Stochastic Soil Water Dynamics, and Ecohydrology, According to Amilcare Porporato

Last March 19 and 20, 2012, was there was the occasion to celebrate Ignacio Rodriguez-Iturbe' 70. In Princeton a lot of friends met and some interesting seminars on the topic covered and/or initiated by Ignacio took place. All of this fantastic material should be available soon on Princeton's web sites. Meanwhile they format the videos, I am summarizing here the first of the talks, the one given by Amilcare Porporato (on the right  in the picture - with purple jacket- with Eric VanMarcke on the left).

The idea behind Amilcares (Ignacio's own, and others like Luca Ridolfi, Paolo d'Odorico and Andrea Rinaldo, naming just the seniors of the group) is assuming a stochastic forcing of the soil water balance as given by rainfall (Ignacio worked a lot on  random model of precipitation, e.g., see the classic Random Function and Hydrology with Raphael Bras) incorporated into a probabilistic description of soil water balance. Soil moisture, in fact, is thougth as the key driver of ecohydrological, biogeochemical and hydrometeorological processes and what comes as a consequence. According to Amilcare, the progenitor of this research has to be found in the paper by P. Eagleson, 1978, and followed by some other relevant contribution by Bras and Cordova, 1981, Rodriguez-Iturbe et al., 1991, Milly, 1993 and Rodriguez-Iturbe et al., 1999.

To these pioneering works followed several works of "generalizations": D'Odorico et al., 2000, Porporato et al., 2006, containing the interannual variability and the "superstatistics"; Salvucci et al., 2000, with experimental verifications; Laio et al., 2001 with a more realistic loss function; Porporato et al., 2004 with classification of soil water balance; Daly et al., 2004, introducing arguments on the plant photosynthesis; Ridolfi et al., 2005,2006 including the water table and the capillary rise.

In the whole set of these papers the strategy followed was:

• Extract low-dimensional components of the dynamics;

• Surrogate external forcing and internal heterogeneities (high-dimensional components) with suitable noise (probabilistic description)

• Use minimalist models:
– analytical solutions;
– general relationships among fundamental groups;
– Coupling with other processes (plant,nutrients, etc.)

• Interpreting more complete simulations and schemes

Other papers cited in the presentation were: Daly et al. AWR, 2008; Gollan et al., 1985 (about the stomata response); Federer, 1979 (about a simple plant-atmosphere model), Porporato et al.,  2004, Daly and Porporato, 2010 (studying analitical steady state solutions of the master equation derived from the application of the assumptions above).

All the previous papers deal with local, point dynamics. However, some papers also have some spatial dynamics and/or descrition. Just looking at the vertical profile: Celia et al., 2001; Laio, 2006, D'Odorico and Ridolfi, 2000. Looking at the spatial soil moisture variability and about scaling of soil moisture: Rodriguez-Iturbe et al., 1995; Isham et al., 2006; about spatial Poisson processes: Manfreda et al., 2006 ; Using a Reynolds averaging approach: Katul et al., 2002; Albertson and Montalto, 2003; looking at the role of topography: Caylor et al., 2007; Instanbulluoglu and Bras et al., 2006.

Some papers, finally, tried to link soil moisture with the rainfall processes and precipitation recycling (D'Odorico and Porporato, 2004; Porporato and D'Odorico, 2004)

The above about the recent past: enough, I think for a novel reader.

However, the more recent work try to embrace a complexity of interactions of which an example is the work he made with Vico: Vico and Porporato, WRR 2010; AWR 2011a,b; Manzoni and Porporato, EOS (2006), Ecology (2012) an other papers of which you can find the reference and sometimes the pdf below.


References

Albertson, J. D., and N. Montaldo, Temporal dynamics of soil moisture variability: 1. Theoretical basis, Water Resour. Res., 39(10), 1274, doi:10.1029/2002WR001616, 2003.

Bras, R. L. and J. R. Cordova (1981), Intraseasonal water allocation in deficit irrigation, Water Resour. Res., 17(4), 866–874, doi:10.1029/WR017i004p00866 ?

Caylor K.K, Manfreda S. and Rodriguez-Iturbe, I., On the coupled geomorphological and ecohydrological organization of river basins, Advances in Water Resour., 28, 69-86, 2005

Daly, Edoardo, Amilcare Porporato, Ignacio Rodriguez-Iturbe, 2004: Coupled Dynamics of Photosynthesis, Transpiration, and Soil Water Balance. Part II: Stochastic Analysis and Ecohydrological Significance. J. Hydrometeor, 5, 559–566

Daly E. Oishi A.C., Porporato A., Katul G., A stochastic model for daily subsurface CO2 concentration and related soil respiration, Advances in Water Resour., 31,987-994, 2008

Daly and Porporato, Effect of different jump distributions on the dynamics of jump processes, Phys. Rev. E., 2010

D'Odorico, P., L. Ridolfi, A. Porporato, and I. Rodriguez-Iturbe (2000), Preferential states of seasonal soil moisture: The impact of climate fluctuations, Water Resour. Res., 36(8), 2209–2219, doi:10.1029/2000WR900103.

D'Odorico, P. and Porporato, A., Preferential states in soil moisture and climate dynamics, PNAS, 2004

Eagleson, P., Climate, Soil, and Vegetation 3. A simplified model of soil moisture movement in the liquid phase, Water Resour. Res., 14(5), 1978

Federer, C. A. (1979), A soil-plant-atmosphere model for transpiration and availability of soil water, Water Resour. Res., 15(3), 555–562, doi:10.1029/WR015i003p00555.

T. Gollan, N. C. Turner and E. -D. Schulze, The responses of stomata and leaf gas exchange to vapour pressure deficits and soil water content, Oecologia, 65 (3), 365-362, 1985

Guswa, A. J., M. A. Celia, and I. Rodriguez-Iturbe, Models of soil moisture dynamics in ecohydrology: A comparative study,Water Resour. Res., 38(9), 1166, doi:10.1029/2001WR000826, 2002

Isham, V., Cox, D.R., Rodríguez-Iturbe,  I., Porporato, A., Manfreda, S. (2005).
Mathematical characterization of the space-time variability of soil moisture, Proceedings
of the Royal Society A: Mathematical, Physical and Engineering Sciences, 461(2064),
4035–4055.

Istanbulluoglu, E. and R. L. Bras (2006), On the dynamics of soil moisture, vegetation, and erosion: Implications of climate variability and change, Water Resour. Res., 42, W06418, doi:10.1029/2005WR004113

Katul, G., P. Wiberg, J. Albertson, and G. Hornberger (2002), A mixing layer theory for flow resistance in shallow streams, Water Resour. Res., 38(11), 1250, doi:10.1029/2001WR000817.

Katul, G., Porporato, A., and Orem R., Stochastic Dynamics of Plant-Water Interactions., Annu. Rev. Ecol. Evol. Syst. 2007. 38:767–91

Laio, F., A. Porporato, C. P. Fernandez-Illescas, and I. RodriguezIturbe, Plants in water-controlled ecosystems: Active role in hydrologic processes and response to water stress, IV, Discussion of real cases, Adv. Water Resour., 24(7), 745–762, 2001.

Laio, F. (2006), A vertically extended stochastic model of soil moisture in the root zone, Water Resour. Res., 42, W02406, doi:10.1029/2005WR004502.

Manfreda, S. and I. Rodríguez-Iturbe (2006), On the spatial and temporal sampling of soil moisture fields, Water Resour. Res., 42, W05409, doi:10.1029/2005WR004548.

Manzoni, A., and Porporato, A., Soil Biology and Biochemistry, A theoretical analysis of nonlinearities and feedbacks in soil carbon and nitrogen cycles, Volume 39, Issue 7, July 2007, Pages 1542–1556 (http://c-h2oecology.env.duke.edu/Duke-FACE/PDF/sbb39-07.pdf)

Manzoni, S.,  Schimel, J.P, and Porporato, A., Responses of soil microbial communities to water stress: results from a meta-analysis, Ecology, 2012, (doi: 10.1890/11-0026.1)

Milly, P. C. D. (1993), An analytic solution of the stochastic storage problem applicable to soil water, Water Resour. Res.,29(11), 3755–3758, doi:10.1029/93WR01934
Porporato, A. & D'Odorico, P. (2004), State transitions driven by state-dependent Poisson Noise, Phys. Rev. Lett. 92

Porporato, A., Daly, E., Rodriguez-Iturbe, I., Soil Water Balance and Ecosystem Response to Climate Change, The American Naturalist, 164(5), 2004

Porporato, A. , Vico, G. , Fay, Philip A., Superstatistics of hydro-climatic fluctuations and interannual ecosystem productivity, NAL, 2006

Rigby, J.R and  Porporato, A., Simplified stochastic soil-moisture models: a look at infiltration, Hydrol. Earth Syst. Sci., 10, 861-871, 2006 www.hydrol-earth-syst-sci.net/10/861/2006/doi:10.5194/hess-10-861-2006

Rodriguez-Iturbe, I., P. D'Odorico, F. Laio, L. Ridolfi, and S. Tamea (2007), Challenges in humid land ecohydrology: Interactions of water table and unsaturated zone with climate, soil, and vegetation, Water Resour. Res., 43, W09301, doi:10.1029/2007WR006073. ???

Rodriguez-Iturbe, I., D. Entekhabi, and R. L. Bras (1991), Nonlinear Dynamics of Soil Moisture at Climate Scales: 1. Stochastic Analysis, Water Resour. Res., 27(8), 1899–1906, doi:10.1029/91WR01035
Rodriguez-Iturbe, I, A. Porporato, L. Ridolfi, V. Isham, and D.R. Cox, Probabilistic modelling of water balance at a point: the role of climate, soil and vegetation, PRSA, 1999

Ridolfi, L., P. D'Odorico, F. Laio, S. Tamea, and I. Rodriguez-Iturbe (2008), Coupled stochastic dynamics of water table and soil moisture in bare soil conditions, Water Resour. Res., 44, W01435, doi:10.1029/2007WR006707.

Rodriguez-Iturbe, I, Gregor K. Vogel, R. Rigon, D. Entekhabi, F. Castelli and A. Rinaldo, On the spatial organization of soil moisture fields, Journal of Geophysical Research, 22(20), 2757-2760, 1995

Salvucci, G. D. (2001), Estimating the moisture dependence of root zone water loss using conditionally averaged precipitation, Water Resour. Res., 37(5), 1357–1365, doi:10.1029/2000WR900336

Tamea, S., F. Laio, and L. Ridolfi (2005), Probabilistic nonlinear prediction of river flows, Water Resour. Res., 41, W09421, doi:10.1029/2005WR004136.

Vico, G. and A. Porporato (2010), Traditional and microirrigation with stochastic soil moisture, Water Resour. Res., 46, W03509, doi:10.1029/2009WR008130.

Vico, Giulia and Porporato, Amilcare, From rainfed agriculture to stress-avoidance irrigation: I. A generalized irrigation scheme with stochastic soil moisture, Advances in Water Resources, vol 34 no. 2 (2011), pp. 263--271.

Vico, G. and Porporato, A., From rainfed agriculture to stress-avoidance irrigation: II. Sustainability, crop yield, and profitability, Advances in Water Resources, vol 34 no. 2 (2011), pp. 272--281.