Categories of systems of equations in ODEs based hydrological systems

This is the continuation of the reservoirology topic saga.  Especially preparatory for understanding  is the Reservoirology #3 post. Here we show that the same topological structure of Petri Nets can address various physical concepts related to a hydrological system conceptualised as a set of reservoir and therefore solvable as a set of ODEs.
The main ODE system, however, does not reveal all of the system. A finer inspection can be obtained by investigating travel times and concentration of tracers (being the theoretical point of view, the first, the experimental one, the second).

To fix some concept we wrote the short presentations above. Or just click here. The pdf contains itself links to other posts and literature.

Anke Hildebrandt's recent research

If you are interested in the hydraulics of plants, you should give a look to the recent production of Anke Hildebrandt. Her production encounter my favor since she is able to put together experimental work and theoretical work on the thermodynamics of trees. A topic on which recently I became interested in. Relevant among her production is the work on hess: A thermodynamic fomulation of root water uptake which was awarded as one of the best paper of 2017 in HESS. No more comments. Just papers to read below. 

Recent papers

Van Stan, J. T., Norman, Z., Meghoo, A., Friesen, J., Hildebrandt, A., Côté, J.-F., et al. (2017). Edge-to-Stem Variability in Wet-Canopy Evaporation From an Urban Tree Row. Boundary-Layer Meteorology, 165(2), 295–310. http://doi.org/10.1007/s10546-017-0277-7

Guderle, M., Bachmann, D., Milcu, A., Gockele, A., Bechmann, M., Fischer, C., et al. (2017). Dynamic niche partitioning in root water uptake facilitates efficient water use in more diverse grassland plant communities. Functional Ecology, 32(1), 214–227. http://doi.org/10.1111/1365-2435.12948

Metzger, J. C., Wutzler, T., Dalla Valle, N., Filipzik, J., Grauer, C., Lehmann, R., et al. (2017). Vegetation impacts soil water content patterns by shaping canopy water fluxes and soil properties. Hydrological Processes, 31(22), 3783–3795. http://doi.org/10.1002/hyp.11274

Weisser, W.W., C. Roscher, S. Meyer, A. Ebeling, G. Luo, E. Allan, H. Beßler, R. Barnard, N. Buchmann, F. Buscot, C. Engels, C. Fischer, M. Fischer, A. Gessler, G. Gleixner, S. Halle, A. Hildebrandt, H. Hillebrand, H. de Kroon, M. Lange, S. Leimer, X. Le Roux, A. Milcu, L. Mommer, P. Niklaus, Y. Oelmann, R. Proulx, C. Scherber, M. Scherer-Lorenzen, S. Scheu, T. Tscharntke, M. Wachendorf, C. Wagg, A. Weigelt, W. Wilcke, E.-D. Schulze, B. Schmid, N. Eisenhauer. Biodiversity effects on ecosystem functioning in a 14-year grassland experiment: patterns, mechanisms, and open questions. Basic and Applied Ecology, doi: 10.1016/j.baae.2017.06.002. (link)

Zimmermann, A., Voss, S., Metzger, J. C., Hildebrandt, A., & Zimmermann, B. (2016). Capturing heterogeneity: The role of a study area’s extent for estimating mean throughfall. Journal of Hydrology, 542(C), 781–789. http://doi.org/10.1016/j.jhydrol.2016.09.047

Guderle, M., D. Bachmann, A. Milcu, A. Gockele, M. Bechmann, C. Fischer, C. Roscher, D. Landais, O. Ravel, S. Devidal, J. Roy, A. Gessler, N. Buchmann, A. Hildebrandt. Dynamic niche partitioning in root water uptake facilitates efficient water use in more diverse plant communities. Functional Ecology, doi: 10.1111/1365-2435.12948. (link)

Metzger, J. C., N. Dalla Valle, T. Wutzler, J. Filipzik, R. Lehmann, M. Roggenbuck, D. Schelhorn, J. Weckmüller, K. Küsel, K. U. Totsche, S. Trumbore, A. Hildebrandt. Tracing spatial variation of canopy water fluxes to the soil with high resolution data. Hydrological Processes. doi: 10.1002/hyp.11274 (link)

Arnold, S., Attinger, S., Frank, K., Hildebrandt, A. 2016. Assessing the structural adequacy of alternative ecohydrological models using a pattern-oriented approach. Ecological Modelling 316: 52-61. doi: doi:10.1016/j.ecolmodel.2015.08.003. (link)

Hildebrandt, A. A. Kleidon and M. Bechmann. A thermodynamic fomulation of root water uptake. Hydrology and Earth System Sciences. 20: 3441-3454, doi: 10.51947hess-20-3441-2016. (link)

Milcu, A., W. Eugster, D. Bachmann, M. Guderle, Ch. Roscher, D. Landais, O. Ravel, A. Gessler, M. Lange, A. Ebeling, W. Weisser, J. Roy, A. Hildebrandt, N. Buchmann. 2015. Plant species and functional diversity increase grassland productivity-related water vapour fluxes: a combined Ecotron and modeling approach. Ecology 97(8): 2044-2054. doi: 10.1890/15-1110.1 (link)


Renner, M., S. K. Hassler, T. Blume, M. Weiler, A. Hildebrandt, M. Guderle, S. J. Schymanski, and A. Kleidon. Dominant controls of transpiration along a hillslope transect inferred from ecohydrological measurements and thermodynamic limits, Hydrology and Earth System Sciences 20: 2063-2083. doi: 10.5194/hess-20-2063-2016. (link)

Fischer, C., Tischer, J., Roscher, C., Eisenhauer, N., Ravenek, J. M., Gleixner, G., Attinger, S., Jensen, B., de Kroon, H., Mommer, L., Scheu, S., Hildebrandt, A. 2015. Plant species diversity affects infiltration capacity in an experimental grassland through changes in soil properties. Plant and Soil. 397(1): 1-16, doi: 10.1007/s11104-014-2373-5 (link)

Guderle M. and Hildebrandt A. 2015. Using measured soil water contents to estimate evapotranspiration and root water uptake profiles - a comparative study. Hydrology and Earth System Sciences. 19: 409-425. doi: 10.5194/hess-19-409-2015 (link)

Bechmann, M., C. Schneider, A. Carminati, D. Vetterlein, S. Attinger, A. Hildebrandt. 2014. Parameterizing complex root water uptake models - the arrangement of root hydraulic properties within the root architecture affects dynamics and efficiency of root water uptake. Hydrology and Earth System Sciences. 18:4189-4206. doi: 10.5194/hess-18-4189-2014 (link)

Fischer, C., C. Roscher, Jensen, N. Eisenhauer, J. Baade, S. Attinger, S. Scheu, W.W. Weisser, A. Hildebrandt. 2014. How do earthworm, soil texture and plant composition affect infiltration in managed grasslands along a plant diversity gradient? PLoS ONE9(6): e98987. doi:10.1371/journal.pone.0098987. (link)

Leimer, S., Kreutziger, Y., Rosenkranz, S., Beßler, H., Hildebrandt, A., Oelmann, Y., Weisser, W., Wirth, C. Wilcke, W., 2014. Plant diversity effects on the water balance of an experimental grassland. Ecohydrology, doi: 10.1002/eco.1464. (link)

Carminati, A., C. L. Schneider, A. B. Moradi, M. Zarebanadkouki, D. Vetterlein, H.-J. Vogel, A. Hildebrandt, U. Weller, L. Schüler, and S. E. Oswald. 2011. How the Rhizosphere May Favor Water Availability to Roots. Vadose Zone Journal 10:988. doi: 10.2136/vzj2010.0113. (link)

Kalbacher, T., C. L. Schneider, W. Wang, A. Hildebrandt, S. Attinger, and O. Kolditz. 2011. Modeling Soil-Coupled Water Uptake of Multiple Root Systems with Automatic Time Stepping. Vadose Zone Journal 10:727. doi: 10.2136/vzj2010.0099. (link)

Alexandrov, G. a., D. Ames, G. Bellocchi, M. Bruen, N. Crout, M. Erechtchoukova, A. Hildebrandt, F. Hoffman, C. Jackisch, and P. Khaiter. 2010. Technical assessment and evaluation of environmental models and software: Letter to the Editor. Environmental Modelling & Software 26:328-336. doi: 10.1016/j.envsoft.2010.08.004. (link)

If I was the head of my Department

I manifested to my colleague my availability to be voted for Department Head. Not an easy task indeed, and a challenge if I want to continue to do some research. However, this is the right time for doing it. In six years I will be too old to plan to for ten years in advance and the baton has to be given to others, while I will give "good advise, if I will not be able to give bad examples".
Today we are asked, the so far three candidates, to give our vision for our mandate in front  our peers and electors.

Below the above figure, you find my talk (in Italian). Have to say my opponents are good guys, and I have not problems to give up if I recognize if their will and view is better than mine.  At the end, I think one of the quality of good academics is to recognize where excellence stands.  My complete program can be found here. 

Towards a new SWMM, JSWMM

You want to design a storm water management system. What you usually get is a rainfall-runoff model. In this specific subfield, the model is SWMM. EPA SWMM contains many features that were implemented to simulate urban storm water depletion network. Meaning that there are specific model's parameters set for that, and that a community gathered around this tool.

However SWMM is not a system for designing sewers. Designing requires that you repeat the modeling actions several times. At the outlet of any pipe, you have to:

• estimate the runoff under a "design rainfall" coming from some intensity-duration-frequency curves.
• get the maximum discharge with an assigned return period (say 10 years)
• Use simplified hydraulics for obtaining the size of the pipe apt to contain the maximum discharge
• repeat the operation for the pipes downhill, without leaving out uphill branches.

Operation 2 above requires a search algorithm to find the rainfall duration that is responsible for the maximum discharge. The complete theory is in Rigon et al., 2011.

The point is that SWMM does not do the sequence of operation above. This is one of the reasons we implemented JSWMM. To see what it does, click on the figure.

News: A ne presentation of the work was given at the 2020 iEMSs biennial Conference and can be found here

On complex networks computation of mountain catchments

From June 12 to June 14 2018 in Trento there is the 5th European IAHR conference. I am convening (and also presenting a contribution) which derives from our modelling within the GEOframe system.

The scope of the presentation is to inform about functionalities of GEOframe and something of what it is hidden under the hood. Clicking on the figure above, please access the pdf of the presentation.

Snow related Ph.D. position (the Stradivari snow project)

The Stradivari project research aims to build better tools for analysing the processes of the hydrological cycle. The project is more focused on the tools (building the violin) but it does not forget the music that has to be played. It is conceived to account for hydrological processes interactions and feedbacks, and develop new mathematics (equations) for their description. Use of appropriate contemporary numerics is also part of the project. The overall project builds on the foundations given by the GEOtop (http://abouthydrology.blogspot.com/2015/02/geotop-essentials.html) model and the GEOframe-NewAGE (http://geoframe.blogspot.com/) infrastructure. 

It is time to move on the generation of snow models. The computation abilities and the physics of snow are now much better known than thirty years ago. However, most of the snow model are based on parameterisations which should be updated. We start from the experience made in GEOtop (versions 0.*,1.* and 2.*) which is capable of reliable snow height, temperature and densities, at operational level over all the Alps, but we look also to the experiences made by CROCUS, SnowPack and Alpine 3D. In particular GEOtop use highlighted various issues that we plan to overcome with a new version of the model, which requires both deepening the thermodynamics of snow and its numerical implementation.

In synthesis we identify the following aspects to be improved:

• Actual GEOtop snow model is 1-d. It can improved including the vapor phase movements explicitly. Besides, we can add modules to have a better account for: density, viscosity and, adding the vapor phase, type of grain. 
• The physics. Analysing the thermodynamics to keep out of the future formulation empirical parameterisations of the processes which revealed obsolete; 
• Adding Richards equation for water percolation; 
• Analysing the separation rainfall, snowfall through a more physical modelling than actual; 
• the description of deposition on canopies, and subsequent effects of vegetation on sublimation; the effect of slope and topography characteristics on snow deposition and sublimation 
• blowing snow in complex terrain 
• assimilation of hydro-meteorological data and calibration 
• integration with remote sensing data 

This research will be implemented in strict collaboration with MobyGIS, EURAC Research (Giacomo Bertoldi, Ph.D), Stephan Gruber,  Professor at Carleton University and with Niccolò Tubini, the Ph.D. student who is actually developing new theory codes for Richards equation and freezing soil. Collaborative and unselfish spirit is required in this research group.
The project has also some practical outcomes that are related to:

• the avalanche triggering 
• the water availability due to snow and glaciers melting (both in the short and long terms) 
• the hydroelectric production 

All the code developed will be done in Github (or similar platform), inside the GEOframe community and will be Open Source according to the GPL v3 license.

The candidate will take care of implementing, besides the code, the appropriate procedures for continuous integration of the evolving source code, and s/he will be also asked to maintain a regular rate of commits to the common open platform. Despite these conditions, and being free and open source, the code will be intellectual property by the coder. This will be guaranteed also by the components-based infrastructure offered by OMS3, which allows to better define the contributions of anyone.
The implementation part will be followed, accompanied by testing activities, either for mathematical consistency, than for physical consistency with experiments and field measurements.
The Ph.D. student is intended to produce, besides working and tested codes, also at least three papers in major journals (VQR Class A), of which, at least one as first Author. Duration of the doctoral studies could be three or four years.

This project can enter either the curriculum C (Environmental Engineering) or the curriculum A (Modelling and Simulation) of our doctoral school.

Further information of the policies of the research group can be found:

• To my students
• Working with us
• The scaring version of “working with us"
• About doing a Ph.D.
• Why Open Source ?
• Going beyond the present state of Art Of Hydrological Modeling (since 2011 but still valid)

Evaporation and Transpiration

This contains the video related to my interpretation of evapotranspiration.

The thermodynamics of evaporation

Definitions

Transport of vapor in the atmospheric boundary layer

Evaporation from soils

Transpiration

The energy and mass budget 

The Penman-Monteith approach