Performance Evaluation of Gene Expression Programming Approach in Layout Design of Drippers in Drip Irrigation systems comparing with empirical method

Background and objectives: One of the essential aspects of design and management of drip irrigation system is soil moisture movement pattern and its dimensions in vertical and horizontal directions. Accurate estimation of soil water distribution in drip irrigation and subsurface drip irrigation is vital, because of its effects on design parameter as: emitters' layout, lateral spaces, plant root grow, efficiency application of water, salt distribution around the dripper, and has evident effects on Successfulness of drip irrigation systems. So deriving design equations between soil texture, emitter discharge, water volume infiltrated in soil, soil wetted volume and irrigation time for prediction of wetting bulb dimensions have major application values. One of these are empirical design equations, which derived based on dimensional analysis and experimental data. The other researchers have developed several empirical equations based on experimental data where need soil condition calibrations. The main objective of this study is to apply genetic expression programming for automatic function finding in DI and SDI wetting front dimensions and prepare design tables in different soil and dripper conditions.
Materials and Methods: in this study GEP approach is used for automatic function finding of dimensionless soil water distribution equations using available extended data. GEP programming is done in MATLAB. The GEP code use operator and functions of: plus, minus, times, divide square, power, tanh, sin, cos, exp, abs, if-then and derive predictor equations based on GEP automatically. This paper presents design equations based on volume water, irrigation time, and emitter discharge and soil hydraulic conductivity. The results of derived equations are compared with observations graphically and by R2, RMSE and MAPE indices. The final form of optimum equations derived based on pareto analysis over generations. Finally design tables for different soil, root depth and emitter discharges are presented.
Results: GEP results are compared with those of 8 empirical equations using graphical and statistical indices of R2, RMSE, and MAPE. Based on the results it is cleared that the GEP model with RMSE=0.2, MAPE=12%, R2=0.99 values for depth and RMSE=0.19, MAPE=18.5%, R2=0.99 values for wetting front diameter have better results the others and is superior for applying in different and extensive design conditions. The Schwartzman and Zur (1985) empirical model have RMSE=0.12, MAPE=18.5%, R2=0.99 values for depth and RMSE=0.72, MAPE=97%, R2=0.97 values for wetting front diameter has some errors. Also design tables based on optimum GEP results based on conventional condition of Iran soil and emitters are developed.
Conclusion: Based on the results GEP equations have extensive validation ranges (discharge ranges 1 to 5 l/s, depth up to 110 cm) than other empirical equations and involves different conditions of emitter and soil and based on the results comparisons using GEP equations will reduce uncertainties in design of drip irrigation systems and will improve water use efficiency and performances of these systems.