Subsurface Temperature Variability Research Articles

An Inconsistent ENSO Response to Northern Hemisphere Stadials Over the Last Deglaciation

AbstractThe dynamics shaping the El Niño‐Southern Oscillation's (ENSO) response to present and future climate change remain unclear, partly due to limited paleo‐ENSO records spanning past abrupt climate events. Here, we measure Mg/Ca ratios on individual foraminifera to reconstruct east Pacific subsurface temperature variability, a proxy for ENSO variability, across the last 25,000 years, including the millennial‐scale events of the last deglaciation. Combining these data with proxy system model output reveals divergent ENSO responses to Northern Hemisphere stadials: enhanced variability during Heinrich Stadial 1 (H1) and reduced variability during the Younger Dryas (YD), relative to the Holocene. H1 ENSO likely intensified through meltwater‐induced changes to ocean/atmospheric circulation, a response observed in models, but the lack of a similar response during the YD challenges model simulations. We suggest the tropical Pacific mean state during H1 primed ENSO for larger fluctuations under meltwater forcing, whereas the YD mean state likely buffered against it.

A preliminary assessment of regional CO2 storage potential in the onshore northern Perth Basin

The Geological Survey of Western Australia (GSWA) is creating a new carbon dioxide (CO2) geological storage atlas for Western Australia. The atlas will incorporate the latest state-wide datasets to provide a regional assessment of the potential for CO2 sequestration across the Perth, Southern Carnarvon, Northern Carnarvon (onshore and State waters), Canning and Officer basins. Multi-1D modelling of subsurface temperature in the northern Perth Basin incorporates newly collated temperature data, updated regional depth maps, and stratigraphic revisions. This modelling captures lateral subsurface temperature variations that are incorporated into isothermal depth and temperature maps identifying reservoir units within the optimum temperature–pressure window for CO2 storage. Isopach maps of associated sealing units indicate where they are of adequate thickness to contain CO2. Modelled present-day temperature maps of seven key reservoir units reveal promising CO2 storage prospectivity, with all postulated reservoir units having significant extents within optimum CO2 storage temperature and pressure ranges. Whereas older reservoir units are prospective for CO2 storage towards the margins of the basin, younger reservoir units in the shallower part of the succession are only prospective in or near the Dandaragan Trough, the deepest part of the basin. The critical upper temperature limit of 31.1°C is shallower in the north and west of the basin, where the modelled geothermal gradient is higher. All state-wide raw and interpreted datasets including temperature and depth maps will be published and available for download on the GSWA Western Australian Petroleum and Geothermal Information Management System website.

Numerical simulation and experimental study of femtosecond laser ablation of copper: A two-temperature model with temperature-dependent properties and multiple phase transitions

A fundamental study of the interaction between femtosecond laser and copper will be useful in optimizing laser parameters and processing quality in practice, and it faces challenges due to very short action time, complex energy transport and phase transition processes of this interaction. In this paper, A 2D two-temperature model was established and improved to include temperature-dependent optical and thermophysical properties and three phase transitions including melting, vaporization, and phase explosion. The temperature evolution of both the top surface and the sub-surface were simulated, thereafter, ablation experiments with different laser peak fluences were conducted using a femtosecond laser. It was found that the interface reflectivity would decrease rapidly, while the optical penetration depth and the ballistic electron penetration depth would increase significantly during laser irradiation. The temperature evolution of electron and lattice subsystems of the top surface could be divided into, respectively, 4 and 5 stages with different temperature trends in each stage. The variation of subsurface temperature was different from that of surface temperature and the temperature distribution showed that there was a temperature peak at near surface. A comparison of the experimental and simulation results showed that the simulated ablation depths were consistent with the experiment results.

Enhancing impacts of mesoscale eddies on Southern Ocean temperature variability and extremes

As a major sink of anthropogenic heat and carbon, the Southern Ocean experienced pronounced warming with increasing extreme temperature events over the past decades. Mesoscale eddies that strongly influence the uptake, redistribution, and storage of heat in the ocean are expected to play important roles in these changes, yet observational evidence remains limited. Here, we employ a comprehensive analysis of over 500,000 historical hydrographic profile measurements combined with satellite-based eddy observations to show enhanced thermal eddy imprints in the Southern Ocean. Our observations reveal that anticyclonic (cyclonic) eddies are responsible for nearly half of the subsurface high (low)-temperature extremes detected, although only 10% of the profiles are located in eddy interiors. Over the past decade (2006 to 2019), both mean and extreme temperature anomalies within eddies in the Antarctic Circumpolar Current increased significantly, promoting the rise in subsurface ocean temperature variability. This enhanced role of eddies is likely a result of enhanced eddy pumping due to the increase in eddy intensity and ocean stratification caused by ocean warming. Our analysis underscores the crucial role of eddies in amplifying ocean temperature variability and extremes, with their effects expected to be even more pronounced as global warming persists.

Photothermal Effects of High-Energy Photobiomodulation Therapies: An In Vitro Investigation.

The purpose of this study was to investigate photothermal aspects of photobiomodulation therapies (PBMT) in vitro to assist in the development of safe clinical parameters with respect to higher-power devices with large surface applicators. Laser wavelengths in the range of 650 nm-1064 nm were investigated using a thermal camera. Thermographic measures of surface and sub-surface temperature variations of similar lean porcine muscle tissue samples were recorded for a series of calibrated experiments. A thermal comparison was then made between Flat-top and Gaussian beam spatial distribution devices. Outcome data were subjected to statistical analysis using an ANOVA model. Results acquired at similar parameters of irradiance indicated that the application of the 980 nm wavelength was associated with the highest rise in temperature, which decreased with other wavelengths in the order 980 > 1064 ≈ 650 >>> 810 nm (p < 5 × 10-20). All wavelengths assessed were associated with a significant temperature increase, and with the exception of 810 nm, all exceeded the threshold of a 6 °C rise within the prescribed parameter limits. Optical scanning by movement of the applied source over a relevant area was found to offer effective mitigation of these temperature increases. An extended discussion is presented, analysing the clinical significance of the study outcomes. Recommendations are made within the limits of this in vitro study in order to assist future clinical investigations.

Distribution of surface heat flow and effects on the subsurface temperatures in the northern part of Thrace Basin, NW Turkey

The Thrace Basin in northwestern Turkey is a deep Eocene–Oligocene hydrocarbon-bearing sedimentary basin. The basin has potential for geothermal energy utilization in the future due to its favorable geological conditions. In this study, we combined the available bottom hole temperature (BHT) data from 70 points with the thermal conductivity and radiogenic heat productions of the basin formations, and generated a detailed thermal model of the northern part of the basin. For heat flow determinations from the BHT data, we applied Bullard’s thermal resistance method on formation thermal conductivities and thicknesses. The results give an average surface heat flow of 65.8 ± 11.3 mW/m2. We obtained high heat flow values (75–80 mW/m2) in the eastern and western sides, and the central part of the study area. These relatively high heat flow values can be explained by the combined effect of basement topography and the variations in the radiogenic heat production of the basement rocks. The calculated subsurface temperatures in selected hydrocarbon fields vary in the range of 45–64 °C at 1 km depth, 99–136 °C at 3 km depth, and 155–208 °C at 5 km depth as a result of local variations of the surface heat flow and formation thermal resistances. These variations in subsurface temperatures can have significant effects on the cost of geothermal energy production in future.

Global ocean reanalysis CORA2 and its inter comparison with a set of other reanalysis products

We present the China Ocean ReAnalysis version 2 (CORA2) in this paper. We compare CORA2 with its predecessor, CORA1, and with other ocean reanalysis products created between 2004 and 2019 [GLORYS12v1 (Global Ocean reanalysis and Simulation), HYCOM (HYbrid Coordinate Ocean Model), GREP (Global ocean Reanalysis Ensemble Product), SODA3 (Simple Ocean Data Assimilation, version 3), and ECCO4 (Estimating the Circulation and Climate of the Ocean, version 4)], to demonstrate its improvements and reliability. In addition to providing tide and sea ice signals, the accuracy and eddy kinetic energy (EKE) of CORA2 are also improved owing to an enhanced resolution of 9 km and updated data assimilation scheme compared with CORA1. Error analysis shows that the root-mean-square error (RMSE) of CORA2 sea-surface temperature (SST) remains around 0.3°C, which is comparable to that of GREP and smaller than those of the other products studied. The subsurface temperature (salinity) RMSE of CORA2, at 0.87°C (0.15 psu), is comparable to that of SODA3, smaller than that of ECCO4, and larger than those of GLORYS12v1, HYCOM, and GREP. CORA2 and GLORYS12v1 can better represent sub-monthly-scale variations in subsurface temperature and salinity than the other products. Although the correlation coefficient of sea-level anomaly (SLA) in CORA2 does not exceed 0.8 in the whole region, as those of GREP and GLORYS12v1 do, it is more effective than ECCO4 and SODA3 in the Indian Ocean and Pacific Ocean. CORA2 can reproduce the variations in steric sea level and ocean heat content (OHC) on the multiple timescales as the other products. The linear trend of the steric sea level of CORA2 is closer to that of GREP than that of the other products, and the long-term warming trends of global OHC in the high-resolution CORA2 and GLORYS12v1 are greater than those in the low-resolution EN4 and GREP. Although CORA2 shows overall poorer performance in the Atlantic Ocean, it still achieves good results from 2009 onward. We plan to further improve CORA2 by assimilating the best available observation data using the incremental analysis update (IAU) procedure and improving the SLA assimilation method.

Simulation of spatiotemporal interannual variability of oceanic subsurface temperature off East Africa

The oceanic subsurface variability off East Africa in the tropical western Indian Ocean plays a crucial role in ocean dynamics and living resources as well as weather and climate variability. A regional ocean model is applied to understand the oceanic subsurface interannual variability off East Africa. The region with the highest sea surface temperature (SST) variability in the offshore region lies adjacent to strong subsurface temperature variations located between 30 and 130 m corresponding with strong variations in the thermocline depth. The weakest SST variations in the Tanzanian shelf waters lie over the subsurface waters with the smallest temperature variations in the upper 200 m with weak variations in the thermocline depth. Such signals are associated with induced forcings from the Indian Ocean Dipole (IOD) and El Niño-Southern Oscillation (ENSO) in both regions with different intensity and peaking times. The IOD-induced forcings are weaker, evolving in October and November-December in the region with the weakest and strongest SST variations, respectively. However, relatively stronger ENSO-induced forcings occur in both regions with stronger signals in the region with the strongest SST variations throughout the years except in August, and it peaks in January. The ENSO-induced forcings occur in January to May peaking in March and April in the region with the weakest SST. Consequently, anomalous Rossby waves as well as local Ekman downwelling and upwelling associated with both large-scale modes occur in the region leading to the subsurface temperature variations.

How temperatures derived from fluid flow and heat transport models impact predictions of deep geothermal potentials: the “heat in place” method applied to Hesse (Germany)

One key aspect in the energy transition is to use the deep geothermal energy stored in sedimentary basins as well as in igneous and metamorphic basement rocks. To estimate the variability of deep geothermal potentials across different geological domains as encountered in the Federal State of Hesse (Germany), it is necessary to understand the driving processes of fluid flow and heat transport affecting subsurface temperature variations. In this study, we quantify the stored energy in a set of geological units in the subsurface of Hesse with the method of “heat in place” (HIP, sensu Muffler and Cataldi in Geothermics 7:53–89, 1978)—HIP is one proxy for the geothermal potential of these units controlled by their temperature configuration as derived from a series of coupled 3D thermo-hydraulic numerical models. We show how conductive, advective and convective heat transport mechanisms influence the thermal field and thereby the HIP calculations. The heterogeneous geology of the subsurface of Hesse ranges from locally outcropping Paleozoic basement rocks to up to 3.8 km thick Cenozoic, porous sedimentary deposits in the tectonically active northern Upper Rhine Graben. The HIP was quantified for five sedimentary layers (Cenozoic, Muschelkalk, Buntsandstein, Zechstein, Rotliegend) as well as for the underlying basement. We present a set of maps allowing to identify geothermally prospective subregions of Hesse based on the laterally varying thermal energy stored within the units. HIP is predicted to be highest in the area of the northern Upper Rhine Graben in the Cenozoic unit with up to 700 GJ text {m}^{-2} and in the Rotliegend with up to 617 GJ text {m}^{-2}. The calculations account for the variable thicknesses and temperatures of the layers, density and heat capacity of the solid and fluid parts of the rocks as well as porosity.

Influence of Winter Subsurface on the Following Summer Variability in Northern California Current System

AbstractTemperature variations in the North and tropical Pacific contribute to the predictability of temperatures along the 26.4σ isopycnal layer off the Northern California Current System (N‐CCS). Monthly temperature variations at this depth in the N‐CCS are related to a linear combination of factors, including North Pacific spice anomalies, and the PDO and ENSO climate indices. However, the mechanisms for seasonal predictability of subsurface temperatures, are not well explored. While wind and buoyancy driven deep winter mixing influence subsurface temperatures during the following summer in the deep basin of the North Pacific, a coupled atmosphere‐ocean reanalysis (the CFSR) reveals that winter prior surface temperatures explain only 25% of the summer subsurface temperatures in the N‐CCS. A heat budget of the intermediate layer between a temporally varying mixed layer and the 26.4σ level is diagnosed here to explore the possible role of oceanic advection in explaining the remaining variance. Warmer waters from the south near the coast drive temperature changes in ENSO‐neutral winters, thereby preconditioning temperatures for the following summer. During ENSO winters, isopycnal variations associated with propagating coastal kelvin waves and other sources of heaving, along with anomalous alongshore currents, drive convergence/divergence of the advective fluxes, thereby reducing the local memory of the winter subsurface temperatures. Variations in winter advection could account for almost 36% of the summer subsurface temperature variability in the N‐CCS; this exceeds the portion explained by the heat fluxes associated with deep winter mixing.

A thermal origin for super-high-frequency marsquakes

Of the marsquakes detected, super-high-frequency marsquakes are dominant (>60%) in number. However, their occurrence mechanism remains unclear. One possibility is local heat-induced ground motion. We model heat conduction under InSight based on measured subsurface thermal parameters and air temperature records, which provide insights into heat flow in the shallow Martian subsurface. Diurnal and seasonal variations of subsurface temperature and their rates of temperature change are analyzed. Diurnal temperature variations >1 K only occur within 25 cm of the surface. The highest rate of temperature change appears around sol 440 (in summer), which coincides closely with the season of the dominant number of super-high-frequency marsquakes observed. Thermal-mechanical finite-element simulations indicate that heat-induced ground motion is evidently stronger in the daytime than at night. These results indicate that super-high-frequency marsquakes are most likely induced by thermal stress in shallow rocks on the surface or partially buried within 10 cm depth.

City-wide monitoring and contributing factors to shallow subsurface temperature variability in Nanjing, China

Shallow temperatures down to a depth of 100 m were measured over one year in 19 closed boreholes located in Nanjing, China, to reveal the conditions and factors influencing the subsurface thermal regime. A monitoring concept with distributed temperature sensing, fiber Bragg grating-based sensor, and a type of Resistance Temperature Detectors, is implemented, providing spatial distribution characteristics of subsurface temperatures. The results show that temperatures near the surface are most dynamic, influenced by the air temperature. The temperature remains stable at the depth of 10–20 m. The mean transition temperature is 18.1 °C. Borehole measurements are interpolated by using satellite images and surface temperature records to obtain large-scale surface temperature distributions and temporal variations of subsurface temperature. Geological and hydrological conditions are primary factors by affecting subsurface upward heat flux and heat loss. Urban land cover change and enhanced heat release from urbanization contribute to a subsurface urban heat island with intensities of 1.0–4.4 °C. The altered subsurface thermal regime is of primary concern for the management of shallow geothermal energy use. The monitoring concept in this study can provide spatially-temporally continuous profiles of subsurface temperature and become a reference for city-wide geothermal monitoring in other urban areas.

Weakening of the Atlantic Niño variability under global warming

The Atlantic Niño is one of the most important patterns of interannual tropical climate variability, but how climate change will influence this pattern is not well known due to large climate model biases. Here we show that state-of-the-art climate models robustly predict a weakening of Atlantic Niños in response to global warming, mainly due to a decoupling of subsurface and surface temperature variations as the upper equatorial Atlantic Ocean warms. This weakening is predicted by most (>80%) models in the Coupled Model Intercomparison Project Phases 5 and 6 under the highest emission scenarios. Our results indicate a reduction in variability by the end of the century by 14%, and as much as 24–48% when accounting for model errors using a simple emergent constraint analysis. Such a weakening of Atlantic Niño variability will potentially impact climate conditions and the skill of seasonal predictions in many regions.

A 15-million-year surface- and subsurface-integrated TEX86 temperature record from the eastern equatorial Atlantic

Abstract. TEX86 is a paleothermometer based on Thaumarcheotal glycerol dialkyl glycerol tetraether (GDGT) lipids and is one of the most frequently used proxies for sea-surface temperature (SST) in warmer-than-present climates. However, GDGTs are not exclusively produced in and exported from the mixed layer, so sedimentary GDGTs may contain a depth-integrated signal that is also sensitive to local subsurface temperature variability. In addition, the correlation between TEX86 and SST is not significantly stronger than that to depth-integrated mixed-layer to subsurface temperatures. The calibration of TEX86 to SST is therefore controversial. Here we assess the influence of subsurface temperature variability on TEX86 using a downcore approach. We present a 15 Myr TEX86 record from Ocean Drilling Program Site 959 in the Gulf of Guinea and use additional proxies to elucidate the source of the recorded TEX86 variability. Relatively high GDGT[2/3] ratio values from 13.6 Ma indicate that sedimentary GDGTs were partly sourced from deeper (&gt;200 m) waters. Moreover, late Pliocene TEX86 variability is highly sensitive to glacial–interglacial cyclicity, as is also recorded by benthic δ18O, while the variability within dinoflagellate assemblages and surface/thermocline temperature records (U37k′ and Mg/Ca) is not primarily explained by glacial–interglacial cyclicity. Combined, these observations are best explained by TEX86 sensitivity to sub-thermocline temperature variability. We conclude that TEX86 represents a depth-integrated signal that incorporates a SST and a deeper component, which is compatible with the present-day depth distribution of Thaumarchaeota and with the GDGT[2/3] distribution in core tops. The depth-integrated TEX86 record can potentially be used to infer SST variability, because subsurface temperature variability is generally tightly linked to SST variability. Using a subsurface calibration with peak calibration weight between 100 and 350 m, we estimate that east equatorial Atlantic SST cooled by ∼5 ∘C between the Late Miocene and Pleistocene. On shorter timescales, we use the TEX86 record as a proxy for South Atlantic Central Water (SACW), which originates from surface waters in the South Atlantic Gyre and mixes at depth with Antarctic Intermediate Water (AAIW). Leads and lags around the Pliocene M2 glacial (∼3.3 Ma) in our record, combined with published information, suggest that the M2 glacial was marked by SACW cooling during an austral summer insolation minimum and that decreasing CO2 levels were a feedback, not the initiator, of glacial expansion.

Mechanisms of asymmetry in sea surface temperature anomalies associated with the Indian Ocean Dipole revealed by closed heat budget

The Indian Ocean Dipole (IOD) is an interannual climate mode of the tropical Indian Ocean. Although it is known that negative sea surface temperature (SST) anomalies in the eastern pole during the positive IOD are stronger than positive SST anomalies during the negative IOD, no consensus has been reached on the relative importance of various mechanisms that contribute to this asymmetry. Based on a closed mixed layer heat budget analysis using a regional ocean model, here we show for the first time that the vertical mixing plays an important role in causing such asymmetry in SST anomalies in addition to the contributions from the nonlinear advection and the thermocline feedback proposed by previous studies. A decomposition of the vertical mixing term indicates that nonlinearity in the anomalous vertical temperature gradient associated with subsurface temperature anomalies and anomalous vertical mixing coefficients is the main driver of such asymmetry. Such variations in subsurface temperature are induced by the anomalous southeasterly trade winds along the Indonesian coast that modulate the thermocline depth through coastal upwelling/downwelling. Thus, the thermocline feedback contributes to the SST asymmetry not through the vertical advection as previously suggested, but via the vertical mixing.

Precession cycles of the El Ni\xf1o/Southern oscillation-like system controlled by Pacific upper-ocean stratification

Modern observations have presented linkages between subsurface waters of the western Pacific warm pool and both El Niño/Southern Oscillation-related and extratropic-controlled upper-ocean stratification on interannual timescales. Moreover, studies have showed that such controls may operate on orbital cycles, although the details remain unclear. Here we present paired temperature and salinity reconstructions for the surface and thermocline waters in the central western Pacific warm pool over the past 360,000 years, as well as transit modeling results from an Earth system model. Our results show that variations in subsurface temperature and salinity in the western Pacific warm pool have consistently correlated with the shallow meridional overturning cell over the past four glacial-interglacial cycles, and they vary on eccentricity and precession cycles. The shallow meridional overturning cell regulates subsurface waters of the western Pacific warm pool by changing subtropical surface water density and thus equatorial upper-ocean stratification, acting as an El Niño/Southern Oscillation-like process in the precession band. Therefore, the western Pacific warm pool is critical in connecting the austral shallow meridional overturning cell to the Earth’s climate system on orbital timescales.

Reply to discussion on ‘Borehole temperature log from the Glasgow Geothermal Energy Research Field Site: a record of past changes to ground surface temperature caused by urban development’ by Watson and Westaway 2020 ( SJG , 56, 134–152)

Watson and Westaway (2020) (WW) quantified subsurface temperature variations caused by anthropogenic climate change and urban/industrial development in Glasgow, using temperature data from the Glasgow Geothermal Energy Research Field Site (GGERFS) well GGC-01 (at site G-10; Fig. 1), noting implications for the thermal physics of this site. Monaghan, Manning and Shipton (2021) (MMS) have queried points, noted in passing by WW, on other aspects: the GGERFS purpose, location, design, heat resource, and cost.

Regime shift in the decadal variability of the Indian Ocean subsurface temperature

The decadal variability in the subsurface temperature of the tropical Indian Ocean shows a strong seasonality and features a prominent east–west dipole structure. The seasonal characteristics of the decadal variability shows a semiannual cycle in the rapid warming period of the twentieth century and then shift to an annual cycle during the recent hiatus period. The semiannual cycle is in phase with the climatological seasonal cycle, and therefore strengthens the climatological seasonal variations. Whereas during the recent hiatus period, the annual cycle shows a negative (positive) Indian Ocean Dipole pattern in the first (second) half of the year. Such regime shift in the decadal variability of subsurface temperature is strongly correlated with that of the surface wind in the tropical Indian Ocean, especially the equatorial zonal wind. Our result suggests that an abrupt weakening in both summer and winter Indian monsoon at the beginning of this century is the major cause of the regime shift in decadal variability of surface winds. • Decadal variability in Indian Ocean subsurface temperature shows strong seasonality. • The decadal variability features a prominent east–west dipole structure. • The decadal variability experienced an abrupt regime shift around 2000. • Such regime shift is correlated with surface wind, especially equatorial zonal wind. • The regime shift in local wind is related to an abrupt weakening in Indian monsoon.

A Linear Inverse Model of Tropical and South Pacific Climate Variability: Optimal Structure and Stochastic Forcing

AbstractA stochastically forced linear inverse model (LIM) of the combined modes of variability from the tropical and South Pacific Oceans is used to investigate the linear growth of optimal initial perturbations and to identify the spatiotemporal features of the stochastic forcing associated with the atmospheric Pacific–South American patterns 1 and 2 (PSA1 and PSA2). Optimal initial perturbations are shown to project onto El Niño–Southern Oscillation (ENSO) and South Pacific decadal oscillation (SPDO), where the inclusion of subsurface South Pacific Ocean temperature variability significantly increases the multiyear linear predictability of the deterministic system. We show that the optimal extratropical sea surface temperature (SST) precursor is associated with the South Pacific meridional mode, which takes from 7 to 9 months to linearly evolve into the final ENSO and SPDO peaks in both the observations and as simulated in an atmosphere-forced ocean model. The optimal subsurface precursor resembles its peak phase, but with a weak amplitude, representing oceanic Rossby waves in the extratropical South Pacific. The stochastic forcing is estimated as the residual by removing the deterministic dynamics from the actual tendency under a centered difference approximation. The resulting stochastic forcing time series satisfies the Gaussian white noise assumption of the LIM. We show that the PSA-like variability is strongly associated with stochastic SST forcing in the tropical and South Pacific Oceans and contributes not only to excite the optimal initial perturbations associated with ENSO and the SPDO but in general to activate the entire stochastic SST forcing, especially in austral summer.

A Concise and Effective Expression Relating Subsurface Temperature to the Thermocline in the Equatorial Pacific

AbstractThe temperature of the subsurface water entrained into the surface mixed layer plays a key role in controlling the sea surface temperature (SST) and its interannual variability in the equatorial Pacific. In this paper, we combine a hyperbolic tangent function bounded by the warm pool SST and centered at the thermocline depth with a variable sharpness parameter to describe the time‐space evolutions of the subsurface temperature. Under simple approximations of the sharpness parameter, this concise expression becomes remarkably efficient in capturing the observed and climate‐model simulated subsurface temperature variability in terms of anomalies of the thermocline depth and SST of the El Niño‐Southern Oscillation (ENSO) phenomenon. The formulations for the subsurface temperature and thermocline sharpness developed in this work should be useful tools for evaluating and understanding the role of the thermocline feedback in ENSO behaviors in both theoretical and comprehensive climate models.