Scale Issues in Remote Sensing: A Review on Analysis, Processing and Modeling <s> The scaling methods for products <s> As regional and global scales become more important to ecologists, methods must be developed for the application of existing fine-scale knowledge to predict coarser- scale ecosystem properties. This generally involves some form of model in which fine-scale components are aggregated. This aggregation is necessary to avoid the cumulative error associated with the estimation of a large number of parameters. However, aggregation can itself produce errors that arise because of the variation among the aggregated components. The statistical expectation operator can be used as a rigorous method for translating fine- scale relationships to coarser scales without aggregation errors. Unfortunately this method is too cumbersome to be applied in most cases, and alternative methods must be used. These alternative methods are typically partial corrections for the variation in only a few of the fine-scale attributes. Therefore, for these methods to be effective, the attributes that are the most severe sources of error must be identified a priori. We present a procedure for making these identifications based on a Monte Carlo sampling ofthe fine-scale attributes. We then present four methods of translating fine-scale knowledge so it can be applied at coarser scales: (1) partial transformations using the expectation operator, (2) moment expansions, (3) partitioning, and (4) calibration. These methods should make it possible to apply the vast store of fine-scale ecological knowledge to model coarser-scale attributes of ecosystems. <s> BIB001 </s> Scale Issues in Remote Sensing: A Review on Analysis, Processing and Modeling <s> The scaling methods for products <s> Abstract We compared estimates of regional biomass and LAI for a tallgrass prairie site derived from ground data versus estimates derived from satellite data. Linear regression models were estimated to predict LAI and biomass from Landsat-TM data for imagery acquired on three dates spanning the growing season of 1987 using co-registered TM data and ground measurements of LAl and biomass collected at 27 grassland sites. Mapped terrain variables including burning treatment, land-use, and topographic position were included as indicator variables in the models to acccount for variance in biomass and LAI not captured in the TM data. Our results show important differences in the relationships between Kauth-Thomas greenness (from TM), LAI, biomass and the various terrain variables. In general, site-wide estimates of biomass and LAI derived from ground versus satellite-based data were comparable. However, substantial differences were observed in June. In a number of cases, the regression models exhibited signific... <s> BIB002 </s> Scale Issues in Remote Sensing: A Review on Analysis, Processing and Modeling <s> The scaling methods for 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> The scaling methods for products <s> An analytical approach is presented to study the effects of spatial heterogeneity of land surface parameters in climate models. This approach does not use any parametric probability density functions for land surface parameters and attempts to account for the effects of subgrid heterogeneity by using grid-level parameters and correlation between parameters. The adequacy of the approach is illustrated by using the influence of spatial variability in soil wetness and temperature on evaporation. It is shown that both the stability of the lower atmosphere and the surface soil wetness conditions could introduce non-linearity in the estimation of grid-scale evaporation. For stable and near neutral conditions, the heterogeneity in surface temperature plays an important role in the estimation of grid-level latent heat flux. The heterogeneous effect of soil wetness is found to be important when the soil is under moisture constraint. With increasing soil wetness, heterogeneous effects of soil wetness diminish and become negligible as we approach saturation. It appears that effects of temperature and soil moisture heterogeneity effects are an order of magnitude larger compared with correlative effects of temperature and soil moisture for a range of soil wetness and temperature conditions. The subtle difficulties associated with non-linear and coupled influence of soil wetness and atmospheric stability on evaporation preclude the use of any simple aggregation procedure to represent subgrid-scale effects in climate models. © 1998 Royal Meteorological Society. <s> BIB004 </s> Scale Issues in Remote Sensing: A Review on Analysis, Processing and Modeling <s> The scaling methods for products <s> The scaling-multiscaling properties of passive microwave remotely sensed soil moisture images from the Washita '92 experiment are investigated. Analysis of moments of the soil moisture shows a log-log linearity of moments with spatial scale and the concavity of corresponding slopes with the order of moments. These properties suggest a deviation from simple scaling and the possible presence of multiscaling. By decomposing the soil moisture images into large-scale and small-scale fluctuation parts using wavelet transforms, it is shown that the small-scale fluctuation features obey a simple scaling law. The implications for such a decomposition and the coupling between the large-scale and small-scale features are discussed. <s> BIB005 </s> Scale Issues in Remote Sensing: A Review on Analysis, Processing and Modeling <s> The scaling methods for products <s> Because Farquhar’s photosynthesis model is only directly applicable to individual leaves instantaneously, considerable skill is needed to use this model for regional plant growth and carbon budget estimations. In many published models, Farquhar’s equations were applied directly to plant canopies by assuming a plant canopy to function like a big-leaf. This big-leaf approximation is found to be acceptable for estimating seasonal trends of canopy photosynthesis but inadequate for simulating its day-to-day variations, when compared with eddy-covariance and gas-exchange chamber measurements from two boreal forests. The daily variation is greatly dampened in big-leaf simulations because the original leaf-level model is partially modified through replacing stomatal conductance with canopy conductance. Alternative approaches such as separating the canopy into sunlit and shaded leaf groups or stratifying the canopy into multiple layers can avoid the problem. Because of non-linear response of leaf photosynthesis to meteorological variables (radiation, temperature and humidity), considerable errors exist in photosynthesis calculation at daily steps without considering the diurnal variability of the variables. To avoid these non-linear effects, we have developed an analytical solution to a simplified daily integral of Farquhar’s model by considering the general diurnal patterns of meteorological variables. This daily model not only captures the main effects of diurnal variations on photosynthesis but is also computationally efficient for large area applications. Its application is then not restricted by availability of sub-daily meteorological data. This scheme has been tested using measured CO2 data from the Boreal Ecosystem–Atmosphere Study (BOREAS), which took place in Manitoba and Saskatchewan in 1994 and 1996 <s> BIB006 </s> Scale Issues in Remote Sensing: A Review on Analysis, Processing and Modeling <s> The scaling methods for products <s> Quantification of biophysical parameters is needed by terrestrial process modeling and other applications. A study testing the role of multispectral data for monitoring biophysical parameters was conducted over a network of grassland field sites in the Great Plains of North America. Grassland biophysical parameters [leaf area index (LAI), fraction of absorbed photosynthetically active radiation (fPAR), and biomass] and their relationships with ground radiometer normalized difference vegetation index (NDVI) were established in this study (r 2 =.66–.85) from data collected across the central and northern Great Plains in 1995. These spectral/biophysical relationships were compared to 1996 field data from the Tallgrass Prairie Preserve in northeastern Oklahoma and showed no consistent biases, with most regression estimates falling within the respective 95% confidence intervals. Biophysical parameters were estimated for 21 ‘‘ground pixels’’ (grids) at the Tallgrass Prairie Preserve in 1996, representing three grazing/burning treatments. Each grid was 30 � 30 m in size and was systematically sampled with ground radiometer readings. The radiometric measurements were then converted to biophysical parameters and spatially interpolated using geostatistical kriging. Grid-based biophysical parameters were monitored through the growing season and regressed against Landsat Thematic Mapper (TM) NDVI (r 2 =.92–.94). These regression equations were used to estimate biophysical parameters for grassland TM pixels over the Tallgrass Prairie Preserve in 1996. This method maintained consistent regression development and prediction scales and attempted to minimize scaling problems associated with mixed land cover pixels. A method for scaling Landsat biophysical parameters to coarser resolution satellite data sets (1 km 2 ) was also investigated. D 2002 Elsevier Science Inc. All rights reserved. <s> BIB007 </s> Scale Issues in Remote Sensing: A Review on Analysis, Processing and Modeling <s> The scaling methods for products <s> Leaf area index (LAI) is one of the surface parameters that has importance in climate, weather, and ecological studies, and has been routinely estimated from remote sensing measurements. Canada-wide LAI maps are now being produced using cloud-free Advanced Very High-Resolution Radiometer (AVHRR) imagery every 10 days at 1-km resolution. The archive of these products began in 1993. LAI maps at the same resolution are also being produced with images from the SPOT VEGETATION sensor. To improve the LAI algorithms and validate these products, a group of Canadian scientists acquired LAI measurements during the summer of 1998 in deciduous, conifer, and mixed forests, and in cropland. Common measurement standards using the commercial Tracing Radiation and Architecture of Canopies (TRAC) and LAI-2000 instruments were followed. Eight Landsat Thematic Mapper (TM) scenes at 30-m resolution were used to locate ground sites and to facilitate spatial scaling to 1-km pixels. In this paper, examples of Canada-wide LAI maps are presented after an assessment of their accuracy using ground measurements and the eight Landsat scenes. Methodologies for scaling from high- to coarse-resolution images that consider surface heterogeneity in terms of mixed cover types are evaluated and discussed. Using Landsat LAI images as the standard, it is shown that the accuracy of LAI values of individual AVHRR and VEGETATION pixels was in the range of 50–75%. Random and bias errors were both considerable. Bias was mostly caused by uncertainties in atmospheric correction of the Landsat images, but surface heterogeneity in terms of mixed cover types were also found to cause bias in AVHRR and SPOT VEGETATION LAI calculations. Random errors come from many sources, but pixels with mixed cover types are the main cause of random errors. As radiative signals from different vegetation types were quite different at the same LAI, accurate information about subpixel mixture of the various cover types is identified as the key to improving the accuracy of LAI estimates. D 2002 Elsevier Science Inc. All rights reserved. <s> BIB008 </s> Scale Issues in Remote Sensing: A Review on Analysis, Processing and Modeling <s> The scaling methods for 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> BIB009 </s> Scale Issues in Remote Sensing: A Review on Analysis, Processing and Modeling <s> The scaling methods for 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> The scaling methods for products <s> Abstract Accurate mapping of land cover at continental to global scales is currently limited by our ability to exploit the spatial, temporal, and radiometric characteristics of the available satellite data. Many ecologically and biogeochemically important landscape features are spatially extensive, but occur at scales much smaller than the ∼1-km footprint of wide-swath, polar orbiting radiometers. This is especially true for land cover changes associated with human activities. Satellite instruments that offer the appropriate spatial detail have much smaller swaths and longer repeat times, resulting in compositing intervals that are too large to resolve the time scales of these changes. In addition, the cost and effort associated with acquisition and processing of high-resolution data for large areas is often prohibitive. Methods for taking advantage of information contained in multiple-scale observations by combining data from high-resolution and moderate resolution sensors are thus of great current interest. In this paper, we retrieve land cover distributions in two different parts of the Brazilian Amazon region by estimating relationships between land cover fractions derived from 30-m resolution ETM+ and reflectance data from ∼1-km resolution MODIS and MISR. The scaling relationships are derived using a Bayesian-regularized artificial neural network (ANN) and compared to results using linear unmixing (LU). We explore the simultaneous use of two significant independent variables in terrestrial optical remote sensing, wavelength, and sun-sensor geometry, by combining nadir-adjusted MODIS reflectances in seven bands (VIS-SWIR) with multiangular (−71° to +71°) bidirectional reflectance data from MISR. This research was motivated by evidence from modeling and field studies demonstrating that: (a) the angular dependence of reflectance (e.g., from MISR) contains information about the structural composition of canopies that is complementary to the wavelength dependence; and (b) the SWIR portion of the spectrum (e.g., from MODIS) is sensitive to canopy moisture and shading conditions and, therefore, to the successional status of the ecosystem. This case study, using the Bayesian artificial neural network with combined MODIS-MISR data to estimate sub-pixel land cover fractions, yielded a quantitative improvement over spectral linear unmixing of single-angle, multispectral data. Our results suggest potential for broad-scale applicability despite a number of challenges related to tropical atmospheric conditions. <s> BIB011 </s> Scale Issues in Remote Sensing: A Review on Analysis, Processing and Modeling <s> The scaling methods for products <s> A wavelet multi-resolution analysis was conducted using vegetation and radiometric temperature data derived from the Advanced Very High Resolution Radiometer (AVHRR) data from the Southern Great Plains 1997 (SGP97) Hydrology Experiment. The wavelet coefficients were used to investigate whether the Normalized Difference Vegetation Index (NDVI) and radiometric temperature fields exhibit self-similar scaling behaviour. Using the first six moments of the wavelet coefficients through eight levels of dyadic decomposition, the NDVI data are shown to be statistically self-similar with a slope of approximately m 0.72 in each of the horizontal, vertical, and diagonal directions of the image over scales ranging from 2000 to 256 000 m. The radiometric temperature data are also shown to exhibit self-similarity with slopes ranging from m 0.9 in the diagonal direction to m 1.0 in the vertical direction over the same scales. These slopes indicate long range behaviour and may imply a methodology for statistically assimila... <s> BIB012 </s> Scale Issues in Remote Sensing: A Review on Analysis, Processing and Modeling <s> The scaling methods for products <s> Routine (i.e., daily to weekly) monitoring of surface energy fluxes, particularly evapotranspiration (ET), using satellite observations of radiometric surface temperature has not been feasible at high pixel resolution (i.e., ∼101–102 m) because of the low frequency in satellite coverage over the region of interest (i.e., approximately every 2 weeks). Cloud cover further reduces the number of useable observations of surface conditions resulting in high-resolution satellite imagery of a region typically being available once a month, which is not very useful for routine ET monitoring. Radiometric surface temperature observations at ∼1- to 5-km pixel resolution are available multiple times per day from several weather satellites. However, this spatial resolution is too coarse for estimating ET from individual agricultural fields or for defining variations in ET due to land cover changes. Satellite data in the visible and near-infrared wavelengths, used for computing vegetation indices, are available at resolutions an order of magnitude smaller than in the thermal-infrared, and hence provide higher resolution information on vegetation cover conditions. A number of studies have exploited the relationship between vegetation indices and radiometric surface temperature for estimating model parameters used in computing spatially distributed fluxes and available moisture. In this paper, the vegetation index–radiometric surface temperature relationship is utilized in a disaggregation procedure for estimating subpixel variation in surface temperature with aircraft imagery collected over the US Southern Great Plains. The disaggregated surface temperatures estimated by this procedure are compared to actual observations at this subpixel resolution. In addition, a remote sensing-based energy balance model is used to compare output using actual versus estimated surface temperatures over a range of pixel resolutions. From these comparisons, the utility of the surface temperature disaggregation technique appears to be most useful for estimating subpixel surface temperatures at resolutions corresponding to length scales defining agricultural field boundaries across the landscape. <s> BIB013 </s> Scale Issues in Remote Sensing: A Review on Analysis, Processing and Modeling <s> The scaling methods for 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> BIB014 </s> Scale Issues in Remote Sensing: A Review on Analysis, Processing and Modeling <s> The scaling methods for 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> BIB015 </s> Scale Issues in Remote Sensing: A Review on Analysis, Processing and Modeling <s> The scaling methods for products <s> A fundamental question in scale research is how to scale up descriptions of hydrological responses from the small scales at which they are developed to the larger scales at which predictions are required or can be validated, in the presence of spatial heterogeneity of soils, vegetation and topography, and of space–time variability of climatic inputs. One scaling approach is the disaggregation–aggregation approach, which involves disaggregating catchment-scale state variables to point-scale distributions, applying a suitable point-scale physical model using these state variables, and aggregating the resulting point-scale responses to yield a catchment-scale response. Thus, the approach provides a way of linking the catchment-scale state variables with the catchment-scale responses and thereby permits the development of empirical large-scale models that still retain some essence of the small-scale physics. In this paper we illustrate the disaggregation–aggregation approach with two examples that deal with developing catchment-scale conceptualizations of (a) infiltration excess runoff and (b) evapotranspiration, using detailed process-based models available at the small scale. These conceptualizations became the building blocks of the large-scale catchment model, LASCAM. Copyright © 2004 John Wiley & Sons, Ltd. <s> BIB016 </s> Scale Issues in Remote Sensing: A Review on Analysis, Processing and Modeling <s> The scaling methods for 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> BIB017 </s> Scale Issues in Remote Sensing: A Review on Analysis, Processing and Modeling <s> The scaling methods for 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> BIB018 </s> Scale Issues in Remote Sensing: A Review on Analysis, Processing and Modeling <s> The scaling methods for products <s> Scaling up ecosystem processes from plots to landscapes is essential for understanding landscape structure and functioning as well as for assessing ecological impacts of land use and climate change. This study illustrates an upscaling approach to studying the spatiotemporal pattern of ecosystem processes in the Changbai Mountain Nature Reserve in northeastern China by integrating simulation modeling, GIS, remote sensing data, and field-based observations. The ecosystem model incorporated processes of energy transfer, plant physiology, carbon dynamics, and water cycling. Using a direct extrapolation scheme, the patch-level ecosystem model was scaled up to quantify the landscape-level pattern of primary productivity and the carbon source-sink relationship. The simulated net primary productivity (NPP) for the entire landscape, consisting of several ecosystem types, was 0.680 kg C m−2 yr−1. The most widely distributed ecosystem type in this region was the mixed broad-leaved and Korean pine (Pinus koraiensis) forest, which had the highest NPP (1.084 kg C m−2 yr−1). The total annual NPP for all ecosystem types combined was estimated to be 1.332 Mt C yr−1. These results suggest that the Changbai Mountain landscape as a whole was a carbon sink, with a net carbon sequestration rate of about 0.884 Mt C yr−1 for the study period. The simulated NPP agreed reasonably well with available field measurements at a number of locations within the study landscape. Our study provides new insight into the relationship between landscape pattern and ecosystem processes, and useful information for improving management practices in the Changbai Mountain Nature Reserve, which is one of the most important forested landscapes in China. Several research needs are discussed to further refine the modeling approach and reduce prediction uncertainties. <s> BIB019 </s> Scale Issues in Remote Sensing: A Review on Analysis, Processing and Modeling <s> The scaling methods for 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> BIB020 </s> Scale Issues in Remote Sensing: A Review on Analysis, Processing and Modeling <s> The scaling methods for products <s> Hydrology and crop water management require daily values of evapotranspiration ET at different time-space scale. Sun synchronous optical remote sensing, which allows for the assessment of ET with high to moderate spatial resolution, provides instantaneous estimates during satellites overpass. Then, usual solutions consist of extrapolating instantaneous to daily values by assuming that evaporative fraction EF is constant throughout the day, providing that daily available energy AE is known. The current study aims at deriving daily ET values from ASTER derived instantaneous estimates, over an olive orchard in a semi-arid region of Moroccan. It has been shown that EF is almost constant under dry conditions, but it depicts a pronounced concave up shape under wet conditions. A new heuristic parameterization is then proposed, which is based on the combination of routine daily meteorological data for characterizing atmospheric dependence, and on optical remote sensing based estimates of instantaneous EF values to take into account the dependence on soil and vegetation conditions. Using the same type of approach, a similar parameterization is next developed for AE. The validation of both approaches shows good performances. The overall method is finally applied to ASTER data. Though performances are reasonably good, their moderate reduction is ascribed to errors on remotely sensed variables. Future works will focus on method portability since its empirical formulation does not account for the direct stomatal response to water availability, as well as on application over different surface and climate conditions. <s> BIB021 </s> Scale Issues in Remote Sensing: A Review on Analysis, Processing and Modeling <s> The scaling methods for 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> BIB022
Compared to the scaling methods of measurements and retrieval models, the scaling methods for products are more widely studied in research. These scaling methods provide a few systematic approaches to characterize the land surface heterogeneity and compensate for scaling effects. Here, we just emphasize the spatial domain. Other scaling methods applied in different domains can be realized by certain approaches. For example, scaling in the temporal domain may consider the general diurnal patterns of meteorological variables BIB006 or assume that the evaporative fraction (EF) is constant throughout the day BIB021 . Scaling in the spectral domain and the directional domain would rely on experimental regression or look-up tables (LUT) to solve the scale problem, respectively. Since land surface is very heterogeneous, up-scaling is probably more important than downscaling in product validation. Therefore, we may be more concerned about the up-scaling method. The downscaling method resorts to relevant literature  . In general, the simple up-scaling method can use statistical algorithms to estimate the spatial means at a large scale by either area-weighted products of homogeneous patches or the integration over the probability density function of products BIB010 . In the following, other extensively used scaling methods in the spatial domain, such as Empirical Regression Method (ERM), Taylor Series Expansion Method (TSEM), Contextural Parameters Method (CPM), Statistical Fractal and Self-similar Method (SFSM) will be analyzed in detail. ERM is simply used to empirically calibrate the relationship of products between fine and coarse scales BIB001 BIB002 BIB007 . The goal is to relate the products at different scales by regression. Fernandes et al. BIB014 simply used empirical relationships between spectral vegetation indices and surface estimations of LAI, which are in-situ measurements from the auxiliary sites, to estimate coarse-scale LAI. Martinez et al.  used a multivariate ordinary least squares (OLS) algorithm which uses an iteratively reweighted least squares (IRLS) algorithm to build an empirical relationship and upscale the field LAI data to the corresponding satellite products. Although the scaling method is simple, the relationship of regression is usually site, time, model and scale dependent. If any one factor is changed, the relationship may need to be recalibrated. Consequently, it would gradually be replaced by other scaling methods. TSEM is based on Taylor's theorem of linearizing the retrieval model around the arithmetic average of measurements   BIB017 . It characterizes the scaling effects as the combined effects of degree of non-linearity of the model and the heterogeneity of the land surface. The key to using this method is to know how to estimate the variance and covariance within the pixel at coarse resolution. Hu and Islam  proposed a novel method based only on the mean values of measurements at pixel scale to parameterize the variance and covariance terms by the half ellipse relationship between the normalized standard deviation of radiance and the normalized average radiance over the pixel. They used this relationship to study the effects of subgrid scale heterogeneity of soil wetness and temperature on gridscale evaporation BIB004 . Garrigues et al. BIB017 used the local dispersion variance and covariance which are calculated by semivariogram and cross semivariogram from concurrent high spatial resolution images or a spatial sampling per type of landscape of the high spatial resolution data to quantify the spatial variability within the moderate resolution pixel. Afterwards, Garrigues et al.  proposed a spatio-temporal model of the variogram to estimate the intra-pixel spatial heterogeneity. It is a novel approach to predict the variogram at a date at which the high spatial resolution scene is not available by the seasonal cycle of phenological variability. Although its validity is argued by Chen  , it is still useful for product scaling. In conclusion, the method is easy to understand and operate. If the intrapixel spatial heterogeneity can be successfully represented, it can give reasonable results. The disadvantage of TSEM is that it must satisfy some hypotheses. The model needs to be continuous and have at least up to second order continuous derivatives in the interval under consideration. If the model has strong non-linearity, the approximation would not be appropriate. When using complicated models with a large number of variables, it would be difficult to find the derivatives of the model  . Again, failure to include high order terms or interactive terms (covariance) may limit the application of this technique. Generally, the variance and covariance within one pixel are important for the traditional textural parameters that can capture the spatial variability of the surface. However, they are difficult to be estimated due to the fact that the concurrencies of high and low resolution images are often not available. In addition, they may not be used to discriminate the situations where the surface heterogeneity can be caused either by the cover type changes or by density change within the same cover type. If the surface heterogeneity is caused by cover type changes, the linear models which have different forms for different cover types may also cause scale effects. In contrast, if the surface heterogeneity is caused only by density change, the non-linearity of the model would generally cause very small scale effects  BIB008 . In short, TSEM would be useless when the model is discontinuous or piecewise against the measurements. In order to break through the limitations of using textural parameters, Chen  proposed a different scheme, CPM. It took the contextural parameters (e.g., the fractions of subcomponents) as a bridge to quantify the scaling effects. Simic et al. BIB015 tried to use such subpixel information to upscale NPP. The result showed that the correlation between the distributed NPP and lumped NPP was greatly improved. El Maayar and Chen BIB018 thought the scale effects resulted from the overlooking of sub-pixel variability of land surface characteristics and proposed a simple algorithm that used contextural parameters of vegetation, soil cover, and surface topography to correct evapotranspiration (ET) estimates. Jin et al. BIB020 developed such algorithms to remove the biases in lumped LAI maps using sub-pixel land cover-type information and correct coarse resolution products of LAI. Here the fractions can be estimated either by the sub-pixel land cover masks at high resolutions or the linear unmixing method. Braswell et al. BIB011 used the Bayesianregularized artificial neural network with combined MODIS-MISR data to estimate sub-pixel land cover fractions and yielded a quantitative improvement result over spectral linear unmixing of singleangle, multispectral data. The result is promising. However, contexture-based methods are usually model-dependent. They cannot provide a general method to compensate for scaling effects. The mapping function needs to be redefined when the model is changed. When the model has several variables, the mapping functions become very hard to be derived. Therefore, contexture-based methods are not alternatives to texture-based methods. They are new attempts to solve scaling effects. In practice, we need to choose the corresponding scaling methods according to actual requirements. SFSM is based on the simple scaling and multiscaling characteristics of products. Dubayah et al.  have found the log-log linearity relationship between the statistical moment and the scale factor, and the non-linear dependence of scaling exponents with order moment. That is to say, the statistical properties (moments) of process can be extended from one scale to the other scale. Hu et al. BIB003 analyzed the statistical characterization of soil moisture retrieved from remotely sensed passive microwaves. They found these properties and suggested a deviation from simple scaling and the possible presence of multiscaling BIB009 BIB005 . Das and Mohanty BIB022 argued that the scaling exponent of soil moisture during dry-down suggests a transition from simple scaling (in wet fields) to multiscaling (in dry fields) behavior. However, the fluctuation parts of soil moisture, which is decomposed by wavelet transforms, showed a simple scaling characteristic which implied the possibility of scaling soil moisture. In addition to soil moisture, other products also behave with self-similarity characteristics, such as NDVI and radiometric temperature BIB012 . Based on the multiple moments scaling law, the wish of scaling between different scales without other prior knowledge may be realized. Table 3 summarizes the general scaling methods discussed above. Besides these methods, we can use other methods for scaling the products, such as disaggregation-aggregation combined methods BIB016 , process simulation methods BIB019 and so on. Again, additional information provided by optical and thermal sensors can be used as auxiliary knowledge to assist the scaling. Kustas BIB013 utilized such information and proposed the DisTrad technique to estimate subpixel variation of surface temperature. On the whole, scaling methods for products have already become a universally recognized problem. Its development needs the development of cross-disciplines in order to achieve theoretical and technical innovation. 