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see [code](https://github.com/Ibasam/IBASAM/blob/master/IBASAM/R/river_climate_model.R)
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The climate in the simulated river was described by daily water temperature and flow. As explained in the input section, the time series of temperature and flow of a real river can be used for parameterization purpose or specific simulations. However, for further simulations and to obtain realistic replicates of time series of these two environmental factors, a random autore- gressive sinusoidal function was used for each of these factors. The mathematical form of these two functions was:
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> sinus_model_resid_ar <-
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function (m, a, cs, alp, bet, d, nbd)
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{
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error <- numeric(length(d))
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tm <- m + a * sin(2 * pi * (d - cs)/nbd)
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error[1] <- 0
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for (dd in d[-1]) {
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error[dd] <- alp * error[dd - 1] + bet * rnorm(1)
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tm[dd] <- tm[dd] + error[dd]
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}
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return(tm)
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}
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where Mean and Amp were the mean and amplitude of the envi- ronmental parameter (temperature or flow) over a year, t was the Julian day, cs was a shifting parameter to adjust the sinusoidal signal and AR(t) was an autoregressive random error of the form:
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where ̨ was a non-zero parameter and was a normal random number centered on 0 and of variance ˇ. The Scorff River data series (over 15 yrs) allowed a parameterization of these two functions: (1) for the river water temperature (T(t)); (2) for the logarithm of the flow (flow(t) in m3 /s) divided by the module of the river (5.03 m3 /s). Table 2 gives the parameters of the adjusted values.
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For further studies simulating climate change, a temporal trend either on the Mean or the Amp parameter could be easily set up.
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![](CC.png) |
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