Providing General Equation for the Advance of the Water at the Border

For evaluating border irrigation, it is needed to use advance data. Due to soil variability, as well as initial and boundary conditions in border irrigation, water advance rate varies considerably indifferent borders. In recent years, Scaling approach has been adopted as a means to reduce measurement data on water and soilissues.The aim of this study is to provide a unique equation, independent of initial and boundary conditions, for evaluation of water advance in border through scaling approach. For this purpose border irrigation was solved under the kinematic wave model and Philips 2-term equation for the infiltration. Physically basedscaling factors were defined, attempted to scale the border irrigation for the advance trajectory. Scaling advance curves followed some certain quations, therefore, power, exponential, and parabolic equations were fitted for water advancing of trajectories. The equations obtained using the scaling and the volume balance equation were evaluated for 25 different borders. Four statistical indicators, i.e. coefficient of determination (R2), distribution around line of perfect aggrement, percentage of model prediction error (Er), and percentage of average relative error (Ea) were used.The results showed that the power model with R2 =0.893, λ=1.003, Er=0.9 and Ea=13.76 performed better than the other two models. In comparison with the volume balance equation, the power equation can be more accurate. Simple form and independent of the soil type equations presented are superior methods over previous researches in this field.