Research on a Key Question in the Parlange Solution

In order to solve the problem that the key parameter c(t) in the Parlange Solution of Richards Equation is difficult to calculate, this paper proposes a variable separation method based on experimental, which transforms the integral equation containing c(t) into transcendental equation and finds the analytical solution. The calculation results show that when the test parameters D(θ) and k(θ) are power functions, the improved method converges quickly, a stable solution can be obtained by more than ten iterations, and the generated trajectory of soil moisture content conforms to the actual situation. The proposed solution converges faster than the simplified Parlange Solution, and is very close to the Philip Solution, with a difference of less than 5%. The proposed solution has strict analytical steps and clear mathematical significance, which can be regarded as a supplement to the Parlange Model in a key step.