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FUSION OF SATELLITE LAND SURFACE ALBEDO PRODUCTS ACROSS SCALES USING A MULTIRESOLUTION TREE METHOD IN THE NORTHCENTRAL UNITED STATES Tao Hea, Member, IEEE, Shunlin Lianga,b, Fellow, IEEE, Dongdong Wanga, Yanmin Shuaic,d, Yunyue Yue a

Department of Geographical Sciences, University of Maryland, College Park, MD 20742, USA

b

College of Global Change and Earth System Science, Beijing Normal University, Beijing 100875, China c

d

Earth Resources Technology Inc. Laurel, MD 20707, USA

NASA Goddard Space Flight Center, Greenbelt, MD 20771, USA e

NOAA/NESDIS/STAR, Camp Springs, MD 20746, USA

Abstract Land surface albedo is a key factor in climate change and land surface modeling studies, which affects the surface radiation budget. Many satellite albedo products have been generated during the last several decades. However, due to the problems resulting from the sensor characteristics (spectral bands, spatial and temporal resolutions, etc.) and/or the retrieving procedures, surface albedo estimations from different satellite sensors are inconsistent and often contain gaps, which limit their applications. Many approaches have been developed to generate the complete albedo dataset; however, most of them suffer from either the persistent systematic bias of relying on only one dataset or the problem of sub-pixel heterogeneity. In this study, a data fusion method is prototyped using multi-resolution tree (MRT) models to develop spatially and temporally continuous albedo maps from different satellite albedo/reflectance datasets. Data from the Multiangle

Imaging

Spectro-Radiometer

(MISR),

Moderate

Resolution

Imaging

Spectroradiometer (MODIS), and Landsat Thematic Mapper (TM)/Enhanced Thematic

2 Mapper Plus (ETM+) are used as examples, at a study area in the north-central United States mostly covered by crop, grass, and forest from June to September 2005. Results show that the MRT data fusion method is capable of integrating the three satellite datasets at different spatial resolutions to fill the gaps and to reduce the inconsistencies between different products. The validation results indicate that uncertainties of the three satellite products have been reduced significantly through the data fusion procedure. Further efforts are needed to evaluate and improve the current algorithm over other locations, time periods, and land cover types. Key words: albedo; data fusion; MRT; MODIS; MISR; TM; ETM+.

1. Introduction Land surface albedo is the ratio of the outgoing to the incoming solar radiation at the Earth’s surface, which is a key component in the radiation budget studies [1, 2]. Surface albedo estimations with accuracy of ±0.02 to ±0.03 are generally required for climate modeling studies [3, 4]. As satellite remote sensing provides unique techniques for monitoring surface albedo at a large spatial scale, many satellite albedo products have been developed at various temporal and spatial resolutions in the past decades [5], which makes it possible to study the long-term regional and global climate change [6]. Extensive examinations on these satellite albedo products have been made, and in some cases the accuracy was reported to be between 10% and 28% [7-12], out of which 3% to 5% error was reported resulting from the band differences in generating the broadband albedos [13]. This accuracy can be translated into absolute values of around 0.03 to 0.09, which suggests that current albedo products may still need improvement to satisfy the requirement of climate modeling studies [14, 15]. Moreover, there is a common problem of data gaps in current albedo products due to either cloud contamination or rapid changes in surface albedo. For example, when using the Moderate Resolution Imaging Spectroradiometer (MODIS) albedo products, the global mean annual probability of obtaining a sufficient number of clear sky observations for a typical 16-day compositing period is 80%, when data from MODIS onboard Terra and Aqua are combined. As the temporal window reduces to 10 days, the percentage of data gaps increases to 40% [16].

3 To reduce the gaps and improve the albedo estimations, researchers have been working on two types of approaches. The first one is to improve the retrieving procedure by introducing some other sources of data, such as the prior information [17, 18]. The second is to improve the albedo datasets from existing satellite data, which can take advantage of the sensor characteristics, and/or retrieving algorithms from different satellites [19-24]. Many researchers have been focusing on reducing the data gaps and producing spatially and temporally continuous albedo maps based on currently available satellite products. There are two major methodologies used to generate this type of albedo dataset to satisfy the needs of land surface modeling studies. The first one is the physical method, which relies on the surface bidirectional reflectance distribution function (BRDF) information. Research has been done using BRDF information from datasets with better angular sampling to convert surface reflectance with reduced angular sampling to albedo [19-22]. However, these methods assume that there are some homogeneous pixels with coarser spatial resolution that correspond to the finer resolution data for each of the land cover types. Therefore, it is sometimes difficult to translate information across scales if pure pixels are hard to be found at the coarser resolution. The second methodology uses the data-driven models that are directly based on the albedo products and utilize the spatial and/or temporal information to fill the gaps [23, 24]. Most of the existing algorithms that follow the second methodology use only one dataset, which may introduce systematic bias in the final albedo maps possibly results from simplified atmospheric/surface condition and/or sensor calibration [12, 13]. Another issue with the data-driven method is that the uncertainty evaluation for the original satellite products must be performed before the implementation of the data-driven models. The framework of the multi-resolution tree (MRT) method has been developed in recent years to make predictions consistent across different spatial resolutions by assuming a statistical model that is autoregressive in levels of resolution [25]. The MRT method has been widely used on large datasets to overcome the computational difficulties that other existing methods (optimal interpolation, kriging, etc.) may have [26]. Many researchers have been applying this method to interpolate and to smooth data over various satellite products [26-30]. Based on its time efficiency and capability of generating interpolations with minimal bias, this method was selected for performing the

4 albedo data fusion for multiple satellite datasets in this study. Since the data fusion on both temporal and spatial domain is very complex, we will focus on reducing spatial inconsistence of different satellite products in this study. The objective of this study is to prototype a data fusion procedure based MRT that combines three satellite albedo products from the Multi-angle Imaging SpectroRadiometer (MISR), MODIS, and Landsat to generate consistent albedo datasets at different spatial resolutions. In this paper, the general methodology and algorithm implementation are introduced in section 2. In section 3, the data from different satellite sensors are evaluated based on the ground measurements and inter-comparisons. Some preliminary results of surface albedo maps generated by the prototype data fusion process are shown and discussed in section 4. Summary and conclusions are given in section 5.

2. Methodology The theoretical basis of the MRT is the assumption that data at different spatial resolutions are autoregressive and can be organized in a tree structure (Fig 1). The linear tree-structure model can be expressed using Eq. (1): = yu Au y pa ( u ) + wu

(1)

where yu is the variable used to estimate at the scale u and y pa (u ) is the variable at the parent node. wu is the spatial stochastic process that follows a Gaussian normal distribution with a variance of Wu . Au is the state conversion matrix that estimates the variable at scale u from its parent node. There is a similar formulation that transfers the variable at scale u from its child node ch ( u ) . To determine the state conversion matrix, the “change-of-support” problem has been widely discussed [28, 31, 32]. In this study, the variable y (surface albedo) is estimated as the ratio of downward to upward solar radiation. If we assume that the downward radiation is the same for each ch ( u ) of a node

u , ideally the yu can be estimated as the average of all the ych (u ) . Other than the state conversion model, an observation model is also used in this method by linking the satellite products to the “truth” data:

5 = zu Cu yu + ε u

(2)

Here, zu is the satellite product with a white noise ε u that follows a normal distribution N ( 0, Φ u ) . Cu is the observation matrix that converts the variable of interest to the satellite data. Both the variable and the satellite data are surface albedo, and hence, the observation matrix Cu is set to one (identity matrix). The MRT algorithm consists of two steps: the leaves-to-root filtering step and the root-to-leaves smoothing step. The basic assumption of the tree model is that the treestructure follows a Markov chain process, which implies that the state variable is only related to its instant child nodes and instant parent node(s). The first step is a high-to-low resolution filtering, which is used to estimate the state variable from higher resolution data (Eq. (3)). The major purpose of this step is to fill in the gaps at different resolutions. In the leaves-to-root filtering step, the Kalman filter is used herein to deal with the Markov chain process. The second step is a low-to-high resolution smoothing to update the state variable with the information at a coarser resolution (Eq. (4)). This step generally assumes that the process at the parent scale provides the foundation of the process at current scale. After the Kalman-smoothing step, the datasets at different spatial scales become smooth and consistent. Details of the Kalman filter derivations can be found in Huang et al. [28].  yu = E ( yu Z u , Z ch (u ) )

(3)

 yu = E ( yu Z u , Z pa ( u ) )

(4)

To implement the MRT using multiple satellite products, there are generally several steps (Fig 2). First, the data uncertainties of different satellite products need to be evaluated and quantified. To do this, the ground measurements of surface albedo are collected to verify the satellite albedo products. An inter-comparison between different satellite datasets also provides accuracy information. Second, there is a basic assumption of zero mean in the spatial process of the variable used and predicted in the MRT. Therefore, the spatial trend surface for each of the satellite products needs to be extracted such that the de-trended albedo datasets can be used in the data fusion process. Based on

6 the detrended datasets, we calculate the variance Wu for the child nodes that are linked with same root node. For the observation error ε u of the leaves node, we obtain the Φ u from standard deviation of the relative difference between the finest resolution data and ground truth. To calculate the observation error of the nodes other than the leaves, we use standard deviation of the relative difference between the nodes and the aggregated values from their child nodes. Third, the leaves-to-root Kalman filtering and root-to-leaves Kalman smoothing procedures are implemented to obtain the updated probability estimation of the data at each scale. Finally, the updated spatial residual “albedo” is added back to the trend surface to obtain the actual updated albedo maps at all the scales involved. In this study, satellite albedo products from MISR, MODIS, and Landsat are used to apply the MRT method.

3. Characterization of the data uncertainties of different satellite products 3.1 Ground measurements The study area is located in the north-central of the United States. The land cover types are mainly cropland, grassland, forest, and some water bodies. Data were collected at eight AmeriFlux sites in the study area. Site information is listed in Table 1. 3.2 Satellite data In this study, we used three satellite albedo products from MODIS, MISR, and Landsat at different spatial resolutions. Band information for these sensors is listed in Table 2. 3.2.1

MODIS albedo products

MODIS Level 3 500 m albedo (MCD43A3) together with the quality flags (MCD43A2) are available every 8 days [33]. These data are based on the surface reflectance [34, 35] observations taken over a period of 16 days. The actual pixel size for this nominal “500 m” Sinusoidal grid is 463.3127 m. Shortwave broadband albedo is included in this product for both white-sky (bi-hemispherical) and black-sky (directional-

7 hemispherical) albedos. In this study, the MODIS tile h11v04 was selected to match with the Landsat scenes. 3.2.2

Landsat albedo data

The Landsat L1T dataset is geometrically and radiometrically calibrated and projected in the Universal Transverse Mercator (UTM) coordinate system from the original Landsat data. To obtain the surface reflectance, we used the Landsat Ecosystem Disturbance Adaptive Processing System (LEDAPS) tool [36] to do the atmospheric correction on Landsat L1T data from 2005. The atmospheric correction on Landsat data is similar to that on MODIS data [34, 35]. The LEDAPS tool relies on 6S software [37] to do the atmospheric correction based on some atmospheric ancillary datasets from reanalysis data. To mitigate the effect of residual cloud contamination on atmospheric correction, only the scenes with no more than 30% cloudy pixels were used in this study. Landsat surface albedo was then estimated from the surface reflectance with the support of MODIS 500 m BRDF/albedo data (details can be found in [20]). Specifically, we used the MODIS BRDF parameter to calculate the reflectance with the Landsat viewing geometry and applied the relationship of the reflectance and spectral albedo on Landsat data to obtain the Landsat albedo (black-sky and white-sky). 245 surface spectrum data (including vegetation, soil, rock, water, snow, and ice) were collected from USGS (U.S. Geological Survey) and ASTER (Advanced Spaceborne Thermal Emission and Reflection Radiometer) spectral libraries [38, 39] to carry out the narrowband-tobroadband albedo conversions proposed in Liang [40]. Eq. (5) and Eq. (6) were applied on the band conversion for both the Thematic Mapper (TM) on board Landsat-5 and the Enhanced Thematic Mapper Plus (ETM+) on board Landsat-7, respectively.

3.2.3

α short = 0.3206α1 + 0.1572α 3 + 0.3666α 4 + 0.1162α 5 + 0.0457α 7 − 0.0063

(5)

α short = 0.3141α1 + 0.1607α 3 + 0.3694α 4 + 0.1160α 5 + 0.0456α 7 − 0.0057

(6)

MISR albedo products

MISR Level 2 albedo products [41] with a spatial resolution of 1100 m were used in this study. The albedo data were stored in the grid system called Space Oblique Mercator (SOM). MISR albedo products contain both white-sky (bi-hemispherical) and black-sky (directional-hemispherical) albedos for each of the spectral bands. MISR shortwave

8 broadband albedo is converted from the spectral albedos using the following equation [40]:

α short = 0.126α 2 + 0.343α 3 + 0.415α 4 + 0.0037

(7)

3.3 Inter-comparison at AmeriFlux sites Validations of the MODIS and MISR surface shortwave broadband albedo products with ground measurements [7, 11, 42] and inter-comparisons between these two datasets [12, 43] have been made in the last decade. Although on a global basis these two products generally agree with each other and ground measurements well, the uncertainties of these products vary with both time and location. The Landsat albedo algorithm has been evaluated over some non-snow surfaces [20]. However, owing to the limited amount of validation dataset, the validation results may not really represent the error distribution of all the satellite albedo datasets. In this study, we mainly focus on prototyping the data fusion algorithm. To fully characterize the albedo accuracies and error distributions is beyond the scope of this paper. Satellite observations cover an area instead of a point. It is therefore not suitable to directly compare the satellite derived albedo products with ground measurements if the area covered by the pixel is not homogeneous. With the large field-of-view pyranometers the AmeriFlux measurements can cover an area of at least several Landsat pixels [20]. In this study, we extracted the average albedo of the site-specific Landsat pixels based on the instrument height in the comparison with ground measurements. In addition, we used the “blue-sky” albedo ( α total ) in validation, which is a combination of black-sky ( α bs ) and white-sky ( α ws ) albedos based on the diffuse skylight ratio ( rdif ) [44].

α total = rdif ⋅ α ws + (1 − rdif ) ⋅ α bs

(8)

Fig 3 shows the time-series of the MODIS, MISR, TM, and ETM+ “blue-sky” albedo values in comparison to the ground measurements at the eight AmeriFlux sites for the year of 2005. MODIS data with the highest quality (quality flag is 0) are labeled as “good” and other data are labeled as “others”. In this comparison, we can see that MODIS data have stable and smooth annual curves. Given that the MODIS algorithm tends to generate snow-free albedo (if the majority of valid clear sky observations are snow-free) and the

9 estimations from the magnitude version algorithm are flagged as low quality [33, 45], the abrupt changes caused by events such as ephemeral snow cannot be seen from good quality MODIS data. Moreover, there is a significant scale difference between MODIS data and ground measurements as MODIS albedo values tend to have an underestimation at vegetation sites if compared directly to ground measurements [7]. MISR data have similar values to MODIS data. However, the fluctuation in MISR data appears to be slightly higher because MISR algorithm only relies on observations taken within a very short time span. Landsat data provide the best match with the ground measurements except for the Lost Creek site, because they have the finest spatial resolution and are instantaneously available. Residual clouds and cloud shadow may be the possible reason for the data uncertainties shown in Fig 3 for Landsat albedo, although the cloud masks from the LEDAPS have been used. At Lost Creek, all three satellite products have underestimated albedos from the beginning of the growing season. Since this site covers some open shrubland, the surrounding forests may be the reason that those satellites observed smaller albedos. The georegistration accuracy of Landsat data might have also contributed to this underestimation. Statistics on the paired comparison of Landsat data and ground measurements are shown in Fig 4. Outliers contaminated by either clouds or cloud shadows were removed in the comparison. No significant differences were found for the data uncertainties on TM and ETM+. The standard deviation of the relative error of Landsat data is 14.59%, which implies the accuracy of Landsat data in our investigation sites. To prototype the data fusion algorithm, we therefore assume that all the Landsat albedo (black-sky) data used in this study have a relative error of 14.59%. In the following sections, we used black-sky albedos from the three sensors for error estimation and data fusion. MODIS and MISR data were reprojected into the UTM projection and Landsat data were aggregated to match MODIS and MISR in order to evaluate their albedo estimation accuracies. The relative errors of MODIS and MISR data were estimated using the aggregated Landsat data and MODIS data for each scene, respectively.

10

4. Results and discussion 4.1 Data selection and preprocess To evaluate this method using three different satellite datasets, a subset of approximately 135 km × 135 km area was extracted from all these products in the UTM projection for the year of 2005. This area is located in the Landsat scene p025r028 and shares the same land cover types as that in the whole MODIS tile h11v04. The uncertainties of the albedo products are assumed to be the same as mentioned in the previous section. Criteria were selected for the selection of data used in the experiment based on cloud coverage and the timing of the data. Landsat surface reflectance is generated through the LEDAPS tool that gives both a cloud flag and a filling value for each of the cloud pixels detected. As shown in Fig 3, there might be some possible residual cloud and shadow pixels from the LEDAPS outputs. The highly cloud covered scene may have high cloud shadow coverage. Moreover, undetected thin clouds may deteriorate the quality of atmospheric correction. To reduce the risk of cloud contamination, only Landsat scenes with less than 30% cloud coverage were used in this study. MODIS and MISR albedo products tend to rely on multiple observations, and hence generate cloud/cloud shadowfree data that suffer less from residual cloud impacts. The assumption that surface BRDF is invariant in 16 days is adopted in the MODIS albedo product. This assumption was followed in this study. In the following context, the DOY date refers to the 16-day time period around the specific date (e.g., DOY 192 implies the temporal window from DOY 185 to DOY 200). Owing to the limited spatial coverage of each MISR swath and cloud contamination problems, the MISR Level 2 albedo product often has many gaps as its albedo value for a pixel comes from the multiangular observations within a day. To reduce the effects of missing data from MISR albedo, data from multiple days within the temporal window were combined and the average was used. The Landsat data closest to the center of the temporal window was used.

11 4.2 Comparison of albedo products before and after MRT One of the basic assumptions in the MRT method is that the data on each scale shall have an expectation of zero mean in the spatial domain for each tree structure. However, the original albedo datasets cannot have a zero mean to satisfy the implementation requirements of MRT. The spatial trend surface needs to be extracted and then removed from the original data. Previous research has used methods such as spline fitting and kriging to find the spatial trend surface. These methods are quite time consuming [26], which limits their application in operational practice. We select a simpler method in our study by applying the median value of a moving window as the spatial mean. On the basis of the MRT theory [28], the window size can be determined by the ratio of spatial resolutions from two satellite products with adjacent scales, e.g., MISR/MODIS and MODIS/Landsat. Hence, for Landsat data, the window size is set to 15, and for MODIS and MISR, it is set to 3. Based on the site validation results, the relative error of Landsat albedo is 14.59%. We assume that this relative error is invariant to time and location in the study area to simply the problem. To obtain the observation error of MODIS, the inter-comparison was made between each pair of detrended MODIS and detrended Landsat obtained within the same time period. The error of MISR data was obtained in the same way but based on the comparison with detrended MODIS. The relative error of each MODIS and MISR scene is listed in Table 3. The observation errors for the satellite products are assumed to be proportional to the magnitude of albedo. Finer resolution data usually carry more information in the spatial domain than the coarser resolution data. Since the coarser resolution data can only provide the average information, the spatial variation of finer resolution data needs to be estimated to reserve the spatial random process. In this study, we characterize the spatial random process using the variance of each satellite product within the window size from the detrended data on the basis of Eq. (1). The two-step MRT algorithm was implemented on the three albedo products. Fig 5 shows the error comparison of three albedo maps on DOY 192. Cloud/shadow pixels and data gaps were masked with dark blue color in Landsat and MISR data, respectively. In this figure, the error of the original albedo dataset was calculated as the product of albedo and relative error, as we assume the observation error is proportional to the albedo

12 magnitude. The right column of Fig 5 shows the posterior error estimation of the albedo map generated by the Kalman filter in the MRT. Errors were significantly reduced after the implementation of MRT. The three satellite datasets and the corresponding results were compared for the date of DOY 192 (Fig 6). In this comparison, four groups of data were plotted in histograms showing the difference between 1) MODIS and aggregated Landsat before MRT; 2) MISR and aggregated MODIS before MRT; 3) MODIS and aggregated Landsat after MRT; and 4) MISR and aggregated MODIS after MRT. All the data in the selected subset were included in these histograms except for the water and filled value pixels. The water pixels were excluded to avoid the potential error of the reprojection. The differences between the satellite products were reduced significantly through data fusion. For MODIS and Landsat data, the difference was constrained to ±0.02 in most cases except for a few outliers and the bias was very close to zero. The outliers with absolute difference (between the original MODIS and Landsat data) larger than 0.02 were more than 33%; while after data fusion, the numbers of outliers dropped to less than 5% for the whole study area. The MISR albedo products provided some overestimated values as compared to the MODIS data; however, the data fusion method reduced the difference. Even then, a small positive bias still remained, which was possibly caused by the residual clouds and/or the difference of albedo algorithms used on the sensors. Fig 7 showed the results separating the input data for “good” and “other” data qualities from MODIS albedo products. The results for pixels with different data qualities do not have statistically significant results (see Table 4); however, the data with lower quality have slightly more outliers than “good” quality data, which could be the residual cloud effects. Nevertheless, the three albedo products have different criteria for “good” and “poor” data qualities and they may not be fully comparable. Thus, we do not separate the data according to the quality flags in generating the fused albedo datasets. The estimated detrended data were then added to the trend surface to generate the surface albedo. A time-series comparison of albedo was made from the results generated using data from DOY 160 to DOY192 and DOY232 to DOY 264 based on the availability of clear scenes (Fig 8). Ten cases in total were included in this time range. It is worth noting that the same Landsat data may be used in two adjacent cases. In addition, some adjacent cases can also share a part of the MISR data, whereas MODIS albedo, in

13 contrast, is always different from case to case. Similar to Fig 5, filled values and cloud/shadow pixels were masked with dark blue color (0 values) in Fig 8. Even the temporal composite MISR data were used there were still many data gaps because MISR algorithm has some strict criteria generating albedo data. For the Landsat ETM+ data, the data gaps were mainly caused by the scan-line corrector problem since the year of 2003. Results showed that the gaps, especially in MISR data and Landsat ETM+ data, could be significantly filled based on the supporting data from the other scale(s). Compared with the original satellite products, the datasets after MRT became consistent across scales. According to the statistical comparison on the data before and after the data fusion (tabulated in Table 3), the bias between different products is reduced and the values are consistent across the time. More significant improvements are that the relative RMSE is reduced to almost half of its original value, and the outliers of the data have been removed in terms of the decrease in the absolute values of maximum differences. These improvements indicate that the data fusion algorithm is capable of generating consistent albedo products at different scales as well as reducing the risks of residual cloud contamination and satellite system failure.

5. Summary and conclusions Land surface albedo is an essential geophysical variable controlling the surface radiation budget. Errors of satellite albedo products may arise from issues such as sensor calibration, temporal/angular composition, cloud contamination, and differences in the albedo retrieving algorithms in considering the atmospheric components and surface anisotropy. To reduce the uncertainty of the albedo products, it is important to take advantage of different albedo datasets. This study proposes a novel approach for combining satellite albedo datasets at different spatial resolutions. This study proposes a data fusion method using MRT to improve current satellite albedo products from multiple datasets. The purpose of using this data fusion method is to generate a set of temporally and spatially complete, continuous, and consistent albedo products across different scales. The MRT algorithm is proven to be capable of generating consistent albedo products across scales while reducing uncertainties. This is

14 the first time, to the best of our knowledge, that data fusion method has been used on more than two albedo datasets at different spatial scales. The proposed method works well to reduce the difference between albedo products at different spatial resolutions. Considering that the MRT method is very time efficient and that the methodology presented here is applicable to other satellite albedo data and scalable to other areas, the proposed method can be used to generate some global albedo datasets at different spatial scales to better serve the albedo retrieving algorithms and other land surface modeling purposes. The proposed prototype approach is currently limited to the three land cover types in the growing season in the north-central United States. Extension of this approach requires extensive uncertainty evaluations of existing satellite albedo products in various seasons and locations. Evaluation of the Landsat albedo data relies on ground measurements. While the ground measurements used here are very limited, so the derived relative error may not fully represent all the land cover types across time and space. In addition, oversimplifications are made on the land surfaces by assuming that the land cover types remain the same within the study area and that the albedo uncertainty is proportional to the magnitude regardless of the surface cover type. In other words, the error estimation may not represent the real accuracy of the satellite albedo products used in this study. In order to extend this approach to other areas with different types of land cover (snow and urban areas, etc.), more research is needed to evaluate the products’ accuracies.

Acknowledgement This research was supported by the Center for Satellite Applications and Research (STAR) of the National Oceanic and Atmospheric Administration (NOAA) under Grant NA17EC1483. Many thanks to the reviewers who provided great suggestions to help improve the contents of the manuscript. We gratefully acknowledge the MODIS, MISR, and Landsat teams for maintaining and providing access to the albedo products. We also thank the LEDAPS project members for providing the LEDAPS tools used for this study.

15

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17 [27] J. Zhu and W. Yue, "A multiresolution tree-structured spatial linear model," Journal of Computational and Graphical Statistics, vol. 14, pp. 168-184, Mar 2005. [28] H. C. Huang, N. Cressie, and J. Gabrosek, "Fast, resolution-consistent spatial prediction of global processes from satellite data," Journal of Computational and Graphical Statistics, vol. 11, pp. 63-88, Mar 2002. [29] X. L. Zhu, J. Chen, F. Gao, X. H. Chen, and J. G. Masek, "An enhanced spatial and temporal adaptive reflectance fusion model for complex heterogeneous regions," Remote Sensing of Environment, vol. 114, pp. 2610-2623, Nov 2010. [30] D. Wang and S. Liang, "Using multiresolution tree to integrate MODIS and MISR-L3 LAI products," in Geoscience and Remote Sensing Symposium (IGARSS), 2010 IEEE International, 2010, pp. 1027-1030. [31] C. Plumejeaud, H. Mathian, J. Gensel, and C. Grasland, "Spatio-temporal analysis of territorial changes from a multi-scale perspective," International Journal of Geographical Information Science, vol. 25, pp. 1597-1612, 2011. [32] C. K. Wikle, "Hierarchical models in environmental science," International Statistical Review, vol. 71, pp. 181-199, Aug 2003. [33] C. B. Schaaf, F. Gao, A. H. Strahler, W. Lucht, X. W. Li, T. Tsang, N. C. Strugnell, X. Y. Zhang, Y. F. Jin, J. P. Muller, P. Lewis, M. Barnsley, P. Hobson, M. Disney, G. Roberts, M. Dunderdale, C. Doll, R. P. d'Entremont, B. X. Hu, S. L. Liang, J. L. Privette, and D. Roy, "First operational BRDF, albedo nadir reflectance products from MODIS," Remote Sensing of Environment, vol. 83, pp. 135-148, Nov 2002. [34] E. F. Vermote, N. ElSaleous, C. O. Justice, Y. J. Kaufman, J. L. Privette, L. Remer, J. C. Roger, and D. Tanre, "Atmospheric correction of visible to middle-infrared EOS-MODIS data over land surfaces: Background, operational algorithm and validation," Journal of Geophysical Research-Atmospheres, vol. 102, pp. 17131-17141, Jul 1997. [35] E. F. Vermote and S. Kotchenova, "Atmospheric correction for the monitoring of land surfaces," Journal of Geophysical Research-Atmospheres, vol. 113, Dec 2008. [36] J. G. Masek, E. F. Vermote, N. E. Saleous, R. Wolfe, F. G. Hall, K. F. Huemmrich, F. Gao, J. Kutler, and T. K. Lim, "A Landsat surface reflectance dataset for North America, 1990-2000," IEEE Geoscience and Remote Sensing Letters, vol. 3, pp. 68-72, Jan 2006. [37] S. Y. Kotchenova, E. F. Vermote, R. Matarrese, and F. J. Klemm, "Validation of a vector version of the 6S radiative transfer code for atmospheric correction of satellite data. Part I: Path radiance," Applied Optics, vol. 45, pp. 6762-6774, Sep 2006. [38] A. M. Baldridge, S. J. Hook, C. I. Grove, and G. Rivera, "The ASTER spectral library version 2.0," Remote Sensing of Environment, vol. 113, pp. 711-715, Apr 2009. [39] R. N. Clark, G. A. Swayze, R. Wise, E. Livo, T. Hoefen, R. Kokaly, and S. J. Sutley, "USGS digital spectral library splib06a," U.S. Geological Survey, Digital Data Series 231, 2007. [40] S. L. Liang, "Narrowband to broadband conversions of land surface albedo I Algorithms," Remote Sensing of Environment, vol. 76, pp. 213-238, May 2001. [41] J. V. Martonchik, D. J. Diner, B. Pinty, M. M. Verstraete, R. B. Myneni, Y. Knyazikhin, and H. R. Gordon, "Determination of land and ocean reflective, radiative, and biophysical properties using multiangle imaging," IEEE Transactions on Geoscience and Remote Sensing, vol. 36, pp. 1266-1281, Jul 1998.

18 [42] A. Cescatti, B. Marcolla, S. K. S. Vannan, J. Y. Pan, M. O. Roman, X. Y. Yang, P. Ciais, R. B. Cook, B. E. Law, G. Matteucci, M. Migliavacca, E. Moors, A. D. Richardson, G. Seufert, and C. B. Schaaf, "Intercomparison of MODIS albedo retrievals and in situ measurements across the global FLUXNET network," Remote Sensing of Environment, vol. 121, pp. 323-334, Jun 2012. [43] M. Taberner, B. Pinty, Y. Govaerts, S. Liang, M. M. Verstraete, N. Gobron, and J. L. Widlowski, "Comparison of MISR and MODIS land surface albedos: Methodology," Journal of Geophysical Research-Atmospheres, vol. 115, Mar 2010. [44] P. Lewis and M. Barnsley, "Influence of the sky radiance distribution on various formulations of the Earth surface albedo," in The 6th International Symposium on Physical Measurements and Spectral Signatures in Remote Sensing, Val d'Isere, France, 1994. [45] W. Lucht, C. B. Schaaf, and A. H. Strahler, "An algorithm for the retrieval of albedo from space using semiempirical BRDF models," IEEE Transactions on Geoscience and Remote Sensing, vol. 38, pp. 977-998, Mar 2000.

19 Tables & Figures Table 1. AmeriFlux sites Site_Name

Latitude

Longitude

Tower Elevation Height IGBP (m) (m) 219 10 CRO

Landsat Scene

Bondville 40.006 -88.290 p023r032 Bondville 40.009 -88.290 219 10 CRO p023r032 Companion Site Brookings 44.345 -96.836 510 4 GRA p029r029 Fermi Agricultural 41.859 -88.223 225 4 CRO p023r031 Fermi Prairie 41.841 -88.241 226 3.8 GRA p023r031 Fort Peck 48.308 -105.102 634 3.5 GRA p035r026 Lost Creek 46.083 -89.979 480 10.2 CSH p025r028 Willow Creek 45.806 -90.080 515 30 DBF p025r028 CRO: cropland; CSH: closed shrub land; GRA: grassland; DBF: deciduous broadleaf forest. Table 2. Reflective bands of the satellite sensors used in this study Sensor

Landsat

MODIS

MISR

Band wavelength

Band 1: 0.45 – 0.52

Band 1: 0.62 – 0.67

Band 1: 0.43 – 0.47

(µm)

Band 2: 0.52 – 0.60

Band 2: 0.84 – 0.88

Band 2: 0.54 – 0.57

Band 3: 0.63 – 0.69

Band 3: 0.46 – 0.48

Band 3: 0.66 – 0.68

Band 4: 0.76 – 0.90

Band 4: 0.55 – 0.57

Band 4: 0.85 – 0.89

Band 5: 1.55 – 1.75

Band 5: 1.23 – 1.25

Band 7: 2.08 – 2.35

Band 6: 1.63 – 1.65 Band 7: 2.11 – 2.16

20 Table 3. Statistical comparison of different datasets before and after MRT MODIS vs Aggregated Landsat Date

Before MRT

After MRT

160

Bias -0.0085

RMSE 0.0182

RMSE(%) 17.9108

Max 0.1067

Min -0.1070

Bias -0.0156

RMSE 0.0181

RMSE(%) 13.9820

Max 0.0970

Min -0.0774

168

-0.0095

0.0180

17.4897

0.1037

-0.1038

-0.0136

0.0164

13.0580

0.0990

-0.0754

176

-0.0143

0.0211

18.1358

0.1084

-0.1157

-0.0125

0.0154

12.1361

0.0994

-0.0706

184

-0.0083

0.0188

18.5690

0.1118

-0.1307

-0.0147

0.0173

13.0931

0.0971

-0.0733

192

-0.0124

0.0209

18.3825

0.0991

-0.1239

-0.0060

0.0108

10.0797

0.1010

-0.0740

232

-0.0065

0.0170

17.9333

0.1000

-0.1216

-0.0052

0.0105

11.4130

0.0936

-0.0780

240

-0.0084

0.0173

17.2759

0.0977

-0.1196

-0.0052

0.0104

11.4145

0.0936

-0.0780

248

-0.0117

0.0195

17.3321

0.0943

-0.1643

-0.0099

0.0128

11.0042

0.0889

-0.0711

256

-0.0064

0.0154

16.1747

0.0912

-0.1204

-0.0063

0.0105

10.6633

0.0890

-0.0772

264

-0.0077

0.0156

16.1652

0.0912

-0.1144

-0.0051

0.0098

10.4847

0.0902

-0.0781

MISR vs Aggregated MODIS Date

Before MRT

After MRT

160

Bias 0.0231

RMSE 0.0268

RMSE(%) 20.8862

Max 0.0861

Min -0.0565

Bias 0.0112

RMSE 0.0115

RMSE(%) 9.6205

Max 0.0395

Min 0.0010

168

0.0288

0.0321

27.6596

0.1100

-0.0705

0.0093

0.0100

8.1748

0.0368

-0.0101

176

0.0318

0.0346

29.0747

0.1105

-0.0710

0.0088

0.0099

7.6991

0.0482

-0.0078

184

0.0259

0.0294

21.8256

0.1004

-0.0770

0.0097

0.0100

7.6436

0.0247

-0.0045

192

0.0285

0.0314

24.2215

0.1099

-0.0741

0.0051

0.0059

4.1192

0.0412

-0.0111

232

0.0108

0.0430

33.8418

0.0682

-0.0663

0.0211

0.0244

16.7703

0.0496

0.0075

240

0.0290

0.0344

30.7421

0.1256

-0.0909

0.0052

0.0067

5.3723

0.0476

-0.0108

248

0.0266

0.0321

29.0905

0.1326

-0.0937

0.0070

0.0078

6.3334

0.0415

-0.0092

256

0.0207

0.0242

21.3517

0.1142

-0.0852

0.0053

0.0059

4.7944

0.0351

-0.0080

264

0.0205

0.0242

22.0446

0.1227

-0.0892

0.0047

0.0054

4.3884

0.0384

-0.0074

RMSE(%): relative RMSE in percentage; Max: maximum value of the difference; Min: minimum value of the difference. The differences are calculated as MODIS minus Aggregated Landsat and MISR minus Aggregate MODIS.

Table 4. Statistical comparison* of differences between MODIS and aggregated Landsat before and after MRT for different data qualities on DOY 192, 2005. Data quality

Before MRT

After MRT

“Good”

Bias -0.0127

RMSE 0.0208

RMSE(%) 17.5803

Max 0.0991

Min -0.0923

Bias -0.0061

RMSE 0.0106

RMSE(%) 9.3643

Max 0.0862

Min -0.0590

“Other”

-0.0118

0.0212

19.8104

0.0904

-0.1239

-0.0058

0.0113

11.2802

0.1010

-0.0740

*: statistics are calculated the same way as those in Table 3.

21

Fig 1. MRT data structure [28]. The “root” node is at the top of the tree structure and the “leave” nodes are at the bottom of the tree structure. In this study, the MISR data serve as the “root”, MODIS data are in the middle of the tree structure, and Landsat data are treated as “leaves”.

22 Satellite albedo products at different scales

Uncertainty evaluation Ground measurements

Products inter-comparison

Trend surface extraction

Albedo anomaly Image-based uncertainty estimation

MRT data fusion (II) Updated uncertainty estimation

MRT data fusion (I) Leaves-to-root Kalman Filtering

Root-to-leaves Kalman Smoothing

Mean of post probability Updated albedo products

Fig 2. Framework of MRT albedo data fusion from multiple satellite products.

23 Bondville Shortwave Albedo

0.8 Insitu MODIS (best quality) MODIS (others) MISR TM ETM+

0.7 0.6 0.5 0.4 0.3 0.2 0.1 0

0

50

100

200

150

250

300

350

250

300

350

250

300

350

250

300

350

DOY

BondvilleCompanionSite Shortwave Albedo

0.8 Insitu MODIS (best quality) MODIS (others) MISR TM ETM+

0.7 0.6 0.5 0.4 0.3 0.2 0.1 0

0

50

100

200

150

DOY

Brookings Shortwave Albedo

0.8 Insitu MODIS (best quality) MODIS (others) MISR TM ETM+

0.7 0.6 0.5 0.4 0.3 0.2 0.1 0

0

50

100

150

200

DOY

FermiAgricultural Shortwave Albedo

0.8 Insitu MODIS (best quality) MODIS (others) MISR TM ETM+

0.7 0.6 0.5 0.4 0.3 0.2 0.1 0

0

50

100

200

150

DOY

Fig 3. Time series comparison of the albedo datasets used in this study.

24 FermiPrairie Shortwave Albedo

0.8 Insitu MODIS (best quality) MODIS (others) MISR TM ETM+

0.7 0.6 0.5 0.4 0.3 0.2 0.1 0

0

50

100

200

150

250

300

350

250

300

350

250

300

350

250

300

350

DOY

FortPeck Shortwave Albedo

0.8 Insitu MODIS (best quality) MODIS (others) MISR TM ETM+

0.7 0.6 0.5 0.4 0.3 0.2 0.1 0

0

50

100

200

150

DOY

LostCreek Shortwave Albedo

0.8 Insitu MODIS (best quality) MODIS (others) MISR TM ETM+

0.7 0.6 0.5 0.4 0.3 0.2 0.1 0

0

50

100

150

200

DOY

WillowCreek Shortwave Albedo

0.8 Insitu MODIS (best quality) MODIS (others) MISR TM ETM+

0.7 0.6 0.5 0.4 0.3 0.2 0.1 0

0

50

100

200

150

DOY

Fig 3 (continued).

25 1 TM(N=52): Bias=-0.001 RMSE=0.020

0.9

Landsat data

0.8 0.7

ETM+(N=52): Bias=0.001 RMSE=0.030

All(N=104): Bias=-0.000 RMSE=0.026

0.6 0.5 0.4 0.3

TM ETM+

0.2 0.1 0

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Ground measurements

(a) 18 16 14

Standard deviation: 14.59%

12 10 8 6 4 2 0 -50

-40

-30

-20

-10

0

10

20

Relative error of Landsat data (%)

30

40

(b) Fig 4. Evaluation of Landsat data using ground measurements: paired comparison (a) and histogram (b).

26

Fig 5. Error comparisons between albedo maps before and after MRT for the three products on DOY 192, 2005 (zero means no data). The error of the original albedo datasets is calculated as the product of the relative error and absolute albedo value.

27

4

Before MRT

3

x 10

2000 1500

2

1000 1

500

0 -0.1

-0.05

0

0.05

0.1

0 -0.1

-0.05

0

0.05

0.1

4

After MRT

6

x 10

4

8000 6000 4000

2

0 -0.1 -0.05 0 0.05 0.1 MODIS - Aggregated Landsat

2000 0 -0.1

-0.05 0 0.05 0.1 MISR - Aggregated MODIS

Fig 6. Comparison of the difference between data from different products on DOY 192, 2005.

28

4

Before MRT

2

x 10

10000

1.5 5000

1 0.5 0 -0.1

-0.05

0

0.05

0.1

0 -0.1

4

After MRT

4

x 10

0

0.05

0.1

4

2

3

1.5

2

1

1

0.5

0 -0.1 -0.05 0 0.05 0.1 MODIS - Aggregated Landsat

-0.05

x 10

0 -0.1 -0.05 0 0.05 0.1 MODIS - Aggregated Landsat

Fig 7. Comparison of the difference between data using different quality flags on DOY 192 (left column is based on data with “good” quality only; right column is based on data with “other” quality).

1

2 3 4

29

Fig 8. Time-series comparison of albedo maps before and after MRT (left-to-right order: original MISR albedo, MISR albedo after MRT, original MODIS albedo, MODIS albedo after MRT, original Landsat albedo, and Landsat albedo after MRT); dark blue color (0 value) means no data.

5

6

30

Fig 8. (continued)s

31 7