Impacts of Forecast Time and Verification Area Setting on the Targeted Observation of Typhoon

Abstract

The results of the identification of sensitive areas are affected by the forecast time and verification area settings in targeted observations. Understanding this setting issue is important for improving the effectiveness of the identification of sensitive areas in real-time field campaigns. To determine this, a series of experiments were carried out based on the Ensemble Transform Sensitivity (ETS) method, and the results are as follows: (1) First, Observation System Simulation Experiments (OSSEs) were conducted to assimilate simulated dropsondes in sensitive areas (SENS) or non-sensitive areas (OTHR). The results showed that the SENS experiment improved forecasts of typhoon intensity, track, precipitation score, and RMSE of forecast elements. However, the OTHR experiment only improved the forecast in some aspects and even had negative effects on other aspects. This indicates that the sensitive areas identified by the ETS method are effective. (2) Different forecast time experiments were carried out. There were significant differences between the sensitive areas of fixed verification times and variable targeted observation times, indicating that the sensitive areas changed greatly with time. In the field campaign, it was necessary to calculate the sensitive area for multiple times in advance and to design or adjust the observation scheme according to the time. (3) Finally, comparative experiments of position deviation and size change in the verification area were carried out. It was found that for a big deviation, too large or too small a verification area will result in significant differences in the sensitive areas. Based on the study in this article, a verification area size of about 6° × 6° is recommended; this can not only accommodate the position deviation of the verification area from the typhoon center caused by forecast errors, but also does not contain too much noise unrelated to typhoons, which may affect the accuracy of identification of sensitive areas.

1. Introduction

Effective monitoring and prediction of severe weather plays a crucial role in the entire process of disaster prevention and reduction [1]. The high dependence of numerical weather prediction (NWP) on the initial condition has led to a strong demand for an observation system, which is the driving force for the development of the observation system. In the early stages of the development of NWPs, meteorologists noticed that the accuracy of numerical forecasting in a certain region was limited by the initial conditions in the local area in the earlier stages [2]. This means that only increasing observations in that local area to improve the initial conditions and thus improve the forecast effect may not be inferior to increasing observations on a large scale. This local area is the sensitive area under observation. In the mid to late 1990s, the idea of increasing observations within sensitive areas to improve the numerical forecasting skills for designated areas, known as targeted observations (or adaptive observations), was developed [3,4,5]. Targeted observation specifically means that in order to improve forecasting skills in the area of concern (verification area) at a future time (verification time, $t_v$), additional observations should be made in the area (sensitive area) at a future time (targeted observation time $t_a$, $t_a<t_v$) that has a greater impact on the prediction of the verification area. These additional observation data are processed by the assimilation system to provide more realistic initial conditions for numerical predictions in order to obtain more accurate forecasts [6]. The key to targeted observation lies in the identification of sensitive areas, which usually have the following characteristics: the initial errors are large, or the errors increase rapidly with the forecast. If observation is strengthened in these areas, the forecasting skills of the numerical model can be improved [7,8].

At present, there are many methods for identifying sensitive areas, such as the singular Vector (SV) method [9], Conditional Nonlinear Optimal Perturbation (CNOP) method [10], Adjoint-Derived Sensitivity Steering Vector (ADSSV) method [11], Ensemble Transform (ET) method [12], Ensemble Kalman Filter (EnKF) method [13], Ensemble Transform Kalman Filter (ETKF) method [14], Ensemble Transform Sensitivity (ETS) method [15], and so on. Because algorithms based on ensemble forecasts (for example, ET, EnKF, ETKF, ETS) have a set of ensemble forecasts in advance, there is no need to calculate the adjoint for the numerical model, resulting in higher computational efficiency compared to adjoint-based methods such as SV and CNOP [8]. However, in order to determine the sensitive area, ET and ETKF need to traverse all the state variables in all grids to find the minimum value of the cost function. So, the computational cost grows exponentially as the model resolution, number of vertical layers, and ensemble members increase. The ETS method is an approximation of the ETKF method and searches for the minimum value of the cost function by calculating its gradient. It does not require traversing all the state variables in all grids to find the minimum value of the cost function, thus its computational efficiency is significantly higher than that of the ETKF method. This method can reduce computational costs by 60–80% while maintaining similar accuracy [15,16]. Peevey et al. used the ETS method to conduct research on winter storms in the United States and verified the effectiveness of this method by assimilating simulated dropsonde data in the identified sensitive areas [17]. Siqi Chen et al. also used this method to identify sensitive areas for five typical typhoons in the Northwest Pacific and found that assimilating fewer observations in the sensitive areas could achieve the effect of assimilating many observations over a larger range [16].

Many previous targeted observation experiments have shown that observation sensitive areas will change with changes in weather systems and observation experiment settings [7,18,19,20,21]. Understanding these changes is particularly important for the design of the field campaign. Small changes are better, which means that one targeted observation may have a positive effect on more times and situations. The main aspects of the setting of the targeted observation experiment are the verification area, targeted observation time, and verification time. Generally, the verification area should be set as the area where the prediction accuracy needs to be improved in the future [22]. However, due to the deviation in prediction, the selection of the verification area may deviate from the ideal area, thus it is necessary to understand the influence of different locations and sizes of verification areas on the identification of sensitive areas. It has also been found that sensitive areas undergo changes over time [21]. Therefore, understanding the differences in the impact of changes in verification time or targeted observation time on the identification of sensitive areas is also meaningful for the setting of targeted observation schemes.

Typhoons are one of the most frequent and severe natural disasters in the world, and the southeastern coastal areas of China are heavily affected by typhoons, causing serious social and economic losses [23,24,25,26,27]. This article focuses on this high-impact weather system and studies the impact of forecast time changes and verification area selection on the identification of sensitive areas, which will provide a reference for the design of typhoon field campaigns and minimize the influence of scheme setting on the results of the identification of sensitive areas. Section 2 of this paper introduces the data, typhoon cases, and methods used in this paper. Section 3 describes the design of the OSSEs, different forecasting time experiments, and different verification area experiments. Section 4 gives the analyses of the experiment results, and Section 5 summarizes and discusses the results.

2. Data, Case and Methods

2.1. Data Description

The data used in this study to estimate sensitive areas were the ensemble forecast from the China Meteorological Administration-Regional Ensemble Prediction System (CMA-REPS), with 15 ensemble forecast members (including 1 control forecast member and 14 perturbance members). The dataset has a temporal resolution of 1 h, a horizontal resolution of 0.1° × 0.1°, and a vertical layer of 50.

2.2. Case Description

In-Fa was a highly catastrophic typhoon with a long life history, a complex track, slow movement speed, long onshore detention time, and strong wind and rain intensity; all of this caused 4.82 million people in China to be affected, including 33 deaths and 8 missing persons. Typhoon In-Fa generated at the east of Taiwan Island at 18:00 on 17 July 2021 (UTC, the same below), moved northwestward and strengthened. It made landfall in Zhoushan City, Zhejiang Province around 04:30 on 25 July, with the intensity of a typhoon and a maximum wind speed of 13 levels (38 m/s) near the center. After landfall, In-Fa remained in northern Zhejiang Province and southern Jiangsu Province for a long time, and broke the record for rainfall caused by landfall typhoons in Zhejiang Province. Furthermore, it was recorded as the typhoon with the largest amount of rainfall affecting Jiangsu Province. In addition, in the process of its slow westward movement on the ocean surface, In-Fa interacted with the subtropical high in the north and the typhoon Chapaka in the southwest, and transported a large amount of water vapor to the inland areas of China [28], which may be closely related to the occurrence of the “21.7” extreme rainstorm in Henan Province.

2.3. The ETS Method

The ETS method was proposed by Yu Zhang et al. (2016). A brief introduction to this algorithm follows in this paper, and for more details, please refer to Zhang et al. (2016) [15]. The ETS method is based on a set of ensemble forecasts, represented by an $N\times K$ matrix $E\left(t\right)$, where $t$ is the forecast time, $N$ stands for the number of state variables of all elements in the entire grids, and $K$ is the number of ensemble members. $\bar{E}$ represents the ensemble mean, where each column is the same ensemble mean vector. The ensemble perturbation $X_e\left(t\right)$ is represented as:

$$X_e\left(t\right)=E\left(t\right)-\bar{E}$$

(1)

where $t_a$, $t_v$ are the targeted observation time and verification time, respectively; $X_e\left(t_a\right)$ represents the ensemble forecast perturbation at the targeted observation time; and $X_e\left(t_v\right)$ represents the ensemble forecast perturbation at the verification time. Therefore, the covariance matrix of the forecast error at the verification time $P_e\left(t_v\right)$ can be expressed as the following equation:

$$P_e(t_v)={\displaystyle \frac{X_e\left(t_a\right)X_e(t_a{)}^T}{K}}$$

(2)

We define a new matrix $Y\left(t_a\right)$ as the ensemble perturbation matrix generated by assimilating adaptive observation data. The goal of ensemble transformation method is to find a transformation matrix $C$ that satisfies the following equation:

$$Y\left(t_a\right)=X_e\left(t_a\right)C$$

(3)

where $C$ is a $K\times K$ matrix. Thus, the covariance matrix of analysis error after assimilating adaptive observation data $A_g(t_a)$ is:

$$A_g(t_a)\approx {\displaystyle \frac{X_e\left(t_a\right)C{C}^T{X}_e(t_a{)}^T}{K}}$$

(4)

Further the covariance matrix of forecast error after assimilating adaptive observation data $P_g(t_v)$ can be expressed as:

$$P_g(t_v)={\displaystyle \frac{X_e\left(t_v\right)C{C}^T{X}_e(t_v{)}^T}{K}}$$

(5)

The forecast error decrease after assimilating new data ΔP is:

$$\Delta P=P_e\left(t_v\right)-P_g\left(t_v\right)$$

(6)

The ensemble perturbation matrix at the targeted observation time and verification time $X_e\left(t_a\right)$, $X_e\left(t_v\right)$ can be obtained from the ensemble forecast. In data assimilation, an estimated analysis error covariance matrix can be provided through first guess using 1999BT [12]. To obtain the reduction of forecast ΔP after assimilating new data, one only needs to obtain $C{C}^T$ through Formula (4). Assuming the first guess analysis error covariance matrix $A_g\left(t_a\right)$ and ensemble perturbation matrix $X_e\left(t_a\right)$ are full rank, Formula (4) can be written as:

$$C{C}^T=K\left(X_e\right(t_a{)}^T{A_g}^{-1}{X}_e\left(t_a\right){)}^{-1}$$

(7)

To obtain the optimal adaptive observation scheme, a measurement standard needs to be selected to verify the forecast accuracy. This study uses the frequently, the commonly used dry air total energy as the measurement standard, and the formula is as follows:

$${\displaystyle \frac{1}{D}}{\displaystyle \underset{D}{\int }{\displaystyle {\int }_0^1\left[{u^{\prime }}^2+{v^{\prime }}^2+\frac{C_p}{T_r}{T^{\prime }}^2+R{T}_r{\left(\frac{P_s^{\prime }}{P_r}\right)}^2\right]}}d\delta dD$$

(8)

where $(u^{\prime },v^{\prime },T^{\prime },P_s^{\prime })$ represent the perturbation of horizontal wind, temperature, and surface air pressure; $D$ represents the integrated horizontal area; $\delta$ represents the vertical coordinate; $C_p$ is the dry air constant volume pressure of 1005.7 Jkg⁻¹K; $R$ is the latent heat of phase change of 287.04 Jkg⁻¹K; and $T_r$ and $P_r$ are the reference temperature and pressure. In this study, only wind and temperature variables were used to calculate the sensitive area, so the pressure term was ignored in the calculation, and the $T_r$ value used was 270 K.

We defined a projection matrix $\mathsf{\wp }=diag\left({\rho }_i\right),i=1,\cdots ,M$, and $i$ represents state variables, when the state variable is wind and is within the verification areas, ${\rho }_i=1$; when the state variable is temperature and is within the verification areas, ${\rho }_i=\sqrt{{\displaystyle \frac{C_p}{T_r}}}$, otherwise ${\rho }_i=0$. We define a vector $\beta =\left({\beta }_1,\cdots ,{\beta }_l\cdots ,{\beta }_M\right)$ as representing the covariance change rate of analysis error caused by the assimilation of adaptive observation data. If β_l = 0.4 represents a 60% reduction in the analysis error of the state variable $l$, the variance matrix of forecast error is: ${\displaystyle \frac{1}{K}}\mathsf{\wp }{X}_e(t_v)C(\beta )C^T(\beta )X_e(t_v{)}^T\mathsf{\wp }$.

We define $Z=\left(Z_1,\cdots ,Z_M\right)=X_e(t_v{)}^T\mathsf{\wp }$, where $Z_i$ is the column $i$ of the matrix $Z$, then the forecast error $J$ can be expressed as:

$$J(\beta )={\displaystyle \frac{1}{K}}\sum _{i=1}^M{Z}_i^{T}C(\beta )C^T(\beta )Z_i$$

(9)

To obtain the observation sensitive area, it is necessary to find the minimum forecast error $J$. Unlike the ET method that traverses all state variables, which reduces computational efficiency, the ETS method calculates the gradient of the forecast error $J$ and finds its minimum value, which can effectively improve efficiency. The gradient expression of the forecast error $J$ is as follows:

$$\begin{array}{l}\nabla J={\left({\displaystyle \frac{\mathsf{\partial }J}{\mathsf{\partial }{\beta }_1}},\cdots ,{\displaystyle \frac{\mathsf{\partial }J}{\mathsf{\partial }{\beta }_l}},\cdots {\displaystyle \frac{\mathsf{\partial }J}{\mathsf{\partial }{\beta }_M}}\right)}^T\\ ={\left({\displaystyle \frac{1}{K}}{\displaystyle {\sum }_{i=1}^M{Z}_i^T}{\displaystyle \frac{\mathsf{\partial }C{C}^T}{\mathsf{\partial }{\beta }_1}}{Z}_i,\cdots ,{\displaystyle \frac{1}{K}}{\displaystyle {\sum }_{i=1}^M{Z}_i^T}{\displaystyle \frac{\mathsf{\partial }C{C}^T}{\mathsf{\partial }{\beta }_l}}{Z}_i,\cdots {\displaystyle \frac{1}{K}}{\displaystyle {\sum }_{i=1}^M{Z}_i^T}{\displaystyle \frac{\mathsf{\partial }C{C}^T}{\mathsf{\partial }{\beta }_M}}{Z}_i\right)}^T\end{array}$$

(10)

The reduction of forecast error is:

$$\mathrm{d}J={\left({\displaystyle \frac{1}{K}}{\displaystyle {\sum }_{i=1}^M{Z}_i^T}{\displaystyle \frac{\mathsf{\partial }C{C}^T}{\mathsf{\partial }{\beta }_1}}{Z}_i,\cdots ,{\displaystyle \frac{1}{K}}{\displaystyle {\sum }_{i=1}^M{Z}_i^T}{\displaystyle \frac{\mathsf{\partial }C{C}^T}{\mathsf{\partial }{\beta }_l}}{Z}_i,\cdots {\displaystyle \frac{1}{K}}{\displaystyle {\sum }_{i=1}^M{Z}_i^T}{\displaystyle \frac{\mathsf{\partial }C{C}^T}{\mathsf{\partial }{\beta }_M}}{Z}_i\right)}^{T}d\beta$$

(11)

3. Experiment Design

This study conducted three sets of experiments. Firstly, to verify the effectiveness of the sensitive area identified via the ETS method, the Observation System Simulation Experiments of assimilating simulated dropsondes within and outside the sensitive area ware carried out. Then, the differences in sensitive areas identified for different forecast times were compared. Finally, the impact of different verification areas on sensitive area identification was analyzed.

3.1. Observation System Simulation Experiment Design

An OSSE study was conducted on Typhoon In-Fa using the CMA-REPS ensemble forecast with a starting time of 00:00 on 24 July 2021. The sea surface wind field of the ensemble control forecast and 14 ensemble members were plotted separately (omitted), and it was found that the average landing time of each ensemble member was 06:00 on the 25th. In order to improve the accuracy of the position and intensity prediction at the time of typhoon landing, this time (06:00, 25th) was selected as the verification time of the experiments. The design of the verification area was centered on the typhoon landing site and included the scope of the strong spiral rain band. For the specific verification area, see the red solid rectangle in Figure 1.

The observation sensitive area at the 24 h before the verification time calculated via the ETS method was mainly located in the first quadrant of Typhoon In-Fa, as shown in the shadowed area in Figure 1. In order to explore the effect of increasing observations in the sensitive area on typhoon prediction, the dropsondes’ data in the sensitive area and non-sensitive area were simulated (positions are shown in Figure 1) for OSSEs. Two sensitivity experiments and one control experiment were designed. The sensitivity experiments assimilated simulated dropsondes from the sensitive area (SENS) and non-sensitive area (OTHR), while the control experiment (CTRL) did not assimilate any observation data.

In these experiments, ERA5 reanalysis data were used for the “Nature Run”. To generate the simulated dropsondes, there were two steps. First, interpolation based on the “Nature Run” was carried out to obtain the basic vertical profiles of the simulated dropsondes. Then, the observation perturbation errors conforming to the Gaussian distribution were superimposed onto the simulated dropsondes. The WRF model and WRF-3DVAR assimilation system were used in these experiments, and GFS was used as the background field and boundary conditions. The numerical experiments started at 00:00 on 24 July 2021, assimilated the dropsondes at 06:00 on 24 July, and predicted the landing time of Typhoon In-Fa at 06:00 on 25 July.

3.2. Design of Different Forecasting Time Experiments

In this part, two sets of experiments were designed to analyze the difference in sensitive areas identified under different prediction time periods. The first group included the experiments with a fixed verification time and variable targeted observation time. The purpose was to explore whether there are differences in the observation sensitive areas at different times for the confirmed verification time, in order to understand the necessity of adjusting the targeted observation scheme with time when the field campaign is carried out. The other group include the experiments with fixed targeted observation time and variable verification time, in order to explore the effectiveness of the targeted observation conducted for a specific future time for other future times.

3.2.1. Experiments of Fixed Verification Time and Variable Targeted Observation Time

These experiments used the CMA-REPS ensemble forecast with the same start time as the OSSEs study in Section 3.1. Taking 06:00 on the 25th as the verification time, the targeted observation time was set at 06, 12, 18, and 24 h earlier than the verification time. The time setting scheme is shown in

Table 1. Test scheme settings with fixed verification time and variable targeted observation time.

Starting Time of Ensemble Forecast	Verification Time (Typhoon Landing Time of Ensemble Forecasting)	Targeted Observation Time
		06 h Before Landing	12 h Before Landing	18 h Before Landing	24 h Before Landing
2021072400	2021072506	2021072500	2021072418	2021072412	2021072406

. The verification area is consistent with the OSSE study in Section 3.1, as shown in the solid rectangular area in Figure 1.

3.2.2. Experiments of Fixed Targeted Observation Time and Variable Verification Time

The same start time of the ensemble forecast from Section 3.1 was also used in this part. Taking 06:00 on the 24th as the targeted observation time, the verification time was set at 06, 12, 18, and 24 h later than the targeted observation time. Since these experiments contains four verification moments, in order to ensure that the verification area included the typhoon center location at all verification moments, the verification area set in these experiments was slightly larger than that set in the experiments in the Section 3.2.1, as shown by the dashed rectangle in Figure 1. The setting scheme of the targeted observation and verification time is shown in

Table 2. Test scheme settings with fixed targeted observation time and variable verification time.

Starting Time of Ensemble Forecast	Targeted Observation Time	Verification Time
2021072400	2021072406	2021072412	2021072418	2021072500	2021072506

.

3.3. Experiments Design of Different Verification Areas

In targeted observation, what we want to look for is the sensitive area which has the greatest impact on improving numerical weather prediction in the verification area at the verification time. For typhoons, the verification area should contain the location of the typhoon at the verification time. However, in real-time operations, due to the fact that the exact location of the typhoon at the verification time cannot be obtained in advance, and it can only be estimated according to the typhoon forecast track. Therefore, this part studies, the impact of a position shift and size change of the verification area on the recognition of sensitive area. The verification area of the control experiment (A) is the same as those in the Section 3.1 and Section 3.2.1, which was designed to be centered on the actual landing site of the Typhoon In-Fa and include the extent of the surrounding strong spiral rain band. To investigate the influence of the typhoon forecast moving faster or slower than the actual moving speed on the identification of sensitive areas, experiments were designed in which the verification area shifted forward and backward in the direction of the typhoon moving track (B1 and B2, see Figure 2a). Then, to investigate the difference between sensitive areas caused by the left and right deviation of the typhoon forecast track compared with the actual track, experiments were designed for the left and right shift of the verification area in the typhoon moving track (C1 and C2, see Figure 2b). In order to study the proper size of the typhoon verification area, experiments to reduce and expand the verification area with the center position unchanged (D1, D2, see Figure 2c) and experiments to change both the center position and size of the verification area (D3–D5, see Figure 2d) were designed. The settings of the targeted observation time and verification time in these experiments were the same as those in the Section 3.2.1 experiments.

4. Results

4.1. Results of the OSSEs Study

Since the OSSEs study used ERA5 data for the “Nature Run”, these data were used as the observed truth value when evaluating the results of these experiments. First, the intensity and track prediction of Typhoon In-Fa through SENS, OTHR, and CTRL experiments were compared with those of ERA5 and the observation, and the results are shown in Figure 3. The black line represents the typhoon intensity and the track of the International Best Track Archive for Climate Stewardship (IBTrACS), the orange line represents those of ERA5 data, the blue line represents those of the control experiment (CTRL), the red line represents the experiment (SENS) that assimilated the simulated dropsondes in the sensitive area, and the green line represents the experiment (OTHR) that assimilated the simulated dropsondes in the non-sensitive area. Compared with ERA5 data and the observation, the intensity forecasts of the typhoon in each group was stronger, and the track forecasts of the typhoon was west and south. Comparing different sensitivity experiments, it can be seen that both the SENS and OTHR experiments had improved the typhoon intensity forecast compared with the CTRL experiment, and the SENS experiment had a more significant improvement of the intensity forecast. The SENS experiment improved the forecast track, but the OTHR experiment increased the track forecast deviation of the typhoon.

By analyzing the differences in the RMSE forecast of different elements at different altitudes of each experiment (Figure 4), it can be concluded that at 06:00 on the 25th (that was, 24 h after assimilation), the OTHR experiment reduced the RMSE forecast of v-wind, temperature, and geopotential height, had little impact on the forecast of specific humidity; but increased the RMSE forecasts of u-winds and vertical winds below 250 hPa, while, the SENS experiment reduced the RMSE of u-wind, v-wind, vertical wind, temperature, geopotential height, and specific humidity, and the reduction ratio was greater than that of the OTHR experiment. In addition, the TS score of rainstorm and heavy rainstorm precipitation in the verification area at the verification time was analyzed (see

Table 3. TS score of each experiment in the verification area at the verification time.

	Rainstorm	Heavy Rainstorm
CTRL	0.816	0.500
SENS	0.878	0.577
OTHR	0.792	0.472

). It was found that compared with the CTRL experiment, the SENS experiment improved the TS score of rainstorm and heavy rainstorm precipitation, but the OTHR experiment reduced it.

In conclusion, compared with the control experiment, the experiment assimilating dropsondes in the sensitive area improved the forecast accuracy of the typhoon intensity, tracking, the RMSE of each forecast element, and the precipitation score. The experiment assimilating dropsondes in the non-sensitive area improved the forecast of typhoon intensity and the individual elements, but the forecasts skill of the typhoon track, precipitation, and some other elements was worse. The sensitive area identified using the ETS method was effective, and increased observations in the sensitive area clearly improved the numerical prediction skill.

4.2. Results of Different Forecasting Time Experiments

4.2.1. Experiments of Fixed Verification Time and Variable Targeted Observation Time

The cumulative sensitive signal strength in the vertical direction of each grid point was calculated and normalized. The distribution of sensitive signals for different experiments of Typhoon In-Fa is shown in Figure 5. It can be seen that for the Typhoon In-Fa, there were significant differences in the observation sensitive areas at the same verification time and different targeted observation times, but they were all around the center position of the typhoon at the targeted observation time, mainly located on the east side of the typhoon. This results was consistent with the findings of many previous studies [9,19,21]. These studies indicated that the movement of typhoons was directly related to the position and intensity of the subtropical high system, so their sensitive areas were mainly distributed at the edge of the subtropical high around the typhoon. In addition, it can be seen that the closer the verification time was, the stronger and wider the sensitive signal was, and the observation sensitive area expanded from being mainly distributed in the first quadrant to the first and fourth quadrants. Overall, there are significant differences in the observation sensitive areas at the same verification time but different targeted observation times. This indicates that the observation sensitive areas are adaptive over time. Therefore, in a real-time field campaign, the observation sensitive areas at different targeted observation times should be calculated in advance, and decision-makers should design the observation time and position of mobile observation vehicles or aircraft dropsonde based on the distribution of sensitive areas at different times.

4.2.2. Experiments of Fixed Targeted Observation Time and Variable Verification Time

The observation sensitive areas of each verification time with the same targeted observation time were all located around the center of the typhoon (Figure 6). However, compared with the Section 4.2.1, the differences in the sensitive areas at each time in this part was small. This means that the distribution characteristics of observation sensitive areas are more related to the distribution of environmental field characteristics at the observation time. As the atmospheric system evolves, the sensitive areas change significantly. In this part of the experiments, as the forecast time increased, the range of sensitive signals gradually narrowed, and the location of sensitive areas gradually decreased from the original first and fourth quadrants to only the first quadrant of the typhoon. Overall, there were some similarities in the sensitive areas of different verification time and the same targeted observation time. Therefore, targeted observations deployed in advance for a specific forecast time are also beneficial for other forecast times, but the improvement for other forecast times is limited. This is also consistent with the result of research by ZHOU Feifan et al. [21].

4.3. Results of Different Verification Areas Experiments

Figure 7 shows an illustration of the distribution for sensitive signals in different verification areas of Typhoon In-Fa (at 12 h before the verification time; the other times were omitted). At the same time, in order to obtain similar quantitative relationships between different sensitive areas, the correlation coefficients of the two-dimensional field distribution of sensitive signals for each verification area experiment with control experiment A were calculated separately. The results are shown in

Table 4. Correlation coefficients of sensitive signals between each verification area experiment and control experiment A of Typhoon In-Fa.

Time Interval Between Targeted Observation Time and Verification Time	Correlation Coefficient with Control Experiment A
	B1	B2	C1	C2	D1	D2	D3	D4	D5
24 h	0.996	0.972	0.989	0.961	0.998	0.990	0.885	0.977	0.977
18 h	0.949	0.967	0.951	0.804	0.977	0.979	0.733	0.960	0.899
12 h	0.927	0.959	0.945	0.831	0.945	0.968	0.744	0.977	0.868
06 h	0.969	0.986	0.979	0.897	0.974	0.994	0.822	0.992	0.957

and Figure 8. The calculation method for the correlation coefficient between two spatial fields (two-dimensional) is shown in Formula (12):

$$S={\displaystyle \frac{⟨X_1,X_2⟩}{\sqrt{⟨X_1,X_2⟩⟨X_1,X_2⟩}}}$$

(12)

where $X_1$ and $X_2$ represent two matrices and $S$ represents the correlation coefficient between the two matrices.

For the schemes B1 and B2, for a verification area with the same size but with its position shifted forward and backward in the direction of the typhoon track, except for at 24 h before the verification time, the similarity of sensitive areas identified by scheme B1 with that in control experiment A was lower than that of scheme B2 at the other three times. In addition, for the schemes C1 and C2, where the size of the verification area was constant but the position shifted left and right around the track, it can be seen that the correlation coefficients of sensitive areas between scheme C2 and control experiment A were lower than those of scheme C1. In these two sets of experiments, the sensitive areas of B1 and C2, which were more different with the control experiment, were both observed in the experiments with the verification area more westward. Moreover, it can be seen from the comparison between these two sets of experiments that the differences in the sensitive areas of schemes C1 and C2 were greater than those of schemes B1 and B2, that is, the distribution of the sensitive areas was more sensitive to the prediction error of the typhoon movement direction than the speed.

The sensitive areas identified by schemes D1 and D2 were in the same central position and only expanded or reduced the size; they had a high correlation coefficient with those of control experiment A, indicating that as long as the actual typhoon was located in the central position of the verification area at the verification time, the size setting of the verification area would not bring significant changes to the identification of the sensitive area. However, when there is an error in typhoon forecasting, the center of the verification area will deviate from the center of the typhoon. Therefore, experiments D3–D5 were set up with changes in both the size and position of the verification area to find a compatible design scheme for the typhoon verification area. It can be seen that there were significant differences between experiments D3 and D5 (D3 having a greater difference) when comparing with the sensitive area of control experiment A, while experiment D4 had a demonstrated a smaller difference. The verification area set in the scheme D3 was relatively small and has a large positional deviation, even without including the actual center position of Typhoon In-Fa at the verification time, which produces significant errors in the identification of sensitive areas. However, if the verification area was set to be too large, such as in scheme D5, it might also contain too many factors unrelated to the typhoon, resulting in the identified sensitive area not representing the most favorable observation area for typhoon forecasting. In scheme D4, although the typhoon center was not at the center of the verification area, the sensitive area identified was not significantly different from that of control experiment A due to the large, but not excessively large, size of the verification area.

In summary, typhoon sensitive areas are more sensitive to larger position shifts (scheme D3) than to small ones (schemes B1, B2, C1, C2), and are relatively more sensitive to left/right position shifts than forward/backward shifts in the track. In order to be compatible with the forecast track error, including the typhoon center location at the future verification time, the verification area should not be set too small, and not too large, otherwise it will be affected by “noise”. Through the comparative analysis of the above experiments, the size range of scheme D4 (about 6° × 6°) is generally recommended. In real-time operations or tests, considering the forecast errors in relation of typhoons, ensemble forecasting can provide uncertainty in typhoon development and is a good reference for selecting the location of the validation area.

5. Conclusions and Discussion

5.1. Conclusions

This study is the first to study that the impact of different forecast times and verification area settings on the identification of sensitive areas via the ETS method, using Typhoon In-Fa as a study case. Firstly, an OSSEs study was conducted to verify the effectiveness of the sensitive areas identified via the ETS method. Then, different forecast time experiments and different verification area experiments were carried out to analyze the impact of changes in the targeted observation time, verification time, and verification area on the identification of sensitive areas. Some interesting results were obtained.

(1)

First, an OSSEs study was conducted with sensitive experiments assimilating simulated dropsondes in the sensitive area (SENS) and non-sensitive area (OTHR). Compared with the non-assimilation experiment (CTRL), it was found that the typhoon intensity forecast was improved after the assimilation of simulated dropsondes, and the improvement in the SENS experiment was more significant than that that in the OTHR experiment. Meanwhile, the SENS experiment improved the forecast track, but the OTHR experiment increased the deviation of the typhoon track prediction. The SENS experiment reduced the RMSE of each forecast element and improved the precipitation score of rainstorm and rainstorm prediction, while the OTHR experiment only reduced the RMSE of v-wind, temperature, and geopotential height, but had negative effects on the forecast of u-wind, vertical wind, rainstorm, and rainstorm precipitation. In short, the sensitive areas identified via the ETS method are indicative, and increasing observation in sensitive areas can significantly improve typhoon forecast skills.

(2)

For the study of different forecast time periods, two sets of experiments were designed. In the first group, the verification time was fixed, and the targeted observation time was changed. It can be seen that the sensitive areas identified at different targeted observation times were very different, but all around the central position of the typhoon at the targeted observation time was, mainly on the east side of the typhoon. Moreover, the closer the verification time, the stronger and wider the sensitive signals were at the targeted observation time. This indicates that the sensitive area undergoes significant changes over time. In many field campaigns, the observation sensitive area is calculated only once a day, which is clearly inappropriate. According to the results of this study, it is necessary to calculate the sensitive areas multiple times every day in advance, and to design or adjust the observation scheme according to the time. Further the targeted observation scheme should be adjusted to the time in the actual field campaign. In the other group of experiments, the targeted observation time was fixed and the verification time was changed. It can be seen that differences in the identified sensitive areas at different verification time were smaller compared to the previous group of experiments, which indicated that deploying targeted observations in advance to improve one certain time also has positive effect on the forecast at other times. In other words, the positive contribution to the numerical prediction of the additional observation data in the sensitive areas at a single time can last for a period of time, which deepens the confidence of scientists in carrying out the targeted observation field campaign.

(3)

In targeted observation, the design of the verification area is an important problem. For typhoons, the verification area setting should include the location of the typhoon at the verification time. However, in operation or in a real-time field campaign, the location at the future time can only be estimated according to the track prediction of the typhoon. Therefore, the influence of the position shift and size change of the verification area on the sensitive areas was studied. The results show that the typhoon sensitive area was more sensitive to left/right shifts in the track than to forward/backward shifst, that is, the area was more sensitive to a direction forecast error than the moving speed forecast error of the typhoon track. If the typhoon center position was almost accurate, the size change had little effect on the sensitive area, but a large central position shift has a significant impact on the identification results of the sensitive area. In order to be compatible with more track prediction errors, including the center location of the typhoon at the future verification time, the verification area should not be set too small, also not too large; if it is too large, the verification area will contain too much "noise". Through the comparison of these experiments, a size of about 6°×6° is generally recommended for the verification area of typhoon. This research result is relatively new, and provides a reference for the design of typhoon verification areas in real-time targeted observation field campaigns.

5.2. Discussion

In the past few decades, many targeted observation field campaigns have been carried out, and sensitive area identification algorithms have also developed rapidly. Finding the key observation areas that can greatly improve numerical forecasting skills is the focus of field campaigns and the development of the observation system. However, many previous studies have shown that different weather conditions and the settings of sensitive area calculations have a huge impact on the identification results of sensitive areas, sometimes resulting in completely unrelated distributions. It can be seen from the research in this study that the distribution of sensitive areas will change greatly with change in the targeted observation time; thus, in field campaigns, the observation sensitive areas for multiple targeted observation times in the future (at least every 6 h) should be calculated in advance. Moreover, the location deviation and size change of the verification area also has a significant impact on the results, and the verification area size of about 6° × 6° is generally recommended. However, this result also has some limitations, because this result is only based on a single typhoon case, and the results of sensitive areas in other typhoon cases under different weather backgrounds may vary. Meanwhile, in the future, sensitive area identification methods based on ensemble forecasting can be compared with the adjoint-based methods in terms of the influence of time and verification area settings to obtain a comprehensive design view. Although the findings outlined in this paper can provide a relatively better scheme for the settings of the typhoon verification areas, further research is still needed for the settings of the verification areas for other weather systems. Finally, it is worth mentioning that Bishop et al. [22] also indicated that using ensemble forecasting with different start times based on the ETKF method can produce obvious differences in the identification of sensitive areas. Further research of all these aspects is required in the future. Understanding these setting issues can help us find the most favorable observation areas for improving numerical forecasting in targeted areas.