Tuesday, December 2, 2014

Evapotranspiration parameters in coarse grained modelling

To have a little rehearsal on Evapotranspiration look first at my post on Potential Evapotranspiration. where its estimation with Dalton equation and simplified model, like Penman-Monteith (PM) or Priestley-Taylor (PT) is covered.  We concentrate here on the simplest of the formulas, the PT's one.

Once your get PT alpha_p, you can estimate pET but still you have to introduce a further reduction to get the actual evapotranpiration (aET). The method popularized by the ecohydrology literature (e.g. read Amilcare Porporato here) is to introduce a linear decrease of pET with water storage in the root zone "reservoir".

Both the passage, the determination of pET in the framework of PT and the linear reduction with storage have, in my view, strong drawbacks from the quantitative point of view.
One can get the alphap, but literature show a huge variability. So literature is quite useless to obtain quantitative results, with a decent certainty.
The (linear) decrease of ET with soil moisture requires the determination of at least one additional coefficient. In fact, it is well known that ET has two stage: stage one, when ET is "at the potential rate", independently from the water content up to a critical soil moisture, well below saturation, when ET is depressed, not by increasing suction (the so called Kelvin effect, which is a second order effect) but by the fact that pores at the soil or leaf surface to which water is supplied are more and more far apart (see recent literature by Dani Or and co-workers). This critical soil moisture, at which the second stage ET starts is a further coefficient, and its identification with saturation implies a clear underestimation of ET. It is usually given for granted by my friends ecohydrologists and my master IRI's literature that it can be determined. But I do not have to remind to you all how much elusive it is the definition of the "root zone soil moisture" just to cite a practical aspect of it.
Even if field-fellow-scientists claim to have measured it, I know that who tried in lab of few square meters really struggled to close the water budget budget under very controlled conditions (let's say: personal communications). In nature, as my hero Pete Eagleson teaches, interaction among plants distribution, atmosphere, and rugged terrain makes any of the above coefficient heterogeneous, and the trials to find a rational to all of it, kind of frustrating to my eyes.

Said all of this, let's go back to PT, and you can give a look to the presentation below to know what happens when you coarse-grain your model resolution in time and space.


[1] Priestley, C.H.B. and Taylor R. J., On the assessment of surface heat flux and evaporation using large scale parameters, Monthly Weather Review, Vol. 100, No 2, 81-92,1972

[2] - Rigon, R.,  Evapotranspiration  Slides

[3] - Rigon, R.,  Solar Radiation Slides

[4] - Rodriguez-Iturbe, I., Porporato, A., Ridolfi, L., Isham, V., & Cox, D. (1999). Probabilistic modelling of water balance at a point: the role of climate, soil and vegetation. Prooceedings of the Royal Society, 455, 3879–3805

[5] - Rigon R., Bertoldi G e T. M. Over, GEOtop: A distributed hydrological model with coupled water and energy budgets, Vol. 7, No. 3, pages 371-388

[6] Bertoldi G. R. Rigon e T. M. Over, Impact of watershed geomorphic char- acteristics on the energy and water budgets, Vol. 7, No. 3, pages 389-394, 2006

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