Land Surface Temperature (LST) has been identified by NASA and other international organizations as an important Earth System Data Record (ESDR). An ESDR is defined as a long-term, well calibrated and validated data set. Identifying uncertainties in LST products with coarse spatial resolutions (>10 km) such as those from hyperspectral infrared sounders is notoriously difficult due to the challenges of making reliable in situ measurements representative of the spatial scales of the output products. In this study we utilize a Radiance-based (R-based) LST method for estimating uncertainties in the Atmospheric Infrared Sounder (AIRS) v5 LST product. The R-based method provides estimates of the true LST using a radiative closure simulation without the need for in situ measurements, and requires input air temperature, relative humidity profiles and emissivity data. The R-based method was employed at three validation sites over the Namib Desert, Gran Desierto, and Redwood National Park for all AIRS observations from 2002 to 2010. Results showed daytime LST root-mean square errors (RMSE) of 2–3 K at the Namib and Desierto sites, and 1.5 K at the Redwood site. Nighttime LST RMSEs at the two desert sites were a factor of two less when compared to daytime results. Positive daytime LST biases were found at each site due to an underestimation of the daytime AIRS v5 longwave spectral emissivity, while the reverse occurred at nighttime. In the AIRS v6 product (release 2012), LST biases and RMSEs will be reduced significantly due to improved methodologies for the surface retrieval and emissivity first guess.
 Land Surface Temperature and Emissivity (LST&E) products such as those produced from sensors on NASA's Terra and Aqua satellites including the Atmospheric Infrared Sounder (AIRS), Moderate-Resolution Imaging Spectroradiometer (MODIS), and Advanced Spaceborne Thermal Emission and Reflection Radiometer (ASTER) have been identified as a key Earth System Data Record (ESDR) by NASA and many national and international organizations [Intergovernmental Panel on Climate Change, 2007; King, 1999] (also NASA, Exploring our Planet for the Benefit of Society, NASA Earth Science and Applications from Space, Strategic Roadmap, 2005, http://images.spaceref.com/news/2005/earth_roadmap.pdf). LST&E data are used for many Earth surface related studies such as surface energy balance modeling [Zhou et al., 2003] and land-cover land-use change detection [French et al., 2008]; they are also critical for accurately retrieving important climate variables such as air temperature and relative humidity [Yao et al., 2011]. LST is an important long-term climate indicator, and is a key variable for drought monitoring over arid lands [Anderson et al., 2011a; Rhee et al., 2010] and as inputs to ecological models that determine important variables used for water use management such as evapotranspiration and soil moisture [Anderson et al., 2011b]. Identifying and resolving uncertainties in LST&E products is essential if they are to be used as effectively as possible by users, in modeling studies, and as long-term ESDRs.
 The AIRS is a hyperspectral infrared sounder on the Aqua platform and produces a twice-daily, coarse resolution (∼45 km) LST product that is critical for retrieval of other atmospheric constituents [Susskind et al., 2003]. The AIRS v5 emissivity product was recently validated to Stage-1 status [Hulley et al., 2009b], and there have been no previous attempts at validating the AIRS LST product with in situ data, except for comparisons between AIRS surface brightness temperatures and 3 m air temperatures measured at Dome Concordia (DomeC), Antarctica [Aumann et al., 2006]. Unknown uncertainties in the AIRS surface products over land have the potential to limit the usefulness of the atmospheric water vapor and air temperature products, particularly in the boundary layer over heterogeneous land surfaces, however very little work has been done on determining the sensitivity of AIRS atmospheric products to uncertainties in retrieved surface products. Yao et al. showed that using a fixed emissivity in AIRS retrievals could lead to errors of 4–6 K in boundary layer air temperature, and up to 20% in water vapor, however using a fixed emissivity is not a realistic assumption. Using data from the High-resolution Infrared Radiation Sounder (HIRS) instrument, a study byKornfield and Susskind  showed that an emissivity error of 15% resulted in temperature profile retrieval errors of 3 K at the surface layer and a 1.34 K RMS error for ten levels in the lower troposphere.
 Conventional temperature-based (T-based) validation methods require ground measurements over thermally homogenous sites concurrently with the satellite overpass. This requirement has limited in situ validation experiments over land to higher spatial resolution sensors such as MODIS (1 km) and ASTER (90 m), both of which have been validated over thermally homogenous surfaces such as lakes [Hook et al., 2007], and at dedicated field campaign sites over agricultural fields [Coll et al., 2005], playas and grasslands [Wan et al., 2004; Wan, 2008]. An alternative method for validating LST products is a radiance-based (R-based) method, which was developed to validate the MODIS LST products [Coll et al., 2009; Wan and Li, 2008] over land. The R-based method is not a true validation in the ‘classic sense’ since it is not based on in situ LST measurements, and it should therefore be regarded as more of an uncertainty analysis tool to assess the long-term accuracy and stability of LST products. The advantages of the R-based method is that it can be applied to coarser resolution sensors over long time periods for both day and nighttime data and to any location homogeneous in emissivity, but not necessarily homogenous in temperature, which is a limiting factor in the T-based method.
 In this study we apply the R-based method to cloud-cleared AIRS radiances in order to assess the uncertainties in the AIRS v5 LST product over three sites representing forests and deserts under different atmospheric conditions: the Redwood forest in California, the Gran Desierto, Mexico, and Namib Desert, Namibia.
 The T-based method provides the best evaluation of the ability for a LST retrieval algorithm to invert the satellite radiometric measurement and accurately account for emissivity and atmospheric effects. The drawback of this method over land is that several accurate, well calibrated ground radiometers are required to make rigorous measurements concurrently with the satellite overpass over a large thermally homogeneous area ideally representing several pixels at the remote sensing scale. Field radiometers typically measure the radiometric temperature of the surface being measured, and this measurement has to be corrected for the reflected downwelling radiation from the atmosphere and the emissivity before the surface skin temperature can be obtained. The T-based method becomes increasingly more difficult for sensor's with coarser spatial resolutions (e.g., MODIS 1 km) over land where surface emissivities become spatially and spectrally more variable. For example, at the ASTER pixel scale (90 m), depending on the homogeneity of the surface, several radiometer measurements are required over the land surface being measured to account for LST variability which could vary by as much as 10 K over a few meters [Coll et al., 2009].
 Consequently the T-based method remains a challenge for validating LST products from current hyperspectral sounders such as AIRS due to their coarse spatial resolutions (typically >10 km). Point measurements from flux towers or radiometer measurements exist but are not fully representative of the surrounding surface variability at coarse spatial scales. Researchers are investigating upscaling techniques from in situ to satellite LST measurements, for example by using the Soil Moisture Monitoring - land surface model (SETHYS) [Coudert et al., 2006; Guillevic et al., 2012]. However, the fact remains that validating satellite LST data at >1 km scale with in situ data over land remains a big challenge due to surface temperature variability that depends on many factors including season, time of day, surface type and meteorological conditions.
 The R-based method was developed for validating the standard MODIS LST products without the need for rigorous ground measurements byWan and Li. . The R-based method is not a true validation in the traditional sense since it does not rely on ground-based LST measurements, however it does have several advantages over T-based validation methods. The R-based method is based on a ‘radiative closure simulation’ with input surface emissivity spectra from either lab or field measurements, atmospheric profiles from an external source (e.g., model or radiosonde), and the retrieved LST product as input. A radiative transfer model is used to forward model these parameters to simulate at-sensor brightness temperatures (BTs) in a clear window region of the atmosphere (11–12μm). The input LST product is then adjusted in 2 K steps until two calculated at-sensor BTs bracket the observed BT value. An estimate of the ‘true’ temperature (LSTR-based) is then found by interpolation between the two calculated BTs, the observed BT, and the initial retrieved LST used in the simulation. The LST error, or uncertainty in the LST retrieval is simply found by taking the difference between the retrieved LST product and the estimate of LSTR-based. This method has been successfully applied to MODIS LST products in previous studies [Coll et al., 2009; Wan and Li, 2008; Wan, 2008]. For MODIS data, band 31 (10.78–11.28 μm) is typically used for the simulation since it is the least sensitive to atmospheric absorption in the longwave region.
 The advantages of the R-based method are its applicability to both day and night data, and its potential use on a global scale over many more sites than is possible with the T-based method. The requirements are spatially homogenous sites with stable long-term characteristics to minimize surface variability, where accurate surface emissivity measurements are available from either field radiometers, or from sand samples collected and measured in the laboratory. The disadvantages are its dependency on a radiative transfer model and it's requirements of accurate atmospheric profiles and surface emissivity data.
2.3. The Atmospheric Infrared Sounder (AIRS)
 AIRS, along with the Advanced Microwave Sounding Unit A (AMSU-A) and Humidity Sounder for Brazil (HSB) were launched onboard NASA's EOS Aqua on May 4, 2002. The AIRS is an infrared spectroradiometer that provides high spectral resolution (ν/Δν = 1200, ν is wave number) observations of outgoing thermal infrared radiation from the Earth and atmosphere in 2738 channels covering the 3.7–15.4 μm (650–2675 cm−1) spectral range.
 Global fields of atmospheric temperature, water vapor, trace gases, land surface temperature/emissivity are produced twice-daily for climate research and weather prediction [Susskind et al., 2003] at ∼45 km spatial resolution. AIRS ‘core products’ such as atmospheric temperature and water vapor are at Stage 2 validation status with reported accuracies of 1 K/km below 100 mb for temperature and 10%/2 km below 100 mb for water vapor in all conditions. ‘Necessary products’ such as emissivity, LST, total ozone, and ozone profiles are critical for obtaining this kind of accuracy. The AIRS footprint or Field Of View (FOV) is 13 km at nadir, with a 3 × 3 array of AIRS footprints termed the Field Of Regard (FOR) corresponding to a single Advanced Microwave Sounding Unit A (AMSU-A) footprint, a microwave sensor accompanying AIRS on Aqua. Observations from multiple AIRS FOVs within the AMSU FOR are used for removing the effects of clouds from the radiances by assuming constant cloud characteristics and that only the cloud fraction changes over the AMSU FOR [Susskind et al., 2003].
2.4. AIRS Surface Retrieval Algorithm
 The AIRS v5 surface retrieval algorithm uses a regression plus simultaneous solution approach to retrieve spectral emissivity, bidirectional reflectance, and LST in one step from fifteen longwave channels (758–1228 cm−1) and ten shortwave channels (2456–2658 cm−1) [Susskind and Blaisdell, 2008; Susskind et al., 2003]. The National Oceanographic Atmospheric Administration (NOAA) surface regression is used as emissivity first guess over land [Zhou et al., 2008]. Version 5 of the NOAA first guess uses a synthetic regression approach based on clear-sky infrared radiances simulated from European Center for Medium Weather Forecasting (ECMWF) forecast and a surface emissivity training model consisting of 12 laboratory derived spectra for ice/snow and 14 for land blended randomly over each surface type.
3. Input Data and Applied Methodologies
 The following section describes the sources and characteristics of input data for the R-based method, an uncertainty analysis of the R-based method, and methodology for application to AIRS data.
3.1. Atmospheric Profiles
 In terms of accuracy, a major limiting factor for the R-based method is the requirement of an accurate independent set of atmospheric profiles (air temperature, relative humidity and geopotential height) that are required for the forward model. Radiosonde profiles may have the highest accuracy, but have limitations in terms of availability since they are usually only available for dedicated field campaigns. An alternative is to use numerical weather data such as those from the National Center for Environmental Prediction (NCEP) Global Data Assimilation System (GDAS) model, available at 1° × 1° resolution, with atmospheric fields produced 4 times daily. The disadvantage is that variables have to be interpolated between the 4 observation times (00, 06, 12, 18 UTC) to the sensor observation time, which could lead to errors in temperature and water vapor depending on time of day.Coll et al.  used both radiosonde and NCEP profiles to successfully validate the MODIS LST product over vegetated surfaces. In this study we used NCEP atmospheric profiles, since radiosonde profiles were not available at the 3 field sites used for validation.
Wan and Li  proposed a quality check to assess the suitability of the atmospheric profiles by looking at differences between observed and calculated BTs in two nearby window regions with different absorption features. For example, the quality check for MODIS bands 31 and 32 at 11 and 12 μm is:
where: T11obs and T12obs are the observed brightness temperatures at 11 and 12 μm respectively, and T11calc and T12calcare the calculated brightness temperatures from the R-based simulation at 11 and 12μm respectively. If δ(T11 − T12) is close to zero, then the assumption is that the atmospheric temperature and water vapor profiles are accurately representing the true atmospheric conditions at the time of the observation, granted the emissivity is already well known. Because water vapor absorption is higher in the 12 μm region, negative residual values of ā(T11 − T12) imply the R-based profiles are overestimating the atmospheric effect, while positives values imply an underestimation of atmospheric effects. A simply threshold can be applied to filter out any unsuitable candidate profiles for validation. AlthoughWan and Li proposed a threshold of ±0.3 K for MODIS data, we performed a sensitivity analysis and found that a threshold of ±0.5 K resulted in a good balance between the numbers of profiles accepted and accuracy of the final R-based LST. Using the BT difference quality check, observations over long time periods are required to obtain reliable statistics since on average almost 1/3 of all observations do not pass the BT difference check.
3.2. Emissivity Spectra and Variability
 An essential requirement for the R-based method is accurate knowledge of surface emissivity in the 11–12μm window region. Emissivities for most terrestrial surfaces are relatively stable in this wavelength range, and only vary from ∼0.94–0.99 for most types of surfaces [Seemann et al., 2008; Snyder et al., 1998]. Large homogeneous sand dune sites have been demonstrated to be ideal targets for the validation of emissivity data due to their homogeneous mineralogy and consistent physical properties over long time periods [Hulley et al., 2009a; Hulley et al., 2009b]. One key advantage that sand dunes offer compared with more traditional ground sites such as playas, salt flats and claypans, is that the sand surface typically dries rapidly after a precipitation event, whereas playa surfaces remain damp for much longer periods and water beneath the surface can be wicked back to the surface through the clay particles that make up many playas resulting in emissivity variability from surface soil moisture [Mira et al., 2007]. Two large homogeneous sand seas in the Namib Desert, Namibia and the Gran Desierto, Mexico were chosen as two desert validation sites, and a dense stand of redwood trees in Redwood National Park, California to represent a vegetated site. The geographic locations of the sites are shown in Figure 1.
 The Namib Desert in Namibia is located in a hyper-arid region with very low annual rainfall and shifting dunes that are almost completely devoid of vegetation except for sparse perennial grasses [White, 1983]. The dune sand is primarily composed of quartz, with the degree of redness increasing from the coast to inland areas, and determined by a coating of hematite (iron-oxide mineral) adhering to the quartz grains [White et al., 2007].
 The Gran Desierto dune system constitutes the largest portion of the Sonoran Desert in Mexico and the largest and most active sand sea in North America. Scheidt et al.  showed that the central dune area consists of a mixture of approximately 90% quartz and 10% feldspar (plagioclase and potassium feldspar). The grain size, composition, texture, color and sorting have been well documented in previous studies [Blount and Lancaster, 1990; Lancaster, 1992]. Spatial variability in emissivity primarily occurs due to the distribution of quartz and feldspars across the central dune system via aeolian deposits [Scheidt et al., 2011].
 The Redwood National park located along the coast of northern California, USA covers roughly 133,000 acres in the Del Norte and Humboldt counties. The dominant tree species is the Coast Redwood, an evergreen tree with linear, sharp needle tips which sheds older needles in autumn. Redwoods are typically found in mixed forests with other evergreens and deciduous trees, but pure stands are often found.
 Sand samples were collected at the Namib Desert and Gran Desierto during separate field campaigns and measured in a controlled laboratory environment to determine the spectral emissivity. During November 2008 ten sand samples were collected over dune and inter-dune areas within the Namib-Naukluft Park in Namibia at Sossussvlei, a dry salt/clay pan extending into the southern part of the dunes. The directional hemispherical reflectance of the samples was measured in the lab at Jet Propulsion Laboratory (JPL) using a Nicolet 520 Fourier transform infrared (FT-IR) spectrometer at 4 cm−1 spectral resolution from 2.5 to 15 μm, and converted to emissivity using Kirchhoff's law. The uncertainty associated with the FT-IR lab emissivities is 0.002 (0.2%) [Korb et al., 1999]. During Dec 2004, 76 sand samples were collected at different locations in the Gran Desierto desert in Mexico [Scheidt et al., 2011]. These samples were measured with a Nicolet Nexus 670 instrument at 2 cm−1 spectral resolution from 5 to 25 μm. The thermal emission was then converted to emissivity spectra using the method by Ruff et al. . For the Redwood forest site (41.4°N, 123.7°W), a conifer spectrum from the ASTER spectral library was used to represent the effective emissivity of the conifer canopy for the AIRS pixel at 45 km resolution [Baldridge et al., 2009]. The conifer spectrum measurement was made at Johns Hopkins University (JHU) and reduced in reflectance by a factor of two to account for canopy scattering effects. Norman and Becker found that the emissivity of canopies normally varies from 0.97 to 0.99 for a leaf emissivity of 0.95. Therefore, the conifer spectrum from JHU which has a minimum emissivity of 0.989 and min-max difference of 0.003 over the measured spectrum gives a good approximation for the effective tree-canopy emissivity.
 Analyzing the spatial homogeneity of the validation sites is important for the R-based method since the average emissivity spectra derived from the field sample locations must be representative of the effective emissivity measured at the remote sensing scale, i.e., 45 km for AIRS. Sampling locations for each field campaign at these two sites are shown inFigure 2, along with the corresponding mean emissivity spectra and spatial variation shown as solid error bars in the 10–13 μm range. Spatial variations in 11 μm emissivity were 0.0057 (0.57%) for the Gran Desierto sample sites, and 0.0044 (0.44%) for the Namib sample sites. These variations can be considered small and are equivalent to ∼0.3 K for a material at 300 K. Spatial variability in emissivity at each validation site was further analyzed using high resolution (100 m) ASTER emissivity data covering an area corresponding to one AIRS pixel (∼45 km) shown in Figure 3. The ASTER emissivities represent a mean composite of all scenes ever acquired since 2000, part of a Level-3 gridded ASTER Global Emissivity Map (ASTER-GEM) currently being produced at JPL, and previously released as the North American ASTER Land Surface Emissivity Database (NAALSED) [Hulley and Hook, 2009]. Figure 3shows ASTER-GEM band 13 (11.3μm) emissivities at each site representing one AIRS pixel (∼45 km). The ASTER emissivities have low variability over the Gran Desierto and Namib sites with spatial standard deviations of 0.0017 (0.17%) and 0.0015 (0.15%) respectively. The Namib site variability primarily occurs due to differences in mineralogy between dune crests (primarily pure quartz) and interdune areas (higher clay content) previously discussed in Hulley et al. [2009b]. The Redwood site spatial variability was higher than the desert sites at 0.0043 (0.43%), mainly due to access roads and areas of open bare ground. Again these variations can be considered low variability, and equivalent to <0.3 K for a material at 300 K.
 Lab-measured emissivity spectra are currently available for more than ten sand dune sites in the southwestern USA, the Namib and the Kalahari Desert (http://emissivity.jpl.nasa.gov). However, the majority of these sites are too small to be representative of the AIRS spatial footprint. This currently limits the R-based method to the largest sites where emissivity spectra are available (Namib and the Gran Desierto).
3.3. Uncertainty Analysis
 The uncertainty in the R-based LST estimate (LSTR-based) was calculated by perturbing the atmospheric temperature and water vapor profiles, and by varying the surface emissivity. Atmospheric effects were simulated by first increasing the relative humidity at each NCEP level by 10%, and then by increasing the air temperature by 1 K at each level. The effect on the accuracy of LSTR-based was estimated as the calculated LST difference between the original and the perturbed profiles for the 11 μm window region. The results are summarized in Table 1. Using a standard profile with total column water vapor of 2 cm, the absolute LST differences where 0.35 K for the water vapor variation (10%), and 0.19 K for the air temperature variation (1 K), resulting in a total atmospheric effect of ±0.39 K. Using an emissivity perturbation of 0.005 (0.5%), which represents the maximum spatial variation found from the lab measured spectra and ASTER data at each site, resulted in an absolute LST difference of 0.23 K. Validation of the Stand-Alone AIRS Radiative Transfer Algorithm (SARTA) with in situ data have shown accuracies approaching 0.2 K depending on the wave number region [Strow et al., 2006], and this uncertainty was considered negligible The total combined root mean square error (RMSE) for the uncertainty in LSTR-based based on estimated atmospheric profile, emissivity and radiative transfer model errors was ±0.47 K. This is within the 1 K accuracy requirement for typical in situ measurements of LST [Hook et al., 2007].
Table 1. Uncertainty Analysis Results Showing How Perturbations in Emissivity, Air Temperature and Relative Humidity Affect the Relative Accuracy of the R-Based LST Derivation
R-Based LST Change
ε + 0.005
Tair + 1 K
RH + 10%
 Further, since air temperature and water vapor errors (and emissivity) typically cancel each other out and may have different signs at different levels, the simulated error of 0.47 K is most likely an overestimate, i.e., a ‘worse-case-scenario’. Also, using the brightness temperature profile quality check would most likely filter out the majority of unsuitable profiles.
3.4. Application of the R-Based Method to AIRS Data
 The R-based method was applied to the AIRS v5 LST product using the standard L2 cloud-cleared radiance product for all available observations at each site from 2002 to 2010 with surface retrieval quality set to good or best (Quality Assurance (QA) = [0,1]). The closest AIRS pixel for each observation was matched to the sampling points for the desert sites, while an AIRS pixel at 41.4°N, 123.7°W over the Redwood forest was chosen for the vegetation site matchup.
 The simulated TOA BTs for AIRS channels in the 11–12 μm region were calculated using the Stand-Alone AIRS Radiative Transfer Algorithm (SARTA) with input NCEP atmospheric profiles. SARTA is a stand-alone version of the full AIRS operational retrieval system which parameterizes atmospheric transmittances in 100 pressure layers [Strow et al., 2003a] using the AIRS spectral response functions (SRFs) [Strow et al., 2003b]. In this study SARTA V107 was used, which is available upon request from http://asl.umbc.edu/pub/rta/sarta. Validation with in situ data has shown accuracies approaching 0.2 K depending on the wave number region [Strow et al., 2006].
 The LSTR-based was calculated from the 11 μm window region using the average radiance of 3 channels between 904 and 912 cm−1, while the average of 27 channels between 848 and 856 cm−1 were used in the 12 μm region for the profile quality check. The LST accuracy is estimated as the difference between the retrieved LST product and the calculated LSTR-based. For each observation, the quality of the NCEP profile was checked using the ā(T11 − T12) BT criterion, which is the difference between the AIRS observed and calculated T11 − T12 BT values as discussed in section 3.1. Any profiles that did not meet the 0.5 K > ā(T11 − T12) > − 0.5 K criterion were discarded. Profiles that met this criteria were considered accurate enough for the simulation. By applying this quality metric, roughly 1/3 of all observations were discarded at each site, although this did not have a big impact on statistical analysis since 9 years of observations were used. Figure 4 shows an example of the differences between calculated and observed AIRS brightness temperatures from 840 to 920 cm−1 (10.9–11.9 μm) for an observation over the Redwood forest. Indicated on the plot are locations of the channels used for the R-based temperature inversion (904–912 cm−1) in a clear window region, and the profile quality test (27 channels between 848–856 cm−1) in a more opaque region of the atmosphere due to water vapor absorption.
 The biggest assumption in the R-based method over long time periods is that the emissivity stays relatively constant at the site, both temporally and spatially. Soil moisture data from the Advanced Microwave Scanning Radiometer (AMSR-E) were used to confirm that no significant rainfall events occurred preceding each AIRS observation at the two desert sites in a similar manner as described inHulley et al. . Regarding the spatial uniformity, the largest variability at the Namib site occurs due to differences in mineralogy between dune crests (primarily pure quartz) and interdune areas (higher clay content) [Hulley et al., 2009b], while at the Desierto site the largest variability occurs due to the distribution of quartz and feldspars across the central dune system [Scheidt et al., 2011]. At both desert sites multiple samples were collected in these different zones and the lab spectra were averaged in order to be representative of the effective AIRS pixel at 45 km.
4. Results and Discussion
 The results in Figure 5show LST scatterplots between AIRS v5 and the R-based method for day and night observations at the validation sites from 2002 to 2010. Axes limits were plotted consistently between day and night to highlight the diurnal LST differences at each site. The Namib Desert had the largest average diurnal LST difference due to persistent dry and clear conditions throughout the year. The Redwood site had the largest number of observations (N values inFigure 1) primarily because the Namib and Desierto sites often fell within ‘gores’ of the AIRS daily granule coverage. Figure 6 shows corresponding mean emissivity spectra between AIRS v5 (blue), the NOAA first guess regression (red) and the laboratory measurements (black). Solid error bars in Figure 6 show the temporal variation in AIRS and NOAA first guess emissivities. Table 2 summarizes the day and night statistics for both LST and emissivity in terms of bias and RMSEs.
Table 2. Statistics Showing Bias and RMSE Between AIRS v5 and R-Based LST, and Between AIRS v5 and Lab-Measured Emissivities for the Redwood Forest, Namib Desert, and Gran Desierto Validation Sites Using AIRS Data From 2002 to 2010a
Emissivity statistics are for all 39 retrieved hinge-points from 3.9 to 15μm.
 The daytime biases in AIRS LST were positive for all sites indicating an overestimation of LST, with Desierto having the largest bias (1.74 K). Nighttime biases were much smaller and almost negligible for all sites. Daytime LST RMSEs were lowest for the Redwood site (1.5 K) and increased substantially for the Namib (2.5 K) and Desierto (3.2 K) sites. Similarly, the nighttime RMSEs, although smaller in magnitude than the daytime RMSEs, were lowest for the Redwood site (0.9 K) and increased for the Namib (1.6 K) and Desierto (1.9 K) sites. The reasons for positive daytime LST biases are emissivity related. Figure 6 shows the mean longwave emissivity spectra (10–15 μm) at the Namib and Desierto sites were too low when compared to the lab spectra, which would result in an overestimation of LST. The primary cause for this is that the NOAA first guess emissivity spectra (red curve) starts off at unreasonably low values. For the majority of surfaces, emissivities <0.9 in the longwave region (10–15 μm) are generally considered unphysical. The result is that the final retrieval struggles to fully capture the correct magnitude and spectral shape, even although the quartz doublet at 9 μm is represented well. For the nighttime results the emissivities matched the lab results more closely resulting in ∼1 K improvement in RMSE at the Namib and the Desierto sites when compared to daytime results. The LST differences are generally much better for the Redwood site due to the lower variability in emissivity both spatially and temporally, and also because of a better first guess.
 Large diurnal differences in shortwave emissivity (3–5 μm) over desert regions are common for the AIRS v5 emissivity product and occur due to large variations in daytime shortwave emissivities due to improper modeling of the reflected shortwave solar radiation [Hulley et al., 2009b; Susskind and Blaisdell, 2008]. If not modeled correctly, the shortwave solar reflectance can be misinterpreted as emissivity and cause systematic errors in retrieved shortwave emissivity and the LST. This problem further degrades the daytime LST product accuracy in v5, however with the release of the v6 product during 2012, the diurnal emissivity differences have been significantly reduced due to an improved surface retrieval methodology [Susskind and Blaisdell, 2008].
5. Summary and Conclusions
 A radiance-based (R-based) method has been established for the long-term uncertainty assessment of LST products over homogenous land surface sites [Wan and Li, 2008]. This method was used to estimate uncertainties in the AIRS v5 LST product over three validation targets, including two desert sites and one vegetated site, for AIRS daily observations from 2002 to 2010. The largest RMSEs in LST occurred for daytime observations at the Namib (2.54 K) and Desierto (3.18 K) sites. The vegetated site over the Redwood forest had the lowest LST biases and RMSEs (<1.5 K) for both day and night data most likely due to a more consistent emissivity with respect to spatial and spectral variations. Positive daytime biases were found at all three sites due to underestimation of longwave spectral emissivity in the 10–15 μm range. Although not conclusive, the primary cause of biases at the two desert sites appear correlated with an unphysical first guess from the NOAA surface regression.
 The advantages of the R-based method is its potential application over long time periods both day and night, whereas the more traditional temperature-based (T-based) method over land surfaces is constrained to more short-term field campaigns. The R-based requirements are homogeneous sites in emissivity, and accurate atmospheric profiles and emissivity data for the radiative transfer calculations. The R-based method was designed for validating the MODIS LST products, but we have successfully shown its applicability to AIRS data, and potential application to other hyperspectral sounders such as the Infrared Atmospheric Sounding Interferometer (IASI) on MetOP-A and the recently launched Cross-track infrared Sounder (CrIS) on the National Polar-Orbiting Operational Environmental Satellite System (NPOESS) Preparatory Project (NPP). The R-based method will be used to validate the future AIRS v6 land surface products (expected release May 2012), in which significant improvements have been made to both the retrieval methodology [Susskind and Blaisdell, 2008], and in using the MODIS Baseline-fit emissivity product as the first guess [Seemann et al., 2008].
 We would like to thank Stephen Scheidt, from the Smithsonian Center for Earth and Planetary Studies, for providing the Gran Desierto emissivity lab spectra. The research described in this paper was carried out at the Jet Propulsion Laboratory, California Institute of Technology, under the contract with the National Aeronautics and Space Administration.