Both ASTER and MODIS LST products were not corrected for terrain angular and adjacency effects. The terrain-induced angular effect can be corrected based on the cosine method [18] as follows [19]: (1) T = ( T ′ 4 cos γ ) 1 / 4where T is the corrected LST and T′ the satellite-derived LST. γ is the angle between the satellite-view path and the normal to the terrain element. To a thermal band, the angle of emitted radiance can be geometrically determined from the following equation: (2) cos γ = cos α cos β + sin α sin β cos ( ϕ s − ϕ )where α is the local slope angle, β the satellite zenith angle, φ_s the satellite azimuth angle, and φ the aspect angle of the terrain element.

In addition to the emittance by the terrain element, the terrain irradiance is also contributed from the adjacent terrain [20-22]. The adjacency effect on the terrain irradiance is accounted for by the terrain-view factor with a trigonometric function as: (3) M a = π L ¯ 1 − cos α 2 ,where M_a is the irradiance from the adjacent terrain and L(x00304) is the local average radiance emitted from the surrounding terrain [23]. The effect needs to be included in terrain correction for satellite data with a fine spatial resolution. In the case of MODIS data with a spatial resolution of 1-km, it is negligible [24].

ASTER LST has a spatial resolution of 90-m, different from MODIS LST, which are directly incomparable with respect to spatial resolution. It is necessary to upscale ASTER LST before a comparison of ASTER and MODIS data. ASTER LST can be upscaled with a scaling function from a fine resolution into a coarse one. In the case of topographic heterogeneity, the angular and adjacency effects can be accounted for in the follow scaling function [11]: (4) T = ( 2 ∑ ɛ i T i 4 sec α i − π L ¯ ∑ ( sec α i − 1 ) cos γ i 2 ɛ cos γ ∑ sec α i ) 1 / 4where the subscript i denotes the pixel i at a sub-pixel or fine scale. The upscaled ASTER LST may serve as a basis for investigating the uncertainty embedded in MODIS 1-km LST.

The MODIS 1-km LST products have been found to be underestimated with the GSW algorithm [25] over semiarid areas [7, 11, 12]. To reduce the underestimation, Liu et al. proposed a correction approach as follows [19]: (5) T s ′ = T s + ( A 2 T 31 + T 32 2 + B 2 T 31 − T 32 2 ) ︸ a ( 1 ɛ ′ − 1 ɛ ) + ( A 3 T 31 + T 32 2 + B 3 T 31 − T 32 2 ) ︸ b Δ ɛ ( 1 ɛ ′ 2 − 1 ɛ 2 )where ε = 0.5(ε₃₁ + ε₃₂) and Δε = ε₃₁ − ε₃₂. T_s is the retrieved LST (K). T₃₁ and T₃₂ are the brightness temperature (K), and ε₃₁ and ε₃₂ are the emissivity used for MODIS TIR bands 31 and 32, respectively. A₂, A₃, B₂, and B₃ are the coefficients in the look-up table defined by Wan and Dozier [25]. ɛ ′ = 0.5 ( ɛ 31 ′ + ɛ 32 ′ ). T s ′ is the rectified LST (K). ɛ 31 ′ and ɛ 32 ′ are the “accurate” emissivities. The components a and b can be estimated from multiple regression approach [19].

With the three approaches, we can reduce the discrepancy between ASTER and MODIS LST. Further incorporated with angular and surface features, we may make more insightful analysis into terrain effects on MODIS LST.

The study area is located on the Loess Plateau of China. Figure 1 shows the land cover features and topography of the area, produced from ASTER data collected on 8 June 2004. The geographic extent was defined by the acquired ASTER image with four corners: (34.44°N, 109.47°E), (34.21°N, 110.27°E), (33.65°N, 110.14°E), and (33.78°N, 109.35°E). Agricultural field, grassland, bare soil surface, forestland, and inland water surface dominant the area [Figure 1(a)]. It has highly variable topographical features suffering from serious soil erosion in the plateau. The elevation of the area ranges from 327 to 1,430 m, with an average of 518.6 m [Figure 1(b)]. The mean slope is 2.8 degrees with a standard deviation (S.D.) of 4.5 degrees, and the maximum slope is 43.6 degrees.

We used ASTER surface emissivity (AST_05) and surface kinetic temperature (AST_08) products, dated on 8 June 2004. Liu et al. [11, 12] detailed these products. Figure 2(a) shows the acquired ASTER LST image. In addition, we used 3D-Ortho product (AST3A01) served as the digital elevation model (DEM) in this study. The 1-km DEM data were generated from the 90-m DEM data [11].

We acquired the same date MODIS products including MOD02_QKM, MOD02_HKM, MOD02_1KM, MOD03_L1A, and MOD11_L2 data. MOD03_L1A geolocation product provided satellite zenith and azimuth angles for each MODIS 1-km pixel. MOD11_L2 data contains LST and band-averaged emissivity in band-31 (10.780–11.280 μm) and band-32 (11.770–12.270 μm) generated using the GSW algorithm. Figure 2(b) shows the segmented MODIS LST image as the ASTER coverage. The scattered white pixels were missing values in the MODIS LST products. Other products were detailed in [11,12].

MODIS has the geolocation with an accuracy of 18±38 m in-track and 4±40 m cross-track [26]. ASTER has the geolocation with an accuracy of 50±15 m in- and cross-track [27]. Liu et al. [11,12] detailed image co-registration and segmentation.

ASTER narrowband emissivity was produced from bands 13 and 14 emissivity data. It was used as “accurate emissivity” in LST correction [13]. The narrow-band emissivity data were upscaled from 90-m to 1-km within the footprint of the corresponding nominal MODIS pixel [10]. The broadband emissivity was generated from all the emissivity in the five bands in the AST_05 product. It was used to upscale ASTER LST from 90-m to 1-km using equation (4). The upscaled LST was used as a reference for exploring the uncertainty embedded in MODIS 1-km LST. The 1-km LST data from MODIS product was rectified using [equation (5)]. The rectified MODIS LST was further corrected for terrain angular effect using equation (1).

Essentially, MODIS LST is determined from surface emissivity in the GSW algorithm. To evaluate the uncertainty in emissivity, we compared the ASTER and the MODIS emissivity at the corresponding wavelength. To investigate the uncertainties related to surface feature, we generated LST difference images from ASTER LST to original MODIS LST, and to that rectified with or without terrain correction. To find the terrain-induced uncertainty in MODIS LST, we analyzed the relationships of MODIS-to-ASTER LST and emissivity with angular matrix (angle of local slope and angle of emitted radiance)

The original 1-km MODIS LST was general lower than the ASTER LST. It had a discrepancy to the upscaled ASTER LST with -2.7±1.28K and a root-mean-square-error (RMSE) of 3.02K [Figure 3(a)]. The major large differences were located at the eastern part of the area along the edge of the valley [Figure 3(b)]. However, this does not mean that a large local slope would necessarily lead to a large LST discrepancy. Indeed, the ASTER-to-MODIS LST discrepancy had a larger range at a small slope than at a large slope [Figure 3(c)]. There was no significant trend in the LST discrepancy varying with the local slope. In contrast, the ASTER-to-MODIS LST difference was general lower than zero, and it had a tendency to change with the angle of emitted radiance (p>0.005). The largest difference was at an angle of around 11 degree [Figure 3(d)]. This demonstrated that the angle of emitted radiance was more important than the slope angle in affecting LST discrepancy.

The original MODIS LST increased generally after rectification with the GSW based approach. Yet, the discrepancy between the rectified LST and the ASTER is as large as 1.2±1.21 K. Even though the S.D. was lower than that of the ASTER-to-original MODIS LST, there existed the relative large differences at the range of 298-305K [Figure 4(a)]. These pixels were distributed mainly at the eastern part of the area [dark blue pixels in Figure 4(b)]. In comparison with Figure 1(a), these pixels are densely vegetated areas with high emissivity. Anyway, the LST discrepancy was close to zero mean from a low to a high slope [Figure 4(c)]. Comparing Figure 4(d) with Figure 3(d), we can see that the distribution of LST difference also changed with the angle of emitted radiance. This suggested that, even without explicit inclusion of terrain factors in the rectification, the original MODIS LST was rectified with the ASTER emissivity in which included already terrain effect.

Further corrected for terrain effect, the discrepancy was reduced to 0.1±1.33 K on average between ASTER and MODIS LST. Likely, there existed some pixels with a relative large difference at the range of 298-305K [Figure 5(a)]. The pixels were mainly vegetated areas with a high emissivity close to unity. It suggested that the conventional terrain correction might be not sensitive to and unsuitable for vegetated areas. To date, few terrain correction approaches incorporated the Bidirectional Reflectance Distribution Function (BRDF) effects, which is more significant to vegetation [28]. A more specific correction needs to be developed for densely vegetated rugged area. With respect to angular effect, the mean of LST difference was generally close to zero within the range of local slope angle. In contract, the LST discrepancy reduced more with a larger angle of emitted radiance [Figure 5(d)], because the terrain correction took effective directly with the angle of emitted radiance rather than the angle of local slope [equation(1)]. Again, the LST discrepancy showed a tendency to change with the angle of emitted radiance, as a result of the comprised angular and emissivity effects (Section 4.4). Further compared with the original MODIS-to- ASTER LST (Section 4.1), the direct terrain-induced effect contributed approximately 30% to the total LST discrepancy. Overall, it made not the major but the important influence on the MODIS 1-km LST.

MODIS emissivity is the key to retrieval of the MODIS 1-km LST. The uncertainty in emissivity directly affects the accuracy of LST. In the present examination, MODIS emissivity in band 31 had a large discrepancy to the corresponding ASTER emissivity and they showed no obvious correlation [Figure 6(a)]. As a result, the overestimated MODIS emissivity led to the underestimated LST.

With respect to terrain features, the ASTER-to-MODIS emissivity difference showed no obvious relation with local slope angle [Figure 6(b)]. In contrast, the discrepancy had a stronger trend with the angle of emitted radiance [Figure 6(c)]. This evidence enhanced our inference in Section 4.2 that terrain effect was included in emissivity used for rectifying the original MODIS LST. As a further inference, terrain features might have taken effects on retrieval of emissivity, and subsequent retrieval of LST. As a result, the significance of the relation in Figure 6(d) decreased after the original MODIS LST was rectified (p<0.001). Changes in the relationship of emissivity difference versus LST discrepancy supported our inferences on terrain effects [Figures 6(d)-6(f)].

The accuracy of MODIS emissivity relies on classification of land cover [25]. Each class has its designed emissivity value. Misclassification, not necessarily related to topographic feature, unavoidably results in errors in surface emissivity. For reliable use of satellite-retrieved LST, classification-induced uncertainty in emissivity needs to be explored in future study.