cross-validation

Predicting river flow is one of the most crucial aspects in water resources management. Improving forecasting methods can lead to a reduction in damages caused by hydrological phenomena. Studies indicate that artificial neural network models provide better predictions for river flow compared to physical and conceptual models. However, since these models may not offer reliable performance in estimating unstable data, using preprocessing techniques is necessary to enhance the accuracy and performance of artificial neural networks in estimating hydrological time series with nonlinear relationships. One of these methods is wavelet transformation, which utilizes signal processing techniques.

In this study, to evaluate the efficiency of discrete and continuous wavelet types in the Wavelet-Artificial Neural Network (WANN) hybrid model for monthly flow prediction, a case study was conducted on the Kardeh Dam watershed in the northeast of Iran, serving as a water source for part of Mashhad city and irrigation downstream agricultural lands. Monthly streamflow estimates for the upstream sub-basin of the Kardeh Dam were obtained from the meteorological and hydrometric stations' monthly statistics over a 30-year period (1991-2020). The WANN model is a hybrid time series model where the output of the wavelet transform serves as a data preprocessing method entering an artificial neural network as the predictive model. The combination of wavelet analysis and artificial neural network implies using wavelet capabilities for feature extraction, followed by the neural network to learn patterns and predict data, potentially enhancing the models' performance by leveraging both methods. The 4-fold cross-validation method was employed for the artificial neural network model validation, where the model underwent validation and accuracy assessment four times, each time using 75% of the data for training and the remaining 25% for model validation. The final results were presented by averaging the validation and accuracy results obtained from each of the four model runs. To evaluate and compare the performance of the models used in this study, three evaluation indices, Nash-Sutcliffe Efficiency (NSE), Root Mean Square Error (RMSE), and Pearson correlation coefficient (R), were employed.

The analysis of meteorological and hydrometric data in this study revealed that monthly streamflow in two time steps, T-1 and T-2, were the most effective predictive variables. Each of the two runoff variables of the previous month (Qt-1) and the previous two months (Qt-2) were analyzed by each of the Haar and Fejer-Korovkin2 discrete wavelet transforms and the two continuous Symlet3 and Daubechies2 wavelets at three levels. The results of each level of decomposition was given as input to the ANN model. The presented results at each decomposition level indicated that hybrid models could accurately predict lower flows compared to the single ANN model, and the estimation of maximum values also significantly improved in the hybrid models. Among the wavelets used, Haar wavelets exhibited the weakest performance, and the less commonly employed Kf2 wavelet showed a moderate performance. Since the Haar and Fk2 wavelets, with their discrete structure, did not perform well in decomposing continuous monthly streamflow data, continuous wavelet models outperformed discrete wavelet models. The hybrid models, combining wavelet analysis and artificial neural networks, demonstrated up to an 11% improvement over the performance of the single neural network model.

Streamflow is a crucial element in the hydrological cycle, and predicting it is vital for purposes such as flood prediction and providing water for consumption. The objective of this research was to evaluate the performance of different types of discrete and continuous wavelet models at various decomposition levels in enhancing the efficiency of artificial neural network (ANN) models for streamflow prediction. Since climate and watershed characteristics can influence the nature of data fluctuations and, consequently, the results of the wavelet model decomposition, choosing an appropriate wavelet model is essential for obtaining the best results. Considering the existing variations in the results of different studies regarding the selection of the best wavelet type, it is suggested to use both continuous and discrete wavelet types in modeling to achieve the best predictions and select the optimal results. Given that a lower number of input variables in neural network models lead to higher accuracy in modeling results, it is recommended to perform decomposition at a two-level depth to reduce input components to the neural network model, thereby reducing the model execution time.

At the arid and semi-arid climates which the rainfed farming has a high degree of importance, it is essential to evaluate both the effective factors on the rainfed crop yield and its predicting as well. In this respect, it is unavoidable to have a special consideration for some tolerable crops such as barley. The aim of the current study was to assess the possibility of rainfed barley annual yield prediction using some drought indices at a semi-arid climate.

By calculating SPEI, EDDI and SPI drought indices for four growth stages of rainfed barley including sowing-emerge, emerge-tillering, tillering-stem and stem-flowering at the Sararoud-Kermanshah station, a number of 12 time series of these indices were extracted during 2000-2015 period. The cross-tabulation was used to evaluating the overall relationship between drought indices and rainfed barley annual yield and to modeling rainfed barley annual yield based on drought indices, the best subset-based multiple linear regression model and Principal Component Regression (PCR) were applied at two different stages. The modelling procedure performed in two overall cases including considering a unique drought index and considering a combination of three different drought indices cases.

the results of cross-tabulation technique showed an appropriate relationship between rainfed barley annual yield and drought indices. Therefore, a potential is available to use drought indices to predict rainfed barley annual yield. Based on the results of considering a unique drought index case, the highest (63.6%) and lowest (54.1%) values of coefficient of determination between rainfed barley annual yield and drought indices were for SPEI and EDDI indices, respectively and a value between them (62.4%) for SPI. The values of these indices were appeared at the model during the sowing-emerge and tillering-stem stages for SPEI and SPI and sowing-emerge and stem-flowering stages for EDDI. By considering the combination of three different drought indices case, the results revealed that the best multiple linear regression model is obtained by presence of SPEI (during tillering-stem and stem-flowering stages) and EDDI (during sowing-emerge and tillering-stem stages) indices in the model with a good coefficient of determination (R2= 78.7% and R2adj= 69.2%). However, the high value of Variance Inflation Factor (VIF) revealed that it is necessary to solve this issue by considering the Principal Component Regression (PCR) model. By applying PCR model to predict rainfed barley annual yield, the coefficient of determination for the PCR (78.2%) showed a negligible decrease compared to the multiple regression model. However, the adjusted coefficient of determination properly improved to 71.7%. By considering the PCR model as the final model of predicting rainfed barley annual yield, the cross-validation results of this model led to obtaining R2=58.5% and RMSE=572.3kg/hec (equal to 22% of the mean of annual yield).

The overall results of this research showed that applying different drought indices could lead to increasing the explained variance of rainfed barley annual yield. The overall results of this research showed that the occurrence of drought during the emerge-tillering stage does not have a considerable impact on the rainfed barley annual yield. With respect to the higher role of the tillering-stem stage in the regression models, this stage was detected as the most important effective period on the rainfed barley annual yield. Therefore, among different growth stages, occurring drought in the tillering-stem period is expected to lead to a lesser amount of annual yield.

The present study demonstrates a method in groundwater quality assessment using the Empirical Bayesian Kriging and Moran Spatial Autocorrelation Index. In this study, concentration of Arsenic, Lead, Iron, Manganese and Nitrate and also groundwater table and Total Dissolved Solid has been measured for 21 point in Azarshahr Plain (East Azerbaijan). Azashahr study area is one of the Lake’s twelve adjacent aquifers that is located between 45°,46’ to 45°,50’ longitudinal and 37°,43’ to 37°,52’ latitudinal. Its total area is about 457 km2, that its plain has an area about 124 km2. The highest and lowest heights in the study area are 3700m and 1282m, respectively. Its average annual precipitation is about 221.2 mm whereas the average annual evaporation is about 1579 mm. The most important stream in Azarshahr Plain is Azarshahrchai which has a southeast-northwest trend and is eliminated before reaching to the lake because of wide agricultural usage. On the other hand, the total annual discharge of aquifer is about 90.64 million that is one of the groundwater depletion and decreasing the quality of groundwater factors in the study area. Moran’s I is a commonly used indicator of spatial autocorrelation. In this study, the Moran’s I was used as the first measure of spatial autocorrelation. Its value ranges from −1 to 1. The value “1” means perfect positive spatial autocorrelation (high values or low values cluster together), while “−1” suggests perfect negative spatial autocorrelation (a checkerboard pattern), and “0” implies perfect spatial randomness. After that, the appropriate weight has given to the aforementioned parameters, considering the international standard of water quality and spatial autocorrelation index of each of them. After determining the layer rules, the Expert Choice software was applied to calculate the comparing binary matrix of analytic hierarchy process. After that, the final weight for each layer with inconsistency of 0.08 was derived that is less than 0.1 and acceptable. In the conventional geostatistical approaches for interpolation and kriging, the variance structure is estimated first, and then the estimated variance is used for interpolation that whereas a Bayesian approach to the interpolation of spatial processes will provide a general methodology for taking into account the uncertainty about parameters on subsequent predictions. The Bayesian approach generalizes automatically to the case which the variogram parameters are unknown, whereas the classical approach essentially makes the assumption that these are known and only deals with the question of uncertainty of model parameters in a very peripheral way. Then replacing the popular interpolation methods, the Empirical Bayesian Kriging prediction method has utilized to expand every parameter to the whole plain. In order to evaluate the prediction results, the cross validation method was used. The study area was divided to 4 sections, as desirable, acceptable, moderate and non-acceptable. The final obtained map reveals that desirable quality is just located in the southeast of the study area in the upstream of the groundwater input. The acceptable quality of the groundwater is located in the east and southeast of the study area. The center, west and northwest of the study area has a moderate quality. The groundwater in the north, northwest and southwest of the study area has a non-acceptable quality that seems due to anthropogenic activities, especially agricultural and industrial during the recent years. On the other hand, the spatial autocorrelation model of effective parameters on water quality in the on hand and Bayesian kriging method with its precise assessment and prediction in some areas without data have a high applicability. The cross validation technique in model accuracy approving, is a valuable tool. Every three methods played an important role in modifying and improving the analytic hierarchy process of the groundwater quality assessment in the study area. The resulted map revealed that the groundwater quality of the east and southeast of the study area are desirable and acceptable with about 32.53 and 44.38 km2, respectively. The center and west section with area about 69.32 and the north and southwest with area about 27.21 km2 have a moderate and non-acceptable quality, respectively. Upon to the analytic hierarchy process of the groundwater quality assessment of the Azarshahr Plain, it has been revealed that 16 percent of aquifer has non-acceptable quality, about the 40 percent has moderate quality and other has an acceptable to desirable quality in the study area. The result of this study has shown the necessity of the groundwater quality precise monitoring in the study area.

Rainfed wheat is a food resource for developing countries that various factors may contribute in its production. The aim of the present study was developing a model that estimate rainfed wheat grain yield based on physico-chemical properties of the soil. Therefore, wheat grain yield was measured at 53 rainfed wheat fields over Zanjan province in agronomical year 2014. Also, 18 soil physico-chemical properties were measured in triplicates in the fields. Using partial least square regression, a model was developed to explain the relationship between rainfed wheat grain yield and soil properties (n=40, R2= 0.6). The highest and lowest standardized coefficients of the model belonged to silt and calcium carbonate percentages which were equal to 0.23 and -0.24, respectively. The results of the present research revealed that some soil physico-chemical properties, in order of priority, including silt, calcium carbonate and potassium has more effects on rainfed wheat grain yield.

In order to protection of water quality in the aquifers, awareness about spatial and temporal distributions of water quality has particular importance. In this study, the spatial and temporal variations of water qualitative variables were analyzed based on the data of 47 selected wells in Tabriz plain over the period of 10 years (1382-1391). For the propose of spatial analyzing, the simple Kriging (SK) as well as the inverse distance weighting methods were carried out leading to derivation of isoquality curves for calcium, chloride, bicarbonate, potassium, magnesium and pH over the aquifer for each year. The study of annual spatial profiles extracted from isoquality curves for each qualitative variable showed that the majority of variables were aggregated on South West and North East part of aquifer. Using Ward method as a multivariate statistical cluster analysis procedure together with S statistics as a homogeneity test procedure, the homogeneous regions for pH were determined over the aquifer. Finally, the annual fluctuation in the qualitative variables were investigated, and according to the results,the majority of variables (except potassium)had incremental trend during the 10 years of statistical period.

Determining the spatial distribution of different contaminants in soil is essential for the pollution assessment and risk control. Interpolation methods are widely used to estimate the concentrations of the heavy metals in the unstudied sites. In this study, the performances of interpolation methods (inverse distance weighting, local polynomials and ordinary Kriging and radial basis functions) were evaluated to estimate the topsoil contamination with copper and nickel in Golestan Province. 216 surface soil samples were collected from Golestan province, and their Cu and Ni concentrations were measured. Soil contamination was determined using different interpolation methods. Cross validation was applied to compare the methods and estimate their accuracy. The results showed that all the tested interpolation methods have an acceptable prediction accuracy of the mean content for soil heavy metals. RBF-IMQ and IDW1 methods had the lowest RMSE, whereas RBF-TPS method with the largest RMSE estimated a larger size for the polluted area. The greater the weighting power, the larger the polluted area estimated by IDW. Compared with the ‘‘sample ratio over the pollution limits” method, the polluted areas of Cu and Ni were reduced by 8.38% and 6.14%, respectively.

Precise mapping of the spatial distribution of salt-affected soils is prerequisite for effective management of these soils. This study was carried out for mapping soil salinity of 78000 hectares of Ardakan soils (0-30 and 0-100 cm) using 151soil samples which were taken based on hyper cube method. The secondary variables used in co-kriging method were ETM data، terrain analysis and EM38 readings. The best model was selected by means of cross validation and error evaluation methods، such as RMSE and ME methods. Results showed that co-kriging method with EM38 data as a secondary variable was the best method for prediction of soil salinity (69. 1، 30. 55، 48. 8 and 20. 41، respectively). Results recommended EM38 as secondary data for mapping soil salinity. Additionally، results showed the largest amount of soil salinity in the north of the area and the smallest values in the areas with more elevation. The concavely shaped plain could help to move soluble salts toward the north of area in which the soils with highest electrical conductivity are found.

Point data of weather stations are not important in and by themselves. Therefore, it is necessary to change these point data into regional information. Undesirable distribution of weather stations and their data deficiency hinder the direct determination of the regional information, unless sufficient data in the study area could be provided. Providing extra data using the geostatistical methods is practical, scientific, simple and quick, but adopting a suitable method is the basic question. The objective of the present study is to find a suitable method to estimate monthly rainfall in the central region of Iran. In this regard, the methods of kriging (ordinary kriging, log-kriging, co-kriging), weighted moving average (WMA, with the power of 1 to 5), thin plate smoothing splines (TPSS, with the power of 2 and 3 and with covariable) were used. Cross validation technique was used to compare these methods. Based on the variography analysis, the range of influence of monthly rainfall in the central region is about 450 km. The results show that TPSS, with the power of 2 and with elevation as a covariable, was the most accurate method to estimate monthly rainfall. In addition, it is preferable to use the selected interpolation method in the sub-basins with homogeneous climates instead of considering the whole region.