Interpolation Methods Research Papers

Assessment of Geostatistical Methods for Determining Distribution Patterns of Groundwater Resources in Sari-Neka Coastal Plain, Northern Iran

by Environmental Resources Research

2017, Environmental Resources Research

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... more

Figure 1. The location of the study area The Sari-Neka Plain is an area of 1607 km? located at Mazandaran Province, Iran,

Interpolation methods unbiasedness of kriging is very important due to removal of systematic errors in such a system (Kalyrad et al., 2013). Kriging is based on the notion that the parameter Kriging The main purpose of calculating the variogram is to evaluate inconsistency of variables to spatial and temporal changes. In order to calculate a variogram, it is necessary to first calculate the average squared difference of points situated by a distance A and then plot it against A (Hassani pak, 2010). Kriging is an unbiased estimator providing the minimum variance of estimation. The necessary to first calculate the average Variogram

The spatial variation of water level over the years 2001 and 2012 are shown in Figures 3 and 4. Figure 3 illustrates a higher water level in the middle part than the eastern and western parts of the plain while forming a U shape from north to south. However, as

Figure 4. The spatial variations in groundwater table in 2012 depicted in Figure 4, groundwater level reduces from east to west and from south to north. It is worth mentioning that regarding DEM and Figure 4, ground water level follows the topography of the plain. The trend of groundwater level and the Z-axis values indicates the lack of rainfall, aquifer over-exploitation and distribution of spatial patterns of water.

Figure 6. The RBF method for water table in 2006 Figure 5. The IDW method with power of 1 for water table in 2002

Fig. 7 The IDW method with power of | for water table in 2012

Table 1. Best-fitted variogram models of water table and depth for the years 2001, 2006 and 2012 and their parameters Based on the water table and the depth to groundwater in Table 1, the spherical model was chosen as the best theoretical model while the linear model provided the best fit with data in all the three years of experiment. The ratio of nugget effect to sill (C/Co+C) was used to assess the strength of a variable. The ratio ranges between 0 and | indicating the worst to best scale. The ratio also represents how much of the total variability may be explained by he nugget effect (Deutsch and Journel, 1998). If the value is less than 0.5, the variable has a weak spatial structure telling hat geostatistical methods will not provide useful results (Hamidianpour et al., 2013). In this study, groundwater level showed a robust spatial structure in three time steps. Although, some other structures of water level indicated a higher value of the nugget effect to sill ratio in the spherical structure, the spherical model was chosen as the best model due to the higher r’ and lower RSS in three time steps. In terms of water depth in the years 2001, 2006 and 2012, the linear model was preferred due to the higher 12 and lower RSS. However, according to the value 0 of the ratio C/Cy+C, applying the geostatistical methods did not provide a useful outcome.

that of the measured sample. However, the IDW method is highly sensitive to the value of power in which increase in the weighting power causes the prediction value to approach the value of the nearest sample Xie et al. 2011). There were three main purposes in this research in order to generate interpolated maps of groundwater able for the coastal plain: (1) determining he spatial distribution, (11) determining the emporal distribution, and (iii) determining he alternations in groundwater table in accordance with over-exploitation of groundwater resources. Interpolation accuracy is a relative concept depending on _ criteria and interpolation objectives. According to Table 7, ordinary kriging was selected as the best method for interpolating depth to groundwater in all the three time steps 2001, 2006 and 2012. Moreover, the value of MAE was calculated 14.52 in all time steps. Therefore, the models of depth to groundwater were used to determine the spatial and temporal distribution patterns of water during the years 2001 to 2012 due to the lack of strong spatial structure of the water table. The best methods to interpolate water table in different years were chosen as follows: for 2001, the IDW method with power | and the least value of MAE (1.63); for 2006, the RBF method with the least value of MAE (2.19), and for 2012, the IDW method with power 1 and MAE value of 2.46. The obtained results in Table 7 reveal that the greater the power of the IDW method, the lower is the accuracy of the results. The outcomes are in line with findings of Xie et al (2011) expressing that increase in the power of IDW method enhances the value of RMSE. The IDW and RBF interpolators predicted exactly similar values to the measured values (Xie et al., 2011). The RBF approach may predict the values higher than the maximum and less than the minimum measured values while the predicted minimum and maximum values of the IDW method exactly follows

Note: The first and last classes were considered the same in order to unify the three periods. Table 4. Area and percentage for different classes of water table

Table 5. Mean annual precipitation of Sari-Neka Plain able accelerated from 2006 to 2012 even hough the precipitation increased almost 110 mm over the same period. In 2002, the class 2.44-3.28 m of the water table covered he largest area (402.54 km’) occupying almost a quarter of the size of the aquifer. In 2006, the class 1.85-2.44 m of the water able occupied the largest area (328.51 km’) covering 20.44% of the aquifer. In 2012, he same class in 2006 covered the biggest Results in Table 4 show no water table classes 1.16, 0.25, 1.45, and 1.16 m in the study area in the year 2001. However, these classes were present in the years 2006 and 2012 indicating a drop in water table. Moreover, the area of aforementioned classes doubled between 2006 and 2012 showing an ongoing utilization of groundwater resources. Meanwhile, as shown in Table 5, the loss of groundwater

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Soft Computing and Conventional Interpolation Methods in Geoid Modelling: A Case Study in Istanbul

by Muge MUGE and

2017, JpGU-AGU Joint Meeting 2017

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... more

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.

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Recepta na dane odstające

by Viktor Lishchuk

PL O odpornej właściwości metody interpolacyjnej ruchomej powierzchni. Metoda interpolacyjna ruchomej powierzchni realizowana metodą najmniejszych kwadratów nie jest odporna na dane odstające. Wpływ danych odstających można... more

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Interpolation Methods

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