Sensitivity Analysis of Microwave Spectrometer for Atmospheric Temperature and Humidity Sounding on the New Generation Fengyun Satellite

The vertical profiles, spatiotemporal distribution, and trends of temperature and humidity in the middle atmosphere are significant for numerical weather prediction and the analysis of global climate change. To better design and apply spaceborne microwave spectrometer on the new generation Fengyun satellite, the sensitivities of the spectrometers at 22.235, 50–60, 118.75, 183.31, 325.153, 380.33, 424.77, 448.0, and 556.94 GHz are analyzed, respectively. Qpack2 included in the atmospheric radiative transfer simulator is used. The results show that the retrieval accuracy of the 50.0–60.0 GHz spectrometer is obviously better than other spectrometers, and the effective detection height (EDH) is the highest, reaching 0.233 hPa. The humidity profiles bigger than 500 hPa are well detected by the seven channels of the Humidity and Temperature Profiler or 22.0–32.0 GHz spectrometer. The retrieval accuracy is better than 6%, which greatly improves the retrieval performance of humidity profiles in the lower troposphere over the sea. In addition, this frequency band is not affected by errors in sea surface temperature or wind speed. The humidity profiles over the sea and land in the middle atmosphere under clear-sky and cloudy-sky conditions are well detected by the 183.31 and 556.94 GHz spectrometer. The EDH can be increased to 1.14 hPa by the 556.94 GHz spectrometer. In the design and application of future spaceborne microwave spectrometers for temperature and humidity profiles detection, the spectrometers mentioned previously are good candidates, and the parameter configuration of these spectrometers can be used as a reference.


I. INTRODUCTION
C LIMATE change is a major global issue, the information such as vertical profiles, spatiotemporal distribution, and trends of temperature and humidity are of great significance to numerical weather prediction and global climate change. The middle atmosphere is sensitive to natural or human activities Manuscript  from the ground and low altitude areas, as well as energy input from the space environment. In addition, the layer of atmosphere can directly affect the lower and upper atmosphere, which makes it an important area for the interaction and feedback between atmospheric dynamics, thermal, chemical, and microphysical processes. Therefore, the detection of the temperature and humidity profiles of the middle atmosphere with high temporal and spatial resolution and high detection accuracy is particularly important.
In 2011, the concept of "microwave hyperspectral" was proposed by Lincoln Laboratory in the United States [1], [2]. This radiometer with hundreds of detection channels and a detection bandwidth of several gigahertz can achieve high spectral resolution and high vertical resolution observations of the atmosphere [3], [4]. This technology is one of the development directions of passive microwave remote sensors for middle atmosphere detection in recent years. The spectrometer is currently widely used in ground-based microwave radiometers, spaceborne infrared detectors, and microwave imagers [5].
The detection of the humidity profiles in the middle atmosphere is achieved with ground-based microwave spectrometers such as the Water Vapor Millimeter-Wave Spectrometer [6], [7], [8], [9] and the Middle Atmospheric Water Vapor Radiometer [10], [11]. Centered at 22.235 GHz, these instruments detected the water vapor profiles of 35-75 km with a spectral resolution of 30.5 kHz. For the detection of temperature profiles in the middle atmosphere, the temperature radiometer has a spectral resolution of 30.5 kHz near 52.4-53.2 GHz, and the effective detection height (EDH) can reach 1.5 hPa [12], [13]. In general, the detection height of atmospheric profiles can be effectively improved by applying spectrometer to ground-based microwave radiometers, but the development of ground-based microwave radiometers is limited to low spatial resolution.
Temperature and humidity profiles in the middle atmosphere can also be detected by infrared spectrometers such as Greenhouse Gas Interferometer [14], Infrared Atmospheric Sounder [15], Interferometric Infrared Atmospheric Sounder [16], Geostationary Interferometric Infrared Sounder [17], or Infrared Hyperspectral Atmospheric Vertical Sounder Instrument [18]. These infrared spectrometers contain several thousands of channels and can provide accurate temperature, humidity, and atmospheric composition data for weather prediction. However, the infrared band is easily affected by cloud, rain, and topography, This work is licensed under a Creative Commons Attribution 4.0 License. For more information, see https://creativecommons.org/licenses/by/4.0/ which will adversely affect the retrieval of atmospheric temperature and humidity profiles.
Different from the infrared band, the microwave band is less affected by the cloud and rain, and can achieve all-weather observation. Since 2003, several studies have already explored the potential of hyperspectral sampling in the microwave band [19], [20], [21]. In 2015, the detection frequencies of Hyperspectral Microwave Sensor (HYMS) were extended to 50-60, 118, 183, 352, 420, and 448 GHz, with 10-1000 MHz spectral resolution [22], [23], [24]. The retrieval performance of HYMS was compared to European meteorological satellites. The results confirmed that the uncertainty of temperature retrieval was reduced by the order of 2-10%, and the improvements for humidity sounding could reach 30%, especially at the atmosphere pressure bigger than 250 hPa. These studies in [21], [22], and [23] show that the retrieval accuracy of temperature and humidity profiles can be effectively improved by spectrometer. But only two spectral resolutions are considered, the smallest of which is only 10 MHz, and the role of each frequency band is not specified.
In this article, the sensitivity of the spectrometer is specifically analyzed for the payload configuration and channel design of the new generation Fengyun satellite. In addition to considering the retrieval performance of the middle atmosphere, the boundary layer is also analyzed. The rest of this article is organized as follows. The theoretical background of weighting function and retrieval method is briefly introduced in Section II. The detection capability of atmospheric temperature profiles is introduced in Section III. Due to the poor detection capability of water vapor in the lower troposphere, we first analyze the sensitivity of spectrometer to detect water vapor in the lower troposphere in Section IV. Spectrometric analysis of water vapor above the troposphere is considered in Section V. Finally, Section VI concludes this article.

II. WEIGHTING FUNCTION AND RETRIEVAL METHOD
The typical atmospheric profiles data set in 1992 and 1993 provided by the Satellite Application Facility for Numerical Weather Prediction (NWP SAF) is used in this article [25]. In total, 215 sets of 60-layer sea and land atmospheric profiles under the clear-sky and cloudy-sky conditions are selected as the simulation data set.

A. Weighting Function of Atmosphere
For the downward-looking spaceborne microwave radiometer, the observed brightness temperature T up [26] is the sum of three parts where T uf is the upward-emitted brightness temperature, which is the first part and the most important radiation contribution observed by satellites, expressed as where θ is the observation angle and is assumed to be 0°in this article, i.e., the nadir-looking. The 0 and ∞ represent the atmospheric path from the surface to the top of the atmosphere. k v , T , τ v , and z are the absorption coefficients of frequency v, physical temperature, optical thickness, and atmospheric altitude. The surface-emitted brightness temperature T ef after atmospheric transmission is the second part, where T ef is defined as where T s is the physical temperature of the surface. e s represents the emissivity of the surface. In this article, the surface emissivity of sea is calculated by TEESEM emissivity model [27] that comes with the atmospheric radiative transfer simulator (ARTS). For the calculation of land surface emissivity, the TELSEM emissivity model [28], [29] is selected because the frequency range to be calculated is 22-565 GHz. The third part is the upward-reflected fraction T rf of the downward-emitted brightness temperature T df after being transmitted by the atmosphere where T df represents the brightness temperature of atmospheric radiation that can be received at the surface, which is the sum of the cosmic background brightness temperature T ba and the downwelling atmospheric brightness temperature where T ba can be further expressed as the brightness temperature of the cosmic background equivalent temperature T c after atmospheric transmission For simplicity, atmospheric transmittance Υ vθ is defined as then, (1) can be expressed in a simple form [26] T up = e s T s Υ vθ (0, ∞) T up = e s T s Υ vθ (0, ∞) where ρ is the water vapor density. W T and W H 2 O are the temperature weighting function and water vapor weighting function, respectively, which can be expressed as The weighting function represents the sensitivity of the radiometer channel to different atmospheres. The height of the peak of the channel weighting function is the most sensitive atmospheric height of the channel. The effect of the surface and the cosmic background is not considered when calculating the weighting function in this paper. Klein and Gasiewski [30], Cimini et al. [31], and Sahoo et al. [32] showed a more comprehensive calculation of the weighting function.

B. Retrieval Method
The optimal estimation method of the ARTS [33], [34] is used in this article for the retrieval of atmospheric temperature and humidity profiles. Among them, the Levenberg-Marquardt method [35], [36], which combines the advantages of the gradient descent method and the Gauss-Newton iteration method, is the most commonly used least-squares optimization method. The state parameters x obtained by this method are where i, γ, and K denote the number of iterations, Levenberg-Marquardt parameter, and the Jacobian matrix, respectively. The subscripts T and −1 represent the transpose and inverse of the matrix. x a is the priori profile. Consider the difference between the priori profile and the real profile, as well as the variation range of atmospheric temperature and humidity under the same weather conditions, the humidity priori profile in this article is obtained by adding a 50% deviation to the input profile, and the temperature priori profile is the input profile adding a 10 K deviation [37]. y and F (x i ) are the observed brightness temperature and the simulated brightness temperature, respectively. The observed brightness temperature in this article is the sum of the simulated brightness temperature and the measurement noise error. Measurement noise is mainly generated by the thermal noise of the instrument. The ideal thermal noise is also called white noise, and within a certain bandwidth, the thermal noise conforms to the Gaussian distribution. Therefore, to facilitate the analysis, the measurement noise error is expressed as white Gaussian noise with the radiometer system sensitivity as the standard deviation. When the receiver noise temperature is 300 K, the system sensitivity of the 50-60 GHz spectrometer with a spectral resolution of 30 MHz over the sea under the clear-sky conditions is about 0.74 K. The measurement noise error of this spectrometer is shown in Fig. 1. The standard deviation of the measurement noise error is consistent with the system sensitivity. S a and S y are the background covariance matrix and the measurement covariance matrix, respectively. In this article, the background covariance matrix is calculated by an exponential function where m and n are the mth row and nth column of the background covariance matrix, respectively. σ is standard deviation, l is correlation length. The standard deviation and correlation length of the temperature background covariance matrix are 5 K and 0.2 km, respectively [38], [39]. The standard deviation and correlation length of the humidity background covariance matrix are 0.2 and 0.5 km, respectively [40], [41].
Assuming that the noise between the radiometer channels is uncorrelated, the measurement error covariance matrix can be expressed as a diagonal matrix. The diagonal elements are the sum of the squares of the system sensitivity and the square of the measurement noise error, and the OFF-diagonal elements are zero. The system sensitivity of radiometer, i.e., noise equivalent temperature difference (NEDT), is defined as where T sys represents the system noise temperature of the radiometer, which is the sum of the receiver noise temperature and the receiving temperature at the antenna end. β is noise equivalent bandwidth. dτ is the integration time for measuring a single spectrum, which is assumed to be 17 ms in this article. The criterion for iterative convergence using the Levenberg-Marquardt method is where nlev is the number of retrieval grids. For the retrieval results, the mean error (ME) and the rootmean-square error (RMSE) are used as quantitative standards for statistical verification. The temperature retrieval results are where x true , x retrieval , and N are the real profile, the retrieval profile, and the number of samples, respectively. In addition, the IC is to quantify the information obtained from the channel measurements. The bigger the IC, the smaller the error caused by the prior information. The degree of freedom is one of the quantitative criteria for evaluating the IC measured by radiometer, and it can be expressed as the trace of the average kernel function matrix [35] where A denotes the average kernel function matrix, which describes the sensitivity of the retrieval state vector to the real state vector, and tr is the trace of the matrix. The closer the retrieval error is to zero, the bigger the degrees of freedom.

III. SPECTROMETRIC ANALYSIS OF ATMOSPHERIC TEMPERATURE PROFILES
The channel parameters of HYMS, MWTS, and MWHS are shown in Table I. Each of the eight spectrometers of HYMS has two bandwidths and corresponding sensitivities, one to the left and one to the right of the slash. MWTS has thirteen channels, where "fo" refers to 57.290344 GHz for easy writing. Eight temperature channels centered at 118.75 GHz and five humidity channels centered at 183.31 GHz are included in MWHS. The channels from top to bottom in Table I correspond    Referring to the receiver noise temperature of MWTS [42], the noise temperature of 300 and 500 K is set here. The retrieval accuracy of 50.0-60.0 and 50.0-70.0 GHz spectrometers deteriorates with the increase of noise temperature. The ME and RMSE of two spectrometers are basically the same at the atmospheric pressure bigger than 0.4 hPa, and only the EDH is slightly different. Based on the consideration of cost performance, increasing the bandwidth from 10 to 20 GHz can only improve EDH by 0.1 hPa, which is not a good choice. Therefore, the spectrometer with 10 GHz bandwidth is further analyzed. The retrieval results of MWTS and the spectrometer with spectral resolution of 30, 10, and 3 MHz over the sea under the clear-sky conditions are shown in Fig. 3.  The ME and RMSE of the 3 MHz spectrometer are slightly smaller than MWTS. With the increase of noise temperature, the ME and RESE of the 10 MHz spectrometer are gradually worse than MWTS. The retrieval accuracy of the 30 MHz spectrometer is significantly worse than MWTS. It can also be seen from Table II that the IC of the spectrometer is significantly bigger than MWTS. The EDH (RMSE T < 2 K) of the 3 MHz spectrometer is the highest, up to 0.233 hPa, and the IC is about 1.4 times that of MWTS.
The results are similar over the sea under the cloudy-sky conditions. But, the retrieval accuracy is worse than MWTS over the land at the atmospheric pressure bigger than 400 hPa, especially at lower noise temperatures. The reason is the effect of surface emission and channel weighting issues. The results at other heights are basically consistent with the results over the sea. The EDH of the 3 MHz spectrometer is 0.271-850 hPa, and the IC is 1.3 times that of the MWTS.

B. Spectrometric Analysis at 118.75 GHz
According to the instrument parameters of MWHS [43], 113.75-123.75 GHz spectrometer with spectral resolutions of 30, 10, and 3 MHz is analyzed at receiver noise temperatures of 400 and 600 K. The retrieval results over the sea under the clear-sky conditions are shown in Fig. 4. The results are similar over the land and under the cloudy-sky conditions. As shown in Fig. 4, the ME and RMSE of the spectrometer increase slightly with increasing receiver noise temperature, which indicates that two receiver noise temperatures have less impact on the system sensitivity and even less impact on the retrieval accuracy. The retrieval results of the spectrometer are obviously better than MWHS at the atmospheric pressure smaller than 850 hPa. The ME and RMSE of the spectrometer with different spectral resolutions are slightly different, and the retrieval accuracy of the 3 MHz spectrometer is the best. As shown in Table III, the EDH of the spectrometer is higher than MWHS, and IC of the spectrometer is bigger than MWHS. The EDH of the 3 MHz spectrometer is 1.96-982 hPa, and the IC is about 1.6 times that of MWHS.

C. Spectrometric Analysis at 424.77 GHz
With reference to the frequency range of HYMS and receiver noise temperature of Ice Cloud Imager (ICI) [23], [44], the 416.77-432.77 GHz spectrometer with 100, 50, and 20 MHz spectral resolution is analyzed at receiver noise temperature of 1500 and 2000 K, respectively. The retrieval results over the sea under the clear-sky conditions are shown in Fig. 5. The results are similar over the land and under the cloudy-sky conditions. The retrieval accuracy of the spectrometer is better than MWHS at the atmospheric pressure smaller than 800 hPa but worse than MWTS. The ME and RMSE of the 20 MHz spectrometer are

IV. SPECTROMETRIC ANALYSIS OF WATER VAPOR IN THE LOWER TROPOSPHERE
At present, the 22.235 GHz spectrometer is widely used in ground-based microwave remote sensing [6], [7], [8], [9], [10], [11]. The application of this frequency band in spaceborne microwave spectrometer is first studied in this section.
The HATPRO developed by Radiometer Physics GmbH in Germany is a very representative radiometer [45], the channel parameters are shown in Table IV The spectrometer is analyzed at 150 and 300 K receiver noise temperature, and three spectral resolutions of 100, 30, and 10 MHz are considered. The retrieval results over the sea under the clear-sky conditions are shown in Fig. 7. The detection accuracy of water vapor degrades slightly with the increase of noise temperature. The results of HATPRO are slightly worse than spectrometer, but the difference is smaller than 1%. The results of different spectral resolutions are basically the same. When the atmospheric pressure is bigger than 500 hPa, the retrieval accuracy of the HATPRO and spectrometer is better than 6%, MWHS is only 16%. The abovementioned conclusions  Table V.
To further analyze the sensitivity of this frequency band, the retrieval results of sea surface temperature and wind speed fluctuations of 2.0 K and 2 m/s, respectively, are shown in Fig. 8. The retrieval accuracy of the 22.0-32.0 GHz spectrometer and HATPRO is smaller than 1% affected by the errors of sea surface temperature and wind speed. In addition, the retrieval accuracy remains within 6% at the atmospheric pressure bigger than 500 hPa.
In general, due to the complexity of land emissivity, the optimization effect of this frequency band is very limited over the land. However, the retrieval accuracy of water vapor in the low troposphere is greatly improved by the HATPRO and 22.0-32.0 GHz spectrometer over the sea under the clear-sky and cloudy-sky conditions, and is not be affected by sea surface temperature and wind speed errors.

V. SPECTROSCOPIC ANALYSIS OF WATER VAPOR ABOVE THE TROPOSPHERE
The ability of high-frequency spectrometers to detect water vapor above the troposphere is discussed in this section. The frequency range, bandwidth, and receiver noise temperature of MWHS, HYMS, and ICI are used as references. Spectrometers at 173.

A. Spectrometric Analysis at 183.31 GHz
The spectrometers at 176. 31-190.31 and 173.31-193.31 GHz with spectral resolutions of 30, 10 and 3 MHz are compared at receiver noise temperatures of 400 and 600 K. The difference between spectrometers with 14 GHz and 20 GHz bandwidth is mainly at the atmosphere pressure bigger than 600 hPa. Within the EDH, the retrieval accuracy of spectrometer with 20 GHz bandwidth is better. Therefore, the spectrometer with   Fig. 9. The results are similar over the land and under the cloudy-sky conditions. As the Fig. 9 shown, the retrieval results of the spectrometer are significantly better than MWHS. The ME and RMSE of spectrometer with different spectral resolutions are almost identical at 400 or 600 K noise temperature. In addition, compared with HATPRO and 22.0-32.0 GHz spectrometer, the retrieval accuracy of the 173. 31-193.31 GHz spectrometer is better at the atmosphere pressure smaller than 660 hPa over the sea and is significantly better over the land. The EDH and IC of the spectrometer shown in Table VI deteriorate with the increase of noise temperature, but are still better than MWHS. The retrieval performance of 3 MHz is best, the EDH is 43.6 hPa, and the IC is about 1.6 times that of MWHS.
The retrieval accuracy of the troposphere and lower stratosphere profiles obtained by the spectrometer is further improved than MWHS, which is agreed to the results of [23].    spectrometer are similar to MWHS, but the retrieval accuracy is slightly better and the EDH is 93.9 hPa. The retrieval results of the 372. 33-388.33 GHz spectrometer over the sea under the clear-sky conditions are shown in Fig. 10. The results are similar over the land and under the cloudy-sky conditions. As the Fig. 10 shown, the retrieval accuracy of the spectrometer is worse than MWHS at the atmospheric pressure bigger than 400 hPa and the opposite is true for other heights. The retrieval accuracy of the 20 MHz spectrometer is the best, the EDH is 59.4-948 hPa. In addition, the ME and RMSE of the 440.0-456.0 GHz spectrometer are similar to this spectrometer, but the retrieval accuracy is slightly worse and the EDH is only 47.7-901 hPa.
The retrieval results of the 548.94-564.94 GHz spectrometer over the sea under the clear-sky conditions are shown in Fig. 11. The results are similar over the land and under the cloudy-sky conditions. The ME and RMSE of the spectrometer increase slightly with increasing receiver noise temperature. The retrieval  accuracy of the spectrometer is obviously better than MWHS at the atmospheric pressure smaller than 230 hPa. The results of spectrometer with different spectral resolutions have a small difference, and the retrieval accuracy of the 50 MHz spectrometer is the best. In addition, as can be seen from Table VII, the EDH and IC of the spectrometer are significantly better than MWHS. The EDH of the 50 MHz spectrometer reaches 1.14-424 hPa at 1500 K receiver noise temperature, and the IC is about 1.6 times that of MWHS.
The retrieval performance of the 548.94-564.94 GHz spectrometer is studied for the first time and is far superior to MWHS at atmospheric pressure smaller than 230 hPa. The detection capability of water vapor profiles above the troposphere using spaceborne microwave sensors is further improved.

VI. CONCLUSION
In this article, 215 sets of global sea and land datasets under the clear-sky and cloudy-sky conditions are used to analyze the sensitivity of the spectrometer with different spectral resolutions and noise temperatures by Qpack2 in ARTS.
Based on the retrieval results of temperature profiles over the sea, the EDH of the 50.0-60.0 GHz spectrometer can reach 0.233 hPa, the retrieval accuracy is kept within 1 K at the atmospheric pressure bigger than 6.5 hPa and the IC is about 1.4 times that of MWTS. The retrieval results over the land are slightly worse, with an EDH of 0.271-850 hPa and IC of 1.3 times that of MWTS. The EDH of the 113.75-123.75 GHz spectrometer reaches 1.96-982 hPa, the IC is about 1.6 times that of MWHS. The EDH of 416.77-432.77 GHz spectrometer is only 5.02-836 hPa and the temperature profiles cannot be more effectively detected compared to low-frequency spectrometers.
In general, the retrieval accuracy of the 50.0-60.0 GHz spectrometer is the highest, followed by the 113.75-123.75 GHz spectrometer and the results of the 416.77-432.77 GHz spectrometer are the worst. The results of the 50.0-60.0 GHz spectrometer are slightly better than the MWTS. Therefore, in the design and application of spaceborne microwave spectrometer on the new generation Fengyun satellite for temperature profiles detection, 50.0-60.0 GHz spectrometer is a better candidate, and the parameter requirements of the spectrometer shown in Table VIII can be as a reference. These parameters are applicable over the sea and land as well as under the clear-sky and cloudy-sky conditions. Based on the retrieval results of the humidity profiles in the lower troposphere over the sea, the retrieval accuracy of HATPRO is slightly worse than the 22.0-32.0 GHz spectrometer. But, the ME and RMSE of HATPRO and the spectrometer are better than MWHS at the atmospheric pressure bigger than 500 hPa. The RMSE of HATPRO and 22.0-32.0 GHz spectrometer is better than 6%, while the MWHS is better than 16%. The retrieval accuracy of water vapor in the low troposphere is greatly improved by the HATPRO and 22.0-32.0 GHz spectrometer over the sea. In addition, the retrieval accuracy of this frequency band is not affected by the errors of sea surface temperature and wind speed with 2.0 K and 2 m/s, respectively. However, limited by the accuracy of surface emissivity, the HATPRO and 22.0-32.0 GHz spectrometer have no more effective detection capability over the land.
The retrieval results of 173. 31-193.31 GHz spectrometer are better than MWHS. The retrieval accuracy of 3 MHz spectrometer is the best, the EDH reaches 43.6 hPa and the IC is 1.6 times that of MWHS. In addition, compared with HATPRO and 22.0-32.0 GHz spectrometer, the retrieval accuracy of this spectrometer is better at the atmosphere pressure smaller than 660 hPa over the sea and is significantly better over the land. For the high-frequency spectrometers, the retrieval results of the 315. 16-335.16 are similar with MWHS, but the retrieval accuracy is slightly better, with an EDH of 93.9 hPa. Similar results are obtained for the 372.33-388.33 and 440.0-456.0 GHz spectrometers, with EDHs of 59.4-948 and 47.7-901 hPa, respectively. The retrieval accuracy of the 372.33-388.33 GHz spectrometer is slightly better. The EDH of 548.94-564.94 GHz spectrometer can reach 1.14-424 hPa and the IC is about 1.6 times that of MWHS. The retrieval accuracy of 548.94-564.94 GHz spectrometer is significantly better than MWHS at the atmospheric pressure bigger than 230 hPa.
In general, the humidity profiles over the sea bigger than 660 hPa can be well detected by the seven channels of HATPRO or 22.0-32.0 GHz spectrometer. The retrieval accuracy of the 173. 31-193.31 GHz spectrometer is the highest at 230-660 hPa. The EDH can be extended to 1.14 hPa by the 548.94-564.94 GHz spectrometer. Humidity profiles over the land are only well detected by the 173. 31-193.31 and 548.94-564.94 GHz spectrometers. The parameter configurations of HATPRO and spectrometers shown in Table IX can be as a reference. According to the parameter configurations, the humidity profiles of the middle atmosphere under the clear-sky and cloudy-sky conditions can be effectively detected by these spectrometers for nadir-looking configuration.