Water in soils
(Storyboard2020)
- The Richardson-Richards equation (Storyboard 2020)
Once precipitations arrive to the ground surface they either infiltrate or generate runoff. We first state how they infiltrate and, actually how water behave in the soil and in the ground. We talk about the complexity of the Earth surface that contains life and call it, the Critical Zone. To study infiltration we introduce the Darcy and Richards equations of which we explain the characteristics.
- 1 - Soils (Vimeo2025)
- 2 - Texture and Structure of soils (Vimeo2025)
- Textbook: Freeze and Cherry: Groundwater, section 2.8
- 3 -Definitions (Vimeo2025)
- 4 - Darcy-Buckingham law
- 5 - Heuristic reasons for assuming that a Darcy like laws is valid also in the unsaturated case (Vimeo2025)
- Darcy (Vimeo2025)
- Textbook: Freeze and Cherry, Groundwater, section 2.1 and section 2.12
- Buckingham (Vimeo2025
- Complementary reading: Freeze and Cherry, Groundwater, section 2.2
- Soil Water RetentionCurves (Vimeo2025)
- SWRC White Board explanation
- On What SWRC depends upon (White Board)
- Complementary reading: Freeze and Cherry, Groundwater, section 2.6
- Hydraulic Conductivity
- Conductivity in unsaturated soils (Vimeo2025)
- Saturated conductivity (Vimeo2025)
- Textbook: Freeze and Cherry, Groundwater, section 2.3 and section 2.
- Additional material: Ning Lu's lectures on soil water
- The Richardson-Richards equation (Storyboard 2020)
- Just the divergence Theorem (Vimeo2025)
- Complementary reading: Freeze and Cherry, Groundwater, section 2.6
- Pedotransfer Functions (Vimeo2025)
- Richards 1D (Vimeo2025)
- Further information:
- The groundwater equation (Vimeo2025)
- (YouTube2019,Vimeo 2021,Vimeo2022, Vimeo2023, Vimeo2024)
- Textbook: Freeze and Cherry, Groundwater (Section 2.9 and section 2.11)
Evaporation generalities (Storyboard2020)
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.
- Definitions (Vimeo2025)
- Evaporation as Entropy growth (Vimeo2025)
- Evaporation causes diffusion of water vapor and the Clausius Clapeyron Equation (Vimeo2025 I, Vimeo2025 II)
- Turbulent transport of vapor (and other quantities): the Daltonian law (Vimeo2025)
- Textbook: M. Bottazzi (cap. 2.2)
- Whiteboards:
- A short reminder (Evaporation as vapor transport and evaporation as phase transition)
- On the parametrization of turbulence
- And again on the logarithm profile
- Blackboard 2024
- Evaporation as energy flux (Vimeo2025)
- Textbook: M. Bottazzi (chap. 2.3)
- Schymanski & Or derivation of Penman-Monteith equation (Vimeo2025 - not recorded)
Evapotraspiration II
- Simplification of the P-M solution (PM-FAO e Priestley-Taylor) (Vimeo2024)
- Evaporation form soils (Vimeo2024)
- Textbook: M. Bottazzi (chap. 2.4.1-2.4.3)
- Transpiration I (Vimeo2024)
- Textbook M. Bottazzi (chap. 3.0-3.3)
- Transpiration II (Vimeo2024)
Supplemental Material
- Plants marvellous physics (Vimeo2025 - In Italian)
- From Leaves Old Material to Canopies (Vimeo2024)
- Textbook M. Bottazzi (chap. 3.4)
- Plants physiology and resistances to transpiration (supplemental material)
Further Reading
D’Amato, Concetta, and Riccardo Rigon. 2025. “Elementary Mathematics Can Help to Shed Light on the Transpiration Budget under Water Stress,” January. https://doi.org/10.1002/ECO70009.
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