Emergent relation between surface vapor conductance and relative humidity profiles yields evaporation rates from weather data

The ability to predict terrestrial evapotranspiration (E) is limited by the complexity of rate-limiting pathways as water moves through the soil, vegetation (roots, xylem, stomata), canopy air space, and the atmospheric boundary layer. The impossibility of specifying the numerous parameters required to model this process in full spatial detail has necessitated spatially upscaled models that depend on effective parameters such as the surface vapor conductance (Csurf). Csurf accounts for the biophysical and hydrological effects on diffusion through the soil and vegetation substrate. This approach, however, requires either site-specific calibration of Csurf to measured E, or further parameterization based on metrics such as leaf area, senescence state, stomatal conductance, soil texture, soil moisture, and water table depth. Here, we show that this key, rate-limiting, parameter can be estimated from an emergent relationship between the diurnal cycle of the relative humidity profile and E. The relation is that the vertical variance of the relative humidity profile is less than would occur for increased or decreased evaporation rates, suggesting that land–atmosphere feedback processes minimize this variance. It is found to hold over a wide range of climate conditions (arid–humid) and limiting factors (soil moisture, leaf area, energy). With this relation, estimates of E and Csurf can be obtained globally from widely available meteorological measurements, many of which have been archived since the early 1900s. In conjunction with precipitation and stream flow, long-term E estimates provide insights and empirical constraints on projected accelerations of the hydrologic cycle

Spectral behavior of the coupled land-atmosphere system

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Civil and Environmental Engineering, February 2010.Cataloged from PDF version of thesis.Includes bibliographical references.The main objective of this thesis is to understand the daily cycle of the energy coupling between the land and the atmosphere in response to a forcing of incoming radiation at their common boundary, the land surface. This is of fundamental importance as that the initial/ boundary conditions of the land-surface state variables (e.g. soil moisture, soil temperature) exert strong control at various temporal scales on hydrologic, climatic and weather related processes. Hence diagnosing these state variables is crucial for extreme hydrological forecasting (flood/ drought), agronomic crop management as well as weather and climatic forecasts. Consequently in this thesis, the daily behavior of a simple land-atmosphere model is examined. A conceptual and linearized land-atmosphere model is first introduced and its response to a daily input of incoming radiation at the land surface is investigated. The solution of the different state and fluxes in the Atmospheric Boundary Layer (ABL) and in the soil are expressed as temporal Fourier series with vertically dependent coefficients. These coefficients highlight the impact of both the surface parameters and the frequency of the radiation on the heat propagation in the ABL and in the soil. The simplified model is shown to compare well with field measurements thus accounting for the main emergent behaviors of the system. The first chapter of the thesis describes the theoretical background of the equations governing the evolution of temperature and humidity in the ABL and in the soil. In the second chapter, the pioneering work of Lettau (1951), which inspired our approach is summarized. In his work Lettau studied the response of a simplified linearized land-atmosphere model to a sinusoidal net radiation forcing at the land surface. The third chapter of the thesis describes the SUDMED project, which took place in Morocco in 2003. During this project a wheat field was fully instrumented with continuous measurements of soil moisture, radiative fluxes, turbulent heat fluxes and soil heat flux. This site will be taken as a reference for model comparison. The fourth chapter of the thesis presents the three studies with distinctive goals. In these studies our linearized land-atmosphere model is first introduced. Then the propagation of the land-surface diurnal heating is presented and the model is compared to observations from the SUDMED project. Finally the repercussion of a land-surface energy budget error noise is investigated. Finally in the last chapter of the thesis we discuss possible evolution and improvements of the analytical coupled model presented in this thesis. In particular, it is emphasized that the non-linearity of the the boundary-layer height is of great importance for the predictability of the ABL state.by Pierre Gentine.Ph.D

Analysis of the diurnal behavior of Evaporative Fraction

Thesis (S.M.)--Massachusetts Institute of Technology, Dept. of Civil and Environmental Engineering, 2006.Includes bibliographical references (leaves 153-160).In this thesis, the diurnal behavior of Evaporative Fraction (EF) was examined. EF was shown to exhibit a typical concave-up shape, with a minimum usually reached in the middle of the day. The influence of the vegetation cover and the soil moisture conditions on EF diurnal shape was also investigated. We also checked the repercussion of a change in environmental conditions on EF. This study will finally allow a better understanding of EF and suggests some new methods to obtain a good estimate of EF and of evapotranspiration.by Pierre Gentine.S.M

Systematic errors in ground heat flux estimation and their correction

Incoming radiation forcing at the land surface is partitioned among the components of the surface energy balance in varying proportions depending on the time scale of the forcing. Based on a land-atmosphere analytic continuum model, a numerical land surface model, and field observations we show that high-frequency fluctuations in incoming radiation (with period less than 6 h, for example, due to intermittent clouds) are preferentially partitioned toward ground heat flux. These higher frequencies are concentrated in the 0–1 cm surface soil layer. Subsequently, measurements even at a few centimeters deep in the soil profile miss part of the surface soil heat flux signal. The attenuation of the high-frequency soil heat flux spectrum throughout the soil profile leads to systematic errors in both measurements and modeling, which require a very fine sampling near the soil surface (0–1 cm). Calorimetric measurement techniques introduce a systematic error in the form of an artificial band-pass filter if the temperature probes are not placed at appropriate depths. In addition, the temporal calculation of the change in the heat storage term of the calorimetric method can further distort the reconstruction of the surface soil heat flux signal. A correction methodology is introduced which provides practical application as well as insights into the estimation of surface soil heat flux and the closure of surface energy balance based on field measurements

Deep learning to represent sub-grid processes in climate models

The representation of nonlinear sub-grid processes, especially clouds, has been a major source of uncertainty in climate models for decades. Cloud-resolving models better represent many of these processes and can now be run globally but only for short-term simulations of at most a few years because of computational limitations. Here we demonstrate that deep learning can be used to capture many advantages of cloud-resolving modeling at a fraction of the computational cost. We train a deep neural network to represent all atmospheric sub-grid processes in a climate model by learning from a multi-scale model in which convection is treated explicitly. The trained neural network then replaces the traditional sub-grid parameterizations in a global general circulation model in which it freely interacts with the resolved dynamics and the surface-flux scheme. The prognostic multi-year simulations are stable and closely reproduce not only the mean climate of the cloud-resolving simulation but also key aspects of variability, including precipitation extremes and the equatorial wave spectrum. Furthermore, the neural network approximately conserves energy despite not being explicitly instructed to. Finally, we show that the neural network parameterization generalizes to new surface forcing patterns but struggles to cope with temperatures far outside its training manifold. Our results show the feasibility of using deep learning for climate model parameterization. In a broader context, we anticipate that data-driven Earth System Model development could play a key role in reducing climate prediction uncertainty in the coming decade.Comment: View official PNAS version at https://doi.org/10.1073/pnas.181028611

Data-Driven Equation Discovery of a Cloud Cover Parameterization

A promising method for improving the representation of clouds in climate models, and hence climate projections, is to develop machine learning-based parameterizations using output from global storm-resolving models. While neural networks can achieve state-of-the-art performance within their training distribution, they can make unreliable predictions outside of it. Additionally, they often require post-hoc tools for interpretation. To avoid these limitations, we combine symbolic regression, sequential feature selection, and physical constraints in a hierarchical modeling framework. This framework allows us to discover new equations diagnosing cloud cover from coarse-grained variables of global storm-resolving model simulations. These analytical equations are interpretable by construction and easily transferable to other grids or climate models. Our best equation balances performance and complexity, achieving a performance comparable to that of neural networks ($R^2=0.94$) while remaining simple (with only 11 trainable parameters). It reproduces cloud cover distributions more accurately than the Xu-Randall scheme across all cloud regimes (Hellinger distances $<0.09$), and matches neural networks in condensate-rich regimes. When applied and fine-tuned to the ERA5 reanalysis, the equation exhibits superior transferability to new data compared to all other optimal cloud cover schemes. Our findings demonstrate the effectiveness of symbolic regression in discovering interpretable, physically-consistent, and nonlinear equations to parameterize cloud cover.Comment: 35 pages, 10 figures, Submitted to 'Journal of Advances in Modeling Earth Systems' (JAMES