Land surface skin temperature climatology: benefitting from the strengths of satellite observations

Surface skin temperature observations (Tskin), as obtained by satellite remote sensing, provide useful climatological information of high spatial resolution and global coverage that enhances the traditional ground observations of surface air temperature (Tair) and so, reveal new information about land surface characteristics. This letter analyzes nine years of moderate-resolution imaging spectroradiometer (MODIS) skin temperature observations to present monthly skin temperature diurnal, seasonal, and inter-annual variations at a 0.05° latitude/longitude grid over the global land surface and combines these measurements with other MODIS-based variables in an effort to understand the physical mechanisms responsible for Tskin variations. In particular, skin temperature variations are found to be closely related to vegetation cover, clouds, and water vapor, but to differ from 2 m surface Tair in terms of both physical meaning and magnitude. Therefore, the two temperatures (Tskin and Tair) are complementary in their contribution of valuable information to the study of climate change.


Introduction
Global averaged land surface temperatures should be increasing with global warming (Jin and Dickinson 2002). They are determined by and respond to land surfaceatmosphere interactions (Schmugge and Becker 1991, Jin et al 1997. Climatological data can be developed for two kinds of surface temperatures: 2 m surface air temperature (T air ) and the skin temperature (T skin ). How are these two surface temperatures related? Are they both needed? This letter addresses these questions by (a) assessing the differences between T skin and T air from their theoretical definitions and from recent global observations; and (b) addressing the strengths of satellite-based T skin temperature data in terms of coverage, resolution, and consistency with other land and atmospheric data. 3 Author to whom any correspondence should be addressed.
Various definitions of land surface temperature have been used in different research communities. Modeling, remote sensing, and boundary layer studies have used the same terminology ('land surface temperature') for different physical concepts. Such differences in usage have made it difficult to interpret data among interdisciplinary communities, and consequently have hindered scientific applications. Skin temperature terminology was previously clarified by Norman and Becker (1995). This letter provides additional clarification in the context of remote sensing and particularly in the context of climate change by assessing the differences between the T skin and T air for various spatial and temporal scales. Its references and their citations should complement this review in summarizing what is currently known about T skin and T air .
Surface temperatures are used for calculating heat and radiative fluxes, e.g., as a possible formulation: where F ↑ is upwelling longwave radiation, SH and LE are sensible and latent heat fluxes respectively, σ is the Stefan-Boltzmann constant, ε is surface spectrally averaged emissivity, U is wind speed, and C DH and C DE are bulk transfer coefficients for heat and moisture, respectively. T air is the air temperature at the reference (shelter) height and T aero is the aerodynamic temperature discussed further in section 3 and is related to T skin . q * skin is the saturated specific humidity at T skin and q air is specific humidity at the same reference level as T aero .
For a given region, the governing equation for land surface energy balance is: where α is the surface albedo, S ↓ is the surface insolation, F ↓ is downward longwave radiation from atmosphere, and G is the ground heat flux. The calculation of heat fluxes and surface radiation terms in equation (4) depends on T skin and other physical properties such as albedo (α) and emissivity (ε). The term T skin differs from T air in its physical meaning, magnitude, and measurement techniques.
As such, it provides additional information on land surface radiation properties because it is closely determined by surface longwave emissions, as shown in equation (1). Therefore, it is necessary to analyze the climatology of T skin as distinct from that of T air .
This letter addresses the issues associated with the use of T skin by focusing on four specific but relevant topics: section 2 examines the different physical meanings of T skin and T air ; section 3 describes the data used; and section 4 provides a climatology of T skin as observed from the recent moderateresolution imaging spectroradiometer (MODIS) instrument and compares this data with T air data obtained from ground observations and NCEP reanalysis. A discussion as to the difficulties that hamper the use of T skin is given in section 5 followed by final recommendations for future directions on this topic in section 6.

Surface temperature
'Surface temperature' is, by itself, vague and may refer to T skin , T air , or T aero , depending on the underlying physical principles of their measurement. This section defines various surface temperature measurements used in calculating land surface heat fluxes and radiation transfer processes, as presented in equations (1)-(3), following the previous overview of Norman and Becker (1995).

Skin temperature (T skin )
The term 'skin temperature' has been used for 'radiometric surface temperature' (Jin et al 1997). It can be measured by either a hand-held or aircraft-mounted radiation thermometer, as derived from upward longwave radiation based on the Stefan-Boltzmann law (Holmes 1969, Oke 1987, or retrieved from satellite observations and mapped over large areas, after removing the effects of atmospheric attenuation on satellitemeasured radiances (Saunders 1967, Anding and Kauth 1970, Sobrino et al 1994, Stephens 1994, Ulivieri et al 1994, Prata 1993. The retrieval techniques for obtaining T skin from satellite measurements for land applications have developed substantially in the last two decades (Price 1984). The accuracy of many T skin algorithms has been improved to within 0.5-1 • C for field measurements and for satellite observations under clear sky conditions (Becker and Li 1995, Wan and Dozier 1996, Coll et al 1994.
The definition of T skin in satellite remote sensing is based on Planck's law. Radiances measured by satellite sensors observing the earth surface consist of both atmospheric and land surface radiation. The surface radiation at a specific wavelength gives the brightness surface temperature, defined as: where L ↑ is the radiance measured by the radiometer, after corrections for atmospheric and emissivity effects, and B −1 is the inverse of Planck's law B λ (T ). Planck's law gives dependence on temperature of the radiative emission from a black body, i.e., surface spectral emissivity ε λ = 1. Since the land surface is typically not a black body, equation (5) needs to be modified to account for variations in ε λ (e.g., Li and Becker 1993): where L ↓ is the downward radiance from the atmosphere. For a homogeneous surface, the temperature from this definition is equal to the thermodynamic temperature of the surface (Norman and Becker 1995). Because the land surface has heterogeneous emissivity, many retrieval algorithms have used the concept of effective emissivity at the pixel level (Prata et al 1995, Schmugge et al 1998. Climate models have generally used the Stefan-Boltzmann law, i.e., the integrated version of equation (6), to calculate F ↓ (i.e., equation (1)). Errors in assuming ε to be some constant value are common in both formulations (equations (1) and (6)) because a correct value for ε is not easily available for large (frequently heterogeneous) surfaces (Jin and Liang 2006). Moreover, satellite-measured radiances correspond to the instantaneous field of view of the instrument and include part of the surrounding sky flux. For this reason, a satellite-based definition of T skin (e.g., T b skin ) is ideally used for measurements over a small area or for calculating fluxes where the emissivity is measured, inferred or otherwise estimated. In the remainder of this letter, T skin is the radiometric temperature derived from the inverse of the Planck's function (namely, T b skin in equation (6)).

Surface air temperature (T air )
Traditionally, thermodynamic temperature (or equivalently kinetic temperature) has been measured by an in situ thermometer in a shelter at 1.5-2 m and with good thermal contact with the air. This is the surface air temperature or, more accurately, air temperature at shelter height. This nearsurface air temperature is correlated with T skin but can differ depending on land cover or sky conditions; differences may be large, e.g., for sparsely vegetated areas with most of the net radiation balanced by sensible heat flux (Sun andMahrt 1995, Jin et al 1997). Norman and Becker (1995) summarize the conceptual differences between thermodynamic and kinetic temperature that are here taken to be essentially equivalent.

Aerodynamic temperature (T aero )
Another surface temperature that is related to T skin and T air is the aerodynamic temperature, i.e., the temperature at the height of roughness length for heat. Unlike roughness length for momentum, where the surface wind speed reduces to zero due to surface friction, roughness length for heat is the level heat transfer at zero. In an aerodynamically smooth flow, roughness length is independent of surface geometry and wind speed. However, for an aerodynamically rough flow, roughness length varies with surface geometry (Garratt 1992, p 87).
Aerodynamic temperature may fall between surface air and radiometric skin temperature, but can be quite different from the latter. Typically, the skin temperature can be 2-6 K higher than the aerodynamic temperature at midday, and lower than the aerodynamic temperature at night (Sun and Mahrt 1995). Some models, however, have approximated the surface radiative temperature by the aerodynamic temperature (Huband and Monteith 1986) while others including BATS (biosphere-atmosphere transfer scheme, Dickinson et al 1986Dickinson et al , 1993 and CLM (community land model, Oleson et al 2008) have assumed a thin boundary layer over the leaves or soil where molecular diffusion generates the difference between T aero and T skin .

Data
Monthly observations of skin temperature, albedo, and land cover data measured by MODIS Terra (Wan and Dozier 1996, Schaaf et al 2002, Gao et al 2005, Friedl et al 2002 from April 2000-December 2008 are used to analyze the climatology of skin temperature and how it relates to surface properties. Details of skin temperature collection four process and validation can be found at Wan (2008) and Wan and Li (2008), or the user's guide at (www.icess.ucsb.edu/modis/Lst UsrGuide/MODIS LST products Users guide C5.pdf). The MODIS data (Collection 5) is at 0.05 • latitude/longitude grid. T skin data is only retrieved on clear days. The daytime and nighttime T skin values in MOD11C3 are averaged from the daytime and nighttime LST values in the daily T skin product (MOD11C1) in clear days only. The daytime T skin in MOD11C1 is around 10:30 am local solar time and the nighttime T skin is around 10:30 pm local solar time. The observation time may differ by 90 min in low latitude regions or up to several hours in high latitude regions. Local solar time is equal to coordinated universal time (UTC) + longitude (in degrees)/15.
In addition, water vapor and cloud observations from MODIS  are also used to examine the connections between surface temperature and atmospheric conditions. Observed surface air temperatures are provided by the global historical climatological network (GHCN, for details see www.ncdc.noaa.gov/temp-and-precip/ghcn-gridded-temp. html, and also Peterson and Russell 1997, Peterson et al 1998, Free et al 2004. These datasets were created from 2 m observations at World Meteorological Organization (WMO) observation sites (namely, screen-level shelters). In order to make the limited coverage of the data sites as useful as possible, an anomaly method (AM) is implemented which first calculates station averages for a selected duration , in this case) and then departures by subtracting this average from the raw data. The data set is given in 5 × 5 degree grid boxes, as calculated from station anomalies for all adjusted stations falling within the 5 × 5 degree box. An adjusted station is one with at least 25 years of data during the 1961-1990 period. For stations which are too new to be adjusted, anomalies were calculated from the raw station data using the same AM approach.
In addition to GHCN, daily T skin and T air data from the atmospheric radiation measurement (ARM) program are used to reveal the differences between T skin and T air . The ARM site used was from surface meteorological observation station (SMOS) at E13: Lamont, OK (36.605 • N, 97.485 • W, altitude 318 m). T air is measured at 2 m height with 30 min intervals. Two days, 1 January 2006 and 1 July 2006 were analyzed. Corresponding T skin data is obtained from the same site. T skin was named as ground surface infrared temperature in the data set and was observed at 10 m and remove atmosphere effects. The interval of T skin is 60 s.

T skin versus T air
Why do we need to use T skin , when T air data have been obtained for decades with much effort going in to constructing a data set for use Russell 1997, Peterson et al 1998)? Figure 1 partly answers this question by showing that T skin and T air are significantly different in terms of magnitude, response to atmospheric conditions, and diurnal phase. On 1 July 2006 at Lamont, OK (figure 1(b); 36.605 • N, 97.485 • W), which was a clear day except for clouds flying across the observation site during the afternoon, T skin was higher than T air during the daytime with the maximum T skin of 50 • C around local noon while T air was only 35 • C. This 15 • C difference is significant for heat and moisture fluxes. At night, T skin was consistently lower than T air by about 3 • C. The reasons for the T skin and T air differences are complex. Clouds may be one of the major reasons. For example, in the afternoon of 1 January 2006 (figure 1(a)), T skin was lower than T air when clouds were present, but during the morning T skin was higher. At night on the same day, T skin was lower than T air by about 4 • C. In addition, in both the January and July cases (figures 1(a) and (b)), the diurnal phase of T air shifted to later in the afternoon compared to that of T skin , because the skin surface warmed up first as a result of absorbing surface insolation and then heated the near surface air.
Another reason for studying T skin is that T skin observations provide more coverage than T air . High spatial resolution is  2(b)). Since the T air observations over the globe are not uniformly distributed (one of the limits of T air observations), many areas cannot have observations over T air . Therefore, solely relying on T air data maybe misleading to accurate land surface change over the globe. In general, the major patterns of T air are consistent with those of T skin , although details differ.

Global distribution of skin temperature
Polar-orbiting satellites monitor global distributions of specific variables. For remotely accessible regions such as Greenland and Antarctica, these measurements provide critical information that is often missing with in situ ground observations. The spatial and temporal variability of T skin is similar to that of T air . In the following paragraphs, we describe and quantify this variability.
The global distribution of T skin varies with the surface insolation depending on the solar zenith angle (figure 3). The north-polar region in January has its minimum T skin in Greenland with its monthly average around 220 K. Temperatures increase southward, with the warmest regions in January occurring over the deserts in South Africa, tropical Africa, South America, and Australia, where the temperature is above 320 K ( figure 3(a)). In July, Greenland has a skin temperature of about 260 K in its central glacier areas, but up to 290 K at the edges where the surface is free of snow and ice ( figure 3(b)). These margins are important for climate change as snowmelt can cause a positive feedback that promotes the melting of ice sheets and glaciers. From January to July the maximum surface insolation has shifted from the Southern Hemisphere to the Northern Hemisphere. Correspondingly, land masses receive the most amount of solar energy in summer, and from the equator to 30 • N reach daytime temperatures of about 320 K. Much of these areas are desert with high albedo and low soil moisture. The coldest region over land in July is the central Antarctic plateau with skin temperature below 210 K. Depending on details of the surface and of the surface boundary layer processes, the minimum skin temperatures are generally colder than air temperatures and maximum daytime values warmer.

Diurnal variations
All land surfaces show significant diurnal variations 4 of T skin (figure 4). The desert regions in the sub-tropics (i.e., the Sahara, southwestern USA, southern Africa, Australia, and India) have the highest daytime skin temperatures up to 310-320 K (figure 4(a)) as well as at the highest nighttime temperatures up to 290-300 K (figure 4(b)), and the largest diurnal range (daytime minus nighttime as large as by 20-25 • C, figure 4(c)). A diurnal range above 25 • C is seen over some mountainous regions, in particular, the Tibetan Plateau. By contrast, most forest regions have low skin temperature diurnal range. For example, the T skin diurnal range of the Amazon is only 2.5-5 • C. Other regions with small diurnal range (values less than 5 • C) are cold, snow-covered regions including Greenland and Antarctica.
Both daytime and nighttime T skin have substantial seasonality (figure 5), with their maxima values occurring in Northern Hemisphere summer months (June, July, and August (JJA)) and minima in the winter months (December, January, and February (DJF)) as a result of solar insolation. The peaks of global averaged, monthly mean T skin are all above 295 K and the minima below 275 K. Furthermore, inter-annual variations are also evident; in 2005 JJA global T skin was about 1 • C higher 4 Note that here the observed MODIS T skin used were taken by NASA MODIS on Terra platform at 10:30 am and 10:30 pm, respectively. Its absolute range is likely to be smaller than the true diurnal range, i.e., the maximum minus the minimum skin temperatures. Nevertheless, the spatial pattern of this diurnal range should still be informative. Scale is critical in climate study. The features or even the signs can be different from one scale to another. Therefore, to get a complete picture of a variable, one needs to examine it at different spatial or temporal scales. Figures provide an example of T skin at global land scale (figure 6(a)), at continental scales (figures 6(b) and (c)), and at regional scales (figure 6(d)).
The smaller spatial scales (individual continents or land masses) have larger seasonality. For example, as shown in figure 6(b), the T skin differences between July and January in USA can be 25 • C (295 minus 270 K), but at global scale the T skin seasonal range (figure 6(a)) is only 14 • C (292 minus 278 K). In addition, different land surfaces have distinct seasonality. For example, Greenland (figure 6(d)) has a seasonal change of about 15 • C, while Africa (figure 6(c)) has a seasonal range of up to 40 • C.

T skin versus land cover
One strength of satellite MODIS data is that MODIS provides simultaneous measurements for many land and atmospheric variables, and so facilitates the combination of T skin data with other variables to study the mechanisms responsible for its changes. For example, land cover data helps to interpret how T skin varies as a function of the underlying land surface vegetation coverage.
Land cover maps are provided by the MODIS land cover group and can be downloaded from www.geog.bu.edu ( figure 7). Evidently, skin temperature is related to land cover. For example, desert regions have higher surface temperature than the surrounding non-desert regions, because deserts have little soil moisture but large surface insolation. The absorbed solar radiative energy is used to heat up the surface instead of giving evaporation. Figure 8 examines the relationship of skin temperature to land cover for four-month averages of T skin (January, April, July, and October) over the globe for each type of land cover. The minimum skin temperature is for land cover type 15 'snow and ice'. Its monthly means are 249.99 K, 233.03 K, 230.85 K and 237.07 K for January, April, July, and October respectively. The maximum skin temperature is for land cover type 16 'barren or sparsely vegetated', with values as 290.28 K, 307.13 K, 314.78 K, and 306.80 K for January, April, July, and October respectively. In addition, the largest seasonal difference occurs for land cover type 3 'evergreen needleleaf forest', varying from 242.48 K in January to 296.13 K in July (total difference is about 55 • C). Also interestingly, 'savannas' (land cover type 9) have a larger T skin in October (308.54 K) than in July, and their January and July T skin are almost the same (∼304 K). Furthermore, 'evergreen broad leaf forest' (land cover type 2), 'woody savannas' (land cover type 8) and 'savannas' (land cover type 9) show little seasonal differences between January and July, while other land cover types have clear seasonal variations.

T skin versus surface albedo
Skin temperature is determined in part by surface albedo, i.e., how much surface insolation is reflected back to space. Figure 9 shows a clear relationship between yearly averaged T skin and land surface albedo. In general, albedo decreases from Northern Hemisphere winter to Northern Hemisphere summer, with the peak in February and March when the surface snow cover reaches a maximum. Global, year-averaged skin temperature has the opposite phase with surface albedo, namely, warm in July and cold in December and January. Another example of T skin and surface albedo over Greenland across 70 • N (figure 10) clearly shows that T skin decreases with the increase of albedo from the edges to the center. Even along the same latitude (70 • N), at the edge T skin is above 280 K at 50 • W and 27 • W, suggesting that the melt of surface snow cover at the edges during summer has an evident influence. a b c Figure 4. Six-year (2001Six-year ( -2006 averaged MODIS skin temperature measured (a) daytime at 10:30 am, (b) nighttime at 10:30 pm, and (c) daytime minus nighttime.
Both T skin versus land cover and T skin versus albedo relationships show that in addition to the changes in air temperature and insolation, T skin also depends on vegetation health, canopy depth, and soil wetness. Because of such interdependencies, it may be difficult to relate changes in T skin to those in T air such as seen as global warming. For example, shifts in precipitation patterns will have a larger influence in one area than in another. Therefore, one may gain more understanding with the use of T skin in global climate change studies.

T skin versus vegetation
Vegetation information is represented by the enhanced vegetation index (EVI) from MODIS remote sensing. In figure 11, EVI less than 0 is related to water or snow surfaces. For EVI from 0 to 0.9, which is the valid vegetation-covered region, T skin almost linearly decreases with the increase of EVI, suggesting that more vegetation would reduce surface skin temperature. Such a decrease is partly because there is more vegetation, more evaportranspiration, and therefore less heat is used to warm up the surface. On the other hand, since T skin is observed from space, larger EVI represents dense, forest area where T skin is mainly the canopy top temperature. In addition, for the studied region 40-60 • N, 80-120 • W, T skin is the highest, upto 265 K, when EVI is 0.1.

T skin versus atmospheric conditions
MODIS measures land and atmospheric conditions at the same time over quite a few years of observations, facilitating the study of land surface-atmosphere interactions. For example, water vapor is closely related to T skin (figure 12), as expected from many earlier studies relating surface air temperature and water vapor. Both water vapor and T skin show the same seasonality-peaking in June, July, and August and minimizing in November, December, January, and February. The higher the surface skin temperature, the more water vapor can be contained in the atmospheric column. (But for desert regions less water vapor is transported or evaporated so there would be less water vapor than in other regions of similar temperatures.) In addition to water vapor, global averaged cloud optical thickness also shows similar seasonality to that of T skin over land (

Issues in constructing data sets for T skin
Given the importance of land surface T skin , why has this variable not been more widely used? For example, IPCC 2001 and 2007 used satellite sea surface temperature (SST) as evidence of global climate change, but did not use land T skin . There appear to be three major reasons that have hampered the use of T skin in global climate change studies.
First, uncertainties in the T skin data set limit its use. T skin can be measured through microwave or thermal infrared channels. Remotely sensed T skin is now widely available due in part to a larger suite of satellites providing these measurements, and due in part to improvements in the recovery of T skin and its accuracy (e.g., Prata et al 1995, Schmugge et al 1998. Nevertheless, the uncertainty in detection of changes in this variable may be large enough to obscure actual change. To retrieve T skin , it is necessary to calculate atmospheric radiative transfer in order to account for atmospheric emission and molecular absorption. Even in the most transparent spectral windows, atmospheric emission and attenuation are not negligible, thus corrections are usually required. These corrections are best accomplished by incorporating atmospheric profile information, for example, through the use of radiosonde measurements in the radiative transfer model calculations. Such measurements, however, are time consuming and rarely available for extensive areas or time periods. For example, within the seven wavelengths that MODIS used to retrieve T skin , where most thermal infrared remote sensing measurements operate, carbon dioxide (CO 2 ) and water vapor (H 2 O) are the chief atmospheric components that attenuate radiation. The mixing ratio of CO 2 is nearly  constant and thus not difficult to correct for. Water vapor is highly variable, however, and correcting for its effect may be difficult over an area of greater than a few kilometers or time periods greater than a few hours (Goody and Yung 1989).
Because of the high heterogeneity of the land surface, surface emissivity is largely unknown and thus induces a substantial uncertainty in the final retrieval. Atmospheric absorption increases with view angle and so also the retrieved values of skin temperature (Francois et al 1997). Instrument noise and variability are additional sources of error (Prata et al 1995), and limitations linked to the instrument itself also need to be recognized.
Second, satellite footprints cover a heterogeneous surface even for fine resolution of MODIS (1 km); its pixels in fact commonly contain several different land types. Thus, the interpretation of T skin from satellite instruments, and its linkage to models or traditional measurements continues to be difficult.
Third, is the issue of the short duration of large-scale T skin data sets. Evidence for climate change requires consistent, reliable, long-term data sets, but T skin measurements first began at the end of the 1970s, and the changes of instrument and orbit drift have made construction of long-duration datasets problematical (Jin 2004).

Concluding remarks
Satellite observations, for example, MODIS data, have strengths such as high spatial and temporal resolutions, global coverage, and high quality. Therefore, satellite data are very useful for studies on land surface climate. The most advanced satellite observations show that: (1) T skin is clearly a different physical parameter from T air .
(2) Land surface skin temperature is determined by both land surface properties and atmosphere interactions (water vapor, clouds, etc). (3) Scale is critical for understanding T skin and its interactions with land surface and the overlying atmosphere.
This letter shows T skin data on the monthly scale, and relates it to T air , to water vapor and to clouds. Different features would be expected at smaller spatial and temporal scales. Improved climatological data sets of T skin could provide considerable benefits. The climatologies of T air are designed primarily to examine long-term and large-scale changes. However, such changes may not be ideal for the study of the predominantly local and regional impacts of climate change. Also, T skin may be more directly connected to systems impacted, such as canopies.
Both the T skin versus land cover and T skin versus albedo relationships show that in addition to the changes in air temperature and insolation, T skin also depends on vegetation health, canopy depth, and soil wetness. Because of such interdependencies, it may be difficult to relate the changes in T skin to one specific physical process.
More field measurements of T skin , together with T air and surface and atmosphere conditions would improve the understanding and modeling of this quantity. The most widely used T skin -included field experiments are still the First ISLSCP Field Experiment (FIFE, Sellers et al 1992), the Boreal Ecosystem-Atmosphere Study (BOREAS, Sellers et al 1997), and the Atmospheric Radiation Measurement (ARM, Xie et al 2010). New carefully designed and implemented field experiments over various land covers would be extremely valuable to validate satellite and model simulations or to examine T skin and T air relationships.
MODIS skin temperature is retrieved for clear days only, which is a limitation of MODIS land skin temperature observations due to the fact that MODIS only uses IR channels to retrieve surface temperature, and therefore cannot see through clouds. When clouds are present at the satellite overpass time, the satellite cannot observe skin temperature. As a result, all the diurnal, seasonal, and interannual variations presented in this paper are for clear days. How to convert the clear-day data into whole-sky data (clear and cloudy) is a challenging research topic (Jin andDickinson 1999, 2002). Furthermore, when climate modelers compare model output with MODIS skin temperatures, satellite limitations need to be kept in mind.
Skin temperatures retrieved from satellite give information about the ground temperature of bare soils, if there is bare soil presented in the field of view of satellite instrument. After the removal of the atmosphere effect, radiances coming from the field of view of the instrument are a combination of the underlying bare soil and vegetation. A skin temperature for one pixel is therefore the average of the effective temperature of the pixel. Similarly, in a land surface model, for a grid box partially covered by bare soil and partially covered by vegetation, skin temperature of the grid is the sum of canopy top temperature and ground temperature weighted by their fractions (Dickinson et al 1986).
Skin temperature, as shown in equations (2) and (3), is critical in calculating heat transfer from land surface to atmosphere (Beljaars and Holtslag 1991, Choudhury et al 1986, Jin and Liang 2006. Nevertheless, this is not the focus of this letter. How to use skin temperature to calculate surface fluxes will be an important ongoing research topic. Remote sensing scientists have made some progress but their results are limited by the uncertainty of their approaches for broader applications (Nemani et al 2001).