1. Introduction
Accurate forecasts of seasonal streamflow volumes assist a broad array of water (and other) resource decision makers (Pagano et al. 2004). Therefore, forecasters have a strong interest in the accuracy of seasonal forecasts, and in the potential for improvement of forecast accuracy. Nonetheless, Pagano et al. (2004) reported that the skill of western U.S. seasonal streamflow forecasts generally has not improved since the 1960s. The current skill of seasonal hydrological forecasts is still limited and far from meeting society’s needs (Luo et al. 2007).
In the United States, the primary operational method for seasonal streamflow forecasting is linear regression (of seasonal streamflow on indicator variables, such as accumulated winter precipitation, and/or observations of snowpack water equivalent). This approach forms the backbone of operational systems in the National Weather Service (NWS) and National Water and Climate Center (NWCC) of the National Resources Conservation Service (NRCS). An alternative approach known as ensemble streamflow prediction (ESP) (Twedt et al. 1977; Day 1985) has been implemented on a more limited basis by both NWS and NWCC, although its use is increasing. In the ESP approach, a hydrologic model is forced up to the time of forecast with observed precipitation, temperature, and other surface variables to produce a “nowcast” of the current hydrologic state (soil moisture and snow water storage), which forms the initial condition for ensemble forecasts that represent the range of future conditions. Although more computationally and data intensive than regression approaches, ESP offers various advantages including better ability to adapt to changing climate conditions and to represent extreme hydrologic behavior (especially droughts), and the ability to provide more information about spatial variations in hydrologic conditions.
Implementation of the ESP approach is complicated, however, by the effect on both the nowcast and predicted ensembles of hydrologic model errors. Model errors can result from errors in the model meteorological forcings, from errors in model structure, and from model parameter errors (Beven 1993; Sorooshian et al. 1993; Wagener et al. 2003). While errors in meteorological forcings and model structure may not be readily reduced, parameter errors can generally be reduced through a process of model calibration, that is, adjustment of parameters to match observations (usually of streamflow) in a retrospective observation period. Model calibration is usually viewed by operational hydrologists, therefore, as a prerequisite for effective implementation of the ESP approach.
Seasonal streamflow forecast errors can be assessed using measures such as root-mean-square error (RMSE). RMSE is the square root of the bias squared plus the variance of the forecasts about the true value, and therefore can be heavily influenced by model bias. Bias in turn is readily reduced by calibration, as shown in Fig. 1. On the other hand, bias can also be reduced by postprocessing (e.g., by “training” a bias removal technique on retrospective simulation error statistics), leaving the variance of the forecasts about the true value as main contributor to RMSE. This invites the question: How much is forecast error reduced by model calibration, beyond what can be accomplished by postprocessing to remove bias (and without the often time consuming process of model calibration)? We address this question through retrospective evaluation of forecast errors at eight streamflow forecast points distributed across the western United States, for forecast periods of length ranging from 1 to 6 months, and for forecasts initiated from 1 December to 1 June, a period during which most runoff occurs in snowmelt-dominated western U.S. rivers. We evaluate ESP forecast errors both for uncalibrated forecasts to which a postprocessing bias correction approach is applied, and for forecasts from a calibrated hydrologic model without explicit bias correction.
2. Study basins
To ensure relatively complete geographic coverage and a range of basin types, eight river basins (see Fig. 2) were selected across the western United States with drainage areas ranging from 831 km2 for the Stehekin River basin to 35 094 km2 for the Salmon River basin. All forecast points were selected so as to have minimal effects of diversions and regulation upstream as noted in U.S. Geological Survey (USGS) metadata, or to have records from which upstream diversion and storage effects had been removed. All forecast points have lengthy streamflow records (spanning at least the period 1971–2001) of high quality. The basins represent different hydroclimatic conditions and are distributed across the western United States. The seasonal hydrologic cycle of all basins is dominated by spring snowmelt runoff. Six of the gages, the Animas River at Durango (ANIMA), Bruneau River near Hot Spring (BRUNE), Yellowstone River (YELLO), Salmon River at Whitebird (SALMO), North Fork Flathead River (NOFOR), and Stehekin River at Stehekin (STEHE), are included in the USGS Hydro-Climatic Data Network (HCDN) (Slack and Landwehr 1992). The data record for the Feather River at Oroville (OROVI) is naturalized (anthropogenic effects upstream removed) monthly streamflow provided by the California Data Exchange Center (CDEC) of the California Department of Water Resources (DWR), while naturalized streamflow data for the Gunnison River near Blue Mesa (BLMSA) were provided by the U.S. Bureau of Reclamation (USBR). The eight forecast points are all locations that are considered critical to water management operations (e.g., inflows to reservoirs or flows at key index sites). Summary characteristics of the eight river basins, along with relevant forecast point information, are shown in Table 1.
3. Methods
Our general procedure was as follows: first, we implemented the Variable Infiltration Capacity (VIC) model (Liang et al. 1994) using methods summarized in Nijssen et al. (1997) for each of the eight river basins. For the initial implementation, we used the VIC continental U.S. parameter set assembled for the North American Land Data Assimilation System (N-LDAS) by Maurer et al. (2002). We then implemented an automated parameter estimation algorithm, which took multiple objective functions to evaluate the difference between simulated and observed monthly streamflows. The ESP technique was then applied using both the calibrated and uncalibrated hydrologic model. Subsequently, a bias correction approach was applied to individual members of the streamflow forecast ensembles produced using the uncalibrated model. Forecast errors (ensemble mean forecast difference from observations) were then assessed for the two sets of forecasts.
a. Hydrologic model implementation
The VIC model was implemented for each of the eight river basins at a daily time step in water balance mode (meaning that no iteration on the effective surface temperature to close the energy balance was performed). When snow was present, however, the embedded snow accumulation and ablation algorithm within VIC was run at a 1-h time step, which resolves the diurnal cycle and helps to accurately estimate day–night variations in snow accumulation and melt. The VIC model produced daily runoff from each grid cell in the simulation domain as baseflow and surface runoff. Grid cell runoff was routed through a grid-based stream network using the routing scheme described by Lohmann et al. (1998a,b). The model was implemented at one-eighth-degree spatial resolution with five elevation bands specified as described by Nijssen et al. (1997) and Maurer et al. (2002).
The VIC model was forced with daily precipitation, maximum and minimum temperature, and daily averaged wind speed taken from the lowest level in the National Centers for Environmental Prediction–National Center for Atmospheric Research (NCEP–NCAR) reanalysis (Kalnay et al. 1996) during both the model run-up period (to the time of forecast) and during the forecast period. Gridded forcing data were produced from National Oceanic and Atmospheric Administration (NOAA) Cooperative Observer (CoOp) station data using the SYMAP method (Shepard 1984) as described in Maurer et al. (2002). As in other VIC implementations (e.g., Nijssen et al. 1997), other surface radiative fluxes and variables (downward solar and longwave radiation, surface humidity) were derived from daily temperature and/or the daily temperature range.
b. Model calibration
Model calibration was performed using the multi objective complex evolution (MOCOM-UA) algorithm of Yapo et al. (1998), which employs a population evolution strategy to find the optimal parameter set. Two objective functions were incorporated in our implementation of the algorithm: the Nash–Sutcliffe efficiency measure of Nash and Sutcliffe (1970), which is the complement of the ratio of the sum of the squares of the predicted minus observed values squared to the (sample) variance of the observations, and the absolute value of annual mean volume error between observed and simulated streamflow. The MOCOM-UA method searches the parameter space by sampling the feasible parameter space at a number of points. At each point, the multi-objective vector is computed and then the population is ranked and sorted using the Pareto-rank procedure of Goldberg (1989). The iterative process causes the parameter set to converge toward the Pareto optimum (see Fig. 3). This algorithm has been applied successfully in a number of studies (Yapo et al. 1998; Wagener et al. 2001; Xia et al. 2002; Meixner et al. 2002; Gupta et al. 2003; among others).
Like most physically based hydrologic models, the VIC model has many (about 20, depending on how the term “parameter” is defined) parameters that must be specified. However, the usual implementation approach (see, e.g., Nijssen et al. 1997) involves the calibration of six parameters, which are 1) the infiltration parameter (bi), which controls the partitioning of rainfall (or snowmelt) into infiltration and direct runoff (a higher value of bi gives lower infiltration and yields higher surface runoff); 2) D2 and D3, the second and third soil layer thicknesses (D1, the top-layer depth, is usually specified a priori), which affect the water available for transpiration and baseflow respectively. Thicker soil depths have slower runoff response (baseflow dominated) with higher evapotranspiration, but result in longer retention of soil moisture and higher baseflow in wet seasons. Number 3) is Dsmax, Ds, and Ws, which are baseflow parameters and also estimated via calibration. The Dsmax is maximum baseflow velocity, Ds is the fraction of maximum baseflow velocity, and Ws is the fraction of maximum soil moisture content of the third layer at which nonlinear baseflow occurs. These three baseflow parameters determine how quickly the water stored in the third layer is evacuated as baseflow (Liang et al. 1994).
Initial values and plausible ranges (see Table 2) of these six VIC model parameters were obtained from the N-LDAS experiment (Mitchell et al. 2004; Maurer et al. 2002) for each of the eight basins. The initial conditions for the calibrations also were used as the uncalibrated parameter sets. They also were used as the initial values for the automatic calibration.
c. Ensemble streamflow prediction
As noted above, the ESP method estimates the hydrologic state of current physical conditions (especially for the soil moisture and snowpack) at the time of forecasts using hydrologic simulations driven by observed surface forcings up to the time of forecast, followed by resampling of hydrologic ensembles from past observed forcings. One issue in application of the ESP method is to assure that the initial conditions at the time of forecast (so-called nowcast) are not affected by model initialization, which ordinarily is in the distant past. For this purpose, we initialized the model with a 10-yr spinup simulation prior to each of the forecast dates. Once the nowcast was simulated for each forecast date, ensembles sampled from past conditions (sequences of gridded data selected from years in the observed record, one year at a time each of length equal to the forecast period) were used to produce forecasts as if they were being made at the time of the nowcast (“hindcasts”). The ESP ensembles were sampled from the climatology period 1970–99 for all sites except BRUNE, where they were sampled from the period 1950–79. Ensemble means were computed for each forecast period and site. Hence, accounting for the 10-yr spinup period, 20 hindcasts were produced for each forecast date and forecast period at all sites, each consisting of the mean of 30 ensemble members. For example, January ESP ensembles were initialized with a 1 January nowcast for the calibration and validation periods (e.g., 1981–2000 for BLMSA), and each hindcast, for forecast periods of length from 1 to 6 months, had 30 ensemble members (1970–99).
d. Bias correction approach
To correct bias, we used the “percentile mapping” approach (Panofsky and Brier 1958), as adopted by Wood et al. (2002) and applied to streamflow simulations by Snover et al. (2003). In this technique, simulated and observed data covering the same period of record are used to create a percentile mapping from one population to the other using probability distributions (in this case, lognormal) fit to the empirical cumulative distribution functions (CDFs) of the two datasets. The bias correction procedure consists of taking the percentile from the fitted CDF corresponding to a simulated flow and extracting the corresponding flow at the same percentile from the fitted CDF of the observations. The percentile mapping bias correction approach not only removes the bias in the mean, but also alters the distribution of the simulated streamflows as well. In this case, we used two-parameter lognormal CDFs fitted to both the simulated and observed flows as the basis for the bias correction approach.
e. Assessment of forecast skill
4. Results and discussion
We computed Cp for all hindcasts of calibrated, uncalibrated bias-corrected, and calibrated bias-corrected implementations of ESP. We summarize results of the model calibration procedure below, followed by the assessment of hindcast accuracy.
a. Calibration and validation results
For each forecast point, we selected a period of 10 yr for model calibration, which differed somewhat across sites. In Fig. 4, we show hydrographs for the calibration period, along with a validation period (either before or after the calibration period) for comparison purposes. The monthly hydrographs illustrate that the annual cycle of the calibrated and validated monthly streamflows matches with that of historical observations quite well. Figure 5 shows the long-term monthly means for the calibrated, uncalibrated, and observed streamflows respectively, which also show a good agreement between observed and predicted streamflow with calibrated parameters in both the calibration and verification periods. Summary statistics for the uncalibrated and calibrated (calibration and verification periods) streamflow simulations are given in Table 3. As expected, the Nash–Sutcliffe efficiency is much higher (0.83 to 0.97) for both the calibration and validation periods across all study basins than for the uncalibrated simulations (0.29 to 0.71). For the validation periods, there is a slight decrease in the Nash–Sutcliffe efficiency relative to the calibration period, also as expected.
b. Retrospective evaluation of forecast errors
The Cp is shown in Fig. 6 for calibrated, uncalibrated, and uncalibrated bias-corrected scenarios, for forecasts made from 1 December to 1 June, and for forecast periods of 1–6-month length with zero-month lead time. As is expected for snowmelt-dominated rivers in the western United States, Cp generally improves as the forecast date advances from 1 December to the winter and into the spring until about the time of maximum snow accumulation, typically April–May depending on the specific basin, and then begins to decline. For forecasts made on 1 December, Cp is often negative or lower, which reflects the fact that much of the snow that will contribute to forecast period runoff has not yet accumulated. Depending on the forecast initial date (which ranged from 1 December to 1 June), forecasts for longer periods tend to have higher Cp s than for shorter forecast periods, primarily because the role of errors in the forecasting of runoff timing are reduced for longer forecast periods.
Comparison of Figs. 6a,b shows that in all cases, calibration improves the forecast accuracy. However, uncalibrated bias-corrected forecasts (Fig. 6c) in many cases have Cp values that are only slightly lower than for calibrated forecasts, and in the case of four of the basins (ANIMA, OROVI, STEHE, and YELLO), bias correction yielded higher Cp values than did calibration (gray boxes in Fig. 6d). Table 4 summarizes the percentage of forecasts for lead times ranging from 0 to 6 months, for which Cp with calibration is higher than without (but with bias correction), by forecast date. All the basins show the consistency as described above in Fig. 6 for zero-month lead time except YELLO for which calibration provides a higher Cp than does bias correction for 3–6-month forecast lead times. In general, there is a good deal of persistence in the results across forecast dates and lengths, that is, the relative performance of calibrated versus bias-corrected forecasts is mostly determined by the site, and not by the forecast date or forecast period. On the other hand, there is no obvious pattern that discriminates against basins for which bias correction performs better than calibration. For instance, in the case of ANIMA, OROVI, and STEHE, where bias correction generally performed better than calibration, Table 3 shows that the calibrated model performed quite well in simulation mode, as measured, for instance, by the Nash–Sutcliffe efficiency, so it is not a matter of those sites having a “bad” calibration.
In addition to forecasts for a range of forecast periods beginning at specified times, we also computed the Cp values for April–July forecasts made for a range of forecast dates (Fig. 7). April–July is often used as a reference period for water management purposes in western river basins. The results are generally consistent with those shown in Fig. 6 for different forecast initiation dates and forecast periods: there is a modest improvement of 0.07 in Cp due to calibration relative to bias correction for BLMSA, BRUNE, NOFOR, SALMO, and YELLO (mean improvement) across all forecasts. In contrast, STEHE and OROVI show a better improvement from uncalibrated bias-corrected forecasts (average Cp increment 0.13), whereas for ANIMA, the effect is nearly equal for model calibration and bias correction.
The scatterplots in Fig. 8 show the forecast ensemble means plotted against observed flow for the uncalibrated, uncalibrated bias-corrected (BC), and calibrated April–July forecasts for BLMSA. For April–July forecasts made on 1 May and 1 June, the observed flow was used for the months prior to the start of the nowcast while those after were ESP predictions. For instance, in the 1 May forecast, we use the observed flow for April since the April flow has already occurred. Figure 8a shows that for this site, the uncalibrated ESP ensemble means have an overestimation bias. The bias correction approach dramatically reduces this bias and increases Cp in Fig. 8b. Figure 8c shows that model calibration reduces not only bias but also the spread of the ESP hindcast ensemble means. The figure also shows that for both the calibrated and uncalibrated bias corrected cases, the spread of the ensemble means narrows and the bias falls as the forecast date progresses from 1 January to 1 June.
The evaluation was also performed for calibrated forecasts with bias correction. The Cp values were calculated for the two scenarios (calibrated bias-corrected and uncalibrated bias-corrected forecasts), respectively, based on Eq. (1). Figure 9 shows the difference between calibrated bias-corrected and uncalibrated bias-corrected forecasts as measured by Cp for the eight river basins. In most cases, Cp values for calibrated bias-corrected forecasts are only slightly higher than for bias correction alone; however, in the case of STEHE, bias correction resulted in substantially lower Cp values.
A somewhat different question is how the forecast reliability is affected by the bias correction process. Reliability “pertains to the relationship of the forecast with the average observation, for specific values of the forecast” (Wilks 2006). A quantitative measure is the deviation from the 1:1 line on a reliability diagram, which essentially measures variations between the predicted probabilities of an event and their corresponding observed frequencies. The reliability diagram is equivalent to a cumulative ranked histogram (Hamill and Colucci 1997; Talagrand and Vautard 1997). Figure 10 shows a typical reliability diagram for calibrated and uncalibrated bias-corrected forecasts (for April–July flows made 1 June at BLMSA). A forecast with perfect reliability would plot on the 1:1 line, and therefore the maximum deviation (in absolute value) of the observed plot from the 1:1 line can be used as a measure of forecast performance in terms of reliability. We computed the maximum deviations for all forecast dates and forecast periods, which are shown as histograms for each site in Fig. 11. In general, the deviations are slightly smaller for the uncalibrated bias-corrected than calibrated forecasts, suggesting that bias correction improves forecast reliability somewhat.
5. Conclusions
By exploring a range of streamflow forecast locations, forecast period lengths, issue dates, and forecast lead times during the year, we find that the reduction in forecast error as measured by Cp that is achieved by bias correction alone is nearly as great as that captured by hydrologic model calibration in essentially all cases, and is greater in many. Moreover, the incremental improvement in forecast accuracy achievable by bias correcting calibrated forecasts in comparison with bias correction alone is minor in most cases. Bias correction is easy to implement and avoids the time-consuming effort required for model calibration (even in the case of automated approaches). It is important to note that we have focused entirely on seasonal forecasts, which depend primarily on the volume, rather than timing, of runoff. For shorter forecast periods, which approach what might be termed the “hydrograph time scale,” bias correction most likely will be less effective. Consider, for instance, the case where the model tends to be biased such that the response time to hydrograph peak is misestimated by the model. The bias correction will effectively be attempting to compensate for this by adjusting rising limb flows to correspond to falling limb observations, or vice versa, an adjustment to which the percentile mapping approach is not well suited.
Acknowledgments
This research was supported by the National Oceanic and Atmospheric Administration under Grant NAOAR50AR4310015 to the University of Washington. The authors appreciate the advice of Ms. Nathalie Voisin in preparation and interpretation of the forecast reliability plots (Figs. 10, 11).
REFERENCES
Beven, K., 1993: Prophecy, reality and uncertainty in distributed hydrological modelling. Adv. Water Resour., 16 , 41–51.
Day, G. N., 1985: Extended streamflow forecasting using NWSRFS. J. Water Resour. Plann. Manage., 111 , 157–170.
Goldberg, D. E., 1989: Genetic Algorithms in Search, Optimization, and Machine Learning. Addison-Wesley, 412 pp.
Gupta, H. V., Sorooshian S. , Hogue T. S. , and Boyle D. , 2003: Advances in automatic calibration of watershed models. Calibration of Watershed Models, Q. Duan et al., Eds., Water Science and Applications Series, Vol. 6, Amer. Geophys. Union, 9–28.
Hamill, T., and Colucci S. J. , 1997: Verification of Eta–RSM short-range ensemble forecasts. Mon. Wea. Rev., 125 , 1312–1327.
Kalnay, E., and Coauthors, 1996: The NCEP/NCAR 40-Year Reanalysis Project. Bull. Amer. Meteor. Soc., 77 , 437–471.
Lettenmaier, D. P., 1984: Limitations on seasonal snowmelt forecast accuracy. J. Water. Resour. Plann. Manage., 108 , 255–269.
Liang, X., Lettenmaier D. P. , Wood E. F. , and Burges S. J. , 1994: A simple hydrologically based model of land surface water and energy fluxes for general circulation models. J. Geophys. Res., 99 , 14415–14428.
Lohmann, D., Raschke E. , Nijssen B. , and Lettenmaier D. P. , 1998a: Regional scale hydrology: I. Formulation of the VIC-2L model coupled to a routing model. Hydrol. Sci. J., 43 , 131–141.
Lohmann, D., Raschke E. , Nijssen B. , and Lettenmaier D. P. , 1998b: Regional scale hydrology: II. Application of the VIC-2L model to the Weser River, Germany. Hydrol. Sci. J., 43 , 143–158.
Luo, L., Wood E. F. , and Pan M. , 2007: Bayesian merging of multiple climate model forecasts for seasonal hydrological predictions. J. Geophys. Res., 112 .D10102, doi:10.1029/2006JD007655.
Maurer, E. P., Wood A. W. , Adam J. C. , Lettenmaier D. P. , and Nijssen B. , 2002: A long-term hydrologically based dataset of land surface fluxes and states for the conterminous United States. J. Climate, 15 , 3237–3251.
Meixner, T., Bastidas L. A. , Gupta H. V. , and Bales R. C. , 2002: Multicriteria parameter estimation for models of stream chemical composition. Water Resour. Res., 38 .1027, doi:10.1029/2000WR000112.
Mitchell, K. E., and Coauthors, 2004: The multi-institution North American Land Data Assimilation System (NLDAS): Utilizing multiple GCIP products and partners in a continental distributed hydrological modeling system. J. Geophys. Res., 109 .D07S90, doi:10.1029/2003JD003823.
Nash, J. E., and Sutcliffe J. V. , 1970: River flow forecasting through conceptual models. Part I—A discussion of principles. J. Hydrol., 10 , 282–290.
Nijssen, B., Lettenmaier D. P. , Liang X. , Wetzel S. W. , and Wood E. F. , 1997: Streamflow simulation for continental-scale river basins. Water Resour. Res., 33 , 711–724.
Pagano, T., Garen D. , and Sorooshian S. , 2004: Evaluation of official western U.S. seasonal water supply outlooks, 1922–2002. J. Hydrometeor., 5 , 896–909.
Panofsky, H. A., and Brier G. W. , 1958: Some Applications of Statistics to Meteorology. The Pennsylvania State University, 224 pp.
Shepard, D. S., 1984: Computer mapping: The SYMAP interpolation algorithm. Spatial Statistics and Models, G. L. Gaille and C. J. Willmott, Eds., D. Reidel, 133–145.
Slack, J. R., and Landwehr J. M. , 1992: Hydro-Climatic Data Network: A U.S. Geological Survey streamflow data set for the United States for the study of climate variations, 1974–1988. U.S. Geological Survey Rep. 92–129, 193 pp.
Snover, A. K., Hamlet A. F. , and Lettenmaier D. P. , 2003: Climate change scenarios for water planning studies: Pilot applications in the Pacific Northwest. Bull. Amer. Meteor. Soc., 84 , 1513–1518.
Sorooshian, S., Duan Q. , and Gupta V. K. , 1993: Calibration of rainfall-runoff models: Application of global optimization to the Sacramento Soil Moisture Accounting Model. Water Resour. Res., 29 , 1185–1194.
Talagrand, O., and Vautard R. , 1997: Evaluation of probabilistic prediction systems. Proc. ECMWF Workshop on Predictability, Reading, United Kingdom, European Centre for Medium-Range Weather Forecasts, 1–25.
Twedt, T. M., Schaake J. C. Jr., and Peck E. L. , 1977: National Weather Service extended streamflow prediction. Proc. 45th Western Snow Conf., Albuquerque, NM, Colorado State University, 52–57.
Wagener, T., Boyle D. P. , Lees M. J. , Wheater H. S. , Gupta H. V. , and Sorooshian S. , 2001: A framework for development and application of hydrological models. Hydrol. Earth Syst. Sci., 5 , 13–26.
Wagener, T., McIntyre N. , Lees M. J. , Wheater H. S. , and Gupta H. V. , 2003: Towards reduced uncertainty in conceptual rainfall-runoff modelling: Dynamic identifiability analysis. Hydrol. Processes, 17 , 455–476.
Wilks, D. S., 2006: Statistical Methods in the Atmospheric Sciences. International Geophysics Series, Vol. 91, Academic Press, 627 pp.
Wood, A. W., Maurer E. P. , Kumar A. , and Lettenmaier D. P. , 2002: Long-range experimental hydrologic forecasting for the eastern United States. J. Geophys. Res., 107 .4429, doi:10.1029/2001JD000659.
Wood, A. W., Kumar A. , and Lettenmaier D. P. , 2005: A retrospective assessment of National Centers for Environmental Prediction climate model–based ensemble hydrologic forecasting in the western United States. J. Geophys. Res., 110 .D04105, doi:10.1029/2004JD004508.
Xia, Y., Pitman A. J. , Gupta H. V. , Leplastrier M. , Henderson-Sellers A. , and Bastidas L. A. , 2002: Calibrating a land surface model of varying complexity using multicriteria methods and the Cabauw dataset. J. Hydrometeor., 3 , 181–194.
Yapo, P. O., Gupta H. V. , and Sorooshian S. , 1998: Multi-objective global optimization for hydrologic models. J. Hydrol., 204 , 83–97.
Scatterplots of (a) uncalibrated ESP forecasts, and (b) calibrated ESP forecasts starting from the first day of June vs observations from 1981 to 2000 for Salmon River at Whitebird. RMSE is (a) 4350 million cubic meters (MCM), which is heavily influenced by bias, and (b) reduced to 710 MCM by model calibration.
Citation: Journal of Hydrometeorology 9, 6; 10.1175/2008JHM1001.1
Location of the eight river basins used in this study.
Citation: Journal of Hydrometeorology 9, 6; 10.1175/2008JHM1001.1
Example of model calibration output for six VIC model parameters showing how the parameter estimates converge toward the Pareto optimum using the MOCOM-UA calibration algorithm; (top) b_inf controls the partitioning of precipitation (or snowmelt) into surface runoff or infiltration; (one below top) Ds is the fraction of maximum baseflow velocity, and (two below top) Ws is the fraction of maximum soil moisture content of the third soil layer at which nonlinear baseflow occurs; (three below top) D2 and (four below top) D3 are the second and third soil layer thicknesses, which affect the water available for transpiration and baseflow, respectively; (bottom) Dsmax is maximum baseflow velocity; and N–S efficiency is the Nash–Sutcliffe efficiency metric of Nash and Sutcliffe (1970).
Citation: Journal of Hydrometeorology 9, 6; 10.1175/2008JHM1001.1
Calibration and validation hydrographs for the eight river basins.
Citation: Journal of Hydrometeorology 9, 6; 10.1175/2008JHM1001.1
Long-term mean monthly hydrographs for the eight river basins.
Citation: Journal of Hydrometeorology 9, 6; 10.1175/2008JHM1001.1
The Cp for ESP hindcasts for (top to bottom) the eight river basins issued from 1 Dec to 1 Jun with forecast period lengths from 1 to 6 months for (a) calibrated forecasts, (b) uncalibrated forecasts, (c) uncalibrated BC forecasts, and (d) the difference between calibrated and uncalibrated BC forecasts. Note that in (d), gray boxes indicate forecast dates and forecast periods for which uncalibrated BC Cp exceeded calibrated.
Citation: Journal of Hydrometeorology 9, 6; 10.1175/2008JHM1001.1
The Cp for operational Apr–Jul streamflow forecasts Cp for the eight river basins issued from 1 Jan to 1 Jun for uncalibrated, BC (uncalibrated), and calibrated.
Citation: Journal of Hydrometeorology 9, 6; 10.1175/2008JHM1001.1
Scatterplots of ensemble means vs observations for (a) uncalibrated ESP forecasts, (b) uncalibrated BC ESP forecasts, and (c) calibrated ESP forecasts for forecast period Apr–Jul starting from the first day of Jan–Jun vs observations for BLMSA.
Citation: Journal of Hydrometeorology 9, 6; 10.1175/2008JHM1001.1
The Cp for ESP hindcasts for the eight stations issued from 1 Dec to 1 Jun with forecast period lengths from 1 to 6 months for the difference between calibrated BC and uncalibrated BC. Gray boxes indicate forecast dates and forecast periods for which uncalibrated BC Cp exceeded BC calibrated.
Citation: Journal of Hydrometeorology 9, 6; 10.1175/2008JHM1001.1
Reliability plot for calibrated and uncalibrated BC Apr–Jul forecasts made 1 Jun for BLMSA showing maximum deviation of observed frequencies from the 1:1 line.
Citation: Journal of Hydrometeorology 9, 6; 10.1175/2008JHM1001.1
Histograms of maximum deviations estimated as in Fig. 10 for all eight sites.
Citation: Journal of Hydrometeorology 9, 6; 10.1175/2008JHM1001.1
Eight river basins and their characteristics. (Latitude and longitude for the location of stream gauge)
The range of six VIC model parameters used in automatic calibration.
The statistics of uncalibrated and calibrated (calibration and validation periods) monthly flows for the eight river basins.
Percentage of forecasts for lead times ranging from 0 to 6 months, for which calibrated Cp is higher than BC uncalibrated, by forecast date.
