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Abstract Desert lakes are important wetland resources in the blown-sand area of western China and play a significant role in maintaining the regional ecological environment. However, large-scale coal mining in recent years has considerably impacted the deposition condition of several lakes. Rapid and accurate extraction of lake information based on satellite images is crucial for developing protective measures against desertification. However, the spatial resolution of these images often leads to mixed pixels near water boundaries, affecting extraction precision. Traditional pixel unmixing methods mainly obtain water coverage information in a mixed pixel, making it difficult to accurately describe the spatial distribution. In this paper, the cellular automata (CA) model was adopted in order to realize lake information extraction at a sub-pixel level. A mining area in Shenmu City, Shaanxi Province, China is selected as the research region, using the image of Sentinel-2 as the data source and the high spatial resolution UAV image as the reference. First, water coverage of mixed pixels in the Sentinel-2 image was calculated with the dimidiate pixel model and the fully constrained least squares (FCLS) method. Second, the mixed pixels were subdivided to form the cellular space at a sub-pixel level and the transition rules are constructed based on the water coverage information and spatial correlation. Lastly, the process was implemented using Python and IDL, with the ArcGIS and ENVI software being used for validation. The experiments show that the CA model can improve the sub-pixel positioning accuracy for lake bodies in mixed pixel image and improve classification accuracy. The FCLS-CA model has a higher accuracy and is able to identify most water bodies in the study area, and is therefore suitable for desert lake monitoring in mining areas.

Spatial land surface heterogeneities are widespread at various scales and represent a great challenge to leaf area index (LAI) retrievals and product validations. In this paper, considering the mixed water and vegetation pixels prevalent at moderate and low resolutions, we propose a methodological framework for conducting global comparisons of heterogeneous land surfaces based on criterion setting and a global search of high-resolution data. We construct a global network, Heterogeneous Surface Network aiming Water and Vegetation Mixture (HESNet-WV), comprised of three vegetation types: grassland, evergreen broadleaf forests (EBFs), and evergreen needle forests (ENFs). Validation is performed using the MCD15A3H Global 500-m/4-day and GLASS 500-m/8-day LAI products. As the water area fraction (WAF), LAI values and LAI inversion errors increase in the MODIS and GLASS products, the GLASS product errors (relative LAI error (RELAI): 94.43%, bias: 0.858) are lower than the MODIS product errors (RELAI: 124.05%, bias: 1.209). The result indicates that the proposed framework can be applied to evaluate the accuracy of LAI values in mixed water-vegetation pixels in different global LAI products.

It is necessary to understand the relationship between the impervious surface area (ISA) distribution, variation trends and potential driving forces over Dongying, Shandong Province. We extracted ISA information from Landsat images with 3–5 year intervals during 1995 to 2018 using Minimum Noise Fraction (MNF) transform, Pixel Purity Index (PPI), and Linear Spectral Mixture Analysis (LSMA), followed by the analysis on three driving forces of ISA expansion (physical geography, socioeconomic factors, and urban cultural features). Our results show the retrieved ISA thematic map fit the limited requirement of root mean square error (RMSE). The correct classification accuracy of ISA is greater than 83.08%. Further, the cross–comparison exhibits the general consistent with the ISA distribution of the land use classification map published by the National Basic Geographic Information Center. The gradual increasing trend can be captured on the expansion of ISA from 1995 to 2018. Despite of the central region always shown as the high ISA density, it still keeps increasing annually and radiating the surrounding region, especially in the southward which has formed into a new large–scale and high intensity of ISA in 2015–2018. Though the ISA patches scattered in the west region or along the northern and eastern part of the ocean coastline are still small, the expansion trend of ISA can be detected. The expansion intensity index (EII) of ISA measuring the situation of its expansion changes from the lowest value 0.12% between 1995 and 2000 up to the highest 0.73% between 2000 and 2005. Richly endowed by nature, the city’s natural geographical environment provides an elevated chance of further urbanization. The rapid increase of regional economy provides a fundamental driving force for expanding ISAs. The development of urban culture promotes the sustainable development of ISAs. Our results provide a scientific basis for future urban land use management, construction planning, and environmental protection in Dongying.

Research on fusion modeling of high spatial and temporal resolution images typically uses MODIS products at 500 m and 250 m resolution with Landsat images at 30 m, but the effect on results of the date of reference images and the ‘mixed pixels’ nature of moderate-resolution imaging spectroradiometer (MODIS) images are not often considered. In this study, we evaluated those effects using the flexible spatiotemporal data fusion model (FSDAF) to generate fusion images with both high spatial resolution and frequent coverage over three cotton field plots in the San Joaquin Valley of California, USA. Landsat images of different dates (day-of-year (DOY) 174, 206, and 254, representing early, middle, and end stages of the growing season, respectively) were used as reference images in fusion with two MODIS products (MOD09GA and MOD13Q1) to produce new time-series fusion images with improved temporal sampling over that provided by Landsat alone. The impact on the accuracy of yield estimation of the different Landsat reference dates, as well as the degree of mixing of the two MODIS products, were evaluated. A mixed degree index (MDI) was constructed to evaluate the accuracy and time-series fusion results of the different cotton plots, after which the different yield estimation models were compared. The results show the following: (1) there is a strong correlation (above 0.6) between cotton yield and both the Normalized Difference Vegetation Index (NDVI) from Landsat (NDVIL30) and NDVI from the fusion of Landsat with MOD13Q1 (NDVIF250). (2) Use of a mid-season Landsat image as reference for the fusion of MODIS imagery provides a better yield estimation, 14.73% and 17.26% higher than reference images from early or late in the season, respectively. (3) The accuracy of the yield estimation model of the three plots is different and relates to the MDI of the plots and the types of surrounding crops. These results can be used as a reference for data fusion for vegetation monitoring using remote sensing at the field scale.

The minimum size of objects or geometrical features that can be distinguished within a laser scanning point cloud is called the resolution capability (RC). Herein, we develop a simple analytical expression for predicting the RC in angular direction for phase-based laser scanners. We start from a numerical approximation of the mixed-pixel bias which occurs when the laser beam simultaneously hits surfaces at grossly different distances. In correspondence with previous literature, we view the RC as the minimum angular distance between points on the foreground and points on the background which are not (severely) affected by a mixed-pixel bias. We use an elliptical Gaussian beam for quantifying the effect. We show that the surface reflectivities and the distance step between foreground and background have generally little impact. Subsequently, we derive an approximation of the RC and extend it to include the selected scanning resolution, that is, angular increment. We verify our model by comparison to the resolution capabilities empirically determined by others. Our model requires parameters that can be taken from the data sheet of the scanner or approximated using a simple experiment. We describe this experiment herein and provide the required software on GitHub. Our approach is thus easily accessible, enables the prediction of the resolution capability with little effort and supports assessing the suitability of a specific scanner or of specific scanning parameters for a given application.

There are a lot of mixed pixels in the remotely sensed imagery, which can seriously limit the utility of classification. Sub-pixel mapping (SPM) is a promising technique to solve this problem. It can generate a fine resolution land cover map from coarse resolution fractional images by predicting the spatial locations of different land cover classes at sub-pixel scale.However, the accuracy and detail are always limited. Especially when the scale factor is large among sub-pixels per pixel, the data volumes are amplified and the sub-pixel distribution becomes complex. The traditional methods are carried out only by the fractions of land cover and the spatial dependence theory, which cannot satisfy the requirement of the SPM. For avoiding the above flaw, a new SPM method based on maximum a posteriori (MAP) model with subpixel/pixel spatial attraction theory aimed at the largescale factor is proposed. First, MAP is proposed to improve the resolution of the fractional images and obtain the initial sub-pixel locations; after that, the pixel swapping algorithm is used to optimize and produce the final SPM result. In this paper, the proposed model is tested by a simple simulated font image and real remotely sensed imagery, which can both demonstrate that it can outperform traditional algorithm with a more accurate sub-pixel scale land cover map.

In this research study, we deal with remote sensing data analysis over high dimensional space formed by hyperspectral images. This task is generally complex due to the large spectral, spatial richness, and mixed pixels. Thus, several spectral un-mixing methods have been proposed to discriminate mixing spectra by estimating the classes and their presence rates. However, information related to mixed pixel composition is very interesting for some applications, but it is insufficient for many others. Thus, it is necessary to have much more data about the spatial localization of the classes detected during the spectral un-mixing process. To solve the above-mentioned problem and specify the spatial location of the different land cover classes in the mixed pixel, sub-pixel mapping techniques were introduced. This manuscript presents a novel sub-pixel mapping process relying on K-SVD (K-singular value decomposition) learning and total variation as a spatial regularization parameter (SMKSVD-TV: Sub-pixel Mapping based on K-SVD dictionary learning and Total Variation). The proposed approach adopts total variation as a spatial regularization parameter, to make edges smooth, and a pre-constructed spatial dictionary with the K-SVD dictionary training algorithm to have more spatial configurations at the sub-pixel level. It was tested and validated with three real hyperspectral data. The experimental results reveal that the attributes obtained by utilizing a learned spatial dictionary with isotropic total variation allowed improving the classes sub-pixel spatial localization, while taking into account pre-learned spatial patterns. It is also clear that the K-SVD dictionary learning algorithm can be applied to construct a spatial dictionary, particularly for each data set.

Accurately mapping urban vegetation carbon density is challenging because of complex landscapes and mixed pixels. In this study, a novel methodology was proposed that combines a linear spectral unmixing analysis (LSUA) with a linear stepwise regression (LSR), a logistic model-based stepwise regression (LMSR) and k-Nearest Neighbors (kNN), to map the forest carbon density of Shenzhen City of China, using Landsat 8 imagery and sample plot data collected in 2014. The independent variables that contributed to statistically significantly improving the fit of a model to data and reducing the sum of squared errors were first selected from a total of 284 spectral variables derived from the image bands. The vegetation fraction from LSUA was then added as an independent variable. The results obtained using cross-validation showed that: (1) Compared to the methods without the vegetation information, adding the vegetation fraction increased the accuracy of mapping carbon density by 1%–9.3%; (2) As the observed values increased, the LSR and kNN residuals showed overestimates and underestimates for the smaller and larger observations, respectively, while LMSR improved the systematical over and underestimations; (3) LSR resulted in illogically negative and unreasonably large estimates, while KNN produced the greatest values of root mean square error (RMSE). The results indicate that combining the spatial modeling method LMSR and the spectral unmixing analysis LUSA, coupled with Landsat imagery, is most promising for increasing the accuracy of urban forest carbon density maps. In addition, this method has considerable potential for accurate, rapid and nondestructive prediction of urban and peri-urban forest carbon stocks with an acceptable level of error and low cost.

Medium resolution satellite data such as Landsat is very potential for mixed pixel (mixel) to occur. Indonesian land use diverse especially urban areas makes high potential mixel in the first Landsat pixel size of 30 meters x 30 meters on the actual condition. Aircraft multispectral aerial photo data LAPAN Surveillance Aircraft (LSA) with a spatial resolution reached 58 cm can display objects in more detail in these sizes. The purpose of this research is to study mixel on Landsat data with multispectral data LSA as a complement Landsat data. The method proposed in this study is a visual interpretation with GEOBIA method for classification of land cover, and then test the validity of the sample to be used in research, and the use of such vegetation index NDVI to see the connection between vegetation index data of vegetation index LSA with Landsat data. The results showed that the regression equation obtained by regression between NDVI of Landsat data and NDVI of LSA with a significance of less than 0.05 is y = 0.732x - 0102 with a value of R2 = 0.887. Through these results we can conclude that the NDVI values on both the data related to one another.

Fraction of Photosynthetically Active Radiation (FPAR) is a critical parameter in land surface energy balance and climate modeling. Several global FPAR products are available, but these still require considerable assessment and validation due to low spatial resolution. Three major FPAR products that have covered China and provided continuous time series data—MODIS, MERIS and GEOV1—were assessed from 2006–2010. Based on the ground measurement data, the accuracies of these three FPAR products were directly validated for maize and winter wheat over northern China. This investigation also assessed the consistencies among the three FPAR products, and analyzed the residential area in mixed pixels effect on the FPAR products accuracy, at each of the main growth stages of maize and winter wheat. The GEOV1 FPAR product was found to be the most accurate with regression R2 values of 0.818 and 0.655 for ground measured maize and winter wheat FPAR. The maize FPAR data were generally more accurate than the winter wheat FPAR data. The MODIS, MERIS and GEOV1 products all indicated that FPAR variations among the growth stages differed from year to year. The scattered residential areas in mixed pixels were found to significantly affect the FPAR data uncertainties, and these were also analyzed in detail. The effect of residential area percentage in mixed pixels on FPAR values differed for different crops, and this was not necessarily in accordance with the FPAR product accuracy. For the mixed pixels, a quadratic polynomial was able to fit the residential area and FPAR data reasonably well with R2 values higher than 0.9 for most relationships. Quadratic polynomial fitting may provide a simple and convenient method to assess and reduce the residential area effect on FPAR in the mixed pixels.

Spatial heterogeneity is present in the land surface at every scale and is one of the key factors that introduces inherent uncertainty into simulations of land surface processes and parameter retrieval based on remotely sensed data. Because of a lack of understanding of the heterogeneous characteristics of global mixed pixels, few studies have focused on modeling and inversion algorithms in heterogeneous areas. This paper presents a parameterization scheme to describe land cover heterogeneity quantitatively by composition and boundary information based on high-resolution land cover products. Global heterogeneity features at the 1-km scale are extracted from the ‘GlobeLand30’ land cover dataset with a spatial resolution of 30 m. The composition analysis of global mixed pixels shows that only 35% of pixels over the land surface of Earth are covered by a single land cover type, namely, pure pixels, and only 25.8% are located in vegetated areas. Pixels mixed with water are more common than pixels mixed with any other non-vegetation type. The fragmentation analysis of typical biomes based on the boundary length shows that the savanna is the most heterogeneous biome, while the evergreen broadleaf forest is the least heterogeneous. Deciduous needleleaf forests are significantly affected by canopy height differences, while crop and grass biomes are less affected. Lastly, the strengths and limitations of the method and the application of the land cover heterogeneity characteristics extracted in this study are discussed.

Land cover (LC) refers to the physical and biological cover present over the Earth’s surface in terms of the natural environment such as vegetation, water, bare soil, etc. Most LC features occur at finer spatial scales compared to the resolution of primary remote sensing satellites. Therefore, observed data are a mixture of spectral signatures of two or more LC features resulting in mixed pixels. One solution to the mixed pixel problem is the use of subpixel learning algorithms to disintegrate the pixel spectrum into its constituent spectra. Despite the popularity and existing research conducted on the topic, the most appropriate approach is still under debate. As an attempt to address this question, we compared the performance of several subpixel learning algorithms based on least squares, sparse regression, signal–subspace and geometrical methods. Analysis of the results obtained through computer-simulated and Landsat data indicated that fully constrained least squares (FCLS) outperformed the other techniques. Further, FCLS was used to unmix global Web-Enabled Landsat Data to obtain abundances of substrate (S), vegetation (V) and dark object (D) classes. Due to the sheer nature of data and computational needs, we leveraged the NASA Earth Exchange (NEX) high-performance computing architecture to optimize and scale our algorithm for large-scale processing. Subsequently, the S-V-D abundance maps were characterized into four classes, namely forest, farmland, water and urban areas (in conjunction with nighttime lights data) over California, USA using a random forest classifier. Validation of these LC maps with the National Land Cover Database 2011 products and North American Forest Dynamics static forest map shows a 6% improvement in unmixing-based classification relative to per-pixel classification. As such, abundance maps continue to offer a useful alternative to high-spatial-resolution classified maps for forest inventory analysis, multi-class mapping, multi-temporal trend analysis, etc.

The Caprivi basin in Namibia has been affected by severe flooding in recent years resulting in deaths, displacements and destruction of infrastructure. The negative consequences of these floods have emphasized the need for timely, accurate and objective information about the extent and location of affected areas. Due to the high temporal variability of flood events, Earth Observation (EO) data at high revisit frequency is preferred for accurate flood monitoring. Currently, EO data has either high temporal or coarse spatial resolution. Accurate methodologies for the estimation and monitoring of flooding extent using coarse spatial resolution optical image data are needed in order to capture spatial details in heterogeneous areas such as Caprivi. The objective of this work was the retrieval of the fractional abundance of water ( γ w ) by applying a new spectral indices-based unmixing algorithm to Medium Resolution Imaging Spectrometer Full Resolution (MERIS FR) data using a minimum number of spectral bands. These images are technically similar to the OLCI image data acquired by the Sentinel-3 satellite, which are to be systematically provided in the near future. The normalized difference wetness index (NDWI) was applied to delineate the water surface and combined with normalized difference vegetation index (NDVI) to account for emergent vegetation within the water bodies. The challenge to map flooded areas by applying spectral unmixing is the estimation of spectral endmembers, i.e., pure spectra of land cover features. In our study, we developed and applied a new unmixing method based on the use of an ensemble of spectral endmembers to capture and take into account spectral variability within each endmember. In our case study, forty realizations of the spectral endmembers gave a stable frequency distribution of γ w . Quality of the flood map derived from the Envisat MERIS (MERIS) data was assessed against high (30 m) spatial resolution Landsat Thematic Mapper (TM) images on two different dates (17 April 2008 and 22 May 2009) during which floods occurred. The findings show that both the spatial and the frequency distribution of the γ w extracted from the MERIS data were in good agreement with the high-resolution TM retrievals. The use of conventional linear unmixing, instead, applied using the entire available spectra for each image, resulted in relatively large differences between TM and MERIS retrievals.

The nonuniformity of the spatial response to surface radiation is a fundamental characteristic of all airborne and spaceborne sensors that inevitably introduces uncertainty into the estimation of object proportions by the spectral unmixing of mixed pixels. Simulated data of the surface radiation distribution and a TM (thematic mapper) response matrix were developed and utilized to imitate the generation of mixed pixels and the extraction of the object proportion via a Monte Carlo simulation, and then, the nonuniformity effect of a sensor’s PSF (point spread function) was explored. The following conclusions were drawn: (1) given a nonuniform spatial response of a sensor to a surface scene with a constant object proportion and various object distribution patterns, the mixed pixel DN (digital number) of a remotely-sensed image becomes a random variable, which causes a PSF nonuniform effect on the object proportion extraction; (2) for the estimated object proportion, the corresponding true object proportion appears with a random variation; its upper and lower bounds take on an asymmetrical spindle shape; and models of these bound curves at any probability level were established; (3) there exists a negative linear relationship between the bias of the spectral unmixing and the estimated proportion; the bias is zero at an estimated proportion of 50%, and when the estimated proportions are approximately 100% and 0%, the object proportion is overestimated by 0.78% and underestimated by 0.78%, respectively; (4) the relationship between the standard deviation of the spectral unmixing and the estimated proportion follows a symmetrical polynomial function opening downward; the standard deviation reaches a maximum of 4.4% at the estimated proportion of 50%, and when the estimated proportion is approximately 100% or 0%, the standard deviation is a minimum, 1.05%. The above findings contribute to a comprehensive understanding of the PSF nonuniformity effect, have the potential to compensate for the bias of proportion estimation and present its confidence interval at any probability level.