Precipitation Probabilistic Forecast Calibration by two approaches Rank histogram and Logistics (Novemer 2008 to April 2009)

Probabilistic forecasts represent forecasts with a value between zero and one. Using ensemble forecasts is a proper way of getting probabilistic forecasts. An ensemble forecast is a group of forecasts which differ from each other in terms of initial conditions and/or physics of the model. A good probabilistic forecast should have reliability, sharpness and resolution (e. g. Wilks, 2006). For assessing reliability and sharpness of the forecasts, scores such as Brier score (BS), reliability diagram and Ranked probability Score (RPS) are used. Relative Operating Characteristic (ROC) curve is used to assess the sharpness of the probabilistic forecasts. Statistical post-processing techniques are used to produce calibrated probabilistic forecast. In this research two methods of rank-histogram (Hamill & Colucci, 1998) and logistic regression (Hamill et al, 2004; Hamill et al, 2008; Wilks & Hamill, 2007) are used to calibrate the raw ensemble outputs. Domain of study and data used Domain of study covers an area between 23-41 N and 42-65 E. Observed precipitations form 257 synoptic meteorological stations for a six month period from 1st Nov 2008 to 30th Apr 2009 are used to verify the EPS output. The EPS in this research is an eight member ensemble and includes five and three different configurations of the WRF and MM5 models respectively. Democratic voting In the so-called democratic voting method (Wilks & Hamill, 2006.) the probability of occurring precipitation less than or equal to a quantile q is calculated as follows: The coefficients b, b1 and b2 are calculated by minimizing likelihood function. Rank-histogram calibration If the nens members and the single observation all have been drawn from the same distribution, then actual future atmospheric state behaves like a random draw from the distribution. This condition is called consistency of the ensemble (Anderson 1997). In other words, if the ensemble members are sorted, then the probability of occurrence of the observation within each bin is equal. Suppose there is a sorted ensemble precipitation forecast X for a given time and location with N members, a verification observation V, and a corresponding verification rank distribution R with N+1 ranks representing the climatological behavior of the verification compared to the ensemble.Reliability diagram: Reliability diagram is graphical representation of observed conditional frequencies versus forecast probability. Forecasts with higher reliability represent lesser deviation from the diagonal line. Parts of the curve lying below (above) the diagonal line represent over-forecasting (under forecasting) for corresponding forecast probabilities. Reliability diagram Reliability diagram is graphical representation of observed conditional frequencies versus forecast probability. Forecasts with higher reliability represent lesser deviation from the diagonal line. Parts of the curve lying below (above) the diagonal line represent over-forecasting (under forecasting) for corresponding forecast probabilities. Fig. 1 1nd 2 show Brier score and skill score for the uncalibrated ensemble and calibrated probabilistic forecasts using Logistic and rank-histogram calibration methods. As shown in the Figures the BS decreases to lower values for calibrated forecasts and the degree of improvement is higher for Logistic method when compared to rank-histogram method. Reliability diagrams for calibrated and uncalibrated ensemble forecasts are presented in Fig. 3 for 24-h forecasts and different thresholds. Comparison of the reliability curves show that for all thresholds, the reliability curves for post processed forecasts are nearer to the diagonal line (perfect reliability) and hence show higher reliability. In other words the using logistic and rank-histogram calibration methods the probabilistic forecasts match better to the relative frequency of the observed occurrence of precipitation. Comparison the reliability curves for Logistic and rank-histogram show that for light precipitation threshold, the Logistic method is more reliable compared to the rank-histogram method while for heavy precipitation threshold the rank-histogram calibration give higher reliability. Calculated RPSs for both calibrated and uncalibrated probabilistic forecasts are shown in Fig. 4. RPS is a negatively oriented score and lower values dente more reliable and sharper forecasts. RPS for calibrated forecasts is smaller when compared to that of the uncalibrated forecasts. Using Logistic and rank-histogram calibration methods has improved the RPS 18 and 16 percent respectively for 24-h forecasts compared to uncalibrated forecasts. In general the results showed that using both Logistic and rank-histogram calibration methods improved the forecast probabilities in terms of both reliability and resolution compared to the raw ensemble forecasts. Also, results showed that for light and moderate precipitation thresholds the Logistic method gives more reliable probabilistic forecasts when compared to the rank-histogram calibration method. While for heavy precipitation threshold the reverse is true.