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The fast radiative transfer models, e.g., the Radiative Transfer for TIROS Operational Vertical Sounder TOVS (RTTOV) and the Community Radiative Transfer Model, allow rapid cross-conversion of model variables to BT and serve as the observation operator role in data assimilation. However, strong absorption of cloud liquid water (CLW) and scattering of ice clouds and precipitation lead to large errors in the BT simulation. Therefore, removing observations affected by clouds is necessary before radiance data assimilation. The 3D precipitation detection is achieved by dynamic selection of clear-sky channels above precipitation, called the DCS method. Under clear-sky conditions, the radiative transfer equation for channel
${i}$ can be written as follows:where
$ {L}_{i,\mathrm{c}\mathrm{l}\mathrm{r}} $ is clear radiance,${\varepsilon }_{i,\mathrm{s}\mathrm{u}\mathrm{r}}$ is the surface emissivity,$ {B\left(T\right)}_{i} $ is the Planck function,$ {\tau }_{i,\mathrm{s}\mathrm{u}\mathrm{r}} $ is the surface-to-space transmittance,$ {T}_{\mathrm{s}} $ is the surface temperature,$ {P}_{\mathrm{t}\mathrm{o}\mathrm{p}} $ is the top layer of pressure coordination used in RTTOV, and${P}_{{\rm{s}}\mathrm{u}\mathrm{r}}$ is the surface pressure.$ {\tau }_{i} $ is the cumulative transmittance of all absorbing gases from the model layer to space and can be presented as below:where
$ {a}_{i,j,k} $ are the transmittance coefficients,$ {X}_{j,k} $ are the predictors,$ m $ and$ n $ are the number of absorbing gases and pressure coordination layers defined by RTTOV respectively, and$ k $ and$ j $ are the$ k $ th and$ j $ th of those. If a non-precipitation cloud has thickness and exists in many layers, the radiance transfer equation should be written as below:where
$ {L}_{i} $ is total radiance,$ {L}_{i,\mathrm{c}\mathrm{l}\mathrm{d}} $ is cloudy radiance, and$ N $ is the fractional cloud cover. For those channels whose weighting function peak heights are already higher than the cloud top height, the absorptions in clouds are strong, and the transmissions below the clouds are small. Therefore, only the transmission of absorbing gases from cloud top to space could be contained in the radiative transfer calculation, while the cloudy radiance$ {L}_{i,\mathrm{c}\mathrm{l}\mathrm{d}} $ can be written as follows:where
$ {P}_{\mathrm{c}\mathrm{l}\mathrm{d}\_\mathrm{t}\mathrm{o}\mathrm{p}} $ is the cloud top pressure. Under this condition, the CLW absorption should be considered for MW radiance. CLW should be added as one of the absorbing gases, and an additional calculation for CLW transmittance is added:where
$ {X}_{j,\mathrm{c}\mathrm{l}\mathrm{w}} $ are the CLW predictors associated with the satellite zenith angle,$ f $ is the central frequency of the channel,$ \mathrm{n}\mathrm{l}\mathrm{e}\mathrm{v}\mathrm{s} $ is the number of model layers, and mw_cldtop is the top layer of clouds in the CLW profile.$ {Z}_{\mathrm{a}} $ and$ {Z}_{\mathrm{b}} $ are empirical coefficients related to frequency. The lack of a calculation for the CLW transmittance in the clear-sky assimilation can cause large simulation errors. The sensitivity of each channel to CLW is different, and the impact of CLW on simulation errors is also different. The DCS method takes these into account and analyzes the difference between total radiance and clear-sky radiance, which can be written as below:Qin et al. (2020) analyzed the influence of CC and CTH on the
$ \mathrm{d}\mathrm{i}\mathrm{f}\mathrm{f} $ values through RTTOV9.2 and established the lookup tables based on different$ \mathrm{d}\mathrm{i}\mathrm{f}\mathrm{f} $ values for 54.4 GHz, 54.94 GHz, and 55.5 GHz. For a given pixel, the accuracy for the simulated BT of which channel is affected by the CC and CTH can be determined according to the lookup tables, and the contaminated channels of this pixel can be simultaneously removed. But MW sounders cannot retrieve CC and CTH directly, so it is necessary to obtain CC and CTH in MW pixels by a pixel-remapping technique with the help of an IR imager onboard the same satellite platform. It is worth noting that the differences in optical properties between IR and MW make IR more cloud-sensitive than MW. Clouds that can affect IR radiances do not always affect MW radiances to the same extent, which may lead to overestimation in cloud-affected MW radiances through IR observations. But it can ensure that the MW radiances that have passed the IR-assistant detection are more likely clear. Since the weighting function peaking height of 53.596 GHz is only 700 hPa, it is much more sensitive to cloud water than other channels. Therefore, the 53.596 GHz channel is not discussed in this study because it is strongly unaffected by low clouds. Three thresholds (0.05 K, 0.1 K, and 0.2 K) of$ \mathrm{d}\mathrm{i}\mathrm{f}\mathrm{f} $ values are selected to determine the accuracy of the simulated BT in Qin et al. (2020), whereas 0.05 K was chosen for this study because of the similar impacts from the three thresholds. -
FY-3D, an afternoon-orbit satellite of the Chinese Fengyun series, was launched in November 2017. The MWTS-II onboard FY-3D has 13 channels in the 50–60 GHz oxygen absorption band and can provide atmospheric temperature information from the surface to 2 hPa. There are 90 FOVs in each scanline with a horizontal resolution of approximately 32 km. The swath width is 2250 km. The central frequency, weighting function peak heights, bandwidth, and noise equivalent differential temperature (NE△T) of the FY-3D MWTS-II are shown in Table 1 (Carminati et al., 2021). In this study, the Level-1c (L1c) products from the FY-3D MWTS-II were provided by the National Satellite Meteorological Centre (NSMC) of the CMA. According to the Medium Resolution Spectral Imager (MERSI) -2 cloud product, the CC and CTH required by the DCS method are already remapped in the L1c dataset and can be obtained from the operational CMA NWP center in near-real time.
Channel Numbers Central frequency (GHz) Weighting function peak heights (hPa) Bandwidth (MHz) NE△T (K) 1 50.3 Surface 180 0.3 2 51.76 Surface 400 0.2 3 52.8 950 400 0.2 4 53.596 700 400 0.23 5 54.40 400 400 0.2 6 54.94 270 400 0.2 7 55.50 180 330 0.3 8 57.290344 90 330 0.4 9 Fo±0.217 50 78 0.5 10 Fo±0.3222±0.048 20 36 0.5 11 Fo±0.3222±0.022 12 16 0.7 12 Fo±0.3222±0.010 5 8 1.2 13 Fo±0.3222±0.0045 2 3 1.5 Note: Fo=57.290344. Table 1. The channel characteristics of FY-3D MWTS-II.
To prevent the assimilation of poor-quality data, necessary preprocessing is required for raw radiance data before assimilation, including bias correction, quality control, and preliminary channel selection. Significant systematic biases between the observations and the first guess exist due to the inaccuracies in the radiative transfer model and the instrument's characteristics. The Variational Bias Correction (VarBC) method, which has been proven to minimize the analysis disruptions (Auligné and McNally, 2007), was used here to correct the systematic biases. The VarBC method expresses the bias as a linear combination of predictors that can be updated adaptively during the minimization of variational analysis. By running a VarBC "off-line" model with 25-day (from 1 to 25 August 201) radiance data, the bias correction coefficient and predictor statistics are obtained for the first cycle analysis. The predictors include 1000–300 hPa and 200–50 hPa layer thickness, surface skin temperature, total column water vapor, the scan position, and the square and cube of scan position. Then, the bias correction coefficients are updated from the previous analysis output.
Quality control (Zhang et al., 2019b) includes (1) outlier detection: the radiances are removed when OMBs (observation minus background) exceed either 15 K or three times the standard deviations (STDV) of the observation error, whichever is smaller, (2) surface type detection: radiances binned into mixed surface-type are removed, (3) scan position check: the data of the eight outermost FOVs are removed, and (4) pressure detection: the observations from channel 5 are removed when the surface pressure is smaller 850 hPa to reduce the influence of the plateau terrain.
Moreover, not all MWTS-II channels are suitable for assimilation. As shown in Table 1, channels 1 and 2 are sensitive to the surface. Channels 3 and 4 are sensitive to CLW and the surface due to their primary goal of measuring lower-troposphere atmospheric temperatures. These channels are not assimilated in this study because the lack of accurate surface emissivity makes it difficult to simulate the corresponding BT accurately. Channels 9–13 are mainly aimed at upper-stratosphere atmospheric temperatures. Accurate atmospheric state profiles with corresponding heights from the first guess are needed to assimilate these channels, which is a challenge for this study because of the model's top setting at 10 hPa. Thus, channels 9–13 are also excluded to avoid excessive simulation errors.
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To quantitatively evaluate the impact of MWTS-II on analysis and forecasting with the DCS method, the analysis fields and forecast fields of the two cases are verified against ECMWF Re-Analysis 5 (ERA5) (Hersbach et al., 2020). ERA5 does not use the MWTS-II on FY-3D. The cycle-averaged root-mean-square error (RMSE) of temperature, relative humidity, U-wind, and V-wind for the 48-h deterministic forecasts in model domain 2 (see Fig. 1) are calculated, and the results for the upper (200 hPa), middle (500 hPa), and lower (850 hPa) troposphere are shown in Fig. 6 and Fig. 7 for Typhoon Lekima (2019) and Typhoon Mitag (2019) respectively. Eight groups of forecasts for the Lekima (2019) case and four groups of forecasts for the Mitag (2019) case are used in the verification. In general, the RMSEs of each variable in the upper troposphere are larger than those in the lower troposphere, and the RMSEs increase with the forecast lead time. To quantify the impacts, the improve ratio (in %) can be defined as:
Figure 6. The cycle-averaged root-mean-square error (RMSE) of (a) temperature, (b) relative humidity, and (c) U- and (d) V-wind 48-h deterministic forecasts for Typhoon Lekima (2019). The blue lines indicate CTRL experiments, and the red lines indicate DCS experiments. Error bars show the confidence interval of the mean RMSE for 95% confidence limit.confidence limit.
and is calculated for every 6-h forecast. The averaged results at different levels are shown in Table 2.
Case Altitude T (%) RH (%) U (%) V (%) Lekima (2019) 200 hPa 1.15 –0.41 0.99 1.20 500 hPa 1.23 0.44 0.40 0.29 850 hPa –0.20 –0.23 0.20 0.33 Mitag (2019) 200 hPa 2.42 1.05 1.45 1.49 500 hPa –0.20 0.56 –0.27 1.34 850 hPa –0.78 0.27 –0.05 0.85 Table 2. The averaged improve ratio at the upper (200 hPa), middle (500 hPa), and lower (850 hPa) troposphere in the two typhoon cases.
For temperature in the middle and upper troposphere, the average RMSEs in the DCS experiments are slightly reduced compared to those in the CTRL experiments; but the average RMSEs are increased in the lower layers. This decreasing trend is most evident in the Mitag (2019) case at 200 hPa (Fig. 7a), where the average improve ratio is 2.42%. RMSE reduction may benefit from more upper channels being assimilated.
For relative humidity, the RMSEs of the DCS and CTRL experiments are relatively close. In the Lekima (2019) case, the RMSEs of the DCS experiment show a slight increase at 200 hPa and at 850 hPa. In the Mitag (2019) case, the DCS experiment shows slight improvements. As a temperature-sounding instrument, the assimilation of additional MWTS-II radiance data produces limited improvement for relative humidity.
However, the improvement of the U- and V-wind component RMSEs with the DCS method is obvious, especially at 200 hPa. The relative change between the DCS and CTRL experiments increases with the forecast lead time. The average improve ratio is 0.99% for Lekima (2019) and 1.45% for Mitag (2019) for 200-hPa U-wind. For 200-hPa V-wind, the values are 1.49% and 1.20%, respectively. The reason for the improvement in the wind forecast is related to the cycle assimilation scheme. As a MW-temperature sounder, MWTS-II is assimilated to provide a noticeable increment in temperature analysis. At the same time, the other model variables of analysis fields (model initial values), such as surface pressure and geopotential height, can also be updated after assimilation. Through cycle assimilation, these model initial values are continuously updated, and the information from observation is transferred to other forecast variables (e.g., wind, etc.) through the dynamical constraints of the dynamic equations of atmospheric motion. After several cycles, this improvement gradually accumulates and becomes evident. Similar results can also be found in Li and Liu (2016b) and other studies. At the same time, because of the large forecast errors of wind, its improvements are obvious. In fact, the improve ratios of wind and temperature are on the same order of magnitude (see Table 2).
The profiles of the averaged RMSEs at different forecast times are shown in Fig. 8, and similar conclusions can be made. The impacts of the DCS method become more evident as the deterministic forecast time extends. The improvement of temperature is mainly concentrated above 500 hPa, and the improvement in the wind field is more evident than temperature due to the larger wind forecast error. The average improvement rates of these four prognostic variables in the upper, middle, and lower troposphere are 1.7%, 0.5%, and 0.05%, respectively.
Figure 8. The vertical profiles of the 6-h (first line), 12-h (second line), 24-h (third line), and 48-h (fourth line) forecasts of T (K, first column), RH (%, second column), U (m s–1, third column), and V (m s–1, fourth column) for Typhoons Lekima (2019, solid lines) and Mitag (2019, dashed lines) for the CTRL (blue) and DCS (red) experiments compared with ERA5.
The error bars in Fig. 6 and Fig. 7 show the 95% confidence interval. For the Lekima (2019) case, the differences between the experiments were not statistically significant. For the Mitag (2019) case, some statistically significant results can be found in temperature and V-wind at 200 hPa. Significant differences between the CTRL and DCS experiments are concentrated only in the upper troposphere, where the average improvement in temperature and wind is 1.5%. The DCS method brings limited improvement, probably because only one MW sounder was assimilated with the DCS approach. As a polar-orbiting satellite, FY-3D has a low temporal resolution. Although it provides a lot of observations from MWTS-II, the increased number of observations in the DCS experiments cover only a part of the model domain, and the impacts are subtle after averaging over multiple forecasts and more than 10 000 grid points. Applying the DCS method to more MW sounders is likely to cause more significant differences.
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The impact of assimilating MWTS-II radiance data is evaluated by examining the 72-h forecasts from each analysis. The average absolute errors for track, CSLP, and MWS in the 72-h forecasts from the Lekima (2019) and Mitag (2019) cases are shown in Fig. 9, as verified against the best track from JTWC. The track and intensity results come from the output of the moving-nest domain.
Figure 9. The average absolute forecast errors of (a) track, (b) central sea level pressure, and (c) maximum wind speed as functions of forecast range from the two experiments, as verified against the best track from the JTWC. The error statistics are obtained from all 72-h forecasts for Typhoon Lekima (2019) and four 72-h forecasts for Typhoon Mitag (2019). The blue lines indicate CTRL experiments, and the red lines indicate DCS experiments. The solid lines indicate the results of Typhoon Lekima (2019) and correspond to the left y-axis, and the dashed lines indicate the results of Typhoon Mitag (2019) and correspond to the right y-axis. The averages of forecast time are the text on the top of the figures.
On average, neither experiment produces superior forecasts. For the stronger typhoon, Lekima (2019), there are slight improvements in track forecasts as forecast time increases. The averaged reduction of track error for the DCS experiment is approximately 4.53% compared to the CTRL experiment. The improvements in track forecasts may be a result of assimilating more observations in the DCS experiment, which improves the environmental field and further increases the accuracy of the steering flow. CSLP and MWS are used to reflect the typhoon intensity forecast. For both typhoons, the intensity forecast errors continue to increase during the first 30 h of the forecast due to the typhoon intensification. However, in the 30-h to 48-h forecasts, the forecast errors decrease as the typhoon matures. After the 48-h forecast, the errors gradually increase again as the typhoon weakens. Both the CTRL and DCS experiments show this “increase–decrease–increase” trend of intensity forecast errors. The intensity forecasts are mixed. For Lekima (2019), except for the 42-h and 48-h forecasts, the DCS experiment has a smaller CSLP forecast error than the CTRL experiment. The maximum improvement of the DCS experiment CSLP forecast error is about 16.97%. Similar conclusions can be drawn for the MWS of Lekima (2019). For the weaker typhoon, Mitag (2019), the results are not as positive as for Lekima (2019). The CSLP forecast results is neutral, and the MWS forecast results is even negative. This may be attributed to the complexity of typhoon intensity forecasting (Wang and Wu, 2004; Yu et al., 2013; Ito, 2016).
The assimilation of FY-3D MWTS-II data using the DCS method slightly improves typhoons track forecasts on average and neutrally impacts intensity forecasts. These results may also be related to the slight increase of STDV in channel 5. As discussed in section 4.1, a small percentage of bad data may compromise the data impact or even cause a negative impact. It is essential to implement more stringent quality control steps when adding a large number of observations in order to minimize the impact of bad observations.
Channel Numbers | Central frequency (GHz) | Weighting function peak heights (hPa) | Bandwidth (MHz) | NE△T (K) |
1 | 50.3 | Surface | 180 | 0.3 |
2 | 51.76 | Surface | 400 | 0.2 |
3 | 52.8 | 950 | 400 | 0.2 |
4 | 53.596 | 700 | 400 | 0.23 |
5 | 54.40 | 400 | 400 | 0.2 |
6 | 54.94 | 270 | 400 | 0.2 |
7 | 55.50 | 180 | 330 | 0.3 |
8 | 57.290344 | 90 | 330 | 0.4 |
9 | Fo±0.217 | 50 | 78 | 0.5 |
10 | Fo±0.3222±0.048 | 20 | 36 | 0.5 |
11 | Fo±0.3222±0.022 | 12 | 16 | 0.7 |
12 | Fo±0.3222±0.010 | 5 | 8 | 1.2 |
13 | Fo±0.3222±0.0045 | 2 | 3 | 1.5 |
Note: Fo=57.290344. |