Improving the accuracy of multimodel short-to-medium-range precipitation and streamflow forecasts over the Upper Bhima river basin, India

ABSTRACT Accurate precipitation forecasting with sufficient lead time is a prerequisite for developing a robust flood warning system (FWS), which is very challenging, particularly in developing countries like India. This study evaluates the utility of the TIGGE multimodel ensemble meteorological forecasts over the Upper Bhima River basin and investigated the hydrological utility of the TIGGE forecasts through a calibrated hydrological (VIC-RAPID) model followed by the post-processing of streamflow through Bayesian model average (BMA) approach. Results show that the quality of the meteorological forecasts of precipitation, and of the simulated streamflow, deteriorated with increasing lead time, which can be ameliorated with a suitable bias-correction technique. The BMA-based post-processing further improved the streamflow simulations, especially in case of extreme events, which highlighted its efficacy in flood forecasting. From the results of the study, it is recommended that a compound system of improved precipitation prediction, calibrated VIC-RAPID model and post-processing of streamflows in an integrated manner would facilitate a reliable FWS for operational purposes.


Introduction
Streamflow forecasting is an important aspect of water resources planning and management.While streamflow forecasts with longer lead times (e.g.ranging from weeks to months) are used for hydropower planning, allocation of irrigation water, drought analysis etc., short-to medium-range (e.g.ranging from hours to days) streamflow forecasts are generally used for flood warning purposes.Riverine flooding causes an annual average loss of US $104 billion globally, more than any other natural hazard (Blöschl et al. 2019).Furthermore, such damages from flooding are expected to increase in the future due to economic growth (Winsemius et al. 2016), population increase (Winsemius et al. 2016), land-use changes (Brath et al. 2006, Rogger et al. 2017, Recanatesi and Petroselli 2020) and a warming climate (Blöschl et al. 2019).
With the advancement of computational resources, processbased continuous hydrological models have gained huge popularity for streamflow and flood estimation applications.For example, Beven (1987) used a semi-distributed continuous hydrological model, namely TOPMODEL (a topography-based hydrological model), along with a stochastic rainfall generator to estimate the 100-year design flood (Beven 1987).Viviroli et al. (2009) applied a process-based distributed hydrological model, namely the Precipitation-Runoff-EVApotranspiration-HRU related model (PREVAH), for flood flow estimation in several gauged and ungauged watersheds in Switzerland.Campbell et al. (2018) used the Soil And Water Assessment Tool (SWAT) model for streamflow estimation in the Pawtuxet River basin, USA, and subsequently analysed the effect of urbanization on flood magnitudes.Grimaldi et al. (2021) applied a continuous hydrological model, namely the COntinuous Simulation Model for Small Ungauged Basins (COSMO4SUB), to an ungauged basin in Belgium and found that the continuous hydrological modelling approach was more suitable for flood modelling, as compared to event-based hydrological modelling, due to the improved design hydrograph estimation in the continuous modelling approach.In the last three decades, many other hydrological models and their modified variants have been developed for improved hydrological simulation.
The variable infiltration capacity model (VIC) by Liang et al. (1994) is one such model that has become increasingly popular in an enormous number of hydrological applications globally (Liu et al. 2017, Nandi andReddy 2020a).It is a process-based macroscale hydrological model which has been applied at spatial scales ranging from 1/16° to several degrees.It can calculate both the water and energy balance at daily or sub-daily time steps for each modelling grid.The VIC model considers sub-grid variation for infiltration capacity, elevation bands, and vegetation classes, making it more suitable for sub-grid heterogeneity representation than other gridbased hydrological models (Liang et al. 1994).It has also shown its potential for streamflow and flood forecasting applications in basin-scale to global-scale hydrological studies.For example, Wu et al. (2014) successfully applied the VIC model for real-time hourly flood estimation globally.Nanda et al. (2019) demonstrated that the VIC model forced with meteorological forecasts from the European Centre for Medium-Range Weather Forecasts (ECMWF) was able to offer satisfactory streamflow forecasts at up to seven days' lead time.Nandi and Reddy (2022a) demonstrated successful integration of the VIC model with the Routing Application for Parallel computation of Discharge (RAPID) river routing model and LISFLOOD Flood-Plain (LISFLOOD-FP) hydrodynamic model for high-resolution streamflow and flood inundation modelling.Nevertheless, like other hydrological models, the VIC model also has a few parameters that cannot be directly measured in the field, and reliable simulation from the model cannot be expected unless these parameters are properly adapted for the study area in question.Automatic calibration of the model using a global optimization algorithm can alleviate this problem by finding the optimal value of the unknown model parameters, thereby enabling the model to deliver more dependable hydrological predictions.
The most common way of producing streamflow forecasts is forcing a well-calibrated hydrological model with meteorological forecasts with the desired lead time.However, producing an accurate meteorological forecast with sufficient lead time is considered to be one of the most challenging tasks in hydrometeorological research.With their increased computational capabilities and improved representation of physical processes, numerical weather prediction (NWP) models have shown potential to produce meteorological forecasts with acceptable accuracy (Yamaguchi andMajumdar 2010, Keller et al. 2011).Among the different meteorological variables, precipitation is the one variable that is most difficult to predict from NWP models (Cuo et al. 2011).The main reason for this is the discontinuous nature of precipitation and its high spatiotemporal variability.But recent studies suggest that with the current advancement in NWP models, it is possible to achieve quality precipitation forecasts from NWP models that can be used for operational streamflow forecasting applications (Khan et al. 2015, Aminyavari andSaghafian 2019).
In 2005, the World Meteorological Organization (WMO) launched a research programme, i.e. the THe Observing-system Research and Predictability EXperiment (THORPEX) Interactive Grand Global Ensemble (TIGGE), with the objective of providing accurate numerical weather forecasts with lead times from one day to two weeks (Buizza 2014).TIGGE is an archive of ensemble forecasts of different models from 10 global NWP centres.The TIGGE dataset has been utilized in numerous previous studies (Froude 2010, He et al. 2010, Keller et al. 2011) for improved meteorological and hydrological forecasting purposes.It is important to note that the performance of different models from TIGGE may vary according to the geographical location; thus, they must be evaluated prior to their respective applications.Consideration of the TIGGE multi-model ensemble can be useful for alleviating such problems.Moreover, the multi-model approach can also capture uncertainties, which is not possible using a deterministic/single NWP model.Therefore, the use of TIGGE multi-model NWP meteorological forecasts with a capable physically-based hydrological model can be useful for streamflow and flood forecasting applications.
As mentioned, precipitation forecasting from NWPs is challenging due to their regional biases.Correcting such biases in the NWP precipitation forecasts is necessary to facilitate better streamflow forecasts (Yang et al. 2020).There are numerous techniques for bias correction, and each has its own advantages and limitations.Spatio-temporal bias correction (STB), power transformation (PT), and quantile mapping (QM) bias correction are examples of popular bias-correction techniques (Yuan et al. 2015, Crochemore et al. 2016).STB is a linear bias-correction approach capable of correcting the mean values of the forecast using the difference between the observed and forecast values.The PT method is a non-linear bias-correction approach, whereas the QM method matches the statistical distribution of the forecast data to that of observed data.Crochemore et al. (2016), in their study over France, demonstrated that the linear and distribution-based bias-correction methods are capable of improving the accuracy and reliability of ECMWF precipitation forecasts, thereby improving their subsequent use in streamflow forecasting.Ratri et al. (2021) reported the QM method was essential for the reliable use of ECMWF seasonal precipitation forecasts in economic and agricultural applications.Nevertheless, applications of bias-correction techniques to reduce precipitation bias must be thoroughly investigated before their use in hydrological models, as they might cause additional uncertainty in streamflow simulation (Lafon et al. 2013).
The streamflow simulations from hydrological models may also suffer from systematic errors due to complex catchment characteristics, assumptions/simplifications in model structure, the model's inability to incorporate the anthropogenic influence on hydrological processes, etc.The possible causes of uncertainty in hydrological model simulations have been explored in previous studies (Yang et al. 2008, Setegn et al. 2010).Streamflow post-processing is carried out to remove the systematic errors in simulated flows, thereby improving the accuracy of flood forecasting.Bayesian moving average (BMA) is an effective method of streamflow post-processing; however, its potency must be evaluated.Given the fact that precise and timely streamflow forecasts are a cornerstone for an operational flood forecasting system, the use of BMA-based post-pro cessing on the outputs of a calibrated VIC model can certainly be useful.
Despite the fact that multiple studies have been conducted to evaluate the performance of global precipitation forecasts from NWP models, there appears to be a lack of studies on the analysis of NWP precipitation forecasts for streamflow forecasting in the monsoon-dominated flood-prone countries in general, and India in particular.It is pertinent to mention that flood management over the Indian region is critical due to the highly seasonal rainfall and huge population, which increases the vulnerability to floods.Further, during the monsoon season, the chance of an extreme event is very high, which necessitates a robust streamflow forecasting system.Furthermore, few studies have utilized TIGGE (NWP) forecasts in a hydrological modelling framework over the Indian region.Moreover, streamflow post-processing using the BMA technique is not explored in detail for streamflow forecasting.
With this in mind, this study aims to improve the use of global NWP forecasts in streamflow forecasting in monsoondominated Indian regions through bias correction of NWP rainfall forecasts and post-processing of streamflow forecasts.The Upper Bhima River basin (UBRB), located in the midwest of India, is an agriculture-dominated part of the state of Maharashtra, which has undergone several floods and other hydrometeorological hazards (Menon and Bhatt 2005).An accurate streamflow forecast system for the area would be highly beneficial for planning and management of water resources.However, no past studies in the basin have analysed the suitability of multiple global NWP models for streamflow forecasting applications.Considering the above gaps, the specific objectives of the study are: (1) to evaluate different types of TIGGE global models for their accuracy in precipitation forecasting, (2) to carry out bias correction of TIGGE model outputs with widely used techniques and assess their performance, and (3) to apply the calibrated VIC-RAPID model for streamflow simulation, and BMA for post-processing of streamflow, to improve the operational efficacy of the streamflow forecasts.The compound system of improved precipitation prediction, calibrated VIC-RAPID model and post-pro cessing of streamflow in an integrated manner would facilitate developing a reliable streamflow system for operational purposes, which is the explicit novelty of this study.
The remaining sections of the paper are organized as follows: The descriptions of the study area, data used, and methodology adopted in this study are presented in the next sections.Then, the results obtained from the study and their implications are discussed in detail in the subsequent sections.Finally, a summary of the entire study, along with the key conclusions derived, is presented in the last section.

Study area
The UBRB was selected as the study area.The location of the basin is presented in Fig. 1.The basin spatially extends from latitude 16°51′06″ to 19°25′39″N and longitude 73°18′09″ to 76°06′36″E, covering an area of ∼48 900 km 2 .The UBRB lies in the western part of India and has a tropical semi-arid climate.The average annual rainfall over UBRB is 697 mm, the majority of which is received during the southwest monsoon (i.e.June-September) season.The mean temperature ranges from 11-16°C in winter to 38-40°C in summer.The basin is characterized by a diverse topography with flat terrain over major portions and the undulating/hilly terrain of the Western Ghats in the upper portions.There is a decreasing topographic gradient from northwest to southeast, and the elevation ranges from 143 to 832 m.a.s.l.(Fig. 1).The soil type is mostly vertisols, whereas the land use/land cover is dominated by agricultural land, with paddy, cotton, sugarcane and jowar as the major crops.

Data used
This study utilizes the control precipitation forecast datasets from the TIGGE archive, which is publicly available to the scientific community.TIGGE contains forecast datasets from multiple centres around the globe, among which data from seven centres (hereafter called models) are selected for this study.The seven selected models are CMA, CPTEC, ECCC, ECMWF, KMA, NCEP, and UKMO.A description of each model, including its core numerical weather prediction model and data assimilation system, is given in Table 1.The CMA model uses the Global and Regional Assimilation and Prediction System (GRAPES) system, while the CPTEC model is based on the Brazilian Global Atmospheric Model (BAM).The ECCC model uses the Global Environmental Multiscale Model (GEM), and the ECMWF model is based on the Integrated Forecasting System (IFS).The KMA and UKMO models both utilize the Unified Model (UM), with different configurations.The NCEP model relies on the Global Forecast System (GFS).These models employ various data assimilation techniques, such as three dimensional variational assimilation (3DVAR) and four dimensional variational assimilation (4DVAR), to improve their forecasts.The quantitative precipitation forecasts (QPF) from these models were collected for 2010-2016 with lead times up to seven days.The cumulative precipitation forecasts are converted into daily incremental forecasts before their application in this study.The wind speed, minimum temperature, and maximum temperature datasets are also collected from the TIGGE archive for the seven models to operate the hydrological models for streamflow forecasting.
This study uses a daily gauge-based gridded rainfall dataset from the India Meteorological Department (IMD) available at 0.25° × 0.25° spatial resolution.This gridded dataset is constructed with data from 6955 raingauges across the country using an inverse distance weighting (IDW) interpolation scheme (Pai et al. 2015).Evaluation and bias correction of TIGGE precipitation forecasts is carried out using this IMD gridded rainfall dataset.Before performing this evaluation, all the TIGGE datasets are resampled to 0.25° × 0.25° resolution to match the spatial scale of the IMD gridded precipitation data.The observed gridded minimum and maximum temperature datasets (1° × 1°, daily) are also collected from IMD. Wind speed data is taken from the US National Centers for Environmental Prediction (NCEP) reanalysis archive, which is available at 2.5° × 2.5° resolution.Soil, land use/land cover (LULC), and topographical information are also required for the operation of the VIC-RAPID hydrological model.The soil data (1 km × 1 km) and LULC data (1 km × 1 km) are obtained from the Food and Agricultural Organization of the United Nations (FAO)'s Harmonized World Soil Database and the US National Aeronautics and Space Administration (NASA)'s Moderate Resolution Imaging Spectroradiometer (MODIS) land cover database, respectively.A 90 m Shuttle Radar Topography Mission (SRTM) digital elevation model (DEM) is used in this study for the operation of the VIC-RAPID model.Moreover, the hydrological model requires river network information to route the flow generated from the individual model grid, which is prepared with the HydroRIVERS database (https://www.hydrosheds.org).The naturalized flow data at the basin outlet is collected from the Global Reach-scale A priori Discharge Estimates for SWOT (GRADES) database (Lin et al. 2019).

Methodology
A schematic outline of the methodology followed in the present study is shown in Fig. 2. First, the daily forecasts of meteorological variables (precipitation, wind speed, minimum temperature, and maximum temperature) at lead times of up to seven days from seven TIGGE models are collected.As precipitation is considered the most complex meteorological variable to forecast and is the key input for streamflow estimation, bias correction is performed only for the precipitation (Tiwari et al. 2021).Three techniques are employed for this bias-correction step.Next, raw and bias-corrected TIGGE precipitation forecasts are evaluated using various deterministic and probabilistic measures.Both the raw and bias-corrected TIGGE forcing are then used with the VIC-RAPID hydrological model to generate streamflow forecasts.However, the VIC-RAPID model is calibrated over the study area against the observed datasets before its use for streamflow forecasting from TIGGE forcing.The verification of forecasted streamflow is carried out similarly to that of precipitation.Statistical post-processing of the simulated streamflow forecasts is performed using the BMA approach and we assess the relative improvement in streamflow forecasting.

Bias correction of precipitation forecasts
Three popular bias-correction techniques, viz.spatio-temporal bias correction (STB), power transformation (PT) and quantile mapping (QM), are investigated for their comparative performance in bias correction of the TIGGE precipitation forecasts.The STB (Tesfagiorgis et al. 2011) computes a multiplicative bias-correction factor (BF), which is multiplied with the raw precipitation forecast.BF is computed as follows: where P F and P G are the forecasted and observed precipitation, respectively; i is the location of the grid; t is Julian day number; df and dp are the day number for forecasted and observed precipitation; and l is a time window for bias correction.
The PT method (Vernimmen et al. 2012) is chosen as the second precipitation bias-correction method in this study.In this method, an exponential bias correction is applied to the raw precipitation forecast, as given below: where P F * is the corrected precipitation forecast; P F is the raw precipitation forecast; and b and a are the factors used to match the standard deviation and mean of the forecasted precipitation to those of the observed precipitation.
QM (Themeßl et al. 2012) is the third bias-correction method used in this study.It has been applied for bias correction of precipitation forecasts in many earlier studies (Verkade  Tiwari et al. 2021).The raw precipitation forecasts are corrected using a transformation function in the QM method.This transformation function is prepared by estimating an empirical cumulative distribution function between the forecasted and observed precipitation values.The QM bias correction of raw precipitation forecast can be expressed as: where P F * is the corrected precipitation forecast; P F is the raw precipitation forecast; F À 1 G is the inverse of the empirical cumulative distribution function of observed precipitation; and F P is the empirical cumulative distribution function of raw precipitation forecast.

Hydrological modelling
A three-layer VIC model (Liang et al. 1994) is employed to perform the rainfall-runoff modelling in this study.It can calculate both the water and energy balance at daily or subdaily time steps for each modelling grid.It uses grid-level meteorological, topographical, soil, and land-cover information to generate the runoff at the each modelling grid.The runoff generated at each VIC modelling grid needs to be routed separately.The vector-based routing application for parallel computation of discharge (RAPID) model (David et al. 2011) is used for routing such VIC-generated runoff across the basin.The combined VIC and RAPID model (hereafter called VIC-RAPID) is used to generate the streamflow forecasts in this study.The VIC-RAPID model has several parameters that need to be calibrated before its practical application.A total of 13 parameters are selected for the calibration of the model by following the feedback from past studies (Xie et al. 2007, Nandi andReddy 2022b).More details on these selected parameters are given in the Supplementary material (Table S1).Automatic calibration of the VIC-RAPID model is performed using a self-adaptive differential evolution algorithm (SaDE) after performing global sensitivity analysis of the selected model parameters using Sobol′'s method (Sobol′ 2001).The formulation of the SaDE algorithm and its linking with a hydrological model is based on Nandi and Reddy (2020b).The VIC-RAPID model is calibrated against the daily observed streamflow at the basin outlet using SaDE, with Nash-Sutcliffe efficiency (NSE) as the objective function.applied in many hydrological forecasting applications (Liu et al. 2017, Aminyavari and Saghafian 2019, Zhang et al. 2020, Hegdahl et al. 2021).In this study, the BMA is used to combine the streamflow generated from the seven TIGGE models into a single streamflow series.The complete formulation of the BMA can be found in Duan et al. (2007).For the sake of completeness, the BMA procedure is briefly described here.In BMA, the conditional posterior probability density function (PDF) of the desired variable (streamflow in this case) q bma is represented as:

Streamflow post-processing
where N and n are the total number of models and their index, respectively; q raw,n represents the raw streamflow from the n th TIGGE model; w n represents p q raw;n jq o À � the posterior probability of the q raw,n model using observed discharge q o ; and g n q bma jq raw;n À � is the conditional distribution of the q bma based on q raw,n .Assuming the q bma follows a Gaussian distribution, the conditional PDF, g n q bma jq raw;n À � , can be approximated by a linear function with mean and standard deviation of a n +b n .q raw,n and σ, respectively, where a k and b k are the regression coefficient.Following Raftery et al. (2005), the posterior mean and standard deviation of the q bma can be calculated as: The BMA posterior mean calculated using Equation ( 5) is deterministic in nature and can be compared with the ensemble mean or the individual models.In this study, the BMA technique is implemented using the BAS package in the R programming environment (Clyde et al. 2011).

Verification measures
Different deterministic and probabilistic performance measures are used for the comprehensive evaluation of the precipitation and streamflow forecasts from the TIGGE models.The description and formulation of these measures are given in Table 2.The deterministic forecast evaluation is carried out using percentage bias (PBIAS), coefficient of correlation (CC), root mean squared error (RMSE), Brier skill score (BSS) and continuous ranked probability skill score (CRPSS) are selected for verifying the probabilistic forecasts.The TIGGE rainfall forecasts are evaluated at four lead times (1, 3, 5, and 7 days) against IMD gridded rainfall data using PBIAS, CC, and RMSE.This evaluation is implemented for both raw TIGGE precipitation (hereafter called TIGGE-RAW) and biascorrected TIGGE precipitation forecast (TIGGE-BC) datasets.Further, each TIGGE model is associated with three different bias-corrected precipitation forecasts coming from three different bias-correction techniques.Probabilistic verification of raw and bias-corrected TIGGE precipitation forecast is made using BSS and CRPSS.Computation of BSS requires defining a threshold to convert numerical rainfall forecast series into a binary series of rain/no-rain events.Three different precipitation thresholds are chosen from IMD to evaluate three different precipitation categories.The precipitation threshold of 2.49, 7.6 and 35.6 mm/day is selected for evaluation of BSS for light, moderate, and heavy precipitation events, respectively.
After evaluating the precipitation forecast, the streamflow forecast is verified by driving the VIC-RAPID with the raw and biascorrected precipitation forecast along with other meteorological forecasts (minimum temperature, maximum temperature and wind speed) from the seven TIGGE models.Deterministic evaluation of streamflow forecasting is carried out using PBIAS, CC and NSE.Similar to precipitation forecast verification, the probabilistic evaluation of streamflow forecasting is carried out using BSS and CRPSS.Next, the improvement of the post-processed streamflow Inclination of forecast to be smaller or larger than the observation PBIAS ¼ 100 � Linear relationship between forecast and observation CC ¼ ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi Root mean squared error (RMSE) Standard deviation of the residual which represents difference between the forecast and observed values RMSE ¼ ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi s 0/large positive number Nash-Sutcliffe efficiency (NSE) Normalized value indicating residual variance as compared to observation variance NSE ¼ 1 À ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi Brier skill score (BSS) Skill score indicating quality of forecast for binary events associated with a threshold Continuous ranked probability skill score (CRPSS) Skill score indicating quality of forecast by comparing the cumulative density function (CDF) of forecast and observation data forecasts (hereafter called TIGGE-BC-PP) is compared against the raw streamflow forecast from TIGGE-BC using similar deterministic and probabilistic performance measures.This verification of the BMA post-processed streamflow forecast is made with the "leave one year out" approach, where the data for all the years except one was used for the post-processing (Tiwari et al. 2021).Finally, a streamflow event corresponding to an extreme precipitation event during 2010-2016 is considered for forecast verification of extreme events over the study area.

Evaluation of the forecast skill of the TIGGE rainfall estimates
In this work, the TIGGE multimodel ensemble precipitation forecast datasets are bias-corrected using three popular biascorrection methods, and their results are compared to identify the most suitable TIGGE model and bias-correction method.
The comparison is carried out between the raw and biascorrected TIGGE models (for seven models) for lead times of 1, 3, 5 and 7 days during 2010-2016.
The deterministic performance evaluation of TIGGE datasets is carried out using PBIAS, CC, and RMSE, and the results are presented in Fig. 3. Figure 3(a) shows that the raw precipitation estimates from all the models (except UKMO) have a large negative bias (overestimation).It is also noted that such biases in the precipitation forecasts increase with increasing lead times for some models (CMA, ECMWF, and KMA) and decrease with longer lead times for the other models (CPTEC, ECC, NCEP, and UKMO).It is also interesting to note that different models perform better at different lead times, i.e.CMA performs better at a one-day lead time and UKMO performs better at a sevenday lead time.Such variation among the model performance encourages the application of the multimodel ensemble precipitation forecasting approaches.Among the three selected biascorrection techniques, PT and QM are able to reduce the biases significantly in all seven models at all lead times.shows the CC statistics for the raw and biascorrected precipitation estimates from the seven TIGGE models for the whole study area.The CC values for the TIGGE models are relatively low, and their improvement after bias correction is not as significant as in the case of PBIAS.Unlike PBIAS, the CC values for all seven models deteriorate consistently as the lead time increases.Considering raw CC skills for the TIGGE models, UKMO performs better at shorter lead times (1-3 days), and ECMWF performs better at longer lead times (5-7 days).However, the ECMWF performs better at all lead times after the bias correction.Among the three bias-corr ection methods, only PT consistently improves the CC values of the TIGGE-RAW precipitation forecasts from all seven models.
Figure 3(c) represents the RMSE statistics for the TIGGE-RAW and TIGGE-BC forecasts from the seven models.Like CC, the RMSE score also deteriorates as the lead time increases, with few exceptions.The RMSE scores from the TIGGE-RAW precipitation forecasts are relatively high (> 6 mm/day).The UKMO model exhibited better RMSE skills than the other models at all lead times for the raw precipitation forecasts.However, the ECMWF showed marginally better RMSE skills after the bias correction.Further, the PT method again performed better among the three selected biascorrection methods and improved the RMSE values by 15-20% for different TIGGE models.
In this work, the probabilistic evaluation of the TIGGE ensemble precipitation forecast from the seven models is carried out using BSS and CRPSS.Figure 4(a-c) represents the BSS statistic of the TIGGE-RAW and TIGGE-BC ensemble precipitation forecast over all the grids in the study area for light, moderate, and heavy rain at different lead times.The BSS values for the TIGGE-RAW forecast are generally less than zero, indicating the TIGGE-RAW forecast has less skill than the climatology for the study area.The BSS performance is marginally improved with a larger threshold, especially for shorter lead times, indicating better performance in heavier rainfall events.
Figure 4 also clearly shows a significant improvement in the BSS values for all the TIGGE-BC forecasts.All three bias-corr ection methods have produced positive BSS values at different thresholds for all the lead times.For light rain (i.e.considering a threshold of 2.49 mm), the mean BSS value over the study area from the TIGGE-RAW forecast at a one-day lead time is −0.16, which is improved to 0.09, 0.13, and 0.08 by the STB, PT, and QM methods, respectively.The PT method achieves noticeably higher BSS skills than the STB and QM methods at all lead times, especially for the shorter rainfall thresholds, indicating it is a more suitable bias-correction technique for the study area.One important observation from Fig. 4 is that the relative improvements with the different bias-correction methods for the BSS performance decrease with higher rainfall thresholds.For example, for a one-day lead time, the improvements in BSS skill with the PT method are rainfall thresholds of 0.29, 0.12, and 0.04 for 2.49, 7.6, and 35.6 mm, respectively.Similar outcomes can also be observed for the longer lead times.Also, the difference in performance between the three bias-correction methods decreases with increasing thresholds.Looking at the spread of the box plots in Fig. 4(a-c), it can also be comprehended that the spatial variation in the BSS values over the study area decreases after applying the bias-correction methods.For example, for a one-day lead time, the BSS values from the raw forecast are positive for a few grids and negative for the others.In contrast, the BSS values are consistently positive and homogeneous for all the grids in the study area from all the bias-corrected forecasts.
Figure 4(d) shows the CRPSS values of the raw and biascorrected TIGGE precipitation forecasts at different lead times for the 79 grids covering the study area.The increasing or decreasing pattern of CRPSS at different lead times is found to be similar to that of BSS.However, unlike the BSS, the CRPSS for the TIGGE-RAW precipitation forecasts is better than the climatology, as indicated by the positive CRPSS values for all the grids.Overall, both the raw and bias-corrected TIGGE precipitation forecasts show a decreasing CRPSS with a higher lead time.All the bias-correction methods have shown a noticeable improvement over the TIGGE-RAW forecasts at one day lead time.The QM method performed better than the STB and PT methods for other lead times (3, 5, and 7 days).

Calibration and validation of the VIC-RAPID model
The variance-based Sobol′ global sensitivity analysis technique is employed to identify the sensitive parameters of the model by computing the first-order (S i ) and total-order sensitivity (S Ti ) indices (Sobol′ 2001).Table 3 shows the results of the Sobol′ sensitivity analysis, which clearly indicates the eight (nine) important parameters of the VIC-RAPID model according to the Sobol′ S i (S Ti ) indices.After sensitivity analysis, the daily calibration of the VIC-RAPID model is performed for seven years (2010)(2011)(2012)(2013)(2014)(2015)(2016), among which the first four years are used for calibration and the remainder for validation.The SaDE-based calibrated parameter values of the VIC-RAPID model are presented in the Supplementary material (Table S2).Three evaluation measures, namely NSE, CC, and PBIAS, are considered to assess the calibration of the VIC models.
Figure 5 compares the simulated streamflow from the VIC-RAPID model with observed streamflow at the basin outlet.It can be noted that the pattern of the simulated flows matches well with the observation.The mean daily streamflow values during 2010-2016 are 340 and 395 m 3 /s for observation and model simulation, respectively.This points towards the slight overestimation of simulated streamflows by the VIC-RAPID model.This can also be  noted from the overprediction of low flows in Fig. 5.The NSE, CC, and PBIAS values are estimated as 0.68, 0.85, and −24.12, respectively, for the calibration period, whereas for the validation period, they are found to be 0.73, 0.86, and 3.6, respectively.Overall, the streamflow simulations from the VIC-RAPID model can be considered satisfactory (Moriasi et al. 2015); therefore, they can be further used to generate the TIGGE-driven streamflow forecasts over the study area.

Assessment of streamflow forecast skill
This subsection presents the verification of the streamflow simulation from the VIC-RAPID model forced with TIGGE-RAW and TIGGE-BC forecast datasets.Here, instead of considering all three bias-correction methods, only the PT method (bias-corrected TIGGE precipitation forecasts) is considered to perform the streamflow simulations.This is mainly due to the better overall performance of the PT than the other two biascorrection methods, which is reflected in its better score for the various deterministic and probabilistic performance measures.
The VIC-RAPID model simulations are performed with the TIIGE-RAW and TIGGE-BC (using PT bias-correction) forecasts from seven models for 2010-2016.The configuration of the VIC-RAPID model is obtained from the calibration of the model with the observed forcing as discussed earlier.
Figure 6 shows the deterministic evaluation of the VIC-RAPID simulations from the TIGGE-RAW and TIGGE-BC forecasts at four different lead times using PBIAS, CC, and NSE.The PBIAS is used for analysing the under-or overestimation of the simulated streamflows and is shown in Fig. 6(a).Daily streamflow simulation with the VIC-RAPID model by inputting TIGGE-RAW precipitation forecasts tends to overestimate, which can be seen from the multiple negative values in Fig. 6(a).The PBIAS skill generally deteriorates (i.e. the value increases) with increasing lead times.However, such an increase in PBIAS score with increasing lead times is more significant for the TIGGE-RAW-than the TIGGE-BC-based simulated streamflows.The application of bias correction for the TIGGE meteorological forecast has been clearly reflected in the streamflow simulations.For example, the PBIAS for the raw CPTEC forced streamflow forecast at a lead time of seven days is reduced to almost one-fifth after applying the bias correction.Among the seven models, the UKMO meteorological forecast forced simulation generally performs better considering the PBIAS score for all lead times for both raw and bias-corrected cases.However, it is closely followed by the bias-corrected CMA, and by the ECMWF meteorological forecast forced VIC-RAPID flow simulations.
The CC values of the streamflow simulation obtained from TIGGE-RAW-and TIGGE-BC-based model forecasts are presented in Fig. 6(b).A high correlation (>0.8) between observed and simulated runoff is found at the one-day lead time even with VIC-RAPID simulation from TIGGE-RAW forecasts.Overall, the CC values for the simulated flows from TIGGE-RAW and TIGGE-BC forecasts decrease with increasing lead times.This is consistent with the variation of the CC skill in the TIGGE-RAW precipitation forecasts (Fig. 6(b)).It is also clear from Fig. 6(b) that bias correction of TIGGE-RAW precipitation forecasts helps to improve the CC values of the corresponding streamflow forecasts.Moreover, such improvement in the CC values increases with increasing lead times.For example, the improvement in CC from the raw to biascorrected UKMO model is 0.08 at a one-day lead time and 0.24 at a seven-day lead time.Unlike PBIAS, no single TIGGE model performs better at all lead times considering the raw forecasts.However, after the bias correction, the ECMWF model consistently produces better CC values at all lead times.
Figure 6(c) shows the NSE score of the streamflow simulation obtained using the VIC-RAPID model forced with TIGGE-RAW and TIGGE-BC meteorological forecasts at four lead times.It can be seen that as the lead time increases, the overall accuracy of the daily streamflow forecast declines.The NSE of simulated streamflow from the TIGGE-RAW precipitation inputs is found to be low (0.25) even at the one-day lead time and showed no skill (<0) at the seven-day lead time.However, the streamflow simulation from the TIGGE-BC forcing of the VIC-RAPID model has improved the NSE scores at all lead times.For example, the NSE values of streamflow forecast obtained using the VIC-RAPID model from the bias-corrected KMA precipitation input enhanced from −1.38 to 0.53 and −8.34 to 0.37 for one-day and sevenday lead times, respectively.The individual model performance in Fig. 6(c) shows that the best (or worst) performing model is different at different lead times.The choice of the best-performing model also changes from raw to biascorrected TIGGE forecasts.
To analyse the performance of ensemble streamflow simulations obtained using VIC-RAPID by inputting TIGGE-RAW and TIGGE-BC, the BSS and CRPSS are computed from the observed and ensemble simulated streamflows at the basin outlet for 2010-2016.Figure 7(a-c) shows the BSS of ensemble streamflow simulation by the TIGGE-RAW and TIGGE-BC models.The BSS values are estimated for three streamflow categories (low flow, medium flow, and high flow) at four lead times (1, 3, 5, and 7 days).The three flow categories, viz.low, medium, and high flow, are defined on the <25%, 25-75%, and >75% quantiles, respectively, of observed streamflow during 2010-2016 to show streamflow simulation at different magnitudes.For low flow, the BSS values for the ensemble streamflows obtained using TIGGE-RAW precipitation forecasts are not skilful (<0) at any lead time.Similar unskilful performance of streamflow forecast obtained using TIGGE-RAW precipitation forecast can also be seen for the medium flows.The BSS values for high flows were skilful and did not improve much after the bias correction.However, the ensemble streamflow obtained using the TIGGE-BC precipitation forecasts showed a noticeable improvement in BSS values for low and medium flows.For example, the BSS values of ensemble streamflow from TIGGE-RAW forecasts are −0.43 and −0.23 for one-and seven-day lead times, which are improved to 0.48 and 0.54 in case of TIGGE-BC precipitation forecasts.Overall, the BSS values improved in all flow classes of streamflow forecasts obtained with inputs of the TIGGE-BC as compared to TIGGE-RAW forecasts.
The CRPSS values of the ensemble streamflow forecasts obtained with input of TIGGE-RAW and TIGGE-BC precipitation forecasts are shown in Fig. 7(d).Unlike BSS, the CRPSS values are skilful (>0) for the raw forecast at all lead times.The CRPSS values at all lead times improved considerably for ensemble streamflow forecasts obtained with inputs of the TIGGE-BC precipitation forecasts.For example, a 46% improvement in CRPSS is achieved for ensemble streamflow simulation at a one-day lead time with the input of TIGGE-BC forecasts.Figure 7(d) also shows that the accuracy of CRPSS for ensemble streamflow simulation decreases with increasing lead times.This may be due to decreasing accuracy of the precipitation forecast at higher lead times (Fig. 3).

Verification of the post-processed streamflow forecasts
This subsection presents the analysis of post-processing of the ensemble streamflow generated from the TIGGE forecasts.As earlier results have confirmed the better performance of TIGGE-BC for streamflow simulation, the post-processing of the streamflow experiment is carried out only for streamflow generated by TIGGE-BC (referred to as TIGGE-BC-PP).The streamflow from TIGGE-BC and TIGGE-BC-PP are compared using both statistical and deterministic performance measures as employed earlier.As the leave-one-year-out approach is utilized for performing the BMA-based post-processing of streamflow, only the last year ( 2016) is used to verify the effect of streamflow post-processing in the current study.Moreover, as discussed earlier, the BMA-derived discharge can be compared with the streamflow from the simple ensemble mean or the individual models.Since the verification results of individual models were shown earlier, the analysis of BMA post-processed streamflow is presented together with the TIGGE-BC ensemble mean streamflow in this section.However, these results can be directly compared with the results of the individual models shown in Fig. 6, which enables a comparison of TIGGE-BC-PP with streamflow from individual TIGGE-BC models.
Figure 8 shows the deterministic analysis of the streamflow simulation from TIGGE-BC and TIGGE-BC-PP using PBIAS, CC, and NSE.It can be seen from Fig. 8(a) that PBIAS from TIGGE-BC is quite high at all lead times.Also, the PBIAS values are always positive for TIGGE-BC, indicating underestimation of the actual streamflow.However, the TIGGE-BC-PP streamflows showed great skill in reducing such large overestimations as compared to the TIGGE-BC streamflows.On average, an 80% reduction in the PBIAS values is observed from TIGGE-BC -PP across all the lead times.The PBIAS values from TIGGE-BC -PP are also within the range of −10 to 10 at all lead times, indicating a very good skill for the post-processed streamflows (Moriasi et al. 2015).9(a-c).The BSS values are computed for three flow categories, namely at low, medium, and high flow (as defined in the previous subsection).For low and high flow, post-processing of streamflow exhibits notable improvement in BSS, and the degree of such improvement increases with progressing lead time.For example, the improvement of BSS is 0.10 at the one-day lead time, which increases to 0.31 at the seven-day lead time.Figure 9(d) shows the CRPSS of streamflow from TIGGE-BC and TIGGE-BC-PP.Similar to BSS, the postprocessing of streamflow notably improved the CRPSS, and the degree of improvement in CRPSS increases with increasing lead time.BMA-based post-processing of streamflow showed an overall improvement in the quality of the streamflow forecasts.

Verification of an extreme event
As the study area has experienced multiple floods during the monsoon season, the extreme flow simulations from TIGGE forecasting are evaluated.Due to the monsoon-driven precipitation in India, flooding is generally observed in the Indian river basins during the June-September season.A recent flooding report highlighted multiple flooding events over the study area for August and September (GOM 2020).Inspection of rainfall events during 2010-2016 revealed that one of the highest rainfall events over the study area occurred during the second half of August 2013.Therefore, this study analyses the performance of the ensemble streamflow simulation from mid-August to mid-September 2013.
Figure 10 shows the time series of observed BMA postprocessed streamflow (TIGGE-BC-PP) and ensemble streamflow from TIGGE-BC and TIGGE-RAW.At a oneday lead time, the ensemble mean streamflow from TIGGE-BC showed underestimation, while the TIGGE-RAW revealed a large overestimation.The NSE values of the ensemble mean streamflow from TIGGE-RAW and TIGGE-BC for one-day forecasts during the event are found to be −9.02 and −2.62, respectively, indicating their poor performance for reliable flood simulations.However, the streamflow forecasts from TIGGE-BC-PP at a one-day lead time showed a very good match with observations in Fig. 10(a).The NSE value of post-processed streamflow is found to be 0.83, indicating a skilful performance of TIGGE-BC-PP.The pattern of overestimation (underestimation) of TIGGE-RAW (TIGGE-BC) remained unchanged for other lead times.However, the performance of TIGGE-BC-PP deteriorated with increasing lead time.For example, the NSE of streamflow forecast from TIGGE-BC-PP goes down to 0.02 for the seven-day forecast as compared to an NSE of 0.83 for the one-day forecast.
The performance evaluation of the individual models' streamflow forecasts from TIGGE-RAW and TIGGE-BC (Supplementary material, Figure S1) showed marginally better performance of the UKMO model for both raw and biascorrected forecasts.An overall analysis of the extreme event shows that only the bias correction of TIGGE meteorological forecasts can improve the overall streamflow simulation, but it may not give satisfactory results for extreme events.Similar results for extreme event forecasting from NWP models were reported by earlier studies (Yang et al. 2020, Amini et al. 2021).However, post-processing of streamflow with bias-corrected TIGGE forecasts can alleviate such problems reasonably well.

Discussion
A reliable short-to medium-range precipitation forecasting system is essential for flood forecasting, reservoir operation, and other water resource applications.Precipitation forecasts from seven TIGGE models at lead times of up to seven days are analysed over the UBRB using different statistical forecast verification measures.From the comparative analysis of the TIGGE-RAW and TIGGE-BC models, it is noted that no single TIGGE model performed better for all performances measures at all lead times.However, overall, the UKMO and ECMWF models performed better, while CPTEC performed the worst among the seven considered models.
Compared to the TIGGE-RAW precipitation forecast, the accuracy and reliability of the TIGGE-BC forecasts were greatly increased.Precipitaion forecasts from all the TIGGE-BC models showed a significant improvement in verification measures, especially for PBIAS and RMSE.The probabilistic verification of TIGGE-BC ensemble precipitation forecasts showed improvements in terms of increasing BSS and CRPSS values.Therefore, the bias-correction of the TIGGE precipitation product is proven to be an effective approach for their further use in hydrological forecasting.The present study also evaluated multiple bias-correction techniques to compare their performance in removing systematic errors from TIGGE precipitation forecasts.Overall, the PT method performed better, closely followed by the QM method.
Upon forcing the precipitation forecasts from both TIGGE-RAW and TIGGE-BC models into the VIC-RAPID hydrological model for streamflow forecasting, the results showed a moderate skill of the TIGGE-RAW models as hydrological input.On the other hand, the TIGGE-BC precipitation forecasts showed the usefulness of bias-correction for the raw precipitation forecasts, especially at higher lead times (Fig. 6).Considering the streamflow forecast from TIGGE-RAW models, the UKMO (as in the case of raw precipitation forecast) performed comparatively better, followed by the ECMWF and CMA models.The NSE values of the streamflow forecasts from TIGGE-RAW models are generally very low (negative) at the seven-day lead time, which is improved to a great extent (>0.35) by all the TIGGE-BC models.Also, the application of post-processing of streamflow forecasts has improved the quality of the streamflow forecasts to a great extent.
The present study evaluated the performance of seven TIGGE models for only seven years of data (2010-2016) due to the limited consistent availability of all the required variables from all seven TIGGE models.However, an extended evaluation period would give more reliable estimates of performance from various TIGGE models.The comparison of the TIGGE models presented in this study cannot be directly associated with the performance of the TIGGE models in the other regions.This is mainly because the various TIGGE models perform differently for different geographical locations  (Froude 2010, He et al. 2010, Yamaguchi and Majumdar 2010, Keller et al. 2011).
It is also important to mention the other probable limitations associated with the methods, data, and the individual TIGGE models used in this study.The adopted methodology, while comprehensive, may have certain limitations that could affect the overall results and conclusions.First, the bias-correction techniques applied only to precipitation forecasts may not fully account for potential biases in other meteorological variables, such as wind speed and temperature, which can also influence streamflow simulations.Second, the use of a single hydrological model (VIC-RAPID) might not capture the full range of hydrological processes and uncertainties associated with different model structures and parameterizations.Third, the soil and LULC data obtained from the FAO and MODIS databases, both at 1 km × 1 km resolution, may not adequately represent the spatial variability of soil properties and land cover types, potentially impacting the performance of the VIC-RAPID hydrological model.Similarly, the naturalized flow data from the GRADES database may not fully account for human-induced alterations to the hydrological system, such as water withdrawals and reservoir operations.Finally, each TIGGE model has its own set of inherent limitations, which could affect the quality of the meteorological forecasts and the subsequent hydrological predictions.For example, CMA is known to have a limited ability to accurately predict convective precipitation (Zhang and Pan 2022); NCEP, UKMO, and CPTEC can significantly underpredict cyclonic precipitation (Froude 2010); KMA can produce low accuracy for heavy rain events as compared to all rainfall events (Kim et al. 2015); forecasts from ECMWF might be negatively impacted by the poor approximations of the terrain and local micro-climate in the model (Frnda et al. 2022); and the ECCC model produces inaccurate forecasts in steep orography (Husain et al. 2019).Despite these limitations, the current study provides valuable insights into the performance of TIGGE models for streamflow forecasting in the study area.The framework presented in this study can be followed for any region of the world to identify suitable TIGGE models for a specific area.Moreover, this study also contributes to improving short-to medium-range streamflow forecasting applications for better water resources planning and management.

Conclusions
The current study proposed an integrated approach for improved streamflow forecasting from TIGGE multimodel ensemble meteorological forecasts over the UBRB and evaluated its efficacy for different lead time forecasts of 1, 3, 5 and 7 days.To this end, first TIGGE-RAW and TIGGE-BC are verified to understand the effects of bias correction on the precipitation forecasts.Next, the effectiveness of the streamflow forecasts from the TIGGE models is evaluated in three distinct configurations, with (1) TIGGE-RAW, (2) TIGGE-BC, and (3) TIGGE-BC-PP.
The major conclusions of this study can be summarized as follows: (1) The TIGGE-RAW precipitation revealed low to moderate forecast skills.The PBIAS showed that all the TIGGE models overestimated the actual precipitation amount over the UBRB.Moreover, the quality of the forecasts deteriorated with increasing lead time.
(2) The bias correction considerably improved the quality of the precipitation forecasts over the UBRB.Moreover, the degree of deterioration with increasing lead time for the precipitation forecasts was ameliorated in the TIGGE-BC forecasts.Among three bias-correction techniques (i.e.STB, PT and QM), PT is found to be the best performing technique over the UBRB.The UKMO and ECMWF models performed marginally better than the other TIGGE models in precipitation forecasting.
(3) The streamflow forecasts from raw TIGGE models showed moderate skill at short lead times (one and three days) and an unskilful performance at longer lead times.Over-estimation of raw precipitation forecasts from the TIGGE models resulted in overestimation of the corresponding streamflow forecasts.However, the bias-corrected TIGGE models improved the overall quality of streamflow forecasts and increased the low NSE skill at higher lead times.Similar to precipitation forecasts, the quality of streamflow forecasts also deteriorated with increasing lead times.(4) The skills of post-processed streamflow forecasts increase significantly at all lead times after applying the BMA.Post-processing of streamflow is also found to be effective for extreme flow simulations, highlighting its efficacy in flood forecasting.

Figure 1 .
Figure 1.Location map of the study area.
Statistical post-processing of the VIC-RAPID simulated streamflow is carried out using the BMA technique.BMA was introduced byRaftery et al. (2005) and then successfully

Figure 2 .
Figure 2. Schematic diagram of the methodological framework used in the present study.

Figure 3 .
Figure 3. Heatmap showing precipitation forecast skill of the TIGGE-RAW and TIGGE-BC models at 1-, 3-, 5-and 7-day lead times in terms of (a) PBIAS, (b) CC, and (c) RMSE.The computation of these verification measures was performed for 2010-2016.In each sub-plot, the performance of the RAW and bias-corrected (STB, PT, and QM) TIGGE models are arranged alphabetically for each of the seven selected TIGGE models.

Figure
Figure3(b)  shows the CC statistics for the raw and biascorrected precipitation estimates from the seven TIGGE models for the whole study area.The CC values for the TIGGE models are relatively low, and their improvement after bias correction is not as significant as in the case of PBIAS.Unlike PBIAS, the CC values for all seven models deteriorate consistently as the lead time increases.Considering raw CC skills for the TIGGE models, UKMO performs better at shorter lead times (1-3 days), and ECMWF performs better at longer lead times (5-7 days).However, the ECMWF performs better at all lead times after the bias correction.Among the three bias-corr ection methods, only PT consistently improves the CC values of the TIGGE-RAW precipitation forecasts from all seven models.Figure3(c) represents the RMSE statistics for the TIGGE-RAW and TIGGE-BC forecasts from the seven models.Like CC, the RMSE score also deteriorates as the lead time increases, with few exceptions.The RMSE scores from the TIGGE-RAW precipitation forecasts are relatively high (> 6 mm/day).The UKMO model exhibited better RMSE skills than the other models at all lead times for the raw precipitation forecasts.However, the ECMWF showed marginally better RMSE skills after the bias correction.Further, the PT method

Figure 6 .
Figure 6.Heatmap showing forecast skill of the VIC-RAPID simulated streamflow by TIGGE-RAW and TIGGE-BC models at 1-, 3-, 5-and 7-day lead times in terms of (a) PBIAS, CC, and (c) NSE.The computation of the verification measures was performed for 2010-2016 at the basin outlet.In each sub-plot, the performance of the TIGGE-RAW and TIGGE-BC models are arranged alphabetically for each of the seven selected TIGGE models.
Figure 8(b) shows the CC values for the streamflow from TIGGE-BC and TIGGE-BC-PP.A high CC value (>0.8) can be seen for TIGGE-BC streamflows at all lead times.Post-pro cessing of streamflow marginally improved the high CC values of streamflow from the TIGGE-BC.The NSE scores of streamflow from TIGGE-BC and TIGGE-BC-PP are shown in Fig. 8 (c).The TIGGE-BC streamflows are associated with a moderate NSE skill (~0.4), whereas the TIGGE-BC-PP streamflows showed a significant improvement in the NSE score.For example, the NSE values from TIGGE-BC streamflows are 0.42, 0.46, 0.41, and 0.40 at 1-, 3-, 5-, and 7-day lead times, which are improved to 0.69, 0.68, 0.67 and 0.68, respectively, by the TIGGE-BC-PP streamflows.Moreover, TIGGE-BC-PP streamflows also performed better than the streamflow from any single model at all lead times, which can be realized by comparing the results of the BMA-post-processed streamflow in Fig. 8 with the streamflow simulation from the individual model in Fig. 6.

Figure 8 .
Figure 8. Bar plots showing (a) PBIAS, (b) CC, and (c) NSE of the BMA-based post-processed streamflow (TIGGE-BC-PP) and ensemble mean streamflow from TIGGE-BC models at the basin outlet for different lead times during 2016.

Figure 9
Figure9compares the probabilistic performance between raw and post-processed streamflow from bias-corrected TIGGE meteorological forecasts.The BSS values of TIGGE-BC and TIGGE-BC-PP are shown in Fig.9(a-c).The BSS values are computed for three flow categories, namely at low, medium, and high flow (as defined in the previous subsection).For low and high flow, post-processing of streamflow exhibits notable improvement in BSS, and the degree of such improvement increases with progressing lead time.For example, the improvement of BSS is 0.10 at the one-day lead time, which increases to 0.31 at the seven-day lead time.Figure9(d)shows the CRPSS of streamflow from TIGGE-BC and TIGGE-BC-PP.Similar to BSS, the postprocessing of streamflow notably improved the CRPSS, and the degree of improvement in CRPSS increases with increasing lead time.BMA-based post-processing of streamflow showed an overall improvement in the quality of the streamflow forecasts.

Figure 10 .
Figure 10.Hydrograph of observed and forecasted streamflow at (a) 1-day, (b) 3-day, (c) 5-day, and (d) 7-day lead times during an extreme rainfall event in 2013.Observed and BMA post-processed (TIGGE-BC-PP) streamflow are shown in black and green lines, respectively.The spread of the streamflow from TIGGE-RAW and TIGGE-BC models is shown in shades of red and blue, respectively, while their ensemble means are shown as solid red and blue lines.

Table 1 .
Details of the selected models (centres) from the TIGGE archives.

Table 2 .
Description, formulation and ideal score of the verification measures used in the study.

Table 3 .
First-order (S i ) and total-order sensitivity (S Ti ) values obtained using Sobol′'s sensitivity analysis for the VIC-RAPID model.