we precipitation,three evapotranspiration analyzed high and annual Alpine runo neighbouring sumsK head subbasins and Klausbachtal overall (1),to Wimbachtal means (2) 1375 mm of and in measuredbasin subbasin Wimbachtal runo Klausbachtal (mean 2091) (meanK and 1207), from from 1197 1045 to 1831 to mm 2808 (mean mm 1604) in in sub- subbasin and Elevation Dependent Regression (weightingannual factor sum IDW: 0.25) of were precipitationprecipitation tested were in for 1559 the mm subbasin for K ear IDW, 1704 combination mm of for both regression methodselevation and (Table dependency 1643 mm of for the the lin- precipitation was not considered (1559 mm). Analyses namics di we conclude unknown storagemismatch. processes to be the most3.3 likely cause for Outcomes the distributed modeling model – identification and quantification of Weighting (IDW), Elevation Dependent Regression and a linear combination of IDW shows modeled runo tion methods to analyzetion whether or precipitation not input were data investigated. was The the precipitation cause interpolation methods for Inverse the Distance devia- 3.2 Analysis of precipitation interpolation methods We found, there to beable a mass to problem reproduce within measured the runo distributed model, because it was not defined for 40 layers with aproach. depth Information of on 0.2 the m hydraulic to saturated 4.0 conductivity m was according derived the from distributed porous ap- and space throughout the model area (Fig. tion parameters are the recessionand constant the interflow drainage density tion. Due to fast infiltrationparameters and for high evapotranspiration evapotranspiration over in rock barespiration surfaces karst for leading area, these we areas. to adapted increasedit Furthermore, evapotran- is we implemented also in allowed thesoil for distributed macropore classification model were – after derived infiltration from as thority the and existing the soil concept database of soiluse the classification map National was provided derived Park by from au- thesified Bavarian 15 Environment land Agency. use Land types and 20 soil types within the model area. Soil stratification was agement o was provided by 33 weather stationsstations whereby (Table 20 are automatic and 15 are mechanical as e ( with a kinematic wave approach, including a flow time table, retardation and transla- were iteratively estimated. River coursesduring were preprocessing. derived from The the discharge digital data elevation was model provided by the Traunstein water man- represents a substitutional porous media model whose parameters must be interpreted ( 5 5 10 25 15 20 25 10 15 20 Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | . ff for (1) (2) (3) ff show ) from ff Q ( a,b shows . In winter ff by the dis- ¨ onigsseetal 9 ff in subbasin ff ff 59 mm) indicating more − underestimates measured . In subbasin Klausbachtal, ff ff ¨ than precipitation income (soil onigssetal. Figure ff and distributed model runo 24 mm; ). 3 − ff indicates a unique hydrology in each ff and 2 c) shows an annual dynamic with a peak 9 2 mm), because water outflow is not calcu- ) storage reduction or buildup is expressed − 226 225 1 during model runs. Since it is the characteristic sub- erent annual sums of measured runo ¨ onigsseetal to be the result of subsurface boundary shows the maximum, minimum and mean of monthly ff ff 4 than precipitation coming in, indicating groundwater in- ff , dependent on precipiation input. Mean annual modeled ¨ onigsseetal. Consequently, a systematic over- and under- ff ). Based on analyses of several precipitation interpolation ) ¨ onigsseetal), respectively. Mean annual evapotranspiration 6 t b shows the water storage derived from the measured runo ( ) 7 t ( meas (Fig. mod Q ) ff t Q d shows water storage derived from the modeled runo − ective precipitation (Eq. ) shows the annual dynamic of main water balance components for each 9 − ff t ¨ ¨ onigsseetal in monthly sums for the summer period in years 2001 to onigsseetal. The measured runo ) ( ET( 9 e shows the water storage derived from the measured runo t ff 9 ( e − ff than incoming precipitation and consequently water inflow into the system. ) P e t ff shows monthly sums for measured runo ( P = a shows the water storage modeled for the subcatchments Klausbachtal, Wim- ) P = 8 t 7 b). There is more runo ¨ ) ( ¨ onigsseetal were analyzed in model runs and reality to gain more information onigsseetal, mean water storage is negative ( = . Figure t 7 ) ( ff real t ( ff ¨ onigsseetal, resulting in an overall mean of 1772 mm (Klausbachtal), 1704 mm (Wim- mod obs e months, the storage is positive due to snow cover build-up. In May there is strong snow due to snow melt,age. while in Figure summer values are slightly positive due to soil water stor- tributed model. In winter months, storage is nearly zero, in spring values are negative P S S hydrological year within the studythe period sum for of subbasin K snowmeltare and hydrological rain input and intoand the snowmelt from system, only. June from to In Februarythe October November, subbasin. to it snowmelt June The is and snowmelt evapotranspiration mainlyin rain (Fig. is rainfall July. dominant, that Figure contributes to the water balance in and K river runo Figure summer months of the yearsruno 2007 to 2011. Modeled runo (Fig. flow and explaining the amountthere of is measured less soil annual storage runo the and annual snow lack melt, of indicating groundwater water.modeled outflow Table and and explaining measured waterwater storage. storage In is subbasin positiveunderestimated Klausbachtal, by (15 mean the mm), of distributed indicating model observed lated ( water and outflow all incoming from precipitation the is subbasin. routed to the It stream. is In subbasins Wimbachtal bachtal and K 2011. Storage is alwaysstorage positive as buildup) there in is the lesspositive distributed values. runo model. Figure The monthlyIt shows sums negative of peaks modeled during runo summer for subbasins Klausbachtal and K and is assumed toand be negative positive in in spring wintera and and systematic autumn summer pattern (snow throughout (snow melt one storageobserved and year. and Deviations water soil soil from storage storage the storage) may decrease), assumedbution give pattern leading at insights for to subbasin the scale into due groundwater toobserved inflow, subsurface water water outflow storage fluxes. or were Monthly redistri- analyzed sums (Eqs. of modeled and Figure surface conditions and resulting wateraquifers, fluxes the that monthly influence sums theand of water K water balance storage in for karst about subbasins the Klausbachtal, annual Wimbachtal dynamicsthe of incoming the e water storage. By substracting the runo discharge was 1325 mm inand subbasin 1201 mm Klausbachtal, in 1280 mm subbasinestimation K in of subbasin discharge Wimbachtal was foundto in measured these sub-catchments runo when comparingapproaches, modeled we assume thatKlausbachtal, di Wimbachtal and K fluxes that were not takenoverestimation of into measured account runo by the distributed model, leading to under and bachtal) and 1681 mmwas (K 367 mm for subbasin Klausbachtal,for 348 subbasin mm K for subbasin Wimbachtalvalley. and 425 After mm distributed modelnual calibration, sums model of runs modeled result runo in equally calculated an- K 5 5 25 25 15 20 10 20 15 10 Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | i f 44 (4) (5) (6) (7) (8) ) to to = i Dixon Neural a m ); ® 2006a Herz et al. ( 1997 56 (85 %) for ). Neural net- ( 2 = m 1 and backtransformed ) and monthly sums of 20) in the hidden layer. t Dou et al. ( = = 65) and tested for m is the calculated input into n ). The exogenous inputs are = Kunstmann et al. max ) as interpolated meteorolog- ) and gives the observed wa- Sm r t shows the weights and biases 10 4 ); m ( Q m 5 1 to 2010 − ( ) (Eq. = t ( ) t ( m ). Table min m r 6 ) during pre- and postprocessing: QS RH 8 i f 228 227 + ) t 2 ( er from surface catchment sizes as they are pre- and m )) ), relative humidity RH ff T t i t 7 ( ( e i + m ) ¨ real onigsseetal each (Fig. b t T ) and air humidity RH ( ), which is t m t ( obs ( min m S r QS m min i T Kurtulus and Razack P − d x + ) + i ); + t ) to calculate the observed water storage (Fig. ( c 2 min ) e ). Explanatory variables for the artificial neural net are outputs / t x min ) 5 ANN ( + x − 2011 1999 m 1 ( ( obs min − 1 x S x n 11 for validation (15 %). Net training to obtain the parameters ). = max SN ) and rain ( i X t 2 − x 1 ) (Eq. = ( + n ) = t + ) i m ( X i t m ( max S a 1 n min Haykin x r m = P v u u t − ) Siou et al. 1)( t = = ( ) + ) and ); t max ( y r ANN ( ( correction m = = obs 1991 2005 derived by the training process. QS S RMSE x Net input and outputusing were the normalized following from equations (Eqs. the objective function to be minimized (Eq. ical variables to capture seasonalitythe hydrological and system. air moisture; Thising study concentrates window on is monthly needed. sums;and therefore, Selection error. no of slid- Best theThe results number ANN were of obtainend was hidden with trained neurons(test 20 and was data). neurons done validated The ( by with datasettraining trial 65 for and training months and ( validationwas done was with split the up Levenberg-Marquardt algorithm into for which the RMSE was chosen as y snowmelt SN ter storage of the distributed modelDuring to the ensure training that process theperform and ANN best. input is Temperature data not testing, based three on input any variables measured turned data. out to monthly means of temperature works have already been applied in karstic environments by 4 Artificial neural net to calculate boundary fluxes and distributedAnalysis model of the mismatchesfluxes, indicate, which that can thereneeds be are to expressed systematic be as subsurface adapted to observedronment. boundary the We water developed special an storage. hydrological Artificial systems Neural in Network The (ANN) the as distributed high introduced Alpine model by karst envi- negative, indicating water inflow throughthat unknown underground subsurface catchment processes. sizes We di sumed assume for distributed modeling,quantities and (Fig. that this is the cause of deviating water storage function in the hiddenKlausbachtal, layer Wimbachtal and and a K linear function in the output layer for the subbasins melt impact, leading to negative storage values. In summer months, storage remains ( ( Input variables are distributed model outputs.usually Artificial Neural implemented Network using approaches libraries, are Network as Toolbox they libraries. are We e.g. presentenable available for implementation the of the analytical this Matlab solution method of within the the neural distributed network model4.1 source to code. Artificial Neural Network (ANN) We implemented a two layer feedforward Artificial Neural Network (ANN) with a sigmoid calculate spring response andstudy stream does discharge. not The calculate ArtificialWith stream this Neural or method Network we spring describe in discharge, the strong our but heterogeneity the and discontinuity observed of water the medium. storage. 5 5 15 20 10 10 25 20 15 Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | (9) 0.43 and = erence was im- ff b represents water 12 quantities and dynam- shows the results of the ff ). The di 9 ers from the size assumed 15 per hour for each month in ff 1 − at the outlet point, but an inflow ), whereby the NSE ). The monthly sum of observed ff 11 2 ) in m s t ( erences in hydrological system at catch- ff 48 (Fig. . bound 0 230 229 Q = a represents modeled water storage based on 2 r 12 ) t ( ). Figure 6 ANN . obs 13 S in the given subbasin from April to October 2007, from June to − ff ) t ( 27 (Table . 0 mod S 444). Correlation of the observed water storage simulated with the ANN = = = ) ¨ onigsseetal for the test period of the neural net from March 2007 to October t m ( saturated zone 44), showing deviations during summer months. The distributed model underes- = bound n distributed model for the hydrological year 2006–2007. It is evident that the grid-based ment scale resulting in consistent model mismatch. Figure Q Within the scope ofin this high study, alpine wesystematic terrain could model show with mismatch the massive atwithin limitations subbasin carbonate these of scale heterogeneous aquifers. a andtions catchments distributed point (Darcy that model We out Flow, deviate were hydrological Porousthese from Media processes able catchments, common Conditions). to which model are quantify Toics, assump- the enable we origin developed distributed a of modeling methodBy lowland within to the river describe runo given and station accounttions data for are the not and the missing interpolation case watermismatch. method, and quantities. could unrealistic Therefore, be we precipitation suspended concluded assump- assub-catchments an the to uneven underlying be the observed reason cause, for water becausein the balance of model other unknown for words, subsurface the boundary the given fluxes. realby Or, catchment the size distributed for model riverthe due gauges model to di is underground unable to fluxes. account for By extreme assuming di porous conditions, routed to river outlets. 5 Results and discussion subsequently considered in consecutive modules of the distributed model and finally This method is not awithin bias the correction groundwater of model, modeledin which runo the the model following accounts modelingwhole for process. subbasin and area. which The We is inflow implementedperiod considered a size boundary of can flux the based vary neural on fromare the net presented one results from of in grid July the Fig. cell to test to October the for the years 2007 to 2009. The results the RMSE We show monthly sumsbasin of K observed water2009 storage ( simulated withand the the observed ANN water in storage give sub- the saturated zone athydrological selected model sites was at constantly the corrected border during of model subcatchments. run. Therefore, the The correction was Performance evaluation – ANN the distributed model and( observed water storagetimates from river June runo 2007September to 2008 October and 2009 froming June the to summer October months when 2009. snow Underestimation melt is also not occurs present. dur- Figure 4.2 Distributed model correction: implementation of boundary flux in the We used the monthly outcomesstant of boundary the flux artificial intowater neural the network storage distributed as simulated model a (Fig. withstorage basis the already for neural calculated the for net con- plemented the was as investigated subtracted period continuous from (Eq. boundary the flux modeled water age during summer months.2007 and It Mai underestimates 2009 observedwater and water storage storage it simulated with in overestimates the water November a ANN constant storage is boundary in then flux implemented June to in 2009. improve the distributed distributed The model model within observed as that time period. storage by the distributed modelstorage and simulated observed with water the storage ANN. and the The observed ANN water is able to represent observed water stor- 5 5 25 15 20 10 10 20 25 15 Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | ff ). in do ff and ff ff 2011 , per time step of 1 306 mm and better − Kraller et al. − . After implementing , modeled runo ff ff shows the mean groundwater after implementing the boundary 15 components of modeled runo ff ff also increases, showing improved dis- ff C at elevated regions. The massive karst ◦ 2 232 231 − presents runo . After implementing the boundary flux, interflow is increased to 1487 mm. Originally, modeled water ff ). NSE increased from 0.34 to 0.57 and the RMSE 16 9 ff ective precipitation (1181 mm) and observed water storage ff C in valleys to ◦ shows monthly sums of measured runo (1094 mm) underestimated measured runo 13 ff after implementing the boundary flux for 2007 to 2009. Measured shows main components of the annual water balance of 2007 in sub- ff 14 ¨ onigsseetal from July to October for the years 2007 to 2009 based on the ). Figure ¨ onigsseetal before and after distributed model correction. As the inflow takes 6 is improved in most months. In June 2008 and July 2009 the influx did not ff 618 mm) are equally calculated before and after the boundary influx. Observed wa- − has been used previously in hydrological studies, but mainly to predict and calculate year 2007 before and afterrun, implementation interflow of and the baseflow boundarymain were flux. calculated contributor almost In to equally, the whereas modeledincreased original direct most, model runo flow whereas is baseflow the groundwater and module directflow and remain unsaturated almostpled zone bidirectionally, unchanged. module baseflow is in As converted the the to distributed interflow model within model are performance. cou- ANN outlet of the wholetributed catchment, modeling modeled for runo the overall study area. Figure ter storage was negative in theplace annual throughout balance, because subbasin subsurface borders waterthe inflow (derived modeled takes by runo thethe DEM). boundary In flux, modeled the runo storage original was model minimal run, (18 mm),water balances because internally. the By distributedon correcting model the a calculates distributed even monthly model annual basis,reproduction with the annual of constant modeled observed inflow water water storage storage. resulted At in river gauge St. Leonhardt, which is the moisture in the rootreached zone within ranges the from saturatedto zero zone the to in unsaturated almost the zone. 100 given %. soil Figure layers, Storage and capacities water are excess is given flux. Figure basin K place in the saturatedtranspiration zone (432 mm), module, e annual sums( of precipitation (1604 mm), evapo- level in the regionhad in to the be year in 2006–2007.face the in Based given valley on range regions, the of as assumed the steep soil distributed layers, gradients model, which lead groundwater to reaches the increased sur- flow in hill slopes. Soil not perfectly match monthly sums of measured runo resentation of observed storage. Consequently, monthly sums of modeled runo results of the ANN.model The run. influx wasthe Performance then constant of involved boundary the in fluxdecreased the distributed (Eq. from consecutive model 6.10 modules improved mm during boundary with to flux implementation 1.66 the mm, of (Table distributed which shows model that was after better implementation at of reproducing the runo the measured runo improve model results. In September 2007, the neural net did not give satisfactory rep- in the hiddenhidden layer layer and gave a best linearwater results. storage. function The in We neuralone the implemented net hour output a is for layer constant satisfactory each withsubbasin representing boundary K month 20 observed flux in neurons in the in m s saturated the zone module of the distributed model for modeled runo a black box. However, basedable on to tracer synthesize experiments that andcorresponds the the with main spring the underground locations results we flowSince of were direction we the tends are distributed to unablecially model be to mismatch the north, quantify ( dynamics which each throughout undergroundcapture a flux unknown hydrological in underground year, the flowsis. we study processes By chose area, developing at a the and catchment artificial statisticaldeviations. espe- scale neural method A net, on to we two a were layer monthly able feedforward to backpropagation ba- reproduce network monthly with storage a sigmoid function annual sum of precipitationmountainous ranges regions. from Evapotranspiration 1300 is mmextreme calculated locations. in from Relative the humidity zero valleys rangestemperature to from to is over 0.70 over % 1400 from mm to 2100 10 mm at overaquifer 0.82 in itself %. and, Mean annual the location of all conduits and subsurface flow channels, remains approach provides detailed information on the heterogeneous Alpine catchment. The 5 5 25 15 10 20 15 20 25 10 Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | 222 e, Staatliche Kraller et al. ff at catchment scale. ¨ unther Kus for helpful com- ff 218 at subbasin scale. Further 227 ff 217 234 233 ¨ ur Geowissenschaften und Rohsto ¨ Ubersichtskarte von Deutschland, Oberer Grund- 223 218 217 217 This project was initiated and financed by the Authority of the Berchtes- er from surface basin sizes. This was also indicated by ff use flow and conduit flow in limestone terrain in the Mendip Hills, Sommerset ff 217 ), who synthesized northerly subsurface water flow direction. Subsurface water 2/1993, 51–62, 2004. wasserleiter, Tech. rep.,Geologische Bundesanstalt Dienste f der BRD, 2007. analysis of hydraulic and physico-chemicalJ. spring Hydrol., responses 286, (Urenbrunnen, 179–193, SW 2004. Germany), puted with MODFLOWNevada and Test Site a and vicinity, mixing J. Hydrol., model 361, 371–385, using 2008. deuterium:GIS-based sensitivity analysis, application J. Hydrol., to 309, the 17–38, 2005. eastern (Great Britain), J. Hydrol., 35, 93–110, 1977. 2005. water bodies on theHydrogeol. regional J., 19, scale 525–546, with 2011. a special focus on the impacts of climate change, 2011 Bonacci, O.: Karst springs hydrographs as indicators of karst aquifers., Hydrolog. Sci. J., 38, Brutsaert, W.: Evaporation into the Atmosphere, Kluwer Academic Publishers, 1982. Caroll, R., Pohll, G., Earman, S., and Hershey, R.: A comparison of groundwater fluxes com- Dixon, B.: Application of neuro-fuzzy techniques in predicting ground-water vulnerability: a BGRSGD: HUEK200, Hydrogeologische Birk, S., Liedl, R., and M, S.: Identification of localised recharge and donuit flow by combined Attkinson, T.: Di Bakalowicz, M.: Karst groundwater: a challenge for new resources, Hydrogeol. J., 13, 148–160, Agency (EEA) for providing Corine Land Cover Data (CLC) for land use classification. References Barthel, R.: A indicator approach to assessing and predicting the quantitative state of ground- gaden National Park.Vogel, The head authors of gratefully acknowledge thethe the Berchtesgaden Berchtesgaden continuous Nationalpark. National support Park Furthermorements. of and we Michael Special want Helmut to thanks Franz, thank goKaspar research G to for coordinator involved motivated of institutes neural and network authorities discussions. for data We supply also and thank to the Severin European Environment Acknowledgements. 6 Summary and conclusions We implemented a distributed water balance modelesgadener in Ache. the watershed The of model thedivides. river area Bercht- was Since derived the during model preprocessingbasins area sizes by is to surface situated di water in high Alpine karst, we expect groundwater fluxes in monthly sums thatrated can zone then of be the implementedrespresent distributed as observed model. inflow water or The storage satisfactorily. outflow resultsfluxes Implementation in obtained in of the with missing the satu- the boundary distributedstudies artificial will model neural show net improved that modeled the approach runo can be generalized on a larger spacial scale. Our new method describesstorage processes the in ANN complex hydrogeological analytically,this environments and method, on enables a the monthly to distributed basis.high model calculate With Alpine reproduces unknown karst storage terrain, conditions which more leads to realistically a in more realistic runo Each of the threedrology. neighbouring Distributed modeling high resulted Alpine in headneighboring systematic model subbasins. sub-catchments mismatch Model is in mismatch the unique isin high a in alpine reality consequence its of and hy- water the storagekarst deviations distributed dominated catchments, model. we developed To an improve artificial the neural net distributed to model calculate in missing high Alpine the discharge of a given river course or spring rather than deviating storage conditions. ( fluxes in the unsaturated zone and saturated zone lead to an uneven water balance. 5 5 25 20 15 10 15 20 10 Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | , 2006b. 217 ¨ oden, Acta ect in tracer ff 218 223 , 217 218 217 , Royal Institute of 217 227 218 217 217 217 227 , 227 ective model equations, Adv. Geosci., ff 223 doi:10.5194/hess-10-395-2006 217 233 , , 2006a. t, H., Scholz, M., and Wagner, B.: Quantitative 231 236 235 ff , 217 ect of Alpine karst on the hydrology of the Bercht- ff 220 221 227 , ftp://www.lwr.kth.se/CoupModel.pdf 219 222 217 ¨ Ubersicht, Grundwasser, 3, 143–156, 2006. 217 222 227 doi:10.5194/adgeo-9-123-2006 222 217 220 223 222 wasserleitern – Eine 1931. case of the Jordan River sources, Israel, J. Hydrol.,speleogenesis, 331, 524–542, The 2006. Step fromgenesis 1-dimensional and to Evolution of 2-dimensional Karst modeling Aquifers, 2, domains, 2004. Speleo- of the Upper Jordan catchment and investigation of e Hydrophys., 22, 39–48, 1977. parkverwaltung Berchtesgaden, 2005. 1994. 191–205, 1948. in karst systems from spring hydrographs, J. Hydrol., 348, 452–463, 2008. terisation of karst aquifers based2001. on spring hydrographs analysis, J. Hydrol., 303, 152–164, esgadener Ache basin: aAlps, comprehensive eco.mont., summary 3, 19–28, of 2011. karst research in the Berchtesgaden catchments, Hydrol. Earth Syst. Sci., 10, 395–412, using soft computing101–111, methods: 2010. Artifical neural network and neuro-fuzzy, J. Hydrol., 381, tiative INTERREG III B, Alpine2006. Space Programme, Tech. rep., Nationalpark Berchtesgaden, evaluation of tracer experiments inBerchtesgaden, Alpine Lands, Karst 48, and 11–18, Porous 2005. Aquifers in the Nationalrecharge Park in of semiarid karst aquifers, J. Hydrol., 388, 389–398,1975. 2010. of Karst Aquifers, 1, 3, 2003. 218 acterized by artificial and environmental tracers, J. Hydrol., 312, 312–321, 2005. ologie, 16, 2011. graphs and chemographs, Ground Water, 40, 608–617, 2002. breakthrough curves in karst conduits, J. Hydrol., 241, 177–193, 2001. systems, Tech. rep.,Technology, Dept available of Civil at: and Environmental Engineering, Stockholm, 2001. 9, 123–130, resources, EEA Report, No. 8/2009, Tech. rep., EEA, 2007. Addison-Wesley, Reading, MA, 1991. fuzzy set approach, Ground Water, 35, 205–215, 1997. Sauter, M., Kovacs, A., Geyer, T., and Teutsch, G.: Modellierung der Hydraulik von Karstgrund- Romanov, D., Gabrovsek, F., and Dreybrodt, W.: Modeling the evolution of karst aquifers and Richards, L.: Capillary conduction of liquidsRimmer, through A. porous and mediums, Salingar, Y.: Physics, Modelling 1, precipitation-streamflow 318–333, processes in karst basin: The Kunstmann, H., Heckl, A., and Rimmer, A.: Physically based distributed hydrological modelling Peschke, G.: Ein zweistufiges Modell der Infiltration von Regen in geschichtete B Fischer, K.: Geomorphologie der Berchtesgadener Alpen – Forschungsbericht 50, National- Langenscheidt, E.: Die Geologie der Berchtesgadener Berge, Berchtesgadener Anzeiger, Penman, H.-L.: Natural evaporation from open water, bar soils and grass, P.ROY. Soc. Lond. A, Kiraly, L.: Karstification and GroundwaterKovacs, Flow, A., Speleo, 1, Perrochet, 155–190, P., Kiraly, 2003. L., and Jeannin, P.-Y.: A quantitative method for the charac- Kunstmann, H., Krause, J., and Mayr, S.: Inverse distributed hydrological modelling of Alpine Monteith, J.: Vegetation and the Atmosphere, vol. 1: Principles, Academic Press, London, Kraller, G., Strasser, U., and Franz, H.: E Lotz, A.: Alpine Habitat Diversity – HABITALP – Project Report 2002–2006, EU Community Ini- Maloszweski, P., Buettner, G., Apel, R., Kra Martinez Santos, P. and Andreu, J.: Lumped and distributed approaches to model natural Ford, D.: Perspectives in karst hydrogeology and cavern genesis, Speleogenesis andGeyer, Evolution T., Birk, S., Liedl, R., and Sauter, M.: Quantification of temporal distribution of recharge Kurtulus, B. and Razack, M.: Modeling daily discharge responses of a large karstic aquifer Einsiedl, F.: Flow system dynamics and water storage of a fissured-porous karst aquifer char- Goldscheider, N.: Alpine Hydrogeologie, Grundwasser – Zeitschrift der Fachsektion Hydroge- Hauns, M., Jeannin, P.-Y., and Atteia, O.: Dispersion, retardation and scale e Jansson, P. and Karlberg, L.: Coupled heat and mass transfer model for soil-plant-atmosphere Grasso, D. and Jeannin, P.-Y.: A global experimental system approach of karst springs’ hydro- EEA: Regional climate change and adaption, The Alps facing the challenge of changing water Haykin, S.: A Comprehensive Foundation,Herz, Macmillan New J., York, 1999. Krough, A., and Palmer, R.: Introduction to the Theory of Neural Computation, Dou, C., Wold, W., Dahab, M., and Bogardi, I.: Transient ground-water flow simulation using a 5 5 30 25 20 30 15 25 10 10 15 20 Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | ?A wind ¨ ff urich, global = , 2004. = atmospheric ¨ onau/NPV/DWD 223 = , ects, dam acqui- ff 217 222 ¨ atzung von Folgen von 1 d1 d1 d1 d NPV NPV 1 d NPV 1 d NPV 1 d1 d NPV 1 d NPV 1 d NPV 1 d NPV 1 d NPV NPV NPV NPV relative humidity, WS = sunshine duration, GR precipitation, AP ¨ urich, 2007. Central Institute for Meteorology H = = = P Bavarian avalanche warning service, doi:10.5194/hess-8-1017-2004 = 218 218 237 238 air temperature, ¨ atzung der potentiellen Verdunstung, Z. Meteorol., = T , GR RR, SD 10 min LWZ , GR, DR, SS, WS, WD, AP 10 min Sch , WS, TS, SD 10 min LWZ , WS, WD, GR, RR, TS, SD, SWE 10 min LWZ , WS, WD, GR, SS, AP 1 h ZAMG , WS, WD, GR, SS, AP 1 h ZAMG , WS, WD, GR, SS, AP 1 h ZAMG , WS, WD, GR, SS, AP 1 h ZAMG relfelcted radiation, P P P P H H H H , WS, WD 10 min LWZ , TS, SD 10 min LWZ , , , , P, 10 min LWZ , WS,WD 10 min LWZ , , , , = H H H H H H H H P P P P , , , , , , , , , , , , T T T T T T T T T T T T P P P P P P P P P P P P snow water equivalent, SS = transfer function approach, Water Resour. Res., 39, 1315–1327, ff surface temperature, LWZ = 217 222 [m a.s.l.] resolution direct radiation, RR 217 227 223 = snow depth, SWE ¨ 218 , a 604 P 1 d NPV Location, altitute and parameters and temporal resolution of the meteorologi- = ¨ ohe 1973 ¨ utterung 840 217 222 222 ¨ anderungen – Diss ETH 12018, Ph.D. thesis, Geographisches Institut ETH Z Administration Berchtesgaden National Park, ZAMG ¨ = onau 617 ¨ ¨ ¨ ¨ ollgraben 653 uhroint 1407 onigsberg Pegeluhroint (mech.) 699 1418 2003. 15, 2003. genesis and Evolution of Karst Aquifers, 1, 2003. 217 combined tracer and runo 105, 2002. Aquifers, 1, 3, 2003. groundwater basins: the Appalachians as a test case, Speleogen. Evol. Karst Aquif., 1, 1– Forschungsbericht 55,2008. Nationalparkverwaltung Berchtesgaden (Hrsg.), Berchtesgaden, sition and field validation,agement 34d of Conference ground on water in hydrogeology, karst ecology, monitoring terranes, Nashville, and USA, man- 25, 17–35, 103–111, 1991. 1976. global scale, Hydrol. Earth Syst. Sci., 8, 1017–1030, karst flood forecasting: the380, case 2011. of the Lez Basin (Southern France), J. Hydrol., 403, 367– Klima 1997. a karst system using equivalent porousaquifer, media USA, models? J. Hydrol., Case study, 276, Barton 137–158, Srpings 2003. Edwards StationReiteralm1 Altitude 1755 Parameters Temporal Operator Reiteralm2 1670 Reiteralm3 1615 Sch Jenner 1200 H K Funtenseetauern 2445 Lofer 625 Loferer Alm 1623 SBG Flughafen 430 Schmittenh K SchapbachK LahneralmSt. Bartholom WimbachschlossBrunftbergtiefe (mech.)Auf dem GriesBindalm 953 1238 Eckau 1240 Lahnwaldf 926 MittereisHalsalm 1435 1119 1015 1325 1088 pressure at sea level,NPV TS and Geodynamics Austria). speed, SD radiation, DR Worthington, S.: A comprehensive strategy for understanding flow in carbonate aquifer, Speleo- Weiler, M., McGlynn, B., Kevin, M., and McDonnell, J.: How does rainfall become runo White, W.: Conceptual models forWhite, karstic W. and aquifers, White, Speleogenesis E.: and Conduit Evolution fragmentation, of cave Karst patterns and the localization of karst White, W.: Karst hydrology: recent developements and open questions, Eng. Geol., 65, 85– Strasser, U.: Modelling of the mountain snow cover in the Berchtesgaden National Park, Van Genuchten, M.: Zur Messung und Sch Viviroli, D. and Weingartner, R.: The hydrological significance of mountains: from regional to Table 1. cal stations used for our investigation ( Teutsch, G. and Sauter, M.: Groundwater modeling in karst terrains: scale e Schulla, J.: Model Description WaSiM-ETH,Siou, Tech. L., rep., ETH Johannet, Z A., Borrel, V., and Pistre, S.: Complexity selection of a neural network for Schulla, J.: Hydrologische Modellierung von Flussgebieten zur Absch Scanlon, B., Mace, R., Barret, M., and Smith, B.: Can we simulate regional groundwater flow in 5 30 20 25 15 10 Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | ¨ onigsseetal ¨ uhroint) ¨ uhroint) – mean IDW) in the year 2006/2007 for + IDW Station Data (K + ¨ onigsseetal IDW for station location (K + 240 239 Year Klausbachtal2002/2003 Wimbachtal2003/2004 K 1652/4052004/2005 1782/3552005/2006 1832/338 1533/3932006/2007 1607/331 1718/3512007/2008 1672/355 1745/319 1469/477 2008/2009 1739/389 1574/310 1639/420 2009/2010 1818/192 1621/355 1655/371 1739/389 1654/353 1511/362 1899/350 1604/423 1654/353 1774/465 2002/2003 1804/434 2003/2004 1375/1260 1774/435 2004/2005 996/13712005/2006 1872/1146 1253/14502006/2007 1235/1291 1045/1265 1634/1002 2007/2008 1783/1351 1259/11752008/2009 2622/1255 1197/1178 1128/1283 1596/1241 2009/2010 2269/1175 1178/1178 1784/1137 2346/1226 1253/1282 1799/1094 2544/1335 1831/1291 2808/1353 1597/1240 1593/1332 [mm] [mm] [mm] [mm] (1407 m a.s.l.) [mm] 1207/1325 2091/1280 1604/1201 ff [mm] 2001/2002 1183/1541 1535/1411 1402/1297 ff ¨ onigsseetal (4). Regression and REG ] 42.79 35.69 163.54 Precipitation interpolation analysis. Inverse Distance Weighting (IDW), Regression 2 Annual sums and mean of precipitation, evapotranspiration, modeled and measured Scale TimeSubbasin period SumStation 2006/2007 1559 Mean 2001–2010 IDW 1704 REG – REG 1643 1468 1670 – 1676 Area [km Precipitation/evapotranspiration [mm] 2001/2002 2112/349 1940/354 1869/446 Mean precipitation/evapotranspiration [mm]Measured/modeled runo 1772/367 1704/348Mean 1681/425 measured/modeled runo Table 3. discharge – subbasins Klausbachtal, Wimbachtal and K 2001–2010. Table 2. (REG) and the combination of Regression and IDW (REG subbasin K Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | weights layer 1 = i f , i e , i real d 349 i ) water storage by the dis- obs f 59 − − /S mod 7.14 2.02 8.72 3.33 4.00 5.72 5.12 5.49 S − − − − − − − − 366/ mod ¨ onigsseetal − S i e 54 ( bias hidden layer to output). . 1.21 5.79 3.36 7.77 1.60 3.49 0.52 5.75 3.00 2.02 2.25 5.19 2.32 6.02 real 0 − − − − − − − − − − − 328 obs 21 1/ − = i i − /S ) in subbasin Klausbachtal, Wimbachtal and d a 8.6 1.46 282/ obs 8.50 4.966.87 2.44 3.88 6.16 4.06 2.001.70 5.99 5.67 3.69 3.38 mod − 10.03 10.26 3.30 11.77 0.54 1.70 11.70 2.143 1.398 S − − − − − − − − 242 241 S − − − − i real weight hidden layer to output. c 199 = obs 1.65 9.21 0.01 1.85 3.07 2.71 3.53 9.02 6.59 4.92 i − 10.03 − − − − − − − b /S 2/15 5/ − − 282/ mod i − S Klausbachtal Wimbachtal K b 1.6 0.050.17 0.63 1.00 0.13 12.27 0.840.56 0.78 3.55 9.94 9.29 3.65 3.76 0.04 0.230.820.17 0.71 0.06 0.68 0.030.74 4.381.65 4.47 5.75 4.38 0.060.37 5.151.57 0.01 3.12 7.94 1.10 0.131.07 2.37 4.53 0.35 4.99 − − − − − − − − MaxMin Mean 264/271 275/207 285/439 bias layer 1 to hidden layer. = i c Minimum, maximum and mean of monthly modeled ( Weights and biases ANN. ¨ onigsseetal (mm) to hidden layer. Table 5. tributed model and observed water storage ( Table 4. K Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | without ANN extention with ANN extention 244 243 ) 0.48 0.80 0.79 2 r ciency (NSE) 0.43 0.34 0.57 ffi Performance evaluation Artificial Neural Net (observed water storage and modeled cient of Determination ( cient of E Study area: river gauges and subbasins. ffi ffi ciency criteria ANN Distributed modeling Distributed modeling ffi E Coe Coe Root Mean Square Error (RSME) [mm] 0.27 6.10 1.66 Fig. 1. Table 6. water storage) and distributed model correction (measured vs. modeled discharge). Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | ) sys- ). The ff ff minus Evap- P ective precipitation (Precipitation 246 245 ff Consistent model mismatch was detected due to ff Overview of the presented method. E Soil classification, landuse classification and main geological units within the study area. tematically over/underestimates observed waterobserved storage (derived water from storage measured ismodule runo then to account calcualted for by the observed the storage ANN processes. and implemented in the groundwater water storage deviations. Modeled water storage (derived from distributed model runo Fig. 3. otranspiration ET) results in modeled runo Fig. 2. Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | ¨ onigsseetal. Inverse Dis- 248 247 erent interpolation methods in subbasin K ff REG). + Comparison of di Locations of weather stations within and outside the study area. tance Weighting (IDW),combined Elevation (IDW dependent Regression (REG) and both methods linearly Fig. 5. Fig. 4. Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | . ff ¨ onigsseetal. ) derived from measured runo real obs S ) derived from results of distributed mod S 250 249 Comparison of the water storage ( (b) Comparison of the water storage ( . Monthly sums July–October 2001–2011 – subbasins Klausbachtal, Wimbach- ff Annual sums of modeled and measured discharge subbasins Klausbachtal, Wimbachtal ¨ onigsseetal. ¨ onigsseetal. Fig. 7. (a) model runo tal, K Monthly sums July–October 2001–2011 – subbasins Klausbachtal, Wimbachtal, K Fig. 6. and K Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | , water stor- (c) ¨ onigsseetal – June in subbasin K ff , evapotranspiration for hydrological years 2001–2010 in (b) (e) 252 251 , snowmelt and modeled runo (a) ff rain + and observed water storage (d) ¨ onigsseetal. Monthly sums of snowmelt Monthly sums of measured runo subbasin K Fig. 9. age distributed model Fig. 8. to October for years 2007 to 2009. Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | 254 253 Performance ANN – Test period. Correlation diagram between simulated monthly Architecture Artificial Neural network. Input Layer, Hidden Layer and Output Layer. Fig. 11. observed water storage by the ANN vs. observed water storages. Fig. 10. Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | ¨ onigsseetal. with and without imple- ff ¨ onigsseetal. The upper graph 256 255 and distributed model runo ff Comparison of observed water storage and observed water storage simulated by the Monthly sums of measured runo mented boundary flux from June to October for years 2007–2009 – subbasin K Fig. 13. Fig. 12. ANN in monthly sums. Test period of the neural net in subbasin K shows the observed waterdiagram storage is and showing the the water simulated storage observed by water the storage by distributed the model. artificial The neural lower network. Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | for St. ff modeled stor- = ective precipitation, mod ff S e = ff e P observed storage, ¨ onigsseetal and modeled runo = obs S , Evapotranspiration; ff 258 257 = modeled runo = Precipitation, ET mod = Q P , ff Water balance components for subbasin K Spatial water balance results of the distributed model. Precipitation and Evapotranspi- measured runo = obs Fig. 15. ration, Relative Humidity, Temperature, Groundwaterlevel and Relative Soil Moisture. Q Leonhard – annualmented sums boundary 2007. flux ( Results for originalage). model run and model run with imple- Fig. 14. Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | ¨ onigsseetal – annual sums [mm] 2007. 259 . Subbasin K ff Components of modeled runo Fig. 16. Results for original model run and model run with implemented boundary flux.