multiple regression

Base flow is one of the most important criteria which is used for assessment, utilization and management of river flow in drought periods. The base flow amount and its variations depends on several factors. Base flow modeling and estimation can be used in assessment of river health as well as planning of surface water utilization. Base flow refers to the flow of the river in times without rainfall. The base flow of the river is the infiltration of groundwater to the river banks or the river bed. The base flow may be significant and flow continuously throughout the year in the permanent rivers. The base flow has reached the underground water table with its deep penetration, and with the increase in the level of the aquifers, it can be connected with the drainage network, they create their own excess water during a long period of time, which sometimes takes several months. Determining the amount of river flow in dry periods, and the proportion of total runoff is one of the important topics in river hydrology. The base flow plays an important role in the river ecosystem, and is critical to human communities and ecosystems. This is especially important for watersheds that are not fed by snowmelt. Different ecological processes occur in different parts of the river's hydrograph. During base flow and during low water seasons, river ecosystems and habitats are dependent on river flow. Land change affect hydrologica; processes such as infiltration rates, groundwater recharge, groundwater and runoff levels. Also, climatic factors can affect the water yield of river basins. The most common method for regionalization in hydrology is bivariate or multivariate regression. Regression analysis is a useful approach to develop the desired factors in the regionalization of ungauged basins. Regression analysis is also one of the most common statistical methods in predicting values based on most important influencing factors. In this study, the multiple regression was used to model the base flow amount and determining the effective factors on base flow discharge. Ardabil province is considered one of the cold mountainous areas and the amount of precipitation in Ardabil province fluctuates on average between 250 and 600 mm/year in different parts of the province. Therefore, the aim of the current research is to model the effective factors in the amount of base flow and its estimation in the watersheds of Ardabil province.

The topographic maps were used to extract parameters of slope, area, average height of sub-basin, drainage density, length of main river, area percentage of different land uses in each sub-basin, precipitation, daily discharge (as independent variables) was used to analyze the factors affecting the amount of base flow. The daily discharge data recorded in 22 hydrometric stations were used. The base flow was calculated from the daily flow hydrograph by one-parameter algorithm method and programming in Excel software. The one-parameter algorithm method is one of the reverse numerical filter methods that are used in the flow rate signal processing, and separating the base flow from the fast flows using a recursive digital filter. In the following, the physiographic characteristics of the basins have been considered as independent variables, and base flow amount has been modelled using regression analaysis. The necessary statistical tests were performed in the screening stage, and the logarithm of the variables and the Box-Cox method were used to normalize the data. Then, collinearity between independent variables was tested using Pearson's correlation coefficient at 99% confidence level and the VIF values has been examined in SPSS software. Therefoe, independent variables with significant correlation (Sig<0.01) and (VIF>10) were excluded from the regression analysis due to collinearity. The multivariable regression model is an extended type of the bivariate linear regression model, in which it is tried to estimate the dependent variable based on several independent variables, Then, the stepwise regression approach has been considered for the modelling purpose. Then, considering base flow as dependent variables, and other physiographic parameters as independent variables, the most suitable methods has been chosen according to the efficiency assessment criteria.

The ANOVA table of the modelling showed that there is a significant relationship between independent and dependent variables. The obtained value showed that the rangeland percentage amount had a significant effect on the base flow amount. The degree of linear relationship between independent variables is measured by the tolerance index. Standardized β shows a very important role in predicting the dependent variable, so the daily discharge variable had a much greater contribution compared to other variables in the estimation of the dependent variable (base flow). According to the results, all the mentioned factors were considered in proposed regression model considering the VIF value less than 10. Based on the value (β), the contribution of independent was interpretated. The results revealed that the discharge, area, the percentage of medium to good rangelands, and the percentage of agriculture-residential area-garden are among the effective factors. The main river length, average height, and average slope were removed from the modelling procedure due to collinearity effect, and then the stepwise multiple regression was performed and the produced model accuracy were proved as significant (p-value <0.005). Also, the results indicate the positive and direct impact of vegetation and land use on the amount of base flow amount. The results of base flow modeling nased on presented model can be used in the ungauged areas adjacent to the studied watersheds in Ardabil province.

It should be noted that the hydrological response of the basins will be different on hourly, daily, monthly or yearly scales. Therefore, modeling can be done in different time scales, which will help to better understanding of base flow contribution in river flow regime. It should also be noted that considering the influence of factors such as extraction or river flow diversion can affect the accuracy of the results. In addition, the effect of human modifications on the change of the contribution of the river's base flow is important that is usually not considered in modeling and will be the source of a significant error. Also, the changes of climatic factors can affect the water flow of the river, and therefore, the study of the changes in the river flow over time can determine the effects of changes in climatic factors.

Estimation of compressional and shear wave velocities is very important in the oil and gas industry. Unlike compressional wave velocity, shear wave velocity is not measured in all wells of a field due to its higher costs. Therefore, using an alternative method that estimates the shear wave velocity at a lower cost and with acceptable accuracy is inevitable. In this study, to estimate the response variable in a well, the correlation of several logs in that well (i.e., acoustic logs, density, neutron porosity, resistivity, gamma ray, dolomite volume, quartz volume, and water saturation) with target log investigated. It was found that the compressional wave velocity, density, dolomite volume, and quartz volume logs are more correlated with shear wave velocity. Therefore, these logs were selected as input features for estimating shear wave velocity using different approaches. In the next step, among the various methods, The estimated values obtained from a method that has the best match with the actual shear wave velocity is introduced as the optimal model. Afterward, it is performed to estimate the shear wave velocity in other wells that do not have a shear wave velocity log. In this paper, multiple regression methods and machine learning algorithms (support vector regression, adaptive Neuro-fuzzy inference system, and deep artificial neural network) were applied to predict the shear wave velocity. In this study, data from seven wells were used. Due to the fact that only in well #7 shear wave velocity has been measured, and in six other wells this feature has not been recorded, this field data limitation has caused the data of well #7 to be divided into training, testing, and validation data. In multiple regression methods (linear and interaction models), support vector regression, and adaptive Neuro-fuzzy inference system, Randomly, 70% of the data has been used for training and 30% for testing, but in the artificial neural network method, Randomly, 70% of the data has been used for training, 15% for validation and 15% for network testing. For all methods, the root means square error and correlation between actual and estimated data are calculated. Linear model, interaction model, support vector regression, adaptive Neuro-fuzzy inference system, and deep artificial neural network have provided 91, 92, 89, 94, and 98% correlation in training data, and 88, 89, 86, 90 and 92% in testing data, respectively. Also, the RMSE for each of the mentioned methods is 125.59, 115.86, 148.23, 84.36, and 80.49 (m/s) in the training data and 139.77, 133.44, 166.03, 126.15, and 98.04 (m/s) in the testing data, respectively. Our results show that deep artificial neural network has provided a better solution than other methods. Hence, in this study deep artificial neural network has been proposed to estimate the shear wave velocity in other blind wells. Moreover, the Castagna empirical model was used to validate the obtained results from the deep artificial neural network in these wells, which show a good fit between the two models.

Updated information in quantitative and qualitative properties of forests are useful in describing ecosystem sustainability, and designing management and conservative plans. According to importance of canopy cover parameter in the Zagros region and cost and time consuming processes of field measurement methods, in this study performance of remote sensing and geostatistics techniques to estimate forest canopy cover of Baghan region, Marivan city, were investigated.

 First, the number of 89 plots (each 0.1 Hectare) were selected based on random sampling method. In each plot, information of tree crown and center geographic coordinates of that plot were recorded. Remote sensing method was carried out using Landsat satellite images (TM) and multiple linear regression model. After image processing, spectral values of the corresponding field plots were extracted from the original images and synthetic bands composed of vegetation indices and principle component analysis. In geostatistic method, the estimation was performed using ordinary kriging from a fitted exponential model to the semivariogram.

 The calculated variograms of canopy cover showed relatively strong spatial autocorrelation fitted by exponential models and cross-validation results showed an unbiased estimation of canopy estimation. Compared with the remote sensing method (with R2= 0/52 and RMSE= 16/47), the results indicated that Kriging model (RMSE= 9.21, R2= 0.69) showed a more accurate estimation of forest canopy cover.

The results showed that geostatistics techniques can be used as an efficient tool for mapping the forest canopy in the same regions (Zagros Forest).

Permeability assessment is one of the important properties in geomechanical investigation of rock mass determined from water pressure test (WPT) and Lugeon number. Results of these tests are used to determine the amount of groutability in tunnel, dam site and other water related constructions. Due to complex discontinuity patterns, it is almost impossible to determine the permeability of rock mass without a proper testing method. The purpose of this study is to develop various multivariate regression models to estimate the rock mass permeability in Khersan 2 dam site. To do this, a dataset including 28 cases with Lugeon test results and corresponding RQD (Rock Quality Designation), spacing of discontinuities and SCR (Surface Condition Rating) properties are employed. Three different models were developed to estimate the rock mass permeability. The inputs of the first model are RQD and SCR (Model 1), the inputs of the second model are discontinuity spacing and SCR (Model 2) and those of the third model are discontinuity spacing and RQD (Model 3). Simple regression analyses indicate that there is no statistically meaningful relationship between the Lugeon values and SCR. There is a statistically meaningful relationship, however, between the Lugeon values with discontinuity spacing and RQD. Non-linear multivariate regression analyses was conducted for two independent variables and one dependent variable because of nonlinear relationships between input and output. Finally, the validation of the results using statistical indicators shows that the accuracy of the proposed multivariate nonlinear regression relationship between Lugeon with RQD and the discontinuity spacing is higher than other relationships and it is more consistent with real data. The results show that with increasing the number of regression variables, the accuracy of the predicted Lugeon values increases and the experimental relationships are obtained with a higher correlation coefficient.