Scale Issues in Remote Sensing: A Review on Analysis, Processing and Modeling <s> Effects of scale on the measurements, retrieval models and products <s> Abstract Models used in remote sensing are based mostly on a relationship between a parameter and the measured reflectance at a given wavelength. They are generally built on the basis of physical considerations at a scale enough small enough so that the media can be considered to be homogeneous. The general practice in remote sensing is to apply these models to reflectances measured from satellites on heterogeneous surfaces, without considering making any correction in order to compensate for the change of scale. It is shown that this usual practice generates errors, the lower and upper bounds of which are given in the form of two functions associated with the physical model. Finally, a general method is proposed to build a new model connected to the physical one, reducing the error introduced by the heterogeneity of the analysed surface. An application to the role of resolution change for the quantification of covered area is also considered. <s> BIB001 </s> Scale Issues in Remote Sensing: A Review on Analysis, Processing and Modeling <s> Effects of scale on the measurements, retrieval models and products <s> Understanding and modelling physical and dynamical processes over heterogeneous land surfaces have becomea central focus of many recent studies. There is aconsiderable debate, however, over how to representthe effects of spatial heterogeneity in mesoscale andglobal scale models. Here, a computationally efficientanalytical approach is presented to evaluate scalingproperties of land surface representations. It isshown that the effects of spatial variability may not benegligible for commonly encountered land surfaces andassociated parameterizations. Second-order correction termsinvolving variances of the parameters and covariancesof each pair of land surface parameters are developedto account for the effects ofheterogeneity. Using this analytical approach, weshow that the detail of spatial heterogeneity may not beimportant for the infrared radiation and reflectedsolar radiation from the surface, while sensible andlatent heat fluxes are shown to be sensitive toheterogeneity. Assumptions related todifferent parameterizations for the same physicalprocess could potentially lead to different inferencesregarding the influence of spatial heterogeneity. Theproposed approach, however, is capable of identifying therole of different parameterizations in estimating theinfluence of spatial heterogeneity. These analyticalresults are consistent with the results of severalrecent numerical and field experiments that deal withthe effects of small-scale heterogeneity in landsurface characteristics. <s> BIB002 </s> Scale Issues in Remote Sensing: A Review on Analysis, Processing and Modeling <s> Effects of scale on the measurements, retrieval models and products <s> Abstract Using ESTAR (Electronically Scanned Thinned Array Radiometer) passive microwave remotely sensed soil moisture data from the Washita 92 experiment, we examine the appropriateness of several probability density functions as a candidate for soil moisture distribution. Although the normal distribution is found to approximate the data well, it is shown that such a distribution cannot capture the inherent spatial structure of soil moisture. We confirm the recent finding that the variance of soil moisture images follows a power law decay and show that such a scaling is valid over a wider range of scales than previously reported. We also relate the scaling exponent of the variance to highly correlated cluster structure: in soil moisture images. Our analysis of scaling for higher-order moments suggests that soil moisture images may not be simple scaling. <s> BIB003 </s> Scale Issues in Remote Sensing: A Review on Analysis, Processing and Modeling <s> Effects of scale on the measurements, retrieval models and products <s> Abstract The spatial scale of soil moisture measurements is often inconsistent with the scale at which soil moisture predictions are needed. Consequently a change of scale (upscaling or downscaling) from the measurements to the predictions or model values is needed. The measurement or model scale can be defined as a scale triplet, consisting of spacing, extent and support. ‘Spacing’ refers to the distance between samples; ‘extent’ refers to the overall coverage; and ‘support’ refers to the area integrated by each sample. The statistical properties that appear in the data, the apparent variance and the apparent correlation length, are as a rule different from their true values because of bias introduced by the measurement scale. In this paper, high-resolution soil moisture data from the 10.5 ha Tarrawarra catchment in south-eastern Australia are analysed to assess this bias quantitatively. For each survey up to 1536 data points in space are used. This allows a change of scale of two orders of magnitude. Apparent variances and apparent correlation lengths are calculated in a resampling analysis. Apparent correlation lengths always increase with increasing spacing, extent or support. The apparent variance increases with increasing extent, decreases with increasing support, and does not change with spacing. All of these sources of bias are a function of the ratio of measurement scale (in terms of spacing, extent and support) and the scale of the natural variability (i.e. the true correlation length or process scale of soil moisture). In a second step this paper examines whether the bias due to spacing, extent and support can be predicted by standard geostatistical techniques of regularisation and variogram analysis. This is done because soil moisture patterns have properties, such as connectivity, that violate the standard assumptions underlying these geostatistical techniques. Therefore, it is necessary to test the robustness of these techniques by application to observed data. The comparison indicates that these techniques are indeed applicable to organised soil moisture fields and that the bias is predicted equally well for organised and random soil moisture patterns. A number of examples are given to demonstrate the implications of these results for hydrologic modelling and sampling design. <s> BIB004 </s> Scale Issues in Remote Sensing: A Review on Analysis, Processing and Modeling <s> Effects of scale on the measurements, retrieval models and products <s> Abstract Information on the exchange of carbon dioxide between the earth’s surface and the atmosphere is critical for successful prediction of future climate. In the present study a model of leaf photosynthesis and stomatal conductance was parameterised based on field measurements of leaf photosynthesis and stomatal conductance. The simulated leaf gas exchange was scaled to the canopy level using the big leaf approach based on estimated radiation capture by the canopy and coupled to calculations of atmospheric resistance and soil carbon dioxide efflux to simulate the fluxes of carbon dioxide over a barley field. The model was found to be applicable for the conditions and simulated values agree well with canopy fluxes measured using the eddy covariance technique for a four-week period during the second field campaign of the Northern Hemisphere Climate processes Land-surface Experiment (NOPEX) in the region around Uppsala, Sweden, during June and July 1995. The rate of canopy development was high during the period and the leaf area index (LAI) changed from 0.7 to 3.5. Evaluation of the sensitivity of the model to driving variables and key canopy parameters showed high sensitivity to information on development and physiological characteristics of the canopy. <s> BIB005 </s> Scale Issues in Remote Sensing: A Review on Analysis, Processing and Modeling <s> Effects of scale on the measurements, retrieval models and products <s> The problem of how the scale, or spatial resolution, of reflectance data impacts retrievals of vegetation leaf area index (LAI) is addressed in this article. We define the goal of scaling as the process by which it is established that LAI values derived from coarse resolution sensor data equal the arithmetic average of values derived independently from fine resolution sensor data. The increasing probability of land cover mixtures with decreasing resolution is defined as heterogeneity, which is a key concept in scaling studies. The effect of pixel heterogeneity on spectral reflectances and LAI retrievals is investigated with 1-km Advanced Very High Resolution Radiometer (AVHRR) data aggregated to different coarse spatial resolutions. It is shown that LAI retrieval errors at coarse resolution are inversely related to the proportion of the dominant land cover in such pixel. Further, large errors in LAI retrievals are incurred when forests are minority biomes in non-forest pixels compared to when forest biomes are mixed with one another, and vice versa. A physically based scaling with explicit spatial resolution-dependent radiative transfer formulation is developed. The successful application of this theory to scaling LAI retrievals from AVHRR data of different resolutions is demonstrated. These principles underlie our approach to the production and validation of LAI product from the Moderate Resolution Imaging Spectroradiometer (MODIS) and the Multi-angle Imaging Spectroradiometer (MISR) aboard the TERRA platform. <s> BIB006 </s> Scale Issues in Remote Sensing: A Review on Analysis, Processing and Modeling <s> Effects of scale on the measurements, retrieval models and products <s> Abstract This paper presents the general methods and some preliminary results of validating Moderate-Resolution Imaging Spectroradiometer (MODIS) land surface reflectance and albedo products using ground measurements and Enhanced Thematic Mapper Plus (ETM+) imagery. Since ground “point” measurements are not suitable for direct comparisons with MODIS pixels of about 1 km over heterogeneous landscapes, upscaling based on high-resolution remotely sensed imagery is critical. In this study, ground measurements at Beltsville, MD were used to calibrate land surface reflectance and albedo products derived from ETM+ imagery at 30 m, which were then aggregated to the MODIS resolution for determining the accuracy of the following land surface products: (1) bidirectional reflectance from atmospheric correction, (2) bidirectional reflectance distribution function (BRDF), (3) broadband albedos, and (4) nadir BRDF-adjusted reflectance. The initial validation results from ground measurements and two ETM+ images acquired on October 2 and November 3, 2000 showed that these products are reasonably accurate, with typically less than 5% absolute error. Final conclusions on their accuracy depend on more validation results. <s> BIB007 </s> Scale Issues in Remote Sensing: A Review on Analysis, Processing and Modeling <s> Effects of scale on the measurements, retrieval models and products <s> Data from passive microwave remote sensing with an ESTAR L-band radiometer, deployed on an aircraft, were used to produce soil moisture images over the area of the Little Washita watershed in Oklahoma in 1992. This area was revisited during the Southern Great Plains 1997 Hydrology Experiment. This offered an opportunity to evaluate the time-specificity of the conclusions, relating to scaling of the surface soil moisture, that have been reported for 1992. The objective of this work was to compare scaling properties of soil moisture fields observed in 1992 and 1997. We analyzed one 1992 data set and three 1997 data sets, each covering several days of continuous drydown. Different resolutions were introduced by aggregating the pixels of original 200-m resolution into bigger square cells. Scaling in dependencies on resolution was observed for the variance of moisture content, for the within-cell variance, and for the first six moments about zero, the latter indicating multiscaling. Parameters of the scaling equations differed among four drying periods studied. However, once a scaling dependency on resolution was established in the beginning of a drying period, its shape was maintained during the drydown both in 1992 and 1997. Slopes of the dependencies changed only slightly, whereas the intercepts decreased as the drying progressed. Having constant slopes and intercepts dependent on average area water contents gives an opportunity to reduce the volume of observations needed to predict scaling of surface soil moisture during drydowns. <s> BIB008 </s> Scale Issues in Remote Sensing: A Review on Analysis, Processing and Modeling <s> Effects of scale on the measurements, retrieval models and products <s> The three-dimensional structure of a coniferous shoot gives rise to multiple scattering of light between the needles of the shoot, causing the shoot spectral reflectance to differ from that of a flat leaf. Forest reflectance models based on the radiative transfer equation handle shoot level clumping by correcting the radiation attenuation coefficient with a clumping index. The clumping index causes a reduction in the interception of radiation by the canopy at a fixed leaf area index (LAI). In this study, we show how within-shoot multiple scattering is related to shoot scale clumping and derive a similar, but wavelength dependent, correction to the scattering coefficient. The results provide a method for integrating shoot structure into current radiative transfer equation based forest reflectance models. The method was applied to explore the effect of shoot scale clumping on canopy spectral reflectance using simple model canopies with a homogeneous higher level structure. The clumping of needles into shoots caused a wavelength dependent reduction in canopy reflectance, as compared to that of a leaf canopy with similar interception. This is proposed to be one reason why coniferous and broad-leaved canopies occupy different regions in the spectral space and exhibit different dependency of spectral vegetation indices on LAI. <s> BIB009 </s> Scale Issues in Remote Sensing: A Review on Analysis, Processing and Modeling <s> Effects of scale on the measurements, retrieval models and products <s> Abstract The interaction between the land surface and the atmosphere is discussed focusing on the recent literature. Of primary importance is the issue of scale and the variation across different levels of pixel resolution for using remotely sensed data in the determination of the different components of the surface energy balance (SEB). This leads into a discussion of various methods of aggregating local scale input parameters in order to calculate larger scale surface fluxes. As an example application, airborne and satellite data are coupled to a soil-vegetation–atmosphere-transfer (SVAT) model and applied to the Southern Great Plains 1997 (SGP97) Hydrology Experiment. A physically based aggregation scheme is suggested for radiometric temperature by decomposing the temperature into vegetation and soil components and then aggregating the radiance field based on the percent cover of vegetation. Fluxes derived from the airborne data agree well with those measured with eddy covariance stations. Satellite data agrees poorly with the surface and airborne estimates. However, after aggregating the airborne data to the resolution of the satellite, the agreement is better. This suggests that the satellite data is useful at estimating the fluxes at the 1 km 2 scale, while the comparison between the 1 km 2 satellite and the surface data may be problematic at such scales. <s> BIB010 </s> Scale Issues in Remote Sensing: A Review on Analysis, Processing and Modeling <s> Effects of scale on the measurements, retrieval models and products <s> Abstract As surface exchange processes are highly non-linear and heterogeneous in space and time, it is important to know the appropriate scale for the reasonable prediction of these exchange processes. For example, the explicit representation of surface variability has been vital in predicting mesoscale weather events such as late-afternoon thunderstorms initiated by latent heat exchanges in mid-latitude regions of the continental United States. This study was undertaken to examine the effects of different spatial scales of input data on modeled fluxes, so as to better understand the resolution needed for accurate modeling. A statistical procedure was followed to select two cells from the Southern Great Plains 1997 hydrology experiment region, each 20 km×20 km, representing the most homogeneous and the most heterogeneous surface conditions (based on soil and vegetation) within the study region. The NOAH-OSU (Oregon State University) Land Surface Model (LSM) was employed to estimate surface energy fluxes. Three scales of study (200 m, 2 and 20 km) were considered in order to investigate the impacts of the aggregation of input data, especially soil and vegetation inputs, on the model output. Model results of net radiation and latent, sensible and ground heat fluxes were compared for the three scales. For the heterogeneous area, the model output at the 20-km resolution showed some differences when compared with the 200-m and 2-km resolutions. This was more pronounced in latent heat (12% decrease), sensible heat (22% increase), and ground heat flux (44% increase) estimation than in net radiation. The scaling effects were much less for the relatively homogeneous land area with 5% increase in sensible heat and 4% decrease in ground heat flux estimation. All of the model outputs for the 2- and 20-km resolutions were in close agreement. The results suggested that, for this study region, soils and vegetation input resolution of about 2 km should be chosen for realistic modeling of surface exchange processes. This resolution was sufficient to capture the effects of sub-grid scale heterogeneity, while avoiding the data and computational difficulties associated with higher spatial resolutions. <s> BIB011 </s> Scale Issues in Remote Sensing: A Review on Analysis, Processing and Modeling <s> Effects of scale on the measurements, retrieval models and products <s> Three definitions of emissivity for non-isothermal pixels are evaluated, and their differences are analysed. On the basis of the experimental data and numerical simulation, a generalized formula is established to scale for land surface emissivity, reflectance, and other variables between pixel scale and sub-pixel scale. Finally, it is pointed out that isothermal concept of land surface temperature and homogeneous concept of some other parameters in one spatial scale are relative according to humans' capability of measurement, and that the heterogeneity in a spatial scale is absolute in the natural world. <s> BIB012 </s> Scale Issues in Remote Sensing: A Review on Analysis, Processing and Modeling <s> Effects of scale on the measurements, retrieval models and products <s> Abstract Leaf area index (LAI) is an important surface biophysical parameter as a measure of vegetation cover, vegetation productivity, and as an input to ecosystem process models. Recently, a number of coarse-scale (1-km) LAI maps have been generated over large regions including the Canadian boreal forest. This study focuses on the production of fine-scale (≤30-m) LAI maps using the forest light interaction model-clustering (FLIM-CLUS) algorithm over selected boreal conifer stands and the subsequent comparison of the fine-scale maps to coarse-scale LAI maps synthesized from Landsat TM imagery. The fine-scale estimates are validated using surface LAI measurements to give relative root mean square errors of under 7% for jack pine sites and under 14% for black spruce sites. In contrast, finer scale site mean LAI ranges between 49% and 86% of the mean of surface estimates covering only part of the sites and 54% to 110% of coarse-scale site mean LAI. Correlations between fine-scale and coarse-scale estimates range from near 0.5 for 30-m coarse-scale images to under 0.3 to 1-km coarse-scale images but increase to near 0.90 after imposing fine-scale zero LAI areas in coarse-scale estimates. The increase suggests that coarse-scale image-based LAI estimates require consideration of sub-pixel open areas. Both FLIM-CLUS and coarse-scale site mean LAI are substantially lower than surface estimates over northern sites. The assumption of spatially random residuals in regression-based estimates of LAI may not be valid and may therefore add to local bias errors in estimating LAI remotely. Differences between fine-scale airborne LAI maps and 30-m-scale Landsat TM LAI maps suggests that, for sparse boreal conifer stands, LAI maps produced from Landsat TM alone may not always be sufficient for validation of coarser scale LAI maps. In addition, previous studies may have used biased LAI estimates over the study site. Fine-scale spatial LAI maps offer one means of assessing and correcting for effects of sub-pixel open area patches and for characterising the spatial pattern of residuals in coarse-scale LAI estimates in comparison to the true distribution of LAI on the surface. <s> BIB013 </s> Scale Issues in Remote Sensing: A Review on Analysis, Processing and Modeling <s> Effects of scale on the measurements, retrieval models and products <s> Spatial scaling is of particular importance in remote sensing applications to terrestrial ecosystems where spatial heterogeneity is the norm. Surface parameters derived at different resolutions can be considerably different even though they are derived using the same algorithms. This article addresses issues related to spatial scaling of net primary productivity (NPP). The main objective is to develop algorithms for spatial scaling of NPP using subpixel information. NPP calculations were performed using the Boreal Ecosystem Productivity Simulator (BEPS). The area of interest is near Fraserdale, Ontario, Canada. It is found from this investigation that lumped (coarse resolution) calculations can be considerably biased (by +14.9% on average) from the distributed (fine resolution) case. Based on these results, algorithms for removing these biases in lumped NPP are developed using subpixel land cover type information. The correlation between the distributed NPP and lumped NPP is improved from r 2 =0.16 to r 2 =0.59 after the correction. In addition, subpixel leaf area index (LAI) information is used to reduce the remaining biases. After the LAI correction, the correlation is further improved to r 2 =0.90. <s> BIB014 </s> Scale Issues in Remote Sensing: A Review on Analysis, Processing and Modeling <s> Effects of scale on the measurements, retrieval models and products <s> Release of an annual global terrestrial net primary production (NPP) data layer has begun in association with the Moderate Imaging Spectro- radiometer (MODIS) sensor, a component of the NASA Earth Observing System. The task of validating this product will be complicated by the mismatch in scale between ground-based NPP measurements and the coarse resolution (1 km) of the NPP product. In this paper we describe three relevant approaches to scaling NPP from the plot level to the approximately 25-km 2 footprint of the sensor, and discuss issues associated with operational comparisons to the MODIS NPP product. All approaches revealed considerable spatial hetero- geneity in NPP at scales less than the resolution of the MODIS NPP product. The effort to characterize uncertainty in the validation data layers indicated the importance of treating the combination of classification error, sampling error, and measurement error. Generally, the optimal procedure for scaling NPP to a MODIS footprint will depend on local vegetation type, the scale of spatial heterogeneity, and available resources. In all approaches, high resolution remote sensing can play a critical role in characterizing land cover and relevant biophysical variables. <s> BIB015 </s> Scale Issues in Remote Sensing: A Review on Analysis, Processing and Modeling <s> Effects of scale on the measurements, retrieval models and products <s> The monitoring of earth surface dynamic processes requires global observations of the structure and the functioning of vegetation. Moderate resolution sensors (with pixel size ranging from 250 m to 7 km) provide frequent estimates of biophysical variables to characterize vegetation such as the leaf area index (LAI). However, the computation of LAI from moderate resolution remote sensing data induces a scaling bias on the LAI estimate if the moderate resolution pixel is heterogeneous and if the transfer function that relates remote sensing data to LAI is non-linear. This study provides a model to evaluate and correct the scaling bias. The model is built first for a univariate semi-empirical transfer function relating LAI directly to NDVI. The scaling bias is a function of (i) the degree of non-linearity of the transfer function quantified by its second derivative and (ii) the spatial heterogeneity of the moderate resolution pixel quantified by the variogram of the high spatial resolution (20 m) NDVI image. Then, the model is extended to a bivariate transfer function where LAI is related to red and near infrared reflectances. The scaling bias depends on (i) the Hessian matrix of the transfer function and (ii) the variograms and cross variogram of the red and near infrared reflectances. The scaling bias is investigated on several distinct landscapes from the VALERI database. Adjusting for scaling bias is critical on crop sites which are the most heterogeneous sites at the landscape level. Regarding the univariate transfer function, the magnitude of the scaling bias increases rapidly with pixel size until this size is larger than the typical spatial scale of the data. For the bivariate transfer function, it results from the addition of several components that may add up or cancel each other out. It is thus more difficult to analyze. The accuracy of the model to estimate the scaling bias is discussed. It depends mainly on the ability of the variograms and cross variogram to represent the local dispersion variances and covariance within the moderate resolution pixel. The model is generally highly accurate at 1000 m spatial resolution for the univariate transfer function and less accurate for the bivariate transfer function. <s> BIB016 </s> Scale Issues in Remote Sensing: A Review on Analysis, Processing and Modeling <s> Effects of scale on the measurements, retrieval models and products <s> Abstract Land surface temperature (LST) is a key parameter in numerous environmental studies. Surface heterogeneity induces uncertainty in pixel-wise LST. Spatial scaling may account for the uncertainty, however, different approaches lead to differences in scaled values. Satellite-retrieved LST may be representative of the pixel-wise LST and useful for scaling analysis, but the limited accuracy of retrieved values adds uncertainty into the scaled values. Based on the Stefan–Boltzmann (S–B) law, this study proposed scaling approaches for LST over flat and relief areas to explore the combined uncertainties in scaling using satellite-retrieved data. To take advantage of simultaneous, multi-resolution observations at coincident nadirs by the Advanced Spaceborne Thermal Emission Reflection Radiometer (ASTER) and the MODerate-resolution Imaging Spectroradiometer (MODIS), LST products from these two sensors were examined for part of the Loess Plateau in China. 90-m ASTER LST data were scaled up to 1 km using the proposed approaches, and variation in the LST was generally reduced after scaling. Amongst the sources of uncertainties, surface heterogeneity (emissivity) and different scaling approaches resulted in very minor differences, with a maximum difference of 0.2 K for the upscaled LST. Terrain features, taken as an areal weighting factor, had negligible effects on the upscaled value. Limited accuracy of the retrieved LST was the major uncertainty. The overall LST increased 0.6 K on average with correction for terrain-induced angular effect and 0.4 K for both angular and adjacency effects over the study area. Accounting for terrain correction in scaling is necessary for rugged areas. With terrain correction, the upscaled ASTER LST achieved an agreement of − 0.1 ± 1.87 K and a root mean square error (RMSE) of 1.87 K overall with the 1-km MODIS LST rectified by Wan et al.'s approach [Wan, Z., Zhang, Y., Zhang Q., Li, Z.-L. (2002b), Validation of the land-surface temperature products retrieved from Terra Moderate Resolution Imaging Spectroradiometer data. Remote Sensing of Environment, 83 , 163–180]. Refining the rectification approach resulted in a better agreement of − 0.2 ± 1.57 K and a RMSE of 1.58 K. <s> BIB017 </s> Scale Issues in Remote Sensing: A Review on Analysis, Processing and Modeling <s> Effects of scale on the measurements, retrieval models and products <s> Abstract There is considerable interest in using remote sensing to characterize the hydrologic behavior of the land surface on a routine basis. Information on moisture fluxes between the surface and lower atmosphere reveals linkages and land–atmosphere feedback mechanisms, aiding our understanding of energy and water balance cycles. Techniques that combine information on land and atmospheric properties with remotely sensed variables would allow improved prediction for a number of hydrological variables. Over the last few decades, there has been a focus on better determining evapotranspiration and its spatial variability, but for many regions routine prediction is not generally available at a spatial resolution appropriate to the underlying surface heterogeneity. Over agricultural regions, this is particularly critical, since the spatial extent of typical field scales is not regularly resolved within the pixel resolution of satellite sensors. Understanding the role of landscape heterogeneity and its influence on the scaling behavior of surface fluxes as observed by satellite sensors with different spatial resolutions is a critical research need. To attend this task, data from Landsat-ETM (60 m), ASTER (90 m), and MODIS (1020 m) satellite platforms are employed to independently estimate evapotranspiration. The range of the satellite sensor resolutions allows analyses that span scales from (point-scale) in-situ tower measurements to the MODIS kilometer-scale. Evapotranspiration estimates derived at these multiple resolutions were assessed against eddy covariance flux measurements collected during the 2002 Soil Moisture Atmospheric Coupling Experiment (SMACEX) over the Walnut Creek watershed in Iowa. Together, these data allow a comprehensive scale intercomparison of remotely sensed predictions, which include intercomparisons of the evapotranspiration products from the various sensors as well as a statistical analysis for the retrievals at the watershed scale. A high degree of consistency was observed between the retrievals from the higher-resolution satellite platforms (Landsat-ETM and ASTER). The MODIS-based estimates, while unable to discriminate the influence of land surface heterogeneity at the field scale, effectively reproduced the watershed average response, illustrating the utility of this sensor for regional-scale evapotranspiration estimation. <s> BIB018 </s> Scale Issues in Remote Sensing: A Review on Analysis, Processing and Modeling <s> Effects of scale on the measurements, retrieval models and products <s> To date, simulating land surface hydrological processes over large areas at spatial resolutions higher than 1 km remains technically unfeasible, because of limitations of data availability and computational resources. Several studies have demonstrated, however, that gridding the land surface into coarse homogeneous pixels may cause important biases on ecosystem model estimations of water budget components at local, regional and global scales. These biases result from the overlook of sub-pixel variability of land surface characteristics. This study suggests a simple algorithm that uses sub-pixel information on the spatial variability of vegetation and soil cover, and surface topography to correct evapotranspiration (ET) estimates, made at coarse spatial resolutions where the land surface is considered as homogeneous within each pixel. The algorithm operates in such a way that the ET rates as obtained from calculations made at coarse spatial resolutions are multiplied by separate simple functions that attempt to reproduce the effects of sub-pixel variability of land cover, leaf area index, soil texture, and topography on ET. Its application to a remote sensing process-based model estimates made at a 1-km resolution over a watershed located in the southern part of the Canadian boreal forest improved estimates of average ET as well as its temporal and spatial variability. <s> BIB019 </s> Scale Issues in Remote Sensing: A Review on Analysis, Processing and Modeling <s> Effects of scale on the measurements, retrieval models and products <s> Abstract The normalized difference vegetation index (NDVI) is the most widely used vegetation index for retrieval of vegetation canopy biophysical properties. Several studies have investigated the spatial scale dependencies of NDVI and the relationship between NDVI and fractional vegetation cover, but without any consensus on the two issues. The objectives of this paper are to analyze the spatial scale dependencies of NDVI and to analyze the relationship between NDVI and fractional vegetation cover at different resolutions based on linear spectral mixing models. Our results show strong spatial scale dependencies of NDVI over heterogeneous surfaces, indicating that NDVI values at different resolutions may not be comparable. The nonlinearity of NDVI over partially vegetated surfaces becomes prominent with darker soil backgrounds and with presence of shadow. Thus, the NDVI may not be suitable to infer vegetation fraction because of its nonlinearity and scale effects. We found that the scaled difference vegetation index (SDVI), a scale-invariant index based on linear spectral mixing of red and near-infrared reflectances, is a more suitable and robust approach for retrieval of vegetation fraction with remote sensing data, particularly over heterogeneous surfaces. The proposed method was validated with experimental field data, but further validation at the satellite level would be needed. <s> BIB020 </s> Scale Issues in Remote Sensing: A Review on Analysis, Processing and Modeling <s> Effects of scale on the measurements, retrieval models and products <s> Abstract There are a number of outstanding important issues in terms of estimating terrestrial carbon fluxes; one of these is the spatial scaling issue. The purpose of the present study is to document the spatial scaling effect in terms of the terrestrial carbon flux measured at the point-scale and satellite-driven modeling at the global scale. To achieve this, the biosphere model BEAMS was used at the point, regional, and global scales using the same model conditions and parameters; we then compared the BEAMS output for the three different scales and ground measurements. The three sets of results showed reasonably similar spatial and temporal patterns. Temporal variations in the estimated GPP at point-scale showed good agreement with the ground measurements ( R 2 = 0.84). The spatial distributions of the annual mean GPP and NPP at the regional-scale revealed high values over hilly areas and plateaus, gradually decreasing toward urban areas and high mountains. Ground-observed, point-scale, and regional-scale GPP values show almost identical seasonal patterns. The correlation coefficient for the regional-scale and global-scale monthly mean NPP values is 0.77. In particular, the NPP calculated at the different scales for three areas showed a strong correlation ( R 2 = 0.81). As ground measurements are strongly reflected in the output of the global-scale simulation, we conclude that model validation at the point-scale is important when performing global-scale simulations. <s> BIB021 </s> Scale Issues in Remote Sensing: A Review on Analysis, Processing and Modeling <s> Effects of scale on the measurements, retrieval models and products <s> Abstract Characterizing the spatial dynamics of soil moisture fields is a key issue in hydrology, offering an avenue to improve our understanding of complex land surface–atmosphere interactions. In this paper, the statistical structure of soil moisture patterns is examined using modelled soil moisture obtained from the North American Land Data Assimilation System (NLDAS) at 0.125° resolution. The study focuses on the vertically averaged soil moisture in the top 10 cm and 100 cm layers. The two variables display a weak dependence for lower values of surface soil moisture, with the strength of the relationship increasing with the water content of the top layer. In both cases, the variance of the soil moisture follows a power law decay as a function of the averaging area. The superficial layer shows a lower degree of spatial organization and higher temporal variability, which is reflected in rapid changes in time of the slope of the scaling functions of the soil moisture variance. Conversely, the soil moisture in the top 100 cm has lower variability in time and larger spatial correlation. The scaling of these patterns was found to be controlled by the changes in the soil water content. Results have implications for the downscaling of soil moisture to prevent model bias. <s> BIB022 </s> Scale Issues in Remote Sensing: A Review on Analysis, Processing and Modeling <s> Effects of scale on the measurements, retrieval models and products <s> Abstract We developed algorithms for spatial scaling of leaf area index (LAI) using sub-pixel information. The study area is located near Liping County, Guizhou Province, in China. Methods for LAI spatial scaling were investigated on LAI images with 960 m resolution derived in two ways. LAI from distributed calculation (LAID) was derived using Landsat ETM+ data (30 m), and LAI from lumped calculation (LAIL) was obtained from the coarse (960 m) resolution data derived through resampling the ETM+ data. We found that lumped calculations can be considerably biased compared to the distributed (ETM+) case, suggesting that global and regional LAI maps can be biased if surface heterogeneity within the mapping resolution is ignored. Based on these results, we developed algorithms for removing the biases in lumped LAI maps using sub-pixel land cover-type information, and applied these to correct one coarse resolution LAI product which greatly improved its accuracy. <s> BIB023 </s> Scale Issues in Remote Sensing: A Review on Analysis, Processing and Modeling <s> Effects of scale on the measurements, retrieval models and products <s> Abstract In this study, we examined the characteristics of soil moisture dynamics of wet and dry fields across hierarchical spatial scales within the region of Soil Moisture Experiment 2002 (SMEX02) hydrology campaign in Iowa. The Polarimetric Scanning Radiometer (PSR)-based remotely sensed surface (∼ 0–5 cm) soil moisture at 800 m × 800 m resolution was used in this study. Wavelet-based multiresolution technique decomposed the soil moisture into large-scale mean soil moisture fields and fluctuations in horizontal, diagonal, and vertical directions at hierarchical spatial resolutions. Results suggested linearity in the log–log dependency of the variance of soil moisture up to a resolution of 6400 m × 6400 m on PSR sampling dates during SMEX02. The wet fields (with high soil moisture) show almost similar variance for all the resolutions signifying the strong spatial correlation. Analysis of the dry fields (with low soil moisture) indicated a log–log linearity of moments with various scales, and the slopes of these relationships exhibit a concave functional form with the order of moments, typically representing a multiscaling process. The scaling exponent of soil moisture during dry-down suggests a transition from simple scaling (in wet fields) to multiscaling (in dry fields) behavior. The fluctuation components of multiresolution analysis in the horizontal, diagonal, and vertical directions for dry and wet fields exhibited self-similarity. Another important finding of this study is the increase of subpixel soil moisture variability with increasing resolution, especially for the wet fields. These findings will help develop appropriate up-and down-scaling schemes of remotely sensed soil moisture data for various hydrologic and environmental modeling applications. <s> BIB024 </s> Scale Issues in Remote Sensing: A Review on Analysis, Processing and Modeling <s> Effects of scale on the measurements, retrieval models and products <s> Global NDVI data are routinely derived from the AVHRR, SPOT-VGT, and MODIS/Terra earth observation records for a range of applications from terrestrial vegetation monitoring to climate change modeling. This has led to a substantial interest in the harmonization of multisensor records. Most evaluations of the internal consistency and continuity of global multisensor NDVI products have focused on time-series harmonization in the spectral domain, often neglecting the spatial domain. We fill this void by applying variogram modeling (a) to evaluate the differences in spatial variability between 8-km AVHRR, 1-km SPOT-VGT, and 1-km, 500-m, and 250-m MODIS NDVI products over eight EOS (Earth Observing System) validation sites, and (b) to characterize the decay of spatial variability as a function of pixel size (i.e. data regularization) for spatially aggregated Landsat ETM+ NDVI products and a real multisensor dataset. First, we demonstrate that the conjunctive analysis of two variogram properties – the sill and the mean length scale metric – provides a robust assessment of the differences in spatial variability between multiscale NDVI products that are due to spatial (nominal pixel size, point spread function, and view angle) and non-spatial (sensor calibration, cloud clearing, atmospheric corrections, and length of multi-day compositing period) factors. Next, we show that as the nominal pixel size increases, the decay of spatial information content follows a logarithmic relationship with stronger fit value for the spatially aggregated NDVI products (R2 = 0.9321) than for the native-resolution AVHRR, SPOT-VGT, and MODIS NDVI products (R2 = 0.5064). This relationship serves as a reference for evaluation of the differences in spatial variability and length scales in multiscale datasets at native or aggregated spatial resolutions. The outcomes of this study suggest that multisensor NDVI records cannot be integrated into a long-term data record without proper consideration of all factors affecting their spatial consistency. Hence, we propose an approach for selecting the spatial resolution, at which differences in spatial variability between NDVI products from multiple sensors are minimized. This approach provides practical guidance for the harmonization of long-term multisensor datasets. <s> BIB025 </s> Scale Issues in Remote Sensing: A Review on Analysis, Processing and Modeling <s> Effects of scale on the measurements, retrieval models and products <s> Directional gap probability or gap fraction is a basic parameter in the optical remote sensing modeling. Although some approaches have been proposed to estimate this gap probability from remotely sensed measurements, few efforts have been made to investigate the scaling effects of this parameter. This paper analyzes the scaling effect through aggregating the high-resolution directional gap probability (pixel size of 20 meters) estimated from leaf area index (LAI) images of VALERI database by means of Beer's law and introduces an extension of clumping index, Ĉ, to compensate the scaling bias. The results show that the scaling effect depends on both the surface heterogeneity and the nonlinearity degree of the retrieved function. Analytical expressions for the scaling bias of gap probability and Ĉ are established in function of the variance of LAI and the mean value of LAI in a coarse pixel. With the VALERI dataset, the study in this paper shows that relative scaling bias of gap probability increases with decreasing spatial resolution for most of land cover types. Large relative biases are found for most of crops sites and a mixed forest site due to their relative large variance of LAI, while very small biases occur over grassland and shrubs sites. As for Ĉ, it varies slowly in the pure forest, grassland and shrubs sites, while more significantly in crops and mixed forest. <s> BIB026 </s> Scale Issues in Remote Sensing: A Review on Analysis, Processing and Modeling <s> Effects of scale on the measurements, retrieval models and products <s> Abstract Understanding the influence of within-pixel land cover heterogeneity is essential for the extrapolation of measured and modeled CO 2 fluxes from the canopy to regional scales using remote sensing. Airborne light detection and ranging (lidar) was used to estimate spatial and temporal variations of gross primary production (GPP) across a jack pine chronosequence of four sites in Saskatchewan, Canada for comparison with the Moderate Resolution Imaging Spectroradiometer (MODIS) GPP product. This study utilizes high resolution canopy structural information obtained from airborne lidar to bridge gaps in spatial representation between plot, eddy covariance (EC), and MODIS estimates of vegetation GPP. First we investigate linkages between canopy structure obtained from measurements and light response curves at a jack pine chronosequence during the growing season of 2004. Second, we use the measured canopy height and foliage cover inputs to create a structure-based GPP model (GPP Landsberg ) which was tested in 2005. The GPP model is then run using lidar data (GPP Lidar ) and compared with eight-day cumulative MODIS GPP (GPP MODIS ) and EC observations (GPP EC ). Finally, we apply the lidar GPP model at spatial resolutions of 1 m to 1000 m to examine the influence of within-pixel heterogeneity and scaling (or pixel aggregation) on GPP Lidar . When compared over eight-day cumulative periods throughout the 2005 growing season, the standard deviation of differences between GPP lidar and GPP MODIS were less than differences between either of them and GPP EC at all sites. As might be expected, the differences between pixel aggregated GPP estimates are most pronounced at sites with the highest levels of spatial canopy heterogeneity. The results of this study demonstrate one method for using lidar to scale between eddy covariance flux towers and coarse resolution remote sensing pixels using a structure-based Landsberg light curve model. <s> BIB027
The mechanism analyses of scale issues undoubtedly involve several questions. The first one is what the main causes of scale issues are in remote sensing, which has already been analyzed above. The following one is what the effects of scale on the measurements, models and products are. With measurements, what we are more concerned about may be the mean, variance and correlation lengths. Bloschl et al.  and Western et al. BIB004 have already demonstrated the effect of the measurement scale on the apparent variance and the apparent integral scale (apparent correlation length). Here, the "apparent" means the statistical properties that appear in the data. The apparent variance decreases with increasing resolution, while the apparent correlation length, the average distance (or time) over which a property is correlated, always increases with increasing resolution. To the retrieval models, the effects of scale may be difficult to analyze. We may select suitable models at the corresponding scale; for example, the radiative transfer model of vegetation at the leaf scale  or canopy scale  . Whether the change of scale has an effect on the retrieval model is dependent on the status of the measurements and the form of the retrieval model. In the case of threedimensional structures, the retrieval models may need to be remodeled. Smolander and Stenberg BIB009 used a clumping index to correct the radiation attenuation coefficient at a shoot scale and proposed the forest reflectance models for coniferous forests. In the case of big-leaf assumptions, if measurements are homogeneous, the scale has no effects on the retrieval model no matter if the model is linear or non-linear. If the measurements are heterogeneous, there is a scale effect on the retrieval model. There is only no effect when the retrieval model is linear and does not vary with the land cover types, which means the model has a uniform form. Otherwise, the retrieval model may need to be simplified or reparameterized. Raffy BIB001 proposed a spatialisation model to overcome the scale effects by using the lower and upper bounds of the retrieval model. Tian et al. BIB006 addressed the problem of how the scale, or spatial resolution of reflectance measurements impacts retrievals of LAI and developed a physically radiative transfer formulation with explicit spatial resolution dependents. To the products, the effects of scale have already been widely discussed. There is conflicting conclusions in the literature as to whether products are scale dependent or scale free. The main reason is that the scaling effects are usually dependent on the real application. If the retrieval model that is used is linear, there may be no scale effects, yet when the retrieval model has a uniform form for all the land covers, for example, if simply mapping the reflected solar radiation to the surface albedo, we can argue that the reflected solar radiation parameterization is scale invariant. Otherwise, the nonlinearity of albedo with topography and spectral dependence of albedo and the reflected solar radiation would be scale dependent. This demonstrates that a different parameterization and different assumptions related to the retrieval model can lead to different conclusions for the same physical process BIB002 . Raffy BIB001 used a convex hull to judge whether products are overestimated or not. The concave retrieval model overestimates the arithmetic average of values derived independently from fine resolution, while the convex retrieval model underestimates them. Garrigues et al. BIB016 pointed out that the magnitude of scaling effects increases rapidly with pixel size until the size is larger than the typical length scale of data for the univariate retrieval model. For the bivariate transfer function, the scaling effects are the combined effects of several components, which may add up or compensate for each other. The effects of scale on specific products are theoretically and practically analyzed. We may resort to relevant literature, such as bidirectional reflectance distribution function (BRDF) and albedo BIB007 , the temperature BIB017 , the emissivity BIB012 , the infrared radiation and the reflected solar radiation from the surface BIB002 , the latent, sensible and ground heat fluxes  BIB002 BIB018 BIB010 BIB011 BIB019 , carbon flux BIB021 BIB005 , soil moisture BIB003 BIB022 BIB008 BIB024 , NDVI and vegetation fraction BIB020 BIB025 , LAI    BIB016 BIB013 BIB023 , net primary production (NPP) and gross primary productivity (GPP) BIB014 BIB015 BIB027 , directional gap fraction BIB026 .