The Role of Wet Processes in Extratropical Thermal Stratification During the Glacial Period

In this study, we differentiate wet processes from dry processes in shaping the extratropical thermal stratification during the Last Glacial Maximum. Our findings indicate that even during the dry glacial period the influence of wet processes on thermal stratification cannot be overlooked. The applicability of dry and wet baroclinic adjustment theory strongly depends on the seasonality rather than the glaciation as the warm season is characterized by a weaker meridional temperature gradient and increased precipitation than the cold season. Despite that the baroclinic adjustment theory based on effective static stability can be proficiently applied to all seasons, the classical dry baroclinic adjustment theory may be better suited for use during relatively cold seasons. These findings have important implications for understanding processes governing the extratropical thermal stratification, particularly in the context of cold climate.

• The study differentiates wet process from dry process in shaping extratropical thermal stratification during the Last Glacial Maximum • Even during the dry glacial period, wet processes still poses a significant influence on thermal stratification • Seasonality governs dry and wet baroclinic adjustment theory applicability, with the dry theory being more suited for cold seasons

Supporting Information:
Supporting Information may be found in the online version of this article.
model (GCM), Frierson (2006) demonstrated that latent heat release from the wet process dominates the increase in extratropical static stability in the global warming scenario, supporting the warming side of the conclusion from Schneider et al. (2010) and highlighting the presence of latent heat release in the midlatitudes under drier conditions.However, there is limited research addressing application of Schneider et al. (2010)'s conclusions in a glacial period.
Indeed, the Last Glacial Maximum (LGM) provides a great opportunity to investigate the applicability of these theories in cold climate.The LGM, occurring approximately 21,000 years ago, was characterized by a cold and arid climate, as well as extensive Northern Hemisphere (NH) ice sheets on midlatitude (Kageyama et al., 2017).
Given the critical role of thermal stratification in shaping key aspects of extratropical general circulation during the LGM (Rivière et al., 2018;N. Wang et al., 2018aN. Wang et al., , 2018b)), it becomes imperative to unravel the dominant processes governing extratropical thermal stratification during this period.Although studies based on proxy data offer insights into LGM thermal stratification (Banerjee et al., 2022;Loomis et al., 2017), the contribution of the wet process remains unclear.Hence, this study aims to fill this gap by quantifying the contributions of both wet and dry processes to thermal stratification in various glacial states and seasons.
The rest of this paper is structured as follows.In Section 2, we describe the data and methodology employed in our study, including a detailed overview of the data sources (Section 2.1) and explanation of the baroclinic adjustment theory (Section 2.2).Section 3 presents our results, namely, the analysis of the applicability of dry and wet baroclinic adjustment theory, impact of seasonality and glaciation on thermal stratification, and role of wet processes.Finally, in Section 4, we offer a comprehensive conclusion and discussion, emphasizing the implications of our findings in understanding the extratropical thermal stratification, particularly in the context of a cold climate.

Data
The data set employed in this research is sourced from the Paleoclimate Modeling Intercomparison Project Phase III and Phase IV (Braconnot et al., 2011;Kageyama et al., 2021;T. Wang et al., 2023, PMIP3/PMIP4) LGM experiment and Pre-industrial (PI) control run.A total of nine models from PMIP3 and five models from PMIP4 were included in our investigation.While climatology results from PMIP3 models were directly used, we obtained the climatology mean state from PMIP4 by averaging the last 100 years of simulations.Detailed information regarding the PMIP3/PMIP4 data set is available at https://pmip3.lsce.ipsl.fr/and https://pmip4.lsce.ipsl.fr/.The following results from both PMIP3 and PMIP4 simulations exhibit no significant difference, allowing for the combination of all data in the subsequent analysis.For detailed PMIP data information in this study, please refer to Table S1 in Supporting Information S1.
Before computing the ensemble mean, we employed linear interpolation to ensure uniform resolution for all data.
For efficient processing and a focus on large-scale signals, a horizontal resolution of COSMOS-ASO with dimensions of 3.75° × 3.75° were utilized.The vertical dimension consisted of 17 levels.The multimodel ensemble mean was obtained using arithmetic averaging.
For zonal mean, all missing data were disregarded.To compare vertical averages between the LGM and PI simulations, we calculated the vertical average for each simulation individually to account for different topography effects.During the LGM, strong surface cooling in the wintertime led to temperature inversions within the polar boundary layer, resulting in a higher static stability at the surface layer compared to other levels (Schneider, 2004b;Schneider & O'Gorman, 2008).To reflect the main stability properties of the troposphere, vertical averaging was performed from the top of the boundary layer (defined as 0.84 times surface pressure, following Schneider and O'Gorman (2008)) rather than at the surface level.

Baroclinic Adjustment Theory
In this study, we compared dry and wet baroclinic adjustment theory in context of the LGM and PI to evaluate the relative importance of wet processes in different climatology.The dry bulk static stability from pressure level p b to p t can be defined as: 10.1029/2023GL106400 3 of 9 where Δ d and θ are the dry bulk static stability and potential temperature, respectively.

Dry Theory
According to Schneider and Walker (2006), Δ d can be estimated by the expression: where f, β, θ mid , S c are Coriolis coefficient, meridional gradient of Coriolis coefficient, potential temperature at mid-level and supercriticity coefficient.

Wet Theory
Based on O'Gorman (2011), we can obtain a similar form of equation like Equation 2 but in terms of effective static stability: where λ and S eff represent the precipitation coefficient (0.6) and the supercriticity coefficient for effective static stability, respectively.The term Δ m is the integral of potential temperature vertical gradient over pressure between two levels along a moist adiabatic process.The term λΔ m in Equation 3 adjusts the estimate of Δ d in Equation 2for biases due to extra latent heat release from precipitation.Please refer to the Data Availability Statement section for the code of effective static stability.
In this study, we set S c as 1.3 for dry theory and S eff as 1.6 for wet theory to give best fit for annual mean simulated dry bulk static stability during PI and corresponding theoretical prediction.And following Frierson (2006), the potential temperature gradient at 500 hPa is used instead of the surface potential temperature in both theories.et al. (2023) demonstrates that during the LGM, in contrast to PI, there is a reduction in dry static stability in the tropics, attributed to decreased moist convection, while dry static stability increases in the high-latitude ocean and ice sheet margins due to surface cooling.Unlike the tropics and high latitudes, the mid-latitudes only exhibit slight decrease in both DJF and JJA in the zonal mean (see Supporting Information S1 for details).Our subsequent discussion will emphasize the role of the wet process in those seasons.

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Figure 1 shows a comparison of predicted bulk dry static stability between the dry and wet versions of the baroclinic adjustment theory in December-January-February (DJF), March-April-May (MAM), June-July-August (JJA), and September-October-November (SON) during the LGM and PI periods for both the LGM and PI periods.For the dry theory (Figures 1a and 1b), the dots in DJF, MAM, and SON are mainly concentrated near the 45° division line, indicating a small discrepancy between theory and simulation.However, the dry bulk static stability predicted by dry theory is lower than what we observed in the simulation in JJA, which makes the dots in JJA outliers for the linear fit during both the LGM and PI.Interestingly, the dry bulk static stability prediction from the dry theory exhibits lower root mean square error and higher correlation coefficients for the LGM than the results from PI, even though we use PI data to obtain the best fit for supercriticity.This finding suggests that during the cold and dry glacial period, the LGM climate is more dominated by the dry processes.
Figures 1c and 1d demonstrates the superior performance of the wet baroclinic adjustment theory during both the LGM and PI periods, with the wet theory outperforming the dry theory in simulating the extratropical thermal stratification, even during the LGM.This improvement is mainly attributed to the inclusion of the latent heat release in the wet theory.The latent heat release tends to warm up the upper-level troposphere while cooling down the lower level, resulting in a positive contribution to the dry bulk static stability.Consequently, in the wet theory, the effect of latent heat release is isolated as an independent term and added to the dry bulk static stability estimates (Equation 3), leading to higher dry bulk static stability estimates, particularly during the warm season, which rectifies the underestimation in the dry theory (Figures 1a and 1b).As a result, Figures 1c and 1d exhibits an absence of JJA outliers in the dry theory, suggesting a substantial contribution from the wet process to the dry bulk static stability during the summer season.This underscores the critical role of seasonality in determining the relative impact of dry and wet processes on the extratropical thermal stratification.
Given that the wet baroclinic adjustment theory agrees well with simulated dry bulk static stability, we can quantify the contributions of wet and dry processes to dry bulk static stability by analyzing the right-hand side term of Equation 3. Figure 2 presents the contributions of dry and wet processes for dry bulk static stability during the LGM and PI in different seasons.Overall, during the LGM, there is a reduced potential temperature difference between two levels compared to PI, suggesting less stable stratification.This is consistent with the zonal mean results in Figure S1 in Supporting Information S1, especially for JJA.In all seasons, the dominant process is dry baroclinic adjustment, accounting for more than 50% of the total in each season.The contribution from the wet process is less than 30% for all seasons except JJA.However, in JJA during both the LGM and PI, the contribution from the dry process decreases while the wet process increases.Consequently, the share of the wet process accounts for one-third during the LGM and almost half during the PI, indicating a strong impact from the wet process in JJA, regardless of the LGM or PI.
We attribute this seasonal difference in dry and wet processes to changes in precipitation and large-scale MTGs, represented by zonal median precipitation and zonal mean 500 hPa meridional temperature difference (referenced to 20°N), respectively (Figure 3).Here, we utilize zonal median precipita tion instead of zonal mean to mitigate the influence of extreme precipitation values in the average (refer to Supporting Information S1 for details).
In NH, precipitation in JJA and SON is heavier than other seasons at 50°N and polewards, mainly due to the relatively warm land in mid-latitudes that can hold more moisture, thereby enhancing the importance of wet processes in these two seasons.On the other hand, the temperature meridional slope in JJA is notably flatter compared to the other seasons, indicating weaker MTGs (Figures 3c and 3d).As a result, in NH summer, with stronger precipitation and weaker MTGs, wet processes make a more significant contribution to extratropical thermal stratification, during both LGM and PI periods.Therefore, the combined effect of wet and dry processes determines the extratropical thermal stratification, and in NH summer, the contribution of wet processes reaches its maximum due to the relatively warm climate.
To gain a deeper insight into why the wet process remains significant during the LGM, despite the climate being colder and drier than the present day, we will examine the influence of seasonality and glaciation on the climatological mean state.Furthermore, our analysis indicates that, during the LGM, the changes in the climatological mean state are more pronounced due to seasonality rather than glaciation.To clarify this, we define temperature change due to seasonality as the temperature difference between JJA and DJF, and temperature change due to glaciation as the annual mean temperature difference between the PI and LGM. Figure 4a shows a comparison of surface temperature climatology change resulting from seasonality and glaciation.At the surface, the temperature change due to seasonality increases from less than 5 K at the equator to more than 30 K at the North Pole during the LGM.The pattern of temperature change due to seasonality of PI is similar to that of the LGM but with lower maximum values at the polar region.In comparison, the temperature change due to glaciation also warms up polewards but with a much less magnitude, reaching 15 K North Poles.Consequently, in the NH extratropics, the temperature change due to seasonality is much greater than that due to glaciation, namely, the seasonality-associated temperature change is nearly twice of the glaciation-associated temperature change.At middle levels (500 hPa, Figure 4b), although the temperature gap between the two types of climatology change becomes smaller, we can still see the dominant role of temperature change due to seasonality.In particular, in the NH extratropics, the seasonality-associated temperature difference is nearly triple of glaciation-associated temperature difference.These analyses suggest that even during the LGM, the climate mean state of warm season in extratropics is still relatively warm.A comparison between the climatology of warm season during the LGM and cold season during PI better illustrates this feature (Figure 4c).Excluding North America and North Europe, which were covered by large ice sheets, most of the land area in the NH was warmer during LGM JJA than PI DJF.As a result, in the NH extratropics during the LGM, the relatively warm climate state in JJA can support more precipitation, and thus the wet process still plays a critical role in thermal stratification.

Conclusion and Discussion
In this study, the role of wet process in extratropical thermal stratification during the LGM is explored.The comparison of wet and dry versions of baroclinic adjustment theory shows that wet processes are important in regulating extratropical thermal stratification even during glacial periods, especially during warm seasons.During all seasons, except NH summer, the dominant process is dry baroclinic adjustment in NH extratropics, accounting for more than 50% of the bulk dry static stability, while the contribution of the wet process is less than 30%.However, in NH summer, owing to the increasing precipitation and decreasing large-scale MTGs, the contribution from the wet process increases in both the LGM and PI, suggesting a strong impact from the wet process upon extratropical thermal stratification during NH summer, regardless of the glaciation.Our findings suggest that during the LGM, the climatology mean state change is more affected by seasonality than glaciation.
A similar mechanism to ours was discussed by O'Gorman (2011), where they showed that as the climate becomes warmer, the extratropical thermal stratification becomes more latent heat release-controlled due to the decreasing MTGs.However, their discussion is based on an idealized GCM simulation without seasonality.In contrast, our study clearly demonstrates the seasonal dependence of the extratropical thermal stratification during the LGM, which is a cold and dry glacial period.Specifically, we show that even during the LGM, the moist process must be considered during the summer in the NH.Frierson and Davis (2011) also examined the seasonal cycle of static stability in observations, with a primary emphasis on the land-sea contrast.In contrast, our main focus lies on understanding the role of moist processes.
Proxy data is essential for comprehending the thermal stratification change during the LGM.Loomis et al. (2017) analyzed proxy data from East Africa's mountainous region, indicating a steeper lapse rate change between the LGM and the modern profile than simulated by models, partly attributed to inadequate representation of condensation processes.Recent studies on Rwenzori Mountain Glaciers confirmed this steeper lapse rate change in the tropics (Doughty et al., 2023).Another work by Banerjee et al. (2022) estimated a global lapse rate of 6.2-7.1°C/kmduring the LGM, slightly deviating from the PI value of 6.5°C, providing a constraint for extratropical static stability.Although the aforementioned studies provide valuable insights, they do not directly offer proxy data for extratropical static stability change.The scarcity of reported proxy data, especially in the extratropics, emphasizes the need for increased interdisciplinary collaboration in future research endeavors in this area.
Figure 3. Zonal median precipitation (upper panel; units: mm day −1 ) and zonal mean 500 hPa temperature referenced to 20°N (lower panel; units: K) in various seasons during the Last Glacial Maximum (left) and pre-industrial (right) periods.The green, red, yellow, and black lines represent March-April-May, June-July-August, September-October-November, and December-January-February, respectively.

Data Availability Statement
The data utilized in this study, including PMIP3 and PMIP4, can be accessed from the Earth System Grid Federation (ESGF) website for the Coupled Model Intercomparison Project 5 (CMIP5) and Project 6 (CMIP6) at https://esgf-node.llnl.gov/projects/cmip5/and https://esgf-node.llnl.gov/projects/cmip6/,respectively.The lgm and piControl experiments are utilized for analysis.Specifically, the model output can be referenced as follows: CCSM4:  ) and the surface temperature difference (units: K) between Last Glacial Maximum (LGM) June-July-August (JJA) and pre-industrial (PI) December-January-February (DJF) (c).The zonal mean temperature change due to seasonality is defined as the temperature difference between JJA and DJF during the LGM (solid line) and PI (dash line).The zonal mean temperature change due to glaciation is defined as the annual mean temperature difference between the PI and LGM.

Figure 1 .
Figure1.Dry bulk static stability and stability estimates based on dry and wet baroclinic adjustment theory at 50°N during the Last Glacial Maximum (LGM) and pre-industrial (PI).Upper panel shows dry theory, while lower panel shows wet theory.Left and right panels correspond to LGM and PI, respectively.Legends indicate correlation coefficient (r), slope (s), and root mean square error (RMSE).The green, red, yellow, and black dots represent the model results in March-April-May, June-July-August, September-October-November, and December-January-February, respectively.

Figure 2 .
Figure2.Dry bulk stability contribution from dry (baroclinic adjustment, green bar) and wet (precipitation, orange bar) processes in March-April-May, June-July-August, September-October-November, and December-January-February during the Last Glacial Maximum and pre-industrial.The percentage in the bracket along the x-axis shows the share of wet process contribution to the total dry bulk stability.

Figure 4 .
Figure 4.The zonal mean temperature change (units: K) due to seasonality and glaciation (a, b) and the surface temperature difference (units: K) between Last Glacial Maximum (LGM) June-July-August (JJA) and pre-industrial (PI) December-January-February (DJF) (c).The zonal mean temperature change due to seasonality is defined as the temperature difference between JJA and DJF during the LGM (solid line) and PI (dash line).The zonal mean temperature change due to glaciation is defined as the annual mean temperature difference between the PI and LGM.