# Assimilation of ASCAT Sea Surface Wind Retrievals with Correlated Observation Errors

## 考虑观测误差相关的ASCAT海表风场反演资料同化

• Corresponding author: Weimin ZHANG, wmzhang104@139.com
• Funds:

Supported by the National Natural Science Foundation of China (41675097 and 41375113) and Key Research and Development Program of Hainan Province (ZDYF2017167)

• doi: 10.1007/s13351-021-1007-0
• Data assimilation systems usually assume that the observation errors of wind components, i.e., u (the longitudinal component) and v (the latitudinal component), are uncorrelated. However, since wind components are derived from observations in the form of wind speed and direction (spd and dir), the observation errors of u and v are correlated. In this paper, an explicit expression of the observation errors and correlation for each pair of wind components are derived based on the law of error propagation. The new data assimilation scheme considering the correlated error of wind components is implemented in the Weather Research and Forecasting Data Assimilation (WRFDA) system. Besides, adaptive quality control (QC) is introduced to retain the information of high wind-speed observations. Results from real data experiments assimilating the Advanced Scatterometer (ASCAT) sea surface winds suggest that analyses from the new data assimilation scheme are more reasonable compared to those from the conventional one, and could improve the forecasting of Typhoon Noru.

资料同化系统通常假定纬向风分量u与经向风分量v的观测误差不相关。然而，由于风分量是从观测的风速和风向推导出来的，所以风分量的观测误差实际上是相关的。本文根据误差传播定律，导出了已知风速和风向误差的前提下，风分量的观测误差和相关系数的显示表达式，并在WRF模式同化系统（WRFDA）中实现了考虑风分量观测误差相关的直接同化。此外，为了更好的利用高风条件下的风场信息，引入了自适应的质量控制方案。基于ASCAT海表风场反演的初步实验结果表明，与常规方法相比，本文的方法更加合理，并且改进了台风“奥鹿”的预报效果。

• Fig. 1.  Region where the wind “truth” might be located when given the wind observation with uncertainties. The red arrow is the wind observation, while the blue ones are the corresponding wind components. The red shadow region is the place where the wind “truth” might be located given the uncertainties of the wind observation. Panel (a) is from the wind-vector perspective, in which the uncertainties of ${\rm{spd}}$ and ${\rm{dir}}$ (${\delta _{{\rm{spd}}}}$ and ${\delta _{{\rm{dir}}}}$) are known. Panel (b) is from the wind-components perspective, in which the uncertainties of $u$ and $v$ (${\delta _u}$ and ${\delta _v}$) are known.

Fig. 2.  Standard errors and corresponding correlation of $u$ and $v$ within a certain range of the observed values: (a) standard errors of $u$, denoted as ${\sigma _u}$; (b) standard errors of $v$, denoted as ${\sigma _v}$; and (c) error correlation of $u$ and $v$, denoted as ${\rho _{u,v}}$.

Fig. 3.  As in Fig. 2, but after variance inflation.

Fig. 4.  ASCAT wind field of Typhoon Noru with a grid size of 25 km: (a) wind speed (spd) field, (b) standard deviation of $u$ component, (c) standard deviation of $v$ component, and (d) error correlation of wind components.

Fig. 5.  Ensemble mean of the wind fields of forecasts and corresponding flow-dependent error of the $u$ and $v$ components: (a) ensemble average of the wind fields of forecasts, (b) standard deviation of the $u$ component, and (c) standard deviation of the $v$ component.

Fig. 6.  QC using different assimilation schemes, in which the blue dots represent the wind observations that are successfully assimilated into the data assimilation system: (a) ($u$, $v$) with independent errors, (b) (spd, dir) with independent errors, and (c) ($u$, $v$) with correlated errors.

Fig. 7.  Wind speed (spd) analysis errors of different experiments: (a) background, (b) ($u$, $v$) components with independent error, (c) (spd, dir) with independent error, and (d) ($u$, $v$) components with correlated error.

Fig. 8.  Mean error and root-mean-square (RMS) of spd analysis errors of different experiments: (a) background, (b) ($u$, $v$) components with independent error, (c) (spd, dir) with independent error, and (d) ($u$, $v$) components with correlated error.

Fig. 9.  As in Fig. 7, but for pressure analysis errors.

Fig. 10.  As in Fig. 8, but for pressure analysis errors.

Fig. 11.  The forecast (a) tracks and (b) track errors of Typhoon Noru (2017).

Fig. 12.  (a) Minimum pressure and (b) maximum spd forecast errors of the typhoon eye.

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###### 通讯作者: 陈斌, bchen63@163.com
• 1.

沈阳化工大学材料科学与工程学院 沈阳 110142

## Assimilation of ASCAT Sea Surface Wind Retrievals with Correlated Observation Errors

###### Corresponding author: Weimin ZHANG, wmzhang104@139.com;
• 1. College of Meteorology and Oceanology, National University of Defense Technology, Changsha 410073
• 2. Laboratory of Software Engineering for Complex Systems, Changsha 410073
• 3. State Key Laboratory of Remote Sensing Science, Chinese Academy of Sciences, Beijing 100101
• 4. Hainan Key Laboratory of Earth Observation, Sanya 572029
• 5. Beijing Institute of Applied Meteorology, Beijing 100029
Funds: Supported by the National Natural Science Foundation of China (41675097 and 41375113) and Key Research and Development Program of Hainan Province (ZDYF2017167)

Abstract:

Data assimilation systems usually assume that the observation errors of wind components, i.e., u (the longitudinal component) and v (the latitudinal component), are uncorrelated. However, since wind components are derived from observations in the form of wind speed and direction (spd and dir), the observation errors of u and v are correlated. In this paper, an explicit expression of the observation errors and correlation for each pair of wind components are derived based on the law of error propagation. The new data assimilation scheme considering the correlated error of wind components is implemented in the Weather Research and Forecasting Data Assimilation (WRFDA) system. Besides, adaptive quality control (QC) is introduced to retain the information of high wind-speed observations. Results from real data experiments assimilating the Advanced Scatterometer (ASCAT) sea surface winds suggest that analyses from the new data assimilation scheme are more reasonable compared to those from the conventional one, and could improve the forecasting of Typhoon Noru.

Reference (27)

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