## Saturday, December 17, 2016

### Lectures on probability and second order random fields

This is a gift from twenty five years ago. These are lectures from a short course held in Padua at the Department of Applied Mathematics. We were younger then ! I remember the lectures by Diego Bricio Hernandez as exciting and interesting. Looking back at the nineties, one of the dominant topics, were random fields and the interplay of randomness with hydrological phenomena. The work of Gedeon Dagan was one of the growing paradigms. But random fields and techniques (see Bras and Rodriguez-Iturbe book) were ubiquitous in Hydrology. Here they come the Lectures by Diego Bricio Hernandez, a Mexican scholar in sabbatical at Padua University.

You can find the same lectures also on Google Books, but clicking on the figure above, you will have the pdf.  Diego also wrote this "On some guiding principles in mathematical modelling with special emphasis on determinism". Oldies but goodies.

## Thursday, December 15, 2016

### A travel time model for estimating the water budget of complex catchments

This is the presentation given by Marialaura Bancheri for her admission to the final exam to achieve a Ph.D. in Environmental Engineering. It contains a synthesis of her studies about spatially integrated models of the water budget, and about travel time theory. A model structure is also presented preliminarily containing five reservoirs.
These reservoirs model the hydrology  of a  Hydrologic Response Unit (HRU) of a basin  which are connected together to treat a river catchment (as shown in Rigon et al. 2016). The figure above is a Petri net representation of the set od ordinary differential equations that  constitute the mathematical models of a HRU. The model uses the river network structure to organise the components execution, a work made conjointly with Francesco Serafin.
By clicking on the Figure, you will see Marialaura's presentation.

## Wednesday, December 7, 2016

### A list of papers estimating the water budget at various scales

Since almost couple of decades I am trying to develop tools that evaluate the surface water budget components, and I look at the closure of the budget equation.  The outcomes of this research are our models GEOtop and our system JGrass-NewAGE, and some applications are listed below. My impression was that many researchers are talking of the water budget closure, since many actually have the knowledge and the tools for estimating the budget, but less are really doing it. We wrote  (more or less)  it in the introduction of one of our paper and we were asked by the reviewers to be more precise. The list below, certainly to be cleaned, improved and enriched, says that there are effectively many papers (out of around a hundred we inspected) that do it. They are distributed according to four  threads.
• The one of “global and continental hydrology” where the water budget of the whole earth or of the largest river basins is studied. The methods used are remote sensing data, global circulation models, large-scale hydrological models.
• One is (but the focus is more often on evaporation) based on the use of Budyko curves, at various scales.
• The  use models plus in-situ data, with various levels of simplification, usually from few kilometers to thousands of kilometers scales. Models are process-based (like  CATHY,  GEOtop  or ParFlow, to cite three of them)  or more conceptualised (as our JGrass-NewAGE). Data are the most various, depending on the spatial scale of the application and the type of model. Process-based models use more data (which is a richness or a weakness, depending on the point of view), while conceptual models use less data. Larger scale applications require a coarse graining of the data set and, obviously, a limitation in the description of spatial heterogeneity.
• Finally there are fully experimental papers, especially in forest and agricultural areas, with accurate measurements, for some specific plant stand, or even single trees.

In the selection of the paper below, I searched for the water budget equation, with all of the terms, its minimal expression being:

$\frac{\Delta S}{\Delta t} = P - ET - R$

where $S$ is the soil/groundwater storage, $P$ precipitation rate, $ET$ evapotranspiration, $R$ runoff. Various papers present a more articulated baudget, but certainly I did not listed the paper that not deals with the equation. Many papers, having “water budget” in the title, actually deal with evapotranspiration and were excluded. As Praveen Kumar (GS) argued to me, all good models preserve mass: but they often deal only with a part of the budget, and/or their authors are  concerned with other specific topic. Also these papers (and some really very  interesting were excluded).  Finally, please find below the list. A different version of the same list (and its LaTeX editable version)  with some comments about the spatial and temporal scales of the budget and some further information can be found here ( where references can be sorted).

P.S. - Another list (to review, just received from Roger Moussa) of water budget studies is here.

References

Adelana, S. M., Dresel, P. E., Hekmeijer, P., Zydor, H., Webb, J. A., Reynolds, M., & Ryan, M. (2014). A comparison of streamflow, salt and water balances in adjacent farmland and forest catchments in south-western Victoria, Australia. Hydrological Processes, 29(6), 1630–1643. http://doi.org/10.1002/hyp.10281

Arnold, J. C., & Allen, P. M. (2016). Estimating hydrologic budgets for three Illinois watersheds. Journal of Hydrology, 176, 57–77.
Azarderakhsh M,  Rossow WB, Papa F,  Norouzi H, Khanbilvardi R. Diagnosing water variations within the Amazon basin using satellite data. Journal of Geophysical Research: Atmospheres 116 (2011).

Batelaan, O., & De Smedt, F. (2007). GIS-based recharge estimation by coupling surface–subsurface water balances. Journal of Hydrology, 337(3-4), 337–355. http://doi.org/10.1016/j.jhydrol.2007.02.001

Bertoldi, G., Rigon, R., & OVER, T. M. (2005). Impact of watershed geomorphic characteristics on the energy and water budgets. Journal of Hydrometeorology, 1–29.

Brye, K. R., Norman, J. M., Bundy, L. G., & Gower, S. T. (2000). Water-Budget evaluation of Prairie and Maize Ecosystems, 64, 715–724.

Chen J,  Lee C, Tian-Chyi Yeh J, Yu J. A Water Budget Model for the Yun-Lin Plain, Taiwan. Water Resources Management 19, 483–504 (2005).

Claessens, L., Hopkinson, C., Rastetter, E., & Vallino, J. (2006). Effect of historical changes in land use and climate on the water budget of an urbanizing watershed. Water Resources Research, 42(3), n/a–n/a. http://doi.org/10.1029/2005WR004131

Cook, P. G., Hatton, T. J., Pidsley, D., Herczeg, A. L., Held, A., O'Grady, A., & Eamus, D. (2016). Water balance of a tropical woodland ecosystem, Northern Australia: a combination of micro-meteorological, soil physical and groundwater chemical approaches. Journal of Hydrology, 210, 161–177.

Dages C, Voltz M,  Bsaibes A,  Prévot L,  Huttel O,  Louchart X, Garnier F, S Negro. Estimating the role of a ditch network in groundwater recharge in a Mediterranean catchment using a water balance approach. Journal of Hydrology 375, 498–512 (2009).

Dean, J. F., Webb, J. A., Jacobsen, G. E., Chisari, R., & Dresel, P. E. (2015). A groundwater recharge perspective on locating tree plantations within low-rainfall catchments to limit water resource losses. Hydrology and Earth System Sciences, 19(2), 1107–1123. http://doi.org/10.5194/hess-19-1107-2015

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Marengo, J. A. (2004). Characteristics and spatio-temporal variability of the Amazon River Basin Water Budget. Climate Dynamics, 24(1), 11–22. http://doi.org/10.1007/s00382-004-0461-6

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