واسنجي پيش‌بيني احتمالي بارش به دو روش بافت‌نگار رتبه‌اي و لجستيك روي ايران (آبان 1387 تا ارديبهشت 1388)

New Method for Climatic Classification of Iran Based on Natural Ventilation Potential (Case study: Yazd)

فرآيند واسنجي منجر به افزايش اطمينان پذيري و تفكيك پذيري پيش بيني هاي احتمالي وضع هوا مي شود. در اين پژوهش يك سامانه همادي هشت عضوي شامل مدلWRF  با پنج پيكربندي مختلف و مدلMM5با سه پيكربندي مختلف تشكيل شده است. براي راست‌آزمايي پيش بيني هاي سامانه همادي، از آمار بارش تجمعي روزانه 257 ايستگاه همديدي در سطح كشور در بازه زماني 11 آبان 1387 تا دهم ارديبهشت 1388 استفاده شده است. داده‌ها شامل يك دوره 90 روزه براي آموزش و يك دوره 90 روزه براي ارزيابي مي باشد. پيش بيني بارش براي آستانه‌هاي كمتر يا مساوي 1/0، بين 1/0 تا 10 و بيشتر از 10 ميلي متر براي هر روز در دوره ارزيابي به دو روش لجستيك و بافت‌نگار رتبه اي واسنجي و سپس ارزيابي شده است.نتايج ارزيابي نشان مي دهد كه هر دو روش سبب بهبود نتايج پيش بيني هاي واسنجيده نسبت به پيش بيني هاي ناواسنجيده در هر سه آستانه مي شود. همچنين نتايج حاصل از مقايسه دو روش واسنجي نشان مي دهد كه در آستانه هاي اول و دوم روش لجستيك نتايج مطلوب‌تري نسبت به بافت نگار رتبه اي دارد، و در آستانه سوم يعني آستانه هاي بزرگتر از 10 ميلي متر روش در هر دوروش تقريبا يكسان است. به عنوان مثال نتايج حاصل از امتياز مهارتي برير نشان مي دهد كه با واسنجي كردن پيش بيني به روش لجستيك مقادير اين امتياز در آستانه اول نسبت به بافت نگار رتبه اي 52 درصد، و در آستانه دوم 57 درصد افزايش يافته است در حاليكه در آستانه سوم 60 درصد كاهش يافته است.

Introduction 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 postprocessing techniques are used to produce calibrated probabilistic forecast. In this research two methods of rankhistogram (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.   Materials and Methods Domain of study and data used Domain of study covers an area between 2341 N and 4265 E. Observed precipitations form 257 synoptic meteorological stations for a six month period from 1st Novr 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 socalled democratic voting method (Wilks Hamill, 2006.) the probability of occurring precipitation less than or equal to a quantile q is calculated as follows:   Where n represent the number of the members in the EPS, Rank (q) shows the rank of q when pooled among the ensemble members and V denotes the verification whose cumulative probability is be predicted. According to Equation (1,) Pr(V ≤ q) = 1 when all ensemble members are smaller than q, and Pr(V ≤ q) = 0 when all ensemble members are larger than q.   Logistic regression Probability forecasts for a binary predictand, defined according to a particular quantile q, can be made using logistic regressions of the form   Where  and  represent the ensemble mean and standard deviation of the ensemble members. The coefficients b0, b1 and b2 are calculated by minimizing the following likelihood function   Rankhistogram calibration If 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. Then using the rankhistogram calibration method proposed by Hamill Colucci (1998) probabilities of precipitation forecast for different thresholds can be estimated as follows: i)                    For V less that the ith member’s forecast (Xi):   ii)                  For V between Xi and Xi+1     iii)                For V less than a threshold that is less than the lowest ensemble member X1 and greater than zero:   For V less than a threshold that is larger than  Xi and smaller or equal to Xi+1   For V between any two thresholds T1 and T2 such that T2 > T1 ≥ Xn     Where F denotes the Gumbel distribution defined as   The distribution parameters are computed using the sle mean  and standard Deviation  s as     – is the Euler constant.   Verification Calibrated probabilistic forecasts produced by Rankhistogram and Logistic regression methods along with no calibrated probabilistic forecasts were verified against the corresponding observations using common statistical scores including Brier score, reliability diagram and Ranked probability Score (RPS).   Brier Score BS is in fact the squared probabilistic forecast errors and is defined as   Where n is the total number of forecast and observation pairs and (fk, ok) is the kth of n pairs of forecasts and observations.   Rankedprobability Score RPS is the sum of squared differences between the components of the cumulative forecast and observation and is given by   Where k is the number of precipitation thresholds and Pk and Ok represent the cumulative forecast and observation probabilities respectively. RPS is zero for a perfect forecast.   Reliability diagram Reliability diagram is a 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 overforecasting (underforecasting) for corresponding forecast probabilities.   Results Brier score and skill score The BS decreases to lower values for calibrated forecasts and the degree of improvement is higher for Logistic method when compared to rankhistogram method.   Reliability diagram Comparison of the reliability curves show that for all thresholds, the reliability curves for postprocessed forecasts are nearer to the diagonal line (perfect reliability) and hence show higher reliability. In other words, when logistic and rankhistogram calibration methods are used, the probabilistic forecasts match better to the relative frequency of the observed occurrence of precipitation. Comparison of the reliability curves for Logistic and rankhistogram show that for light precipitation threshold, the Logistic method is more reliable compared to the rankhistogram method while for heavy precipitation threshold the rankhistogram calibration give higher reliability.   Ranked Probability Score 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 no calibrated forecasts. Using Logistic and rankhistogram calibration methods has improved the RPS 18 and 16 percent respectively for 24h forecasts compared to no calibrated forecasts.   Conclusion In general the results showed that using both Logistic and rankhistogram 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 rankhistogram calibration method. While for heavy precipitation threshold the reverse is true.