interpolation methods

Iran is characterized by a dry and semi-arid climate. The limited irrigated arable land in and the need for increasing food production due to the upward trend in population growth, coupled with water scarcity and Iran's heavy reliance on irrigation, have led to a heightened importance of water productivity in agricultural sector. In this regard, for the purpose of identifying and understanding the agricultural potential of farmlands, the analysis and estimation of physical water productivity can be utilized. The main objective of conducting this research is to evaluate various interpolation methods and to select the most appropriate method for estimating the physical water productivity of the sugar beet. Additionally, the study aims to investigate the spatial distribution pattern of sugar beet production in its major cultivation centers across Iran.

To accomplish this research, 108 field measured data obtained from selected sugar beet farms across Iran for the agricultural year 2016-2017 were used. Data on crop yield, irrigation water, and a ten-year average effective precipitation were collected, and the water productivity index of sugar beet was calculated for the selected farms.To achieve this goal, initially, the data was analyzed using the capabilities of the SPSS software. Descriptive statistical analysis was conducted, and similar regions were classified into independent and homogeneous groups (by drawing a dendrogram). Additionally, the spatial analysis of the data was carried out using the GS+ software. Furthermore, various interpolation methods were employed to create a classification map using the Geographic Information System (GIS) software. These methods encompass algebraic methods, including weighted inverse distance, radial basis function, global polynomial, and local polynomial methods, as well as geostatistical methods like ordinary kriging, simple kriging, and universal kriging. To assess the different interpolation methods, validation methods were employed, and accuracy index values such as Mean Bias Error (MBE), Mean Absolute Relative Error (MARE), Mean Squared Error (MSE), Mean Absolute Deviation (MAD), and Root Mean Square Error (RMSE) were utilized.

The results of the present study revealed that the water productivity index for sugar beet ranged from 2.60 to 13.11 kg/m³, with an average of 6.30 kg/m³. Despite the high standard deviation, the findings indicate a significant potential and high capacity for improving water productivity and crop performance in the sugar beet production hubs in Iran. Among the examined interpolation methods, the Radial Basis Function method with a completely regular spline model (CRS) exhibited acceptable accuracy (MBE=0.009) for generating the water productivity zoning map. The analysis of the generated map suggested that the western regions of the country, especially Kermanshah province, have higher water productivity index values compared to other parts of the country, making them more suitable for sugar beet cultivation. Furthermore, cluster analysis results for influential factors such as variety type, soil salinity, and irrigation water salinity indicated that within the study area, about 5% of the potential sugar beet cultivation areas could be divided into 23 distinct clusters. The minimum and maximum water productivity index were observed in cluster 11 (2.64 kg/m³) and cluster 3 (11.025 kg/m³), respectively.
Based on the low level of correlation coefficient according to the results of the Pearson correlation test, the physical productivity of water utilization can be influenced by various factors other than precipitation and climate parameters. These factors include salinity of water, soil salinity, total irrigation water, average effective precipitation (over a ten-year period), and crop yield. It can be concluded that, in addition to precipitation and climatic parameters, other constant factors including management factors have an impact on improving the physical efficiency of water utilization.

Given the high water consumption in agricultural sector and the need for increased production in cultivated lands, evaluating the water produvtivity of high-water-demand crops such as sugar beet in Iran is essential. Understanding its current state and obtaining comprehensive information from fields, as well as monitoring cultivated fields, are necessary for decision-making and macro-level planning to enhance and improve water productivity of sugar beet cultivation in Iran. However, due to the extensive cultivation area, costs, limited resources, and time constraints, this task is challenging and often unfeasible. To address this, the potential of interpolation tools can be utilized. These tools have the capability to extrapolate point-based information to spatial information (area-wide). Results have shown that the highest and lowest error values were associated with the kriging interpolation method and the radial basis function (completely regularized spline) method, respectively, for creating zoning maps. In conclusion, it can be stated that through interpolation, if there is a strong correlation between the data, a better understanding of the spatial distribution of water productivity can be achieved in the study area.

This study was conducted with the aim of understanding the temporal and spatial variations of groundwater levels in the Meshgin Plain Aquifer, located in Ardabil Province, with the application of spatial statistics and temporal regression and using groundwater depth data on an annual scale from 2007 to 2016. In order to achieve the optimal method of zoning spatial changes in groundwater level, a comparison of different interpolation methods including Radial Basis Functions (RBFs), Inverse Distance Weighted (IDW), and Kriging (KRG) based on cross-validation was used. In addition, regression relationships between groundwater level and the study years were fitted to determine how the data series ascended or descended. A comparison of interpolation methods based on cross-validation showed that the root mean square error (RMSE) of RBF, IDW, and KRG methods were 21.98, 22.85, 22.57 in 2007; and 23.45, 27.88, 26.25 in 2016, respectively. Therefore, the RBF method with the lowest estimation error due to the power applied to scattered data and low sampling points in both years was selected as the optimal method for estimation of groundwater level in the aquifer. The weighted average of groundwater table loss was calculated as equal to nine meters. Furthermore, the iso-decline map of groundwater level was indicative of a decrease in groundwater level in the western half and its increase in the eastern half of the aquifer which is related to anthropogenic factors (withdrawal of groundwater in agricultural lands). In general, it can be stated that the accuracy and efficiency of interpolation methods depend on the region and data characteristics. In the case of Meshgin Plain Aquifer, the discharge factor has been more effective than the recharge factor in annual fluctuations of groundwater level. Accordingly, it is necessary to establish a balance between the pattern of cultivation and irrigation and the pattern of spatio-temporal variations of groundwater level in managerial plans for Meshgin Plain Aquifer.

It is important to be aware of the spatial dependence structure of different soil properties in natural resources to achieve more production and better management. This study aimed to determine the determining factors controlling spatial variations of macronutrient (NPK) by geostatistics. In the present study, 150 surface soil samples were collected from forests of northern Iran and some variables, including nitrogen, phosphorus and potassium were measured. The half-variance was selected to determine the spatial correlation and the best fitted models on half-variance for variables of nitrogen, phosphorus and potassium were spherical. Also, the effective range for these variables was obtained, which was equal to 530/80, 720/20 and 520/80 meters, respectively. Interpolation was performed using traditional Ordinary Kriging (OK), the inverse distance weighting (IDW) and radial basis function (RBF) techniques using ARC GIS and GS+ software and the accuracy of the distribution map of these variables was calculated using mean absolute error (MAE) and Root Mean Square Error (RMSE). According to the results, the OK technique for the variables of nitrogen, phosphorus and potassium variables was considered as the best interpolation method for estimating the variables in areas where sampling was not performed, because it had the highest accuracy and lowest error.

Water resource deficiency and the necessity of sustainable production in irrigated lands have attracted much attention to water productivity issues. In this regard, analysis, estimation, and preparation of water productivity map are necessary as an influential factor to recognize cultivation potential in irrigated lands. The aim of this study was to select a proper interpolation method for water productivity and investigate spatial changes in water productivity in Iranian wheat production centers. In this research, 241 field data were used, of which range of water productivity (irrigation water + effective precipitation) was estimated between 0.3 to 2.58 kg.m-3 with the average of 0.79 kg m-3, in 2016-2017 season. Interpolation methods used included Ordinary Kriging, Inverse Distance Method (IDW), and Radial Basis Function (RBF). Cross Validation technic was applied to evaluate methods by statistical measures such as Root Mean Square Error (RMSE), Mean Bias Error (MBE), and Mean Absolute Relative Error (MARE). Interpolation methods evaluation showed that between available procedures, typical Kriging method with exponential semi-variogram model had the most proper condition to prepare wheat water productivity zoning map. The results of the spatial analysis of water productivity confirmed that geostatistics could be used with acceptable accuracy (MBE=0.005) to provide water productivity mapping. Results of Cluster analysis of the effective factors (salinity of irrigation water, soil salinity, and crop cultivar) on wheat water productivity index showed that the areas suitable for wheat cultivation were separated into 13 independent groups (at the 5 percent level), such that the highest and lowest mean water productivity of wheat were observed in group 5 (Mean = 0.84 kg.m-3) and group 10 (Mean = 0.41 kg.m-3), respectively.

Drought is recognized as a slow, creeping phenomenon that can accelerates the expansion of desertification in different regions especially in arid and semi-arid area with its effect on the agricultural sectors, water resources and vegetation cover. Positioning of Iran in the world arid and semi-arid belt is exposed to drought and water crisis and desertification. Drought monitoring and zoning with the goal of planning and water resources management are very important in different area especially in arid and semi-arid regions. One of the methods for drought study is monitoring and mapping of drought using meteorological indices and Geographic Information System techniques. In order to investigate and drought monitoring in present research during the period of 29 years (1989 to 2017) in Qoum-Kahak study region we used annual rainfall data from four stations (i.e. Qoume, Kahak, Koohsefid and Janatabad) which are located inside and around the Qoume-Kahak catchment. Then we applied meteorological indices such as Standard of Precipitation Index (SPI), Percent of Normal Index (PNi), Deciles Index (DI), Chinese Z Index (CZI) and Z-Score Index (ZSI) for drought monitoring during the study period. Afterward for drought mapping, four interpolation methods included Simple Kriging (SK), Ordinary Kriging (OK), Inverse Distance Weighting (IDW) and Radial Basis Functions (RBF) were used and compared. After determination of best method in each year, yearly drought map were produced based on the best interpolation methods in ArcGIS software environment. According to the result of meteorological indices the near-normal class occurred more than other classes in study stations. SPI results indicated that Jannatabad and Kahak stations have the highest and lowest frequency of extremely dry class during the study period, respectively. The most extremely dry class with the SPI of -2.35 was occurred in Janatabad station in the year of 1997-98. Based on the results of PNI and ZSI indexes there was no occurred extremely dry class in all stations. The result of PNI index indicated that Koohsefid station has the highest frequency of very dry class between all stations. According to the result of CZI index the extremely dry class was occurred only for Kahak and Janatabad stations in the water years of 2016-2017 and 1997-98 respectively. Extremely wet class was occurred also for Kahak and Janatabad stations during the water years of 2009-2010 and 1992-1993 respectively. The results of DI index illustrated that the class of very much below normal was occurred in Qoume and Koohsefid stations 4 times and in Kahak and Janatabad stations 3 times during the study period. We applied geostatistical analyst tools in ArcGIS software to produce zoning maps for rainfall and drought. Its result showed that ordinary kriging with RMSE of 28 mm is the best method to create rainfall map. Accordingly mean annual rainfall was 136 mm/year during the study period. We selected SPI index for drought monitoring and zoning because of according to the results of all meteorological indices,only for this index the extremely and severely drought classes for all stations have occurred Simultaneous with the minimal rainfall during the study period. Afterward we compared different interpolation methods to produce drought zoning maps for each year during the study period. Based on the results of RMSE ordinary kriging and simple kriging were the best methods for most years. The results of all meteorological indices suggested that in all stations the near-normal class has the most frequency during the study period. According to the results of SPI and CZI indices, the highest (7 years) and lowest (3 years) number of drought were occurred in Kahak and Jannatabad stations, respectively. While according to PN index the highest (9 years) and lowest (3 years) number of drought were observed in Qoum and Jannatabad stations, respectively. Also the results of PN index illustrated that there was no wet period during the study period. According to the ZSI Index, the extremely dry class did not occurred in the region and the ZSI results about the frequency of extremely wet class was similar to the SPI results. The results of drought zoning indicated that in the years of 1990, 1995 and 1997, most of the region has been in a state of extremely to slightly drought. In the years 2010 and 2017, slight to sever drought classes were occurred in most parts of the study area and the slight wet class was observed in the eastern part of region. While during the years of 1992, 1996 and 2009 whole of the study area has experienced moderate and severe wet conditions. In the year of 2011, half of the study area which is located in the eastern part of the region has been in a state of moderate wet condition.

As one of the most important natural disasters “drought” is a phenomenon, which has an important impact on water resources, natural ecosystems and human societies economic, social, political and cultural from the point of view. Therefore, it is essential and inevitable to create a proper management system based on the recognition of the drought characteristics including frequency, severity, continuity and spatial extend, and its monitoring to reduce the damages and its consequences. In this study, with the aim of better understanding of droughts in Jazmorian watershed and recognizing dry and wet periods, eight special characteristics of drought were studied using the SPI and CZI Meteorological drought indices and Geographic Information System (GIS). For this the rainfall data of 24 rain gauge stations were used over a 30year period of 1983-2013 and the drought condition were assessed. In order to interpolate and prepare the most suitable zoning map for the studied features, Kriging, Co-kriging and Inverse Distance Weighted (IDW) methods were selected and compared. To select the appropriate model for fitting on the experimental variogram, the ratio of Sill to Nugget was used. To choose the right interpolation method, the mean absolute error (MAE), mean bias error (MBE), root mean square error (RMSE), and general standard deviation (GSD) were calculated then selected with lower values indicating stronger spatial structures. The results showed that in studying the majority of drought features, the co-kriging method was better than the other two methods, and the SPI index evaluated the drought condition in more detail than the CZI index. On the other hand, the Jazmourian watershed, especially in the eastern part of the province of Sistan- Baluchestan, has a relatively high sensitivity to the drought phenomenon, in which increases the frequency, continuity and severity of droughts to the eastern and southeast regions, and affect the inhabitants of these areas heavily by the consequences of the drought. Therefore, it is suggested that in macro planning and drought management plans for Jazmorian watershed, studying drought in different monthly and annual time scales and providing a suitable strategy for the management of drought in the highlands and plains areas separately.

The aim of the present study was to evaluate the spatial and temporal changes of NPP in different biomes of Isfahan province from 2000 to 2014 and their response to climatic factors. For this purpose, the NPP data of the MODIS satellite were collected and the map of climatic variables was produced using various interpolation methods. The investigation of the spatial and temporal variations of NPP was carried out by combining these data. The results indicated that the spatial distribution of annual NPP changed significantly, with higher NPP in the west and southwest and the lower NPP in the east of the province. The mean annual NPP values for rangeland, forest, desert, Haloxylon forest and agricultural lands were 16.7, 58.77, 1.66, 5.76 and 51.43 grCm-2yr-1, respectively. The temporal changes of the NPP annual average during 2000-2014 had no significant trend. In 82.14% of the total area, the slope of changes was less than zero and in 17.86%, the value of this index was more than zero. The highest and lowest changes in the slope were observed in the biomes of forest and desert, respectively. The amounts of NPP of biomes in rangeland, desert and Haloxylon forest were influenced by precipitation, while the temperature was the main controlling factor in the forest and agriculture biomes

Groundwater is the main source of agricultural, drinking and industrial needs, especially in arid and semi-arid regions. The aim of this study was to investigate the relationship between groundwater quality and water level in Mashhad Plain. In this study, qualitative information of 41 underground water piezometer wells for months of feeding and evacuation was investigated in 2001-2015. The GS software and the GIS environment were used to map and Zonation using different interpolation methods. The results showed that the ordinary Kriging method with the lowest RMSe and the highest R2 had the best estimate in the region. The study of the predominant class of groundwater in Mashhad plain was classified as "good" and "moderate" for agricultural use, with Wilcox, C2-S1 and C3-S1 charts for drinking purposes. The results of the review of water quality parameters showed that, other than Mg, the rest of the parameters had incremental changes over the years, and among these parameters, electrical conductivity (EC) and the total dissolved solids (TDS) had a more significant increase, which reduced water quality during this It's been years. The average correlation between the spatial variation of the surface of the stand and the EC is -0.35 and -0.45, which indicates increased salinity by decreasing the aquifer's water level. The results of this research indicate that the main cause of water quality decline in Mashhad plain was the existence of industrial and residential areas and agricultural land development.

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.
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.
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.
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.

Geostatistical approaches have great importance because they include spatial correlation of geographic data. Present study evaluated the efficiency of geostatistical techniques and demonstrated their capabilities in studying the soil variables(soil texture (sand percent), EC and So4-2) in the important plant community of Nitraria schoberi in Meighan desert, Arak. A regular grid on the map comprising rectangular cells was designed and situated over the experimental area with 98 points for vegetation type. The grid was laid out in the field using the global positioning system. Soil samples were taken between 0-20 and 20-100 cm layers for each point. Analysis using the best view at semivariogram model were applied to select the Gaussian models of soil characteristics with R2 higher than 0.95. Among ordinary Kriging, simple Kriging and Inverse distance weighting methods, ordinary kriging method showed the best cross-validation criteria (mean square error and average error) and had higher prediction accuracy than others. Finally, spatial estimates of the soil characteristics were performed using ordinary kriging.

Rainfall erosivity is usually represented by indices based on rainfall characteristics. So far، many rainfall erosivity indices have been developed، out of which the R index (EI30 in the model of RUSLE) is the most acceptable one. By calculating the EI30 in various points، erosivity maps can be produced for the country، some provinces or any other parts of the country. In this study، erosivity map for Lorestan Province was produced using this index. In order to estimate this index for regions lacking data from recording rain gauges، regression analysis was used. Thus the EI30 index and a few easily obtainable rainfall erosivity indices were calculated for 13 recording rain gauges with long term and intensive rainfall data. A regression analysis was then carried out between EI30 index and other indices. The best regression equation was established using Modified Fournier index (MF) with determination coefficient and standard error of estimate of 0. 955 and 112، respectively. To mapping rainfall erosivity، all of rain gauges (both having rainfall intensity and daily rainfall depth records) existed in the province and that of the surrounding regions were then assessed، and 61 rain gauges having more than 15 year daily rainfall data were selected. The EI30 were then estimated for the selected ones using the regression equation. Mean، Maximum، Minimum and coefficient of variation of the rain gauges were 594. 94، 2257. 3، 98. 54 Mj-mm-ha-1hr-1year-1 and 66. 38 percent. For converting point erosivity data to a map، a number of common interpolation methods were assessed and in order to select the suitable one، cross- validatin method were used. from the interpolation methods، Co Kriging was found to be the most suitable in terms of low error measures based on cross validation. Therefore rainfall erosivity map were produced for Lorestan Province using Co Kriging.