Forecast products were evaluated against observed data from the India Meteorological Department (IMD). We used the 0.25∘ daily gridded precipitation product from the IMD which was developed based on ground observations from 6995 stations across India using an inverse distance weighing scheme (Shepard, 1984) and is available for the period of 1901–2015 (Pai et al., 2015). The IMD precipitation captures the spatial variability of the monsoon season rainfall and features related to orographic rainfall in the Western Ghats and foothills of the Himalayas. We used 0.5∘ daily observed maximum and minimum temperatures from the IMD, which were developed based on 395 stations across India (Srivastava et al., 2009). The gridded air temperature dataset is available for 1951–2013 and has been used in many previous studies (Mishra et al., 2014; Shah and Mishra, 2015, 2014; R. D. Shah and Mishra, 2016; Mishra et al., 2016).

We evaluated prediction skill of precipitation, maximum and minimum temperatures from the CFSv2 reforecast (Saha et al., 2014), GEFSv2 reforecast (Hamill et al., 2013) and forecast products from IITM. Reforecast from the CFSv2 are based on a dynamical coupled model and are available at every 5th day from the start of year from the National Centre of Environmental Prediction (NCEP). Moreover, 6-hourly forecasts at every 5th day from CFSv2 are available with up to 9 months' lead time and at 1∘ resolution for 1982–2009. Climate forecast System (CFS) model's atmospheric component is operational at T126 spectral truncation (∼ 100 km horizontal resolution) and 64 sigma-pressure hybrid vertical resolution. Shukla and Lettenmaier (2011) using CFSv2 reported that initial hydrologic conditions dominate skill of hydrologic prediction in the continental US (CONUS) up to a 1-month lead time, beyond which skill from meteorological forcing dominated. McEvoy et al. (2016) recently demonstrated higher skill for potential evapotranspiration than precipitation using the CFSv2. Moreover, Yuan et al. (2011) reported that CFSv2 performs better than CFSv1 for prediction of precipitation and air temperature in the United States. Mo and Lettenmaier (2014) found that for shorter lead times (about 1 month), CFSv2 forecast has higher skill for soil moisture prediction than the benchmark forecast (climatological mean). Moreover, Tian et al. (2016) evaluated CFSv2 for the CONUS and found that extreme indices based on temperature were better predicted than that of precipitation.

Other than CFSv2, we compared precipitation and temperature forecast from GEFSv2 reforecast (Hamill et al., 2013), which is based on the Global Forecast System (GFS) model, for 7 and 15 days' lead time. Ensemble members are generated in GEFS by making perturbations in initial atmospheric conditions which lead to 11 ensemble members. The GEFS model runs at T254L42 resolution (∼ 40 km horizontal resolution) for the first 8 days' lead time and at T190 (∼ 54 km) for lead time beyond 7.5 days. The GEFS reforecasts are available at 1∘ resolution for lead times of up to 16 days and at 0.5∘ for an 8-day lead from 1985 to the present. R. D. Shah and Mishra (2016) evaluated the skill of GEFSv2 reforecast for drought prediction in India for an accumulation period of 7 days and found that the GEFS reforecast showed a correlation of more than 0.5 with drought estimates from the observed data.

We obtained four forecast products from the IITM. The forecast products of the IITM are generated from the same CFSv2 model that has been described above. Abhilash et al. (2014b) developed an ensemble prediction system using CFSv2 at T126 horizontal resolution (∼ 100 km) (hereafter: IITM-CFST126) for prediction of monsoon intraseasonal oscillations (MISOs) over the Indian monsoon region 15–20 days in advance. They found that though the skill was reasonable, there was a significant dry bias over the Indian land. Sharmila et al. (2013) reported that CFSv2 simulates the northward propagating MISO reasonably well, but it has a cold bias in sea-surface temperature (SST) and tropospheric temperatures. Thus, Abhilash et al. (2014a) implemented a lead-time-dependent SST bias correction, forced the GFS (atmospheric component of CFSv2) with slightly different physics and showed that it has improved skill over India compared to the CFSv2 (hereafter: IITM-GFST126). Subsequently, Sahai et al. (2015a) implemented a high-resolution version of CFSv2 (at T382 horizontal resolution ∼ 35 km; hereafter: IITM-CFST382) and showed that it has better skills in steep orographic regions. Although these three individual models show similar prediction skill and their errors saturate at about the same lead time of around 25 days, there are many instances where the three models disagree in predicting particular events, such as the amplitude and phase of MISO propagation. Considering these facts, Abhilash et al. (2015) proposed a CFS-based multimodel ensemble mean (MME), which improved the spread error relationship and added value to both the deterministic and probabilistic forecasts. Real-time skill for these models has been reported in the previous studies (Borah et al., 2015; Joseph et al., 2015a, b; Sahai et al., 2013, 2015b). Subsequently, bias corrected SST forced GFS was also run at T382 resolution (hereafter: IITM-GFST382). Thus the IITM's forecasts are available for four models, named IITM-CFST126, IITM-GFST126, IITM-CFST382, and IITM-GFST382. Model integrations for the years from 2001 to 2015 are carried out from 16 May and continued up to 28 September at every 5-day interval (16, 21, 26 May, …, 23, 28 September) for the next 45-day period. Forecast ensemble members from the IITM are available at 1∘ resolution. The ensemble mean of all four IITM products (hereafter: IITM ensemble) and individual products were compared with CFSv2 and GEFSv2 to evaluate the hydrologic prediction skill. The aim of this comparison was to evaluate whether IITM forecast products provide better prediction skill than CFSv2 and GEFSv2. Moreover, the product that provides the best hydrologic prediction skill in India can be used operationally to forecast hydrologic conditions and rainfall and temperature anomalies that can help in decision making in agricultural and water resources.

We used the ensemble mean (of all available ensemble members) of individual forecast products for evaluation. We selected forecasts at every 15th day, which was evaluated for the 7-, 15-, 30-, and 45-day accumulation periods using accumulated precipitation and average temperature. We use the term “accumulation period” instead of “lead time” as forecast evaluation was performed for accumulated precipitation and mean temperature for 7, 15, 30, and 45 days. We selected forecasts starting from 16 May till the end of September as currently the IITM provides forecast during the monsoon season. However, the IITM will extend forecast to the non-monsoon season in the near future. We aggregated all the observed and forecast variables (precipitation, maximum and minimum air temperatures) to the daily scale (if they were available at a sub-daily time period) and regridded to 0.25∘ horizontal resolution to make them consistent with the spatial resolution of observed data. We regridded precipitation and air temperature using Maurer et al. (2002), which uses the Synergraphic Mapping System (SYMAP) algorithm (Shepard, 1984) for precipitation and lapse rate based on elevation data for air temperature. We, however, carefully evaluated all the products at their original spatial resolution and at 0.25∘ to make sure that datasets are consistent at both resolutions for spatial and temporal variability. We found that the bias in the forecast products at coarser and higher resolution was consistent.

We considered a common period of 2001–2009 for comparison and evaluation of different forecast products against the observed gridded data from the IMD.

For evaluation of the forecast from each product against the observations, we prepared yearly time series of precipitation and temperature forecast for each forecast date by accumulating precipitation and averaging temperature for a given lead time (7–45 days). For instance, if the date of forecast was 1 June and the lead time 15 days, accumulated precipitation and mean temperature for 15 days from 1 June for each of the products were estimated for the period 2001–2009. As the period for evaluation was 2001–2009, the sample size was 10, and we acknowledge that a larger sample size with data for a longer retrospective record will help us to better categorize uncertainty in forecast skill. We used the coefficient of correlation, mean absolute error (MAE), and critical success index (CSI) to evaluate the performance of the forecast products. A non-parametric Spearman rank correlation coefficient (Wilks, 2006) was used to evaluate the performance of forecast products in capturing the temporal relationship with observations (OBS). For this the forecast product and the corresponding OBS are assigned ranks and then the correlation was estimated using the following Eq. (1): rs=1-6∑di2nn2-1, where rs is the Spearman rank correlation coefficient; di is the difference in rank between paired forecast and OBS; and n is the sample size (here 10). Significance of correlation was tested using the exact permutation distribution test (Robson, 2002). Observed samples were permuted and rank correlations were estimated. Estimated correlation is significant if it rejects the null hypothesis at the 5 % significance level.

The MAE was used to estimate error in the forecast products as compared to OBS. Absolute error was estimated in all the forecast products for each year as compared to OBS and then the mean of all the years was taken to estimate MAE. The critical success index (CSI; Wilks, 2006) was used to evaluate anomalies predicted using forecast products as compared to OBS, similar to (AghaKouchak and Mehran, 2013). The CSI is ratio of hit events and the sum of hit and miss, and false events (hit + miss + false).

We used the Variable Infiltration Capacity (VIC, version 4.1.2) (Liang et al., 1994, 1996) model to simulate hydrologic variables (total runoff and root-zone soil moisture) using meteorological forcing (daily precipitation, and maximum and minimum temperatures) from the IMD and the forecast products. Soil moisture and runoff predicted using forecast products were evaluated against soil moisture and runoff simulated using the observed forcing from the IMD. The VIC model simulates water and energy fluxes at each grid cell, and sub-grid variability of precipitation, elevation, soil, and vegetation is well represented (Gao et al., 2010). The soil parameters used were developed based on the Harmonized World Soil Database (HWSD) v1.2. The vegetation parameters used in this study were developed using 1 km Advanced Very High Resolution Radiometer (AVHRR) global land cover information. We used the vegetation library that was developed at the University of Washington. The vegetation parameters were not specifically developed to incorporate crops that are grown in India. However, the existing parameters were successfully used in the model application over India (Shah and Mishra, 2015, 2016). The VIC model's version that was used in this study does not explicitly represent groundwater; rather, it only accounts for baseflow. We acknowledge that India-specific soil and vegetation parameters along with the representation of irrigation, reservoir, and groundwater can improve the water budget; however, these were not considered in the present study due to the unavailability of either observations or the model version that has the representation of human interventions. The VIC model set-up used in this study is well calibrated and evaluated against observed streamflow and satellite-based evapotranspiration and soil moisture in H. L. Shah and Mishra (2016) and R. D. Shah and Mishra (2016). The VIC model has been widely used for hydrologic prediction at watershed and regional scales (Mo and Lettenmaier, 2014; R. D. Shah and Mishra, 2016; Shukla and Lettenmaier, 2011; Yuan and Wood, 2012b).

Improvements in hydrologic prediction can be achieved by post-processing the forecast of meteorological variables (precipitation, maximum and minimum temperatures). We corrected precipitation forecast using the linear scaling approach as described in R. D. Shah and Mishra (2016) and Shah and Mishra (2015). For each forecast date, we corrected precipitation for the selected (7-, 15-, 30- and 45-day) accumulation period. We first corrected accumulated precipitation due to extreme events (above the 90th percentile) for each forecast date in the training period and a scaling factor was obtained for each forecast date based on the ratio of precipitation for the 45-day accumulation period due to extreme events in the observed and forecast products. In the second step, after the correction for extreme precipitation, scaling factors were obtained based on precipitation for the 45-day accumulation period, for each forecast date from the forecast products and OBS for the entire training period. Scaling factors were estimated for the training period (9 years), which were evaluated in the testing period (1 year). More detailed information on this method can be obtained from R. D. Shah and Mishra (2016).

To correct the daily mean (of maximum and minimum) temperature from the forecast, we performed quantile–quantile (Q–Q) mapping (Wood et al., 2002). Initially, we prepared yearly time series of a 45-day accumulation period average temperature forecast for all the forecast dates along with the corresponding observed time series. For each forecast date and for each grid cell, we estimated quantiles of mean temperature for the 45-day accumulation period for each year using the climatology of the entire period. To estimate quantiles, cumulative distribution functions (CDFs) were fitted. The Weibull plotting position was used to map the cumulative distribution function when percentiles fall between 1/(N + 1) and N/(N + 1), where N is the number of climatological years during the training period. In cases when percentiles fall beyond these limits, normal distribution was fitted and values were extrapolated. More details on the Q–Q mapping can be obtained from R. D. Shah and Mishra (2016). Similarly, quantiles were estimated for OBS temperature for corresponding time series. Based on estimated quantiles, Q–Q mapping was done and forecast was replaced with the corresponding value based on OBS. We estimated the bias corrected mean temperature using Q–Q mapping. Bias (difference between the corrected and uncorrected 45-day average mean temperature) was then added equally to daily raw Tmax and Tmin to get the corrected values of daily maximum and minimum temperatures. We did not bias correct Tmax and Tmin individually, as that will affect the diurnal temperature range (Tmax–Tmin). We adopted the multifold validation approach of leaving 1 year out for testing both precipitation and mean temperature (R. D. Shah and Mishra, 2016).

Forecast of soil moisture and runoff is essential for planning and decision making in agriculture and water resources (Asoka and Mishra, 2015). Hence, we evaluated the forecast skill of soil moisture and runoff simulated using meteorological variables from the IITM ensemble. Using the raw and bias corrected forecasts (precipitation, maximum and minimum temperatures), the Variable Infiltration Capacity (VIC) model was run to obtain a soil moisture and total runoff (surface runoff + baseflow) forecast. We evaluated improvements in the correlation of runoff and soil moisture predicted using the bias corrected precipitation and temperatures from the IITM ensemble (IITM ensemble-bc) against uncorrected (raw) precipitation and temperatures from the IITM ensemble mean (IITM ensemble) and CFSv2 (Fig. S14). For simulating runoff and soil moisture, forcings from all three products were used to run the VIC model at 0.25∘ and daily resolution, while initial hydrologic conditions were generated using the observed forcing from the IMD. Forecast skill in hydrologic prediction was evaluated for mean total runoff and soil moisture for the 7–45-day accumulation period. We considered the 45-day accumulation period to evaluate the hydrologic prediction skill, as for shorter lead times forecast skill is generally higher owing to persistence of initial hydrologic conditions.

Our results show that the bias correction resulted in a reduction in all-India median MAE in precipitation predictions for all the forecast dates during the monsoon season months (Fig. 3c), especially in the Himalayan range and the northeastern region (Fig. 3a and b). We find substantial improvements in the MAE of maximum and minimum temperatures after the bias correction (Fig. 3d and e). For instance, all-India median MAE was reduced for all the forecast dates after the bias correction (Fig. 3f). Median reduction in MAE for all dates was observed as 2.1 ∘C. We find that the bias correction substantially improved temperature forecast from the IITM ensemble. This improvement in temperature forecast can be valuable for hydrologic applications. For instance, air temperature influences the energy budget in hydrologic models and therefore can affect the partitioning of evapotranspiration and runoff. Due to high intraseasonal variability in the monsoon season precipitation, bias correction resulted in only marginal improvements in the precipitation forecast.

We find that linear scaling improved negative bias in precipitation forecast in central India and the Western Ghats and positive bias in the Himalayan range and the southern peninsula. During the testing period (1 year), improvement in bias is consistent with the training period (9 years; Fig. S15c and d). Improvements in the correlation of all-India average precipitation predictions from the IITM ensemble before and after bias correction can be noticed (Fig. S16). At a 45-day accumulation period a substantial improvement was noticed as compared to other accumulation periods (Fig. S16d). Overall, we noticed that the IITM ensemble mean showed improved forecast skill after the bias correction for most of the regions. We bias corrected the forecast products for the accumulation period of 45 days. However, the bias in the forecast products may have temporal variability and may not be constant for the entire period of 45 days. Therefore, bias correction approaches based on the variable lead time (Stockdale, 1997) need to be evaluated in future when IITM forecast for a long-term retrospective period is available. However, the bias correction approach that we presented can be applied to evaluate seasonal forecast skill.

The VIC model was calibrated and evaluated using observed streamflow, satellite soil moisture and evapotranspiration (H. L. Shah and Mishra, 2016; R. D. Shah and Mishra, 2016). In this study, we used the calibrated VIC model forced with observed IMD data to simulate soil moisture and runoff, which was considered as a reference to evaluate the forecast of soil moisture and runoff. Forecast of root-zone soil moisture and runoff was simulated using the VIC model forced with the forecast products (IITM ensemble-bc, IITM ensemble, and CFSv2), which were evaluated against the soil moisture/runoff obtained from the VIC model simulation using the observed forcing from the IMD (Fig. S17). For all the forecast dates, predicted root-zone soil moisture (top 60 cm soil moisture; Fig. S14) showed a higher correlation than total runoff (Fig. S17), which is due to a higher persistence in soil moisture as compared to runoff (R. D. Shah and Mishra, 2016). The bias corrected IITM ensemble showed higher correlations than the uncorrected IITM ensemble and CFSv2. The CSI of predicting the dry anomaly in precipitation using the IITM ensemble was higher in the northwestern region but lower in the Himalayan range and southern peninsula as compared to CFSv2, which is consistent with the results based on correlation and MAE (Fig. 4). The bias corrected IITM ensemble showed an improved CSI in comparison to the raw forecast from the IITM ensemble and CFSv2 for the majority of the regions in India. However, the CSI of predicting warm temperature anomalies was lower than that of the CSI of predicting dry precipitation anomalies (Fig. 4), especially in the Himalayan range. This can be due to higher uncertainty among observations in this region (Mishra, 2015). The CSI in runoff and soil moisture is higher as compared to precipitation and temperature due to persistence in initial hydrologic conditions (Fig. 4). For the 7-, 15- and 30-day accumulation periods the CSI is higher than that of the 45-day accumulation period (Fig. S18). We observed that as the accumulation period was increased from 7 to 45 days, the CSI of runoff declines in the arid and semi-arid regions of the northwest. Overall, we found that the bias correction of the forecast improves the CSI of precipitation, temperature, total runoff, and soil moisture anomalies in India.

To show the utility of bias corrected forecast in hydrologic prediction in India, we analysed the forecast for one of the recent drought years in India. Anomalies of total runoff and root-zone soil moisture predicted on 15 July 2009 for the 45-day accumulation period using the VIC model with the bias corrected IITM ensemble forecast were compared against the observed anomalies (Fig. 5). Forecast of these hydroclimatic anomalies at a sufficient lead time can be helpful in decision making related to water resources and agriculture. We found that the IITM ensemble-bc successfully captured the spatial pattern of observed anomalies, which demonstrates the utility of hydroclimatic forecast for various applications. Persistence in initial hydrologic conditions simulated using the observed forcing and the ability of the IITM ensemble-bc to capture anomalies in precipitation and temperature (Fig. S19) resulted in an improved forecast of total runoff and root-zone soil moisture in the majority of regions in India. However, some overestimation in the areal extent and severity of hydroclimatic anomalies can be noted in central India. These results show that the framework developed using the IITM ensemble-bc forecast and the VIC model can be used to predict runoff and soil moisture up to a 45-day accumulation period of forecast. Early warning based on predictions can be helpful in decision making in the water resource and agricultural sectors so as to minimize risk.