Topographic Correction Algorithm Research Articles

A methodology for mapping annual flood extent using multi-temporal Sentinel-1 imagery

A novel automated approach for mapping nonurban flood extents using satellite-based Sentinel-1C-band SAR data is presented and applied in the Republic of Ireland. The methodology mapped the maximum flood extent of over 25,000 detected water bodies across Ireland over a five-year period (2016–2021). Flood extents were classified using a semi-automatic tile-based histogram thresholding approach and refined using a series of post processing filters. These included multi-temporal filters which exploited the timing and orbit position of the Sentinel-1 satellite to identify likely false positives, and contextual information based filters which used external information such as topography and land use to estimate the likelihood of flooding and constrain its extent. A topographic correction algorithm was also applied to hydrologically-correct flood bodies. The methodology produced a user accuracy of above 0.95 for each annual map when compared to observed flood level data, overall accuracy values above 0.97 and kp values above 0.7 when compared to mapping process based on Sentinel-2 validation imagery, and the capacity to detect over 90% of recorded permanent water bodies larger than 2 ha. As an additional step, confidence information was provided for each flood polygon based on the quantity of consistently flooded pixels used in its definition. The mapping process represents a stable and systematic nonurban flood mapping methodology that enables inter-annual comparison of flood extent at gauged and ungauged sites.

Evaluation and Intercomparison of Topographic Correction Methods Based on Landsat Images and Simulated Data

Topographic effects in medium and high spatial resolution remote sensing images greatly limit the application of quantitative parameter retrieval and analysis in mountainous areas. Many topographic correction methods have been proposed to reduce such effects. Comparative analyses on topographic correction algorithms have been carried out, some of which drew different or even contradictory conclusions. Performances of these algorithms over different terrain and surface cover conditions remain largely unknown. In this paper, we intercompared ten widely used topographic correction algorithms by adopting multi-criteria evaluation methods using Landsat images under various terrain and surface cover conditions as well as images simulated by a 3D radiative transfer model. Based on comprehensive analysis, we found that the Teillet regression-based models had the overall best performance in terms of topographic effects’ reduction and overcorrection; however, correction bias may be introduced by Teillet regression models when surface reflectance in the uncorrected images do not follow a normal distribution. We recommend including more simulated images for a more in-depth evaluation. We also recommend that the pros and cons of topographic correction methods reported in this paper should be carefully considered for surface parameters retrieval and applications in mountain regions.

Response of topographic control on nearest-neighbor diffusion-based pan-sharpening using multispectral MODIS and AWiFS satellite dataset

Remote sensing plays a significant role in monitoring of the undulating the Himalayas. With continuous monitoring, the preservation of natural resources and mitigation of natural hazards is possible. Currently, satellite sensors are not capable enough to deliver the earth surface image at a very high temporal, spectral, and spatial resolution, simultaneously. Therefore, it is essential to perform the pan-sharpening of spatially high-resolution (HR) panchromatic (PAN) spectral band with low-resolution (LR) multispectral (MS) imagery which must be acquired on the same temporal date from multiple sensors. On the other hand, due to the rugged topography of the Himalayas, topographic effects are generally induced in the form of shadow and affect the spatial information or spectral information. Therefore, the focus of the present work is to implement and analyze the performance of topographic correction on nearest-neighbor diffusion (NND)-based pan-sharpening algorithm. In order to evaluate the effectiveness, K-mean classification (KMC) has been implemented over topographically corrected and topographically uncorrected NND pan-sharpened images. From the experimental outcomes, it is inferred that topographically corrected NND pan-sharpened classified image has achieved better accuracy (81.33%) as compared with topographically uncorrected NND pan-sharpened classified imagery (78%). It is expected that the integration of topographic correction and NND algorithm facilitates the better extraction of spectral and spatial information and leads to improvement in results for further analysis such as change detection procedure and classification. The applications of the present study are in monitoring of climate change and mapping land cover changes over rugged terrain regions.

Comparision of Eight Topographic Correction Algorithms Applied to Landsat-8 OLI Imagery Based on the DEM

Topographic correction is one of the most important procedures for remote sensing image preprocessing, and it is also the premise for quantitative remote sensing. According to the latest calibration parameters provided by the USGS website, four Lambert body reflectance models and four Non-Lambert body reflectance models were used to carry out the topographic correction combining the DEM data in R platform. A total of three indicators were used to assess the effects including visual contrast, normalized evaluation of shady slopes and sunny slopes, and linear fitting. The results show that the corrected image of Cosine correction method based on the Lambertian reflectivity model is visually overexposed, and the DN value on the shady slope is over-corrected. The corrected images of Minnaert and Minaret-scs based on the Non-Lambertian reflectivity model visually reduce the amplitude of the terrain fluctuations, and the linear fitting has a small separation factor, which produces a better correction effect.

Unsupervised Atmospheric Compensation of Airborne Hyperspectral Images in the VNIR Spectral Range

Atmospheric compensation (AC) is a fundamental and critical step for quantitative exploitation of hyperspectral data. It is the means by which the reflectance of an object/material is estimated from the measured at-sensor radiance. Such reflectance is the inherent signature that is used to identify various materials in a monitored scene. AC is quite complex and is hampered by the large amount of uncontrollable variables that play a role: just think about the spatial variability of some atmospheric constituents such as water vapor and aerosols, or to the rapidly spatially varying effects of the radiation coming from adjacent areas. Though, in principle, some atmospheric parameters and radiometric quantities such as solar irradiance and sky irradiance can be measured during the flight, in practice such measures are rarely available in an operational framework or are taken at a single point of the surface ignoring their spatial variation. Thus, a prompt quantitative exploitation of hyperspectral data for operational purposes, such as material identification and object detection, requires unsupervised and accurate AC procedures that can learn from the image itself the parameters of the inversion model and follow their variability within the scene. In this framework, we present a new unsupervised methodology for AC of airborne hyperspectral images in the visible and near-infrared spectral range. The proposed methodology relies on a radiative transfer model accounting for the adjacency effect and allows the estimation of relevant atmospheric parameters. Specifically, it embeds two new algorithms for the estimation of: 1) aerosol and atmospheric visibility and 2) the water vapor content of the atmosphere accounting for the spatial variability of such a parameter. The two algorithms significantly differ from those adopted by existing state-of-the-art approaches or in commercial packages such as fast line-of-sight atmospheric analysis of spectral hypercubes and airborne atmospheric and topographic correction algorithm. In this paper, we present the detailed description of the new AC methodology, and we analyze the results provided by the algorithm over real data.

A coupled atmospheric and topographic correction algorithm for remotely sensed satellite imagery over mountainous terrain

Radiometric correction is an important issue in the quantitative remote-sensing community. By integrating dark object subtraction (DOS)-based atmospheric correction with physics-based topographic correction, a coupled land surface reflectance retrieval algorithm (coupled atmospheric and topographic correction algorithm, named the CAT algorithm) for rugged mountainous regions is proposed. Terra MODIS-derived atmospheric characterization data (including aerosol optical depth, integrated precipitable water, surface pressure, and ozone concentration) are employed as inputs for the proposed algorithm. A physics-based path radiance estimation model is proposed and embedded in the CAT algorithm, and band-specific per-pixel path radiance values are calculated. After the CAT algorithm was performed, the correlation between reflectance and terrain was dramatically reduced, with correlation coefficients nearly equal zero, especially for the near infrared and short-wave infrared bands, meanwhile the image information content increased over 20%. To provide a comparison with previous studies, two commonly used methods in the literature (DOS + Cosine and DOS + C) were employed. The results of the comparison show that the proposed algorithm performed better in both atmospheric and topographic corrections without empirical regression.

The Added Value of Stratified Topographic Correction of Multispectral Images

Satellite images in mountainous areas are strongly affected by topography. Different studies demonstrated that the results of semi-empirical topographic correction algorithms improved when a stratification of land covers was carried out first. However, differences in the stratification strategies proposed and also in the evaluation of the results obtained make it unclear how to implement them. The objective of this study was to compare different stratification strategies with a non-stratified approach using several evaluation criteria. For that purpose, Statistic-Empirical and Sun-Canopy-Sensor + C algorithms were applied and six different stratification approaches, based on vegetation indices and land cover maps, were implemented and compared with the non-stratified traditional option. Overall, this study demonstrates that for this particular case study the six stratification approaches can give results similar to applying a traditional topographic correction with no previous stratification. Therefore, the non-stratified correction approach could potentially aid in removing the topographic effect, because it does not require any ancillary information and it is easier to implement in automatic image processing chains. The findings also suggest that the Statistic-Empirical method performs slightly better than the Sun-Canopy-Sensor + C correction, regardless of the stratification approach. In any case, further research is necessary to evaluate other stratification strategies and confirm these results.

Evaluation of Topographic Correction on Subpixel Impervious Cover Mapping With CBERS-2B Data

This study compared the effectiveness of six commonly used topographic correction methods for subpixel impervious surface mapping in selected mountainous areas of Southwest Virginia. One 2008 China–Brazil Earth Remote Sensing 2B (CBERS-2B) image was processed using selected topographic algorithms and then used as input for subpixel impervious cover mapping. High-resolution National Agriculture Imagery Program (1-m resolution) images were used to build proportional subpixel impervious cover as training/validation data. We then applied a classification and regression tree algorithm to establish relationships between CBERS signals and impervious surfaces. Accuracy assessment showed that both $R^{2} $ (0.644–0.767) and RMSE (0.118–0.150, reported as proportion of impervious surface) values vary across different topographic correction algorithms. The accuracy differences ( $R^{2} $ : 0.448–0.771; RMSE: 0.118–0.247) were most pronounced for areas facing away from the sun azimuth angle, suggesting aspect–sun azimuth-dependent map accuracy. For terrain shadowing areas, the Minnaert method, the minslope method, and the C-correction substantially outperformed the cosine and improved cosine correction. These findings indicate that users should apply caution in using topographic correction algorithms and that aspect-stratified accuracy assessment needs to be conducted for detailed comparisons. We also repeated the analyses using Landsat TM and obtained better overall results compared to the CBERS-2B data. The differences in $R^{2} $ (or RMSE) for two data sources were not substantial, suggesting the high potential of CBERS data for subpixel impervious surface mapping.

Estimation of high-resolution land surface net shortwave radiation from AVIRIS data: Algorithm development and preliminary results

Hyperspectral remote sensing provides unique and abundant spectral information for quantification of the land surface shortwave radiation budget, which can be used to calibrate climate models and to estimate surface energy budget for monitoring agriculture and urban environment. However, only single broadband or multispectral data have been used in previous studies. In the present study, two methods are proposed to estimate the instantaneous land surface net shortwave radiation (NSR) with high spatial resolutions using hyperspectral remote sensing observations from the Airborne Visible Infrared Imaging Spectrometer (AVIRIS) data. Method A calculates the NSR based on separate estimation of downward radiation and surface broadband albedo, which requires ancillary information for aerosol optical depth; and Method B directly estimates the NSR from the observed radiance. Results based on radiative transfer simulations showed that the use of hyperspectral data can significantly improve NSR estimation compared with the multispectral data method. Atmospheric water vapor correction was applied to adjust the surface radiation estimation. Validation of AVIRIS NSR estimates against ground measurements from two flux networks for the period of 2006–2014 showed that the two methods were similar and had consistent accuracy in the all-sky instantaneous NSR estimation with root-mean-square-errors (RMSEs) of approximately 28–56W/m2. The pixel-based water vapor content estimation from AVIRIS data provided slightly different results than those obtained using coarse resolution remote sensing data. A simplified topographic correction algorithm was found to be able to improve the results generated from Method A; however, the degree of improvement provided by Method B was unclear, possibly because of the lack of consideration of horizontal atmospheric scattering effects from adjacent pixels. In general, hyperspectral remote sensing data have been shown to improve the NSR estimation accuracies compared with results obtained in previous studies. Additional efforts are needed to refine the NSR estimation for application to future satellite hyperspectral data.

Validation of a Simplified Model to Generate Multispectral Synthetic Images

A new procedure to assess the quality of topographic correction (TOC) algorithms applied to remote sensing imagery was previously proposed by the authors. This procedure was based on a model that simulated synthetic scenes, representing the radiance an optical sensor would receive from an area under some specific conditions. TOC algorithms were then applied to synthetic scenes and the resulting corrected scenes were compared with a horizontal synthetic scene free of topographic effect. This comparison enabled an objective and quantitative evaluation of TOC algorithms. This approach showed promising results but had some shortcomings that are addressed herein. First, the model, originally built to simulate only broadband panchromatic scenes, is extended to multispectral scenes in the visible, near infrared (NIR), and short wave infrared (SWIR) bands. Next, the model is validated by comparing synthetic scenes with four Satellite pour l'Observation de la Terre 5 (SPOT5) real scenes acquired on different dates and different test areas along the Pyrenees mountain range (Spain). The results obtained show a successful simulation of all the spectral bands. Therefore, the model is deemed accurate enough for its purpose of evaluating TOC algorithms.

Expansion of Empirical-Statistical Based Topographic Correction Algorithm for Reflectance Modeling on Himalayan Terrain using AWiFS and MODIS Sensor

Irregular shape of terrain causes variable illumination angles and diverse reflectance values within same land cover type in optical remote sensing image. It causes problems in image segmentation and misclassification (snow with other land cover). This perception leads to develop an empirical-statistical based topographic correction (ESbTC) algorithm for reflectance modeling after compared with existed topographic correction methods like Cosine correction, C-correction, Minnaert correction, sun–canopy–senor with c-correction (SCS + C) and slope matching, in the context of snow reflectance. An image based atmospheric correction has used in present study included dark-object subtraction (DOS) and effect of Rayleigh scattering on the transmissivity in different spectral bands of AWiFS and MODIS image data. The performance of different models is evaluated using (1) visual analysis, (2) change in snow reflectance on sunny and shady slopes after the corrections, (3) validation with in situ observations and (4) graphical analysis. Further snow cover area (SCA) has been estimated with normalized difference snow index (NDSI) and validated with support vector machine (SVM), a supervised classification technique. The result shows that the proposed algorithm (ESbTC) and slope-matching technique could eliminate most of the shadowing effects in Himalayan rugged terrain and correctly estimate snow reflectance from AWiFS and MODIS imagery as compared with in situ observations whereas other methods significantly underestimate reflectance values after the corrections.

Synthetic Images for Evaluating Topographic Correction Algorithms

In the last years, many topographic correction (TOC) methods have been proposed to correct the illumination differences between the areas observed by optical remote sensors. Although the available number of TOC methods is high, the evaluation of their performance generally relies on the existence of precise land-cover information, and a standardized and objective evaluation procedure has not been proposed yet. In this paper, we propose an objective procedure to assess the accuracy of these TOC methods on the basis of simulated scenes, i.e., synthetically generated images. These images represent the radiance an optical sensor would receive under specific geometric and temporal acquisition conditions and assuming a certain land-cover type. A simplified method for creating synthetic images using the state-of-the-art irradiance models is proposed, both considering the real topography of a certain area [synthetic real (SR) image] or considering the relief of this area as being completely flat [synthetic horizontal image (SH)]. The comparison between the corrected image obtained by applying a TOC method to the SR and SH images of the same area, allows assessing the performance of each TOC algorithm. This comparison is quantitatively carried out using the structural similarity index. The proposed TOC evaluation procedure is applied to a specific case study in northern Spain to explain its implementation and demonstrate its potential. The procedure proposed in this paper could be also used to assess the behavior of TOC methods operating under different scenarios considering diverse topographic, geometrical, and temporal acquisition configurations.

Restoration of Information Obscured by Mountainous Shadows Through Landsat TM/ETM+ Images Without the Use of DEM Data: A New Method

Shadows in remotely sensed imagery occur when objects totally or partially occlude direct light from a source of illumination, generating great difficulty in land cover interpretation and classification because of the loss of spectral information of shaded pixels. In a mountainous environment with rough terrain, shadows are especially pronounced due to the differentiation of direct illumination between sunny and shady slopes. Topographic correction methods, which are widely used to adjust for differences in solar incidence angles, can partly alleviate the impacts of shadows. However, there are two limitations: one is that the contemporary topographic corrections have little effect on areas that have very low incidence angles and areas that are completely without direct solar illumination (cast shadow); another is that their effectiveness is restricted by the data quality and completeness, spatial resolution, and elevation accuracy of the Digital Elevation Model (DEM) data, which is not currently available in all parts of the world. Thus, noise and errors may be introduced in topographic correction during resampling and geometric registration of the target image. This paper proposes a new approach to restore the radiometric information of mountainous cast shadows using a spectral processing technique called “continuum removal” (CR) without the aid of DEM. The CR-based approach makes full use of the spectral information derived from both the shaded pixels and their neighboring nonshaded pixels of the same land cover type. Several Landsat TM images were used to assess the performance of the proposed method. Results indicated that the proposed method can effectively restore the spectral values of shaded pixels more accurately than the ATCOR_3 correction method, especially for very low incidence angle areas and cast shadows. By comparing data values of shaded pixels with nonshaded pixels (pure reference pixels) of their same class, images processed by the proposed method had the lowest average root mean square error (RMSE) between them in visible, NIR and SWIR bands, followed by the ATCOR_3 correction method and the original image. In addition, the proposed method achieved the best classification accuracy, higher than those from the original test image and the ATCOR_3 corrected image generated using 90 m or 30 m spatial resolution DEM. Therefore, the Continuum Removal method is a better alternative for restoring objects obscured by mountainous shadow when adequate DEM data are unavailable and the quality of DEM cannot satisfy the requirements of topographic correction algorithms.

A physics-based atmospheric and BRDF correction for Landsat data over mountainous terrain

Steep terrain affects optical satellite images through variations it creates in both irradiance and bidirectional reflectance distribution function (BRDF) effects. To obtain the corrected land surface reflectance and detect land surface change through time series analysis over rugged surfaces, it is necessary to remove or reduce the topographic effects. In this paper a physics-based BRDF and atmospheric correction model that handles both flat and inclined surfaces in conjunction with a 1-second SRTM (Shuttle Radar Topographic Mission) derived Digital Surface Model (DSM) product was applied to 8 Landsat scenes covering different seasons and terrain types in eastern Australia. Visual assessment showed that the algorithm removed much of the topographic effect and detected deep shadows in all 8 images. An indirect validation based on the change in correlation between the data and terrain slope showed that the correlation coefficient between the surface reflectance factor and the cosine of the incident (sun) angle reduced dramatically after the topographic correction algorithm was applied. The correlation coefficient typically reduced from 0.80–0.70 to 0.05 in areas of significant relief. It was also shown how the terrain corrected surface reflectance can provide suitable input data for multi-temporal land cover classification in areas of high relief based on spectral signatures and spectral albedo, while the products based only on BRDF and atmospheric correction cannot. To provide comparison with previous work and to validate the proposed algorithm, two empirical methods based on the C-correction were used as well as the established SCS-method to provide benchmarks. The proposed method was found to achieve the same measures of shade reduction without empirical regression.

Topographic correction algorithm for remotely sensed data accounting for indirect irradiance

The solar irradiance incidents upon terrain surface are composed of three parts, i.e. direct solar irradiance, diffuse sky irradiance and reflected irradiance from the adjacent surface, respectively. Most of the topographic correction models only account for the topographic effect induced from direct solar irradiance, and few models take the topographic effects from the last two components of solar irradiance into account. A physically based topographic correction algorithm aiming to overcome this shortcoming, called a three-factor correction model, was developed based on theoretical analysis of radiation transferring processes along an undulating surface, atmosphere and satellite sensor geometry under the assumption of Lambertian surface. On the basis of this three-factor correction model, an advanced algorithm accounting for the bidirectional reflectance distribution function (BRDF) nature of non-Lambertian surface, called the three-factor+C topographic correction model, was developed by introducing an empirical parameter C to approximate the indirect irradiance contribution of non-Lambertian surface. Performances of these two newly developed algorithms were tested and compared with those of Cosine and C correction algorithms for a selected rugged terrain on the south flank of the Qinling Mountain, China. Visual comparison and statistical analysis were adopted for quantitative evaluation on topographic corrections of a Landsat-7 Enhanced Thematic Mapper Plus (ETM+) image in the study. The results suggested that the general performance of the algorithms for topographic correction ranks the three-factor+C correction, C correction, three-factor correction and Cosine correction from excellent to poor in order, which implies the promising potential of the proposed algorithms in effective topographic correction applications in remote sensing techniques.

A simultaneous inversion for deformation rates and topographic errors of DInSAR data utilizing linear least square inversion technique

We demonstrate here a computer code for calculation of time series and also mean and linear deformation rates from a set of coregistered unwrapped differential interferograms using a linear least-squares inversion technique based on the small baseline subset (SBAS) algorithm. The computer code is written in C and uses a singular value decomposition (SVD) routine from the LAPACK library and the fast Fourier transform for spatial filtering from the FFTW library. Various offset estimation and topographic correction algorithms are implemented, including simultaneous inversion for deformation rates and residual topographic error. This approach is particularly useful when applied to ALOS PALSAR interferograms that are coherent even at large perpendicular baselines and acquired with orbital parameters correlated with the time of acquisition. This methodology is applied to produce time series of ground deformation at Tauhara and Wairakei geothermal fields (Taupo Volcanic Zone, North Island, New Zealand) from 12 ALOS PALSAR images acquired between July 2007 and December 2009. We also present here a high-resolution deformation map of the ground subsidence caused by the extraction of geothermal groundwater for power generation, with maximum rates of subsidence of about 7 cm/y.

Operational Two-Stage Stratified Topographic Correction of Spaceborne Multispectral Imagery Employing an Automatic Spectral-Rule-Based Decision-Tree Preliminary Classifier

The increasing amount of remote sensing (RS) imagery acquired from multiple platforms and the recent announcements that scientists and decision makers around the world will soon have unrestricted access at no charge to large-scale spaceborne multispectral (MS) image databases make urgent the need to develop easy-to-use, effective, efficient, robust, and scalable satellite-based measurement systems. In these scientific and industrial contexts, it is well known that, to date, the operational performance of existing stratified non-Lambertian (anisotropic) topographic correction (SNLTOC) algorithms has been limited by the need for <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">a priori</i> knowledge of structural landscape characteristics, such as surface roughness which is land cover class specific. In practice, to overcome the circular nature of the SNLTOC problem, a mutually exclusive and totally exhaustive land cover classification map of a spaceborne MS image is required <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">before</i> SNLTOC takes place. This system requirement is fulfilled by the original operational automatic two-stage SNLTOC approach presented in this paper which comprises, in cascade, 1) an automatic stratification first stage and 2) a second-stage ordinary SNLTOC method selected from the literature. The former combines 1) four subsymbolic digital-elevation-model-derived strata, namely, horizontal areas, self-shadows, and sunlit slopes either facing the sun or facing away from the sun, and 2) symbolic (semantic) strata generated from the input MS image by an operational fully automated spectral-rule-based decision-tree preliminary classifier recently presented in RS literature. In this paper, first, previous works related to the TOC subject are surveyed, and next, the novel operational two-stage SNLTOC system is presented. Finally, the original two-stage SNLTOC system is validated in up to 19 experiments where the system's capability of reducing within-stratum spectral variance while preserving pixel-based spectral patterns (shapes) is assessed quantitatively.

LULC Classification and Topographic Correction of Landsat-7 ETM+ Imagery in the Yangjia River Watershed: the Influence of DEM Resolution

DEM-based topographic corrections on Landsat-7 ETM+ imagery from rugged terrain, as an effective processing techniques to improve the accuracy of Land Use/Land Cover (LULC) classification as well as land surface parameter retrievals with remotely sensed data, has been frequently reported in the literature. However, few studies have investigated the exact effects of DEM with different resolutions on the correction of imagery. Taking the topographic corrections on the Landsat-7 ETM+ images acquired from the rugged terrain of the Yangjiahe river basin (P.R. China) as an example, the present work systematically investigates such issues by means of two commonly used topographic correction algorithms with the support of different spatial resolution DEMs. After the pre-processing procedures, i.e. atmospheric correction and geo-registration, were applied to the ETM+ images, two topographic correction algorithms, namely SCS correction and Minnaert correction, were applied to assess the effects of different spatial resolution DEMs obtained from two sources in the removal of topographic effects and LULC classifications. The results suggested that the topographic effects were tremendously reduced with these two algorithms under the support of different spatial resolution DEMs, and the performance of the topographic correction with the 1:50,000-topographic-map DEM was similar to that achieved using SRTM DEM. Moreover, when the same topographic correction algorithm was applied the accuracy of LULC classification after topographic correction based on 1:50,000-topographic-map DEM was similar as that based on SRTM DEM, which implies that the 90 m SRTM DEM can be used as an alternative for the topographic correction of ETM+ imagery when high resolution DEM is unavailable.

Simple correction of multiple reflection effects in rugged terrain

Operational correction of optical satellite sensor imagery usually models radiation reflected from surrounding terrain with a first‐order reflection function. In rugged areas and snowy environments, the trapping of radiation between adjacent slopes can make such an approximation inadequate, leading to underestimation of the amount of irradiance, and overestimation of the ground reflectance. It is shown that a multiple reflection model, based on mean parameters computed from the terrain neighbourhood, converges to a simple correction factor. Comparison between first‐order and multiple reflection models shows that the reflectance of snow targets, in very rugged terrain, may be overestimated by up to 30% if disregarding multiple reflections. This potentially explains saturated values obtained from topographic correction algorithms which only use a first‐order terrain function, e.g. ATCOR3, and demonstrates that correction for multiple reflections should be implemented in specific environments.