problem of SPDE and NS combined model prediction

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Sep 26, 2023, 12:16:01 PM9/26/23
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Hi, I want to add the time(year) to the spde model as a natural spline. the formula as follows,
formulate ~ -1 + Intercept + f(field, model = spde) + f(loc_id, model = "iid") + c("ns(year, 2)")

The Fixed effects is:
                  mean    
Intercept   -2.022 
1                0.858 
2                0.057 ,

①how can we to interpret The “1” , and “2”?(I read the example of NS smoothing in Chapter 9, and it seems that there is no explanation for this, is this a degree of freedom? https://becarioprecario.bitbucket.io/inla-gitbook/ch-smoothing.html
②How should we draw the graph after NS combined spde model fitting? or can  we get the   expression of the equation for a natural spline for further prediction?

thanks 

Helpdesk (Haavard Rue)

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Sep 27, 2023, 3:50:27 AM9/27/23
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you can use either RW1 or RW2 model, indexed by year ?
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Oct 3, 2023, 3:58:25 AM10/3/23
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thanks for your kind answer. I used the “rw1” model before, but i do not know how to explain the result and how to predict by year which is already become a hyperparameters.
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