On 23rd March 2024, Sarosh gave an invited talk at the International water conference on sustainable development goals (IWCSDG-2024) held at NIT Bhopal, India. His presentation focused on using thermodynamic limits as an additional constraint to model the hydrological cycle and estimate the hydrological fluxes.
Sarosh explained that thermodynamics provides a set of laws that put limit and direction to energy conversion and energy transport. For instance, it explains why a hot cup of coffee in a room cools over time and and why the reverse does not occur. It does it by describing “entropy” and stating that entropy of a system cannot decrease. Additionally, it introduces the concept of thermodynamic equilibrium (a state of maximum entropy) and explains how the dynamics is organized in order to achieve this state. So, what is its role in shaping the hydrologic cycling?
Hydrologic cycling refers to the movement of water in the surface-atmosphere system. While it is indeed fluxes of water that are shaping this cycle, each process within this cycle is closely related to thermodynamics. For example, hydrologic cycling is associated with phase transitions between ice, water and vapor. These transitions require significant amount of energy, hence intimately linked to energy conversions and entropy changes.
Thermodynamics also imposes limits to maximum evaporation that can take place for a given change in net radiation at the surface, through the concept of equilibrium energy partitioning. To maintain the exchange of heat and water from the surface to the atmosphere, work must be performed, and thermodynamics limits the maximum work that can be achieved. The atmosphere’s water-holding capacity is another concept closely related to thermodynamics and described by the Clausius-Clapeyron equation. Furthermore, the pathways water takes to reach runoff in the form of organized networks reflect thermodynamic states. Thus, hydrologic cycling is intricately connected to thermodynamics, and modelling the hydrological cycle using this approach can provide additional constraints for better predicting hydrological fluxes and understanding their response to global warming.
In his talk, Sarosh showed two applications of this approach to hydrologic cycle. The first one is to apply this concept to atmospheric convection, which facilitates the exchange of heat and water from surface to the atmosphere. He viewed this exchange as an outcome of a heat engine operated between the hotter surface and a cooler atmosphere (A framework that we have been working on for quite sometime, see Kleidon & Renner, 2013; 2018; Ghausi et al., 2023) . This engine performs work to generate kinetic energy and sustain vertical motion. We describe this exchange by writing the energy and entropy budgets for this system (first and second law of thermodynamics). As a combination of these equations, we get a limit to how much work can maximally be performed for given turbulent flux exchange. We then maximized this generated work and estimated the corresponding optimal turbulent flux. This optimal turbulent flux was then compared with independent observations and showed an excellent agreement. This flux was further partitioned into latent and sensible heat using the equilibrium energy partitioning. The latent heat flux estimated from this method was compared to observations and again showed a very good agreement.
What these findings imply is that the turbulent flux exchange between surface and atmosphere operate at its thermodynamic limit leading to an emergent predicable pattern in these inherently complex processes. To know more about this work, read this blogpost or check out our publication in PNAS.
He showed another application of this approach to estimate the rainfall-temperature sensitivities from observations. Rainfall amount per event is expected to increase with temperature at a rate of 7%/K; a rate set by thermodynamics based on the amount of moisture the atmosphere can hold (based on the Clausius-Clapeyron relationship, CC in short). However, observations from tropical regions show large deviations in the precipitation sensitivities from the CC rate. He used observations from India and showed that a large part of the uncertainty in this response comes from the radiative effect of clouds on surface temperatures during the precipitation events. This results in a covariation between precipitation and temperature that needs to be accounted for when using observations to infer how precipitation events scale with temperature.
He minimized this covariation by removing the cloud effects on surface temperature using the thermodynamically constrained surface energy balance approach and estimated sensitivities that are consistent with physical arguments and model projections. This implies that the argued intensification of heavy rainfall events is consistent with observations after the cloud effects are accounted for. It also shows that the rainfall sensitivity to global warming is mainly determined by the clear-sky conditions. To know more about this work read this blogpost or see this paper in HESS.
To conclude, Sarosh’s talk highlights that thermodynamics imposes relevant constraints to hydrologic cycling as the atmosphere works as hard as it can to deplete the disequilibriums. Assimilating this kind of approach together with state-of-art process based hydrological models should be a viable next step which may further enhance their performance, particularly in the ungauged basins.
References:
A. Kleidon, M. Renner, Thermodynamic limits of hydrologic cycling within the Earth system: Concepts, estimates, and implications. Hydrol. Earth Syst. Sci. 17, 2873–2892 (2013), https://doi.org/10.5194/hess-17-2873-2013.
A. Kleidon, M. Renner, Diurnal land surface energy balance partitioning estimated from the thermodynamic limit of a cold heat engine. Earth Syst. Dynam. 9, 1127–1140 (2018), https://doi.org/10.5194/esd-9-1127-2018.
Ghausi, S. A., Tian, Y., Zehe, E., & Kleidon, A. (2023). Radiative controls by clouds and thermodynamics shape surface temperatures and turbulent fluxes over land. Proceedings of the National Academy of Sciences, 120(29), e2220400120 https://doi.org/10.1073/pnas.2220400120.
Ghausi, S. A., Ghosh, S., & Kleidon, A. (2022). Breakdown in precipitation–temperature scaling over India predominantly explained by cloud-driven cooling. Hydrology and Earth System Sciences, 26(16), 4431-4446. https://doi.org/10.5194/hess-26-4431-2022,.
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