A Fast Forward Modelling Method for Simulating Satellite Observations Using Observing Path Tracking

Abstract

The higher the atmosphere is, the larger the deviations in atmospheric temperature and humidity are between the vertical column atmosphere above the cross-section of a satellite instrument and a ray’s trajectory from the cross-section to the satellite. In general, satellite instruments that observe using cross-orbit scanning result in the difference between the observed radiance and the simulations using this method becoming incrementally larger and larger as the cross-section moves to the edge of the satellite’s orbit. The deviations depend on the distance from the column to the ray trajectory and on the horizontal gradient of variables in the distance. In fact, the horizontal gradient of water vapour is larger than the gradient of temperature in clear scenarios, which could introduce an impact of temperature and water vapour on the simulated radiance of a satellite. In this study, a new method to simulate upgoing and downgoing radiation synchronously was developed, using the observing path tracking method. The conventional vertical initial atmospheric profile (Exp.1) and the profiles along the upgoing and downgoing rays of the satellite’s observation (Exp.2) were established, in order to simulate the observed radiance of MWHS-II of FY-3D using global numerical forecasts with resolutions of 15 km and 25 km. The results showed that, for channels in the oxygen and water vapour absorption line on the microwave spectrum, deviations of the two atmospheric profiles were larger at the scan edge (0.01 K) than those at the nadir (0.001 K), and were larger in the upper atmosphere than in the lower atmosphere. The deviation was usually negative in low-latitude regions and was positive in southern high-latitude regions. Such results were obtained in experiments using both the numerical forecast method with 15 km grids and the forecast method with 25 km grids. Deviations were analysed for representative channels at 118 GHz and 183 GHz. Then, the results indicated that bigger deviations between the two experiments were observed in the water vapour absorption line than in the oxygen absorption line in the microwave spectrum. In conclusion, this indicates that, because of the greater horizontal gradient of water vapour, the stronger localisation of water vapour makes the atmospheric profile along the satellite’s observing ray have more increments in the simulated radiance at the scan edge, compared to the atmospheric column profile.

1. Introduction

The fast radiative transfer model is a tool that uses real-time atmospheric temperature and humidity profiles to simulate the radiance of satellite instruments. It is a mapping function from a space of atmospheric and surface parameters to a space of the observed radiance of a satellite. It is key to the simulation of a satellite sensor’s observed radiance, to the physical retrieval of atmospheric parameters using satellite observations, and to the assimilation of satellite data in numerical prediction models [1,2].

In 1976, McMillion et al. first proposed a theory that atmospheric transmittance to a satellite channel can be calculated using a linear function related to the absorption coefficient of the channel and the transmittance prediction factors in transmittance space, as in [3], where the absorption coefficient is only related to the channel spectrum and the transmittance prediction factor is an explicit function of the atmospheric temperature and humidity profiles [4]. In general, this function is a regulative Taylor expansion. In 1988, Eyre et al. proposed that, in a parallel plane atmosphere, the fast calculation of channel transmittance can be performed by a Taylor expansion calculation in the observing thickness space [5]. In an overview of the current dominant fast radiative transfer models, RTTOV (Radiative Transfer for TOVS) was identified as one important model, originally developed by ECMWF (the European Centre for Medium-Range Weather Forecasts) in the early 1990s [6]. After the mid-1990s, RTTOV was developed using NWP SAF (numerical weather prediction SAF), which is one of the SAFs supported by the European Organization for the Exploitation of Meteorological Satellites (EUMETSAT) [7,8,9]. Another important model is CRTM (the Community Radiative Transfer Model), which was developed by JCSDA (the Joint Center for Satellite Data Assimilation) in the United States [10,11]. Up to now, more than 120 satellite sensors in the visible/near-infrared, infrared, microwave, and ultraviolet spectra have been introduced into these fast radiative transfer models [12].

Three types of radiation, the upgoing radiation from the atmosphere, the surface emission radiation, and the downgoing radiation from the atmosphere reflected by the underlay, are involved in the fast calculation of the observed channel radiance of a satellite [2]. While a vertical column is obtained, corresponding to the ground projection of a cross-section of the satellite instrument, profiles of mean temperature and water vapour in the column are used to simulate observed channel radiance. To a cross-section at a non-nadir point, transmittances between neighbouring pressure levels are calculated layer by layer within profiles in the column and are transmitted to the observing path tracking of the satellite’s observations, using the trigonometric function of the satellite’s zenith angle. In general, to such satellite instruments observing using cross-orbit scanning, the increments between the observed radiance and the results of simulations using this method become larger and larger as the cross-section moves to the edge of the satellite’s orbit [13,14].

The higher the atmosphere is, the larger the deviations in atmospheric temperature and water vapour are between the column atmosphere above the cross-section of a satellite instrument and a ray from the cross-section to the satellite. When the NWP model’s top height is approximately 60–80 km, the horizontal offset of the vertical atmospheric column of the cross-section and the observing path tracking at the top of the atmosphere can reach 150–160 km for the cross-section at the edge of the satellite’s orbit [15]. Similar phenomena have been found in corrections to sounding balloon drifts, in simulations of the occultation bending angle, etc. A general solution is to construct two-dimensional observation profiles, using the target travelling paths and projections at sea level [16], and then to compute the simulated observations on the corresponding paths separately, along the projection of the target’s moving path. Benefits have been obtained regarding corrections of observation errors during sounding balloon drift with this method by Laroche and Sarrazin [17]. Zou et al. developed a ray-tracing algorithm to simulate the bending angle along the ray trajectory of an occultation event. Compared to local bending angle prophetization algorithms, the ray-tracing method decreases the error between observations and simulations of extreme weathers, such as typhoons [18]. Bormann et al. established an initial atmospheric profile in segments along an observing path tracking projection, and experiments showed that this method was more effective in revising the mid- and upper-level temperature channels and the mid-latitude low-level water vapour channels to ATMS [15]. The Meteorological Service of Canada applied this method in its global numerical prediction system. The operational results indicated a positive impact on the assimilation increment and a reduction in forecast errors [19]. Previous experience shows that the horizontal gradient of water vapour is larger than the gradient of temperature, both longitudinal and latitudinal, in clear scenarios. In regions with abundant water vapour and with large horizontal gradients, local changes have a significant effect on the simulations of a channel. In current satellite observation simulations, a vertical column is obtained that corresponds to the ground projection of the cross-section of a satellite instrument. To a cross-section at a non-nadir point, the vertical atmospheric column profiles are usually revised into the observation path using the scan angle. For atmospheric variables with strong local characteristics such as water vapour, as the pixel scanning angle increases, the NWP mode grid crossed by the satellite’s observing path also increases, causing the simulation deviation to increase accordingly. In order to validate the impact of water vapour in the calculation of fast radiative transfer and to improve the accuracy of the simulations, the following impacts should be involved in the forward calculations: the high-altitude water vapour content from surface to 300 hPa, the modelling of changes in horizontal gradient of water vapour at every pressure level, and the corrections performed using data assimilation. We are conducting similar work to further evaluate the application of this method in the data assimilation system of the China Meteorological Administration. In view of the method of simulating satellite observations along the observing path tracking of Bormann et al. [15], which only considers the observing path tracking integral of the atmospheric upgoing radiation, in this paper, a new method has been developed to simulate the upgoing and downgoing radiation synchronously, using the observing path tracking method. The global forecast variables of YHGSM with a resolution of 15 km [20] and CMA-GFS in 25 km grids [21] are used to establish the traditional atmospheric profile segmentally in a vertical column atmosphere above the cross-section, and the profile of the observing path tracking method both in the upgoing path and the downgoing path. The FY-3D MWHS-II data are used to conduct a comparative analysis of the simulations, comparing them to the upgoing radiation, downgoing radiation, and observed radiation. The method used to show the initial atmospheric profile along the observing path tracking segments is shown in the second section of this paper. In the third section of the paper, analyses are performed to simulate radiance with the two initial temperature and water vapour profiles, using NWP data and the observations of FY-3D MWHS-II. The conclusions are drawn in the fourth section.

2. Radiation Transfer Calculation Based on the Observing Path Tracking Method

2.1. Fast Radiative Transfer Model

Observed vertical profiles of atmospheric temperature, water vapour, O3, and other trace gases, as well as surface emissivity, surface temperature and humidity, and other underlying surface parameters, are input into the RTTOV model [22] to simulate satellite radiance observations. A fast linearized calculation, to calculate the channel transmittance of the satellite instrument layer by layer, and a linearized radiative transfer equation are also involved in RTTOV, allowing a comparison with a line-by-line transmittance model, performing fast simulations of satellite observations. A radiative transfer equation [23] can be shown in clear scenarios using a cumulative method, as follows:

$$\begin{array}{c}{\mathit{Rad}}_i=B_i^{surf}·{\tau }_i^{surf}+{\displaystyle \underset{k=1}{\overset{j}{\int }}{B}_{k,i}·}d{\tau }_{k,i}\\ \hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}+(1-{\epsilon }_i)·{({\tau }_i^{surf})}^2·{\displaystyle \underset{k=1}{\overset{j}{\int }}\frac{B_{k,i}}{{({\tau }_{k,i})}^2}·}d{\tau }_{k,i}\end{array}$$

(1)

where Rad is the upgoing radiance at the top of the atmosphere, B is Planck radiance, τ is the transmittance of the channel, and ε is surface emissivity. The superscript surf denotes the surface, the subscript k is the pressure level, i is the channel number, and j is the number of model layers of RTTOV. In Equation (1), the first term on the right-hand side is the surface emission, the second term is the calculation of the upgoing radiation in the atmosphere, and the third term is the calculation of the downgoing radiation reflected at the surface.

2.2. Observing Path Tracking Method to Construct the Initial Profile of RTTOV

When the earth’s curvature is ignored, the geometric parameter distribution along the observing path is calculated as shown in Figure 1. In the figure, o is the centre of a satellite’s cross-section, and a three-dimensional coordinate system is established with o as the origin. In the coordinates, the three axes are a ray in the easterly direction (E), a ray in the northerly direction (N), and a ray along the vertical atmospheric column. In addition, $∆H$ is the height between pressure levels, $\theta$ is the satellite’s zenith angle, and $∆D$ is the projection of a segment from o to the intersection of the observing path and a pressure level. $\mathrm{l}\mathrm{e}\mathrm{n}\left(\mathrm{E}\right)$ indicates the offset distance of o and the satellite’s cross-section on a pressure level in the E direction. $\mathrm{l}\mathrm{e}\mathrm{n}\left(\mathrm{N}\right)$ indicates the offset distance of o and the cross-section on a pressure level in the N direction, and α is an angle between ΔD and the E direction of a pressure level.

Firstly, we calculate the $∆H$ between each profile in the NWP model level, and the $∆D$ of the satellite in a pressure level of RTTOV corresponding to the $∆H$ and the satellite’s zenith angle θ. ${lon}_{star}$ and ${lat}_{star}$ at the nadir are calculated by Equations (2) and (3), as follows:

$${lon}_{star}=({lon}_i+{lon}_{i+1})/2$$

(2)

$${lat}_{star}=({lat}_i+{lat}_{i+1})/2$$

(3)

where ${lon}_i$ and ${lon}_{i+1}$ indicate the longitudes corresponding to the 49th and 50th cross-sections in a scanline of MWHS from the FY-3D satellite, and ${lon}_{star}$ indicates the corresponding longitude.

$$Lon=lon\pm ∆D\ast \cos \left(\arctan \frac{\left(lat-{lat}_{star}\right)\ast R}{\left(lon-{lon}_{star}\right)\ast R\ast \cos \left(\mathrm{l}\mathrm{a}\mathrm{t}\right)}\right)/\mathrm{d}$$

(4)

$$Lat=lat\pm ∆D\ast \sin \left(\arctan \frac{\left(lat-{lat}_{star}\right)\ast R}{\left(lon-{lon}_{star}\right)\ast R\ast \cos \left(\mathrm{l}\mathrm{a}\mathrm{t}\right)}\right)/\mathrm{d}$$

(5)

where $lon$ and $lat$ indicate the vertical projected latitude and longitude of the satellite, and $Lon$ and $Lat$ indicate the projected longitude and latitude of the cross-section along the observing path in each isobaric plane. The latitude and longitude of the intersection of the observing path at each pressure level of the RTTOV are calculated according to Equations (4) and (5), regarding both upgoing radiation and downgoing radiation. R is the radius of the Earth and d is 111.2 km, which is the distance represented by 1 degree in the mid-latitude region.

There are three components for the construction of an atmospheric profile algorithm for observing path tracking (shown in Figure 2), as follows:

 (i) 

Atmospheric temperature and water vapour profiles of the NWP forecast are bilinearly interpolated with the location of the satellite’s cross-section at the NWP model level. Then, the profiles are interpolated with the pressure level of the RTTOV from the surface to 0.01 hPa.

 (ii) 

The offset of the vertical atmospheric column above a satellite’s cross-section and the intersection between the upgoing observing path of the satellite and the pressure level of the RTTOV is calculated. Then, the offset of the downgoing observing path of the satellite is calculated. A comparison is performed between the offsets and grids of the NWP model to obtain the corresponding ID of the NWP grid at each pressure level. Thus, an atmospheric temperature and water vapour profile is set up for the observing path of a satellite by constructing the temperature and water vapour at each ID of the NWP grid, layer by layer.

3. Datasets

3.1. FY3D MWHS-II

The FY-3D MWHS-II has 15 channels. Eight channels are used to conduct temperature sounding and are located in the oxygen absorption line at 118.75 GHz. The vertical distribution of atmospheric temperatures from 1000 hPa to 10 hPa can be retrieved [24], as shown in Figure 3a. There are another five sounding channels near the 183.31 GHz water vapour absorption line, which are used to obtain the vertical distribution of atmospheric water vapour from 1000 hPa to 300 hPa, as shown in Figure 3b. A tensor angle of 1.1°, with a corresponding resolution of 15 km for the cross-section at the nadir, has been set for channels at 183 GHz. For channels at 118 GHz, the tensor angle has been set to 2.2°, and the corresponding resolution of the cross-section is 30 km at the nadir. There are 98 consecutive cross-sections per each scan line of the MWHS-II, with a maximum scan angle of 53.35°, and an orbital amplitude of about 2600 km [25].

3.2. Global Numerical Prediction Fields

CMA-GFS is a global numerical weather prediction model system developed by the China Meteorological Administration (CMA) [26]. YHGSM is a global medium-range and monthly extended numerical forecast system developed by the National University of Defence Technology [27,28]. Both models are numerical model systems of the atmosphere and ocean and land surfaces, based on multi-scale and multi-physical processes, and are used to provide refined global weather forecasts. CMA-GFS and YH4DVAR [29] were both adopted as four-dimensional variational assimilation methods to combine observations with model forecasts, in order to correct the error of the initial field of the model, thereby improving the forecast accuracy. In actuality, data assimilation is carried out four times a day, at 00:00 UTC, 06:00 UTC, 12:00 UTC, and 18:00 UTC, respectively. In this study, CMA-GFS was used to provide a global analysis field in 25 km grids and YHGSM was used to provide a global analysis field in 15 km grids.

4. Experiments and Discussion

4.1. Experimental Program

The experiments were divided into two sets, according to the resolution of the global NWP model. In each set of experiments, the global radiance of the channels of the MWHS-II aboard FY-3D were calculated using the temperature and humidity profiles in the vertical atmospheric column above a cross-section (Exp.1) and the profiles based on the zenith angle (Exp.2) constructed using the observing path tracking method [30,31]. These simulations were compared to satellite observations in clear cross-sections over open ocean, and variations in the O-B between the two simulation methods were analysed in each latitude zone between 1 July and 31 July 2021. In these experiments, the O-B (Observed Brightness Temperature—Simulated Brightness Temperature) of channels 2, 4, 6, 7, and 8 at 118 GHz and all five channels at 183 GHz [32] were calculated. The method used to select a clear cross-section is described in the following equation. When the O-B exceeds 3 K in a channel at 89 GHz, the corresponding cross-section could be contaminated by precipitation [33].

$${|\left(obs-FG\right)}_{89\mathrm{G}\mathrm{H}\mathrm{z}}|<3K$$

(6)

In the formula, obs is the observed brightness temperature of a channel, and FG represents the simulated brightness temperature of the NWP forecast. Upgoing radiation flux, downgoing radiation flux, and the simulated satellite radiation flux are more intuitively expressed as channel brightness temperature, using the following formula [6,34]:

$$T_i=\frac{c_2}{\log (1+\frac{c_1}{R_i})}-1$$

(7)

where T is the brightness temperature of a channel, R is the radiation flux of a channel, C₁ and C₂ are the pre-calculated coefficients for each channel, and the subscript i is the channel sequence number.

When selecting a cross-section over an ocean, not only the longitude and latitude of the cross-section but also the projections of the lines connecting the cross-section up to the top of the NWP model layer on the ground should be over an ocean. The projection of the downgoing radiation along the observing path cannot be located over an ocean, because the calculation of the downgoing radiation is conducted from the top of the NWP model layer, using the cosmic brightness temperature as the source of emission, and calculating the emission of the downgoing gas layer by layer, with the radiation emitted from the ground not involved in the calculations. The temperature and humidity profiles established by the observing path tracking method based on the zenith angle are then constructed by constructing the atmospheric temperature and humidity profiles, according to the method described in Section 2.

4.2. Results of the Observing Path Tracking Method for the Construction of Atmospheric Profiles

The average deviation of the global temperature and humidity profiles along the upgoing and downgoing observed observing paths and in the vertical atmospheric column on 1 July 2021 is shown at each pressure level of RTTOV in Figure 4. The temperature differences are small between the profiles in the vertical atmospheric column and the profiles in the observing paths in the middle and lower atmosphere (<500 hPa), and the large deviations in the temperature profiles for the 15 km grids are mainly concentrated in the upper atmosphere above 100 hPa. This phenomenon can be found in profiles both in upgoing observing paths (Figure 4a) and in downgoing observing paths (Figure 4b). As the cross-section moves toward the edge of a scan line, the impact of the scan angle on the temperature deviation becomes larger. The maximum value is 0.002 K for the 97th cross-section at 5 hPa. The vertical distribution of the deviation of the humidity field is the opposite to that of the temperature field, and most of the large values are concentrated in atmosphere with a pressure below 250 hPa. The largest humidity deviation is located at the edge of the scan line and the value decreases gradually as the image element moves closer to the nadir. Another humidity deviation with a larger value is found near 300 hPa at the nadir in Figure 4c.

In the upgoing observed observing path (Figure 4c), large humidity deviations with a value of 2 kg/kg are presented in the fourth cross-section on the left end of the scan line at 800 hPa. Above 400 hPa, similar humidity deviations appear in the 4th and 25th cross-sections. Additionally, maximum deviations appear at the 70th and 85th cross-sections, with a value of 4 kg/kg. In Figure 4d, all humidity deviations are negative. The distribution of the larger deviations is similar to the distribution shown in Figure 4c. Therefore, between profiles in the vertical atmospheric column over the cross-section and profiles along the observing path in clear cross-sections, few temperature deviations appeared in all cross-sections in a scan line at every pressure level and, therefore, will introduce few deviations to the simulated brightness temperature. If the deviations were larger, bias would be introduced into the simulations of the humidity profiles at the edge of a scan line.

4.3. The Influence of the Forecast in 25 km Grids on the Two Radiative Transfer Calculations

Channels 2, 4, 6, 7, and 8 are used to detect the temperature at 10 hPa, 70 hPa, 200 hPa, 500 hPa, and 700 hPa, respectively. Then, the O-B of these channels can be calculated using a global NWP forecast and using RTTOV v13. In Figure 5, deviations of Exp.1 and Exp.2 within the forecast with a 25 km grid are calculated for upgoing radiation, in order to obtain the average bias between the two O-B at each cross-section in various latitude zones between 1 July and 31 July 2021. In the figure, from left to right and from top to bottom, deviations of the two experiments are analysed for upgoing radiance every 10° along the latitude circle. In the subplot, the x-axis indicates scan points, and the y-axis indicates the brightness temperature differences between Exp.1 and Exp.2. The average deviations are much smaller for cross-sections at the nadir than at the edge of the scan lines for the five channels at 118 GHz. The minimum deviation is about 0.001 K, at the nadir, and the maximum value is 0.01 K, at the edge of a scan line. However, the variation in the deviations shows a non-monotonic acyclic vibration, with viewing angles and the amplifications decrease following an arranged in order to detecting altitudes of the channels. Further, the deviations decrease from the polar region to the equator.

Similar experiments have been conducted on the five 183 GHz channels of MWHS-II as well, and the results are shown in Figure 6. The distribution in Figure 6 is similar to that in Figure 5. Global average deviations are about 0.001 K between Exp.1 and Exp.2 for all channels; they vary in a consistent trend for every pressure level and in every latitude zone with gaps less than 0.0001 K. The maximum deviation is 0.025 K at the polar region. Additionally, on the scan line, the deviation is smaller at the nadir than at the scan edge. There is an oscillation as the viewing angle increases, and the bias is larger than 0.02 K between the maximum deviation and the minimum value. The deviations of the simulated upgoing radiances of Exp.1 and Exp.2 do not show a symmetric distribution centred at the nadir, and in the region of latitude of 20°–70°, the deviation at the left end of the scan line (scan point number <48) is significantly larger than that at the right end of the scan line. A conclusion could be that deviations between Exp.1 and Exp.2 are larger for 183 GHz channels than for 118 GHz channels, as the stronger localisation of water vapour causes atmospheric contour orthogonalisation along the observing path to be more adjusted to the edges of the scan line, relative to the atmospheric column contour orthogonalisation.

In the calculation of downgoing radiation, it is assumed that the atmospheric downgoing radiation is specularly reflected at the centre of a cross-section. Then, the atmospheric temperature and humidity profile of Exp.2 can be constructed along the mirror symmetry direction of the upgoing observed observing path. When temperature and humidity profiles of Exp.1 are used, the profiles used for the upgoing radiation are identical to those used for the downgoing radiation calculations. The profiles in Exp.2 construct the temperature and humidity profiles in the same normal direction of symmetry as the observation of the upgoing observing path, which is distinctly different from the upgoing atmospheric profiles. The errors of representativeness of the profiles in two radiation directions can be reduced, because profiles along downgoing observing paths are quite different from profiles along upgoing observing paths and from the profiles in vertical columns. Downgoing emissions are calculated for the five channels with profiles using the forecast in 25 km grids, and average deviations are shown in Figure 7, using observations of MWHS-II in clear cross-sections over the ocean from 1 July to 31 July 2021. It can be seen that the average deviation is about 0.001 K for all channels and the variation in deviations of these channels is not significantly correlated with differences in channel detection height. The distribution of these deviations is similar to that for upgoing radiation, but the maximum deviation is smaller than that of the values for upgoing radiation. In all latitudinal bands, the deviation is smallest at the nadir and grows with an increasing scan angle. For all channels at 118 GHz, the deviations in high-latitude regions are larger than the values for low-latitude regions, and the deviations are larger for the upper atmosphere sounding channels than for lower atmosphere sounding channels, in most regions of the world except the equatorial region (10°N–10°S).

Deviations within the two experiments are shown in Figure 8, for downgoing radiation for the five MWHS-II channels at 183 GHz, and all sets are the same as the test in Figure 5. It can be seen that the overall average deviation for the five channels is 10⁻³ K, the maximum deviation is about −0.03 K in high-latitude regions, and the deviations have a consistently changing trend for all channels. The conclusions obtained for other characteristics are the same as in Figure 6.

For 1 July 2021, the global deviations obtained by the two methods are indicated by channels 2, 4, 6, 7, and 8 of MWHS-II in the ascending orbit of FY-3D. Observed brightness temperatures when over clear ocean are indicated in figures in the left column. Additionally, deviations in brightness temperature are shown by figures in the right column, using the simulations of Exp.1 and Exp.2. At 10 hPa, deviations between the two experiments show few differences and are negative, and the maximum value is −0.019 K at the scan line edge in low-latitude regions of all orbits in the northern hemisphere. However, the deviations are 0.016 K at the edge of orbits in the southern hemisphere. As the channel detection altitude decreases, negative zones of the deviations at the scan line edge move in a southerly direction. Comparing this to the positive deviations of upper channels in the southern hemisphere, negative deviation appears for channel 4 in the region of 30°S, and positive deviation appears in the region of 30°N. For channels with a detecting altitude less than 100 hPa, the same distribution of these deviations between Exp.1 and Exp.2 as that found in the upper atmosphere can be found for channels 6, 7, and 8, but the value is obviously smaller than that in the upper atmosphere. The deviation is smaller the lower the atmosphere that the channel detects. On the other hand, for the five channels at 118 GHz, while cross-sections are distributed in high-latitude regions with low brightness temperatures, the deviations are actually positive between Exp.1 and Exp.2. This is in contrast to cross-sections in low-latitude regions with high brightness temperatures (for example, the observation is larger than 220 K for channel 2), in which the deviations are negative for all channels.

Similar to Figure 9, the deviations are shown for channels 11–15 of MWHS-II in Figure 10. In this figure, the deviations are distributed between −0.2 K and 0.2 K. All large deviations are located at the edge of the orbit and in the precipitation region. Simulations from Exp.2 are larger than the simulations from Exp.1, for all channels at all latitudes and longitudes, because of positive deviations at the edge of the satellite’s orbit. While observing path tracking in the vertical atmosphere column is in clear cross-sections, precipitation could occur along real observed observing paths in certain pressure layers. Therefore, simulations from Exp.2 have smaller values than the simulations from Exp.1, because of scat by hydrated particles, and negative deviations are actually found at the edge of the precipitation region. In addition, the differences in brightness temperature between Exp.1 and Exp.2 decrease gradually with the channel detection height, and the distribution interval of the brightness temperature difference for channel 15 is in the range of [−0.1 K, 0.1 K].

A linearized difference in radiance of satellite channels simulated by Exp.1 and Exp.2 can be calculated using the following equation:

$${\delta R}_i^{tot}={\delta R}_i^{\uparrow }+\frac{(1-{\epsilon }_i){\tau }_{s,i}^2}{{\int }_{k=1}^j{\tau }_{k,j}^{2}d\tau }{\delta R}_i^{\downarrow }$$

(8)

where R^tot is the radiance of a satellite channel, R↑ is the upgoing radiance, ${\delta R}_i^{\uparrow }$ is the equivalent to $B_i^{surf}·{\tau }_i^{surf}+{\int }_{k=1}^J{B}_{k,i}·d{\tau }_{k,i}$ in Equation (1), R↓ is the downgoing radiance, $\frac{\left(1-{\epsilon }_i\right){\tau }_{s,i}^2}{{\int }_{k=1}^j{\tau }_{k,j}^{2}d\tau }{\delta R}_i^{\downarrow }$ is integrated separately to obtain $(1-{\epsilon }_i)·{({\tau }_i^{surf})}^2·{\int }_{k=1}^j\frac{B_{k,i}}{{\left({\tau }_{k,i}\right)}^2}·d{\tau }_{k,i}$, ε is the surface emissivity, τ is the transmittance, τ_s is the transmittance from the surface to the top of the atmosphere, the subscript i is the channel’s ordinal number, and j is the total number of RTTOV mode surfaces. The average deviations of simulated brightness temperature between Exp.1 and Exp.2 are shown, with profiles, in July of 2021 in Figure 11. R^tot should be transferred into brightness temperature by Equation (5). In addition, the deviations are in the range of [−0.01 K, 0.01 K] for all channels at 118 GHz. The distribution characteristics of the deviations are the same as the results for the upgoing scenarios shown in Figure 5 and the results for the downgoing scenarios shown in Figure 7.

Using the same calculation method as in Figure 11, deviations in simulated brightness temperatures between Exp.1 and Exp.2 are shown for five channels at 183 GHz, using data obtained in July of 2021, in Figure 12. The deviation distribution and value range characteristics in this figure are basically the same as in Figure 6 and Figure 8.

There are conclusions that can be obtained from the analysis of the deviations, which are calculated using Exp.1 and Exp.2, for upgoing radiance, downgoing radiance, and observed radiance for the selected channels at 118 GHz and 183 GHz, using global NWP forecasts in 25 km grids. For the five channels at 118 GHz, deviations at the nadir are less than those in the cross-section at the edge of a scan line, where the maximum deviation is 0.01 K. The deviations become smaller with a decrease in latitude and are stable with variations in the detecting altitude of the channel. Additionally, no obvious impact of downgoing radiance along downgoing observing paths on the simulation of brightness temperature can be found. For the five channels at 183 GHz, there is a consistent trend in the mean deviations, with a value of 10⁻³ K for all channels. The deviation is the smallest at the nadir and increases with the increase of the scan angle. It is similar to the impact of downgoing radiance along downgoing observing paths. In general, the deviations increase with increasing scan angles, as increments in the simulations are less than the increments in the observations during a cross-section move to the scan line edge. Larger deviations can be seen in the absorption spectrum of water vapour than in the oxygen spectrum because, in contrast to the radiance of the profiles in the vertical atmosphere column, more radiance could be calculated along the observing path due to the strong localization of distribution of the water vapour.

4.4. The Influence of the 15 km Grid of the Forecast Field on the Two Radiative Transfer Calculations

In this section, all experiments are conducted using the global NWP forecast in 15 km grids of YH4DVAR. The methods and time period of data collection are the same as those used in the analysis of the experiments in Section 4.3.

In Figure 13, the deviations of simulated brightness temperatures are shown for five selected MWHS-II channels at 118 GHz of FY-3D. Observed brightness temperatures during ascending orbit on 1 July 2021 are indicated by the left column in Figure 13, and deviations between Exp.1 and Exp.2 are indicated, for the corresponding channels, in the right column. The maximum positive deviation value is 0.01 K at 10 hPa, which can be found on the scan edge at 40°S. The deviations decrease as the detection altitudes of the channels become lower and lower. Negative deviations may appear below 100 hPa, but the largest deviation observed is −0.05 K at 700 hPa.

The method used to obtain the results in Figure 14 is same as that used for Figure 13, except the deviations are from the five channels at 183 Ghz. It can be seen that the maximum deviation is 0.1 K and that the average deviations are less than the values simulated by the NWP forecast in 25 km grids. The same results can be obtained pertaining to the location of the maximum deviation, the horizontal distribution of the deviation, and the variation in the deviations with decreasing detected altitudes of the channels, in contrast to the results in Figure 10.

The mean deviations at the top of the atmosphere, calculated using Equation (8), are indicated by five channels at 118 GHz using an NWP forecast between 1 July and 31 July 2021. The minimum deviation between Exp.1 and Exp.2 can be found at the nadir and the maximum value is located at edge of a scan line at all latitudes.

The deviations between Exp.1 and Exp.2 decrease gradually from the polar region to the equator.

The experimental setup and conclusions are basically the same as those in Figure 15, Figure 16 shows the results of the analyses for the five channels at 183 GHz.

4.5. Effect of the Two NWP Forecast Fields on the Forward Bias

In this section, deviations in brightness temperature for selected channels of the MWHS-II are calculated, with samples from clear cross-sections over the ocean from 1 to 31 July 2021, using Exp.1 and Exp.2.

The deviations between Exp.1 and Exp.2 are shown in Figure 17 for NWP forecasts in 25 km grids. Deviations are indicated by the five channels at 118 GHz in Figure 17a. In these figures, the curves are mean deviations, and the boxes represent the maximum and minimum values, using profiles from Exp.1 and Exp.2 for each channel. Mean deviations show few differences for all channels, no matter whether they pertain to upgoing radiation or to downgoing radiation, except the radiance at the top of the atmosphere, which indicates larger deviations with decreasing detecting altitudes of the channels. The smallest box is available for channel 2 at 10 hPa and the larger box for channel 4 at 75 hPa. In atmospheres below 100 hPa, the range of the deviations remains unchanged for channel 6 and channel 7 in the middle atmosphere and is largest for channel 8 in the lower atmosphere. This phenomenon can also be found for deviations in both upgoing downgoing scenarios. For deviations of radiance at the top of the atmosphere, the same distribution can be seen for deviations above 100 hPa, and the range of deviations increases with decreasing detecting altitudes of the channels, below 100 hPa.

For the five channels at 183 GHz, the mean deviations remain stable around 0 K in upgoing calculations and have a range between −0.46 K and −0.6 K in downgoing calculations. The deviations are the smallest for channel 11 at 300 hPa and become larger and larger with a decreasing detecting altitude of the channel; the deviation is largest for channel 15 at 800 hPa. Boxes become monotonic and smaller with the decreasing altitude of channels in upgoing scenarios. The minimum deviation is 0.005 K and the maximum value is 0.4 K for radiance at the top of the atmosphere. Additionally, the range of the boxes is disordered for the calculation of downgoing radiation and radiance at the top of the atmosphere.

The results in Figure 18 are calculated using the NWP forecast in 15 km grids. A smaller range of deviations is indicated for upgoing radiation, downgoing radiation and radiance at the top of the atmosphere, when compared to the range of deviations obtained when using forecasts in 25 km grids. For channels at 118 GHz, the maximum deviation can be obtained for channel 2 at 10 hPa, for the calculation of both upgoing radiation and radiance at the top of the atmosphere. Deviations remain stable and have values near 0 K for the remaining four channels. The largest box is available for channel 2, and the smallest box can be found for channel 4, for upgoing scenarios. For downgoing radiation and radiance at the top of the atmosphere, the box for channel 2 is still larger than for channel 4, but the largest box is for channel 8, at a lower atmosphere.

For the five channels at 183 GHz, similar results can be obtained for mean deviations, for both upgoing radiation and downgoing radiation, contrasting with the results in Figure 17. However, for radiance at the top of the atmosphere, the maximum deviation is larger than 0.2 K for channel 11 at 300 hPa. The minimum value is −0.1 K for channel 15 near 800 hPa. Variations in boxes are similar to the variation shown in Figure 17.

5. Conclusions

In regions with abundant water vapour and large horizontal gradients, local changes have a significant effect on the simulations of a channel. In order to validate the impact of water vapour in fast radiative transfer calculations and to improve the accuracy of the simulated radiance of satellite instruments, several impacts should be involved in forward calculations; for example, modelling the changes in the horizontal gradient of water vapour at every pressure level, etc. In this study, a new method was developed to simulate upgoing and downgoing radiation synchronously, using the observing path tracking method. Global forecast variables of YHGSM, with a resolution of 15 km, and of CMA-GFS, with a resolution of 25 km, were used to establish the traditional vertical initial atmospheric profile segmentally along the column atmosphere above the cross-section and the profile along the observing path, for both the upgoing path and the downgoing path. The FY-3D MWHS-II data were used to conduct a comparative analysis of the simulations for the upgoing and downgoing radiation, and the results of these two simulations were analysed in comparison with the observed radiation. The conclusions obtained are as follows.

Statistical analysis was performed using observations of FY-3D MWHS-II data between 1 and 31 July 2021, and small deviations between Exp.1 and Exp.2 could be seen for channels at 118 GHz. Larger deviations were obtained for channels at 183 GHz, due to the strong localization of the distribution of water vapour. Mean deviations were approximately 10⁻² K for channels at both 118 GHz and 183 GHz, but the maximum deviation was 1.0 K for a certain channel at 183 GHz. For the simulated brightness temperatures in upgoing scenarios, downgoing scenarios, and in radiance calculation at the top of the atmosphere, deviations between Exp.1 and Exp.2 were smallest at the nadir (0.001 K) and demonstrated maximum values at the edge of the scan line (0.01 K). Additionally, larger deviations were found in upper altitude detecting channels, and smaller deviations were located in channels in the lower atmosphere, no matter whether the channel was at 118 GHz or at 183 GHz. When the CMA-GFS forecast in 25 km grids was replaced by the YH4DVAR forecast in 15 km grids, the same conclusions were obtained for the deviations, and we can say that few impacts of the variation in horizontal resolution of the NWP forecasts could be seen on the radiative transfer calculation.