multivariable regression

Density current is one of the most important factors in the sedimentation process of dams. Because this current is one of the important factors affecting the reduction of life efficiency of large dams, so understanding sedimentation patterns to manage the reservoir of dams is very effective. Accordingly, in this study, the reduction percentage of the density current head flux under the influence of trapezoidal permeable barriers (filled with sand grains with a diameter of 0.5 cm) is investigated also variable parameters effect such as discharge, slope, concentration and height of obstacles on density current control is examined experimentally, based on the results, the reduction percentage of the density current head flux was modeled using the artificial neural network feed-forward method and the classical multivariable regression method, and the performance of these two methods was compared. The results showed that the intelligent method of feed-forward artificial neural network has a significant advantage over the multivariable regression method in modeling the reduction percentage of the density current head flux.

Air temperature is one of the major variables required for agroclimatic classifications. For spatial zoning of temperature point observations, the interpolation approaches in which the horizontal and vertical gradients are included may be applied. In this research, the skill of Kriging, Co-Kriging, geographically weighted regression and Linear Multivariate Regression was evaluated for the interpolation of the monthly mean temperature values using the data of 56 synoptic stations located in the northern and central regions of Iran. The results of the statistical analysis indicated that the geographically weighted regression have the greatest difference with the other methods in month of December, with root mean square error (RMSE) equal to 0.83 °C, Based on the RMSE values of all months, the geographically regression method (with RMSE of 1.26°C) is the most suitable approach for temperature spatial zoning in this region. and then linear multiple regression method with RMSE of 2.24 °C, Kriging with RMSE of 2.52 °C and Cokriging with highest RMSE of 2.86 °C were ranked second to fourth, respectively. Besides, it is concluded that for high altitude areas where almost no weather station exist, the geographically weighted regression method provided the most accurate interpolated data of the air temperature.

Greenhouse cultivation is a steadily developing agricultural sector throughout the world. In addition, it is known that water is a major issue almost all part of the world especially for countries which have insufficient water source. With this great expansion of greenhouse cultivation, the need of appropriate irrigation management has a great importance. Accurate determination of irrigation scheduling (irrigation timing and frequency) is one of the main factors in achieving high yields and avoiding loss of quality in greenhouse tomato and cucumber. To do this, it is fundamental to know the crop water requirements or real evapotranspiration. Accurate estimation on crop water requirement is needed to avoid the excess or deficit water application, with consequent impacts on nutrient availability for plants. This can be done by using appropriate method to determine the crop evapotranspiration (ETc). In greenhouse cultivation, crop transpiration is the most important energy dissipation mechanisms that influence ETc rate. There are a large number of literatures on methods to estimate ETc in greenhouses. ETc can be measured or estimated by direct or indirect methods. The most common direct method estimates ETc from measurements with weighing lysimeters. Thisalsoincludes the evaporation measuring equipment, class A pan, Piche atmometer and modified atmometer. Indirect method includes the measurement of net radiation, temperature, relative humidity, and air vapour pressure deficit. A large number of models have been developed from these measurements to estimate ETc. Due to the fast development of under greenhouse cultivation all around the world, the needs of information on how it affects ETc in greenhouses has to be known and summarized. The existing models for ETc calculation have to be studied to know whether it is reliable for greenhouse climate (hereafter, microclimate) or not. Regression and artificial neural network models are two important models to estimate ETc in greenhouse. The inputs of these models are net radiation, temperature, day after planting and air vapour pressure deficit (or relative humidity).
In this study, daily ETc of reference crop, greenhouse tomato and cucumber crops were measured using lysimeter method in Urmia region. Several linear, nonlinear regressions and artificial neural networks were considered for ETc modelling in greenhouse. For this purpose, the effective meteorological parameters on ETc process includes: air temperature (T), air humidity (RH), air pressure (P), air vapour pressure deficit (VPD), day after planting (N) and greenhouse net radiation (SR) were considered and measured. According to the goodness of fit, different models of artificial neural networks and regression were compared and evaluated. Furthermore, based on partial derivatives of regression models, sensitivity analysis was conducted. The accuracy and performance of the employed models was judged by ten statistical indices namely root mean square error (RMSE), normalized root mean square error (NRMSE) and coefficient of determination (R2).
Based on the results, the most accurate regression model to reference ETc prediction was obtained three variables exponential function of VPD, RH and SR with RMSE=0.378 mm day-1. The RMSE of optimal artificial neural network to reference ET prediction for train and test data sets were obtained 0.089 and 0.365 mm day-1, respectively. The performance of logarithmic and exponential functions to prediction of cucumber ETc were proper, with high dependent variables especially, and the most accurate regression model to cucumber ET prediction was obtained for exponential function of five variables: VPD, N, T, RH and SR with RMSE=0.353 mm day-1. In addition, for tomato ET prediction, the most accurate regression model was obtained for exponential function of four variables: VPD, N, RH and SR with RMSE= 0.329 mm day-1. The best performance of artificial neural network for ET prediction of cucumber and tomato were obtained with five inputs include: VPD, N, T, RH and SR. The RMSE values of test data sets for cucumber and tomato ET were obtained 0.24 and 0.26 mm day-1. Moreover, the sensitivity analysis results showed that VPD is the most sensitive parameter on ETc.
The greenhouse industry has expanded across many parts of the word and the need of information on a reliable ETc method especially by indirect method is crucial. In this research, the artificial neural network models indicated good performance compared with linear and nonlinear regressions. The evaluated method could be used for scheduling irrigation of greenhouse tomato and cucumber.