Interpolation Methods

Uno tra i problemi di matematica elementare, a tutt'oggi irrisolto, è la congettura di Collatz (dal matematico Lothar Collatz). Essa riguarda la seguente funzione tra numeri naturali: f: N →N N/2 se N è pari f(N)= 3*N+1 se N è dispari Iterando la funzione più volte dopo un certo numero di iterazioni si ottiene il numero 1 e continuando le iterazioni si ha il ciclo 1-4-2-1. Quindi il numero iniziale N, nelle iterazioni successive, viene moltiplicato per 3 (sommando 1) e diviso per 2 per cui è una successione di passaggi dispari (quando si moltiplica per 3 e si aggiunge 1) e di passaggi pari (quando si divide per 2) che, dopo un certo numero totale di passaggi pari bi e un certo numero totale di passaggi dispari ai, converge ad 1 in base alla relazione

Digital Elevation Models (DEM) are defined as numerical data structures that represent the spatial distribution of elevation above the surface. From the 70’s was established the representation of surfaces generated by the TIN model as the most appropriate, but by its nature, this algorithm follows a linear function, while the geometry of nature is showing a chaotic behavior, for that reason could achieve a better representation of these forms with the implementation of Kriging algorithm allowing to analyze the statistical variation over different distances and directions, causing the minimum error in estimated elevation; this work seeks to establish the relationship between surface geometry and the interpolation algorithm, through an analysis of variance (ANOVA) of Root Mean Square Error (RMSE) of a sample of 80 different models ranked according to their slope.

Uno tra i problemi di matematica elementare, a tutt’oggi irrisolto, è la congettura di Collatz (dal matematico Lothar Collatz). Essa riguarda la seguente funzione tra numeri naturali:
f: N →N
f(N)=N/2 se N è pari
f(N)=3*N+1 se N è dispari
Iterando la funzione più volte dopo un certo numero di iterazioni si ottiene il numero 1 e continuando le iterazioni si ha il ciclo 1–4–2–1. Quindi il numero iniziale N, nelle iterazioni successive, viene moltiplicato per 3 (sommando 1) e diviso per 2 per cui è una successione di passaggi dispari (quando si moltiplica per 3 e si aggiunge 1) e di passaggi pari (quando si divide per 2) che, dopo un certo numero totale di passaggi pari bi e un certo numero totale di passaggi dispari ai, converge ad 1 in base alla relazione 𝟑^𝒂𝒊∗𝑵∗𝑹𝒆𝒔𝒊/𝟐^𝒃𝒊=𝟏 dove 𝑹𝒆𝒔𝒊 è il residuo finale che è compreso tra 1,1 ed 1,25 per il riferimento [2] e dipende dalla somma di 1 nelle iterazioni in cui vi è il passaggio dispari (cioè 3*N+1) e quindi si avrà 𝟑^𝒂𝒊∗𝑵/𝟐^𝒃𝒊<𝟏.
In questo lavoro si presenta una successione personalizzata della funzione di Collatz, formulata su base modulare e orientata alla riduzione del numero di iterazioni necessarie per la convergenza. L’approccio si fonda sulla classificazione dei numeri naturali modulo 4, concentrando l’analisi sui soli numeri dispari congrui a 1 e 3 modulo 4. Grazie a una codifica algoritmica e a una struttura diagrammatica, il metodo consente un tracciamento semplificato dei passaggi pari e dispari, con evidenti vantaggi computazionali. Il confronto con la successione canonica di Collatz, applicato al numero N=27, evidenzia una riduzione significativa delle iterazioni (da 111 a 21), pur mantenendo la convergenza finale. L’introduzione del concetto di orbite isopath rafforza l’efficienza del modello e apre prospettive teoriche per una dimostrazione costruttiva della celebre congettura.

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...

The present work aims to study the spatial variability of ash Total Carbon (TC%) and Total Nitrogen (TN%) after a wildfire occurred in Portugal. Ash TC% a mean of 26.72 % (±8.76 %) and ash TN% of 1.20 % (±0.32 %). We observed that the area recover very fast to wildfire and two years the great part of soil was cover by vegetation. The fire severity (assessed with ash color and CaCO 3 content) was more related with ash TC%, than ash TN% due the different vulnerability and response of these two elements to fire temperature and as consequence severity. Previous to model data we tested their normality that only was achieved in the case of TC% after a neperian logarithmic transformation (ln). TN% respected gaussian distribution, however showed a high skewness, thus this variable was also ln transformed. Ash TC%(ln) presented an excellent spatial structure and the experimental model fits better with the rational quadratic model and ash TN%(ln) with the lineal model. Among all interpolation methods tested, the most accurate to interpolate ash TC%(ln) was IDW2 and the less suitable LP3. In relation to ash TN%(ln) the best interpolation technique was SPT and the less precise LP3. This allow us to observe differences that the spatial distribution of both variables is different, that is due the small scale variability observed in ash TC%(ln). In general the models were well performed because the residuals mean were closed to 0 and no differences between average of predicted and estimated values were identified. Ash TC%(ln) spatial distribution was in higher amounts in western, northern part and southeast and northeast corner of the plot and lower in the centre and south of the interested area and ash TN%(ln) was observed in higher amounts in the southwest and southeast part of the plot and lesser in the central part.

Bu çalışma ile Samsun ilinin güneyinde bulunan Kavak ilçesi sınırları içerisinde yer alan Seyitali, Kaya, İdrisli, Muhsinli, Beyköy ve Çayırlı mahallelerine ait toplam 1523 parselden oluşan ve 397.3 ha alan kaplayan tarım arazilerin bazı fiziksel, kimyasal ve verimlilik özelliklerinin belirlenmesi ile CBS yardımıyla farklı enterpolasyon modeller kullanarak 14 farklı parametre açısından dağılım haritalarının hazırlanması amaçlanmıştır. Alanın yıllık ortalama sıcaklık 10.2 °C ve yıllık ortalama yağış miktarı da 512.5 mm’dir. Newhall simülasyon modeline göre, toprak sıcaklık rejimi Mesic ve toprak nem rejimi ise Typic Xeric olarak belirlenmiştir. Çalışma sahasından 200m x 200m aralıklarla oluşturulan grit sistemden yüzey (0-20 cm) ve yüzey altı (20-40 cm) toplam 233 adet yer koordinatları ölçülerek toprak örnekleri alınmıştır. Laboratuvara getirilen topraklar, pH, EC, CaCO3, OM, N, Ca, Mg, K, P, Na, Fe, Cu, Zn ve Mn analizleri yapılmıştır. Analiz sonuçlarına göre, toprakların tamamı tuzsuz, pH değerleri ise nötr-hafif alkali arasında değişmektedir. Kireç içerikleri az ve orta düzeylerde, OM ve çinko ise genel olarak yeterli olarak belirlenmiştir. Ayrıca, toplam azot, magnezyum, fosfor, demir ve mangan yeterli düzeyde bulunmuştur. Ayrıca, uygun gübreleme ve arazi yönetimi pratikleri için uygun enterplasyon model kullanılarak bu parametrelerin dağılım haritalarının oluşturulmuştur.

Este trabajo analiza la calidad final de diferentes cartografías continuas de precipitaciones y temperaturas realizadas a partir de distintos métodos de interpolación. El análisis se ha realizado en el sector central del valle del Ebro, un espacio de topografía suave pero que se encuentra dominado por cornplejos patrones climáticos. Se han realizado 23 cartografías con diferentes tipos de métodos (locales, globales y geoestadísticos). Los mejores resultados en la cartografía de precipitaciones se han obtenido mediante la aplicación de métodos geoestadísticos, en concreto las técnicas de block-kriging y cokriging. Las temperaturas se han cartografiado con mejores resultados a partir de un modelo de regresión múltiple. Se discute acerca de la utilidad de las diferentes técnicas cartográficas en función de la variable analizada.

Este trabajo analiza la calidad final de diferentes cartografías de la temperatura máxima y mínima absoluta de Navarra (N. de España) en 2009. Se han realizado 12 cartografías para cada una de esas variables utilizando diferentes métodos de interpolación local, geoestadística, global y mixta. Su calidad se ha evaluado a partir de una muestra independiente de datos y mediante el cálculo del Error Medio Absoluto (MAE) y del Error Cuadrático Medio (RMSE). Los resultados señalan que las cartografías con un error estimado más bajo son las elaboradas a partir de modelos de regresión múltiple por pasos y corrección posterior del error mediante la cartografía de residuales.

Dokumen ini membahas berbagai metode interpolasi sebagai pendekatan dalam analisis numerik untuk memperkirakan nilai fungsi pada titik-titik yang tidak diketahui berdasarkan data yang ada. Penjelasan mencakup tiga metode utama: interpolasi linear, kuadratik, dan kubik, dengan masing-masing langkah-langkah prosedural, kelebihan, serta keterbatasannya. Analisis ini menyoroti pentingnya pemilihan metode berdasarkan karakteristik data, seperti distribusi, kelengkungan, dan jumlah titik data yang tersedia. Selain itu, dokumen ini membahas faktor-faktor yang memengaruhi akurasi dan efisiensi interpolasi, serta konsep terkait seperti ekstrapolasi dan spline. Kesimpulan menekankan bahwa tidak ada metode interpolasi yang universal; pilihan metode harus disesuaikan dengan kebutuhan dan konteks analisis.

In the paper is described the process of creating digital terrain models (DTM) using different interpolation methods. The analyses show the accuracy of the DTM obtained from topographic maps at different scales and using different interpolation methods. The quality and accuracy of DTM depends on the complexity of the terrain, data sources, and methods of height interpolation. The basic idea is the creation of the DTM for the selected area and the comparison of the results by applying appropriate interpolation methods. The aim of the research is to analyse the quality of the DTM model and to consider suitability of certain interpolation methods, based on the obtained results, i.e. their advantages and disadvantages. The experiment was done in the software environment ERDAS IMAGINE 2014.

Despite the modern technological advancements, contemporary methods of data gathering still rely on point samples, which means they feature a precise variable info only on specific x, y -coordinates. In order to get a continual representation of a surface necessary for research, it is necessary to approximate various data values on those surfaces which have not been sampled by using various methods of interpolation. The main aim of this research is to evaluate two different methods of interpolation based on the quality of digital terrain models used for geomorphometric analyses. For the purposes of developing and comparing these methods, a set of elevation data was attained by vectorization of contour lines from HOK. Two methods of interpolation were tested: triangulated irregular network (TIN) and ANUDEM (Topo to Raster). In order to get a more appropriate method, the research employed eight statistical parameters, various graphical representations (both two-and three-dimensional) and geomorphometric parameter of slope inclination. The research shows that ANUDEM is a better method for geomorphometric analyses than TIN is. After the analysis of geomorphometric parameters (slope), the conclusion is that there are no significant differences between the digital terrain models developed on the bases of different sets of elevation data.

Groundwater is the main water resource in La Gomera (Canary Islands) where it represents almost 70% of the consumption. Since the elaboration of the preliminary works of the Insular Hydrological Plan in 1996 there has not been other estimation of the island's rainfall. For an accurate estimation of the future hydrogeological resources of the island it is necessary to know and assess carefully the recharge estimates. It is for this reason that the choice of the rainfall interpolation method is so important. In this study two different interpolation methods have been used to compare their results with the real data of the gauges and to obtain doing that the best precipitation estimate in the area. Results show the kriging with external drift to be the best interpolation method in the study area and that the use of the relationship between elevation and precipitation increase the accuracy of the model.

The accuracy and computational efficiency of various interpolation methods for the implementation of non grid-confirming boundaries is assessed. The aim of the research is to select an interpolation method that is both efficient and sufficiently accurate to be used in the simulation of vortex induced vibration of the flow around a deformable cylinder. Results are presented of an immersed boundary implementation in which the velocities near nonconfirming boundaries were interpolated in the normal direction to the walls. The flow field is solved on a Cartesian grid using a finite volume method with a staggered variable arrangement. The Strouhal number and Drag coefficient for various cases are reported. The results show a good agreement with the literature. Also, the drag coefficient and Strouhal number results for five different interpolation methods were compared it was shown that for a stationary cylinder at low Reynolds number, the interpolation method could affect the drag coeffi...

Background: This aimed to compare the interpolation of lead and zinc concentration at the National Lead and Zinc Corporation using Landsat satellite and laboratory data to introduce an optimal interpolation method. Methods: After collecting the laboratory data, geostatistical approaches were applied to model the spatial distribution of lead and zinc, including radial basis functions, inverse distance weighting, and ordinary kriging (Gaussian, spherical, exponential, and circular). Estimation accuracy was evaluated by cross-validation and MAE, MBE, and RMSE diagnostic statistics. Results: The Gaussian model had the lowest error and was the optimal method for modeling lead and zinc. After investigating the correlations between the Landsat 5 satellite bands and soil element concentrations, the spatial distribution of lead and zinc was re-zoned in the ArcGIS software. In both methods, estimation accuracy was evaluated by cross-validation and MAE, MBE, and RMSE diagnostic statistics. Con...

In this paper is given a description of Neville’s algorithm which is generated from Lagrange interpolation
polynomials. Given a summary of the properties of these polynomials with some applications. Then, using the
Lagrange polynomials of lower degrees, Neville algorithm allows recursive computation of those of the larger
degrees, including the adaption of Neville’s method to trigonometric interpolation. Furthermore, using a
software application, such as in our case, Matlab, we will show the numerical experiments comparisons between
the Lagrange interpolation and Neville`s interpolation methods and conclude for their advantages or
disadvantages.

The Artificial Neural Networks (ANNs) are mathematical models method capable of estimating non-linear response plans. The advantage of these models is to present different responses of the statistical models. Thus, the objective of this study was to develop and to test ANNs for estimating rainfall erosivity index (EI30) as a function of the geographical location for the state of Rio de Janeiro, Brazil and generating a thematic visualization map. The characteristics of latitude, longitude e altitude using ANNs were acceptable to estimating EI30 and allowing visualization of the space variability of EI30. Thus, ANN is a potential option for the estimate of climatic variables in substitution to the traditional methods of interpolation.

Corrosion in general is a complex interaction between water and metal surfaces and materials in which the water is stored or transported. Water quality monitoring in terms of corrosion and scaling is crucial, and a key element of preventive maintenance, given the economic and health hurts caused by corrosion and scaling in water utilities. The aim of this study is to determine the best model for zoning and interpolation corrosive potential of water distribution networks. For this purpose, 61 points of Sanandaj, Iran, distribution network were sampled and using Langelier indices, we investigated corrosivity potential of drinking water. Then, we used geostatistical methods such as ordinary kriging (OK), global polynomial interpolation, local polynomial interpolation, radius-based function, and inverse distance weighted for interpolation, zoning and quality mapping. Variogram analysis of variables was performed to select appropriate models. The results of the calculation of the Langeli...

Multipoint secant and interpolation methods are effective tools for solving systems of nonlinear equations. They use quasi-Newton updates for approximating the Jacobian matrix. Owing to their ability to more completely utilize the information about the Jacobian matrix gathered at the previous iterations, these methods are especially efficient in the case of expensive functions. They are known to be local and superlinearly convergent. We combine these methods with the nonmonotone line search proposed by Li and Fukushima (2000), and study global and superlinear convergence of this combination. Results of numerical experiments are presented. They indicate that the multipoint secant and interpolation methods tend to be more robust and efficient than Broyden's method globalized in the same way.

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...

In this study, daily-observed data from 481 rain gauges were used to build a new gridded rainfall dataset for Vietnam based on the Spheremap interpolation technique. The new dataset, called Vietnam Gridded Precipitation (VnGP) Dataset has the resolution of 0.25° and covers the period 1980−2010. The validation was done for VnGP by assessing the spatial distribution, correlations, mean abosolute errors, root mean square errors with gauge observations. Results showed that VnGP had a relatively better performance compared to the datasets that used different interpolation techniques or used less number of input rain gauges. VnGP is currently available at the Data Integration and Analysis System (DIAS) managed by the

The article presents the experience in developing digital elevation models (DEMs) of Sulska Cove's territory and water area near the national park «Nyzhnosulskyy». General digital models were created using existing topographic and bathymetric maps. The processing and data visualization were performed with GIS technologies applications. DEMs present as the basis for a comprehensive study of the national park's landscape diversity as well as means of fundamental ways of its functioning and activity optimization. The required usage of 3D-modeling representation of NNP «Nyzhnosulskyy» is explained by its better visualization and interpretation of the data. In general, it allows information exchange about the changes of the environmental objects under research. At the same time, it decreases a list of applied tasks which were not possible to be solved using two dimensional data.

La Armada Nacional, en su buque ARC Providencia, cuenta con el magnetómetro G-882, con el cual se obtuvieron los datos de profundidad del lecho marino de la falla Rocha inferida en islas del Rosario, puntos que fueron representados por métodos de interpolación geoestadísticos como el IDW, Kriging, Shepard y B-Spline, que generaron los modelos digitales batimétricos correspondientes, basados en las correcciones asociadas a las mareas y alturas elipsoidales. Partiendo de ello, se evaluó que el fondo marino no influye de una forma sustancial en la bondad de ajuste del modelo generado, de ahí que fue preciso identificar los diversos cambios del relieve submarino para escoger los datos necesarios en la representación del modelo batimétrico y así realizar la selección del mejor método a través de la evaluación y comparación del error medio cuadrático (EMC), y evaluar la calidad del modelo, a través de los criterios de calidad de validación cruzada, la exactitud altimétrica y la incertidumbre total vertical. El resultado del estudio permitió establecer la confiabilidad del magnetómetro G-882, como herramienta admisible para representar las profundidades marinas.

The Artificial Neural Networks (ANNs) are mathematical models method capable of estimating non-linear response plans. The advantage of these models is to present different responses of the statistical models. Thus, the objective of this study was to develop and to test ANNs for estimating rainfall erosivity index (EI30) as a function of the geographical location for the state of Rio de Janeiro, Brazil and generating a thematic visualization map. The characteristics of latitude, longitude e altitude using ANNs were acceptable to estimating EI30 and allowing visualization of the space variability of EI30. Thus, ANN is a potential option for the estimate of climatic variables in substitution to the traditional methods of interpolation.

Groundwater is the main water resource in La Gomera (Canary Islands) where it represents almost 70% of the consumption. Since the elaboration of the preliminary works of the Insular Hydrological Plan in 1996 there has not been other estimation of the island's rainfall. For an accurate estimation of the future hydrogeological resources of the island it is necessary to know and assess carefully the recharge estimates. It is for this reason that the choice of the rainfall interpolation method is so important. In this study two different interpolation methods have been used to compare their results with the real data of the gauges and to obtain doing that the best precipitation estimate in the area. Results show the kriging with external drift to be the best interpolation method in the study area and that the use of the relationship between elevation and precipitation increase the accuracy of the model.

The article considers the question of estimating the accuracy of interpolation methods for building digital elevation models using Soviet topographic maps. The territory of the Kursk region of the Russian Federation was used as the study area, because it is located on the Central Russian Upland and characterized by the complex structure of the vertical and horizontal dissection of the relief. Contour lines automatically obtained using a Python algorithm were used as the initial elevation data to build a digital elevation model. Digital elevation models obtained by thirteen different interpolation methods in ArcGIS and Surfer software were built and analyzed. Special attention is paid to the ANUDEM method, which allows to obtain hydrologically correct digital elevation models. Recommendations for the use of one or another method of interpolation are given. The results can be useful for professionals who use topographic maps in their work and deals with the design using digital elevat...

SUNTO.-I1 lavoro si compone di due parti. Nella prima, dopo aver richiamato la generalized cross validation, vengono brevemente illustrate alcune fondamentali propriet~ di approssimazione e le pii~ significative tecniche di costruzione della relativa smoothing spline. Nella seeonda parte viene deseritto un metodo eomputazionalmente efficiente per la utilizzazione della generalized cross validation neUa regolarizzazione mediante polinomi ortogonali.

La Armada Nacional, en su buque ARC Providencia, cuenta con el magnetómetro G-882, con el cual se obtuvieron los datos de profundidad del lecho marino de la falla Rocha inferida en islas del Rosario, puntos que fueron representados por métodos de interpolación geoestadísticos como el IDW, Kriging, Shepard y B-Spline, que generaron los modelos digitales batimétricos correspondientes, basados en las correcciones asociadas a las mareas y alturas elipsoidales. Partiendo de ello, se evaluó que el fondo marino no influye de una forma sustancial en la bondad de ajuste del modelo generado, de ahí que fue preciso identificar los diversos cambios del relieve submarino para escoger los datos necesarios en la representación del modelo batimétrico y así realizar la selección del mejor método a través de la evaluación y comparación del error medio cuadrático (EMC), y evaluar la calidad del modelo, a través de los criterios de calidad de validación cruzada, la exactitud altimétrica y la incertidumbre total vertical. El resultado del estudio permitió establecer la confiabilidad del magnetómetro G-882, como herramienta admisible para representar las profundidades marinas.

Corrosion in general is a complex interaction between water and metal surfaces and materials in which the water is stored or transported. Water quality monitoring in terms of corrosion and scaling is crucial, and a key element of preventive maintenance, given the economic and health hurts caused by corrosion and scaling in water utilities. The aim of this study is to determine the best model for zoning and interpolation corrosive potential of water distribution networks. For this purpose, 61 points of Sanandaj, Iran, distribution network were sampled and using Langelier indices, we investigated corrosivity potential of drinking water. Then, we used geostatistical methods such as ordinary kriging (OK), global polynomial interpolation, local polynomial interpolation, radius-based function, and inverse distance weighted for interpolation, zoning and quality mapping. Variogram analysis of variables was performed to select appropriate models. The results of the calculation of the Langeli...

La Armada Nacional, en su buque ARC Providencia, cuenta con el magnetómetro G-882, con el cual se obtuvieron los datos de profundidad del lecho marino de la falla Rocha inferida en islas del Rosario, puntos que fueron representados por métodos de interpolación geoestadísticos como el IDW, Kriging, Shepard y B-Spline, que generaron los modelos digitales batimétricos correspondientes, basados en las correcciones asociadas a las mareas y alturas elipsoidales. Partiendo de ello, se evaluó que el fondo marino no influye de una forma sustancial en la bondad de ajuste del modelo generado, de ahí que fue preciso identificar los diversos cambios del relieve submarino para escoger los datos necesarios en la representación del modelo batimétrico y así realizar la selección del mejor método a través de la evaluación y comparación del error medio cuadrático (EMC), y evaluar la calidad del modelo, a través de los criterios de calidad de validación cruzada, la exactitud altimétrica y la incertidumbre total vertical. El resultado del estudio permitió establecer la confiabilidad del magnetómetro G-882, como herramienta admisible para representar las profundidades marinas.

Introduction Climate changes and global warming have caused changes in weather patterns and the occurrence of serious events in different regions of the earth. Therefore, it is necessary to predict destructive floods, especially in coastal areas, to announce flood warnings and control them. Satellite precipitation estimation systems often generate data with global coverage that can provide information in areas where data from other sources are not available. Satellite retrieval and estimation systems, rain gauges, and radar networks complement each other regarding coverage and rainfall monitoring capabilities. Satellite precipitation estimation systems often produce data with global coverage. One of the main advantages of satellite-based precipitation products is the ease of real-time data availability and high spatial-temporal resolution. Currently, various satellite precipitation products such as GPM, TRMM, GSMap, CMORPH, CHIRPS, etc. are available to the public. Materials and Methods In this study, the southwest coastline of Caspian Sea, Gilan province is considered as the study area and the accuracy of fou r satellite-based products namely CHIRPS, GPIM-IMERG, PERSIANN CDR, TRMM-3B42V7 is compared in order to estimate the heavy precipitation from 2017 to 2021. Estimates are performed using categorical indices including PC, CSI, BIAS, and HSS and statistical criteria of correlation coefficient (Corr) and normalized root mean square error (nRMSE). Results and Discussion Evaluations and statistical criteria are conducted by comparing estimated satellite precipitation with ground stations through definitive indicators as well as the height of each station and the average of all stations respectively. The results show th at in the PC index in eight stations, all of which are located at an altitude of fewer than 40 m above sea level and on the Caspian coast, the product IMERG scores higher than other products. The weakest performance in the PC index at the threshold of more than 5 mm belongs to TRMM and PERSIANN-CDR, which have the lowest scores jointly in eight stations. According to the results obtained from CSI, IMERG product had better performance in all stations except the Manjil station. Additionally, evaluation of the height of stations and the results obtained from this index demonstrate the fact no relationship was found between station height and product performance. In the Bias quality index, in IMERG and CHIRPS products, the bias of each station is directly related to its height, so that in higher stations, rainfall is overestimated, and vice versa in lower altitudes, the precipitations have been underestimated less than the amount of observation. Conclusion The IMERG product has performed better than the other three products in all categorical indices and correlation criteria. Finally, to evaluate and analyze heavy precipitation in the coastal strip of Gilan province and studies related to precipitat ion estimation, it is suggested that the IMERG product be used as a priority. The analysis carried out in this study, from the collection of satellite precipitation bases in estimating heavy precipitation in coastal areas, reveals the need to study and investigate this issue as much as possible in future research.

The article considers the question of estimating the accuracy of interpolation methods for building digital elevation models using Soviet topographic maps. The territory of the Kursk region of the Russian Federation was used as the study area, because it is located on the Central Russian Upland and characterized by the complex structure of the vertical and horizontal dissection of the relief. Contour lines automatically obtained using a Python algorithm were used as the initial elevation data to build a digital elevation model. Digital elevation models obtained by thirteen different interpolation methods in ArcGIS and Surfer software were built and analyzed. Special attention is paid to the ANUDEM method, which allows to obtain hydrologically correct digital elevation models. Recommendations for the use of one or another method of interpolation are given. The results can be useful for professionals who use topographic maps in their work and deals with the design using digital elevat...

This study aimed to develop artificial neural networks for the estimation of tractor fuel consumption during soil preparation, according to the adopted system. The multilayer perceptron network was chosen. As input data: the soil mechanical penetration resistance, the mobilized area by implements, the working gear and the tractor engine speed. The number of layers and neurons varied to form different architectures. The adjustment was verified based on various statistical criteria. The values estimated by the networks did not differ significantly from those obtained experimentally. The conclusion was that the networks showed adequate reliability and accuracy to predicting the fuel consumption in each tillage system, in function of the input data and this can be a useful tool for planning and management of agricultural operations.

Increasing numbers of patients request lipolytic injection therapy for aesthetic indications instead of surgical procedures. Deoxycholic acid (DC) with or without phosphatidylcholine (PC) is widely used to reduce localized fat accumulation and lipomas. DC induces inflammation and reduces the adipocytes by necrosis, and the usefulness is controversially debated.

Geoid is the fundamental geodetic infrastructure for rational use of Global Navigation Satellite System (GNSS) technology. For this reason, definition a &quot;cm geoid&quot; is an actual subject in all countries. Development of geoid modelling is based on geodetic, gravimetric and astrogeodetic techniques, which are maintained using the geopotential models produced by the combination of gravity measurements, astrogeodetic vertical deflections, GNSS/Levelling data, satellite gravity data, satellite altimetry data and the combination of these data. GNSS/Levelling geoid determination has great importance with regard to the transformation of GNSS-derived ellipsoidal height (h), into the orthometric height (H), which is used in engineering projects and determined by levelling. Instead of levelling, which is an expensive and time-consuming method, orthometric heights can be calculated by using a well-defined geoid models. These geoid models enable us to compute the geoid height (N), which...

Wireless communication networks offer subscribers to have free mobility and possibility to access information in any where at any time. Therefore, electromagnetic coverage calculation is important for wireless mobile communication systems, especially in Global System for Mobile communications (GSM) and Wireless Local Area Networks (WLAN). In this study, electromagnetic coverage calculations using neural network algorithm is presented and mobile GIS interrogation System (GIS) is improved with measurements and simulation data to make queries about electromagnetic coverage and electromagnetic pollution. The proposed GIS system realizes mapping and graphical presentation in real time including a Global Positioning System (GPS), a notebook or pocket PC and a GIS software.

Wireless communication networks offer subscribers to have free mobility and possibility to access information in any where at any time. Therefore, electromagnetic coverage calculation is important for wireless mobile communication systems, especially in Global System for Mobile communications (GSM) and Wireless Local Area Networks (WLAN). In this study, electromagnetic coverage calculations using neural network algorithm is presented and mobile GIS interrogation System (GIS) is improved with measurements and simulation data to make queries about electromagnetic coverage and electromagnetic pollution. The proposed GIS system realizes mapping and graphical presentation in real time including a Global Positioning System (GPS), a notebook or pocket PC and a GIS software.

This paper presents the results of a Two-Way Particle-Tracking Model (PTM) to detect possible crash sites of MH370. The methodology, the algorithms used and the program technical implementation are presented in detail in Eichhorn2016. In contrast to Eichhorn2016, the influence of wind on the particle drift is considered in the simulations for this paper. This paper also examines 31 additional items of debris discovered  on the east coast of Africa and Madagascar and on islands over a time period of 1 1/2 years after the first found on La Réunion on 29 July 2015. The focus of the paper is to show: 1. The influence of the leeway coefficient on the particle tracking simulation. 2. The influences on the results of simulation settings and uncertain information about the date when the debris beached. 3. The plausibility of possible classified crash locations.

This paper presents a system based on a Two-Way Particle-Tracking Model to analyze possible crash positions of flight MH370. The particle simulator includes a simple flow simulation of the debris based on a Lagrangian approach and a module to extract appropriated ocean current data from netCDF files. The influence of wind, waves, immersion depth and hydrodynamic behavior are not considered in the simulation.

Wireless communication networks offer subscribers to have free mobility and possibility to access information in any where at any time. Therefore, electromagnetic coverage calculation is important for wireless mobile communication systems, especially in Global System for Mobile communications (GSM) and Wireless Local Area Networks (WLAN). In this study, electromagnetic coverage calculations using neural network algorithm is presented and mobile GIS interrogation System (GIS) is improved with measurements and simulation data to make queries about electromagnetic coverage and electromagnetic pollution. The proposed GIS system realizes mapping and graphical presentation in real time including a Global Positioning System (GPS), a notebook or pocket PC and a GIS software. 1.

Geoid is the fundamental geodetic infrastructure for rational use of Global Navigation Satellite System (GNSS) technology. For this reason, definition a &quot;cm geoid&quot; is an actual subject in all countries. Development of geoid modelling is based on geodetic, gravimetric and astrogeodetic techniques, which are maintained using the geopotential models produced by the combination of gravity measurements, astrogeodetic vertical deflections, GNSS/Levelling data, satellite gravity data, satellite altimetry data and the combination of these data. GNSS/Levelling geoid determination has great importance with regard to the transformation of GNSS-derived ellipsoidal height (h), into the orthometric height (H), which is used in engineering projects and determined by levelling. Instead of levelling, which is an expensive and time-consuming method, orthometric heights can be calculated by using a well-defined geoid models. These geoid models enable us to compute the geoid height (N), which...

Original scientific paper Despite the modern technological advancements, contemporary methods of data gathering still rely on point samples, which means they feature a precise variable info only on specific x, y- coordinates. In order to get a continual representation of a surface necessary for research, it is necessary to approximate various data values on those surfaces which have not been sampled by using various methods of interpolation. The main aim of this research is to evaluate two different methods of interpolation based on the quality of digital terrain models used for geomorphometric analyses. For the purposes of developing and comparing these methods, a set of elevation data was attained by vectorization of contour lines from HOK. Two methods of interpolation were tested: triangulated irregular network (TIN) and ANUDEM (Topo to Raster). In order to get a more appropriate method, the research employed eight statistical parameters, various graphical representations (both t...

Background and objectives: Rainfall estimation in regions facing lack meteorological stations is critical in hydrology and meteorology studies. The problem in Iran that lacks dense weather station network, especially in the highlands, is more important. Aphrodite is a dense network that provides daily precipitation data in a resolution of 0.25*0.25 degree. But before operating network, its accuracy and uncertainty should be evaluated. About this database, few studies have been conducted in Iran and the world. This study aimed to evaluate the accuracy of Aphrodite in Golestan province at daily, monthly and yearly scales. Also its accuracy compared with two conventional interpolation techniques and for more data operation, the network was modified.
Materials and methods: In this study, 19 rain gauges and 5 synoptic stations were used to evaluate the Aphrodite network. Grid points network were selected based on the nearest point to meteorological station and data analysis was performed in daily, monthly and yearly scales. After accuracy evaluation of network, the correction factor of means ratio was employed for modification of monthly and annual rainfall network data. As well modified network data were compared with interpolation methods of Ordinary Kriging (OK) and Inverse Distance Weighting (IDW). Cross-validation technique was used for evaluation and error indices was calculated for comparison of different methods.
Results: The results of MBE in all studied scales showed that in spite of good correlation of Aphrodite and meteorological data, Aphrodite data has large underestimation error that this is higher in high rainfall areas. Obtained modification factors of the monthly and annual data vary from 1.2 to 1.8 in cold and warm months, respectively. In addition to removal underestimation error from modified network, the average of error is reduced remarkably. Also RMSE of annual rainfall data, is declined from 247 to 194 mm. considering that, network modification needs to be multiplied in a constant (correction factor) so the correlation coefficients remained unchanged. Comparison of modified data network with interpolation methods showed that modified network is more efficient than both interpolation methods. Correlation coefficients of actual and estimated data showed that the correlation of modified network with actual data is positive in all the months but in case of IDW and OK, correlation coefficients was negative in some months that represent modified network in addition to fewer error also in the detection of low and high rainfall points is more efficient than the interpolation methods.
Conclusion: This study showed that high resolution Aphrodite network has good accuracy in rainfall estimation especially in high elevation regions. Also this network is more accurate than interpolation methods of OK and IDW. But because of its underestimation error, before than operating Aphrodite data, the network must be modified.

This study aimed to evaluate the temporal change and accuracy of interpolation techniques used for spatial zonation of two groundwater quantity parameters including water table and depth to water table over 11 years. The study was conducted based on the data collected from piezometric wells of Sari-Neka Plain in Mazandaran Province, Iran. The investigated methods included a set of geostatistical approaches involving simple Kriging, ordinary Kriging, Radial Basis Function (RBF), and a deterministic interpolation method called Inverse Distance Weighting (IDW) with powers of 1 and 5. Subsequent to quality control and data normalization, the most appropriate variogram was chosen based on low RSS and high r 2 while the most suitable interpolation technique was determined regarding the cross validation, Mean Absolute Error (MAE), and Mean Bias Error (MBE). The results demonstrated that Simple Kriging was the most suitable method for zoning the depth to groundwater over the years 2001, 2006, and 2012. Meanwhile, the most suitable methods for zoning the water table included IDW with a power of 1for the year 2001, RBF for the year 2006, and IDW with a power of 5 for the year 2012. The important finding was that the interpolation methods showed a lower error for estimating water table than estimating depth to groundwater. This study also revealed a drop in water table in the study area over the 11 years' period. Meanwhile, new water table classes have been added and extended between the years 2006 and 2012 that had not existed five years earlier. The highest water table losses were observed in three points at 13m depth to water table in the middle and northern parts of the study area.

IMPLEMENTAZIONE DEL METODO GMRES Il metodo GMRES (Generalized Minimum Residual) è un metodo iterativo per la risoluzione di sistemi lineari del tipo A x = b, con A matrice generica n x n. Il metodo GMRES fa parte della famiglia dei metodi di Krylov, i quali consistono essenzialmente nella ricerca di una soluzione del tipo: x (i) =x (0) +w (i) Il vettore x (i) viene cercato sommando a un generico vettore iniziale x (0) , un vettore w (i) appartenente al sottospazio di Krylov di ordine i, capace di minimizzare l'errore rispetto alla soluzione esatta. L'errore, dipendendo dalla soluzione esatta, è una quantità incognita. Una stima dell'errore " a posteriori " , è realizzabile a partire da quantità già calcolate: come, ad esempio, nel caso della valutazione del residuo o del controllo dell'incremento. Il sottospazio di Krylov di ordine i è lo spazio generato all' i-esimo passo da: r (0) , Ar (0) ,… , A (i−1) r (0) con: r (0) = b – A x (0) residuo associato al vettore iniziale x (0). Lo spazio Ki (A;r (0)) ha dimensione al più uguale a i ≤ n. La parte iniziale dell'implementazione di un metodo di Krylov consiste nello sviluppo dell'Algoritmo di Arnoldi. Si introduce la matrice: K i =[r (0) Ar (0) ⋯ A (i−1) r (0) ] L'algoritmo di Arnoldi è una procedura iterativa analoga all'ortogonalizzazione di Gram-Schmidt. Si costruiscono così, uno dopo l'altro, i vettori q (i) costituenti la base ortonormale del sottospazio di Krylov di ordine i-esimo.

Geoid is the fundamental geodetic infrastructure for rational use of Global Navigation Satellite System (GNSS) technology. For this reason, definition a "cm geoid" is an actual subject in all countries. Development of geoid modelling is based on geodetic, gravimetric and astrogeodetic techniques, which are maintained using the geopotential models produced by the combination of gravity measurements, astrogeodetic vertical deflections, GNSS/Levelling data, satellite gravity data, satellite altimetry data and the combination of these data. GNSS/Levelling geoid determination has great importance with regard to the transformation of GNSS-derived ellipsoidal height (h), into the orthometric height (H), which is used in engineering projects and determined by levelling. Instead of levelling, which is an expensive and time-consuming method, orthometric heights can be calculated by using a well-defined geoid models. These geoid models enable us to compute the geoid height (N), which is the difference between ellipsoidal and orthometric height values (N=h-H). Then orthometric heights can be computed using these geoid heights and known ellipsoidal heights. Therefore, this will reduce the measurement work in the basic land surveying to a great extent and make economic contribution. In geoid modelling several methods can be employed. Such a geoid model has been developed for the metropolitan area of Istanbul city. In this context, Istanbul GPS Triangulation Network (IGN) and the Istanbul Levelling Network (ILN) provided reliable data, ellipsoidal and orthometric heights, respectively. This study focuses on the development of Istanbul geoid model with soft computing techniques and its comparison with conventional interpolation algorithms used for modelling. For this purpose, geoid heights in Istanbul metropolitan area have been computed by soft computing methods, namely Adaptive Network based Fuzzy Inference System (ANFIS) and Artificial Neural Networks (ANN) and modeled by twelve different interpolation methods. For computations and modelling in the study area, homogenously distributed 1005 model and 178 test points were selected. These are the common points in IGN and ILN whose latitude, longitude, ellipsoidal heights and orthometric heights are known to construct ANFIS and ANN models in Istanbul. To construct these models in model and test points, latitude and longitude are taken as inputs and geoid heights are taken as outputs. The results obtained from ANFIS and ANN methods are quite satisfactory. The model derived orthometric heights were compared with the known orthometric heights for model and test points. The standard deviation has been obtained in ANFIS as ±4.3cm and ± 4.0cm for model and test areas, respectively. On the other hand, the standard deviation in ANN model are ±4 cm and 3.1 cm, for model and test areas, respectively. In addition, conventional interpolation methods as modified Sheapard's method, radial basis function, Kriging, Nearest neighbor, minimum curvature, inverse distance to a power and local polynomial yield better results than ANFIS and ANN in model and test areas. The others interpolation methods such as polynomial regression, moving average, triangulation with linear interpolation, natural neighbor and data metrics yield worse results than ANFIS and ANN in each area.