1. Introduction
Satellite radiances and the assimilation of them have significantly contributed to advances in numerical weather prediction (NWP), especially in regions with sparse conventional observations, such as the Southern Hemisphere and oceans (Bauer et al. 2015). Hyperspectral infrared (IR) satellites provide high-resolution vertical information related to temperature, humidity, and other atmospheric variables, which have demonstrated excellent impact in NWP (Le Marshall et al. 2006; Hilton et al. 2009; Okamoto 2017; Li et al. 2022). Early IR sounders were limited by spectroscopy technology and provided a few channels, such as the High-Resolution Infrared Radiation Sounder (HIRS) with 19 channels (Singh et al. 2012). Given the development of grating/interferometric spectral sounders, the spectral resolution of IR sounders has vastly improved (Menzel et al. 2018), like the Atmospheric Infrared Sounder (AIRS; Chahine et al. 2006), Infrared Atmospheric Sounder Interferometer (IASI; Cayla 2001; Chalon et al. 2001) and the Cross-track Infrared Sounder (CrIS; Gambacorta and Barnet 2012) with over a thousand channels. The high spectral resolution of the hyperspectral IR sounders can well capture the detailed atmospheric vertical structures, and thus the hyperspectral IR sounders have played an important role in meteorological disaster monitoring, assimilation, and predictions (Li et al. 2016; Menzel et al. 2018). The advantages of the hyperspectral sounders have been extended by enabling such measurements in geostationary orbits (Smith et al. 2009; Schmetz 2021). However, due to the large data volume and interchannel correlations, it has been a great challenge to efficiently and effectively assimilate the hyperspectral IR sounders.
In December 2016, China launched the second-generation geostationary meteorological satellite Fengyun-4A (FY-4A), with a Geostationary Interferometric Infrared Sounder (GIIRS) onboard. As a Michelson interferometer sounder, the GIIRS spectrum covers the longwave infrared (700–1130 cm−1) and midwave infrared (1650–2250 cm−1), with a spectral resolution of 0.625 cm−1 and a total number of 1650 detection channels. Previous studies have shown that geostationary hyperspectral IR sounders could improve the forecasts for both global (Okamoto et al. 2020; Wang et al. 2021) and regional applications (Zhang et al. 2016; Cintineo et al. 2016; Jones et al. 2017). Given the high temporal- and spectral-resolution data for a fixed area, GIIRS has shown great promise for NWP (Ma et al. 2021; Di et al. 2021; Yin et al. 2021). Assimilation of the clear-sky GIIRS water vapor channels improved the forecasts of location and precipitation for the “21⋅7” (21 July 2012) extreme rainstorm in Henan, China (Yin et al. 2022). Feng et al. (2022) assimilated temperature retrievals from GIIRS and obtained improved typhoon predictions. Yin et al. (2021) showed that frequent assimilation of the GIIRS IR data improved the forecasts of Typhoon Maria (2018).
Among the thousands of hyperspectral IR channels, the almost monochromatic atmospheric IR observations are provided with signals varying in strength due to the intrinsic nature of atmospheric absorption (Menzel et al. 2018). Due to limited computational resources, it is currently impractical to assimilate all the hyperspectral IR channels for operational real-time NWP. Moreover, the overlap of weighting functions among the hyperspectral channels results in interchannel correlations and correlated observation errors (Bormann et al. 2010). Thus, channel selection has been widely adopted for assimilating the hyperspectral IR radiances (Rabier et al. 2002; Collard 2007; Gambacorta and Barnet 2012; Noh et al. 2017; Di et al. 2022). Previous studies have shown that assimilation of the channel-selected radiances could help to reduce the forecast errors (e.g., Collard 2007; Ventress and Dudhia 2014; Noh et al. 2017). Various channel selection methods have been proposed and applied, including the statistical methods based on the degrees of freedom of the signal (DFS; e.g., Rabier et al. 2002; Collard 2007; Collard et al. 2010), and the physical methods based on the channel spectral sensitivity to the state variables (e.g., Dudhia et al. 2002; Gambacorta and Barnet 2012; Martinet et al. 2014).
One commonly applied statistical method for channel selection is based on the Shannon’s information entropy (Rodgers 1998). Using simulated IASI data, Rabier et al. (2002) evaluated various channel selection methods, including one using the Jacobian matrix (gradient of the forward operator matrix) and selecting the channels with the most appropriate Jacobian characteristics, and another iteratively selecting channels with the largest information content according to the analysis error covariances. The iterative method produced better results than the Jacobian method, but with larger computational costs, while both methods can provide additionally selected channels to improve the radiance assimilation in cloudy conditions (Martinet et al. 2014). Based on the maximum entropy reduction (ER), an optimal subset of channels over the entire spectrum can be selected (Collard 2007; Di et al. 2022). Using the ER-based channel selection method, the optimal channels of AIRS (McNally et al. 2006) and IASI (Collard 2007) are selected, which have been used for the European Centre for Medium-Range Weather Forecasts (ECMWF) and the National Centers for Environmental Prediction (NCEP) (e.g., McNally et al. 2006; Collard and McNally 2009; Ventress and Dudhia 2014; Martinet et al. 2014). However, the ER-based channel selection method is based on the linear theory of optimal estimation, which often provides the optimal subset of channels without time variations. Along with the increased spatial resolutions of numerical models and satellite radiances, more detailed features and associated evolutions of the multiscale weather can be revealed, which requires follow-dependent and time-varying channel selections. Thus, the traditional ER-based method that gives time-invariant selected channels could become suboptimal.
Besides the ER-based channel selection method, another method for reducing data volumes via dimensionality reduction is the principal component analysis (PCA). The PCA-based approach transfers observation information from spectral space to principal component space, and thus the main observation information is represented by the leading principal components while the less valuable observation information is contained by the trailing principal components. But the nonlocalized Jacobians associated with the principal components can mix contributions from clear and cloudy atmosphere and also result in broad vertical influences from the stratosphere to the troposphere. Collard et al. (2010) demonstrated that assimilation of the IASI radiance spectra reconstructed from the principal components could mitigate the nonlocality of the Jacobians. Matricardi and McNally (2014) assimilated 20 IASI principal components in the ECMWF four-dimensional variational (4D-Var) system with a significant reduction of computational cost, compared to the assimilation of the original 165 channels. Using an ensemble Kalman filter (EnKF), Lu and Zhang (2019) showed that the analysis increment by assimilating 10–20 AIRS principal components was similar to that of assimilating all channels. In addition to the reduction of data dimensionality, assimilating the leading principal components can reduce noise (Geer et al. 2019), and the transformation from spectral space to principal component space can achieve uncorrelated principal component scores. But the PCA-based channel selection method requires a PCA-based radiative transfer model, such as the PC_RTTOV (Matricardi 2010) or PCRTM (Liu et al. 2006).
This work proposes an alternative way to select channels for hyperspectral IR radiances, by performing the channel selection along with data assimilation. Using an EnKF, Whitaker et al. (2008) proposed an adaptive assimilation order for spatially dense observations, in order to reduce the computational cost and avoid duplicate observation information. Similar to the ER-based channel selection, the adaptive assimilation order serially assimilates the observations by the sequence of the reduction of the background error variances. The assimilation stops when a threshold of the reduction of the background error variances is reached, which indicates that the unassimilated observations cannot significantly improve the analysis, but only reduce the posterior ensemble spread. Expanding upon this idea, it is straightforward to apply the adaptive assimilation order as a channel selection method. The adaptive assimilation order can naturally provide an adaptive channel selection with spatial and temporal variations, along with data assimilation. The adaptive channel selection is investigated in this study for the GIIRS radiances, under both clear-sky and all-sky conditions. Moreover, the performance of the adaptive channel selection with varying model resolutions from kilometers to subkilometers is examined.
The paper is organized as follows. Section 2 describes the channel selection methods, including ER-based and proposed adaptive techniques. Section 3 presents the experimental design. The selected radiance data from the ER-based method and adaptive method are compared in section 4. Section 5 discusses the results of two channel selection methods under clear-sky and all-sky conditions, respectively. Section 6 summarizes the conclusions.
2. Methodology
a. ER-based method
b. Adaptive selection method
It is straightforward to apply the assimilation order based on the reduction of analysis error variances in observation space (Whitaker et al. 2008) as an adaptive channel selection method for the hyperspectral IR radiances, by assuming that radiance observations have no correlated observation errors. Compared to the ER-based method that differentiates the radiance observations by channels, the adaptive channel selection method treats the multichannel radiance observations as independent and assimilates them by the order of increasing Pa/Pb. Therefore, the hyperspectral IR radiance observations that have large contributions to the reduction of observation analysis error variances are assimilated before the other. Once the preset threshold is reached, the remaining hyperspectral IR radiance observations are not assimilated. Note that the adaptive channel selection method does not consider interchannel correlations from which the correlated channels could be simultaneously assimilated (Bormann et al. 2010; Weston et al. 2014). This issue will be discussed in section 6.
3. Experimental design
To examine the channel selection methods, a noncycled observing system simulation experiment (OSSE) is used with configurations following Zhou et al. (2023). The nature run (NR) and ensemble simulations are conducted using the Weather Research and Forecasting (WRF) Model version 3.8.1 (Skamarock et al. 2008). The applied physical parameterization schemes are the WRF 6-class microphysical scheme (Hong and Lim 2006), the surface parameterization based on the Monin-Obukhov similarity theory (Monin and Obukhov 1954; Dudhia 2005), the five-layer thermal diffusion scheme (Dudhia 2005), and the Yonsei University (YSU) planetary boundary layer (PBL) scheme (Hong et al. 2006). As atmospheric radiation is one of the effects represented in the relaxation term, no other parameterization of it was used (Rotunno et al. 2009). Two-way feedback is on for nested domains.
The initial condition for NR contains an initial vortex, whose maximum wind at the lowest level, radius of the maximum wind, and radius of zero wind are 15 m s−1, 82.5 km, and 412.5 km, respectively. The whole NR simulates the vortex evolution for 13 days. The first two nested domains of NR have 1200 × 1200 horizontal grid points with horizontal grid spacings of 7.5 and 1.5 km, respectively (Fig. 1). Starting on the beginning of the fourth day (0000 LT day 4), two additional nest domains are initialized from the 1.5-km simulation, both of which have 3200 × 3200 horizontal grid points with horizontal grid spacings of 300 and 60 m, respectively; and the large eddy simulation is integrated for 12 h. There are 100 vertical levels with the model top at 15 hPa. The output frequencies of the four nested domains are 180, 180, 5, and 5 min, respectively. Details of NR simulations are shown in Fig. 2.
Nested domains for (a) NR and (b) ensemble simulations. Red boxes denote the domains for LES simulations.
Citation: Monthly Weather Review 152, 3; 10.1175/MWR-D-23-0131.1
Configurations for NR and ensemble simulations. Red stars and bars denote times for synthetic observations and assimilations, respectively.
Citation: Monthly Weather Review 152, 3; 10.1175/MWR-D-23-0131.1
The initial conditions for the 50-member ensemble simulations are generated by adding random perturbations on a control initial vortex that is slightly different from the true one. The initial vortex for the control has the maximum wind at the lowest level of 14 m s−1 and radius of the maximum wind of 80 km. Random perturbations have mean 0 and standard deviation of 2.1 m s−1 and 12 km for the lowest-level maximum wind and radius of the maximum wind, respectively. Ensemble simulations are conducted with the outermost domain of 7.5-km horizontal grid spacing on 240 × 240 horizontal grids for 13 days, with 3-h outputs except for 30-min outputs from 0000 to 0300 LT day 4. After a 10-min spin up from 0000 LT, a 1.5-km resolution domain with 700 × 700 horizontal grids is nested from the 7.5-km domain and integrated for 3 h with 10-min outputs. Similarly, after a 10-min spin up from 0010 LT day 4, a 300-m resolution domain with 1000 × 1000 horizontal grids is nested from the 1.5-km domain and integrated for 1 h with 5-min outputs. Thus by discarding the first few outputs to avoid the transient, there are 2, 4, and 7 assimilation times from 0030 to 0100 LT day 4 for 7.5-km, 1.5-km, and 300-m horizontal grid spacings, respectively (Table 1). Nested domains for ensemble simulations and configurations for ensemble assimilations are shown in Figs. 1 and 2, respectively.
Configurations and assimilation parameters for data assimilation experiments with varying model resolutions.
Synthetic observations are the brightness temperature observed by GIIRS. The radiative transfer model RTTOV version 11 (Saunders et al. 2013; Hocking et al. 2015) is used as the observation forward operator that converts the model state variables to the observed brightness temperature using the simulation coefficients of GIIRS (Di et al. 2018). A simple cloud scheme of RTTOV is applied, which uses inputted cloud fraction and cloud top pressure and assumes uniform gray cloud without complex scattering calculations. Synthetic observations are generated by adding independent random errors with mean 0 and standard deviation 1.5 K to the simulated brightness temperature from the 60-m NR, and then masked to the 7.5-km horizontal grids without spatial averaging. For simplicity, a single observation error of 1.5 K that is around the average observation errors from realistic GIIRS radiance observations (Niu et al. 2023), is used for all channels. The synthetic observations are available every 5 min, and they are assimilated at the according assimilation times so that the same number of synthetic observations are assimilated at each assimilation time.
To assimilate the synthetic radiance observations, an EnSRF (Whitaker and Hamill 2002, https://dtcenter.org/sites/default/files/EnKF_UserGuide_v1.3.pdf) is used. The ensemble size is set to 50. To remedy the spurious sample error correlations caused by a limited ensemble size and model errors, covariance localization is applied. For both horizontal and vertical localizations, the Gaspari and Cohn (GC; Gaspari and Cohn 1999) function is adopted. The GC localization function is a fifth-order piecewise polynomial function whose localization length scale is determined by a parameter. For each data assimilation experiment, the horizontal and vertical localization length scales are optimally tuned based on the analysis errors relative to the NR (Table 1). The vertical localization length scale is 1 ln(hPa) for assimilation experiments with varying model resolutions, while the horizontal localization length scale reduces from 30 to 10 km as the model resolution increases from 7.5 km to 300 m. These tuned localization length scales are consistent with previous studies (e.g., Zhou et al. 2023; Honda et al. 2018; Dowell et al. 2011). No covariance inflation is used since the assimilation is not cycled.
Following Okamoto et al. (2014), the synthetic observations with a “symmetric” cloud influence parameter smaller than 1.0 are seen as cloud-free observations (ClearSky), and the others are considered as cloud-affected observations. Note that this criterion for cloud is a strict one, which covers all grid points with nonzero cloud fractions. AllSky contains both cloud-free and cloud-affected observations. Inappropriate analysis increments could result from the excessive radiative bias between the simulations and observations in the presence of cloud (Zupanski et al. 2011). Thus, observations whose innovations (observation minus prior ensemble mean) exceed 3 times the observation error for ClearSky and observations whose innovations exceed 5 times the observation error for AllSky, are discarded. To account for the representativeness errors of the cloud-affected radiances, error standard deviations of the cloud-affected radiances are inflated to 3 × 1.5 K (Geer et al. 2019). Following Zhou et al. (2023), the linearized observation forward operator is used for assimilating the ClearSky radiances, and the full operator is used for assimilating the AllSky radiances, since the linearized operator has advantages over the full operator for the ClearSky radiances but vice versa for the AllSky radiances.
The two channel selection methods described in section 2 are examined, with different amounts of selected observations by adjusting the threshold. A group of cumulative ER proportions for the ER-based channel selection method is set to [0.80 0.85 0.90 0.95], from which a larger value indicates more selected channels. A group of thresholds for the adaptive channel selection method is set to [0.90 0.95 0.96 0.97 0.98 0.99], from which a larger threshold denotes more selected observations. Note that the threshold of the adaptive channel selection method is not equivalent to that of the ER-based method.
4. Comparison of selected hyperspectral IR radiances
Before applying the channel selection, the GIIRS channels are first preprocessed to eliminate channels with surface and trace gas sensitivity (Collard 2007), using the averaged profile over D01 at time 0030 LT day 4. Due to large uncertainties of the emissivity from the surface and ocean, channels whose weighting functions peak near the surface, i.e., the pressure at which the weighting function peaks (Pmax) larger than 950 hPa, are eliminated for simplicity (Di et al. 2021). Since the model top is set to 15 hPa, the upper channels with Pmax smaller than 50 hPa are also neglected. Channels for which the limited representation of trace gases (O3, N2O, and CO) results in an error of >1 K when a 10% change in gas concentration is made during the simulation, are eliminated (Matricardi 2003). The preprocess leads to 690 rejected channels, and the remaining 960 channels are used for data assimilation (Fig. 3). Using the ensemble mean prior of temperature and specific humidity from D01 at analysis time 0300 LT day 4, the channels selected by the ER-based method for ClearSky are calculated using (6), as shown in Fig. 4. Similar ER-based channels are selected when background error covariances at different times are used. As expected, more channels are selected when the cumulative ER proportion increases. Given the group of cumulative ER proportions, there are 15, 41, 82, and 161 selected channels from the ER-based method, which give observation numbers from 8453 to 42 974.
The spectra of the GIIRS hyperspectral radiances, with rejected channels (black dot) and the remaining 960 channels after preprocessing (red dot). For each GIIRS channel, the left y axis is the brightness temperature and the right y axis is the pressure at which the weighting function peaks.
Citation: Monthly Weather Review 152, 3; 10.1175/MWR-D-23-0131.1
The reduction of information entropy (black curve) and the cumulative ER proportion (red curve) along with numbers of selected channels. The blue triangles denote the numbers of selected channels with thresholds of ER reduction at [1.33, 0.18, 0.08, and 0.03] and proportions of cumulative ER at 0.80, 0.85, 0.90, and 0.95.
Citation: Monthly Weather Review 152, 3; 10.1175/MWR-D-23-0131.1
The differences between the ER-based and adaptive channel selection methods are first examined. The assimilated observation number given each channel (Fig. 5) and the assimilated channel numbers at each horizontal observation location (Fig. 6) are analyzed with cumulative ER proportion of 0.95 and adaptive thresholds of 0.9 and 0.98, respectively. For ClearSky, the ER-based channels are mainly located between 200 and 400 hPa (Fig. 5), where the observation height is determined by the correlation rather than the weighting function. The vertical observation location given by the level at which correlations between the observed brightness temperature and state variables maximize, has advantages over that given by the peak of weighting functions, for radiance data assimilation (Lei et al. 2016). For the ER-based method, the channel numbers at each horizontal observation location are the same, but the assimilated ones could be different due to quality control (Figs. 6a,c). Comparatively, the adaptive channel selection method with threshold of 0.9 has more numbers of selected lower-level channels below 400 hPa (Fig. 5a). The adaptive method has much smaller assimilated channel numbers at each horizontal observation location than the ER-based method (Fig. 6a). However, the information content, defined as one minus the mean Pa/Pb for the selected channels at each horizontal observation location, is generally larger for the adaptive selection method compared to the ER-based method (Fig. 7a).
The distributions of selected GIIRS radiance observations of ER-based (blue cross) and Pa/Pb (red dot) methods at time 0300 LT (day 4) under ClearSky. The cumulative ER proportion is 0.95 and Pa/Pb with the threshold of (a) 0.9 and (b) 0.98. For each channel, the x axis is the number of selected radiance observations, and the y axis is the pressure at which the correlation between the observed brightness temperature and state variable of either temperature or specific humidity maximizes.
Citation: Monthly Weather Review 152, 3; 10.1175/MWR-D-23-0131.1
Selected channel numbers at each horizontal observation location for ER-based (blue) and Pa/Pb (red) methods at time 0300 LT day 4 with (a),(b) ClearSky and (c),(d) AllSky. The cumulative ER proportion is 0.95 and adaptive thresholds of (left) 0.9 and (right) 0.98.
Citation: Monthly Weather Review 152, 3; 10.1175/MWR-D-23-0131.1
Information content for each horizontal observation location for ER-based (blue) and Pa/Pb (red) methods at time 0300 LT day 4 with (a),(b) ClearSky and (c),(d) AllSky. The cumulative ER proportion is 0.95 and adaptive thresholds of (left) 0.9 and (right) 0.98.
Citation: Monthly Weather Review 152, 3; 10.1175/MWR-D-23-0131.1
When the threshold of the adaptive method increases from 0.9 to 0.98, many more channels are adaptively selected, but the assimilated channel numbers are still smaller than those of ER-based method (Figs. 6b,d). The increased adaptively selected channels are mainly between 200 and 700 hPa (Fig. 5b). With increased adaptive thresholds, the information content for the adaptive selection method increases, especially for the observation locations with small magnitudes of information content (Fig. 7). With different adaptive thresholds, the assimilated channel numbers do not significantly differ over horizontal observation locations. Although flow- and time-dependent channels are adaptively selected, analyses with homogeneity are expected due to spatially well distributed observations. When the sky condition is shifted from ClearSky to AllSky, the selected channels from the ER-based method are similar, except for several more selected channels due to additionally assimilated observations. Similar comparisons between the ER-based and adaptively selected channels for ClearSky are obtained for AllSky. Compared to ClearSky, many more channels are adaptively selected for AllSky. With different adaptive thresholds, the information content of the adaptive selection method is still larger than that of the ER-based method for AllSky.
Moreover, the selected channels and associated number of radiance observations through data assimilation for the ER-based and adaptive methods are shown for two assimilation times (Fig. 8). The channels selected by the ER-based method are time-invariant, although the assimilated radiance observations can be temporally different due to quality control. Comparatively, the adaptive channel selection method can capture the time dependence of the observation variance reduction for the radiance observations, which can provide flow-dependent and time-dependent channel selections.
The selected channels and associated number of radiance observations through data assimilation for the ER-based (the cumulative ER proportion is equal to 0.95) and Pa/Pb (with a threshold of 0.98) method at different assimilation times under AllSky.
Citation: Monthly Weather Review 152, 3; 10.1175/MWR-D-23-0131.1
5. Assimilation results
To evaluate radiance assimilation using different channel selection methods, the root-mean-square (RMS) errors of priors and posteriors are verified against the 60-m NR masked to the corresponding resolutions. The RMS error differences between the posteriors and priors from the ER-based and adaptive selection methods are shown in Fig. 9. Given the 7.5-km horizontal grid spacing, the ER-based selection method has decreased RMS errors as increased cumulative ER proportion, i.e., more assimilated channels, for state variables of temperature, specific humidity, and u and υ wind components (Figs. 9a,d,g,j). Given the cumulative ER proportion of 0.95, assimilation of all channels has smaller RMS errors than the ER-based channels for state variables of temperature and u wind component, while similar RMS errors are obtained for assimilating all channels and ER-based channels for state variables of specific humidity and υ wind component. This indicates that the ER-based method can effectively select informative channels, but it cannot outperform that with all channels since the RMS errors of ER-based channels converge to those with all channels.
For the state variable of (a)–(c) temperature, (d)–(f) specific humidity, (g)–(i) u wind component, and (j)–(l) υ wind component, RMS error differences between posteriors and priors from data assimilation experiments at (left) 7.5-km, (center) 1.5-km, and (right) 300-m horizontal grid spacings, under the ClearSky condition. Blue represents the proportion of cumulative ER of 0.80, 0.85, 0.90, and 0.95; red represents Pa/Pb with thresholds of 0.90, 0.95, 0.96, 0.97, 0.98, and 0.99; and gray represents the assimilation of all channels.
Citation: Monthly Weather Review 152, 3; 10.1175/MWR-D-23-0131.1
Comparatively, the adaptive selection method in general has V-shaped RMS errors, except for specific humidity (Figs. 9a,d,g,j). The RMS errors of adaptive selection method first decrease as the adaptively selected channels increase, and then increase when the adaptively selected channels further increase. The minimum RMS errors of the adaptive selection method for the state variables of temperature, specific humidity, and u and υ wind components are smaller than those with all channels assimilated. Intuitively, the RMS errors with increased adaptive thresholds should converge to the one with all observations assimilated. However, this is the ideal situation when all assumptions are valid, e.g., Gaussian error distributions, noncorrelated observation errors, linear error growth, etc. One possible situation is that the observations that have assimilation sequences toward the end cannot improve the posterior ensemble mean, but just decrease the posterior ensemble spread, given the known truth. When approaching the end of the assimilation sequence, the observation departure (observation minus background) can still have a large magnitude, but the observation spread is very small (Fig. 10a). By assimilating this additional observation with sample correlations that could be contaminated by sampling errors or nonlinearities, the posterior ensemble mean error could be larger than the prior mean error, although the posterior ensemble spread becomes smaller than the prior ensemble spread. Thus, the V-shaped RMS errors indicate that the EnKF analyses could be contaminated by sampling errors, nonlinearities, etc. In addition to selecting informative observations, the adaptive selection method can consider the assimilation impact of the selected observations and then obtain the best ensemble analyses, compared to assimilating all observations. Moreover, the adaptive selection method generally produces smaller RMS errors than the ER-based method, especially with similar amounts of assimilated observations. Thus compared to the ER-based method, the adaptive selection method can effectively assimilate the most informative radiance observations and neglect the redundant radiance observations.
Observation departure (observation minus background) and observation spread along with assimilation sequence for (a) ClearSky and (b) AllSky, with adaptive threshold of 0.98.
Citation: Monthly Weather Review 152, 3; 10.1175/MWR-D-23-0131.1
To examine the impacts of channel selection methods on TC intensity, the errors of the minimum dry air mass (MU) and error profiles of the maximum wind speed (Vmax) relative to the 60-m NR are shown in Fig. 11. Dry air mass is used rather than surface pressure for verification, because it is a prognostic variable that is updated by assimilation while surface pressure is diagnostic and not updated. Given the 7.5-km horizontal grid spacing, assimilation of the ER-based channels underestimates the TC intensity, whereas the assimilation of adaptively selected channels overestimates the intensity (Fig. 11d). Meanwhile, the adaptive selection method has smaller magnitudes of errors for the dry air mass than all channels and the ER-based method. The error differences for the maximum wind speed between two selection methods are mainly between 300 and 800 hPa (Fig. 11a). Assimilation of all channels generally has the smallest errors of the maximal wind speed. The ER-based method underestimates the maximal wind speed, and the underestimation is reduced with more channels assimilated. Similar results are obtained for the adaptive selection method. Compared to the ER-based method, the adaptive selection method has smaller errors in the maximal wind speed. When the assimilated radiance observations increase, the adaptive selection method has errors converging to those with all channels assimilated. Thus, compared to the ER-based channels, the adaptive selection method can improve the analyses of TC intensity.
Error profiles (top) of the maximum wind speed (Vmax) and errors (bottom) of the minimum dry air mass (MU) at (a),(d) 7.5-km; (b),(e) 1.5-km; and (c),(f) 300-m horizontal grid spacings, under the ClearSky condition. Blue represents the proportion of cumulative ER of 0.80, 0.85, 0.90, and 0.95; red represents Pa/Pb with thresholds of 0.90, 0.95, 0.96, 0.97, 0.98, and 0.99; and gray represents the assimilation of all channels.
Citation: Monthly Weather Review 152, 3; 10.1175/MWR-D-23-0131.1
When the horizontal grid spacing decreases from 7.5 to 1.5 km and then to 300 m, similar results are generally obtained. For the state variables of temperature, specific humidity, and u and υ wind components, the RMS errors using the ER-based channels decrease when assimilated channels increase, and the RMS errors converge to those with all channels assimilated (Fig. 9). Comparatively, the adaptive selection method has V-shaped RMS errors, and the minimum RMS errors are smaller than those with all channels assimilated. The adaptive selection method has smaller RMS errors than the ER-based method, when similar numbers of radiance observations are assimilated. Since the synthetic observations have the same horizontal resolution of 7.5 km for assimilation experiments with increasing model resolutions from 7.5 to 1.5 km and then to 300 m, the observations can be better represented when the model resolution increases. Compared to the ER-based method, the adaptive selection method chooses the assimilated radiance observations along with serial data assimilation. Thus, the adaptive method implicitly considers the impact of model resolution, and has the advantage in dealing with the representative error. Given 1.5-km and 300-m horizontal grid spacings, the comparisons of the minimum dry air mass and maximum wind speed between the ER-based and adaptive selection methods are generally consistent with those given 7.5-km horizontal grid spacing (Fig. 11). One difference is that the adaptive selection and all channels underestimate the TC intensity when the horizontal grid spacing decreases to 300 m. In general, the adaptive selection method has improved analyses for the TC intensity than the ER-based method. Therefore, the advantages of the adaptive selection method over the ER-based method are retained with varying horizontal grid spacings from kilometers to subkilometers.
Assimilating all-sky radiances can give improved analyses relative to using only clear-sky radiances, due to additional information provided by all-sky radiance observations (e.g., Honda et al. 2018; Zhou et al. 2023). The RMS error differences between the posteriors and priors using the two channel selection methods to assimilate AllSky radiances are shown in Fig. 12. Given the 7.5-km horizontal grid spacing, the ER-based method has decreased RMS errors as the cumulative ER proportion increases for the state variables, except for the υ wind component. The RMS errors of the υ wind component are not reduced along with increased cumulative ER proportion, because the analysis increment does not effectively correct the prior error (figures are not shown). The inaccurate υ wind analysis increment could be the result of sampling errors and nonlinearities with AllSky. The adaptive selection method has V-shaped RMS errors as the assimilated radiances increase except for the specific humidity. As the assimilation sequence increases, the observation departure of AllSky is still large (larger than ClearSky), while the observation spread is very small (Fig. 10b). By assimilating the additional observations with assimilation sequences toward the end, the ensemble analysis is not improved, although the ensemble spread is reduced. Consistent with ClearSky, the V-shaped RMS errors with AllSky could be resulted from sampling errors, forward operator errors, nonlinearities, etc. Thus, the adaptive selection method can select the informative observations along with assimilation, which leads to improved ensemble analyses compared to the assimilation of all observations.
As in Fig. 9, but for the AllSky condition.
Citation: Monthly Weather Review 152, 3; 10.1175/MWR-D-23-0131.1
Different from assimilating ClearSky radiances, the ER-based method with cumulative ER proportion of 0.95 has smaller RMS errors than all channels except for the specific humidity, and the minimum RMS error of adaptive selection method is smaller than that of ER-based method only for the υ wind component (Figs. 12a,d,g,j). One possible reason for these inconsistent comparisons between the two channel selection methods at 7.5-km horizontal grid spacing is that AllSky has more observations than ClearSky (Fig. 6) and AllSky radiances at 7.5-km horizontal grid spacing cannot be well represented by the model simulation at 7.5-km horizontal grid spacing. Figure 13 shows the RMS error differences between the posterior and prior for assimilating AllSky radiances with a reduced observation resolution of 15 km, while keeping the model resolution of 7.5 km. Given the thinned AllSky radiances, the adaptive selection method generally has smaller RMS errors than the ER-based method with similar numbers of assimilated observations, except for u and υ wind variables with the smallest assimilated observation numbers. Moreover, when the horizontal grid spacing decreases from 7.5 to 1.5 km and then to 300 m, the adaptive selection method has smaller RMS errors than the ER-based method when similar numbers of radiance observations are assimilated, and the minimum RMS errors of the adaptively selected channels are generally smaller than those with all channels assimilated (Fig. 12). These results of assimilating AllSky radiances at 1.5-km and 300-m horizontal grid spacings are consistent with those of assimilating ClearSky radiances.
For the state variable of (a) temperature, (b) specific humidity, (c) u wind component, and (d) υ wind component, RMS error differences between the posteriors and priors from assimilation experiments at 7.5-km horizontal grid spacing and with 15-km observational horizontal grid spacings (60-m NR mask to 15-km horizontal grids), under the AllSky condition. Blue represents the proportion of cumulative ER of 0.80, 0.85, 0.90, and 0.95; red represents Pa/Pb with thresholds of 0.90, 0.95, 0.96, 0.97, 0.98, and 0.99; and gray represents the assimilation of all channels.
Citation: Monthly Weather Review 152, 3; 10.1175/MWR-D-23-0131.1
Figure 14 displays the error of minimum dry air mass and error profiles of the maximum wind speed verified against the 60-m NR with assimilation of AllSky radiances. Given the horizontal grid spacing decreasing from 7.5 to 1.5 km and then 300 m, the ER-based method underestimates the maximum wind speed, especially between 300 and 900 hPa, and the underestimation decreases as assimilated channels increase. Compared to ClearSky radiances, the improvements in analysis error below 800 hPa among the different ER-based methods with AllSky radiances are mainly due to the additionally assimilated cloud-affected radiance observations whose information are spread below the cloud. The ER-based method also underestimates the TC intensity as shown by the dry air mass, with varying horizontal grid spacings. In general, along with more selected channels, the ER-based method has TC intensity converged to that of assimilating all channels. Similar to the ER-based method, the adaptive method underestimates the maximum wind speed and TC intensity for the horizontal grid spacings of 7.5 km, 1.5 km, and 300 m. The adaptive selection method has smaller errors of the maximum wind speed and dry air mass than the ER-based method. The adaptively selected channels have smaller errors of dry air mass than all channels assimilated, and have errors of the maximum wind speed with increased assimilated radiances converging to those of all channels. Thus, the advantages of adaptive selection method over ER-based method are demonstrated for both ClearSky and AllSky with horizontal grid spacings of 7.5 km, 1.5 km, and 300 m.
As in Fig. 11, but for the AllSky condition.
Citation: Monthly Weather Review 152, 3; 10.1175/MWR-D-23-0131.1
6. Discussion and conclusions
Hyperspectral IR satellites can provide high-resolution vertical profiles of the atmospheric state. But the hyperspectral channels with overlapped weighting functions could have interchannel correlations and correlated observation errors, which imposes challenges for assimilating the hyperspectral radiances. To effectively extract information from the hyperspectral radiances, an adaptive channel selection method that is implemented within data assimilation and selects the radiance observation with the maximum reduction of variance in the observation space, is proposed. Compared to the commonly used channel selection method based on the maximum ER, the adaptively selected radiances have broader vertical distributions with temporal variations. Thus the adaptive method can provide flow-dependent and time-dependent channel selections.
The performance of the adaptive selection method is evaluated by assimilating the synthetic FY-4A GIIRS IR radiances with model resolutions from 7.5 km to 300 m. For the ClearSky condition, the assimilation experiments with 7.5-km horizontal grid spacing show that the ER-based method can effectively select channels that contribute to the analysis error reduction but it does not outperform the assimilation with all channels. Comparatively, the adaptive channel selection method can have the minimum RMS errors of the state variables smaller than the assimilation with all channels. The performance of adaptively selected channels may converge to that of all channels, given sufficiently large ensembles and well represented model errors. Moreover, given similar amounts of assimilated radiances, the adaptive method produces smaller RMS errors of the state variables than the ER-based method. For TC intensity, the adaptive method also produces smaller errors for the minimum dry air mass and maximal wind speed at different levels. The advantages of the adaptive method over the ER-based method are held as the model resolution increases from 7.5 to 1.5 km and then 300 m.
Given the 7.5-km model resolution with AllSky condition, both the ER-based method and adaptive method have smaller RMS errors than that with all channels assimilated for state variables of temperature and u and υ wind components, except for specific humidity. Different from the ClearSky condition with 7.5-km horizontal grid spacing, the adaptive method has the minimum RMS error of υ wind component smaller than the ER-based method, but vice versa for the state variables of temperature, specific humidity, and the u wind component. One possible reason for the inconsistent comparisons between the ER-based and adaptive methods for the ClearSky and AllSky conditions is that there are much more assimilated radiances under the AllSky condition than the ClearSky condition, and the model resolution of 7.5 km is insufficient to resolve the dense observations. When the observation resolution is thinned from 7.5 to 15 km, the adaptive method outperforms the ER-based method. When the model resolution increases from 7.5 to 1.5 km and then 300 m, results under the AllSky condition are consistent with those under the ClearSky condition. The adaptive method produces smaller RMS errors than the ER-based method given similar amounts of assimilated radiances. The adaptive method has the minimum RMS errors smaller than those with all channels assimilated for temperature and the υ wind component, and it has the minimum RMS errors approaching those with all channels assimilated for specific humidity and the u wind component. For TC intensity, the adaptive method also produces smaller errors for the minimum dry air mass and maximal wind speed at different levels than the ER-based method.
Therefore, the advantages of the adaptive channel selection method over the ER-based selection method have been demonstrated, with model resolutions varying from kilometers to subkilometers for both ClearSky and AllSky conditions in an OSSE. Despite the computational cost for channel selection of the ER-based method, the adaptive selection method requires more computational cost for data assimilation than the ER-based one. The adaptive selection method needs additional computational cost to compute and sort the Pa/Pb for remaining observations, when each observation is serially assimilated. Figure 15 shows the computational cost for the two selection methods with different model resolutions. Since the same synthetic observations are used by assimilation experiments with different model resolutions, the differences of computational cost between the two selection methods become smaller when the model resolution increases.
Computational costs of the ER-based and adaptive selection methods for (a) 7.5-km, (b) 1.5-km, and (c) 300-m horizontal grid spacings.
Citation: Monthly Weather Review 152, 3; 10.1175/MWR-D-23-0131.1
Acknowledgments.
Thanks to the editor and three anonymous reviewers who help to significantly improve the manuscript. This work is supported by the National Natural Science Foundation of China under Grants 41922036, 42192553, and 41775057, the Frontiers Science Center for Critical Earth Material Cycling Fund JBGS2102, and the Fundamental Research Funds for the Central Universities 0209-14380097.
Data availability statement.
To generate the nature run and assimilation experiments, the WRF V3.8.1 data available at https://www2.mmm.ucar.edu/wrf/users/wrf_files/wrfv3.8/wrf_model.html are used. The channel sets selected by the ER-based selection method with different thresholds, and the analysis fields assimilated by the ER-based selection method and the adaptive method are available at https://zenodo.org/record/8092868.
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