My reflections and notes about hydrology and being a hydrologist in academia. The daily evolution of my work. Especially for my students, but also for anyone with the patience to read them.
Monday, May 4, 2026
Stomata close to maximize transpiration ?
The slides of the talk can be found here. The various figures were created within Jupyter Notebooks that are here with the helps of Claude. Please also consider to watch my other presentation on a new statistical theory on the dynamics of soil water in vadose zone, also presented at EGU 2026. This latter presentation is here.
Tuesday, April 16, 2024
Elementary Mathematics sheds light on plant Transpiration
However, here you can find also the Jupyter Notebooks and the data that were used to produce the figures in the presentation. The presentation itself can be found by clicking on the figure above. The paper, submitted to Ecohydrology, can be found as an Authorea preprint here.By examining the derivation of Penn-Monteith-like equations for estimating evapotranspiration, one can uncover valuable insights into plant functionality. In essence, equations talk. For a more comprehensive and in-depth exploration of this topic, refer to this erlier post.
Tuesday, January 2, 2024
Elementary Mathematics sheds light on the transpiration budget under water stress
Saturday, September 30, 2023
Constraints to transpiration in a simple (but not too simple) model of transpiration
In our collaborative work with Concetta D'Amato for the WATERSTEM project, we encountered the initial constraint of transpiration imposed by the hydraulic conductance of the stem-root system. Through our research, inspired by Manzoni et al. [2013], we discovered that the sigmoidal form of conductivity leads to an optimum for transpiration. We attempted to reproduce this phenomenon using the data provided by Kroeber et al. [2-13]. After considerable effort, we successfully generated the gray curve in the Figure, which exhibits a peak just before -4 MPa and enables too high transpiration.
However, we realized that the soil resistance was missing from our analysis. To address this, we incorporated the conductivity of a Silt Loam soil using the van Genuchten Mualem parameterization. The resulting brownish curves serve as evidence that the soil plays a crucial role, as anticipated by Carminati and Javaux [2020]. It is important to note that these curves depict the limits imposed by the soil and stem, which determine the potential sapflow rates, but do not reflect the constraints imposed by plant physiology. To account for plant physiology, we introduced the stomatal resistance, represented by the three dashed curves under different working hypotheses whose parameterization was taken from Daly et al. [2004]. The red points in the Figure represent the plant's working points (although the coupling with the atmospheric boundary layer is not depicted). One notable aspect of the Figure is that at typical soil suctions, the sapflow curves appear relatively flat, and the working points result in relatively constant sapflow despite variations in xylem/leaves pressure. The complete story will soon be available in Concetta's Ph.D. thesis, and the detailed process of creating the Figure can be found in its supplemental material notebooks.
References
Carminati, Andrea, and Mathieu Javaux. 2020. “Soil Rather Than Xylem Vulnerability Controls Stomatal Response to Drought.” Trends in Plant Science 25 (9): 868–80. https://doi.org/10.1016/j.tplants.2020.04.003.
Daly, Edoardo, Amilcare Porporato, and Ignacio Rodriguez-Iturbe. 2004. “Coupled Dynamics of Photosynthesis, Transpiration, and Soil Water Balance. Part I: Upscaling from Hourly to Daily Level.” Journal of Hydrometeorology 5 (3): 546–58. https://doi.org/10.1175/1525-7541(2004)005<0546:cdopta>2.0.co;2.
Kröber, Wenzel, Shouren Zhang, Merten Ehmig, and Helge Bruelheide. 2014. “Linking Xylem Hydraulic Conductivity and Vulnerability to the Leaf Economics Spectrum—A Cross-Species Study of 39 Evergreen and Deciduous Broadleaved Subtropical Tree Species.” PloS One 9 (11): e109211. https://doi.org/10.1371/journal.pone.0109211.
Manzoni, Stefano, Giulia Vico, Gabriel Katul, Sari Palmroth, Robert B. Jackson, and Amilcare Porporato. 2013. “Hydraulic Limits on Maximum Plant Transpiration and the Emergence of the Safety-Efficiency Trade-Off.” The New Phytologist 198 (1): 169–78. https://doi.org/10.1111/nph.12126.
Wednesday, June 15, 2022
Evaporation and Transpiration as you have never seen before
A consistent part of root zone and surface water evaporates and returns to the atmosphere to eventually form clouds and precipitation again. The process follows quite complicate routes and is different when happening from liquid surfaces, soil or vegetation (and BTW animals). In this group of lectures we try to figure out the physical mechanisms that act in the process and give some hint on methods to estimate evaporation and transpiration with physically based models.
| Courtesy of Luca Chisté (http://www.lucachiste.it/) |
- The generation of Water vapor (Vimeo2022)
- Turbulent transport of vapor (and other quantities): the Daltonian law (Vimeo2022)
- Textbook: M. Bottazzi (cap. 2.2)
- Evaporation as energy flux (Vimeo2022)
- Textbook: M. Bottazzi (chap. 2.3)
- Evaporation is water limited or energy limited (Budyko approach) (Vimeo2022)
- Textbook: M. Bottazzi (chap. 2.1.0)
- Evaporation form soils (Vimeo2022)
- Textbook: M. Bottazzi (chap. 2.4.1-2.4.3)
- Transpiration (Vimeo2022)
- Plants physiology and resistances to transpiration (supplemental material)
- Textbook M. Bottazzi (chap. 3.0-3.3)
- The derivation of the generalized PM equation (Vimeo2022)
- Textbook: M. Bottazzi (cap. 2.3.2-2.3.5)
Tuesday, June 15, 2021
How CO2 and H2O Flux Mesurements have contributed to our understanding of Global Change Biology
Dennis Baldocchi (GS) is a myth for me, for his knowledge of the processes and issues related to the soil atmosphere interactions, for the wide range of materials he shared with the community and for his efforts in the FLUXNET. So it was a great pleasure when I heard that he accepted to give a talk to our class (held by Mirco Rodeghiero, GS) "Biosphere Atmosphere and Climate Interactions" of the Master in Environmental Meteorology. His talk was very dense and illuminating and, fortunately, he agreed with us to share the videos that are presented here below.
- The talk (Vimeo)
- The Discussion (Vimeo)
Thursday, May 13, 2021
Evaporation and Transpiration
Evaporation and transpiration are the topics more discussed in this blog, due to the interests I grew in the last few years (almost without publishing). However, I believe I collected enough information to be able to summarize a new view on these processes. Certainly shared with others, but not so widely shared, and not already present in other posts of this blog. In this presentation, that I shrinked in less than half an hour, I tried to summarize part of my current knowledge. For complimentary information, please see the lectures I gave at the GEOframe Winter School, or during the class of hydrology I do.
Friday, December 18, 2020
Lysimiter GEO - Webinar I
Land-Vegetation-Atmosphere interactions are an exciting field of Hydrology. Within our system GEOframe, one branch of work is improving the physics of GEOtop and this talk shows some of the work we made to this goal. Lysimiter GEO builds a virtual lysimiter and modeling infiltration and energy transfer in soil and evaporation and transpiration. The infiltration is modeled by the component WHETGEO 1D (Water, HEat and Transport in GEOframe) that integrates the 1D Richards developed by Niccolò Tubini. The evaporation and Transpiration are modeled by the GEOframe component Prospero developed by Michele Bottazzi in his Ph.D. Thesis. Lysimeter GEO, however, was completed by Concetta D'Amato who is pursuing her Ph.D. on these topics within the PRIN project WATZON.By clicking on the Figure below you can access the slides.
Thursday, October 22, 2020
On putting plants in hydrological models in practice
The work of Concetta D’Amato Ph.D. started with joining together a reasonable evapotranspiration model with a solid infiltration model building a virtual lysimeter.
Monday, January 20, 2020
Video Lectures on Hydrology
Here they are below subdivided by arguments with their companion slides:
Catchments Delineation and Geomorphometry
- The basic theory (YouTube video 2019,YouTube2020)
- The derived quantities (YouTube video 2019,YouTube2020)
- Extracting the hillslope (YouTube Video 2019,YouTube2020)
- A little on some geomorphic laws (YouTube video 2019, YouTube2020)
Data Interpolation with Kriging
- The Kriging's equations (YouTube2019 - Slides were a little modified for 2020, YouTube2020)
- Variography (YouTube video 2019, YouTubeVideo2020)
- The GEOframe Spatial interpolation Package (SIK) (YouTube2019, YouTube2020)
- Error estimation (leave one out) within SIK (YouTube video 2019, YouTube2020)
Richards equation
Radiation for Hydrologists
- The Sun
- Stefan-Boltzmann law
- From Sun to Earth
- Copying with Earth Surface
- Shortwave absorptions by the atmosphere (YouTube video)
- Considering clouds (YouTube video)
- Shortwave-Terrain geometries (YouTube video)
- Longwave radiation (YouTube video)
- Table of Symbols
- Momentum and water vapor transport in atmosphere (YouTube2020)
- Evaporation as energy flow (YouTube2020)
- Derivation of the simplified energy budget (a là Penman-Monteith after Schymanski and Or) (YouTube2020)
- Simplified relatives of PMSO (YouTube2020)
- Leaf Temperature feedbacks
- Transpiration (YouTube2020)
- Further discussions on resistances and the physiology of plants in this video.
- Evaporation from soil (YouTube2020)
- From leaves to canopies (YouTube2019 Video, YouTube2020)
- Models in Hydrology
- The GEOframe type of models (YouTube2020)
- Representing the Hydrological Dynamical Systems (YouTube2020)
- The Embedded Reservoir Model (YouTube2020)
- Other Videos, that I am providing for my Hydrological Modelling Class are here.
- Video collected by Kevin McGuire (GS) are here.
If you do not want to be just a tourist, you can go deeper and exercise with Jupyter lab and GEOframe. For the latter, please see the material of the GWS2020. To anyone requesting, I can provide the original slides.
Wednesday, September 4, 2019
Stomatal resistance and Transpiration
The other big topic is the physiological reaction to water scarcity. Plants in fact can close stoma: they are like a tap which is being closed with an effect in literature is known as “stomatal resistance”. It cuts the evaporative flux to oppose to the evaporation demand and the reduction is usually represented as a multiplicative factor, the stomatal conductance (actually the inverse of a resistance) which multiply the driving force, which is given as a different of water vapor concentration between the zone very close to the available liquid water and a zone in the viscous boundary layer (VBL) a little apart, such that:
$$Tr = g_l (c(z_0) - c(z))$$
where $T_r$ is transpiration, $g_l$ the stomatal conductance, $c(z_0)$ is the water vapor concentration close to the leaves surface and $c(z)$ is is the vapor concentration at distance $z$.
There is a variety of plants actions that regulate the stomatal resistance which are summarised in the isohydric and anisohydric behavior (Martinéz-Vilalta and Garcia-Forner, 2016). In the first case, the plant progressively closes the stoma as reaction to water stress to maintain as much as possible a balanced water content. In the other case the plant delays stoma closure in the measure it can resist to manifestation of cavitation and produces in its interior a very uneven water distribution. Actually the stomatal resistance $g_s$ is not the only one affecting plants. Plants have roots and a steam that convey water fluxes and also the flux there is traditionally treated as a viscous flow with some resistance. In that cases though, the driving force is the gradient of water potential or, if we prefer the Nobel (1999) view, of the chemical potential (of which the water potential is a particular expression).
Assuming an almost stationary situation along the root-stem-leaves system, the connection between plants compartments can be manipulated within the electric circuitry analogy (resistances sums to obtain a total resistance, as $g_v = 1/g_r+1/g_s+1/g_l$).
This model allows to obtain the suction in leaves, which, in turn, controls the quantity of water vapor in stomatal cavities.
The resistances are further unknown in the coupled water-energy-momentum system that determines evaporation, heat transfer and the water budget, however $g_l$ has been found to be connected to carbon cycle productivity trough the so called Ball-Berry formula (1987, BB). BB (see also Collatz et al, 1991) has been built out of empirical bases and it was subsequently modified (e.g Verhoef and Egea, 2014) to include physiological reactions and the production of abscisic acid, ABA (Buckley, 2017).
To obtain the final result of transpiration, (besides the determination of roots and stem resistances), there is the further problem of the coupling of stoma with the VBL. Again the tradition assume quasi-stationarity of the fluxes and therefore uses the resistance metaphor, assigning to the VBL a resistance according to an integrated Fick’s law. Also in this case, resistances are summed to obtain the comprehensive flux law that regulates the water ascending.
New questions arise: which is the dominant between the two resistances ? Is the resistance metaphor really applicable ?
A couple of papers, in particular, Manzoni et al., 2013 and Bonan et al. 2014 offer two remarkable points of view of the matter. Manzoni is more interested to processes, equations and general issues with plants hydraulics. Bonan et al. goal is the implementation of a model of the soil-plant-atmosphre continuum and therefore its appendixes can be useful to understand some of the details that can be perceived as ambiguous by the beginners in the field. Bonan's treatment is “traditional” being based on the set of assumptions all literature use which give you back an already well packaged simplification of the physics involved. Manzoni et al. put more emphasis on the biophysical aspects and their connections with plants physiology and use partial differential equations to illustrate the concepts. Both of them have a large list of references and, together with the recent work of Verohef and Egea (2016, VE) and the work of Dewar, 2002, can be a solid start for any study of the subject. VE in particular, compare various approaches to modelling the water stress and discuss their ability to reproduce experimental data. One of its main interest is to clarify if either water content or the water pressure explains better plant’s transpiration behavior. VE approach is very practical, since it does not discuss the rational behind the different approaches but just use and test them. The final verdict that pressure explain more properly: this is not so clear indeed until the end. Apparently the result is counter-intuitive with respect the organization of the paper that starts from empirical observation that transpiration follow a two-stage behavior (similar to the one seen in soils) when actual (daily) relative transpiration is plotted against the water available. Therefore there is no better that read it to get the vision clear.
References
- Ball, J. T., Woodrow, J. B., & Berry, J. A. (1987). A model predicting stomatal conductance and its contribution to the control of photosynthesis under different environmental conditions. Progress in Photosynthesys Research, 4, 221–224. http://doi.org/10.1007/978-94-017-0519-6_48
- Bonan, G. B., Williams, M., Fisher, R. A., & Oleson, K. W. (2014). Modeling stomatal conductance in the earth system: linking leaf water-use efficiency and water transport along the soil–plant–atmosphere continuum. Geoscientific Model Development, 7(5), 2193–2222. http://doi.org/10.5194/gmd-7-2193-2014
- Buckley, T. N. (2017). Modeling Stomatal Conductance. Plant Physiology, 174(2), 572–582. http://doi.org/10.1104/pp.16.01772
- Collatz, G. J., Ball, J. T., Grivet, C., & Berry, J. A. (1991). Physiological and environmental regulation of stomatal conductance, photosynthesis and transpiration: a model that includes a laminar boundary layer,. Agricultural and Forest Meteorology, 54, 107–136.
- Dewar, R. C. (2002). The Ball-Berry-Leunning and Trdieu-Davis stomata models: synthesis and extension with a spatially ggregated picture of guard cell function, 25, 1383–1398. http://doi.org/10.1046/j.1365-3040.2002.00909.x
- Martínez-Vilalta, J., & Garcia-Forner, N. (2016). Water potential regulation, stomatal behaviour and hydraulic transport under drought: deconstructing the iso/anisohydric concept. Plant, Cell and Environment, 40(6), 962–976. http://doi.org/10.1111/pce.12846
- Manzoni, S., Vico, G., Porporato, A., & Katul, G. (2013). Biological constraints on water transport in the soil-plant-atmosphere system. Advances in Water Resources, 51(C), 292–304. http://doi.org/10.1016/j.advwatres.2012.03.016
- Nobel, P. (1991). Pysicochemical and environmental plant physiology (pp. 1–637). S.Diego (CA): Academic Press, Inv.
- Verhoef, A., & Egea, G. (2014). Modeling plant transpiration under limited soil water: Comparison of different plant and soil hydraulic parameterizations and preliminary implications for their use in land surface models. Agricultural and Forest Meteorology, 191, 22–32. http://doi.org/10.1016/j.agrformet.2014.02.009
Wednesday, April 11, 2018
Schymanski & Or model for Evapotranspiration in GEOFRAME
You can find it directly at the blog TranspirAction (by Michele Bottazzi) or clicking on the Figure above. The portrait version used in Tübingen is here.









