Energy Balance Model Research Articles

Assessment of satellite-based water requirements for a drip-irrigated apple orchard in Mediterranean agroclimatic conditions

Accurate assessment of evapotranspiration (ETa) and crop coefficient (Kc) is crucial for optimizing irrigation practices in water-scarce regions. While satellite-based surface energy balance models offer a promising solution, their application to sparse canopies like apple orchards requires specific validation. This study investigated the spatial and temporal dynamics of ETa and Kc in a drip-irrigated ‘Pink Lady’ apple orchard under Mediterranean conditions over three growing seasons (2012/13, 2013/14, 2014/15). The METRIC model, incorporating calibrated sub-models for leaf area index (LAI), surface roughness (Zom), and soil heat flux (G), was employed to estimate ETa and Kc. These estimates were validated against field-scale Eddy Covariance data. Results indicated that METRIC overpredicted Kc and ETa with errors less than 10 %. These findings highlight the potential of the calibrated METRIC model as a valuable decision-making tool for irrigation management in apple orchards.

Effective Spatial Degrees of Freedom of Natural Temperature Variability as a Function of Frequency

Abstract A fundamental statistic of climate variability is its spatiotemporal correlation function. Its complex structure can be concisely summarized by a frequency-dependent measure of the effective spatial degrees of freedom (ESDOF). Here we present, for the first time, frequency-dependent ESDOF estimates of global natural surface temperature variability from purely instrumental measurements, using the HadCRUT4 dataset (1850–2014). The approach is based on a newly developed method for estimating the frequency-dependent spatial correlation function from gappy data fields. Results reveal a multicomponent structure of the spatial correlation function, including a large-amplitude short-distance component (with weak time scale dependence) and a small-amplitude long-distance component (with increasing relative amplitude toward the longer time scales). Two frequency-dependent ESDOF measures are applied, each responding mainly to either of the two components. Both measures exhibit a significant ESDOF reduction from monthly to multidecadal time scales, implying an increase of the effective spatial scale of natural surface temperature fluctuations. Moreover, it is found that a good approximation to the global number of equally spaced samples needed to estimate the variance of global mean temperature is given, at any frequency, by the greater one of the two ESDOF measures, decreasing from ∼130 at monthly to ∼30 at multidecadal time scales. Finally, the multicomponent structure of the correlation function together with the detected ESDOF scaling properties indicate that the ESDOF reduction toward the longer time scales cannot be explained simply by diffusion acting on stochastically driven anomalies, as it might be suggested from simple stochastic-diffusive energy balance models.

SSEBop Evapotranspiration Estimates Using Synthetically Derived Landsat Data from the Continuous Change Detection and Classification Algorithm

The operational Simplified Surface Energy Balance (SSEBop) model has been utilized to generate gridded evapotranspiration data from Landsat images. These estimates are primarily driven by two sources of information: reference evapotranspiration and Landsat land surface temperature (LST) values. Hence, SSEBop is limited by the availability of Landsat data. Here, in this proof-of-concept paper, we utilize the Continuous Change Detection and Classification (CCDC) algorithm to generate synthetic Landsat data, which are then used as input for SSEBop to generate evapotranspiration estimates for six target areas in the continental United States, representing forests, shrublands, and irrigated agriculture. These synthetic land cover data are then used to generate the LST data required for SSEBop evapotranspiration estimates. The synthetic LST, evaporative fractions, and evapotranspiration data from CCDC closely mirror the phenological cycles in the observed Landsat data. Across the six sites, the median correlation in seasonal LST was 0.79, and the median correlation in seasonal evapotranspiration was 0.8. The median root mean squared error (RMSE) values were 2.82 °C for LST and 0.50 mm/day for actual evapotranspiration. CCDC predictions typically underestimate the average evapotranspiration by less than 1 mm/day. The average performance of the CCDC evaporative fractions, and corresponding evapotranspiration estimates, were much better than the initial LST estimates and, therefore, promising. Future work could include bias correction to improve CCDC’s ability to accurately reproduce synthetic Landsat data during the summer, allowing for more accurate evapotranspiration estimates, and determining the ability of SSEBop to predict regional evapotranspiration at seasonal timescales based on projected land cover change from CCDC.

Effect of gangue on CO2 emission for different decarbonisation pathways

At present, iron and steelmaking industry worldwide is going through the transition of decarbonisation to meet its goal of reaching net zero by 2050. In addition, Australian iron and steelmaking industry is facing its own challenge of processing lower grade ores with increasing gangue content. Two major pathways are direct reduction of iron – electric arc furnace pathway (DRI-EAF) and direct reduction of iron – electric smelter-BOF (DRI-electric smelter-BOF) pathway. In the present work, a mass and energy balance model of basic oxygen furnace (BOF) and electric arc furnace (EAF) have been developed using thermodynamic software. The EAF model showed that with 100 wt-% cold DRI, the specific electric energy requirement varied between 514 and 651 kWh/tls whereas in case of hot DRI, it varied between 399 kWh/tls and 510 kWh/tls. As the gangue content increased from 10.7 wt-% to 19.1 wt-%, yield decreased from 88 wt-% to 75.5 wt-% and slag weight increased from about 200 kg/tls to 630 kg/tls. The BOF model showed that the slag produced in a BOF varied between 63 kg/tls and 73 kg/tls for lower to higher grade ores reflecting different hot metal chemistry (P, Mn) coming from different ores. The results indicated that electric smelter-BOF is more compatible to process lower grade ores than EAF where quantity of slag and loss of yield are very high with increasing gangue content. CO2 emissions from H2DRI-EAF and H2DRI-electric smelter-BOF pathway for different types of ores increased with the increasing gangue content. For H2DRI-EAF pathway, as gangue content increases from 10.7 wt-% to 19.1 wt-%, CO2 emission rises from 0.10 t/tls to 0.19 t/tls as more limestone is needed to remove the gangue which also increases the production of CO2. In case of H2DRI-electric smelter-BOF pathway, CO2 emission increases from 0.12 t/tls to 0.19 t/tls with increasing gangue content. CO2 emissions from both pathways are significantly lower than the current BF-BOF pathway.

Comparative analysis of process selection and carbon emissions assessment of innovative steelmaking routes

Innovative emission reduction technologies combined with optimized processes can effectively reduce the environmental pressure in the iron and steel industry (ISI). Identifying and comparatively analyzing the carbon emissions (CE) from steel productions is conducive to achieving China's ambitious carbon reduction targets. In this paper, we investigated two innovative routes: the shaft furnace-induction furnace-basic oxygen furnace route (SF-IF-BOF) and shaft furnace-electric smelting furnace-basic oxygen furnace route (SF-ESF-BOF), alongside two traditional routes: the blast furnace-BOF route (BF-BOF) and SF-electric arc furnace route (SF-ESF). The analysis was based on a functional unit of 1000 kg of crude steel (CS). By establishing the mass and energy balance models and decision criteria, 12 typical smelting scenarios for these routes were analyzed and compared in terms of materials consumption and CE. The results showed that increasing the proportion of scrap was beneficial for reducing CE. Under the condition of a 50% scrap ratio, the CE of the SF-IF-BOF, SF-ESF-BOF, BF-BOF, and SF-EAF routes were 768, 823, 946, and 870 kg, respectively. The SF-IF-BOF route displayed the most significant advantage of CE reduction. In addition, by using 100% zero-carbon electricity substitution, the SF-EAF route exhibited the greatest CE reduction effect of 41% (from 870 to 510 kg/t). While deploying 100% biomass fuels to replace coal, the CE of the BF-BOF route reduced by 80%. Finally, after introducing biomass fuels and zero-carbon electricity, the CE of the SF-IF-BOF route was minimized to a significantly low 13 kg/t (from 768), nearing zero CE. This research is expected to provide a novel solution for further CE reduction in the future of ISI, contributing to environmental sustainability and carbon reduction goals.

Quantifying Supraglacial Debris‐Related Melt‐Altering Effects on the Djankuat Glacier, Caucasus, Russian Federation

AbstractWe use a spatially distributed and physically based energy and mass balance model to derive the Østrem curve, which expresses the supraglacial debris‐related relative melt alteration versus the debris thickness, for the Djankuat Glacier, Caucasus, Russian Federation. The model is driven by meteorological data from two on‐glacier weather stations and ERA‐5 Land reanalysis data. A direct pixel‐by‐pixel comparison of the melt rates obtained from both a clean ice and debris‐covered ice mass balance model results in the quantification of debris‐related relative melt‐modification ratios, capturing the degree of melt enhancement or suppression as a function of the debris thickness. The main results show that the distinct surface features and different surface temperature/moisture and near‐surface wind regimes that persist over debris‐covered ice significantly alter the pattern of the energy and mass fluxes when compared to clean ice. Consequently, a maximum relative melt enhancement of 1.36 is modeled on the glacier for thin/patchy debris with a thickness of 0.03 m. However, insulating effects suppress sub‐debris melt under debris layers thicker than a critical debris thickness of 0.09 m. Sensitivity experiments show that especially within‐debris properties, such as the thermal conductivity and the vertical debris porosity gradient, highly impact the magnitude of the sub‐debris melt rates. Our results also highlight the scale‐dependency as well as the dynamic nature of the debris thickness‐melt relationship for changing climatic conditions, which may have significant implications for the climate change response of debris‐covered glaciers.

Robust Polar Amplification in Ice-Free Climates Relies on Ocean Heat Transport and Cloud Radiative Effects

Abstract A fundamental divide exists between previous studies that conclude that polar amplification does not occur without sea ice and studies that find that polar amplification is an inherent feature of the atmosphere independent of sea ice. We hypothesize that a representation of climatological ocean heat transport is key for simulating polar amplification in ice-free climates. To investigate this, we run a suite of targeted experiments in the slab ocean aquaplanet configuration of CESM2-CAM6 with different profiles of prescribed ocean heat transport, which are invariant under CO2 quadrupling. In simulations without climatological ocean heat transport, polar amplification does not occur. In contrast, in simulations with climatological ocean heat transport, robust polar amplification occurs in all seasons. What is causing this dependence of polar amplification on ocean heat transport? Energy-balance model theory is incapable of explaining our results and in fact would predict that introducing ocean heat transport leads to less polar amplification. We instead demonstrate that shortwave cloud radiative feedbacks can explain the divergent polar climate responses simulated by CESM2-CAM6. Targeted cloud locking experiments in the zero ocean heat transport simulations are able to reproduce the polar amplification of the climatological ocean heat transport simulations, solely by prescribing high-latitude cloud radiative feedbacks. We conclude that polar amplification in ice-free climates is underpinned by ocean–atmosphere coupling, through a less negative high latitude shortwave cloud radiative feedback that facilitates enhanced polar warming. In addition to reconciling previous disparities, these results have important implications for interpreting past equable climates and climate projections under high-emissions scenarios. Significance Statement Polar amplification is a robust feature of climate change in the modern-day climate. However, previous climate modeling studies fundamentally do not agree on whether polar amplification occurs in ice-free climates. In this study, we find in a state-of-the-art climate model that, if ocean heat transport is neglected, the response to an increase in CO2 is not polar amplified, whereas robust polar amplification occurs if ocean heat transport is included. Using targeted model experiments, we diagnose cloud radiative effects as the driver of this divergent behavior. We conclude that polar amplification is a robust feature of the atmosphere–ocean system. Our results have important implications for interpreting past warm climates and future projections under high-emissions scenarios.

Climate Model Simulations of the Effects of Orbital Parameters on Glacier Equilibrium Line Altitude

AbstractThe effects of obliquity and precession on conditions favorable for Northern Hemisphere glaciation are explored using an energy balance and mass balance model of equilibrium line altitude (ELA), the height on a glacier where accumulation and ablation are in balance annually. Climate forcing for the ELA model is obtained from idealized single‐forcing orbital simulations with two atm‐ocean general circulation models, Geophysical Fluid Dynamics Laboratory (GFDL) CM2.1 and National Center for Atmospheric Research (NCAR) Community Earth System Model version 1.2. Over Scandinavia and Baffin Island, the respective locations in which the Scandinavian and Laurentide ice sheets are thought to have originated, low obliquity and perihelion at the boreal winter solstice are associated with lower ELA values, as would be expected from the orbital theory of the ice ages. Linear reconstructions of ELA variations over the past 800 kyr indicate that precession dominated ELA variations in Scandinavia and Baffin Island in the GFDL model, and in Scandinavia in the NCAR model. Obliquity and precession played equal roles in Baffin Island in the NCAR model. A decomposition of the ELA responses finds that the effects of ablation on ELA are much larger than the effects of precipitation. Overall, the findings of this study point to precession being a more important factor in glacial inception than obliquity, which contrasts with previous findings in which obliquity had a slightly larger effect on positive degree days (PDDs), a simple metric for ablation. This is likely due to differences in seasonality of melt from the ELA model and PDDs.

Estimation of ecosystem water consumption and the suitable scale of cultivated land in the Karamay region and Muzat River basin based on the optimized SEBAL energy balance model and water resource constraint model

Food security is closely related to the development of human society, and the root of food production lies in cultivated land, with water conservancy as its lifeline. This study estimates the ecological water consumption of located in the arid region of Northwest China (the Karamay region and Muzat River basin) from 1990 to 2020 based on the optimized Land Surface Energy Balance Algorithm. The verification accuracy of SEBAL energy balance model is greatly improved after optimization. It was showed an increasing trend in the Karamay region and Muzat River basin, increasing at the rates of 2.84 mm/year and 2.86 mm/year respectively. The suitability of cultivated land was evaluated by combining four periods of 30 m spatial resolution land use/land cover data from 1990, 2000, 2010, and 2020, as well as the Hydrological Statistical Yearbook and Xinjiang Statistical Yearbook. Through the analysis of spatial optimization for cultivated land, it can be inferred that the primary limiting factors affecting cultivated land suitability in the Karamay region are irrigation guarantee rate (54.03%) and soil salinity (11.98%). Muzat River region are irrigation guarantee rate (32.19%) and soil salinity (18.62%). By comparing the scenarios of setting ecological priority and cultivated land priority, it is concluded that under the conditions of water resource constraints and 50%, 75% and 90% design irrigation assurance rates, Karamay still has cultivated land expansion potential, which can be used as the main preparatory reclamation area. In addition to the traditional agriculture irrigation area, the Muzat River basin still has development potential under the condition of ecological priority and no more than 75% irrigation design assurance rate. The study on the cultivated land suitability under the condition of water resource constraints can provide new ideas for food security.

Gravimetric and Thermal-Imaging Characterization of Water-Free Reflux Condensers for Laboratory Applications.

Water-free reflux condensers, which use convective cooling from the surrounding air to condense vapors, avoid the need for cooling water, which is more sustainable than water-cooled condensers, and eliminates the risk of flooding, but these devices are newer and less familiar to many chemists, who may never have used them before. To facilitate the shift to water-free condensers, several types of water-free condensers (simple glass tube, Vigreux column, Condensyn, Findenser, and air-cooled Dimroth) were characterized using three different solvents (ethyl acetate, acetone, and tetrahydrofuran) under both gentle and vigorous refluxing conditions to compare their relative performance and determine the condensing capacity/failure point. In addition to experimentally quantifying the performance of each condenser both gravimetrically and via infrared thermal imaging, energy-balance models were developed to gain insight into which factors were most important in driving their performance. Several of the water-free condensers, including the Findenser, Condensyn, and air-cooled Dimroth condenser, were shown to provide suitable performance for most refluxing operations.

Dynamics of large-scale solar PV adoption feedback effects: A technical, economic, and environmental assessment

Large residential solar photovoltaic (PV) penetration has a compound effect on the grid load reductions, PV hosts’ economic savings, and the achievable environmental benefits, which is not fully understood. This study combines process-based energy balance modeling, life cycle assessment, regression analysis, and stochastic demand simulations to assess the technical, economic, and environmental tradeoffs under increased residential solar PV adoption, using Boston, MA as a testbed. It was found that increased PV adoption may lead to a steeper ramp-up in the grid during winter months, but a flattened peak load curve during summer months, emphasizing the need for seasonal time-of-use rates and energy storage. It also reduces electricity wholesale prices, lowering PV hosts' economic benefits by about $15 million under 100 % adoption. The largest buildings present the highest load reduction (top 5.5 %) and environmental benefits (top 16.6 %), but they are the least cost efficient (top 14.5 %), requiring tradeoff balance.

Developing a New ANN Model to Estimate Daily Actual Evapotranspiration Using Limited Climatic Data and Remote Sensing Techniques for Sustainable Water Management

Accurate estimations of actual evapotranspiration (ETa) are essential to various environmental issues. Artificial intelligence-based models are a promising alternative to the most common direct ETa estimation techniques and indirect methods by remote sensing (RS)-based surface energy balance models. Artificial Neural Networks (ANNs) are proven to be suitable for predicting reference evapotranspiration (ETo) and ETa based on RS data. This study aims to develop a methodology based on ANNs for estimating daily ETa values using NDVI and land surface temperature, coupled with limited site-specific climatic variables in a large irrigation catchment. The ANN model has been applied to the two different scenarios. Data from only the 38 days of satellite overpass dates was selected in Scenario I, while in Scenario II all datasets, i.e., the 769-day data were used. An irrigation scheme, located in the Mediterranean region of Turkiye, was selected, and a total of 38 Landsat images and local climatic data collected in 2021 and 2022 were used in the ANN model. The ETa results by the ANN model for Scenarios I and II showed that the R2 values for training (0.79 and 0.86), testing (0.75 and 0.81), and the entire dataset (0.76 and 0.84) were all remarkably high. Moreover, the results of the new ANN model in two scenarios showed an acceptable agreement with ETa-METRIC values. The proposed ANN model demonstrated the potential for obtaining daily ETa using limited climatic data and RS imagery. As a result, the suggested ANN model for daily ETa computation offers a trustworthy way to determine crop water usage in real time for sustainable water management in agriculture. It may also be used to assess how crop evapotranspiration in drought-prone areas will be affected by climate change in the 21st century.

Quantifying the compound hazard of freezing rain and wind gusts across CONUS

The co-occurrence of freezing rain, ice accumulation and wind gusts (FZG) poses a significant hazard to infrastructure and transportation. However, quantification of the frequency and intensity of FZG is challenged by the lack of direct icing measurements. In this work, we evaluate and then apply an energy balance model to high-frequency data collected during 2005–2022 to derive hourly ice accumulation at 883 stations across the contiguous USA. These estimates are combined with wind gust observations to compute time series of hourly FZG hazard magnitude using the Sperry–Piltz Ice Accumulation (SPIA) index. Results are evaluated using Storm Reports of damage and economic disruption. The hourly SPIA estimates are also used to (i) derive a geospatial atlas of the hazard including the 50 yr return period event intensities for each US state derived using superstations, and (ii) describe storylines of significant events in terms of meteorological drivers and socioeconomic impacts. The highest values of SPIA during the 18 yr study period occur in a region extending from the Southern Great Plains over the Midwest into the densely populated Northeast. States in these regions also have high 50 yr return period maximum radial ice accumulation of 3–5 cm and co-occurring wind gusts >30 ms−1. These values are comparable to past estimates for the 500 yr event which may imply this hazard has been previously underestimated. This atlas can be used to inform optimal FZG hazard mitigation strategies for each state/region.

Sea-surface temperature pattern effects have slowed global warming and biased warming-based constraints on climate sensitivity

The observed rate of global warming since the 1970s has been proposed as a strong constraint on equilibrium climate sensitivity (ECS) and transient climate response (TCR)-key metrics of the global climate response to greenhouse-gas forcing. Using CMIP5/6 models, we show that the inter-model relationship between warming and these climate sensitivity metrics (the basis for the constraint) arises from a similarity in transient and equilibrium warming patterns within the models, producing an effective climate sensitivity (EffCS) governing recent warming that is comparable to the value of ECS governing long-term warming under CO[Formula: see text] forcing. However, CMIP5/6 historical simulations do not reproduce observed warming patterns. When driven by observed patterns, even high ECS models produce low EffCS values consistent with the observed global warming rate. The inability of CMIP5/6 models to reproduce observed warming patterns thus results in a bias in the modeled relationship between recent global warming and climate sensitivity. Correcting for this bias means that observed warming is consistent with wide ranges of ECS and TCR extending to higher values than previously recognized. These findings are corroborated by energy balance model simulations and coupled model (CESM1-CAM5) simulations that better replicate observed patterns via tropospheric wind nudging or Antarctic meltwater fluxes. Because CMIP5/6 models fail to simulate observed warming patterns, proposed warming-based constraints on ECS, TCR, and projected global warming are biased low. The results reinforce recent findings that the unique pattern of observed warming has slowed global-mean warming over recent decades and that how the pattern will evolve in the future represents a major source of uncertainty in climate projections.

Variational techniques for a one-dimensional energy balance model

Abstract. A one-dimensional climate energy balance model (1D EBM) is a simplified climate model for the zonally averaged global temperature profile, based on the Earth's energy budget. We examine a class of 1D EBMs which emerges as the parabolic equation corresponding to the Euler–Lagrange equations of an associated variational problem, covering spatially inhomogeneous models such as with latitude-dependent albedo. Sufficient conditions are provided for the existence of at least three steady-state solutions in the form of two local minima and one saddle, that is, of coexisting “cold”, “warm” and unstable “intermediate” climates. We also give an interpretation of minimizers as “typical” or “likely” solutions of time-dependent and stochastic 1D EBMs. We then examine connections between the value function, which represents the minimum value (across all temperature profiles) of the objective functional, regarded as a function of greenhouse gas concentration, and the global mean temperature (also as a function of greenhouse gas concentration, i.e. the bifurcation diagram). Specifically, the global mean temperature varies continuously as long as there is a unique minimizing temperature profile, but coexisting minimizers must have different global mean temperatures. Furthermore, global mean temperature is non-decreasing with respect to greenhouse gas concentration, and its jumps must necessarily be upward. Applicability of our findings to more general spatially heterogeneous reaction–diffusion models is also discussed, as are physical interpretations of our results.

Influence of shunt currents in industrial-scale alkaline water electrolyzer plants

The aim of this paper is to analyze through simulation how the energy efficiency of a single electrolysis stack at various loads is affected by shunt currents and to determine the energy-optimal load distribution between lines in a multiline electrolysis system under various magnitudes of shunt current losses. A dynamic energy and mass balance model of an industrial 3MW, 16bar alkaline water electrolyzer (AWE) process was developed using MATLAB. The optimization goal is to determine the power supply for each AWE line so that it can meet any hydrogen demand while minimizing the global specific energy consumption (SEC). The Particle Swarm Optimization (PSO) algorithm is used to minimize the objective function. According to the results of the single stack investigation, shunt current reduction could significantly improve the energy efficiency of partial-load operation. In addition, the optimization study revealed that whenever two or more lines are required to run in order to satisfy the hydrogen demand, the global SEC is minimized when the lines operate at equal loads.

Energy absorption and dissipation characteristic of FG honeycomb reinforced laminate embedded with viscoelastic material in hygrothermal conditions under low-velocity impact

A novelty FG honeycomb-reinforced laminate (FGHRL) with viscoelastic material is constructed for an industrial exoskeleton. The study examines how FGHRL dissipates energy under hygrothermal conditions. Low-velocity impacts on the exoskeleton’s load-bearing structure are simulated using a spherical object. Parameters for the FGHRL, made of a two-phase material, are estimated using the Halpin-Tsai model and macroscopically uniform theory. In-plane deformations are determined using Reddy’s HSDT, while the impact response is evaluated with Newmark-β and Wilson-θ methods. Energy dissipation properties are calculated using the energy balance model, validated through CUF-based FEM and LS-DYNA explicit solution, and factors influencing energy dissipation are investigated.

Evaluation of surface urban energy and water balance scheme (SUEWS) using scaled 2D model experiments under various seasons and sky conditions

Urban energy balance models are essential for better understanding of urban climate processes and mitigating urban heat island intensity. In this study, the Surface Urban Energy and Water Balance Scheme (SUEWS) is evaluated using scaled outdoor experiments of idealized city models consisting of street canyons (aspect ratio H/W = 2, H = 0.5) and hollow concrete building models, under various seasonal and sky conditions in a humid subtropical climate in 2020, using three evaluation approaches. The results indicate that the model effectively simulates net all-wave radiation (Q∗), with the coefficient of determination (R2) exceeding 0.970. Storage heat flux (ΔQS) derived from the Objective Hysteresis Model (OHM) is compared to those obtained from the residual term method (RTM) and element surface temperature method (ESTM), revealing the RTM tend to overestimate ΔQS compared to the observation-based ESTM. Compared to using default OHM coefficients, applying fitted OHM coefficients obtained under seasons and sky conditions improves the simulations of ΔQS and sensible heat flux (QH), reducing statistical errors by approximately 50% for ΔQS and increasing R2 in rainy summer from 0.353 to 0.793 for QH, respectively. Additionally, the improved available energy simulation suggests the importance of accurately partitioning between QH and latent heat flux (QE) for the future development of SUEWS.

Spherical geometry convection in a fluid with an Arrhenius thermal viscosity dependence: The impact of core size and surface temperature on the scaling of stagnant-lid thickness and internal temperature

The rock and rock-ice mixtures of the core-enveloping spherical shells comprising terrestrial body interiors have thermally determined viscosities well described by an Arrhenius dependence. Accordingly, the implied viscosity contrasts determined from the activation energies (E) characterizing such bodies can reach values exceeding 1040, for a temperature range that spans the conditions found from the lower mantle to the surface. In this study, we first explore the impact of implementing a cut-off to limit viscosity magnitude in cold regions. Using a spherical annulus geometry, we investigate the influence of core radius, surface temperature, and convective vigour on stagnant lid formation resulting from the extreme thermally induced viscosity contrasts. We demonstrate that the cut-off viscosity must be increased with decreasing curvature factor, f (=rin/rout, where rin and rout are the inner and outer radii of the annulus, respectively), if the solutions are to be not only computationally manageable but physically valid. We find that for statistically-steady systems, the mean temperature decreases with core size, and that a viscosity contrast of at least 107 is required for stagnant lid formation as f decreases below 0.5. Inverting the results from over 80 calculations featuring stagnant lids (from a total of approximately 180 calculations), we apply an energy balance model for heat flow across the thermal boundary layers and find that the non-dimensionalized temperature in the Approximately Isothermal Layer (AIL) in the convecting region under a stagnant lid is well predicted by TAIL′=12−2Tout′+γ+γ2+4γ1+Tout′ where γ is a function of E and f, and Tout′ is the non-dimensionalized surface temperature. Moreover, the normalized (i.e., non-dimensional) thickness of the stagnant lid, L′, can be obtained from a measurement of the non-dimensional surface heat flux once TAIL′ is determined. Stagnant-lid thicknesses increase from 10 to 30% of the shell thickness as f is decreased, and thick lids can overlie vigorously convecting underlying layers in small core bodies, potentially delaying secular cooling and suggesting that small objects with small cores may have developed thick elastic outer shells early in the solar system's history while maintaining vigorously convecting interiors. However, we also find that for the small number of 3-D calculations that we examined, parametrizations based on 2-D calculations overestimate the temperature of the convecting layer and the thickness of the conductive lid when f is small (less than 0.4).

Evaluation of a single-layer urban energy balance model using measured energy fluxes by scaled outdoor experiments in humid subtropical climate

Urban energy balance models can simulate the localized climate and fluxes in urban areas. They are often evaluated using real urban site observations. However, uncertainties in anthropogenic emission, geometry and materials can hinder interpretation. These uncertainties can be eliminated by scaled outdoor models. We assess the performance of a single-layer urban canopy model (SLUCM) offline in predicting surface energy balance (SEB) fluxes within a street canyon-like urban configuration using field measurements from a scaled outdoor setup in Guangzhou, China. We utilize observations of SEB fluxes and surface temperature from a homogenous scaled urban site characterized by street canyons. The scaled observations in June–December 2020 in a dense urban environment with a height-to-width ratio (H/W) of 2 are employed to assess seasonal variations in model performance. Additionally, the December data from two distinct urban scenarios (H/W = 2(2020) and 0.5(2019)) are utilized to compare model performance in deep and shallow street canyon settings. Results show that QS(R2 = ∼0.47, RMSE = ∼46.0) is the most challenging to predict, followed by QH (R2 = ∼0.92, RMSE = ∼65.5), Q*(R2 = ∼0.99, RMSE = ∼39.5), L↑(R2 = ∼0.95, RMSE = ∼33.7), and K↑(R2 = ∼0.99, RMSE = ∼6.2). SLUCM faces difficulties simulating L↑ particularly during nighttime and cloudy conditions. It also tends to underestimate daytime net radiation (Q*), especially during hot, humid months. Moreover, H/W ratio slightly affects SLUCM's performance in simulating SEB fluxes under dry cool conditions denser urban settings (H/W = 2) show better model performance in K↑, QH, and QS but worse performance in L↑ and Q*.