Spatiotemporal Distribution Analysis of Rainfall in the Harirud-Murghab River Basin, Afghanistan

Rain is one of the elements that make up the climate. Rainfall in an area can be influenced by many factors. The rainfall data at a point in the rain station only represents the area at that point. Interpolation is done to present the rainfall data so that it can be easily understood. This study was conducted to determine the characteristics of the spatial distribution of rain in Jember Regency using the Thiessen Polygon and Inverse Distance Weigthed (IDW) methods and to determine the best method between the two. The data used in this study are the annual average rainfall data that has been obtained Perusahaan Daerah Perkebunan (PDP) Kahyangan Jember, Dinas PUPR Sumber Daya Air, and PTPN XII. Data processing is carried out using the ArcGIS program, and then a rainfall distribution map is made. The RMSE (Root Mean Square Error) calculation was carried out using the IDW method using 5 power levels, namely 0.5, 1, 2, 3, and 4. The results of calculations using the Thiessen polygon method produce a characteristic distribution of rainfall in which the rainfall decreases with the area moving south towards the coast. The Inverse Distance Weighted (IDW) method shows diversity with the lowest value being 94.71 mm and the highest being 406.92 mm per year. The power value 4 shows the RMSE calculation result of 0.00026 which is the lowest value.

Comparison of methods to estimate areal means of short duration rainfalls in small catchments, using rain gauge and radar data

Accurate assessment of spatial and temporal precipitation is crucial for simulating hydrological processes in basins, but is challenging due to insufficient rain gauges. Our study aims to analyze different precipitation interpolation schemes and their performances in runoff simulation during light and heavy rain periods. In particular, combinations of different interpolation estimates are explored and their performances in runoff simulation are discussed. The study was carried out in the Pengxi River basin of the Three Gorges Basin. Precipitation data from 16 rain gauges were interpolated using the Thiessen Polygon (TP), Inverse Distance Weighted (IDW), and Co-Kriging (CK) methods. Results showed that streamflow predictions employing CK inputs demonstrated the best performance in the whole process, in terms of the Nash–Sutcliffe Coefficient (NSE), the coefficient of determination (R2), and the Root Mean Square Error (RMSE) indices. The TP, IDW, and CK methods showed good performance in the heavy rain period but poor performance in the light rain period compared with the default method (least sophisticated nearest neighbor technique) in Soil and Water Assessment Tool (SWAT). Furthermore, the correlation between the dynamic weight of one method and its performance during runoff simulation followed a parabolic function. The combination of CK and TP achieved a better performance in decreasing the largest and lowest absolute errors compared to any single method, but the IDW method outperformed all methods in terms of the median absolute error. However, it is clear from our findings that interpolation methods should be chosen depending on the amount of precipitation, adaptability of the method, and accuracy of the estimate in different rain periods.

In order to incorporate the influence of collected in-situ data, the spatial correlation between the data and the foundation needs to be explored. However, risk and uncertainty are the characteristics of the soil that cannot be eliminated. Statistical information of the soil property can be estimated from available field data obtained from testing at discrete locations across the site. In this research, several well-established spatial interpolation methods like ordinary kriging (OK), simple kriging (SK), inverse distance weight (IDW), spline, natural neighbor (NaN) and universal kriging (UK) were incorporated to evaluate the best method. Six CPT (Cone penetration test) (Tip Resistance data) cases (Case 1, 3, 4, 5, 6 and 9) and four soil boring (SU and SPT data) cases (Case 2, 7 ,8 and 10) were investigated in this research. According to the results, for Case 1, 2, 3, 4, 7, 9 and 10, if the first priority is given to bias factor followed by coefficient of variation (COV) and root mean square error (RMSE), the best three spatial interpolation techniques are IDW, OK and SK sequentially, based on their performance. For Case 5 (CPT data), the best three spatial interpolation techniques are OK, IDW and SK sequentially. For Case 6 (CPT data), the best three spatial interpolation techniques are SK, IDW and OK sequentially. For Case 8 (Soil Boring data), the best three spatial interpolation techniques are IDW, SK and OK sequentially. It can be concluded that the average COV of bias factor λ (for qc, SU and SPT data) for different spatial interpolation methods are less than the average measured COV of predicted average tip resistance and the measured COV of undrained shear strength and SPT (standard penetration test).

Rainfall stations in small and medium-sized river basins in China are sparsely distributed and unevenly spaced, resulting in insufficient spatial representativeness of precipitation data and posing challenges to the accuracy of flood forecasting. Spatial interpolation methods for rainfall data are a key tool for bridging the gap between discrete rainfall station data and continuous surface rainfall data; however, their applicability in flood forecasting for small and medium-sized river basins with sparse rainfall stations requires further investigation. Taking the Hezikou basin as the study area and focusing on the Liuxihe model, this study analyzes the distribution characteristics of the seven rainfall stations in the basin and the interpolation effectiveness of the original Thiessen Polygon Interpolation (THI) method in the model. It compares and discusses the applicability of the THI, the Inverse Distance Weighting (IDW) method, and the Trend Surface Interpolation (TSI) method in flood forecasting for this basin. Different rainfall station distribution scenarios (full coverage, upstream only, downstream only, single rainfall station) were set up to study the performance differences in each method under extremely sparse conditions. The results indicate that, under the sparse condition of only 0.0068 rainfall stations per square kilometer in the Hezikou basin, IDW interpolation yields the best flood forecasting results, with model Nash–Sutcliffe Efficiency (NSE) values all above 0.85, Kling–Gupta Efficiency (KGE) values exceeded 0.78, and the Peak Relative Error (PRE) was controlled within 0.09, significantly outperforming THI and TSI. Additionally, as rainfall station sparsity increased, IDW exhibited the smallest decline in performance, showing a weak negative correlation (p ≤ 0.05) between prediction performance and rainfall station sparsity, demonstrating stronger adaptability to sparse scenarios. When station information is extremely limited, IDW performs more stably than THI and TSI in terms of certainty coefficients (NSE, KGE) and flood peak error control. The Inverse Distance Weighting method (IDW) can provide reliable rainfall spatial interpolation results for flood forecasting in small and medium-sized basins with sparse rainfall stations.

The water table is an important piece of data for hydrogeological studies, particularly as input data to groundwater simulation models. Since the accuracy of groundwater simulation models significantly depends on input data, this study highlights the application of fuzzy kriging to improve the accuracy of water table interpolation. The results of the fuzzy kriging approach are compared with common methods in water table interpolation like ordinary kriging, inverse distance weighting (IDW), and Thiessen polygon methods to justify the suitability of the fuzzy kriging. The Gilan and Zanjan plains, located in the northwest of Iran, are used as case study areas. The Gilan Plain is characterized by a dense and regular piezometric network and gentle hydraulic gradient. The longitudinal plain of Zanjan has a sparse and irregular piezometric network and steep hydraulic gradient. Since these plains have different piezometric network configurations, the sensitivity of the interpolation methods to the monitoring point configuration is analyzed. The cross-validation method is employed to validate the accuracy of interpolation methods in water table interpolation. In control points, the average of root-mean-square errors associated with groundwater water table values estimated using fuzzy kriging, ordinary kriging, IDW, and Thiessen polygon methods are obtained to be respectively 1.36, 1.93, 3.49, and 9.10 in the Gilan Plain and 13.60, 22.86, 32.30, and 59.81 in the Zanjan Plain. The results indicate that the fuzzy kriging technique has greater precision in comparison with other methods, especially under the conditions of the sparse piezometric network and steep hydraulic gradient. The results also demonstrate that the used methods generally have higher accuracy in the Gilan Plain with a regular piezometric network than in the Zanjan Plain. Furthermore, Thiessen polygon, IDW, and ordinary kriging methods overestimated water table in comparison with the fuzzy kriging method in our cases. This overestimation may cause large error values in subsequent calculations such as water budget and aquifer storage which play a major role in the appropriate management of water resources.

Although water availability for paddy production in Mahaweli System H is abundant, paddy yield is lower in Nochchiyagama (278 km2), chosen for soil assessment. Paddy yield data were used to identify the low-yielding division using the area-weighted average. Twenty-five random locations were generated, and soil samples were collected for pH, soil conductivity (EC), salinity, and total dissolved solids (TDS) analysis. ArcGIS software was used to create spatial distribution maps and related geostatistical analyses for each parameter. Vector files were created with their associated properties, and thematic maps were generated using spatial interpolation techniques, such as universal kriging (UK), ordinary kriging (OK), and inverse distance weighted (IDW) methods of interpolation techniques to identify the best interpolation method for soil chemical parameters mapping. The entire Nochchiyagama land was observed to have a slightly acidic pH (5.6-5.9) range that may have affected rice crop growth due to nutrient mobility and uptake issues. The spatial interpolation evaluation suggests that at least two-thirds of the area observed for lower TDS levels (591-654 mg/L) is potentially unsafe paddy production. Elevated levels of EC (3.1-7.24 dS/m) along with TDS may lead to physiological drought due to interferences in ion uptake. In overall, spatial interpolation evaluation indicators suggest that the UK method was observed with a lower mean relative error (MRE) than the other two interpolations. However, EC distribution showed low MRE in both IDW and OK interpolation techniques. The IDW method was observed to have a lower RMSE (Root mean square error). The UK spatial interpolation performed better for TDS and salinity predictions than other methods. This study found consistent regional differences in low paddy yields in Mahaweli system H using the UK method for analyzing soil chemical parameters. 
 Keywords: Electrical conductivity, Interpolation errors, Salinity, Spatial interpolation

Evapotranspiration estimations are not common in developing countries though most of them have water scarcities for agricultural purposes. Therefore, it is essential to estimate the rates of evapotranspiration based on the available climatic parameters. Proper estimations of evapotranspiration are unavailable to Sri Lanka, even though the country has a significant agricultural contribution to its economy. Therefore, the Shuttleworth–Wallace (S-W) model, a process-based two-source potential evapotranspiration (PET) model, is implemented to simulate the spatiotemporal distribution of PET, evaporation from soil (ETs), and transpiration from vegetation canopy (ETc) across the total landmass of Sri Lanka. The country was divided into a grid with 6 k m × 6 k m cells. The meteorological data, including rainfall, temperature, relative humidity, wind speed, net solar radiation, and pan evaporation, for 14 meteorological stations were used in this analysis. They were interpolated using Inverse Distance Weighting (IDW), Universal kriging, and Thiessen polygon methods as appropriate so that the generated thematic layers were fairly closer to reality. Normalized Difference Vegetation Index (NDVI) and soil moisture data were retrieved from publicly available online domains, while the threshold values of vegetation parameters were taken from the literature. Notwithstanding many approximations and uncertainties associated with the input data, the implemented model displayed an adequate ability to capture the spatiotemporal distribution of PET and its components. A comparison between predicted PET and recorded pan evaporations resulted in a root mean square error (RMSE) of 0.75 mm/day. The model showed high sensitivity to Leaf Area Index (LAI). The model revealed that both spatial and temporal distribution of PET is highly correlated with the incoming solar radiation fluxes and affected by the rainfall seasons and cultivation patterns. The model predicted PET values accounted for 80–90% and 40–60% loss of annual mean rainfall, respectively, in the drier and wetter parts of the country. The model predicted a 0.65 ratio of annual transpiration to annual evapotranspiration.

In order to incorporate the influence of collected in-situ data, the spatial correlation between the data and the foundation needs to be explored. Statistical information of the soil property can be estimated from available field data obtained from testing at discrete locations across the site. In this research, several well-established spatial interpolation methods like ordinary kriging (OK), simple kriging (SK), inverse distance weight (IDW), spline, natural neighbor (NaN), and universal kriging (UK) were incorporated to evaluate the best method for generating synthetic cone penetration test (CPT) data. To remove the spikes, continuous five points averaging was done to generate the smoothed tip resistance. For the analysis, the spatial interpolation was performed in each foot (depth wise). Six CPT cases were investigated in this study. According to the results, four out of six cases, if the first priority is given to bias factor followed by coefficient of variation (COV) and root mean square error (RMSE), the best three spatial interpolation techniques are IDW, OK, and SK sequentially, based on their performance. For the other two cases, in one case, the best three spatial interpolation techniques are OK, IDW, and SK, sequentially, and the other case shows SK, IDW, and OK sequentially are the best three spatial interpolation techniques.

Rainfall is one of the frequent data used in weather-related studies. Sometimes the data have missing information that needs the treatment to make sure the data can be useful, complete and reliable. There are many methods in treating missing data suggested by previous studies. The best selected method to estimate missing rainfall data in different regions may vary depending on the rainfall pattern and spatial distribution. Therefore, this paper discussed and compared 3 different methods in missing data treatment. The selected methods are Expectation Maximization (EM), Inverse Distance Weighted (IDW) and Multiple Imputation (MI). After analysis, the best method is IDW based on root mean square error (RMSE), mean absolute error (MAE), correlation coefficient (r) and percentage of error (% of error) values. The IDW method has RMSE, MAE values and the lowest % of error values. In addition, the r value of IDW method is highest compared to EM and MI method. MI method recorded the highest values of RMSE, MAE and % of error with the lowest r value that proved MI method is the least accurate method to use in missing data treatment. After all methods were implemented, it proved that the IDW method is the best way to treat missing data because the analysis shows monthly rainfall distribution for 4 treatment stations in line to 3 missing data stations compared to EM and MI methods.

The cone penetration test (CPT) has been widely used in many geotechnical engineering applications, including soil identification and classification, and evaluation of different soil properties. However, the uncertainties associated with site variation are typical characteristics of subsurface soil conditions that cannot be ignored. Therefore, the effect of site variability on the correlated soil properties from collected field data, such as CPT data, obtained from discrete locations across the site needs to be evaluated. In this study, six well-established spatial interpolation techniques — ordinary kriging (OK), simple kriging (SK), universal kriging (UK), inverse distance weight (IDW), spline, and natural neighbor (NaN) — were investigated to evaluate the best interpolation method for incorporating site variability. Six CPT test sites were used to evaluate the performance of these spatial interpretation methods. For each site, CPT profiles at specified locations were generated using the different interpolation techniques, and the generated CPT profiles were compared with the measured CPT profiles. The best-fit line of measured versus predicted cone tip resistance (qc) values, mean bias factor (λ), coefficient of variation (COV), and root mean square error (RMSE) were calculated for each CPT profile and used as a criteria for evaluating the different spatial interpolation methods. The results of this study demonstrated the ability of these spatial interpolation methods for generating CPT profiles with good accuracy. The slope of best-fit line of measured versus predicted qc ranges from 0.93 to 0.95, the mean of λ ranges from 0.90 to 0.98, and the COV ranges from 0.34 to 0.53. The IDW, OK, and SK showed the best spatial interpolation methods (in order) for four out of the six CPT sites. For site 4, OK, IDW, and SK showed the best spatial interpolation methods (in order); while for site 5, the three best spatial interpolation techniques are SK, IDW, and OK (in order).

Rainfall analysis is important to managing water resources. Mean rainfall is usually used to calculate the spatial rainfall status of a region and is the input into various rainfall-runoff models. However, this method relies on an adequate raingauge network. This study identifies the effects of raingauge distribution based on estimation results of areal rainfall using the Thiessen polygon and block Kriging methods. Twelve rainfall events with complete data from 14 raingauges were selected to complete the goal of this study. The block Kriging method in this study uses a dimensionless semivariogram to obtain hourly semivariograms based on a standardized rainfall depth. The power semivariogram model was used to describe the temporal-spatial variation of rainfall. The analytical process in this study uses raingauge weight and rainfall volume as evaluation criteria. All raingauges were in turn removed from the original raingauge network. The effects of removing each raingauge were compared with computations using all raingauges. Comparison results indicate that (1) the block Kriging method can accurately describe rainfall processes in terms of the spatiotemporal structure of a semivariogram. (2) the block Kriging method is better than the Thiessen polygon method at obtaining exact mean rainfall, and (3) the effects of different raingauge distributions on a mean hyetograph warrant further investigation.

The synthetic unit hydrograph methods of Nakayasu, HEC-HMS (Snyder), SCS, ITB-1, and ITB-2 are used to calculate peak discharge and flood hydrograph shape in this Kadumalik Dam study. The maximum daily rainfall data analysis used the Thiessen Polygon and Arithmetic Mean methods. Of these two frequency analysis methods, the Thiessen Polygon method was chosen. Rainfall transformation into runoff using the FJ MOCK and NRECA methods has been applied in the Kadumalik Dam analysis. Compared to NRECA, the FJ MOCK method with the Thiessen Polygon method for frequency rainfall analysis provided a better performance rating with calibration values of 0.911 for R2, 0.627 for NSE, 0.606 for RSR, 18.141 for RMSE, and 30.764 for PBIAS. The validation values were 0.911 for R2, 0.661 for NSE, 0.582 for RSR, 16.086 for RMSE, and 34.420 for PBIAS. The Kadumalik Dam uses a side-channel spillway model with an ogee spillway crest type. Technically, it is planned based on the design flood discharge Q100 and controlled by discharging the flood discharge Q1000 and QPMF. The purpose of this study is to determine the hydraulic flow behavior that occurs in the numerical model based on CFD with ANSYS Fluent and CFX, along with Flow 3D in the diversion, regulation, and launching channels, to obtain the optimum design of the structures, where the flow classification is steady and transient. From the numerical analysis results, it was found that the water velocity streamline in the launch channel for Q100 with steady flow is 0.1644 – 0.2643 m.s-1, for Q1000 it is 0.2176 – 0.2869 m.s-1, and for QPMF it is 0.1592 – 0.2262 m.s-1. For transient flow, the water velocity streamline in the launch channel for Q100 is 0.1555 – 0.2250 m.s-1, for Q1000 it is 0.1541 – 0.2232 m.s-1, and for QPMF it is 0.1559 – 0.2255 m.s-1. Wet, normal, and dry hydraulic conditions are used in the analysis of the Kadumalik Dam operation pattern. The wet hydraulic condition before the reservoir had an average discharge of 25.51 m3/s, and after the reservoir, the average discharge was 26.89 m3/s, an increase of 5.125%. The normal hydraulic condition before the reservoir had an average discharge of 15.54 m3/s, and after the reservoir, the average discharge was 18.75 m3/s, an increase of 17.105%. The dry hydraulic condition before the reservoir had an average discharge of 1.74 m3/s, and after the reservoir, the average discharge was 7.97 m3/s, an increase of 78.157%.

This paper presents spatial interpolation techniques to produce finer-scale daily rainfall data from regional climate modeling. Four common interpolation techniques (ANUDEM, Spline, IDW, and Kriging) were compared and assessed against station rainfall data and modeled rainfall. The performance was assessed by the mean absolute error (MAE), mean relative error (MRE), root mean squared error (RMSE), and the spatial and temporal distributions. The results indicate that Inverse Distance Weighting (IDW) method is slightly better than the other three methods and it is also easy to implement in a geographic information system (GIS). The IDW method was then used to produce forty-year (1990–2009 and 2040–2059) time series rainfall data at daily, monthly, and annual time scales at a ground resolution of 100 m for the Greater Sydney Region (GSR). The downscaled daily rainfall data have been further utilized to predict rainfall erosivity and soil erosion risk and their future changes in GSR to support assessments and planning of climate change impact and adaptation in local scale.

Optimal interpolation approach for groundwater depth estimation