Improvement of the Ensemble Methods in the Dynamical– Statistical–Analog Ensemble Forecast Model for Landfalling Typhoon Precipitation

The Dynamical–Statistical–Analog Ensemble Forecast model for landfalling 2 typhoon precipitation (the DSAEF_LTP model) identifies tropical cyclones (TCs) 3 from history data that are similar to a target TC, and then assembles the 4 precipitation amounts and distributions of those identified to obtain those of the 5 target TC. Two original ensemble methods in the DSAEF_LTP model, mean 6 and maximum, tend to under- and over-forecast TC precipitation, respectively. 7 In addition, these two methods are unable to forecast precipitation at stations 8 beyond their maxima. To overcome the shortcomings and improve the forecast 9 performance of the DSAEF_LTP model, the following five new ensemble 10 methods are incorporated: optimal percentile, fuse, probability matching mean, 11 equal difference-weighted mean, and TSAI (Tropical cyclone track Similarity 12 Area Index)-weighted mean. Then, model experiments for landfalling TCs over 13 China in 2018 are conducted to evaluate the forecast performance of the 14 DSAEF_LTP model with the new ensemble methods. Results show that the 15 overall performance of the optimal percentile (the 90th percentile) ensemble 16 method is superior, with the false alarm rate lower than that of the original 17 ensemble methods. As compared to five operational numerical weather 18 prediction models, the improved DSAEF_LTP model shows advantages in 19 predicting accumulated rainfall, especially with the rainfall of over 250 mm. 20 When implementing the experiments, above results, however, it is found that 21 the model forecast performance varies, depending on the type of TC tracks. That is, the accumulated rainfall forecast for westbound TCs is significantly 23 better than that of northbound TCs. To address this issue, different schemes 24 are used to forecast the accumulated rainfall of TCs with the two different track 25 types. The precipitation forecast performance for westbound and northbound 26 TCs, using the 90th percentile and the probability-matched ensemble mean 27 ensemble method, respectively, is much better than that using a single 28 ensemble method for all the TCs. 29


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China is the country with the world's most frequent landfalling tropical cyclones The specific steps of the DSAEF_LTP model are given in section 3.2.

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To identify TCs whose tracks are similar to the target TC, the objective TC track 134 Similarity Area Index (TSAI) (Ren et al., 2018) is used. The principle of the TSAI is to 135 calculate the area enclosed by the track of the historical TCs and the target TC over a 136 certain region. The smaller the TSAI value is, the higher is the similarity.

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The threat score ( ) and bias score ( ), which are widely used in the operational 138 weather prediction, are the two basic criteria for determining the forecast performance 139 in this study. TS is defined as = ℎ ℎ + + , indicating the fraction of 140 correctly predicted forecast events. It varies from 0 to 1. The closer it is to 1, the higher is the hit rate. BIAS is defined as = ℎ + ℎ + , indicating whether the 142 forecast system has a tendency to underestimate ( < 1) or overestimate ( > 143 1). denotes the number of stations which the event is forecast to occur, and does 144 occur; is the number of stations which the event is forecast not to occur, but 145 does occur; is the number of stations which the event is forecast to 146 occur, but does not occur.  equal difference-weighted mean (ED-WM), and TSAI-weighted mean (TSAI-WM).

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The specific calculation steps of the seven ensemble methods are given in Table 2.

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The mean and maximum ensemble methods forecast the precipitation at each station by 219 calculating the average and max precipitation, respectively, at each station of the 220 selected analogs. Since these two methods always tend to underestimate and 221 overestimate precipitation, respectively, percentiles were introduced. To get the optimal 222 percentile of the best forecast performance, the 60th to 95th percentiles, at 5 percentile 223 intervals, are applied to simulating the precipitation of the 10 LTCs. Results show that 224 the 90th percentile is the optimal one. Thus, the 90th percentile is adopted in this study.

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The fuse ensemble method is also adopted to obtain the target TC's precipitation by 226 employing different percentile ensemble methods determined by the precipitation of m 227 analogs in order to achieve better forecast performance. This method can be 228 implemented by following the calculation rules shown in Table 2. The criteria in the fuse are checked in order. If one criterion is met, the rest will not be checked.

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Because the forecasted precipitation at a station by using these four methods (i.e.,

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Historical precipitation data from the remaining stations are directly used when using 240 PM to forecast the precipitation at a station. By using this method, the higher the 241 average precipitation of the selected analogs at a certain station, the higher is the 242 forecasted precipitation. The forecast values, whose algorithm is given in Table 2, 243 depend on the precipitation of the similar TCs selected at all stations.

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The ED-WM ensemble method can be achieved by assigning equal differential 245 weights to the precipitation amounts of the selected m analogs in order of similarity.

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That is, the higher the similarity is, the more weight will be given to the precipitation 247 of that analog is. Thus, the weight of precipitation for each similar TC selected is  performance of the DSAEF_LTP model.

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As can be seen from Fig.3, the station-based ensemble methods (the first four 301 ensemble methods in Table 2) show better forecast performance than the field-based 302 ensemble methods; the overall forecast performance of the 90th percentile is the best, 303 i.e., the TSsum of the best scheme with the 90th percentile ensemble method is the 304 highest. This may be due to the fact that the precipitation distribution of the selected 305 analogs by the DSAEF_LTP model is very similar to that of the target TC. Therefore, 306 obtaining the ensemble forecast using the precipitation of the station itself performs 307 better. The fuse and maximum ensemble schemes rank the second. They have the same 308 TSsum value because they obtain the same forecast of precipitation of more than 100 309 mm. A difference between the two methods is that the fuse scheme reduces the rate of 310 misses for less than 100 mm precipitation. The TS250 is maximized when the 90th 311 percentile is adopted, while the TS100 is the highest when the ensemble method is fuse 312 or maximum. This is consistent with the conclusion of some previous studies (e.g., is the same as that for the 10 TCs. That is, the parameters of P1-P7 take values of 1, 20, 371 1, 6, 3, 2, 5, and 3 (Table 3) As indicated in the preceding subsection, TC1808 is a northbound TC, which is best 409 forecasted by the 90th percentile (Fig.3) and PM ensemble method (Fig.6)  TC1816 is a westbound typhoon, and best forecasted when the 90th percentile ensemble method is used (Fig. 6) Fig. 9 shows that for precipitation above 250 432 mm, the GFS forecast is better than that of the other models, but there is severe It is evident that the forecast performance for TC1823 is the best with the 90th 450 percentile ensemble method, followed by the maximum and fuse ensemble methods, 451 whereas precipitation of more than 100 mm cannot be simulated by the other ensemble 452 methods (cf. Figs. 10 and 7). This TC produced more than 100 mm accumulated 453 precipitation at 12 stations, with four of them recording more than 250 mm. The

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DSAEF_LTP model using the 90th percentile ensemble method predicts more than 100 455 mm precipitation at 7 stations, and more than 250 mm precipitation at 3 stations.

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However, this method setup underestimates the precipitation of above 250 mm and 457 overestimates the precipitation over 100 mm (Fig. 10d). As compared to the original 458 ensemble methods in the DSAEF_LTP model, the 90th percentile outperforms the mean 459 (Fig. 10b) and maximum (Fig. 10c) Table 1 Parameters of the DSAEF_LTP model. 777 Table 2 The improved ensemble methods in the DSAEF_LTP model.  Table 3 Parameter values for the best schemes with seven ensemble methods.  Table 2 Total number of schemes: 6 × 20 × 3 × 6 × 5 × 4 × 5 × 10 × 7 = 15,120,000 782 Table 2 The improved ensemble methods in the DSAEF_LTP model.