scales and hydrology in 2020
TRANSCRIPT
Scales & Hydrology in 2020
Potenza, 24 Febbraio 2017
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Riccardo Rigon, Marialaura Bancheri, Niccolò Tubini, Giuseppe Formetta, Francesco Serafin
Three quarks for Muster Mark
J. Joyce
The computational effort and the quantity of information to manage in a hydrologcial modelling project of areas of many thousands or even millions of square kilometers become easily so demanding to become impossible to support. This statement has been always a motivation to discard any trial to investigate what could actually be done or not in advance. Through the experience made with the model GEOtop, we analyse in this talk the state-of-art in this field.
The mathematical (formal) aspects of the hydrological problem to treat seamlessly different spatial and temporal scale, can be framed by saying that model process-based (as GEOtop) have at their core systems of partial differential equations (PDEs), while lumped models (with their physics aggregated at the basin or at at hillslope scale) constitute systems of ordinary differential equations (ODEs). Almost no other choice is available, if we excludes statistical models and machine learning techniques. Despite lumped models are built for reducing the degree of freedom of the hydrological problems through an informed set of simplifications, even they end to produce quite complicate systems that, as the process based models do, cause identifiability and computational problems.
However, it is evident that the issues, before to be computational and about information (the one necessary to obtain a given prognosis), are theoretical. The topic here debated is which would be, at any scale, the hydrological aspects (or quantities) that dominate and a certain spatial and temporal scale.
The research questions raised are: which are the techniques and the approaches that can be used to aggregate the spatial information. Which are the physical-mathematical directions towards which we should look ?
This talk aims to give some effective indications, immediately practicable by researchers.
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The experience of “Process Based” models
What is a “Process Based” model ?
Fatichi,S; Vivoni e.R.; Ogden F.L.; Ivanov V.Y.; Mirus,B; Gochis, D; Downer C.W.; Camporese, M; Davison J.H., Ebel, B; Jones, N; Kim, J., Mascaro, G; Niswonger, R; Restrepo, P.; Rigon, R.; Shen, C.; Sulis, M.,Tarboton, D.; An overview of current applications, challenges, and future trends in distributed process-based models in hydrology, Journal of Hydrology, 537 (2016) 45-60, 2016
Paniconi, C., & Putti, M. (2015). Physically based modeling in catchment hydrology at 50: Survey and outlook. Water Resources Research, 1–46. http://doi.org/10.1002/(ISSN)2169-8996/homepage/billing_faqs.pdf
Freeze and Harlan, Blueprint for a physically-based digitally-simulated hydrological response model, Jour. of Hydrology, 1969
Abbot et al., An Introduction to the European Hydrological System - Systeme Hydrologique Europeen, SHE. 1. History and Philosophy of a Physically-Based, Distributed Modeling System 1986
Dunne Saturation Overland Flow
Unsaturated Layer
Surface Layer
Saturated Layer:
Horton Overland Flow
Modified from Abbot et al., 1986
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Beven, K. J. (2001). How far can we go in distributed hydrological modelling? Hydrology and Earth System Sciences, 5(1), 1–12.
“…The modelling results were never published. They were simply not good enough. The model did not reproduce the stream discharges, it did not reproduce the measured water table levels, it did not reproduce the observed heterogeneity of inputs into the stream from the hillslopes.”
Critiques were not missing
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An analysis of this question reveals a number of issues. These will be summarised here as the problems of
nonlinearity; of scale; of uniqueness; of equifinality; and of uncertainty.
Problems
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My first answer is
We discover ... that all our laws can be
written in mathematical form; and that
this has a certain simplicity and beauty
about it. So, ultimately, in order to
understand nature it may be necessary to
have a deeper unders tanding of
mathematical relationships*
R. Feynman
http://abouthydrology.blogspot.it/2013/06/ezio-todini-70th-symposium-my-talk.html
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On a practical base
I (we) built GEOtop
mass, momentum and energy conservation are
the most “true” equations we know
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Richards equation is “wrong” !
9
Sure. But then, what else I should use:
•Green-Ampt ? •SCS ? •Topmodel ? •Reservoirs ?
I use all of them when I find convenient. However, all of them are even more “wrong” than Richards. So for the first part of this talk I stick with Richards’ assumptions.
Take it as my null hypothesis
Better wrong than “not even wrong”
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To exaggerate
•energy budget: turbulent flows, heat equation, soil
freezing, snow budget
we added
still Freeze and Harlan, 1968 ?En
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Better wrong than “not even wrong”
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In What GEOtop is different ?
Water mass budgetR
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In What GEOtop is different ?
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In What GEOtop is different ?
Snow height, density, temperature)Freezing Soil - Permafrost
Snow and freezing soil: see also me on Thursday talk
Zanotti et al, 2004; Dall’Amico et al., 2011
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Many models do the water budget
Many models do the energy budget
Many model do the snow budget
How many models do the whole stuff together ?
Obviously is also matter of the degree of
physical simplification (i.e. the equations) used.
To study the interactions all is modelled together
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Some misconceptions about distributed modelling
“Distributed models are overparameterised”
“Model parameters cannot be identified”
“These models require too high computational time”
“They cannot be used for ungauged basins”
“Reality is simpler than that (and we learn just from simple models)”
see also http://www.nature.com/nature/journal/v469/n7328/abs/469038a.html
To sum up our position
not completely wrong but not completely true.
eat the apple before talking!
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Endrizzi et al. 2014
see also http://abouthydrology.blogspot.com/search/label/GEOtop
The whole story here
Geosci. Model Dev., 7, 2831–2857, 2014www.geosci-model-dev.net/7/2831/2014/doi:10.5194/gmd-7-2831-2014© Author(s) 2014. CC Attribution 3.0 License.
GEOtop 2.0: simulating the combined energy and water balance atand below the land surface accounting for soil freezing, snow coverand terrain effectsS. Endrizzi1, S. Gruber2, M. Dall’Amico3, and R. Rigon41Department of Geography, University of Zurich, Winterthurerstrasse 190, 8057 Zurich, Switzerland2Carleton University, Department of Geography and Environmental Studies, 1125 Colonel By Drive, Ottawa,ON K1S 5B6, Canada3Mountaineering GmbH, Siemensstrasse 19, 39100 Bozen, Italy4Dipartimento di Ingegneria Civile, Ambientale e Meccanica e CUDAM, Università di Trento, Via Mesiano 77,38123 Trento, Italy
Correspondence to: S. Endrizzi ([email protected])
Received: 4 October 2013 – Published in Geosci. Model Dev. Discuss.: 3 December 2013Revised: 25 September 2014 – Accepted: 30 September 2014 – Published: 3 December 2014
Abstract. GEOtop is a fine-scale grid-based simulator thatrepresents the heat and water budgets at and below the soilsurface. It describes the three-dimensional water flow in thesoil and the energy exchange with the atmosphere, consider-ing the radiative and turbulent fluxes. Furthermore, it repro-duces the highly non-linear interactions between the waterand energy balance during soil freezing and thawing, andsimulates the temporal evolution of the water and energybudgets in the snow cover and their effect on soil tempera-ture.Here, we present the core components of GEOtop 2.0 and
demonstrate its functioning. Based on a synthetic simula-tion, we show that the interaction of processes represented inGEOtop 2.0 can result in phenomena that are significant andrelevant for applications involving permafrost and seasonallyfrozen soils, both in high altitude and latitude regions.
1 Introduction
Frozen soil and snow cover interact in various ways withhydrology, climate, ecosystems and with human infrastruc-tures. These natural systems are complex and characterisedby many non-linear processes that operate and interact overdifferent scales. Their mathematical representation and quan-tification is gaining in importance, especially in the light of
global climate change. This importance derives on one handfrom the requirement to study more and more complex sys-tems, and, on the other hand, this representation of morecomplex systems can inform decisions about their simpli-fication (Freeze and Harlan, 1969). In fact, the systems ofequations required for representing such environments areoften simplified by excluding processes that are consideredless important for the problems addressed. Such an a prioriexclusion, however, may not be quantitatively justified andmostly dictated by the need for mathematical tractability. Es-timating the error inherent in model simplifications is there-fore desirable for weighing the costs and benefits of differingoptions.There is a great diversity of models (understood here as
mathematical representations of one or more processes) andsimulators (computer programs, usually comprising imple-mentations of several models to represent a natural system)to simulate cold-region processes. For example, models ap-plied in permafrost environments are normally: (i) modelsapplied at a local, regional, and continental scale that inte-grate a one-dimensional form of heat and water flow equationwith phase change and predict the evolution of the depth ofthaw; (ii) hydrological models commonly applied at a largescale that predict river discharge without accurately describ-ing the coupling with the soil energy balance; and (iii) mod-els that very accurately describe and couple water and en-ergy subsurface flow in frozen soil, but do not consider the
Published by Copernicus Publications on behalf of the European Geosciences Union.
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Will you suggest, from the point of view of computational time, to use distributed models (like SHE) and continuous, since we think to use weather time series of thousands of years ? Personally I see the danger to be overwhelmed by data, and by so long computational time that we will not able to perform all the analysis we require with the adequate rigor (sensitivity analysis, and so on ...).
Different people have different ideas of what a distributed model is. Kampf and Burges (2007) offered a review a few years ago. However, taking as reference our GEOtop, that is probably one of the more complex existing hydrological models, we can observe that it runs, in our laptop, a year long simulation for a 10-20 square kilometer basin at 10 m of resolution, in, say, a day. So, simulating 1000 years would require approximately 3 years: which is clearly too long for any project. Using faster machine would probably increase the time by a factor of two. GEOtop is not parallelized, so, after an investment in rewriting the code, we could probably cut the time of simulation of a factor 100, by using also large parallel computers. Thus, we will reduce one year of simulation to 3/4 days: this could then be feasible. But this is obviously wishful thinking.
A practical concern from: Which hydrological model (is better) ?
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However
Condon, L. E., & Maxwell, R. M. (2016). Analyzing the impact of groundwater flow and storage changes on Budyko relationships across the continental US. Hydrology and Earth System Sciences Discussions, 1–40. http://doi.org/10.5194/hess-2016-408
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So the bottom line here is:
Maybe scale problem could became not so important from the computational point of view in the next future.
Similar systems can be implemented also for:
• rainfall• runoff• evapotranspiration• groundwater
With resolution of few hundreds meter. Just a problem of investments.
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Is the scale problem so important anymore ?
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This doesn't imply that
nonlinearity; of scale; of uniqueness; of equifinality; and of uncertainty.
issues are not solved. But that
“…The modelling results were never published. They were simply not good enough. The model did not reproduced the stream discharges, it did not reproduced the measured water table levels, it did not reproduced the observed heterogeneity of inputs into the stream from the hillslopes.”
maybe this is still not true
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Issues
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So we do not care anymore about scale issues ?
Certainly not. We want do it more easily. Implying less time and facing a whole
set of interactions and feedbacks. Especially with vegetation and ecosystems.
Some problems complexity grows more than exponentially and are not computable.
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What is the real scale problem ?
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Please join the number and the letter
Scales & Hydrology
simplifications
Potenza, 24 Febbraio 2017
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Riccardo Rigon, Marialaura Bancheri, Niccolò Tubini, Giuseppe Formetta, Francesco Serafin
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The problem here can be enunciated as follows:
• Do, at certain scale, are we interested just in “averages” of the hydrological quantities ?
• Are fluxes of the (at boundaries of the control volumes of interest) computable just on the basis of these averages (or on their gradients) ?
• How can we exploit the fact that mass, energy and momentum are conserved
Rigon & Al.Rigon & Al.
Scaling by simplification
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2D - de Saint Venant equations with some smart subgrid parameterization (e.g. Casulli, 2009)
1D - Kinematic equation So many to cite here but ... Liu and Todini, 2002
Various aggregation strategies for runoff, including residence time theories (a.k.a GIUH)
Rodriguez-Iturbe and Valdes, 1979; Rinaldo et al., 1991, D’Odorico and Rigon, 2003 Rigon et al. 2016a
Less is more: Ranfall runoff
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3D-Richards’ equation (Richards, 1931; Celia et al. 1990)
1D-Richards + Boussinesq
Topkapi
HsB
Topog/Topmodel
Cord
ano a
nd
Rig
on
, 2008 (Cordano and Rigon, 2013)
Liu and Todini, 2002
Troch et al., 2003
O’Loughlin, 1986; Beven and Kirkby, 1979
Less is more: soil science
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Dalton’s Equation e.g. Brutsaert 1982
Penman Penman, 1948
Monteith Monteith, 1965
Priestley-Taylor Priestley and Taylor, 1972
Less is more: Evapotranspiration
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Energy Budget Jordan, 1991
Radiation + Temperature Brubaker et al., 1996 Hock, 1999
Degree-day (Just temperature) Martinec and Rango, 1975
Less is more: snow
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Models “complexity” and computational time increase going from bottom up.
More complexity, more processes physics.
Scales of application usually* decrease from top to bottom
* But not anymore necessarily
Less is more
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Parameters pretend to be estimated ex-ante (measured) in more complex models (with a lot of disclaimers ... obviously)
Are certainly calibrated (ex-post) in the simplest models (but in some models preserve a physical significance)
From top to bottom heuristic and statistics substitute processes analysis
Less is more
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A more theoretical but abstract treatment of the subject can be found in
Reggiani, P., Sivapalan, M. and Hassanizadeh, S.M., 1998. A unifying framework for watershed thermodynamics: balance equations for mass, momentum, energy and entropy and the second law of thermodynamics, Adv. Water Resour., 23, 15-40.
Reggiani, P., Hassanizadeh, S.M., Sivapalan, M. and Gray, W.G., 1999. A unifying framework for watershed thermodynamics: constitutive relationships, Adv. Water Resour., 23, 15-40.
Reggiani, P., Sivapalan, M. and Hassanizadeh, S.M., 2000. Conservation equations governing hillslope responses: exploring the physical basis of water balance, Water Resour. Res., 36, 1845- 1863.
Well, my opinion on those papers is that they are a must read. However notation does not help and they lack of insight of physics, with repect to the more “bottom up” paper and procedures I cited before. Then .. c’mon everybody when does not what to say talks about entropy but does not really reveals the mystery around it.
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A systematic approach
Scales & Hydrology
The Richards’ case
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Riccardo Rigon, Marialaura Bancheri, Niccolò Tubini, Giuseppe Formetta, Francesco Serafin
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Everything is statistical, and statistics is more than simple integration
integration interpretation simplification
Is
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Statistical-Mechanical-Hydrology
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Soil is made up of various stuff
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Take the case of Richards equation
But we concentrate on pore distribution
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Interpretation and simplification: As in Mualem (1976), we think that soil is a bundle of pores and that they are filled (or emptied) systematically. Filled from the smaller to larger. Emptied from larger to smaller. Then a partially filled soil is represented by figure below.
Statistics is represented here by the pdf f(r) and the water content is
Interpretation & Simplification
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Thus the variation in time of the water content is:
pores distribution
largest pore size
dimensionless liquid water content
The first member of the equation
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Young-Laplace law
pore radius
liquid water density
acceleration of gravity
surface tension of water
contact angle
water pressure
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As a result (see Kosugi et al., 2008):
l.h.s. of Richards’ equation
hydraulic capacity
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r.h.s. of Richards’ equation
We could continue with the r.h.s. of the equation to express Richards equation as a function of the largest pore size
hydraulic conductivity
details in Rigon et al. 2017 (in preparation)
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scales up
because we can think to any control volume as a bundle of pores of a given statistics. For fluxes to be right though some more hypothesis has to be made.
Rigon & Al.
it scales up
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Another good example of “scaling up” is offered by
Mualem, Y. (1976). A new model fro predicting the hydraulic conductivity of unsaturated porous media. Water Resources Research, 12(3), 513–522.
which is also the most cited paper in Water Resources Research.
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read the masters!
Scales & Hydrology
ET’s case
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tte,
R.,
La r
ech
erch
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solu
, Oil
on
can
va, 1
94
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Riccardo Rigon, Marialaura Bancheri, Niccolò Tubini, Giuseppe Formetta, Francesco Serafin
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Admitting that scaling in Richards can be obtained
With other processes like evapotranspiration is more complicated
computationally demanding. Therefore, several eco-hydrological models still use simplified solutions ofthe energy budget such as the Penman–Monteith orPriestley-Taylor equations (e.g., Refs260,265,269,273).
Carbon BudgetThe carbon cycle is linked to the water and energycycles because carbon assimilated through photosyn-thesis uses the same pathway between the outeratmosphere and leaf interior as transpired water (seethe ‘Stomatal Controls’ section) and because changesin vegetation properties (e.g., plant height and LAI)modify boundary conditions for energy and waterexchanges (Figure 6). For instance, a change in LAImodifies interception capacity, energy absorption andemission as well as roughness; a change in photosyn-thetic rate, An (Eq. (1)), may change stomatal con-ductance and therefore transpiration. Thecomputation of carbon assimilation can be carriedout with various degrees of complexity. Some modelsuse a biochemical model of photosynthesis in whichAn and leaf internal CO2 concentration (ci) are com-puted as prognostic variables in a non-linear equa-tion (e.g., Refs 164,165,259,275,276); others havesimpler approaches exploiting the water use effi-ciency (WUE; i.e., the ratio between net carbonassimilation and transpiration284) or light use effi-ciency (LUE; i.e., the efficiency through which radia-tion absorbed by vegetation is converted into
carbon285) concepts that empirically link carbonassimilation to the transpired water or interceptedlight (e.g., Refs 264,265,271,286,287). In some eco-hydrological models, vegetation dynamics are essen-tially reduced to the simulation of carbonassimilation only (e.g., Refs 262,276). In others, theassimilated carbon is used to grow plants and toevolve a given number of carbon pools. Carbonpools are the way models account for the size anddynamics of different plant compartments.288 Thenumber of carbon pools varies from model to model,but a typical set is composed of at least of a foliagepool, a fine-root pool, a sapwood or stem pool, and,more recently, a carbon reserve pool (e.g., Refs165,273). Carbon reserves have been ignored in earlyecohydrological models and ESMs with rare excep-tions (e.g., Ref 289), but it is currently recognizedthat plant dynamics cannot be simulated meaning-fully without accounting for carbon reserves.290–292
Models that use carbon pools can also simulate thedynamics of the biophysical structure of vegetation,e.g., LAI, vegetation height, and root biomass.
Soil BiogeochemistryWater, energy, and carbon fluxes are additionallyconnected through soil biogeochemistry and nutrientdynamics (Figure 6). Soil biogeochemistry is typicallysimulated to account for a given number of carbonand nitrogen pools.293 Other nutrients, such as phos-phorous, sulfur, or potassium, are not typically
Energy exchangesLongwaveradiationincoming
Longwaveradiationoutgoing
Shortwaveradiation
Latent heat
Latentheat
Sensibleheat
Soil heat flux
Geothermal heatgain
Bedrock Bedrock Bedrock Bedrock
Momentum transfer
Rain Snow Photosynthesis
Phe
nolo
gy
DisturbancesAtmosphericdeposition
Fertilization
Nutrient resorption
Nutrient uptake
Nutrients in SOM
Mineral nutrientsin solution
Mineralization andimmobilizationOccluded or not
available nutrients
Primary mineralweathering
Biologicalfixation (N)
Tectonic uplift
Denitrification (N)
Volatilization
Growth respiration
Maintenance respiration
Fruits/flowers production
Heterotrophicrespiration
Wood turnover
Litter Litter
Litterfallnutrient flux
DecompositionMycorrhizalsymbiosis
Microbialand soil
faunaactivity
SOM
DOCleaching Leaching
Fine and coarseroot turnover
Carbon allocationand translocation
Carbon reserves (NSC)
Leaf turnover
Transpiration
Evaporation frominterception
Evaporation/sublimationfrom snow
Evaporation
Throughfall/dripping
Snow melting
Infiltration
LeakageRoot water uptakeLateral subsurface flow
Base flowDeep recharge
Runoff
Sensible heatAlbedo
Energy absorbedby photosynthesis
Water cycle Carbon cycle Nutrient cycle
FIGURE 6 | Ecohydrological and terrestrial biosphere models have components and parameterizations to simulate the (1) surface energyexchanges, (2) the water cycle, (3) the carbon cycle, and (4) soil biogeochemistry and nutrient cycles. Many models do not include all thecomponents presented in the figure.
WIREs Water Modeling plant–water interactions
© 2015 Wiley Per iodica ls , Inc.
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Rigon & Al.
45
computationally demanding. Therefore, several eco-hydrological models still use simplified solutions ofthe energy budget such as the Penman–Monteith orPriestley-Taylor equations (e.g., Refs260,265,269,273).
Carbon BudgetThe carbon cycle is linked to the water and energycycles because carbon assimilated through photosyn-thesis uses the same pathway between the outeratmosphere and leaf interior as transpired water (seethe ‘Stomatal Controls’ section) and because changesin vegetation properties (e.g., plant height and LAI)modify boundary conditions for energy and waterexchanges (Figure 6). For instance, a change in LAImodifies interception capacity, energy absorption andemission as well as roughness; a change in photosyn-thetic rate, An (Eq. (1)), may change stomatal con-ductance and therefore transpiration. Thecomputation of carbon assimilation can be carriedout with various degrees of complexity. Some modelsuse a biochemical model of photosynthesis in whichAn and leaf internal CO2 concentration (ci) are com-puted as prognostic variables in a non-linear equa-tion (e.g., Refs 164,165,259,275,276); others havesimpler approaches exploiting the water use effi-ciency (WUE; i.e., the ratio between net carbonassimilation and transpiration284) or light use effi-ciency (LUE; i.e., the efficiency through which radia-tion absorbed by vegetation is converted into
carbon285) concepts that empirically link carbonassimilation to the transpired water or interceptedlight (e.g., Refs 264,265,271,286,287). In some eco-hydrological models, vegetation dynamics are essen-tially reduced to the simulation of carbonassimilation only (e.g., Refs 262,276). In others, theassimilated carbon is used to grow plants and toevolve a given number of carbon pools. Carbonpools are the way models account for the size anddynamics of different plant compartments.288 Thenumber of carbon pools varies from model to model,but a typical set is composed of at least of a foliagepool, a fine-root pool, a sapwood or stem pool, and,more recently, a carbon reserve pool (e.g., Refs165,273). Carbon reserves have been ignored in earlyecohydrological models and ESMs with rare excep-tions (e.g., Ref 289), but it is currently recognizedthat plant dynamics cannot be simulated meaning-fully without accounting for carbon reserves.290–292
Models that use carbon pools can also simulate thedynamics of the biophysical structure of vegetation,e.g., LAI, vegetation height, and root biomass.
Soil BiogeochemistryWater, energy, and carbon fluxes are additionallyconnected through soil biogeochemistry and nutrientdynamics (Figure 6). Soil biogeochemistry is typicallysimulated to account for a given number of carbonand nitrogen pools.293 Other nutrients, such as phos-phorous, sulfur, or potassium, are not typically
Energy exchangesLongwaveradiationincoming
Longwaveradiationoutgoing
Shortwaveradiation
Latent heat
Latentheat
Sensibleheat
Soil heat flux
Geothermal heatgain
Bedrock Bedrock Bedrock Bedrock
Momentum transfer
Rain Snow Photosynthesis
Phe
nolo
gy
DisturbancesAtmosphericdeposition
Fertilization
Nutrient resorption
Nutrient uptake
Nutrients in SOM
Mineral nutrientsin solution
Mineralization andimmobilizationOccluded or not
available nutrients
Primary mineralweathering
Biologicalfixation (N)
Tectonic uplift
Denitrification (N)
Volatilization
Growth respiration
Maintenance respiration
Fruits/flowers production
Heterotrophicrespiration
Wood turnover
Litter Litter
Litterfallnutrient flux
DecompositionMycorrhizalsymbiosis
Microbialand soil
faunaactivity
SOM
DOCleaching Leaching
Fine and coarseroot turnover
Carbon allocationand translocation
Carbon reserves (NSC)
Leaf turnover
Transpiration
Evaporation frominterception
Evaporation/sublimationfrom snow
Evaporation
Throughfall/dripping
Snow melting
Infiltration
LeakageRoot water uptakeLateral subsurface flow
Base flowDeep recharge
Runoff
Sensible heatAlbedo
Energy absorbedby photosynthesis
Water cycle Carbon cycle Nutrient cycle
FIGURE 6 | Ecohydrological and terrestrial biosphere models have components and parameterizations to simulate the (1) surface energyexchanges, (2) the water cycle, (3) the carbon cycle, and (4) soil biogeochemistry and nutrient cycles. Many models do not include all thecomponents presented in the figure.
WIREs Water Modeling plant–water interactions
© 2015 Wiley Per iodica ls , Inc.
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ra) works for this:
Rigon & Al.
is the same true for transpiration ?
46
Admitting that scaling in Richards can be obtained
Why should this work for this ?
How to scale up this complexity ?
computationally demanding. Therefore, several eco-hydrological models still use simplified solutions ofthe energy budget such as the Penman–Monteith orPriestley-Taylor equations (e.g., Refs260,265,269,273).
Carbon BudgetThe carbon cycle is linked to the water and energycycles because carbon assimilated through photosyn-thesis uses the same pathway between the outeratmosphere and leaf interior as transpired water (seethe ‘Stomatal Controls’ section) and because changesin vegetation properties (e.g., plant height and LAI)modify boundary conditions for energy and waterexchanges (Figure 6). For instance, a change in LAImodifies interception capacity, energy absorption andemission as well as roughness; a change in photosyn-thetic rate, An (Eq. (1)), may change stomatal con-ductance and therefore transpiration. Thecomputation of carbon assimilation can be carriedout with various degrees of complexity. Some modelsuse a biochemical model of photosynthesis in whichAn and leaf internal CO2 concentration (ci) are com-puted as prognostic variables in a non-linear equa-tion (e.g., Refs 164,165,259,275,276); others havesimpler approaches exploiting the water use effi-ciency (WUE; i.e., the ratio between net carbonassimilation and transpiration284) or light use effi-ciency (LUE; i.e., the efficiency through which radia-tion absorbed by vegetation is converted into
carbon285) concepts that empirically link carbonassimilation to the transpired water or interceptedlight (e.g., Refs 264,265,271,286,287). In some eco-hydrological models, vegetation dynamics are essen-tially reduced to the simulation of carbonassimilation only (e.g., Refs 262,276). In others, theassimilated carbon is used to grow plants and toevolve a given number of carbon pools. Carbonpools are the way models account for the size anddynamics of different plant compartments.288 Thenumber of carbon pools varies from model to model,but a typical set is composed of at least of a foliagepool, a fine-root pool, a sapwood or stem pool, and,more recently, a carbon reserve pool (e.g., Refs165,273). Carbon reserves have been ignored in earlyecohydrological models and ESMs with rare excep-tions (e.g., Ref 289), but it is currently recognizedthat plant dynamics cannot be simulated meaning-fully without accounting for carbon reserves.290–292
Models that use carbon pools can also simulate thedynamics of the biophysical structure of vegetation,e.g., LAI, vegetation height, and root biomass.
Soil BiogeochemistryWater, energy, and carbon fluxes are additionallyconnected through soil biogeochemistry and nutrientdynamics (Figure 6). Soil biogeochemistry is typicallysimulated to account for a given number of carbonand nitrogen pools.293 Other nutrients, such as phos-phorous, sulfur, or potassium, are not typically
Energy exchangesLongwaveradiationincoming
Longwaveradiationoutgoing
Shortwaveradiation
Latent heat
Latentheat
Sensibleheat
Soil heat flux
Geothermal heatgain
Bedrock Bedrock Bedrock Bedrock
Momentum transfer
Rain Snow Photosynthesis
Phe
nolo
gy
DisturbancesAtmosphericdeposition
Fertilization
Nutrient resorption
Nutrient uptake
Nutrients in SOM
Mineral nutrientsin solution
Mineralization andimmobilizationOccluded or not
available nutrients
Primary mineralweathering
Biologicalfixation (N)
Tectonic uplift
Denitrification (N)
Volatilization
Growth respiration
Maintenance respiration
Fruits/flowers production
Heterotrophicrespiration
Wood turnover
Litter Litter
Litterfallnutrient flux
DecompositionMycorrhizalsymbiosis
Microbialand soil
faunaactivity
SOM
DOCleaching Leaching
Fine and coarseroot turnover
Carbon allocationand translocation
Carbon reserves (NSC)
Leaf turnover
Transpiration
Evaporation frominterception
Evaporation/sublimationfrom snow
Evaporation
Throughfall/dripping
Snow melting
Infiltration
LeakageRoot water uptakeLateral subsurface flow
Base flowDeep recharge
Runoff
Sensible heatAlbedo
Energy absorbedby photosynthesis
Water cycle Carbon cycle Nutrient cycle
FIGURE 6 | Ecohydrological and terrestrial biosphere models have components and parameterizations to simulate the (1) surface energyexchanges, (2) the water cycle, (3) the carbon cycle, and (4) soil biogeochemistry and nutrient cycles. Many models do not include all thecomponents presented in the figure.
WIREs Water Modeling plant–water interactions
© 2015 Wiley Per iodica ls , Inc.
computationally demanding. Therefore, several eco-hydrological models still use simplified solutions ofthe energy budget such as the Penman–Monteith orPriestley-Taylor equations (e.g., Refs260,265,269,273).
Carbon BudgetThe carbon cycle is linked to the water and energycycles because carbon assimilated through photosyn-thesis uses the same pathway between the outeratmosphere and leaf interior as transpired water (seethe ‘Stomatal Controls’ section) and because changesin vegetation properties (e.g., plant height and LAI)modify boundary conditions for energy and waterexchanges (Figure 6). For instance, a change in LAImodifies interception capacity, energy absorption andemission as well as roughness; a change in photosyn-thetic rate, An (Eq. (1)), may change stomatal con-ductance and therefore transpiration. Thecomputation of carbon assimilation can be carriedout with various degrees of complexity. Some modelsuse a biochemical model of photosynthesis in whichAn and leaf internal CO2 concentration (ci) are com-puted as prognostic variables in a non-linear equa-tion (e.g., Refs 164,165,259,275,276); others havesimpler approaches exploiting the water use effi-ciency (WUE; i.e., the ratio between net carbonassimilation and transpiration284) or light use effi-ciency (LUE; i.e., the efficiency through which radia-tion absorbed by vegetation is converted into
carbon285) concepts that empirically link carbonassimilation to the transpired water or interceptedlight (e.g., Refs 264,265,271,286,287). In some eco-hydrological models, vegetation dynamics are essen-tially reduced to the simulation of carbonassimilation only (e.g., Refs 262,276). In others, theassimilated carbon is used to grow plants and toevolve a given number of carbon pools. Carbonpools are the way models account for the size anddynamics of different plant compartments.288 Thenumber of carbon pools varies from model to model,but a typical set is composed of at least of a foliagepool, a fine-root pool, a sapwood or stem pool, and,more recently, a carbon reserve pool (e.g., Refs165,273). Carbon reserves have been ignored in earlyecohydrological models and ESMs with rare excep-tions (e.g., Ref 289), but it is currently recognizedthat plant dynamics cannot be simulated meaning-fully without accounting for carbon reserves.290–292
Models that use carbon pools can also simulate thedynamics of the biophysical structure of vegetation,e.g., LAI, vegetation height, and root biomass.
Soil BiogeochemistryWater, energy, and carbon fluxes are additionallyconnected through soil biogeochemistry and nutrientdynamics (Figure 6). Soil biogeochemistry is typicallysimulated to account for a given number of carbonand nitrogen pools.293 Other nutrients, such as phos-phorous, sulfur, or potassium, are not typically
Energy exchangesLongwaveradiationincoming
Longwaveradiationoutgoing
Shortwaveradiation
Latent heat
Latentheat
Sensibleheat
Soil heat flux
Geothermal heatgain
Bedrock Bedrock Bedrock Bedrock
Momentum transfer
Rain Snow Photosynthesis
Phe
nolo
gy
DisturbancesAtmosphericdeposition
Fertilization
Nutrient resorption
Nutrient uptake
Nutrients in SOM
Mineral nutrientsin solution
Mineralization andimmobilizationOccluded or not
available nutrients
Primary mineralweathering
Biologicalfixation (N)
Tectonic uplift
Denitrification (N)
Volatilization
Growth respiration
Maintenance respiration
Fruits/flowers production
Heterotrophicrespiration
Wood turnover
Litter Litter
Litterfallnutrient flux
DecompositionMycorrhizalsymbiosis
Microbialand soil
faunaactivity
SOM
DOCleaching Leaching
Fine and coarseroot turnover
Carbon allocationand translocation
Carbon reserves (NSC)
Leaf turnover
Transpiration
Evaporation frominterception
Evaporation/sublimationfrom snow
Evaporation
Throughfall/dripping
Snow melting
Infiltration
LeakageRoot water uptakeLateral subsurface flow
Base flowDeep recharge
Runoff
Sensible heatAlbedo
Energy absorbedby photosynthesis
Water cycle Carbon cycle Nutrient cycle
FIGURE 6 | Ecohydrological and terrestrial biosphere models have components and parameterizations to simulate the (1) surface energyexchanges, (2) the water cycle, (3) the carbon cycle, and (4) soil biogeochemistry and nutrient cycles. Many models do not include all thecomponents presented in the figure.
WIREs Water Modeling plant–water interactions
© 2015 Wiley Per iodica ls , Inc.
computationally demanding. Therefore, several eco-hydrological models still use simplified solutions ofthe energy budget such as the Penman–Monteith orPriestley-Taylor equations (e.g., Refs260,265,269,273).
Carbon BudgetThe carbon cycle is linked to the water and energycycles because carbon assimilated through photosyn-thesis uses the same pathway between the outeratmosphere and leaf interior as transpired water (seethe ‘Stomatal Controls’ section) and because changesin vegetation properties (e.g., plant height and LAI)modify boundary conditions for energy and waterexchanges (Figure 6). For instance, a change in LAImodifies interception capacity, energy absorption andemission as well as roughness; a change in photosyn-thetic rate, An (Eq. (1)), may change stomatal con-ductance and therefore transpiration. Thecomputation of carbon assimilation can be carriedout with various degrees of complexity. Some modelsuse a biochemical model of photosynthesis in whichAn and leaf internal CO2 concentration (ci) are com-puted as prognostic variables in a non-linear equa-tion (e.g., Refs 164,165,259,275,276); others havesimpler approaches exploiting the water use effi-ciency (WUE; i.e., the ratio between net carbonassimilation and transpiration284) or light use effi-ciency (LUE; i.e., the efficiency through which radia-tion absorbed by vegetation is converted into
carbon285) concepts that empirically link carbonassimilation to the transpired water or interceptedlight (e.g., Refs 264,265,271,286,287). In some eco-hydrological models, vegetation dynamics are essen-tially reduced to the simulation of carbonassimilation only (e.g., Refs 262,276). In others, theassimilated carbon is used to grow plants and toevolve a given number of carbon pools. Carbonpools are the way models account for the size anddynamics of different plant compartments.288 Thenumber of carbon pools varies from model to model,but a typical set is composed of at least of a foliagepool, a fine-root pool, a sapwood or stem pool, and,more recently, a carbon reserve pool (e.g., Refs165,273). Carbon reserves have been ignored in earlyecohydrological models and ESMs with rare excep-tions (e.g., Ref 289), but it is currently recognizedthat plant dynamics cannot be simulated meaning-fully without accounting for carbon reserves.290–292
Models that use carbon pools can also simulate thedynamics of the biophysical structure of vegetation,e.g., LAI, vegetation height, and root biomass.
Soil BiogeochemistryWater, energy, and carbon fluxes are additionallyconnected through soil biogeochemistry and nutrientdynamics (Figure 6). Soil biogeochemistry is typicallysimulated to account for a given number of carbonand nitrogen pools.293 Other nutrients, such as phos-phorous, sulfur, or potassium, are not typically
Energy exchangesLongwaveradiationincoming
Longwaveradiationoutgoing
Shortwaveradiation
Latent heat
Latentheat
Sensibleheat
Soil heat flux
Geothermal heatgain
Bedrock Bedrock Bedrock Bedrock
Momentum transfer
Rain Snow Photosynthesis
Phe
nolo
gy
DisturbancesAtmosphericdeposition
Fertilization
Nutrient resorption
Nutrient uptake
Nutrients in SOM
Mineral nutrientsin solution
Mineralization andimmobilizationOccluded or not
available nutrients
Primary mineralweathering
Biologicalfixation (N)
Tectonic uplift
Denitrification (N)
Volatilization
Growth respiration
Maintenance respiration
Fruits/flowers production
Heterotrophicrespiration
Wood turnover
Litter Litter
Litterfallnutrient flux
DecompositionMycorrhizalsymbiosis
Microbialand soil
faunaactivity
SOM
DOCleaching Leaching
Fine and coarseroot turnover
Carbon allocationand translocation
Carbon reserves (NSC)
Leaf turnover
Transpiration
Evaporation frominterception
Evaporation/sublimationfrom snow
Evaporation
Throughfall/dripping
Snow melting
Infiltration
LeakageRoot water uptakeLateral subsurface flow
Base flowDeep recharge
Runoff
Sensible heatAlbedo
Energy absorbedby photosynthesis
Water cycle Carbon cycle Nutrient cycle
FIGURE 6 | Ecohydrological and terrestrial biosphere models have components and parameterizations to simulate the (1) surface energyexchanges, (2) the water cycle, (3) the carbon cycle, and (4) soil biogeochemistry and nutrient cycles. Many models do not include all thecomponents presented in the figure.
WIREs Water Modeling plant–water interactions
© 2015 Wiley Per iodica ls , Inc.
computationally demanding. Therefore, several eco-hydrological models still use simplified solutions ofthe energy budget such as the Penman–Monteith orPriestley-Taylor equations (e.g., Refs260,265,269,273).
Carbon BudgetThe carbon cycle is linked to the water and energycycles because carbon assimilated through photosyn-thesis uses the same pathway between the outeratmosphere and leaf interior as transpired water (seethe ‘Stomatal Controls’ section) and because changesin vegetation properties (e.g., plant height and LAI)modify boundary conditions for energy and waterexchanges (Figure 6). For instance, a change in LAImodifies interception capacity, energy absorption andemission as well as roughness; a change in photosyn-thetic rate, An (Eq. (1)), may change stomatal con-ductance and therefore transpiration. Thecomputation of carbon assimilation can be carriedout with various degrees of complexity. Some modelsuse a biochemical model of photosynthesis in whichAn and leaf internal CO2 concentration (ci) are com-puted as prognostic variables in a non-linear equa-tion (e.g., Refs 164,165,259,275,276); others havesimpler approaches exploiting the water use effi-ciency (WUE; i.e., the ratio between net carbonassimilation and transpiration284) or light use effi-ciency (LUE; i.e., the efficiency through which radia-tion absorbed by vegetation is converted into
carbon285) concepts that empirically link carbonassimilation to the transpired water or interceptedlight (e.g., Refs 264,265,271,286,287). In some eco-hydrological models, vegetation dynamics are essen-tially reduced to the simulation of carbonassimilation only (e.g., Refs 262,276). In others, theassimilated carbon is used to grow plants and toevolve a given number of carbon pools. Carbonpools are the way models account for the size anddynamics of different plant compartments.288 Thenumber of carbon pools varies from model to model,but a typical set is composed of at least of a foliagepool, a fine-root pool, a sapwood or stem pool, and,more recently, a carbon reserve pool (e.g., Refs165,273). Carbon reserves have been ignored in earlyecohydrological models and ESMs with rare excep-tions (e.g., Ref 289), but it is currently recognizedthat plant dynamics cannot be simulated meaning-fully without accounting for carbon reserves.290–292
Models that use carbon pools can also simulate thedynamics of the biophysical structure of vegetation,e.g., LAI, vegetation height, and root biomass.
Soil BiogeochemistryWater, energy, and carbon fluxes are additionallyconnected through soil biogeochemistry and nutrientdynamics (Figure 6). Soil biogeochemistry is typicallysimulated to account for a given number of carbonand nitrogen pools.293 Other nutrients, such as phos-phorous, sulfur, or potassium, are not typically
Energy exchangesLongwaveradiationincoming
Longwaveradiationoutgoing
Shortwaveradiation
Latent heat
Latentheat
Sensibleheat
Soil heat flux
Geothermal heatgain
Bedrock Bedrock Bedrock Bedrock
Momentum transfer
Rain Snow Photosynthesis
Phe
nolo
gy
DisturbancesAtmosphericdeposition
Fertilization
Nutrient resorption
Nutrient uptake
Nutrients in SOM
Mineral nutrientsin solution
Mineralization andimmobilizationOccluded or not
available nutrients
Primary mineralweathering
Biologicalfixation (N)
Tectonic uplift
Denitrification (N)
Volatilization
Growth respiration
Maintenance respiration
Fruits/flowers production
Heterotrophicrespiration
Wood turnover
Litter Litter
Litterfallnutrient flux
DecompositionMycorrhizalsymbiosis
Microbialand soil
faunaactivity
SOM
DOCleaching Leaching
Fine and coarseroot turnover
Carbon allocationand translocation
Carbon reserves (NSC)
Leaf turnover
Transpiration
Evaporation frominterception
Evaporation/sublimationfrom snow
Evaporation
Throughfall/dripping
Snow melting
Infiltration
LeakageRoot water uptakeLateral subsurface flow
Base flowDeep recharge
Runoff
Sensible heatAlbedo
Energy absorbedby photosynthesis
Water cycle Carbon cycle Nutrient cycle
FIGURE 6 | Ecohydrological and terrestrial biosphere models have components and parameterizations to simulate the (1) surface energyexchanges, (2) the water cycle, (3) the carbon cycle, and (4) soil biogeochemistry and nutrient cycles. Many models do not include all thecomponents presented in the figure.
WIREs Water Modeling plant–water interactions
© 2015 Wiley Per iodica ls , Inc.
Rigon & Al.
47
In fact our models are like this:
and they are called big-leaf models
Rigon & Al.
the big-leaf model
48
The knowledge here is too simplified for being scaled up decently.
My guess:we should go back to pore scale processes as well and combine properly with boundary layer dynamics
Schymanski, S. J., & Or, D. (2016). Leaf-scale experiments reveal important omission in the Penman-Monteith equation. Hydrology and Earth System Sciences Discussions, 0, 1–33. http://doi.org/10.5194/hess-2016-363
Rigon & Al.
new insight are needed
!49
2. VERTICAL PERSPECTIVE
As overviewed in section 1, any aspects of land-surface characteristics which influence the heating andmoistening of the atmospheric boundary layer will affectthe potential for cumulus convective rainfall. Thereforevertical radiosonde soundings over adjacent locationsthat have different surface conditions offer opportuni-ties to assess alterations in thunderstorm potential. Thisinfluence of surface conditions on cumulus cloud andthunderstorm development has been discussed, for ex-
ample, by Clark and Arritt [1995], Crook [1996], Cutrim etal. [1995], Garrett [1982], and Hong et al. [1995].
Figure 6 illustrates two soundings made over twolocations in northeastern Colorado at 1213 local stan-dard time (LST) on July 28, 1987 [Segal et al., 1989;Pielke and Zeng, 1989]. The soundings were made priorto significant cloud development. The radiosondesounding over an irrigated location had a slightly coolerbut moister lower troposphere than the sounding overthe natural, short-grass prairie location. Aircraft flightsat several levels between these two locations on July 28,
Figure 4. Schematic of the differences in surface heat energy budget and planetary boundary layer over atemperate forest and a boreal forest. The symbols used refer to equation (1). Horizontal fluxes of heat andheat storage by vegetation are left out of the figure. Adapted from P. Kabat (personal communication, 1999).Reprinted with permission.
Figure 5. Same as Figure 4 except between a forest and cropland. Adapted from P. Kabat (personalcommunication, 1999). Reprinted with permission.
39, 2 / REVIEWS OF GEOPHYSICS Pielke: PREDICTION OF CUMULUS CONVECTIVE RAINFALL ● 155
Pie
lke,
20
01
Feedbacks - Retroazioni sull’atmosfera
~ 10 km
not disconnect from what happens in the heavens
Rigon & Al.
!50
Not even to life processes
.. though warned at the outset that the subject-matter was a difficult one a …, even though the physicist’s most dreaded weapon, mathematical deduction, would hardly be utilized. The reason for this was not that the subject was simple enough to be explained without mathematics, but rather that it was much too involved to be fully accessible to mathematics
What is life ?
E. Schroedinger
The large and important and very much discussed question is: How can the events in space and time which take place within the spatial boundary of a living organism be accounted for by physics and chemistry? The preliminary answer which this little book will endeavor to expound and establish can be summarized as follows: The obvious inability of present-day physics and chemistry to account for such events is no reason at all for doubting that they can be accounted for by those sciences
A programmatic manifesto based on Schroedinger booklet
Rigon & Al.
Scales & Hydrology
How can we make our model more physically based ?
Potenza, 24 Febbraio 2017
Mgri
tte,
R.,
La r
ech
erch
e d
e l’ab
solu
, Oil
on
can
va, 1
94
0
Riccardo Rigon, Marialaura Bancheri, Niccolò Tubini, Giuseppe Formetta, Francesco Serafin
!52
See my comment here:
http://abouthydrology.blogspot.it/2016/09/on-how-to-make-our-models-more.html
Savenije, H. H. G., & Hrachowitz, M. (2016). Opinion paper: How to make our models more physically-based. Hydrology and Earth System Sciences Discussions, 1–23. http://doi.org/10.5194/hess-2016-433*
The title was inspired by this paper
Which was eventually renamed
Catchments as meta-organisms – a new blueprint for hydrological modelling
Rigon & Al.
Hydrological modelling in 2020
!53
“Alexander von Humboldt (1769–1859) considered nature and its processes as an inseparable entity, where all forces of nature are connected and mutually dependent (Wulf, 2015). Although these concepts were not formulated specifically to describe the movement of water through the natural environment, they very pointedly summarize what controls hydrological functioning at the catchment scale.”
“Ironically, state-of-the-art catchment-scale hydrological models, for varying reasons depending on the model under consideration, frequently do a poor job in addressing overall system behaviour emerging from the characteristics above. This results in many models being inadequate representations of real-world systems, haunted by large model and/or parameter uncertainties and unreliable predictions. “
Rigon & Al.
Hydrological modelling in 2020
!54
They have good points
“capacity of the ecosystem to manipulate the system in response to the temporal dynamics of the atmospheric drivers, as encapsulated in the above two quotes, is only insufficiently or often not at all accounted for in these models.”
“many others rely on simple and straightforward aggregation of processes from the lab scale to the catchment scale, assuming that there is no structure and organization in the system”
Although most models take Newtonian theory at heart, as best they can, what they generally miss is Darwinian theory on how an ecosystem evolves and adjusts its environment to maintain crucial hydrological functions.
Rigon & Al.
Hydrological modelling in 2020
!55
http://seismo.berkeley.edu/~kirchner/reprints/2002_55_Kirchner_gaia.pdf
https://en.wikipedia.org/wiki/Gaia_hypothesis
Rigon & Al.
in late XX century
!56
Rigon & Al.
in late XX century
!57
“River networks morphology self-organise to obtain minimal energy expenditure”
1096 RODFffGUEZ-ITURBE ET AL,' STRUCTURE OF DRAINAGE NETWORKS
233.1, •-- 303,3
L- 3.73
Fig. 1. Different patterns of connectivity of a set of equally spaced points to a common outlet. L r is the total length of the paths, and L is the average length of the path from a point to the outlet. In the explosion case, L •2) refers to the case when there is a minimum displacement among the points so that there is a different path between each point and the outlet [from Stevens, 1974].
network; (2) the principle of equal energy expenditure per unit area of channel anywhere in the network; and (3) the principle of minimum energy expenditure in the network as a whole. It will be shown that the combination of these principles is a sufficient explanation for the treelike structure of the drainage network and, moreover, that they explain many of the most important empirical relationships observed in the internal organization of the network and its linkage with the flow characteristics. The first principle expresses a local optimal condition for any link of the network. The second principle expresses an optimal condition throughout the network regardless of its topological structure and later on in this paper will be interpreted in a probabilistic frame- work. It postulates that energy expenditure is the same everywhere in the network when normalized by the area of the channel on which it takes place. Thus even with the first principle there will be channels that spend much more energy per unit time than others only because of their larger discharge. The second principle makes all channels equally efficient when adjusted for size. The third principle is ad- dressed to the topological structure of the network and refers to the optimal arrangement of its elements.
The first principle is similar to the principle of minimum work used in the derivation of Murray' s !aw in physiological vascular systems. Murray [1926] derived a relation which states that the cube of the radius of a parent vessel should
equal the sum of the cubes of the radii of the daughter vessels (see, for example, Sherman [ 1981]). He assumed that two energy terms contribute to the cost of maintaining blood flow in any vessel: (1) the energy required to overcome friction as described by Poiseuille's law, and (2) the energy metabolically involved in the maintenance of the blood volume and vessel tissue. Minimization of the cost funcfi0a leads to the radius of the vessel being proportional to the lB power of the flow. Uylings [1977] has shown that when turbulent flow is assumed in the vessel, rather than lain'mar conditions, the same approach leads to the radius be'rag proportional to the 3/7 power of the flow. The secorot principle was conceptually suggested by Leopold and Lang. bein [1962] in their studies of landscape evolution. It is of interest to add that minimum rate of work principles have been applied in several contexts in geomorphic research. Optimal junction angles have been studied in this context by Howard [1971], Roy [1983], and Woldenberg and Horsfield [1986], among others. Also the concept of minimum work as a criterion for the development of stream networks has been discussed under different perspectives by Yang [1971] a•d Howard [1990], among others.
ENERGY EXPENDITURE AND OPTIMAL NETWORK CONFIGURATION
Consider a channel of width w, length L, slope $, and flow depth d. The force responsible for the flow is the downslope component of the weight, F1 = ptldLw sin /3 = ptIdLwS where sin/3 = tan/3 = S. The force resisting the movement is the stress per unit area times the wetted perimeter area, F2 = •(2d + w)L, where a rectangular section has been assumed in the channel. Under conditions of no acceleration of the flow, F1 = F 2, and then r = p.qSR where R is the hydraulic radius R = Aw/Pw = wd/(2d + w), Aw and being the cross-sectional flow area, and the wetted perimeter of the section, respectively. In turbulent incompressible flow the boundary shear stress varies proportionally to the squa• of the average velocity, r = Cfpv 2, where Cf is a dimen. sionless resistance coefficient. Equating the two expressions for ,, one obtains the well-known relationship, S = Cfv2/ (R•/), which gives the losses due to friction per unit weight of flow per unit length of channel. There is also an expendi• of energy related to the maintenance of the channel w•ch may be represented by F(soil, flow)P•L where F( ) is a complicated function of soil and flow properties represenf• the work per unit time and unit area of channel involved 'm the removal and transportation of the sediment which 0th- erwise would accumulate in the channel surface. From the equations of bed load transport one may assume that F = KT m where K depends only on the soil and fluid prope•es and m is a constant.
In a channel of length L and flow Q the rate of ene• expenditure may then be written as
v 2 Q3 P = Cfp •- QL + KTmpw L = CfpPw '•- L Aw
+ KC•p mv2mpwL The coefficient Cf depends mainly on the channel roughness which tends to decrease only slightly in the downstr-.eaga direction; on the whole the downstream reduction in rough-
Energy dissipation, runoff production and the three dimensional structure of river networks
Rigon & Al.
!58
Rigon & Al.
in late XX century
!59http://www.larssono.com/musings/sandpile/
Rigon & Al.
the emerging of power laws
!60
On the coupled geomorphological and ecohydrologicalorganization of river basins
Kelly K. Caylor a,*, Salvatore Manfreda a,b, Ignacio Rodriguez-Iturbe a
a Department of Civil and Environmental Engineering, Engineering Quadrangle, Princeton University, Princeton, NJ 08540, USAb Dipartimento di Ingegneria e Fisica dell!Ambiente, Universita degli Studi della Basilicata, Potenza I-85100, Italy
Received 17 March 2004; received in revised form 27 August 2004; accepted 27 August 2004
Abstract
This paper examines the linkage between the drainage network and the patterns of soil water balance components determined bythe organization of vegetation, soils and climate in a semiarid river basin. Research during the last 10 years has conclusively shownan increasing degree of organization and unifying principles behind the structure of the drainage network and the three-dimensionalgeometry of river basins. This cohesion exists despite the infinite variety of shapes and forms one observes in natural watersheds.What has been relatively unexplored in a quantitative and general manner is the question of whether or not the interaction of veg-etation, soils, and climate also display a similar set of unifying characteristics among the very different patterns they presents in riverbasins. A recently formulated framework for the water balance at the daily level links the observed patterns of basin organization tothe soil moisture dynamics. Using available geospatial data, we assign soil, climate, and vegetation properties across the basin andanalyze the probabilistic characteristics of steady-state soil moisture distribution. We investigate the presence of organizationthrough the analysis of the spatial patterns of the steady-state soil moisture distribution, as well as in the distribution of observedvegetation patterns, simulated vegetation dynamic water stress and hydrological fluxes such as transpiration. Here we show that thedrainage network acts as a template for the organization of both vegetation and hydrological patterns, which exhibit self-affine char-acteristics in their distribution across the river basin. Our analyses suggest the existence of a balance between the large-scale deter-minants of vegetation pattern reflecting optimality in the response to water stress and the random small-scale patterns that arisefrom local factors and ecological legacies such as those caused by dispersal, disturbance, and founder effects.! 2004 Elsevier Ltd. All rights reserved.
Keywords: Soil moisture dynamics; Plant water stress; River network; Geomorphology; Ecohydrology; Semi-arid; Vegetation patterns
1. Introduction
Recent years have seen dramatic advances in thequantitative description of the geomorphologic struc-ture of river basins [26]. The interconnected system ofhillslopes and the channel network possesses a profoundorder that manifests itself in a number of probabilistic
features whose basic characteristics remain unchangedregardless of scale, geology, or climate [18]. Despitethe deep symmetry of structural organization in geo-morphologic properties, the convergence of the biologi-cal and geophysical study of river basins is a remainingfrontier in hydrological science. In particular, there ex-ists a need to understand the interrelationship amongbiological, geophysical and geochemical approaches tothe study of the earth system. In this regard, soil mois-ture is a crucial link between hydrological and biogeo-physical processes through its controlling influence ontranspiration, runoff generation, carbon assimilationand nutrient absorption by plants. Therefore, efforts to
0309-1708/$ - see front matter ! 2004 Elsevier Ltd. All rights reserved.doi:10.1016/j.advwatres.2004.08.013
* Corresponding author. Tel.: +1 949 824 4327; fax: +1 949 8243672.
E-mail addresses: [email protected] (K.K. Caylor), [email protected] (S. Manfreda), [email protected] (I. Rodri-guez-Iturbe).
Advances in Water Resources 28 (2005) 69–86
www.elsevier.com/locate/advwatres
P[T > t], we find that the Rio Salado basin (and all sub-basins therein) exhibits characteristic scaling propertiesthat are consistent with known scaling properties of riv-er networks. In particular, the exceedance probability ofcumulative upstream evapotranspiration for any ran-domly chosen point in the basin is a power law withslope !0.43 (Fig. 15b), which is very similar to the ob-served geomorphological scaling exponent in the distri-bution of contributing areas within river basins [26].Thus, despite the presence of a geographic trend inatmospheric losses per unit area (Fig. 15a), there is notrend manifested within evapotranspiration per unitarea when analyzed according to stream magnitude
(Fig. 15b), where magnitude is a surrogate of upstreamcontributing area. The reason for the above is that basintopology tends to smooth many geographical differencesacross the river basin. As an example, the average nor-malized distance from the outlet is approximately 0.5for streams of almost all magnitudes (Fig. 15c), exceptfor the very highest magnitude streams whose directlycontributing areas are very close to the outlet. There-fore, the topological structure of river basins tends topreserve an average value of hydrological quantitieswithin the network structure (here expressed as constantevapotranspiration per unit area) even in the presence ofpronounced inhomogeneous geographical distributions
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9-0.2
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104 105 106 107
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100 101 102 103 1040
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m
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(b)
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∆χ a(x
)P
[T ≥
t]<x
>
0.43
Fig. 15. Normalized atmospheric losses per unit area, Dva , increasing with distance from the outlet, x, measured through the network (a). Exceedanceprobability of total upstream evapotranspiration above a randomly chosen point in the drainage network, P[T > t], (b). Normalized average distancefrom the outlet for links of different magnitudes (c).
K.K. Caylor et al. / Advances in Water Resources 28 (2005) 69–86 83
Statistical organisation “at large”. Exceedance of upstream total evapotranspiration
Rigon & Al.
eco-hydrology
!61
Does the Thermodynamics of the Earth System has a subchapter in Hydrology ?
Rigon & Al.
Thermodynamics
!63
My own path in two questions
(Where is the great optimism of the old century ?)
Where are the experiments ?
Where is the mathematics?
Rigon & Al.
My own tradition
!64
Where are the measurements ?
I mean which type of measurements can we depict to identify spatial and temporal patterns ?
Are power laws the only way to identify organisation ?
How can we use these measurements to constrain our models ?
Can information theory help ?
2005 drought-afflicted ecohydrological system. The result-ing weighted-cut process network for July 2005 is visual-ized in Figure 8. The first salient observation is that thedrought process has fewer couplings than the healthyprocess network; in fact, roughly half of the couplingsdisappear during the drought state (adjacency matrix re-sults not shown). Not a single new coupling exists duringthe drought, which did not occur during healthy condi-tions. In general, then, the drought state is characterizedby decoupling.[62] The most important decoupling is that of the turbu-
lent type 2 land surface subsystem from the other twosubsystems. In the process network, neither the synopticnor the ABL subsystems are coupled to the turbulentsubsystem during drought conditions, with the same type3 12 h couplings that existed during healthy conditions.Because less information is flowing between the subsys-tems, the surface energy balance and carbon flux processesare not being organized as strongly by the weather patternsand boundary layer processes. The ‘‘engine of variability’’that is necessary for the land surface ecohydrological systemto thrive [Kumar, 2007] appears to be broken down during
drought because of insufficient information input from thesynoptic weather patterns. The moisture fluxes which carrythe information may be reduced below a key thresholdduring drought.[63] The absence of information flow from the ABL
subsystem to the turbulent subsystem means that the circu-lar type 3 feedback between these two subsystems is brokenduring drought. The regional self-organizing type 3 subsys-tem that binds the turbulent and ABL subsystems into alarger hierarchical subsystem at longer time scales around12 h dissolves because of the disappearance of the feedbackthat defined this structure during healthy conditions. Aphysical interpretation of this breakdown is that individuallocal-scale land surface ecosystems are not able to commu-nicate with each other via the medium of the ABL, or tocollectively organize and influence their atmospheric envi-ronment on a regional scale. The reduction of informationflow and feedback between the turbulent and ABL sub-systems on longer ‘‘regional’’ time scales is characteristic ofdrought.[64] At one time it was believed that the plant ecosystem
is passively forced by climate conditions, but as far back as
Figure 7. The process network for July 2003, a healthy system state. Types 1, 2, and 3 relationshipsresult in the interpretation of the system as three subsystems linked at time scales ranging from 30 min to12 h. Thin arrows represent type 2 couplings. Thick arrows represent type 3 couplings. A type 1‘‘synoptic’’ subsystem including GER, q, Qs, Qa, and VPD forces the other subsystems at all studied timescales from 30 min to 18 h. A type 2 ‘‘turbulent’’ self-organizing subsystem including gH, gLE, NEE, andGEP exists with a feedback time scale of 30 min or less and inhabits a feedback loop with P and Rg attime scales from 30 min to 12 h. The P, CF, and Rg variables form a loose subsystem of mixed types,which interact with each other on a time scale of roughly 12 h.
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W03419 RUDDELL AND KUMAR: ECOHYDROLOGIC PROCESS NETWORKS, 1 W03419
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My own tradition
!65
Where is the mathematics?
Can we formulate a mathematics of the interactions ?
My own idea is that this mathematics comes out from networks (graph) analysis
I think that an interesting working hypothesis is that "the whole is the sum of its parts and the interactions among the parts", and that part of the quality of the system, seen as a whole, derives from parts' interactions and feedbacks. A system is itself a quite unidentified entity, and its definition is certainly recursive, meaning that, most of the time, a system is a system of systems, and reality is “stratified”. But having a "basic system" at some scale should be feasible.
Rigon & Al.
My own tradition
!66
Look at the interfaces !!!
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My own advise
!67
Ezio Todini 70th Symposium: my talk
Sparse thoughts (on the foundations of a Thermodynamics of Hydrological Systems)
Reservoirology
On " How to make our models more physically-based"
Critical Zone
Which Hydrological model is better ?
What is life ? (by Erwin Schroedinger) and Hydrology
Some talk and thoughts I’ve not already mentioned
Rigon & Al.
Link to posts in my blog: some further reading for a sleeping night
!68
Find this presentation at
http://abouthydrology.blogspot.com
Ulr
ici, 2
00
0 ?
Other material at
Questions ?
Rigon & Al.
https://www.slideshare.net/GEOFRAMEcafe/scales-and-hydrology-in-2020