Application of a medium range global hydrologic probabilistic forecast scheme to the Ohio River. Basin

Transcription

1 Application of a medium range global hydrologic probabilistic forecast scheme to the Ohio River Basin Nathalie Voisin 1, Florian Pappenberger 2, Dennis P. Lettenmaier 1,4, Roberto Buizza 2, John C. Schaake 3 1 Department of Civil and Environmental Engineering, University of Washington, Seattle, WA European Centre for Medium-Range Weather Forecasts (ECMWF), Shinfield Park, Reading, RG2 9AX, UK 3 Consultant to Office of Hydrologic Development, National Weather Service National Oceanic and Atmospheric Administration, Silver Spring MD 4 Corresponding author, dennisl@u.washington.edu 1

2 Abstract A 10-day globally applicable flood prediction scheme was evaluated using the Ohio River basin as a test site for the period The Variable Infiltration Capacity (VIC) hydrology model was initialized with the European Centre for Medium Range Weather Forecasts (ECMWF) analysis temperatures and wind, and Tropical Rainfall Monitoring Mission (TRMM) precipitation up to the day of forecast. In forecast mode, the VIC model was then forced with a calibrated and statistically downscaled ECMWF ensemble prediction system (EPS) 10-day ensemble forecast. A parallel set up was used where ECMWF EPS forecasts were interpolated to the spatial scale of the hydrology model. Each set of forecasts was extended by 5 days using monthly mean climatological variables and zero precipitation in order to account for the effect of initial conditions. The 15-day spatially distributed ensemble runoff forecasts were then routed to four locations in the basin, each with different drainage areas. Substitutes for observed daily runoff and flow were provided by the reference run, i.e. the VIC simulation forced with ECMWF analysis fields and TRMM precipitation.. The flood prediction scheme using the calibrated and downscaled ECMWF EPS forecasts was shown to be more accurate and reliable than interpolated forecasts for both daily distributed runoff forecasts and daily flow forecasts. Initial and antecedent conditions dominated the flow forecasts for lead times shorter than the time of concentration depending on the flow forecast amounts and the drainage area sizes. The flood prediction scheme had useful skill for the 10 following days at all sites. 2

3 1.0 Introduction In-situ precipitation observations derived from gauges and precipitation radars are often used for real-time or near real-time flood forecasting (Hopson and Webster 2009, Thielen et al. 2009, or are used to downscale precipitation forecasts issued by global weather forecast models for short (up to 48 hours, American Meteorological Society s glossary of meteorology) and medium range (up to 15 days) flood forecasts (Schaake et al. 2007, Clark and Hay 2004). When available, regional scale atmospheric models can provide medium range forecasts at a finer spatial resolution than is available from global weather models, and the forecasts so derived can be used for flood forecasting (Westrick et al. 2002, de Roo et al. 2003, Pappenberger et al., 2005). Flood forecasting capabilities are, however, especially limited in areas where in-situ observations are sparse and/or where there are no regional scale atmospheric models, a situation that includes much of the underdeveloped world (Hossain and Katiyar, 2006). Improvements in global weather prediction, and in precipitation observations and nowcasts, both from satellite and numerical weather prediction systems, are beginning to be implemented in parts of the world that are under gauged. Asante et al. (2007) describe a flood monitoring system that uses satellite precipitation data and a semi distributed hydrologic model which they apply over the poorly gauged Limpopo River basin in Africa. Hopson and Webster (2009) describe a method of producing flood forecasts at two locations in the Ganges and Brahmaputra River basins in Bangladesh that the Flood Forecasting and Warning System of Bangladesh now integrates in their automated flood forecast system. Their streamflow forecasts are derived using European Centre for Medium Range Weather Forecasts (ECMWF) Ensemble Prediction System (EPS) precipitation forecasts, Tropical Rainfall Monitoring Mission (TRMM) 3B42 (Huffman et al. 2007) and Climate Prediction Center (CPC) MORPHing technique (CMORPH, Joyce et al. 2004) precipitation nowcasts, and NOAA Global Telecommunication System (GTS) precipitation gauge data. Thiemig et al. (2010) describe an African Flood Alert System with application to the Juba-Shabelle Rivers basin. It draws heavily from the 3

4 European Flood Alert system (Thielen et al. 2009, Bartholmes et al. 2009). The system uses ECMWF EPS weather forecasts which drive the fully distributed rainfall-runoff model LISFLOOD (Van der Knijff et al., 2008) at a 0.1-degree spatial resolution. The model is initialized using either ERA-40 (Uppala et al. 2004, 1-degree) or CHARM (Funk et al. 2003, 0.1-degree) atmospheric forcings. An alternative global flood forecast approach that uses TRMM data in conjunction with a rainfall-runoff model has been developed for near real-time global flood monitoring (Hong et al. 2007, Yilmaz et al. 2009) and shows promise for filling the void in ungauged basins. Buizza (2008a) and Cloke and Pappenberger (2009) summarize the benefits of ensemble-based probabilistic forecasting; not only the most-likely scenario is provided by the deterministic forecast (or ensemble mean forecast), but also information on the uncertainty of this scenario, i.e. the probabilistic forecasts, with longer lead times than the basin concentration time. In view of those benefits, global ensemble forecasts will be used instead of the finer spatial resolution deterministic forecasts. Similarly, several operational flood forecasts systems have upgraded to incorporate those probabilistic forecasts: see Cloke and Pappenberger (2009) for a summary. We expand here on such approaches, using a strategy that combines remotely sensed precipitation observations with downscaling of global weather models ensemble forecasts to force a macroscale hydrology model. Our objective is to test a global approach to producing hydrological ensemble forecasts in river basins where in-situ data are sparse. The strategy is to incorporate satellite precipitation data and use precipitation forecasts produced by global weather prediction models in conjunction with a semi-distributed macroscale land surface hydrology model a strategy similar to the designing of EFAS (Figure 1).This paper utilizes for the first time analysis fields in medium range weather predictions, along with satellite precipitation data in order to warm up the hydrology model and create the initial conditions for the hydrology forecasts. A companion paper Voisin et al. (2010, V2010 hereafter) evaluated several methods for calibrating and spatially downscaling ensemble precipitation forecasts, produced by global weather prediction models using globally available remote sensing 4

5 observations, to the scale used by macroscale hydrology models. Specifically, we considered degree latitude-longitude spatial resolution, which is consistent with the capabilities of current generation global land models (see for example Balsamo et al., 2010). In V2010, three methods were evaluated for downscaling European Center for Medium Range Weather Forecasts (ECMWF) ensemble prediction system (EPS) 10-day daily 51-ensemble precipitation forecasts from 1-degree to 0.25-degree spatial resolution over the Ohio River basin with respect to remotely sensed precipitation: simple interpolation, a bias correction with spatial disaggregation and an analog method. The goal was to select which approach was most appropriate for calibrating and downscaling global ensemble weather forecasts for daily hydrologic forecasting with realistic precipitation patterns that maintain or improve the original ensemble forecast skill. They found that the analog method had the smallest absolute biases, competitive RMSEs and the best reliability of the downscaled precipitation ensemble forecasts, but lower predictability than the interpolation method. The analog method had the most realistic high resolution precipitation patterns, due at least in part to the fact that the analogs were patterns that had occurred in the historic record. A variation of the analog method (RMSDmean) was chosen by V2010 to be used for further development of the hydrological prediction scheme for global application. In this paper, the V degree calibrated ECMWF EPS 10-day daily ensemble forecasts using the RMSDmean variation of the analog method force the Variable Infiltration Capacity (VIC) semi-distributed hydrology model (Liang et al. 1994) to produce ensemble daily runoff and streamflow forecasts in the Ohio River basin (Figure 1). The paper has three objectives. First, we assess the skill of the system. Secondly, we evaluate the improvement of skill in spatially distributed runoff forecasts and in flow forecasts when the spatially distributed meteorological forecasts are calibrated (pre-processor). Third, because the approach is using a semi-distributed model and distributed weather forecasts, skill may be different for basins of different sizes in particular when the concentration time is different. To address those objectives, we compare two set ups of the system, one that use interpolated forecasts and one using the calibrated weather forecast as input into the hydrological model. Spatially distributed 5

6 runoff forecast verifications similar to the precipitation forecast verifications in V2010 are performed. Streamflow forecast verifications are then made at several locations with drainage areas ranging from km 2 to km 2. This range of drainage areas allows us to assess the effect of different concentration times on the forecast skill. The analog method used to calibrate and downscale the weather forecasts is based on resampling remotely sensed precipitation (Tropical Rainfall Monitoring Mission (TRMM) Multi-satellite Precipitation Analysis 3B42 V6 research product; TMPA, Huffman et al. 2007). In V2010, gridded insitu gauge station data were substituted for the remote sensing precipitation data in order to evaluate potential differences in skill when using different observed precipitation data sets. The Ohio River basin, which has an extensive in-situ gauge network, was used for this evaluation. This paper follows from V2010, which motivates our choice of the Ohio River basin for evaluation of the hydrologic forecasts. The remainder of the paper is organized as follows. Section 2 summarizes the observations, forecasts and analysis fields. Section 3 describes the experiments that were designed to evaluate the flood forecast system. Results and their interpretation are in Section 4, discussion in Section 5 and conclusions in Section Data sets Three data sets were used. TMPA precipitation and ECMWF wind and temperature analysis fields were used to force the hydrology model up to the time of forecast. ECMWF EPS forecasts (precipitation, temperature and wind) were calibrated and downscaled as in V2010 (summarized below) and then used to force the hydrology model during the forecast period (Figure 1). A VIC simulation, forced with TMPA and ECMWF analysis fields was used as a surrogate for observations for streamflow forecast verification purposes. 2.1 ECMWF EPS forecasts 6

7 The ECMWF EPS has been operational since 1992: it simulates initial condition uncertainties using singular vectors, which are the perturbations with the fastest growth over a finite time interval, and model uncertainties using a stochastic scheme (Palmer et al. 2007). The ECMWF EPS products available for this study are day forecasts at 6-hour time increments, which we aggregated or averaged to a daily time step ( GMT). From November 2000 to February 2006, the EPS was running with horizontal spectral truncation T255 (~80 km grid spacing at mid-latitudes), T399 (~50 km) in February 2006, and T639 (~32km) at the time of writing (2010). In September 2006 the ECMWF EPS was extended to 15 days with a variable resolution approach (VAREPS, Buizza et al. 2007) and to 32 days once a week in March 2008 (Vitart et al. 2008), i.e. a 63 km spatial resolution for lead times beyond day 10. For consistency, we aggregated the forecasts to a one degree spatial resolution and considered only the 10-day forecast period over the entire period. The following surface variables, which are required to force the VIC hydrologic model, were taken from the EPS forecasts: daily precipitation (convective and stratiform fields), maximum and minimum temperatures (MN2T and MX2T) and wind speed (U10 and V10). Those variables had to be calibrated and spatially downscaled from the 1-degree spatial resolution to 0.25-degree, the spatial scale at which the VIC model was implemented (as explained below). We reduced the 51 ensemble members to 15 as described in V2010 in order to reduce computation time. Because the random selection of the 15 ensemble members follows a discrete uniform distribution, the impact on the ensemble mean and spread skills is minimized. With constant development to the forecast models (see Section 2.1.4), the calibration and downscaling of the forecasts (analog method) is expected to work best when using a resampling of a retroforecast dataset as in Hamill and Whitaker (2006), which most often is a reduced size ensemble and coarser spatial resolution. The number 15 was chosen in order to be consistent with the NCEP GFS reforecasts dataset (Hamill et al., 2006) used in Hamill and Whitaker (2006). The following subsections describe how the calibration and downscaling of the different forecast variables was performed. 7

8 2.1.1 Temperature and wind forecasts Daily minimum (maximum) temperatures were first derived by extracting the minimum (maximum) temperature of the four 6-hourly minimum (maximum) temperature forecasts (MN2T and MX2T fields) of each day of the 10-day forecast. They were then interpolated to 0.25-degree spatial resolution using the SYMAP algorithm (Shepard 1984); a simple inverse squared distance from nearest neighbors algorithm where interpolated temperatures are also lapsed using the elevation difference between the 1-degree and the 0.25-degree cells using a degree per 100 meter lapse rate (approximately pseudo adiabatic). Different interpolation algorithms can (but must not) lead to significantly different results (Pappenberger et al for a comparison of interpolation methods applied on a network of gauge station data), but the SYMAP algorithm has been judged to be the most optimum in terms of computational efficiency and quality for this area in comparison to other approaches because the forecasts are already gridded and have a uniform spatial and temporal density. Six-hourly wind forecasts were computed as the square root of the sum of the squares of U10 and V10 fields. These values were averaged to a daily time scale and then interpolated from one degree to 0.25 degrees using the SYMAP algorithm of Shepard (1984) Precipitation forecasts We calibrated and spatially downscaled the EPS 10-day 1-degree ensemble precipitation forecasts from 1 to 0.25 degrees on a daily basis using what V2010 define as the analog RMSDmean method. The reader is referred to V2010 for a step-by-step description and evaluation of the method. In brief though, the analog method is based on resampling from remotely sensed precipitation (TMPA) fields. A moving (5-by-5 degrees, or 25 forecast points) spatial window (rather than the entire Ohio River basin) was used as the spatial domain for purposes of choosing the analogs, hence the method is applicable to any domain (see V2010 for details). Over the 5-by-5 degree window, the daily ensemble 8

9 mean forecast at day n, year X, for lead time Y, was compared with all daily retrospective ensemble mean forecasts in the same spatial window, for the same lead time Y, in a +/- 45 days temporal window around day n over the period (excluding day n of year X). The 15 retrospective ensemble mean forecasts that corresponded most closely to the ensemble mean forecast for the given lead time Y in the root mean square sense (15 smallest sums of the root mean square differences over the 25 grid points in the spatial window) became the 15 analogs for the center point of the spatial moving window for lead time Y. The corresponding finer spatial resolution remote sensing observations (four 0.25 grid cells at the center point of the moving spatial window) for those days (analog dates) became the downscaled ensemble forecasts, following V2010, Hamill and Whitaker (2006), and Hamill et al. (2006). A Schaake Shuffle (Clark et al. 2004) was then performed in order to construct a spatio-temporal rank structure over the 10-day period and over the Ohio River basin domain that was necessary for subsequent hydrologic simulation; This Schaake Shuffle (V2010, Appendix A.3) was also necessary to create the correlation between all downscaled forecast fields (precipitation, temperatures and wind). In this last step, 15 dates (and the subsequent 9 days) were selected in the period in the +/-45 days window around day n. This resample was done for each daily forecast for the entire Ohio River basin domain and the same resample was used for precipitation, temperatures and wind forecast fields. For each forecast lead time (day in the 10-day resampled period) and 0.25-degree grid cell, each downscaled forecast member (resampled observed date) was ranked from 1 to 15 (number of ensemble members). This ranking was done for each forecast fields (precipitation, temperatures and wind) where 0.25-degree TMPA was used as observed precipitation and 0.25-degree downscaled ECMWF analysis fields were used as observed temperatures and wind). Precipitation, temperature and wind forecast ensemble members were then re-ordered so that the forecast rank matrix (space, time, variable, members) was similar to the day resampled observed periods. The calibrated and downscaled 9

10 ensemble forecasts at each grid cell were not modified in values by the Schaake Shuffle, only the ordering of the members was changed. V2010 showed that the downscaled ensemble precipitation forecasts were more accurate and largely more reliable than those downscaled using a simple interpolation technique. V2010 also showed that the observed-predicted Spearman rank correlation was maintained although slightly lower Consistency of the raw EPS forecasts The quality of probabilistic weather predictions in general has significantly improved over the last decade (Palmer et al., 2007). Precipitation forecasts, which are of particular significance for this study, have gained about 1 day of lead time every 10 years over Europe for the ECMWF forecasts (Ghelli and Primo, 2009; Rodwell, 2010). It is important to point out that improvements over the years have varied with parameter as well as verification region (Palmer et al., 2007; Rodwell, 2010; Pappenberger and Buizza, 2009). Over the period considered here, the ECMWF forecast model has undergone several changes (spatial resolution, convection scheme), of which it is likely that the change in spatial resolution has had the largest impact on meteorological forecast skill (Buizza, 2010; Buizza et al., 2008a). Further changes in the meteorological forcing, usually occurs in 2-3 updates per year and are documented in ECMWF webpages. In this paper, the impact of the change in spatial resolution (the major change over the period) is minimized because we aggregated the EPS forecasts to a 1-degree spatial resolution over the entire period. The current spatial resolution of the EPS forecasts (32 km at time of writing, 2010) would allow bypassing the spatial disaggregation step of the V2010 calibration and downscaling approaches but a long retrospective period is necessary for the calibration step. The need for the longest possible forecast period motivated us to choose the period as one with reasonably consistent model physics. 10

11 2.2 Observed precipitation The three-hourly Tropical Rainfall Monitoring Mission (TRMM) Multisatellite Precipitation Analysis 3B42 V6 research product (TMPA, Huffman et al. 2007) is a near-global data set at degree latitude-longitude spatial resolution. It was used as the observation data set from which the analogs were derived during the calibration and downscaling of the EPS precipitation forecasts (V2010). Daily TMPA estimates are accumulations of the 3-hourly values from 0000 to 2100 UTC. TMPA rescales the monthly sums of the 3-hourly fields to a monthly gauge analysis. One evolution in the TMPA product during the period is that the Climate Assessment and Monitoring System (CAMS) 0.5-by-0.5 degree monthly gauge analysis is used to adjust the TMPA estimates from January 1998 to March 2005 and the Global Precipitation Climatology Center (GPCC) 1.0-by-1.0 degree monthly monitoring product is used to adjust the TMPA estimates after March 2005, resulting in some inconsistencies (Su et al. 2008). 2.3 ECMWF analysis Daily ECMWF analysis wind and temperature fields were downscaled from 1 to 0.25-degree using the same method as was used to downscale the forecasts. Similarly to the EPS forecasts, the analysis fields spatial resolution increased from T511 (~40 km) to T799 (~25 km) between 2002 and 2007 and underwent the same model changes (convective scheme upgrades in 2003 and 2007). These analysis data were used with TMPA precipitation for the spin up of the VIC hydrological model and for the reference hydrological simulation, which produces the VIC initial conditions (soil moisture and snow accumulation) for the hydrologic forecasts as explained in the methodology section. 3.0 Methodology 3.1 Experimental design The study was based on four simulations (Figure 2). 11

12 i) Reference The first simulation was the reference, in which the semi distributed VIC hydrology model was forced with the downscaled ECMWF analysis temperatures and wind fields, and TMPA precipitation for the period. The gridded runoff was then routed using the Lohman et al. (1996, 1998) routing model to four stream gauge locations (forecast points) for the simulation period; 2002 was used as a spin up of the hydrology and routing models. The four forecast points are the Monongahela River at Elizabeth, PA (USGS , km 2 ), the Wabash River at Mt Carmel, IL (USGS , km 2 ), the Ohio River at Louisville, KY (USGS , km 2 ) and the Ohio River at Metropolis, IL (USGS , km 2 ), which have varying drainage areas. It allows the assessment of the role of drainage area in the resulting streamflow forecast errors. The reference run served as a surrogate for the observed spatial distribution of daily runoff over the Ohio River basin and for observed daily streamflow at the four locations for the forecast verifications. Use of the reference run (essentially hydrology model forced with observations) avoids confounding forecast errors with the effect of hydrological modeling error, and as such allows for a focused assessment of individual uncertainty contributions. Nonetheless, a final system will need to integrate all error sources (Pappenberger and Beven 2006, Pappenberger et al. 2006). Regulation of the Ohio River basin for water management purposes is mostly for navigation and flood control, the effects of which are minimal at the monthly time scale. However, these effects, in addition to several small hydropower plants, can affect daily flows significantly. The VIC model does not simulate these effects; however, Figure 3 shows that the combination of the VIC hydrology and routing model did capture observed daily streamflow reasonably well at all four stations following calibration (performance described in detail in the next section). Given this agreement, the reference simulation is considered as truth rather than the daily streamflow observations, in order to focus attention on the hydrologic effects of the errors in the downscaled forecasts. One could also apply post processing and error corrections to the observed and forecasted flows (Seo et al. 2006, Bogner et al. 12

13 2010), however, our eventual intent is to apply the system described herein to ungauged catchments, for which observed flow may not be readily available (Schumann et al. 2009, Neil et al. 2009). ii) Interpolation method (interpolated weather forecasts) The second simulation used the reference forcing to spin up the hydrologic model until the day of the forecast. The simulation subsequently used the downscaled ECMWF EPS temperatures and wind speed, and ECMWF EPS interpolated precipitation forecasts to force the hydrology model. The routing model was also spun up using the gridded runoff from the reference run. Next, the forecasted gridded runoff was routed to derive daily streamflow forecasts at the four forecast points. This simulation is referred to as the interpolation method. iii) Analog RMSDmean method (calibrated and downscaled weather forecasts) The third simulation used the same spin ups and setup as the interpolation method, except that the ECMWF EPS precipitation forecasts were calibrated and downscaled using the V2010 RMSDmean analog technique described above. This method is termed RMSDmean hereafter. iv) Zero precipitation and climatology forecast The fourth simulation isolates the impact of initial conditions (and concentration time) from the skill of the forecasts in the early lead times. The VIC hydrology model was run as for the reference run until the day of the forecast, and then was forced with a 15-day deterministic forecast with null precipitation and temperature and wind climatology monthly means (Figure 2). Depending on the size of the drainage basin (hence concentration time), the forecasted daily streamflow for the first few days of the forecasts responds mostly to the hydrologic initial and antecedent conditions. The initial conditions include snow water equivalent (SWE) and soil moisture. Initial and 13

14 antecedent conditions also include streamflow throughout the basin at the time of forecast. Table 1 shows for the four different locations the daily fraction of grid cells, in their corresponding watershed, which contribute to the daily flow at the station. Those fractions are derived using unit hydrographs created by the calibrated routing model (see next section on the calibration of the routing model). On day 1 (day of the precipitation event), only a minimal fraction of the grid cells in each drainage area (stations) contributes to the flow at the forecast points, i.e. initial conditions prevail. As expected, the fraction of contributing grid cells increases faster with time for smaller drainage areas. Table 1 also shows the daily fraction of grid cells for which 100% of the generated runoff has been routed to the station. Because of the assumed grid cell unit hydrograph shape (Table 2), no grid cell (and hence no basin) can be fully drained in less than four days. Table 1 shows that initial conditions will impact the flow at Metropolis, IL (outlet) for up to 14 days, and up to six days at Elizabeth, the smallest drainage area considered in this paper. This also implies that there could be skill in the forecasted streamflow beyond the 10 days of the weather forecast. We therefore extended by 5 days each of the 10-day ensemble forecast members of the interpolation and the RMSDmean methods using the downscaled ECMWF analysis monthly mean temperatures and wind (climatology), and null precipitation, which resulted in an ensemble streamflow forecast period of 15 days (Figure 2). 3.2 Calibration of the hydrology and routing models The semi distributed VIC hydrology and routing models are two independent entities. For monthly applications, a default calibration is usually used for the routing model (routing makes little difference for monthly streamflow aggregations) and VIC is calibrated independently. For daily application, VIC and the routing component were considered as one model and were calibrated jointly. This one-step approach avoided over-fitting because the calibration of the two entities cannot be fully independent due to the absence of observed gridded runoff. The calibration of the VIC-routing model was performed at a daily time scale, for 10/2005 through 9/2007 at the downstream-most station 14

15 (Metropolis, IL). The period 10/2002 9/2005 was used for evaluation. VIC was forced with ECMWF analysis daily minimum and maximum temperatures and wind, and TMPA daily precipitation. The calibration was performed using the Multi-Objective COMplex Evolution of the University of Arizona (MOCOM-UA) method (Yapo et al. 1998), as applied in Shi et al. (2008). Multi-objective automatic calibration is time-saving and allows fitting the simulated hydrograph to different characteristics of the observed hydrograph. In particular, three objective function terms were used: variance explained, Nash-Sutcliffe efficiency (NSE) factor (Nash and Sutcliffe 1970) and the absolute value of annual mean volume error. A lumped calibration approach was chosen here for simplicity. Ajami et al. (2004) showed that representing spatial variability in the calibrated parameters (distributed calibration approach) did not improve the flow calibration at their basin outlet. Feyen et al. (2008) however showed that a spatially distributed approach for calibration parameters (in particular for the most uncertain soil parameters like soil depth) was necessary to represent sub-basin hydrological processes. They argued that the distributed approach reduces the overall model uncertainty and therefore increases the accuracy of flow predictions, especially at the sub basin level. In ungauged basins, regionalization of the calibration parameters can be performed by linking the calibration parameters to long term climate and hydrological properties, and physical basin characteristics (Abdulla and Lettenmaier 1997, Yadav et al amongst other). The implementation of regional calibration approaches for ungauged basins will be the topic of future work. Here we use the lumped approach, which arguably is justifiable given our emphasis on forecast errors at the basin level. Table 3 shows the correlations between predicted and observed, and NSE statistics for the daily flow at Metropolis for the calibration period (2005/ /09) and for a verification period (2002/ /09). Both the correlations and NSE values for the verification period are considerably smaller than for the calibration period, which is due in part to the evolution in the TMPA precipitation dataset in March The top panel in Figure 3 shows the 5-day moving average of the daily basin average 15

16 difference between TMPA and a gridded station precipitation dataset (extension of Maurer et al. 2002). Figure 3 also shows reasonable agreement between the simulated and observed daily flows at Metropolis, and at the three other locations (Louisville, KY, Mt Carmel, IL, and Elizabeth, PA). 3.3 Forecast verification Both runoff and streamflow forecasts were verified. i) Runoff forecast verification Runoff forecasts were verified by comparing the daily gridded runoff forecast (interpolation and RMSDmean methods) with the reference runoff (derived from the model forced with observations). Similar to V2010, commonly used skill measures like biases (mean errors), RMSEs (accuracy) and predicted-observed Pearson correlation (predictability) were used to verify the daily forecasted runoff. Other skill measures specific to probabilistic quantitative forecasts were used: ensemble spread (range) reliability (Talagrand histograms; Hamill and Collucci 1997; Talagrand and Vautard 1997) and Continuous Rank Probability Skill Score (CRPSS; see Hersbach, 2000; Wilks, 2006 and V2010 Appendix C for details). Those measures were assessed as an average over the period over the Ohio River basin for the 15-day lead times for three forecast categories: all forecasts in the period, and lower and upper terciles of forecasts. It is important to note that the categories used in the evaluations are conditioned on the forecasts and not the observation. Conditioning on observations is common when comparing, for instance, forecasts from different sources (Demargne et al. 2009). Here however, we want to assess the value of hydrologic forecasts for a potential real time decision What can I expect if the forecasts falls into a certain forecast category? What should I do with this forecast? rather than how good are those forecasts for those particular events. The analysis was made on both spatially distributed and basin average runoffs. The distributed runoff analysis provides a parallel with V2010, whereas the basin average runoff analysis confirms the conservation of the spatial rank structure in the ensemble weather forecasts. 16

17 ii) Streamflow forecast verification Daily streamflow (routed runoff) at the four forecast points for each of the 15 lead times was verified using the reference simulation as truth. Not only are the ensemble flow forecasts the end product of the flood prediction scheme, but their accuracy also confirms the spatio-temporal rank structure of the downscaled weather forecasts; i.e. if there was unsatisfactory spatio-temporal rank structure in the ensemble weather forecasts forcing the hydrology model, the ensemble routed runoff (flow) forecasts would have similar biases and RMSEs as using a deterministic climatology mean forecast with a narrow (and unreliable) ensemble spread that would not grow in size with increasing lead times. Furthermore we assess the skill due to initial conditions rather than weather forecast skill in the first few lead times of the flow forecasts by comparing the scores of the RMSDmean and interpolation methods with those of the climatology and zero precipitation 15-day deterministic forecast experiment. 4.0 Results The forecast verifications for the interpolation and the RMSDmean methods were made with respect to the reference simulation for the period over the entire Ohio River basin. Unless indicated otherwise, an improvement indicates that the RMSDmean method performed better than the interpolation method. Three forecast categories were evaluated: all forecast (no conditioning), and lower and upper terciles of the runoff/flow forecasts. For simplicity, only the all and high runoff forecast categories and two flow forecast points are shown. The means and relative biases, i.e. the ratio of bias to the mean, in each category are shown. The relative RMSEs, CRPSSs and Talagrand histograms are indicative of the accuracy. CRPSS in particular is indicative of how the cumulative distribution function (CDF) of the forecast ensemble (daily forecast CDF based on 15 values, i.e. members, for one lead time) matches the observation for each individual forecast; it is indicative of bias, but also of the ensemble spread reliability, resolution and predictability. The Talagrand histograms or rank histograms (Hamill 17

18 and Collucci 1997, Talagrand and Vautard 1997) show the normalized rank of the observation within the ensemble forecast. Perfect ensemble reliability corresponds to a uniform histogram, a U-shaped histogram indicates an ensemble spread that is too small (forecast is overconfident), while an asymmetric histogram indicates a systematic bias in the forecast. We define here the ensemble spread as the ensemble range, i.e. the difference between the maximum and the minimum member values. The predicted-observed Pearson correlation is indicative of the predictability of the ensemble mean forecast. The reader is referred to V2010 Appendix C for a detailed description of the measures. 4.1 Forecast verification for daily runoff over the period, Ohio Basin The forecast verification for the forecasted spatially distributed runoff was performed by computing the various performance measures at each grid cell independently, and then averaging over the basin (V2010, Appendix C). For the basin average runoff forecast verification, the scores were computed using the basin average runoff values. Figure 4 shows the forecast verification for spatially distributed (solid lines) and for basin average (dashed lines) runoff forecasts for the interpolation method (grey, set up 2) and the RMSDmean method (black, set up 3) with respect to the simulated truth (set up 1); relative bias and RMSE, CRPSS and Pearson correlation. Results for the spatially distributed and the basin average runoff forecasts are consistent. The basin average runoff scores are usually higher, as expected. On day 11 of the extended forecasts, the mean runoff values drop sharply, and consequently, relative biases and RMSEs increase sharply. This implies that for runoff, there is no extension in skill beyond 10 days (through initial conditions) when forecasts are extended using the assumed zero precipitation and temperature climatology beyond forecast day 10. Note that with the EPS forecast extension to 15 days in 2006 and 32 days in 2008, runoff forecasts for more recent periods should have a useful skill for longer than 10 days, but no extension in skill through initial conditions. In agreement with the forecast verifications for spatially distributed precipitation in V2010, the biases of the runoff forecasts produced by the analog method improved relative to those of the interpolation method. 18

19 The RMSDmean CRPSS was lower than the interpolation CRPSS, due to an increase in ensemble spread, as shown by the Talagrand histograms (Figure 5). The predictability (Pearson correlation) was similar between the interpolation and the analog RMSDmean methods. In V2010, the RMSDmean Spearman rank correlation for the daily precipitation forecasts was slightly lower than for the interpolation method. Figure 4 shows an improvement in RMSDmean reliability relative to the interpolation method for both the distributed and basin average runoff. At day 1, there was a large improvement in reliability for the RMSDmean method for all forecast categories for both spatially distributed and basin average runoff. The improvement for basin average runoff for the RMSDmean method was important at small lead times, however the interpolation and RMSDmean reliabilities were similar after day 5 (averaging effect). The RMSDmean method improved reliability for all forecast categories and all lead times for spatially distributed runoff, which is consistent with precipitation as reported in V2010. The RMSDmean method showed high forecast ensemble spread reliability. The interpolation method lacked reliability (U-shape histograms), and also showed a consistent overestimation of distributed runoff (asymmetric histogram), which is explained by the fact that the VIC model is calibrated to the reference forcings (TMPA precipitation) and the interpolated precipitation forecasts are wetter than TMPA in general (Figure 3 in V2010, all forecast categories, all lead times). 4.2 Forecast verification for daily streamflow at four locations over the period. Figures 6 and 7 show the daily ensemble streamflow forecast verifications for lead times 1 to 15 days for the Ohio River in Metropolis, IL, and Monongahela River in Elizabeth, PA with respect to the reference. The number of lead times (days) when initial conditions control the streamflow forecasts decreases with decreasing drainage area as shown by the lead time at which the interpolation and RMSDmean method performance scores diverge from the climatology and zero precipitation deterministic forecast scores (dashed line, 4 th simulation). As shown on the first and second rows of Figure 6, the initial conditions control the forecast mean flow values in each forecast category for the 19

20 first 2 days at Metropolis (and Louisville, not shown) forecast point. For the Mt Carmel forecast point, the climatology and zero precipitation deterministic mean flow and relative bias values dropped slightly on day 2, i.e. initial conditions control the forecast flow values on day 1 and partially on day 2 (not shown). For the Elizabeth forecast point (Figure 7), which has the smallest drainage area, the initial conditions control forecast value only on day 1. On the basis of the correlation between forecast and observations (Figures 6 and 7), initial conditions had an influence on the forecasts performance for up to 3 days at Elizabeth and Mt Carmel, and 4 days at Louisville and Metropolis. The influence of initial conditions on the correlation was shorter (longer) for low (high) flow forecasts, i.e for lower and upper tercile forecast categories. Similarly, the control through initial conditions of the flow forecasts for short lead times results is an extension in skill beyond 10 days, when interpolated and analog RMSDmean forecasts are extended to 15 days using the assumed zero precipitation and temperature climatology (forecast discontinuity). This extension in skill spans from day 11 to when the performance skill scores drop sharply. tended to have some skill for day 11 (one day beyond the duration of the forecasts) at Elizabeth, day 12 at Mt Carmel, Louisville and Metropolis in terms of relative biases, and day 12 at Elizabeth and Mt Carmel and day 14 at Louisville and Metropolis on the basis of forecast-observed correlation. These are average maximum lead times and it could be possible that longer lead times would be achieved for particular events (see.g. Thielen et al, 2009). Following the extension of the EPS forecasts beyond day 10 in 2006, it should be possible to generate flood forecasts with longer lead times when using more recent forecasts. The relative biases were reduced by the RMSDmean method relative to the interpolation method at all forecast points. Relative RMSEs were usually improved, or equivalent with the exception of Elizabeth. The analog RMSDmean method focused on improving bias and reliability, in contrast to RMSEs (V2010). Consequently, the RMSE for flow was not improved for short concentration time forecast points, but was reduced or maintained for longer concentration times due to an improved bias. The RMSDmean method CRPSSs were either equivalent (Elizabeth) or lower than those for the 20

21 interpolation method. As with forecast verification for precipitation (V2010) and runoff (Section 4.1), improvement in CRPSSs is due to increased reliability, discussed below. The observed-predicted correlations were similar for the interpolation and the RMSDmean methods. Figure 8 shows Talagrand histograms at two stations (columns) for two forecast categories and lead times 1, 5 and 8 days. As expected on day 1 (not shown), the ensemble spreads were too narrow and therefore the reliability was poor for both methods at all stations because initial conditions controlled the streamflow forecasts. On day 2, the RMSDmean method improved the reliability with respect to the interpolation method especially at Elizabeth and Mt Carmel (not shown), as the effect of initial conditions decayed more rapidly for the smaller drainage areas. By day 5, the RMSDmean method improved the reliability of the forecasts considerably at all four stations for all forecast categories. At day 8, the RMSDmean method still improved the reliability for the larger basin. Reliabilities between the interpolation and the RMSDmean methods were equivalent at day 8 for smaller basins and by day 10 for larger basins due to a very large ensemble spread. 5.0 Discussion We have described a hydrological forecast scheme that is intended for global application, particularly in regions where in situ data are sparse. The potential improvement in ensemble streamflow forecast skill that is realizeable from calibrating the ensemble weather forecasts (upstream of the hydrology model) in comparison to a simple interpolation of the forecasts was investigated. The system using the calibrated weather forecasts (analog RMSDmean method) reduced the relative biases and improved the reliability of the spatially distributed and basin average runoff and daily streamflow forecasts relative to no calibration (interpolated forecasts). Relative RMSEs and the observed-predicted correlations, on the other hand, were similar for the interpolation and RMSDmean methods for all forecast categories. The RMSDmean CRPSS values were lower than those for the interpolation method due mostly to the improved reliability of the ensemble spread. As a result of the 21

22 routing time in the runoff to streamflow transformation, initial conditions controlled the forecast performance for the first 1-4 days (depending on drainage basin size), and useful streamflow forecast skill was, therefore, derived from the 10-day forecasts for up to 4 additional days depending on the drainage area and the forecast category (flow magnitude). This is valid even for locations in which no site specific calibration of the hydrologic-routing model was performed (surrogate for ungauged basins).our results suggest that spatially distributed runoff and flow can be forecasted in regions with sparse precipitation observation networks in a more reliable and accurate way when the hydrology model is forced with calibrated and downscaled precipitation forecasts using the RMSDmean method as compared with the interpolation method. Forecast reliability is an important consideration in real-time forecast applications: What can I expect if the forecast falls into a certain forecast category? What should I do with this forecast? The improvement in streamflow forecast accuracy achieved through use of the method we evaluated is similar for basins with varying drainage areas, but the timing of the improvement varies with the time of concentration at the forecast point, which in turn depends on the drainage area and the streamflow magnitude. For lead times shorter than the time of concentration, the calibration of the weather forecasts has little impact on the streamflow forecasts. The ensemble mean streamflow forecasts are of expected accuracy (as good at the streamflow simulation forced with observations) but the probabilistic streamflow forecasts are not reliable (ensemble spread is too narrow). For lead times longer than the time of concentration, the analog RMSDmean ensemble flow forecasts are more accurate and reliable than the flow forecasts without calibration upstream of the hydrology model. The EPS short-range under dispersion (U-shape Talagrand diagrams at forecast day 1 and 2 for precipitation, Figure 3 in V2010, and runoff forecasts, Figure 5) was due to the strategy used to define the EPS initial perturbations. Since June 2010, the perturbations have been defined by adding to the singular vectors a new set of perturbations defined by the new ECMWF Ensembles of Data Assimilation system (Palmer et al. 2007). This change has lead to an improved spread-skill reliability in the extra- 22

23 tropics during the first 2 days (Buizza et al 2008). Work is progressing at ECMWF to further improve the EPS spread-skill reliability by further improving the simulation of the initial uncertainties by introducing land-surface perturbations, and by further improving the simulation of model uncertainties by upgrading the stochastic scheme. These changes are expected to have a positive impact on EPS-based probabilistic flood applications. Future work could include calibration and evaluation of accuracy and reliability of routed flow forecasts in ungauged basins. 6.0 Conclusions The hydrologic forecasting scheme we have outlined consists of precipitation EPS forecasts calibrated and downscaled using the RMSDmean method (developed in V2010) and, in turn, used to force the semi-distributed VIC macroscale hydrology model. It is of most practical interest in ungauged basins where calibration of the ensemble flow forecasts (post-processor, downstream of the hydrology model) is complicated by the absence of or large uncertainties in observed streamflow. It should also have useful applications for related purposes such as landslide prediction and forecasting of flood inundation extent. Our main conclusions are: The system has useful skill and reliability for spatially distributed runoff and streamflow forecasts for about 10-days beyond the time of concentration, more or less independent of the basin drainage area. Following the extensions of the EPS forecasts beyond day 10 in 2006 and day 15 in 2008, the system should have useful skill for longer lead times beyond the time of concentration of the basin. For forecast lead times shorter than the time of concentration, hydrologic initial conditions control the streamflow forecast skill Reduction in the number of ensemble members (which helps computational feasibility) was successfully compensated by calibrating the reduced ensemble of forecasts. Furthermore, the 23

24 improvement in reliability and bias that results from calibration of the weather forecast ensemble is realized in the runoff and streamflow forecasts. Finally, the Schaake Shuffle was successful not only for creating a spatial and temporal ensemble forecast matrix (space, time, variable, ensemble member), its traditional use; but also for imposing a lost correlation/structure in the rank-correlation matrix. This is the key element for transforming a spatially distributed calibrated ensemble weather forecast (with focus on reliability) into a reliable flow forecast. It also allows the system to be appropriate for river basins large enough that the average time of travel exceeds the time step of the hydrological model (one day in the application we have illustrated here). 24

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31 LIST OF FIGURES Figure 1: Schematic of the probabilistic quantitative hydrological forecast system for global application. The calibration and downscaling technique was developed in V2010. In this paper, the calibrated and downscaled meteorological forecasts derived and verified in V2010 force the hydrology model. Derived hydrologic forecasts (runoff and discharge) are then verified. Figure 2: The verification of the system includes four hydrologic simulations (experiments): the reference (1-middle), the interpolation method (2-left), the RMSDmean method (3-right) and the climatology forecast with zero precipitation (4-far right). Figure 3: Daily calibration of VIC-routing model at Metropolis (10/ /2007), and verification in Metropolis (10/ /2005) and at 3 other stations (10/ /2007). The first row shows the 5-day moving average of the TMPA and the gauge-station based Maurer et al. (2002)daily basin average precipitation. Figure 4: day daily forecast verification for the spatially distributed (solid lines) and basin average (dashed lines) runoff, for 2 categories of forecasts: all and upper terciles for the 2 experiments (interpolation, grey, and RMSDmean, black). The reference is the runoff simulated by forcing VIC with ECMWF Analysis fields and TMPA precipitation. Figure 5: Talagrand histograms for daily 1) distributed and 2) basin average runoff for 3 forecast categories (all, lower tercile, upper tercile), at days 1, 5 and 10. Figure 6: Day 1-15 daily flow forecast verification at Metropolis, IL (outlet) for 3 forecast categories (all, lower and upper terciles) for 2 downscaling methods (interpolation-grey, RMSDmean-black) and climatology with zero precipitation with respect to the reference (dashed). Figure 7: Same as Figure 6 but for the Monongahela River at Elizabeth, PA. Figure 8: Talagrand histograms for daily flow forecast for 2 forecast categories (all, lower and upper terciles) at 2 different stations (Metropolis and Elizabeth - with decreasing drainage areas) at days 2, 5 and 8 (rows 1-2, 3-4 and 5-6 respectively). 31

32 FIGURES Figure 1: Schematic of the probabilistic quantitative hydrological forecast system for global application. The calibration and downscaling technique was developed in V2010. In this paper, the calibrated and downscaled meteorological forecasts derived and verified in V2010 force the hydrology model. Derived hydrologic forecasts (runoff and discharge) are then verified. 32

33 Figure 2: The verification of the system includes four hydrologic simulations (experiments): the reference (1-middle), the interpolation method (2-left), the RMSDmean method (3-right) and the climatology forecast with zero precipitation (4-far right). 33

34 Figure 3: Daily calibration of VIC-routing model at Metropolis (10/ /2007), and verification in Metropolis (10/ /2005) and at 3 other stations (10/ /2007). The first row shows the 5-day moving average of the TMPA and the gauge-station based Maurer et al. (2002)daily basin average precipitation. 34