LAND SURFACE Long-wave (LWIR). For most terrestrial surfaces (340 K to 240 K), peak thermal emittance occurs in the LWIR (8–14 mm). Alan Gillespie Mid-infrared (MIR). Forest fires (1,000–600 K) have Department of Earth and Space Sciences, University peak thermal emittances in the MIR (3–5 mm). of Washington, Seattle, WA, USA Noise equivalent D temperature (NEDT). Random mea- surement error in propagated through Planck’s law to give the equivalent uncertainty in temperature. Definitions Path radiance S↑. The per unit area incident on Land surface emissivity (LSE). Average emissivity of a detector and emitted upward from within the atmosphere an element of the surface of the Earth calculated (W m 2 sr 1). from measured radiance and land surface temperature Planck’s law. A mathematical expression relating spectral (LST) (for a complete definition, see Norman and Becker, radiance emitted from an ideal surface to its temperature 1995). (Equation 1, in the entry Land Surface Temperature). Atmospheric window. A spectral region in Radiance. The power per unit area from a surface directed which the atmosphere is nearly transparent, separated by toward a sensor, in units of W m 2 sr 1. at which atmospheric gases absorb radiation. Reflectivity r. The efficiency with which a surface reflects The three pertinent regions are “visible/near-infrared” energy incident on it. (0.4–2.5 mm), mid-wave infrared (3–5 mm) and Reststrahlen bands. Spectral bands in which there is long-wave infrared (8–14 mm). a broad minimum of emissivity associated in silica Blackbody. An ideal material absorbing all incident energy minerals with interatomic stretching vibrations of Si and or emitting all thermal energy possible. A cavity with O bound in the crystal lattice. a pinhole aperture approximates a blackbody. SEBASS. Spatially Enhanced Broadband Array Spectro- temperature. The temperature of a blackbody graph System, a hyperspectral TIR imager (Hackwell that would give the radiance measured for a surface. et al., 1996). Color temperature. Temperature satisfying Planck’s law Short-wave infrared (SWIR). Erupting basaltic lavas for spectral measured at two different (1,400 K) have their maximum thermal emittance at wavelengths. 2.1 mm in an atmospheric window at 0.4–2.5 mm. Part Contrast stretch. Mathematical transform that adjusts the of this spectral region (1.4–2.5 mm) is called the SWIR. way in which acquired radiance data translate to the Sky I#. The irradiance on the Earth’s surface black/white dynamic range of the display monitor. originating as thermal energy radiated downward by the Emissivity e. The efficiency with which a surface radiates atmosphere (W m 2) (spectral irradiance: W m 2 mm 1). its thermal energy. Spectral radiance L. Radiance per wavelength, in units of Irradiance. The power incident on a unit area, integrated Wm 2 mm 1 sr 1. over all directions (W m2). Thermal infrared (TIR). Thermal energy is radiated from Graybody. A material having constant but non-unity a body at or wavelengths in proportion to its emissivity. temperature. The wavelengths for which this

E.G. Njoku (ed.), Encyclopedia of , DOI 10.1007/978-0-387-36699-9, © Springer Science+Business Media New York 2014 304 LAND SURFACE EMISSIVITY is significant for most terrestrial surfaces (1.4–14 mm) are de-emphasizes the temperature, shown as dark/ inten- longer than the wavelength of visible red light and hence sity. In addition to composition, the daytime image gives are known as thermal infrared. The TIR is subdivided into a good sense of topography, because sunlit slopes are three ranges (LWIR, MIR, SWIR) for which the atmo- warmer than shadowed slopes. In the nighttime image, sphere is transparent (atmospheric “windows”) so that the most temperature effects are subdued, and the image energy can be measured from space. closely resembles the Land Surface Emissivity (LSE) alone. Introduction Exceptions include standing , which is cooler than Thermal emissivity e is the efficiency with which a surface the land during the day but warmer at night. Standing emits its stored heat as thermal infrared (TIR) radiation. water (C) in the floor of Death Valley shows dark green It is useful to know because it indicates the composition in the daytime image but light pink in the nighttime image. of the radiating surface and because it is necessary as Vegetation (A) appears dark in the daytime image, when it a control in atmospheric and energy-balance models, since is cooling its canopy by evapotranspiration. The toe of an it must be known along with brightness temperature to alluvial fan (B) appears darker at night, when soil moisture establish the heat content of the surface. The first practical rises to the surface and evaporates. demonstration of multispectral TIR imaging for composi- The colors in Figure 1 indicate rock type. For example, the emissivity of quartzite is low (0.8) at 8.3 and 9.1 mm tional mapping was from a NASA airborne scanner flown m over Utah (Kahle and Rowan, 1980). (blue and green) but high at 10.4 m (red); therefore, it is Emissivity differs from wavelength to wavelength, just displayed as red. Other rock types and display colors can as reflectivity r does in the spectral region of reflected be understood by comparing the images and emissivity (0.4–2.5 mm). Emissivity is defined as spectra in Figure 1. The discussion below focuses on algorithms designed Lðl; TÞ to recover from remotely sensed spectral radi- eðlÞ¼ (1) Bðl; TÞ ance data. Figure 2, of a desert landscape, compares spec- tral radiance to temperature and emissivity images where L is the measured spectral radiance and B is the recovered from it. Also shown are emissivity spectra of theoretical blackbody spectral radiance for a surface vegetation and the geologic substrate. As explained in with a skin temperature T. B is given by Planck’s law the entry Land Surface Temperature, temperature and which, together with the basic of TIR radiative emissivity recovery is an underdetermined problem, and transfer, is discussed in the entry Land Surface Tempera- dozens of approaches have been proposed and published ture (LST). that break down the indeterminacy. These fall in four clas- Unlike T, which is a variable property of a surface ses: deterministic algorithms that solve for LST and LSE controlled by the heating history and not directly by com- exactly, algorithms that recover the shape of the LSE spec- position, e(l) is independent of T and is a function directly trum only, model approaches that make key assumptions, of composition. Furthermore, e(l) in the TIR wavelengths and algorithms that attempt also to scale or calibrate the (3–14 mm) responds to different aspects of composition normalized spectra to their actual emissivity values. than reflectivity r(l) at 0.4–2.5 mm. In general, r at wave- In evaluating the algorithms, it is useful to ask how lengths 0.4–2.5 mm is controlled by the amounts of accurately it is necessary to recover LSE and LST. For oxides, chlorophyll, and water on the surface; e in the example, many analytic algorithms that seek to identify TIR is controlled more by the bond length of Si and O in surface composition rely not so much on actual emissivity silicate minerals. Examples of emissivity spectra are given values, but on the central wavelengths of emissivity min- in Figure 1. ima (e.g., reststrahlen bands), which can be diagnostic TIR spectroscopy is especially important because for many rocks and minerals. If this is your goal, it may silicate minerals are the building blocks of the geologic not be necessary to scale the spectra, relying instead on surface of Earth, and their presence and amounts can be the simpler algorithms that just recover spectral shape. inferred only indirectly at shorter wavelengths. Thus TIR Errors in LST may affect some algorithms by warping spectroscopy is complementary to spectroscopy of the spectra over several mm of wavelength. This happens reflected sunlight. Good summaries of TIR spectroscopy because the shape of the Planck function changes with and its significance in terms of surface composition may temperature (Land Surface Temperature, Figure 2). be found in Lyon (1965), Hunt (1980), and Salisbury A 5 K error at 300 K, for example, will cause a slope in and D’Aria (1992). A good introduction to spectral the recovered emissivity spectrum of 0.05 from 8 to analysis may be found in Clark et al. (2003). 14 mm. However, the sharp mineralogical features Figure 1 shows daytime and nighttime false-color com- (0.2–0.5 mm wide) are readily distinguished against this posite images of spectral radiance from a sparsely vege- distorted continuum. tated part of Death Valley, California, enhanced using The TIR is commonly a difficult spectral region in a decorrelation contrast stretch (Soha and Schwartz, which to measure spectral radiance, and the images are typ- 1978; Gillespie et al., 1986). This stretch emphasizes the ified by a low signal–noise ratio. This ratio is commonly emissivity component of the signal, shown as color, and represented by the “noise equivalent D temperature” or LAND SURFACE EMISSIVITY 305

Land Surface Emissivity, Figure 1 Airborne thermal infrared multispectral scanner (TIMS: Palluconi and Meeks, 1985) false-color TIR radiance images of Death Valley, California (RGB ¼ 10.4, 9.1, 8.3 mm). Letters A, B, and C indicate sites discussed in the text. Central column shows laboratory spectra for field samples. Inset shows similar ASTER image “draped” over topography, looking north up Death Valley. The TIMS images cross the central part of the ASTER footprint (Courtesy Harold Lang and Anne Kahle, JPL).

NEDT, which is the temperature difference corresponding deterministic. It is additionally necessary that the LST be to the standard deviation of the radiance within significantly different between acquisitions. a homogeneous, isothermal scene region. For TIR imagers such as ASTER, NEDT300K 0.25 K. Also for ASTER, the Two-time, two-channel approach NEDT, atmospheric correction, and radiometric calibration If well-registered multispectral day–night radiance mea- all introduce errors of about the same size, leading to a total surements are available, it is possible to determine T and uncertainty in the recovered LST of about 1.5 K and in the e uniquely (Watson, 1992a). Although this approach is LSE of 0.015. esthetic, for most TIR data, the recovered temperatures and emissivities tend to be imprecise. For example, for image channels at 8 and 12 mm, day–night temperatures Deterministic solutions for emissivity of 290 and 310 K, and for NEDT ¼ 0.3 K, recovered As discussed in Land Surface Temperature, recovering LST would have an uncertainty of 20 K. This arises both LST and LSE from a single image is because of the flat shape of the Planck curve in the spectral underdetermined. In principle, this problem can be range around 300 K. removed by increasing the number of images acquired Wan (1999) showed that using an image channel in the for the same scene. For each n-channel image, after atmo- 3–5 mm window, where the slope of the Planck function is spheric compensation, there are n + 1 unknowns, but only steep, can improve the precision greatly and used the day– n measurements; for two images of the same scene, there night algorithm to make a standard MODIS LST product. are n + 2 unknowns, but 2n measurements (assuming However, for daytime data, reflected sunlight at 3–5 mm LST has changed but LSE has remained constant). There- must be accounted for (see Land Surface Temperature, fore, a two-channel image taken at two different times is Figure 3). Furthermore, acquiring data 12 h or more apart 306 LAND SURFACE EMISSIVITY

Land Surface Emissivity, Figure 2 TIR images and spectra, South Mountain, Arizona, looking SE. (a) Natural color; (b) TIR radiance at 9 mm; (c) brightness temperature; (d) emissivity (RGB ¼ 8, 8.5 and 9 mm, respectively); (e) emissivity spectra measured with the TELOPS, Inc., FIRST hyperspectral imaging spectrometer, August 8, 2007. The shrub spectrum was taken from the site in d marked the green cross; the rock spectrum from the red cross. Differences in the “rock” spectra likely relate to differences in the pixel field of view and exact location, and in the length of the atmospheric path between the sample and sensor. adds complexity because the scene may have changed how well emissivity limits are known a priori, and imple- between images, for example, because of dew. mentation would probably require some sort of image It is also advantageous to use more than two channels, classification to establish them closely. in which case the inversion for LST and LSE is overdeter- mined. This has the advantage of reducing the impact of Spectral-shape solutions measurement errors. The exaggeration of measurement Although it is not possible to invert the modified Planck error in this otherwise esthetic technique will become less equation for both e and T without external constraints, it severe as high-precision imagers such as SEBASS is possible to estimate spectral shape for e, at the expense < (NEDT300K,11mm 0.05 K: Hackwell et al., 1996) become of T and of the amplitude of the recovered spectrum, that widely available. is, the recovered spectra are essentially normalized, so that only relative amplitudes (wavelength to wavelength) are Emissivity bounds method known. This is nevertheless useful, since composition is Jaggi et al. (1992) observed that for every pixel and every generally determined from spectral shape, and not the absolute amplitudes. channel i there exists a locus of (T, ei) vectors that are possible solutions for the modified Planck equation (Equation 1, Land Surface Temperature). Because T must Ratio methods be the same for all image channels, some (T, ei) pairs can Watson (1992b) observed that ratios of spectrally adjacent be ruled out as candidate solutions. The range of solutions channels i and j described spectral shape accurately, pro- is even more limited if e and/or T can be restricted a priori. vided that T could be estimated even roughly: For the land surface, it is commonly possible to assume 5 < < ej Ljl ðÞexpðÞc2=ðliTÞ 1 that 0.8 e 1.0, for example. ¼ i (2) 5 ð Þ This elegant approach is not truly deterministic, ei Lilj exp c2 ljT 1 because it requires assumed limits to e and/or T. However, it requires no empirical assumptions. The technique does (c2 is a constant from Planck’s law, Equation 1, Land not appear to have been widely used, perhaps because it Surface Temperature). To calculate the e ratios, it is nec- does not identify the most probable values of e or T, only essary first to approximate the temperature T from the possible ranges. In practice, performance depends on measured radiances Li and Lj.Ife can be estimated LAND SURFACE EMISSIVITY 307

12 where C is spatially variable and atmosphere 310 K k specific. The TISI is found by rationing spectral radiances 305 K 10 for image channels i and j:

1 301.5 K − ai ai ai niai ai

sr Li ei ai Ts Ci 1 8 L (λ)*ε(λ) ¼ (6) − 300K aj aj aj njaj aj

m Lj ej aj Ts Cj μ 2

− 6 1 1 Here ai is defined as ni (and aj ¼ nj ), chosen to 1.0 make Equation 6 independent of T. Since for a wide range

), W m 4 ε λ 0.8 λ *( ) of temperatures the C ratio is close to unity, TISI is then ( ) L 0.6

λ ( = = 1=n 1=n 1=n 2 0.4 ε 1 ni 1 nj i i i Li Lj ei Ci ei TISI ; ¼ ¼ (7) 0.2 i j 1=n 1=n 1=n ai aj e j C j e j 0 0.0 j j j 8101214 Wavelength, μm The ratio spectra are insensitive to temperature, for nor- mal terrestrial ranges. The approaches are adaptable for most sensors. Land Surface Emissivity, Figure 3 Emissivity e(l) and spectral radiance spectra L(l) for basalt at 300 K. L(l) was calculated as the product of measured e(l) and a 300 K blackbody (B(l)) spectrum. In “Planck draping,” blackbody spectra are calculated Alpha-residual method for successively lower temperatures (e.g., 310, 305 and 301.5 K, The alpha-residual algorithm produces a relative emissiv- above) until emax B(l)=L(l) at some wavelength. The maximum ity spectrum that preserves spectral shape but, like the emissivity, e must be estimated, usually as a value near 0.95 as max ∗ ratio methods, does not yield actual e or T values. The in the example shown. e (l), the recovered e(l), is calculated as L alpha residuals are calculated utilizing Wien’s approxima- (l)/B(l). Both it and the found LST (301.5 K, above) will be ’ “ ” inaccurate unless the Planck functions are scaled correctly by tion of Planck s law, which neglects the 1 term in the emax. In the example shown, LST is in error by 1.5 K. The error denominator. This makes it possible to linearize the warps e∗(l) slightly. approximation with logarithms, thereby separating l and T:

c2 lj lnðejÞlj lnðLjÞ T (8) within 0.075, the uncertainty in T is 5K,andthee þ lj lnðc1Þ5lj lnðljÞlj lnðpÞ: ratios can be estimated with an average error of 0.007 (this estimate does not include the effects Here c1 and c2 are the constants defined in Planck’s law of measurement error). (Equation 1, Land Surface Temperature) and j is the image Becker and Li (1990) proposed a similar approach they channel. Wien’s approximation introduces a systematic “ ” called the temperature-independent spectral indices error in ej of 1 % at 300 K and 10 mm wavelength. (TISI) method. TISI begins with the observation (Slater, The next step is to calculate the means for the parame- 1980) that Planck’s law may be represented by ters of the linearized equation, summing over the n image channels: ð Þ ð Þ¼ ð Þ nk To Bk Ts ak To T (3) Xn Xn Xn c2 1 5 1 lj lnðejÞ lj lnðljÞ lj lnðLjÞ where B is the spectral radiance in image channel k T n j¼1 n j¼1 n j¼1 for a blackbody at temperature T and T is a reference tem- (9) s o 1 Xn perature. Constants nk and ak are given by þ ðÞlnðc1ÞlnðpÞ lj: n j¼1 c2 1 nkðToÞ¼ 1 þ ; lkTo exp ðc2=lkToÞ1 The residual is calculated by subtracting the mean from (4) the individual channel values. Collecting terms, a set of n BkðToÞ akðToÞ¼ equations is generated relating ei to Li, independent of T: nk ðToÞ To 1 Xn l lnðe Þm ¼ l lnðl Þ l lnðL Þþk : (10a) (Dash, 2005). The land-leaving spectral radiance j j a j j n j j i L , corrected for atmospheric absorption and path radiance j¼1 k # but not down-welling spectral irradiance L , is thus Xn k # ki 5li lnðliÞ lj lnðliÞðÞðlnðc1ÞlnðpÞ lj lÞ ð1 ekÞL ¼ nk ; ¼ þ k j¼1 Lk ekakTs Ck Ck 1 ð Þ (5) ekBk Ts (10b) 308 LAND SURFACE EMISSIVITY

Xn Xn ¼ 1 1 Retaining the assumption eref emax but allowing the m ¼ lj ln ðejÞ; l ¼ lj (10c) reference channel to vary, pixel by pixel, allows the model a n n j¼1 j¼1 emissivity approach to be accurate for a wider range of materials. This approach is called the normalized emissiv- Note that ki contains only terms which do not include ity method (NEM) (Gillespie, 1985; Realmuto, 1990). the measured spectral radiances, Li, and hence may be cal- First, the brightness temperature Tb is found for each culated from the constants. Although dependency on T has image channel, using Planck’s law. Tb differs from chan- been eliminated, it has been replaced by the unknown ma, nel to channel only if ej does also, since the actual skin related to the mean emissivity, such that the total number temperature must be the same. The channel j with the of unknowns is unchanged. The components of the maximum Tb is also the channel for which the maximum alpha-residual spectrum vary only with the measured ej occurs and becomes the reference channel. For 81 spec- radiances. They are defined as tra evaluated by Hook et al. (1992), 58 % of the tempera- tures found by the NEM algorithm were accurate to within ð Þ ai liln ei ma (11) 1 K, compared to only 21 % of temperatures recovered using the model emissivity method. and are equivalent to the right-hand side of Equation 10a Finding the maximum Tb has been called the “Planck (a is defined differently than in the TISI method). draping” method (Figure 3). This approach has been used to estimate e(l) from high-resolution radiance spectra col- lected by hyperspectral imagers such as SEBASS or by Model approaches field spectrometers. In this section, three algorithms distinguished by their Instead of examining the same scene element at two model assumptions are described. The most specific different times and temperatures, as in the day–night requires that both a value of e and the wavelength at which method, the scene element may be measured at different it occurs be known. The next requires only that the value wavelengths li and lj, chosen such that ei ¼ ej. In such be known. The third does not require the value of the emis- a case, it is necessary to find T (the “color temperature,” sivity to be known, only that the emissivity at two known Tc; see Equations 10 and 11, Land Surface Temperature) wavelengths be the same. and only a single e for the two channels, and the situation The model emissivity (or reference channel) method is deterministic (two measurements, Li and Lj, and the two (Kahle et al., 1980) assumes that the value of e for one unknowns, Tc and ei ¼ ej). As for the reference channel ’ of the image channel s ref is constant and known method, Tc can then be used to calculate a blackbody spec- a priori, reducing the number of unknowns to the number trum B, from which e(l) can be found. This treatment has of measurements. First, the temperature is estimated using been called the “graybody emissivity method” (Barducci !! and Pippi, 1996). 1 c2 c1eref The strength of the technique lies in its ability to recover T ¼ ln þ 1 (12) emissivities even if the value of e is unknown. The main l 5 ref pLref lref weaknesses are that for imagers with only a few TIR chan- nels, the basic requirement, ei ¼ ej, is not met for much of Lyon (1965) suggested that, for most rocks, the maxi- the land surface, and it is not always possible to know li mum emissivity (emax) was commonly 0.95 and and lj. If the assumption is valid, the accuracy for T is com- occurred at the long-wavelength end of the 8–14 mm parable to NEM, provided li and lj are widely separated TIR window. This observation has been used to (e.g., Mushkin et al., 2005), but for most rock spectra, errors justify the assumption eref ¼ emax, typically for 10 < lref are 5 K. Barducci and Pippi (1996) proposed the < 12 mm. graybody emissivity method for hyperspectral scanners, Blackbody spectral radiances Bj for the remainder of for which the basic requirement is more likely to be met. the channels are next calculated from T and Planck’s law. The model emissivities are ej ¼ Lj/Bj. No single value of eref is appropriate for all surfaces. Scaling approaches For example, for vegetation, emax 0.983; if the value Once relative spectra have been calculated, they can be is assumed to be 0.95, the emissivities will be calibrated to “absolute” emissivity provided a scaling fac- underestimated, the spectrum warped, and T tor is known. Applied to the ratio approach of Watson overestimated by 2.3 K. Vegetation, snow, and water (1992b) or the TISI approach of Becker and Li (1990), this are all subject to this kind of error. Also, reststrahlen bands is basically the same as one of the model algorithms. How- for some types of rocks, for example, peridotite, occur ever, scaling can also be done from empirical regression near 10 mm, and emax occurs at shorter wavelengths. For relating the shape of the emissivity spectrum to an abso- these rock types, the errors may be even greater. Neverthe- lute value at one wavelength. The regression is typically less, the model emissivity approach is robust and has the based on laboratory spectra of common scene compo- virtue of simplicity. It produces reliable results for nents. More complex approaches also are possible: the a wide range of surface materials. first example given below combines the “two-channel, LAND SURFACE EMISSIVITY 309 two-time,” and TISI approaches to convert the relative relationship between the mean emissivity e and the TISI spectra to emissivities. variance of alpha-residual emissivities, MMD utilizes an The hybrid TISI approaches requires first that assumed linear relationship between e and the range of daytime and nighttime MIR and LWIR images be the emissivities themselves, represented by the maxi- acquired and co-registered and that their TISI ratios be mum–minimum difference or MMD. calculated. Essentially, there are four measurements The MMD algorithm requires that the e spectrum be (LMIR,day, LLWIR,day, LMIR,night, and LLWIR,night), four estimated (e.g., using NEM) in order to calculate MMD, unknowns (eMIR, eLWIR), and one model assumption from which e is predicted. The apparent spectrum is then (the on the target). The MIR reflectivity rescaled according to this average, T is calculated, and is the complement of eMIR by Kirchhoff’s law (for the the process is iterated until the change in T is less than complete mathematical development, see Dash, 2005). the NEDT. Using widely separated image channels improves the pre- TES uses land-leaving spectral radiance and down- cision of T and e recovery (e.g., Mushkin et al., 2005). welling sky irradiance as input and provides a first guess for T and ej using the NEM algorithm. The correction for Alpha-derived emissivity (ADE) method reflected sky irradiance is The ADE method (Kealy and Gabell, 1990; Hook et al., 1992; Kealy and Hook, 1993) is based on the alpha- 0 ð1 ejÞ L j ¼ Lj I# (14) residual approach. To recover ei, ma may be estimated via p an empirical regression to the variance parameter na found for laboratory spectra: where Lj is the ground-leaving spectral radiance, compen- sated for atmospheric absorption and path radiance, I#is Xn the down-welling sky irradiance, and (1e ) is the scene ¼ 1 2 j va aj (13) ’ reflectivity (Kirchhoff s law).0 The NEM emissivities are n 1 j¼1 then recalculated from Lj and normalized: where a is defined in Equation 11. The best-fitting curves e ¼ 1/x b ¼ j (15) relating ma and na are of the form ma cna , where c and x j e are empirically determined coefficients (c ¼0.085, n ¼ 0.40, and r2 ¼ 0.935 for ASTER). MMD is calculated from the b spectrum and used to a Once the emissivities have been estimated, the temper- predict emin (instead of e, as in the MMD approach), which ature may be calculated using Planck’s law. For 95 % of is used for scaling: the library spectra, T was recovered within 1.6 K of the correct value, and Hook et al. (1992) showed that 67 % ¼ : : 0:737; ¼ emin emin 0 994 0 687 MMD ej bj were accurate to within 1 K, compared to 58 % for bmin the NEM. (16) The key innovation of the ADE approach is to utilize the empirical relationship between the average e and After early 2009, a linear regression (emin ¼ 0.8625MMD a measure of the spectral contrast or complexity in order + 0.955) was used for scaling in TES (Gustafson et al., 2006) to restore the amplitude to the alpha-residual spectrum. in order to improve TES precision for low-contrast spectra in The regression is based on the observation that, for standard ASTER data products. The TES algorithm differs a blackbody, the mean emissivity is unity and the spectral from the MMD approach in using a better estimate of the variance is zero. For minerals with reststrahlen bands or emissivity andinbasingthe“absolute” measure of emissiv- other emissivity features, the variance is greater than zero ity on emin rather than e, a difference that results in less scatter and, of course, the mean is less than unity. In use, the mean of the data about the regressed line and, hence, improved is predicted from the variance, which is calculated from performance (1.5 K; 0.015 e). the measured radiances.

Temperature–emissivity separation algorithm (TES) Classification-based algorithms The TES algorithm (Gillespie et al., 1998) uses a variant of Classification approaches exploit the relationship between the “minimum–maximum difference” or MMD approach composition and e and/or r to estimate e pixel by pixel in of Matsunaga (1994) to scale relative emissivity spectra. at least one-image channel, generally in order to find T. TES is used to generate standard T and e products from T can then be used to calculate e(l) in the other channels. ASTER, but it has been generalized for different scanners. Approaches that use channels in reflected sunlight TES can work with as few as three channels provided the (0.4–2.5 mm) require imagers with multiple, co-registered channel wavelengths are well chosen to capture the range telescopes. They also make the assumption that TIR emis- of emissivities in scene spectra. sivities and visible–SWIR reflectivities are correlated. The MMD algorithm is related to the ADE algorithm, In some cases, for example, vegetation or water, the TIR but is simpler. Whereas ADE utilizes the empirical emissivities can be predicted accurately; in others, for 310 LAND SURFACE EMISSIVITY example, many rocks, this assumption is less robust. Nev- Gillespie, A. R., Kahle, A. B., and Walker, R. E., 1986. Color ertheless, simply being able to distinguish rock and/or soil enhancement of highly correlated images I. Decorrelation and 20 from vegetation can improve accuracy by 1–2K.Asan HSI contrast stretches. Remote Sensing of Environment, , 209–235. example, the NDVI approach (see Equation 9, Land Sur- Gillespie, A. R., Matsunaga, T., Rokugawa, S., and Hook, S. J., face Temperature) makes use of co-registered visible red 1998. Temperature and emissivity separation from advanced (0.65 mm) and near-infrared (NIR: 0.7–1.2 mm) daytime spaceborne thermal emission and radiometer image channels in order to recognize pixels that have (ASTER) images. IEEE Transactions on Geoscience and a significant fraction of vegetation. Remote Sensing, 36, 1113–1126. Gustafson, W. T., Gillespie, A. R., and Yamada, G., 2006. Revi- sions to the ASTER temperature/emissivity separation algo- Conclusions rithm. In Sobrino, J. A. (ed.), Second Recent Advances in – Quantitative Remote Sensing. Spain: Publicacions de la Only a fraction of published temperature emissivity Universitat de València, pp. 770–775, ISBN 84-370-6533-X; separation algorithms have been discussed here. (For an 978-84-370-6533-5. alternative summary, see Dash (2005).) Increasingly Hackwell, J. A., Warren, D. W., Bongiovi, R. P., Hansel, S. J., sophisticated approaches are being devised to improve Hayhurst, T. L., Mabry, D. J., Sivjee, M. G., and Skinner, on old treatments, for example, by using neural net tech- J. W., 1996. LWIR/MWIR imaging hyperspectral sensor for air- nology to tune algorithms (e.g., Mao et al., 2008; Liang, borne and ground-based remote sensing. Proceedings- SPIE The International Society For Optical Engineering, 2819, 102–107. 1997). However, the basic categories discussed above Hook, S. J., Gabell, A. R., Green, A. A., and Kealy, P. S., 1992. still apply. A comparison of techniques for extracting emissivity informa- For the most part, calibration inaccuracies, measurement tion from thermal infrared data for geologic studies. Remote uncertainty, and inaccurate atmospheric characterization all Sensing of Environment, 42, 123–135. contribute to errors in the recovered LST and LSE. These Hunt, G., 1980. Electromagnetic radiation: the communication link in remote sensing. In Siegal, B. S., and Gillespie, A. R. (eds.), errors are commonly as large as or larger than those – attributable to the algorithms themselves, at least for Remote Sensing in Geology. New York: Wiley, pp. 5 45. Jaggi, S., Quattrochi, D., and Baskin, R., 1992. An algorithm for the the high-resolution imagers commonly used for Earth- estimation of bounds on the emissivity and temperatures from surface studies. Therefore, algorithms themselves are now thermal multispectral airborne remotely sensed data (Abstract). not the dominant factor limiting recovery accuracy. In Realmuto, V. J. (ed.), Summary of the Third Annual JPL Air- However, the next few years may see the introduction of borne Geoscience Workshop, June 1–5, Jet Propulsion a new generation of sensors, such as SEBASS, with dramat- Laboratory Publication 92–14. Pasadena, CA: Jet Propulsion – ically improved measurement characteristics. In this case, Lab, pp. 22 24. Kahle, A. B., and Rowan, L. C., 1980. 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Scientific usefulness Quantifying surface roughness One important surficial geologic process is aeolian erosion, Good reviews of techniques for describing quantitatively transport, and deposition of sediments. The shear stress surface roughness can be found in Dierking (1999), wind produces at the earth's surface is strongly affected Thomas (1999), Shepard et al. (2001), and Campbell by the surface roughness. The aerodynamic roughness (2002), Chap. 3. The simplest description of surface http://www.springer.com/978-0-387-36698-2