Advances in Meteorology

Volume 2017 (2017), Article ID 4861765, 12 pages

https://doi.org/10.1155/2017/4861765

## A New Variational Assimilation Method Based on Gradient Information from Satellite Data

^{1}Institute of Meteorology and Oceanography, PLA University of Science and Technology, Nanjing, China^{2}National Satellite Meteorological Center, Beijing, China

Correspondence should be addressed to Yun-Feng Wang

Received 22 December 2016; Revised 27 March 2017; Accepted 10 April 2017; Published 24 April 2017

Academic Editor: Rossella Ferretti

Copyright © 2017 Bo Zhong et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

With the development of meteorological observation technology, satellite data have found increasingly wide use in the numerical weather prediction field. However, there are various observational biases in satellite data, including a random bias brought about by complex weather systems and a systematic bias caused by the instrument itself, which greatly influence the quality of satellite data. A gradient information assimilation method is proposed in this paper to eliminate systematic bias. This method uses a gradient operator for gradient transformation between the model variable and observation variable and reaches the objective of eliminating systematic bias. An ideal experiment of variational data assimilation is conducted using the Community Radiative Transfer Model (CRTM) and Advanced Microwave Sounding Unit-A (AMSU-A) data, indicating that only assimilating gradient information can eliminate the smooth systematic bias in observation data. Then, a numerical simulation of tropical cyclone (TC) Megi and data assimilation experiment are conducted using the Weather Research Forecast (WRF) and WRF Data Assimilation (WRFDA) model as well as the Atmospheric Infrared Sounder (AIRS) data. The results show that the method of gradient information assimilation can improve the accuracy of TC tracks forecast and is also applicable for dealing with unreliable satellite data.

#### 1. Introduction

With the rapid development of space technology and remote sensing technology, satellite data have been widely used in data assimilation, weather analysis, and forecasting by virtue of their high temporal and spatial resolution. In particular, satellite data play a key role in TC research because of a lack of observations over the ocean. For example, Kidder et al. [1] studied the warm core structure of TCs and gradient wind inversion with the data obtained by Advanced Microwave Sounding Units (AMSU). The study shows that the AMSU data provide improvement to track forecasts of TC [2]. Wang et al. [3] used BDA Method combined with AMSU-A Data Assimilation Method to reconstruct the Mesoscale Information of TC. McNally et al. [4] added AIRS data to the assimilation system of the European Centre for Medium-Range Weather Forecast (ECMWF) and found that assimilating AIRS data improved the quality of analysis and forecasting. The distribution of clouds, precipitation, and thermal structure in the TC’s evolution were described in detail using Cloudsat data [5]. Although satellite data have been successfully applied to many studies, the bias of the observation instruments on satellites can lead to most of the analytical errors in the model of the initial field and cannot be ignored [6]. Due to the bias of production accuracy as well as a variety of calibration, positioning, and other aspects of observatory instruments carried out by satellites, the final observation results also contain bias. At present, bias avoidance mainly includes quality control and bias correction. Quality control can eliminate obvious bias by deleting data that are too disperse or of low reliability but cannot eliminate bias from the source and can only reduce the use of unreliable satellite data. In addition, systemic bias is a problem of global data rather than individual data that cannot be eliminated by quality control. The purpose of bias correction is to eliminate or reduce systematic bias, the sources of which include bias in radiative transfer modes and instrument calibration, and systematic bias forms the response characteristics of the sensor over time. At present, systematic bias cannot be fundamentally removed by bias correction. Therefore, satellite observation data need to be revised before utilization. Wang et al. [7] proposed that, based on the GRAPES model variational system and assuming a known bias correction, forcing the initial state of the model mapping bias to be consistent with satellite observations of the air mass bias can achieve the effect of bias correction. However, in practice, the mechanism of generating bias is unknown, so it is difficult to eliminate the impact of systematic bias. The ECMWF initially adopted global scan correction and linear air mass correction to reduce satellite bias. However, the change of radiation angle and air mass modification were not taken into the consideration [8] in these methods, so Eyre [9] cited cloud radiation to adjust the scheme. Harris and Kelly [10] first considered the latitude dependency of scan correction and divided the globe into 18 latitudes. Then, air mass bias correction was performed on the result of the scan line scan correction using the air mass bias prediction factor from the mode background field. Liu [11], with reference to the previous TIROS Operational Vertical Sounder (TOVS) bias correction scheme of ECMWF combined with the radiation characteristics of the Chinese Advanced TIROS Operational Vertical Sounder (ATOVS), performed the correction of the scanning line bias and air mass bias, and the former was obtained by multiple linear regression modelling based on the selected air mass forecasting factor. The experimental results show that the error distribution tends to a Gaussian distribution before and after the bias correction and that the bias standard deviation is also reduced accordingly. Bao et al. [12] developed the FY3A-Microwave Temperature Sounder (FY3A-MWTS) satellite data bias correction system based on the classical satellite data bias correction method, which can effectively eliminate the air mass deviation. Furthermore, the deviation of the corrected image after averaging the observation residuals is greatly improved, approaching 0. At present, the bias correction method can reduce but not eliminate systematic bias. Wang et al. [13] proposed a method to eliminate systematic bias by using a gradient operator for gradient transformation between the model variable and observation variable based on a shallow water wave mode. This method makes the assimilation effect better able to absorb the spatial and temporal distribution tendency rather than the data itself and is also applicable to low confidence data. However, this method only studies shallow water equations and other ideal experiments and has not been used in practical applications.

With the popularization and rapid development of satellite observation data, the quality control of satellite data and elimination of systematic bias of observation data urgently need to be addressed. In this paper, the gradient information of AMSU-A observed TBB data is introduced into the model as new assimilation data using the CRTM model and the feasibility of the gradient information assimilation method for satellite observation data is verified by comparing assimilation results between gradient information assimilation method and original variational assimilation method. On this basis, the WRFDA module was used to assimilate AIRS observations with higher horizontal resolution. Then, the TC “Megi” was simulated with the WRF model. Finally, the results were analyzed by comparing the assimilation effect under different schemes. Although AMSU-A data and AIRS data are different in objections, channels, and resolutions, gradient information extraction and model variation replacement are only in the horizontal direction. Therefore, characteristics of these data do not interfere with the assimilation results. The AMSU-A observational data are used to verify the feasibility of the gradient information assimilation method. The advantage of assimilating AMSU-A observational data is that it avoids the complex channel selection problem and reduces the computational complexity of the assimilation algorithm.

#### 2. Assimilation Principle of Satellite Data

##### 2.1. Cost Function

In the conventional assimilation method, the cost function is defined aswhere is the difference between the mode control variable and the background variable and is the difference between the simulated and observed AIRS data. The detailed variable settings are as follows:

where represents background error covariance matrix, the superscript represents matrix transpose, represents weight coefficient matrix which reflects the quality of the observed data credibility, represents forward radiative transfer operator, and represents the brightness temperature of the observed data.

##### 2.2. CRTM Mode

CRTM, a rapid radiation transmission model developed by the US Joint Center for Satellite Data Assimilation (JCSDA), is one of the software programs in the numerical weather forecasting data assimilation system. In this paper, the CRTM model is used to transform the existing atmospheric profile information (including barometric pressure, temperature, humidity, and ozone level) into the required observation brightness temperature information using the clear sky module (ClearSky), which acts as the observation operator in the ideal experiment. In addition, the descent algorithm adopted in the process of assimilation is the finite inner quasi-Newton method (Nocedal [14], 1980; Liu and Nocedal [15], 1989).

##### 2.3. WRFDA

WRFDA is an assimilation module of the WRF mode that assimilates the observed data into a background field obtained by numerical prediction and uses the variational assimilation technique to obtain the required analysis field. The current WRF-3DVar system can assimilate conventional observations and unconventional data like radar, occultation data, satellite radiometric data, and so on.

#### 3. Variational Assimilation Scheme of Gradient Information

##### 3.1. Construction of Horizontal Gradient Information

Suppose there exists the following truth vector of satellite bright temperature observation data:

where is the number of data in the data sequence and superscript represents the transpose. Assuming there exists systematic bias and random bias vector of satellite data,and the bias has an unbiased stochastic distribution. The mode status variable is . The observation operator is . It is equivalent to use the CRTM mode to convert the profile containing the temperature information into the brightness temperature.

The observed data vector with bias can be expressed as :

To eliminate , it is necessary to rebuild the model variables and observation vectors. First, the model variable is transformed into gradient information. Then, consider the mapping of the model variable to the observation space vector.

Then, performing the gradient information transformation,and is the new pattern variable after the gradient information transformation. is the spatial distance between the two data locations. The observation vector is rewritten as :

is the gradient information after the transformation of the observed vector, which eliminates the impact of , and is the residual expectation of the new variables after transformation:

##### 3.2. Gradient Information Assimilation

The gradient information is introduced into the assimilation of satellite data. When only the gradient information is assimilated, the cost function is defined as

is the difference between the new control variable and new observation variable after the gradient information is transformed.

represents the gradient information transformation operator.

#### 4. Ideal Test

The standard profile used in this paper is from the CRTM model. According to the range of pressure in the actual model, it extracts the 63 layer temperature profile (51.5–1010 hPa) that contains the atmospheric temperature profiles, humidity profiles, ozone profiles, and other information. In this paper, the temperature variation in profile is chosen as the assimilation test. According to the distribution of the pressure layer and channel weight function map of the AMSU-A satellite data, it selects 4–9 channel as a channel assimilation which is also the mode of the commonly used AMSU-A satellite data assimilation channel.

Table 1 shows the specific test settings of the ideal scheme. The purpose of gradient information assimilation is to eliminate the systematic bias of the instrument. To highlight the impact of systematic bias and not consider the background error covariance matrix, a fixed random bias is set in the range of ±1 K. The systematic bias is set to 0, 0.5, 1, 1.5, or 2.0 K. According to the test settings, , represent the true value of the brightness temperature of two standard profiles. , represent the brightness temperature of the two standard profiles that are a superposition of random bias and systematic bias. , represent the brightness temperature of two profiles obtained by variational assimilation, which set , as the initial profile, and set , as the true value of the brightness temperature. Then, the RMSE of , , and , is calculated as an average of the 4–9 channel. The results are shown in Figure 1.