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![Surface energy balance equations over (a) land surfaces; (b) ocean (water–snow–ice) surface. RS↑,RS↑,RL↑,RL↑\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$R_{S}^{ \uparrow } ,R_{S}^{ \uparrow } ,R_{L}^{ \uparrow } ,R_{L}^{ \uparrow }$$\end{document} are downward shortwave, upward shortwave, downward longwave, upward longwave radiation; Rn the net radiation; E, H, Q the latent, sensible, and ground/surface water–snow–ice heat flux; R0 is the (net) solar radiation entering the (water–snow–ice) media. Radiation fluxes are positive (negative) when the surface receiving (emitting or reflecting). Thermal energy fluxes are positive when entering the atmosphere and/or surface media](publication/309281336/figure/fig8/AS:960096683180032@1605916295002/Surface-energy-balance-equations-over-a-land-surfaces-b-ocean-water-snow-ice.gif)
Surface energy balance equations over (a) land surfaces; (b) ocean (water–snow–ice) surface. RS↑,RS↑,RL↑,RL↑\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$R_{S}^{ \uparrow } ,R_{S}^{ \uparrow } ,R_{L}^{ \uparrow } ,R_{L}^{ \uparrow }$$\end{document} are downward shortwave, upward shortwave, downward longwave, upward longwave radiation; Rn the net radiation; E, H, Q the latent, sensible, and ground/surface water–snow–ice heat flux; R0 is the (net) solar radiation entering the (water–snow–ice) media. Radiation fluxes are positive (negative) when the surface receiving (emitting or reflecting). Thermal energy fluxes are positive when entering the atmosphere and/or surface media
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The maximum-entropy-production (MEP) model of surface heat fluxes, based on contemporary non-equilibrium thermodynamics, information theory, and atmospheric turbulence theory, is used to re-estimate the global surface heat fluxes. The MEP model predicted surface fluxes automatically balance the surface energy budgets at all time and space scales wi...
Citations
... Lots of land surface models have been used to calculate the SEB in the TP (Gao et al., 2004;Han et al., 2017;Han et al., 2021;Ma et al., 2018;Niu et al., 2011;Yang et al., 2009;Yuan et al., 2021;Zhong et al., 2019). In these models, the parameterizations of transfer coefficients and surface roughness for the bulk flux formula are inevitable, which has large uncertainties as reported in previous studies (Huang et al., 2017;Huang and Wang, 2016;Shi and Liang, 2014). Besides, the surface heat fluxes in land surface models are estimated separately, which does not conserve surface energy balance. ...
... In order to present the spatiotemporal variation of land surface heat flux more accurately in the TP, a new method, the maximum entropy production (MEP) model, is proposed based on the maximum entropy principle, dissipation function, and Monin-Obukhov similarity theory (Wang and Bras, 2009). Different from the traditional land surface models and approaches, the MEP model estimates the surface heat fluxes from the partitioning of surface net radiation (hereinafter R n ) under the surface energy balance condition, not needing the input of temperature and moisture vertical gradients in the near-ground layer and surface roughness (Huang et al., 2017;Wang and Bras, 2011;Wang et al., 2014). The Monin-obukhov similarity equation is modified in the MEP model in estimating the surface heat fluxes according to its extreme solution. ...
... The Monin-obukhov similarity equation is modified in the MEP model in estimating the surface heat fluxes according to its extreme solution. The MEP model has been used to estimate the surface heat fluxes on various land cover types such as bare soil, vegetation, water/snow/ice, and ocean in previous studies (Alves et al., 2019;Hajji et al., 2018;Huang et al., 2017;Isabelle et al., 2021;Maheu et al., 2019;Xu et al., 2019). Besides, it also has been used to replace the bulk transfer method in the numerical forecast model, which remarkably improves the simulations of tropical precipitation oscillation and land cold or wet events Jia et al., 2023). ...
... MEP model formulates energy dissipation partitioning of land-surface net radiative energy into latent, sensible, and ground heat fluxes. The model requires fewer inputs than classical ET algorithms, avoiding typical parameterization uncertainties (Text S2 in Supporting Information S1), and it has demonstrated a well-proven accuracy for a variety of land-cover conditions (Huang et al., 2017;Isabelle et al., 2021;Nearing et al., 2012;Shanafield et al., 2015;Sun et al., 2022;Wang et al., 2014;Xu et al., 2019), offering the potential to elucidate mechanisms controlling future ET changes. ...
The 21st century evapotranspiration (ET) trends over the continental U.S. are assessed using innovative, energy‐based principles. Annual ET is projected to increase with high confidence at the rate of 20 mm for every 1℃ of rise in near‐surface air temperature, or 0.45 or 0.98 mm/year/year, depending on the emission scenario. The ET trajectory is dominated (58%) by the increase of land‐surface net radiative energy. An enhancement of the fraction of energy taken up by ET becomes a more important controller (53%) in late 21st century, under the high emission scenario. This increase is explained by the “tug of war” between atmospheric vapor demand and land‐surface ability to supply water. An assessment of future water availability (precipitation minus ET) shows no significant changes at the continental scale. This outcome nevertheless hides strong spatial variability, emphasizing the role of ET in shaping the distribution of water availability among human populations.
... Are there any liquidromes in our heliodrome? The MEPP drives the dynamics of the liquid shells of our earth (Ozawa et al., 2003;Kleidon, 2010;Huang et al., 2017). Hence those shells make our earthly liquidrome. ...
If we take on board the classic Durkheimian (1995 [1915]: 208) notion that religions and societies reflect and maintain one another—that societies create “God” in their own image—it is unsurprising that animism’s popularity as a religious path, often referred to as the “new animism” (Harvey, 2005, 2013), is growing amid current global anxieties about the destruction of natural environments, species depletion and extinction, pollution and climate change. This is happening even as many indigenous heirs of the world’s traditional animisms find themselves increasingly absorbed into cosmopolitan societies and urban contexts where their worldviews are a minority and access to traditional territories, food sources, trans-generational knowledge and lifeways is now more difficult, diminished or threatened. Many indigenous heirs of animism and non-indigenous “new animists” find themselves configuring heterodox paths within the cosmopolitan societies they now inhabit—embracing worldviews which are arguably broadly similar to one another, but needing to negotiate the fallout from the ongoing, often fraught socio-politics of indigenous/non-indigenous relations over the last half century and more.
... Surface temperature of the earth plays a uniquely important role in solar radiation energy entering the Earth system through the surface energy balance, that is, the partition of solar radiation into long-wave radiation and turbulent and conductive heat fluxes into the atmosphere and the earth. A fundamental physical principle governing the dynamics of surface temperature is the conservation of energy represented by the energy balance equation linking radiation and conductive/turbulent heat fluxes at the earth-atmosphere interface (Huang et al., 2017). Surface temperature and heat fluxes are commonly related through the temperature gradient-flux relationships that couple the surface temperature and fluxes to the temperature and heat fluxes of the interior atmosphere and earth. ...
... The MEP model has been extensively validated and widely applied for example,(Chen et al., 2017;El Sharif et al., 2019;Hajji et al., 2018Hajji et al., , 2021Isabelle et al., 2021;Nearing et al., 2012;Shanafield et al., 2015;Tang et al., 2021;Yang et al., 2017;Yang & Wang, 2014) either reproducing or outperforming the bulk flux formula. The MEP parameterization of Q has been used in the FRM of soil surface temperature(Huang et al., 2017). ...
Plain Language Summary
Surface temperature of the Earth is a primary indicator of Earth climate system. Change of surface temperature depends on conductive and turbulent heat transport processes at either side of Earth surface and the media (soil, air, water, snow, etc.) specific absorption of solar radiation. Understanding and simulating surface temperature is a long‐standing challenge in the study of energy and mass exchange at the Earth‐atmosphere interface. This study postulates a unified governing equation of the dynamics of surface temperature for all surface types (soil, water, snow/ice, etc.). The new dynamic equation is independent of the parameterization of heat transfer processes within the atmosphere and surface media. The classical force‐restore equation of surface soil temperature is shown to be a special case of the general equation. The new dynamic equation can be used for simulating surface temperature without using the coupled earth‐atmosphere models or for the specification of surface boundary conditions of temperature and/or heat fluxes required by coupled earth‐atmosphere models.
... This timing suggests that the longwave radiation anomalies arise mostly in response to the reduction in the poleward heat flux. Other terms in the surface energy budget (Clark & Feldstein, 2020;ECMWF, 2019;Huang et al., 2016;Lee et al., 2017;Lesins et al., 2012) are also examined, and the result shows that sensible and latent heat flux are small and scattered, while the residual, or ground flux, essentially offsets incoming radiation anomalies ( Figure S5 in Supporting Information S1). ...
Plain Language Summary
The poleward heat transport by atmospheric circulation is an important process of maintaining the meridional temperature gradient. However, a recent study showed that the heat transport by atmospheric waves in the Northern Hemisphere has been decreasing over the past few decades. As a cause of this weakening trend, the decrease of the equator‐to‐pole temperature gradient due to Arctic warming has been suggested. In this study, we examine the monthly trends of the equator‐to‐pole temperature gradient and poleward heat transport by atmospheric waves that are decomposed into synoptic‐scale waves and large‐scale waves. We find that during the winter half‐year, the trend of heat transport by synoptic‐scale waves is more closely tied to that by large‐scale waves, than to the temperature gradient trend. From June to August, it is shown that the poleward heat transport by synoptic‐scale waves decreases after a warming of the high‐latitude land areas. Therefore, these findings underscore the importance of the planetary‐scale waves and summer land warming for understanding future changes in atmospheric heat transport.
... Nevertheless, studies focusing on evaluating the overall ET across various land covers are lacking, especially at a global scale. The only attempt at a global study using the MEP model was conducted by Huang et al. (2017), wherein the surface energy budgets were revisited; however, the study failed to verify the ET because of the coarse spatial resolution and the 10-year temporal coverage that was insufficient to reveal long-term ET variations. Since currently derived global ET estimates for the past decades vary in absolute values and trends (Brutsaert et al., 2020;Jung et al., 2010;Pascolini-Campbell et al., 2021;Rodell et al., 2015), establishing a highly accurate long-term global ET product with finer spatial resolution is essential for understanding ET variability. ...
... The extremum solution of the Monin-Obukhov similarity theory (MOST) formulates the thermal inertia parameters in dissipation as an analytical function of turbulent sensible heat flux without using the surface-to-air temperature gradient (Wang and Bras, 2009). Unlike the traditional physical methods, which calculate ET merely using physical laws and processes, the MEP method predicts ET from the perspective of "What is the best prediction of energy partitioning of surface radiation based on the available information?" (Huang et al., 2017). Unlike the P-M method, which requires six input variables (net radiation, ground heat flux, air temperature, relative humidity, wind speed, and crop coefficients) and surface resistance parameters, the MEP model is an input parsimonious method that requires only three input variables (net radiation, surface temperature, and specific humidity) and two simple parameters (thermal inertia and the parameter z represents the reference height) with robust values. ...
... The MEP estimated H (33.7 W m − 2 ) during 2001-2010 was similar to that of Huang et al. (2017) within the same period (33 W m − 2 ), who concluded an interval ranging from 27 to 51 W m − 2 with eight different products. For a longer temporal coverage, the MEP H (31.7 W m − 2 ) in this study during 1979-2008 was slightly lower than the estimate of 33.5 W m − 2 by MERRA during the same period , reflecting that the MEP H estimate was consistent with previous studies. ...
An accurate estimation of evapotranspiration (ET) is vital for understanding the global hydrological cycle. However, large uncertainties in the present global ET products originate from the distinct model structures, assumptions, and inputs. The maximum entropy production (MEP) model provides a novel method for modeling ET based on parsimonious inputs and energy conservation. In this study, an R package for MEP (RMEP) was presented to facilitate MEP model implementation. Based on RMEP, a global ET analysis was conducted using inputs from the Global Land Data Assimilation System (GLDAS) and Global Land Surface Satellite (GLASS) products during 1978–2018, and the Mann-Kendall and Theil–Sen’s methods were employed to detect the ET trends. The MEP-estimated average annual global land ET was 517 mm yr⁻¹ during 1978–2018, and showed a close agreement with eddy-covariance (EC) measurements from 475 flux sites, with a correlation coefficient of 0.74 and root-mean-square error of 26.99 mm mon⁻¹. The overall performance of MEP was evaluated across various land covers, and a higher ET accuracy was revealed for forestlands, wetlands, and cropland land covers. The MEP-derived ET trend corresponded well with the EC-observed ET trend, and the results indicated that the global land ET declined continuously during 1999–2018. Overall, the MEP model provided an accurate ET estimate with parsimonious inputs, which outperformed the GLDAS-Noah ET product and can serve as a global analytical method for the hydrological cycle and climate change.
... Remote sensing approaches have also been widely used in global ET estimation (Wang and Dickinson 2012). These approaches mainly contain (1) surface energy balance (SEB) based method, including single-source SEB model and dual-source SEB model, such as the operational Simplified Surface Energy Balance (SSEBop) developed by Senay et al. (2013); (2) water balance (WB) based method, including surface water balance and atmospheric water balance, such as the WB with Model Tree Ensemble (WB-MTE) developed by Zeng et al. (2014); (3) Penman-Monteith (PM) method, such as the Moderate Resolution Imaging Spectroradiometer (MODIS) ET product (PM-MOD) developed by Mu et al. (2011) and the Penman-Monteith-Leuning model (PML and PML-V2) developed by Zhang et al. (2016bZhang et al. ( , 2019b; (4) Priestley-Taylor (PT) method, such as the Global Land Evaporation Amsterdam Model (GLEAM) developed by Martens et al. (2017); (5) Surface temperaturevegetation index space (Ts-VI) method, such as the Surface Energy Balance System (SEBS) developed by Su (2002); (6) maximum entropy production method (MEP) applied to global estimation by Huang et al. (2017); (7) empirical or machine learning (EML) method, such as the Gridded FLUXNET ET with Model Tree Ensemble (GFET-MTE) developed by Jung et al. (2010); and (8) Assimilation method, such as the North American Land Data Assimilation System (NLDAS) developed by Xia et al. (2012). The common disadvantage of SEB, WB, Ts-VI, and MEP is only available for clear-sky. ...
An accurate assessment of terrestrial ecosystem transpiration (T) is important to understand the vegetation-atmosphere feedbacks under climate change. Solar-induced chlorophyll fluorescence (SIF) shows great potential to estimate T because of its mechanical linkage with photosynthesis and stomatal conductance. However, a global and spatially estimation of terrestrial T based on remotely sensed SIF remains unresolved and novel strategies are challenged to entail a precise partition of T from evapotranspiration (ET) across various biomes. Here, with far-red SIF from Sentinel-5 Precursor satellite and ground observations for a total of 30 sites encompassing ten primary plant functional types (PFTs), we extend a SIF-driven semi-mechanism canopy conductance (g c) model for different plant functional types (PFTs), and use the optimized Penman-Monteith model (PM opt) to calculate T and T/ET. We reveal that the relationship between SIF and the product of g c and 0.5 power of vapor pressure deficit (g c × VPD 0.5) is tighter than the relationship between SIF and ecosystem productivity. The SIF-g c × VPD 0.5 linear regressions show improved R 2 and increased magnitude in slopes across PFTs when aggregating daily to 16-day. Our T/ET results show high correlations with the results of the Ball-Berry-Leuning model combined with PM opt at the site scale (R 2 = 0.69), and with the results calculated by leaf area index in a previous study at the PFT scale (0.70). We further determine the global mean T/ET (0.57 ± 0.14), close to the ensemble mean of global averaged T/ET (0.55), using 36 different methods. The global T estimated using the SIF-based approach is compared with two other remote sensing products. Our method provides a valuable tool for T and ET estimation using remote sensing data and is critical to understanding ecohydrological processes under climate change.
... The model partitions net radiation (R n ) into ground (G), sensible (H), and latent heat fluxes (λE, the energy version of E), while requiring relatively few data inputs. The MEP model is steadily gaining attention as an alternative evaporation model after extensive tests over a wide range of climates and ecosystems (Alves et al., 2019;Hajji et al., 2018Hajji et al., , 2021Huang et al., 2017;Nearing et al., 2012;Shanafield et al., 2015;Wang et al., 2014;Xu et al., 2019;Yang et al., 2013) and hydrological applications (Maheu et al., 2019). ...
The maximum entropy production (MEP) approach has been little used to simulate evaporation in forests and its sensitivity to input variables has never beenyet to be systematically evaluated. This study addresses these shortcomings. First, we show that the MEP model performed well in simulating evaporation during the snow-free periods at six sites in temperate and boreal forests (0.68 ≤ NSE ≤ 0.82). Second, we computed a sensitivity coefficient S representing the proportion of change in the input variable transferred to the latent heat flux (λE). Net radiation (Rn) was the most influential variable (S ~ 1) at all sites, indicating that an increase in Rn translates into an equivalent increase in λE. The MEP model avoided the issue of oversensitivity to air temperature (S < 0.5 at peak evaporation) and captured limitations to transpiration associated with the atmospheric evaporative demand. Overall, the MEP model offers a promising tool for climate change studies.
... Besides the LE estimation methods described above, a new approach, the maximum entropy production (MEP) model, has been developed to estimate the surface heat fluxes over bare soil, vegetation, water/snow/ice, and ocean surfaces [20]. The MEP model has been successfully applied to estimate the surface heat fluxes over the alpine steppe terrain of the central TP [21]. However, the MEP model has not yet been applied to estimate LE in the bare ground condition over the western TP. ...
... In addition, the difference in the parameterization of the moisture transfer coefficient, surface roughness lengths, and wind speed may also lead to the conspicuous differences among the six reanalysis LE data [34][35][36].While the parameterization scheme of the MEP model may be able to reflect the surface humidity condition directly. The uncertainties of the estimated LE can be substantially reduced compared with the reanalysis LE [21,30]. Previous studies showed that the increased could lead to an increase of LE [37][38][39]. ...
The Tibetan Plateau (TP) has been experiencing warming and wetting since the 1980s. Under such circumstances, we estimated the summer latent heat flux (LE) using the maximum entropy production model driven by the net radiation, surface temperature, and soil moisture of three reanalysis datasets (ERA5, JRA-55, and MERRA-2) at the Ali site over the western TP during 1980-2018. Compared with the observed LE of the Third Tibetan Plateau Atmospheric Scientific Experiment, the coefficient of determination, root-mean-square error, and mean bias error of the estimated summer LE are 0.57, 9.3 W m−2, and −2.25 W m−2 during 2014-2016, respectively, which are better than those of LE of the reanalysis datasets. The estimated long-term summer LE presents a decreasing (an increasing) trend of −7.4 (1.8) W m−2 decade−1 during 1980-1991 (1992-2018). The LE variation is closely associated with the local soil moisture influenced by precipitation, glacier, and near-surface water conditions at the Ali site. The summer soil moisture also presents a decreasing (an increasing) trend of −0.082 (0.022) decade−1 during 1980-1991 (1992-2018). The normalized difference vegetation index generally shows the consistent trend with LE at the Ali site.
... Hence, it is urgent for us to constraint the global warming under some level to mitigate the change of high runoff seasonality, for instance, the 1.5 • C target set by Paris Agreement. accounts for 60% of the land precipitation (Oki and Kanae, 2006), and over half of the net radiation is used in this process (Huang et al., 2017;Trenberth et al., 2009) at the global scale. The temperature is projected to continue increasing until the end of the 21 century due to human activities, which has an impact on ET. ...
... The only parameter is soil thermal inertia of the surface where the radiative exchange takes place. This model has been validated with field observations for a diverse range of biomes (e.g., bare soil, sparse dry shrubs, grazed pasture, temperate forest, ocean, snow, and ice surface) with satisfactory performance (Huang et al., 2017;Nearing et al., 2012;Shanafield et al., 2015;Wang et al., 2014;Yang et al., 2013). But the MEP model was not yet assessed for highly bio-diverse regions such as the Amazon to obtain ET estimates at regional scales. ...
... To estimate the basin scale ET over the Amazon, net radiation, and surface temperature from the SYN-1deg monthly Clouds and the Earth's Radiant Energy System (CERES) product (Wielicki et al., 1996), as well as the MERRA product, are used to drive the MEP model. The finer 3-hourly SYN-1deg CERES product was previously used by Huang et al. (2017) to produce global ET. Since direct observations of ET do not exist, the MEP-simulated ET at the basin scale was assessed against MODIS ET product and water budget analysis. ...
Outputs from the Global Climate Model are always used to study the impacts of climate change on the hydrological cycle. But the inferences suffer from significant uncertainties, which need to be addressed before any robust conclusion of climate change can be made. Specifically, I applied a Bayesian weighted averaging (BWA) method to investigate the change of peak annual runoff seasonality in the future period based on outputs from GCMs contributing to CMIP5. Because of the circular nature of the time variable, we modified the BWA method before we apply it. A high-quality daily runoff dataset is used in this BWA framework to reduce the bias of model projections. Based on the Bayesian inference, we identified a robust spatial pattern for the change of peak annual runoff timing, which is attributed to the change of snowmelt and soil wetness seasonality due to increased temperature. Evapotranspiration (ET) is a crucial component of the surface water, and energy balance, whose reliability of estimation at any scale remains challenging since observations of ET are sparse in space and time. Therefore, models are required to simulate ET at any scale using in situ or remote sensing observations. This dissertation applied a novel method based on the Maximum Entropy Production (MEP) theory to estimate ET, which requires only net radiation, temperature, and specific humidity as inputs. Using site-level eddy flux data in the Amazon rainforest, the MEP method shows high skill at the hourly, daily, and monthly scales. Consistent performance under different levels of land-surface dryness is revealed, hinting that drought signal is appropriately resolved. The site-level MEP-based estimates outperform the estimates of the MODIS ET product, which is commonly used for large-scale assessments. We then applied MEP to project the change of ET in the future with GCMs’ forcing. MEP based projections are shown to be more robust than the original GCMs’ ET projections, implying the uncertainty of ET in climate models can be reduced by using a parsimony algorithm. This dissertation has also presented a framework for quantifying the uncertainty of urban flooding simulation. A physically rigorous “hyper-resolution” hydraulic and hydrologic model - tRIBS-OFM - is used here to simulate flood propagation, advance numerical representation and understanding of interactions between flooding and the urban environment. Due to the steep computational cost and constraints associated with resolving the 2D Saint-Venant equations at very high resolutions, no effort has been made to address the uncertainty systematically. The uncertainty quantification remains challenging even the model is run in parallel with multiple cores. We approach this problem by training a surrogate model for tRIBS-OFM. Specifically, this surrogate model relies on polynomial chaos expansions, which creates a mapping of flooding outputs from the uncertain inputs. The surrogate model is very computationally inexpensive, therefore, the uncertainty in the inputs/parameters can be propagated to outputs efficiently through the surrogate model. Within this uncertainty quantification framework, we propose a real-time high-fidelity urban flooding forecasting framework, which is able to predict near-instantaneous quantities of interest (e.g., river discharge, inundation field) given a forecasted rainfall with uncertainty warranted. For this study, we reproduce a flooding event in a catchment located in the city of Houston during the 2017 Harvey event and validate the performance of the uncertainty quantification framework with streamflow, high watermarks, and inundation depth data.
