TyphoonMariaPrecipitationRetrieval andEvolutionBasedonthe Infrared Brightness Temperature of the Feng-Yun 4A/Advanced Geosynchronous Radiation Imager

Anhui Meteorological Observatory, Key Lab of Strong Weather Analysis and Forecast, Hefei, Anhui 230031, China Anhui Institute of Meteorological, Anhui Key Lab of Atmospheric Science and Satellite Remote Sensing, Hefei, Anhui 230031, China Anhui Meteorological Bureau, Hefei, Anhui 230031, China National Meteorological Center of China, Numerical Weather Prediction Center of China Meteorological Administration, Beijing 100081, China


Introduction
Precipitation plays an important role in the global energy and water cycle, and monitoring and forecasting it is crucial when a typhoon, rainstorm, or severe convection develops and occurs. China is the country that is most affected by typhoons; it is hit by an average of about seven typhoons every year. Typhoons are mainly caused by gales, rainstorms, and storm surges, but compared with typhoons caused by gales, those caused by rainstorms cause more disasters [1]. For example, after the severe Tropical Storm Bilis made landfall in the Fujian province on July 12, 2006, it led to heavy rains in the Hunan, Jiangxi, and Guangdong provinces, which caused serious landslides and mud-rock flows. e disaster caused more than 600 deaths and direct economic losses of about 4.4 billion U.S. dollars [1]. erefore, quantitative research on typhoon precipitation is an important component of disaster prevention and reduction.
Due to the insufficient density of ground rain gauges and the ground-based rain measuring radar observation network, it is difficult to monitor and track rainstorms and other catastrophic weather systems, not to mention the spatial distribution and changes in the intensity of typhoon precipitation [2]. Meteorological satellites can effectively obtain information such as brightness temperature in unattended areas, such as oceans, mountains, and deserts. e precipitation products obtained through retrieval have become the only effective means to cover global precipitation observation [3]. Satellite remote sensing can be divided into active microwave remote sensing, passive microwave remote sensing, and visible/infrared remote sensing. Active and passive microwave remote sensing can detect the vertical structure of precipitation and the structural information inside the cloud, respectively. However, at present, the microwave remote sensing device is carried by the polar orbit meteorological satellite, and the time resolution is low [2]. In contrast, geostationary meteorological satellites are characterized by high spatial and temporal resolution, wide coverage, and strong time continuity, and they can effectively monitor precipitation. e cloud top brightness temperature, which is located at the highest level of the atmospheric vertical layer and is provided by the stationary meteorological satellite, can reveal significant characteristics about the existence of clouds and the evolution stage of clouds and can reflect the distribution of rain areas of typhoons to a certain extent [1].
Researchers have conducted a series of studies on satellite data retrieval of precipitation. Ferraro and Marks [4] and Alishouse et al. [5] achieved good inversion results by using statistical methods. Based on the statistical relationship between convective cloud top brightness temperature and precipitation intensity in an infrared cloud image, Lan et al. [6] developed a short-time convective precipitation intensity forecast. Moreover, Behrangi et al. [7] adopted the GOES-R satellite multichannel, PERSIANN-MSA method to estimate precipitation. ey found that scheme 12 effectively recognized the presence and absence of rain with a probability of detection (POD) of 0.530 and a false-alarm ratio (FAR) of 0.355. Similarly, based on the brightness temperature of a satellite infrared and water vapor channel, Tao et al. [8] proposed the deep neural network to estimate the precipitation and the detect the presence or absence of rain in the study area. e POD was 0.418, and the FAR was 0.528. At present, precipitation retrieval algorithms focus on information from a visible, infrared window area and water vapor channel. For example, Himawari-8 remote sensing data contain other infrared channel information that can improve the accuracy of precipitation retrieval. Moreover, Min et al. [9] used random forests (RF) to carry out precipitation retrieval based on a numerical model weather forecast index and GPM and H8 data and obtained good results. Sun et al. [2] used a lookup table to carry out a study on the H8 infrared brightness temperature retrieval of precipitation. e more dimensions the lookup table had, the higher the retrieval accuracy was. Ebtehaj et al. [10] proposed the shrunken locally linear embedding (SLLE) algorithm for the retrieval of precipitation, which was applied to the precipitation retrieval of TRMM data with high retrieval accuracy. Because this method only uses satellite brightness temperature, the operation is relatively simple. erefore, Wang et al. [11] applied this algorithm to the precipitation retrieval of H8 infrared data.
In summary, this paper focuses on Typhoon Maria and applies the retrieval algorithm proposed by Ebtehaj et al. to the infrared brightness temperature data of Advanced Geosynchronous Radiation Imager (AGRI) data from Feng-Yun 4A satellite [12,13] in order to explore the role of AGRI data in typhoon precipitation monitoring. Furthermore, the information from a typhoon's dominant cloud system was extracted from the AGRI infrared window channel brightness temperature image based on the fuzzy c-means (FCM) clustering method [13,14] to monitor the generation and change of typhoons and potentially eliminate them [15].

Precipitation Retrieval Algorithm Based on Improved Shrunken Locally Linear Embedding.
is section briefly describes the satellite retrieval precipitation algorithm; the algorithm details can be found in the study of Ebtehaj et al. [10,16]. Satellite channel brightness temperature retrieval precipitation can be defined as a mathematical inverse problem. Suppose that at a certain pixel point (field of view), brightness temperature is observed in n c channels denoted by y � (y 1 , y 2 , . . . , y n c ) T ∈ R n c , and the corresponding n r level precipitation profile is denoted by x � (x 1 , x 2 , . . . , x n r ) T ∈ R n r . e superscript T indicates the vector transpose. e satellite observed brightness temperature and precipitation profiles have the following nonlinear mapping relationship: where H: x ⟶ y represents the forward projection function and v ∈ R n c represents the model or measurement error. e historical sample set used in this paper was defined as a matching dictionary of "brightness temperature" and "precipitation," denoted by D � (b i , r i ) M i�1 . i is the ith "atoms" in the dictionary; it could also be called the ith sample. Each set of matches in the dictionary was the basic "atom" of the channel observation brightness temperature retrieval of the precipitation field. Moreover, b i � (b 1i , b 2i , . . . , b n c i ) ∈ R n c and r i � (r 1i , r 2i , . . . , r n c i ) ∈ R n r represent the brightness temperature of n c channels and the n r -dimensional precipitation profile, respectively. e dictionary entries on "brightness temperature" and "precipitation" were denoted as B � [b 1 | . . . | b M ] ∈ R n c ×M and R � [r 1 | . . . | r M ] ∈ R n r ×M , respectively. e basic idea of the precipitation retrieval model proposed by Ebtehaj et al. [10] is to look for a group of "atoms" in the dictionary B � [b 1 | . . . | b M ] ∈ R n c ×M to represent the brightness temperature of the pixel (field of view, FOV) to be inverted and then perform the following calculation: 2 Advances in Meteorology where B S is a subset of the dictionary composed of a found set of "atoms"; c is the atomic coefficient; and v is the observation error. By applying the atomic coefficient c to the matched subset of precipitation dictionary R s , we obtained the precipitation retrieval x as follows: where R S is the subset of R � [r 1 | . . . | r M ] ∈ R n r ×M dictionary corresponding to B S ; c is the atomic coefficient of the combined precipitation subdictionary; and e is the error. Equations (2) and (3) convert the problem into a solution for atomic coefficient c.
Based on the algorithm of Ebtehaj et al. [10], the atomic coefficient c can be obtained by minimizing the objective function constrained by the regular term of L1 norm, as follows: where W is the contribution rate of channel observation of brightness temperature to objective function. Moreover, λ 1 and λ 2 are regularization parameters; L1 and L2-norm are ‖c‖ 1 � i |c i | and ‖x‖ 2 A � x T Ax, respectively, and A represents a positive definite matrix.
Since the L1 norm is not differentiable at the origin, equation (4) is a nonsmooth convex problem. Moreover, the L1 norm proved to be an effective method to solve sparse solutions, i.e., a small number of atoms retained the maximum amount of original information [17].
e key to the algorithm is precipitation signal identification. Compared with nonprecipitation, precipitation falls in the probability category of a "small event." erefore, before precipitation retrieval, the K-nearest neighbor (KNN) method was adopted to identify the channel brightness temperature "precipitation" and "nonprecipitation" signals. e specific process was as follows: for a given channel brightness temperature y � (y 1 , y 2 , . . . , y n c ) to be inverted into a dictionary pair (B, R), we searched for two "optimal" joint subdictionaries (B s ∈ R n c ×K , R s ∈ R n r ×K ) based on KNN. Given the probability threshold predefined value p, based on the "probability vote" method detection, if there was more than p k "precipitation" in the precipitation dictionary, the channel brightness temperature contained the "precipitation" signal.
In the "precipitation signal" subspace, the representation coefficient c was obtained by solving equation (4), and the precipitation profile x � R S c was obtained by satellite brightness temperature inversion. In the equation, x is the approximation of x.
e improvement to the method proposed by Ebtehaj et al. [10,16] is as follows: (1) e brightness temperature gradient information of "precipitation" and "nonprecipitation" from the infrared spectrum of AGRI, which was obtained by statistics, was taken as the prior information and coupled to the K-nearest neighbor (KNN) model.
(2) e contribution rate W of the brightness temperature at different spectral channels to the objective function of the retrieval model (see formula (4)) was "optimized" by the Bayesian model averaging (BMA) that could be implemented with the Markov Chain Monte Carlo (MCMC) method [18,19]. (3) Relevant parameters in the KNN model (such as the detection probability p and the neighborhood K) were optimized, and the two regularization parameters of λ 1 and λ 2 were also optimized [10]. (4) e membership degree information of the dominant cloud system in AGRI typhoon, which was obtained by the fuzzy c-means (FCM) clustering algorithm, was applied to the precipitation retrieval. us, the main structure of typhoon precipitation could be acquired [13].

Fuzzy c-Means Clustering Model.
e fuzzy c-means (FCM) algorithm was used to divide the data sample set into several categories by minimizing a quadratic objective function [14]. Each pixel in the image was classified individually into the corresponding category, and the minimum sum of the error squares of each sample and the cluster center were adopted as the discriminant criterion. e clustering center and membership value were searched iteratively to obtain the minimum value of the objective function so as to realize the optimal classification of the image. e FCM objective function was defined as follows: e constraint conditions of equation (5) are as follows: where p is the dimension of each "feature" vector x j ; n is the number of feature vectors; u ij is the membership degree of the j data belonging to the i category; m is the fuzzy index (m � 2 in this study); v i is the i fuzzy clustering center; and c is the number of categories. e Euclidean norm was used to measure the distance between the "feature" vector x j and the clustering center v i , as follows: According to the Lagrange extremum method, through derivation, the fuzzy membership u ij and clustering center v i were obtained as follows: Advances in Meteorology 3

Data Description.
China's new geostationary FY4A satellite was successfully launched on December 11, 2016. e FY4A/AGRI has 14 channels, including three visible, three near-infrared, and eight infrared [12,13]. Because only the AGRI infrared channels ranging from 8 to 14 were assimilated in the numerical weather prediction system [12,13], we only considered the brightness temperatures of these seven channels for typhoon precipitation retrieval. eir central wavelengths were 3.72, 6.25, 7.10, 8.5, 10.8, 12, and 13.5 micron (unit: μm), respectively. e time interval between two consecutive images of the AGRI brightness temperature was 15 min during observation encryption, and only integral data at hourly times such as 0000 UTC, 0100 UTC, and so on were used in this paper. e domain of the Global Precipitation Measurement (GPM) IMERG precipitation data used in this investigation covered 89.95°S─89.95°N latitude and 179.95°W─179.95°E longitude, with a spatial resolution of 0.1°× 0.1° [13,20]. e time resolution was hourly (mm/h), i.e., 24 precipitation observation times per day. e GPM IMERG data are available at https://pmm.nasa.gov/data-access/downloads/gpm.
Due to the different spatial resolutions of FY4A/AGRI and GPM data, when constructing the dictionary of the historical sample base, the "nearest neighbor" method was adopted to interpolate the channel brightness temperature of FY4A/ AGRI to the GPM FOV. For evaluation of the precipitation retrieval accuracy, the "nearest neighbor" method was adopted to interpolate the retrieval precipitation to the GPM FOV.

Precipitation Signal Identification Based on the AGRI Infrared Brightness Temperature.
e brightness temperature of AGRI infrared channel in the region of Typhoon Maria on July 09, 2018, to July 11, 2018, was used to identify precipitation signals. e matching GPM data were used to judge the precipitation FOVs. e FY4A/AGRI brightness temperature gradient (ΔTB, unit: K), defined as the difference between the brightness temperature of nonprecipitation and precipitation (unit: K) in different channels, is shown in Figure 1(a).
For AGRI channels with different grades of precipitation, the mean brightness temperature (TB Mean, unit: K) is shown in Figure 1(b). Figure 1(a) reveals that for FY4A/AGRI infrared channels 8 to 14, when precipitation occurred, the brightness temperature gradient of the channels all changed. Channel 9 underwent the smallest change range, at only 13.93 K, and channel 12 had the largest range change, at 40.28 K. Figure 1(b) reveals that even with only weak precipitation, AGRI channel's brightness temperature variation range was still large. When the precipitation intensity increased, the change range of the brightness temperature gradient in the AGRI channel was small, which may be related to the small number of precipitation samples in the statistical history sample database and the insufficient representation. It may be also related to the infrared channel's sensitivity to clouds, which can generally only detect cloud top brightness temperature and cannot penetrate clouds [21]. Precipitation is related to cloud top height, cloud top temperature, and cloud vertical structure. Channels of different wavelengths (the peak layer of the weight function varies; see Figure 2(b)) can reflect different aspects of clouds. erefore, the responses of the brightness temperatures of different AGRI channels to the precipitation signal vary (Figure 1(a)). Precipitation can be successfully retrieved using the combined information of brightness temperatures from different channels. Generally, the cloud bodies of precipitation clouds are thicker, the cloud tops are higher, and the cloud top temperatures are lower. us, cold cloud tops generally correspond to heavy precipitation intensity, and the responses of different channels to different levels of precipitation vary (Figure 1(b)).

Optimization of Channel Contribution Rate Based on
BMA. In this paper, the "precipitation signal" of the AGRI infrared channel was obtained based on the K-nearest neighbor (KNN) approach. Based on BMA, we estimated the contribution rate of different channels of AGRI to the objective function of the retrieval model. In the optimization process, BMA-Gamma, BMA-Normal, and BMA-Heteroscedastic were adopted to obtain the channel contribution rates, which are shown in Figure 2(a). Gamma, Normal, and Heteroscedastic represent the conditional probability distributions of Heteroscedastic Gamma, Homoscedastic Normal, and Heteroscedastic Normal, respectively [18]. We adopted radiative transfer for the Tiros Operational Vertical Sounder [22] to determine the weight function of the AGRI channels from 8 to 14 by calculating the standard American atmospheric profile, as shown in Figure 2(b). Figure 2(a) reveals that the contribution rate of channel 9 (the weight function peak was 358.28 hPa, as shown in Figure 2(b)) based on BMA-Gamma was large, which may be related to channel 9's main detection of atmospheric water vapor. e contribution value of other channels was small. e contribution rates of different AGRI channels obtained based on BMA-Gamma were better than those in the precipitation retrieval, which may be related to the characteristics of the "Gamma" distribution of precipitation [23].

Dominant Cloud System Identification and Tracking
Based on the FCM Method. e key to solving the problem of cloud system extraction is to identify the "dominant cloud system," which often leads to typhoon precipitation [15]. In order to analyze the structure of a typhoon's dominant cloud     system, we used the FCM to identify the dominant cloud system based on the 10.8-micron window channel of the AGRI. Specific details on the identification of the dominant cloud system can be found in the work of Wang et al. [13]. Figure 3 shows the original brightness temperature of AGRI and the dominant cloud system based on the FCM and GPM precipitation distribution in the formation of Typhoon Maria.
As shown in Figure 3, the brightness temperature distribution of typhoon's dominant cloud system identified by the FCM was consistent with the GPM precipitation field, and the AGRI brightness temperature low value area corresponded to the strong precipitation area of GPM. is may be related to the inherent characteristics of the FCM method. e typhoon spiral cloud band structure in the original AGRI brightness temperature image has not been effectively identified [13,15], which may be related to the inherent characteristics of the FCM method. A great deal of information concerning a typhoon's motion, wind field, and heavy rainfall is contained in its spiral cloud bands. Moreover, based on the GPM precipitation field (time: 2018071016), we know that GPM data can reflect the "spiral rain belt" of a typhoon.
Comparing the precipitation field U and V, SSIM is defined as where c 1 and c 2 are two constants to stabilize the computation; u and v are partial datasets of precipitation field U and V, respectively; and u and v are the mean values of selected neighborhoods (typically 5 × 5 and 7 × 7 FOVs, etc.) around a certain FOV of u and v, respectively. e overbar (− ) indicates the mean value.
Defining the peak signal-to-noise ratio (PSNR): where L refers to the dynamic range of the GPM precipitation field. MSE � (U − V) 2 , in which U and V are GPM and retrieval precipitation field, respectively.
where A is the number of FOVs in which both U and V are smaller than the threshold; B is the number of FOVs in which U is smaller than the threshold while V is greater than the threshold; and C is the number of FOVs in which U is greater than the threshold while V is smaller than the threshold. e threshold is set as 5.0 mm/h in this paper.

Precipitation Retrieval Experimental of AGRI Infrared Channel Brightness Temperature Based on an Improved Local
Linear Embedding Method. In this study, the brightness temperature obtained from AGRI channels 8-14 was used to retrieve precipitation. e precipitation field at different development stages of Typhoon Maria retrieved with the improved SLLE method is shown in Figure 4. Moreover, to get the main structure of typhoon precipitation, taking the membership degree of the dominant cloud system from the AGRI channels as the prior information, which was obtained by the FCM clustering algorithm, the modified precipitation retrieval result (denoted as "precipitation retrieval (FCM)") could be acquired. e observed data (namely, "true value") in Figure 4 corresponds to the GPM precipitation at different times in Figure 3.
Moreover, the accuracy assessment on the precipitation of "Typhoon Maria" retrieved from AGRI is shown in Table 1.
As shown in Figure 4 and Table 1, the retrieval precipitation field based on the improved SLLE method agreed with GPM and successfully retrieved the spiral cloud rain bands of the typhoon. In addition, the precipitation field after the membership degree modification of the dominant cloud system based on FCM could identify the main morphological structure of typhoon precipitation, especially in high-precipitation value areas, but the precipitation information of the spiral cloud rain belt of "typhoon" was excessively removed [15]. It can be seen that (formulas (9)-(13)), compared with the retrieval precipitation field obtained by the improved SLLE method, part of the field of view (FOV) values was eliminated (that is, the FOV value was assigned to 0) in the precipitation field obtained by the FCM modification. erefore, the retrieval result by the FCM modification exhibits a decrease in the SSIM, NMI, and PSNR values and an increase in the POD and FAR values, whereas there is a decrease in the CSI value, as shown in 6 Advances in Meteorology   Table 1. is may be related to the inherent characteristics of the FCM method, which we will study in greater detail in the future.

Analysis of Time Series Changes of Dominant Cloud System Development of Typhoon Maria Based on the FCM
Method. In this study, FCM was used to identify the dominant cloud system of typhoons with a brightness temperature in the AGRI 10.8-micron window channel, and the time series changes of the typhoon's dominant cloud system were measured through radiation parameters (cloud top average brightness temperature and minimum brightness temperature) and shape parameters (cloud area) [26]. e cloud area was defined as the number of pixel points (FOVs) in this paper. Figure 5 shows the FCM dominant cloud system identification results from 0000 UTC to 1800 UTC on July 10, 2018, and the time series changes of cloud top average brightness temperature (denoted as TB Mean; unit: K), minimum brightness temperature (denoted as TB Min; unit: K), cloud area (denoted as Area (FOVs)), and average brightness temperature gradient (denoted as ΔTB Mean; unit: K).
As shown in Figure 5, at 1600 UTC on July 10, 2018, the typhoon's dominant cloud system had the largest change in the mean brightness temperature, the minimum brightness temperature was 194.1 k, and the cloud system contained the  e brightness temperature gradient had the largest variation range, and there was a "jump" point. Combined with a typhoon path (website: http:// typhoon.nmc.cn/web.html) analysis, we observed the moment when the typhoon turned from a supertyphoon into a typhoon.
us, it can be concluded that the brightness temperature gradient of the dominant cloud system identified by FCM could be used as an indicative factor to a certain extent, which is favorable for the analysis on the intensity change of typhoons. It also shows the feasibility of FY4A/ AGRI data in typhoon monitoring and precipitation retrieval.

Summary and Future Work
Retrieval of precipitation by satellite infrared data has always been a research hotspot. In this study, infrared data from Typhoon Maria in 2018 were selected and applied to typhoon precipitation monitoring based on the statistical analysis of the brightness temperature gradient in different infrared channels of "precipitation" and "nonprecipitation" FOVs by using Feng-Yun 4A/AGRI infrared channel brightness temperature.
Our main results were summarized as follows: (1) Identification of "precipitation" and "nonprecipitation" signals based on FY4A/AGRI infrared brightness temperature: when precipitation occurred, the brightness temperature gradient of channels 8 to 14 all changed, and channel 12 had the largest change range. According to statistics on different precipitation grades, even when there is weak precipitation, the brightness temperature of each channel changes greatly, so the infrared data of AGRI have a good response to precipitation signal identification. (2) Retrieval of typhoon precipitation information based on the improved SLEE method: the L1 norm regularization in the retrieval model can promote sparsity; that is, the maximum amount of original information can be retained with fewer dictionary atoms. From the precision evaluation index, we concluded that the typhoon precipitation retrieval field with the channel contribution rate based on BMA-Gamma is close to GPM and can retrieve the spiral rain band of a typhoon. GPM. e dominant cloud system membership degree information obtained by precipitation FCM modified the precipitation retrieval field and obtained the main precipitation morphological structure of the typhoon. (4) Dominant cloud system change analysis during the development of Typhoon Maria: based on FCM, the changes in the average brightness temperature, minimum brightness temperature area, and brightness temperature gradient of the dominant cloud system can be used to preliminarily analyze the development and change of typhoons.
In this study, only the application of the algorithm was considered. However, the period of statistical analysis data was short, there were few case studies conducted, and the historical sample base was not representative enough. In a future stage of this study, a large number of practical case studies will be carried out, starting from data mining to carry out the study on the optimal data volume of dictionary. When constructing features, numerical "model space" information, such as K index and convection-effective potential energy index, will be added [25]. In addition, the texture information of the visible channel will be integrated into the infrared channel.
at said, a robust statistical method was introduced into the retrieval of objective function, the Huber norm of the M-estimator was added [21], and the overall morphological structure of precipitation field was considered. e results of this study can be further applied to typhoon precipitation monitoring, forecasting, and early warning to improve meteorological services for the public.

Data Availability
e data used to support the findings of this study are available from their corresponding websites. e FY4A/ AGRI data are available at http://satellite.nsmc.org.cn/ portalsite/default.aspx?currentculture�en-US. e GPM IMERG data are available at https://pmm.nasa.gov/dataaccess/downloads/gpm.

Conflicts of Interest
e authors declare that they have no conflicts of interest.

Authors' Contributions
Gen Wang performed the experiments, analyzed the data, optimized and built the model, and drafted the manuscript. Kefu Wang provided technical support for using the precipitation retrieval method and contributed to the analysis and discussion. Wei Han and Dongyong Wang provided technical support for using the FCM method and contributed to the analysis, discussion, and editing of the manuscript. Xuexing Qiu provided important suggestions regarding the precipitation assessment of infrared data as well as manuscript editing.