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Influences of Sensitive Initial Error on the Numerical Forecast of Typhoon Kammuri (0809)
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摘要: 基于WRF四维变分伴随模式建立数值预报敏感初始误差计算流程并对台风北冕 (0809) 进行了分析。结果表明：基于线性化近似的伴随敏感分析方法对台风系统在24 h内适用。构造敏感初始误差的参考系数存在一个合理的取值范围，参考系数取为0.08效果最好。在初始场中去除敏感初始误差能够有效减少预报误差，改善台风路径预报效果，依据24 h预报误差计算出的敏感初始误差订正对24 h后台风数值预报效果也有明显影响。另外，敏感初始误差分布在台风中心附近，伴随台风系统环流且各物理量分布形态相似。对流层下层和中上层的敏感初始误差均对数值预报效果有所影响，对流层中上层的作用略大于对流层下层。敏感初始误差中各物理量对数值预报改善的贡献各不相同，相对而言，风场的贡献最大。Abstract: Initial error is one of the key factors that have great effects on the accuracy of numerical forecast. To study the characteristics of initial error and its influence on the numerical prediction, an analysis procedure of the sensitive initial error of numerical forecast is developed based on WRF adjoint model and is used in the investigation of typhoon Kammuri (0809). The validity of the linear assumption on the study of typhoon case is firstly assessed prior to discussing any adjoint analysis results. It is done by evaluating the evolution differences of the perturbation between linear and nonlinear development, showing that the nonlinear perturbation evolution is well represented by the linear assumption during 24-h forecast. The sensitive initial error is then constructed using the information derived from adjoint sensitivity analysis, finding that the reference coefficient from 0.01 to 0.08 is proper to build the sensitive initial error. The result of 0.08 is the best in this case study. The numerical forecast error could be reduced and the prediction bias of typhoon trace could be improved greatly by removing the sensitive initial error from the initial field. This effect of the sensitive initial error derived from 24-h numerical forecast error affects the numerical forecast even within 60 hours. In addition, the analysis reveals that the sensitive initial error of regional short-term numerical forecast concentrates mainly around the weather system. It goes with typhoon circle and the pattern is almost consistent for all physical variables. The sensitive initial error in the middle-upper troposphere has slightly more contribution to the forecast than that in lower troposphere. Comparing the contribution of different physical variable, it is found that wind is the main contributor with pressure and humidity following.
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Key words:
- WRF adjoint model;
- typhoon Kammuri;
- initial error;
- numerical forecast
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图 1 850 hPa风场u分量小扰动24 h演变结果 (单位：m·s-1)
(a) 线性演变, (b) 非线性演变
Fig. 1 24-h development of u perturbation at 850 hPa (unit: m·s-1)
(a)linear development, (b)nolinear development
图 2 模式层小扰动24 h线性和非线性演变结果的干能量
Fig. 2 The dry energy of 24-h linear and nolinear perturbation development at model levels
图 3 不同试验方案台风模拟路径与NCEP再分析场偏差统计
Fig. 3 The bias of typhoon track between experiments and NCEP reanalysis
图 4 控制试验CNR和敏感性试验EXP4 δ=0.4735模式面扰动气压 (单位：Pa) 和500 hPa风场u分量 (单位：m·s-1) 24 h预报误差对比(黑框区域为目标区)
(a) CNR扰动气压, (b) EXP4扰动气压, (c) CNR u分量, (d) EXP4 u分量
Fig. 4 The contrast of 24-h forecast error of pressure perturbation (unit:Pa) at δ=0.4735 and u perturbation (unit:m·s-1) at 500 hPa between control experiment CNR and sensitivity experiment EXP4 (the black box denotes the target area)
(a) pressure perturbation in CNR, (b) pressure perturbation in EXP4, (c) u perturbation in CNR, (d) u perturbation in EXP4
图 5 敏感初始误差在700 hPa的水平分布 (扰动气压在δ=0.7365模式面上，背景均为水平风矢量)
(a) u分量 (单位：m·s-1)，(b) v分量 (单位：m·s-1)，(c) 风矢量, (d) 扰动气压 (单位：Pa)，(e) 位温 (单位：K)，(f) 比湿 (单位：g·kg-1)
Fig. 5 The horizontal distribution of sensitive initial error at 700 hPa (expect that pressure perturbation is at δ=0.7365, and all with background wind vector)
(a) u (unit: m·s-1), (b) v (unit: m·s-1), (c) wind vector, (d) pressure perturbation (unit: Pa), (e) potential temperature(unit: K), (f) humility (unit: g·kg-1)
图 6 沿20°N台风中心敏感初始误差的垂直剖面
(a) u分量 (单位：m·s-1)，(b) v分量 (单位：m·s-1)，(c) 扰动气压 (单位：Pa)，(d) 位温 (单位：K)，(e) 比湿 (单位：g·kg-1)
Fig. 6 The section of sensitive initial error along 20°N
(a) u (unit:m·s-1), (b) v (unit: m·s-1), (c) pressure perturbation (unit: Pa), (d) potential temperature (unit: K), (e) humility(unit: g·kg-1)
图 7 不同时刻台风路径预报
(a) 2008年8月5日00:00, (b) 2008年8月5日12:00, (c) 2008年8月6日00:00
Fig. 7 The forecast of typhoon track for different initial time
(a) 0000 UTC 5 Aug 2008, (b) 1200 UTC 5 Aug 2008, (c) 0000 UTC 6 Aug 2008
表 1 试验方案和目标区域24 h预报误差的干能量积分
Table 1 The experiment design and the integrated dry energy of 24-h forecast error in the target area
试验方案 参考系数 24 h预报误差干能量
/(105 J)误差减少
率/%CNR 15.4869 EXP1 0.01 14.3733 7.19 EXP2 0.03 12.6838 18.10 EXP3 0.05 11.5815 25.22 EXP4 0.08 10.5205 32.07 
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表 2 不同试验的预报误差干能量统计
Table 2 The dry energy of forecast error
试验 24 h预报误差干能量/(105J) 误差减少率/% 试验1 12.7473 17.69 试验2 12.3248 20.42 EXP4 10.5205 32.07 CNR 15.4869
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表 3 不同试验的预报误差干能量统计
Table 3 The dry energy of forecast error
物理量 24 h预报误差干能量/(105J) 减少率/% 水平风场 11.3685 26.48 位温 13.9362 10.01 扰动气压 14.2984 7.67 湿度 15.2984 1.22
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表 4 不同起报时间24 h小扰动线性和非线性演变的干能量整层积分
Table 4 The integrated dry energy of 24-h perturbation between linear and nolinear development for different initial time
起报时间 非线性演变/(105J) 线性演变/(105J) 误差/% 2008-08-03T18:00 1.8083 1.40394 22.36 2008-08-05T00:00 3.9387 3.63357 14.85 2008-08-06T00:00 3.0678 1.98890 35.16
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