I have a very simple hydrological model. The model can be simply conceptualised as below: [Simple Hydro model 492x394] I am trying to learn the values of the parameters a, b and c. Where: P = Precipitation Inputs L = Losses S = Storage (groundwater / soil) Qf = Fast Flow Qs = Slow Flow a = Pro…

Have you taken a look at some of the case studies? I found @Bob_Carpenter ’s case studies to be very helpful in getting me started with coding ODE models. See https://mc-stan.org/users/documentation/case-studies/soil-knit.html Since Q is observed, as is indicated by your data block, indeed, you wil…

Thanks @xiehw really appreciate the help! 1) Stiff system? If I’m honest I am not certain what a stiff system is. From my brief glance at Wikipedia I don’t think it’s a particularly sensitive system and so I would say it’s not stiff. 2) Univariate / Bivariate Model So P_t is the input / forcing …

[image] tommylees112: Qt=Qft+QstQ_t = Qf_t + Qs_t Qft=(1−a−b)PtQf_t = (1-a-b) P_t Qst=cStQs_t = c S_t St=(1−c)St−1+aPtS_t = (1-c) S_{t-1} + aP_t Lt=bPt Before getting into the priors, it looks like you have a delay differential equation (DDE) system with a discrete delay. You may definite…

[image] xiehw: Difference equations, you solve through by just looping through the times, and then you would not use differential equation integrators at all. Interesting! I think it might be a difference equation for this simple model. I was hoping that adding in complexity (for example when…

[image] tommylees112: If it is just a simple loop does that make it easier? Then I could have something like: Yep, for solving a difference equation, a loop will be the way to go about it. Glad we got the difference/differential equation distinction classified! A difference equation model is …

One thing that I am trying to understand a bit more is how to incorporate both measurement error and process error. In this model there will be A LOT of process error. Where would I incorporate error in the process? Would I have to move the ABCModel process-model statements: transformed parameters…

[image] tommylees112: Because ultimately I would be interested in modelling the errors in the process-model using a Gaussian Process. I’m not familiar enough with GPs or process errors unfortunately to comment on that for now; do you have a link to a paper that the model is from or based on t…

For sure thanks so much! What we’re trying to emulate is this paper (with a much simpler model to begin with). They are looking at simulating soil moisture, whereas we are interested in predicting discharge (y_t = Q_t). translating their notation: f = our ABC model (a process-based model PBM) \…

Having got the very simple optimisation working, the results do return similar values for the parameters as the Python code! I fit the model on a single basin’s data, River Cherwell at Enslow Mill, Station: 39021 . I recover similar parameter estimates from both methods! Which is a start. Original…

Great to hear! What error terms or implementations did you end up using?

Fitting parameters of a simple process model (optimisation & uncertainty)

Modeling

tommylees112 December 21, 2021, 8:35pm 14

I’d be so excited to hear more! Haven’t looked at this since, because I moved onto simply using the scipy optimsation procedures.

Sorry for slow response, just getting back into Stan for some Christmas fun!

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Fitting parameters of a simple process model (optimisation & uncertainty)

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