Using GEOET's Prospero model with minimal variations for simulating the non capacitive energy budget of snow and soil

This post is not self-explanatory and requires digging into other posts and some papers. 

Please review Section 2 of Concetta's paper (https://onlinelibrary.wiley.com/doi/10.1002/eco.70009?af=R) and verify the calculations presented there.

The model in D'Amato and Rigon (2025) uses a non-capacitive approach (it doesn't account for the thermal capacity of plants), and so will be if the same derivation is specialized for snow (or soil), which is a limitation. However, this approach is still more physically based than semi-empirical formulations or degree-day methods commonly used. In the literature, these are referred to as "stationary solutions" of the system. Despite the name, these solutions respond instantaneously to changing boundary conditions (radiation, latent and sensible heat fluxes), as evident in equation (10), which varies with radiation, wind velocity, and roughness.

Equation (10) and subsequent equations in Concetta's paper are essentially the Prospero solutions (though exact implementation should be verified in Concetta's code). The time interval of integration is, in principle instantaneous, but eventually you would like to integrate it over a finite time step (a hour, or a day, for instance). 

A non negligible aspect is that snow can melt into water and for any temperature you get from the energy budget, you need to partition the water in liquid water and ice. For this reason you probably need a partitioning function, like the one used for partitioning precipitation in rainfall and snowfall or you can simply use a melting law like  in simple models but now the temperature used should not be the air tempeature but the snow temperature.  See melting in simple models in  the links below

• Simplified snow models   (Vimeo2024)

for further information. 

An important term is missing from the formulation: heat exchange by conduction with the ground, which should be represented as:

G = C_s T_Δg := C_s (T_g - T_s)

Where:

• C_s is an appropriate exchange coefficient (can be taken as C_s = K/L, where K is the bulk thermal conductivity of the layer and L is its depth)
• T_g is the ground temperature (which could be taken as the multi-annual air temperature average)
• T_s is the snow temperature

Since this flux depends on the independent variable, it introduces additional terms that modify solution (10). Please derive these calculations independently.

Other terms that don't depend on the independent state variables can be included in the S_nk term. With these modifications, the Prospero code can effectively simulate the snow energy budget. Similar arguments apply to soil modeling.

A further consideration is the proper parameterization of the conductances C and C_E fluxes in equation (10), which differ from transpiration cases. For soil, according to Lehman-Or theory, evaporation should be modeled as potential until the water storage exceeds a threshold S_T, then decreasing proportionally with storage below this threshold when implementing an integrated model (Details ? I do not know).

I know that there are several missing aspects in this post. Who is interested, please ask. 

P.S. - These components have then to be carefully coupled to the other components. With respect to this, please consider the following: 

First review the presentation materials I've shared:

Getting new features to the linear systems (Vimeo2025)

The topic is that, based on my analysis, the second option is clearly the one should be applied in integrated distributed models (like GEOframe-NewAGE). However, this means we cannot simply subtract ET (or any other sink) from total rainfall - we need to incorporate this directly into the equation solver. While the example in the presentation uses a linear system with an analytical solution, the same principle applies to our non-linear fluxes where we use numerical integration. Therefore appropriate modifications could be necessary to the basic GEOframe-NewAGE codes. 

GEOSPACE or Soil-Plants-Atmosphere-Continuum Estimator in GEOframe first paper

The soil-plant-atmosphere continuum (SPAC) system is a complex and interconnected network of physical phenomena, encompassing heat transfer, evapotranspiration, precipitation, water absorption, soil water flow, substance transport, and gas exchange. These processes govern the exchange of energy, matter, and water within the SPAC system. To better understand and model SPAC interactions, interdisciplinary approaches are essential due to the inherent complexity of the system. Instead of relying on a single monolithic model, we propose a component-based modeling approach, where each component addresses a specific aspect of the system. Object-oriented programming (OOP) is adopted as the foundational framework for this approach, providing flexibility and adaptability to accommodate the ever-changing nature of the SPAC system.

Please find the paper by clicking on the Figure

The Soil Plant Atmosphere Continuum Estimator in GEOframe (GEOSPACE) is presented in this paper, in particular the one-dimensional development, GEOSPACE-1D. The framework is a tool designed to facilitate robust, reliable and transparent simulations of SPAC interactions. It embraces the principles of open-source software and modular design, aiming to promote open, reusable, and reproducible research practices. By implementing the OOP, GEOSPACE-1D breaks down the complexity of SPAC modeling into smaller, self-contained structures, each responsible for a specific scientific or mathematical concept. This modular architecture adheres to the "open to extensions, closed to modifications" philosophy, enabling easy model extension without disrupting existing components. Equations are implemented in an abstract manner, emphasizing the use of common interfaces over concrete classes, a hallmark of contemporary OOP. GEOSPACE-1D adopts a generic programming framework, where distinct classes adhere to a common interface. This compartmentalization serves two critical purposes: validating individual processes against analytical solutions and facilitating the integration of novel processes into the system.

The paper emphasizes the significance of modeling the coupling between infiltration and evapotranspiration for accurate hydrological simulations. It explores the interplay between plant transpiration, soil evaporation, and soil moisture dynamics, highlighting the need to account for these interactions in SPAC models. The paper concludes by underlining the importance of modularity, transparency, and openness in SPAC modeling, principles that underlie the development of GEOSPACE-1D and its components. Overall, GEOSPACE-1D represents a promising approach to SPAC modeling, providing a flexible and extensible framework for studying complex interactions within the Earth's Critical Zone. It is worth recalling that the fundamental premise of GEOSPACE-1D is not to create a single soil-plant-atmosphere model, but to establish a system that allows the creation of a series of soil-plant-atmosphere models, adapted to the specific needs of the user's case study.

Exploring the Soil-Plant-Atmosphere Continuum: Advancements, Integrated Modeling and Ecohydrological Insights, a Ph.D. Thesis by C. D'Amato

This thesis aims to address the complex issue of SPA interactions by developing a comprehensive set of models capable of representing the intricate dynamics of this system. At the core of this research lies the integration of sophisticated descriptions of hydrological and plant biochemical processes into a novel ecohydrological model, GEOSPACE-1D (Soil Plant Atmosphere Continuum Estimator model in GEOframe).

Through a combination of theoretical exploration, engineering methodologies, and empirical experiments, this thesis aims to advance our understanding of SPA interactions. The development of adaptable models, represents a significant contribution to the field. The thesis emphasizes the practical implications of employing models to analyze experimental data, thereby enhancing our comprehension of various phenomena.

In conclusion, this thesis provides valuable insights into SPA interactions and lays the groundwork for future research and applications. By embracing the challenge of under- standing and modeling the SPA continuum, this work contributes to the ongoing efforts to address environmental challenges and promote sustainable practices.  The thesis draft can be dowloaded by clicking on the figure. 

 

Elementary Mathematics sheds light on the transpiration budget under water stress

This paper aims to establish a method to accurately describe transpiration by employing appropriate physical equations. Although some simplifications are made, including use of a simplified treatment of turbulence and neglecting of the thermal capacity of transpiring leaves, it is argued that the chosen scheme has general validity in identifying the primary mechanisms governing transpiration. 

To achieve this objective, a traditional treatment involving five equations, including the mass budget, is used. Initially, a simplified approach that does not consider the water budget is introduced to outline the general procedure to explicitly ad- dress canopies. Subsequently, the water budget is incorporated to appropriately account for water stress in transpiration. In this context, a novel linearization of the extended Clausius- Clapeyron equation, incorporating the Kelvin effect, is employed. It is demonstrated that the well-known Penman formula emerges as one of the solutions within a system of equations, providing estimates for temperature (T), vapor content in air (e), and the thermal transport of heat (H). The method, initially conceived for homogeneous canopies, is expanded to encompass sun-shade canopy layers. By employing the water mass balance, the trade-off between atmospheric evaporation demand and the water delivery capacity of the soil and stem is eluci- dated. Notably, it is revealed that the pressure potential within leaves is not solely determined by capillarity, but rather represents the dynamic outcome of the intricate interactions within the soil-plant-atmosphere continuum. These findings highlight differences from more simplistic approaches commonly employed, particularly concerning canopies. Overall, this study presents a methodological framework to accurately describe transpiration, incorporating key equations and addressing the complex dynamics involved in the soil-plant-atmosphere continuum, and suggests various directions of research in the field. The preprint manuscript can be found here.  The reviews and the answer to reviewers are here. The published paper can be found here. 

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.

The DICAM-EXC Hydrological day

 As a conclusion of what done for the DICAM  excellence project we organized half a day of seminars. As keynote speaker we invited Andrea Rinaldo (GS), one of our mentors, who gave a keynote talk entitled "Reflected In Water". 

The contribution by Andrea was followed by the talk given by Giuseppe Formetta (GS) who was hired upon financial support of the project and presented his research activities. His talk was: Modeling multiple natural hazards with the GEOframe system in the Trentino Alto-Adige region (Video). 

Finally we had contributions from the three doctoral students also hired on the project, 

• Concetta D'Amato, Steps toward a comprehensive treatment of the soil-plant-atmosphere continuum: the GEOSPACE model.
• Maria Grazia Zanoni, Machine Learning for predicting and mapping hydrological and environmental variables.
• Nerea Karmele Portilo de Alberoa. Microplastics in Riverine Systems: A Network-Based Model for Transport and Fate

Here please find the talk of Concetta D'Amato

The LysGEO modelling solution @ Italian Hydrological Society Hydrology days

 @ The Italian Hydrological Society Hydrology days, Concetta D'Amato presented her work on the LysGEO model. As some knows LysGEO put together the WHETGEO 1D component with the (revised) Prospero component. The first estimates infiltration, the second performs evaporation and transpiration. Together they constitute a soil-water-atmosphere model, that it is what LysGEO is. Or if you prefer, it is a tool to investigate the critical zone. 

LysGEO was already described elsewhere in the blog. However, in this case there is a relevant addition, derived from the work done utilizing the funding support of the WATSON cost action in Lausanne with Andrea Rinaldo e Paolo Benettin. They built a lysimeter whose seems to be the right experiment to test LysGEO. The presentation shows the first results (with almost no calibration). Clicking on the image above, you get the slides (in English). Here you can appreciate the presentation in Italian given by Concetta.   LysGEO is a product of the WATZON PRIN project.

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.

The basic is to have the two models to connect, and we, in GEOframe, have them, due to the work of Michele Bottazzi and Niccolò Tubini. The first built Prospero, the GEOframe component that use a novel formulation of the Penman-Monteith solution for evapotranspiration, the second designed and coded a Richardz 1D solver based on a novel algorithm. 

Obviously attaching the two models was not as easy as it can be thought, since the goal was to have a coupled system in which transpiration depends on water content and water content depends on transpiration with feedbacks among the few systems. The presentation illustrate how the coupling works and some simulations. At present the simulations are virtual reality, meaning that they are not parametrized according to some real case, but we hope to find appropriate data in the Watzon project. The figure, under which, by clicking you’ll find Concetta’s presentation, illustrates the directions her research can take in the following years. One goal was to do better than Hydrus 1D, being more reliable, more robust, more flexible, multiplatform and open source. Maybe we already accomplished it :-) ?