Estimation Of Surface Heat Flux Research Articles

Estimation of Surface Temperature and Heat Flux over a Hollow Cylinder and Slab using an Inverse Heat Conduction Approach

A non-iterative approximation of the inverse heat conduction problem has been developed through energy balance between the control volumes. The heat flow domain along the surface normal was divided into three control volumes and studied in three cases, specifically on a heated hollow metallic cylinder cooled in crossflow of air, a heating flat plate in still air, and a heated flat plate when cooled in still air with random air blows. The time derivatives of temperature and heat flux estimates at the surface appearing in derived equations were evaluated by approximate expressions. Both estimates were obtained from the derived equations by simultaneous measurement of temperature-time histories at two locations: one at the inner surface and the other anywhere within the control volume along the surface normal. The deviation was checked by real-time simultaneous measurement of temperature-time history at the outer surface along the normal surface. Comparison between the estimated surface temperature-time history using the derived equations and the real-time measurement showed deviations within 0.5 % for the cylinder, within 0.03 % for the plate in still air and within 0.5 % when air blows were given. Heat fluxes estimated using these time histories were correspondingly arrived at consistent and close approximations for all cases. Estimates from the derived equations were compared with reported equations from the literature, and a wind tunnel experiment for the validation of circumferential distribution of heat transfer was conducted, for which they also showed reasonably good agreements.

Ground Heat Flux Reconstruction Using Bayesian Uncertainty Quantification Machinery and Surrogate Modeling

AbstractGround heat flux (G0) is a key component of the land‐surface energy balance of high‐latitude regions. Despite its crucial role in controlling permafrost degradation due to global warming, G0 is sparsely measured and not well represented in the outputs of global scale model simulation. In this study, an analytical heat transfer model is tested to reconstruct G0 across seasons using soil temperature series from field measurements, Global Climate Model, and climate reanalysis outputs. The probability density functions of ground heat flux and of model parameters are inferred using available G0 data (measured or modeled) for snow‐free period as a reference. When observed G0 is not available, a numerical model is applied using estimates of surface heat flux (dependent on parameters) as the top boundary condition. These estimates (and thus the corresponding parameters) are verified by comparing the distributions of simulated and measured soil temperature at several depths. Aided by state‐of‐the‐art uncertainty quantification methods, the developed G0 reconstruction approach provides novel means for assessing the probabilistic structure of the ground heat flux for regional permafrost change studies.

Surface heat flux estimation with embedded thermocouples and Fiber Bragg Grating sensor in ITER-like plasma facing components

The main objective of WEST is to study the behavior of the ITER-like divertor monobloc components, test their resistance and ageing under ITER relevant heat loads. For the upcoming phase 2 of WEST, the lower divertor is now fully equipped with the ITER-like actively cooled bulk tungsten Plasma Facing Units (PFU), designed to withstand 10MW/m² in steady state. This divertor is also equipped with an enlarged set of ThermoCouples (TCs x 16) and Fiber Bragg Gratings (FBGs) probes (x5) with 14 measurement spots each to evaluate the heat loading during the experiments. This paper presents the new TC and FBG diagnostics as well as the associated inverse method used to estimate the surface heat flux from the embedded temperature measurements in the divertor. The performance of each diagnostic will be evaluated with synthetic measurements generated with realistic heat flux intensity and distribution. The results of a parametrical analysis shows that each diagnostic is able to estimate the spatial distribution of the expected heat fluxes in WEST.

Seasonal cycle of sea surface temperature in the tropical Angolan Upwelling System

Abstract. The Angolan shelf system represents a highly productive ecosystem. Throughout the year the sea surface is cooler near the coast than further offshore. The lowest sea surface temperature (SST), strongest cross-shore temperature gradient, and maximum productivity occur in austral winter when seasonally prevailing upwelling-favourable winds are weakest. Here, we investigate the seasonal mixed layer heat budget to identify atmospheric and oceanic causes for heat content variability. By using different satellite and in situ data, we derive monthly estimates of surface heat fluxes, mean horizontal advection, and local heat content change. We calculate the heat budgets for the near-coastal and offshore regions separately to explore processes that lead to the observed SST differences. The results show that the net surface heat flux warms the coastal ocean stronger than further offshore, thus acting to damp spatial SST differences. Mean horizontal heat advection is dominated by meridional advection of warm water along the Angolan coast. However, its contribution to the heat budget is small. Ocean turbulence data suggest that the heat flux, due to turbulent mixing across the base of the mixed layer, is an important cooling term. This turbulent cooling, being strongest in shallow shelf regions, is capable of explaining the observed negative cross-shore temperature gradient. The residuum of the mixed layer heat budget and uncertainties of budget terms are discussed.

Exploring CYGNSS mission for surface heat flux estimates and analysis over tropical oceans

The Cyclone Global Navigation Satellite System (CYGNSS) mission can measure sea surface wind over tropical oceans with unprecedented temporal resolution and spatial coverage, so as to estimate surface latent and sensible heat fluxes (LHF and SHF). In this paper, the satellite-derived LHF/SHF estimates from CYGNSS are quantitatively evaluated and analyzed by those from the Global Tropical Moored Buoy. Comparisons of the LHF and SHF estimates demonstrate the good performance and reliability of CYGNSS heat flux products during the period of 2017–2022, including CYGNSS Level 2 Ocean Surface Heat Flux Climate Data Record (CDR) Version 1.0 and Version 1.1. Different latent heat characteristics in the tropical oceans are evaluated separately based on each buoy array, suggesting better agreement in the Atlantic for LHF/SHF products. Based on the Coupled Ocean-Atmosphere Response Experiment 3.5 algorithm, the impact of wind speed on the LHF/SHF estimates is analyzed by using the the Science Data Record V3.1 and NOAA V1.2 science wind products. The results show that the performance of satellite-derived wind speed directly affects the accuracy of LHF products, with an improvement of 17% in root-mean-square error over that of LHF CDR V1.0. Especially, in the Indian Ocean, accuracy can be improved by 26.8%. This paper demonstrates that the heat flux estimates along the orbit of the CYGNSS are an important supplement to in situ observational data and will benefit the study of global climate change.

Using MARSIS signal attenuation to assess the presence of South Polar Layered Deposit subglacial brines

Knowledge of the physical and thermal properties of the South Polar Layer Deposits (SPLD) is key to constrain the source of bright basal reflections at Ultimi Scopuli detected by the MARSIS (Mars Advanced Radar for Subsurface and Ionosphere Sounding) radar sounder. Here we present a detailed analysis of attenuation, based on data acquired by MARSIS at 3, 4, and 5 MHz. We show that attenuation is frequency dependent, and that its behavior is consistent throughout the entire region. This suggests that the SPLD are compositionally homogeneous at Ultimi Scopuli, and our results are consistent with dust contents of 5 to 12%. Using these values as input, and plausible estimates of surface temperature and heat flux, we inferred basal temperatures around 200 K: these are consistent with perchlorate brines within liquid vein networks as the source of the reflections. Furthermore, extrapolation of the attenuation to higher frequencies explains why SHARAD (Shallow Radar) has thus far not detected basal reflections within the SPLD at Ultimi Scopuli.

Estimation and analysis of surface heat flux during gas quenching through IHC method

Gas Quenching is a process of quenching steel components with a gas quenchant. This process, due to its several advantages is being extensively used now a days. This work studies the effect of the variation of gas jet pressure and the standoff distance (SOD), which is the distance between the quench probe and the tip of the nozzle on the quenching heat transfer during gas quenching. A gas quenching chamber of octagonal cross-section of side 100 mm was used for quenching experiments, in which an array of nozzles was fixed. The cylindrical workpieces of 20 mm diameter and 50 mm length were machined from stainless steel 304L and K-type thermocouples were fixed at the selected locations inside the workpiece to read the temperature during quenching. Compressed air as the quenchant at different pressures of 4 bar, 6 bar and 8 bar and different SOD of 9 cm, 10 cm and 11 cm were used to study the effect of these two parameters on the quenching heat transfer rates. Surface heat flux computations were made using Inverse Heat Conduction (IHC) method using the measured time–temperature data as input. It was found out that as the pressure increased, the cooling rate and the peak surface heat flux increased and as the nozzle standoff distance was increased, the cooling rate and the peak surface heat flux dropped. The effect of increasing the nozzle SOD by 1 cm was more than the reduction of gas jet pressure by 2 bar.

A quick surface heat flux estimation method for typical structures of high-speed aircrafts

Surface heat flux estimation of high-speed aircrafts is an inverse problem and high system ill-posedness usually leading to instability and low accuracy. In this study, an efficient method is proposed to solve it stably. The heat flux identification equation is established based on the superposition principle. Tikhonov regularization method with the parameter determined by generalized cross validation is applied to reduce the sensitivity to measurement error. A calibration method is presented to correct the pulse sensitivity coefficient matrix so that the estimation method can be used for complex three-dimensional structures. Numerical studies demonstrate the efficiency and accuracy.

Inaccuracies in the inverse heat conduction problem solution and their effect on the estimation of heat fluxes during quenching

Solving the Inverse Heat Conduction Problem (IHCP) is a common approach to estimate the surface heat fluxes involved in transient, quenching experiments. The inverse problem presents several challenges, such as accounting for the non-uniqueness of its solution, for the effects of noise, or for other practical issues affecting the experimental input data, such as the thermal contact of the internal temperature sensors. In this paper, possible sources of inaccuracy in the IHCP solution and their effect on the estimated surface heat flux in experiments on quenching by water jet impingement are systematically investigated. A “virtual experiment” approach is followed to analyze the effect of a noise cancelling technique, the ambiguity in initial conditions and the quality of the thermocouple contact on the accuracy of the heat flux estimations. The results show that the invalid assumption of perfect thermal contact between thermocouple and test plate leads to overestimation of surface temperature in the initial stages of quenching. Based on these results, two measures are proposed to avoid misinterpretation of quenching heat flux estimations when solving the IHCP.

Influences of changing sea ice and snow thicknesses on simulated Arctic winter heat fluxes

Abstract. In the high-latitude Arctic, wintertime sea ice and snow insulate the relatively warmer ocean from the colder atmosphere. While the climate warms, wintertime Arctic surface heat fluxes remain dominated by the insulating effects of snow and sea ice covering the ocean until the sea ice thins enough or sea ice concentrations decrease enough to allow for direct ocean–atmosphere heat fluxes. The Community Earth System Model version 1 Large Ensemble (CESM1-LE) simulates increases in wintertime conductive heat fluxes in the ice-covered Arctic Ocean by ∼ 7–11 W m−2 by the mid-21st century, thereby driving an increased warming of the atmosphere. These increased fluxes are due to both thinning sea ice and decreasing snow on sea ice. The simulations analyzed here use a sub-grid-scale ice thickness distribution. Surface heat flux estimates calculated using grid-cell mean values of sea ice thicknesses underestimate mean heat fluxes by ∼16 %–35 % and overestimate changes in conductive heat fluxes by up to ∼36 % in the wintertime Arctic basin even when sea ice concentrations remain above 95 %. These results highlight how wintertime conductive heat fluxes will increase in a warming world even during times when sea ice concentrations remain high and that snow and the distribution of snow significantly impact large-scale calculations of wintertime surface heat budgets in the Arctic.

Application of the profile method for the estimation of urban sensible heat flux using roadside weather monitoring data and satellite imagery

This study explores the possibility of estimation of the sensible surface heat flux using satellite-derived surface temperature and road pavement temperature together with in-situ wind and air temperature measurements by the profile method. A 10-year series of data from the roadside weather observation network was used. This dataset contained wind (measured at 5.8–9.5 m above ground) and air temperature (measured at 2.6–4.8 m) together with road surface temperature. Another dataset consisted of 254 simultaneous MODIS observations. A high correlation (0.94) of the surface temperature measured by both methods was noted despite coarse pixel size. We considered satellite-derived surface temperature to determine the sensible heat flux by the profile method; these results were compared to the values obtained using road temperature measured by pavement-mounted sensors. While the overall correlation is relatively strong (0.70) and considerable systematic differences exist, the values of heat flux calculated at different locations show a high spatial coherence - either when using the in situ pavement temperature (correlation ranging from 0.84 to 0.94 for daytime and 0.63–0.84 for nighttime) or the satellite-derived temperature (correlation coefficient 0.72). In most cases, differences between the two flux estimates can be linked to local factors such as the land use structure.

Mantle convection and possible mantle plumes beneath Antarctica – insights from geodynamic models and implications for topography

Abstract This chapter describes large-scale mantle flow structures beneath Antarctica as derived from global seismic tomography models of the present-day state. In combination with plate reconstructions, the time-dependent pattern of palaeosubduction can be simulated and is shown from the rarely seen Antarctic perspective. Furthermore, a dynamic topography model demonstrates which kind and scales of surface manifestations can be expected as a direct and observable result of mantle convection. The last section of this chapter features an overview of the classical concept of deep-mantle plumes from a geodynamic point of view and how recent insights, mostly from seismic tomography, have changed the understanding of plume structures and dynamics over past decades. The long-standing and controversial hypothesis of a mantle plume beneath West Antarctica is summarized and addressed with geodynamic models, which estimate the excess heat flow of a potential plume at the bedrock surface. However, the predicted heat flow is small, while differences in surface heat-flux estimates are large; therefore, the results are not conclusive with regard to the existence of a West Antarctic mantle plume. Finally, it is shown that global mantle flow would cause the tilting of whole-mantle plume conduits beneath West Antarctica such that their base is predicted to be displaced about 20° northward relative to the surface position, closer to the southern margin of the Pacific Large Low-Shear Velocity Province.

Implementation of total variation regularization-based approaches in the solution of linear inverse heat conduction problems concerning the estimation of surface heat fluxes

In this work, we propose the extension of total variation regularization strategies in principle formulated to be implemented in image processing and signal analysis research fields, to the solution of one-dimensional linear inverse heat conduction problems concerning the estimation of surface heat fluxes. Three solution procedures are considered in the current study, and these include the lagged diffusivity fixed point iteration, the iteratively reweighted least-squares, and the split Bregman iteration methods. The performance of such procedures is tested using four cases, and the regularization parameter is selected via the L-curve criterion. The results are compared to the reconstruction obtained via a classical Tikhonov-like strategy. The main outcome is that the staircase effect dominated all the reconstructions. Despite it deteriorated the quality of the solutions in some specific cases, it did not prevent the appropriate fulfillment of the reconstruction task. The results achieved in this communication have been useful to demonstrate the suitability and reliability of extending total variation approaches to the solution of linear inverse heat conduction problems concerning the estimation of surface heat fluxes, as an appropriate and novel alternative to standard procedures.

Evaporation time and vapor generation limit of a droplet on a hot surface

The characteristic of heat flux was analyzed during the heat conduction regime after a water droplet deposited onto a hot surface at the temperature bringing the minimum evaporation time. A two-dimensional solution for estimating surface heat flux was newly derived, in place of the existing one-dimensional one, when a finite size of the liquid droplet suddenly contacted a high-temperature surface of a semi-infinite thick solid. The estimated surface heat fluxes at the minimum evaporation time point for several materials with different thermal properties were consistent within an uncertainty of 20%, although the corresponding surface temperatures for different materials were much different. In addition, a simple equation was developed to estimate the surface heat flux at the minimum evaporation time point, which was validated for the liquid subcooling of 70-80 K and the water droplet radius of 1.0-1.5 mm. Visual observation revealed that the characteristic of the droplet behavior on the hot surface was much different whether the homogeneous bubble nucleation condition was satisfied or not.

Real-time estimation and control of divertor surface heat flux on the DIII-D tokamak

Future tokamaks will require robust technologies for the mitigation of heat exhaust onto the plasma-facing components. As a first step towards this development, a system has been developed at DIII-D that estimates and controls in real-time the heat flux to the PFCs. Real-time estimation of the peak power flux from this model-based approach is validated with off-line infra-red measurements for various DIII-D plasma discharges. A nonlinear free-boundary simulation code (GSevolve) is used for simulating the closed loop response and for the off-line determination of the control parameters. The implementation and first experimental results of the application during the DIII-D plasma campaign are reported.

Evapotranspiration partitioning assessment using a machine-learning-based leaf area index and the two-source energy balance model with sUAV information.

Accurate quantification of the partitioning of evapotranspiration (ET) into transpiration and evaporation fluxes is necessary to understanding ecosystem interactions among carbon, water, and energy flux components. ET partitioning can also support the description of atmosphere and land interactions and provide unique insights into vegetation water status. Previous studies have identified leaf area index (LAI) estimation as a key descriptor of biomass conditions needed for the estimation of transpiration and evaporation. LAI estimation in clumped vegetation systems, such as vineyards and orchards, has proven challenging and is strongly related to crop phenological status and canopy management. In this study, a feature extraction model based on previous research was built to generate a total of 202 preliminary variables at a 3.6-by-3.6-meter-grid scale based on submeter-resolution information from a small Unmanned Aerial Vehicle (sUAV) in four commercial vineyards across California. Using these variables, a machine learning model called eXtreme Gradient Boosting (XGBoost) was successfully built for LAI estimation. The XGBoost built-in function requires only six variables relating to vegetation indices and temperature to produce high-accuracy LAI estimation for the vineyard. Using the six-variable XGBoost-based LAI map, two versions of the Two-Source Energy Balance (TSEB) model, TSEB-PT and TSEB-2T were used for energy balance and ET partitioning. Comparing these results with the Eddy-Covariance (EC) tower data, showed that TSEB-PT outperforms TSEB-2T on the estimation of sensible heat flux (within 13% relative error) and surface heat flux (within 34% relative error), while TSEB-2T outperforms TSEB-PT on the estimation of net radiation (within 14% relative error) and latent heat flux (within 2% relative error). For the mature vineyard (north block), TSEB-2T performs better than TSEB-PT in partitioning the canopy latent heat flux with 6.8% relative error and soil latent heat flux with 21.7% relative error; however, for the younger vineyard (south block), TSEB-PT performs better than TSEB-2T in partitioning the canopy latent heat flux with 11.7% relative error and soil latent heat flux with 39.3% relative error.

Model-based real-time surface heat flux and temperature estimation for the DIII-D tokamak

A control-oriented model for monitoring of wall power flux densities on the DIII-D tokamak has been successfully implemented and validated experimentally. Future reactors will have to withstand severe steady state high heat flux loads on plasma-facing components (PFCs). Due to the difficulty of directly-measuring local heat fluxes on these components, monitoring and protection of PFCs during the plasma discharge can benefit from simplified physics-based real-time functional models to estimate and guide heat load control. As a first step into the development, a control-oriented model for monitoring of wall power flux densities and temperatures on DIII-D tokamak has been successfully implemented. The paper discusses the experimental demonstration and comparison of the 2D model-based wall heat flux algorithm on the DIII-D inner wall limiter (IWL) against infra-red (IR) camera heat flux measurements for limited plasma configurations. The paper also reports on the benchmarking of the field line tracing environment, SMITER, developed at ITER organization on DIII-D tokamak against experimental IR diagnostic data and the derivation of the component shaping weighting factors for the 2D model-based approach. Extension of the model-based approach for surface temperature estimation on the DIII-D IWL is also presented.

Variability in the global energy budget and transports 1985\u20132017

The study of energy flows in the Earth system is essential for understanding current climate change. To understand how energy is accumulating and being distributed within the climate system, an updated reconstruction of energy fluxes at the top of atmosphere, surface and within the atmosphere derived from observations is presented. New satellite and ocean data are combined with an improved methodology to quantify recent variability in meridional and ocean to land heat transports since 1985. A global top of atmosphere net imbalance is found to increase from 0.10 ± 0.61 W m−2 over 1985–1999 to 0.62 ± 0.1 W m−2 over 2000–2016, and the uncertainty of ± 0.61 W m−2 is related to the Argo ocean heat content changes (± 0.1 W m−2) and an additional uncertainty applying prior to 2000 relating to homogeneity adjustments. The net top of atmosphere radiative flux imbalance is dominated by the southern hemisphere (0.36 ± 0.04 PW, about 1.41 ± 0.16 W m−2) with an even larger surface net flux into the southern hemisphere ocean (0.79 ± 0.16 PW, about 3.1 ± 0.6 W m−2) over 2006–2013. In the northern hemisphere the surface net flux is of opposite sign and directed from the ocean toward the atmosphere (0.44 ± 0.16 PW, about 1.7 ± 0.6 W m−2). The sea ice melting and freezing are accounted for in the estimation of surface heat flux into the ocean. The northward oceanic heat transports are inferred from the derived surface fluxes and estimates of ocean heat accumulation. The derived cross-equatorial oceanic heat transport of 0.50 PW is higher than most previous studies, and the derived mean meridional transport of 1.23 PW at 26° N is very close to 1.22 PW from RAPID observation. The surface flux contribution dominates the magnitude of the oceanic transport, but the integrated ocean heat storage controls the interannual variability. Poleward heat transport by the atmosphere at 30° N is found to increase after 2000 (0.17 PW decade−1). The multiannual mean (2006–2013) transport of energy by the atmosphere from ocean to land is estimated as 2.65 PW, and is closely related to the ENSO variability.

Improving Soil Moisture and Surface Turbulent Heat Flux Estimates by Assimilation of SMAP Brightness Temperatures or Soil Moisture Retrievals and GOES Land Surface Temperature Retrievals

AbstractSurface heat fluxes are vital to hydrological and environmental studies, but mapping them accurately over a large area remains a problem. In this study, brightness temperature (TB) observations or soil moisture retrievals from the NASA Soil Moisture Active Passive (SMAP) mission and land surface temperature (LST) product from the Geostationary Operational Environmental Satellite (GOES) are assimilated together into a coupled water and heat transfer model to improve surface heat flux estimates. A particle filter is used to assimilate SMAP data, while a particle smoothing method is adopted to assimilate GOES LST time series, correcting for both systematic biases via parameter updating and for short-term error via state updating. One experiment assimilates SMAP TB at horizontal polarization and GOES LST, a second experiment assimilates SMAP TB at vertical polarization and GOES LST, and a third experiment assimilates SMAP soil moisture retrievals along with GOES LST. The aim is to examine if the assimilation of physically consistent TB and LST observations could yield improved surface heat flux estimates. It is demonstrated that all three assimilation experiments improved flux estimates compared to a no-assimilation case. Assimilating TB data tends to produce smaller bias in soil moisture estimates compared to assimilating soil moisture retrievals, but the estimates are influenced by the respective bias correction approaches. Despite the differences in soil moisture estimates, the flux estimates from different assimilation experiments are in general very similar.

Estimation of surface heat fluxes using multi-angular observations of radiative surface temperature

The retrieval of canopy and soil component temperatures for estimating evapotranspiration in the two source energy balance (TSEB) model depends on a relatively accurate partitioning of soil/substrate evaporation and canopy transpiration along with the soil and vegetation temperature components. To avoid the need for a Priestley-Taylor based transpiration formulation, this study applies the TSEB model using radiometric land surface temperature observations at multiple view angles from an airborne sensor for estimating soil and canopy temperatures directly. This direct partitioning between soil and canopy temperatures applied with the TSEB formulation improved the agreement between observed and modeled surface heat fluxes, reducing mean absolute percentage error (MAPE) in latent heat fluxes (LE) with flux tower observations from nearly 20% using the original Priestley-Taylor based TSEB model (TSEB-PT) to 15% using TSEB with thermal infrared observations from two substantially different view angles (TSEB-2AG) to nearly 5% using multiple (~6) view angles (TSEB-6AG). Moreover, TSEB-6AG is shown to compute physically realistic spatially-distributed LE for a range of vegetation cover and environmental conditions over the imaged domain. Values of MAPE for sensible heat (H) tended to be larger for all three models due to the fact that tower measurements tended to be located in well irrigated and densely vegetated sites having relatively low H values. This increased accuracy of soil and vegetation component temperature separation using multiangle radiometric temperature observations is useful for evaluating the utility of single and dual view angle thermal radiometer measurements currently available for applying the TSEB model.