Abstract

The information content of high-spectral-resolution midinfrared (MIR; 650–2300 cm−1) and far-infrared (FIR; 200–685 cm−1) upwelling radiance spectra is calculated for clear-sky temperature and water vapor profiles. The wavenumber ranges of the two spectral bands overlap at the central absorption line in the CO2 ν2 absorption band, and each contains one side of the full absorption band. Each spectral band also includes a water vapor absorption band; the MIR contains the first vibrational–rotational absorption band, while the FIR contains the rotational absorption band. The upwelling spectral radiances are simulated with the line-by-line radiative transfer model (LBLRTM), and the retrievals and information content analysis are computed using standard optimal estimation techniques. Perturbations in the surface temperature and in the trace gases methane, ozone, and nitrous oxide (CH4, O3, and N2O) are introduced to represent forward-model errors. Each spectrum is observed by a simulated infrared spectrometer, with a spectral resolution of 0.5 cm−1, with realistic spectrally varying sensor noise levels. The modeling and analysis framework is applied identically to each spectral range, allowing a quantitative comparison. The results show that for similar sensor noise levels, the FIR shows an advantage in water vapor profile information content and less sensitivity to forward-model errors. With a higher noise level in the FIR, which is a closer match to current FIR detector technology, the FIR information content drops and shows a disadvantage relative to the MIR.

1. Introduction

High-spectral-resolution measurements of earth’s upwelling infrared radiation have proven extremely useful in a variety of atmospheric science applications. Originally developed as atmospheric sounders to infer profiles of water vapor and temperature, current instruments [Atmospheric Infrared Sounder (AIRS) and Infrared Atmospheric Sounding Interferometer (IASI)] routinely produce high-quality spectral observations. These instruments (as well as most infrared sensors) are based on cooled semiconductor detectors (e.g., InSb or HgCdTe), which work extremely well for the midinfrared (MIR) spectral regions. Roughly speaking, this region covers 650–2500 cm−1, and the relevant absorption bands are the CO2 ν2 band at 600–750 cm−1 and the water vapor absorption band covering roughly 1200–2000 cm−1. Typically these MIR spectral observations stop near the middle of the CO2 ν2 band, and do not cover lower frequencies. Since the absorption band is roughly symmetric about the central absorption line, the low-frequency side contains partially redundant information. In addition, the semiconductor detectors lose sensitivity very quickly at these low energies. Although HgCdTe detectors can be designed for lower frequencies (Knuteson et al. 2004; Serio et al. 2008a), the cutoff at 650 cm−1 is more common. Therefore, while defining the low-frequency edge of the MIR at 650 cm−1 is arbitrary, it is justified by the fact that making the low-frequency cutoff for an MIR observation at that point is a sensible trade-off. The far-infrared (FIR) portion of the infrared spectrum is not as well observed. As mentioned above, common semiconductor detectors are not sensitive to FIR because the photon energies will be lower than the band gap energy. Thus, different detector technologies are required, and the technology is not as mature.

Recently, interest in the FIR has increased. New developments in detector technology have allowed improvements in FIR sensors, and the community has renewed interest in this spectral regime as it relates to many atmospheric scientific questions. Several ground-based and aircraft research sensors have been developed, and deployed in field campaigns (Turner and Mlawer 2010; Bhawar et al. 2008; Serio et al. 2008b; Harries et al. 2008; Cox et al. 2007; Mlynczak et al. 2006).

These campaigns have primarily focused on estimating the water vapor continuum coefficients and water vapor spectral line parameters. It is challenging to retrieve profiles of temperature and water vapor from downwelling infrared radiance spectra since the strong water vapor continuum absorption tends to cause a large optical depth at all spectral frequencies. However, the upwelling spectrum contains a large amount of potential profiling information. The water vapor rotational absorption band in the FIR has many absorption lines with larger optical depth than the MIR (Harries et al. 2008), which implies an increased sensitivity to water vapor changes in the upwelling radiance spectrum. The increased sensitivity is especially important in the upper troposphere, where the water vapor concentration is low. Previous studies have investigated profiling using the FIR spectrum (Serio et al. 2008a; Palchetti et al. 2008), using the limited datasets available from ground campaigns and balloon flights. In Rizzi et al. (2002), the sensitivity of the upwelling radiance in the two water vapor absorption bands was compared using a line-by-line radiative transfer code. The FIR showed significantly larger sensitivity, as well as relatively lower retrieval error.

In addition to the relation to water vapor profiling, one of the key scientific questions is the role of the FIR in earth’s outgoing longwave radiation (OLR) in the overall energy budget. Although the full OLR (MIR and FIR) is routinely measured from space by the Clouds and the Earth’s Radiant Energy System (CERES)–Earth Radiation Budget Experiment (ERBE) programs, the spectrally resolved FIR radiance has not been observed from space since the Infrared Interferometer Sounder (IRIS) instrument on Nimbus-3 (Conrath et al. 1970). The future National Aeronautics and Space Administration (NASA) mission Climate Absolute Radiance and Refractivity Observatory (CLARREO) (Sandford et al. 2010) is designed to measure the OLR at a high spectral resolution with excellent absolute calibration.

Our study borrows CLARREO’s general instrument characteristics to model observations of MIR and FIR spectra, and we investigate how these modeled spectra perform when processed by optimal estimation retrieval techniques. Although CLARREO’s design is not optimized for atmospheric sounding, the excellent calibration and spectral resolution of the collected spectra will still be very useful for sounding applications. So, this study uses the general CLARREO characteristics as a basis for analyzing the potential clear-sky profiling information contained within satellite-based observations of the upwelling spectra.

Our goal is to compare and contrast the information content and sensitivity to certain forward-model errors of the MIR and FIR spectral ranges. The present study extends the earlier analysis of Rizzi et al. (2002) to a wider range of atmospheric conditions and prior constraints utilized in the retrieval algorithm. For simplicity, we have assumed clear-sky conditions and nadir pointing for the simulated sensors in all cases. In section 2, we describe our simulation and retrieval methodology, including full details on the assumed a priori information and sensor characteristics. The different sensitivities of the retrievals to the forward-model errors are described in section 3. The information content analysis is described in section 4. We discuss the results in section 5.

2. Retrieval and simulation design

The retrieval methodology follows the optimal estimation technique (Rodgers 2000), which is a standard method for physical retrievals. The state vector x is equal to the temperature and the logarithm of the water vapor mixing ratio at the simulated levels. Specifically, our levels are specified at 40 pressure values, so the state vector is an 80-element vector with elements 1–40 equal to the temperature and elements 41–80 equal to the logarithm of the water vapor mixing ratio. The measurement vector y is equal to the high-resolution spectral radiance measurement, with O(103) elements. The retrieval is performed with the Gauss–Newton method, where the forward model is linearized at the first guess (which we set equal to the a priori mean state vector), according to

 
formula

where represents the linearization of the forward model at the first guess (i.e., ), and ε is the measurement error vector. No forward-model error has been included in the measurement error. The Gauss–Newton method is an iterative calculation that computes a new estimate for the state vector at each iteration i using a forward-model linearization at the current state vector estimate :

 
formula

where is the a priori covariance of the state vector and is the covariance of the measurement error. The superscript T and −1 denote the matrix transpose and matrix inverse, respectively. The first guess, x0, is always set to the a priori state vector mean, so x0 = xa. The iteration proceeds until the convergence criteria are met or the iteration limit (10) is reached. The convergence criteria tests the change in the state vector estimate against the squared Mahalanobis distance computed from the expected covariance of the state estimate, with a conservative limiting factor of 0.1 (meaning, the iteration will repeat until the change is well below the “noise level”):

 
formula

The optimal estimation retrieval framework is strongly dependent on the choice of the a priori, forward model, and instrument model, so we will discuss each in further detail.

a. Optimal estimation retrieval framework

1) A priori

The a priori consists of the mean and covariance of the state vector, computed from radiosonde data collected at the Atmospheric Radiation Measurement Climate Research Facility (ACRF) ground sites (Ackerman and Stokes 2003). To sample a wide range of possible climate conditions, we selected the North Slope Alaska (NSA) site at Barrow, Alaska; the Southern Great Plains (SGP) site at Lamont, Oklahoma; and the Tropical West Pacific (TWP-C3) site at Darwin, Northern Territory, Australia. The magnitude of the variance over an entire year is quite large at all three sites, so the climatology was split into four seasonal composites, covering the usual 3-month groupings [December–February (DJF), March–May (MAM), June–August (JJA), and September–November (SON)], with each 3-month period expanded by 15 days at the start and end.

For all sites, bad radiosonde profiles were removed by various automatic checks: extremely high or low temperatures, large data gaps, or truncation below the tropopause. In addition, some manual outlier removal was performed to remove bad humidity measurements that showed unphysical variations. The outlier removal process removed at most a few percent of the total radiosonde data list. These raw radiosonde profiles were then interpolated to a common altitude grid with a dense vertical sampling (Δz = 20 m).

After the initial processing, a humidity correction was applied to eliminate some of the dry bias associated with the Vaisala radiosondes (Cady-Pereira et al. 2008). The corrected humidity was converted to relative humidity over water, and relative humidity over ice for (T < −10°C), to enable a crude cloud detection method. Any profile that contained more than two samples above 100% relative humidity was classified as cloudy and removed from the climatology. Since the altitude increment is 20 m, this corresponds to a layer thicker than 40 m. For the Arctic climatology, these thresholds caused a large majority of the available profiles to be classified as cloudy. To get a statistically significant sample for the climatological composites, we increased the count threshold to five (from two), and also ignored any points in the lowest 200-m altitude. Our physical justification for these ad hoc additional thresholds is that many high-humidity samples at low altitudes are likely due to blowing snow or diamond dust conditions, and that the much lower water content due to the lower temperatures implies that a relatively thicker saturated layer would be needed to constitute a cloud layer with enough optical thickness to have an impact on the infrared emission. With the adjusted thresholds, all prior composites had enough total samples to create a statistically significant sample (102 or more samples per composite).

Since the radiosonde humidity measurements above the tropopause are known to have large systematic errors because of the extremely low water vapor mixing ratios, all data above the tropopause were replaced with synthetic profile data. The synthetic profiles used the closest representative standard atmosphere profile (tropical, summer–winter midlatitude, summer–winter subarctic) or the average of the two closest standard profiles. Specifically, for the SGP data, the winter composite uses the winter midlatitude standard profile, while the spring composite uses the average of the winter and summer midlatitude standard profiles. Each profile also had a small-amplitude (1-K RMS for temperature and 30% RMS for log water vapor mixing ratio) random fluctuation added to the standard profile with no interlevel correlation. The cutoff between the synthetic high-altitude profile and the radiosonde-derived low-altitude profile occurs at the tropopause, which has a different altitude depending on the site location and season. Through the year, the tropopause height is assumed to vary sinusoidally between the two heights suggested by the standard atmosphere profiles. In terms of the level numbers, this cutoff occurs at level 19 for the subarctic winter profile, and level 32 for the tropical profile, with the other profiles intermediate between these two extremes.

For the most part, the retrievals from our simulated infrared spectrometers are not very sensitive to the stratospheric levels because of the low pressure and thus extremely narrow spectral lines. So, the exact details of the synthetic stratospheric profiles are not critical. The most important impact of the synthetic stratosphere is to ensure that realistic optical depths from the top of atmosphere (TOA) down to the tropopause are simulated. If the stratosphere was removed from the simulation, there would be a false sensitivity to tropospheric levels for those high optical depth spectral frequencies where the true weighting functions contain significant amplitude in the stratosphere.

To illustrate the shape of these measured covariance matrices, Fig. 1 shows the covariance matrix for the Darwin ACRF site for the DJF season. Because of the construction of the state vector (level temperature followed by level water vapor concentration logarithm), the covariance consists of blocks of T covariance, Q covariance, and TQ cross covariance, as shown in the figure. The associated correlation matrix is shown on the right. Note the large interlevel correlation, especially for temperature. The stratospheric levels also stand out, as no interlevel correlation was added to these synthetic levels, so the corresponding portion of the covariance and correlation matrices is diagonal.

Fig. 1.

(left) Covariance matrix and (right) correlation matrix for the ACRF radiosondes from the Darwin site for the DJF season. The T, Q, and TQ labels denote the portions of the covariance matrix representing temperature covariance, water vapor mass mixing ratio logarithm covariance, and the temperature–water vapor cross covariance.

Fig. 1.

(left) Covariance matrix and (right) correlation matrix for the ACRF radiosondes from the Darwin site for the DJF season. The T, Q, and TQ labels denote the portions of the covariance matrix representing temperature covariance, water vapor mass mixing ratio logarithm covariance, and the temperature–water vapor cross covariance.

2) Forward model

The forward model used for our nonlinear retrieval is the line-by-line radiative transfer model (LBLRTM) from Atmospheric and Environmental Research (AER) (Clough et al. 2005, 1992). The LBLRTM computes the Jacobian analytically [the term in Eq. (2)], instead of requiring an approximation through finite differencing. One important aspect of the forward model is the reduction of the vertical resolution of the original radiosonde data. The radiosonde data is gridded at 20-m vertical resolution, and the raw data has a vertical resolution of the same order (although it is not regularly gridded because of the random nature of the balloon ascent). However, this is far too high a vertical resolution for the forward model, partly because of computational limitations, and partly because of the poor vertical resolution of the retrieved state estimate. Following the information density analysis of Purser and Huang (1993), the vertical resolution of the temperature and water vapor content reaches a maximum of roughly 0.5 km−1 in the middle troposphere, and drops rapidly above 12 km in altitude. Therefore, a conservative coarse level set was selected, with the level spacing in the troposphere at 0.5 km (implying a resolution of 2.0 km−1). Above 11 km, the spacing increases smoothly, up to 2.6 km at the last level, at an altitude of 31.9 km.

3) Instrument model

The two simulated spectrometers (MIR and FIR) have a common spectral resolution (0.5 cm−1) and independent spectral coverage that overlaps at the Q branch of the CO2 ν2 absorption band. The instruments were modeled as classic interferometers, having a sinc function for the instrument line shape. The spectral coverage of the FIR instrument is 200–685 cm−1, and the spectral coverage of the MIR instrument is 650–2050 cm−1. Each instrument thus captures the central Q branch of the CO2 absorption band at 667 cm−1, with roughly 17 cm−1 of extra spectral coverage on the opposite side. Figure 2 shows the upwelling radiance spectra as simulated with LBLRTM for mean Arctic winter (NSA DJF) and tropical (Darwin DJF) profiles. These two profiles represent approximate lower and upper bounds in radiance, since the other profiles have intermediate temperatures. The figure also shows the spectral coverage and overlap between the two simulated spectrometers.

Fig. 2.

Simulated upwelling radiance spectra for the two extreme climatological composites: Darwin summer (gray) and NSA winter (black): (left) FIR and (right) MIR with (top) radiance and (bottom) brightness temperature. These two spectra are approximate upper and lower bounds for all simulated spectra.

Fig. 2.

Simulated upwelling radiance spectra for the two extreme climatological composites: Darwin summer (gray) and NSA winter (black): (left) FIR and (right) MIR with (top) radiance and (bottom) brightness temperature. These two spectra are approximate upper and lower bounds for all simulated spectra.

For the sensor noise covariance [ in Eq. (2)], a diagonal matrix was assumed, meaning no spectrally correlated noise is present in the measurement. A lack of correlated noise implies the noise is fully described by the noise-equivalent delta radiance (NEDR) curve—the matrix is simply a diagonal matrix, with the NEDR values along the diagonal. The assumed NEDR curves are shown in Fig. 3. In our information content analysis, additional comparisons are made with higher noise levels in each instrument, which is just a simple multiplicative factor of 3 at all frequencies. The dashed lines in Fig. 3 represent the high-noise levels. The spectral coverage and NEDR curves are intended to roughly approximate the expected characteristics of CLARREO (Mlynczak 2010). The noise of the real interferometers will likely be a combination of the low-noise MIR and the high-noise FIR NEDR curves. The low-noise curve for the FIR NEDR is mainly hypothetical, but allows comparison between two simulated instruments that have roughly similar minimum noise levels in radiance units.

Fig. 3.

NEDR curves for FIR and MIR sensors, with the “high-noise” version shown with dashed curves.

Fig. 3.

NEDR curves for FIR and MIR sensors, with the “high-noise” version shown with dashed curves.

In addition to the high-noise-level comparison, a high-spectral-resolution variant of the basic instrument is also compared with the information content analysis. The high-resolution version has a factor of 4 increase in spectral resolution, so the wavenumber increment is reduced to 0.125 cm−1 in those cases. The same NEDR curve is used in this case, sampled at the higher-resolution wavenumber grid. This does imply the observation would require a factor of 4 longer in dwell time, since the interferogram would need to be measured over a longer optical path difference with the same scan rate.

b. Channel selection

Since our study is focused on the retrieval of the atmospheric temperature and water vapor profile, the surface characteristics are not modeled or retrieved, and we assumed a gray surface with ε = 0.95. The large number of channels in the MIR “window” contains completely redundant information because of our surface assumption. In addition, because the stratospheric ozone profile is not contained within our radiosonde data, we have no good a priori information about the ozone mean and covariance. Thus, we ignore most of the MIR window region, and the primary ozone absorption band at 1040 cm−1, by removing the spectral channels in the range 770–1228 cm−1 in all of our modeling and analysis.

It is well known that many of the O(103) spectral elements in the high-spectral-resolution measurements contain highly correlated and thus redundant information. Of course, the redundant information can sometimes be used to increase the effective signal-to-noise ratio, but in other cases removing the redundant information will make the retrievals more robust to potential forward-model errors and improve convergence. To quantify some aspects of the impact of channel selection, we perform channel selection in two ways and investigated the impact on the retrieval statistics.

The first channel selection method is intended to improve performance in the presence of the forward-model errors. The simple ad hoc method simply removes channels that show radiance changes larger than half the NEDR level after the forward model is perturbed. The channel identification was performed for the three primary trace infrared absorbers—namely methane, ozone, and nitrous oxide. The “ignore list” consists of those channels in the strongest parts of the absorption bands for these molecular species—approximately 1300 cm−1 for methane and nitrous oxide, 700 cm−1 for ozone (this is the second most important absorption band, after the absorption band at 1040 cm−1, which is removed from our analysis—see above), and 590 cm−1 for nitrous oxide. The ignored channels are identified in Fig. 4 for the spectrum simulated from the Darwin DJF prior profile.

Fig. 4.

Simulated spectrum for Darwin DJF prior profile, with circles overlying channels ignored because of interference by trace gas absorption or primary sensitivity to surface emission. Channels at 590 cm−1 are associated with nitrous oxide; 700 cm−1, ozone; and 1300 cm−1, methane and nitrous oxide.

Fig. 4.

Simulated spectrum for Darwin DJF prior profile, with circles overlying channels ignored because of interference by trace gas absorption or primary sensitivity to surface emission. Channels at 590 cm−1 are associated with nitrous oxide; 700 cm−1, ozone; and 1300 cm−1, methane and nitrous oxide.

The second channel selection method is more sophisticated, and uses the method suggested by Rodgers et al. (1996), which selects channels in order to maximize the information content. By truncating the selection at a number smaller than the total number of available channels, the retrieval can operate with a much smaller dimension measurement space, while theoretically utilizing almost the same information content and achieving the same retrieval performance. Since the selection algorithm depends on the prior covariance and sensor-noise covariance, the algorithm must be run independently on each prior composite (e.g., for each seasonal composite) for each choice of the NEDR and sensor resolution. The channel selection algorithm is run on the full set of 40 state levels, even though the stratospheric levels contain synthetic information. In later analysis the information content will be computed only for the tropospheric levels, since these contain the “real” profile information derived from radiosonde data.

c. Simulated forward-model errors

Since the state vector in the retrieval algorithm only contains the temperature and water vapor concentration per level, the surface temperature, surface emissivity, and trace gas profiles are not retrieved. These state variables are set to the a priori values for all baseline retrievals. For the surface properties, the assumed a priori value is the mean temperature in the lowest atmospheric level with a gray emissivity of 0.95. For the trace gas profiles, the corresponding standard atmosphere profile is assumed.

If the upwelling radiance is simulated with a different surface property or trace gas profile, the difference essentially creates a forward-model error. The retrieval assumes the a priori value for that property, but it is not allowed to vary that parameter to find a more optimal solution. We applied random differences to several such state variables to create such forward-model errors. For the surface perturbation, since we assumed a gray emissivity, perturbations to temperature or emissivity would produce identical effects, so the perturbation is only applied to temperature. The perturbation in this case in an additive error, drawn from a Gaussian probability distribution function (PDF) with a standard deviation of 0.25 K. For trace gas profiles, we focused on methane, ozone, and nitrous oxide, since these are the primary infrared active trace gases. Since we do not have any detailed a priori information about profile variation, we used a single multiplicative error applied to the entire standard atmosphere profile. The assumed error is again drawn from a Gaussian PDF with a standard deviation of 2.5%. These variations are roughly consistent with observed seasonal variations in total column methane and nitrous oxide (Dils et al. 2005).

3. Retrieval error statistics

The first set of simulation experiments consisted of retrievals of the prior profile over an ensemble of random sensor-noise realizations. The baseline set has no forward-model perturbation, so these retrievals represent the best possible performance, where the random variation in the retrieved state profiles is caused by the random sensor noise. The error statistics can thus be compared to the baseline results to determine if the noise level is significantly above the noise “floor” because of the sensor.

The basic retrieval error statistic is the RMS of the difference between the mean retrieved profile and the truth (prior) profile. The mean profile is computed by averaging over the set of 30 retrievals computed with independent sensor-noise realizations. Any retrieval that did not converge were discarded; this only occurred for surface temperature perturbations to profiles with low water vapor.

RMS results

Our original a priori climatologies were drawn from the three ARM sites: TWP-Darwin, SGP, and NSA. To simplify the analysis we focused on four particular composites that span the full range in temperature and total column water vapor: TWP-Darwin summer (DJF), SGP summer (JJA), SGP winter (DJF), and NSA winter (DJF). The prior profiles for these four composites are shown in Fig. 5.

Fig. 5.

Prior (left) temperature and (right) water vapor profiles for the four climatological composites used in the analysis. The precipitable water vapor (PWV) amounts for these profiles are 38 mm (Darwin DJF), 25 mm (SGP JJA), 6.2 mm (SGP DJF), and 1.3 mm (NSA DJF).

Fig. 5.

Prior (left) temperature and (right) water vapor profiles for the four climatological composites used in the analysis. The precipitable water vapor (PWV) amounts for these profiles are 38 mm (Darwin DJF), 25 mm (SGP JJA), 6.2 mm (SGP DJF), and 1.3 mm (NSA DJF).

We also decided to focus analysis on methane and nitrous oxide and ignore ozone, because the retrieval errors due to the forward-model perturbations in ozone were much less significant than methane and nitrous oxide. We are not implying that ozone perturbations in general would be less significant than the other trace gases. Given our simplifying assumptions (2.5% changes to the total gas profile), ozone is less important. In the real atmosphere, the reverse may be true if the ozone has the most variable concentration.

The results of the RMS errors for these four climatologies are shown in Fig. 6. The solid lines in each plot show the errors using the full continuous channel sets for each retrieval (though the MIR does not use the main ozone absorption band or the redundant surface channels; see section 3). Note the RMS temperature error plots have a common y axis range except for the plot corresponding to the surface temperature perturbation. The RMS water vapor error plots have identical y axis ranges on a logarithmic scale.

Fig. 6.

(left) RMS error for temperature and (right) water vapor mass mixing ratio for various simulated forward-model errors. The results are shown for MIR (square markers, dark gray lines) and FIR (X markers, light gray lines). Solid lines use maximum channels, and dashed lines ignore channels with significant interference. Note the y-axis range for temperature errors is identical for all perturbation plots, except for the larger range for the surface temperature perturbation. The y-axis display range for all water vapor errors is identical and logarithmic.

Fig. 6.

(left) RMS error for temperature and (right) water vapor mass mixing ratio for various simulated forward-model errors. The results are shown for MIR (square markers, dark gray lines) and FIR (X markers, light gray lines). Solid lines use maximum channels, and dashed lines ignore channels with significant interference. Note the y-axis range for temperature errors is identical for all perturbation plots, except for the larger range for the surface temperature perturbation. The y-axis display range for all water vapor errors is identical and logarithmic.

The baseline temperature error is in the range 0.05–0.12 K, while the baseline water vapor error is in the range 0.05 g kg−1 for the tropical profile down to 0.003 g kg−1 for the Arctic profile. The baseline errors are approximately equal when comparing the MIR and FIR retrievals.

The different sensitivities qualitatively follow our expectations, given knowledge of the location of the absorption bands and the impact of the highly variable total column water vapor on the different climatologies. First, the surface temperature perturbation shows a steep increase in temperature error as the water vapor decreases, which is expected since the lower water vapor means relatively more radiance from the surface is detected. The induced error in the retrieved water vapor is also relatively larger for the drier profiles. The tropical summer profile (Darwin DJF) shows no sensitivity to the surface temperature perturbation in the FIR, since all channels are effectively opaque from the surface to space.

The perturbation to methane only affects the MIR, since there are no strong absorption features in the FIR. The magnitude of the temperature error caused by the methane perturbation drops significantly for the NSA DJF profile, since the water vapor absorption lines that occur in the same channels as the methane absorption lines are weaker and thus there is less interference. At the other extreme of high water vapor in the Darwin DJF profile, many of the channels are saturating with water vapor absorption, which also reduces the impact of the methane perturbation. The same approximate pattern is seen in the water vapor error in that the NSA DJF profile has the smallest induced error, but the error in the other three profiles is of similar magnitude.

Finally, the perturbation to nitrous oxide produces a large temperature error for the SGP DJF profile in the MIR, but small errors in the other three profiles. The water vapor error is increased for all but the NSA DJF profile. Since the FIR has a significant nitrous oxide absorption feature, the temperature error for the FIR retrievals shows increased error. The nitrous oxide absorption feature is at the edge of the carbon dioxide absorption band, so the effect on the water vapor error is insignificant.

The second set of dashed lines in each plot show the errors after removing the ignore list of channels with strong absorption features for the trace gases (see section 3). The baseline and surface temperature perturbation results are not changed in any significant way, as expected. The error results for the methane and nitrous oxide perturbations are significantly improved, with most results equivalent to the baseline error levels. The methane perturbation still causes small temperature errors for SGP DJF in the MIR, and small water vapor errors for all profiles except for NSA DJF. The nitrous oxide perturbation still causes small water vapor errors for the SGP JJA profile. These small residual errors are caused by the remaining aggregate effects of the weaker absorption lines.

Figure 6 does not show the error results for the further experiments with increased sensor noise, increased spectral resolution, or with further channel “thinning” with the optimal selection techniques (section 3). These other experiments had only marginal impact on the resulting RMS errors. In all cases, the errors were less than 0.2 K for the retrieved temperature profiles, and less than 0.1 g kg−1 for the retrieved water vapor mass mixing ratio profiles. These other experiments are the focus of the information content analysis in the next section.

4. Information content

For our information content analysis, we use the degrees of freedom for signal (DFS), which is defined as the trace of the averaging kernel matrix . The averaging kernel is defined as the product of the Jacobian and its generalized “inverse” matrix (Rodgers 2000):

 
formula

Since we are primarily interested in the tropospheric information, and the stratospheric data is synthetic, all of our calculations of the DFS for comparison purposes are based on the tropospheric levels. The DFS presented in this section is a partial trace of , where the diagonal elements corresponding to the tropospheric levels are summed. The number of elements summed is equal to the average level number of the tropopause for one entire year, since the tropopause level changes with season (see section 1). The number of levels in the sum is 20, 24, and 32 for the NSA, SGP, and TWP-Darwin data, respectively.

As a complement to the information content estimate from DFS, direct examination of the averaging kernels can be used to estimate the vertical resolution of the retrieved profile. The averaging kernels are the rows of the matrix in Eq. (4), and represent the smoothing kernel that acts at each level in the retrieved state estimate (Rodgers 2000). Figure 7 shows a subset of the averaging kernels (every fifth kernel) for a single retrieval using the Darwin DJF a priori. By computing the full width, half maximum (FWHM) of the linearly interpolated kernel (the short black vertical segment in Fig. 7), the vertical resolution as a function of altitude can be estimated.

Fig. 7.

Selected averaging kernels for (left) temperature and (right) water vapor. Every fifth averaging kernel is plotted in order to clearly separate the different lines. The thick vertical line on the third water vapor averaging kernel shows the FWHM computed from the linear interpolation.

Fig. 7.

Selected averaging kernels for (left) temperature and (right) water vapor. Every fifth averaging kernel is plotted in order to clearly separate the different lines. The thick vertical line on the third water vapor averaging kernel shows the FWHM computed from the linear interpolation.

The experiments using forward-model perturbations did not result in significant differences in the information content, so in this section we focus only on the sensor configuration modifications (increased noise level and increased spectral resolution) and the optimal estimation channel selection. For the channel selection, we chose to retain 250 channels within each spectral range for the baseline and increased noise experiments and 500 channels for the increased-spectral-resolution experiment. This choice was arbitrary, but guided by the shapes of the information content curve. Figure 8 shows the information content as channels are selected for one of the climatological composites. The shapes of the curves for the other composites are nearly identical, although the magnitude differs. Typical of these plots, the information rises rapidly for the first O(10) channels, as the initially selected channels are almost statistically independent. As more channels are added, the information increase slows rapidly. By examining Fig. 8, we see that our choice of 250 channels (500 for increased spectral resolution) retains at least 80% of the total DFS in all cases.

Fig. 8.

DFS as a function of the number of channels selected by the optimal selection technique. Each curve is normalized by the total DFS within that configuration.

Fig. 8.

DFS as a function of the number of channels selected by the optimal selection technique. Each curve is normalized by the total DFS within that configuration.

The selected channels are displayed in Fig. 9 for the Darwin DJF and NSA DJF composites. Several key features can be noted in these plots. The lack of selected channels in the range 800–1200 cm−1 was forced by our initial removal of the redundant surface channels from any analysis. The lack of selected channels at wavenumbers larger than 1700 cm−1 is not forced a priori, and it is simply a consequence of the low signal-to-noise ratio in the high wavenumber half of the water vapor vibrational–rotational absorption band. The only strong difference in selection between the two climatological composites appears to be in the edge of the MIR water vapor absorption band. The low wavenumber absorption lines are too weak in the NSA DJF composite to contain useful information, so they are not selected by the algorithm. No significant differences are noted between the FIR channel selection in each climatological composite.

Fig. 9.

Selected channels within the Darwin DJF and NSA DJF brightness temperature spectra. The black circles mark the 250 channels selected within each spectral range by the optimal selection method.

Fig. 9.

Selected channels within the Darwin DJF and NSA DJF brightness temperature spectra. The black circles mark the 250 channels selected within each spectral range by the optimal selection method.

a. MIR and FIR spectrometer comparison

Figure 10 shows the information content, in terms of DFS, for various sensor configurations applied to each of the four climatological composite priors. The solid lines show the DFS for the full channel set, minus the small number of channels ignored because of interference from methane and nitrous oxide. The dashed lines show the DFS after the optimal estimation selection algorithm reduced the channel number to 250 (500 for the higher-spectral-resolution configuration).

Fig. 10.

DFS for the (left) temperature profile and (right) water vapor profile. The results are shown for MIR (square markers, dark gray lines) and FIR (X markers, light gray lines). Solid lines use most channels (only ignore list channels are not used), and dashed lines use the optimally selected subset (250 channels, or 500 channels with the higher spectral resolution).

Fig. 10.

DFS for the (left) temperature profile and (right) water vapor profile. The results are shown for MIR (square markers, dark gray lines) and FIR (X markers, light gray lines). Solid lines use most channels (only ignore list channels are not used), and dashed lines use the optimally selected subset (250 channels, or 500 channels with the higher spectral resolution).

The temperature profile information content in the two spectral bands is nearly equal in most cases, with a slight advantage with the FIR, mostly in the higher-spectral-resolution simulations. For the Darwin prior, the advantage is lost, probably because of the loss in sensitivity to the lower troposphere as the high water vapor concentration makes the atmosphere completely opaque throughout the FIR. All scenarios show more temperature information content in the midlatitude winter composite, compared to the tropical, midlatitude summer or Arctic profiles. Since some temperature information can be obtained from the water vapor lines, the loss of information content in the tropical and midlatitude summer profiles is likely due to increased saturation of water vapor lines. Similarly, the decrease in the Arctic profile is likely due to the opposite effect, in which the weak water vapor absorption causes weaker lines to fall below the useful detection limit imposed by the sensor noise.

The water vapor DFS shows a slightly different pattern, in that the FIR has a slightly larger information content (by 0.5–2.0 DFS) in all scenarios. The increase is largest for the tropical profiles, which is somewhat surprising since the large water vapor absorption implies the lowest level is not detectable. However, much of the water vapor variation in the tropical profile is in the middle-to-upper troposphere, so the “invisible” lower troposphere carries less weight in terms of DFS because there is little available information outside the climatological prior PDF. The increased DFS relative to the MIR is related to upper-tropospheric information. The FIR has an advantage in a signal-to-noise ratio sense for upper-tropospheric water vapor emission, since the lower emission temperatures will favor observations at the lower wavenumbers because of the wavenumber and temperature dependence of the Planck function.

In Fig. 11, the average vertical resolution for the troposphere levels is shown for the various sensor configurations and priors. The layout and symbols match those shown in Fig. 10 for the degrees of freedom for signal. The overall comparison is fairly similar to the DFS, but in this case the FIR shows a resolution advantage in a larger number of different conditions. The poorer resolution in temperature for the Darwin prior, for both sensors, is primarily due to the inclusion of the upper-troposphere levels in the tropical atmosphere. The FWHM of the averaging kernel increases with altitude, so the inclusion of the high-altitude (12–17 km) kernels will inflate the overall mean FWHM as seen in the plot.

Fig. 11.

Average vertical resolution within the troposphere from the mean averaging kernel FWHM for (left) temperature and (right) water vapor. Markers identical to Fig. 10.

Fig. 11.

Average vertical resolution within the troposphere from the mean averaging kernel FWHM for (left) temperature and (right) water vapor. Markers identical to Fig. 10.

b. Combined spectrometer

As a way of visualizing the different information content in the two spectral bands, we performed an additional set of constrained channel selections using the optimal selection algorithm. First, a set of 250 channels was selected from the MIR spectral band using the optimal selection technique as previously described. The total channel sets are then merged into one combined set, and the optimal selection is continued, but with the constraint that the initial 250 MIR channels are fixed. A further 250 channels are selected from the merged channel set. The process is repeated in another channel selection experiment by using 250 channels from the FIR spectral band as the constraint. The approach is similar to the constrained sequential selection in Rabier et al. (2002).

First, by comparing the selection ranks, we can get a qualitative picture of which channels contain useful information. Figure 12 shows the selection ranks by applying the method to the Darwin DJF prior. The first 250 channels in each selection are constrained to one spectral band, and the following 250 channel selections are pulled from the combined FIR + MIR channel set. The top plot shows the results for the initial channel selection from the FIR channels, and the bottom plot shows the results for the initial channel selection from the MIR channels. The channel selection from the combined channel set after the FIR selection shows that new information is gained by adding additional channels in the carbon dioxide absorption band. Even though the MIR and FIR sensors’ spectral coverage overlaps here, the information is not completely redundant since the wavenumber grids are offset from one another. Since the true absorption lines are much narrower than the 0.5 cm−1 width of the spectral channels, the weighting functions can be quite different even though there is much spectral overlap. The high wavenumber side of the carbon dioxide absorption band also sees less interference from water vapor absorption lines, so these MIR channels introduce some independent temperature information. Some MIR water vapor channels are also selected, only at the low wavenumber edge of the water vapor absorption band. After roughly 100 channels are selected, the combined selection switches back to selecting water vapor channels primarily from the FIR spectral band. The selection order implies that the residual information in the FIR channels is higher.

Fig. 12.

Constrained combined channel selection from both baseline sensors. The vertical axis is the selection rank. (top) The first 250 channels are constrained to the FIR sensor, and the next 250 selections are made from the combined FIR+MIR channel set. (bottom) The ranks for the initial 250 selections are constrained to the MIR sensor.

Fig. 12.

Constrained combined channel selection from both baseline sensors. The vertical axis is the selection rank. (top) The first 250 channels are constrained to the FIR sensor, and the next 250 selections are made from the combined FIR+MIR channel set. (bottom) The ranks for the initial 250 selections are constrained to the MIR sensor.

The same conclusion about the water vapor information content is supported by the selection initially constrained to the MIR channels (bottom plot of Fig. 12). In this case, the channel selection in the merged set moves almost entirely into the FIR channels. There is less of a concentration of selected channels inside the carbon dioxide absorption band (600–685 cm−1), compared to the FIR-only selection in the top plot, indicating that relatively more water vapor information is gained in the channel selection from the combined channels.

The actual number of DFS involved is listed in Table 1. For each of the four climatological composite priors, the DFS is shown for a 250- and 350-channel selection from one spectral band (the first and second columns). The third column shows the DFS for a selection using 250 channels selected from the single spectral band and the remaining 100 channels drawn from the merged channel set. The fourth column, labeled Δ, shows the difference between the third and second columns. For example, with the Darwin DJF prior (the first row in Table 1), the FIR channel selection with 250 channels has 12.2 DFS, and extending the selection to 350 channels increases this to 12.5 DFS. Instead, if the 100 channels (251–350) are selected from the merged FIR and MIR channel set, the final DFS is 13.7, implying 1.2 additional DFS are obtained by including MIR spectral information. Thus the fourth column shows the additional DFS included from the other spectral band; in Table 1 we see that the DFS gain from “adding” the FIR to the MIR is significantly higher than the DFS gain from adding the MIR to the FIR.

Table 1.

Tropospheric DFS for various scenarios with constrained channel selection across the combined spectrometer. Both channel selections derived from baseline sensors.

Tropospheric DFS for various scenarios with constrained channel selection across the combined spectrometer. Both channel selections derived from baseline sensors.
Tropospheric DFS for various scenarios with constrained channel selection across the combined spectrometer. Both channel selections derived from baseline sensors.

The initial comparison summarized in Table 1 involved the two baseline sensors. As described in section 3, the more realistic representation of CLARREO would compare the higher-noise FIR sensor to the baseline-noise MIR sensor. By repeating the same constrained channel selection experiment with the more realistic pair of sensors, we see the increased information content in the FIR spectra is lost. Figure 13 and Table 2 show the results from this second experiment, and are directly comparable to Fig. 12 and Table 1 derived from the comparison between both low-noise sensors. The channel selection ranks in Fig. 13 show skew toward selection of MIR channels in the selection from the combined channel list instead of the preference for FIR channels in Fig. 12. The DFS metric, summarized in Table 2, shows a much larger DFS gain from the MIR channels, which is in agreement with the results from channel selection ranks.

Fig. 13.

As in Fig. 12, but using the high-noise FIR sensor with ×3 NEDR.

Fig. 13.

As in Fig. 12, but using the high-noise FIR sensor with ×3 NEDR.

Table 2.

Tropospheric DFS for various scenarios with constrained channel selection across the combined spectrometer. MIR selections from baseline sensor, and FIR selections from high-noise sensor (×3 NEDR).

Tropospheric DFS for various scenarios with constrained channel selection across the combined spectrometer. MIR selections from baseline sensor, and FIR selections from high-noise sensor (×3 NEDR).
Tropospheric DFS for various scenarios with constrained channel selection across the combined spectrometer. MIR selections from baseline sensor, and FIR selections from high-noise sensor (×3 NEDR).

5. Discussion

To quantitatively compare the FIR and MIR spectral bands for water vapor and temperature sounding, we performed several sets of simulation and retrieval experiments. The first experiments with simulated forward-model errors showed a similar sensitivity to surface radiance (temperature or emissivity) errors for low integrated water vapor column amounts, but much less sensitivity for high water vapor column amounts where the FIR becomes completely opaque. The MIR is also more sensitive to perturbations in the two infrared active trace gases (methane and nitrous oxide), although the sensitivity can be eliminated by removing the trace gas sensitive channels from the retrieval. The absorption features of the trace gases are narrow enough that little water vapor and temperature information is lost by removing the trace gas sensitive channels.

The next experiments involved simulation of spectra for several different sensor configurations. The temperature and water vapor profile information content was computed within each spectral band for these different configurations. The two spectral bands showed very similar changes for increased spectral resolution and increased sensor noise. The primary difference between the two spectral bands is in the high water vapor (tropical) prior profile, where the FIR shows less information content in the temperature profile, and has no advantage over the MIR for temperature. For the water vapor information content in this profile, the FIR shows the largest advantage relative to the MIR. In the other conditions, the FIR shows a small advantage over the MIR in both temperature and water vapor. The comparison based on the width of the averaging kernels shows similar results, with the FIR showing a resolution advantage in almost all conditions and equivalent resolution in the remaining case (SGP DJF).

Although in almost all cases (except for temperature information in the tropical profile) the FIR shows a larger information content and improved vertical resolution compared to the MIR, we stress that these comparisons were made with roughly equivalent NEDR levels with each simulated sensor. Initial work on the CLARREO system design (Mlynczak 2010) suggests that the FIR sensor will have a noise that matches our higher-noise configuration, so the most realistic sensor comparison would match the low-noise MIR with the high-noise FIR sensor within our framework. In the case of higher noise in the simulated FIR sensor, the information content in the MIR is larger.

The final set of experiments investigated the relative information tropospheric content of the two spectral ranges in terms of the DFS. The first comparison used equivalent noise levels in the two simulated sensors. Using a selection of 250 MIR channels, followed by a selection of 100 channels from the merged FIR+MIR, we calculated an increase of 15%–19% tropospheric DFS relative to the MIR-only channel selection. When the FIR channels were selected first, the MIR added 1%–11% additional DFS relative to the FIR-only channel selection. Switching to a more realistic noise level for the FIR instrument, the additional DFS by adding the FIR channels to the MIR drops to approximately 4%–6%, and the additional DFS by adding the MIR to the FIR increases to 8%–23%. These precise values are of course strongly dependent on the number of channels selected in each step, but the relative comparison between the FIR and MIR is consistent. Clearly, the DFS is quite sensitive to the sensor noise level, and it is important to note that the comparison shows the information advantage changes significantly within a small range of plausible NEDR figures. At the same noise level, the FIR clearly has an advantage, and the extra information is primarily in the water vapor profile. The advantage is likely due to the increased signal-to-noise ratio (SNR) of the FIR measurements. The larger SNR is mainly a consequence of the shape of the blackbody emission curve for terrestrial atmospheric temperatures. Inspection of Fig. 2 shows how much more radiance is shown in the FIR water vapor absorption lines compared to the MIR absorption lines, and the difference is larger for the colder (Arctic) profile. The fact that the FIR contains a roughly constant DFS advantage over the MIR for varying total column water vapor supports this comparison, since the constant DFS implies a relatively larger fraction in the FIR for the smaller total water vapor.

Acknowledgments

The radiosonde data utilized in this study were obtained from the Atmospheric Radiation Measurement (ARM) Program sponsored by the U.S. Department of Energy, Office of Science, Office of Biological and Environmental Research, Climate and Environmental Sciences Division. This work was supported by NASA Grant NNX08AP44G as part of the CLARREO program, and DOE Grant DE-FG02-06ER64167 as part of the ARM program.

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