An improved fast radiative transfer model for special sensor microwave imager/sounder upper atmosphere sounding channels

Authors

  • Yong Han,

    1. Center for Satellite Applications and Research, National Environmental Satellite, Data, and Information Service, NOAA, Camp Springs, Maryland, USA
    2. Joint Center for Satellite Data Assimilation, Camp Springs, Maryland, USA
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  • Paul van Delst,

    1. Science Applications International Corporation, Camp Springs, Maryland, USA
    2. Environmental Modeling Center, National Center for Environmental Prediction, NOAA, Camp Spring, Maryland, USA
    3. Joint Center for Satellite Data Assimilation, Camp Springs, Maryland, USA
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  • Fuzhong Weng

    1. Center for Satellite Applications and Research, National Environmental Satellite, Data, and Information Service, NOAA, Camp Springs, Maryland, USA
    2. Joint Center for Satellite Data Assimilation, Camp Springs, Maryland, USA
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Abstract

[1] Special sensor microwave imager/sounder (SSMIS) on board the U. S. Defense Meteorology Satellite Program satellites includes six upper atmosphere sounding (UAS) channels for probing air temperature in the upper stratosphere and mesosphere. Three of the UAS channels 19–21 are sensitive to the Doppler frequency shift due to Earth's rotation. The sensitivity to the frequency shift in large degree depends on the O2 Zeeman splitting effect, which is a function of the Earth's magnetic field strength and the angle between the Earth's magnetic field and propagation direction of the electromagnetic wave. Since the brightness temperatures can change up to 2 K as a result of the Doppler shift, the fast radiative transfer model developed earlier for the SSMIS UAS channels has recently been improved to take the Doppler shift into account. In the fast model, an averaged transmittance within the channel frequency passbands is parameterized and trained with a line-by-line radiative transfer model that accurately computes the monochromatic transmittances at fine frequency steps within each passband. The model is evaluated by comparing it with the line-by-line model in an independent experiment. The root mean square differences between the two models are 0.21, 0.39, 0.34, and 0.19 K for channels 19–22, respectively. Using the model, the sensitivities of the radiances to the Doppler shift are analyzed through simulations. A theoretical explanation is given for the dependence of the sensitivities on the Zeeman splitting effect. Results from the analysis are then compared to the observations and a good agreement is achieved.

1. Introduction

[2] Special sensor microwave imager/sounder (SSMIS) [Kunkee et al., 2008] on board the U. S. Defense Meteorology Satellite Program (DMSP) satellites includes six upper atmosphere sounding (UAS) channels, channels 19–24. Some of the channel parameters are listed in Table 1. These channels have narrow spectral passbands near the line centers of the O2 magnetic dipole transitions and their sensitivities peak in the upper stratosphere and mesosphere. Due to Zeeman splitting, the energy received in some of the UAS channels is partially polarized and depends strongly on the geomagnetic field and its orientation with respect to the propagation direction of the electromagnetic wave. To assimilate measurements from the UAS channels, a radiative transfer (RT) model was developed for rapid radiance and radiance derivative (Jacobian) calculations, in which the Zeeman splitting effect was taken into account [Han et al., 2007]. However, the frequency shift of the radiation spectrum due to Earth's rotation is ignored in the model.

Table 1. SSMIS Upper-Atmosphere Channel Parametersa
ChannelNumber PassbandsOffset (Line Center) (MHz)Bandwidth (MHz)NEΔT (K)
  • a

    Offset: passband central frequency offset from the unsplit O2 transition line center. The line centers of the transitions, represented with 7+, 9+, 15+, and 17+, are 60.434776, 61.150560, 62.997977, and 63.568518 GHz, respectively. The noise-equivalent delta temperature (NEΔT) is for instrument temperature 273.15 K and calibration target 260 K with integration times 12.6 ms for channel 24 and 25.2 ms for channels 19–23.

1920 (15+), 0 (17+)1.352.7
2020 (7+), 0 (9+)1.352.7
214±2 (7+), ±2 (9+)1.31.9
224±5.5 (7+), ±5.5 (9+)2.61.3
234±16 (7+), ±16 (9+)7.350.8
244±50 (7+), ±50 (9+)26.50.9

[3] SSMIS is a conical scanner viewing the Earth at a constant 45o angle from nadir on a polar orbit with an inclination of 98.8° and an average orbital altitude of approximately 850 km. Both the satellite orbital motion and Earth's rotation can have a velocity component in the direction between the sensor and radiation emitter, resulting in Doppler shift in the received radiation spectrum. The Doppler frequency shifts due to the spacecraft motion and Earth's rotation are thereafter referred to as SCDS (SpaceCraft Doppler Shift) and ERDS (Earth Rotation Doppler Shift), respectively. The SCDS has been compensated instrumentally by tuning the frequency of the receiver phase-locked local oscillator as a function of scan angle. This onboard “hardware Doppler” compensation removes the requirement for the RT model to deal with the Doppler shift effect when brightness temperatures are calculated and compared to satellite measurements. However, a similar measure is not implemented for the ERDS. Kerola [2006] gives an example of the simulated brightness temperature (BT) measurements near the equator, where the ERDS is the largest at certain scan positions, showing the affect of the ERDS is up to a couple of tenths of a degree in Kelvin (K). However, it will be shown later that in certain regions the effect can be as large as 2 K, which is significant when compared to the noise level of the radiance data in the sensor data record (SDR), and therefore, the effect should not be ignored in radiance assimilations in these regions.

[4] Work has recently been done to improve the earlier model to take the ERDS into account. The model has been implemented as a module in the community radiative transfer model (CRTM) [Weng et al., 2005; Han et al., 2006] developed at the U. S. Joint Center for Satellite Data Assimilation (JCSDA) for satellite radiance data applications. In the following sections, the model algorithms are described in section 2, followed by an analysis of the radiance sensitivities to the ERDS in section 3. Comparisons of the simulated and observed ERDS effect are presented in section 4. Section 4 also provides evidences confirming that the radiation received by the SSMIS instrument on the DMSP-16 spacecraft is right-circularly polarized (RCP), not left-circularly polarized (LCP), under the Institute of Electrical and Electronics Engineers definition.

2. Model Algorithm

[5] The Zeeman splitting effect is an important factor in modeling radiances for the UAS channels and algorithms to deal with the effect have been developed and implemented in the earlier model [Han et al., 2007]. Since the algorithms are retained in the improved model, a brief summary of the model is given below.

2.1. Fast Model With No Spectral Frequency Shift

[6] The SSMIS UAS channels measure radiation originating mainly from the upper stratosphere and mesosphere. In these regions, the O2 transition lines are narrow, and the Zeeman splitting [Lenoir, 1968] may occur. The line can split into three groups of sublines, usually referred as the π, σ+, and σ− components. The total spread width of the sublines is on the order of 0.05B MHz, where B is the magnitude of the Earth magnetic field vector, which may take a value in the range of 23–65 μT near the Earth surface. SSMIS channels 19 and 20 have passbands centered on the transition lines, designated as 7+, 9+, 15+, and 17+ [Rosenkranz, 1993], with passband widths about 1.3 MHz and therefore are strongly influenced by the Zeeman effect. The differences in radiance modeling with and without considering this effect may exceed 10 K in BT. The other four channels each have four passbands, paired, and situated symmetrically on opposite sides of the transition lines 7+ or 9+ with increased bandwidths and band frequency offsets from the line centers as the channel number increases. Thus, their sensitivity to the Zeeman effect decreases with the channel number. For channels 23 and 24, the Zeeman effect is negligible.

[7] For circular polarization, the spectral intensity of thermal microwave radiation may be expressed by a 2 × 2 BT coherent matrix with the RCP and LCP components Tb,R,ν and Tb,L,ν as the diagonal elements and the coherency Tb,RL,ν and its complex conjugate T*b,RL,ν as the off-diagonal elements, where ν is the frequency. The solution solving the radiative transfer equation for the coherent matrix at the top of atmosphere (TOA) is given in the work of Rosenkranz and Staelin [1988]. The SSMIS channel radiance, either RCP or LCP, represented by Tb,ch, is computed by convolving Tb,R,ν or Tb,L,ν with the channel's spectral response function (SRF). The Tb,ch is a function of air temperature Ta, B, and cos(θB), which is the cosine of the angle between the Earth's magnetic field and propagation direction of the electromagnetic wave. For a monochromatic model, this computational process is usually referred as line-by-line (LBL) calculation. An LBL model for channel radiance calculations is computationally expensive because it requires the averaging of multiple monochromatic calculations within a spectral band. The fast model for operational applications such as radiance assimilations was developed to mimic the performance of the LBL model. In the fast model, the channel transmittance, defined as the convolution of the SRF with the transmittance spectrum, is predicted for an atmosphere divided into N layers, as

equation image

where

equation image

and

equation image

where i and k are layer or level indexes starting from the top of the atmosphere, θ is the zenith angle, σi is optical depth of the ith layer, xi,j and ci,j are the jth predictor and the corresponding coefficient, τch,i is channel transmittance, and Ta,i is the air temperature of the ith layer. The predictors are combinations of Ta,i, B, and cos(θB) [Han et al., 2007].

[8] The coefficients ci,j were obtained via regression, for which the channel transmittances were computed using an LBL model [Rosenkranz and Staelin, 1988] and a diverse set of profiles. The profiles are based on the profile set developed at the University of Maryland, Baltimore county (UMBC) [Strow et al., 2003], which contains 48 atmospheric profiles spanning the expected range of profile variability and were mostly selected from the TOVS Initial Guess Retrieval (TIGR) database [Achard, 1991]. The top of each profile was extended vertically from its original 0.005 hPa to 7 × 10−5 hPa (approximately at 110 km) by adding layers from one of the five model profiles [McClatchey et al., 1972], selected according the profile's location and season. The extended portion of the profile is then shifted to preserve vertical continuity at 0.005 hPa.

2.2. Method to Handle Doppler Shift

[9] It can be shown that the radial velocity of the radiation emitters due to the Earth's rotation at a given wave propagation direction k is independent of the distance between the emitters and satellite. The ERDS Δν due to the velocity is given by [Swadley et al., 2008]

equation image

where equation image is the mean frequency of the channel passbands, c is the speed of light, Ω is the angular velocity of the Earth's rotation, Rs is the distance of the satellite from the center of the Earth, ψ is the viewing angle (45°), io is the inclination of the orbit, λ is the latitude (positive in Northern Hemisphere, negative in Southern Hemisphere, and zero at equator) of the satellite nadir point, and ϕ is the scan angle from the satellite orbital motion direction, positive on the right side when facing the motion direction. Scan position 1 in each scan data set with the 30 scan positions corresponds to the east-most pixel for the ascending observations and west-most for the descending observations. The plus and minus signs before the second term in (4) correspond to the ascending and descending orbits, respectively. The first term in (4) is due to the departure of io from 90° and is a positive contribution at ϕ = 0°, since k has a component to the east at this angle. The second term is due to an angle from the north and is zero at ϕ = 0°. Examples of the frequency shift as a function of scan position are shown in Figure 1. It is seen that the shift may reach 75 kHz in the tropical region at the edges of the scan tracks.

Figure 1.

Doppler frequency shift as a function of the scan positions at several satellite latitude positions with solid curves for ascending orbits and dashed curves for descending orbits. Each curve represents two latitude positions with the same absolute latitude value, one with a positive sign in Northern Hemisphere and the other with a negative sign in Southern Hemisphere.

[10] The method applied to handle the ERDS is to use a series of the transmittance coefficient sets, conditioned at different values of Δν added to the radiation spectrum. Each set of coefficients are generated in a similar process as described in section 2.1, in which the radiation spectrum is shifted by a specified amount. The transmittances at an arbitrary value of Δν are obtained through interpolation from the transmittances computed at two adjacent Δν nodes which bracket the desired value. Nine sets of transmittance coefficients are used in the model covering the range from −80 to 80 kHz with a 20 kHz interval. The interval value was adopted after the results of using the interval were compared with those of using finer intervals (the differences were less than 0.05 K). The model was evaluated by comparing it with the LBL model using a profile set independent of the data used to generate the transmittance coefficients. The profile set is from the COSPAR International Reference Atmosphere [Fleming et al., 1988] (CIRA-88). The lower part (0–120 km) of the model profile includes monthly values of the temperature field on the latitude grid points with a 5° interval from 80°N to 80°S, generated from data including ground-based and satellite measurements. Radiances were computed at real SSMIS pixels with the parameters B, cos(θB), and Δν obtained from real data on the following four dates in 2006: 1 January, 1 April, 1 July, and 1 October, with a total sample size of 856,290. The bias and root mean square (RMS) BT differences between the two models are listed in Table 2 for channels 19–22. Channels 23 and 24 are not included in Table 2 since they are not affected by the frequency shift. Listed also in Table 2 are errors evaluated on the dependent profile set (the UMBC 48 profile set), which is used to generate the transmittance coefficients. The RMS differences between the two models from the independent profile set are 0.21, 0.39, 0.34, and 0.19 K for channels 19–22, respectively.

Table 2. Bias and Root Mean Square (RMS) Differences on Dependent and Independent Data Sets Between the Fast and LBL Model Calculations
 Channel 19Channel 20Channel 21Channel 22
Brightness temperature errors (K) on dependent data set
Bias0.01−0.01−0.050.02
RMS0.180.310.250.13
Brightness temperature errors (K) on independent data set (size = 856,290)
Bias−0.09−0.06−0.080.06
RMS0.210.390.340.19

[11] The model described above is the Forward model for radiance simulations. Its Jacobian model has also been developed and implemented in CRTM for radiance derivative calculations with respect to the temperature variables.

3. Radiance Sensitivities to Doppler Shift

[12] The impact of the ERDS on the SSMIS UAS channel radiances is dependent on the Zeeman splitting effect, which is a function of B and cos(θB). Furthermore, the dependence for an RCP system differs from an LCP system. Figures 2a and 2b show the BT differences for an RCP radiometer between the calculations with and without the Doppler shift for channels 19–22 as a function of the frequency shift with the values of B fixed at 30 and 60 μT, respectively. The solid, long-dashed and short-dashed curves in the figures correspond to the three values of cos(θB) (−1, 0, 1), respectively. For an LCP radiometer, the pattern of the BT differences may also be described by Figure 2 but with the three curves corresponding to the three values of cos(θB) (1, 0, −1), respectively. It can be seen that the BTs from RCP and LCP radiometers vary with the Doppler frequency in opposite directions. For channels 19 and 20, the BT differences can reach a value of about 2 K when cos(θB) is near 1 or −1 and become small when cos(θB) is near zero. The dependence of the BT differences on B is larger for smaller B, since the width of the Zeeman splitting becomes narrower for smaller B, resulting in a larger sensitivity to the ERDS. Small B occurs near equator, which may coincide with large ERDS. The temperature profile used in the calculations for Figure 2 is an annual mean of the CIRA-88 profile set at 15°N. It should be pointed out that the magnitude of the BT difference also depends on the temperature lapse rate of the portion of the atmosphere which the channels are sensitive to. As the frequency of the radiation spectrum is shifted, the peak height of the channel's weighting function may shift up or down accordingly, resulting in a decrease or increase of the amount of BT depending on the temperature lapse rate. For channel 21, the situation is complicated by the factor that the peak of the channel weighting function is near the stratopause [Han et al., 2007] at a height which may differ significantly in different locations and seasons. For the temperature profile used for Figure 2, the sensitivity dependency on cos(θB) is similar but the sign with a change of Δν is opposite to those in channels 19 and 20. For channel 22, as well as channels 23 and 24, the effect of the frequency shift is negligible.

Figure 2.

Simulated brightness temperature (BT) differences using the RT models with and without the inclusion of the Doppler shift effect, BT(Δν) − BT(Δν = 0) for an RCP radiometer. The solid, long-dashed and short-dashed curves correspond to cos(θB) = −1, 0, 1, respectively. (a) B = 30 μT and (b) B = 60 μT.

[13] The patterns of the curves in Figure 2 for channels 19 and 20 may be explained with the assistance of Figure 3, which shows an example of the Tb,R,ν and Tb,L,ν spectra near the 9+ line, computed for the United States 76 standard atmosphere at B = 50μT and three values of θB (0°, 90°, and 180°). It can be seen that the spectra of Tb,R,ν and Tb,L,ν are in mirror symmetry, that is, Tb,R,ν at νν0 is the same as Tb,L,ν at ν0ν, where ν0 is the center of the unsplit line. This property may be proved by applying Theorem 3 and equation (45) in the work of Stogryn [1989] and holds in general at other values of B and θB near the line center ν0, where the contributions from other lines may be ignored. The property implies that the LCP and RCP systems with symmetrical passbands would receive the same amount of energy if there is no frequency shift in the radiation spectrum. However, if the spectrum is shifted, the two systems would in general receive a different amount of energy when θB ≠ 90°. The passbands of channels 19 and 20 are about 1.3 MHz in width and are centered on the transition lines of the original spectrum (Δν = 0). It can be seen from Figure 3 that a small positive frequency shift of the spectrum (add a constant to the spectral frequency) would increase Tb,ch for an RCP system at θB = 180° and an LCP system at θB = 0°, but decrease Tb,ch for an RCP system at θB = 0° and an LCP system at θB = 180°. The situation is reversed for a small negative frequency shift. At θB = 90°, the three Zeeman components are all linear polarized and the LCP and RCP systems would observe the same radiance. Notice also that the curves for θB = 90° in Figure 3 are quite flat near the center of the line, implying that the sensitivity to the ERDS would be small under this condition.

Figure 3.

A brightness temperature spectrum near the 9+ transition line centered at ν0 = 61.150560 GHz, for the United States 76 standard atmosphere and B = 50 μT. Note that the curve for the right-circularly polarization (RCP) at θB is identical with that for the left-circularly polarization (LCP) at 180° - θB.

[14] On a global scale, we simulated the measurements of channel 20 for the full day of 1 January 2006. The result is shown in Figure 4, plotted as BT differences between the simulations with and without the inclusion of the effect of the Earth's rotation. It can be seen from Figure 4 that the BT differences can be as large as 2 K, but not necessarily occur in the tropical region where the tangent velocity of the Earth's rotation is the largest, because of the dependence of the effect on the angle θB discussed earlier. For clarity, the corresponding cos(θB) and B data are plotted and shown in Figures 5 and 6, respectively. It can be seen that the BT differences are large at the pixel positions where the ERDSs are large and the values of ∣cos(θB)∣ are close to 1. They become small in high latitudes, where the ERDSs are small, and in regions where the values of cos(θB) are near zero (θB ≈ 90°). Note also the difference of the patterns of the BT differences between the ascending and descending orbits, which is in large degree due to the differences of the angle θB between the two sets of data. Finally, we observe from the cos(θB) images that between 10°N and 40°N from the ascending observations and −40°S and 0° from the descending observations, on some of the scan tracks, the parameter cos(θB) on the east and west sides with respect to the scan position 15 or 16 of the scan track can have approximately the same values and is close to −1 or 1. This feature as well as the fact that the signs of Δν are opposite between the two sides will be used in the following section to compare model results with observations.

Figure 4.

Simulated brightness temperature (BT) differences for channel 20 using the RT models with and without the inclusion of the Doppler shift effect for the ascending and descending observations on 1 January 2006.

Figure 5.

The cosine of the angle between the magnetic field and wave propagation direction for the ascending and descending observations on 1 January 2006.

Figure 6.

The Earth's magnetic field strength in μT at 00:00 Greenwich mean time on 1 January 2006 at the height of 60 km, computed using the 10th International Goemagnetic Reference Field (IGRF) model [Mandea et al., 2000].

4. Comparisons of Simulated and Observed Doppler Shift Effect

[15] It is difficult to compare the model results with observations due to the lack of reliable temperature profiles collocated with radiance measurements at the scan positions where the ERDS is significant. In an experiment discussed below, the CIRA-88 profile set as the model input was used to compare the model results with measurements in a way that the bias originating from the CIRA-88 profiles will be minimized. The difference of the BTs at two scan positions was simulated and then compared with the observation. With a focus on the ERDS effect, the two scan positions were selected at which the values of the ERDS are large and the two parameters B and cos(θB) have respectively about the same values. Specifically, the data selection criteria are the following. The latitudes of the data are confined between 10°N and 40°N for the ascending orbits and between −40°S and 0° for the descending orbits for the reason discussed in section 3. These data were further filtered by selecting data with the absolute values of Δν to be greater than 55 kHz and the variations in B and ∣cos(θB)∣ are less than 1 μT and 0.01, respectively. Finally, the data points on the east and west sides of the same scan were paired according to the smallest difference in cos(θB). The BT differences, BT(west point) - BT(east point), were then computed for each pair of the data points. Note that the ERDS is positive on the west data points and negative on the east data points.

[16] The set of data meeting the above criteria were collected from the SDRs in the period of the entire year of 2006, which include 41,772 pairs of data samples from ascending orbits and 65,476 pairs from descending orbits. The SDR data for channels 19–21 are averages of 6 × 6 footprints with an effective spatial resolution of 75 × 75 km and their NEΔT values in these channels are 1.2, 1.2, 1.18, and 0.86 K (for 305 K scene), respectively [Northrop-Grumman, 2002]. The RMS differences in B and cos(θB) between the paired data points are 0.6 μT and 0.006, respectively, for both the ascending and descending data. The mean values and standard deviations of B, cos(θB), Δν and scan positions of the data set are summarized in Table 3. As listed in Table 3, the values of ∣cos(θB)∣ in the data set are about 0.7, which are the highest value we could obtain for such paired data in order to maximize the radiance sensitivity to the ERDS. The BT differences between the paired data points are plotted as histograms shown in Figure 7, with the solid curves for ascending observations and dashed curves for descending observations. The corresponding mean values and standard deviations of the BT differences are listed in Table 4 in the rows labeled “Measured.” The results show that for channels 19 and 20, there is a positive mean BT difference of about 2 K for the ascending set of data whose cos(θB) values are negative, and a negative difference of approximately the same magnitude from the descending data whose cos(θB) values are positive. For channel 21, the BT differences are relatively small but the signs are opposite to those for channels 19 and 20. Since, as mentioned earlier, Δν is negative on the east edge and positive on the west edge, of the scan track, this pattern of the BT differences in channels 19–21 is consistent with the analysis given in section 3 and is matched to that of an RCP system. The BT differences for channels 22–24 are small, as expected since the ERDS effect is negligible in these channels.

Figure 7.

The histograms of the differences of the measured brightness temperature (BT) between the paired data points on the east and west edges of the scans, BT(west) - BT(east), with the solid curves from the ascending observations (sample size = 41,772) and the dashed curves from the descending observations (sample size = 65,476).

Table 3. Means and Standard Deviations Over the Data Set of n Samples Corresponding to the Results in Table 4 and Figure 7a
 B (μT)cos(θB)East Δν (kHz)West Δν (kHz)East PositionWest Position
  • a

    Means (the first numbers) and standard deviations (the second numbers) of the Earth's magnetic field strength B, cosine of the angle between the magnetic field and the wave propagation direction cos(θB), Doppler frequency shift Δν, and pixel position, over the data set of n samples corresponding to the results in Table 4 and Figure 7. The words “East” and “West” refer to the data pixel positions on the east and west edges of the scans, which containing 30 pixel positions (1–30), numbered sequentially from east to west for ascending orbits and west to east for descending orbits.

Ascending (n = 41,772)41.3, 4−0.66, 0.05−62.2, 3.265.3, 4.52, 126, 2
Descending (n = 65,476)45.3, 70.68, 0.06−63.0, 3.867.4, 4.729, 14, 2
Table 4. Means and Standard Deviations of the Brightness Temperature Differences Between the Paired Data Points on the East and West Edges of the Scansa
 Channel 19Channel 20Channel 21Channel 22Channel 23Channel 24
  • a

    Means (the first numbers) and standard deviations (the second numbers) of the brightness temperature (BT) differences between the paired data points on the east and west edges of the scans, BT(West) - BT(East). The words “measured” and “simulated” refer to the measured and simulated data, respectively, and “RCP” and “LCP” refer to the radiometer systems with right-circularly and left-circularly polarizations, respectively. The issue of polarization is not important in the simulations with no Doppler shift (Δν = 0).

Ascending orbit (n = 41,772)
Measured2.54, 2.142.03, 2.40−0.72, 1.38−0.14, 1.49−0.05, 1.01−0.07, 0.68
Simulated RCP1.79, 0.361.80, 0.37−0.60, 0.280.02, 0.220.04, 0.230.01, 0.14
Simulated LCP−1.71, 0.32−1.67, 0.310.65, 0.210.06, 0.220.03, 0.230.02, 0.14
Simulated Δν = 00.02, 0.24−0.01, 0.240.04, 0.200.04, 0.220.04, 0.230.01, 0.14
Descending orbit (n = 65,476)
Measured−1.84, 2.08−2.02, 2.320.01, 1.80−0.26, 1.45−0.14, 0.97−0.05, 0.65
Simulated RCP−1.59, 0.39−1.82, 0.360.83, 0.260.15, 0.350.14, 0.400.03, 0.26
Simulated LCP1.94, 0.461.72, 0.54−1.01, 0.410.10, 0.350.14, 0.400.03, 0.25
Simulated Δν = 00.16, 0.260.03, 0.340.01, 0.180.15, 0.350.14, 0.400.03, 0.25

[17] Statistics of the BT differences of the above data set are compared with those simulated using the fast model. The results are listed in Table 4. Three sets of simulations were performed. The first two are for RCP and LCP systems, respectively, and the third for an RCP system but without the inclusion of the ERDS. It can be seen that, with the uncertainties in the measurements and model temperature profiles, the model calculations agree with the measurements, except those for channel 21 in the descending orbit. The measured BT difference in channel 21 taken from the descending orbits is near zero, while the simulated BT difference for an RCP radiometer is 0.83 K. The fast model was then checked by repeating the comparisons in which the fast model was replaced by the LBL model described in section 2. The results are similar to those listed in Table 4. The LBL model simulated BT difference in channel 21 is 0.91 K for an RCP radiometer in the descending orbit. Thus, the inconsistency is not due to the error of the fast model. Unfortunately, the inconsistency remains unexplained. Possible causes include errors in the temperature profiles used in the simulations and uncertainties in the measurements. Results in Table 4 also show clearly that the measured radiation is not LCP, because the signs of the simulated BT differences in channels 19–21 under the LCP assumption are opposite to those observed in both the measurements and the simulations for an RCP radiometer. The sign difference shown in Table 4 between the LCP and RCP radiometers can be explained with the theory discussed in section 3. Finally, it is noted that the widths (standard deviations) of the measured BT differences are larger than the simulations, but they decrease with the channel number. One cause for the large widths is likely related to the instrument noise. Another possible cause is the variations of the temperature profiles, which are not possible to be taken into account fully in the simulations with the CIRA-88 profile model.

[18] The BT difference comparisons were also performed with low ∣cos(θB)∣ but large ERDS. As discussed in section 3, in these cases the radiance sensitivity to the ERDS is relatively small even at large values of Δν. Following the procedure discussed earlier, data pairs were selected with the latitudes of the data confined between −40°S and −10°S for ascending orbits and between 15°N and 50°N for descending orbits and the values of ∣cos(θB)∣ limited to be less than 0.3. The statistics of B, cos(θB), Δν and the scan positions over the data set are listed in Table 5. The BT differences between the paired data points are summarized in Table 6. It can be seen that the effect of the ERDS is indeed smaller for smaller ∣cos(θB)∣ and the simulations are in agreement with the observations, considering the uncertainties in the measurements and temperature profiles.

Table 5. The Same as Table 3 Except the Statistics Corresponds to the Results in Table 6a
 B (μT)cos(θB)East Δν (kHz)West Δν (kHz)East PositionWest Position
  • a

    Note the values of ∣cos(θB)∣, which are smaller than those listed in Table 3.

Ascending (n = 36,247)36.9, 11.70.18, 0.07−61.5, 2.564.4, 4.52, 127, 2
Descending (n = 36,247)38.5, 3.50.13, 0.07−60.4, 1.965.6, 4.729, 13, 2
Table 6. The Same as Table 4 Except That the Data Set Is Collected for Low Values of ∣cos(θB)∣
 Channel 19Channel 20Channel 21Channel 22Channel 23Channel 24
Ascending orbit (36,247 samples)
Measured0.05, 2.290.14, 2.470.26, 1.81−0.11, 1.30−0.15, 0.88−0.05, 0.59
Simulated RCP−0.42, 0.44−0.45, 0.350.11, 0.29−0.03, 0.23−0.06, 0.26−0.01, 0.14
Simulated Δν = 0−0.04, 0.31−0.01, 0.24−0.03, 0.21−0.05, 0.23−0.06, 0.26−0.01, 0.14
Descending orbit (57,580 samples)
Measured−0.39, 2.19−0.83, 2.55−0.71, 1.93−0.87, 1.59−0.50, 1.17−0.26, 0.77
Simulated RCP−0.34, 0.37−0.27, 0.44−0.09, 0.33−0.16, 0.36−0.19, 0.39−0.05, 0.24
Simulated Δν = 0−0.05, 0.330.05, 0.40−0.17, 0.32−0.18, 0.36−0.19, 0.39−0.05, 0.24

[19] The main features of the BT differences seen in the measurements are unlikely caused by others factors, such as variations in B and cos(θB), inadequate hardware SCDS compensation and a dependence of instrumental errors on the scan position. The BT differences originating from the differences in B and cos(θB) between the paired data points were evaluated through simulations. The BT variations from the differences in B and cos(θB) between the paired data points are less than 0.2 K, almost an order smaller than the BT differences seen in the measurements. The issue of the inadequate SCDS compensation was discussed in the work of Swadley et al. [2008]. Even if there is a significant SCDS residual, its impacts on the results shown in Table 4 would likely not be significant for the reason discussed below. The SCDS is a symmetric function of the scan azimuth angle about the center of the scan track, varying from a maximum at the center of scan track to ∼34% of the maximum near the scan edges. If the SCDS residual is also symmetric, its effect would be cancelled out by taking the BT differences at the two data points near the opposite edges of the same scan track. On the other hand, if the residual is asymmetric, the patterns of the BT differences would likely be different from those seen in Table 4. This is because the SCDS residual at the east (west) edge of the scan track in the ascending orbit will be at the west (east) edge in the descending orbit, unlike the ERDS which is always negative on the east edge and positive on the west edge. Since the values of cos(θB) associated with the radiance data used in the comparisons change sign from ascending to the descending orbit, according to the theory discussed in section 3, the BT differences between the two scan positions due to the SCDS residual in the ascending orbit will have the same sign as those in the descending orbit, unlike those due to the ERDS, which have different signs in the two orbits as shown in Table 4. The dependence of the measurements of the low atmosphere sounding (LAS) channels on the scan position has been detected in the temperature data record (TDR) data [Yan and Weng, 2008] and corrected for the SDRs. To check the issue for the UAS channels, we note from Table 4 that for channels 23 and 24, whose sensitivity to the ERDS is negligible, the BT differences are very small in both measured and simulated data. This may be an indication that the BT asymmetry of the scans seen in the LAS channels is not significant for channels 19–21 in the experiment, since they share the same antenna feedhorn with channels 23 and 24. Furthermore, the clear dependence of the BT difference on cos(θB) shown in the comparisons discussed earlier further suggests the BT differences seen in the measurements are mainly caused by the ERDS.

5. Conclusions

[20] The ERDS can have an effect of up to 2 K on the BT simulations for SSMIS channels 19–21. This effect has been taken into account in the fast model developed for SSMIS UAS channel radiance assimilations and temperature profile retrievals. The model is evaluated by comparing it with the LBL model on an independent profile set. The RMS BT differences are 0.21, 0.39, 0.34, and 0.19 K for channels 19–22, respectively. Simulations are also compared with observations in an experiment in which the differences of BTs at two selected scan positions are computed and compared to observations. A good agreement is achieved, considering the instrument noises and the use of climatology as the model input. The experiment also confirms the measured radiation in the UAS channels is RCP.

[21] The radiance sensitivity to the ERDS has a strong dependence on cos(θB) and B. Although the magnitude of the ERDS can reach maximum near equator at the pixels on the edges of the scan tracks, the largest impact of the ERDS does not necessary occur near equator because of the dependence on cos(θB). The sensitivity is large if ∣cos(θB)∣ is large and B is small and become small if cos(θB) is near zero. B is usually small in low latitudes, but cos(θB) can vary significantly in these regions. The ERDS is small at high latitudes and therefore can be neglected at high latitudes in radiance simulations. For channels 22–24, the effect of the ERDS is insignificant.

Acknowledgments

[22] The contents of this paper are solely the opinions of the authors and do not constitute a statement of policy, decision, or position on behalf of NOAA or the U. S. Government.

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