Radiative transfer model and its linearization

If scattering by the atmosphere is neglected, the true clear radiance exiting the earth–atmosphere system for a given MODIS IR band with center wavenumber υ is approximated by

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where R_υ is the spectral radiance with wavenumber υ, τ(0, p) is the total transmittance from the top of the atmosphere to the atmospheric pressure p, ε is the surface emissivity, B is the Planck radiance, which is a function of pressure p, subscript s denotes surface, τ* = τ²_s/τ is the downwelling transmittance, and R′ represents the contribution of reflected solar radiation in the infrared region. The reflected infrared solar radiation is considered negligible for bands with wavelengths longer than 4.0 μm during the day.

To linearize Eq. (1), the first-order variations of the Planck and spectral radiances δB = (∂B/∂T)δT and δR = (∂R/∂Tb)δTb are used, where Tb is the brightness temperature. The linearized form of Eq. (1) is

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where Tb_υ is the brightness temperature for the MODIS IR spectral band with center wavenumber υ; W_T, W_q, and W_o3 are the weighting functions (sensitivity functions) of the atmospheric temperature profile, water vapor mixing ratio profile, and ozone mixing ratio profile, respectively. The weighting functions can be calculated efficiently from a given atmospheric state (Li 1994; Li et al. 2000):

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where β(p) = ∂B/∂T/∂R/∂Tb and τ_q and τ_o3 are the water vapor and ozone component transmittance functions, respectively. Figure 2a shows the temperature-weighting functions for the MODIS IR bands 20–25 and bands 27–36 calculated for a U.S. Standard Atmosphere, 1976. Bands 27 and 28 are water vapor absorption bands. However, these bands also provide information about the atmospheric temperature if there is enough moisture in the atmosphere, and provided that the water vapor profile is known or estimated accurately. Bands 33–36 are CO₂ absorption bands that also provide atmospheric temperature information; they can be used to infer the cloud properties with a known atmospheric temperature profile (Frey et al. 1999; Li et al. 2001). The moisture-weighting functions in Fig. 2b show that bands 27 and 28 provide information about the distribution of moisture in the troposphere, and that the window bands 29, 31, and 32 also provide some moisture information due to weak water vapor absorption. The weighting functions in Figures 2a and 2b were computed without any contrast between surface air temperature and surface skin temperature. Under these conditions, MODIS has limited skill in retrieving boundary layer temperature and moisture information. However, if contrast exists between the surface air temperature and surface skin temperature, information about the boundary layer moisture structure can be retrieved with more success. A skin temperature of 5 K warmer than the surface air temperature was used in computing the moisture-weighting functions in Fig. 2c, where increased sensitivity to moisture can be seen near the surface, particularly in the window channels (bands 29, 31, and 32).

Statistical synthetic regression retrieval processing

A computationally efficient method for determining the distribution of atmospheric temperature, moisture, and ozone from satellite sounding measurements uses previously determined statistical relationships between observed or modeled radiances with corresponding atmospheric profiles. In the regression procedure, temperature and moisture are regressed together against radiances from CO₂, water vapor, and window bands. This method is often used to generate a first guess for a physical retrieval algorithm, as is done in the International Television and Infrared Observation Satellite (TIROS) Operational Vertical Sounder (TOVS) Processing Package (ITPP; Smith et al. 1993). The statistical regression algorithm for atmospheric temperature is described in detail in Smith et al. (1970), and is summarized below for cloud-free skies.

The general inverse solution of Eq. (2) for the atmospheric profile can be written as (Smith et al. 1970)

i,ki,nn,k(5)

where i is the number of parameters to be retrieved, k is the number of profiles and surface data in the training sample, and n is the number of channels and other predictors used in the regression procedure. The statistical regression algorithm seeks a “best fit” operator matrix 𝗔 that is computed using least squares methods with a large sample of atmospheric temperature and moisture soundings and collocated radiance observations. Minimizing the difference between synthetic observations and the regression model,

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yields

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where (𝗬^T 𝗬) is the covariance of the radiance observations and (𝗬^T 𝗫) is the covariance of the radiance observations with the atmospheric profile.

In the MODIS regression procedure, the primary predictors [𝗬 in Eq. (5)] are infrared spectral band brightness temperatures. The algorithm uses 12 infrared bands with wavelengths between 4.465 and 14.235 μm (see Table 2). Quadratic terms of all brightness temperature predictors are also used as separate predictors to account for the nonlinear relationship of moisture to the MODIS radiances. Surface emissivity effects in the shortwave window bands are mitigated by regressing against band differences [e.g., instead of BT(4.5 μm) and BT(4.4 μm), the difference, BT(4.5 μm) − BT(4.4 μm) is used in the regression, where BT represents brightness temperature]. See section 3d for more discussion on surface emissivity uncertainty. In addition to the primary predictors, estimates of surface pressure, latitude, month, and percentage of land are also used as predictors to improve the retrieval.

Ideally, the radiance predictors 𝗬 would be taken from actual MODIS measurements and used with time- and space-collocated radiosonde profiles 𝗫 to directly derive the regression coefficients 𝗔. In such an approach, the regression relationship would not involve any radiative transfer calculations. However, radiosondes are only routinely launched 2 times per day at 0000 and 1200 UTC simultaneously around the earth; Terra passes occur at roughly 1100 and 2300 LST each day. It is, therefore, not possible to obtain many time- and space-collocated radiosondes and MODIS radiances that are globally distributed at a wide range of locations. Alternatively, synthetic regression coefficients can be generated from MODIS radiances calculated using a transmittance model with profile input from a global temperature and moisture radiosonde database. The advantage of this approach is that it does not need MODIS radiances collocated in time and space with atmospheric profile data; it requires only historical profile observations. However, it involves the radiative transfer calculations and an accurate forward model in order to obtain a reliable regression relationship. Any uncertainties (e.g., a bias of the forward model) in the radiative calculations will influence the retrieval. To address model uncertainties, radiance bias adjustments have been implemented in the retrieval algorithm, as discussed in section 3b.

In the MODIS retrieval algorithm, the National Oceanic and Atmospheric Administration (NOAA)-88b global dataset of radiosonde observations is used for training the regression. The NOAA-88b dataset was chosen for this purpose to build on previous experience with the sounding algorithm from the Advanced TOVS (ATOVS; Li et al. 2000). See section 3c for more information about the NOAA-88b dataset. Other radiosonde datasets such as the Thermodynamic Initial Guess Retrieval (TIGR)-3 are also being tested for possible operational implementation. The original NOAA-88b data contains 7547 globally distributed clear-sky radiosonde profiles of temperature, moisture, and ozone, along with observations of surface temperature and pressure. Additional radiosonde observations have been added to this dataset for the MODIS retrieval algorithm, as described in section 3c. The radiative transfer calculation of the MODIS spectral band radiances is performed with the PFAAST model for each profile from the training dataset to produce a temperature–moisture–ozone profile–MODIS radiance pair. The synthetic regression coefficients [see Eq. (7)] are generated using the calculated radiances and the matching atmospheric profile. For each training profile, 680 coefficients are generated, corresponding to different local zenith angles from nadir to 65°, with an increment of approximately 0.1°.

The estimated MODIS instrument noise was added to the calculated spectral band radiances before creating the coefficients. The noise was randomly generated with a Gaussian distribution, a standard deviation equal to the NEΔT in Table 2, and an average of zero. The noise used in the algorithm is larger than estimates of postlaunch detector noise to account for variability between the 10 detectors (striping). The correlation in the noise between the spectral bands was not considered in the regression, and it is assumed that any impact of spectral noise correlation on the retrievals should be small. This impact will be further studied in future work.

The predictands, or the parameters to be retrieved by regression, include the temperature profile, logarithm of the water vapor mixing ratio profile, logarithm of the ozone mixing ratio, surface skin temperature, and longwave and shortwave infrared surface emissivities. To perform the retrieval, Eq. (5) is applied to the actual MODIS measurements, where 𝗬 is now the observed MODIS radiances. Integration of the retrieved profiles yields the total precipitable water (TPW) or total column ozone. Other atmospheric parameters, such as layer temperature and moisture and stability indices, can also be calculated from the predictands. The retrieved water vapor mixing ratio at each pressure level is checked for saturation and the mixing ratio at any level with relative humidity greater than 100% is set equal to the saturation mixing ratio at that level. In addition to integrating retrieved mixing ratio profiles to obtain TPW, TPW is also retrieved directly by integrating the training data profiles and including TPW as a predictand.

To analyze the information contribution from various predictors to the retrieval, a simulation study was performed. In the simulation, 90% of the NOAA-88b profile data samples were used for training, while radiances calculated from the remaining 10% of the profiles were used for testing the retrieval algorithm. The noise added in the simulation is the same as the noise used in the operational algorithm for Terra (see Table 2). Figure 3 shows the root-mean-square error (rmse) of the retrieved vertical profiles of temperature and moisture compared with the actual profiles for the 844 independent regression retrievals. The most accurate MODIS temperature retrievals are between 800–400 hPa, where the rmse is approximately 1 K. Near the surface, rmse increases to 2 K. Moisture retrieval accuracy decreases with height from an rmse maximum of 1.5 g kg⁻¹ at the lowest levels. The rmse of the ozone profiles reaches a maximum of 0.75 ppmv at the highest levels.

The impact of various predictors on the total precipitable water retrieval was also investigated using retrievals from the simulated data. Figure 4 shows comparisons between actual TPW (integrated from the 844 independent test profiles) and TPW retrieved from radiances calculated from the same profiles. For the simulation results in Fig. 4a, the same NEΔT and predictors were used as in the operational Terra MODIS algorithm. Calculating the coefficients without adding artificial noise to the calculated radiances (Fig. 4b) leads to improvement of the rmse from 4.15 mm with added noise to 2.9 mm without. However, for retrievals with true MODIS radiances, it is necessary to add artificial noise to the radiances calculated in the synthetic coefficients to account for striping and other instrument noise. Removing the quadratic terms (individual brightness temperatures squared) from the predictor list shows an increase in the rmse to 3.2 mm (not shown) from 2.9 mm, computed with no added noise.

Nonlinear physical retrieval processing

The statistical regression algorithm has the advantage of computational efficiency, numerical stability, and simplicity. However, it does not account for the physical properties of the radiative transfer equation (RTE). After computing atmospheric profiles from the regression technique, a nonlinear iterative physical algorithm (Li et al. 2000) applied to the RTE often improves the solution. The physical retrieval approach is described in this section.

A comparison between the regression-based first-guess brightness temperatures and the physical retrieval brightness temperatures is presented in Fig. 5. The results are based on simulated data similar to that detailed in section 2b for Figs. 3 and 4, except that retrievals were performed on only the 394 moist profiles with TPW greater than 17 mm. Only moist cases were used in this comparison because the current physical retrieval algorithm has very little effect on dry cases; the moisture signal is weak in the MODIS IR radiance measurements for a dry atmosphere. The rmse of actual minus retrieved brightness temperature decreased from the regression-based guess to the physical retrieval. The most significant improvement is apparent in the water vapor bands 27 and 28, with the rmse decreasing from 0.8 to 0.2 K for band 27 (6.7 μm), and from 0.6 to 0.2 K for band 28 (7.3 μm). The improvements evident in the brightness temperature calculations using the physical algorithm are also apparent in the retrieved products. For the same 844 simulated radiances as in Fig. 4, the rmse of the actual TPW minus that retrieved using the physical retrieval was 3.6 mm with added noise and 2.5 mm without, compared with 4.15 and 2.9 mm for the regression retrievals with and without noise, respectively.

In summary, a nonlinear physical retrieval shows some improvement over a synthetic regression retrieval for MODIS retrievals. However, the physical retrieval requires more computation time and, like the synthetic regression used in the MODIS processing, is dependent on the accuracy of the radiative transfer model.

Cloud detection algorithm

MODIS atmospheric and surface parameter retrievals require clear-sky measurements. The operational MODIS cloud-mask algorithm (Ackerman et al. 1998) is used to identify pixels that are cloud free. The MODIS cloud-mask algorithm determines if a given pixel is clear by combining the results of several spectral threshold tests. A confidence level of clear sky for each pixel is estimated based on a comparison between observed radiances and specified thresholds. The MODIS atmospheric retrieval algorithm requires that at least 5 of the 25 pixels in a 5 × 5 field-of-view area have a 95% or greater confidence of clear by the cloud mask. The retrieval for each 5 × 5 field-of-view area is performed using the average radiance of only those pixels that were considered clear. Experimentation with MODIS retrievals for different requirements for the minimum number of clear pixels showed that requiring that 5 of 25 pixels be clear maximized retrieval coverage, while minimizing undetected cloud contamination. A more strict requirement would further reduce cloud contamination effects but also lead to fewer retrievals. Since the decision to perform a retrieval depends on the validity of the cloud-mask algorithm, cloud contamination may occur if the cloud mask fails to detect a cloud, or the retrieval may not be processed if the cloud-mask falsely identifies a cloud.

Radiance bias adjustment in the retrieval processing

The forward model–calculated radiances have biases with respect to the MODIS-measured radiances. There are several possible causes, including calibration errors, spectral response uncertainty, temperature and moisture profile inaccuracies, and forward model error. The synthetic regression and physical retrieval methods use both measured and calculated radiances and thus require that this bias be minimized. Some of the techniques developed for computing GOES sounder radiance biases with respect to the forward model (Hayden 1988) were adapted to the MODIS atmospheric temperature, moisture, and ozone retrieval algorithm. Bias adjustment for radiative transfer calculation of MODIS spectral band radiances is demonstrated to have a positive impact on the atmospheric product retrievals.

MODIS radiance bias calculations are routinely computed for the Southern Great Plains (SGP) Atmospheric Radiation Measurement (ARM) Cloud and Radiation Test Bed (CART) for clear scenes with MODIS sensor zenith angle less than 35°. Observed MODIS radiances, averaged from a 5 × 5 field-of-view area, are compared with those computed using the 101-level PFAAST model, with temperature and moisture profile input from National Center for Environmental Prediction (NCEP)'s Global Data Analysis System (GDAS) global analysis data. Skin temperature and emissivity are estimated by regression with MODIS radiances. To establish credibility for the synthetic regression-derived skin temperature input, actual observed skin temperature from the SGP ARM CART ground-based downward-looking infrared thermometer (IRT) measuring the radiating temperature of the ground surface was also used. Figure 6 shows that, on average over 72 clear-sky day and night cases from April 2001 to August 2002, the observed minus calculated radiance biases computed using the regression-based skin temperature differ very little from those computed using the IRT skin temperature. A comparison of the two skin temperatures for the same cases used in computing the biases shows good agreement (Fig. 7); the rmse of the IRT skin temperature compared with MODIS regression-based skin temperature is 1.75 K, and the slope of a linear best fit is 1. Most CART site MODIS radiance biases (expressed as observed minus calculated BT) shown in Fig. 6 are positive, indicating that, on average, the observed MODIS brightness temperatures are warmer than those predicted by the model. Case-to-case variability for each spectral band can be seen in Fig. 8. The high variability in the radiance bias for band 27 is partially due to the significant detector-to-detector differences, or striping, that exists in the radiance data for this band. Some of the variability in this band is also related to differences in the atmospheric moisture; band-27 radiance bias calculations vary as a function of TPW. For this reason, a different band-27 radiance bias correction is applied to moist scenes (TPW > 17 mm) than to dry scenes (TPW > 17 mm).

A comparison of MODIS products at the SGP ARM CART site with and without the radiance bias corrections confirms a significant improvement with the bias corrections. The rmse for TPW sensed by the CART site microwave radiometer (MWR) compared with MODIS TPW for 80 clear-sky cases between April 2001 and October 2002 decreased from 5.9 to 4.1 mm when the bias corrections were applied (not shown). The improvements were primarily apparent for moist cases; the average MWR minus MODIS TPW difference for the 43 cases with TPW greater than 17 mm was 5.6 mm without bias corrections, as compared with 1.24 mm after correction. Because the MODIS retrieval algorithm is applied globally, the biases computed at the SGP ARM CART site are not appropriate for application at other latitudes and for other ecosystem types. Thus, radiance bias corrections have been computed for other regions of the globe; however, they are less well validated.

To compute the global radiance biases, observed MODIS brightness temperatures were compared with calculated brightness temperatures for clear-sky scenes distributed globally with a MODIS-viewing zenith angle >30°. Calculations of brightness temperatures were performed as outlined above for the SGP CART site with skin temperature and emissivity estimated from regression of MODIS radiances, and temperature and moisture profiles taken from NCEP GDAS analysis. Because there are known difficulties in retrieving skin temperature and emissivity over the desert, these cases were excluded from the global averages. The global radiance biases are separated into six latitudinal zones each for land and ocean. The average global radiance bias calculations for northern midlatitude land agree fairly well with those calculated at the SGP CART site; the rmse of MODIS minus MWR TPW for 80 cases increased only 0.3 mm when using the global radiance bias instead of the SGP CART biases (not shown).

The radiance bias corrections applied in the operational MODIS atmospheric retrieval algorithm will be updated regularly to account for adjustments in the instrument calibration and improvements in the forward model. Future versions of the algorithm will include a more advanced global bias scheme that uses a regression based on predictors that characterize the air mass (e.g., brightness temperatures, surface skin temperature, TPW, and atmospheric layer thickness) similar to that employed on the TOVS (Eyre 1992; Harris and Kelly 2001).

Adjustments to the NOAA-88b training dataset

The NOAA-88b dataset contains 7547 globally distributed clear-sky radiosonde observations. Profiles of temperature, moisture, and ozone and surface data from this dataset were used to compute the synthetic regression coefficients for the MODIS statistical retrieval. The temperature and mixing ratio profiles are from radiosondes launched in 1998 at a wide range of locations distributed globally; ozone was derived from solar backscatter ultraviolet (SBUV) collocated profiles. All profiles were extended to 0.005 hPa and interpolated to 101 levels by researchers at NOAA–National Environmental Satellite, Data, and Information Service (NESDIS) who created the dataset.

A surface emissivity and skin temperature were assigned to each training profile to be used as input to the forward model because observed surface information is not included in the NOAA-88b profile dataset. The characterization of the surface used in the calculation of the synthetic coefficients is described below. Infrared emissivity spectra were assigned randomly to the training profiles with a Gaussian distribution, standard deviation of 0.05, mean of 0.95 for longwave IR bands (8–13 μm), mean of 0.88 for the 6.7-μm band, and mean of 0.84 for shortwave IR bands (4–5 μm). The difference between the lowest-level radiosonde temperature and the skin temperature to be assigned to the profile was also generated randomly with a Gaussian distribution, but with a mean of 0 K and standard deviation of 10 K. To better represent the range of conditions sensed by MODIS, a second skin temperature was assigned to each training profile in a similar manner. This created a second set of radiance–profile pairs with different skin temperatures, thus, doubling the amount of training data used in the regression. Future work will improve upon this choice of skin temperature and emissivity by employing techniques with more physical bases, including the use of ecosystem-dependent emissivities (Wilber et al. 1999) and deriving physical relationships between surface air and skin temperature.

To limit the retrievals to training data with physical relevance to the observed conditions, the NOAA-88b data were partitioned into seven zones based on the 11-μm brightness temperatures (BT11) calculated from the profiles. The seven zones are BT11 >245, 245–269, 269–285, 285–294, 294–300, 300–310, and >310 K. Any profiles corresponding to BT11 within 2 K of a zone end point were included in both closest zones. When each retrieval is performed, it uses only that subset of the training data in the same zone as the observed MODIS BT11.

After partitioning, there were insufficient training data in the NOAA-88b dataset for the very warm surfaces (the last two zones, BT11 >300 K). Figure 9a shows that many measurements over the North African deserts with BT11 >300 K had little to no training data corresponding to a similar BT11 (Fig. 9b). To address this problem, new radiosonde data from the North African desert regions for January–December 2001 were added to the training dataset. Spread equally through the 12 months, 900 radiosonde observations met the criteria of relative humidity <90% at each level and physically reasonable behavior; profiles of temperature and moisture from these radiosondes were added to the NOAA-88b dataset. A skin temperature was assigned to the new profiles by adding a positive increment to the temperature of the lowest level in the profile. The increment was derived by taking the absolute value of a random number from a Gaussian distribution with mean of zero and standard deviation of 15 K. These warm skin temperatures were necessary to generate brightness temperatures in the desert region, representative of conditions observed by MODIS, and to add more training in the highest BT11 zones. Figure 10 compares the frequency of occurrence of the 11-μm brightness temperatures for both the original and enhanced NOAA-88b dataset with the extra desert profiles.

Results from a study of retrievals using simulated data (similar to that described in section 2b for Figs. 3 and 4) illustrate the benefit of separating the training data into brightness temperature zones and adding the warm desert profiles. For the 844 independent cases with no noise added to the radiances used in the coefficients, the rmse of retrieved TPW compared with actual TPW decreased to 2.9 mm with BT zones and new profiles (see Fig. 4b) from 4.2 mm without (not shown). The most improvement was evident for moist cases with TPW >30 mm.

One example of the improvement in retrievals from MODIS data after partitioning the BT11 into seven zones and adding desert training data is presented in Fig. 11. True color reflectance and 11-μm radiance images from 20 August 2001 are shown in Figs. 11a and 11b, respectively. A large area of clear sky exists from Texas through Oklahoma and southeastern Kansas. Figures 11c–e compare GOES-8 TPW with MODIS TPW retrieved with and without the BT zones and new profiles. The MODIS results with the zones and new profiles compare considerably better with the GOES. The area in Kansas and Oklahoma that shows the most improvement has a warm BT11 that falls within the highest two classes (see Fig. 12). This is consistent with results of other cases; the most significant improvements occurred for scenes with BT11 in the two highest classes.

Surface emissivity for IR 4.5-μm spectral bands

In most situations the infrared emissivity assigned to the NOAA-88b training dataset accounts for the global variations in emissivity. However, for some regions, such as the deserts of North Africa, the surface emissivity has the potential to be significantly lower at 4 than at 11 μm (Salisbury and d'Aria 1992). Figure 13 shows measurements of emissivity spectra from data obtained through the NASA Jet Propulsion Laboratory's spectral library (information available online at http://speclib.jpl.nasa.gov) for two silicates commonly found in desert regions: cyclosilicates and tectosilicates. The emissivity at the 4.5-μm spectral region is extremely low for both minerals, indicating that emissivities in the desert may be as low as 30%–40%. Because emissivities this low are not included in the training dataset, the surface characteristics in the 4.4- and 4.5-μm bands (MODIS bands 24 and 25) were not accurately represented and the MODIS retrievals were excessively moist in the desert regions. To remedy this problem, the difference between these two bands is used as a single predictor instead of using bands 24 and 25 independently; this subtraction removes most of the surface emissivity signal in the regression equation. The BT difference between band 25 and band 24 is found to be much less sensitive to the surface emissivity change than the BT of either of the bands independently. Figure 14 illustrates the advantages of this approach by showing the BT increment, defined as the difference between the BT calculated at a given emissivity and that calculated with emissivity equal to 0.4. The BT increment for the individual bands 24 and 25 is greater than 2.0 K for a surface emissivity of 0.85, while the BT increment for the difference between them is less than 0.8 K. Taking the BT difference between band 25 and band 24 instead of using the bands individually reduces the error in the retrieval due to surface emissivity uncertainties over the desert region. In addition to the surface emissivity effects on 4.5-μm region, there are also effects of nonlocal thermodynamical equilibrium on that region for the radiative transfer modeling. Taking the difference between bands 24 and 25 also minimizes this effect in the retrieval.

Comparison of MODIS temperature and moisture with ARM CART observations

Specialized instrumentation at the SGP ARM CART site in Oklahoma facilitates comparisons of MODIS atmospheric products with other observations collocated in time and space. Terra passes over the SGP CART daily between 0415 and 0515 UTC and between 1700 and 1800 UTC. Radiosondes are launched 3 times per day at approximately 0530, 1730, and 2330 UTC. Observations of total column moisture are made by the MWR every 40–60 s. An additional comparison is possible with the GOES-8 sounder (Menzel and Purdom 1994; Menzel et al. 1998) that retrieves TPW hourly.

MODIS retrieved products were compared for 80 clear-sky cases from April 2001 to October 2002. Manual inspection of visible and infrared images excluded any scenes with the possibility of cloud contamination. MODIS sensor zenith angle was less than 50° to the CART site for all cases. To reduce noise due to striping, all retrievals in a 3 × 3 retrieval area were averaged in this comparison. TPW from MODIS synthetic regression retrievals, the GOES-8 sounder, radiosondes, and the MWR are compared in Fig. 15. MODIS shows general agreement with the MWR for these cases; however, GOES-8 sounder and radiosonde observations show better agreement with the MWR. The rmse between MODIS and MWR TPW collocated in time and space is 4.1 mm for regression retrievals, as compared with 1.9 and 1.2 mm for GOES-8 and radiosondes, respectively. For the 43 cases with moist atmospheres (TPW > 17 mm), MODIS compares better to the MWR; the rmse between MODIS and MWR TPW is 3.9 mm, as compared with 2.5 mm for GOES and MWR TPW (not shown). On average, for these moist cases, MODIS is 1.2-mm drier than the MWR. For dry atmospheres, MODIS consistently overestimates the total column moisture; MODIS is on average 3.7 mm more moist than the MWR for the 37 dry cases with MWR TPW less than 17 mm. Stephens et al. (1994) observed similar behavior in TOVS total column water vapor and attributed it to a limitation of low spectral resolution infrared sounders in subsidence regions. Use of different band-27 bias corrections for moist and dry cases (see section 3b) improved the retrievals for moist cases but had little effect on the dry cases.

An example comparison of temperature and moisture profiles from a radiosonde at the SGP CART with MODIS regression retrievals of temperature and moisture is shown in Fig. 16. For atmospheres with a fairly monotonic, smooth temperature and moisture distribution, such as that shown here, MODIS retrievals compare well to radiosonde observations. However, in situations with isolated layers of sharply changing temperature or moisture, MODIS is not able to capture the finer-scale structure. Improved sounding capability is expected from the high spectral resolution AIRS on Aqua (Susskind et al. 1998).

Continental-scale comparisons between MODIS and GOES TPW

On the continental scale, MODIS TPW was compared with GOES-8 and GOES-10 sounder retrievals of TPW over the continental United States and Mexico. GOES TPW has been well validated (Schmit et al. 2002) and has a resolution at the subsatellite point of 10 km. GOES uses radiances measured from a 3 × 3 field-of-view area (approximately 30-km resolution) to retrieve one atmospheric profile, while MODIS has nadir resolution of 1 km and uses a 5 × 5 field-of-view area (5-km resolution). Unlike the MODIS retrieval, GOES hourly radiance measurements are supplemented with hourly surface observations of temperature and moisture as additional information in the GOES retrieval. MODIS and GOES retrieval procedures also use different first-guess profiles; GOES uses a numerical model forecast, while MODIS uses the previously described synthetic regression retrieval.

Figure 17 compares MODIS TPW with TPW retrieved by the GOES-8 and GOES-10 sounders over North America for 2 June 2001 during the day and at night. MODIS and GOES show fairly good agreement except the daytime MODIS TPW retrieved by regression is drier than GOES over Oklahoma, Arkansas, and the Gulf of Mexico. TPW retrieved by physical retrieval shows better agreement with GOES in these areas.

Global comparisons of MODIS products with SSMI and TOMS

Global TPW from MODIS atmospheric retrievals is compared with TPW from the Defense Meteorological Satellite Program (DMSP) SSM/I (Alishouse 1990; Ferraro et al. 1996; Wentz 1997) for 22 May 2002 in Fig. 18. The SSM/I (resolution 12.5 km) TPW retrievals for clear or cloudy skies over ocean use the 22- and 37-GHz microwave channels. MODIS and SSM/I show similar patterns of TPW distribution and similar magnitudes, however, MODIS retrievals are somewhat less moist over tropical oceans. Some of the differences can be attributed to MODIS TPW retrievals occurring only in clear pixels and, thus, not capturing the moist environment associated with clouds. Other differences may be attributed to the time differences between the two satellite overpasses.

In order to predict the evolution of ozone on timescales of a few days to 1 week, reliable measurements of ozone distribution are needed. The NASA Goddard Space Flight Center (GSFC) TOMS instrument (Bowman and Krueger 1985; McPeters et al. 1998) onboard the Earth Probe (EP) satellite measures backscattered ultraviolet solar radiation and cannot provide measurements at night. High-spatial-resolution IR radiance measurements at 9.6 μm (band 30) from MODIS allow ozone estimates during both day and night.

MODIS total column ozone retrievals are compared with TOMS ozone from 22 May 2002 in Fig. 19. The general distribution of ozone from TOMS is similar to that from MODIS. A quantitative comparison for the same day between TOMS and MODIS ozone (Fig. 20) shows percent errors of less than 10% for latitudes between ±20°. Errors increase toward the Poles, with the highest errors at the South Pole, where very few training data exist.