Water-land Boundary Research Articles

Evaluating the performance of Bayesian geostatistical prediction with physical barriers in the Chesapeake Bay.

The Chesapeake Bay is one of the most widely studied bodies of water in the United States and around the world. Routine monitoring of water quality indicators (e.g., salinity) relies on fixed sampling stations throughout the Bay. Utilizing this rich monitoring data, various methods produce surface predictions of water quality indicators to further characterize the health of the Bay as well as to support wildlife and human health research studies. Bayesian approaches for geostatistical modelling are becoming increasingly popular and can be preferred over frequentist approaches because full and exact inference can be computed, along with more accurate characterization of uncertainty. Traditional geostatistical prediction methods assume a Euclidean distance between two points when characterizing spatial dependence as a function of distance. However, Euclidean approaches may not be appropriate in estuarine environments when water-land boundaries are crossed during the modelling process. In this study, we compare stationary and barrier INLA geostatistical models with a classic kriging geostatistical model to predict salinity in the Chesapeake Bay during 4 months in 2019. Cross-validation is conducted for each approach to evaluate model performance based on prediction accuracy and precision. The results provide evidence that the two Bayesian-based models outperformed ordinary kriging, especially when examining prediction accuracy (most notably in the tributaries). We also suggest that the non-Euclidean model accounts for the appropriate water-based distances between sampling locations and is likely better at characterizing the uncertainty. However, more complex bodies of water may better showcase the capabilities and efficacy of the physical barrier INLA model.

Using Sentinel images for analyzing water and land separability in an agricultural river basin.

The presence or absence of water can result in floods or droughts, potentially impacting agricultural productivity to a great extent. With advancements in remote sensing technology, the reliability of identifying water bodies has significantly improved, particularly in terms of distinguishing between water and land. This study introduced remote sensing methods to improve the accuracy of differentiating water within the Dawenhe River basin. Various water body scenarios were examined, and the performance of these methods was evaluated to determine the proper approach for water-land separation. In applying water body indices to Sentinel-2 images, it was found that the normalized difference water index (NDWI) outperformed the modified normalized difference water index (MNDWI) in identifying water bodies. Consequently, histograms of frequency distribution for Sentinel-1 were generated, revealing that water and land were more distinguishable in VV polarization than in VH polarization. Using histogram thresholding on VV polarized images in Dongping Lake resulted in an overall classification accuracy of 97.58%, surpassing that of Otsu's method at 97.36%. To address the persisting misclassifications, this study identified three leading causes and proposed corresponding solutions. These solutions included (1) employing the morphological dilation algorithm to expand the water area, mitigating pixel mixing issues at the water-land boundary that caused the water bodies to appear smaller; (2) utilizing incidence angles and digital elevation model (DEM) to locate and remove shadows; and (3) slightly lowering the thresholds and manually correcting misclassifications. As a result, the average accuracy of the four areas increased from 95.56 to 96.94%.

Shifting Sands, Land from the Sea: A Microhistory of Coastal Land Titling in Thailand

ABSTRACT This microhistory of a shoreline place in Thailand details the socio-natural process by which a piece of coastal land came to be recognised as private property by the state. It demonstrates that intimate and long-term attention to specificities of how property comes into being has more explanatory power than synoptic theorisations of accumulation and dispossession. Using ethnography, archives and affective co-narration, this paper probes the shifting ground of water and land to show how the fluidity of water plays a key role in the politics and legal procedures of enclosure, and how fluctuating boundaries become an ambiguous arena for property claims contestations amid entanglements of slippery legal semantics. It argues that the expanded notion of agency in the Anthropocene presents new challenges for thinking about property relations, and that thinking from a shoreline place of shifting water-land boundaries engenders novel questions to do with fluid dispossessions at a time of rising oceans.

Using Remote Data and GIS in Research of Morphometric Characteristics of the Coastal Area in Bulgaria

Remote methods provide information on both the natural objects on the earth's surface, water bodies, water-land boundaries, and relief and relief forms. Satellite images were used to determine the characteristics of the coastline and Black Sea area (about 50 km distance) of the Republic of Bulgaria. Its fractal dimension and curvature are determined. A number of thematic maps have been generated through the digital relief model to assist in the interpretation and geomorphologic characteristics of the study area. A database was created as part of the project MARINEGEOHAZARD – “Set-up and implementation of key core components of a regional early-warning system for marine geohazards of risk to the Romanian-Bulgarian Black Sea coastal area” from CBC Romania-Bulgaria Programme.

Deep Feature and Domain Knowledge Fusion Network for Mapping Surface Water Bodies by Fusing Google Earth RGB and Sentinel-2 Images

Mapping surface water bodies from fine spatial resolution optical remote sensing imagery is essential for the understanding of the global hydrologic cycle. Although satellite data are useful for mapping, the limited spectral information captured by some satellite systems can be suboptimal for the task. For example, the very high-resolution images of Google Earth (GE) only contain RGB bands, which often means many water bodies and land objects are confused. Sentinel-2 (S2) imagery has a spectral resolution more suitable for mapping water bodies, but its medium spatial resolution limits the ability for detailed mapping of water-land boundaries. This letter proposes a deep feature and domain knowledge fusion network (DFDKFNet) for mapping surface water bodies by fusing GE and S2 images while incorporating domain knowledge. DFDKFNet uses the remote sensing indices of normalized difference water index (NDWI) and normalized difference vegetation index (NDVI) derived from the S2 image as the representative domain knowledge to better extract water bodies from terrestrial features. A similar pixel-based approach is used to downscale the NDWI and NDVI maps to match the spatial resolution between the GE and S2 images. The DFDKFNet uses the GE and downscaled NDWI and NDVI images to extract the deep semantic features of water bodies, which are fused with the domain knowledge extracted from the NDWI and NDVI images. DFDKFNet was compared with several state-of-the-art algorithms, and the results show that DFDKFNet can enhance water body mapping accuracy.

Applicability Analysis of GF-2PMS and PLANETSCOPE Data for Ground Object Recognition in Karst Region

Remote sensing image with high spatial and temporal resolution is very important for rational planning and scientific management of land resources. However, due to the influence of satellite resolution, revisit period, and cloud pollution, it is difficult to obtain high spatial and temporal resolution images. In order to effectively solve the “space–time contradiction” problem in remote sensing application, based on GF-2PMS (GF-2) and PlanetSope (PS) data, this paper compares and analyzes the applicability of FSDAF (flexible spatiotemporal data fusion), STDFA (the spatial temporal data fusion approach), and Fit_FC (regression model fitting, spatial filtering, and residual compensation) in different terrain conditions in karst area. The results show the following. (1) For the boundary area of water and land, the FSDAF model has the best fusion effect in land boundary recognition, and provides rich ground object information. The Fit_FC model is less effective, and the image is blurry. (2) For areas such as mountains, with large changes in vegetation coverage, the spatial resolution of the images fused by the three models is significantly improved. Among them, the STDFA model has the clearest and richest spatial structure information. The fused image of the Fit_FC model has the highest similarity with the verification image, which can better restore the coverage changes of crops and other vegetation, but the actual spatial resolution of the fused image is relatively poor, the image quality is fuzzy, and the land boundary area cannot be clearly identified. (3) For areas with dense buildings, such as cities, the fusion image of the FSDAF and STDFA models is clearer and the Fit_FC model can better reflect the changes in land use. In summary, compared with the Fit_FC model, the FSDAF model and the STDFA model have higher image prediction accuracy, especially in the recognition of building contours and other surface features, but they are not suitable for the dynamic monitoring of vegetation such as crops. At the same time, the image resolution of the Fit_FC model after fusion is slightly lower than that of the other two models. In particular, in the water–land boundary area, the fusion accuracy is poor, but the model of Fit_FC has unique advantages in vegetation dynamic monitoring. In this paper, three spatiotemporal fusion models are used to fuse GF-2 and PS images, which improves the recognition accuracy of surface objects and provides a new idea for fine classification of land use in karst areas.

Atmospheric Correction Model for Water–Land Boundary Adjacency Effects in Landsat-8 Multispectral Images and Its Impact on Bathymetric Remote Sensing

Atmospheric correction (AC) is the basis for quantitative water remote sensing, and adjacency effects form an important part of AC for medium- and high-spatial-resolution optical satellite images. The 6S radiative transfer model is widely used, but its background reflectance function does not take the radiance changes at water–land boundaries into account. If the observed land possesses bright features, the radiance of the adjacent water will be affected, leading to deviations in the AC results and increasing the uncertainty of water depth-based optical quantitative remote sensing. In this paper, we propose a model named WL-AE (a correction model for water–land boundary adjacency effects), which is based on the obvious radiance differences at water–land boundaries. This model overcomes the problem by which the background reflectance calculation is not terminated due to the highlighting pixel. We consider the influences of different Rns (neighborhood space) on the target pixel. The effective calculation of the equivalent background reflectance of the target pixel is realized, and the influence of the land area anomaly highlighting the pixel on the adjacent water is avoided. The results show that WL-AE can effectively improve the entropy and contrast of the input image and that the water–land boundary is greatly affected by adjacency effects, especially in the green and near-infrared bands, where the Mrc (mean rate of change) are as high as 14.2% and 20.1%, respectively. In the visible wavelength, the Sd of Rrc (the relative rate of change) is positively correlated with Rns, and the Sd reaches 16.9%. Although the adjacency effect is affected by ground object types, its influence area remains within 3 km offshore. Based on the WL-AE and 6S results, the comparative test regarding bathymetric inversion shows that the influence is significant in the 0–5 m depth section. In Penang, the MRE of the 0–4 m inversion results is 31.4%, which is 10.5% lower than that of the 6S model.

Traveling Waves in Shallow Seas of Variable Depths

The problem of the existence of traveling waves in inhomogeneous fluid is very important for enabling an explanation of long-distance wave propagations such as tsunamis and storm waves. The present paper discusses new solutions to the variable-coefficient wave equations describing traveling waves in fluid layers of variable depths (1D shallow-water theory). Such solutions are obtained by using the transformation methods when variable-coefficient equations can be reduced to the constant coefficient equation when the existence of traveling waves is evident. It is shown that there is a wide class of monotonic bottom profiles (discrete set) that allow the existence of traveling waves that are not reflected in a strongly inhomogeneous water medium. Their temporal shape changes with distance, mainly near the water–land boundary (shoreline). Traveling waves can transfer the wave energy over a long distance that is often observed at the transoceanic propagation of tsunami waves.

Mapping inter- and intra-annual dynamics in water surface area of the Tonle Sap Lake with Landsat time-series and water level data

Surface water monitoring is the foundation of water resources management. However, large-scale surface water monitoring based on long-sequence Landsat images is easily affected by cloud cover. In this study, taking the Tonle Sap Lake in the lower Mekong as an example, a series of water-land boundaries with height attributes based on water level data were extracted from multi-temporal Landsat images without cloud cover using the optimal water index and the lakeshore elevation model (LEM) of Tonle Sap Lake was constructed. On this basis, with the help of the limited land-water boundary provided by the Landsat image over a longer period, long-term monitoring of the changes in the water area of the entire lake area was realized. The results show that the Landsat image data in conjunction with the LEM can effectively remove the effect of cloud cover in monitoring the change of long time series water bodies. Reconstruction of historical data on changes in the waters of Tonle Sap Lake with the proposed method shows that in the past 30 years, there has been no significant change in the water areas of Tonle Sap Lake in either the dry or rainy seasons. Water area changes of the lake have a delayed response of 1-3 months to changes in the water level of the Mekong River, which is more affected by the mainstream recharge. The water area of the lake is unaffected in the dry season; however, it is weakly affected in the rainy season by the Xiaowan and Nuozhadu hydropower stations in China.

EVALUATING DIFFERENT WATER-LAND-BOUNDARY APPROXIMATIONS TO IMPROVE SAR-DERIVED DIGITAL ELEVATION MODELS

Abstract. The coastline of the German Wadden Sea is constantly subjected to the tides and the tidal-induced environmental changes like erosion and accumulation of sediments need to be monitored constantly. This task requires digital elevation models (DEMs), which are derived from remote sensing data. To model those DEMs, a separation of data collected over landmasses and water bodies is required. In the GeoWAM project the potential of airborne SAR-data (F-SAR) is investigated for monitoring purposes in the Wadden Sea. As part of the project, this paper focuses on the suitability of F-SAR data regarding the derivation of water-land-boundaries (WLBs). Therefore, water-land-boundaries based on independent data sets are compared and evaluated. Analyzed data sets include data collected via F-SAR, airborne laserscanning (ALS), on site GNSS measured WLB points and sea-level data from two acoustic gauges. The algorithms were tested on a study site on Spiekeroog island. Our results show, that the accuracies of the derived WLBs mostly depend on the on-site topography and sediments. The spatial deviation between the reference data and the approximated WLBs is mostly less than 2 m horizontally and 0.15 m vertically. Identified challenges to overcome are mostly related to processing of F-SAR data in areas with highly water saturated sediments. Our results suggest, that F-SAR data in tidal flats is not necessarily dependent on further supplementing surveys, as one of the main advantages of the F-SAR data is the potential to derive DEMs and WLBs from the same data set.

СОСТОЯНИЕ МИКРОФИТНЫХ ЦЕНОЗОВ НА УРЕЗЕ ВОДЫ В ОКРЕСТНОСТЯХ ПОРТА ЕРСАЙ И ПОС. КУРЫК (ВОСТОЧНЫЙ КАСПИЙ)

Microphytic cenoses that develop on coastal rocks in the area of the water's edge can serve as particularly bright indicator biosystems that clearly display any harmful effects on their habitat. Developing, in fact, in the water-land boundary conditions, in the area of direct impact of the surface film of continuously moving water, they are a kind of " sponges " that collect a variety of agents carried by sea currents from sources of pollution. Accumulating in these communities, such agents are able to change the balance of species in the structure of these coenoses in a short time, as well as cause morphological changes in the species themselves. These modifications of the appearance can be caused both by their phenotypic norm of reaction to the presence and high concentrations of the contaminating agent, and by mutations provoked by one or another agent. Based on the obtained results describing the state of microepiphytic and microepilitic cenoses in various locations located at the end of July 2019 in the vicinity of the port of Ersai and the village of Kuryk, it can be concluded that the communities of all three locations were under stress – however, to a significantly different degree.

ИСПОЛЬЗОВАНИЕ ДАННЫХ СПУТНИКА SENTINEL-2 ДЛЯ ОЦЕНКИ СГОННЫХ ЯВЛЕНИЙ В ДЕЛЬТЕ ДОНА

Drifting phenomena pose a significant threat to human life and the economy. The estuary of the Don is an ideal testing ground for surge phenomena. The largest surges can reach 2.8 m at the sea edge of the Don delta, the largest surges – 3.3 m. In addition, this area is highly urbanized and has great economic importance. The work is devoted to the use of Sentinel 2 satellite imagery data to assess the areas of drainage of the bottom of the Taganrog Bay and the sea part of the Don delta as a result of wind-driven phenomena. The paper considers the period from 2015 to 2020. The study of surges and overshoots in the mouth area of the Don River is based on observational data of the standard hydrometeorological network of Roshydromet. A combination of spectral channels has been determined, which allows to clearly distinguish the water-land boundary. The main research methods are the method of classification with training, which allows you to identify the most characteristic classes of objects. To assess the quality of the classification carried out, the classification accuracy was assessed using the inconsistency matrix, which confirmed the validity of the method. As a result of the classification carried out, the areas of bottom drying were calculated. The dependence of the bottom drainage value on the speed and duration of northeast and east winds is shown. Analysis of the data showed that a combination of satellite information, meteorological data and data from level gauges is required to monitor the overshoot phenomenon. This publication was prepared as part of the GZ SSC RAS, № g. project 01201363188

The Ozone Water-Land Environmental Transition Study (OWLETS): An Innovative Strategy for Understanding Chesapeake Bay Pollution Events.

Coastal regions have historically represented a significant challenge for air quality investigations due to water-land boundary transition characteristics and a paucity of measurements available over water. Prior studies have identified the formation of high levels of ozone over water bodies, such as the Chesapeake Bay, that can potentially recirculate back over land to significantly impact populated areas. Earth-observing satellites and forecast models face challenges in capturing the coastal transition zone where small-scale meteorological dynamics are complex and large changes in pollutants can occur on very short spatial and temporal scales. An observation strategy is presented to synchronously measure pollutants 'over-land' and 'over-water' to provide a more complete picture of chemical gradients across coastal boundaries for both the needs of state and local environmental management and new remote sensing platforms. Intensive vertical profile information from ozone lidar systems and ozonesondes, obtained at two main sites, one over land and the other over water, are complemented by remote sensing and in-situ observations of air quality from ground-based, airborne (both personned and unpersonned), and shipborne platforms. These observations, coupled with reliable chemical transport simulations, such as the NOAA National Air Quality Forecast Capability (NAQFC), are expected to lead to a more fully characterized and complete land-water interaction observing system that can be used to assess future geostationary air quality instruments, such as the NASA Tropospheric Emissions: Monitoring of Pollution (TEMPO) as well as current low earth orbiting satellites, such as the European Space Agency's Sentinel 5-Precursor (S5-P) with its Tropospheric Monitoring Instrument (TROPOMI).

Comparison of Classification Techniques on Fused Optical and SAR Images for Shoreline Extraction: A Case Study at Northeast Coast of Peninsular Malaysia

Shoreline is a very important element to identify exact boundary at the coastal areas of a country. However, in order to identify land-water boundary for a large region using traditional ground survey technique is very time consuming. Alternatively, shoreline can be extracted by using satellite images that minimizes the mapping errors. The trend of extracting shoreline has been shifted from image processing to machine learning and data mining techniques. By using machine learning technique, the satellite images could be classified into land and water classes in order to extract shoreline. However, the result is meaningless if it has cloud and shadow on the water-land boundary. In this study, we compare the accuracy and Kappa Coefficient of six machine learning techniques namely Maximum Likelihood, Minimum Distance, Mahalanobis Distance, Parallelepiped, Neural Network and Support Vector Machines on three type of images; single optical multispectral, single SAR and fused image. A case study for this research is done alongside Tumpat beach, located at the Northeast Coast of Peninsular Malaysia. All the machine learning techniques have been tested on the three types of images. The experimental results show that classification using SVM on single multispectral image has the highest accuracy among all. However, the classified of fused image using SVM is considered much more accurate because it can cater the cloud and shadow problem. Additionally, the classification on 5 and 10 m fused images also tested and the result shows that with the increase of spatial resolution of fused image, the classification accuracy also increases.

Improving the Accuracy of the Water Surface Cover Type in the 30 m FROM-GLC Product

The finer resolution observation and monitoring of the global land cover (FROM-GLC) product makes it the first 30 m resolution global land cover product from which one can extract a global water mask. However, two major types of misclassification exist with this product due to spectral similarity and spectral mixing. Mountain and cloud shadows are often incorrectly classified as water since they both have very low reflectance, while more water pixels at the boundaries of water bodies tend to be misclassified as land. In this paper, we aim to improve the accuracy of the 30 m FROM-GLC water mask by addressing those two types of errors. For the first, we adopt an object-based method by computing the topographical feature, spectral feature, and geometrical relation with cloud for every water object in the FROM-GLC water mask, and set specific rules to determine whether a water object is misclassified. For the second, we perform a local spectral unmixing using a two-endmember linear mixing model for each pixel falling in the water-land boundary zone that is 8-neighborhood connected to water-land boundary pixels. Those pixels with big enough water fractions are determined as water. The procedure is automatic. Experimental results show that the total area of inland water has been decreased by 15.83% in the new global water mask compared with the FROM-GLC water mask. Specifically, more than 30% of the FROM-GLC water objects have been relabeled as shadows, and nearly 8% of land pixels in the water-land boundary zone have been relabeled as water, whereas, on the contrary, fewer than 2% of water pixels in the same zone have been relabeled as land. As a result, both the user’s accuracy and Kappa coefficient of the new water mask (UA = 88.39%, Kappa = 0.87) have been substantially increased compared with those of the FROM-GLC product (UA = 81.97%, Kappa = 0.81).

Tide-induced groundwater level fluctuation in a U-shaped coastal aquifer

Summary The prediction of groundwater level fluctuation due to tidal waves propagation in coastal aquifers is important for the planning and management of water resources in coastal areas. A two-dimensional (2-D) analytical solution is derived to describe the tidal groundwater fluctuation in an aquifer bounded by three water–land boundaries that form a U-shaped coastline. Two opposite sides represent estuary–land boundaries on which the amplitude attenuation and phase shift of the tidal movement in the estuary are considered while the third side is an ocean–land boundary. The effects of wave interaction due to the propagation of oscillating oceanic tides in the cross-shore direction inland and the transmission of the two opposite estuarine tides in the along-shore direction are investigated. Three existing head-fluctuation solutions can be considered as special cases of the present solution; one is for one-dimensional flow and the other two are for 2-D flow. A transition distance ranging from 10 to 15 times of tidal propagation length along the shoreline can be estimated based on the solution. This distance can be used to judge whether the interaction among tides is significant. The influences of hydraulic properties on the tidal fluctuations within the aquifer can therefore be assessed quantitatively. Based on sensitivity analyses, one can conclude that the tidal head is most sensitive to the transmissivity and storativity of the aquifer, and least to the damping coefficient of tidal amplitude and wave number along the estuary. The sensitivities of head fluctuation to the changes of transmissivity and storativity depend on the shoreline length and whether the interaction among waves is significant. On the other hand, the sensitivities of head fluctuation to the changes of damping coefficient and wave number increase with diagonal distance from the entry of estuary and reach the largest magnitude near the estuary far away seashore.

Shoreline movement monitoring based on SAR images in Shanghai, China

In this article, a divide-and-combine approach and multiscale normalized cut techniques are combined to extract water–land boundaries from synthetic aperture radar (SAR) images. A validation study shows that waterline extraction from SAR using the proposed algorithm is consistent with that derived from Landsat optical remote-sensing imagery. Analysis of six European Remote Sensing-1/2 (ERS-1/2) satellite and Envisat SAR images acquired at spring tides in Lingang New City, a new land-reclamation city in the suburb of Shanghai, China, between 1993 and 2005 shows the shoreline movement of the study region. We find that the shoreline had minimum seaward movement in the region due to natural forces between 1993 and 1996. Between 1996 and 1999, the shoreline moved more in the eastern and slower in the western part due to artificial impelling siltation and deposition of silt in the Yangtze River. Later, between 1999 and 2005, the shoreline significantly changed following commencement of a tidal flat reclamation project.

Testate amoebae community pattern in different types of boundary structures at the water-land contact zone

The patterns of changes in the species richness, abundance, species composition, and species structure of the testate amoebae community along six different types of water-land boundaries in the Medveditsa River (Don river Basin) were studied, namely, a new boundary, terrigenous and reogeneous edges, reogeneous and terrigenous hemiecotones, and the full ecotone. The testate amoebae communities are divided into terrestrial and aquatic variants for all types of boundaries. Hydrophilic species of the genera Arcella, Diffugia, Cyphoderia, and Pseudodifflugia dominate in the aquatic types of communities while pedobiont and eurybiont groups from the genera Centropyxis, Euglypha, Plagiopyxis, and Trinema are characteristic of the terrestrial communities. A decrease in the abundance and species richness of testate amoebae in the boundary zones was detected.

A technique for spatial sharpening of thermal imagery of coastal waters and of watercourses

Although satellite thermal infrared (TIR) remote sensing is a valuable tool for the thermal mapping of coastal waters and watercourses, it has many problematic issues, the most important of which are linked to spatial resolution. In the literature, several algorithms for sharpening thermal imagery can be found. Nevertheless, most of them are devoted to land temperature and are not applicable to water–land mixed pixels. In this article, a new algorithm for sharpening water thermal imagery (SWTI) at the water–land boundaries is presented. SWTI is based on the assumption that a relationship exists between the TIR radiance emitted by the pixels of the scene and the fractional water coverage, the fractional non-vegetated soil coverage and a variable describing the presence of vegetated soils. The algorithm works on a pixel by pixel basis and the results are accepted or refused using an analysis of variance (ANOVA) test. SWTI was applied to two Advanced Spaceborne Thermal Emission and Reflection Radiometer (ASTER) scenes acquired on areas where complex water surfaces are present: the delta of the Po river and the lagoon of Venice (Italy). The spatial resolution of ASTER TIR scenes was improved from 90 to 30 m. Different variables were tested to represent vegetated soils, and the SWTI sensitivity to them has been inspected. The performance of SWTI has been studied using visual inspection and statistical and simulation methods. Visual inspection indicated that the spatial enhancement was significant for most of the water surfaces and, in particular, for watercourses. Most of the details with dimension ≥60 m (i.e. 2 pixels at the final spatial resolution) were discernible. Quantitative analysis showed that the algorithm was successfully applicable for 94% and for 84% of the mixed pixels at the water–land boundary in the Po and in the Venice case studies, respectively. Expected and maximum errors were 1 and 1.4 K in the Po case, and 1 and 2.1 K in the Venice case. These values can be considered satisfactory when compared with the ASTER thermal accuracy (1 K). Further research is required to confirm the accuracy and performance analysis using methods based on accurate and higher resolution thermal imagery and on ground measurements.

Use of analytic solutions in the statement of difference boundary conditions on a movable shoreline

Solutions to initial boundary value problems are constructed for the shallow water equations in the form of series locally convergent in the neighbourhood of a movable water–land boundary for an arbitrary bottom relief. The motion law and the velocity of this boundary are determined for various wave–shore interaction modes. The obtained results of analytic study of the solutions are used for the development of approximations of boundary conditions on the movable shoreline. Test problems are numerically solved using an explicit predictor-corrector scheme of the second order of approximation on adaptive grids retracing the position of the water–land boundary. The results of these calculations are presented.