Old water contribution to streamflow: Insight from a linear Boussinesq model

This is a paper by Aldo Fiori one one of the most interesting issues in Hydrology, just appeared in Water Resources Research (Fiori, 2012). I already talk on this issue in the blog one year ago or so. Now Aldo comes back with a new paper which I will start to read avidily.

This is an excerpt from his  introduction, with some references:

"The understanding of the main physical processes which rule runoff generation in catchments is limited by the so-called ‘‘old water paradox.’’ The latter states that a (sometimes significant) fraction of the runoff volume after a rainfall event is pre-event, or ‘‘old.’’ Experiments with passive tracers suggest that most of the water contributing to stormflow is pre-event [Neal and Rosier, 1990; Sklash, 1990; McDonnell, 2003; Kirchner, 2003; Botter et al., 2010], with percentages often close to 75% of the total flow [Buttle, 1994]. This experimental evidence, which seems to invalidate most of the existing rainfall-runoff models, have been explained by means of a few mechanisms [Beven, 2002]. Among the latter is the propagation of pressure waves with high celerity [e.g., Beven, 1981], the capillary fringe-ridging hypothesis [see, e.g., Sklash and Farvolden, 1979 ; Gillham, 1984 ; McDonnell, 1990 ; Cloke et al., 2006; Fiori et al., 2007], and transmissivity feedback or macropore flow [McDonnell and Buttle, 1998]. The issue is still a matter of debate [McDonnell et al., 2010], and the principal physical processes controlling the release of old water and the partition between old and new water are still poorly understood. This problem has a crucial impact on several processes of interest in hydrology, for example, the development of meaningful rainfall-runoff models and the analysis of solute transport in catchments, which is often performed in terms of travel time distribution [e.g., McGuire and McDonnell, 2006]. Among the processes which may control the age of water we point here at the ‘‘potentially under-appreciated importance of old ground- water input to streams,’’ and ‘‘we thus need to have a better understanding of where and when old groundwater inputs are important’’ (both statements by McDonnell et al. [2010])."

On the side of pressure wave, I would add the reference to the work by Rasmussen et al., (2000) which refers to an experiment of percolation through saprolite, and the  paper by Torres et al. (1998) where these pressure waves are seen in the field (see also the Commentary by Torres 2002).

Certainly in producing a retardation in travel times concurs also the slowness of flow in unsaturated conditions (e.g. Lanni et al., 2012a,b which apparently talk about shallow landslides, but, in fact, talk also about hillslopes' residence time) but still they do not explain enough of the very large age of water in streams.

However,  measuring travel times and interpreting them is not all that easy (e.g. Rinaldo et al. 2011, with an important reference to Niemi, 1977), and maybe some measurements should be rethought.

Talking about vague references (to me, obviously), some work by Jean Yves Parlange, on fast propagation of water in soils, could be interestingly related to this topic.  But this is just a stub for future literature investigations (for instance the paper on sound waves referred here should be related to the fast propagation of pressure waves).

In any case, again a lot of stuff to read.

References

Beven, K. (1981), Kinematic subsurface stormflow, Water Resour. Res., 17, 1419–1424.

Beven, K. J. (2002), Rainfall-Runoff Modelling, The Primer, 360 pp., John Wiley, Hoboken, N. J.

Botter, G., E. Bertuzzo, and A. Rinaldo (2010), Transport in the hydrologic response: Travel time distributions, soil moisture dynamics, and the old water paradox, Water Resour. Res., 46, W03514, doi:10.1029/ 2009WR008371.

Buttle, J. M. (1994), Isotope hydrograph separations and rapid delivery of pre-event water from drainage basins, Prog. Phys. Geogr., 18(1), 16–41.

Cloke, H. L., M. G. Anderson, J. J. McDonnell, and J. P. Renaud (2006), Using numerical modelling to evaluate the capillary fringe groundwater ridging hypothesis of streamflow generation, J. Hydrol., 316, 141–162.

Fiori, A., and D. Russo (2007), Numerical analyses of subsurface flow in a steep hillslope under rainfall: The role of the spatial heterogeneity of the formation hydraulic properties, Water Resour. Res., 43, W07445, doi:10.1029/2006WR005365.

Fiori, A. (2012), Old water contribution to streamflow: Insight from a linear Boussinesq model, Water Resour. Res., 48, W06601, doi:10.1029/2011WR011606.

Gillham, R. W. (1984), The capillary fringe and its effect on water table response, J. Hydrol., 67, 307–324.

Kirchner, J. W. (2003), A double paradox in catchment hydrology and geo- chemistry, Hydrol. Processes, 17, 871–874.

Lanni C., J.J. McDonnell, L. Hopp, R. Rigon, 2012. Hydrological controls on shallow landslide triggering: the role of soil depth and bedrock topography. Earth Surface Processes and Landforms, in print (see http://abouthydrology.blogspot.it/2012/01/simulated-effect-of-soil-depth-and.html)

C. Lanni, M. Borga, R. Rigon, and P. Tarolli, Modelling catchment-scale shallow landslide occurrence by means of a subsurface flow path connectivity index, Hydrol. Earth Syst. Sci. Discuss., 9, 4101-4134, 2012, www.hydrol-earth-syst-sci-discuss.net/9/4101/2012/doi:10.5194/hessd-9-4101-2012

McDonnell, J. J. (1990), A rationale for old water discharge through macro- pores in a steep, humid catchment, Water Resour. Res., 26 (11), 2821– 2832.

McDonnell, J. J., and J. M. Buttle (1998), Comment on ‘‘A deterministic empirical model of the effect of the capillary-fringe on nearstream area runoff. 1. description of the model’’ by Jayatilaka CJ, Gillham RW (J. Hydrol. 184 (1996) 299–315), J. Hydrol., 207, 280–285.

McDonnell, J. J. (2003), Where does water go when it rains? Moving beyond the variable source area concept of rainfall-runoff response, Hydrol. Processes, 17(9), 1869–1875.

McDonnell, J., et al. (2010), How old is the water ? Open questions in catchment transit time conceptualization, modelling and analysis, Hydrol. Processes, 24(12), 1745–1754.

McGuire, K. J., and J. J. McDonnell (2006), A review and evaluation of catchment transit time modelling, J. Hydrol., 330, 543–563.

Niemi, A. J. (1977), Residence time distribution of variable flow processes, Int. J. Appl. Radiat. Isotopes, 28, 855–860.

Neal, C., and P. T. W. Rosier (1990), Chemical studies of chloride and sta- ble oxygen isotopes in two conifer afforested and moorland sites in the British uplands, J. Hydrol., 115(1–4), 269–283.

Rasmussen, T.C., Baldwin, R.H. Jr.,  Dowd, J. F., and  Williams, A.G., Tracer vs. Pressure Wave Velocities through Unsaturated Saprolite, Soil Sci. Soc. Am. J. 64:75–85 (2000).

Rinaldo, A. Beven, K. J., Bertuzzo, E., Nicotina, L., Davies, J., Fiori, A., Russo D. and G. Botter G., Catchment travel time distributions and water flow in soils, Water Resources Research, vol. 47, p. -, 2011.

Sklash, M. G., and R. N. Farvolden (1979), The role of groundwater in storm runoff, J. Hydrol., 43, 45–65.

Sklash, M. G. (1990), Environmental isotope studies of storm and snowmelt runoff generation, in Process Studies in Hillslope Hydrology, edited by M. G. Anderson and T. P. Burt, pp. 401–435, John Wiley, N. Y.

Torres R, Dietrich WE, Montgomery DR, Anderson SP, Loague KM. 1998. Unsaturated zone processes and the hydrologic response of a steep, unchanneled catchment. Water Resources
Research 34(8): 1865– 1879.

Torres R., A threshold condition for soil-water transport, Hydrol. Process. 16, 2703–2706 (2002) DOI: 10.1002/hyp.5060