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The Probabilistic Flood Prediction Based on Implementation of the Schaake Shuffle Method over the Huaihe Basin
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摘要: 采用条件亚正态模型方法，生成了具有包含不同可能性的降水集合预报。为了保持各子流域降水集合预报变量之间的空间相关性，采用集合预报重组方法对降水集合预报进行重新排列。使用重组后的降水集合预报驱动水文模型，实现了淮河上游大坡岭-息县、淮河上游息县-王家坝和汝河-洪河上游3个子流域的12次洪水过程的洪水概率预报，并对1988年9月7日和1991年7月31日两次洪水概率预报进行个例分析。结果表明：相对于单一确定性预报，通过条件亚正态分布模型生成降水集合预报后，再经过Schaake洗牌法空间相关性重新组合的降水集合预报，捕捉洪峰出现时间和流量的能力更强。对洪水概率预报来说，降水概率预报更能达到对未来的水文事件进行最大可能估计的目的，并尽可能综合了降水预报不确定性因素，同时也说明维持变量原有的空间相关特征对于降水概率预报具有重要意义。
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关键词:
- Schaake洗牌法;
- 条件亚正态分布;
- 洪水概率预报;
- 集合预报;
- 概率定量降水预报
Abstract: Daily precipitation records of 19 rain gauges over the Huaihe Wangjiaba-Dapoling catchment and single-value forecasts of 24-hour cumulative precipitation of the Global Forecast System (GFS) with lead time up to 14 days from 1 January 1981 to 31 December 2003 are employed to construct a probability forecast model which can generate ensemble forecast based on conditional meta-Gaussian distribution. Several single-value forecasts could be computed by this model using forecasts of the GFS for daily mean areal precipitation (MAP) and cumulative MAP for each lead time (1-14 days) over 3 sub-catchments in the Huaihe Basin. Then a method is implemented to reorder the ensemble output to recover the space-time variability in precipitation, namely Schaake shuffle method. Ensembles are then reordered to match the original order of the selection of historical data. Using this approach, the observed inter sub-catchments correlations, intervariable correlations, and the observed temporal persistence are almost entirely recovered. This reordering methodology is applied in recovering the space-time variability in modeled streamflow for twelve flood processes over the Huaihe Basin. Results demonstrate that the observation of discharge is included in the interval between the 5th percentage and the 95th percentage forecasts of discharge that is generated by MAP ensemble forecasts which is calculated from the conditional meta-Gaussian distribution model and Schaake shuffle. Several members can capture the flood peak flow and the corresponding peak time. Using approach of Schaake Shuffle, sub-catchment correlations of each ensemble member forecasting could be recovered, which are closer to the observation.A test of flood forecasting result from precipitation probability forecasts of conditional meta-Gaussian distribution model and Schaake shuffle for the stream between Dapoling to Wangjiaba Hydrologic Station is carried out. It shows that MAP ensemble forecasts can provide the maximum estimation of possibility of the future hydrologic events for flood forecasting comparing to the single-value MAP forecast of GFS model. And a comprehensive interval which includes the factor that can lead to hydrologic uncertainty is also given. -
图 1 研究区域及流域内气象观测站示意图
Fig. 1 Illustration of the catchment and the location of 19 stations over the Huaihe Basin
图 2 1988年9月7日—9月20日王家坝水文站流量和流域面雨量
流量预报与观测，(b)流域面雨量预报与观测
Fig. 2 The discharge and drainage areal rainfall of Wangjiaba Hydrologic Station from 7 Sep to 20 Sep in 1988
(a)forecasted discharge in comparison with observation, (b)forecasted areal rainfall in comparison with observation
图 3 1991年7月31日—8月13日王家坝水文站流量和流域面雨量
(a)流量预报与观测, (b)流域面雨量预报与观测
Fig. 3 The discharge and drainage areal rainfall of Wangjiaba Hydrologic Station from 31 Jul to 13 Aug in 1991
(a)forecasted discharge in comparison with observation, (b)forecasted areal rainfall in comparison with observation
表 1 Schaake洗牌法在3个流域间相关性重建示例：升序排列的集合预报
Table 1 The ensemble reordering method: The ranked ensemble output
子流域1 子流域2 子流域3 集合成员
排列序号面雨量/mm 集合成员
排列序号面雨量/mm 集合成员
排列序号面雨量/mm 1 0 1 0 1 0 2 0 2 0 2 0.1 3 0.2 3 0 3 0.1 4 0.4 4 0.1 4 0.2 5 1.0 5 0.3 5 0.2 6 1.1 6 0.5 6 0.3* 7 1.2* 7 0.9* 7 0.8 8 2.1 8 1.0 8 1.2 9 3.1 9 1.1 9 1.7 10 6.1 10 1.2 10 2.3 
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表 2 Schaake洗牌法在3个流域间相关性重建示例：历史观测资料时间序列
Table 2 The ensemble reordering method: Randomly selected historical observations
序号 时间 面雨量/mm 子流域1 子流域2 子流域3 1 1991-09-20 2.3* 1.2* 0.5* 2 1992-09-20 1.8 0.2 0.1 3 1993-09-20 0 0 0.1 4 1994-09-20 0 0.1 0 5 1995-09-20 0 0.3 0 6 1996-09-20 0 0.5 0 7 1997-09-20 7.6 3.9 6.8 8 1998-09-20 15.9 9.0 9.9 9 1999-09-20 19.8 30.1 12.7 10 2000-09-20 1.1 1.2 2.3
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表 3 Schaake洗牌法在3个流域间相关性重建示例：升序排列的历史观测资料序列
Table 3 The ensemble reordering method: The ranked historical observations
子流域1 子流域2 子流域3 集合成员
排列序号面雨量/mm 集合成员
排列序号面雨量/mm 集合成员
排列序号面雨量/mm 3 0 3 0 4 0 4 0 4 0.1 5 0 5 0 2 0.2 6 0 6 0 5 0.3 3 0.1 10 1.1 6 0.5 2 0.1 2 1.8 10 1.2 1 0.5* 1 2.3* 1 1.2* 10 2.3 7 7.6 7 3.9 7 6.8 8 15.9 8 9 8 9.9 9 19.8 9 30.1 9 12.7
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表 4 Schaake洗牌法在3个流域间相关性重建示例：最终集合预报排序结果
Table 4 The ensemble reordering method: Final ensemble(shuffled output)
序号 子流域1 子流域2 子流域3 集合成员
排列序号面雨量/mm 集合成员
排列序号面雨量/mm 集合成员
排列序号面雨量/mm 1 7 1.2 7 0.9 6 0.3 2 6 1.1 3 0 5 0.2 3 1 0 1 0 4 0.2 4 2 0 2 0 1 0 5 3 0.2 4 0.1 2 0.1 6 4 0.4 5 0.3 3 0.1 7 8 2.1 8 1.0 8 1.2 8 9 3.1 9 1.1 9 1.7 9 10 6.1 10 1.2 10 2.3 10 5 1.0 6 0.5 7 0.8
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表 5 对12次洪水过程洪峰概率预报检验
Table 5 Validation results of probabilistic 12 flood process prediction
洪水起始时间 洪峰流量预报相对误差/% 峰现预报时间误差/d 第5百分位 中位数 第95百分位 第5百分位 中位数 第95百分位 1985-05-01T08:00 -88 -52 166 7 -1 0 1985-06-17T08:00 -85 -76 88 -6 4 3 1988-09-07T08:00 -94 -78 33 -4 5 1 1989-08-03T08:00 -82 -81 -18 -8 -8 -3 1990-07-16T08:00 -95 -90 -49 -4 7 7 1991-06-09T08:00 -92 -90 -7 -7 0 1 1991-07-31T08:00 -97 -93 20 -9 1 1 1992-04-26T08:00 -91 -75 22 -12 0 0 1994-06-02T08:00 -87 -83 57 -6 3 -1 1998-06-28T08:00 -96 -92 39 -4 1 1 2000-06-20T08:00 -98 -86 -12 -11 1 -4 2003-06-25T08:00 -80 -80 0 -8 -8 4
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