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The Experiment of Hydrologic Probabilistic Forecast Based on the Precipitation Forecast Calibrated by Bayesian Model Averaging
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摘要: 利用淮河流域加密站点2008年6月1日—8月31日逐日降水资料、对应的T213模式的24 h, 48 h以及72 h集合预报，采用贝叶斯模型平均 (Bayesian Model Averaging，BMA) 方法对集合预报15个成员的降水预报进行了概率集成与偏差订正，采用排序概率评分 (CRPS)、平均绝对误差 (MAE) 对BMA的订正结果进行检验，并将订正后的降水预报输入VIC (Variable Infiltration Capacity) 水文模型中进行水文概率预报。结果表明：经BMA订正后的24 h, 48 h, 72 h降水预报精度较订正前有所提高；BMA模型给出的有效区间 (第25百分位数至第75百分位数) 预报将实况降水量包含在内的可能性比订正前更大；由水文概率预报检验指标分析可知，经BMA订正的降水集合预报，由VIC水文模型模拟得到的径流量变化趋势与实况较吻合。Abstract: Based on 24-h accumulated precipitation data of the Huaihe Basin from 1 June to 31 August in 2008 and the corresponding ensemble forecast of 24 h, 48 h, 72 h from T213 model, the method of Bayesian Model Averaging (BMA) is used to calibrate quantitative precipitation forecasts of 15 members from the ensemble forecast based on the training data of 30 days. The calibrated results are verified by continuous ranked probability score (CRPS) and mean absolute error (MAE). Second, the Dapoling—Wangjiaba Catchment in the upper stream of the Huaihe River, which is subdivided into Dapoling—Xixian Catchment and Xixian-Wangjiaba Catchment, is investigated with the hydrological simulation experiment. The Xixian and Wangjiaba hydrologic stations in the upper stream of the Huaihe River are selected as representative stations. The rain process occurring from 23 June to 3 August in 2008 is investigated to simulate the runoff tendency. Then, the 25th and the 75th percentiles of 24-h, 48-h and 72-h precipitation ensemble forecast which are calibrated by BMA are used to force the Variable Infiltration Capacity (VIC) hydrological model respectively to obtain the corresponding runoff, and finally the simulate results are analyzed comparing with daily runoff observations.Results show that the precision of 24-h, 48-h, 72-h precipitation forecast of BMA model is improved after the calibration. The raw ensemble forecast of 24 h is calibrated well by BMA model. As the leading hours increase, the calibration of 48 h and 72 h is as good as that of 24 h. Although BMA calibrates on the raw ensemble forecast, the improvement of calibrated forecast depends on the accuracy of raw ensemble forecast. The valid interval given by BMA model, namely the interval from the 25th percentile to the 75th one of ensemble forecast, is more likely to contain the true value of observations according to the verification analysis of hydrological probabilistic forecast. From this aspect, the performance of BMA forecast outperform deterministic forecast. It can improve the accuracy of forecast and reduce the error by BMA, describing forecast uncertainty in the form of a probability distribution. Known from the analysis of verification index of hydrologic probabilistic forecast, it shows that the hydrological simulation forced by the calibrated precipitation is almost consistent with the runoff tendency of observations. It is effective to grasp the trend of runoff change. It indicates that the precipitation forecast calibrated by BMA can be established coupling with the VIC hydrological model as well as increasing the forecast accuracy significantly. It can meet the more and more objective, quantitative needs of decision-making service, and improve the benefit of weather forecast greatly.
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图 1 淮河流域位置与范围 (a)、淮河上游大坡岭至王家坝流域范围及插值格点示意图 (b)
(Ⅰ代表大坡岭至息县子流域，Ⅱ代表息县至王家坝子流域)
Fig. 1 The location and coverage of Huaihe Basin (a) and the coverage of Dapoling—Wangjiaba Catchment with the illustration of interpolation (b)
(Ⅰ represents the coverage of Dapoling—Xixian Catchment, Ⅱ represents the coverage of Xixian—Wangjiaba Catchment)
图 2 基于贝叶斯模型平均的集合预报-水文概率预报流程
Fig. 2 The schematic chart of hydrologic probabilistic forecast based on precipitation forecast calibrated by Bayesian Model Averaging
图 3 息县站2008年7月21—30日24 h的BMA模型预报 (a)、REF集合预报 (b) 盒须图与实况对比
Fig. 3 The comparison of Box-Whisker plot and observation plot between probabilistic forecast calibrated by Bayesian Model Averaging (a) and raw ensemble forecast (b) at Xixian Station from 21 to 30 in July 2008
图 4 王家坝站2008年7月21—30日24 h的BMA模型预报 (a)、REF集合预报 (b) 盒须图与实况对比
Fig. 4 The comparison of Box-Whisker plot and observation plot between probabilistic forecast calibrated by Bayesian Model Averaging (a) and raw ensemble forecast (b) at Wangjiaba Station from 21 to 30 in July 2008
图 5 息县站BMA 24 h (a)、48 h (b) 和72 h (c) 降水预报的流量模拟与实况对比图
Fig. 5 The comparison between runoff simulations forcing by probabilistic forecast calibrated by Bayesian Model Averaging (BMA) and runoff observations at Xixian Station of 24 h (a), 48 h (b) and 72 h (c)
图 6 王家坝站BMA 24 h (a)、48 h (b) 和72 h (c) 降水预报的流量模拟与实况对比图
Fig. 6 The comparison between runoff simulations forcing by probabilistic forecast calibrated by Bayesian Model Averaging (BMA) and runoff observations at Wangjiaba Station of 24 h (a), 48 h (b) and 72 h (c)
表 1 24 h, 48 h和72 h原始集合预报 (REF) 与BMA概率预报的CRPS及MAE评分对比
Table 1 The comparison of CRPS and MAE scores between raw ensemble forecast (REF) and probabilistic forecast calibrated by Bayesian Model Averaging (BMA) for 24 h, 48 h and 72 h
预报日期 评分 24 h 48 h 72 h REF BMA REF BMA REF BMA 07-21 CRPS 2.05 0.62 0.71 1.21 0.86 1.52 MAE 2.52 0.43 0.88 0.70 1.02 1.16 07-22 CRPS 9.36 9.13 9.82 8.73 8.99 8.73 MAE 10.84 10.02 11.02 10.96 10.74 10.71 07-23 CRPS 31.45 45.59 37.79 47.12 40.26 48.42 MAE 38.62 56.36 45.28 56.64 49.28 57.47 07-24 CRPS 12.01 11.52 12.32 13.31 14.72 12.07 MAE 14.80 14.55 14.97 14.84 18.34 17.05 07-25 CRPS 5.11 3.16 4.25 3.31 3.52 2.96 MAE 6.81 3.41 5.31 3.71 4.58 3.39 07-26 CRPS 8.63 4.23 4.38 3.56 4.50 3.86 MAE 10.78 4.96 5.38 4.28 5.74 4.70 07-27 CRPS 6.97 4.74 5.75 4.79 5.33 4.82 MAE 8.91 5.96 7.25 6.32 6.65 6.42 07-28 CRPS 7.14 4.14 6.36 3.60 3.52 3.04 MAE 9.53 4.66 8.63 3.93 4.89 3.31 07-29 CRPS 2.82 1.18 1.56 1.08 3.20 1.63 MAE 3.64 0.86 2.17 0.49 4.62 0.85 07-30 CRPS 8.91 6.39 8.15 6.97 7.85 6.59 MAE 11.22 8.85 8.78 8.64 8.94 8.35 
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表 2 水文概率预报的各项检验指标统计
Table 2 The statistics of verification index of hydrologic probabilistic forecast
站点 预报时效/h 确定性系数 洪峰相对误差 峰现时间差/d 第25百分位数 第75百分位数 第25百分位数 第75百分位数 息县 24 0.56 0.70 -0.41 -0.36 0 48 -1.13 -1.85 -0.60 -0.50 1 72 -0.56 -2.65 -0.81 -0.70 2 王家坝 24 0.58 0.60 0.16 0.26 -1 48 0.71 0.82 0.04 0.17 -1 72 0.34 0.55 0.19 0.03 0 注：峰现时间差为正，表示预测提前；峰现时间差为负，表示预测滞后。
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