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Non-unique inversed model result

Posted: Mon Oct 28, 2019 7:57 am
by litlux
Dear all,

Hope everyone is doing great.

I have one question regarding to non-unique result from inversed model. I am running inversed model in HYDRUS 1-D to find some key hydraulic parameters of soil column. I have fixed values of theta-r, theta-s,... The values of Ks, n and alpha are fitted. But if I change the initial guess of fitted parameters, the results are changed (non-unique solution).

What should I do in this case? and reason behind this problem (mathematic or experimental data input)?

I am looking forwards to seeing your replies.

Best regards,

Tho Tran

Re: Non-unique inversed model result

Posted: Mon Oct 28, 2019 7:43 pm
by Jirka
HYDRUS uses the Marquardt-Levenberg optimization method to minimize the objective function (the sum of wighted squared deviations), which is a gradient method, i.e., it searches for a local minimum.
inverse.png
inverse.png (39.52 KiB) Viewed 996 times
You need to either use multiple initial parameter estimates and then select the one with the minimal value of the objective function, or use external global optimization method. These issues are discussed in detail in:

Šimůnek, J., and J. W. Hopmans, Parameter Optimization and Nonlinear Fitting, In: Methods of Soil Analysis, Part 4, Physical Methods, Chapter 1.7, Eds. J. H. Dane and G. C. Topp, Third edition, SSSA, Madison, WI, 139-157, 2002.

Hopmans, J. W., J. Šimůnek, N. Romano, and W. Durner, Inverse Modeling of Transient Water Flow, In: Methods of Soil Analysis, Part 4, Physical Methods, Chapter 3.6.2, Eds. J. H. Dane and G. C. Topp, Third edition, SSSA, Madison, WI, 963-1008, 2002.

J.

Re: Non-unique inversed model result

Posted: Tue Oct 29, 2019 12:18 am
by litlux
Dear Sir,

Thank you so much for your quick response.

I will definitely read those.

Best regards

Tho Tran