Scaling characteristics of remotely-sensed surface net radiance over densely-vegetated grassland in Northern China

Scaling characteristics of remotely-sensed surface net radiance over densely-vegetated grassland in Northern China Wenjiang Zhang a,b and Zhiqiang Gao a a Institute of Geographical Sciences and Natural Resources Research, CAS, Beijing 100101, China; b Graduate School, Chinese Academy of Sciences, Beijing 100049, China ABSTRACT The surface heterogeneity of densely vegetated region is often ignored as it doesn t show such an obvious spatial variation as sparse region. This paper is to examine to which degree the estimation difference with scale change would be. The surface net radiation and related variables between six consecutive scales from 30 to 960 m over a dense grass covered region in Northern China are calculated with a simplified scheme based on Landsat ETM data. The estimation agreements between neighboring scales are evaluated with the mean absolute percent difference and the index of agreement. The two indices indicated variation is not so obvious and can t determine whether the study area is homogeneous or not. Further analyses of the fraction variation of land covers with scales and the change of related mean variables for individual land cover with scale, reach a consistent result that the major covers with larger patches are more insensitive to scale change than the minor ones with smaller patches. The introduction of land cover information improves detecting the effect of patches with different covers when the surface net radiation is considered. Keywords: Scaling, Surface net radiance, Densely-vegetated grassland, heterogeneity 1. INTRODUCTION Net radiance of land surface, the fraction of solar energy finally intercepted by earth surface and above atmosphere, is the essential drive of different terrestrial processes, including water cycle, heat exchange and biological activities [1~3]. One widely noticed problem in estimating regional net radiance, is that to what degree the surface heterogeneity, and thus the resulting variables (such as reflectance, emission, micro-meteorological characteristics), will influence the spatial variation of net radiance [4, 5]. In the calculation of land surface input energy, the reflectance (Refl) and land surface temperature (LST) are among the most important elements, if the regional atmospheric attenuation is considered identical. So, many researches are dedicated to exploring the introduction vegetation index (VI) and vegetation fraction (vfr) to improve the modeling of land surface energy balance [6, 7]. Therefore, the studies of land surface thermal flux diverge into two trends, i.e. the dense vegetation intended one-source model and the two-source one for sparsely vegetated region, the latter of which is exposed to many uncertainties and thus attracted most attentions [1, 2, 8~10]. For the densely vegetated land, the surface seems able to be homogeneously treated. But is it the fact? To determine the spatial resolution error in calculating regional evapotranspiration (ET), Bresnahan and Miller compared the estimations of different schemes for a heterogeneous area at eight spatial resolutions [11]. Their result indicated that the critical scale in the study area for ET appeared to be at about 1 Km (960 m). Brunsell et al discussed the scale issues in land-atmosphere interactions with data collected in SGP97 Hydrology Experiment and suggested that the flux at 1 Km 2 estimated by remotely sensed data can t be compared with surface data. Anthoni and Gillies intensively analyzed the variation of net radiance, but their work was still focused on heterogeneous surface [12]. This paper aims to examine the scaling characteristics of remotely sensed net radiance over dense grass covered region in eastern Inner Mongolia of North China with Landsat ETM data, which are resampled to six different resolutions to represent scale change. The surface situations of study area will presented in Section 2. Data and methodology of net radiance modeling at different scales will be detailed in Section 3. And the next followed section will give the modeling results and detailed analyses. The paper will end with a short section of discussion and conclusion. 2. STUDY AREA The study area covers a 71 49 Km region in eastern Inner Mongolia of North China (116.20 ~ 117.08E, 43.35 ~ 43.79N, Address correspondence to zhangwj.04b@igsnrr.ac.cn, phone 81 10 64889832; fax 86 10 64889630 Remote Sensing and Modeling of Ecosystems for Sustainability III, edited by Wei Gao, Susan L. Ustin, Proc. of SPIE Vol. 6298, 62981O, (2006) 0277-786X/06/$15 doi: 10.1117/12.675930 Proc. of SPIE Vol. 6298 62981O-1

the little black rectangle in Fig. 1a). As eastern part of Inner Mongolia Plateau, the region ranges from 1100 ~ 1300 m in evaluation [13]. And it is the middle watershed of Xilin River, which runs across the area northwestwardly, as showed by Landsat ETM composite image in Fig. 1b. The temperate climate bears typical continental characteristics, with most of its annual 400 mm precipitation occurring in summer. So, the natural ecosystem is the temperate typical grassland, which is dominated by two gramineous communities: Stipa grandis and Leymus chinensis, respectively [13]. a b Figure 1. The location (a) and Landsat ETM composite image by band 4, 3 and 2 (b) of the study area. The fractions of different land covers are showed in Table 1, which indicates grass the dominant cover type in the study area. In Table 1, the dense grass has the vegetation fraction over 50%, and the temperate one ranges from 20% to 50%, while the sparse covered region is below 20%. Totally, about 80% of study area is grassland with vegetation fraction over 20%, most of which (about 58% of total area) are densely vegetated. If the riverside marsh is included, the fraction of vegetation cover will be over 91%. So, this densely-vegetated study area provides chance to examine to which degree the scale of land surface variable will affect the net radiance estimation over densely-vegetation region. Table 1. The land cover fractions at different resolutions. Land Cover LC ID 30 60 120 240 480 960 Forest F21 0.13 0.13 0.13 0.13 0.11 0.08 Shrub F22 0.21 0.21 0.21 0.20 0.20 0.05 Dense G31 57.98 57.96 57.99 58.14 58.65 60.20 Grass Temperate G32 21.76 21.78 21.77 21.82 21.81 22.15 Sparse G33 6.34 6.34 6.31 6.30 6.16 5.94 Lake W42 0.78 0.78 0.77 0.76 0.76 0.69 Reservior W46 0.32 0.32 0.32 0.32 0.32 0.24 Village T52 0.58 0.58 0.59 0.54 0.45 0.29 Sand D61 0.95 0.95 0.96 0.91 0.86 0.64 Salina D63 0.52 0.53 0.53 0.52 0.48 0.37 Marsh D64 4.70 4.70 4.69 4.67 4.69 4.32 Rocky D66 0.52 0.51 0.51 0.47 0.42 0.29 Dry farmland A123 5.21 5.21 5.21 5.21 5.07 4.74 However, absolute homogeneous vegetated region is almost absent in natural world. As showed in Figure 2, the study area, though highly vegetated, is some heterogeneous. Besides the dominant grass covers, the patches of other minor cover types are studded among the grassland. Therefore, whether the patches in dense grassland are sensitive to scale will be answered. Proc. of SPIE Vol. 6298 62981O-2

Fig. 2. The area fraction of different land cover in study area. In the following section, the data of Landsat ETM and land use will be resampled to different resolutions to examine the variation of regional net radiance over study area. 3. DATA AND METHODOLOGY 3.1. Data In the study, the remotely sensed data were observed by Landsat 7 ETM at about 10:49 am of local standard time on July 10 and October 14, 2000. The sun elevation and azimuth are 61.81, 130.84 and 36.01, 157.61 for July and October scene, respectively. These two scenes are chosen to represent summer and autumn. The original resolutions of ETM data are 28.5 m for band 1-5, 7, and 57 m for band 61 (low gain) and 62 (high gain). Since the reflectance of study area isn t low, the thermal band of low gain is taken. All the bands of 1~7 are resampled to six resolutions with bilinear interpolation, as showed in Table 2. The resolution of 30 represents the typical scale of Landsat TM/ETM, while the coarsest resolution (960 m) is designed to model the scale of widely used MODIS products. Table 2. The pixel resolutions and numbers of for different scaling schemes. Scale 1 2 3 4 5 6 Resolution (m) 30 60 120 240 480 960 Pixel Number 2368 1632 1184 816 592 408 296 204 148 102 74 51 The land cover data are taken from the Landsat TM derived 2000 version of Chinese LUCC Dataset. Firstly, the vector LUCC data are converted to grids of 30 m resolution. Then, the data of fine grid are further degraded to produce data of other coarser scales as Table 2 indicated. What should be noted here is that the resampling method of land cover is different from that of ETM data. When the neighboring fine grids are aggregated into coarse one, the land cover type of resulting grid will be assigned as the one that has the largest area in the grid. 3.2. Methodology The regional surface net radiance is often estimated through surface energy balance, which can be formulated as: Proc. of SPIE Vol. 6298 62981O-3

R n (x,y) = (1 - r 0 (x,y)) K (x,y) + L (x,y) - 0 (x,y) T s 4 (x,y) (1) where r 0 (x, y) is the total surface albedo of certain pixel (x, y), is the average of atmospheric transmissivity, K and L represent downward short-wave (0.3-3 μm) and long-wave (3-100 μm) radiation components respectively, and 0 (x, y) is the thermal emissivity of pixel (x, y). Related parameters or elements are obtained as following steps, which consist of the simple methodology to estimate surface net radiance in this study. a) r 0 (x, y). The priority here is not the high accuracy but the scaling effect of estimation, the whole land surface reflectance r 0 (x, y) is derived from simplifying the albedo conversion scheme from narrowband to broadband suggested by Liang [14, 15] : r 0 (x,y) = 0.356 r 1 (x,y) + 0.130 r 3 (x,y) + 0.373 r 4 (x,y) + 0.085 r 5 (x,y) + 0.072 r 7 (x,y) 0.0018 (2) where r i is the land reflectance of i th TM/ETM band, which can be calculated with related radiation calibration and solar radiation at top of atmosphere (TOA). b) K (x,y). The downward solar radiation is estimated as K (x,y) = K 0 * cos ( s ) (3) where K 0 is solar radiance constant, which is usually assigned as 1369 W/m 2 and s is the solar zenith angle when the sensor acquired the ETM data in use. c) L (x, y). The downward long-wave radiation L (x, y) is mainly contributed by the atmospheric thermal radiation, so it can be obtained by: K (x,y) = T 4 a (x,y) (4) where is the Stephen-Boltzman constant. T a is the estimated atmospheric temperature with statistical equation suggested by Ma et al [16] : T a - 273.15 = (T s - 273.15) * a + b (5) The parameters of a and b can be defined by regressing surface data. And Ma et al [16] also gave the simple scheme for calculating T s (LST) with TM/ETM band 6 through Formulae (6) ~ (11). T sat (x,y) = C 1 / ln(c 2 / L 6 (x,y) + 1) (6) TOA = T 4 sat (x,y) (7) 0 = c TOA + d (8) T s = [ 0 / 0 (x,y)] 0.25 (9) 0 (x,y) = v (x,y)p v (x,y) + g (x,y) (1-P v (x,y)) + 4< >[1- P v (x,y)] P v (x,y) (10) P v (x,y) = [(NDVI(x,y) - NDVI min ) / (NDVI max - NDVI min )] (11) With surface observation data, the parameters of c and d also can be determined. d) 0 (x,y) T 4 s (x, y). This term is the component of land surface upward thermal radiation. It is the function of LST (T s ) and emissivity 0 (x, y), and can be determined from above Formulae (6) ~ (11). 4. ANALYSIS With the practical methodology presented in Section 3.2, the net radiation over the study area at six scales is calculated, respectively. The followed analyses include three aspects: a) the first is to examine the fraction variation of land covers with scale, b) the second is to compare the estimation difference of every neighbouring scales with mean absolute percent difference (MAPD) and the index of agreement (idx) suggested by Wilmott [17], c) and the final is to check the change of related mean variables with scales for each land cover. 4.1. Fraction variation of land covers with scales Within the study area, totally 13 different land covers are found: forest, shrub, dense, temperate and sparse grasses, lake, reservoir, village, sand, salina, marsh, rocky and dry farmland. Area fraction of these land covers at six different resolutions are shown in Table 1. As indicated by Figure 2, the covers other than grass, marsh and farmland (which consist of over 96% total study area at all scales) are small sparse patches. So, with increase of grid area the fraction of Proc. of SPIE Vol. 6298 62981O-4

minor land covers decreases, though not sharply. On the other hand, only the two most dominant cover types (dense and temperate grasses) experience an increase in fraction with grid area. This will influence estimation averages for individual land cover when the scale changes, as discussed in Section 4.3. 4.2. Estimation difference of every neighbouring scales Willmott [17] suggested several useful statistic indices to evaluate model performance, including the mean absolute percent difference (MAPD) and the index of agreement (idx), which will be adopted in the study to examine the estimation difference of scales. Equations for the two indices respectively are: n 100 Pi Oi MAPD n (12) O i 1 n n 2 2 1 [ ( i i) / ( i i )] i 1 i 1 (13) Idx P O P O O O where P i and O i are respectively the predication and observation values of pixel i for the variable in discussion, while O is the observation value average of all pixels for the variable. Only of July scene the MAPD (Table 3) and idx (Table 4) are presented, for the page consideration. Table 3. Mean absolute percent difference (MAPD) of neighbouring scales for July scene. vfr NDVI Refl Ts Rn 030-060 5.9 6.9 2.4 0.1 0.8 060-120 5.8 6.7 2.5 0.2 0.9 120-240 5.7 6.6 2.5 0.2 1.0 240-480 5.8 6.8 2.6 0.3 1.1 480-960 6.1 7.2 2.8 0.3 1.2 Note: vfr, Refl and Rn represents vegetation fraction, surface reflectance and net radiance, respectively. 030-060 means that estimation of 30m is the observation while 60m is thought as predication. The expressions are shared by later tables. Table 4. Index of agreement (idx) of neighbouring scales for July scene. vfr NDVI Refl Ts Rn 030-060 0.9787 0.9722 1.0000 0.9967 0.9932 060-120 0.9767 0.9851 1.0000 0.9942 0.9909 120-240 0.9744 0.9839 1.0000 0.9903 0.9879 240-480 0.9714 0.9825 1.0000 0.9860 0.9841 480-960 0.9677 0.9600 1.0000 0.9810 0.9795 In the Table 3 and 4, the vegetation fraction, NDVI, surface reflectance, LST and net radiation are compared between different scales. It is indicated that variation between scales for these variables are not very obvious, though vegetation index related variables (vfr and NDVI) relatively show a little more different. However, this can t validate the study area to be homogeneous. The weak contribution of minor land covers may be drowned in the mean indices of whole area dominated by a few major types. The followed analysis for individual land cover is necessary to discover more definitive facts. 4.3. Variation of related mean variables for each land covers with scales For the page limit, only mean estimation of LST and surface net radiation for individual land cover at six scales of July scene are presented (Table 5 and 6) and will be discussed in detail. In Table 5, the lake has the lowest mean LST (284.88 K) while the highest (312.54 K) is found in the village (or small town), which is at least 1 K higher than that of surrounding grassland. Through jointly comparing the scale differences and land cover fraction, the scale induced variation shows some relationship with the patchiness of land cover. The eight minor land covers (less than 1% of fraction) experience a mean LST difference of 2.17 K between the lowest and Proc. of SPIE Vol. 6298 62981O-5

highest scales, while this number for other five major covers is only 0.51 K. So, when the spatial heterogeneity of regional net radiation is examined, not only the traditional fraction of vegetated area but also the further fraction distribution of vegetated area among different vegetated covers should be carefully taken into account. When the fraction of vegetation area is considered the study area is highly densely vegetated (96.65%), however it is dominated by more than five different land covers that show diverse response to scale change. Table 5. Mean estimation of LST for individual land cover at six scales (July scene). LC Fraction% 30 60 120 240 480 960 F21 0.13 309.51 309.44 309.59 310.24 311.49 306.83 F22 0.21 310.91 310.90 311.08 311.11 311.42 313.70 G31 57.98 311.43 311.45 311.54 311.64 311.71 311.78 G32 21.76 311.40 311.40 311.50 311.61 311.70 311.65 G33 6.34 311.95 311.96 312.06 312.17 312.43 312.44 W42 0.78 284.88 284.76 284.96 284.77 284.86 284.42 W46 0.32 303.07 303.09 303.21 303.17 303.16 306.69 T52 0.58 312.54 312.54 312.67 312.84 310.06 309.18 D61 0.95 311.58 311.67 311.65 311.80 312.39 312.07 D63 0.52 309.56 309.53 309.70 309.86 311.62 310.94 D64 4.70 306.23 306.13 306.34 306.44 306.88 307.57 D66 0.52 309.72 309.68 309.87 309.97 309.94 312.26 A123 5.21 307.94 307.89 308.05 308.13 308.38 308.08 The mean estimations of surface net radiation for each land cover are listed in Table 6. On the whole, the differences of net radiation between scales are not obvious, with a cover averaged difference of 7.2 W/m 2. For individual land cover, the scale related estimation difference is the direct function of cover patchiness, which agrees with the situation of LST. The five major covers are less sensitive (3.7 W/m 2 ) to scale change than the other eight minor ones (9.3 W/m 2 ). So, the smallest fraction of forest cover (0.13%) has the largest difference of 21.7 W/m 2, which would be uninterpretable without relating to the cover patchiness. The net radiation estimation of October scene indicates similar scale related variety thought the variation is not so obvious as that of July scene. Table 6. Mean estimation of net radiation for individual land cover at six scales (July scene). LC Fraction% 30 60 120 240 480 960 F21 0.13 542.68 542.91 542.69 536.39 526.08 557.21 F22 0.21 552.24 552.15 550.88 550.54 547.50 530.51 G31 57.98 548.85 548.60 547.83 547.08 546.39 545.34 G32 21.76 531.65 531.45 530.64 529.90 529.26 529.61 G33 6.34 518.67 518.17 517.90 517.00 515.73 516.40 W42 0.78 724.28 724.95 723.68 725.15 724.45 727.68 W46 0.32 575.06 574.07 574.21 575.29 574.81 559.75 T52 0.58 525.15 524.96 523.94 522.52 527.09 517.50 D61 0.95 499.55 497.73 499.34 497.22 494.47 497.18 D63 0.52 549.31 549.13 548.09 546.82 546.42 540.45 D64 4.70 567.80 568.01 566.80 565.99 563.13 559.13 D66 0.52 557.33 557.44 556.23 554.95 555.58 556.61 A123 5.21 557.85 557.74 556.78 556.16 554.66 555.74 Proc. of SPIE Vol. 6298 62981O-6

5. DISCUSSION AND CONCLUSION 5.1 Discussion With respect to the spatial heterogeneity of regional surface net radiation, the only discrimination of vegetated with unvegetated land cover can t safely describe the potential spatial difference. So, the information of land cover fraction can be introduced to improve detecting the effect of patches with different covers. However, the study pays emphasis on the scale induced difference of related surface variables. The adopted methodology to estimate surface net radiation with Landsat ETM data in Section 2.2 can t escape estimation deviations because of its simplification. The potential estimation errors may lie in the simple average of atmospheric attenuation, fitting thermal light of TOA with surface thermal light, and regressing atmosphere temperature with LST. If more physical schemes are taken for these steps, it is reasonable to be optimistic of reaching more convictable result that the introduction of land cover can improve detecting the effect of patches with different covers. 5.2 Conclusion To examine the ignoring surface heterogeneity of densely vegetated region, this paper focused on the spatial variation of surface net radiance and related variable between six consecutive scales from 30 to 960 m of a dense grass region. The estimation agreements between neighbouring scales are evaluated with the mean absolute percent difference and the index of agreement. The variation indicated by the two indices is not very obvious and can t determine whether the study area to be homogeneous or not. Further analyses of the fraction variation of land covers with scale and the change of related mean variables for individual land cover with scales, reached consistent result that the major covers with larger patches are more insensitive to scale change than the minor ones with smaller patches. With the analyses of this study, two points can be reaches: 1) For the densely vegetated region as the study area, different from sparse situation the area fraction of vegetation doesn t always safely work to provide an accurate determination whether the region is homogenous or not; 2) The introduction of land cover information will improve detecting the effect of patches with different covers when the surface net radiation is considered. ACKNOWLEDGEMENT This work was supported by National Natural Science Foundation of China (Project:40471097) and National 973 Key Project of China (2002CB412507),USDA UV-B Monitoring and Research Program under a grant from USDA CSREES 2005-34263-14270. Outstanding Overseas Chinese Scholars Fund of Chinese Academy of Sciences(2004-7-1). Chuihui Plan of Ministry of Education of China (Z2004-1-65010). REFERENCES 1. Lhomme J P, Chehbouni A, Comments on dual-source vegetation-atmosphere transfer models, Agricultural and Forest Meteorology 94, pp. 269~273, 1999. 2. Kustas W P, Norman J M, Reply to comments about the basic equations of dual-source vegetation-atmosphere transfer models, Agricultural and Forest Meteorology 94, pp. 275~278, 1999. 3. Zhan X, Kustas W P, Humes K S, An intercomparison study on models of sensible heat flux over partial canopy surfaces with remotely sensed surface temperature, RS Envi.58, pp. 242~256, 1996. 4. Woodward F I, Lomas M R,,Integrating fluxes from heterogeneous vegetation, Global Ecology & Biogeography 10, pp. 595~601, 2001. 5. Lyons T J, Halldin S, Surface heterogeneity and the spatial variation of fluxes, Agricultural and Forest Meteorology 121, pp. 153~165, 2004. 6. Blyth E M, Representing heterogeneity at the Southern Super Site with average surface parameters, Journal of Hydrology 188-189, pp. 869~877, 1997. 7. Susan Moran M, Humes K S, Pinter J P J, The scaling characteristics of remotely-sensed variables for sparsely-vegetated heterogeneous landscapes, Journal of Hydrology 190, pp. 337~362, 1997. 8. Norman J M, Kustas W P, Humes K S, A two-source approach for estimating soil and vegetation energy fluxes in observations of directional radiometric surface temperature, Agricultural and Forest Meteorology 77, pp. 263~293, 1995. Proc. of SPIE Vol. 6298 62981O-7

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