Ordinary Kriging

Arid mountainous regions are vulnerable to extreme hydrological events such as floods and droughts. Providing accurate and continuous rainfall records with no gaps is crucial for effective flood mitigation and water resource management in these and downstream areas. Satellite data and geospatial interpolation can be employed for this purpose and to provide continuous data series. However, it is essential to thoroughly assess these methods to avoid an increase in errors and uncertainties in the design of flood protection and water resource management systems. The current study focuses on the mountainous region in northern Oman, which covers approximately 50,000 square kilometers, accounting for 16% of Oman's total area. The study utilizes data from 279 rain gauges spanning from 1975 to 2009, with varying annual data gaps. Due to the limited accuracy of satellite data in arid and mountainous regions, 51 geospatial interpolations were used to fill data gaps to yield maximum annual and total yearly precipitation data records. The root mean square error (RMSE) and correlation coefficient (R) were used to assess the most suitable geospatial interpolation technique. The selected geospatial interpolation technique was utilized to generate the spatial distribution of annual maxima and total yearly precipitation over the study area for the period from 1975 to 2009. Furthermore, gamma, normal, and extreme value families of probability density functions (PDFs) were evaluated to fit the rain gauge gap-filled datasets. Finally, maximum annual precipitation values for return periods of 2, 5, 10, 25, 50, and 100 years were generated for each rain gauge. The results show that the geostatistical interpolation techniques outperformed the deterministic interpolation techniques in generating the spatial distribution of maximum and total yearly records over the study area.

Using reliable stochastic or deterministic methods, it is possible to rearrange an existing network by eliminating, adding or moving monitoring locations producing the optimal arrangement among any possible. In this paper, some spatial optimization methods have been selected as more effective among those reported in literature and implemented into a software M-Sanos able to carry out a complete redesign of an existing monitoring network. Both stochastic and deterministic methods have been embedded in the software with the option of choosing, case by case, the most suitable with regard to the available information. Finally, an application to the existing regional groundwater level monitoring network of the aquifer of Tavoliere located in Apulia (south Italy) is presented.

The aims of this paper are to present a brief review of techniques used to generate random fields of hydraulic conductivity (K) and to develop a hypothetical case study of stochastic simulation of the flow and transport of contaminants in saturated porous media. The sequential Gaussian
simulation method (SGS) is applied to generate the random fields of K in order to represent uncertainty and spatial variability of hydraulic conductivity. The spatial structure of hydraulic conductivity is described by three distinct models of spatial variability, represented by Gaussian, Exponential and Spherical theoretical variograms. The hypothetical case study consisted in spreading a contamination plume from an area contaminated with benzene. The contaminated area is 80 m long x 80 m wide and the study area is 2 km long x 1 km wide. The assumed benzene concentration of the contaminated area was 200 ppb. The simulations comprised a 30-year period and the results showed a greater development of the contamination plume when the Gaussian and Exponential models were used compared to the Spherical model. It also presented the
cumulative frequency distributions of benzene concentration for one hypothetical receptor located within the study area. The frequency associated to an assumed threshold concentration (10 ppb) is highlighted.

La disponibilidad de informacion de precipitacion con alta resolucion espacial es de fundamental importancia en el campo de los recursos hidricos. Comunmente, los datos de lluvia se obtienen mediante estaciones pluviometricas. Sin embargo, investigaciones demuestran que las medidas tradicionales pueden no reflejar la variacion espacial de la precipitacion efectiva. Por otro lado, cuando se aplican datos de satelite a regiones locales su resolucion espacial es demasiado gruesa. Este trabajo presenta un enfoque para identificar un metodo de reduccion de escala mediante la regionalizacion geoestadistica para mejorar los modelos de recursos hidricos que contienen escalas cortas espaciales y temporales y datos de precipitacion limitada. Se aplicaron tres modelos diferentes: Cokriging, Peso Inverso de la Distancia (IDW) y Kriging. Se calcularon parametros estadisticos como el error medio absoluto (MAE) y la raiz del error cuadratico medio (RMSE). Un proceso de validacion cruzada mostro un...

The availability of rainfall information with high spatial resolution is of fundamental importance in many applications in the field of water resources. Commonly, the rainfall data in developing countries are obtained by rain gauge stations. However, many studies show that traditional measures based on rain gauge stations may not reflect the spatial variation of rainfall effectively. Although satellite data have been widely used around the world, when applied to local regions the spatial resolution of these products is too coarse. In this paper, an approach to identify a downscaling method through geostatistical regionalization to improve water resources models with short spatial and temporal scales and with limited rainfall data is presented. Three different models were applied: Cokriging, Inverse Distance Weight (IDW) and Kriging. Statistical parameters such as mean absolute error (MAE) and root mean square error (RMSE) were computed. A cross-validation process showed a better fit for most of the stations using the Cokriging method. The regionalization results were quite comparable with the rain gauge stations data. Although the model outcomes did not improve remarkably, the contribution of this approach may have the potential to provide useful rainfall data at spatial scales shorter than the present resolution.

Accurate prediction of mineral grades is a fundamental step in mineral exploration and resource estimation, which plays a significant role in the economic evaluation of mining projects. Currently available methods are based either on geometrical approaches or geostatistical techniques that often considers the grade as a regionalised variable. In this paper, we propose a grade estimation technique that combines multilayer feed-forward neural network (NN) and k-nearest neighbour (kNN) models to estimate the grade distribution within a mineral deposit. The models were created by using the available geological information (lithology and alteration) as well as sample locations (easting, northing, and altitude) obtained from the drill hole data. The proposed approach explicitly maintains pattern recognition over the geological features and the chemical composition (mineral grade) of the data. Prior to the estimation of grades, rock types and alterations were predicted at unsampled locatio...

Groundwater is an important source of fresh drinking water in Pakistan and it has a great impact on human and ecological health. Therefore, it is imperative to evaluate the quality of groundwater. This study aims to explore the spatial variability of groundwater quality and to predict the unmeasured locations in Sheikhupura, Pakistan. For this purpose, hydro-chemical results of 105 water samples were taken from the Pakistan Council of Research in Water Resources (PCRWR). The water quality parameters including total dissolved solids, calcium (Ca), magnesium (Mg), hardness, sodium (Na) and sulfate (SO 4 ) were measured from each sample at every location and compared with the permissible limits of the World Health Organization (WHO). Initially, descriptive statistical measures along with normality tests are carried out to assess the shape of water quality parameters. Later on, two geostatistical prediction techniques: inverse distance weighting (IDW) and ordinary kriging (OK) were considered to predict the unmeasured locations within the study domain. In this case, the parameters of the experimental variogram (sill, range and nugget) were estimated using the best-fitted variogram models including exponential, spherical, matern and Gaussian. Crossvalidation statistics were carried out to evaluate the performance of IDW and OK. Results showed that the OK better performed than IDW. Furthermore, the water quality index was plotted to demonstrate the overall quality of groundwater in District Sheikhupura. It was observed that the area (South-West) with latitude 31.55°-31.66° and longitude 73.79°-73.93° have a very poor quality of groundwater. On the whole, only 9.6% of locations have excellent water for drinking. Thus results showed that the quality of groundwater is not satisfactory in Sheikhupura, Pakistan; therefore, serious preventive measures are required to reduce possible threats to human and ecological health.

The importance of accurate ore reserve estimates has consistently been recognized in the past. Mining companies need accurate ore reserve estimates since the quality of the estimate may directly affect the company's profitability. Accurate ore reserve estimates are also becoming crucial to governmental bodies that must make policy decisions regarding nonrenewable natural resources. Based on ore estimated value, we convert the estimated ore into ore resources and ore reserves And ore estimated values can vary according to level of geological knowledge, type of sample obtained, competent person qualifications doing estimation. The paper explain the analysis of orebody modeling carried out, which is explained in detail. Furthermore, the geostatistical method of reserve estimation has been compared with other conventional methods. The conventional methods tested are the polygon method, the inverse of the distance square (IDS) method, and ELIP, similar to IDS but allows different wei...

Accurate spatial distribution information of rainfall is essential to rainfallinduced hazard predictions and statistical interpolation methods may serve as a useful tool to produce a detailed distribution from coarse data sources. Although numerous comparison studies about different interpolation methods have been conducted on irregular rain-gauge networks, there is a need to perform such work on the increasingly available gridded rainfall data. Carried out in the Emilia-Romagna region (Italy) from 2008 to 2018, this study aims to examine accurate and appropriate interpolation methods to produce finer rainfall surface maps based on the 0.25° × 0.25° ERA5 gridded precipitation datasets. Five interpolation techniques, namely Thiessen polygons, Inverse Distance Weighting (IDW), Thin Plate Spline (TPS), Ordinary Kriging (OK), and ordinary Co-Kriging (CoK), have been selected and compared at different time scales (annual, monthly, and annual maximum daily precipitation). To assess the accuracy, the leave-one-out-cross-validation(LOOCV)test was used by using the indexes of Bias, Correlation coefficient (CC), the Nash-Sutcliffe Efficiency (NSE), Root Mean Square Error (RMSE) and the Kling-Gupta Efficiency (KGE). Additionally, visual inspections are employed to evaluate the plausibility of the interpolated maps. Results show: (1) All five interpolation methods have certain capabilities to improve spatial resolution, but they fail on accuracy at the daily scale. The OK generally outperforms the other four methods, while TPS shows better performance through the visual inspection at the monthly scale; (2) Unlike in the case of the interpolation using conventional point-based rain-gauge data, the multivariate method CoK is inferior to the univariate ones and the p-power of the IDW also differs; (3) Winter and spring results are better than those of summer and autumn. This study has provided useful guidance on choosing suitable rainfall interpolation methods for gridded datasets, which can be expanded in other regions and data sources to explore the generality of the conclusions.

Extreme precipitation episodes are very common in Mediterranean area and can lead to serious and catastrophic environmental hazards. They have special incidence during autumn months, September, October and November (SON) with important impacts on society, leading frequently to significant economic losses and mortality. These events have special impact in mountainous areas where steep slopes enhance the effects of extreme precipitation. In mountainous areas rain gauge stations are sparse and normally in lower amount. Due to these reasons it is very important to map with higher accuracy the distribution of extreme precipitation. Also, in mountainous environments precipitation patterns can change in small distances that make the prediction more difficult, but also more important. A better prediction of areas with higher values of extreme precipitation will contribute to a better land use planning and avoid the effects of flash floods, land‐slides and soil erosion recognized as environm...

Sea-salt input over the land masses is known to have deleterious effects on man-made structures, plants crops and . natives and soilrwater resources. Recent work has shown the ability of some epiphytic-lichen species to monitor the deposition of airborne salts of marine origin. The atmospheric transport and inland deposition of marine salts can thus be assessed by measuring saline elements in lichens growing over coastal areas. The concentration of Cl y and Na q was determined in lichen thalli collected on three different occasions in south-western Portugal. The extracellular fraction of Na q was obtained by a sequential elution procedure and surface Cl y was recovered after leaching samples with water. The dispersion of element concentration in the area was studied through geostatistical analysis. Numerical values were estimated by two interpolation methods: ordinary kriging and kriging with an external drift. The latter method used the logarithm of the distance to the coast as an auxiliary variable and yielded more reliable results. Every set of data produced a similar spatial pattern, showing a steep gradient in the first 3 km from the coast. However, considerable variation can be observed between surveys. The variability of results is interpreted using the precipitation data obtained for the region under consideration.

Digital soil mapping (DSM) has emerged an effective tool for the classification of soil using auxiliary landscape data. Various pedometrical methods have been developed to deduce soil characteristics using geographical information, global positioning system, statistical techniques, geostatistical methods and field data. The use of auxiliary environmental variables is less expensive versus field-intensive methods and it also allows soil properties prediction through inter and intra relationships. In this paper, we report digital mapping of soil phosphorus from Qazvin region, Iran through regression-kriging method. Soil samples were collected from 77 points (1000 ha) through grid method and multivariate geostatistical method was used for mapping of soil phosphorus. The performance of the interpolation technique in term of the accuracy of predicted values were assessed by comparing the deviation of estimates from the measured data by performing a cross-validation technique over the validation data set by using the root mean square error. Based on analysis, the best model was selected for estimation of soil phosphorus. The phosphorus distribution varied significantly in selected area and up to 48.32% was observed which indicates a good efficiency of regression-kriging method for the estimation of soil phosphorus by computing easily measurable variables. The results indicated that the regression-kriging method is efficient method for the measurement of target variables and thus, the soil properties can be predicted with low cost and high accuracy which might be helpful to manage soil farming practices.

The analysis and modeling of the spatial variability associated with geophysical data such as hydrological and environmental data, have been of concern to geophysicists for many decades. For instance, the spatial characterization of rainfall, the variability of parameters describing groundwater flow such as transmissivity and hydraulic conductivity, the variation of water quality properties in a lake or reservoir, the spatial distribution of acid rainfall, and the spatial variability of droughts, are only a few examples. The analysis of spatial data can be made by using traditional methods such as Thiessen polygons and linear interpolation based on distance between sites. Likewise, Geostatistical methods such as Kriging [Bras and Rodriguez-Iturbe, 1985] have been commonly applied for spatial analysis of hydrological, meteorological, and geohydrological variables such as soil properties [

An understanding of water needs in agriculture is a critical input in resolving the water resources issues that confront many southeastern states. In Georgia, the water usage in the agricultural sector is higher than in any other sector and hence its estimation is of utmost significance in order to determine the total water usage . Water is used for a g r i c u l t u r a l w a t e r m a n a g e m e n t 8 9 ( 2 0 0 7 ) 1 9 9 -2 0 7 a r t i c l e i n f o Article history:

Introduction Safeguarding Venice is a national priority since 1973 when the so called “special legislation for Venice” regime was established with the aim to protect urban centers from tidal floods and sea storms, prevent erosion, restore typical lagoon habitats and abate pollution. National, regional and local administrations are in charge of implementing programs, plans and projects to achieve the “special legislation” goals (Amorosino 2002; Bevilacqua 1998). The national government regularly allocates funds and takes the most important political decisions regarding measures to implement.

Kebakaran hutan dan lahan merupakan peristiwa yang dapat terjadi secara alamiah ataupun diakibatkan oleh kegiatan manusia. Upaya pembukaan hutan dan lahan untuk hutan tanaman industri, perkebunan, pertanian, pembalakan liar dan lain-lain merupakan penyebab terjadinya kebakaran hutan oleh manusia. Berdasarkan data Kementrian Lingkungan Hidup dan Kehutanan, dalam lima tahun terakhir ini jumlah titik panas di suatu daerah terus mengalami peningkatan. Kalimantan Barat merupakan salah satu provinsi yang terus mengalami peningkatan banyaknya titik panas setiap tahunnya. Tahun 2015 merupakan puncak jumlah titik panas jika dibandingkan dengan 5 tahun sebelumnya yaitu sebanyak 105.289 titik panas [1]. Meningkatnya jumlah titik panas setiap tahun memerlukan suatu metode yang dapat digunakan untuk memodelkan perilaku dari kebakaran hutan. Hal ini bertujuan untuk mengestimasi titik-titik panas yang berpotensi kebakaran hutan. Jika kebakaran hutan terus terjadi maka luas hutan akan semakin berkurang setiap tahunnya dan dapat menyebabkan menurunnya fungsi hutan sebagai paru-paru dunia. Metode penaksiran yang dapat digunakan untuk menangani kasus fenomena alam adalah metode Kriging. Metode Kriging yang sesuai untuk menyelesaikan kasus tersebut antara lain adalah Simple Kriging, Ordinary Kriging dan Universal Kriging. Simple Kriging digunakan pada saat rata-rata populasi diketahui, sedangkan Ordinary Kriging digunakan pada saat rata-rata populasi tidak diketahui dan Universal Kriging digunakan untuk data yang mengandung kecendrungan tertentu [2]. Geostatistika berperan dalam menyelesaikan kasus fenomena alam berdasarkan lokasi untuk meminimalisir tingkat kesalahan. Metode yang sesuai untuk kasus data titik panas pada kebakaran hutan adalah Ordinary Kriging. Penelitian ini bertujuan untuk mengaplikasikan metode Ordinary Kriging dalam mengestimasi confidence titik panas pada kasus kebakaran hutan yang terjadi di Desa Nanga Tayap dan Kendawangan, Kabupaten Ketapang Kalimantan Barat. Confidence adalah cakupan luas titik panas pada area 1 km 2 dengan satuan persen (%). Penelitian ini dibatasi pada kasus kebakaran hutan dengan tidak melibatkan faktor arah sudut atau anisotropi. Selain itu, pada estimasi confidence di suatu daerah diasumsikan bahwa antar lokasi memiliki jenis tanah yang homogen.

Future Satellite Based Navigation Systems based on GPS, like US Wide Area Augmentation Sysytem (WAAS), are of global interest to the scientific community. Precise estimation of ionospheric delay is most crucial for successful implementation of the systems. Due to the complex ionospheric structure and large variation of Total Electron Content (TEC) in low latitudes, it is necessary to compare and validate the efficiency of the existing algorithms in this region. In this study, performances of the various interpolation algorithms for TEC calculation at ionospheric grid point (IGP) and user position for gridbased Single Shell Model have been tested for 72 test days of 2005. Based on the results obtained from this analysis, it has been found that, for the Indian region, it would be more suitable to use Ordinary Kriging in place of Planar Fit to estimate delay at an IGP (as used by US WAAS). It has also been found that Ordinary Kriging performs better than the Bilinear Interpolation technique at the user end.

The paper proposes a new randomized Cross Validation (CV) criterion specially designed for use with data acquired over non-uniformly scattered designs, like the linear transect surveys typical in environmental observation. Numerical results illustrate the impact of randomized cross-validation in real environmental datasets showing that it leads to interpolated fields with smaller error at a much lower computational load. Randomized CV enables a robust parameterization of interpolation algorithms, in a manner completely driven by the data and free of any modelling assumptions. The new method proposed here resorts to tools and concepts from Computational Geometry, in particular the Yao graph determined by the set of sampled sites. The method randomly chooses the hold-out sets such that they reflect, statistically, the geometry of the design with respect to the unobserved points of the area where the observations are to be extrapolated, minimizing biases due to the particular geometry ...

Due to substantial effect of classification of resource models on future mine planning, one should come with an accurate method of estimation to guarantee that the minimum error is acquired in the estimation process. The known world class Cu-Mo deposit, Sarcheshmeh Porphyry deposit (central Iran) selected as the study area. The Hypogene zone of the deposit was chosen as the space in which estimation processes should be done. The mean value of Molybdenum and Copper extracted from the top part of this zone, where sampling operations have been done on a dense grid. The correlation coefficient of 0.45 allowed going through the process of interpolation. It was shown that taking account Cu as an auxiliary variable the interpolation process, the estimation had been improved. Simple Cokriging interpolation technique is applied and it was proved that using Cu, with mean value of 0.61 percent, as secondary variable will decrease the estimation variance of Mo interpolation which has the mean v...

Geochemical anomaly separation, using concentration-area method at Zarshuran Au-As deposit, NW Iran, is studied in this work. Lithogeochemical dataset was used in this geochemical survey, which was conducted for exploring Au mineralization in green schist units at Zarshuran Carlinlike gold deposit. Similar surveys were also carried out for Ag and As exploration in these rock units, and obtained results have been interpreted using detailed geological mapping. The correlation between these threshold values and ore grades is clearly interpreted in this investigation. Also, the logarithmic plots show existence of two stages for Au, Ag, and As. According to the SEM studies, it can be concluded that the proposed algorithm is verified technically in order to identify economically valuable Au concentrations in the area under study.

Os interpoladores sao utilizados para geracao de mapas tematicos, buscando a melhor caracterizacao da variabilidade espacial de caracteristicas de solo e planta, sendo que quanto mais real for a distribuicao espacial destes atributos, melhor o manejo e gerenciamento das lavouras e consequentemente, maior a lucratividade do produtor. Neste sentido, o objetivo deste trabalho foi criar uma funcao para comparar os resultados de interpolacao realizadas pelo interpolador inverso da distância elevado a uma potencia (IDP) com o interpolador Krigagem ordinaria (KRI), pois a implementacao do interpolador da KRI e complexa, sendo necessario entender conceitos da geoestatistica. Desta forma, pretende-se mostrar que quando o IDP e utilizado de forma correta, pode ter resultados tao bons ou melhores que o interpolador da KRI, de forma mais rapida e simples. Para a criacao da funcao foi utilizado o banco de dados PostgreSQL com a linguagem PLPG/SQL. Os dados para teste sao dados de produtividade d...

The aims of this study were: 1) to map the different soil parameters using three geostatistical approaches, including; ordinary kriging (OK), cokriging (CK), and regression kriging (RK), 2) to compare the accuracy of maps created by the mentioned methods, and 3) to evaluate the efficiency of using ancillary data such as satellite images, elevation, precipitation, and slope to improve the accuracy of estimations. In the rangelands of the Poushtkouh area of central Iran, 112 soil samples were collected. The maps of different soil parameters were created using the mentioned methods. To assess the accuracy of these maps, cross-validation analyses were conducted. The cross-validation results were assessed by the root mean square error (RMSE) and normal QQ-plot together with sum and average error to suggest the best estimation approach for mapping each soil parameter. The results have shown that, in most cases, taking the ancillary data into account in estimations has increased the accura...

Resumo -O objetivo deste trabalho consistiu na inferência de Planta de Valores Genéricos (PVG) a partir da interpolação por krigagem ordinária, considerando-se os casos de isotropia e anisotropia, e variação do tamanho do raio de busca. O ajuste da superfície ocorreu com base no Valor do Metro Linear de Testada Corrigida (VMLTC) para uma amostra de 71 observações. Outros seis atuaram como pontos de verificação do modelo. Adotou-se dois modelos, esférico e gaussiano, e três distintos raios de busca (500m, 1000m e 2951m). A validação das superfícies ocorreu pela determinação da Raiz quadrada do Erro Médio Quadrático (REMQ) no VMLTC, para os pontos da amostra e de verificação. A modelagem anisotrópica, com raio de busca de 1000m, apresentou melhor resultado nos pontos amostrais (REMQ = R$154,76). Nos pontos de verificação, o melhor resultado obtido foi para isotropia e modelo gaussiano (REMQ = R$ 264,84). Conclui-se que a krigagem pode auxiliar na produção de PVG, uma representação cartográfica temática de importância para o planejamento urbano. No caso em estudo, para um mesmo raio de busca, verificou-se que as modelagens são equivalentes, sendo a isotrópica ligeiramente melhor em alguns casos. Palavras-chave: Interpolação de superfície; Representação cartográfica temática; Planejamento urbano.

Soil fertility mapping is essential when planning land use and developing crop fertilization strategies. Interpolation techniques are widely used for the mapping processes in varied fields of soil sciences to estimate the soil property values at unsampled sites. The aim of this work was to evaluate and compare the performances of three spatial interpolation methods (inverse distance weighting IDW; ordinary kriging OK; and spline) using the statistical criterion of root mean square error (RMSE) for cross validation and then generate a set of accurate soil property maps (pH, organic matter, phosphorus, and potassium). The study covers an area of 45 000 ha in the Loukkous irrigated district, Northwest of Morocco and includes 934 soil samples. These samples were collected from irregular cross-line nodes grids and were analyzed in the laboratory. Exploratory data analyses were first adopted to identify and remove all spatial outliers and to validate the normal distribution required for geostatistical analyses. In all cases, the distributions were found strongly skewed and needed to be transformed. Box-Cox transformations were used; they performed well for all soil properties. Experimental variograms were fitted with the exponential, spherical and Gaussian models. With the use of the lowest RMSE approach, ordinary kriging model was selected as the best method compared to IDW and spline for interpolating with the exponential variogram for pH, organic matter and potassium, and the spherical model for phosphorus. A map was generated for each soil property. The maps indicated the low level of potassium and organic matter soil content throughout the study area. These maps could be used for optimizing crop fertilizing considering the different soil fertility levels.

Remote sensing data are typically collected at a scale which is larger in both grain and extent than traditional ecological measurements. To compare with remotely sensed data on a one-to-one basis, field measurements frequently must be rescaled to match the grain of image data. Once a one-to-one correspondence is established, it may be possible to extrapolate site based relationships over

This work proposes to generalize the method of kriging when data are spatially sampled curves. A spatial functional linear model is constructed including spatial dependencies between curves. Under some regularity conditions of the curves, an ordinary kriging system is established in the infinite dimensional case. From a practical point-of-view, the decomposition of the curves into a functional basis boils down the problem of kriging in infinite dimension to a standard cokriging on basis coefficients. The methodological developments are illustrated with temperature profiles sampled with dives of elephant seals in the Antarctic Ocean. The projection of sampled profiles into a Legendre polynomial basis is performed with a regularization procedure based on spline smoothing which uses the variance of the sampling devices in order to estimate coefficients by quadrature.

This work proposes to generalize the method of kriging when data are spatially sampled curves. A spatial functional linear model is constructed including spatial dependencies between curves. Under some regularity conditions of the curves, an ordinary kriging system is established in the infinite dimensional case. From a practical point-of-view, the decomposition of the curves into a functional basis boils down the problem of kriging in infinite dimension to a standard cokriging on basis coefficients. The methodological developments are illustrated with temperature profiles sampled with dives of elephant seals in the Antarctic Ocean. The projection of sampled profiles into a Legendre polynomial basis is performed with a regularization procedure based on spline smoothing which uses the variance of the sampling devices in order to estimate coefficients by quadrature.

Exploration and mining success of a mineral deposit rely greatly on an adequate modelling of spatial characteristics of constituent geo-variables through an understanding of deposit geology, because it is the geology that governs the process of mineralisation. Geostatistics pro vide its meaningful role in spatial characterization of constituent geo-variables and thus constitutes an essential input to integrated geostatistical modelling for mineral resource assessment. Geostatistics recognise that sample values in a mineral deposit are spatially correlated with one another. The methods are based on a set of theoretical concepts known as the theory of 'Regionalised Variables'. Geological-geostatistical modelling for spatial characterisation of a mineral deposit is of fundamental importance for mineral inventory estimation and grade-tonnage modelling. Deposit geology when integrated with appropriate geostat istical techniques provide an impro ved understanding of the mineralization type and specifics. The present research has focused on an integrated approach to geostatistical modelling involving geological understanding of depositional process for bauxite formation to analyse stat istical and geostat istical characteristics of an east coast bauxite deposit of Odisha, India. The bauxite deposit studied is Panchpatmali deposit, located in East Coast Bauxite zone of India in the southern part of Koraput district, Odisha. The research study comprised of (i) an understanding of geology of the bauxite deposit; (ii) probability modelling using classical statistics; (iii) quantification of spatial variability using semi-variogram; (iv) estimation of block values using kriging. Due to prolonged r esidual concentration and lateralizat ion of Precambrian khonadalites and charnockites, the bauxite deposit formed is geologically ferruginous type (high in iron) and spat ially heterogeneous. Modelling results of statistical and geostatistical analyses have been related to the process of bau xite formation Estimation of mineral inventory and grade-tonnage mo dels made on the basis of geo-mathematical models provided a persuasive means to subsequent engineering and economic decisions.

Kriging is an important statistical method used in spatial studies within regional planning and predictive studies. It is employed to achieve optimal predictions, such as pollutant quantities or various environmental and health impacts. There are many types of pollutants, including: 1. Water Pollution: The leakage of chemicals from mining sites into groundwater and water bodies can affect water quality and vitality.

The lack of randomisation in irrigation experiments is usually a disadvantage. The introduction of spatial variable experimental design offers a convenient tool to help solving this problem. In order to understand the variation of some soil physical and chemical properties in an experimental block and its effect on lettuce (Lactuca sativa L.) production, graphical interpretation of those soil properties was done with the use of geostatistics in a geographic information system (GIS). In this work three techniques of geostatistics were used for the creation of several maps of soil properties in an experimental plot cultivated with lettuce. Lettuces were evaluated for individual weight and diameter at the end of the cropping season. The soil properties studied were: total mineral nitrogen, phosphorus, potassium, pH, electric conductivity and saturated soil hydraulic conductivity. The techniques used were: ordinary kriging, inverse distance and Thiessen polygon. Cross validation used to compare the prediction performances of the three geostatistical interpolation algorithms determined that kriging was the best technique for each soil property. Prior to the creation of the maps, semivariograms were produced for each soil property. The maps resulting from the interpolation techniques were introduced in a GIS and their values reclassified. After that, spatial modelling was used to develop a final overlay map from all the information of the analysed soil properties simulating a "lettuce production capability map". This final map was created with the objective to determine which areas in the plot had optimal conditions for lettuce development. It was concluded that the plot did not had an optimal area for lettuce production. Localized problems with soil properties were found that could be solved with simple geographically restricted amendment treatments. Final lettuce yield had high correlation (r 2 = 0.83) with the lettuce capability map derived.

A auten cidade deste documento pode ser conferida no site h ps://www.sei.ufu.br/sei/controlador_externo.php? acao=documento_conferir&id_orgao_acesso_externo=0, informando o código verificador 3643084 e o código CRC CB0F21F0. Referência: Processo nº 23117.038448/2022-16 SEI nº 3643084 AGRADECIMENTOS Eu não teria chegado até aqui se não tivessem passado pessoas maravilhosas na minha vida que me incentivassem a estudar, me dando apoio pessoal e profissional, ou me servissem como exemplo. Primeiramente, à minha família, minha mãe Célia, meu pai Darci e meu irmão Davi, muito obrigado por tudo, a minha vida e tudo que eu alcancei até hoje eu devo tudo a vocês. Eu os amo incondicionalmente. Agradecimento especial ao meu orientador, professor doutor Luiz Antônio de Oliveira pela paciência e pelas maravilhosas reflexões que tivemos juntos, por todo apoio científico e emocional, esse trabalho não teria saído do projeto se não fosse por você. Ao Dr. Samuel Maciel, Me. Rafael Silva e Dra. Camila Carpenedo por todo apoio técnico e científico, todo meu agradecimento por dispor de seus tempos e trabalhos para me ajudar a elaborar e/ou entender os "mistérios" da climatologia, estatística e geoestatística. A todos os meus amigos, em especial, José Rojas, Breno Rezende, Luiz Ricardo Soldi,

To utilise DSMs effectively it is necessary to ensure that they are sufficiently accurate to meet the requirements of our specific application. In order to assess the accuracy of a model two basic aspects must be considered: the measured data accuracy and the modelling quality. In this work we show a geostatistical approach to the surface modelling. The geostatistical methods are well suited to assessing accuracy and they allow treat the entire modelization process. These methods allow the study of phenomena that fluctuate in space. The process begins with a data capture using a dense grid in a representative zone of the study area. Those data are used for the spatial variability estimation, obtaining information about the influence zones and presence of anisotropies. The modeled spatial variability functions will be used for the final grid design considering the maximum admissible estimation error, that depends only of the spatial variability functions and the data positions -not data values-. Once the grid to be measured is defined, the final capture is made and the data are debugged using the cross validation method. Using the debugged data and the information derived from the structural analysis the modelization is made. The estimation will be optimum (non-biased and minimum estimation error). The estimation error will be known for the entire model and it will be a very important information for the evaluation of the model quality. Finally, we present an example of analysis using the Factorial Kriging method that allows the filtering using a structural space depending filter schema.

This paper presents an overview of the preliminary evaluation results of the new Earth Gravitational Model (EGM08) in Uganda. The evaluation was based on a network of 12 GNSS/levelling points in Kampala and was performed in point wise (absolute) and relative (varying baselines) sense. For completeness the evaluation tests were also performed for EGM96. Our preliminary results were inconclusive as in the absolute tests, EGM96 was unexpectedly significantly better than EGM08. However, in the relative tests, EGM08 was consistently better than EGM96 for all baseline lengths considered. Subsequently further tests with much higher density and distribution than our test network should be carried out to conclusively determine the best global model for geodetic applications in Uganda Keywords: EGM08, geoid, ellipsoidal and orthometric heights, GNSS/levelling.

The majority of navigation satellite receivers operate on a single frequency. They compensate for the ionospheric delay using either an ionospheric model which typically only corrects for 50% of the delay or a thin-shell map of the ionosphere. A 4D tomographic imaging technique is used to map the free electron density over the fullheight of the ionosphere above North America during autumn 2003. The navigation solutions computed using correction based upon the thin-shell and the full-height maps are compared in this paper. The maps are used to calculate the excess propagation delay on the L1 frequency experienced by GPS receivers at selected locations across North America. The excess delay is applied to correct the single-frequency pseudorange observations at each location, and the improvements to the resulting positioning are calculated. It is shown that the thin-shell and full-height maps perform almost as well as a dual-frequency carriersmoothed benchmark and for most receivers better than the unfiltered dual-frequency benchmark. The full-height corrections perform well and are considerably better than thinshell corrections under extreme storm conditions.

Geostatistical spatial models are widely used in many applied fields to forecast data observed on continuous three-dimensional surfaces. We propose to extend their use to finance and, in particular, to forecasting yield curves. We present the results of an empirical application where we apply the proposed method to forecast Euro Zero Rates (2003-2014) using the Ordinary Kriging method based on the anisotropic variogram. Furthermore, a comparison with other recent methods for forecasting yield curves is proposed. The results show that the model is characterized by good levels of predictions' accuracy and it is competitive with the other forecasting models considered.

Groundwater is a vital source of freshwater, but its quality is often compromised by various physicochemical factors. Despite the importance of groundwater quality, there is a gap in understanding the spatial distribution of physicochemical factors controlling groundwater quality, particularly in regions with limited data. This study bridges the gap in groundwater quality assessment by applying advanced statistical and spatial analysis techniques. The research aims to assess groundwater quality in a data-limited region, identify physicochemical factors controlling quality, and analyze physicochemical parameters of samples, examining correlations and chemical characteristics. To achieve these objective groundwater samples were collected from 103 different sampling locations and their physiochemical parameters such as hydrogen ion concentration (pH), total dissolved solids (TDS), electrical conductivity (EC), dissolved oxygen (DO), nitrate, sulfate, phosphate, chloride, fluoride, total hardness (TH), calcium, magnesium, and bicarbonate were tested and analyzed. Correlation coefficient analysis revealed a strong correlation between TDS, chloride, and sulfate. Hierarchical cluster analysis (HCA) divided the collected samples into three clusters based on similarities in chemical characteristics related to groundwater quality. HCA showed groundwater properties similar to groups I, II, and III (less, moderate, and severely mineralized, respectively). In the spatial analysis, the physio-chemical variables were interpolated by the application of Empirical Bayesian Kriging (EBK). In this interpolation, the lowest root mean square error (RMSE) values for TDS (1.03) and EC (0.98) were calculated using the exponential model. Using the K-Bessel model of the EBK interpolation approach, the lowest RMSE values were determined for pH, HCO 3-, F-, Cl-, Mg 2+ , TH, SO 4 2-, PO 4 3-, and DO. The Whittle model of the EBK interpolation determined the lowest RMSE for NO 3-(0.98) and Ca 2+ (1.22). Water quality index (WQI) value ranges from 31.77 to 131.76 in the study area. The spatial distribution of the WQI values showed that the southeastern, northern, and central regions of the research area have unsuitable groundwater quality. In 8% samples of the study area, the water is not suitable for drinking before proper treatment. These findings have significant implications for the government and society, highlighting the need to take notice of the possible health dangers to the people living in the study region.

Coal is one of the extractive energy in indonesia to very large potentials, Sumatra is known as one of area which has potential resources of coal. The location area PT Andhika Yoga Pratama at Taman Bandung Village, Subdistrict Pauh, District Sarolangun, Province of Jambi. As the efforts to estimate the deposit of resources in contained in mining permit area (area Ijin Usaha Penambangan), the company should conduct an exploration process. Which consist of outcrop monitoring (outcrop descriptions, strike and dip measurements) and conducted mapping under surface with monitoring cutting from the the result of drill process. Data obtained is an the outcrop data and data of drill result. Research was commenced with generated histogram graph based on the thickness of coal, so it could from general overview of the thickness in research area. Based on correlation among drill points, there are 4 coal seam with condition of geometry straight with slope 5,1 0 to the South west, average of thickness seam A is 15,38 m, seam B 6,02 m, C is 1,15 m, and seam D 3,92 m, resperctively. There is also dwindling of thickness towards the Northwest and splitzing of seam B to the Northwest. This is could be assumed has moderate geological condition. Based on SNI 5015-2011 the distance of drilling point ≤ 500 m is counted as indicated resource classification. Volume calculated for measured resources is 46.189.441,45 m³, mean while indicated resource is 13.893.930,34 m³.

The present study was conducted at Almashanah area, Ibb city in the Republic of Yemen to evaluate the quality of groundwater for drinking and irrigation. Water samples were collected from twenty different wells. The physicochemical parameters of water samples, In-situ parameters include: pH value, temperature, electrical conductivity (EC), total dissolved solids (TDS) were measured in-situ during the sampling, Furthermore, the cations, anions and nitrogenous compound (F-, Cl-, NO2, NO3, NH3, Mg2+, Ca2+, K+, Na+, Fe2+, Zn2+, Cu2+) were analyzed.The suitability of water for irrigation was evaluated by estimating of Electrical Conductivity (EC), calculating of Sodium Absorption Ratio (SAR), Soluble Sodium Percentage (SSP), Exchangeable Sodium Percentage (ESP), Permeability Index (PI), Magnesium Hazard (MH) and Kelly’s Ratio (KR). The highest concentration of TH, EC, TDS, F, Cl, PO4, NH3, NO3, NO2, Mg, Na, K, Cu and Znfound in borehole (BH3) followed by(BH1 and BH2) which were not suitable for drinking.The boreholessamples can be used for irrigation with need for leashing only in thewells (BH1,BH2 andBH3). This study concluded that the boreholesnear to the wastewater treatment plant (WWTP) has been affected by the effluent of (WWTP) Therefore, it is suggested that the location of the (WWTP) is either to be shaft or its effluent is to be transfer further beyond the groundwater aquifer 20 km. Furthermore, the groundwater in the boreholes should be continuously monitored in order to prevent further ecological contamination and to guarantee public health.

The spatial distribution of total and CaCl 2 -extracted Cd, Pb and Zn concentrations in smelter-impacted soils was investigated over a polluted site (40 km 2 ) in Northern France. The study was conducted on 262 soils sampled in woody habitats. Total and extracted concentrations of trace metals (TMs) rose up to 2402 and 59.5 mg kg À1 for Cd, 41 960 and 13.7 mg kg À1 for Pb, 38 760 and 143.0 mg kg À1 for Zn, respectively. The spatial dependence of both total and extracted concentrations showed a high spatial auto-correlation and ordinary kriging was used to predict soil concentrations. Investigating which variables influenced metal concentrations and their spatial distribution, we found that total concentrations mostly depended on the distance from the smelter, the wind and the organic carbon, while extracted concentrations were mainly modulated by the pH. Conditionally to those variables, other soil properties and landscape characteristics influenced both total and extracted concentrations. We conclude that total and extracted TM concentrations are governed by different processes which act at various spatial ranges: total concentrations are mainly related to input and retention of metals (large scale) whereas extracted concentrations were mainly explained by factors controlling metal solubility in soils (local scale). Spatial distributions of total and extracted TMs differed over the area, which should be considered for risk assessment. Maps of risk based on the US EPA's Eco-SSLs (for plants, invertebrates and vertebrates) were realized, showing that wildlife may be at risk but that the relevance of Eco-SSL values is questionable.

Soil and water conservation is one of the most fundamental bases of sustainable development. Knowing the distribution manner of soil physical and chemical properties is one of the most important factors in recognition, management and exploitation of water and soil resources. Estimating the soil moisture curve plays an important role in modeling water and solutes movement through soils. Soil saturated moisture is among the most significant parameters in soil studies that is used for estimating the soil moisture curve and soil unsaturated hydraulic conductivity. This investigation was done with the purpose of investigating spatial variation of soil sp parameter by geostatistical methods and then selecting the most suitable method in estimating the above-mentioned parameter in Farahan area. For this purpose, at first, 54 soil samples were taken from the given area. Then, the soil samples were transferred to the lab for determining the soil saturated moisture (sp). After determining the sp values, data were inserted to GIS software. Afterward, the interpolation map of soil saturated moisture was prepared by interpolation and ordinary kriging. The results obtained from interpolation method showed that among the various models, Spherical model with nearest RSS value to number 1 was chosen as the best map. According to the map prepared by this method, the spatial variation of soil saturated moisture in the direction of westnorth-eastsouth of the area was more. While in the direction of eastnorth-southwest there were gradual changes.

The Sn-W Panasqueira mine, in activity since the mid-1890s, is one of the most important economic deposits in the world. Arsenopyrite is the main mineral present as well as rejected waste sulphide. The long history is testified by the presence of a huge amount of tailings, which release considerable quantities of heavy metal(loid)s into the environment. This work assesses soil contamination and evaluates the ecological and human health risks due to exposure to hazardous materials. The metal assemblage identified in soil (Ag-As-Bi-Cd-Cu-W-Zn; potentially toxic elements (PTEs)) reflects the influence of the tailings, due to several agents including aerial dispersion. PTEs and pH display a positive correlation confirming that heavy metal mobility is directly related to pH and, therefore, affects their availability. The estimated contamination factor classified 92.6% of soil samples as moderately to ultra-highly polluted. The spatial distribution of the potential ecological risk index classified the topsoil as being of a very high ecological risk, consistent with wind direction. Non-carcinogenic hazard of topsoil, for children (1-6 years),

A obtenção da correta distribuição espacial para atributos do solo é relevante no planejamento agrícola, no que diz respeito à instalação e manutenção das culturas. O objetivo desse trabalho foi comparar métodos de interpolação estatísticos (krigagem ordinária) e métodos determinísticos (inverso do quadrado da distância) na estimativa de CTC e V% em um Latossolo vermelho amarelo distrófico. O estudo foi realizado no Estado do ES na fazendo experimental do Instituto Capixaba de Pesquisa, Assistência Técnica e Extensão Rural (INCAPER), em uma grade irregular com 109 pontos. Os dados foram coletados na camada de 0-0,20 m na projeção da copa das plantas, na parte superior do declive. A performance dos interpoladores foi obtida e comparada usando o critério do erro médio. As observações são espacialmente dependentes até um alcance máximo de 14,1 m, considerando a isotropia. O IDW apresentou maior erro na estimação dos dados, entretanto sua diferença em relação à KRIG foi pequena para ambas as variáveis. Palavras-chave: Geoestatística, métodos de interpolação, zonas de manejo

Military training activities disturb ground and vegetation cover of landscapes and increases potential soil erosion. To monitor the dynamics of soil erosion, there is an important need for an optimal sampling design in which determining the optimal spatial resolutions in terms of size of sample plots used for the collection of ground data and the size of pixels for mapping. Given a sample size, an optimal spatial resolution should be cost-efficient in both sampling costs and map accuracy. This study presents a spatial variability-based method for that purpose and compared it with the traditional methods in a study area in which a soil erosion cover factor was sampled and mapped with multiple plot sizes and multi-sensor images. The results showed that the optimal spatial resolutions obtained using the spatial variability-based method were 12 and 20 m for years 1999 and 2000, respectively, and were consistent with those using the traditional methods. Moreover, the most appropriate spatial resolutions using the high-resolution images were also consistent with those using ground sample data, which provides a potential to use the high-resolution images instead of ground data to determine the optimal spatial resolutions before sampling. The most appropriate spatial resolutions above were then verified in terms of cost-efficiency which was defined as the product of sampling cost and map error using ordinary kriging without images and sequential Gaussian co-simulation with images to generate maps.

Kriging is a geostatistical interpolation technique that performs the prediction of observations in unknown locations through previously collected data. The modelling of the variogram is an essential step of the kriging process because it drives the accuracy of the interpolation model. The conventional method of variogram modelling consists of using specialized knowledge and in-depth study to determine which parameters are suitable for the theoretical variogram. However, this situation is not always possible, and, in this case, it becomes interesting to use an automatic process. Thus, this work aims to propose a new methodology to automate the estimation of theoretical variogram parameters of the kriging process. The proposed methodology is based on preprocessing techniques, data clustering, genetic algorithms, and the K-Nearest Neighbor classifier (KNN). The performance of the methodology was evaluated using two databases, and it was compared to other optimization techniques widely...

The spatial variability of soil pH for engineered Weathered Oxford Clay is described using 35 samples collected from the base of a new cell in an existing land®ll. Soil pH variability in¯uences the reactivity of Cr, Cu and Zn in the site. The reactivity of these metals as natural components was determined using a sequential extraction method. The total concentration of Cr, Cu and Zn and the mineralogical composition were also determined. The results showed that due to the presence of a layer rich in pyrite in the base, a natural acidi®cation may occur which can produce a soil pH as low as 2.7. The spatial variability of soil pH in this area has been described with an anisotropical variogram model and the estimation of its values at unsampled locations was carried out using the ordinary kriging algorithm. From the spatial modelling of the soil pH, it was found that the metals in the soil solid phases follow a similar distribution.

Myrionecta rubra patchiness in a Mexican coastal lagoon was studied. The 3 objectives were to (1) characterize the spatial distribution of M. rubra patches through time; (2) characterize and model the spatial distribution of M. rubra at scales ranging from m to km, and from 1 wk to more than 1 yr; and (3) to place the patchiness patterns of M. rubra into an ecological context. Geostatistical analysis was applied to data collected from simple and nested sampling grids in different seasons; autocorrelation analysis was used to detect temporal regularities over 55 wk. Classical statistics were applied to data from 10 sites in the lagoon to identify trends relating ciliate abundance to environmental conditions. Patches were detected and characterized using empirical variograms and modelled by omnidirectional Gaussian and exponential functions. For most of the analysis variance was low in the nugget parameter, indicating a strong spatial resolution of the data, and the range parameter indicated that M. rubra formed patches of 10, 20, 80, 130, and 170 m. Spatial analysis using hierarchical grids produced a more detailed assessment of patches than single grids alone. Conditional simulation of patches indicated the presence of a > 2 km patch covering most of the western lagoon. Patch densities varied from between 4 and 700 cells ml-1. M. rubra abundance exhibited a temporal, pulse-like pattern; autocorrelation revealed a 13 wk periodicity. At the lagoonal level, multiple regression revealed a trend towards higher abundance in the northwest of the lagoon and a decrease during the dry season. Finally, we speculate on the forces causing heterogeneity at large (>1000 m), meso (100 to 1000 m), and fine (1 to 100 m) scales by examining physical-chemical environmental factors and physiological behavioural properties of the ciliate and its potential predators. We propose that M. rubra patches originate by fragmentation of larger patches, growth of smaller patches, and physical-behavioural aggregation of cells.

Dissertação (Mestrado) --USP / Escola Superior de Agricultura "Luiz de Queiroz". 1. Análise de cluster 2. Regiões hidrologicamente homogêneas 3. Modelagem hidrológica 4. krigagem ordinária . I. Título À minha mãe Simone, que com toda sua força e dedicação me mostrou que a educação é a chave da mudança. Ao meu padrasto Adriano, que com toda sua paciência, respeito e honestidade me ajudou a ser uma pessoa melhor. Aos meus irmãos João Pedro e Ana Clara, amores da minha vida, que entendem minha ausência e são o motivo pelo qual busco ser melhor a cada dia. Aos meus avós Irany, Gentil (in memorian) e Carolina (in memorian), que com humildade e muito amor me proporcionaram os maiores ensinamentos. As minhas tias, que posso chamar de mãe, Elizete, Maria Aparecida e Sandra, por todo amor e carinho e por sempre acreditarem no meu potencial. Aos meus primos André, Taynara, Tamires, Isabela e Juan, por estarem sempre dispostos a me escutar, tenho sorte de ter vocês ao meu lado.