Thursday, January 28, 2016

Daily, Hourly: Instantaneous or averaged ? Answering a question on how to consider the outputs of lumped models

Dear Professor Rigon,

I would like to thank you for your help regarding my last question.

I have another problem that I would like to share with you and your followers, if you consider the question interesting and relevant, of course. 

A -  Your last questions had a lot of readers. So I assume you share issues with many others. 

The question is related to the meaning of the results of lumped models like HBV or HYMOD. These models are usually run with an hourly or daily time-step, therefore hourly or daily evapotranspiration and precipitations are introduced in the models. 

Q - The hydrological algorithm usually calculates the next time-step tank states and the discharges through an Euler explicit algorithm. Once the precipitation, ETP and the internal states are known at the time t0, the model calculates the discharge and the tank states in the next time step t0 + Dt. It is my understanding that these values are point values and not mean values in the interval between t0 and t0 + Dt, even if the input has been averaged.

A - This is also my understanding. However … 

Q - Contrary to my understanding, in most of the applications of these models the results are compared directly with mean values over the interval between t0 and t0 + Dt which, in my opinion, only makes sense if the analysed hydrological regimes are slow, i.e. the change rate in a station is great because the watershed area is great too, or if the analysis focuses on water budget, in which case the peaks are not the most relevant key point.

A - effectively, I think that it depends also on how you calibrated the model. If you calibrated it using average quantities, it is reasonable to assume that the answers the model does are average quantities. Those model are conceptual (especially in the determination of separation of flows between subsurface and surface) and, it is in general questionable what they actually do. So I would stick with:

- consistency with the nature (daily instantaneous, daily averaged, hourly instantaneous or averaged) of data used for calibration of the parameters
- a-posteriori verification in of the results in a control period on the same type of data. 

To be more clear, having data, I would split them  into two sets, and I would use one of them for calibration and the second for validation.  Validation has to be performed to give an estimate of prediction error (before having new data).  Last year, I heard a colleague, who investigated the minimal data set for doing this type of inferences. He said that a four-five years time series length (for daily data) was the optimal choice. As a consequence, to do some good forecasting one is expected to have a time serie of such length. 

Obviously speaking of discharges is one thing, speaking of evapotranspiration is another. In particular, I criticised the concept of potential evapotranspiration, and I have some problems in saying what is the daily potential evapotranspiration, if it is not the daily total potential evapotranspiration (mean evapotranspiration would be fine too, obviously), since this quantity is strongly varying during the day. Its use inside lumped models can  add further fuzziness depending on the internal structure of the model in use. 


Yours sincerely,

Christian Stocker

You are welcomed

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