粒子滤波同化在厄尔尼诺-南方涛动目标观测中的应用 粒子滤波同化在厄尔尼诺-南方涛动目标观测中的应用
 大气科学  2018, Vol. 42 Issue (3): 677-695 PDF

1 中国科学院大气物理研究所大气科学和地球流体力学数值模拟国家重点实验室, 北京 100029
2 成都信息工程大学大气科学学院/高原大气与环境四川省重点实验室/气候与环境变化联合实验室, 成都 610225
3 中国科学院大学地球科学学院, 北京 100049
4 南京信息工程大学大气科学学院, 南京 210044

Application of Particle Filter Assimilation in the Target Observation for El Niño-Southern Oscillation
DUAN Wansuo1,3, FENG Fan2, HOU Meiyi4
1 State Key Laboratory of Numerical Modeling for Atmospheric Sciences and Geophysical Fluid Dynamics(LASG), Institute of Atmospheric Physics, Chinese Academy of Sciences, Beijing 100029
2 School of Atmospheric Sciences/Plateau Atmosphere and Environment Key Laboratory of Sichuan Province/Joint Laboratory of Climate and Environment Change, Chengdu University of Information Technology, Chengdu 610225
3 College of Earth Sciences, University of Chinese Academy of Sciences, Beijing 100049
4 College of Atmospheric Sciences, Nanjing University of Information Science & Technology, Nanjing 210044
Abstract: Considering the limitation of particle filter-target observation approach, the present study proposes a new target observation approach that can overcome this limitation. This new approach is then applied to the study of the predictability of El Niño-Southern Oscillation and reveals the sensitive areas for targeting observation associated with eastern-and central-Pacific El Niño events. By assimilating the target observations, the prediction uncertainties for the two types of El Niño events are significantly reduced. This result confirms that the sensitive areas revealed by the new approach, compared with other areas, can play a much more important role in improving the El Niño forecast skill.
Key words: El Niño-Southern Oscillation      Particle filter      Target observation
1 引言

El Niño事件通常呈现最大的海表温度暖异常中心在热带东太平洋。然而，自20世纪90年代以来，区别于传统厄尔尼诺事件的一种新型El Niño事件开始频繁发生，该类El Niño事件最大海表温度暖异常中心位于热带中太平洋。根据海表温度暖中心位置的不同，上述两类El Niño通常被称为东太平洋型El Niño事件和中太平洋型El Niño事件（EP-El Niño事件和CP-El Niño事件，Kao and Yu 2009）。两类El Niño事件发生的周期与物理机制具有显著差异（Kug et al., 2009, 2010; Weng et al., 2007; Xiang et al., 2013），而且对全球天气和气候的影响也存在较大差别（Feng et al., 2011; Taschetto and England, 2009; Weng et al., 2007; Zhang et al., 2011; Wang and Wang, 2013）。所以，采用数值模式预报ENSO事件时，不仅需要预报El Niño事件是否发生，还需提前对El Niño事件的类型做出判断，因而更增加了ENSO预测的挑战性。

2 基于粒子滤波同化的目标观测新方法

2.1 粒子滤波同化方法

 ${\mathit{\boldsymbol{X}}_{k + 1}} = {\mathit{\boldsymbol{M}}_k}\left({{\mathit{\boldsymbol{X}}_k}, {\mathit{\boldsymbol{\zeta }}_k}} \right),$ (1)

 ${p_N}\left({{\mathit{\boldsymbol{X}}_k}} \right) = \sum {w_k^i} \delta \left({{\mathit{\boldsymbol{X}}_k} - \mathit{\boldsymbol{X}}_k^i} \right),$ (2)

 ${p_N}({\mathit{\boldsymbol{X}}_k}|{\mathit{\boldsymbol{Y}}_{1:\left({k - 1} \right)}}) = \sum\limits_{i = 1}^N {w_{k - 1}^i} \delta ({\mathit{\boldsymbol{X}}_k} - \mathit{\boldsymbol{X}}_k^i),$ (3)

 ${p_N}\left({{\mathit{\boldsymbol{X}}_k}|{\mathit{\boldsymbol{Y}}_{1:k}}} \right) = \frac{{p({\mathit{\boldsymbol{Y}}_k}|{\mathit{\boldsymbol{X}}_k}){p_N}({\mathit{\boldsymbol{X}}_k}|{\mathit{\boldsymbol{Y}}_{1:\left({k - 1} \right)}})}}{{p({\mathit{\boldsymbol{Y}}_k})}},$ (4)

 $w_k^i = \frac{{p({\mathit{\boldsymbol{Y}}_k}|\mathit{\boldsymbol{X}}_k^i)}}{{p({\mathit{\boldsymbol{Y}}_k})}}w_{k - 1}^i,$ (5)

 $p({\mathit{\boldsymbol{Y}}_k}|\mathit{\boldsymbol{X}}_k^i) - \exp \left\{ { - \frac{1}{2}{{\left[ {{\mathit{\boldsymbol{Y}}_k} - \mathit{\boldsymbol{H}}\left({\mathit{\boldsymbol{X}}_k^i} \right)} \right]}^{\rm T}}\sum {^{ - 1}\left[ {{\mathit{\boldsymbol{Y}}_k} - \mathit{\boldsymbol{H}}\left({\mathit{\boldsymbol{X}}_k^i} \right)} \right]} } \right\},$ (6)

2.2 粒子滤波同化预报技巧的度量：Predictive Power指数

 ${P_{\rm{P}}} = 1 - \exp (- {S_{q\left(X \right)}} + {S_{p\left(X \right)}}),$ (7)

 ${S_{p\left(\mathit{\boldsymbol{X}} \right)}} = - \kappa \int {p\left(\mathit{\boldsymbol{X}} \right)} \ln p\left(\mathit{\boldsymbol{X}} \right){\rm{d}}\mathit{\boldsymbol{X, }}$ (8)

2.3 基于粒子滤波的目标观测新方法

（1）计算同化结束时集合样本离散度和集合预报误差呈现较强正相关的区域；

（2）在该正相关区域，用粒子滤波同化不同区域观测计算系统状态变量的信息熵；

（3）根据上述信息熵，计算PP指数值，将PP指数大值区作为目标观测敏感区。

3 试验方案和资料

4 中太平洋型厄尔尼诺事件的目标观测敏感区

 图 1 CNRM-CM5、GFDL-ESM2M、GISS-E2-R和CCSM4模式中，用KD方法计算的CP-El Niño的PP指数的集合平均 Figure 1 Ensemble means of the PP (Predictive Power) index calculated by the KD approach for CP-El Niño in the models of CNRM-CM5, GFDL-ESM2M, GISS-E2-R and CCSM4, respectively

 图 2 热带太平洋区域（15°S~15°N，120°E~80°W）均分为9个区域的示意图 Figure 2 Diagram of the equally-shared nine regions over the tropical Pacific Ocean (15°S–15°N, 120°E–80°W)

 图 3 同图 1，图中黑色打点区域是各模式PP指数最大值前M个格点（CNRM-CM5模式选取前60个格点，GFDL-ESM2M、GISS-E2-R和CCSM4模式均选取前80个格点）所在的位置 Figure 3 As in Fig. 1, but with black-dotted regions for the first M grid points with much large PP values (the first 60 grid points are for model CNRM-CM5 while the first 80 grid points are for models GFDL-ESM2M, GISS-E2-R, and CCSM4)

 图 4 （a）CCSM4模式中一次CP-El Niño事件（红线）的Niño4指数，及其同化PP_max区域观测的SST（黑线）和随机区域Rand1、Rand2和Rand3区域观测的SST（蓝线、绿线、紫线）的集合平均预报的Niño4指数；（b）a图中集合平均预报的预报误差 Figure 4 (a) Niño4 index of a CP-El Niño event (red line) in the model CCSM4, its ensemble-mean forecast by assimilating the observed SST over the PP_max region (black line), and over three randomly selected regions denoted by Rand1, Rand2, and Rand3 (blue, green, and purple lines). (b) Prediction errors of the ensemble-mean forecasts shown in Fig. a

 图 5 CCSM4模式中的15个CP-El Niño个例的集合平均预报误差，其中包含同化PP_max（红色柱状）观测的SST集合预报，以及同化Rand1、Rand2和Rand3区域（蓝色柱状）内观测的SST集合预报 Figure 5 Ensemble-mean forecast errors for the selected fifteen CP-El Niño events simulated by model CCSM4, including the forecasts with assimilation of the observed SST in the PP_max region (red bar) and in three randomly selected regions denoted by Rand1, Rand2, and Rand3 (blue bars)

 图 6 CNRM-CM5、GFDL-ESM2M、GISS-E2-R和CCSM4模式同化1~3月观测的SST后，所得到的Niño4指数的集合离散度和集合平均误差的空间相关系数 Figure 6 Correlation coefficients between ensemble spread and ensemble-mean forecast errors for the ensemble forecasts generated by models CNRM-CM5, GFDL-ESM2M, GISS-E2-R, and CCSM4 with assimilation of observed SST observations from January to March

 图 7 同图 3，但为新方法计算的PP指数的集合平均 Figure 7 As in Fig. 3, but for ensemble means of the PP index calculated by the new approach

 图 8 图 4中CCSM4模式的CP-El Niño的Niño4指数的概率预报：（a）模式同化了PP_max的观测SST后；（b）同化PP_max_R的观测SST后。红线代表真值CP-El Niño事件，灰色区域代表概率预报结果 Figure 8 Niño4 index of probability forecast (NIPF) in the CP-El Niño by model CCSM4 shown in Fig. 4: (a) Assimilation of observed SST in the PP_max region; (b) assimilation of observed SST in the PP_max_R region. Red lines represent the truth values, the areas shaded in gray represent the results of probability forecast

 图 9 对CNRM-CM5、GFDL-ESM2M、GISS-E2-R和CCSM4模式中所有CP-El Niño个例，在分别同化PP_max_R（黄）、PP_max（红）和其他三个随机区域（蓝、绿、紫）观测的SST后，关于其Niño4指数集合平均预报的结果与“真值”的相关系数。图中虚线表示通过置信水平为95%的显著性检验的临界值 Figure 9 Correlation coefficients between the predicted Niño4 index for CP-El Niño events and that of true events. The predicted Niño4 index is obtained by conducting ensemble-mean forecast with assimilation of observed SST in the PP_max_R (yellow), PP_max (red) regions, and other randomly selected three regions (blue, green, and purple), respectively, using models CNRM-CM5, GFDL-ESM2M, GISS-E2-R, and CCSM4. The dashed lines denote significance correlation at the 95% confidence level
5 东太平洋型厄尔尼诺事件的目标观测敏感区

 图 10 用新方法计算得到的表 1中各数值模式EP-El Niño个例的PP指数空间分布的集合平均，打点区域是PP指数最大值的前M个格点 Figure 10 Ensemble means of the PP index calculated by the new approach for the EP-El Niño cases in each model listed in Table 1. The black-dotted regions are for the first M grid points with much large PP values

 图 11 表 1中每个模式中所有EP-El Niño个例，在分别同化PP_max_R（黄色线）、PP_max（红色线）和其他三个随机区域（蓝色线、绿色线、紫色线）观测的SST后，对Niño3指数集合平均预报与“真值”的相关系数。图中虚线是各模式的相关系数通过置信水平为95%的显著性检验的临界值 Figure 11 Correlation coefficients between the predicted Niño3 index for EP-El Niño events and that of true events. The predicted Niño3 index is obtained by conducting ensemble-mean forecast with assimilation of observed SST in PP_max_R (yellow lines), PP_max (red lines) regions, and three randomly selected regions (blue, green, and pink lines) respectively using the selected models listed in Table 1. The dashed lines denote significance correlation at the 95% confidence level
6 总结和讨论

KD提出的粒子滤波—目标观测方法利用集合样本离散度度量初值敏感性，但该敏感性不能保证等同于集合平均预报误差度量的初值敏感性，从而使得KD目标观测敏感区的有效性往往在预报试验中得不到验证。针对KD方法的这种局限性，该研究依据集合预报系统的可靠性条件——集合样本离散度和集合平均预报误差呈正相关关系，提出了新的粒子滤波—目标观测方法，即在应用KD方法之前，首先计算集合样本离散度和集合平均预报误差呈现较强正相关关系的区域，然后在该区域考察PP指数的大值区，将该大值区作为目标观测敏感区。