Spatial scale and pattern dependences of

Landscape Ecol DOI 10.1007/s10980-016-0357-y

RESEARCH ARTICLE

Spatial scale and pattern dependences of aboveground biomass estimation from satellite images: a case study of the Sierra National Forest, California Shengli Tao . Qinghua Guo . Fangfang Wu . Le Li . Shaopeng Wang . Zhiyao Tang . Baolin Xue . Jin Liu . Jingyun Fang

Received: 8 November 2015 / Accepted: 29 February 2016 Ó Springer Science+Business Media Dordrecht 2016

Abstract Context Spatial scale and pattern play important roles in forest aboveground biomass (AGB) estimation in remote sensing. Changes in the accuracy of satellite images-estimated forest AGBs against spatial scales and pixel distribution patterns has not been evaluated, because it requires ground-truth AGBs of fine resolution over a large extent, and such data are difficult to obtain using traditional ground surveying methods. Objectives We intend to quantify the accuracy of AGB estimation from satellite images on changing spatial scales and varying pixel distribution patterns,

Electronic supplementary material The online version of this article (doi:10.1007/s10980-016-0357-y) contains supplementary material, which is available to authorized users.

in a typical mixed coniferous forest in Sierra Nevada mountains, California. Methods A forest AGB map of a 143 km2 area was created using small-footprint light detection and ranging. Landsat Thematic Mapper images were chosen as typical examples of satellite images, and resampled to successively coarser resolutions. At each spatial scale, pixels forming random, uniform, and clustered spatial patterns were then sampled. The accuracies of the AGB estimation based on Landsat images associated with varying spatial scales and patterns were finally quantified. Results The changes in the accuracy of AGB estimation from Landsat images are not monotonic, but increase up to 60–90 m in spatial scale, and then decrease. Random and uniform spatial patterns of

S. Tao  Q. Guo  F. Wu  B. Xue  J. Liu State Key Laboratory of Vegetation and Environmental Change, Institute of Botany, Chinese Academy of Sciences, Beijing 100093, China

L. Li State Key Laboratory of Earth Processes and Resource Ecology, Beijing Normal University, Beijing 100875, China

S. Tao  Z. Tang  J. Fang Department of Ecology, College of Environmental Sciences, and Key Laboratory of Earth Surface Processes of the Ministry of Education, Peking University, Beijing 100871, China

S. Wang German Centre for Integrative Biodiversity Research (iDiv) Halle-Jena-Leipzig, Leipzig, Germany

Q. Guo (&) School of Engineering, Sierra Nevada Research Institute, University of California at Merced, Merced, CA 95343, USA e-mail: [email protected]

S. Wang Institute of Ecology, Friedrich Schiller University Jena, Jena, Germany

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pixel distributions yield better accuracy for AGB estimation than clustered spatial patterns. The corrected NDVI (NDVIc) was the best predictor of AGB estimation. Conclusions A spatial scale of 60–90 m is recommended for forest AGB estimation at the Sierra Nevada mountains using Landsat images and those with similar spectral resolutions. Keywords LiDAR  Above ground biomass (AGB)  Landsat  Scale  Pattern  Vegetation index  NDVIc

Introduction Forest ecosystems are among the most important carbon sinks in terrestrial ecosystems (Fang et al. 2001; Pan et al. 2011). Accurately estimating forest aboveground biomass (AGB) is of fundamental importance for investigating a broad range of issues such as bioenergy policies, sustainable forest management, and, in particular, terrestrial carbon cycling, in the context of global warming and climate change (Le Toan et al. 2011). Allometric equations, which express tree biomass as a function of diameter at breast height (DBH) or tree height, have been widely adopted in conventional approaches to AGB estimation (Brown 2002; Chave et al. 2005). Chave et al. (2005, 2014) provided allometric equations that can be used to predict forest AGB reliably across different tropical forests. TerMikaelian and Korzukhin (1997) reviewed biomass equations for 65 North American tree species. Jenkins et al. (2003) compiled diameter-based allometric equations for estimating total aboveground and component biomasses for United States tree species. These allometric equations, either generic or species specific, greatly facilitate the estimation of forest AGB, carbon stocks, and fluxes at the regional scale. However, these allometric equations were acquired by destructively harvesting trees, which is not environmentally friendly, labor intensive, and almost impossible to cover a large area. The need for a less expensive and more efficient approach has prompted much research into obtaining reliable estimates of forest AGB over large areas from optical remote-sensing images. Compared with conventional approaches, passive remote-sensing

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techniques significantly reduce the amount of field work and improve the efficiency. Classical space-borne remote-sensing data, for example MODIS (Muukkonen and Heiskanen 2007; Li et al. 2015), SPOT (Fransson et al. 2001; Soenen et al. 2010), ASTER (Muukkonen and Heiskanen 2005; Heiskanen 2006), NOAA AVHRR (Hame et al. 1997), and Landsat Thematic Mapper (TM) and enhanced thematic mapper (ETM) (Franklin 1986; Tomppo and Katila 1991; Trotter et al. 1997), have performed well in forest AGB mapping in various forest types on local, national, and global scales, including tropical forest (Steininger 2000; Foody et al. 2003; Lu et al. 2004; Lu 2005), coniferous forest (Tomppo and Katila 1991; Hame et al. 1997; Muukkonen and Heiskanen 2005; Labrecque et al. 2006; Muukkonen and Heiskanen 2007), and temperate mixed forest (Zheng et al. 2004). The accuracy of satellite images for AGB estimation depends on the spatial scale and spatial pattern (namely, the distribution pattern of image pixels) (Franklin 1986; Woodcock and Strahler 1987; Trotter et al. 1997; Hyyppa¨ and Hyyppa¨ 2001; Lu 2006). Spatial scale and pattern are the most essential features in ecology (Levin 1992; Shugart et al. 2010; Chave 2013; Wang and Loreau 2014). The spatial scale matters in AGB estimation by the way of altering the spatial structure of a forest, resulting in a dynamic range of the spectral from the optical images (Franklin 1986; Woodcock and Strahler 1987; Trotter et al. 1997). The spatial distribution pattern of pixels matters because the spectral information associated with different pixel distributions (e.g., clustered, random, or uniform distributions) can differ greatly (Foody and Mathur 2004). Quantification of the accuracy of AGB estimation over large areas from satellite images with different spatial scales and patterns is therefore beneficial in selecting the best spatial scale and pattern at which the remotely sensed image can be used to its maximum utility. However, to the best of our knowledge, a comprehensive evaluation of changes in the accuracy of AGB estimation from satellite images against continuously increasing spatial scales (resolution-cell size) and varying spatial patterns has not been conducted, mainly because of the lack of fine-resolution ground-truth data over large areas. A few studies in the 1980s–2000s reported spatial-scale dependence of AGB estimation from Landsat images, but the spatial scales examined were not continuously increased and limited up to 40 ha

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(Trotter et al. 1997). In addition, without ground-truth AGB data over a large area, previous research could only resample optical images, with ground-truth AGB still on the original scale, causing a mismatch between the resolution of resampled pixel and of the groundtruth AGB (Franklin 1986; Trotter et al. 1997; Hyyppa¨ and Hyyppa¨ 2001). In other words, field data were often inadequate for covering the spatial extent of the resampled pixel size, and this hindered extensive evaluation of the spatial scale and spatial pattern dependences of AGB estimation from satellite images. Airborne light detection and ranging (LiDAR) is a state-of-the-art active remote-sensing technique (Lim et al. 2003). By emitting pulses and determining the elapsed time between the return signals from the target objects, airborne LiDAR is able to measure the vertical distribution of the tree canopy, and enables large-scale biomass estimation without missing detailed information at the individual tree level (Lim et al. 2003; Tao et al. 2014). Specifically, tree height information, which has been widely reported as a robust and saturation-free metric for estimating AGB, can be derived directly from LiDAR data (Lefsky et al. 1999). At regional scales, airborne LiDAR provides the most accurate AGB product compared with other remote-sensing techniques such as MODIS, Landsat, and radar (Lefsky et al. 2002; Asner 2009; Koch 2010; Marvin et al. 2014). Because of their high accuracies, airborne-LiDAR-derived AGB and AGB-related products have recently been used as ground-truth data when assessing the accuracy of traditional passive optical images, which are less accurate than LiDAR images (Chen 2007, 2010). In this study, we used airborne-LiDAR-derived AGB products across 143 km2 in Sierra Nevada mountains and Landsat images as typical examples of optical satellite images, to conduct a comprehensive evaluation of the dependences on spatial scale and pattern of coniferous AGB estimation from optical imagery. Landsat imagery was chosen because of its free availability to the scientific community, its temporal resolution continuity since the 1970s, its global coverage, and its fine spatial resolution, which is compatible with our forest inventory plots (Labrecque et al. 2006). All these merits make it favorable for forest AGB mapping. With the launch of Landsat 8, Landsat will continue to benefit the scientific community in increasing numbers of applications (Roy et al. 2014). We resampled Landsat images on

different spatial scales and generated three different patterns (i.e., random, uniform, and clustered) at each spatial scale, and focused on answering the following questions: (1) What is the accuracy of AGB estimation from Landsat images at continuously increasing spatial scales, and will the accuracy continue to increase or decrease as the spatial scale increases? (2) Will the accuracy change with different spatial patterns? Meanwhile, we are also interested in identifying the most effective vegetation index for AGB estimation in coniferous forests.

Materials and methodology Study site and field data The Sugar Pine site in the Sierra National Forest (Fig. 1) (37°260 N, 119°350 W, 499–2644 m above sea level) encloses around 143 km2 of the west slope of the Sierra Nevada mountains. As a typical mixedconifer site, the Sugar Pine site is characterized by sierra mixed conifer forest dominated by white fir (Abies concolor), ponderosa pine (Pinus ponderosa), incense cedar (Calocedrus decurrens), sugar pine (P. lambertiana), and giant sequoia (Sequoiadendron

Fig. 1 Sugar Pine study site (143 km2) in the Sierra National Forest, California, USA. The locations of surveyed plots were indicated by black dots. Backgrounds are hill-shaded DEMs generated from LiDAR data with a resolution of 0.5 m

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Landscape Ecol Table 1 Site conditions and descriptive statistics for field inventory data for Sugar Pine site Site condition

Value

Area (km2)

143

Slope (degree)

0–45 (99.49 %) 46–90 (0.51 %)

Elevation range (m)

499–2644

Mean tree height (m)

13.60

Number of surveyed trees

4944

Mean DBH (cm)

35.46

Number of hardwoods

801

Basal area proportion of hardwoods (%)

11.01

giganteum). Major hardwoods within the stands are black oak (Quercus kelloggii) and canyon live oak (Q. chrysolepis) (Table 1). A total of 121 plots (500 m2) in the Sugar Pine site were ground surveyed. The plot centers were regularly spaced at 500 m intervals, at even Universal Transverse Mercator (UTM) coordinates. The plots were offset by 25 m in an arbitrary direction when the desired coordinates encountered physically inaccessible locations such as road surfaces and rivers. The ground-truth data were collected by fieldwork carried out in summer 2007, as previously described by Collins et al. (2011). Trees within the plot with a DBH C 19.5 cm were identified by unique numbers, and their height, DBH, and species were recorded. Smaller trees (with a DBH C 5 cm) were also measured, and the coordinates of the center of each plot and the stem center location of every single tree were determined using Trimble GeoXH GPS and TruPulse TM 360 (Collins et al. 2011). The AGBs for individual trees (DBH C 5 cm), measured in megagrams per hectare (Mg/ha), were calculated using the regional allometric equations provided by the USDA Forest Service Forest Inventory and Analysis (FIA) for California (Waddell et al. 2005). The plot-level AGB was calculated as the sum of the individual tree AGBs within the plot and regressed against airborne-LiDAR-derived height variables for upscaling the AGB to the entire study site. Airborne LiDAR data The study area was flown by the National Center for Airborne Laser Mapping using an Optech GEMINI

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Airborne Laser Terrain Mapper (ALTM) mounted in a twin-engined Cessna Skymaster. Five survey flights were conducted during September 13–15, 2007. One hundred and three flight lines were required, with a flight height of 700 m and planned overlap of 341 m. The Optech ALTM sensor was operated at 100 kHz, with a scanning frequency of 40 Hz and a total scan angle of 24°. Up to four echoes per pulse were recorded by the sensor and the final point density was 9.5 points/m2 (Tao et al. 2014). Pre-processing of the raw data was performed by the data vendor using TerraSolid’s TerraScan (http://www. terrasolid.fi). The AGBs for the research site were estimated by regressing canopy quantile height and statistical metrics with the ground-truth AGB of each plot, including H1, H5, H10, H25, H50, H75, H90, H95, H99, maximum height, mean height, minimum height, stdv, and cv (Hx is the xth percentile of the canopy height distribution, stdv is the standard deviation, and cv is the coefficient of variation). Four different regression techniques, namely support vector regression (SVR), artificial neural networks (ANN), linear regression, and exponential growth modeling, were used and compared under tenfold cross-validation conditions (Li et al. 2015). The LiDAR-derived AGB map for the study site was used as ground-truth AGB to assess the accuracies of AGB estimations from Landsat images with different spatial scales and spatial patterns. Landsat image processing Landsat TM images for September 9, 2007 were acquired for the Sugar Pine site; this maximized the correspondence between the data acquired using ground survey and airborne LiDAR. After geo-rectification to UTM projections, the images of bands 1–5 and 7 were calibrated radiometrically and corrected for the atmosphere using the FLASHH model in ENVI 5.0 software (ESRI Inc.). We then resampled the Landsat images from 30 m to successively coarser resolutions to 990 m using different resampling techniques: nearest neighbor resampling, bilinear interpolation and average value resampling, with increases of 30 m. Notice that without knowledge of the sensor’s point spread function, the resampling techniques can only change the pixel size but not in a manner that replicates a sensor operating at a spatial resolution associated with the resampled pixel size. The number of pixels

Landscape Ecol Table 2 Band values, band value transformations, and vegetation indexes for forest AGB estimation Feature

Formula

Reference

Band values (except band 6)

TMi

DVI

DVI = NIR - RED

Tucker (1979)

NIR RED

SR or RVI

SR ¼

OSAVI

NIRRED OSAVI ¼ ð1 þ LÞ NIRþREDþL ; L was set to 1.5

Rondeaux et al. (1996)

MSI

MSI ¼ SWIR NIR NIRRED ð1 SAVI ¼ NIRþREDþL

Huete (1988)

SAVI NDVIC MSAVI2 NDVI Tasseled cap Tasseled cap Tasseled cap

Birth and McVey (1968) and Jordan (1969) Rock et al. (1986)

þ LÞ; L was set to 0.5   MIRMIRmin NIRRED NDVIc ¼ NIRþRED 1  MIR MIR max min qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi MSAVI2 ¼ NIR þ 0:5  ðNIR þ 0:5Þ2  2ðNIR  REDÞ NDVI ¼ ðNIRREDÞ ðNIRþREDÞ P Brightness = bi 9 TMi, where bi is a coefficient for the calculation of brightness P Greenness = vi 9 TMi, where vi is a coefficient for the calculation of greenness P Wetness = hi 9 TMi, where hi is a coefficient for the calculation of wetness

Nemani et al. (1993) Qi et al. (1994) Rouse et al. (1974) Kauth and Thomas (1976) Kauth and Thomas (1976)

Band difference of all band combinations

dij = TMi - TMj

Kauth and Thomas (1976) Hyyppa¨ et al. (2000)

NDVI-type ratio of bands for all band combinations

NDVIij ¼ TMii þTMjj

TM TM

Hyyppa¨ et al. (2000)

decreased as the spatial scale changed from 30 to 990 m after resampling, therefore to ensure comparability among different spatial scales, fixed amounts of pixels were randomly selected on each spatial scale. Different pixel amounts were tested, including N990, N990/2, N990/5 and N990/7, where N990 is the number of pixels at a spatial scale of 990 m, i.e., the largest pixel size (or spatial resolution) examined. Random selection at each spatial scale was repeated 100 times, and their mean accuracy for AGB estimation was used. At each spatial resolution/scale, pixels forming random, uniform, and clustered spatial patterns were then sampled (Fig. A1), and their accuracies of AGB estimation were compared. A random spatial pattern was generated by choosing both the x-coordinate and the y-coordinate from uniform distributions. A uniform spatial pattern was generated by first selecting an arbitrary (random) location, and then placing points at fixed x and y spacings. A clustered spatial pattern was generated by randomly placing several seed points across the whole study site, and then growing each seed point to a cluster. To ensure comparability among different spatial patterns, each pattern at the same

spatial scale was generated 500 times, and the numbers of pixels for different spatial patterns were kept consistent to 1/10 of the total pixel amounts. The band values, band value transformations, and the vegetation indexes that are widely used in previously works (Hyyppa¨ et al. 2000; Zheng et al. 2004; Heiskanen 2006; Hall et al. 2006; Sarker and Nichol 2011) were calculated for each pixel, and finally regressed with AGB values generated from airborne LiDAR data (Table 2). The differences among the accuracies of AGB estimations using the three spatial patterns were quantified by multiple comparison tests using MATLAB 2013b (MathWorks 2013).

Results Forest AGB map We calculated the AGBs of the Sugar Pine site using four regression techniques, namely SVR, ANN, linear, and exponential; ANN yields the best accuracy, with R2 and RMSE of 0.81 and 153.4 Mg/ha, respectively

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Landscape Ecol Table 3 Accuracy of AGB estimation using LiDAR-derived height variables for Sugar Pine site Method

Sugar Pine site R2

RMSE (Mg/ha)

Linear regression

0.71

209.4

Exponential growth

0.77

172.0

Support vector regression

0.67

230.4

Neural network

0.81

153.4

(Table 3). ANN method was therefore chosen to upscale plot-level AGBs to the whole study site (Fig. A2). An obvious gradient in AGB values was identified for the Sugar Pine site and the highest AGB value is 1375.9 Mg/ha. AGBs respond roughly to the gradient in altitudes, with high AGB values found at the mountain valley areas and low AGBs at very low or high altitude areas (Fig. A3). Landsat accuracy at different spatial scales The regressions between LiDAR-derived forest AGB and vegetation indexes at different spatial scales are all strongly significant, with p \ 0.001. A trend in the changes in the R2 values with changing spatial scales can be observed: the accuracies increase up to spatial scales of 60–90 m, followed by a decrease at greater spatial scales with some fluctuations (Fig. 2a, c, e). The highest R2 values are around 0.57 and the differences between R2 values at different spatial scales are as large as or greater than 0.25 (Fig. 2a, c, e). This trend holds when various techniques were used for resampling the Landsat images. Besides, this trend also holds when different numbers of Landsat pixels are used for regressing with forest AGB (Fig. 3). For nearest neighbor resampling and bilinear interpolation resampling, the overall trends in the changes in the R2 values at different spatial scales are similar. However, for average value resampling, the decreasing trend in the R2 values after 60–90 m is not as dramatic as that of nearest neighbor resampling and bilinear interpolation resampling. The RMSE values also decrease at large spatial scales, and their values show roughly the opposite trend to that of the R2: a high R2 corresponds to a low RMSE (Fig. 2b, d, f). An overall decreasing trend in the RMSEs was found regardless of different resampling techniques; the RMSEs up to spatial scales of 60–90 m decrease dramatically, but decrease at a

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relatively slower speed at greater spatial scales, especially for nearest neighbor resampling and bilinear interpolation resampling. Landsat accuracy for different spatial patterns The differences between the R2 values for random and uniform spatial patterns are not significant, based on multiple comparison tests, at almost all spatial scales. This trend holds for different resampling techniques (Figs. 4, A4, A5), indicating equal accuracies of AGB estimation when random and uniform spatial patterns were selected. Random/uniform spatial patterns and clustered patterns give no significant differences at fine spatial scales for all interpolation methods (Figs. 4, A4, A5). However, the differences between random/ uniform spatial patterns and clustered patterns are significant with p \ 0.001 at large spatial scales for nearest neighbor and bilinear resampling methods; the accuracies of AGB estimation using clustered spatial patterns are lower than those achieved using random/ uniform spatial patterns (Figs. 4, A4,A5). For average value resampling, almost all the differences associated with the three spatial patterns are not significant except for a few spatial scales (Figs. A4, A5). Most effective predictor for AGB estimation Among the 47 vegetation indexes used for regression with forest AGB, NDVI-type ratios are effective predictors of forest AGB, including NDVIc, NDVI23, NDVI15, and NDVI13 (Fig. 5). Although the effective predictors are not same for different resampling techniques in Sugar Pine site, NDVIc is always the most effective predictor of forest AGB (Fig. 5); among ca. 3300 regressions with p \ 0.001, NDVIc was selected by 1858 regressions, 2377 regressions, and 2411 regressions for nearest neighbor, bilinear interpolation, and average value resampling, respectively, with 1825 times, 2346 times, and 2407 times, respectively, in the first step, indicating that NDVIc explains most variances in the dependent variable (forest AGB).

Discussion Spatial scale and pattern are recognized as key issues in remote sensing and landscape ecology research

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Fig. 2 Changes in accuracy of AGB estimation from Landsat images with increasing spatial scale. The grey bar indicates the spatial scale around which the highest R2 was achieved. Band values and vegetation indexes listed in Table 2 are used as explanatory variables. Number of pixels used for regressing

forest AGB is N990 for all spatial scales. For each spatial scale, N990 pixels were selected randomly 100 times and the mean accuracy for AGB estimation was used. All relationships are significant, with p \ 0.001

(Turner et al. 1989; Wu et al. 2002). The effects of spatial scale and pattern on the accuracy of forest AGB estimation from optical images has not been evaluated thoroughly because of the lack of ground-truth data over large areas. In the current research, we evaluated the effects of different spatial scales (resolution-cell size) and spatial patterns of the distribution of image pixels on the accuracy of forest AGB estimation from satellite images. We used Landsat images as an example of satellite images and airborne-LiDARderived AGB maps as validation data, and found a

unique trend in the changes in the accuracies of AGB estimation from Landsat images with increasing spatial scale and changing spatial pattern. First, the regressions between satellite-imagebased vegetation indexes and forest AGB are strongly significant, but of relatively low accuracy in terms of R2 and RMSE. This is consistent with previous reports (Trotter et al. 1997; Fazakas et al. 1999). The low R2 values may be associated with signal saturation problems. The optical sensors carried by passive remote-sensing platforms can suffer from serious

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Fig. 3 Changes in accuracy of AGB estimation with continuously increasing spatial scale. Different numbers of pixels are randomly selected for regression, and the overall trend is consistent with Fig. 2, in which a pixel amount of N990 is adopted. N990 means the total number of pixels at a spatial scale of 990 m. Random selection at each spatial scale was repeated 100 times, and the mean accuracy for AGB estimation was used

signal saturation problems, leading to a biased result for some forestry parameters such as forest AGB. This phenomenon is common for optical sensors and is

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observed with Landsat (Steininger 2000; Lu 2005, 2006; Gleason and Im 2011; Lu et al. 2012), MODIS (Blackard et al. 2008; Phillips et al. 2008; Li et al. 2015), SPOT XS (Fransson et al. 2001), ASTER (Heiskanen 2006), and radar signals (Mitchard et al. 2009), and some other systems. Secondly, the R2 values increase up to spatial scales of 60–90 m, followed by a decrease at greater spatial scales. This trend holds even if different numbers of pixels, i.e., N990, N990/10, N990/5, and N990/2, are used for regression (N990 is the number of pixels at a spatial resolution of 990 m), and different resample methods were used (Figs. 2, 3). This phenomenon has not been reported by previous researchers, probably because ground-truth AGB values over large areas are not available, therefore only the spatial scale of the plot size was explored by some researchers. De Wulf et al. (1990) estimated a number of AGB-related parameters, including stand basal area, average canopy height, and stand volume, using SPOT-1 spectral data, and found that using spectral data averaged at a large window gave better results than those averaged at smaller windows. Trotter et al. (1997) noticed that the accuracy of wood volume estimation using Landsat data was poor at the pixel scale, but acceptable accuracy can be obtained by averaging the pixel-scale estimates at an area of 40 ha. Similar conclusions were drawn by Franklin and McDermid (1993), who reported that a modest increase in the R2 value for volume estimation was achieved by averaging the band information over a 5 9 5 window. Fazakas et al. (1999) also found that the RMSEs for forest biomass and wood volume decreased with increasing size of aggregated image cell. In all of these studies, the image pixels were averaged over a window size, but the ground-truth AGB stayed at the plot level. The difference between our study and previous ones is that we not only upscaled the pixel size of the satellite imagery but also of the ground-truth AGB. The use of LiDAR data as ground-truth data over large areas allows the examination of accuracy at continuous spatial scales. Why the R2 values at spatial scales of 60–90 m are higher than those at other spatial scales? Although answering this question is not the object of this study, we presume that the reason might rest on the scale dependence of forest stability, i.e., the dynamics of the spatial structure of forest at different spatial scales. Spatial structure and spatial stability/variability affect

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Fig. 4 Multiple comparison test results for R2 values. Each spatial pattern at every spatial scale was repeated 500 times. Nearest neighbor method was used for resampling Landsat

images to coarser resolution. See Figs. A4, A5 for the results of bilinear interpolation and average value resampling

the functioning of forest (Levin 1992; Shugart et al. 2010; Chave 2013; Wang and Loreau 2014). Satellite images record and reflect the spatial stability/variability of forests by spectral imaging. To quantify the changes of forest AGB of Sugar Pine forest at different spatial scales, the local variance, defined by Woodcock and Strahler (1987) as a measure of the spatial variability, was calculated for the forest AGB at different spatial scales. We found that spatial variability of Sugar Pine forest dropped sharply from spatial scale of 30 m to 60–90 m, and changed slowly and little at greater spatial scales (Fig. A6), forming a negative variability–area relationship. This suggests that the forest structures in Sugar Pine site stay stable since 60–90 m in spatial scale, which corresponds to the spatial scale at which highest R2 values of AGB estimation was achieved. We therefore presume that the mechanisms responsible for the trend in changes in the R2 values might rest on the

interacting effects of scale dependence of forest stability and its corresponding spectral values. However, without quantitative analysis, no conclusion can be drawn. A thorough investigation on this issue will be our main task in the near future. Thirdly, the effects of spatial pattern are significant at large spatial scales for nearest neighbor and bilinear resampling methods; random and uniform spatial patterns are better than clustered spatial patterns. This may be attributed to the fact that clustered spatial patterns tend to sample limited information from the entire study site compared with random and uniform sampling patterns, especially when pixel numbers are low at large spatial scales. However, for average value resampling, the effects of spatial pattern are not significant at almost all spatial scales. Pixel values can be homogenized when resampled to coarser resolutions using average value resampling, covering the effects of different sampling strategies. In contrast,

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The superiority of NDVIc to other vegetation indexes is supported by our results (Fig. 5), when evaluated using selected times and selected orders of stepwise regression for identifying the best predictor (Franklin and McDermid 1993). NDVIc is the midinfrared-radiance-corrected NDVI, which accounts for understory effects, and has been reported to be an effective predictor of leaf area index and biomass (Nemani et al. 1993; Zheng et al. 2004). The overwhelming advantage of NDVIc might highlight the importance of middle-infrared information for AGB estimation (Boyd et al. 1996; Boyd 1999; see text in Supplementary Material). Furthermore, our results indicate that the effectiveness of NDVIc for AGB estimation is robust, regardless of changes in the spatial scales. It is worth noting that the main conclusion of this study should hold if satellite images of similar spectral resolution are used. The same work was conducted using National Agriculture Imagery Program (NAIP) aerial images containing four bands (red, green, blue, and near infrared), and the trend in the changes in the R2 values still held for the study site. The NAIP images were not calibrated, therefore the results are not presented in this paper.

Conclusions

Fig. 5 Numbers of selected times and numbers of first selected times for each of the 47 vegetation indexes and band transformations obtained by stepwise regression across different spatial scales. Only the top predictors are labeled. NDVIc is the best predictor for all spatial scales

nearest neighbor and bilinear resampling methods might retain the dynamics of pixel values when resampled to coarser pixel resolutions. The homogenized pixel values with average value resampling might also contribute to the slower decreasing trend in the R2 values compared to nearest neighbor and bilinear interpolation resamplings (Fig. 2e).

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This study provides a comprehensive evaluation of the effects of spatial scale and pattern on the accuracy of coniferous AGB estimation from satellite images. Using small-footprint airborne-LiDAR-derived forest AGB map of a 143 km2 area in Sierra Nevada mountains and Landsat TM images as examples of optical images, we found the trend in the changes in the accuracy of AGB estimation in Sugar Pine forest is not monotonic; the accuracy increases up to a spatial scale of 60–90 m, and then decreases. This holds true when different resampling methods for resampling optical images and different number of pixels were used for regressing with forest AGB. The spatial pattern affects the accuracy of AGB estimation, but show dependence of resampling methods. We also found NDVIc is the best predictor for AGB estimation in coniferous forest. This research is a case study, and its conclusions might be of use to researchers who are seeking the appropriate spatial scale and spatial pattern for

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estimating AGB (and AGB-related forest parameters) using optical remotely sensed images in Sugar Pine forest. More airborne LiDAR data from other forest types will enable a more comprehensive evaluation on the problem of spatial scale and spatial pattern in the near future. Acknowledgments This study was supported by the National Natural Science Foundation of China (Grants Nos. 41471363 and 41401505), the National Key Basic Research Program of China (2013CB956604), and the Sierra Nevada Adaptive Management Project (SNMAP). We are grateful for the constructive comments from the anonymous reviewers of an earlier version of the manuscript.

References Asner GP (2009) Tropical forest carbon assessment: integrating satellite and airborne mapping approaches. Environ Res Lett 4(3):4–11 Birth GS, McVey GR (1968) Measuring the color of growing turf with a reflectance spectrophotometer. Agron J 60(6):640–643 Blackard JA, Finco MV, Helmer EH, Holden GR, Hoppus ML, Jacobs DM, Lister AJ, Moisen GG, Nelson MD, Riemann R, Ruefenacht B (2008) Mapping US forest biomass using nationwide forest inventory data and moderate resolution information. Remote Sens Environ 112(4):1658–1677 Boyd DS (1999) The relationship between the biomass of Cameroonian tropical forests and radiation reflected in middle infrared wavelengths (3.0-5.0 lm). Int J Remote Sens 20(5):1017–1023 Boyd DS, Foody GM, Curran PJ, Lucas RM, Honzak M (1996) An assessment of radiance in Landsat TM middle and thermal infrared wavebands for the detection of tropical forest regeneration. Int J Remote Sens 17(2):249–261 Brown S (2002) Measuring carbon in forests: current status and future challenges. Environ Pollut 116(3):363–372 Chave J (2013) The problem of pattern and scale in ecology: what have we learned in 20 years? Ecol Lett 16:4–16 Chave J, Andalo C, Brown S, Cairns MA, Chambers JQ, Eamus D, Fo¨lster H, Fromard F, Higuchi N, Kira T, Lescure JP (2005) Tree allometry and improved estimation of carbon stocks and balance in tropical forests. Oecologia 145(1):87–99 Chave J, Re´jou-Me´chain M, Bu´rquez A, Chidumayo E, Colgan MS, Delitti WB, Duque A, Eid T, Fearnside PM, Goodman RC, Henry M (2014) Improved allometric models to estimate the aboveground biomass of tropical trees. Glob Chang Biol 20(10):3177–3190 Chen Q (2007) Airborne lidar data processing and information extraction. Photogramm Eng Remote Sens 73(2):109 Chen Q (2010) Retrieving vegetation height of forests and woodlands over mountainous areas in the Pacific Coast region using satellite laser altimetry. Remote Sens Environ 114(7):1610–1627

Collins BM, Stephens SL, Roller GB, Battles JJ (2011) Simulating fire and forest dynamics for a landscape fuel treatment project in the Sierra Nevada. For Sci 57(2):77–88 De Wulf RR, Goossens RE, de Roover BP, Borry FC (1990) Extraction of forest stand parameters from panchromatic and multispectral SPOT-1 data. Int J Remote Sens 11(9):1571–1588 Fang J, Chen A, Peng C, Zhao S, Ci L (2001) Changes in forest biomass carbon storage in China between 1949 and 1998. Science 292(5525):2320–2322 Fazakas Z, Nilsson M, Olsson H (1999) Regional forest biomass and wood volume estimation using satellite data and ancillary data. Agric For Meteorol 98:417–425 Foody GM, Boyd DS, Cutler ME (2003) Predictive relations of tropical forest biomass from Landsat TM data and their transferability between regions. Remote Sens Environ 85(4):463–474 Foody GM, Mathur A (2004) Toward intelligent training of supervised image classifications directing training data acquisition for SVM classification. Remote Sens Environ 93(1):107–117 Franklin J (1986) Thematic Mapper analysis of coniferous forest structure and composition. Int J Remote Sens 7(10):1287–1301 Franklin S, McDermid G (1993) Empirical relations between digital SPOT HRV and CASI spectral response and lodgepole pine (Pinus contorta) forest stand parameters. Int J Remote Sens 14(12):2331–2348 Fransson J, Smith G, Askne J, Olsson H (2001) Stem volume estimation in boreal forests using ERS-1/2 coherence and SPOT XS optical data. Int J Remote Sens 22(14): 2777–2791 Gleason CJ, Im J (2011) A review of remote sensing of forest biomass and biofuel: options for small-area applications. GI Sci Remote Sens 48(2):141–170 Hall R, Skakun R, Arsenault E, Case B (2006) Modeling forest stand structure attributes using Landsat ETM? data: application to mapping of aboveground biomass and stand volume. For Ecol Manag 225(1):378–390 Hame T, Salli A, Andersson K, Lohi A (1997) A new methodology for the estimation of biomass of conifer dominated boreal forest using NOAA AVHRR data. Int J Remote Sens 18(15):3211–3243 Heiskanen J (2006) Estimating aboveground tree biomass and leaf area index in a mountain birch forest using ASTER satellite data. Int J Remote Sens 27(6):1135–1158 Huete AR (1988) A soil-adjusted vegetation index (SAVI). Remote Sens Environ 25(3):295–309 Hyyppa¨ HJ, Hyyppa¨ JM (2001) Effects of stand size on the accuracy of remote sensing-based forest inventory. IEEE Trans Geosci Remote Sens 39(12):2613–2621 Hyyppa¨ J, Hyyppa¨ H, Inkinen M, Engdahl M, Linko S, Zhu Y-H (2000) Accuracy comparison of various remote sensing data sources in the retrieval of forest stand attributes. For Ecol Manag 128(1):109–120 Jenkins JC, Chojnacky DC, Heath LS, Birdsey RA (2003) National-scale biomass estimators for United States tree species. For Sci 49(1):12–35 Jordan CF (1969) Derivation of leaf-area index from quality of light on the forest floor. Ecology 50:663–666

123

Landscape Ecol Kauth RJ, Thomas G (1976) The tasselled cap—a graphic description of the spectral-temporal development of agricultural crops as seen by Landsat. In: LARS symposia, West Lafayette, p 159 Koch B (2010) Status and future of laser scanning, synthetic aperture radar and hyperspectral remote sensing data for forest biomass assessment. ISPRS J Photogramm Remote Sens 65(6):581–590 Labrecque S, Fournier R, Luther J, Piercey D (2006) A comparison of four methods to map biomass from Landsat-TM and inventory data in western Newfoundland. For Ecol Manag 226(1):129–144 Le Toan T, Quegan S, Davidson MWJ, Balzter H, Paillou P, Papathanassiou K, Plummer S, Rocca F, Saatchi S, Shugart H, Ulander L (2011) The BIOMASS mission: Mapping global forest biomass to better understand the terrestrial carbon cycle. Remote Sens Environ 115(11):2850–2860 Lefsky MA, Cohen W, Acker S, Parker GG, Spies T, Harding D (1999) Lidar remote sensing of the canopy structure and biophysical properties of Douglas-fir western hemlock forests. Remote Sens Environ 70(3):339–361 Lefsky MA, Cohen WB, Harding DJ, Parker GG, Acker SA, Gower ST (2002) Lidar remote sensing of above-ground biomass in three biomes. Glob Ecol Biogeogr 11(5):393–399 Levin SA (1992) The problem of pattern and scale in ecology. Ecology 73(6):1943–1967 Li L, Guo Q, Tao S, Kelly M, Xu G (2015) Lidar with multitemporal MODIS provide a means to upscale predictions of forest biomass. ISPRS J Photogramm Remote Sens 102:198–208 Lim K, Treitz P, Wulder M, St-Onge B, Flood M (2003) LiDAR remote sensing of forest structure. Prog Phys Geogr 27(1):88–106 Lu D (2005) Aboveground biomass estimation using Landsat TM data in the Brazilian Amazon. Int J Remote Sens 26(12):2509–2525 Lu D (2006) The potential and challenge of remote sensingbased biomass estimation. Int J Remote Sens 27(7):1297–1328 Lu D, Chen Q, Wang G, Moran E, Batistella M, Zhang M, Vaglio Laurin G, Saah D (2012) Aboveground forest biomass estimation with Landsat and LiDAR data and uncertainty analysis of the estimates. Int J For Res. doi:10. 1155/2012/436537 Lu D, Mausel P, Brondızio E, Moran E (2004) Relationships between forest stand parameters and Landsat TM spectral responses in the Brazilian Amazon Basin. For Ecol Manag 198(1):149–167 Marvin DC, Asner GP, Knapp DE, Anderson CB, Martin RE, Sinca F, Tupayachi R (2014) Amazonian landscapes and the bias in field studies of forest structure and biomass. Proc Natl Acad Sci 111(48):E5224–E5232 MathWorks Inc. (2013) MATLAB version 8.2.0., Natick, Massachusetts Mitchard ET, Saatchi SS, Woodhouse IH, Nangendo G, Ribeiro NS, Williams M, Ryan CM, Lewis SL, Feldpausch TR, Meir P (2009) Using satellite radar backscatter to predict above-ground woody biomass: a consistent relationship across four different African landscapes. Geophys Res Lett 36(23):L23401

123

Muukkonen P, Heiskanen J (2005) Estimating biomass for boreal forests using ASTER satellite data combined with standwise forest inventory data. Remote Sens Environ 99(4):434–447 Muukkonen P, Heiskanen J (2007) Biomass estimation over a large area based on standwise forest inventory data and ASTER and MODIS satellite data: a possibility to verify carbon inventories. Remote Sens Environ 107(4):617–624 Nemani R, Pierce L, Running S, Band L (1993) Forest ecosystem processes at the watershed scale: sensitivity to remotely-sensed leaf area index estimates. Int J Remote Sens 14(13):2519–2534 Pan Y, Birdsey RA, Fang J, Houghton R, Kauppi PE, Kurz WA, Phillips OL, Shvidenko A, Lewis SL, Canadell JG, Ciais P (2011) A large and persistent carbon sink in the world’s forests. Science 333(6045):988–993 Phillips LB, Hansen AJ, Flather CH (2008) Evaluating the species energy relationship with the newest measures of ecosystem energy: NDVI versus MODIS primary production. Remote Sens Environ 112(12):4381–4392 Qi J, Chehbouni A, Huete A, Kerr Y, Sorooshian S (1994) A modified soil adjusted vegetation index. Remote Sens Environ 48(2):119–126 Rock B, Vogelmann J, Williams D, Vogelmann A, Hoshizaki T (1986) Remote detection of forest damage. BioScience 36:439–445 Rondeaux G, Steven M, Baret F (1996) Optimization of soiladjusted vegetation indices. Remote Sens Environ 55(2):95–107 Rouse Jr JW, Haas R, Schell J, Deering D (1974) Monitoring vegetation systems in the great plains with ERTS. In: Third ERTS symposium, NASA SP-351, Washington, pp 309–317 Roy DP, Wulder MA, Loveland TR, Woodcock CE, Allen RG, Anderson MC, Helder D, Irons JR, Johnson DM, Kennedy R, Scambos TA (2014) Landsat-8: science and product vision for terrestrial global change research. Remote Sens Environ 145:154–172 Sarker LR, Nichol JE (2011) Improved forest biomass estimates using ALOS AVNIR-2 texture indices. Remote Sens Environ 115(4):968–977 Shugart HH, Saatchi S, Hall FG (2010) Importance of structure and its measurement in quantifying function of forest ecosystems. J Geophys Res. doi:10.1029/2009JG000993 Soenen SA, Peddle DR, Hall RJ, Coburn CA, Hall FG (2010) Estimating aboveground forest biomass from canopy reflectance model inversion in mountainous terrain. Remote Sens Environ 114(7):1325–1337 Steininger M (2000) Satellite estimation of tropical secondary forest above-ground biomass: data from Brazil and Bolivia. Int J Remote Sens 21(6–7):1139–1157 Tao S, Guo Q, Li L, Xue B, Kelly M, Li W, Xu G, Su Y (2014) Airborne Lidar-derived volume metrics for aboveground biomass estimation: a comparative assessment for conifer stands. Agric For Meteorol 198:24–32 Ter-Mikaelian MT, Korzukhin MD (1997) Biomass equations for sixty-five North American tree species. For Ecol Manag 97(1):1–24 Tomppo E, Katila M (1991) Satellite image-based national forest inventory of Finland. Int Arch Photogramm Remote Sens 28:419–424

Landscape Ecol Trotter C, Dymond J, Goulding C (1997) Estimation of timber volume in a coniferous plantation forest using Landsat TM. Int J Remote Sens 18(10):2209–2223 Tucker CJ (1979) Red and photographic infrared linear combinations for monitoring vegetation. Remote Sens Environ 8(2):127–150 Turner MG, O’Neill RV, Gardner RH, Milne BT (1989) Effects of changing spatial scale on the analysis of landscape pattern. Landscape Ecol 3(3–4):153–162 Waddell KL, Hiserote BA, Inventory F (2005) The PNW-FIA integrated database user guide: a database of forest inventory information for California, Oregon, and Washington. Forest Inventory & Analysis Program, Pacific Northwest Station, Portland, Oregon

Wang SP, Loreau M (2014) Ecosystem stability in space: alpha, beta and gamma variability. Ecol Lett 17(8):891–901 Woodcock CE, Strahler AH (1987) The factor of scale in remote sensing. Remote Sens Environ 21(3):311–332 Wu J, Shen W, Sun W, Tueller PT (2002) Empirical patterns of the effects of changing scale on landscape metrics. Landscape Ecol 17(8):761–782 Zheng D, Rademacher J, Chen J, Crow T, Bresee M, Le Moine J, Ryu SR (2004) Estimating aboveground biomass using Landsat 7 ETM? data across a managed landscape in northern Wisconsin, USA. Remote Sens Environ 93(3):402–411

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