Surface Temperature History Research Articles

Transient behavior of ablation and swelling for C/C composite and HfC-coated C/C composite in an arc-heated wind tunnel

This study investigated and modeled the transient behavior of surface recession, defined as the difference between ablative length and swelling length, for thermal protection materials within a high-enthalpy flow. Needle punch carbon-carbon (NPCC) and hafnium carbide coated carbon-carbon (HfC-coated NPCC) were exposed to high-enthalpy flow with a heat flux of 7.67 MW/m2 generated by an arc-heated facility. The NPCC and the HfC-coated NPCC represent an ablative surface and a non-ablative surface, respectively. Surface recession histories were estimated through an image analysis and visualizations monitored by a high-speed camera. Moreover, measured data including surface temperature histories, mass loss, and total length were presented. We proposed the models for the transient recession on the ablative surface and the non-ablative surface considering the ablation and the swelling. The ablative length was calculated using non-dimensional parameter B′, which computes ablation rates under equilibrium air conditions. While B’ modeling accurately predicted the ablation rates, it could not reflect the swelling phenomenon during an initial heating phase. The swelling was modeled with consideration of the thermal expansion. Specifically, the effect of increased porosity near the ablative surface was incorporated into the thermal expansion coefficient. The model developed in this study well agreed with the experimental data.

Localized Evaporative Cooling Explains Observed Ocular Surface-Temperature Patterns.

We determined interblink corneal surface-temperature decline and tear-film evaporation rates of localized tear breakup cold regions (LCRs) and localized tear unbroken warm regions (LWRs) of the corneal surface, as well as that of the overall average corneal surface. Each subject underwent 4 inter-day visits where the interblink corneal surface-temperature history of the right eye was measured using a FLIR A655sc infrared thermographer. Corneal surface temperature history was analyzed to determine the overall, LCR, and LWR temperature-decline rates. Evaporation rates of LCR and LWR regions were determined from the measured LCR and LWR temperature data using the physical model of Dursch et al. Twenty subjects completed the study. Mean (SD) difference of LCR temperature-decline rate was -0.08 (0.07)°C/s faster than LWR (P < 0.0001). Similarly, evaporation rates of LCR and LWR were statistically different (P < 0.0001). At ambient temperature, mean LCR and LWR evaporation rates were 76% and 27% of pure water evaporation flux, respectively. There was no statistically significant difference between the inter-day measured temperature-decline rates and the interblink starting temperature. Significant differences in corneal temperature-decline rate and evaporation rate between LCR and LWR were quantified using infrared thermography. In agreement with literature, LCRs and LWRs correlate directly with fluorescein break-up areas and unbroken tear areas, respectively. Because lipid-evaporation protection is diminished in breakup areas, higher local evaporation rates and faster local cooling rates occur in LCRs relative to LWRs. Our results confirm this phenomenon clinically for the first time.

Cellulase-assisted refining in a paperboard mill: Avoided emissions from energy savings. A case study of a Finnish paperboard mill

The 2023 being on its way to be the warmest year in the 174-year global surface temperature history it is becoming more and more evident how crucial it is to break the linkage between economic growth and greenhouse gas emissions.The pulp and paper industry is highly energy intensive industry sector. It is the fourth largest industrial energy user and currently produces approximately 1.3% of global greenhouse gas emissions. While the demand for paper and paperboard products keeps rising, it is essential for the industry to find energy efficient solutions for reducing the environmental impact of the pulp and paper products. 80% of the progress in energy efficiency in Finnish paper mills is due to improved technology and more optimal operational modes. Optimizing existing processes has bigger effect on energy efficiency than closing old and starting new paper mills.Pulp refining is one of the most energy intense steps in the paperboard production, representing 15%–18% of the total energy consumption of a paper mill. The effect of a commercial cellulase enzyme product was evaluated for energy savings and avoided emissions in the refining process of a paperboard mill. Data from a paperboard line using Bleached Softwood Kraft Pulp (BSKP) from a separate pulp mill was provided by a Finnish paperboard mill containing production runs both with and without commercial cellulase product ECOPULP® R. Data was collected from the mill automation system to evaluate and compare a refining capacity restricted run and a run that was not refining capacity restricted.Analysis of the data showed a reduction of refining energy by approximately 16%–17% when the cellulase enzyme was used. This corresponds to 2 kg of CO2 emissions avoided per tonne of pulp refined when calculated using the Finnish average electricity emissions intensity in 2022. Use of the cellulase enzyme enabled the refining results that could not have been reached with the bare mechanical refining capacity of the mill.Cellulases can be efficient processing aids in pulp refining. The reduction of required mechanical refining and electrical power to run the refiners to achieve the required freeness can significantly affect the carbon footprint of the paperboard products, whereas the negative impact of emissions from enzyme production is negligible. Reduction of CO2 emissions is especially significant in the areas where the electricity mix used for the production is based heavily on fossil fuels.

Identification of the surface heat flux of charring ablative materials using dynamic Bayesian network based on multisource information fusion

In order to solve the dual uncertainty problem between heat flux and thermophysical properties in the identification of the heat flux of charring ablative materials, a dynamic Bayesian network (DBN) based on multisource information fusion is proposed. The method is divided into two stages, with thermophysical properties identified in the former stage and the heat flux identified in the latter stage. A one-dimensional pyrolysis layer model is adopted to characterize the ablation process of materials. In the DBN, the multisource information of surface recession and temperature history data are considered as observation nodes. Sensitivity analysis is used to determine the key parameters in each time step in the DBN, and only key parameters are identified in the corresponding time step. Thus, with the increase of types of information and the decrease of the number of simultaneous identification parameters, the identification accuracy can be improved. The method was verified by numerical and experimental cases. In the numerical cases with noise and experimental cases, the maximum error of using the proposed method was 3.27% and 2.55%, respectively. Compared with only considering the temperature information, the relative errors of the identification results considering multisource information fusion were reduced by 83.95% and 47.53%, respectively.

Validation of Ablation and Thermal Response Model for Three-Dimensional Multifunctional Ablator

A semi-empirical physics-based ablation and thermal response model was developed for the 3-Dimensional Multifunctional Ablative Thermal Protection System (3D-MAT) material. Model validation was achieved through comparison between computation and available data obtained in the arc-jet test series, which were conducted at NASA Ames Research Center from 2014 to 2020. The charring ablator simulations for arc-jet test models presented in this work were computed by the Two-Dimensional Implicit Thermal Response and Ablation (TITAN) code, and the Data-Parallel Line Relaxation Method (DPLR) code was used for arc-jet flow simulations to estimate the arc-jet stream total enthalpy and define the aerothermal boundary conditions over the test model surface for TITAN simulations. Because of low surface catalytic efficiency of 3D-MAT char, the exact surface heating could not be determined. Thus, three different types of boundary conditions, including 1) fully catalytic surface heating, 2) noncatalytic surface heating, and 3) surface temperature and recession, were used in the TITAN simulation for model validation. The predicted surface and in-depth temperature history for arc-jet test models were compared with pyrometer and thermocouple data, and the predicted test model surface recession and char depth were compared against the posttest measurements.

Asymptotic and approximate solutions for piloted ignition of thermally thick solids under power-law heat flux

New asymptotic solutions are established in this work to describe the piloted ignition behaviors of thermally thick solids exposed to power-law thermal radiation accounting for convective, radiative and their combined heat loss effects. In all scenarios, the derived surface temperature and ignition time correlations share a similar form. The ignition time to the power of −0.5 linearly depends on the transient radiation. The asymptotic solutions are validated by comparison with numerical solutions and compared for accuracy with previous approximate correlations. Moreover, according to the surface temperature history, an asymptotic mass flux solution is attained. Accuracy of all solutions are verified by numerical and experimental results where vertical PMMA was heated by five power-law heat fluxes. The predicted surface temperatures fit the numerical and experimental curves well if the ignitor is located at the top sample holder. However, for center ignitor the developed model overestimates experimental surface temperatures at ignition time due to the neglected pyrolysis caused by increased thermal penetration effects. Effects of ignitor location are important for low heat fluxes. The asymptotic mass loss rates agree well with numerical and experiential results. Both critical temperature and critical mass loss rate are used to estimate ignition times, and good agreement is found except for the experimental cases of top ignitor.

Analysis of transient characteristics of droplets in the DFFB regime during single-rod channel reflood experiment

This study aims to explore the dynamic distribution and hydrodynamic characteristics of droplets during the highly transient process of reflood. However, the quasi-steady state analysis is generally adopted in existing studies reported in the literature, ignoring the dependence of droplet formation and breaking mechanism in the Dispersed flow film boiling (DFFB) mechanism on the time-related historical behaviors such as the propagation of the quench front. A series of reflood cooling visualization experiments of zirconium alloy high-temperature rod-shaped heating surface were carried out to achieve this research goal. The wall surface and fluid temperature history curves were recorded, and the parameters, such as the size and velocity of DFFB regime droplets, were quantitatively extracted by visual image processing technology. Based on the formation and breakup mechanism of droplets in the dispersed flow, the reasons for droplet size distribution and velocity change with input heat flux, initial wall temperature, inlet subcooling, and inlet flow rate are well analyzed and explained. At the same time, the experimental results also show a strong correlation between droplet behavior and the reflood process in time. This study can provide more detailed physical support for the subsequent development of droplet behavior models more suitable for the strong transient reflood process and the evaluation of existing models.

Forecast uncertainty and ensemble spread in surface currents from a regional ocean model

An operational ocean Ensemble Prediction System (EPS) for the coastal seas off Northern Norway is evaluated by comparing with high-frequency radar current speed estimates. The EPS is composed of 24 members for which the ocean current is not perturbed nor constrained but forced with an atmosphere ensemble. The ocean ensemble spread stems from (i) accumulated differences in wind-forcing history and (ii) constraints of sea surface temperature by data assimilation. The intention of the ensemble is to reflect the actual uncertainty in initial conditions, which are largely unknown in terms of mesoscale circulation. We find a low but pronounced predictive skill in surface currents along with a good statistic skill. Additionally, current speeds show deterioration of the validation metrics over the forecast range. Further, high-resolution wind forcing seems to provide better forecast skill in currents compared to lower resolution forcing. In general, the ensemble exhibits the ability to predict forecast uncertainty.

Ground Surface Temperature History Since the Last Glacial Maximum in Northeast Asia: Reconstructions From the Borehole Geotherms of the International Continental Scientific Drilling Program

AbstractPast ground surface temperature (GST), one of the important aspects of paleoclimate reconstructions, can be inverted from borehole temperature measurements. Here, we report continuous 6,100‐m temperature logs in the International Continental Scientific Drilling Program SK‐2e. We inverted the past GST changes from upper borehole temperature logging (&lt;600 m). Below this depth, localized fluid flow masks the paleoclimate record. Inversions yield an approximately 2 K GST rise since 0.1–0.6 Kyr BP and an approximately 10 K rise since 20 Kyr BP. Assuming a ±5 K influence from the deep groundwater flow, the inverted temperature rise has varied between 8 and 12 K since 20 Kyr BP, which is consistent with previous reports since the Last Glacial Maximum. Our results emphasize the potential of borehole heat‐flow profiles as a record of climate changes and the importance of climate correction for heat‐flow determinations.

Heat flow variations in 2 km deep borehole Litoměřice, Czechia

Temperature in 2 km deep borehole Litoměřice, drilled in 2007, was repeatedly logged down to 1700 m in the period 2007 – 2020. We were able to monitor a return of the temperature to the equilibrium temperature-depth profile undisturbed by drilling. The uppermost part of the profile contains signal of the recent warming manifested by a negative temperature gradient close to the surface and a temperature minimum at a depth of about 40 m. The minimum has been migrating downward at a rate of 1.5 – 2 m per year in the period 2015 – 2020.A detailed knowledge of temperature gradient together with thermal conductivity, diffusivity and heat production measurements on the drill-core samples of mica-schist that occurs below 900 m depth enabled us to analyze the heat flow vertical variations in the lithologically homogeneous depth section 900 – 1700 m. We came to the conclusion that temperature-depth profile in this section contains a robust climate signal of the last glacial cycle. The reconstructed ground surface temperature history indicates the magnitude of the last glacial – Holocene warming 13 -15 K and existence of a minimum 15 – 20 ka. The long-term mean ground surface temperature +1 - +2 °C suggests that the borehole site was permafrost free for most of the glacial cycle. Existence of about 100 m deep permafrost is possible in the coldest part of the last glacial.The steady-state surface heat flow has been estimated at 88 mW/m2. The reconstructed ground surface temperature history used as a surface forcing function in a numerical solution of the transient heat conduction equation provided an estimate of the present-day heat flow in the well. The estimate is practically independent from the poorly constrained conductivity of the 900 m thick sedimentary cover. According to it the present-day heat flow is lower than the steady-state one by 20 - 30 mW/m2 in the first hundreds of meters below the surface and still by about 10 mW/m2 at a depth of 1 km.

Review Study on Thermal Characteristics of Bell Nozzle used in Supersonic Engine

The nozzle is an important component of the rocket motor system, and a rocket’s overall performance is highly reliant on its aerodynamic design. The nozzle contour can be meticulously shaped to improve performance significantly. The design and shape of rocket nozzles have evolved over the last several decades as a result of extensive research. The nozzle design is composed of two components, an integrated throat, an entry and an exit cone, and a thermal protection system. The Bell Nozzle is designed to provide clearance space for placing the ITE and exit cone, with a cone inflection angle of 16 and a thermal protection system. This paper intends to review and summarize all such developments. Small-scale engine testing allows for the analysis of rocket nozzle materials, but the history of nozzle surface temperature and thermal stress may be adversely affected by side effects. The review focuses primarily on the nozzle shape which has the largest radiative flux past the neck, but the nozzle shape has the highest heat flux in the throat due to the mass-flow rate per unit area. The distribution of nozzle wall pressure is strongly influenced by the Mach number of the injected secondary flow, leading to undesirable side loads. Finally, future development possibilities are suggested.

The Search for a Generalized Analytical Solution for the Inverse Problem; Some Surprisingly Simple Approximate Methods for Problems of Practical Importance

Advances in numerical algorithms for Inverse problems has led to significant leaps in our ability to model complex situations of importance. Nonetheless, there is still a strong need for analytical approaches that can be used to calibrate/validate numerical simulations since the old adage of Trust, but Verify is sound advice. Moreover, access to Inverse codes is often limited despite a strong need. Fortunately, generalized Inverse formulations capable of good approximations can be obtained for linear problems by using a known Direct solution. Duhamel’s Integral (convolution) and a systems Unit Response are first employed to derive a Direct solution, with generality maintained via an arbitrary function with coefficients such as polynomials to described the time-dependent boundary condition. For the ensuing Inverse problem, the Direct solution in the form of a more complex polynomial with its coefficients now considered unknown are then used to enforce remotely measured data using the Levenberg–Marquardt algorithm. Once the coefficients are determined, the original function (polynomial or alternative) now describes the unknown boundary condition. Intriguingly, an approximate Inverse Laplace Transform method applied to the Convolution Integral allows for relatively simple formulations for both the Direct and Inverse problems; for this approximation, only the remotely measured data along with the Unit Response as the solitary system information are required. However, the predicted boundary temperature history tends to be shifted forward in time indicating the influence of the thermal thickness and will also reflect any errors in the data. Accuracy can be enhanced by correcting (back-shifting) for the penetration time to the measurement depth and/or using least-squares smoothing. When the various generalized solutions were used for a plate and a thick-cylinder with a time-dependent thermal boundary-condition on one surface and convection on the other, good-to-excellent Inverse predictions were observed; the methods can be adapted so that remotely measured and near instantaneous surface-strains can also be used to determine an unknown surface temperature history. Finally, the convolution-based approach can easily be adapted for 1-degree of freedom vibration problems.

The Cretaceous (early Albian to early Campanian) biostratigraphy and palaeotemperature reconstruction of the eastern Tethys: Calcareous nannofossil evidence from southern Tibet, China

Studies of geochemical proxies, such as carbonate δ18O and TEX86, show that the Earth's climate has changed significantly during the Cretaceous Period. However, knowledge about the sea surface temperature (SST) history of the eastern Tethys is limited. Based on the calcareous nannofossil record of the Nirang section, Tethys Himalayas, this paper attempts to establish the biostratigraphic framework and SST evolution of the Cretaceous Period in the southern Tibet. A total of 131 species were identified from the studied succession. Twelve bioevents were recognized, allowing for early Albian to the early Campanian (CC8 to CC18 biozones) in the section. Meanwhile, a disconformity within 81–71 Ma was also identified. The SST evolution was analysed by the calcareous nannofossils modified temperature index (mTI), and the results reveal that the long-term SST changes in the Tethys Himalayas of southern Tibet experienced progressive warming from the early Albian to the early Turonian and the warm interval persisted until the early Campanian. Short-term warming and cooling events, e.g., rapid warming in the early and late Albian, subsequent cooling in the latest Albian and peak warmth at the Cenomanian–Turonian transition, are also recorded in the study area. The SST history of the Albian-Cenomanian in the eastern Tethys can be well correlated to the western Tethys (central Italy). However, the compilation of TEX86 data indicates substantial global cooling during the Coniacian to Campanian. This study suggests that the northward drift of the Indian continent towards the equator is likely to be responsible for the sustained warmth in the Tethys Himalayas from the middle Turonian to the early Campanian.

A machine learning methodology for the diagnosis of phase change material-based thermal management systems

Phase change materials (PCM) have received significant interest in various thermal energy storage and management applications due to their ample latent heat during the phase transition process. As PCM plays a vital role in these systems, knowledge of the state of the PCM is crucial for the sustained usage of the thermal management system. The energy absorbed by PCM as latent heat directly correlates with the average liquid fraction of the PCM; this can be used as a metric to monitor the thermal state of the system. Direct measurement of liquid fraction is quite challenging and is possible only through a thermal management system designed with a transparent material. This study proposes a machine learning-based diagnosis technique for a PCM-based thermal management system to predict the liquid fraction using surface temperature history. Recurrent neural networks (RNN) are chosen to predict the liquid fraction of PCM due to their non-linear and time-dependent nature. The data set required for the training of RNN is generated using numerical simulations. An RNN model is trained with a data set containing 345 samples which cover heat input types of constant, pulsating, random, Wiener, and discharging with corresponding temperatures as input and liquid fractions as target values of RNN. The results show that for all the heat inputs, the RNN can predict the temporal liquid fraction of PCM by showing a correlation up to 0.99 and RMSE less than 0.015 with the numerically obtained liquid fraction. Further, the RNN model takes a significantly lower computational time and power for predicting liquid fractions and can be deployed in real-life situations. Moreover, the study shows that challenging heat transfer problems are amenable to treatment with machine learning algorithms.

A new bootstrap technique to quantify uncertainty in estimates of ground surface temperature and ground heat flux histories from geothermal data

Abstract. Estimates of the past thermal state of the land surface are crucial to assess the magnitude of current anthropogenic climate change as well as to assess the ability of Earth System Models (ESMs) to forecast the evolution of the climate near the ground, which is not included in standard meteorological records. Subsurface temperature reacts to long-term changes in surface energy balance – from decadal to millennial time scales – thus constituting an important record of the dynamics of the climate system that contributes, with low-frequency information, to proxy-based paleoclimatic reconstructions. Broadly used techniques to retrieve past temperature and heat flux histories from subsurface temperature profiles based on a singular value decomposition (SVD) algorithm were able to provide robust global estimates for the last millennium, but the approaches used to derive the corresponding 95 % confidence interval were wrong from a statistical point of view in addition to being difficult to interpret. To alleviate the lack of a meaningful framework for estimating uncertainties in past temperature and heat flux histories at regional and global scales, we combine a new bootstrapping sampling strategy with the broadly used SVD algorithm and assess its performance against the original SVD technique and another technique based on generating perturbed parameter ensembles of inversions. The new bootstrap approach is able to reproduce the prescribed surface temperature series used to derive an artificial profile. Bootstrap results are also in agreement with the global mean surface temperature history and the global mean heat flux history retrieved in previous studies. Furthermore, the new bootstrap technique provides a meaningful uncertainty range for the inversion of large sets of subsurface temperature profiles. We suggest the use of this new approach particularly for aggregating results from a number of individual profiles, and to this end, we release the programs used to derive all inversions in this study as a suite of codes labeled CIBOR v1: Codes for Inverting BORholes, version 1.

Significance of eigenstresses and curling stresses for total thermal stresses in a concrete slab, as a function of subgrade stiffness

ABSTRACT Thermally induced stresses of a concrete slab are quantified based on in situ temperature measurements. PT100A sensors recorded the temperature at four specific depths during 23 days in autumn. Best-fit quadratic polynomials are used to extrapolate the measured temperatures to the top and the bottom of the slab. The obtained surface temperature histories are used as boundary conditions for the solution of the transient heat conduction problem in thickness direction. Postprocessing the thermal eigenstrains provides access to the eigencurvatures of the plate and to the eigendistortions of the plate-generators. Stresses resulting from the constrained eigencurvatures of the plate are computed numerically, for values of the modulus of subgrade reaction amounting to 50, 100, 200, and 300 MPa/m. Self-equilibrated eigenstresses resulting from the prevented eigendistortions of the plate-generators are quantified analytically. Daily maxima of tensile stresses in corner regions at the top of the slab, and in the central region at its bottom, are found in the early morning and in the early afternoon, respectively. Disregarding the eigenstresses leads to an underestimation of tensile stresses in corner regions by at least 33 % and an overestimation in the central region by at least 26 % . The misestimations increase with decreasing modulus of subgrade reaction.

Thermal modeling and validation via time-resolved temperature measurements for nanosecond laser irradiation of a powder bed of micro metal particles

Continuous-wave (CW) lasers are often used in selective laser sintering or melting; but short-pulsed lasers (e.g., with a pulse duration on the nanosecond scale) have their own potential advantages, such as high resolutions and small residual thermal effects. Compared with CW lasers, nanosecond lasers involve additional parameters (such as the pulse frequency) and more complicated relations between laser parameters and the powder bed thermal responses in laser sintering or melting. To help fundamentally understand the relations and guide efficient parameter selections, it is highly desirable to develop a thermal model for nanosecond laser irradiation of a metal powder bed and directly validate the model via in-situ transient temperature measurements. However, research work integrating such model development and validation has been rarely reported to the authors’ best knowledge. In this paper, a thermal model has been developed for nanosecond laser irradiation of a powder bed of micro metal particles. The model-predicted transient surface temperature history of the powder bed agrees reasonably well with that measured by a fast pyrometry system. Under the conditions studied, the model simulations show that high-frequency nanosecond laser pulses can induce a significant thermal accumulation effect in a metal powder bed due to its lower thermal conductivity than that for a bulk metal. With the same time-averaged laser power, by changing the pulse frequency, a nanosecond laser can induce very different temperature histories, melt pool evolutions and lifetimes, suggesting the laser has a potential advantage of good adjustability and flexibility in laser sintering. It also means a parameter-selection challenge due to the complicated parameter-thermal response relations, implying the importance of a thermal model validated by time-resolved temperature measurements.

Analytical Thermal Boundary Condition for Quasi-Transient Simulation of Internal Flow Experiments

Transient thermochromic liquid crystal (TLC) experiments can provide high-fidelity spatially resolved heat transfer data for complex geometries, particularly where infrared techniques cannot be applied. One challenge when applying transient methods to internal geometries is the local definition of the driving gas temperature. The transient nature of the streamwise driving gas temperature profile has led to comparisons with steady-state computational fluid dynamics being questioned. This paper explores simulating the temporal behavior of transient TLC experiments directly. A novel technique is developed to account for differences in the gas and solid time scales, where surface temperature is calculated at each spatial location analytically from the surface heat flux, using an impulse response method assuming one dimensional, semi-infinite conduction. Postprocessing of the simulated surface temperature history is performed using the same method as experimentally, allowing for direct comparison. This analytical thermal boundary condition (ATBC) is applied to simulate a transient TLC experiment of a stationary superscaled rib turbulated internal cooling passage in a gas turbine engine. Traditional steady-state simulations were also performed with constant temporal and spatial temperature boundary conditions. Results show that calculations using the new ATBC and traditional steady-state method give very similar Nusselt number distributions and mean values in relation to the experimental data, suggesting the larger discrepancy between simulations and the experiments is not the definition of the driving gas temperature. Analysis of transient variation of Nusselt number indicated brief highly localized maximum variations up to 40%, although this was not found to significantly affect the mean values, and passage-averaged values converged to within 0.5% of the final value within 0.2 s.

Deducing flux from single point temperature history when relative spatial variation of flux is prescribed

Surface heat transfer in convective and radiative environments is sometimes measured by recording the surface temperature history in a transient experiment and interpreting this surface temperature with the aid of a suitable model for transient conduction within the substrate. The semi-infinite one-dimensional model is often adopted, and several well-developed techniques for application of this model to surface temperature data are available. However, when a spatial variation of heat flux exists across the surface, the application of the semi-infinite one-dimensional approach may not always be a reasonable approximation because the errors are transient and typically increase with time. In this paper we introduce a method for treatment of the measured surface temperature history that is more accurate than the semi-infinite one-dimensional approximation when substrate lateral conduction is significant and the relative spatial distribution of the flux is known a priori. This new method uses the so-called Neumann heat kernel, which evolves a temperature over an insulated domain with unit energy initially deposited at a specified point. A useful impulse response function is formed by integrating this Neumann heat kernel against the spatial variation of flux over the surface of the domain. By applying the heat kernel result for the sphere to the analysis of a convective experiment using hemispherical-nosed probes, we demonstrate how the theoretical results enhance the practical analysis of transient surface temperature measurements. The current approach is superior to former methods relying on semi-empirical approximations because the multi-dimensional heat conduction within the substrate is modelled with greater fidelity using the heat kernel analysis.

Distinct sources of interannual subtropical and subpolar Atlantic overturning variability

The Atlantic meridional overturning circulation (AMOC) is pivotal for regional and global climate due to its key role in the uptake and redistribution of heat and carbon. Establishing the causes of historical variability in AMOC strength on different timescales can tell us how the circulation may respond to natural and anthropogenic changes at the ocean surface. However, understanding observed AMOC variability is challenging because the circulation is influenced by multiple factors that co-vary and whose overlapping impacts persist for years. Here we reconstruct and unambiguously attribute intermonthly and interannual AMOC variability at two observational arrays to the recent history of surface wind stress, temperature and salinity. We use a state-of-the-art technique that computes space- and time-varying sensitivity patterns of the AMOC strength with respect to multiple surface properties from a numerical ocean circulation model constrained by observations. While, on interannual timescales, AMOC variability at 26° N is overwhelmingly dominated by a linear response to local wind stress, overturning variability at subpolar latitudes is generated by the combined effects of wind stress and surface buoyancy anomalies. Our analysis provides a quantitative attribution of subpolar AMOC variability to temperature, salinity and wind anomalies at the ocean surface.