A Comparison of Channel Selection for the Assimilation of CrIS Radiances for NWP

Laurence Coursol aUniversité du Québec à Montréal, Montréal, Québec, Canada

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Sylvain Heilliette bData Assimilation and Satellite Meteorology Research Section, Environment Canada, Dorval, Quebec, Canada

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Pierre Gauthier aUniversité du Québec à Montréal, Montréal, Québec, Canada

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Abstract

With hyperspectral instruments measuring radiation emitted by Earth and its atmosphere in the thermal infrared range in multiple channels, several studies were made to select a subset of channels in order to reduce the number of channels to be used in a data assimilation system. An optimal selection of channels based on the information content depends on several factors related to observation and background error statistics and the assimilation system itself. An optimal channel selection for the Cross-track Infrared Sounder (CrIS) was obtained and then compared to selections made for different NWP systems. For instance, the channel selection of Carminati has 224 channels also present in our optimal selection, which includes 455 channels. However, in terms of analysis error variance, the difference between the two selections is small. Integrated over the whole profile, the relative difference is equal to 15.3% and 4.5% for temperature and humidity, respectively. Also, different observation error covariance matrices were considered to evaluate the impact of this matrix on channel selection. Even though the channels selected optimally were different in terms of which channels were selected for the various R matrices, the results in terms of analysis error are similar.

Significance Statement

Satellites measure radiation from Earth and its atmosphere in the thermal infrared. Those radiance data contain thousands of measurements, called channels, and thus, a selection needs to be done retaining most of the information content since the large number of individual pieces of information is not usable for numerical weather prediction systems. The goal of this paper is to find an optimal selection for the instrument CrIS and to compare this selection with selections made for different numerical weather prediction systems. It was found that even though the channels selected optimally were different in terms of which channels were selected compared to other selections, the results in terms of precision of the analysis are similar and the results in terms of analysis error are similar due to the nature of hyperspectral instruments, which have multiple Jacobians overlapping.

© 2024 American Meteorological Society. This published article is licensed under the terms of the default AMS reuse license. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

Corresponding author: Laurence Coursol, laurence.coursol@gmail.com

Abstract

With hyperspectral instruments measuring radiation emitted by Earth and its atmosphere in the thermal infrared range in multiple channels, several studies were made to select a subset of channels in order to reduce the number of channels to be used in a data assimilation system. An optimal selection of channels based on the information content depends on several factors related to observation and background error statistics and the assimilation system itself. An optimal channel selection for the Cross-track Infrared Sounder (CrIS) was obtained and then compared to selections made for different NWP systems. For instance, the channel selection of Carminati has 224 channels also present in our optimal selection, which includes 455 channels. However, in terms of analysis error variance, the difference between the two selections is small. Integrated over the whole profile, the relative difference is equal to 15.3% and 4.5% for temperature and humidity, respectively. Also, different observation error covariance matrices were considered to evaluate the impact of this matrix on channel selection. Even though the channels selected optimally were different in terms of which channels were selected for the various R matrices, the results in terms of analysis error are similar.

Significance Statement

Satellites measure radiation from Earth and its atmosphere in the thermal infrared. Those radiance data contain thousands of measurements, called channels, and thus, a selection needs to be done retaining most of the information content since the large number of individual pieces of information is not usable for numerical weather prediction systems. The goal of this paper is to find an optimal selection for the instrument CrIS and to compare this selection with selections made for different numerical weather prediction systems. It was found that even though the channels selected optimally were different in terms of which channels were selected compared to other selections, the results in terms of precision of the analysis are similar and the results in terms of analysis error are similar due to the nature of hyperspectral instruments, which have multiple Jacobians overlapping.

© 2024 American Meteorological Society. This published article is licensed under the terms of the default AMS reuse license. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

Corresponding author: Laurence Coursol, laurence.coursol@gmail.com

1. Introduction

Previous generations of thermal infrared vertical sounders such as HIRS provided measurements over a few spectral bands referred to as channels. From those measurements, it was possible to retrieve atmospheric vertical profiles of temperature and humidity with a coarse vertical resolution, since at those wavelengths, the radiance varies with temperature, humidity, and other constituents. This small number of channels per measurement made it possible to assimilate most of the channels in NWP centers (Prunet et al. 1998). With the advancement of spaceborne hyperspectral instruments containing thousands of sounding channels (3.7 μm < λ < 15 μm), research aimed at finding an optimal subset of channels that would provide most of the information available from those measurements started because they were too many (computationally unaffordable) for assimilation and highly correlated. Rodgers (1998) did a case study to explore the use of the information content [or degrees of freedom for signal (DFS)] to optimize the channel selection of a spectrometer for remote sounding. The instrument AIRS with 2378 channels measuring in the thermal infrared was used (Aumann et al. 2003), and they found that most of the information content on atmospheric temperature and humidity could be retrieved from a subset of up to 1000 channels.

Several studies were done on channel selection for the instruments AIRS, IASI, and Cross-track Infrared Sounder (CrIS). Rabier et al. (2002) tested different methods to obtain an optimal subset of channels in an operational NWP context for the instrument IASI, including the iterative DFS and the Jacobian method, which is based on the characteristics of the Jacobians. They concluded that an iterative method using the DFS gives better results at reducing the analysis error than the Jacobian method, but it is more expensive in computational time. Similarly, Fourrié and Thépaut (2003) compared the operational channel selection with the iterative DFS method introduced by Rabier et al. (2002) for the instrument AIRS. They concluded that the iterative DFS method was slightly better and the channels selected were different but gave similar results in terms of analysis error for temperature, humidity, and ozone. Gambacorta and Barnet (2012) also did a channel selection for CrIS based on the Jacobians and their physical properties. A subset of 399 channels was selected, representing the full atmospheric variability contained in the original spectrum, this selection being the one officially distributed. However, the goal of channel selection, from an NWP perspective, is to find a selection of channels that reduce the most the uncertainty in the analysis and not to represent the full atmospheric variability. Carminati (2022) compared the previous selection with one based on the iterative DFS. They observed that there is a large variability in the channels selected by the two methods with only one-third being identical. Still, the selection made with the DFS gave better results in improving most of the forecasts. This shows that there are still a lot of questions to be explored regarding the channel selection of an instrument since it is dependent on the method used and also the assumptions made. For example, the impact of correlations of the observation error covariance matrix (Coopmann et al. 2020) on channel selection and the variation of the selection with respect to seasons and regions (Fourrié and Thépaut 2003) have been examined previously.

The goal of this paper is to investigate the influence of observation covariance error and the input profile for the optimal channel selection of the instrument CrIS. Comparison of channel selections using the same method has not been previously done in other studies. The channel selection methodology is explained in section 2. The results of the channel selection are discussed in section 3. Section 4 examines the impact of assimilating separately the long-, mid-, and shortwave bands. The selection will be compared to the one based on Jacobians used at Environment and Climate Change Canada (ECCC) and the one from Carminati (2022) in section 5. This will be followed by a discussion on the impact of the observation error covariance matrix on the selection in section 6. Conclusions are drawn in section 7.

2. Methods

a. Theoretical framework

This study is based on linear statistical estimation theory in the context of NWP (Rodgers 2000). The different notations, definitions, approximations, and data used are described in this section. The general framework presented in Coursol et al. (2020) is followed.

The atmospheric profiles of temperature T, the logarithm of specific humidity s = lnq, and surface temperature at a given location define the state vector represented by the vector x. The observations, represented by a vector y, are satellite radiance measurements chosen at nadir at different wavelengths taken at the TOA. The satellite observation is related to the atmospheric state through the following equation:
y=H(x)+ϵO+ϵF,
where H is an observation operator including the radiative transfer model, while ϵo is the measurement error with the associated error covariance matrix O. The observation error covariance R = O + F includes not only the measurement error covariance matrix but also the forward model errors’ covariance F.
Ozone and other trace gases are kept constant to climatological values, whereas the assumption was made that the surface temperature is equal to the first atmospheric temperature level near the surface. Linearization of the forward model is done around the background state xb, which gives
H(x)H(xb)+H(xxb),
assuming that the radiative transfer equation to be weakly nonlinear near the background state.
In the last equation, H(xb) is the background state in the observation space and H=[H(x)/x]|xb is the linearized observation operator with respect to x evaluated at x = xb, referred to as the Jacobian. Jacobians are used to evaluate the changes in radiances associated with a perturbation of the background state. Assuming also that the background error covariance matrix B is known, the analysis xa can be obtained as
xa=xb+K(yHxb),
with K = BHT(R + HBHT)−1 being the gain matrix, which minimizes the total analysis error variance (Rodgers 2000). Superscripts T and −1 denote the transpose and inverse of a matrix, respectively.

1) Atmospheric profiles and Jacobians

Radiosonde profiles were obtained from the Integrated Global Radiosonde Archive (IGRA) database (https://www.ncei.noaa.gov/products/weather-balloon/integrated-global-radiosonde-archive) (Durre et al. 2006). Ten stations were selected to cover different regions and to have some atmospheric variability. Figure 1 shows the location of the selected radiosonde profiles. For each station, five profiles were randomly selected between the years 2015 and 2019. The profiles were interpolated to the RTTOV v.12 (Saunders et al. 2018) 101 pressure levels. The maximum and minimum pressures are 1100 and 0.005 hPa, respectively. For levels higher than 70 hPa, an extrapolation was done for humidity. The humidity at a level i (si) is replaced by si=sp=70hPa(pi/70hPa)3, where sp=70hPa is the humidity at 70 hPa and pi is the pressure at level i (Smith 1966).

Fig. 1.
Fig. 1.

Locations of the stations selected.

Citation: Journal of Applied Meteorology and Climatology 63, 6; 10.1175/JAMC-D-23-0188.1

For each channel, the Jacobian indicates how temperature and humidity variations at each wavelength impact the radiance measured at the TOA. The Jacobians were calculated with an NWP Satellite Application Facilities operational product, RTTOV v.12, a fast radiative transfer model for data assimilation and retrieval systems. It was done for each profile provided by the background state. The Jacobians were computed for each channel of CrIS, for a total of 2211 channels. To avoid selecting bands sensitive to unwanted gases and spectral regions, certain bands were eliminated. In this case, bands sensitive to ozone, methane, and CO and also bands too sensitive at the TOA were excluded similarly to Collard (2007). After this step, there were 1614 channels that remain available.

2) Error covariance matrices

The R matrix normally includes the measurement error, the forward model error, the representativeness error, and the error associated with quality control and other sources (Bormann et al. 2010). For this study, only the measurement error was considered for the experiment with the central field of view (number 5) taken since it has the best characteristics and is the one received at NWP centers (Denis A. Tremblay 2020, personal communication). This approximation was taken since it is a theoretical experiment and the specific details of the composition of the observation error covariance matrix have less importance. Also, this approximation was taken in order to be consistent with our previous paper (Coursol et al. 2020) and with previous studies such as Merrelli and Turner (2012), Shahabadi and Huang (2014), and Mertens (2002). Noh et al. (2017) also gave an explanation to why considering the measurement error is sufficient for this type of experiment since theoretically generated observations and background data are independent of the scale mismatch between the observation and model.

Radiances are assumed to be apodised, which increases the correlation between adjacent channels. The measurement error is assumed to be Gaussian and unbiased, which are assumptions used especially in data assimilation (Rodgers 2000). Nevertheless, matrix R is taken to be diagonal with the noise equivalent radiance (NER) values on the diagonal. In section 6 related to the sensitivity to the R matrix, a complete observation error covariance matrix from ECCC will be used. Also, an R matrix composed of the measurement error and a forward model error of 0.2 K in radiance space with a radiance spectrum associated with the scene as in Fourrié and Thépaut (2003) and Rabier et al. (2002) will be used.

We took the stationary version of the B matrix for temperature and humidity that has been used in the ECCC assimilation system (Buehner et al. 2015). Those matrices were evaluated at the locations of the radiosondes profiles used and averaged over the whole year. The units used are K2 and log(L L−1)2, where L L−1 represents the ratio of volume of water vapor over the volume of air, for temperature and humidity, respectively. For the time being, the surface temperature has not been included in the control variables. The cross-terms of the B matrix between temperature and humidity are neglected. In this study, the B matrices for temperature and humidity are kept constant in time at each station but differ from one station to another.

b. Information content

To quantify the gain in information brought by measurements, the analysis error covariance and information content are needed. The analysis error, assumed here to be unbiased, is εa = xaxt, where xt is the true state of the atmosphere. So, A=εaεaT, with 〈…〉 being the statistical average. At optimality, the best linear unbiased estimate is obtained, and it can be shown that (Rodgers 1998)
A=(IKH)B.
The reduction of analysis error due to the assimilation of observations is measured by
tr(AB1)=Ntr(KH),
where tr(KH) = tr(HK), in which tr is defined as the trace of a matrix and N is the number of pressure levels. The gain in information is defined as
DFS=tr(HK),
where DFS stands for degrees of freedom for signal. It gives a measure of the reduction of uncertainty brought in by the analysis based on the relative errors between the observations and the prior information (Purser and Huang 1993) and only depends on the background error covariance matrix B, the observation error covariance matrix R, and the Jacobian matrix H. The DFS will be computed for subsets of channels and used to find an optimal selection that provides the most information for CrIS.

3. Channel selection

With the background and observation error covariance matrices defined, it is possible to calculate the DFS for temperature and humidity for the 50 atmospheric profiles for all channels sequentially. For each profile, the DFS for each channel of CrIS is calculated and the channel with the largest DFS is selected. The DFS is calculated again for the channel selected in combination to one of the remaining channels not selected previously. The combination of channels which yields the largest DFS is then taken. This calculation is done until 400 channels are selected. The cutoff of 400 channels was selected to reduce the calculation time since the information content becomes saturated at this limit as can be seen in Fig. 2. This cutoff conforms with the one chosen in Carminati (2022) and Coopmann et al. (2020).

Fig. 2.
Fig. 2.

Averaged DFS over the 50 profiles for temperature (orange) and humidity (blue) (full lines), whereas the dotted lines show the associated total DFS for the respective variable. The shaded area shows the standard deviation associated with the variables.

Citation: Journal of Applied Meteorology and Climatology 63, 6; 10.1175/JAMC-D-23-0188.1

Figure 2 shows the averaged DFS over the 50 atmospheric profiles for temperature and humidity as a function of the number of channels selected up to 400. The DFS grows rapidly as the first few channels are selected since most of the information required for improving the background state is contained in those first few. The DFS for temperature increase more rapidly compared to humidity for the first 40 channels, and afterward, the growth rate is similar. At 400 channels, the DFS for both temperature and humidity is close to the total averaged DFS (dashed lines) obtained when assimilating all channels. The values of the DFS at 400 channels are 11.4 and 8.0 for temperature and humidity, respectively. At 400 channels, over 97% of the total information is contained out of the total averaged DFS for both temperature and humidity. The shaded area in Fig. 2 shows the variability from the different atmospheric conditions from the set of 50 atmospheric profiles. As expected, the standard deviation is bigger for humidity than temperature.

Another way to view these results is through the analysis error variance, since the information gained from the addition of channels translates as error reduction. Figure 3 shows the analysis error variance for both temperature and humidity for different configurations. With respect to temperature, CrIS significantly reduces the analysis error variance, up to 27.2% of the background error when 100 channels are considered (orange curve), and 29.7% when 400 channels are assimilated optimally (blue curve). Also, the shaded area shows the variability of the results among the 50 profiles. Among the profiles, there are cases from summer and winter which can have a large variability for regions such as the midlatitudes. This shows the impact of the observations on the analysis varies with the atmospheric conditions. It can also be seen that the difference between 400 channels (blue curve) and all the channels (dark purple curve) is small and that the largest difference is near the surface. For humidity, the bulk of the analysis error reduction is between 800 and 200 hPa where the background error variance is the largest (black curve), i.e., 41.6% when 100 channels are considered (orange curve) and 46.2% when 400 channels are assimilated optimally (blue curve). The larger variability with respect to reducing the analysis error variance is between 800 and 400 hPa, which corresponds to a region with large variability in humidity. Similarly to temperature, the difference in the analysis error between 400 channels and all the channels is minimal.

Fig. 3.
Fig. 3.

Analysis error variance profile averaged over the 50 atmospheric profiles for (left) temperature and (right) humidity. The black curve represents background error B, the orange curve represents the analysis error when 100 channels are taken optimally, the blue curve represents the analysis error when 400 channels are selected optimally, whereas the shaded area represents its associated standard deviation and the dark purple curve represents the analysis error when all the channels are assimilated.

Citation: Journal of Applied Meteorology and Climatology 63, 6; 10.1175/JAMC-D-23-0188.1

To find an optimal selection of channels for CrIS and to analyze more specifically the selection process, Fig. 4 illustrates the number of times a band is selected out of the 50 atmospheric cases for both temperature and humidity taken together (hence, out of 100) at the wavenumber associated with this channel. Separately, for the 50 atmospheric profiles, 149 and 200 channels are always selected for temperature and humidity, respectively. If taken together for temperature and humidity as in Fig. 4, it represents 40 different channels that are always selected. On the other hand, there are 858 and 1030 out of 1614 available channels that are never selected for temperature and humidity, respectively. There are then 738 channels that are never selected when considered together. Figure 4 shows as expected that channels are selected in the 650–770 cm−1 band, which is normally used for temperature sounding. Similarly, many channels are selected in the 1210–1750 cm−1 band, which is used for sounding humidity. Moreover, no channel is selected in the ozone band (1000–1070 cm−1) since the channel selection was not optimized with respect to that variable. The channels selected at least once as shown in Fig. 4 can be sorted according to their selection frequency. Therefore, the 400 most frequently selected channels will become the optimal selection of channels for both temperature and humidity. This method of taking the most frequently selected channels was compared in Coopmann et al. (2022) to a selection made by taking the first rank selected channels and showed that for a larger number of channels selected, the first method yields better results with respect to the information content. The averaged DFS for both the most frequently selected channels and the first rank selected channels were calculated, and the same conclusions as in Coopmann et al. (2022) were obtained. In our case, if we stop at exactly 400 channels, there are still channels left out that have the same frequency of selection, and since they have the same frequency, they were added so that 455 channels were retained for the optimal selection. Those channels selected for the rest of the experiment, shown in Fig. 5, will represent the optimal selection of channels for CrIS. The complete list of selected channels is available in the online supplemental material.

Fig. 4.
Fig. 4.

Frequency of selection of the different channels out of 100 (50 for temperature and 50 for humidity) shown by the color superposed with a spectral radiance as a function of wavenumber.

Citation: Journal of Applied Meteorology and Climatology 63, 6; 10.1175/JAMC-D-23-0188.1

Fig. 5.
Fig. 5.

Position of the channels selected for the optimal selection of 455 channels superposed with a spectral radiance as a function of wavenumber.

Citation: Journal of Applied Meteorology and Climatology 63, 6; 10.1175/JAMC-D-23-0188.1

4. Information content per bands

Another way that the information content can be used is for a comparison of different bands of an instrument. CrIS is composed of three bands, a longwave (LW) band (650–1095 cm−1), a midwave (MW) band (1210–1750 cm−1), and a shortwave (SW) band (2155–2550 cm−1). The LW band is used for temperature and surface sounding, whereas the MW band is used for humidity sounding. At most operational meteorological centers, the LW band is crucial for cloud detection and characterization. The SW band is often less assimilated as its daytime use requires care due to potential solar contamination and the need of nonlocal thermodynamic equilibrium (NLTE) radiative transfer modeling.

With the current satellites (AIRS, IASI, and CrIS) getting older, it can be interesting to investigate the value of different bands for future satellite requirements and if all the bands are necessary for NWP centers. Barnet et al. (2023) found that the SW band could be used for atmospheric temperature retrieval like the normally used LW band if issues are managed including a smaller noise. Smith et al. (2021) reiterate the importance of the LW band for weather forecasting especially for temperature at the troposphere and near-surface humidity. On a more hands-on aspect, in case of malfunction of the instrument, decisions could be made with the aid of information content, for example, the failure of the CrIS detector. There are two sides of the CrIS detector: in case of failure of one side, side 1, the other one, side 2, can be used. In 2019, the MW band failed on side 1 and the switch was made to side 2. In 2021, the LW band failed on that side (Iturbide-Sanchez et al. 2022). Thus, it was decided to switch back to side 1 but without MW measurements. Thus, with band-denial experiments, it can show the impact of the different bands for sounding variables and the impact of losing measurements.

The total DFS for temperature and humidity was calculated for each band separately and also for all the combinations of two bands as seen in Table 1. For temperature, the highest DFS is with the MW band, the LW band being close to it. This shows the signature of humidity in the atmospheric profiles selected, as explained in Smith et al. (2021). This is expected since we did not consider only dry atmospheric profiles, but various profiles are expected to be encountered in NWP systems. There is a gain in using two bands instead of one, especially for the combination of LW + MW. For the SW band, the DFS is small compared to the other bands for both temperature and humidity. As expected, almost all the information with respect to humidity is in the MW band. It should be noted that the DFS for a combination of two bands is not the sum of the total DFS of each individual band since there can be redundancy in the information from the different bands.

Table 1.

DFS total for different bands.

Table 1.

This shows the importance of the LW and MW bands for sounding temperature and humidity and how the two bands complement each other for temperature. Those simple calculations can be useful for quantifying the requirements of future satellites such in Wang et al. (2023) and to design OSSEs. Also, it can help to make decisions when there is instrument failure. In the present case, when comparing the LW + MW experiment to the LW experiment, the degradation is not only very important mostly for humidity but also significant for temperature as well. Given that others instruments provide information on temperature and humidity, the results from OSSEs would be needed to quantify this degradation in the full assimilation system.

5. Comparison with other selections of CrIS

Since the selection is dependent on the observation error covariance matrix R and the background error covariance matrix B, the selection of channels can change for different NWP systems. In this section, the previous optimal selection will be compared with two selections for CrIS previously done: one from ECCC and one from Carminati (2022).

a. ECCC selection

To compare the selection of ECCC composed of 103 channels selected with the Jacobian method, a subset of channels of the selection done in this paper was considered. To have around the same number of channels as the selection of ECCC, a subset of 104 channels were considered optimally selected. A total of 104 channels were selected instead of 103 for the same reason as previously explained, since channels had the same frequency of selection.

To show the added value of the different selections, Fig. 6 shows the analysis error variance for different selections for both temperature and humidity. The dark blue curve represents the averaged analysis error when the selection of 103 channels of ECCC is considered, whereas the light blue curve represents the averaged analysis error when 104 channels are selected optimally. For temperature, the selection of 103 channels of ECCC reduces more the error compared to the optimal selection of 104 channels, whereas it is the inverse for humidity. To show the variability associated with the profiles, the standard deviation is represented with the horizontal bars for the 104 channels configuration. The standard deviations were not shown for the configuration of 103 channels and the optimal selection for figure’s clarity.

Fig. 6.
Fig. 6.

Profiles of analysis error variance for different selections for (left) temperature and (right) humidity with the horizontal bars representing the standard deviation at each level. The different selections are 104 optimal channels (light blue), 103 channels from ECCC (dark blue), selection from Carminati (2022) (431 channels) (red), and the optimal selection of 455 channels (gray).

Citation: Journal of Applied Meteorology and Climatology 63, 6; 10.1175/JAMC-D-23-0188.1

Integrated through the whole profile, the relative difference in reducing the analysis error is equal to 5.7% and −11.6% for temperature and humidity, respectively, between the optimal selection of 104 channels and the ECCC one. Those nonoptimal results for the selection of 103 channels is expected since, as shown in Fig. 2, the selection of 103 channels does not contain most of the information available as the curve for the averaged DFS for temperature and humidity is still increasing as more channels are selected. The 103 channels selected by ECCC contain only 69.6% and 49.1% of the total information available with respect to temperature and humidity, respectively, when the DFS are compared. Six channels are identical between the selection of ECCC and the optimal selection of 104 channels.

b. Carminati selection

Similarly, the optimal selection from this experiment can be compared to the selection made by Carminati (2022). The biggest difference between the selections from the Carminati experiment is the observation error covariance matrix R, estimated with the method of Desroziers et al. (2005). Also, the DFS was calculated for ozone and surface temperature, which are not considered in our study. The optimal selection of Carminati (2022) retains 431 channels to match the number of channels previously selected in other studies such as in Gambacorta and Barnet (2012). Hence, the optimal selection of 455 channels is compared to the selection of Carminati (2022). Figure 6 shows also the analysis error variance corresponding to the assimilation of the channels selected by Carminati (2022) (red) and an optimal selection of 455 channels (gray). These were averaged over the 50 atmospheric cases.

For temperature, the Carminati selection is better at reducing the analysis error compared to the optimal selection. The largest differences are between the surface and 800 hPa and between 400 and 100 hPa, which is expected since it is where there is the largest variability with respect to temperature. For humidity, both selections give almost identical results as can be seen in Table 2. The difference in the reduction of the analysis error between the two selections could be explained by the different atmospheric profiles selected for the different experiments. Carminati (2022) used one profile for each region for a total of 40 cases, whereas in our study, five profiles per region were considered in order to account for the atmospheric variability possible in different regions. The fact that even though the channel selections are different, the analysis error is quite similar could be explained by the Jacobians. Hyperspectral instruments have Jacobian heavily overlapping; therefore, two, three, or more consecutive channels will broadly speaking be sensitive to the same layer of atmosphere and in consequence bear a similar (although not identical) information content. This is why there is a potentially large number of possible combinations yielding similar results with respect to DFS and analysis error. Also, the Carminati selection and the optimal selection share 224 identical channels out of the 455 contained in the optimal selection. One of the differences is due to ozone being considered as one of the variables for the channel selection of Carminati. This shows that even if channel selections for an instrument are different, the final impact on analysis variance is similar.

Table 2.

Averaged DFS and the reduction in error compared to the background error covariance over the 50 atmospheric profiles for the optimal selection and the Carminati selection.

Table 2.

6. Impact of the observation covariance error matrix

The previous section showed that various experiments’ configurations from NWP centers can lead to different results with respect to the CrIS selection of optimal channels. For instance, the channel selection depends on the observation error covariance used. This section examines the sensitivity of the selection to this particular aspect for one region in the midlatitudes. Figure 7 shows the variance associated with different observation error covariance matrices R used as a function of the wavenumber. The yellow curve represents the measurement error that was considered for the main part of our study, whereas two other types of observation error covariance matrices were considered. The green curve represents the operational observation error covariance matrix used at ECCC for the data assimilation system. Another observation error covariance matrix normally used for the channel selection of an instrument is to take the measurement error and to add a constant error of 0.2 K to consider the radiative transfer model error (Fourrié and Thépaut 2003), called the forward error. However, those infrared instruments measure radiance in milliwatts per centimeter per steradian per square meter and not in brightness temperature. Hence, to convert those, a constant brightness temperature of 250 K is considered and not the temperature of the scene, which is dependent on the wavelength. An error is introduced with this assumption. To illustrate this, to the measurement error, two forward errors are added separately, both of 0.2 K but one at 250 K (orange curve) and one evaluated at the brightness temperature of the scene (blue curve).

Fig. 7.
Fig. 7.

Variance of different observation covariance error matrices. The yellow curve represents the measurement error, whereas the green curve represents the variance of the operational observation error covariance matrix used at ECCC. The orange and blue curves represent the sum of the measurement error variance and two forward errors, one constant evaluated at 250 K and one variable evaluated at the temperature scene, respectively.

Citation: Journal of Applied Meteorology and Climatology 63, 6; 10.1175/JAMC-D-23-0188.1

Also, the analysis error variance for both temperature and humidity behaves as expected: a larger observation error variance matrix leads to a larger analysis error variance (not shown). Thus, in order of less reduction to most reduction, there is the operational observation error covariance matrix, the measurement error with the constant forward error, and then the measurement error with the variable forward error. However, even though the operational observation error is one order of magnitude bigger than the measurement error with a forward error, the analysis error reduction is comparable. The percentage of total analysis error variance reduction for the operational observation error and the measurement error with a forward error (green and blue curves) is 10.3% for temperature and 8.3% for humidity.

To compare the impact of the observation error covariance matrices on the channel selection, for each different R matrix shown in Fig. 7, an optimal channel selection was done for up to 455 channels. For the different selections, there are 163 channels always selected for temperature and 214 for humidity. The positions of those channels are in the LW band and MW band for temperature and in the MW band for humidity. There is some variability in the channel selection that can be linked to the observation error covariance matrices chosen for the experiments. However, even if the channel selections are different for various R matrices, the results in terms of analysis error are similar as discussed in the previous paragraph.

Also, the analysis error variance was compared between the averaged optimal selection of 455 channels and the selections of 455 channels made individually for each atmospheric case illustrated in Fig. 8. For temperature, both configurations with the measurement error with a forward error give similar results between both configurations except between 300 hPa and the TOA where the optimal configuration gives better results at reducing the analysis error. There are 291 identical channels between those two configurations, which can explain the similarity in the analysis error variance. For the results with the operational error, the selection made individually is better at reducing the error compared to the averaged selection close to the surface and up to 850 hPa, since the channel selection is tailored for the atmospheric case. For humidity, configurations with the operational R matrix and with the measurement error with a variable forward error, the optimal configuration is better at reducing the analysis error variance compared to the selections made individually between 700 and 400 hPa. Also, for all configurations, between 400 hPa and the TOA, the selections made individually are better at reducing the error.

Fig. 8.
Fig. 8.

Difference in averaged analysis error between two optimal selections. The first selection is the optimal selection of 455 channels, and the second is the selections calculated of 455 channels made individually for each atmospheric case averaged. It shows the difference in the analysis error variance for the operational error in green, the measurement error with the variable forward error in red, and the measurement error with the constant forward error in blue. The horizontal bars represent the standard deviation at each level.

Citation: Journal of Applied Meteorology and Climatology 63, 6; 10.1175/JAMC-D-23-0188.1

Even though the observation error covariance matrices for the variable forward error vary more than the constant forward error at 250 K and are on average larger, the results with respect to analysis error are quite similar. The relative difference with respect to the vertical sum for the analysis error variance is 1.9% and 0.6% for temperature and humidity, respectively, the observation error covariance matrix with the constant forward error being slightly better. For the channels always selected for those two configurations, 291 and 334 channels are identical out of 455, which is similar to the number of channels compared to the optimal selection. Thus, it is impossible to make conclusions at this stage with respect to the use of a constant brightness temperature or of the brightness temperature of the scene.

7. Conclusions

The goal of this paper was to present a channel selection for the instrument CrIS on the basis of information content from the point of view of a specific system (ECCC) and to study the impact of different selections on the analysis error. Hence, channel selections were done for 50 atmospheric profiles selected in different regions for up to 400 channels of the instrument. An optimal configuration for both temperature and humidity of 455 channels was then considered representing around 97% of the total DFS for both temperature and humidity. In terms of analysis error, this optimal configuration reduces the error by 29.5% and 45.8% compared to the background error covariance for temperature and humidity, respectively. This optimal configuration was then compared to two previous selections of channels done for the instrument CrIS, which are from ECCC and Carminati (2022). The channel selection of ECCC contains 103 channels, which is not enough since there is still available information that could be gained by assimilating more channels. However, compared to the selection made by Carminati (2022), there are 233 channels common to the two selections. The results in terms of analysis error are similar, the reduction being 38.8% and 43.3% for temperature and humidity, respectively. The difference in the reduction of analysis error could be due to the different sets of atmospheric profiles used for the evaluations. Finally, different observation covariance matrices were considered to evaluate the impact of this matrix on channel selection. Even though the channels selected optimally were different for the various R matrices, the results in terms of analysis error are quite similar.

The DFS calculations used for a channel selection of an instrument depend on the background error covariance matrix B, the observation error covariance matrix R, and the Jacobian matrix H defined with respect to the atmospheric profiles chosen. It can be stated then that the same number of atmospheric profiles should be taken for each region to give the same statistical weight and also to take into consideration the variability in terms of the different atmospheric variables considered. The background error covariance matrix B being intrinsic to NWP centers, to study its impact on the channel selection of an instrument, an experiment could be constructed where it is the only matrix varied. Another experiment worth considering is to take the dynamic background error covariance matrix B instead of the static one considered in this paper. Thus, we could see the impact of those changes on the channel selection. Also, since some channel selection studies used the Desroziers method to evaluate the observation error covariance matrix, B and R are linked. The results of this study show that there are two subsets of results in terms of analysis error. The analysis error for the operational and the R matrices containing a forward error gives similar results even though there is a factor of 10 between those two types of R matrices. On the other hand, the analysis error for the configuration with only the measurement error when compared to the previous ones results in a much smaller analysis error variance, which is expected since the NER is much smaller. Nevertheless, as seen with the comparison with the channel selection of Carminati (2022), there is only a small difference in terms of analysis error whichever selection is considered as long as there are enough channels considered. These results can help the research on channel selection with respect to the type of R matrices used and also bring improvement in the use of CrIS measurements for NWP systems. Further experiments will be done using R matrices containing interchannels covariance errors since it has been shown to improve the channel selection (Coopmann et al. 2020) and the assumption of a diagonal R matrix is a limitation of this paper. Also, the channels selected for CrIS could be diversified to correspond to different atmospheric conditions. An adaptive selection of channels could be considered with respect to humidity since there is a large variability in terms of this variable for channel selection. In the future, an experiment could focus on finding such an adaptive selection of channels for humidity by taking a training set of atmospheric profiles larger and that includes a sample of cases containing also extreme atmospheric situations.

This study is using a simple 1D system to find the selection of channels that provide the most information on temperature and humidity. However, it remains to be seen if similar conclusions are obtained in a complete assimilation system with all available observations. The next step will then be to perform observing system experiments (OSEs) and evaluate the DFS from diagnostics based on departures with respect to the analysis and the background state. This would provide an estimate of the added value of the observations to confirm the conclusions presented here regarding the impact of additional CrIS channels on both the analyses and forecasts of ECCC.

Acknowledgments.

The authors thank Dr. Josep Aparicio and Dr. Maziar Bani Shahabadi for their comments that led to improvements in the manuscript. The authors are also grateful to two anonymous reviewers, who helped them in improving this manuscript. This research has been funded by the grants and contribution program of ECCC and a grant from the Natural Sciences and Engineering Research Council of Canada (NSERC) Discovery Grant program.

Data availability statement.

The atmospheric profiles used are from radiosondes taken from the IGRA database (https://www.ncei.noaa.gov/products/weather-balloon/integrated-global-radiosonde-archive). These simulations and the codes used to generate the figures are available from Laurence Coursol.

REFERENCES

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    • Export Citation
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    • Search Google Scholar
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  • Merrelli, A., and D. D. Turner, 2012: Comparing information content of upwelling far-infrared and midinfrared radiance spectra for clear atmosphere profiling. J. Atmos. Oceanic Technol., 29, 510526, https://doi.org/10.1175/JTECH-D-11-00113.1.

    • Search Google Scholar
    • Export Citation
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    • Search Google Scholar
    • Export Citation
  • Noh, Y.-C., B.-J. Sohn, Y. Kim, S. Joo, W. Bell, and R. Saunders, 2017: A new infrared atmospheric sounding interferometer channel selection and assessment of its impact on Met Office NWP forecasts. Adv. Atmos. Sci., 34, 12651281, https://doi.org/10.1007/s00376-017-6299-8.

    • Search Google Scholar
    • Export Citation
  • Prunet, P., J.-N. Thépaut, and V. Cassé, 1998: The information content of clear sky IASI radiances and their potential for numerical weather prediction. Quart. J. Roy. Meteor. Soc., 124, 211241, https://doi.org/10.1002/qj.49712454510.

    • Search Google Scholar
    • Export Citation
  • Purser, R. J., and H.-L. Huang, 1993: Estimating effective data density in a satellite retrieval or an objective analysis. J. Appl. Meteor., 32, 10921107, https://doi.org/10.1175/1520-0450(1993)032<1092:EEDDIA>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Rabier, F., N. Fourrié, D. Chafäi, and P. Prunet, 2002: Channel selection methods for infrared atmospheric sounding interferometer radiances. Quart. J. Roy. Meteor. Soc., 128, 10111027, https://doi.org/10.1256/0035900021643638.

    • Search Google Scholar
    • Export Citation
  • Rodgers, C. D., 1998: Information content and optimisation of high spectral resolution remote measurements. Adv. Space Res., 21, 361367, https://doi.org/10.1016/S0273-1177(97)00915-0.

    • Search Google Scholar
    • Export Citation
  • Rodgers, C. D., 2000: Inverse Methods for Atmospheric Sounding: Theory and Practice. Vol. 2. World Scientific, 256 pp.

  • Saunders, R., and Coauthors, 2018: An update on the RTTOV fast radiative transfer model (currently at version 12). Geosci. Model Dev., 11, 27172737, https://doi.org/10.5194/gmd-11-2717-2018.

    • Search Google Scholar
    • Export Citation
  • Shahabadi, M. B., and Y. Huang, 2014: Measuring stratospheric H2O with an airborne spectrometer. J. Atmos. Oceanic Technol., 31, 15021515, https://doi.org/10.1175/JTECH-D-13-00191.1.

    • Search Google Scholar
    • Export Citation
  • Smith, W. L., 1966: Note on the relationship between total precipitable water and surface dew point. J. Appl. Meteor. Climatol., 5, 726727, https://doi.org/10.1175/1520-0450(1966)005<0726:NOTRBT>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Smith, W. L., H. Revercomb, E. Weisz, D. Tobin, R. Knuteson, J. Taylor, and W. P. Menzel, 2021: Hyperspectral satellite radiance atmospheric profile information content and its dependence on spectrometer technology. IEEE J. Sel. Top. Appl. Earth Obs. Remote Sens., 14, 47204736, https://doi.org/10.1109/JSTARS.2021.3073482.

    • Search Google Scholar
    • Export Citation
  • Wang, S., Y. Feng, D. Fu, L. Kong, H. Li, B. Han, and F. Lu, 2023: Stratospheric temperature observations by narrow bands ultra-high spectral resolution sounder from nadir-viewing satellites. Remote Sens., 15, 1967, https://doi.org/10.3390/rs15081967.

    • Search Google Scholar
    • Export Citation

Supplementary Materials

Save
  • Aumann, H. H., and Coauthors, 2003: AIRS/AMSU/HSB on the aqua mission: Design, science objectives, data products, and processing systems. IEEE Trans. Geosci. Remote Sens., 41, 253264, https://doi.org/10.1109/TGRS.2002.808356.

    • Search Google Scholar
    • Export Citation
  • Barnet, C. D., N. Smith, K. Ide, K. Garrett, and E. Jones, 2023: Evaluating the value of CrIS shortwave-infrared channels in atmospheric-sounding retrievals. Remote Sens., 15, 547, https://doi.org/10.3390/rs15030547.

    • Search Google Scholar
    • Export Citation
  • Bormann, N., A. Collard, and P. Bauer, 2010: Estimates of spatial and interchannel observation-error characteristics for current sounder radiances for numerical weather prediction. II: Application to AIRS and IASI data. Quart. J. Roy. Meteor. Soc., 136, 10511063, https://doi.org/10.1002/qj.615.

    • Search Google Scholar
    • Export Citation
  • Buehner, M., and Coauthors, 2015: Implementation of deterministic weather forecasting systems based on ensemble–variational data assimilation at environment Canada. Part I: The global system. Mon. Wea. Rev., 143, 25322559, https://doi.org/10.1175/MWR-D-14-00354.1.

    • Search Google Scholar
    • Export Citation
  • Carminati, F., 2022: A channel selection for the assimilation of CrIS and HIRAS instruments at full spectral resolution. Quart. J. Roy. Meteor. Soc., 148, 10921112, https://doi.org/10.1002/qj.4248.

    • Search Google Scholar
    • Export Citation
  • Collard, A. D., 2007: Selection of IASI channels for use in numerical weather prediction. Quart. J. Roy. Meteor. Soc., 133, 19771991, https://doi.org/10.1002/qj.178.

    • Search Google Scholar
    • Export Citation
  • Coopmann, O., V. Guidard, N. Fourrié, B. Josse, and V. Marécal, 2020: Update of Infrared Atmospheric Sounding Interferometer (IASI) channel selection with correlated observation errors for Numerical Weather Prediction (NWP). Atmos. Meas. Tech., 13, 26592680, https://doi.org/10.5194/amt-13-2659-2020.

    • Search Google Scholar
    • Export Citation
  • Coopmann, O., N. Fourrié, and V. Guidard, 2022: Analysis of MTG-IRS observations and general channel selection for numerical weather prediction models. Quart. J. Roy. Meteor. Soc., 148, 18641885, https://doi.org/10.1002/qj.4282.

    • Search Google Scholar
    • Export Citation
  • Coursol, L., Q. Libois, P. Gauthier, and J.-P. Blanchet, 2020: Optimal configuration of a far-infrared radiometer to study the Arctic winter atmosphere. J. Geophys. Res. Atmos., 125, e2019JD031773, https://doi.org/10.1029/2019JD031773.

    • Search Google Scholar
    • Export Citation
  • Desroziers, G., L. Berre, B. Chapnik, and P. Poli, 2005: Diagnosis of observation, background and analysis-error statistics in observation space. Quart. J. Roy. Meteor. Soc., 131, 33853396, https://doi.org/10.1256/qj.05.108.

    • Search Google Scholar
    • Export Citation
  • Durre, I., R. S. Vose, and D. B. Wuertz, 2006: Overview of the integrated global radiosonde archive. J. Climate, 19, 5368, https://doi.org/10.1175/JCLI3594.1.

    • Search Google Scholar
    • Export Citation
  • Fourrié, N., and J.-N. Thépaut, 2003: Evaluation of the AIRS near-real-time channel selection for application to numerical weather prediction. Quart. J. Roy. Meteor. Soc., 129, 24252439, https://doi.org/10.1256/qj.02.210.

    • Search Google Scholar
    • Export Citation
  • Gambacorta, A., and C. D. Barnet, 2012: Methodology and information content of the NOAA NESDIS operational channel selection for the Cross-track Infrared Sounder (CrIS). IEEE Trans. Geosci. Remote Sens., 51, 32073216, https://doi.org/10.1109/TGRS.2012.2220369.

    • Search Google Scholar
    • Export Citation
  • Iturbide-Sanchez, F., and Coauthors, 2022: Recalibration and assessment of the SNPP CrIS instrument: A successful history of restoration after midwave infrared band anomaly. IEEE Trans. Geosci. Remote Sens., 60, 121, https://doi.org/10.1109/TGRS.2021.3112400.

    • Search Google Scholar
    • Export Citation
  • Merrelli, A., and D. D. Turner, 2012: Comparing information content of upwelling far-infrared and midinfrared radiance spectra for clear atmosphere profiling. J. Atmos. Oceanic Technol., 29, 510526, https://doi.org/10.1175/JTECH-D-11-00113.1.

    • Search Google Scholar
    • Export Citation
  • Mertens, C. J., 2002: Feasibility of retrieving upper tropospheric water vapor from observations of far-infrared radiation. Proc. SPIE, 4485, 191201, https://doi.org/10.1117/12.454251.

    • Search Google Scholar
    • Export Citation
  • Noh, Y.-C., B.-J. Sohn, Y. Kim, S. Joo, W. Bell, and R. Saunders, 2017: A new infrared atmospheric sounding interferometer channel selection and assessment of its impact on Met Office NWP forecasts. Adv. Atmos. Sci., 34, 12651281, https://doi.org/10.1007/s00376-017-6299-8.

    • Search Google Scholar
    • Export Citation
  • Prunet, P., J.-N. Thépaut, and V. Cassé, 1998: The information content of clear sky IASI radiances and their potential for numerical weather prediction. Quart. J. Roy. Meteor. Soc., 124, 211241, https://doi.org/10.1002/qj.49712454510.

    • Search Google Scholar
    • Export Citation
  • Purser, R. J., and H.-L. Huang, 1993: Estimating effective data density in a satellite retrieval or an objective analysis. J. Appl. Meteor., 32, 10921107, https://doi.org/10.1175/1520-0450(1993)032<1092:EEDDIA>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Rabier, F., N. Fourrié, D. Chafäi, and P. Prunet, 2002: Channel selection methods for infrared atmospheric sounding interferometer radiances. Quart. J. Roy. Meteor. Soc., 128, 10111027, https://doi.org/10.1256/0035900021643638.

    • Search Google Scholar
    • Export Citation
  • Rodgers, C. D., 1998: Information content and optimisation of high spectral resolution remote measurements. Adv. Space Res., 21, 361367, https://doi.org/10.1016/S0273-1177(97)00915-0.

    • Search Google Scholar
    • Export Citation
  • Rodgers, C. D., 2000: Inverse Methods for Atmospheric Sounding: Theory and Practice. Vol. 2. World Scientific, 256 pp.

  • Saunders, R., and Coauthors, 2018: An update on the RTTOV fast radiative transfer model (currently at version 12). Geosci. Model Dev., 11, 27172737, https://doi.org/10.5194/gmd-11-2717-2018.

    • Search Google Scholar
    • Export Citation
  • Shahabadi, M. B., and Y. Huang, 2014: Measuring stratospheric H2O with an airborne spectrometer. J. Atmos. Oceanic Technol., 31, 15021515, https://doi.org/10.1175/JTECH-D-13-00191.1.

    • Search Google Scholar
    • Export Citation
  • Smith, W. L., 1966: Note on the relationship between total precipitable water and surface dew point. J. Appl. Meteor. Climatol., 5, 726727, https://doi.org/10.1175/1520-0450(1966)005<0726:NOTRBT>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Smith, W. L., H. Revercomb, E. Weisz, D. Tobin, R. Knuteson, J. Taylor, and W. P. Menzel, 2021: Hyperspectral satellite radiance atmospheric profile information content and its dependence on spectrometer technology. IEEE J. Sel. Top. Appl. Earth Obs. Remote Sens., 14, 47204736, https://doi.org/10.1109/JSTARS.2021.3073482.

    • Search Google Scholar
    • Export Citation
  • Wang, S., Y. Feng, D. Fu, L. Kong, H. Li, B. Han, and F. Lu, 2023: Stratospheric temperature observations by narrow bands ultra-high spectral resolution sounder from nadir-viewing satellites. Remote Sens., 15, 1967, https://doi.org/10.3390/rs15081967.

    • Search Google Scholar
    • Export Citation
  • Fig. 1.

    Locations of the stations selected.

  • Fig. 2.

    Averaged DFS over the 50 profiles for temperature (orange) and humidity (blue) (full lines), whereas the dotted lines show the associated total DFS for the respective variable. The shaded area shows the standard deviation associated with the variables.

  • Fig. 3.

    Analysis error variance profile averaged over the 50 atmospheric profiles for (left) temperature and (right) humidity. The black curve represents background error B, the orange curve represents the analysis error when 100 channels are taken optimally, the blue curve represents the analysis error when 400 channels are selected optimally, whereas the shaded area represents its associated standard deviation and the dark purple curve represents the analysis error when all the channels are assimilated.

  • Fig. 4.

    Frequency of selection of the different channels out of 100 (50 for temperature and 50 for humidity) shown by the color superposed with a spectral radiance as a function of wavenumber.

  • Fig. 5.

    Position of the channels selected for the optimal selection of 455 channels superposed with a spectral radiance as a function of wavenumber.

  • Fig. 6.

    Profiles of analysis error variance for different selections for (left) temperature and (right) humidity with the horizontal bars representing the standard deviation at each level. The different selections are 104 optimal channels (light blue), 103 channels from ECCC (dark blue), selection from Carminati (2022) (431 channels) (red), and the optimal selection of 455 channels (gray).

  • Fig. 7.

    Variance of different observation covariance error matrices. The yellow curve represents the measurement error, whereas the green curve represents the variance of the operational observation error covariance matrix used at ECCC. The orange and blue curves represent the sum of the measurement error variance and two forward errors, one constant evaluated at 250 K and one variable evaluated at the temperature scene, respectively.

  • Fig. 8.

    Difference in averaged analysis error between two optimal selections. The first selection is the optimal selection of 455 channels, and the second is the selections calculated of 455 channels made individually for each atmospheric case averaged. It shows the difference in the analysis error variance for the operational error in green, the measurement error with the variable forward error in red, and the measurement error with the constant forward error in blue. The horizontal bars represent the standard deviation at each level.

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