Spatial Variability Research Articles

Spatial Variability of Ground Deformation of Coastal Regions of the Krishna Delta, East Coast of India Using SAR Interferometry

Spatial Variability of Ground Deformation of Coastal Regions of the Krishna Delta, East Coast of India Using SAR Interferometry

Mapping stem volume in fast-growing eucalypt plantations: integrating spectral, textural, and temporal remote sensing information with forest inventories and spatial models

Abstract Key message Accurate volume estimation in Eucalyptus plantation stands was achieved by a linear model using SPOT and Landsat multispectral imagery, specifically texture indices and pixel-scale NDVI time integrals, which reflect the local plantation growth history. Spatial modelling techniques such as Kriging with External Drift and Generalized Additive Model slightly improved predictions by accounting for spatial correlation of volume between sample points. Context Forest inventories are widely used to estimate stand production. To capture the inherent spatial variability within stands, spatial modelling techniques such as Kriging with External Drift (KED) and the generalized additive model (GAM) have emerged. These models incorporate information on spatial correlation and auxiliary variables that can be obtained from satellite imagery. Aims Our study explored the use of reflectance data from SPOT and Landsat multispectral imagery. We focused on texture indices and temporal integration of vegetation indices as auxiliary variables in KED and GAM to predict stem volume of fast-growing Eucalyptus sp. plantations in Brazil. Methods The components extracted from the high-resolution SPOT-6 image included spectral band values, band ratio metrics, key vegetation indices (NDVI, SAVI, and ARVI), texture measurements, and indices derived from texture analysis. Additionally, we included the accumulated NDVI time series acquired from Landsat 5, 7, and 8 satellites between the planting date and the forest inventory measurement date. Results The best linear model of stem volume using remotely sensed predictors gave an R-squared value of 0.95 and a Root Mean Square Error (RMSE) of 12.44 m3/ha. The R-squared increased to 0.96 and the RMSE decreased to 10.6 m3/ha when the same predictors were included as auxiliary variables in the KED and GAM spatial models. Conclusion The linear model using remotely sensed predictors contributed most to volume prediction, but the addition of spatial coordinates in the KED and GAM spatial models improved local volume predictions.

Spatial variability in residence time of Beryllium in the Indian Ocean

Residence time of an element in the ocean is a consequence of its chemical behaviour and the various biogeochemical processes governing its distribution, sources, and sinks. Precise estimation of the residence time of beryllium(Be) is necessary for its application as a tracer for understanding present and paleo-environmental processes. We utilise cosmogenic 10Be and terrestrially derived 9Be measurements from surface sediments to estimate the residence time of Be in the Indian Ocean. Significant variation in Be residence time is observed, which ranges between 370 and 620 years in the central Indian Ocean, 64–205 years in the Bay of Bengal, 41–117 years in the Andaman Sea, and 179–443 years in the Arabian Sea. Large heterogeneity in the residence time of Be can be attributed to its variable scavenging efficiency in different regions. Active scavenging of Be by sediment particles contributed through various major rivers draining into the northern Indian Ocean results in short residence time of Be. The results of this study have significant implications for the selection of sample sites and the use of Be as a tracer in paleo reconstructions.

Correlates of spatial structure variability in Bushehr port-city: A comprehensive analysis using fuzzy cognitive mapping methodology

It is critical for urban and regional planners to examine spatial relationships and interactions between a port and its surrounding urban areas within a region’s spatial structure. This paper seeks to develop a targeted framework of causal relationships influencing the spatial structure changes in the Bushehr port-city. Hence, the study utilizes Fuzzy Cognitive Maps (FCMs), a computational technique adept at analyzing complex decision-making processes. FCMs are employed to identify concepts that act as drivers or barriers in the spatial structure changes of Bushehr port-city, thereby elucidating the causal relationships within this context. Additionally, the study evaluates these concepts’ relative significance and interrelationships. Data was collected through interviews with ten experts from diverse backgrounds, including specialists, academics, policymakers, and urban managers. The insights from these experts were analyzed using FCMapper and Pajek software to construct a collective FCM, which depicts the influential and affected concepts within the system. The resulting collective FCM consists of 16 concepts, representing the varied perspectives and expertise of the participants. Among these, the concepts of management and planning reform, economic growth of the city-port, and port development emerged as the three most central concepts. Moreover, the effects of all influential concepts on the spatial structure change in Bushehr port-city were evaluated through simulations conducted across four different scenarios. The analysis demonstrated that the system experiences the most significant impact under the fourth scenario, where the most substantial changes are observed in commercial and industrial growth and the planning of port-city separation policies.

Mapping coastal resilience: a Gis-based Bayesian network approach to coastal hazard identification for Queensland’s dynamic shorelines

Coastal regions worldwide face increasing threats from climate change-induced hazards, necessitating more accurate and comprehensive vulnerability assessment tools. This study introduces an innovative approach to coastal vulnerability assessment by integrating Bayesian Networks (BN) with the modern coastal vulnerability (CV) framework. The resulting BN-CV model was applied to Queensland's coastal regions, with a particular focus on tide-modified and tide-dominated beaches, which constitute over 85% of the studied area. The research methodology involved beach classification based on morphodynamic characteristics, spatial subdivision of Queensland's coast into 78 sections, and the application of the BN-CV model to analyze interactions between geomorphological features and oceanic dynamics. This approach achieved over 90% accuracy in correlating beach types with vulnerability factors, significantly outperforming traditional CVI applications. Key findings include the identification of vulnerability hotspots and the creation of detailed exposure and sensitivity maps for Gold Coast City, Redland City, Brisbane City, and the Sunshine Coast Regional area. The study revealed spatial variability in coastal vulnerability, providing crucial insights for targeted management strategies. The BN-CV model demonstrates superior precision and customization capabilities, offering a more nuanced understanding of coastal vulnerability in regions with diverse beach typologies. This research advocates for the adoption of the BN-CV approach to inform tailored coastal planning and management strategies, emphasizing the need for regular reassessments and sustained stakeholder engagement to build resilience against climate change impacts.Recommendations include prioritizing adaptive infrastructure in high-exposure areas like the Gold Coast, enhancing flood management in Brisbane, improving socio-economic adaptive capacity in Redland, and maintaining natural defences in Moreton Bay. This study contributes significantly to the field of coastal risk management, providing a robust tool for policymakers and coastal managers to develop more effective strategies for building coastal resilience in the face of climate change.

Spatial Variation of Microclimatic Parameters Inside a Polyhouse with Fog Cooling System

The importance of protected cultivation is increasing day by day due to its capability of producing crop all round the year and increase in the crop productivity. This advantage of protected cultivation can be efficiently achieved by adapting the polyhouse cultivation. To obtain the maximum crop productivity inside a polyhouse, it is necessary to understand the variability of microclimate inside it. The present study aims to understand the spatial variability of microclimate inside a naturally ventilated polyhouse installed with fog cooling system during summer season. The main aim of the study is to understand the effect of fogging system in spatial variability of microclimate. For the study, the data of microclimatic parameters were collected daily from April to June at four different time intervals 8.30 AM, 12.30 PM, 4.30 PM and 8.30 PM. The data recorded was then analyzed in Golden Surfer Software to generate contour plots of weekly averages of microclimate parameters. The analysis revealed that the temperature and relative humidity varied across the polyhouse depending upon the wind velocity and its distribution pattern. The light intensity varied based upon the orientation of polyhouse and the position of sun. Carbon dioxide concentration varied based on temperature, light intensity, crop transpiration and respiration. It can be concluded that, inside a naturally ventilated polyhouse, the microclimate varied both spatially and temporally with fogging system also due to wind effect. Thus, having accurate understanding of the microclimate inside a polyhouse helps to maintain optimal conditions for plant growth and thus improve crop yield and productivity.

Multi-objective calibration and evaluation of the ORCHIDEE land surface model over France at high resolution

Abstract. Here we present a strategy to obtain a reliable hydrological simulation over France with the ORCHIDEE land surface model. The model is forced by the SAFRAN atmospheric reanalysis at 8 km resolution and hourly time steps from 1959 to 2020 and by a high-resolution DEM (around 1.3 km in France). Each SAFRAN grid cell is decomposed into a graph of hydrological transfer units (HTUs) based on the higher-resolution DEM to better describe lateral water movements. In particular, it is possible to accurately locate 3507 stations among the 4081 stations collected from the national hydrometric network HydroPortail (filtered to drain an upstream area larger than 64 km2). A simple trial-and-error calibration is conducted by modifying selected parameters of ORCHIDEE to reduce the biases of the simulated water budget compared to the evapotranspiration products (the GLEAM and FLUXCOM datasets) and the HydroPortail observations of river discharge. The simulation that is eventually preferred is extensively assessed with classic goodness-of-fit indicators complemented by trend analysis at 1785 stations (filtered to have records for at least 8 entire years) across France. For example, the median bias of evapotranspiration is −0.5 % against GLEAM (−4.3 % against FLUXCOM), the median bias of river discharge is 6.3 %, and the median Kling–Gupta efficiency (KGE) of square-rooted river discharge is 0.59. These indicators, however, exhibit a large spatial variability, with poor performance in the Alps and the Seine sedimentary basin. The spatial contrasts and temporal trends of river discharge across France are well represented with an accuracy of 76.4 % for the trend sign and an accuracy of 62.7 % for the trend significance. Although it does not yet integrate human impacts on river basins, the selected parameterization of ORCHIDEE offers a reliable historical overview of water resources and a robust configuration for climate change impact analysis at the nationwide scale of France.

Spatial and temporal mush heterogeneity during eruptions recorded in clinopyroxene from the 2021 paroxysms at Mt. Etna, Italy

Textural and compositional zoning of volcanic minerals archives pre-eruptive magma processes. Crystals erupted simultaneously may be sampled from different regions of the plumbing system and hence record variable histories due to complex magma dynamics. In addition, crystals erupted throughout the course of an eruption may record temporal variations in the plumbing system. To resolve mush variability on both spatial and temporal scales, we investigate clinopyroxene erupted during a series of paroxysmal episodes between February–April 2021 at Mt. Etna, Italy. Using a combination of high-resolution geochemical techniques, we observe that Cr enrichments in clinopyroxene mantle zones, grown upon eruption-triggering mafic rejuvenation, exhibit both temporal and spatial (sample-scale) variability. Temporal variability correlates with changes in glass compositions, attesting to the ability of clinopyroxene to track magma maficity throughout an eruption. Spatial variability, indicated by the scatter of Cr concentrations, is greatest for the first event and lowest for the final paroxysm. In conjunction with core textures, degree of sector enrichment and thermobarometry, our data suggest that the onset of the paroxysms was preceded by the remobilisation of a mid-crustal clinopyroxene mush (534 ± 46 MPa) by hot, mafic magma causing variable resorption of mush-derived crystal cores. Towards the end of the eruption, waning magma supply led to less efficient mush remobolisation and mixing, resulting in homogenous crystal populations. Our results highlight that clinopyroxene Cr contents and sector enrichment can be used to track mafic rejuvenation and magma evolution throughout eruptions, while also reflecting spatial heterogeneities within the plumbing system.

Temporal consistency and spatial variability in detection: implications for monitoring of macroinvertebrates from shallow groundwater aquifers

Implementing and optimizing biodiversity monitoring is crucial given the current, worldwide biodiversity decline. Compared to other ecosystems, monitoring of biodiversity is lagging behind in groundwater ecosystems, both because of sparse taxonomic knowledge and methodological constraints. We here assessed temporal variation in the occurrence and abundance of macroinvertebrates collected systematically from shallow groundwater aquifers of Switzerland to establish general principles on seasonality and repeatability of assessment outcomes. We found no seasonal abundance pattern for obligate groundwater amphipods and isopods, indicating temporal consistency. In contrast, other macroinvertebrates (predominantly stygophiles and stygoxenes) showed pronounced seasonality in their detection rate. However, we found variability in detection rates across groundwater amphipod species and especially across sampling sites. For groundwater communities, characterized by narrowly-distributed and rare species, our results highlight the need for tailored and extensive sampling strategies. When setting up monitoring programs on groundwater fauna, detection probability, temporal autocorrelation, and standardization of sampling effort should be carefully considered. Applying novel, systematic approaches, can offer promising methodologies for understanding and conserving groundwater ecosystems.

Immunologic aspects of asthma: from molecular mechanisms to disease pathophysiology and clinical translation

In the present review, we focused on recent translational and clinical discoveries in asthma immunology, facilitating phenotyping and stratified or personalized interventions for patients with this condition. The immune processes behind chronic inflammation in asthma exhibit marked heterogeneity, with diverse phenotypes defining discernible features and endotypes illuminating the underlying molecular mechanisms. In particular, two primary endotypes of asthma have been identified: “type 2-high,” characterized by increased eosinophil levels in the airways and sputum of patients, and “type 2-low,” distinguished by increased neutrophils or a pauci-granulocytic profile. Our review encompasses significant advances in both innate and adaptive immunities, with emphasis on the key cellular and molecular mediators, and delves into innovative biological and targeted therapies for all the asthma endotypes. Recognizing that the immunopathology of asthma is dynamic and continuous, exhibiting spatial and temporal variabilities, is the central theme of this review. This complexity is underscored through the innumerable interactions involved, rather than being driven by a single predominant factor. Integrated efforts to improve our understanding of the pathophysiological characteristics of asthma indicate a trend toward an approach based on disease biology, encompassing the combined examination of the clinical, cellular, and molecular dimensions of the disease to more accurately correlate clinical traits with specific disease mechanisms.

Delimitation of Differentiated Management Units (DMUs) based on productivity maps, slope maps and vegetation indices

According to several projections, the planet's demographic density will continue to increase in the coming decades, a fact that makes it necessary to increase food production to meet population demand. However, there are factors that can make it difficult to achieve production goals, such as the high cost of inputs. Therefore, aiming to increase productivity and reduce costs through optimizing the use of resources and the area available for production, it is necessary to implement alternatives to traditional production control methods. In this aspect, precision agriculture stands out. For precision agriculture to be applied to crops, it is first necessary to observe the spatial and temporal variability of the area, through georeferenced data on the attributes that involve the production system. The correlation of these attributes can indicate sub-regions within the production areas that can receive homogeneous treatment; these fractions of the area can also be called Differentiated Management Units (DMUs). Therefore, the objective of this study was to evaluate the viability of DMU delimitations using data on productivity, slope and vegetation indices, referring to the 2020 harvest for corn cultivation. To this end, geoprocessing of the data obtained using the QGIS software was carried out, so that 3 DMUs were generated for the area evaluated in the study. Thus, the DMUs were compared with the 2021 corn harvest. The results show that the DMUs, produced with data from the 2020 corn harvest, delimited regions with different productivity data in the 2021 harvest, indicating that the possibility of obtaining better parameters in production if differentiated management were carried out in the field, and such planning can be carried out based on the assessments that DMUs allow to be carried out.

Tidal levels significantly change bacterial community composition in a tropical estuary during the dry season

AbstractEstuaries are usually characterized by strong spatial and temporal variability in water physicochemical conditions and are often largely affected by human activities. One important source of variability is caused by tides that can swiftly alter not only physicochemical conditions but also the abundance and composition of the biota. The effect of the diurnal tidal cycle on microbial community composition during different seasons remains uncertain, although this knowledge underlies having effective monitoring programs for water quality and potential identification of health risk conditions. In this study, we assessed the bacterioplankton community composition and diversity across four tidal water levels in a tropical estuary characterized by a mixed semidiurnal tide regime (i.e., two high and two low tides of varying amplitudes) during both dry and wet seasons. The bacterial community composition varied significantly among the four tidal levels, but only during the dry season, when the influence of the seawater intrusion was largest. Bacterial indicators’ taxa identified using the Indicator Value Index were found within Cyanobacteria, Actinobacteriota, Bacteroidota, and Proteobacteria. The indicator taxon Cyanobium sp. had a prominent presence across multiple tidal levels. The main predicted phenotypes of the bacterial communities were associated with potential pathogenicity, gram-negative, and biofilm formation traits. While there were no marked predicted phenotypic differences between seasons, pathogenic and gram-negative traits were more prevalent in the dry season, while biofilm formation traits dominated in the wet season. Overall, our findings underscore the intricate relationship between river hydrodynamics and bacterial composition variability and hint a significant human impact on the water quality of the Bangpakong River.

Spatial Chlorophyll Estimation from Rice Field using Drone-derived Spectral Indices

Background: Precision farming has significantly advanced the agricultural sector by enabling real-time canopy monitoring and crop condition evaluation, thus facilitating precise management strategies to enhance yields. This study investigated the use of drone-derived vegetation indices (VIs) for assessing spatial variability in crop conditions, offering a more cost effective and practical alternative to satellite data. Methods: The field experiment was conducted during the Kuruvai season (July - November 2023) on a short-duration rice variety CO 55. Several vegetation indices viz., BGI, CI, EVI, GNDVI, MCARI, MSAVI, NDRE and NDVI were calculated to predict chlorophyll content and correlated with the measured SPAD values. Result: The results showed that indices like MCARI, GNDVI, and NDVI had strong positive correlations with SPAD values, with MCARI exhibiting the highest correlation (R = 0.914) and an R² value of 0.836. The findings underscore the effectiveness of using drone-derived indices for precise chlorophyll estimation, which is crucial for variable rate fertilizer application in precision agriculture.

A New NDSA (Normalized Differential Spectral Attenuation) Measurement Campaign for Estimating Water Vapor Along a Radio Link

The Normalized Differential Spectral Attenuation (NDSA) technique was proposed years ago as an active method for measuring integrated water vapor (IWV) along a Ku/K-band radio link immersed (totally or partially) in the troposphere. The approach is of the active kind, as it relies on the transmission of a couple of sinusoidal signals, whose power is measured at the receiver, thus providing the differential attenuation measurements from which IWV estimates can be in turn derived. In 2018, a prototype instrument providing such differential attenuation measurements was completed and set up for a first measurement campaign aimed at demonstrating the NDSA method. By the end of June 2022, the instrument was profoundly modified and upgraded so that a second measurement campaign could be carried out from 1 August to 30 November 2022. The transmitter was placed on the top of Monte Gomito (44.1277°lat, 10.6434°lon, 1892 m a.s.l.) and the receiver on the roof of the Department of Information Engineering of the University of Florence (43.7985°lat, 11.2528°lon, 50 m a.s.l.). The resulting radio link length was 61.15 km. Four ground weather stations of the regional weather service were selected among those available. In this paper, we describe the upgraded instrument and present the outcomes of the new measurement campaign, whose purpose was mainly to compare the IWV estimates provided by the instrument with the ground sensor measurements of air temperature, air humidity, barometric pressure, and rainfall. In particular, we show that the temporal trends of the two IWV estimates are qualitatively consistent, and that the instrument is able to provide IWV estimates also in the presence of fog and rainfall. Conversely, a quantitative evaluation through comparison with IWV data from point weather station measurements appears challenging due to the significant spatial variability in temperature and relative humidity, even between couples of stations that are quite close to each other.

A method to spatially assess multipass spray deposition patterns via UV fluorescence and weed population shifts

AbstractSpray deposition patterns from agricultural sprayers are traditionally sampled discretely along a field transect accounting for 0.5% or less of the treated area. Such methods may not fully capture the dimensional variability inherent in large‐scale, multiple‐pass spray applications, especially evident from an agricultural spray drone (ASD). This study investigated the utilization of UV‐fluorescent dye and nighttime aerial imaging techniques to assess large‐scale, multipass spray deposition patterns. Accuracy of digital hue from UV‐fluorescent photography to predict deposition of proxy dye was confirmed via fluorometry assessed intensity levels of extracted UV‐fluorescent dye from 384 Petri dishes placed prior to treatment. Results showed that ASD applications, regardless of nozzle type, exhibited greater spatial variability within the target area compared to ride‐on sprayer applications, primarily due to overapplication. Additionally, the ASD generated spray drift to adjacent nontarget areas that was at least three times more than that of ride‐on and spray‐gun sprayers. Multipass deposition was further assessed via in situ smooth crabgrass infestation following treatment with quinclorac or topramezone by multipass ASD or hand‐held, four‐nozzle spray boom. Weed infestation annotated from overlaid grids with 9.3‐dm2 ground resolution inconsistently detected spatial heterogeneity between transects assessed along the center and edge of each sprayer pass. The ASD controlled smooth crabgrass 11% more than the hand‐held sprayer, albeit with an 18% increase in spray drift to nontarget areas, similar to the UV‐fluorescence study. Digitally assessed average hue of fluorescence photography appears to be a viable method to assess multidimensional and continuous spatial relationships of spray deposition.

Spatial Heterogeneity of Soil Nutrient in Principal Paddy and Cereal Production Landscapes of Fengtai County within the Huai River Basin, Eastern China

The problem of cultivated land soil quality in the Huaihe River Basin has become increasingly prominent. How to accurately and quantitatively evaluate the soil quality of regional cultivated land and realize its efficient use has become an urgent problem. In order to explore the spatial autocorrelation and variation in soil nutrients in cultivated land in the plain of Fengtai County in the Huaihe River Basin, a total of 306 soil samples and mature wheat samples were collected in the study area to analyze soil pH, total nitrogen (TN), available nitrogen (AN), available phosphorus (AP), available potassium (AK) and slow-release potassium (SK) content and wheat biomass, and combined with geostatistical methods and GIS technology. The Kriging interpolation method and Moram‘s I index method were systematically analyzed. Principal component analysis (PCA) and Pearson correlation analysis were used to establish the minimum data set (MDS) of soil quality, which was used to calculate the soil quality index (SQI) and determine the key factors affecting soil quality. The results showed that the soil pH was in weak variation, and the other nutrient indexes were in medium variation. The spatial variability of soil-available potassium nutrients was affected by random factors such as human activities and structural factors such as soil parent materials. The spatial autocorrelation of organic matter, total nitrogen, alkali-hydrolyzable nitrogen, available phosphorus, available potassium and mitigation potassium was weak, which was mainly affected by random factors such as human activities. An unequivocal positive spatial nexus was discerned across all nutrients. Cumulatively, the nutrient dispersion across the investigated territory was somewhat diffuse, manifesting in a mosaic pattern with pronounced zonal nutrient allocation disparities in the meridional, median, and septentrional segments. An explicit latitudinal dichotomy delineating zones of nutrient opulence and paucity was also observed. These insights can pave the way for tailored fertilization strategies and judicious pedological stewardship in Fengtai County.

Компоненты микробной пищевой сети в пелагиали фьордов о. Западный Шпицберген в современных климатических условиях

The spatial variability of quantitative indicators of prokaryotes and virus-like particles in the waters of three Arctic fjords was studied in connection with the structure of their dominant water masses in the summer. A comparison of the abundance and biomass of prokaryotes showed that their average value in mesotrophic surface waters (0.60 million cells/ml and 28.64 mg/m3, respectively) exceeded the values in deeper oligotrophic waters – intermediate (0.33 million cells/ml and 16.82 mg/m3) and winter (0.32 million cells/ml and 19.72 mg/m3). The abundance of virus-like particles in different trophic conditions positively correlated with the parameters of prokaryotic communities and in the isolated water masses averaged 1.01 million, 0.09 million and 1.31 million per ml respectively. The factors determining the distribution of the most abundant representatives of the microbial food web and the nature of their interaction are considered.

Earth observation reveals the shifting patterns of China's lake colour driven by climate change and land cover

Water colour has been recognized as one of the most important Essential Climate Variables of the lake ecosystem, as it is directly related to changes in water constituents and almost all of the lake's ecological changes could alter water colour. Given the high retrieval accuracy from existing Earth observation satellite data, water colour, in terms of Forel Ule Index (FUI), can be a realistic indicator to track the long-term changes in the lake ecosystem and further explore the lake response to environmental changes. This paper aims to comprehensively investigate the spatiotemporal variation patterns of FUI in 159 large lakes (≥25 km2) across China during 2000–2022 based on the MODIS data and detect the climatic and anthropogenic driving forces of these changes. The 23 years of MODIS records revealed an overall downward trend of lake FUI across China, indicating the lakes in China shifted to bluer colour during the past two decades. Through driving factor analyses, the complicated interplay among lake colour, lake morphology, regional climate shifts and human interference dynamics was uncovered. In the long term, it was found the pronounced change in lake colour in the western lake zones was primarily attributed to climate warming and humidification, whereas that in the eastern lake zones was mainly related to the alterations in regional land cover during the past two decades. Seasonally, lake basin's air temperature was identified as the main factor impacting the seasonal patterns of lake colour, followed by wind speed and runoff. Spatially, there was high spatial variability in lake colour across China, which was mainly associated with lake elevation and lake basin's precipitation rate, although the factors exhibited considerable divergence across different zones. Based upon the above findings, the implications for lake environment protection and management in different regions of China were further discussed.

Evaluation of the Spatial Variability of the Mechanical Properties of Rocks Using Non‐Iterative Green's Function Approach and the FOSM Method

ABSTRACTThe present work proposes a new version of the Green‐FOSM (first‐order second moment) method, which eliminates the iterative calculation process of the original version and, simultaneously, solves the convergence problems related to the mechanical properties of rocks that form the geological formation. In this calculation scheme, the iterative process is eliminated by using a matrix that correlates the nodal displacement vector with the strain vector. Considering the same computational resources, this non‐iterative version of the Green‐FOSM method is up to 200 times faster than the original iterative process. In addition, it allows analyzing problems with more than 10,000 random variables, value that in the original method is less than 3000. To demonstrate its validity, the proposed method is applied to two hypothetical models subjected to different fluid extraction processes. For all the different levels of correlation and spatial variability, the statistical results obtained by the proposed method agree well with the results obtained via Monte Carlo Simulation (MCS). The relationship between CPU times demonstrates that the proposed method is at least 50 times faster than MCS. In the end, the non‐iterative Green‐FOSM method is used to obtain the displacement, strain, and stress fields of a geological section constructed from a seismic image of Brazilian pre‐salt oil region. The results found show that, depending on the levels of spatial variability, the analyzed fields can assume values up to 30.6% higher or lower than the values obtained deterministically.

Exact analytical solution of the equations for a quasiequilibrium two-phase domain: permeability and interdendritic spacing

This study is concerned with the theoretical description of a quasi-stationary process of directional crystallization of binary melts and solutions in the presence of a quasi-equilibrium two-phase region. The quasi-equilibrium process is ensured by the fact that the system supercooling is almost completely compensated by heat released during the phase transformation. Quasi-stationarity of the process determining constancy of the crystallization rate is ensured by given temperature gradients in the solid and liquid phases. The system of heat and mass transfer equations and boundary conditions to them under these assumptions is dependent on a single spatial variable in the reference frame moving with the crystallization rate relative to a laboratory coordinate system. Exact analytical solutions to the formulated problem in parametric form are obtained. The parameter of the solution is the solid phase fraction in a two-phase region. The distributions of temperature and impurity concentration in the solid, liquid and two-phase regions of the crystallizing system, the rate of solidification, and the spatial coordinate in the two-phase region depending on the solid phase fraction in it are found. An algebraic equation for the solid phase fraction at the interface between the solid material and the two-phase region is derived. Exact analytical solutions show that the impurity concentration in the two-phase layer increases as the solid phase fraction increases. Moreover, the solid phase fraction at the interface solid phase — two phase region and its thickness increase as the temperature gradient in the solid phase and the solidification rate increase. The developed theory allows us to determine analytically the permeability of the two-phase region and a characteristic interdendritic spacing in it. Analytical solutions show that the relative permeability in the two-phase region increases from a certain value at the interface with the solid phase to unity at the interface with the liquid phase. The selection theory of stable dendritic growth allows us to determine analytically a characteristic interdendritic distance in the two-phase layer that decreases as the temperature gradient in the solid phase increases. An increase of impurity in the molten phase gives a decrease in the interdendritic spacing within a two-phase region.