This paper presents the conditioning of a precipitation model to objectively classified circulation patterns (CP). The application of CPs is considered useful with regards to model accuracy improvement and preparation of a downscaling model by using CPs classified with climate model data. As this study aims to produce rainfall as input for derived flood frequency analyses, the validation focuses on extreme values and precipitation events. The analysis is carried out by modifications of a well tested alternating renewal precipitation model

Belli, A.

Haberlandt, Uwe

Advances in Geosciences

Institutionelles Repositorium der Leibniz Universität Hannover

Adv. Geosci., 32, 93–97, 2012www.adv-geosci.net/32/93/2012/doi:10.5194/adgeo-32-93-2012© Author(s) 2012. CC Attribution 3.0 License.Advances inGeosciencesStochastic precipitation modeling using circulation patterns toanalyze climate impact on floodsA. Belli and U. HaberlandtInstitute of Water Resources Management, Hydrology and Agricultural Hydraulic Engineering, Leibniz University Hannover,Hanover, GermanyCorrespondence to: A. Belli (belli@iww.uni-hannover.de)Received: 30 January 2012 – Revised: 30 September 2012 – Accepted: 4 November 2012 – Published: 20 December 2012Abstract. This paper presents the conditioning of a precipita-tion model to objectively classified circulation patterns (CP).The application of CPs is considered useful with regards tomodel accuracy improvement and preparation of a downscal-ing model by using CPs classified with climate model data.As this study aims to produce rainfall as input for derivedflood frequency analyses, the validation focuses on extremevalues and precipitation events. The analysis is carried out bymodifications of a well tested alternating renewal precipita-tion model.1 IntroductionExtreme value statistics of floods are of key importance inclimate impact analyses. Changes in floods cannot directlybe derived from climate models. Therefore it is necessary toobtain long time series of future high resolution precipitationdata as input for rainfall-runoff models.Different downscaling methods were developed to utilizeclimate model data on a local scale. First there are dynami-cal downscaling methods, which use regional climate mod-els (RCM) to obtain regional data which is consistent to thelarge scale data gained from the general circulation models(GCM). An alternative are statistical downscaling methods,which use statistical relations between regional data and se-lected parameters of the GCMs to access changes on a localscale.For climate impact analyses focusing on floods inmesoscale catchments some features are of major interest.The precipitation data must be available in a high tempo-ral resolution (e.g. hourly) and for a long time period. Along time period is necessary to minimize the sampling error.This effect is shown in Fig. 1 which compares confidenceintervals of a bootstrap of different sample sizes of simu-lated discharge values. A larger sample produces a signifi-cantly smaller confidence band and, hence, the uncertaintiesare minimized.This is where we see the main disadvantages of existingmodels. In northern Germany the major RCM is the REMOmodel (see e.g. Jacob and Podzun, 1997). This model has acomparably short time series output and only few realizationsare available. Although different statistical downscaling datasets are available, e.g. WETTREG (Spekat et al., 2007) orSTAR (Werner and Gerstengarbe, 1997), most of these con-centrate on a daily time step, which is insufficient for floodmodeling.Therefore alternatives are desirable which feature longsimulation periods and high resolution data. Here a precip-itation model is proposed with parameters conditioned tospecial GCM predictors. This model has to be tested to de-liver usable flood model input data. The hybrid precipitation-model according to Haberlandt et al. (2008) was chosen tobe the basis of the new downscaling approach. The modelparameters will be estimated related to circulation patterns(CP). As CPs can be obtained using climate model pressuredata as input for an objective CP-classification (see Ba´rdossyet al., 2002) a downscaling is thus possible. Nevertheless re-cent research concluded that merely of CPs is not sufficientto accomplish a downscaling. This is shortly discussed in theconclusions chapter and will hopefully be addressed in a laterarticle.This work presents the results of the precipitation modelconditioned on circulation patterns.Published by Copernicus Publications on behalf of the European Geosciences Union.94 A. Belli and U. Haberlandt: Stochastic precipitation modelingFig. 1. 90 % bootstrap confidence band of simulated flood values(resampled 1000 times) using different sample sizes.2 MethodsThe precipitation model creates synthetic data on the pointsof observed precipitation. For hydrological use it is possi-ble to regionalize the model to places without observations.This is not discussed in this paper though. The model consistsof two separate parts. First part of the model is a statisticalprecipitation generator consisting of an alternating-renewal-model (ARM) to simulate rainfall for single points. Secondpart is an optimization algorithm which reproduces the spa-tial dependencies of the synthetic data with a simulated an-nealing resampling (SA).2.1 First part: Alternating-Renewal-Processes-Model(univariate)The ARM differentiates between external and internal struc-tures. The methods core is the external part which definesrainfall as events (Fig. 2). These events are sub divided intowet spells and dry spells. The wet spells are defined throughlength (wsd) and mean intensity (wsi). They are illustrated asred empty boxes. The dry spells are only defined by length(dsd).In the synthesis the spells (wsd + wsi and dsd) are gener-ated alternately with theoretical distribution functions (Ta-ble 1). The fitting is accomplished with l-moments. In orderto choose the best fitting distribution function several good-ness of fit tests and graphical analyses were carried out. Inthis study other distribution found to be best fitting than inHaberlandt et al. (2008), which is plausible as Haberlandt etal. (2008) focused on low mountain range, while this studyconsiders stations from the coastal area (0 m a.m.s.l.) up tomountainous areas (609 m a.m.s.l.). The dependency of wsdand wsi is considered with a copula function. Copulas allowconsidering dependencies of the two variables, while usingunivarite distribution functions. The internal structure of theprecipitation events is reproduced with statistical model pro-files (see Haberlandt, 1998). In Fig. 2 they are shown as greyfilled boxes. To consider the differences in summer and win-ter rainfall different parameter sets are used for each of thetwo seasons.Table 1. Methods used in the ARM.Variable Methoddsd Kappa distributionwsd generalized Pareto distributionswsi generalized Pareto distributionswsd-wsi dependency Franks CopulaFig. 2. Alternating Renewal Model (wsd-wet spell duration, dsd-dryspell duration, wsi-wet spell intensity).2.2 Second part: Simulated AnnealingSecond part of the model is a simulated annealing algo-rithm (SA). This non-linear optimization method is usedto reproduce the spatio-temporal dependencies in syntheticrainfall data. For more information on the algorithm seeBa´rdossy (1998). The principal of the algorithm is:1. calculation of the objective function for the original sta-tus of the time series;2. two events are switched;3. calculation of the objective function for the new statusof the time series;4. decision about the acceptance of the switch accordingto the SA (worsening of the objective function is al-lowed to a certain degree, so the global optimum canbe found);5. repetition of the procedure until the objective functionis minimal.The elements of the objective function are shown in the Ap-pendix. The single parts are added together to a single objec-tive function with the use of weights. A detailed discussioncan be found in Haberlandt et al. (2008).The 1st station is optimized univariately only regarding theCP transition probabilities. The 2nd station is compared tothe 1st station, the 3rd station compared to both other stationsand so on until the nth station is compared to the 1st up to the(n− 1)th station.Adv. Geosci., 32, 93–97, 2012 www.adv-geosci.net/32/93/2012/A. Belli and U. Haberlandt: Stochastic precipitation modeling 95Table 2. Percentage deviation between observed and simulated statistical moments with and without using CPs as mean values over allstations (Var-Variance; Skew-Skewness, Kurt-Kurtosis); grey indicates an improved and dark grey a reduced accuracy through using CPs;light grey indicates when no changes occurred.Season Version Mean (dsd) Var (dsd) Skew(dsd) Kurt(dsd) Mean(wsd) Var(wsd) Skew(wsd) Kurt(wsd)Winter no CP 1 4 9 25 1 5 21 57with CP 2 5 5 17 0 5 13 10Summer no CP 1 5 15 38 1 5 25 68with CP 2 6 16 40 1 4 11 30Year no CP 1 4 12 28 1 5 19 45with CP 2 5 13 31 0 4 12 27Season Version Mean(wsi) Var(wsi) Skew(wsi) Kurt(wsi) Mean(wsa) Var(wsa) Skew(wsa) Kurt(wsa)Winter no CP 2 9 20 47 2 20 81 461with CP 1 6 14 33 0 8 56 251Summer no CP 1 11 40 148 3 70 122 529with CP 1 10 43 163 2 58 108 463Year no CP 1 9 37 132 2 46 126 582with CP 1 8 39 147 1 37 108 5002.3 Circulation patternCirculation patterns (CP) can be defined using the mean pres-sure distribution on sea level or in the middle troposphereover a large area and a time period of several days (Wernerand Gerstengarbe, 2010). There are two principles to defineCPs. It can be either classified by experts or by means ofan objective classification. The other one is to use an ob-jective classification. Here the fuzzy rule based method ofBa´rdossy et al. (2002) is used to realize an objective classi-fication, where the applied method has two advantages. Firstit is possible to define the objective function in a way whichis especially fitted to the hydrological purpose. Secondly theautomatic classification allows fast processing of hundredsof years of data using reanalysis or GCM data as input. Thusthe model is usable to project future CPs in a daily solution.As pressure data of a very large area (in this case Europeplus outskirts) is necessary NCAR reanalysis data (Kistler etal., 2001) is used for the CP classification. For climate pro-jections ECHAM GCM data (Roeckner et al., 2003) will beused in the classification of CPs for current and future cli-mate in the following studies.Under the assumption that change in precipitation iscaused by change in the CP frequency it is possible to com-bine the precipitation model with the CP prognosis to form adownscaling model. For the ARM the conditioning to CPs issimply done by using a specific parameter set (see Sect. 2.1)for each CP. The frequency of the CPs is calculated from theempirical probability distribution. In the SA algorithm the se-quence and synchrony of the CPs are considered via adjust-ing the objective function. For the first station the temporalsequence and for all other stations the synchrony of the CPshad to be included. This study was carried out with 8 CPs.Fig. 3. Study Area Lower Saxony (Niedersachsen) and precipitationnetwork with two stations indicated for extreme value comparison(see. Fig. 5); the station shown in Fig. 5 marked with slightly biggerpoints than the other stations.3 Study area and dataThe study area is the north-German federal state of LowerSaxony (Niedersachsen) while a validation with a hydro-logical model is planned in the Aller-Leine-catchment (seeFig. 3). As the data availability for hourly rainfall is not ideala compromise between data length and station density is nec-essary. As a result a core data set of twenty recording precip-itation stations with an observation length of 11–15 yr withwww.adv-geosci.net/32/93/2012/ Adv. Geosci., 32, 93–97, 201296 A. Belli and U. Haberlandt: Stochastic precipitation modelingFig. 4. Scatter-plots of statistical moments of observed (9–15 yr) vs. synthetic (1000 yr, CP-conditioned model) rainfall time series.at least 11 overlapping years has been selected. This core setconsists only of data from the German Meteorological Ser-vice (DWD). The extended data set also considers 9 stationswith a length of 7–9 yr and data from the Meteomedia AG.4 Analyses and resultsFirst step was to fit the precipitation model without CPs to thenew study area. Afterwards, the results of the original ARMwere compared to the CP-conditioned model results. For thevalidation statistical rainfall characteristics and extreme val-ues were considered.Figure 4 compares observed short term and synthetic1000 yr precipitation data of the model conditioned to CPs.The statistical properties of the events are overall satisfy-ingly reproduced. Only the dsd’s moments are slightly un-derestimated in the synthesis. As a result of the dsd’s un-derestimation the mean yearly event number is overesti-mated. Combined with the correctly modeled average wetspell amounts, the overestimation of the number of wet spellsleads to a slight overestimation of the mean yearly precipita-tion. Changing the dsd’s distribution function may solve thisissue.Table 2 shows the comparison of statistical parameters ofthe synthetic precipitation data modeled with and withoutCPs. The results are indifferent as the accuracy of the repro-duction of some parameters is improved, while reduced forothers. Nevertheless, more than half of the parameters are im-proving and the changes in the improved parameters are moresignificant (higher delta) than those in the parameters that getFig. 5. Extreme values, 10 synthetic time series (100 yr) vs. obser-vation (9–15 yr).reproduced less accurate. Thus we can conclude that overallthe use of CPs lead to an improvement in the reproductionof rainfall time series. Only the accuracy of the estimationof the dsd values has been slightly reduced. The synthesis ofwsd and wsa (wet spell amount) is significantly improved byincluding CPs. For the variable wsi the lower order statisti-cal moments are modeled slightly better and the higher ordermoments slightly less accurate.Figure 5 compares observed and simulated extremes ofhourly and 3-hourly sums of both model types. Overall theextremes are reproduced quite well. Hourly extremes are re-produced slightly better than extreme values of longer rain-fall duration. The conditioning of the model to CPs did notimprove the simulation of hourly extremes. However theAdv. Geosci., 32, 93–97, 2012 www.adv-geosci.net/32/93/2012/A. Belli and U. Haberlandt: Stochastic precipitation modeling 973-hourly extremes are simulated significantly better, as visi-ble in the example given in the figure. This visual observationwas confirmed by statistical tests. So overall the reproductionof extreme values in the synthetic data could be improved byusing CPs.The results of the simulated annealing resampling are notmeasurably affected by considering CPs.5 ConclusionsIn this paper a precipitation model was fitted to circulationpatterns. This is the first step towards a stochastic downscal-ing of high resolution precipitation with projected CPs. Theconditioned model was compared to the original version. TheCPs were classified using reanalysis data. Through the con-ditioning of the precipitation model an improvement of per-formance in respect of reproduction of statistical parametersand extreme values was achieved.An analysis carried out by Haberlandt et al. (2011) foundthat not only the occurrence frequency of the CPs will changein the future but also their internal structure. This means thate.g. a wet CP can get wetter or dryer. Therefore the condi-tioning of a precipitation model to CPs alone is not sufficientfor downscaling. The internal changes of the CPs have to beaddressed too. For this reason a simple statistic-dynamic ap-proach will be developed.Appendix AElements of the simulated annealing objective functionProbability of bivariate occurrence:Pij(zi > 0|zj > 0)= n11(n01 + n10 + n11 + n00) ,nxy – number of intervals with rain in station x and y; 1: rain-ing 0: not raining; zx – precipitation at station X. Bivariatecorrelation:ρij = cov(zi,zj)√var(zi) · var(zj )zi > 0,zj > 0.Bivariate continuity:Cij = E(zi |zi > 0,zj = 0)E(zi |zi > 0,zj > 0) E(...)− expected value,see Wilks (1998).Acknowledgements. This work was realized with financial supportof the Ministry of Science and Culture of Lower Saxony within theclimate impact and adaptation research in Lower Saxony (KLIFF)project. The authors thank the DWD and Meteomedia GmbH forthe meteorological observation data.Edited by: K. Schneider and S. AchleitnerReviewed by: two anonymous refereesReferencesBa´rdossy, A.: Generating precipitation time series using simulatedannealing, Water Resour. Res., 34, 1737–1744, 1998.Ba´rdossy, A., Stehlı´k, J., and Caspary, H.-J.: Automated objectiveclassification of daily circulation patterns for precipitation andtemperature downscaling based on optimized fuzzy rules, Clim.Res., 23, 11–22, 2002.Haberlandt, U.: Stochastic rainfall synthesis using regionalizedmodel parameters, J. Hydrol. Eng., 3, 160–168, 1998.Haberlandt, U., Ebner von Eschenbach, A.-D., and Buchwald, I.:A space-time hybrid hourly rainfall model for derived floodfrequency analysis, Hydrol. Earth Syst. Sci., 12, 1353–1367,doi:10.5194/hess-12-1353-2008, 2008.Haberlandt, U., Belli, A., and Ba´rdossy, A.: Eignung von Großwet-terlagen als Pra¨misse fu¨r das statistische Niederschlagsdownscal-ing, in: Forum fu¨r Hydrologie und Wasserbewirtschaftung, Tagder Hydrologie Wien, 2011, Heft 30.11, 136–143, 2011.Jacob, D. and Podzun, R.: Sensitivity Studies with the Regional Cli-mate Model REMO, Meteorol. Atmos. Phys., 63, 119–129, 1997.Kistler, R., Kalnay, E., Collins, W., Saha, S., White, G., Woollen, J.,Chelliah, M., Ebisuzaki, W., Kanamitsu, M., Kousky, V., Dool,H. V. D., Jenne, R., and Fiorino, M.: The NCEP-NCAR 50-Year Reanalysis: monthly means CD-ROM and documentation,B. Am. Meteorol. Soc., 82, 247–267, 2001.Roeckner, E., Ba¨uml, G., Bonaventura, L., Brokopf, R., Esch,M., Giorgetta, M., Hagemann, S., Kornblueh, L., Schlese,U., Schulzweida, U., Kirchner, I., Manzini, E., Rhodin, A.,and Tompkins, A.: The atmospheric general circulation modelECHAM5 Max-Planck-Institut fu¨r Meteorologie, Hamburg 140,2003.Spekat, A., Enke, W., and Kreienkamp, F.: Neuentwicklung vonregional hoch aufgelo¨sten Wetterlagen fu¨r Deutschland undBereitstellung regionaler Klimaszenarios auf der Basis vonglobalen Klimasimulationen mit dem Regionalisierungsmod-ell Wettreg auf der Basis von globalen Klimasimulationen mitECHAM5/MPI-OM T63L31 2010 bis 2100 fu¨r die SRESSzenar-ios B1, A1B und A2, 1–149, 2007.Werner, P. C. and Gerstengarbe, F.-W.: Proposal for the develop-ment of climate scenarios, Clim. Res., 8, 171–182, 1997.Werner, P. C. and Gerstengarbe, F.-W.: Katalog der Großwetter-lagen Europas (1881–2009) nach Paul Hess und Helmut Bre-zowsky, 7. verbesserte und erga¨nzte Auflage PIK Report, 119,146 pp., 2010.Wilks, D. S.: Multisite generalization of a daily stochastic precipi-tation generation model, J. Hydrol., 210, 178–191, 1998.www.adv-geosci.net/32/93/2012/ Adv. Geosci., 32, 93–97, 2012

Stochastic precipitation modeling using circulation patterns to analyze climate impact on floods

This paper presents the conditioning of a precipitation model to objectively
classified circulation patterns (CP). The application of CPs is considered
useful with regards to model accuracy improvement and preparation of a
downscaling model by using CPs classified with climate model data. As this
study aims to produce rainfall as input for derived flood frequency
analyses, the validation focuses on extreme values and precipitation events.
The analysis is carried out by modifications of a well tested alternating
renewal precipitation model

A. Belli

U. Haberlandt

Directory of Open Access Journals

Adv. Geosci., 32, 93–97, 2012www.adv-geosci.net/32/93/2012/doi:10.5194/adgeo-32-93-2012© Author(s) 2012. CC Attribution 3.0 License.Advances inGeosciencesStochastic precipitation modeling using circulation patterns toanalyze climate impact on floodsA. Belli and U. HaberlandtInstitute of Water Resources Management, Hydrology and Agricultural Hydraulic Engineering, Leibniz University Hannover,Hanover, GermanyCorrespondence to:A. Belli (belli@iww.uni-hannover.de)Received: 30 January 2012 – Revised: 30 September 2012 – Accepted: 4 November 2012 – Published: 20 December 2012Abstract. This paper presents the conditioning of a precipita-tion model to objectively classified circulation patterns (CP).The application of CPs is considered useful with regards tomodel accuracy improvement and preparation of a downscal-ing model by using CPs classified with climate model data.As this study aims to produce rainfall as input for derivedflood frequency analyses, the validation focuses on extremevalues and precipitation events. The analysis is carried out bymodifications of a well tested alternating renewal precipita-tion model.1 IntroductionExtreme value statistics of floods are of key importance inclimate impact analyses. Changes in floods cannot directlybe derived from climate models. Therefore it is necessary toobtain long time series of future high resolution precipitationdata as input for rainfall-runoff models.Different downscaling methods were developed to utilizeclimate model data on a local scale. First there are dynami-cal downscaling methods, which use regional climate mod-els (RCM) to obtain regional data which is consistent to thelarge scale data gained from the general circulation models(GCM). An alternative are statistical downscaling methods,which use statistical relations between regional data and se-lected parameters of the GCMs to access changes on a localscale.For climate impact analyses focusing on floods inmesoscale catchments some features are of major interest.The precipitation data must be available in a high tempo-ral resolution (e.g. hourly) and for a long time period. Along time period is necessary to minimize the sampling error.This effect is shown in Fig. 1 which compares confidenceintervals of a bootstrap of different sample sizes of simu-lated discharge values. A larger sample produces a signifi-cantly smaller confidence band and, hence, the uncertaintiesare minimized.This is where we see the main disadvantages of existingmodels. In northern Germany the major RCM is the REMOmodel (see e.g. Jacob and Podzun, 1997). This model has acomparably short time series output and only few realizationsare available. Although different statistical downscaling datasets are available, e.g. WETTREG (Spekat et al., 2007) orSTAR (Werner and Gerstengarbe, 1997), most of these con-centrate on a daily time step, which is insufficient for floodmodeling.Therefore alternatives are desirable which feature longsimulation periods and high resolution data. Here a precip-itation model is proposed with parameters conditioned tospecial GCM predictors. This model has to be tested to de-liver usable flood model input data. The hybrid precipitation-model according to Haberlandt et al. (2008) was chosen tobe the basis of the new downscaling approach. The modelparameters will be estimated related to circulation patterns(CP). As CPs can be obtained using climate model pressuredata as input for an objective CP-classification (see Bárdossyet al., 2002) a downscaling is thus possible. Nevertheless re-cent research concluded that merely of CPs is not sufficientto accomplish a downscaling. This is shortly discussed in theconclusions chapter and will hopefully be addressed in a laterarticle.This work presents the results of the precipitation modelconditioned on circulation patterns.Published by Copernicus Publications on behalf of the European Geosciences Union.94 A. Belli and U. Haberlandt: Stochastic precipitation modelingFig. 1. 90 % bootstrap confidence band of simulated flood values(resampled 1000 times) using different sample sizes.2 MethodsThe precipitation model creates synthetic data on the pointsof observed precipitation. For hydrological use it is possi-ble to regionalize the model to places without observations.This is not discussed in this paper though. The model consistsof two separate parts. First part of the model is a statisticalprecipitation generator consisting of an alternating-renewal-model (ARM) to simulate rainfall for single points. Secondpart is an optimization algorithm which reproduces the spa-tial dependencies of the synthetic data with a simulated an-nealing resampling (SA).2.1 First part: Alternating-Renewal-Processes-Model(univariate)The ARM differentiates between external and internal struc-tures. The methods core is the external part which definesrainfall as events (Fig. 2). These events are sub divided intowet spells and dry spells. The wet spells are defined throughlength (wsd) and mean intensity (wsi). They are illustrated asred empty boxes. The dry spells are only defined by length(dsd).In the synthesis the spells (wsd + wsi and dsd) are gener-ated alternately with theoretical distribution functions (Ta-ble 1). The fitting is accomplished with l-moments. In orderto choose the best fitting distribution function several good-ness of fit tests and graphical analyses were carried out. Inthis study other distribution found to be best fitting than inHaberlandt et al. (2008), which is plausible as Haberlandt etal. (2008) focused on low mountain range, while this studyconsiders stations from the coastal area (0 m a.m.s.l.) up tomountainous areas (609 m a.m.s.l.). The dependency of wsdand wsi is considered with a copula function. Copulas allowconsidering dependencies of the two variables, while usingunivarite distribution functions. The internal structure of theprecipitation events is reproduced with statistical model pro-files (see Haberlandt, 1998). In Fig. 2 they are shown as greyfilled boxes. To consider the differences in summer and win-ter rainfall different parameter sets are used for each of thetwo seasons.Table 1.Methods used in the ARM.Variable Methoddsd Kappa distributionwsd generalized Pareto distributionswsi generalized Pareto distributionswsd-wsi dependency Franks CopulaFig. 2.Alternating Renewal Model (wsd-wet spell duration, dsd-dryspell duration, wsi-wet spell intensity).2.2 Second part: Simulated AnnealingSecond part of the model is a simulated annealing algo-rithm (SA). This non-linear optimization method is usedto reproduce the spatio-temporal dependencies in syntheticrainfall data. For more information on the algorithm seeBárdossy (1998). The principal of the algorithm is:1. calculation of the objective function for the original sta-tus of the time series;2. two events are switched;3. calculation of the objective function for the new statusof the time series;4. decision about the acceptance of the switch accordingto the SA (worsening of the objective function is al-lowed to a certain degree, so the global optimum canbe found);5. repetition of the procedure until the objective functionis minimal.The elements of the objective function are shown in the Ap-pendix. The single parts are added together to a single objec-tive function with the use of weights. A detailed discussioncan be found in Haberlandt et al. (2008).The 1st station is optimized univariately only regarding theCP transition probabilities. The 2nd station is compared tothe 1st station, the 3rd station compared to both other stationsand so on until thenth station is compared to the 1st up to the(n − 1)th station.Adv. Geosci., 32, 93–97, 2012 www.adv-geosci.net/32/93/2012/A. Belli and U. Haberlandt: Stochastic precipitation modeling 95Table 2. Percentage deviation between observed and simulated statistical moments with and without using CPs as mean values over allstations (Var-Variance; Skew-Skewness, Kurt-Kurtosis); grey indicates an improved and dark grey a reduced accuracy through using CPs;light grey indicates when no changes occurred.Season Version Mean (dsd) Var (dsd) Skew(dsd) Kurt(dsd) Mean(wsd) Var(wsd) Skew(wsd) Kurt(wsd)Winterno CP 1 4 9 25 1 5 21 57with CP 2 5 5 17 0 5 13 10Summerno CP 1 5 15 38 1 5 25 68with CP 2 6 16 40 1 4 11 30Yearno CP 1 4 12 28 1 5 19 45with CP 2 5 13 31 0 4 12 27Season Version Mean(wsi) Var(wsi) Skew(wsi) Kurt(wsi) Mean(wsa) Var(wsa) Skew(wsa) Kurt(wsa)Winterno CP 2 9 20 47 2 20 81 461with CP 1 6 14 33 0 8 56 251Summerno CP 1 11 40 148 3 70 122 529with CP 1 10 43 163 2 58 108 463Yearno CP 1 9 37 132 2 46 126 582with CP 1 8 39 147 1 37 108 5002.3 Circulation patternCirculation patterns (CP) can be defined using the mean pres-sure distribution on sea level or in the middle troposphereover a large area and a time period of several days (Wernerand Gerstengarbe, 2010). There are two principles to defineCPs. It can be either classified by experts or by means ofan objective classification. The other one is to use an ob-jective classification. Here the fuzzy rule based method ofBárdossy et al. (2002) is used to realize an objective classi-fication, where the applied method has two advantages. Firstit is possible to define the objective function in a way whichis especially fitted to the hydrological purpose. Secondly theautomatic classification allows fast processing of hundredsof years of data using reanalysis or GCM data as input. Thusthe model is usable to project future CPs in a daily solution.As pressure data of a very large area (in this case Europeplus outskirts) is necessary NCAR reanalysis data (Kistler etal., 2001) is used for the CP classification. For climate pro-jections ECHAM GCM data (Roeckner et al., 2003) will beused in the classification of CPs for current and future cli-mate in the following studies.Under the assumption that change in precipitation iscaused by change in the CP frequency it is possible to com-bine the precipitation model with the CP prognosis to form adownscaling model. For the ARM the conditioning to CPs issimply done by using a specific parameter set (see Sect. 2.1)for each CP. The frequency of the CPs is calculated from theempirical probability distribution. In the SA algorithm the se-quence and synchrony of the CPs are considered via adjust-ing the objective function. For the first station the temporalsequence and for all other stations the synchrony of the CPshad to be included. This study was carried out with 8 CPs.Fig. 3.Study Area Lower Saxony (Niedersachsen) and precipitationnetwork with two stations indicated for extreme value comparison(see. Fig. 5); the station shown in Fig. 5 marked with slightly biggerpoints than the other stations.3 Study area and dataThe study area is the north-German federal state of LowerSaxony (Niedersachsen) while a validation with a hydro-logical model is planned in the Aller-Leine-catchment (seeFig. 3). As the data availability for hourly rainfall is not ideala compromise between data length and station density is nec-essary. As a result a core data set of twenty recording precip-itation stations with an observation length of 11–15 yr withwww.adv-geosci.net/32/93/2012/ Adv. Geosci., 32, 93–7, 201296 A. Belli and U. Haberlandt: Stochastic precipitation modelingFig. 4.Scatter-plots of statistical moments of observed (9–15 yr) vs. synthetic (1000 yr, CP-conditioned model) rainfall time series.at least 11 overlapping years has been selected. This core setconsists only of data from the German Meteorological Ser-vice (DWD). The extended data set also considers 9 stationswith a length of 7–9 yr and data from the Meteomedia AG.4 Analyses and resultsFirst step was to fit the precipitation model without CPs to thenew study area. Afterwards, the results of the original ARMwere compared to the CP-conditioned model results. For thevalidation statistical rainfall characteristics and extreme val-ues were considered.Figure 4 compares observed short term and synthetic1000 yr precipitation data of the model conditioned to CPs.The statistical properties of the events are overall satisfy-ingly reproduced. Only the dsd’s moments are slightly un-derestimated in the synthesis. As a result of the dsd’s un-derestimation the mean yearly event number is overesti-mated. Combined with the correctly modeled average wetspell amounts, the overestimation of the number of wet spellsleads to a slight overestimation of the mean yearly precipita-tion. Changing the dsd’s distribution function may solve thisissue.Table 2 shows the comparison of statistical parameters ofthe synthetic precipitation data modeled with and withoutCPs. The results are indifferent as the accuracy of the repro-duction of some parameters is improved, while reduced forothers. Nevertheless, more than half of the parameters are im-proving and the changes in the improved parameters are moresignificant (higher delta) than those in the parameters that getFig. 5. Extreme values, 10 synthetic time series (100 yr) vs. obser-vation (9–15 yr).reproduced less accurate. Thus we can conclude that overallthe use of CPs lead to an improvement in the reproductionof rainfall time series. Only the accuracy of the estimationof the dsd values has been slightly reduced. The synthesis ofwsd and wsa (wet spell amount) is significantly improved byincluding CPs. For the variable wsi the lower order statisti-cal moments are modeled slightly better and the higher ordermoments slightly less accurate.Figure 5 compares observed and simulated extremes ofhourly and 3-hourly sums of both model types. Overall theextremes are reproduced quite well. Hourly extremes are re-produced slightly better than extreme values of longer rain-fall duration. The conditioning of the model to CPs did notimprove the simulation of hourly extremes. However theAdv. Geosci., 32, 93–97, 2012 www.adv-geosci.net/32/93/2012/A. Belli and U. Haberlandt: Stochastic precipitation modeling 973-hourly extremes are simulated significantly better, as visi-ble in the example given in the figure. This visual observationwas confirmed by statistical tests. So overall the reproductionof extreme values in the synthetic data could be improved byusing CPs.The results of the simulated annealing resampling are notmeasurably affected by considering CPs.5 ConclusionsIn this paper a precipitation model was fitted to circulationpatterns. This is the first step towards a stochastic downscal-ing of high resolution precipitation with projected CPs. Theconditioned model was compared to the original version. TheCPs were classified using reanalysis data. Through the con-ditioning of the precipitation model an improvement of per-formance in respect of reproduction of statistical parametersand extreme values was achieved.An analysis carried out by Haberlandt et al. (2011) foundthat not only the occurrence frequency of the CPs will changein the future but also their internal structure. This means thate.g. a wet CP can get wetter or dryer. Therefore the condi-tioning of a precipitation model to CPs alone is not sufficientfor downscaling. The internal changes of the CPs have to beaddressed too. For this reason a simple statistic-dynamic ap-proach will be developed.Appendix AElements of the simulated annealing objective functionProbability of bivariate occurrence:Pij(zi > 0|zj > 0)=n11(n01+ n10+ n11+ n00),nxy – number of intervals with rain in stationx andy; 1: rain-ing 0: not raining;zx – precipitation at stationX. Bivariatecorrelation:ρij =cov(zi,zj)√var(zi) · var(zj )zi > 0,zj > 0.Bivariate continuity:Cij =E(zi |zi > 0,zj = 0)E(zi |zi > 0,zj > 0) E(...) − expected value,see Wilks (1998).Acknowledgements.This work was realized with financial supportof the Ministry of Science and Culture of Lower Saxony within theclimate impact and adaptation research in Lower Saxony (KLIFF)project. The authors thank the DWD and Meteomedia GmbH forthe meteorological observation data.Edited by: K. Schneider and S. 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Stochastic precipitation modeling using circulation patterns to analyze climate impact on floods

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