Residence time approaches to the hydrological budgets

The natural evolution of geomorphic unit hydrograph approach to the hydrologic response is the analysis of residence time of water for any of the processes in the hydrological budget. Indeed,  there exists something already done in this direction of research, and can be found in the work of Andrea Rinaldo and collaborators. Gianluca Botter talked about the topic in his speech reported here, in a recent post. Without the claim to be very general, very deep, or very informed, I am collecting here some papers of the group on the subject.
Residence time is important under several aspects. The more direct application of theories per residence time seems to be the estimation of pollutants transport around the catchments, but the use of isotopic tracers to determine the age of water, immediately move their applications also the  understanding of the dynamics of runoff formation with mixing between various "waters". If plants are included, also evapotranspiration can become part of the game thus modifying what we expect (See also the post here with related references). Why not, then, make a step forward and use the theory also for temperature (as a passive tracer) ?
This could disclose a way to follow the entropy production and fluxes in the hydrological cycle at catchment scale: a topic in itself.

References

Benettin, P., A. Rinaldo, and G. Botter (2013), Kinematics of age mixing in advection-dispersion models, Water Resour. Res., 49, 8539–8551, doi:10.1002/2013WR014708.

E. Bertuzzo, M. Thomet, G. Botter, A. Rinaldo, Catchment-scale herbicides transport: Theory and application, Advances in Water Resources 52 (2013), p. 232–242

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.

Botter, G., E. Bertuzzo, and A. Rinaldo (2011), Catchment residence and travel time distributions:
The master equation, GEOPHYSICAL RESEARCH LETTERS, VOL. 38, L11403, doi:10.1029/2011GL047666

Botter, G., Catchment mixing processes and travel time distributions, Water Resour. Res., 48, W05545, doi:10.1029/2011WR011160.

F. Comola, B. Schaefli, A. Rinaldo and M. Lehning, Thermodynamics in the hydrologic response: Travel time formulation and application to Alpine catchments, Water resour. Res., Accepted manuscript online: 13 FEB 2015 03:59AM EST | DOI: 10.1002/2014WR016228

Cornaton, F., and P. Perrochet (2006), Groundwater age, life expectancy and tran- sit time distributions in advective-dispersive systems: 1. Generalized reservoir the- ory, Advances in Water Resources, 29(9), 1267–1291, doi:10.1016/j.advwatres.2005. 10.009. 

Cornaton, F. J. (2012), Transient water age distributions in environmental flow systems: The time-marching Laplace transform solution technique, Water Resources Research, 48(3), n/a–n/a, doi:10.1029/2011WR010606. 

Cvetkovic, V., C. Carstens, J.-O. Selroos, and G. Destouni (2012), Water and solute transport along hydrological pathways, Water Resources Research, 48(6), W06,537, doi:10.1029/2011WR011367. 

Ginn, T. R. (1999), On the distribution of multicomponent mixtures over generalized ex- posure time in subsurface flow and reactive transport: Foundations, and formulations for groundwater age, chemical heterogeneity, and biodegradation, Water Resources Research, 35(5), 1395–1407. 

Ginn, T. R., H. Haeri, A. Massoudieh, and L. Foglia (2009), Notes on Groundwater Age in Forward and Inverse Modeling, Transport in Porous Media, 79(1), 117–134, doi:10.1007/s11242-009-9406-1. 

Harman, C. J. (2014), Time-variable transit time distributions and transport: Theory and application to storage-dependent transport of chloride in a watershed, Water Resources Research, doi:10.1002/2014WR015707. 

Kirchner, J., X. Feng, and C. Neal (2001), Catchment-scale advection and dispersion as a mechanism for fractal scaling in stream tracer concentrations, Journal of Hydrology, 254(1-4), 82–101, doi:{10.1016/S0022-1694(01)00487-5}. 

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. Isot., 28, 855–860.

Rinaldo, A. and Rodriguez-Iturbe, I., Geomorphological theory of the hydrologic response, Hydrol Proc., vol 10, 803-829, 1996

Rinaldo, A., K. J. Beven, E. Bertuzzo, L. Nicotina, J. Davies, A. Fiori, D. Russo, and G. Botter (2011), Catchment travel time distributions and water flow in soils, Water Resour. Res., 47, W07537, doi:10.1029/2011WR010478. (See also the complimentary material: here)

van der Velde, Y., P. J. J. F. Torfs, S. E. A. T. M. van der Zee, and R. Uijlenhoet (2012), Quantifying catchment-scale mixing and its effect on time-varying travel time distributions, Water Resources Research, 48, doi:{10.1029/2011WR011310}. 

Weiler, M., B. L. McGlynn, K. J. McGuire, and J. J. McDonnell (2003), How does rainfall become runoff? a combined tracer and runoff transfer function approach, Water Resources Research, 39(11), n/a–n/a, doi:10.1029/2003WR002331. 

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

Water table position in GEOtop simulations

One thing I learn from Aldo Fiori at CATHY's meeting in Padua on Monday, Jan. 17, was that having a water table at the base of a hillslope is changing the way that the hillslope responds to the rainfall input. This is particularly important for getting the right residence time of water, that through this water table is recirculated and resides more time.

The assumption seems to me reasonable. This has also clear implications on the setting of the initial conditions. In fact, it seems reasonable to put a water table at the same level where there are surface water, at least for most of the year, interpolating the water levels of the blue lines.

This obviously does not mean that the spin-out runs can be avoided (see previous posts), which should be performed to gain a dynamical equilibrium level of the water tables.

Certainly this implies a radical change with respect to the habit to assume an impermeable bedrock a few meters below the terrain surface, and imposes the necessity of a more deep discussion of the hydraulic properties of the bedrock itself.

Notable References to Aldo's work

Fiori, A., M. Romanelli, D.J. Cavalli, D.Russo, Numerical experiments of streamflow generation in steep catchments, JOURNAL OF HYDROLOGY, 339, 183-192, 2007.

Fiori, A., D. Russo, Numerical Analyses of Subsurface Flow in a Steep Hillslope under Rainfall: The Role of the Spatial Heterogeneity of the Formation Hydraulic Properties, WATER RESOURCES RESEARCH, 43, W07445, doi:10.1029/2006WR005365, 2007

Russo, D., A. Fiori. Equivalent Vadose Zone Steady-State Flow: An Assessment of its Capability to Predict Transport in a Realistic Combined Vadose Zone - Groundwater Flow System. WATER RESOURCES RESEARCH, 44, W09436, doi:10.1029/ 2007WR006170, 2008.

Fiori, A., D. Russo, Travel Time Distribution in a Hillslope: Insight from Numerical Simulations. WATER RESOURCES RESEARCH, 44, W12426, doi:10.1029/2008WR007135, 2008.

Russo, D., and A. Fiori, Stochastic analysis of transport in a combined heterogeneous vadose zone–groundwater flow system. WATER RESOURCES RESEARCH, 45, W03426, doi:10.1029/2008WR007157, 2009.

Fiori, A., D. Russo, M. Di Lazzaro. Stochastic analysis of transport in hillslopes: Travel time distribution and source zone dispersion. WATER RESOURCES RESEARCH, 45, W08435, 2009.