Analysis of Characteristics of the Forecast Jump in the NCEP Ensemble Forecast Products

The limit of numerical prediction and ensemble prediction can be further understood by the study of the forecast jump. By using the ensemble average forecast and control forecast product output data for the United States National Environmental Prediction Center (NCEP) global ensemble forecast system (GEFS), and the concept of Jumpiness index from Zsoter et al., we analyzed the statistical characteristics of forecast jump. Results show that, on average, in the NCEP ensemble forecast product, the time average prediction jump index increases with the increase of the forecast aging, and the actual forecast experience can reflect this phenomenon. The consistency of ensemble average forecast is better than the corresponding control forecast. Also, in summer, the frequency of “forecast jump” phenomenon is fluctuating by 17.5%.

vious [5] [6] [7] [8]. Especially for the strong convection, heavy rain and other severe weather events, if there is a forecast jump, it will seriously affect the forecast and the user's decision-making, leading to the loss of the severe weather. Therefore, the forecast of jumping in-depth study is very necessary, and the limit of numerical prediction and ensemble prediction can be further understood by the study of the jump. Then we can improve the numerical forecast and ensemble forecast system, promote the forecasting accuracy rate unceasing enhancement, and enhance the confidence of users for numerical forecast products. Finally, we will provide a more scientific basis for reliable decision-making in user's dealing with severe weather events.
At present, the studies of forecast jump just begin, and most of the research work is focused on the analysis of the NCEP and ECMWF and UKMO ensemble forecast product performance in North America or Europe [8] [9]. Recently, the European center through the establishment of "jump forecast index" method to forecast jumping question has carried on the quantitative research, and tentatively explored the causes of forecast jump on the basis of quantitative study [10] [11] [12]. Study forecast leap in Asia, however, has not been deeply involved yet.
In view of the above questions, we will use the NCEP ensemble mean forecast and control forecast product data to carry on the statistical analysis and the contrast research on its forecast jump in the Asian region in this paper. Through the study of this chapter, it is helpful to recognize the forecast jump features of NCEP ensemble forecast, and the forecaster's ability of releasing with NCEP ensemble forecast products was improved, in order to provide more high quality weather forecast service to the users.

Data and Methods
The data used in this paper is the ensemble average forecast and control forecast product output data for the United States National Environmental Prediction Center (NCEP) global ensemble forecast system (GEFS). The forecast factors are selected as 500 hPa height field, forecast the starting time is on March 1, 2011 to February 28, 2013, a total of 731 days. Forecast start time is 00 and 12 times per day (the same below), the forecast time is 6 hours. Forecast area is 15˚N -18˚N and 40˚E -160˚E, the horizontal spatial resolution is 1˚ × 1˚ latitude and longitude. This area was selected based on GEFS' application of Northwest China.
At present, it is usually used to make objective and quantitative analysis of the forecast jump by the forecast jump index. In this paper, one of forecast jump index, Jumpiness index can be used to analyze and compare the forecast jump. Zsoter et al. first proposed the concept of Jumpiness index [2], and give the definition of Jumpiness index type: (1) In the formula, f denotes forecast fields, d and d + δ denote starting time forecasts, t and t − δ denote prediction time, δ denote repay twice the time interval, in this study, for 12 hours. In this way, the forecast time of these two forecasts are d + t. Therefore this article says ( )  show the difference between the two prediction results of t − δ and T, respectively; in Equation (1) the right side of the denominator expressed respectively forecast time t and t − δ the standard deviation of two forecast arithmetic average operations, the introduction of the standard deviation of the jump to forecast index standardized treatment. Standardization can make different forecast system of forecast jump index to compare directly.
The time averaged prediction jump index [2] is defined as In Equation (2),

Statistical Characteristics and Analysis of Forecast Jump
According to this paper, the definition and the calculation formula of the jump index are given, the NCEP ensemble average forecast and the corresponding control forecast are calculated respectively, and the calculation results are shown in Figure 2.
The results of Figure 2 show, in NCEP ensemble forecast product, on average, the   To synthesize the above results, for NCEP ensemble prediction products, the frequency difference of the "flip" phenomenon is not obvious in the ensemble average forecast and the corresponding set control forecast, however, the frequency of "flipflop" and "flip-flop-flip" phenomenon is obviously smaller than that of the corresponding set control forecast, which should be greatly concerned is that the difference between the two frequencies will become easier to distinguish when the forecast time is relatively long. The above phenomena show that the ensemble average forecast is quite low compared with the control forecast.
In this paper, the variation characteristics of "forecast jump" in different seasons are also analyzed, namely, the frequency size of "forecast jump" in the NCEP ensemble average forecast and control forecast in each season ( Figure 6), and the difference of "jumping" frequency in ensemble average forecast and control forecast of NCEP Figure 6. Seasonal variation characteristics of the frequency of "prediction jump" in the NCEP ensemble mean (a) and control forecast (b). ensemble in summer is compared. As shown in Figure 6(a) & Figure 6(b), both ensemble average and its corresponding control forecast are the highest in the summer, and the lowest frequency of occurrence of "forecast jump" is winter, in spring and autumn, the frequency of "forecast jump" is located between the summer and winter, and the difference between the frequency of the occurrence of "forecast jump" in the spring and autumn period is small. In summer, with the extension of the forecast period, both the NCEP ensemble average forecast and the corresponding control forecast, the occurrence frequency of the "predicted jump" is shown to be a slight downward trend, at the same time, the change of the frequency of the ensemble average forecast and control forecast is roughly the same, and their frequency is between 15% -20%; there is a slight difference between the frequency of the ensemble average forecast and the control forecast in the short range of prediction. In addition to the summer season, the other three seasons, that is, autumn, winter and spring, their "predicted jump" frequencies show a slight upward trend. But throughout the year, whether the NCEP ensemble average forecast and its corresponding control forecast, the frequency fluctuation of the phenomenon of "forecasting jump" is small, the above two kinds of forecast in the four seasons of the year, the frequency of "forecast jump" phenomenon is basically in between 10% -20%. To sum up, the phenomenon of "prediction jump" has only limited seasonal sensitivity.

Conclusions
The verification method of NCEP ensemble prediction is introduced firstly in this paper, and then the concept and the statistical analysis method of the forecast jump are described. Finally, the advantages and disadvantages of the forecast consistency of the NCEP ensemble mean forecast and the corresponding control forecast, and the consistency and variability of "forecast jumps" in the ensemble mean forecast and control forecast are studied. The results are summarized as follows: Two main attributes of NCEP ensemble forecast product inspection system are reliability and resolution. The main methods are: SPRD, RMSE, histogram, CRPS score, RPS score, BS score, etc.
Through the statistical analysis of average prediction time jump index, we found that, on average, in the NCEP ensemble forecast product, the time average prediction jump index increases with the increase of the forecast aging, and the actual forecast experience can reflect this phenomenon. At the same time, the consistency of ensemble average forecast is better than the corresponding control forecast.
The frequency of "flip", "flip-flop" and "flip-flop-flip", three different grades of "forecast jumping" phenomenon in the NCEP ensemble mean forecasts and corresponding control forecast decrease in turn. The frequency of occurrence of "forecast jump" phenomenon in the ensemble average and the corresponding control forecast at the same time is lower than the frequency of occurrence of "forecast jump" phenomenon in the ensemble average or the corresponding control forecast alone. For NCEP ensemble prediction products, generally speaking, the difference between the frequency of occurrence of "flip" phenomenon in the ensemble average forecast and its corresponding control forecast is small, however, especially in the longer forecast period, the frequency of "flip-flop" and "flip-flop-flip" phenomenon is obviously smaller than that of the corresponding control forecast. This fully shows that the inconsistent level average level of the ensemble average forecast is lower than the ensemble control forecast.
The frequency of occurrence of "forecast jump" phenomenon in the NCEP ensemble average forecast and its corresponding control forecast in summer is greater than in spring and autumn season, which is more than that in winter. But the occurrence frequency of "forecast jump" is limited to the sensitivity of the season. In summer, the frequency of "forecast jump" phenomenon is fluctuating by 17.5%, which does not appear significant growth.