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IMPRINTS Milestone Report Contract No: FP7-ENV-2008-1-226555 SP3 Milestone October 2010 Milestone M3.3 Date 02.12.2010 Report Number M_SP3-2010-11 Revision Number draft Due data for Milestone: November 2010 Actual submission date: December 2nd 2010 Subproject Leader ULANC IMPRINTS is co-funded by the European Community Seventh Framework Programme for European Research and Technological Development IMPRINTS is a Collaborative Project focused on Theme 6.1.3.3 - ENVIRONMENT: Preparedness and risk management for flash floods including generation of sediment and associated debris flow. Start date 15th January 2009, duration 42 Months Document Dissemination Level PU Public RE Restricted to a group specified by the consortium (including the Commission Services) CO Confidential, only for members of the consortium (including the Commission Services) Coordinator: Centre de Recerca Aplicada en Hidrometeorologia (CRAHI-UPC) Universitat Politècnica de Catalunya Project Contract No: FP7-ENV-2008-1-226555 IMPRINTS Milestone Report Contract No: FP7-ENV-2008-1-226555 Table of Contents 1. Description of Milestone..................................................................................................... 2 2. Summary of the work to carried up .................................................................................... 2 3. Difficulties arisen (if any) and actions................................................................................ 3 4. Further Recommendations .................................................................................................. 3 5. Associated Publications ...................................................................................................... 3 6. APPENDIXES (if any) ....................................................................................................... 4 SP3_M3.3_toPartners.doc 1 02.12.2010 IMPRINTS Milestone Report Contract No: FP7-ENV-2008-1-226555 1. Description of Milestone Milestone 3.3 (“1st version of the probabilistic conditioning methodology”) has been realized by propagating ensemble rainfall inputs into hydrological models. The methodology follows the work initiated by Germann et al. (2009) with the use of the radar ensemble generator REAL for operational hydrological modelling with PREVAH (Viviroli et al., 2009) for the Verzasca river basin. 2. Summary of the work to carried up The work has been split into three perspectives: a. Operational simulations. The simulations with PREVAH conditioned by the radar ensemble generator REAL are fully operational. Simulations are projected into the future for up to three days lead time by nudging the REAL inputs with precipitations forecasts obtained from a high resolution numerical weather prediction model. A very recent event is presented in Figure 1. Figure 1: Operational hydrological ensemble nowcasting with REAL and PREVAH (Germann et al., 2009), computed on the 16 November 2010 in real-time with deterministic initial conditions from the 10 November 2010 for the Verzasca basin in southern Switzerland (186 km2). The nowcasting is conditioned by 25 members from REAL (light grey) are shown with corresponding interquartile range (REAL IQR, red area) and the median (red line). Additionally, two deterministic runs are shown: deterministic radar QPE (yellow line) and forcing with interpolated pluviometer data (green line). The observed runoff is shown in blue. Spatially interpolated observed precipitation as ensemble precipitation from the REAL members (orange whisker-plots). All deterministic and probabilistic members are chained to a three day forecasts by the COSMOCH7 NWP of MeteoSwiss. b. Probabilistic verification of ensemble runoff simulations conditioned by hourly ensemble weather radar fields. Results have been presented on a poster at the IMPRINTS Workshop in Barcelona [Appendix] and have been accepted for poster presentation in the “Weather Radar and Hydrology” (WRaH) conference to be held in the United Kingdom in 2011 from 18 to 21 April at the University of Exeter. A paper for a Red-Book Paper of IAHS is in preparation. The corresponding Abstract with the title “Flood nowcasting in the Southern Swiss Alps using radar ensemble” can be found in the appendix. SP3_M3.3_toPartners.doc 2 02.12.2010 IMPRINTS Milestone Report Contract No: FP7-ENV-2008-1-226555 c. Off-line experiments of propagation and superposition of three sources of uncertainty. A full paper is close to acceptance in "Atmospheric Research." The paper describes an experimental framework for investigating the relative contribution of meteorological forcing uncertainties, initial conditions uncertainties and hydrological model parameter uncertainties in the realization of hydrological ensemble forecasts. Simulations were done for the Verzasca river basin (186 km2). For seven events in the time frame June 2007 to November 2008 it was possible to quantify the uncertainty for a five- day forecast range yielded by inputs of an ensemble numerical weather prediction (NWP) model (COSMO-LEPS, 16 members), the uncertainty in real-time assimilation of weather radar precipitation fields expressed using an ensemble approach (REAL, 25 members), and the equifinal parameter realizations of the hydrological model adopted (PREVAH, 26 members). Combining the three kinds of uncertainty results in a hydrological ensemble of 10400 members. An analysis of sub-samples from the ensemble provides insight in the contribution of each kind of uncertainty to the total uncertainty. The submitted paper (Zappa et al., submitted to Atmospheric Research) and the correspondent poster presented at the IMPRINTS Workshop in Barcelona are attached to this milestone report [Appendix]. The conditioning (superposition) methodology is presented in detail in sections 3.2 and 3.4 of the attached paper. 3. Difficulties arisen (if any) and actions No significant difficulties arose. 4. Further Recommendations Conditioning with ensemble rainfall information should be extended to the first two to four hours in the future. Work for conditioning PREVAH with new tools from IMPRINTS SP1 will start in 2011. MeteoSwiss gave a talk on the progresses of SP1 on December 1st 2010 at WSL. First conditioning of PREVAH with NORA and PREVAH could be presented at the next Meeting in Toulouse. 5. Associated Publications Viviroli D, Zappa M, Gurtz J and Weingartner R. An introduction to the hydrological modelling system PREVAH and its pre- and post-processing-tools. Environmental Modelling & Software. 24(10): 1209–1222. doi:10.1016/j.envsoft.2009.04.001 Germann U, Berenguer M, Sempere-Torres D, Zappa M. 2009. REAL - Ensemble radar precipitation for hydrology in a mountanious region. Quarterly Journal of the Royal Meteorological Society. 135: 445–456. doi:/10.1002/qj.375 Zappa M, Jaun S, Germann U, Walser A, Fundel F. Superimposition of three sources of uncertainties in operational flood forecasting chains. Submitted to Atmospheric Research in revised version. Thematic Issue on COST731. SP3_M3.3_toPartners.doc 3 02.12.2010 IMPRINTS Milestone Report Contract No: FP7-ENV-2008-1-226555 6. APPENDIXES (if any) The cited paper and the two cited posters presented at the IMPRINTS workshop held in Barcelona in June 2010 are attached to this milestone summary. Liechti K., Fundel F., Germann U. and Zappa M. “Flood nowcasting in the Southern Swiss Alps using radar ensemble”. Abstract for WRaH2011 Exeter. SP3_M3.3_toPartners.doc 4 02.12.2010 Flood nowcasting in the Southern Swiss Alps using radar ensemble K. Liechti, F. Fundel, U. Germann, M. Zappa Since April 2007 the MeteoSwiss radar ensemble product REAL has been in operation and used for operational flash flood nowcasting by the WSL. REAL consists of 25 members and is generated hourly by the current radar quantitative precipitation estimates (QPE). REAL covers an area in the Southern Swiss Alps where orographic and convective precipitation is frequent. This ensemble QPE is processed by the semi-distributed hydrological model PREVAH. This provides operational ensemble nowcasts for several basins with areas from 44 to 1500 km2. The smaller basins are prone to flash floods, whereas the larger ones are rather affected by large floods after long-lasting rainfall. In this contribution the performance of nowcasts driven by REAL are compared to nowcasts driven by deterministic radar and rain gauge data. First results for the Verzasca river basin (186 km2) demonstrate, that REAL outperforms deterministic radar over the whole range of discharges, while the results with rain gauge data are threshold dependent. The spread of the hydrological nowcast grows dependently to the time the system is allowed to develop forced by the radar ensemble. Therefore the performance of ensemble nowcasts is expected to improve when using the radar ensemble for a certain time before the initialisation of a nowcast (initialisation period). It will be analysed how long the initialisation period should be to gain the optimal spread for a subsequent hydrological nowcast. First results for the Verzasca river basin indicate that the maximum skill in discharge nowcasts is reached with an initialisation period of 7 days. Forthcoming, it is planned to combine REAL and numerical weather predictions from atmospheric models for flash flood forecasting. In addition, new nowcasting radar QPE products including blending with rain gauge data will be tested. Radar Ensemble for Operational Hydrology Probabilistic Verification of a 33 Months Long Time Series of Verzasca Runoff F. Fundel, K. Liechti and M. Zappa (WSL) U. Germann (MeteoSwiss) Introduction (Germann et al., QJRMS, 2009; Zappa et al., ASL, 2010) In the past decade a series of sophisticated algorithms to obtain the best radar estimates of surface precipitation rates over all of Switzerland have been developed. In spite of significant improvements, for hydrological applications the residual uncertainty is still relatively large. A novel solution to express this residual uncertainty is to generate an ensemble of radar precipitation fields by combining stochastic simulation and detailed knowledge of the radar error structure. A prototype ensemble generator (REAL) has been implemented and is running in real-time since April 2007. The ensemble of precipitation field time series from REAL consists of 25 members and is updated operationally every 60 minutes REAL: Radar Ensemble and propagated through the semi distributed hydrological model PREVAH. for Hydrology in the Alps Methods In numerical weather prediction spread increases with lead time. In analogy the spread of radar ensemble products increases with the number of hours in which one allow them to diverge from initialization conditions. We allow each of the 25 REAL members to build up a 10 day chain of spatially and temporally correlated precipitation values. Thus spread can develop from day to day. During long dry spells the spread can converge. During long wet spell the spread can grow. Our setup starts from “Day minus 10” with identical initial conditions for the hydrological simulations. In case of rainfall the 25 chains of weather radar precipitation propagate First Verification Results separately through the hydrological model. We repeated the 10-days simulations starting them at each consecutive day since April 2007 until Mai 2010. Our particular setup allows then to create chains of discharge values with identical “spread-time” and to evaluate such data with standard probabilistic verification metrics as generally used for evaluating ensemble discharge forecasts (e.g. : Jaun and Ahrens, HESS, 2009). Here first analysis for the period until December 2009 are shown. Talagrand diagram of Verzasca daily maxima runoff . Building maximum discharge daily chains with growing “spread-time” . driven with REAL precipitation for different “spread-times” Brier Skill Score for the 80th, 90th, 95th and 99th quantile Relaibility component of the Brier Score as measure for calibration. Resolution component of the Brier Score of Verzasca daily maximum runoff driven with REAL precipitation. Dashed lines are the 5% and 95% confidence intervals. Conclusion REAL driven runoff ensemble analysis are underdispersive and biased yet skillful. They could provide a good initialization for an ongoing forecast. FP7-ENV-2008-1 IMPRINTS 226555 Superposition of three sources of uncertainties in operational flood forecasting chains in mountainous areas M. Zappa, S. Jaun (WSL) U. Germann, A. Walser (MeteoSwiss) Introduction (Germann et al., QJRMS, 2009; Zappa et al., ASL, 2010) We set up an experimental framework for investigating the relative contribution of meteorological forcing uncertainties, initial conditions uncertainties and hydrological model parameter uncertainties in the realization of hydrological ensemble forecasts. Simulations were done for a representative mesoscale basin of the Swiss Alps, the Verzasca river basin (186 km2). Methods For different events in the time frame June 2007 to November 2008 it was possible to quantify the uncertainty for a five-day forecast range yielded by inputs of an ensemble numerical weather prediction model (C-LEPS, 16 members), the uncertainty in real-time assimilation of weather radar precipitation fields expressed using an ensemble approach (REAL, 25 members), and the parameter uncertainty of the adopted hydrological model PREVAH (MOD, 26 members). The simultaneous propagation of all three ensembles generates a hydrological ensemble of 10400 members. Targeted analyses of members’ sub-samples provide insights on uncertainty superposition. Results Results confirm the expectations and show that for the opera- tional simulation of peak-runoff events the hydrological model uncertainty is less pronounced than the uncertainty obtained by propagating radar precipitation fields (by a factor larger than 4) and NWP forecasts through the hydrological model (by a factor larger than 10). The use of weather radar ensembles for generat- ing hydrologically consistent ensembles of initial conditions pre- vious to the propagation of COSMO-LEPS through the hydrologi- MOD: Uncertainty of the tunable parameters of the hydrological model cal model show that the uncertainty in initial conditions decays within the first 48 hours of the forecast. Another finding from the experiments is that the spread obtained when superposing two or more sources of uncertainty is larger than the cumulated spread of experiments when only one uncertainty source is propagated through the hydrological model. The spread obtained from uncertainty superposition is growing non-linearly. Conclusions The experimental setup provides interesting answers to questions linked to uncertainty propagation and superposition in a hydro- meteorological forecasting system. By use of radar ensembles input uncertainties are considered for nowcasting. The simultaneous application of REAL and parameter uncertainties REAL/MOD: Superposing weather radar uncertainty with MOD generates ensembles that nicely envelop the observed hydrograph. The magnitude of the uncertainty attributed to the difference in initial conditions is smaller than the uncertainty attributed to the hydrological model parameters and almost negligible with respect to the spread owed to COSMO-LEPS. Further efforts are planned in order to implement interpolation- based ensembles within our experimental chain. An objective quantitative verification of the ensemble simulations against observed data will be presented in follow-up studies. Submitted to Atmospheric Research, Special Issue on “ COST 731 LEPS/MOD: Superposing COSMO-LEPS NWP uncertainty with MOD FP7-ENV-2008-1 IMPRINTS 226555 *Manuscript Click here to view linked References 1 "Superposition of three sources of uncertainties in operational 2 flood forecasting chains" 3 4 Massimiliano Zappa1, Simon Jaun1,2, Urs Germann3, André Walser3 and Felix Fundel1 5 6 (1) Swiss Federal Research Institute WSL, Birmensdorf, Switzerland 7 (2) Institute for Atmospheric and Climate Science, ETH Zurich, Switzerland 8 (3) Swiss Federal Office of Meteorology and Climatology MeteoSwiss, Switzerland 9 10 11 12 13 Submitted to Atmospheric Research, Special Issue on “COST 731 - UNCERTAINTY 14 PROPAGATION IN ADVANCED HYDRO-METEOROLOGICAL FORECAST 15 SYSTEMS” Guest Editors, Dr. Andrea Rossa and Dr. Massimiliano Zappa 16 17 18 1st Submission: 31. May 2009 19 2nd Submission: 22. October 2010 20 3rd Submission: 30. November 2010 21 22 23 Corresponding Author: 24 Dr. Massimiliano Zappa 25 Swiss Federal Institute for Forest, Snow and Landscape Research WSL 26 Mountain Hydrology and Torrents 27 Zürcherstrasse 111, CH-8903 Birmensdorf 28 massimiliano.zappa@wsl.ch 1 29 Abstract 30 One of the less known aspects of operational flood forecasting systems in complex 31 topographic areas is the way how the uncertainties of its components propagate and superpose 32 when they are fed into a hydrological model. This paper describes an experimental framework 33 for investigating the relative contribution of meteorological forcing uncertainties, initial 34 conditions uncertainties and hydrological model parameter uncertainties in the realization of 35 hydrological ensemble forecasts. Simulations were done for a representative small-scale basin 36 of the Swiss Alps, the Verzasca river basin (186 km2). 37 For seven events in the time frame June 2007 to November 2008 it was possible to 38 quantify the uncertainty for a five-day forecast range yielded by inputs of an ensemble 39 numerical weather prediction (NWP) model (COSMO-LEPS, 16 members), the uncertainty in 40 real-time assimilation of weather radar precipitation fields expressed using an ensemble 41 approach (REAL, 25 members), and the equifinal parameter realizations of the hydrological 42 model adopted (PREVAH, 26 members). Combining the three kinds of uncertainty results in 43 a hydrological ensemble of 10400 members. An analyses of sub-samples from the ensemble 44 provides insight in the contribution of each kind of uncertainty to the total uncertainty. 45 The results confirm our expectations and show that for the operational simulation of 46 peak-runoff events the hydrological model uncertainty is less pronounced than the uncertainty 47 obtained by propagating radar precipitation fields (by a factor larger than 4 in our specific 48 setup) and NWP forecasts through the hydrological model (by a factor larger than 10). The 49 use of precipitation radar ensembles for generating ensembles of initial conditions shows that 50 the uncertainty in initial conditions decays within the first 48 hours of the forecast. We also 51 show that the total spread obtained when superposing two or more sources of uncertainty is 52 larger than the cumulated spread of experiments when only one uncertainty source is 53 propagated through the hydrological model. The full spread obtained from uncertainty 54 superposition is growing non-linearly. 55 56 Keywords: flood forecasting, uncertainty superposition, weather radar ensemble, atmospheric 57 EPS, model uncertainty, PREVAH, MAP D-PHASE, COST 731 2 58 1. Introduction 59 Operational flood forecasting is an important task in order to detect potentially 60 hazardous extreme rainfall-runoff events in time. This is particularly challenging in 61 mountainous areas, where the orography strongly complicates the setup and operational 62 workflow of most components of an end-to-end flood forecasting system. Such systems 63 consists of atmospheric models (e.g. Rotach et al., 2009), hydrological prediction systems (e.g. 64 Zappa et al., 2008), nowcasting tools used for estimating initial conditions (e.g. Germann et 65 al., 2009) and warnings for end-users (Bruen et al., 2010; Frick and Hegg, this issue). 66 Each component of the system is affected by uncertainties linked to the physical 67 representation of orography, to the parameterization schemes of the models involved and the 68 limitations of the observing platforms providing real-time data (Zappa et al., 2010). For an 69 integral consideration of uncertainty three key sources of errors have to be considered: a) the 70 uncertainty arising from incomplete process representation including the error in the 71 estimation of model parameters (Vrugt et al., 2005), b) the uncertainty in the initial conditions 72 and c) the uncertainty of the observed/forecasted hydrometeorological input. This 73 “uncertainty triplet” (Figure 1) superposes when data are fed into a hydrological model. The 74 integral uncertainty is the result of the interactions of all sources of uncertainty that are 75 propagating. 76 In the field of numerical weather prediction, ensemble systems are established as 77 standard tools to estimate and describe predicition uncertainties. Deterministic numerical 78 weather predictions (NWPs) are intrinsically limited by the chaotic nature of the atmospheric 79 dynamics. Already in the 1960s, Lorenz (1963) demonstrated in a seminal study that small 80 errors in the initial conditions of a weather forecast can grow rapidly, leading to highly 81 diverging solutions. In order to estimate predictability, much research has been undertaken to 82 develop probabilistic forecasting methodologies (see the reviews by Ehrendorfer, 1997 and 83 Palmer, 2000). In the last years, several studies have been devoted to the regional scales using 84 limited-area ensembles, in particular for forecasting heavy precipitation events (e.g. Stensrud 85 et al., 2000; Walser et al., 2004). Motivated by the reported results, initiatives for operational 86 limited-area ensemble prediction systems (EPSs) have emerged, e.g. the SRNWP-PEPS 87 (Quiby and Denhard 2003) and COSMO-LEPS (Marsigli et al., 2005). It is nowadays 88 common to apply atmospheric EPS as a forcing in operational flood-forecasting systems 3 89 (Siccardi et al., 2005; Verbunt et al., 2007; Bartholmes et al., 2009 and see Cloke and 90 Pappenberger, 2008 for a review). 91 One of the advantages all meteorological ensemble approaches have in common is the 92 simple interface with hydrological impact models. Each member of the ensemble can be fed 93 into the hydrological model and generate forecast. The spread arising from the outcomes of all 94 members represents the sensitivity of the hydrological system to the meteorological ensemble. 95 Recently, ensemble techniques have been proposed to quantify uncertainties in observing 96 systems (Collier, 2007), such as radar precipitation estimation and nowcasting (e.g. Berenguer 97 et al., 2005; Bowler et al., 2006; Szturc et al., 2008; Lee et al., 2009; Germann et al., 2009), 98 pluviometer-based ensembles (Ahrens and Jaun, 2007; Villarini and Krajewski, 2008; Moulin 99 et al., 2009; Pappenberger et al., 2009), or satellite rainfall retrieval (e.g. Bellerby and Sun, 100 2007; Clark and Slater, 2006). In addition the use of observation-based ensembles allows 101 obtaining a hydrologically consistent ensemble of initial conditions for simulations coupled 102 with atmospheric EPS. 103 The hydrological model uncertainty is a further measure that is needed being accounted 104 and communicated in hydrological forecasting. The problem of parameter estimation and 105 equifinality is not a prerogative of hydrology (Beven, 1993; Beven and Freer, 2001; Vrugt et 106 al., 2003; Pappenberger and Beven 2006), but is a common issue in environmental modelling 107 (see Matott et al., 2009 for a review). 108 This paper describes an experimental flood-forecasting chain emerging from the joint 109 activities of the MAP–D-PHASE project (Rotach et al., 2009) and the COST action 731 110 (Rossa et al., this issue). A novel approach from our study is the superposition (or “cascading”, 111 Pappenberger et al., 2005) of the “uncertainty triplet” described above. To summarize we will: 112 - Propagate COSMO-LEPS (section 2.3) and the radar ensemble fields from REAL 113 (Germann et al., 2009; section 2.2) through the hydrological model PREVAH (Viviroli et al., 114 2009a; section 2.1) 115 - Estimate the uncertainty of PREVAH tunable parameters by Monte Carlo sampling 116 and select different parameter sub-samples (section 3.2) 117 - Define different experimental settings for superposing the uncertainties from 118 PREVAH, REAL and COSMO-LEPS (section 3.4) 4 119 - Quantify uncertainty and express it as average spread for a forecast period of 120 120 hours, as defined by the lead-time of COSMO-LEPS forecasts (section 3.5). 121 As experimental area the Swiss Verzasca river basin (186 km2, section 3.1) has been 122 selected. This was the authors' main test bed during MAP D-PHASE. Data are available since 123 beginning of the MAP D-PHASE demonstration period in June 2007. 124 Our main goal is to estimate the different magnitudes of spread generated by our 125 particular definitions of input uncertainties (REAL and COSMO/LEPS), initial conditions 126 uncertainties (REAL for estimating initial conditions before feeding COSMO/LEPS into 127 PREVAH) and hydrological model uncertainties (use of different set of calibrated parameters). 128 As a further goal we want to identify how spread grows when different sources of uncertainty 129 are superposed. 130 131 2. Methods 132 2.1 The operational hydrological model PREVAH 133 We adopt the semi-distributed hydrological catchment modelling system PREVAH 134 (Precipitation-Runoff-Evapotranspiration HRU Model; Viviroli et al., 2009a), which has been 135 developed to improve the understanding of the spatial and temporal variability of hydrological 136 processes in catchments with complex topography. A review on previous work with 137 PREVAH is presented in Viviroli et al. (2009a), which also thoroughly introduces the model 138 physics, parameterizations and pre- and post-processing tools. 139 Besides application for investigating water resources in mountainous basins (Zappa et 140 al., 2003; Zappa and Kan, 2007; Koboltschnig et al., 2009), in recent times PREVAH has 141 been more and more used in quasi-operational hydrological applications and re-forecasts of 142 flooding events in Switzerland. Verbunt et al. (2006) presented an indirect verification of 143 deterministic quantitative precipitation forecasts (QPF) for the river Rhine. Verbunt et al. 144 (2007) and Jaun et al. (2008) presented case studies on coupling PREVAH with the ensemble 145 numerical weather prediction system COSMO-LEPS. Jaun and Ahrens (2009) verify a two- 146 year reforecast experiment of the PREVAH/COSMO-LEPS forecasting chain for the Swiss 147 Rhine basin. Romang et al. (2011) introduce the application of PREVAH for early flood 148 warning in Swiss mesoscale basins. PREVAH is adopted as a “hydrological engine” for 149 superposing three sources of uncertainty (Figure 1). 5 150 151 2.2 Dealing with uncertainties within operational weather radar systems 152 In the past decade MeteoSwiss, the Swiss Federal Office of Meteorology and 153 Climatology, developed and implemented a series of sophisticated algorithms to obtain best 154 estimates of surface precipitation rates over Switzerland using a radar network (Germann et 155 al, 2006). In spite of significant improvements, the residual uncertainty is still relatively large. 156 A novel promising solution to express this residual uncertainty is to generate an ensemble of 157 radar precipitation fields by combining stochastic simulations and detailed knowledge of the 158 radar signal error structure. The method is called REAL, which stands for Radar Ensemble 159 generator designed for usage in the Alps using LU decomposition (Germann et al., 2009). 160 In REAL, the original (deterministic) radar precipitation field (1x1 km2 resolution) is 161 perturbed with a stochastic component, which has the same mean and covariance structure in 162 space and time as the covariance matrix of the radar errors. In a first step mean and 163 covariance structure of radar errors are determined by comparing radar estimates with rain 164 gauge measurements. Radar errors are defined as the logarithm of the ratio between the true 165 (unknown) precipitation values divided by the radar estimate. This is a reasonable definition 166 given the fact that most radar errors are actually multiplicative (Germann et al., 2006). In a 167 second step REAL generates a number of perturbation fields using singular value 168 decomposition of the radar error covariance matrix, stochastic simulation using the LU 169 decomposition algorithm, and autoregressive filtering. Each ensemble member is a possible 170 realization of the unknown true precipitation field time series given the radar reflectivity 171 measurements and the radar error covariance matrix. For the complete mathematical 172 derivation of REAL we refer to Germann et al. (2009). 173 A prototype ensemble generator has been implemented as part of MAP D-PHASE and 174 COST-731 and is running in real-time in an automatic mode since spring 2007. The ensemble 175 of precipitation field time series from REAL consists of 25 members and is updated 176 operationally every 60 minutes and propagated through PREVAH. 177 178 2.3 Quantification of uncertainty from ensemble NWP-systems 179 Early identification of severe long-lasting rainfall events within the next five days is 180 obtained from the Limited-area Ensemble Prediction System of the COnsortium for Small- 6 181 scale MOdelling COSMO-LEPS (Marsigli et al., 2005). In the current configuration, 182 COSMO-LEPS provides once a day a 16 member ensemble forecast with 132 hours lead-time 183 for large parts of Europe. COMSO-LEPS is initialized at 12:00 UTC whereas the first 12 184 forecast hours are not used due to misrepresentations during model spin up. Initial and 185 boundary conditions are taken from the European Centre for Medium-Range Weather 186 Forecast EPS (Molteni et al., 1996). The horizontal grid-spacing of COSMO-LEPS is 10x10 187 km2 which is rather coarse for the small Verzasca basin, but due to the high computational 188 costs ensemble forecasts with higher resolutions are not yet available for the medium-range. 189 Six meteorological surface variables (air temperature, precipitation, humidity, wind, sunshine 190 duration derived from cloud cover, global radiation) are obtained from the ensemble NWP 191 and downscaled for hydrological modeling. The setup adopted for downscaling information 192 from COSMO-LEPS for hydrological applications is the same as presented in Jaun et al. 193 (2008) and relies on bilinear interpolation. Air temperature is adjusted according to elevation 194 by adopting a constant lapse rate of 0.65 °C per 100 m. 195 196 3. Experimental design 197 3.1 Study area 198 The Verzasca basin has an area of 186 km² up to the main gauge in Lavertezzo (Figure 199 2). The basin is located in the southern part of Switzerland and is little affected by human 200 activities. Its elevation range is 490-2870 m a.s.l. Forests (30%), shrub (25%), rocks (20%) 201 and alpine pastures (20%) are the predominant land cover classes. Soils are rather shallow 202 (generally smaller than 30 cm) and the plant available field capacity is below 5% volume. The 203 discharge regime is governed by snowmelt in spring and early summer and by heavy rainfall 204 events in fall (Ranzi et al., 2007). The river is rather prone to flash floods (Wöhling et al., 205 2006) and leads into the “Lago di Vogorno” an artificial reservoir maintained by a private 206 Hydropower Company. 207 The hydrological properties of the catchment are derived from gridded maps of 208 elevation, land use, land cover and soil properties (Gurtz et al., 1999), which are available at 209 100x100 m2 resolution. For the present application a resolution of 500x500 m2 is generated 210 previous to the delineation of hydrological response units (Viviroli et al., 2009a). The runoff 211 gauging station at the catchment outlet is maintained by the Swiss Federal Office for 212 Environment, which provides data at 10 minutes resolution operationally. Flood peaks at 7 213 Lavertezzo may exceed 600 m3s-1 (~3.2 m3s-1km²). Base flow in winter can be less than one 214 m3s-1. 215 The operational meteorological forcing is obtained from several sources. MeteoSwiss 216 maintains a network of automatic stations providing a detailed set of meteorological variables 217 with a sampling interval of up to 10 minutes (Figure 2). The administration of the Canton 218 Ticino (UCA Ct. Ticino on Figure 2) maintains an additional network of pluviometers, which 219 samples precipitation data in real-time with a temporal resolution of 30 minutes. One of the 220 latter is the only automatic pluviometer within the basin. Furthermore weather radar 221 precipitation fields are available (Section 2.2.). 222 223 3.2 Consideration of hydrological uncertainty 224 The initial setup and calibration of the hydrological model was based on previous 225 applications in the Verzasca river basin (Wöhling et al., 2006; Ranzi et al., 2007). The used 226 default calibration is focused on the identification of a single parameter set with highest 227 performance in the simulation of the average flows and with the smallest volume error 228 between observed and simulated time series (Zappa and Kan, 2007; Viviroli et al., 2009a). 229 Since the target of this study is the quantification of uncertainty propagation in 230 hydrometeorological flood forecasting chains, only seven parameters being relevant for 231 surface runoff generation were allowed to randomly change during the MC experiment (Table 232 1). The identification of these seven sensitive parameters relies on experience (Zappa, 2002), 233 on consideration of the model structure (Gurtz et al., 2003) and targeted sensitivity studies on 234 flood peak calibration (Viviroli et al., 2009b). Table 1 indicates the basic value of the seven 235 parameters after the default calibration and the ranges allowed for parameter sampling during 236 the MC experiment. Further uncertainties linked to the parameters controlling snow 237 accumulation, snow melting and base-flow have been disregarded. A total of 2527 MC runs 238 were computed for the period 1996-2001, whereby the year 1996 was only used as a spin-up 239 year. Please note, that we are not addressing the full predictive uncertainty of the forecasting 240 chain as defined in Draper (1995) and Todini (2009), but we focus on the parameter 241 uncertainty as obtained by selecting equifinal realizations from a Monte Carlo (MC) 242 experiment, as well as observation and algorithm uncertainty by the ensemble methods for the 243 NWP and the radar systems (see above). However, for the model chain used, the obtained 244 uncertainty is the best available estimate of the full predictive uncertainty and our 8 245 hydrological experiments which rely on assessing different sets of model parameters to fit 246 past observations provide a practicable way to quantify how parameter uncertainty might 247 contribute to the full predictive uncertainty of the system (Figure 1). 248 The decision if a model run is behavioural or not is based on a subjective choice of 249 likelihood function(s) (Beven, 1993; Madsen, 2000 and 2003; Viviroli et al., 2009b; Bosshard 250 and Zappa, 2008). As the goal of the modelling experiments is the estimation of flood peaks, 251 two goodness-of-fit measures focused on peak-discharge have been computed for each MC 252 realization. As a first measure, the well-known Nash and Sutcliffe (1970) (NSE) efficiency is 253 used: ∑ n Qt − qt 2 254 NSE = 1 − t =1 , NSE ∈] − ∞,1] (1) ∑ n 2 t =1 Qt − Q 255 where Qt is the observed hourly runoff at the time step t, Q the average of observed 256 runoff, qt the simulated runoff at the time step t and n the number of time steps. NSE 257 quantifies the relative improvement of the model compared to the mean of the observations. 258 NSE is particularly adequate for our present application, since it is particularly sensitive to 259 high flows. Its use is less advisable for studies focussed on obtaining the best calibrated 260 values for both high and low-flows (Legates and McCabe, 1999; Schaefli and Gupta, 2007). 261 In addition to NSE a second function is used. Lamb (1999) and Viviroli et al. (2009b) 262 introduce and discuss several scores for obtaining tailored parameters sets for flood-peak 263 estimations. One of them is the sum of weighted absolute errors (SWAE), which is defined as: ( ) n SWAE = ∑ Qt Qt − qt , SWAE ∈ [0, ∞[ a 264 (2) t =1 265 A value of a = 1.5 was used as proposed by Lamb (1999) for evaluation of peak flow 266 conditions. Behavioural simulations show a lower SWAE. 267 The 2527 MC runs (Figure 3) were ranked according to their performance in the 268 defined calibration period. As a compound measure of performance a weighted product of 269 NSE (weight=3) and SWAE (weight=1) was adopted to build a single score Li: 3 ⎛ NSE i ⎞ SWAE AVG 270 Li = ⎜ ⎜ NSE ⎟ ⋅ ⎟ (3) ⎝ AVG ⎠ SWAEi 9 271 A MC realization i having NSEi above the average NSEAVG of all realizations and 272 SWAEi lower than the average SWAEAVG of all realizations will be ranked higher than MC 273 runs showing an opposite behaviour with respect to the average NSE and SWAE. The analysis 274 of the MC runs showed that SWAE varied between 3500 and 6000 while the range of NSE 275 was 0.71 to 0.84 (Figure 3). Finally a Li range between 0.5 and 1.34 was obtained for all runs. 276 Figure 3 shows a dot-plot of all MC realizations with NSE on the y-axis and SWAE on 277 the x-axis. The obtained pattern allows for a visual discrimination between realizations with 278 higher and lower performance, with the best realizations being in the upper-left region of the 279 dot-plot. For the analysis in the remaining sections of the paper three sub-samples of 26 280 parameter sets each were isolated by ranking all realizations by sorting Li. The first sub- 281 sample consists of the best 26 realizations (99.5%; Li: 1.289/1.339). The second sub-samples 282 collects the 26 sets around the 95% ranking (Li: 1.238/1.246). The third sub-sample is a 283 selection of 26 runs around the 80% ranking (Li: 1.152/1.157). Table 2 displays some 284 statistical measures about the three sub-samples of 26 parameter sets. Except for the storage 285 coefficient controlling the generation of interflow K1, the 26 runs with highest performance 286 present for all seven tuneable parameters the lowest standard deviation within the sub-sample 287 itself. The highest variability is computed within the 80% sub-sample. 288 289 3.3. The selected peak-flow events 290 All experiments rely on a long-term simulation with PREVAH using the basic 291 parameter calibration (Table 1). Initial conditions for September 1st 2005 (Figure 4) are 292 generated by a reference run using interpolated observed pluviometer data. This reference run 293 starting on January 1st 1996 was obtained from an offline meteorological database, which also 294 includes stations that are not available in real-time. Starting from September 1st 2005 a second 295 long-term simulation relying on operationally available data only has been run to produce 296 initial conditions for March 1st 2007. This run used precipitation data from the operational 297 pluviometers operated by MeteoSwiss and the river network administration of the Canton of 298 Ticino (Figure 2) as an input. From March 1st 2007 operational time series of radar QPE and 299 REAL are also available. 300 The time frame for the implementation of PREVAH in operational mode was decided 301 in order to have good initial conditions for the MAP-D-PHASE demonstration period. In the 302 period March 1st 2007 to November 23rd 2008 seven events with peak-runoff ranging between 10 303 77 and 541 m3s-1 have been identified (Table 3). The return period of the highest flood peak in 304 the considered period on September 7th 2008 is approximately 5 years on the basis of extreme 305 value statistics of a time series starting in 1990 and having an average yearly flood of 385 306 m3s-1. The cumulative precipitation in the period previous to the 7 events is also indicated in 307 Table 3, both as spatially interpolated pluviometer data (areal precipitation estimate with 308 inverse distance weighting interpolation) and as assimilated QPE from the weather radar. It 309 can be observed, that the event on October 29th 2008 occurred after a relative dry antecedent 310 period, while in the days and weeks previous to the August 22nd 2007 over 150 mm rainfall 311 were estimated for the Verzasca basin. In the antecedent cumulative precipitation for the 312 November 5th 2008 event the precipitation event that triggered the October 29th 2008 peak 313 flow are included. 314 315 3.4 The seven experiments towards estimation of uncertainty superposition 316 The availability of several different data sets of deterministic and probabilistic 317 precipitation measurements and forecasts and the identification of sets of hydrological model 318 parameters allows the computation of uncertainty superposition. Seven different experiments 319 (Figure 4 and Table 3) have been completed: 320 1) MOD/PLUV: in this experiment the simulations from March 1st 2007 have been continued 321 until November 25th 2008 with the same configuration used since September 1st 2005. No 322 sources of uncertainty were considered. During the simulation a series of model starting 323 points were stored 10 to 20 days ahead of a major discharge event (see section 3.3 and 324 Table 3). The timing for saving the initial conditions was chosen in order to guarantee that 325 almost only base-flow is contributing to the discharge at initialization and that a minor 326 rainfall event is included in the time span between the models restart point and the peak- 327 flow event. In a second stage a temporally nested simulation was run starting from the 328 defined initialization date (Day -10/-20, Table 3) until 10 to 15 days after the event. For 329 the nested sub-period 3 times 26 model runs were run (Figures 3 and 4 and Table 2). 330 2) MOD/RAD: this experiment is identical to the MOD/PLUV experiment, with the only 331 change that the precipitation forcing is obtained from the weather radar (see section 2.2). 332 Also in this case model runs for temporally nested sub-periods in correspondence to peak- 333 flow events were run by accounting the uncertainty in the determination of calibrated 334 model parameters. It is important to declare here that in the case of simulations forced 11 335 with radar data (either deterministic or estimated with REAL) no bias in rainfall and 336 snowfall is accounted for. The radar QPE is already corrected for biases during the pre- 337 processing (Germann et al., 2006). Therefore: the two parameters of PREVAH controlling 338 such corrections are set to 0% (Table 2). 339 3) REAL: in this experiment only the uncertainty arising from the weather radar QPE is 340 accounted for. 25 ensemble members from the radar ensemble generator (section 2.2) are 341 used to force PREVAH. The initial conditions at initialization of the nested runs are 342 obtained from the MOD/RAD experiment, being forced with the deterministic radar QPE 343 since March 1st 2007 (Figure 4). 344 4) REAL/MOD: this experiment is the first one where uncertainty superposition is 345 considered. To reduce the computational effort, only one of the 3 parameter sub-sets is 346 accounted for (see section 4.1), namely the 95% sub set (Table 2), which includes the 26 347 model runs being ranked in the top 94.5% to 95.5% among the 2527 MC realizations (see 348 section 3.2). In detail: for each nested period 25 (REAL) x 26 (MOD_95%) runs were 349 completed in order to estimate the interaction between the radar-QPE and the uncertainties 350 of the hydrological model. Also in this case restart points for the hydrological model were 351 saved for later initialization of probabilistic forecasts with COSMO-LEPS (see below and 352 Table 4). 353 5) LEPS: in this experiment only the uncertainty arising from feeding PREVAH with the 16 354 COSMO-LEPS ensemble members is accounted for. The initial conditions at initialization 355 of COSMO-LEPS forecasts (Table 4 and Figure 4) are obtained from the model being 356 forced with the deterministic radar QPE since March 1st 2007 (Figure 4). A total of 19 357 COSMO-LEPS 5-day forecasts for the Verzasca river basin were selected (Table 3). 358 COSMO-LEPS QPF are not bias corrected (Table 2). 359 6) LEPS/MOD: in this experiment both the uncertainty of the model parameters and of the 360 NWP forecasts are considered. In detail: for each COSMO-LEPS initialization point 16 361 (COSMO/LEPS) x 26 (MOD-95%) runs were completed. This gives an ensemble of 416 362 5-days forecasts. 363 7) FULL: the final experiment is the combination of REAL/MOD and LEPS/MOD. For each 364 of the 19 COSMO-LEPS ensemble forecasts 650 different initial conditions are available 365 from the superposition of REAL with the model parameter uncertainty (see above). Thus, 366 650 (REAL/MOD) x 16 (COSMO-LEPS) runs were computed for all 19 forecasts (Figure 12 367 4 and Table 3). An overall ensemble of 10400 members results for evaluation and 368 quantifying uncertainty superposition by simultaneous consideration of uncertainties in 369 the QPE (REAL), in the NWP forecasts (COSMO-LEPS) and in the determination of the 370 parameters of the hydrological model (MOD-95%). 371 372 3.5. Quantification of uncertainty 373 We aim at quantifying the propagation and superposition of uncertainty when forcing 374 PREVAH with different meteorological time series and different configuration of its tunable 375 parameters. In all experiments a time frame of 120 hours is evaluated (Figure 4). The time 376 frame is defined by the initialization time of the COSMO-LEPS forecast used. We assume 377 that the average spread of the simulated ensemble hydrographs is related to the uncertainty of 378 the experimental settings used. For allowing intercomparison between experiments all 379 statistics have been computed for the same 120 hours period. We take the average of the 380 ensemble quantiles during the 120 hours as an objective measure for quantifying the i 381 uncertainty. Prior to the averaging, quantiles ( q % ) are determined for each of the 120 hours 382 being evaluated. Equation 4 defines the computation of the average of quantiles q % for the 383 defined time frame: i =n ∑q i % 384 q% = i =1 , n=120 time steps (4) n 385 q % denotes the “average quantile” of discharge during n=120 time steps. q % has been 386 computed for the levels 0%, 25%, 50% (the median), 75% and 100%. The average 387 interquartile range IQR can be obtained by subtracting q 25 from q 75 , while the average range 388 of spread is computed by subtracting q 0 from q100 . 389 390 4. Results 391 In this section the findings from the different experiments are discussed. The observed 392 runoff hydrograph and the average discharge during the events are also plotted, and should 393 give a subjective indication on the plausibility of the obtained result. The evaluation of long 394 series of operational forecasts with COSMO-LEPS and nowcast runs with REAL, 13 395 MOD/PLUV and MOD/RAD are not detailed here. Nevertheless Appendix A1 and Figure A1 396 give a concise summary on the quality of the probabilistic (COSMO-LEPS, REAL) and 397 deterministic (MOD, RAD) simulation during the period June 2007 to November 2008, in 398 which all selected events are included in and for which there is a detailed verification report 399 (Diezig et al., 2010). The verification indicates that all used deterministic and probabilistic 400 meteorological inputs results in discharge estimations that perform better than climatology. 401 Even if REAL and COSMO-LEPS present similar skill against observations, the following 402 sections will outline that the spread of these two sources of ensemble precipitation input may 403 differ quite a lot for events leading to high discharge events. 404 405 4.1 Parameter uncertainty 406 The MOD/PLUV and MOD/RAD experiments have been evaluated by quantifying the 407 average ensemble spread ( q100 - q 0 ) during the seven events (Table 4). MOD/PLUV was run 408 using each of the three different sub-sets of parameter realizations (Table 2). For MOD/RAD 409 only the results from the 26 realizations from the set MOD_95% are shown. Depending on the 410 intensity of the event (peak-flow) and the differences in antecedent precipitation (Table 3) 411 different values of spread are obtained for the different events. The largest average ensemble 412 spread (about 30 m3s-1 for both MOD_95%/PLUV and MOD_95%/RAD) is found during the 413 event leading to the September 7th 2008 peak-flow of 541 m3s-1. 414 The application of parameter sub-samples with higher NSE and SWAE results in 415 reduced spread. The average spread resulting by propagating the MOD_99.5% sub-sample is 416 30% lower than the one computed when propagating MOD_95%. The spread obtained by 417 propagating the MOD_80% sub-sample is on 30% higher than the one obtained from 418 MOD_95% (Table 4). 419 The average spread for the seven events obtained from 26 realizations of PREVAH 420 forced with weather radar QPE is about 14% (MOD95%/RAD) lower than the corresponding 421 spread of the runs forced with interpolated pluviometer data (MOD95%/PLUV). Only for the 422 event leading to the July 13 2008 peak flow the spread of the weather radar-driven 423 simulations are larger than the ones run with rain gauge data. This is due to a local convective 424 rainfall event that was not recorded by the pluviometers, but that resulted in locally very high 425 radar QPE. The main reason for having a lower spread with radar QPE than with pluviometer 14 426 forcing is the effect of bias correction, which is applied to the pluviometer data only. The 427 variation in the bias correction (Table 3) covers both the input and model uncertainties. This 428 is the way errors in estimating precipitation are currently accounted for. However, there is an 429 important constraint as compared to state-of-the-art observation-based precipitation 430 ensembles (e.g. Ahrens and Jaun, 2007; Moulin et al., 2009; Pappenberger et al., 2009). The 431 hydrological model uses the precipitation bias corrections (Table 2) as a global tunable 432 parameter for accounting for different sources of error in the treatment of rain gauge data: a) 433 direct measurement errors, b) systematic errors due to the choice, location and availability of 434 meteorological stations and, c) uncertainties in the generation of spatially interpolated fields. 435 Additionally the bias correction parameters also contribute to a compensation of systematic 436 errors in the estimation of evapotranspiration and other water fluxes by PREVAH (Zappa, 437 2002; Viviroli et al., 2009a). Methods for generating observation-based ensembles (both 438 based on weather radar and simulations) are only focusing on the estimation uncertainties in 439 the gridding of precipitation information and are therefore better suited for the propagation of 440 input uncertainties. 441 Figure 5 shows in detail simulations for the November 5th 2008 event. The related 442 evaluation of the average spread for the 120 hours window starting from November 3rd 2008 443 00:00 is summarized in Table 4. The spread arising from adopting three different parameter 444 sub-sets clearly increases by using sets with lower Li during the calibration period. While the 445 shape of the simulated ensembles above and below the median remains very similar among 446 the three cases, the distance of the upper and lower ensemble envelopes grows with 447 decreasing likelihood within the calibration period. As a consequence, the number of 448 observations falling within the uncertainty band drawn by the ensembles increases when using 449 MOD_80 as compared to both MOD_99.5% and MOD_95%. The spread computed when 450 using weather radar information is slightly higher at the start of the event. During the event 451 the spread obtained from radar forcing gets clearly smaller as the one obtained from forcing 452 using interpolated data from pluviometers. This is confirmed by the average values of spread 453 during the event (Table 4). 454 Spreads resulting from this analysis range between 7 and 30 m3s-1 for the seven 455 investigated events (MOD_95%). We selected MOD_95% as a benchmark against which to 456 compare spreads resulting from the other sources of uncertainty from now on. This decision is 457 taken with the intent of avoiding over fitting (when using MOD_99.5% as a benchmark). 15 458 459 4.2 Weather radar uncertainty and superposition with parameter uncertainty 460 Following the proof-of-concept presented in Germann et al. (2009), PREVAH was run 461 by adopting ensemble radar QPE ensembles obtained from REAL. The runs forced by REAL 462 members use the initial conditions of a deterministic run forced by the operational radar QPE 463 of MeteoSwiss until some days ahead of the event (Figure 4 and Table 4). From that 464 initialization point the procedure described in section 3.4 (experiment “REAL”) is applied. As 465 for the results presented in the previous section the average ensemble spread of the seven 466 selected events has been computed for a 120 hours time frame (Table 5). In analogy also the 467 experiment REAL/MOD was completed by varying both, the REAL member and the 468 calibrated parameter realization from the MOD_95% set one after the other. 469 The model runs resulted in an average spread ranging between 25 and 167 m3s-1 for 470 REAL and between 34 and 216 m3s-1 for REAL/MOD. If we compare these results with the 471 outcomes of MOD_95%/RAD, the REAL and REAL/MOD runs (Table 4) present a higher 472 spread by a factor of 4.3 (REAL) and 5.6 (REAL/MOD). 473 Figure 6 shows two examples of 5-days ensemble hydrographs obtained for the 474 experiments REAL and REAL/MOD. Contrarily to the ensembles shown in Figure 5 almost 475 all observed values fall within the ensemble envelopes. Only the falling limbs close to the end 476 of the simulation are underestimated by both REAL and REAL/MOD ensembles. For the 477 cases August 22nd 2007 and November 5th 2008 events there is clear evidence that the spread 478 arising by joint consideration of two sources of uncertainty is higher than the one obtained by 479 propagating only the REAL members through the hydrological model. The spread from the 480 REAL/MOD ensemble is 25% to 40% higher than that of the REAL realizations. The average 481 additional spread for the seven events is 17 m3s-1 (Table 5). Combining the analyses of Tables 482 4 and 5, the following findings can be stated for simulations REAL and REAL/MOD: 483 - The average spread for the seven events stemming from the parameter ensemble is 484 about 12 m3s-1 (PREVAH forced by deterministic radar QPE and 26 parameter 485 realizations from MOD_95%). 486 - The coupling of PREVAH with REAL results in hydrograph ensembles with an 487 average spread of over 55 m3s-1 for the same seven events. 16 488 - If both REAL and MOD_95% are applied an ensemble of 650 members is generated. 489 The obtained average spread in this case is about 72 m3s-1. 490 This means that REAL/MOD generates a 6% to 7% larger spread than the sum of the 491 spread obtained from the experiment MOD/RAD_95% and REAL (67 m3s-1). This indicates 492 that an amplification of spread by superposition of two sources of uncertainty is occurring. 493 Our particular modeling system is characterized by non-linear responses, mostly explained by 494 conceptual threshold processes in the runoff generation module of PREVAH (Gurtz et al., 495 2003). At the level of interquartile range amplification of spread has been observed in only 496 one of the 19 cases considered (Table 3). Thus only a subset of all considered REAL and 497 MOD combinations triggers a non linear reaction within the runoff generation module of 498 PREVAH. In all other cases the IQR-spread of REAL/MOD is in average 9% smaller than the 499 cumulative spread of REAL and MOD. 500 501 4.3 COSMO-LEPS uncertainty and superposition with model uncertainty 502 As expected the average spread obtained by propagating NWP forecasts through the 503 hydrological model is much larger than the one obtained from the experiments discussed 504 above (Figure 7 and Table 4). The computation of LEPS generates average spreads that are 505 about 10 times higher than the ones of MOD_95%/RAD and 2.3 times higher than the ones 506 from REAL (Tables 4 and 5). Contrary to previous experiments, that are always related to an 507 occurred precipitation event, the LEPS ensemble (initialized as declared in Table 5) also 508 includes members that are forecasting very low or no precipitation at all for the respective 509 event (e.g. Figure 7 for the August 22nd 2007 event, upper panels). The forecast initialized on 510 August the 20th 2007 includes a relevant number of members that show no runoff increase at 511 all within the 120 forecast hours. Even the 25% quantile shows a maximum discharge that is 512 slightly higher than the discharge at initialization time. In case of this event the whole 513 observed time series falls within the envelope drawn by the LEPS experiment. Unfortunately, 514 that the spread is very large. This makes any kind of decision making related to that case 515 almost impossible. Anyway, in this specific case a potential end-user taking actions on the 516 basis of the 75% quartile would have been very efficient in his decision making. Further 517 considerations on skill for decision making are only possible after sound verification of long- 518 term time series of consecutive forecasts (e.g., Fundel and Zappa, 2010) 17 519 The results from the November 5th 2008 event (lower panels in Figure 7) show different 520 characteristics. All LEPS ensemble members agree that the first runoff first peak is to be 521 expected in the second half of the first day of the forecast, and that a second (higher) peak will 522 arrive about 60 hours after initialization of the forecast. Potential users focusing on the 75% 523 quantile would have probably over-reacted at the start of the event, but would have been able 524 to cope with the peak on November 5th 2008. 525 The LEPS/MOD experiments represents a second series of simulations, for which 526 parameter uncertainty is accounted for and superposed to the uncertainty originating from the 527 LEPS (right panels in Figure 7). The average spread from the LEPS/MOD ensemble is 13% to 528 25% higher than the one of the model realizations based on LEPS only. The average 529 additional spread for the seven events is 23 m3s-1 (Table 5). 530 In analogy to joint consideration of Tables 4 and 5 in Section 4.2 the experiments with 531 LEPS and LEPS/MOD allow the following statements: 532 - Average spread from MOD_95%/RAD is about 12 m3s-1 (see above). 533 - The coupling of PREVAH with LEPS generated hydrograph ensembles with an 534 average spread of over 130 m3s-1 for the seven events considered. 535 - Applying both LEPS and MOD_95% results in an ensemble of 416 members. The 536 obtained average spread is larger than 150 m3s-1. 537 This means that REAL/MOD generates a 9% to 10% larger spread than the sum of the 538 spread obtained from the experiment MOD/RAD_95% and LEPS (142 m3s-1). Also in this 539 case the superposition of the two sources of uncertainty causes an amplification of the full 540 spread. In this case an amplification of spread measured by the interquartile range has been 541 observed in seven cases (Table 3). On average the IQR-spread of REAL/MOD is 2% smaller 542 than the cumulative spread of LEPS and MOD. 543 When propagating numerical forecasts from an ensemble prediction system such as 544 COSMO-LEPS through a hydrological model for mesoscale areas such as the Verzasca basin 545 (186 km2), the big mismatch between the basin area and the resolution of the ensemble 546 prediction system (10x10 km2 mesh size) has to be kept in mind. Nevertheless studies with 547 such kind of hydrological ensemble predictions have been very popular in the last few years 548 (Cloke and Pappenberger, 2008; Jaun et al., 2007) and have found already application in 18 549 operational chains. This scale restriction is less problematic for applications in macro-scale 550 basins (Pappenberger et al., 2005; Batholomes et al., 2009). 551 552 4.4. Superposition of three sources of uncertainty 553 The last experiment combines the initial conditions obtained from the REAL/MOD 554 experiment (650 members) with the 16 ensemble members of COSMO-LEPS (see Section 3.4 555 and Figure 4) and thus considers the entire “uncertainty triplet” (Figure 1). The LEPS/MOD 556 experiment discussed above is extended by additionally perturbing the initial conditions 557 forcing PREVAH with REAL, up to start of the COSMO-LEPS propagation through 558 PREVAH. By accounting for these additional perturbations the average spread for the seven 559 events increases by about 4.5%, from 153 (LEPS/MOD) to 160 m3s-1 (FULL, Table 5). Only 560 the run initialized on August 12th 2008 shows a distinctly higher additional uncertainty (~15% 561 more) in the FULL experiment, as compared to the LEPS/MOD experiment (Figure 8). The 562 FULL ensemble shows already a large spread at initialization, as determined by the 563 antecedent conditions obtained from REAL/MOD runs. This difference in the overall spread 564 gradually converges but it is still well defined at the time of the first runoff peak shortly after 565 2:00 on August 13th 2008, where the maximum peak-flow of FULL is about 50 m3s-1 higher 566 than the corresponding LEPS/MOD peak. The difference is also well visible in the IQR. The 567 second peak, late in the evening of August 15th 2008 shows nearby identical shape and ranges 568 for both FULL and LEPS/MOD. The uncertainties owed to the REAL influence on 569 REAL/MOD decays during the first part of the event. 570 Figure 9 shows an overview on all 19 “FULL” experiments, each of them summarizing 571 the spread arising from 10400 5-days forecasts. In 12 cases the observed average discharge is 572 found within the IQR. Only the experiment with the longest lead time initialized on August 573 10th 2008 produced a q100 lower than the observed average discharge during the 120 forecast 574 hours considered. The model run initialized 24 hour later (August 11th 2008) generates an 575 ensemble spread that strongly overestimates the observed value. The correspondent runs for 576 three following days show a gradual reduction in ensemble spread. The reason for the large 577 spread is that some COSMO-LEPS members are forecasting severe convective precipitation, 578 while others predicted no precipitation at all. Finally a moderate thunderstorm occurred in the 579 evening of August 11th 2008. REAL also generated large spread in its members with 580 cumulated rainfall for August 11th 2008 ranging between 3 and 40 mm. This explains the 19 581 large discrepancy in initial conditions observed at initialization of the LEPS forecasts on 582 August 12th 2008 (see Figure 8). 583 584 4.5 Attributing the contribute to the total uncertainty 585 The outcome from the three experiments dealing with uncertainty superposition (FULL, 586 REAL/MOD, LEPS/MOD) can be sorted out in order to allocate the contribution of one of the 587 sources of spread to the whole experimental uncertainty. For this analysis we put the focus on 588 one event only, namely the November 5th 2008 event with COSMO-LEPS forecasts initialized 589 on November 3rd 2008 (see also Figures 5 to 7). The following procedure was applied: 590 - Calculate the quantiles of all runs of the experiment (Eq. 4); 591 - Grouping in turn all runs sharing the same MOD, REAL or LEPS member (Table 6); 592 - Averaging the quantiles of the sub-sample and calculate correspondent spread metrics 593 (Figure 10). 594 The three main findings from Table 6 are: 595 a) FULL: The 10400 FULL runs give an average ensemble spread “ q100 – q 0 ” of 139.0 596 m3s-1. There are 400 model runs sharing the same parameter set. This means that we 597 can compute 26 different “ q100 – q 0 ” and average them to obtaining an integral 598 measure indicating the spread attributed to the two sources of uncertainty that have 599 been varied in this specific case (REAL & LEPS). In this example the “ q100 – q 0 ” that 600 cannot be attributed to MOD is 125.4 m3s-1 (90% of the total spread). When REAL is 601 used as a filter and both MOD and LEPS are varied, then almost 98% of the “ q100 – 602 q 0 ” is obtained. REAL contributes in a very limited way to the whole ensemble 603 spread. Finally, if the influence of LEPS is averaged then only 11.5% of the FULL 604 spread can be attributed (Table 6). Similar outcomes are observed when looking at the 605 IQR “ q 75 – q 25 ”. 606 b) REAL/MOD: The REAL/MOD ensemble generates a “ q100 – q 0 ” of 56.3 m3s-1. Here 607 the “ q100 – q 0 ” that cannot be allocated to MOD is 45.9 m3s-1 (80% of the total spread). 20 608 When REAL is used as a filter and only MOD is varied, then 17.9% of the spread can 609 be allocated (Table 6). 610 c) LEPS/MOD: The 400 LEPS/MOD realizations are resulting in an average “ q100 – q 0 ” 611 of 138 m3s-1. When focusing on the role of changing MOD and averaging the 612 influence of LEPS then “ q100 – q 0 ” is only 15.6 m3s-1 (11% of the total spread). If we 613 make a sub-sample that filters the spread of MOD, then about 88% of the whole 614 spread of LEPS/MOD can still be allocated (Table 6). 615 Figure 10 is a graphic rendering of Table 6 in form of box-plots. All experiments in 616 which LEPS contributes to the spread variation show an average spread close to the one of the 617 spread of the whole experiment. If only LEPS is propagated then the average spread is 130 618 m3s-1 (Table 5). If also model uncertainty is propagated, then the average spread increases by 619 about 23 m3s-1 to 153 m3s-1. If different initial conditions from REAL are also considered the 620 additional increases is 7 m3s-1 only (total:160 m3s-1, Table 5). If REAL is used to generate 621 initial conditions only, its influence to the total spread is smaller than the influence of the 622 hydrological model uncertainty. Using REAL as a forcing during the event increases the 623 spread by about 4.5 times (in the specific case of November 5th 2008) compared to the spread 624 that can be attributed to the model parameters. This confirms the outcomes summarized in 625 Tables 4 and 5. 626 627 5. Discussion and conclusions 628 The experimental setup, accounting for three sources of uncertainty, presented in this 629 paper, provides interesting answers to questions linked to uncertainty propagation and 630 superposition in a hydrometeorological forecasting system. 631 The used setup showed that the hydrological model (PREVAH) uncertainty is less 632 pronounced than the uncertainty obtained by propagating radar precipitation fields (REAL) 633 and NWP forecasts (COSMO-LEPS) through the hydrological model. The average difference 634 in spread for a five-days forecast range in the seven events considered results in a factor larger 635 than four between MOD/RAD and REAL and in a factor above ten between MOD/RAD and 636 LEPS . 21 637 Since the size of the Verzasca basin is only a few square kilometers larger than the 638 mesh size of COSMO-LEPS there is almost no averaging effect. This contributes to the large 639 spread of the obtained hydrographs when COSMO-LEPS is used. Gallus (2002) warns about 640 using NWPs grid-point information as for verification against point data. In the case of the 641 Verzasca this is almost the case, since we use information of few COSMO-LEPS grid points 642 in order to force our impact model and compare it to observations. 643 The estimation of PREVAH parameter uncertainty is strongly depending on the way the 644 parameters have been sampled and ranked. Numerous approaches are possible for this kind of 645 problem (Matott et al., 2009). We are confident, that the chosen approach is appropriate to 646 estimate the parameter uncertainty of PREVAH within the presented superposition 647 experiment. Of course the parameter uncertainty is estimated on the basis of the whole 648 calibration period. Current literature (He et al., 2009; Cullmann and Wriedt, 2008 and 649 Pappenberger and Beven, 2004) offers some examples of approaches that try to combine 650 parameter configurations being successful in the complete data basis with other parameter 651 configurations estimated for single events or series of events. 652 Amplification of spread is obtained if the combination of LEPS (or REAL) and triggers 653 a non linear reaction of the runoff generation module of PREVAH (Gurtz et al., 2003; Viviroli 654 et al., 2009a) which includes a threshold parameter for activating the generation of surface 655 runoff (Table 1). Such a non linear response needs to be accounted for by hydrological 656 models, since a sudden increase of discharge coefficients has been observed in many basins 657 during long lasting heavy precipitation events (e.g. Naef et al., 2008). Such threshold 658 processes can be also identified in for of step-structures in the flood frequency statistic (e.g. 659 Merz and Blöschl, 2008). In all considered cases we observed an amplification of the full 660 spread, while the corresponding interquartile range is mostly smaller when two error sources 661 are superposed. 662 By use of REAL, input uncertainties are considered for nowcasting. We showed that the 663 simultaneous application of REAL and parameter uncertainties generates ensembles that 664 nicely envelop the observed hydrograph. Besides weather-radar based approaches, 665 observation-based ensembles with pluviometer data have been recently proposed. Recent 666 studies propose the use of the Kriging variance (Ahrens and Jaun, 2007; Moulin et al., 2009; 667 Pappenberger et al., 2009) for the estimation of the interpolation uncertainty of ground-based 668 precipitation data for hydrological purposes. Jaun (2008) showed that hydrological simulation 22 669 forced by observation-based ensembles is sensitive to the density and number of stations 670 available. The interpolation uncertainty increases with decreasing number of representative 671 stations available. These restrictions do not apply to REAL, which is able to operationally 672 generate high resolution observation-based ensembles for hydrology. Nevertheless, 673 observation-based pluviometers ensembles are certainly a feasible way to consider input 674 uncertainty in regions where the weather radar coverage is not adequate. Further efforts are 675 planned in order to implement interpolation-based ensembles within our experimental chain. 676 The use of weather radar ensembles for generating hydrologically consistent ensembles 677 of initial conditions previous to the propagation of COSMO-LEPS through the hydrological 678 model show that the uncertainty in initial conditions decays within the first 48 hours of the 679 forecast. The magnitude of the uncertainty attributed to the difference in initial conditions is 680 smaller than the uncertainty attributed to the hydrological model parameters and almost 681 negligible with respect to the spread owed to COSMO-LEPS. 682 The operational implementation of this experiment for the small Verzasca river basin 683 would be a priori possible. To realize a run with all 10400 ensembles including 650 runs for 684 the determination of initial conditions requires about 6 hours CPU time. The application on 685 larger river basin requires a reduction in number of simulations. The adaptive forecasting 686 concept proposed by Romanowicz et al. (2006 and 2008) could be a possible approach to 687 estimate which members need to be computed. 688 689 690 Acknowledgments: 691 We want to acknowledge the Swiss Federal Office for Environment providing us runoff data 692 from their operational networks. Thanks to the Ufficio dei corsi d’acqua (Canton Ticino) and 693 Istituto Scienze della Terra (SUPSI) for additional rain-gauge data. This study is part of 694 COST-731 and MAP D-PHASE, and was funded by MeteoSwiss, WSL and the State 695 Secretariat for Education and Research SER (COST 731). The comments of the two reviewers 696 F. Pappenberger and L. Moulin and of the Guest Editor A. Rossa helped clarifying the paper. 697 698 Appendix A1: 699 In this appendix we give a concise summary on the verification of the probabilistic (COSMO- 700 LEPS, REAL) and deterministic (MOD, RAD) simulations during the period June 2007 to 23 701 November 2008, expressed with probabilistic measures of skill. Such kind of verification is 702 established in atmospheric sciences (Brier, 1950; Wilks, 2006; Weigel et al., 2007; Ahrens 703 and Walser, 2008) and is enjoying increasing popularity in hydrological sciences both for the 704 analysis of single events and for verification of long time series (Jaun et al., 2008; Jaun and 705 Ahrens, 2009; Bartholmes et al., 2009; Roulin and Vannitsem, 2005, Roulin 2007; Laio and 706 Tamea 2007, Brown et al., 2010). 707 Figure A1 shows the relative operating characteristic curves (ROC, Wilks, 2006) of LEPS and 708 REAL for the period June 2007 to November 2008. The ROC for the deterministic 709 simulations MOD/RAD and MOD/PLUV are also indicated as a point. The analysis has been 710 completed for three different thresholds, all of them representing a percentile (50%, 75%, 711 95%) of the observed discharge during these 18 months. Additionally the Brier Skill Score 712 (BSS, Wilks, 2006) of the ensemble products is declared. For LEPS the analysis has been 713 completed for different lead-times (Jaun and Ahrens, 2009). The lead-time of one and five 714 days are displayed in Figure A1. 715 The obtained ROC and BSS show that both REAL and LEPS are skillful for all selected 716 thresholds. When low discharge percentiles are tested (50% and 75%) BSS of LEPS decreases 717 only slightly between day one and day five forecasts. The skill of forecast for discharges 718 above 75.8 m3s-1 (95% percentile) is better for LEPS forecasts with lead time of one day than 719 for LEPS with five days lead time. 720 BSS of REAL is high for the lowest and the highest percentiles considered. For the 75% 721 discharge (17.2 m3s-1) percentile, REAL tends to have an increased rate of false alarms. 722 MOD/RAD und MOD/PLUV show similar behavior as the ensemble products. MOD/RAD 723 has a higher hit rate than MOD/PLUV when the 75% discharge percentile is tested. On the 724 other hand MOD/PLUV has fewer false alarms than MOD/RAD when discharge above 5.97 725 m3s-1 (50% percentile) is verified. An extended objective quantitative verification of the 726 ensemble simulations against observed data will be presented in follow-up studies. 727 728 References 729 Ahrens, B. and Jaun, S., 2007. On evaluation of ensemble precipitation forecasts with 730 observation-based ensembles. 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Atmospheric Science Letters, 9(2): 80-87. 948 29 949 Table 1: Definition of model parameters allowed varying in the Monte-Carlo runs. The “default” 950 parameters are the result of a standard calibration procedure (Viviroli et al., 2009a). The random 951 sampling of the parameters was limited to values included in the interval defined by MCMin and MCMax. 952 Symbol Parameter Unit Default MCMin MCMax Pcorr Rainfall adjustment* [%] 12.8 0.0 30.0 Scorr Snow adjustment* [%] 37.4 20.0 50.0 BETA Soil moisture recharge exponent - 3.8 3.0 6.0 SGR Threshold for surface runoff mm 41 30 50 K0 Storage coefficient for surface runoff h 21 10 30 K1 Storage coefficient for interflow h 127 100 150 PERC Deep Percolation mm h-1 0.153 0.10 0.20 953 * The two parameters controlling the bias adjustment of the precipitation input (rain or snow) are only used if 954 the hydrological model is fed by interpolated pluviometers data. Although the NWP models and precipitations 955 estimates with the weather radar contain systematic errors, it was decided to avoid bias-corrections (Verbunt et 956 al., 2006). 957 30 958 Table 2: Summary of the three parameter-sets of 26 members each after inferring Monte 959 Carlo simulations (see text for details). The numbers declare the median (Med.) and standard 960 deviation (St.Dev) of the seven parameters that were randomly varied. "Range" indicates the 961 ratio between St.Dev. and the dimension of the interval allowed for this parameters (Table 1). 962 Symbol Unit MOD_99.5% MOD_95% MOD_80% Med. / St.Dev / Range Med. / St.Dev / Range Med. / St.Dev / Range Pcorr [%] 11.54 / 2.8 / 0.09 14.3 / 5.1 / 0.17 19.3 / 6.6 / 0.22 Scorr [%] 32.1 / 7.2 / 0.24 29.6 / 9.2 / 0.31 33.6 / 9.5 / 0.32 BETA - 4.6 / 0.87 / 0.29 4.5 / 0.82 / 0.27 4.1 / 1.03 / 0.34 SGR mm 33.2 / 3.6 / 0.18 39.1 / 5.1 / 0.26 38.1 / 5.8 / 0.29 K0 h 12.7 / 0.97 / 0.05 11.8 / 2.0 / 0.1 15.6 / 2.4 / 0.12 K1 h 127 / 14.5 / 0.29 122 / 15.6 / 0.31 129 / 12.8 / 0.26 PERC mm h-1 0.11 / 0.013 /0.13 0.13 / 0.022 / 0.22 0.14 / 0.031 / 0.31 31 963 Table 3: Accumulated precipitation during the five day previous to the seven peak-flow 964 events investigated. The column “Day -10/-20” declares the moment where initial conditions 965 from a deterministic run are stored in order to trigger experiments on uncertainty propagation 966 and superposition (Figure 4). The list of the used COSMO-LEPS forecasts is sorted after the 967 lead time in days before the event. 968 Event Peak Accumulated 120 hours COSMO/LEPS Day -10/-20 (year/month Runoff precipitation until forecast initialization (month/day) /day) [m3s-1] Day-5 [mm] (month/day) pluviometers radar Day-5 Day-4 Day-3 Day-2 Day-1 Day-0 2007/08/22 100.7 08/01 151 153 08/19 08/20 08/21 2008/07/07 80.3 06/28 10 38 07/04 07/05 07/06 2008/07/13 163.0 06/28 87 113 07/10 07/11 2008/08/15 76.9 07/20 45 98 08/10 08/11 08/12 08/13 08/14 2008/09/07 541.0 08/20 28 29 09/04 2008/10/29 210.6 10/09 9 4 10/27 10/28 10/29 2008/11/05 157.5 10/09 219 186 11/03 11/04 969 32 970 Table 4: Average ensemble spread ( q100 - q 0 ) in m3s-1 for seven peak-runoff events when 971 adopting different sets of model parameter realizations and either pluviometers 972 (MOD_%/PLUV) or weather radar QPF (MOD_%/RAD) as precipitation forcing. 973 Event Initialization MOD_%/PLUV MOD_%/RAD (year/month/day) (month/day) 99.5% 95% 80% 95% Members - 26 26 26 26 2007/08/22 08/20 10.3 14.2 18.5 9.3 2008/07/07 07/05 4.9 8.3 10.4 6.5 2008/07/13 07/11 5.3 7.2 10.0 9.5 2008/08/15 08/12 5.9 10.3 11.7 8.3 2008/09/07 09/04 22.8 30.0 38.9 30.4 2008/10/29 10/27 9.9 14.6 19.6 10.8 2008/11/05 11/03 10.8 13.9 18.8 9.9 Average [m3s-1] 10.0 14.1 18.3 12.1 974 33 975 Table 5: Average ensemble spread ( q100 - q 0 ) in m3s-1 for seven peak-runoff events when 976 adopting different experimental settings for propagating and superposing uncertainty in 977 operational hydrological simulations. 978 REAL LEPS Event Initialization REAL LEPS FULL /MOD /MOD (year/month/day) (month/day) Members - 25 650 16 416 10400 2007/08/22 08/20 37.2 48.9 117.0 137.0 141.0 2008/07/07 07/05 24.8 33.8 84.5 100.0 105.0 2008/07/13 07/11 42.0 53.9 123.7 146.0 146.0 2008/08/15 08/12 37.9 48.6 100.0 123.0 142.0 2008/09/07 09/04 167.0 216.0 288.0 328.0 338.0 2008/10/29 10/27 34.9 48.9 82.0 102.0 110.0 2008/11/05 11/03 43.3 56.3 116.0 138.0 139.0 Average [m3s-1] 55.3 72.3 130.0 153.0 160.0 979 34 980 Table 6: Attributing the contribution of different sources of uncertainty to the average spread 981 ensemble spread ( q100 – q 0 ) and IQR ( q 75 – q 25 ) in m3s-1 for the November 5th 2008 peak 982 runoff event. The observed value and the correspondent ensemble median ( q 50 ) are also 983 summarized. Sub-samples of three experiments are evaluated to estimate the different 984 contribution of MOD, LEPS and REAL to the total experimental uncertainty. Details on the 985 experiments and acronyms are found in Section 3.4. 986 987 Average of n Observation q 50 q100 – q 0 q 75 – q 25 Experiment Filter Varying realizations Members [m3s-1] 3 -1 [m s ] [m3s-1] [m3s-1] FULL None All three 1 10400 62.4 67.0 139.0 68.4 MOD REAL & LEPS 26 400 62.4 65.3 125.4 62.3 REAL MOD & LEPS 25 416 62.4 66.8 136.1 67.0 LEPS REAL & MOD 16 650 62.4 71.9 15.9 10.8 REAL/MOD NONE Both 1 650 62.4 56.7 56.3 31.0 REAL MOD 25 26 62.4 57.7 10.1 6.9 MOD REAL 26 25 62.4 55.7 45.9 25.5 LEPS/MOD None Both 1 416 62.4 66.9 138.0 67.9 MOD LEPS 26 16 62.4 64.4 121.8 59.6 LEPS MOD 16 26 62.4 71.5 15.7 10.1 988 35 989 Figures captions: 990 991 Figure 1: Main sources of uncertainties propagating and superposing through a hydrological 992 model in hydrometeorological forecasting chains. 993 994 Figure 2. Situation map of the Verzasca river basin in southern Switzerland including 995 hydrometric (FOEN) and meteorological networks (MeteoSwiss and UCA). Additionally, the 996 location of the Monte Lema weather radar few kilometers southern of the basin is displayed. 997 Graphic elements reproduced by kind authorization of “swisstopo” (JA022265) and BFS 998 GEOSTAT. 999 1000 Figure 3: Dot-plot of the 2527 Monte Carlo realizations for the application of PREVAH in the 1001 Verzasca river basin during the calibration period 1996-2001. NSE and SWAE are used to 1002 select three sub-samples (99.5%, 95% and 80%) of acceptable parameter sets consisting of 26 1003 realizations each. 1004 1005 Figure 4: Design of the seven experiments run for quantification of uncertainty superposition. 1006 The time window for the statistics is defined by the lead time of the C-LEPS forecasts. 1007 1008 Figure 5: November 5th 2008 event: visualization of the spread obtained by adopting different 1009 sets of model parameter realizations for simulations with PREVAH. The observed hydrograph 1010 is drawn as black line. The shaded dark and light grey areas are delimitated by the quantiles of 1011 the ensemble realizations (q0, q25, q75, q100). The dashed black line draws the ensemble median 1012 (q50). Top left: realizations obtained from pluviometric data and the MOD_99.5% set. Top 1013 right: same but MOD_95% set is applied. Bottom left: same for MOD_80%. Bottom right: 1014 weather radar data are used combined with the MOD_95% parameters realizations set. 1015 1016 Figure 6: Ensemble hydrographs for the August 22nd 2007 (upper panels) and November 5th 1017 2008 (bottom panels) events as obtained by forcing PREVAH with 25 radar ensemble 1018 members (REAL, left panels) and by jointly accounting for both radar and model parameter 36 1019 uncertainty (REAL/MOD, right panels). The observed hydrograph is drawn as black line. The 1020 shaded dark and light grey areas are delimitated by the quantiles of the ensemble realizations 1021 (q0, q25, q75, q100). The dashed black line draws the ensemble median (q50). 1022 1023 Figure 7: As Figure 6 but with PREVAH forced by 16 COSMO-LEPS ensemble members 1024 (LEPS, left panels) and by jointly accounting for both COSMO-LEPS and model parameter 1025 uncertainty (LEPS/MOD, right panels). 1026 1027 Figure 8: Ensemble hydrographs for the August 15th 2008 with PREVAH initialized on 1028 August 12th 2008 and forced by jointly accounting for both COSMO-LEPS and model 1029 parameter uncertainty (LEPS/MOD, left panel) and by accounting all three sources of 1030 uncertainty in the experimental chain (FULL, right panel). Legend as Figures 6 and 7. 1031 1032 Figure 9: Box plots summarizing the average ensemble discharge quantiles related 19 1033 experiments (lower captions on the x-axis) of superposing the uncertainty from three sources. 1034 The experiments related to different events (upper captions of the x-axis) are separated by a 1035 vertical line crossing the x-axis. The observed average discharge during the 120 hours of each 1036 experiment is displayed as a thick horizontal black line. The thick horizontal white line 1037 depicts q 50 within the box plot drawn by q 0 , q 25 , q 75 and q100 . 1038 1039 Figure 10: Box plots summarizing the average ensemble discharge quantiles for the 1040 November 5th 2008 event initialized on November 3rd 2008. Three experiments (upper 1041 captions of the x-axis) are evaluated as complete set (“no filter”) and by separating the 1042 influence of different sources of uncertainty (“filter MOD/REAL/LEPS”). The observed 1043 average discharge during the 120 hours of each experiment is displayed as a thick horizontal 1044 black line. The thick horizontal white line depicts q 50 within the box plot drawn by q 0 , q 25 , 1045 q 75 and q100 . 1046 37 1047 Figure A1: Relative operating characteristic curves (ROC, Wilks, 2006) of LEPS and REAL 1048 for the period June 2007 to November 2008. The ROC for the deterministic simulations 1049 MOD/RAD and MOD/PLUV is indicated as a point. ROC are plot for three different 1050 discharge thresholds corresponding to the 0.5 (left), 0.75 (middle) and 0.9 (right) quantiles. 1051 38 Figure Click here to download high resolution image Figure Click here to download high resolution image Figure 3 Click here to download high resolution image Figure 4 Click here to download high resolution image Figure 5 Click here to download high resolution image Figure 6 Click here to download high resolution image Figure 7 Click here to download high resolution image Figure 8 Click here to download high resolution image Figure 9 Click here to download high resolution image Figure 10 Click here to download high resolution image Figure Click here to download high resolution image

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