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.

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.

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

Fang, Z., H.R. Bogena, S. Kollet, J. Koch and H. Vereecken (2015): Spatio-temporal validation of long-term 3D hydrological simulations of a forested catchment using empirical orthogonal functions and wavelet coherence analysis. J. Hydrol. 529: 1754-1767, doi:10.1016/j.jhydrol.2015.08.011.

Fleischbein, K., Wilcke, W., Valarezo, C., Zech, W., & Knoblich, K. (2006). Water budgets of three small catchments under montane forest in Ecuador: experimental and modelling approach. Hydrological Processes, 20(12), 2491–2507. http://doi.org/10.1002/hyp.6212

Graf, A., Bogena, H. R., Drüe, C., Hardelauf, H., Pütz, T., Heinemann, G., & Vereecken, H. (2014). Spatiotemporal relations between water budget components and soil water content in a forested tributary catchment. Water Resources Research, 50(6), 4837–4857. http://doi.org/10.1002/2013WR014516

Harder, S. V., Amatya, D. M., Callahan, T. J., Trettin, C. C., & Hakkila, J. (2007). Hydrology and water budget for a Forested atlantic coastal plain watershed, South Carolina. Journal of the American Water Resources Association, 43(7), 563–575.

Hentschel, R., Bittner, S., Janott, M., Biernath, C., Holst, J., Ferrio, J. P., et al. (2013). Simulation of stand transpiration based on a xylem water flow model for individual trees. Agricultural and Forest Meteorology, 182-183, 31–42. http://doi.org/10.1016/j.agrformet.2013.08.002

Herron, N., & Wilson, C. (2001). A water balance approach to assessing the hydrologic buffering potential of an alluvial fan. Water Resources Res., 37(2), 341–351.

Hingerl L, Kunstmann H, Wagner S, Mauder M, Bliefernicht J, Rigon R. Spatiotemporal variability of water and energy fluxes - A case study for a meso-scale catchment in pre-alpine environment. Hydrological Processes 1–20 (2016).

Högström, U. (1968). Studies on the water balance of a small natural catchment area in southern Sweden, XX(4), 623–631.


Huntington, J.L., and Niswonger, R.G., 2012, Role of surface-water and groundwater interactions on projected summertime streamflow in snow dominated regions: An integrated modeling approach : Water Resources Research, vol. 48, W11524, doi: 10.1029/2012WR012319.

Hutley, L. B., Doley, D., Yates, D. J., & Boonsaner, A. (1997). Water Balance of an Australian Subtropical Rainforest at Altitude: the Ecological and Physiological Significance of Intercepted Cloud and Fog. Australian Journal of Botany, 45(2), 311–20. http://doi.org/10.1071/BT96014

Jothityangkoon, C., Sivapalan, M., & Farmer, D. L. (2001). Process controls of water balance variability in a large semi-arid catchment: downward approach to hydrological model development. Journal of Hydrology, 254, 174–198.

Kochendorfer, J. P., & Ramirez, J. A. (2010). Modeling the monthly mean soil-water balance with a statistical-dynamical ecohydrology model as coupled to a two-component canopy model. Hydrology and Earth System Sciences, 14(10), 2099–2120. http://doi.org/10.5194/hess-14-2099-2010

Landerer, F. W., Dickey, J. O., & Güntner, A. (2010a). Terrestrial water budget of the Eurasian pan-Arctic from GRACE satellite measurements during 2003–2009. Journal of Geophysical Research, 115(D23), D23115–14. http://doi.org/10.1029/2010JD014584

Lewis, C., Albertson, J., Zi, T., Xu, X., & Kiely, G. (2012). How does afforestation affect the hydrology of a blanket peatland? A modelling study. Hydrological Processes, 27(25), 3577–3588. http://doi.org/10.1002/hyp.9486

Lewis D, Singer MJ, Dahlgren RA, Tate KW. Hydrology in a California oak woodland watershed: a 17-year study. Journal of Hydrology 240, 106–117 (2000).

Lorenz, C., & Kunstmann, H. (2012). The Hydrological Cycle in Three State-of-the-Art Reanalyses: Intercomparison and Performance Analysis. Journal of Hydrometeorology, 13(5), 1397–1420. http://doi.org/10.1175/JHM-D-11-088.1

Luxmoore, R. J. (1983). Water Budget of an Eastern Deciduous Forest Stand. Soil Science Soc. Am. J., 47, 785–791. 

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

Maxwell, R. M., & Condon, L. (2016). Connections between groundwater flow and transpiration partitioning. Science, 353(6297), 377–379. http://doi.org/10.1126/science.aaf8589

Mitchell, V. G., McMahon, T. A., & Mein, R. G. (2003). Components of the total Water Balance of an urban Catchment. Environmental Management, 32(6), 735–746.

Munier S, Aires F, Schlaffer S, Prigent C, Papa F, Maisongrande P, Pan M. Combining data sets of satellite-retrieved products for basin-scale water balance study: 2. Evaluation on the Mississippi Basin and closure correction model. Journal of Geophysical Research: Atmospheres 119 (2014).


Niedzialek, J.M., and F.L. Ogden, 2012, First-order catchment mass balance during the wet season in the Panama Canal watershed, J. Hydrol. doi: 10.1016/j.jhydrol.2010.07.044.

Obojes, N., Bahn, M., Tasser, E., Walde, J., Inauen, N., Hiltbrunner, E., et al. (2014). Vegetation effects on the water balance of mountain grasslands depend on climatic conditions. Ecohydrology, 8(4), 552–569. http://doi.org/10.1002/eco.1524

Ogden, F.L., T.D. Crouch, R.F. Stallard, and J.S. Hall, 2013. Effect of land cover and use on dry season river runoff and peak runoff in the seasonal tropics of central Panama, Water Resour. Res. 49(12):8443-8462, doi:10.1002/2013WR013956.

Oliveira PTS, Nearing MA, Moran MS, Goodrich DC, Wendland E, Gupta HV. Trends in water balance components across the Brazilian Cerrado. Water Resources Research 50, 7100–7114 (2014).

Pan, M., & Wood, E. F. (2006). Data Assimilation for Estimating the Terrestrial Water Budget Using a Constrained Ensemble Kalman Filter. Journal of Hydrometeorology, 7, 534–547.

Pan X, Helgason W, Ireson A, Wheater H. Field-scale water balance closure in seasonally frozen conditions. Hydrology and Earth System Sciences Discussions 2016, 1–37 (2016)

Qu, W., H. R. Bogena, J. A. Huisman, M. Schmidt, R. Kunkel, A. Weuthen, B. Schilling, J. Sorg and H. Vereecken (2016): The integrated water balance and soil data set of the Rollesbroich hydrological observatory. Earth Syst. Sci. Data, 8: 517–529, doi:10.5194/essd-8-1-2016.

Sahoo, A. K., Pan, M., Troy, T. J., Vinukollu, R. K., Sheffield, J., & Wood, E. F. (2011). Reconciling the global terrestrial water budget using satellite remote sensing. Remote Sensing of Environment, 115(8), 1850–1865. http://doi.org/10.1016/j.rse.2011.03.009

Scarascia Mugnozza, G., Valentini, R., Spinelli, R., & Ervedo, G. (1988). Osservazioni sul ciclo dell'acqua in un bosco ceduo di Quercus cerris L. Annali Accademia Italiana Scienze Forestali, 3–22.

Schaake, J., Koren, V., Duan, Q., Mitchell, K., & Chen, F. (2007). Simple water balance model for estimating runoff at different spatial and temporal scales. Journal of Geophysical Research, 101(D3), 7461–7475.

Schreiner-McGraw, A. P., Vivoni, E. R., Mascaro, G., & Franz, T. E. (2016). Closing the water balance with cosmic-ray soil moisture measurements and assessing their relation to evapotranspiration in two semiarid watersheds. Hydrology and Earth System Sciences, 20(1), 329–345. http://doi.org/10.5194/hess-20-329-2016

Scott, R. L. (2010). Using watershed water balance to evaluate the accuracy of eddy covariance evaporation measurements for three semiarid ecosystems. Agricultural and Forest Meteorology, 150(2), 219–225. http://doi.org/10.1016/j.agrformet.2009.11.002

Sheffield, J., Ferguson, C. R., Troy, T. J., Wood, E. F., & McCabe, M. F. (2009). Closing the terrestrial water budget from satellite remote sensing. Geophysical Research Letters, 36(7), n/a–n/a. http://doi.org/10.1029/2009GL037338

Silberstein, R. P., & Sivapalan, M. (1995). MODELLING VEGETATION HETEROGENEITY EFFECTS ON TERRESTRIAL WATER AND ENERGY BALANCES. Environmental International, 21(5), 477–484.

Sottocornola, M. (2007, July). Four years of observations of carbon dioxide fluxes, water and energy budgets, and vegetation patterns in an Irish Atlantic blanket bog. Ph.D. Thesis (Chapter 6), (G. Kiely, Ed.).

Su, F., & Lettenmaier, D. P. (2009). Estimation of the Surface Water Budget of the La Plata Basin. Journal of Hydrometeorology, 10(4), 981–998. http://doi.org/10.1175/2009JHM1100.1

Tomasella, J., Hodnett, M. G., Cuartas, L. A., Nobre, A. D., Waterloo, M. J., & Oliveira, S. M. (2008). The water balance of an Amazonian micro-catchment: the effect of interannual variability of rainfall on hydrological behaviour. Hydrological Processes, 22(13), 2133–2147. http://doi.org/10.1002/hyp.6813

Vertessy, R. A., Watson, F. G. R., & Sullivan, S. K. (2001). Factors determining relations between stand age and catchment water balance in mountain ash forests. Forest Ecology and Management, 143, 13–26.

Wagner, S., Kunstmann, H., Bárdossy, A., Conrad, C., & Colditz, R. R. (2009). Water balance estimation of a poorly gauged catchment in West Africa using dynamically downscaled meteorological fields and remote sensing information. Physics and Chemistry of the Earth, Parts a/B/C, 34(4-5), 225–235. http://doi.org/10.1016/j.pce.2008.04.002

Wang H, Guan H, Gutiérrez-Jurado HA, Simmons CT. Examination of water budget using satellite products over Australia. Journal of Hydrology 511, 546–554 (2014).

Whitehead, D., & Kelliher, F. M. (1991). Modeling the water balancevof a small Pinus radiuta catchment. Tree Physiology, 9, 17–33.

Wilson, K. B., Hanson, P. J., Mulholland, P. J., Baldocchi, D. D., & Wullschleger, S. D. (2001). A comparison of methods for determining forest evapotranspiration and its components: sap-flow, soil water budget, eddy covariance and catchment water balance. Agricoltural and Forest Meteorology, 106, 153–168.

Yang, Dawen, Sun, F., Liu, Z., Cong, Z., Ni, G., & Lei, Z. (2007). Analyzing spatial and temporal variability of annual water-energy balance in nonhumid regions of China using the Budyko hypothesis. Water Resources Research, 43(4), n/a–n/a. http://doi.org/10.1029/2006WR005224

Yao, Y., Liang, S., Xie, X., Cheng, J., Jia, K., Li, Y., & Liu, R. (2014). Estimation of the terrestrial water budget over northern China by merging multiple datasets. Journal of Hydrology, 519, 50–68. http://doi.org/10.1016/j.jhydrol.2014.06.046

Yoshiyukiishii YK, Nakamura R., Water balance of a snowy watershed in Hokkaido, Japan. Northern Research Basins Water Balance 13 (2004).

Zhang, L., Potter, N., Hickel, K., Zhang, Y., & Shao, Q. (2008a). Water balance modeling over variable time scales based on the Budyko framework – Model development and testing. Journal of Hydrology, 360(1-4), 117–131. http://doi.org/10.1016/j.jhydrol.2008.07.021