Effect of condensation latent heat release on the relative vorticity tendency in extratropical cyclones:a case study

SHEN Yang,SUN Yan and LIU Duanyang

aKey Laboratory of Transportation Meteorology,China Meteorological Administration,Nanjing,China; bMedium and Short Term Forecast Department,Jiangsu Meteorological Observatory,Nanjing,China; cNumerical Prediction Department,Jiangsu Academy of Meteorological Sciences,Nanjing,China

ABSTRACT Taking an extratropical cyclone that produced extreme precipitation as the research object, this paper calculates the contribution of condensation latent heat release (LHR) to relative vorticity tendency based on the complete-form vertical vorticity tendency equation.The results show that the heating rate of convectional condensation LHR can reach up to about 40 times that of stable condensation LHR. Both the stable and convectional heating centers are higher than 700 hPa,which would cause ∂Q/∂z>0 and a positive vorticity source in the lower troposphere.The vertical gradient of stable condensation LHR contributes little to the growth of relative vorticity,while the relative vorticity tendency associated with the vertical gradient of convectional condensation LHR can be an order of magnitude higher than the former. The positive vorticity source is always located right below the latent heating center,and its maximum value can always be found in the lower troposphere. Convectional LHR is the primary factor for cyclone development from the perspective of diabatic heating.The horizontal gradient of total condensation LHR can contribute about 65% of the actual vorticity growth, but the effect of the vertical gradient of convectional condensation(LHR)can reach twice as much.The adiabatic heating from LHR can cause vorticity tendency directly. However, it can also change the vertical and horizontal gradient of potential temperature,which can further induce vorticity tendency.

KEYWORDS Complete-form vertical vorticity tendency equation;stable condensation latent heat;convectional condensation latent heat;vorticity tendency

1. Introduction

The role of latent heat release(LHR)has been a focus of research on extratropical cyclones for decades. Potential vorticity (PV) is a well-established theoretical framework(Hoskins,McIntyre,and Robertson,1985)used in explaining the relationship between diabatic heating and cyclone development.Comparison of PV fields in numerical simulations with and without latent heating revealed that a large source of anomalous low-level (850 hPa) PV appeared in the wet experiment,but was not present in the dry run,and without the heating the 24-h deepening was reduced from 31 to 12 hPa (Reed, Grell, and Kuo 1993).A positive PV anomaly produced by LHR was maintained in an approximately steady-state manner near the 800-hPa level, which contributed about 70% of the balanced height anomalies of a simulated baroclinic cyclone (Stoelinga 1996). From the perspective of minimum surface pressure without regeneration of low-level PV anomalies, the LHR could also produce a diabatic reduction of upper-level PV, and the removal of LHR only formed a much weaker extratropical cyclone(Ahmadi-givi, Graig, and Plant 2004). Heo et al. (2015)also found LHR contributed to roughly 50% of the decrease in sea level pressure and 50% of the central cyclone’s low-level PV generation in an explosive cyclone.

Besides the importance of PV anomalies produced by LHR on the cyclone intensity,its impact on the precipitation distribution and weather system pattern has also been studied in detail. A numerical study of an extratropical cyclone that caused heavy snow suggested the incipient LHR led to the initial formation of a PV maximum in the lower troposphere, and the balanced flow associated with the PV anomalies induced sufficient moisture transport (Brennan and Lackmann 2005). The LHR could also contribute to the warm occluded thermal structure and upper-tropospheric dynamics by producing (destroying) PV below (above) the maximum diabatic heating(Posselt and Martin 2004;Joos and Wernli 2012;Chagnon,Gray,and Methven 2013).

Previous studies have confirmed that a PV framework can clearly demonstrate how LHR influences the development of extratropical cyclones(Brian,James,and Edmund 2015),and in these studies they finally choose some variables(e.g.,height,central pressure)as evaluation criteria to quantify the cyclone intensity. Wu and Liu (1999)deduced the complete-form vertical relative vorticity(hereafter referred to simply as vorticity)tendency equation from Ertel’s PV formula(Ertel 1942).This equation is completely based on a PV framework and explicitly includes the contribution of diabatic heating to relative vorticity enhancement,providing another perspective for quantifying the impact of LHR on cyclone development.

The increase in relative vorticity will lead to the development of cyclones (Xiong, Zhang, and Tao 2016; Guo,Xiong, and Zhang 2017). Therefore, it is necessary to make a budget of the relative vorticity, so as to further understand the contribution of convective condensation latent heat and other factors to the enhancement of relative vorticity, and the mechanism of the significant intensification of cyclones.

An extratropical cyclone that caused regional heavy rainstorms in the provinces of Jiangsu and Anhui in China in June 2017 (hereinafter referred to as the ‘610’ cyclone) is studied in this paper. The ‘610’cyclone was a typical Jiang-Huai cyclone, and LHR was the main factor in its development (Lv, Zhou,and Chen 2000). The movement of the ‘610’ cyclone(Figure 1(a)) from 0000 UTC 9 June 2017 to 1200 UTC 10 June 2017 shows that, after the initial formation in eastern Sichuan Province, the cyclone migrated eastwards and entered the sea via Jiangsu Province. Its circulation center sloped roughly northwards with height. Its maximum extension height was about 700 hPa, and the minimum sea level pressure was about 1000.9 hPa during its life cycle. The diameter of the cyclone was 500-600 km, based on its outermost closed isobar. Obviously, it was a sub-synoptic scale system (Shen et al. 2019).

Accumulated precipitation based on CMORPH(Climate Prediction Center morphing technique) in mainland China (Shen et al. 2014) from 1200 UTC 9 June to 1200 UTC 10 June 2017 (Figure 1(b)) showed that the‘610’cyclone caused regional torrential precipitation in Jiangsu and Anhui provinces. The 24-h accumulated precipitation at Nanjing Station, Changzhou Station, Jurong Station, and Jintan Station reached 245.3 mm,234.1 mm,259.9 mm,and 265.3 mm,respectively (Table S1). The precipitation at Nanjing Station broke the historical record that had stood since 1951,and the precipitations of the other three stationsbecame the new second-highest ponit in history. Regional extreme precipitation associated with extratropical cyclones covering such large areas in East China is rare in June before the mei-yu period. The generation and development of this cyclone deserves in-depth study from the perspective of LHR because of the large amount of precipitation it produced.

2. Data and methods

Based on the superiority of the ERA-I nterim dataset(Decker et al. 2012; Bao and Zhang 2013; Martineau,Son, and Taguchi 2016), the meteorological elements involved in the diagnostic analysis of this paper were a total of 37 vertical levels of 6-hourly global reanalysis grid data downloaded from the ECMWF (http://apps.ecmwf.int/datasets/data/interim-full-daily/levtype=pl/)with a horizontal resolution of 0.25°.

The complete-form vertical vorticity tendency equation under the Z-coordinate system (Wu and Liu 1999;Liu et al.1999)can be written as in which ζzand ζaare the vertical components of relative vorticity(hereinafter referred to as‘relative vorticity’)and the three-dimensional relative vorticity, respectively; β means the β effect, Ω is the earth rotation angular velocity(7.29×10−5s−1),φ is the latitude,and a is the earth radius (6.37 × 106m); V is the horizontal velocity vector;∇2and ∇3are the horizontal Hamiltonian operator and the three-dimensional Hamiltonian operator, respectively; PEis the Ertel PV and the subscript ‘E’ means‘Ertel’; ξz(ξs) is the vertical (horizontal) component of PE; θz(θs) is the vertical (horizontal) gradient of the potential temperature; ρ is the air density and α is the reciprocal of ρ;ξais the product of α and ζa.Q represents all non-adiabatic factors; and Fζis the frictional dissipation. Some researches have confirmed the advantage of the complete-form vertical vorticity tendency equation in synoptic diagnostic analysis and theoretical studies (Cui,Gao,and Wu 2003;Zhou et al.2004).

Figure 1.(a)Circulation center movement at 700 hPa(solid line)and 850 hPa(dashes line),along which T1 to T7 represent the time from 0000 UTC 9 June 2017 to 1200 UTC 10 June 2017 in 6-h intervals;D1 and D2 are the research domains based on the cyclone movement at 700 hPa. (b) 24-h accumulated precipitation (shaded; units: mm) at 1200 UTC 10 June 2017. (c, d) 6-h accumulated precipitation(shaded;units:mm)at(c)0000 UTC 10 June 2017 and(d)0600 UTC 10 June 2017.

Terms ①②③(-V·∇2ζz, -βv, - （ζz+f）∇2·V)on the right-hand side of Equation (1) represent the contribution of dynamic factorsto the relative vorticity source.Term④ (-（PE-ξsθs）++］) represents the contribution of static stability, baroclinity and vertical wind shear. Term⑤(θ·Fζ) is the frictional factor. Term ⑥(·∇3Q) is the contribution of diabati cheating to the relative vorticity generation rate,and we only focus on the condensation LHR of precipitation in this paper.

3. Condensation LHR and vorticity tendency

3.1 Calculation of LHR

The release of condensation latent heat includes the stable heating QLand the cumulus convectional heating QC,as follows:

in which L is the coefficient of latent heat of condensation(2.5×106J kg−1);F is the condensation function;ω is the vertical velocity.The conditions for QLare air saturation (q=qs) and ascending motion (ω<0). See Ding(1989)for the meaning and specific calculation method of Equations(7)-(9).

The subgrid-scale cumulus convectional heating QCcan be calculated by the cumulus convection parameterization scheme proposed by Kuo(1965,1974),as follows:

where PTand PBare the heights of the cloud top and cloud bottom, and they are set to 200 hPa and 900 hPa respectively; Rdis the gas constant of dry air(287.05 J (kg K)−1); ωBand qBis the vertical velocity and specific humidity of cloud bottom; TSand T are the temperature in the cloud and the ambient temperature respectively. In Kuo (1965, 1974), cumulus development depends on moisture convergence and conditional instability. When cumulus develops, the temperature of the cumulus bottom is the same as the ambient temperature. However, the TSdecreases following the wet adiabatic process, while T decreases following the dry adiabatic process. Finally, τ is the characteristic time scale of cumulus, but it can be removed because it is a common factor in Equations(11) and (13).

3.2. Contribution of LHR vertical gradient to relative vorticity tendency

On the right-hand side of Equation (1), term ⑥ζa·∇3Q) can be further decomposed intoandζx·. These two terms indicate the contributions of the vertical and horizontal gradient of condensation latent heat,respectively.

Figures 2 and 3 show latitude-pressure vertical cross sections of the latent heating rate and relative vorticity tendency along the dashed line in Figure S1, with the 700-hPa shear line roughly falling in the cross. From 1200 UTC 8 June 2017 to 1800 UTC 8 June 2017(Figure 2(a1,a2)),the main heating zone is located on the north side of the shear line, with a maximum heating rate of 0.03-0.04°C h−1at 500 hPa.The maximum vorticity tendency is more than 0.5×10−10s−2,which is just beneath the heating center in the lower troposphere (below 700 hPa). At 0000 UTC 9 June 2017 (Figure 2(a3)), the maximum heating rate increases to more than 0.05°C h−1,while the heating center that is just above the shear line extends from 600 hPa to 400 hPa. Beneath the heating center, the maximum vorticity tendency has accordingly increased to 1.5 × 10−10s−2at around 700 hPa. In the following 18 hours (Figure 2(a4-b1)),the primary heating zone moves to the south side of the shear line. The location of the positive vorticity source center relative to the heating center remains fixed. However, its maximum value reduces to 0.5×10−10s−2.

From 1800 UTC 9 June 2017 to 0600 UTC 10 June 2017 (Figure 2(b1-b3)), when Jiangsu and Anhui provinces experienced their heaviest precipitation(Figure 1(c,d)),the latent heating zone develops on both sides of the shear line and the heating rate restrengthens to more than 0.05°C h−1. The vorticity generation zone is still located right below the heating center and its maximum intensity increases to about 2.5×10−10s−2around 800 hPa.

Figure 3 indicates that, compared with the stable latent heating rate, the maximum convectional heating rate(more than 2°C h−1;Figure 3(a3,a5,b2))could be 40 times that of the former.The vorticity generation zone is still beneath the heating center and its maximum intensity could be more than 200 × 10−10s−2(Figure 3(b3)),which corresponds to the increasing heating rate.

Figure 2.Latitude-height cross sections of vorticity tendency(contours;units:10−10 s−2)associated with the vertical gradient of the stable condensation latent heating rate(shaded;units:°C h−1)along dashed lines as illustrated in Figure S1(a1-a5)for research area D1;(b1-b3)for research area D2.The cross indicates the position of the shear line at 700 hPa.

Based on Figures 2 and 3, we can conclude that the vorticity generation zone was always located right below the latent heating center and its maximum value could always be found in or below the layer of 700 hPa(lower troposphere). Term⑥(ζa·∇3Q) on the right-hand sideofEquation (1) showsthatthe positive heating vertical gradient (i.e., ∂Q/∂z > 0) is conducive to the generation of the positive vorticity source. Both the stable heating center and convectional heating center are higher than 700 hPa,and this vertical distribution of the heating zone would have caused ∂Q/∂z > 0 and the positive vorticity source in the lower troposphere.

Near the 700-hPa shear line, the maximum vorticity tendency associated with stable LHR is only 1×10−10s−2,while the convectional LHR could be 5-50 × 10−10s−2.This means the vorticity generated by stable LHR is only 2.16×10−6s−1in six hours,while the vorticity associated with convectional LHR is 1.08×10−5to 1.08×10−4s−1.It is obvious that convectional LHR could have caused equal vorticity in the real cyclone(Figures 4 and 5),and it is the primary factor for cyclone development from the perspective of diabatic heating(Joos and Wernli 2012).

Figure 3.Latitude-height cross sections of vorticity tendency(contours;units:10−10 s−2)associated with the vertical gradient of the convectional condensation latent heating rate(shaded;units:°C h−1)along dashed lines as illustrated in Figure S1.(a1-a5)for research area D1;(b1-b3)for research area D2.The cross indicates the position of the shear line at 700 hPa.

The vorticity tendency caused by the vertical gradient of convectional condensation latent heat at 700 hPa is illustrated in Figure 4.From the initial generation of the‘610’ cyclone to the period of highest precipitation, the vorticity tendency caused by the convectional condensation latent heat at the cyclone center is not stable,so it makes almost no contribution to the vorticity growth at the cyclone center.When the cyclone moves eastwards,a sheet-like vorticity generation center is formed on the south of the shear line; the intensity can maintain at 50 × 10−10s−2at least, and vorticity of 10.8 × 10−5s−1can be generated within six hours (Figure 4(a4-a5,b1)).The maximum vorticity growth rate of convectional latent heat from 0000 UTC 8 June 2017 to 1800 UTC 9 June 2017 (Figure 4(a4,a5,b1)) is almost 50 times that associated with stable latent heat (Figure S2).Meanwhile, the shear line vorticity is about 10 × 10−5s−1in the same period. Therefore, their magnitudes are very close.

From 0000 UTC 10 June 2017 (Figure 4(b2)) to 0600 UTC 10 June 2017(Figure 4(b3)),with the most precipitation, the shear line vorticity increases from 10 × 10−5s−1to 20×10−5s−1,an increase of 10×10−5s−1.In the same period,the maximum vorticity tendency is maintained at about 100 × 10−10s−2. Assuming that the frictional dissipation and other factors are not considered,the vorticity produced by the vertical gradient of convectional latent heat is 21.6 × 10−5s−1within six hours, which is double the actual growth rate of vorticity. However, it is still reasonable when considering frictional dissipation.

From the above, the latent heat of convectional condensation did not contribute to the central vorticity of the cyclonic center. However, in the process of the cyclone moving eastwards, the vorticity generated within six hours associated with the convectional latent heat could reach up to the same order of magnitude as the growth rate of the shear line vorticity within the same period of time-even more than the growth rate of shearline vorticity.In the process of vorticity growth that is related to the vertical gradient of condensation latent heat,the convectional component was absolutely dominant.

Figure 4.Wind vector(units:m s−1),relative vorticity(contours;units:10−5 s−1),and vorticity tendency(shaded;units:10−10 s−2)at 700 hPa associated with vertical gradient of convectional condensation latent heat:(a1-a5)for research area D1;(b1-b3)for research area D2.

3.3. Contribution of LHR horizontal gradient to relative vorticity tendency

According to the previous analysis, the horizontal gradient of condensation latent heat can also cause a growth in vorticity.Figure 5 shows the vorticity tendency caused by the horizontal gradient of total condensation LHR (the sum of stable condensation LHR and convectional condensation LHR)at 700 hPa.In the formation stage of the‘610’ cyclone (e.g., from 1200 UTC 8 June 2017 to 1800 UTC 8 June 2017; Figure 5(a1,a2)), there is almost no vorticity generation zone in the circulation center.When the cyclone moves eastwards (Figure 5(a3-a5,b1-b3)),there is no vorticity generation near the circulation center,and the intensity and area of the vorticity generation zone near the east shear line are small.The maximum vorticity tendency near the shear line maintains at about 10-30 × 10−10s−2from 0000 UTC 9 June 2017 to 1800 UTC 9 June 2017(Figure 5(a3-a5,b1)),and only increases to 50 × 10−10s−2even in the period with the most intensive precipitation from 0000 UTC 10 June 2017 to 0600 UTC 10 June 2017 (Figure 5(b2,b3)). Calculated as the growth of 30×10−10s−2,a vorticity of 6.48×10−5s−1can be generated within six hours, which is only about 65% of the actual vorticity growth (15 × 10−5s−1) in the same period. This shows the horizontal gradient of the total condensation LHR contributes less to the vorticity growth than that of the vertical gradient of convectional condensation latent heat.

The LHR caused by precipitation will lead to a positive vorticity source in the lower troposphere and be conducive to inducing and strengthening cyclones (Wu and Lin 1999). However, the center of the positive vorticity source is located near the shear line in the east of the ‘610’ cyclone instead of the cyclone circulation center (Figures 4 and 5). In this case, the condensation LHR is obviously not the main cause for the generation of cyclones, because the vorticity tendency in the cyclone center caused by LHR is very small.Nonetheless,the impact of LHR on strengthening the cyclone after its generation cannot be ignored. The vertical gradient of condensation LHR has a greater contribution to the growth of positive vorticity than the horizontal gradient in the ‘610’ case,which is consistent with existing research (Liu et al.1999; Zheng, Wu, and Liu 2013).

Figure 5.Wind vector(units:m s−1),relative vorticity(contours;units:10−5 s−1),and vorticity tendency(shaded;units:10−10 s−2)at 700 hPa associated with the horizontal gradient of total condensation latent heat:(a1-a5)for research area D1;(b1-b3)for research area D2.

3.4. Contribution of slantwise vorticity development to the vorticity tendency

The slantwise vorticity development (SVD) is an important application of the complete-form vertical vorticity tendency equation. This theory can be summarized as:when the air slides upwards (downwards) along the down-concave (up-protruding) isentropic surface, the vorticity will increase rapidly (Wu and Liu 1999; Cui,Gao,and Wu 2003).SVD is the combined effect of static stability,baroclinity,and vertical wind shear in Equation

where Ω is earth rotation angular velocity and φ is the latitude.

The criterion of SVD is as follows:CD<0,0,and0(Wu,Zheng,and Liu 2013).In Figure S3,the CDis negative around the cyclone center and shear line. Its intensity has decreased from −1 × 10−5m3s−1kg−1to−5 × 10−5m3s−1kg−1(from 1200 UTC 8 June to 1200 UTC 9 June;Figure S3(a1-a5)).In the stage of maximum cyclone intensity (precipitation intensity), the minimum CDis less than −5×10−5m3s−1kg−1.It can be concluded that the CDdecreased with time in the‘610’case.

The static stability around the cyclone center and shear line is about 45-60 × 10−4K m−1from 1200 UTC 8 June to 1200 UTC 9 June (Figure S3(a1-a5)) and has increased to more than 75 × 10−4K m−1when the maximum precipitation happens (1800 UTC 9 June to 0600 UTC 10 June; Figure S3(b1-b3)). Thus, there is a slight increase in the static stability over time.

The evolution of CDsatisfies the condition of SVD,while static stability does not. However, the wind vector at the 315-K isentropic surface(figure omitted)indicates that the southerly around the shear line slides upward along the down-concave isentropic surface. Although an accurate vorticity tendency could not be calculated because of the coarse temporal resolution in the reanalysis data,it can be concluded that SVD does happen to a certain extent.

In Chen, Song, and Li (2016), another form of the vorticity tendency equation, which contains adiabatic heating, was used to research the evolution of atmospheric circulation and draw two important conclusions:(1) adiabatic heating is the primary cause of vorticity tendency in the lower troposphere; and (2) adiabatic heating can cause vorticity tendency directly and indirectly by changing the vertical and horizontal gradient of potential temperature. The results of this study, especially the CDand SVD results, coincide with the above conclusions.

To summarize, besides the direct adiabatic heating form LHR, which can cause vorticity tendency (Term ⑥·∇3Q) in Equation (1)), the adiabatic heating can change the vertical and horizontal gradient of potential temperature and cause further vorticity tendencyEquation (1)).

4. Conclusion and discussion

Using the 0.25° × 0.25° reanalysis data provided by ECMWF and taking an extratropical cyclone that triggered heavy regional rainstorms and extreme precipitation events in June 2017 as the object of analysis, this paper quantitatively calculated the tendency of vorticity associated with condensation latent heat by the complete-form vertical vorticity tendency equation. The following conclusions were obtained:

The vorticity generation zone was always located right below the latent heating center, and both the stable heating center and convectional heating center were higher than the 700-hPa layer. This vertical gradient of the heating zone would have caused ∂Q/∂z>0 and a positive vorticity source in or below the layer of 700 hPa, and its maximum value could always be found in the lower troposphere. The convectional condensation latent heating rate could be up to 40 times the stable heating rate,and was mainly distributed south of the shear line,and seldom in the cyclone center.

The vorticity tendency caused by stable LHR was much less than the convectional LHR, and contributed little to the growth of vorticity. In the process of the cyclone moving eastwards, the accumulated vorticity tendency within six hours associated with convectional LHR could reach up to the actual growth of vorticity within the same period of time, or at least up to the same order of magnitude.

The vorticity tendency, which is related to the horizontal gradient of total LHR,could be the same order of magnitude as the vorticity tendency caused by the vertical gradient of convectional LHR.It can be regarded as the mechanism of generation of the incipient vorticity,though it could only generate 65% of the vorticity growth produced by convectional LHR.

The adiabatic heating from LHR could cause vorticity tendency directly.However,it could also change the vertical and horizontal gradient of potential temperature,inducing vorticity tendency indirectly.The SVD contributed to the vorticity development to a certain extent.

The PV framework has been applied in many studies to reveal how diabatic heating impacts on cyclone dynamics.In summary, diabatic heating will cause positive (negative)PV anomalies in the lower(upper)troposphere,and the lower-level positive PV anomalies are associated with a stronger cyclonic circulation, which usually induces an intensification of the cyclone (Hoskins, McIntyre, and Robertson 1985;Brian,James,and Edmud,2015).Studies using the PV framework as the research approach often choose a particular single variable(e.g.,pressure,height)to ultimately indicate the cyclone intensity (Reed, Grell,and Kuo 1993; Stoelinga 1996; Ahmadi-givi, Graig, and Plant 2004;Heo et al.2015).Though vorticity is relatively rarely chosen,it is still a reasonable and direct criterion to demonstrate the impact of diabatic heating on cyclone dynamics. The complete-form vertical vorticity tendency equation is derived from Ertel’s PV formula.It presents the relationship between diabatic heating and relative vorticity tendency directly and distinctly.

However, this study still has certain inadequacies and requires further research in the future. The cumulus formation condition, vertical heating distribution function,and moistening coefficient in the cumulus convection parameterization scheme proposed by Kuo (1965, 1974)contains some irrationality. Using reanalysis data or numerical simulations with a higher temporal resolution and an improved cumulus convection parameterization scheme may improve the conclusions of this paper.

Disclosure statement

No potential conflict of interest was reported by the authors.

Funding

This study was supported by the Natural Science Foundation of Jiangsu Province [grant number BK20161603]; the National Natural Science Foundation of China [grant numbers 41575010 and 41575070]; the China Meteorological Administration[grant number CMAYBY2018-028].