Assessing Latent and Kinetic Energy Trend Changes in Extratropical Cyclones From 1940 to 2020: Results From ERA‐5 Reanalysis

Baroclinic or extratropical cyclones (ETCs) transport heat and moisture to higher latitudes, making it fundamentally important to understand how their influence changes as Earth's climate evolves. A 2–8‐day Lanzcos bandpass filter is applied to European Center for Medium Range Weather Forecasting 5th Generation Reanalysis latent energy (LE) and kinetic energy (KE) data to assess how ETCs have changed from 1940 to 2020 relative to full‐scale changes in LE and KE. Full‐scale KE trends are more positive at high latitudes relative to mid‐latitudes, confirming several previous studies that ETCs have shifted poleward. LE increases have occurred globally, and trends in both full‐scale LE and KE are statistically significant in the southern high latitudes. The high relative fractional contribution of 2–8‐day LE wave power and trend clearly suggest that ETCs have an increasingly important role in poleward moisture transport but are not solely responsible for the observed statistically significant increases.

roles of moist and dry dynamical processes in wave activity amplification and decay.For ETCs, however, the role of moisture has additional complexities since increased moisture in ETCs may decrease eddy kinetic energy (Catto et al., 2019).Several modeling studies have discussed the sensitivity between ETCs and initial temperature/moisture fields (Grise et al., 2019;Krishbaum et al., 2018), which has contributed to some contradiction in models either under-or over-estimating forced changes to mean and extreme precipitation (de Vries et al., 2023).Existing literature clearly highlights the importance and effects of increasing moisture on baroclinic eddies and ETCs, but numerous uncertainties remain in how their evolving energetics will manifest as changes to important climate system components such as the Hadley Circulation and the stratification of the extratropical troposphere (O'Gorman, 2011) or the El Nino Southern Oscillation (Machado et al., 2021).Furthermore, to the authors' knowledge, no multi-decade analysis quantifying regional changes in moisture specifically to baroclinic eddies and ETCs has been done.
Understanding how increasing moisture in baroclinic eddies and ETCs has evolved in recent decades can offer important clues toward how ETCs might respond to further climate warming, and subsequent effects on poleward heat and moisture transport.The magnitude of both cold and warm temperature anomalies is expected to increase (Tamarin-Brodsky et al., 2020).In the Arctic, some of the prior variance in temperature anomalies is potentially explained by expansion in the amplitude of the climatological ridge over northern Europe, which implies stronger poleward heat and moisture transport (Monahan et al., 2000) and subsequently increased precipitation (Field & Wood, 2007).The North Atlantic Oscillation (NAO) also explains variability in the polar Northern Hemisphere, though the NAO alone (or trends following the NAO) cannot solely be linked to climatological changes in poleward heat and moisture transport (Hurrell & Deser, 2010).Whether or not changes to atmospheric circulation patterns are driven by anthropogenic activity, Corti et al. (1999) showed that changes to the thermodynamic structure of mid-and high-latitude circulation patterns are responsible for warming in the northern hemisphere.Given the role midlatitude cyclones play in transporting heat and moisture poleward from the tropics to the polar regions, and the disproportionate amount of heating in the northern hemisphere over the last century (Kang et al., 2015), it is natural to ask how properties of midlatitude cyclones have changed over the last century.This work aims to answer a few basic questions about changes in midlatitude cyclones and decadal changes to kinetic and latent energy using the European Center for Medium-Range Weather Forecasting 5th Generation Reanalysis (ERA-5) data set (Hersbach et al., 2020).It is hypothesized that the warming over the last century has enabled midlatitude cyclones to carry increased amounts of latent energy (water vapor) poleward.ERA5 reanalysis data is examined to address two questions related to this hypothesis: 1. Given the general increase in global temperature, are ETCs carrying more moisture (latent energy) poleward now compared to previous decades?2. Are changes associated with ETC LE and KE statistically significant over the last 80 years?

ERA-5 Data Set
The ERA-5 data set was used as the basis for identifying cyclones and characterizing their energetics.Hereafter, "cyclones" or "ETCs" imply any synoptic-scale process taking place over 2-8 days, though we note that other processes such as propagating Rossby waves and mesoscale convective systems frequently occur over these time scales and will manifest in 2-8 days results.Data are available for every 3 hr and a 0.25° × 0.25° spatially, however, due to the size and longevity of ETCs, 2° × 2° spatial coverage and 6-hourly data were used for this study.Column-integrated dry static energy (DSE), moist static energy (MSE), and kinetic energy (KE), as well as mean sea-level pressure (MSLP) are included in this analysis.The next sub-section describes DSE, MSE, and KE in more detail, and includes information on how latent energy (LE) is derived from DSE and MSE.
Previous studies have used reanalysis data sets for the purpose of evaluating long-term trends in ETC LE and KE content.O'Gorman (2011) used National Center for Environmental Prediction 2nd generation (NCEP-2; Kanamitsu et al., 2002) data from 1992 to 2001 to evaluate zonal and time averaged changes to effective static stability in ETCs, showing how incorporating moisture to static stability can improve ETC evolution and effects to the extra tropical troposphere in a global climate model.Lim and Simmonds (2007) evaluated southern hemispheric ETCs from 1979 to 2001 using ERA-Interim (ERA-5's predecessor) to find that ETCs became more numerous, stronger and faster moving but decreased in spatial scale.Trenberth and Smith (2008) evaluated 10.1029/2023GL105207 3 of 11 multiple reanalysis products and found that all of them accurately captured short-term, synoptic-scale atmospheric properties very well.Results from these studies are extended by presenting a multi-decadal reanalysis-based study of ETC energetics spanning eight decades from 1940 to 2020.

Energetics of Midlatitude Cyclones
To simplify the analysis of this large data set, total climate energy is considered.The moist static energy (MSE) of the climate system is simplified as (Back & Bretherton, 2006;Inoue & Back, 2015;Wing et al., 2019): where c p is the specific heat of dry air at constant pressure, T is the temperature, g is the gravitational constant, z is the height above ground level, L v is the latent heat of vapourization, and q is the water vapor mixing ratio of the air.Combined, c p + gz is DSE, and L v q the latent energy (LE) of system.E is therefore representative of MSE.LE is derived from Equation 1 by subtracting DSE: Kinetic energy (KE) is a very important part of the climate system but is several orders of magnitude smaller than DSE or MSE.Furthermore, typically, Equation 1does not include KE because KE is assumed to be dissipated by heat.To explicitly account for KE in this study, Equation 1 is rewritten as: where ρ is the density of the air and v the speed of the air parcel.In the ERA-5 data set, DSE, MSE, LE, and KE are all column-integrated quantities and unless otherwise stated have units of J/m 2 .Figure 1 illustrates an example of global LE and KE for a given point in time.Throughout the year, the highest LE is concentrated in the tropics.ETCs aid in the transport of this LE poleward and denoted by values of 9-15 × 10 7 J/m 2 appearing as "plumes" moving poleward and occurring downstream of regions of low MSLP (Mecikalski & Tripoli, 1998).These plumes of high LE reaching poleward are also associated with regions of high KE (values greater than 8.0 × 10 6 J/m 2 ), whereby these large values are exclusive to latitudes poleward of 30°.
To isolate the contribution of midlatitude cyclones to global energy trends over the last century, a 2-8-day Lanczos bandpass filter is constructed with a window size of 120 (i.e., 30 days) and applied to all 80-year KE and LE time series in the ERA-5 data set.A key assumption of this work is that variability in LE and KE explained by ETCs is represented by changes in 2-8-day periods.In previous studies 2-8-day and 2-10-day periods for filtering midlatitude cyclones and baroclinic eddies was frequently used, with the choice of 8 or 10 days as an upper limit exhibiting little influence on the results (e.g., Blackmon & White, 1982;Wu et al., 2011).Increasing the range from 2-8 days to 2-10 days, for example, would increase the magnitude of the LE and KE slopes from ETCs since the Lanczos filter would include a wider range of data in the final computation.Finally, to contextualize the role of LE and KE from 2-8-day ETCs against LE and KE from all time scales, all results are presented in terms of (a) overall global (full-scale) trend and (b) trend from 2-8-day cyclones.

Statistical Significance Testing and Trend Analysis
The statistical significance of trends in LE and KE over the last 80 years are established by comparing against their variance.The variance in LE and KE across the 80-year time series varies latitudinally and is known to be much higher at the mid-and high-latitudes compared to the tropics.To detect a trend at each grid point, the "time to emergence" (TTE hereafter; Weatherhead et al., 1998;Hawkins & Sutton, 2012;Sledd & L'Ecuyer, 2021) the trend in each grid point is compared to the "noise" for statistical significance.The noise is computed using 5 of 11 variance and 1-lag autocorrelation calculated from detrended time series of KE and LE similar to Sledd and L'Ecuyer (2021), assumes every time series follow a linear trend, and statistics computed from the noise of these data are only valid for the aforementioned 80-year time period.Since both LE and KE are insensitive to diurnal cycles and given that the data have a time resolution of 6 hr, the autocorrelation for both variables is almost always positive given both variables rise and fall with longer-term trends (i.e., weekly to monthly time scales).Following Weatherhead et al. (1998) the number of years of data at each grid point required to find a statistically significant signal (with 90% confidence) can be found following where n* is the number of years (i.e., the TTE), σ N is the standard deviation, ω 0 is the magnitude of the slope, and ϕ is the autocorrelation.This method has the advantage of accounting for variance and autocorrelation when considering if a trend at a specific location is significant, especially considering LE and KE vary with latitude.
Given that LE and KE slopes are computed at each grid point for an 80-year period, a time-to-emergence of less than 80 years indicates that the slope at each grid point is statistically significant.Put another way, the slope at each grid point is statistically significant if ω 0 is much larger than σ N .Finally, as in Sledd and L'Ecuyer (2021) and references therein, the TTE is intended to provide a rough approximation for when a significant trend emerges, not pinpoint an exact year when a significant trend would have emerged.

Latent and Kinetic Energy Trends of Midlatitude Cyclones
Decadal changes in LE and KE highlight clear regional trends across the globe (Figure 2).In the Northern Hemisphere, the trend in LE has been positive in nearly every region of the globe except for parts of Eastern Asia from 1940 to 2020.This is especially true when examining the contribution by 2-8-day ETCs, where LE has  2015) and other studies showing that the Northern Hemisphere has warmed more than the Southern Hemisphere, thereby allowing increased atmospheric water vapor due to higher saturation vapor pressure.This is particularly notable in the polar regions, where LE increases have been relatively subdued (but still positive) in the southern high latitudes compared to the northern high latitudes.
Full Another way to assess the role of ETCs on LE transport is to examine their contribution compared to other atmospheric processes at longer time scales.Figure 3 shows the fractional wave power of 2-8 periods relative to all time periods (computed using a Fourier transform as the fraction of total power from 2-8-day Lanczos filtered data relative to full-scale data).Given that KE changes are well correlated to ETCs at approximately 2-8-day periods, it is unsurprising to see the highest fractional percentage of KE between 40 and 70° in both hemispheres with 2-8-day ETCs representing over 20% in both the northern and southern mid/high latitudes.The omnipresence of jet streams in both hemispheres is responsible for a high fraction of KE and persists at scales much longer than 1-2 weeks.Fractional LE power from 2-8-day cyclones tells a similar story.LE power from 2-8-day ETCs represents over 15% of total LE power in the North Atlantic and Northeast Pacific basins.A similar result is found for the southern high latitudes, with the contribution of LE by 2-8-day cyclones exceeding 15% but for a much larger area of the southern mid-and high-latitudes, implying that ETCs have a more important relative role in the poleward transport of moisture.This notable increase in LE and poleward shift of KE in these cyclones supports the conclusions drawn in Lapeyre and Held (2004), which found increasingly strong baroclinic cyclones result when both horizontal moisture (LE) and vorticity (a proxy for KE) are advected.This study does not explicitly evaluate atmospheric vorticity, but these results suggest cyclonic vorticity in mid-and high-latitude cyclones has strengthened given the increase in both full-scale and 2-8-day KE.

Signal Time to Emergence for Energetic Changes in ETCs
To understand if the recorded trends in hemispheric LE and KE are statistically significant for both full-scale (unfiltered) data and 2-8-day filtered data, the Weatherhead et al. (1998) methodology for TTE is applied using the observed trends between 1940 and 2020 and presented in Figure 4. Statistically significant trends in full-scale KE emerged between 45 and 70°S across the Southern Ocean, which is offset by ∼15°S of the center of the dipole KE trends (Figure 2), though statistically significant trends in 2-8 days filtered data do not arise in these same locations.This result provides strong evidence that the increases in full-scale KE south of 45°S are not solely explained by poleward-shifting ETC tracks.Similar dipole features are noted in the northern hemisphere, particularly off the east coast of the United States and along the west coast of Mexico/Baja Peninsula, though the trends 10.1029/2023GL105207 8 of 11 associated with full-scale data are not statistically significant.The largest slopes in both full-scale and 2-8-day KE occur in the North Atlantic, especially west and north of the British Isles, as well as across the northwest Pacific.However, no statistical significance is observed in these regions either, possibly due to the increased temperature gradient resulting in weaker eddy heat and moisture transport (Franzke & Harnik, 2023).
The TTE signal for statistically significant LE has several similarities to the TTE signal in full-scale KE trends.Statistically significant trend in full-scale LE across the Southern Ocean match closely with the trends appearing in full-scale KE over the same region, except for most of the SE Pacific region.Two regions where the TTE signal is less than 80 years occur (a) east of the southern tip of South America and (b) east of the southern tip of Africa, which are climatologically consistent with regions of ETC strengthening.No statistical significance in full-scale or 2-8-day LE occurs in the North Atlantic, consistent with the result found for full-scale and 2-8-day KE in the North Atlantic.It is interesting to note, however, that a small region of full-scale LE and KE statistical significance occurs in near the equator in the east Pacific, which is located near a climatological origin point of tropical plumes that ultimately bring moisture and precipitation to the western coasts of Mexico and the United States.
Overall, statistically significant trends in full-scale LE and KE have emerged over the last 80 years in the Southern Ocean.One possible explanation for this might be explained by inter-decadal variability in full-scale KE and LE trends: since the TTE calculation requires autoconversion of the noise as an input, the Southern Ocean likely saw emerging statistical significance due to less noise or variability in the time series relative to the same latitudes in the northern hemisphere.This idea also most likely explains why trends in 2-8-day LE and KE were not statistically significant, given the larger variance and decreased autocorrelation in 2-8-day LE and KE (result not shown).In any case, this analysis provides very clear evidence that ETCs have become increasingly responsible over the last 80 years for transporting moisture in the southern mid-latitudes but cannot solely explain the statistically significant increases in full-scale LE and KE.Overall, the global increases in LE and the poleward shift in KE qualitatively agree with several previous studies showing a poleward shift in ETC activity but suggest further

Conclusions
This study investigated full-scale and 2-8-day LE and KE properties from 1940 to 2020.Regional trend analysis of full-scale and 2-8-day KE shows poleward increases of KE at 40-60° latitude with concurrent decreases in KE at 30-40° latitude, confirming several previous studies (e.g., Marciano et al., 2015;Pan et al., 2017;Yin, 2005) that ETC tracks have shifted poleward.Trends in full-scale LE are statistically significant across much of the Southern Hemisphere midlatitudes, particularly in the Southern Ocean between 45 and 70°S latitude but are not statistically significant when filtering for 2-8 days ETC activity.Trends in full-scale KE across these same latitudes indicate that ETCs are very important but not solely responsible for moisture transport across the South Atlantic and Southeast Pacific Ocean basins.Recent results from Franzke and Harnik (2023) used the Japan Reanalysis Dataset (JRA-55) from 1958 to 2018 to show that southern hemisphere baroclinic eddies and poleward energy fluxes increased.Their analysis also notes a significant weakening of eddy heat and moisture fluxes, which could explain why the observed trends in the 2-8-day filtered ERA-5 LE and KE are not statistically significant for the northern hemisphere.
Though not discussed in the previous sections, an unexpected result beyond the scope of this study shows up in Figure 4: statistically significant trends in both full-scale LE and KE occurred in regions across the equator including the Amazon Basin in South America, the western Sahel region in Africa, and the far West Pacific Ocean.Franzke and Harnik (2023) showed an increase in zonal moisture across the equatorial lower and upper troposphere using the Japan Reanalysis Dataset (JRA-55) from 1958 to 2018.Their result agrees with the current finding of higher LE in this part of the globe, with results here confirming statistical significance of the latent energy increase.Particularly interesting is the fact that significant increases in full-scale KE over the Central Pacific Ocean are somewhat offset to the east of the significant increases in full-scale LE over the West Pacific Ocean.It is speculated that these regions have observed these statistically significant increases in both LE and KE due to surface warming over the last century, allowing for higher convective available potential energy to convert to kinetic energy.Given that the equatorial region is influenced by (among other processes) Kelvin wave activity, further research would be needed to investigate and explain these statistically significant trends in equatorial LE and KE.
The evidence of increased moistening in mid-and high-latitude cyclones has several implications.For example, the quasi-geostrophic approximations for modeling of cyclones do not account for moisture (e.g., Lapeyre & Held, 2004;Zhang et al., 2022) whereas this study clearly suggests that moistening of midlatitude cyclones with time needs to be accounted for.Furthermore, this work supports the idea that latent heat release from future moistening represents a key driver for cyclone strengthening (Marciano et al., 2015).Increased ocean heat content in both hemispheres, especially in the subtropical oceans, could also warrant examination and provide additional context for the increase in ETC moisture (Wu et al., 2011).Future climate modeling studies could also focus on the moistening of baroclinic eddies, where internal variability obfuscates cloud-radiation effects from decreased sea-ice coverage despite strong satellite-based evidence (Sledd & L'Ecuyer, 2021).In fact, given the record of satellite-based observations from platforms such as CloudSat and CALIPSO, measurement-based studies could provide additional evidence supporting these results and other studies using solely reanalysis data (e.g., Binder et al., 2020;Pilewskie & L'Ecuyer, 2022).This study also corroborates previous studies showing evidence of shifting storm tracks poleward, noting increased LE and KE poleward in both hemispheres.Overall, this study supports several previous studies showing a poleward migration of midlatitude cyclones while demonstrating (a) sustained decadal increases of LE within midlatitude cyclones and (b) increased importance of midlatitude cyclones for moisture transport.

Figure 2 .
Figure 2. Changes in latent energy (top) and kinetic energy (bottom) from 1940 to 2020 for all data (left) and 2-8-day filtered data (right).

Figure 3 .
Figure 3.The 80-year averaged latent energy (top panel) and kinetic energy (bottom panel) power fraction, represented as the Lanczos-filtered 2-8-day contribution relative to the full-scale (unfiltered) time series at each point across the globe, between 1940 and 2020.

Figure 4 .
Figure 4.The time to emergence (TTE) for latent energy (top) and kinetic energy (bottom) trends for all data (left) and 2-8 days filtered data (right) highlighted in Figure 2. Filled contours represent regions of the globe where the emerging trend was less than or equal to 80 years, implying that a statistically significant trend emerged from 1940 to 2020.
-scale KE, compared to full-scale LE, exhibits different patterns in both hemispheres.In the Northern Hemisphere, full-scale KE decreases between 15 and 30°N across the far East Pacific and North Atlantic and increases between 35 and 60°N latitude as shown by a red/blue "dipole" feature in Figure2.This dipole feature is also apparent in the Southern Hemisphere with KE decreasing between 15 and 30°S in the southeast Indian and south Pacific Oceans and decreasing between 15 and 20°S in the south Atlantic Ocean.Between 40 and 70°S, both full-scale KE and 2-8-day KE have the largest positive slopes anywhere on the globe, suggesting ETC activity has increased in frequency and/or strength.For both hemispheres, the dipole features in full-scale KE and relative Chemke (2022)019)ay KE poleward of 30° indicate a poleward shift in ETC tracks and verifies previous findings such asYin (2005),Wu et al. (2011),Pan et al. (2017)andTan et al. (2019)showing a poleward shift in midlatitude storm tracks.This result also supports the findings ofChemke (2022), who showed a similar dipole feature for poleward eddy kinetic energy shifts in Coupled Model Intercomparison Project (CMIP) model projections.As with LE, the results for KE provide further evidence that southern hemispheric subtropical high-pressure systems have moved poleward.