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. 

Long wave radiation

I have already dedicated some posts and a paper to radiation. Radiation is deemed necessary to drive evapotranspiration and snow models. However, our previous efforts were dedicated mainly to shortwave radiation. Especially Giuseppe Formetta, however, was pushing to have a solid parametrisation also for long wave radiation (a.k.a as infrared radiation). The preliminary results are shown in the talk here given at the iEMSs conference in S.Diego.

In the talk we used Ameriflux measurements to calibrate a quite long list of parameterisations. No new theory, but testing of theories developed by others, in that kind of agnostic approach suggested by the use of modelling by component, supported by OMS and used in the JGrass-NewAGE system. The same topic in a poster by Marialaura Bancheri, my youngest Ph.D., here.

Four academic brothers (of mine)

I have many academic brother since Andrea Rinaldo is very prolific in generating first class researchers. I have even more I consider the inheritance of Ignacio Rodriguez-Iturbe, my postdoc advisor at (that time at) Texas A&M Unversity. Of the many three agreed to send me the presentations they gave at the Honour doctorate of Andrea Rinaldo, and you can find them with a little comment here below. 

The older (of the three) brother, Marco Marani, from Padova University and Duke, presented a work on the soil-water-plants continuum. He emphasize the role of roots in modifying the soil water distribution, otherwise controlled by Darcy flows. However, he also studied and talked about the influence of the soil-plants-atmosphere continuum. The presentation is here. The couple of references cited are: Volpe et al., 2013 and Manoli et al., 2014. 

Gianluca Botter talked about the travel time distribution approach to catchment scale transport. A topic that intersects also the “old water paradox” querelle, but is, in general, pretty effective in getting the distribution of pollutants. This approach has a long story that put its roots, in Gedeon Dagan’s work, as well as in Rodriguez-Iturbe geomorphic unit hydrograph. Andrea own papers on Mass response function with Sandro Marani can also be considered at the foundations of this presentation. 

Among the reference, recent papers on the topic are Botter et al., 2010 and Benettin et al., 2013. The presentation is here

Enrico Bertuzzo (GS) covered instead the new topic of water borne  diseases and their spreading along rivers. The way Enrico and coworkers analysed the problem, certainly inherited many notions and ideas sprout the early studies on river networks structure by Andrea (I had a part in it), but also on recent and domain specific achievements and findings. In the presentation he cited just one paper, but the research outcomes on the topic are certainly copious and exciting. The presentation is here. 

Andrea D’Alpaos (GS)  talked about tidal networks, their formation, their shapes, their similarity or dissimilarity from river networks. All of it in a blend of equations, analysis in the field and lab experiments. Another fascinating topic that was started with Andrea.  The presentation is here.

Overall is interesting to judge the differentiation of topics and methods used by the authors, expressing that each developed his on research personality and attitude.

Thermodynamics

It is strange that I did not dedicate any post to thermodynamics, since it was one of "the topics" of my work during the last years. As usual I approached Thermodynamics by analysing  a physical process. It was the dynamics of freezing soil (e.g. see Dall’Amico et al., 2011) where phase transitions in soil under capillary effects was the problem under scrutiny.  To get rid of the tens of empirical equations, and desperate after the reading of some nonsensical books and papers, I literally understood what the words of C. Truesdall wanted mean with:

“Thermodynamics today is a blend of statements from most of the founders: Gibbs, Planck, Boltzmann, even from information theory. Confusion is nearly universal. Constitutive properties are not delimited, just pulled out from under the table as needed.”

I decided to calm down, and face it from the scratch. 

Reading the firsts chapters of Dall’Amico thesis would give you a quick synthesis of what I learned with Matteo: it is a good introduction to the topic. Dall'Amico introduces a new and fresh notation that can help the understanding. 

For a more in-deep information, I selected the following list of books and papers (which you should read, with Dall'Amico notation in mind).

I would start from:

• Callen, H. (1985), Thermodynamics and an Introduction to Thermodynamics, John Wiley and & Sons.

And continue with:

• Aharon Katzir Katchalsky, P.F. Curran (1965), Nonequilibrium Thermodynamics in Biophysics, Harvard University Press,  - 248 pp

the latter was a revelation (I really loved their chapter on diffusion). Callen, on his side, with his axiomatic approach, frees your mind from several encrustations that you can have learnt before.

Those three references above should do the main work. However, I would add some other books and papers:

• Zia, R. K. P., Redish, E., & McKay, A. (2009). Making sense of the Legendre Transform. American Journal of Physics, 77(7), 614–622. 

the above, for really understanding the role of Legendre transform

• Bohren, C., and B. Albrecht (1998), Atmospheric Thermodynamics, 402 pp. (I understand, not a cheap book but it also contains a lot of good stuff)

This book above made me gain consciousness about the nonsensical algebra notation of Thermodynamics: I  agree with their criticism, which I completely endorse (actually also  Callen and  Katchalsky-Curran books mildly use the traditional notation. I say mildly because, once you are advised, you can read through it, in their books).  Other clarifying chapters can be found in:

• Müller, I and Weiss, W (2005),  Entropy and Energy: A Universal Competition, Springer & Verlag (Müller is also author of a history of thermodynamics).

Particularly I liked Muller and Weiss chapters on ideal gas and ideal rubber, and many other parts, indeed.

The classic on non-equilibrium thermodynamics is the old Dovers’book by De Grot and Mazur. However, in reading it one gets the idea of a great generality, and I keep in my bookshelf, but, at the same time, inherits a sense of frustration for the too concise treatment of the subject.

I would also mention one (defeated ?) but stimulating view on thermodynamics, the Jaynes one's   explained in

• W.T. Grandy’s book: Entropy and Time Evolution of Macroscopic Systems, Oxford University Press, 2008 

Going more specialised, I would also read

• Zdunkowsky, W. , and Bott, A., Thermodynamics of the atmosphere, A course in theoretical meteorology, Cambridge University Press, 2004.
• Ganguly, J. Thermodynamics in Earth and Planetary Sciences, Springer 2010

and finally I would also include in the lectures

• Reguera, D., Rubi, J. M. and Vilar J.M.G.,  The mesoscopic dynamics of thermodynamic systems, Phys. Chem. B, 2005, 109 (46), pp 21502–21515, DOI: 10.1021/jp052904, 2005

This last contribution open the way to the generalisation of thermodynamics to include small systems, in which the presences of few atoms would otherwise prevent to apply thermodynamics.

There are other books are in my bookshelf, but which I mentioned above can be enough for starting. I am pretty sure that also some good web coursewares is out there, and I would thanks if someone can address them to me.