Download Case studies of the effect of latent heat release on extratropical

Case studies of the effect of latent
heat release on extratropical
cyclogenesis
Bachelor thesis in meteorology
Danny Høgsholt
Pernille Kirstein Hansen
Niels Bohr Institute
Faculty of Science
University of Copenhagen
Denmark
May 28, 2010
Internal supervisor: Eigil Kaas
External supervisor: Niels Woetmann Nielsen (DMI)
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1
Abstract
This bachelor thesis examins the effect of latent heat release on the development of two strong
extratropical cyclones affecting Northern parts of Europe in January 2005 and June 2009. The
issue is interesting because latent heat release is mostly perceived as a secondary effect during the
development of extratropical disturbances. These studies are carried out by comparing the cyclone
developments in an unperturbed run and two perturbed runs regarding the release of latent heat,
using the HIRLAM-T15 numerical model developed by the Danish Meteorological Institute. In
the first perturbed run, the release of latent heat has been set to a very small value (essentially
zero) in all model routines whereas in the second one, the perturbation is only applied to model
routines controling cloud formation, cloud water and precipitation.
The studies reveal both the direct and especially the indirect effects of latent heating on these two
cyclones. It was found that the difference in mean sea level pressures in the centres of the cyclones
between the unperturbed run and the second of the perturbed runs were 32 hPa and 6 hPa at
peak intensities for the winter and summer cyclone, respectively. The direct effect of latent heat
release was most easily analysable during the evolution of the summer cyclone, where convection
near the cyclone centre releasing latent heat kept the surface low from weakening by reducing
surface pressure. The indirect effect, amplifying and shortening the associated upper level waves,
contributed to more rapid developments and shorter life times of the cyclones, mainly through
enhanced positive differential vorticity advection.
The results are in good agreement with former studies by e.g. Kuo et. al. (1990) and Nielsen and
Sass (2003). Furthermore, they also support the studies indicating shorter geopotential waves and
more intense cyclones in future climate, e.g. by Kaas et. al. (2002).
Resumé
Dette bachelorprojekt undersøger effekten af latent varmefrigørelse på udviklingen af to kraftige
ekstratropiske cykloner, der ramte det nordlige Europa i januar 2005 og juni 2009. Emnet er
interessant, fordi frigørelse af latent varme ofte opfattes som en sekundær effekt på ekstratropiske
lavtryksudviklinger. Undersøgelserne er baseret på HIRLAM-T15 modellen fra Danmarks
Meteorologiske Institut, og bygger på en sammenligning af lavtryksudviklingerne i henholdsvis en
uperturberet og to perturberede kørsler med hensyn til frigørelsen af latent varme. I den første
perturberede kørsel er frigørelsen af latent varme sat til en meget lille værdi (essentielt set nul) i
alle modelrutiner, hvorimod det i den anden perturberede kørsel kun er gjort i de rutiner, der
styrer dannelse af skyer, skyvand og nedbør.
Undersøgelserne afslørede både de direkte og især indirekte påvirkninger af latent varmefrigørelse
på disse to cyklonudviklinger. Resultaterne viste, at forskellen i luftrykket i lavtrykscenteret
reduceret til havniveau ved kulminationen i den upertuberede kørsel og den anden af de
perturberede kørsler var henholdsvis 32 hPa og 6 hPa for vinter- og sommerlavtrykket. Den
direkte påvirkning af latent varmefrigørelse var lettest at analysere under udviklingen af
sommerlavtrykket, hvor frigjort latent varme, i forbindelse med konvektion tæt på
lavtrykscenteret, forhindrede lavtrykket i at svækkes. Den indirekte påvirkning, som var med til
at amplificere og forkorte de tilhørende øvre bølger, bidrog til lavtrykkenes hurtigere udviklinger
og kortere levetider, primært på grund af forøget advektion af positiv differentiel vorticitet.
Resultaterne er i god overensstemmelse med tidligere studier af f.eks. Kuo m. fl. (1990) og Nielsen
og Sass (2003). Endvidere underbygger de også studier, der indikerer, at de geopotentielle bølger
vil blive kortere og cyklonerne kraftigere i det fremtidige klima, f.eks. af Kaas m. fl. (2002).
2
Contents
1 Introduction
2 Types of cyclones
2.1 Extratropical cyclones . .
2.1.1 The Bergen School
2.2 Polar cyclones . . . . . . .
2.3 Tropical cyclones . . . . .
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3 Quasi-geostrophic theory
3.1 Quasi-geostrophic equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.2 Geopotential height-tendency equation . . . . . . . . . . . . . . . . . . . . . . . . . .
3.3 Omega equation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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and Shapiro-Keyser models
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4 Extratropical cyclogenesis
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4.1 Cyclogenesis in uniform upper level flow . . . . . . . . . . . . . . . . . . . . . . . . . 10
4.2 Cyclogenesis affected by jet streaks . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
4.3 Cyclogenesis affected by latent heat release . . . . . . . . . . . . . . . . . . . . . . . 11
5 Case studies
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5.1 The HIRLAM-T15 model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
5.2 Study of a winter cyclone, January 2005 . . . . . . . . . . . . . . . . . . . . . . . . . 14
5.3 Study of a summer cyclone, June 2009 . . . . . . . . . . . . . . . . . . . . . . . . . . 19
6 Extratropical cyclones in future climate
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7 Summary and conclusion
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8 Acknowledgement
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9 References
25
3
1
Introduction
It is important to understand the development of cyclones and their properties in order to foresee
their impact on the weather. Since the foundation of the Polar Front Theory1 by Norwegian meteorologists around 1920 and the pioneering theoretical work on baroclinic instability by Charney
and Eady in the late 1940’s2 , the understanding of extratropical weather systems has gradually
improved, but researh on this issue still proceeds.
Today it is known that horizontal temperature gradients and the interaction between lower and
upper level tropospheric disturbances play a key role in the evolution of an extratropical surface
cyclone, mainly through differential advection of heat and vorticity (section 4). But several forcing
mechanisms may contribute to the formation and strengthening of a mid-latitude cyclone. One of
them, diabatic heating through the release of latent heat, is to be investigated in this thesis.
The investigation will be carried out through case studies of two previous cyclone developments,
a 2009 summer cyclone and a 2005 winter cyclone. These cyclones are chosen because of the appropriate thought to examine the effect of latent heat release on extratropical developments in the
warm and cold seasons, respectively, and because of their respective intensities considering the time
of year. Furthermore, the effect of latent heat release on exactly these two storms has not previously
been examined.
These case studies are based on the HIRLAM-T15 model3 from the Danish Meteorological Institute (DMI) with the execution of three model runs of which two have been perturbed in two
different ways regarding latent heat release (section 5). In the first of the perturbed runs, the release of latent heat has essentially been set to zero in all model routines whereas in the second one,
latent heat release has only been eliminated in routines controling cloud formation, including cloud
water and precipiation. In the latter run, evaporation and condensation is, though, still allowed so
that the energy budget at the surface is not directly influenced by the perturbation.
This thesis begins with an introduction to the three main types of cyclones on Earth. Before
the discussion of the development of extratropical cyclones in section 4, the fundamentals of quasigeostrophic theory is treated in section 3. This theory works as basis for the case studies in section 5.
The development of extratropical cyclones is also an interesting subject concerning future climate. In order to have an idea of how cyclones will act in another climate it is essential to know
how they act in the present climate. How will extratropical cyclones behave if the climate proceeds
getting warmer as global models anticipate? This issue is briefly treated in section 6.
1 See
e.g. Bjerknes and Solberg (1922)
(1947) and Eady (1949)
3 Sass et. al. (2002)
2 Charney
4
2
Types of cyclones
Different kinds of cyclones are parts of the global weather system. The three main types are the
extratropical cyclones, the tropical cyclones and the polar cyclones.
In the following, a brief introduction to the three main types of cyclones will be given. A more
comprehensive discussion of the extratropical cyclone will be given in section 4.
2.1
Extratropical cyclones
The extratropical cyclones are low pressure weather systems on synoptic scale that occur all the
year round. They can form anywhere in the extratropical regions of the earth through the process
of cyclogenesis (see section 4). They rotate, like any other low pressure system, counter clockwise in
the Northern Hemisphere (NH) and clockwise in the Southern Hemisphere (SH) due to the Coriolis
force, and they appear in many different magnitudes concerning both size and strength. Their
counterparts are the high pressure weather systems, also known as anticyclones.
Extratropical cyclones form along baroclinic zones which are characterized by strong horizontal temperature gradients and strong vertical wind shear. They usually develop downstream from
upper level troughs in an enviroment characterized by low static stability.
In association with the extratropical cyclone three types of fronts occur. West of the closed
surface circulation, cold polar air is advected southward replacing the warm tropical airmass. This
southward and eventually eastward moving frontal boundary is called the coldfront.
East of the surface cyclone warm air is replacing cold air in a southerly flow. This northward
advancing frontal boundary is called the warmfront. Gradually the cold front catches up with the
warm front cutting off the warm air from the surface. This third frontal boundary is called an
occlusion or the occluded front. A more thorough treatment of the aspects of fronts is beyond the
scope of this report4 .
2.1.1
The Bergen School and Shapiro-Keyser models
Two different models usually work as foundation for describing the evolution of an extratropical
cyclone. One of them is the Bergen School model, sometimes also refered to as the Polar Front Theory5 . It describes the development of a classical mid-latitude cyclone relatively slowly deepening as
it moves up along a frontal boundary. Eventually it occludes often aquireing a cold core structure
in an equivalent barotropic environment beneath the upper level trough, downstream from which
it originally formed.
Contrary to the Bergen School model, the life cycles of the most explosive developments are often
explained with the so-called Shapiro-Keyser model6 as basis. These rapidly developing cyclones
generally form over the oceans during the winter, to some degree because of weak friction, low
static stabiliy and horizontal sea surface temperature gradients. The main differences with the
Bergen School model are the fracture of the cold front and the formation of a warm core, that arise
when air originating in the warm sector is wrapped around the cyclone. In this way, a part of the
4 For
a discussion of fronts, see e.g. Bluestein (1993)
e.g. Bjerknes and Solberg (1922)
6 Shapiro and Keyser (1990)
5 See
5
Figure 1: Illustration of an idealized developing cyclone according to the Bergen School (Norwegian)
model (a) and Shapiro-Keyser model (b). Upper: Sea level pressure and frontal structure. Lower:
Isotherms. Note the warm core in stage 4 by Shapiro and Keyser. From Cooperative Institute for
Mesoscale Meteorological Studies (http://www.cimms.ou.edu)
cold front closest to the low pressure centre dissolves and the warm front and the occlusion can be
treated the same.
2.2
Polar cyclones
The polar cyclone is an intense and small cyclone which occurs north and south of the polar front
in the NH and the SH, respectively, in an unstable environment. It is a meso-scale storm which is
short lived and usually lasts only between 12 and 36 hours.
It forms over open seas within the polar or arctic airmass during wintertime. A weak baroclinic zone downstream from an upper level trough may trigger strong convection due to differential
positive vorticity advection and thereby initiate polar cyclogenesis. The convection occurs due to
very cold air travelling over relatively warm oceans causing low static stability which eases upward
vertical motion. As the rising air cools widespread cumulonimbus clouds form releasing latent heat.
Together with the sensibel heat flux from the sea surface the airmass warms and surface pressure
falls leading to enhanced surface winds and thereby increased evaporation7 .
Polar lows are capable of producing severe weather in form of heavy snow and strong surface
winds of at least 15 m/s. They develop rapidly and often dissipate just as quickly as they have
formed, especially if they reach land or an area of lower sea surface temperatures. Here they lose
the warm moist flux of air from the sea surface inhibiting cumulus convection.
7 See
e.g. Hamilton (2004)
6
2.3
Tropical cyclones
The tropical cyclone is a synoptic-scale phenomenon which occurs in the tropical regions of the
earth, thereby its name. It is usually more intense than the extratropical cyclone and is often
longer lived.
The cyclone forms as warm moist air from the tropical oceans ascends, often forced by differential positive vorticity advection, and causes convective clouds to form. In this process its water
vapor condenses and significant amounts of latent heat is released. The resulting diabatic warming
of the air mass leads to surface pressure falls and an increased vorticity of the vortex. Surrounding
the low pressure centre is a rapidly rotating wall of convective clouds containing huge amounts of
precipitation. Below these cloud bands the strongest winds of the storm are found as well, since
pressure gradients decrease away from the centre of the storm.
The cyclone can only develop from convective clouds under the right conditions and cannot
form too close to the equator (within about 5◦ latitude) because of a too weak Coriolis force. It
primarily gains its energy from the warm oceans which usually need a certain temperature of around
27 degrees Celsius before the cyclone can develop8 . In addition there must be weak vertical wind
shear so that the upper level part of the vortex remains superimposed over the lower level part.
Therefore, tropical cyclones only form in areas of weak horizontal temperature gradients in contrast
to the extratropical cyclone. If the cyclone travels over cooler waters or land surfaces it will begin
to weaken and eventually dissolve.
The release of latent heat is the most important mechanism for development of both the polar
and the tropical cyclone.
3
Quasi-geostrophic theory
In the previous chapter the characteristics of the three main types of cyclones on Earth were shortly
discussed. In this chapter the development of the extratropical cyclone will be treated.
The development of synoptic-scale weather disturbances is usually refered to as cyclogenesis,
which is different from one type of disturbance to the other as just discussed in section 2.
Even though baroclinity is the leading part of extratropical cyclogenesis, the release of latent
heat does play an important role in extratropical low pressure formation. This leads one to the
essence of this report; to study the impact of latent heat release on extratropical cyclogenesis.
First of all extratropical cyclogenesis needs to be discussed in general which can be done in
several ways, e.g. based on quasi-geostrophic theory or theory of potential vorticity. In this report
the former will be used.
8 See
e.g. Wallace and Hobbs (2006)
7
3.1
Quasi-geostrophic equations
In the quasi-geostrophic theory the complete set of dynamical equations for the atmosphere on the
rotating earth is approximated by simplifying the governing equations by utilizing scale analysis.
While hydrostatic balance is roughly valid on synoptic scales and therefore seems like a good approximation, scale analysis is applied to exclude the insignificant terms of the equations which are
generally an order of magnitude or even smaller than the leading parts.
The quasi-geostrophic equations take the following form in isobaric coordinates9 ,
1 ~
V~g =
(k × ∇p Φ)
f0
(1)
Dg V~g
= −f0 (~k × V~a ) − βy(~k × V~g )
Dt
(2)
∂ω
∇ · V~a +
=0
∂p
(3)
∂T
p
J
= −V~g · ∇p T + ωσ +
(4)
∂t
R
cp
where f0 is a constant Coriolis paramater for a given latitude, which is an acceptable assumption
when working on relatively small meridional length scales. β = ∂f
is assumed constant10 , ω = Dp
is
∂y
Dt
RT dlnθ
the vertical velocity in isobaric coordinates and σ = − p dp is a positive static stability parameter.
These equations form a complete set in the dependent variables Φ, Vg , Va and ω provided that
the diabatic heating rate is known, cJp . Note that in these equations, unlike the governing equations
(as listed in e.g. Holton (1992)), the rate of change of momentum and temperature following the
motion are replaced by the geostrophic rate of change of momentum and temperature following the
geostrophic motion.
3.2
Geopotential height-tendency equation
It is, though, more suitable to carry on with the derivation of other equations capable of working as
a more practical applicable geostrophic prediction system. Deriving the quasi-geotrophic vorticity
equation from the geostrophic wind (Eq. 1) and replacing the divergence term with its relation to
omega through the continuity equation (3) yields the quasi-geostrophic vorticity equation
∂ζg
∂ω
= −V~g · ∇p ζg − βVg + f0
(5)
∂t
∂p
where ζg is geostrophic relative vorticity. If the temperature T is then related to the geopotential
in the thermodynamic energy equation (Eq. 4), a few mathematical steps can be taken to eliminate
ω which yields one of two major equations in quasi-geostrophic theory, the geopotential heighttendency equation11 .
(∇p 2 +
f0 2 ∂ 2
f0 2 ∂ R ~
~
( [−Vg · ∇p T +
2 )χ = f0 [−Vg · ∇p (ζg + f ) − Kζg ] −
σ ∂p
σ ∂p p
1 dQ
])
Cp dt
| {z }
diabatic heating
9 See
e.g. Bluestein 1992
a further explanation of the beta-plane approximation, see e.g. Holton (1992) section 6.2.1
11 Bluestein (1992) section 5.6.4
10 For
8
(6)
where χ = ∂φ
and K = K(p) is a pressure dependent friction coefficient. Quasi-geostrophic friction
∂t
~ = −KVg .
is defined by F
This equation couples the geopotential height tendency with geostrophic absolute vorticity advection, vorticity induced by friction, differential temperature advection and diabatic heating. Note
that if all terms on the right hand side of the geopotential tendency equation are known at a specific time the future geopotential distribution can be calculated given some predetermined boundary
conditions. This is possible because the right hand side of the equation is a diagnostic part of the
full expression which contains only a second order differential in χ on the left hand side.
In a qualitative sense the left hand side of the equation can be regarded as being proportional to
−χ because of the second order differential operator applied on it and because of the wavelike structures (i.e. troughs and ridges) in which these fields are most commonly organized. Thus, cyclonic
differential vorticity advection and the advection induced by friction tend to decrease geopotential
heights by forcing upward vertical motion and thereby adiabatic cooling. On the other hand, warm
air advection and diabatic heating tend to increase geopotential heights by expanding the air column.
A remarkable thing is that amplification of a zonally oriented baroclinic wave (and the decay
as well) is contained in the temperature terms alone. The reason for that is that the advection of
geostrophic absolute vorticity is zero both at the trough and ridge axes, since the gradient of Φ and
the meridional part of the geostrophic wind vanish. In other words, temperature advection (and
diabatic heating) is able of amplifying the wave and advection of geostrophic vorticity is able of
moving the wave. Both do, though, often contribute to a speed up of low pressure formation.
3.3
Omega equation
The evolution of the geopotential height field has now qualitatively been discussed, but the vertical
motion field still needs to be involved because of its strong correlation with synoptic-scale weather
disturbances. The ω-field links together the processes of the upper and lower troposphere and gives
arise to feedbacks between these processes. The release of latent heat to the atmosphere is dependent on the ω-field as well.
It is possible to estimate the vertical velocity from the quasi-geostrophic vorticity equation
(Eq. 5) as well as the continuity equation, but neither of these two methods makes use of the
thermodynamic energy equation. Combining the thermodynamic energy equation with the quasigeostrophic vorticity equation - e.g. as done in Holton section 6.4.1 - yields the second of the two
major equations in quasi-geostrophic theory, the omega equation12 .
(∇p 2 +
f0 2 ∂ 2
f0 ∂
R
)ω = −
[−V~g · ∇p (ζg + f ) − Kζg ] −
∇p 2 (−V~g · ∇p T +
σ ∂p2
σ ∂p
σp
1 dQ
Cp dt
| {z }
) (7)
diabatic heating
It is a diagnostic equation for the field of omega and provides a relationship between vertical
velocity on the left hand side and differential absolute vorticity advection, differential vorticity induced by friction, temperature advection and diabatic heating on the right hand side. It should
also be noticed that every term on the right hand side is inversely proportional to static stability
(σ) as expected since high static stability tends to suppress upward vertical motion.
12 Bluestein
1992 section 5.6.4
9
The geopotential height-tendency equation (Eq. 6), the omega equation (Eq. 7) and the quasigeostrophic vorticity equation (Eq. 5) will be the fundamentals for the discussion of extratropical
cyclogenesis in the following section.
4
Extratropical cyclogenesis
Basically extratropical cyclogenesis converts available potential energy in the flow into kinetic energy
lowering the centre of mass of the total airmass. This requires the air motions in a developing
extratropical cyclone to be organized in such way that, in general, cool upper-tropospheric air sinks
and moves equatorward and warm lower-tropospheric air rises and moves poleward both undergoing
adiabatic warming and cooling, respectively13 .
4.1
Cyclogenesis in uniform upper level flow
Extratropical cyclones often intensify when an area of differential cyclonic vorticity advection becomes superimposed over a strong frontal zone which is a zone of enhanced horizontal temperature
gradients, with the warm air to the right and the cold air to the left relative to the upper level flow
direction. This is usually equivalent to, initially, having the warm air to the south or southeast and
the cold air to the north or northwest (in the NH).
For convenience, consider a sinusoidal zonal wave in mid-latitudes (figure 2). If the upper level
trough is positioned to the west of the surface cyclone and is part of a short wave so that the advection of negative planetary vorticity is small, then there is differential cyclonic vorticity advection
above the cyclone which according to the omega equation (ignoring any temperature advection)
forces upward vertical motion.
If static stability is not too strong, the
upward motion may be present in the entire air column along with the formation of
convergence near the surface and divergence
at the top of the troposphere. Thus, according to the stretching term in the vorticity equation, f0 ∂ω
, the vorticity of the whole
∂p
vortex increases resulting in enhanced surface
winds.
As a result warm air advection and cold
air advection increase to the east (and partly
northeast) and west (and partly southwest) of
the cyclone, respectively. The warm air rises
and the cold air sinks in order to maintain thermal wind balance, and the conversion of potential energy into kinetic energy is thereby in
progress.
Figure 2: Regions of cyclonic (positive) vortcity
advection (CVA) and anticyclonic (negative) vorticity advection (AVA) in a short sinusoidal zonal
geopotential wave. Solid lines: Isohypses. From
Bluestein (1993)
The temperature advection amplifies the upper level wave in order to maintain hydrostatic balance. That is, geopotential height rises and falls to the east and west of the surface cyclone resulting
13 Nielsen
2003
10
in an increase of negative and positive vorticity, respectively, according to the vorticity equation.
This makes the difference between vorticity at the trough and ridge axes even larger leading to
increased upper level vorticity advection.
Gradually, the temperature gradient becomes more meridionally oriented resulting in poleward
movement of the surface cyclone. Step by step the cold air originated to the west of the cyclone
spreads further south and east ’wrapping’ around the surface low. Eventually, the upper level
trough becomes superimposed over the surface cyclone and both vorticity advection and temperature
advection above and to the east of the cyclone, respectively, come to a halt inhibiting further
development. At this time the surface cyclone has peak intensity.
4.2
Cyclogenesis affected by jet streaks
In the discussion above it is assumed, that the upper level winds constituting the jet stream associated with the trough are uniform such that no embedded wind maximum exists, i.e. a jet streak.
However, such embedded maximum does often exist within the jet stream, complicating the interpretation of extratropical cyclogenesis.
For convinience, consider a straight zonal jet streak with a jet core located at the centre (figure
3). It can be seen that the vorticity maximum/minimum is positioned on the cyclonic/anticyclonic
shear side of the jet core (north/south side). Thus, maximum cyclonic vorticity advection occurs
both at the right entrance and left exit region of the jet streak14 .
Again, according to the omega equation, upward vertical motion is forced in these particular
areas while downward vertical motion is forced in the opposite regions. Assuming uniform static
stability in the entire area, the forcing mechanisms induce an ageostrophic circulation both at the
surface and aloft.
Below the entrance region of the jet, at the surface, a southerly ageostrophic wind component
occurs, while a notherly component is induced aloft. In the exit region the southerly component
is induced aloft and the notherly component at the surface. These ageostrophic motions leads to
surface frontolysis and frontogenesis in the entrance and exit region of the jet streak, respectively,
making the jet streak progress downstream.
Therefore, even though differential cyclonic vorticity advection dominates two regions of the jet
streak, extratropical cyclones often develop more rapidly in the left exit region. This is due to both
frontogenesis and the destabilization of the troposphere owing to the ageostrophic motions, cooling
and warming upper and lower tropospheric levels, respectively. In case of a cyclonically curved jet
streak the forcing in the left exit region becomes even stronger.
4.3
Cyclogenesis affected by latent heat release
As just seen the cyclogenesis process involves positive feedback mechanisms between the surface
and upper level low pressure systems. The coupling between these two tropospheric levels is necessary for cyclone development, and that is why low static stability plays a key role in extratropical
cyclogenesis.
14 Nielsen
2003
11
Figure 3: Regions of extrema of vorticity advection in a linear jet streak. Areas of negative vorticity
advection (NVA) and positive vortiticty advection (PVA) in red circles. Isotachs marked by yellow
ellipses. From Wetter-Server Österreich (www.zamg.ac.at)
The release of latent heat is commonly greatest in the lower troposphere owing to greater
amounts of moisture. Thus, even though static stability may increase between the surface and
lower troposphere, it will decrease in the layer between the upper and lower parts of the troposphere, easing the establishment of a secondary circulaton. This is, though, not the only way in
which diabatic heating can nourish the development of a cyclone.
Again, considering an idealized sinusoidal zonal geopotential wave, upward vertical motion is
forced downstream from the upper level trough. If stability permits rising motion, latent heat is
released through condensation. Thus, geopotenial heights increases downstream from the trough
and shortens the entire wave15 , creating even more vorticity at the trough axis and consequently
more vorticity advection above the surface low.
Former studies have detected the importance of the vertical distribution of latent heating. E.g.
Sardie and Warner in 1985 found that for a given amount of latent heating, surface cyclogenesis
was stronger when the heating maximum occured in the lower part of the air coloumn.
Regarding the warm front associated with an extratropical cyclone, latent heat release have
also been found to enhance frontogenesis. A case study by Kuo. et al. (1990) of an extremely
fast developing cyclone (≈60 hPa in 24 hours) off the coast of New Foundland in 1978 revealed
the effect of massive latent heating within the frontal upgliding motion in the warm sector. This
latent heating, having a heating rate of ≈550 K/day at 750 hPa, was found to induce upward vertical motion in phase with the adiabatic frontal circulation. Thus, the direct heating on the warm
side of the front acted as a frontogenetical proces. The upward vertical motion induced by this
15 See
e.g. Nielsen (2008) fig. 7
12
diabatic heating reinforced the adiabatic frontal circulation and enhanced low-level cross-frontal
convergence, constituting a positive feedback mechanism that enhanced baroclinity.
Furthermore it can be seen from the geopotential height-tendency equation, that if diabatic
heating is strongest at some height above ground level, isobaric surfaces above this level tend to
rise. Nature’s response to this air column expansion is upper level divergence and thereby falling
surface pressure.
Note that in the same proces surface convergence also increases (according to the quasi-geostrophic
vorticity equation) tending to minimize the reduction of airmass in the air coloumn. That is why
it is important to have the maximum release of latent heat in the lower troposphere so that the
integrated divergence in the air column becomes more positive, leading to larger pressure falls at
the surface16 .
5
Case studies
In order to examine the effect of latent heat release on extratropical cyclogenesis, the subsections
5.2 and 5.3 contain case studies of the development of two independent cyclones across the North
Atlantic and the European continent.
The first case study deals with the strong hurricane-like winter storm, which developed extremely fast across the United Kingdom and the North Sea on the 7th and 8th of January 2005,
with centre pressure falls of more than 40 hPa in just 24 hours. The cyclone especially affected the
United Kingdom, Denmark and Southern Sweden causing extensive material damage.
The second study focuses on a developing summer low on the 11th and 12th of June 2009. This
unusually strong cyclone considering the time of year especially affected the Northern and Central
parts of Germany as well as Eastern Denmark, the Western Baltic Sea and Northwestern Poland.
5.1
The HIRLAM-T15 model
The examination of these two cyclones is carried out using the HIRLAM-T15 model developed
by The Danish Meteorological Institute with 48 hour runs. While the operational run as well as
the reference run (TREF) were drawn up for normal use in the weather service in 2005 and 2009,
respectively, two seperate runs with the same analysis have later been made exclusively for this
purpose.
The HIRLAM-T15 model uses the semi-lagrangian numerical method for integration of the
equations governing atmospheric motions. It has a horizontal resolution of 0.15◦ (approximately
equivalent to 15 km) and 40 vertical layers. Model parameterizations are of great importance for
calculating subgrid-scale phenomena, that is to say e.g. radition, latent heat release and transport
of momentum and moisture, the latter needing to describe phase changes as well. For more information on the HIRLAM model, including parameterization schemes, see Sass et. al. 2002.
The seperate runs mentioned above, in the following named ’TE1’ and ’TE2’, has been perturbed regarding model routines controling the release of latent heat. In TE1 the release of latent
16 Niels
Woetmann Nielsen, personal communication
13
heat has globally (regarding the actual model) been set to a very small value (essentially zero).
In TE2, the release of latent heat in routines controling cloud formation, including cloud water
and precipitation, has been set to the same very small value. Evaporation and condensation at
the surface are, though, still allowed in this run so that the energy budget at the surface is not
directly influenced by the perturbation. Therefore, due to the fact that moisture fluxes from the
surface are not allowed in TE1, this run is expected to show slightly weaker developments than TE2.
The results of TREF and TE2 have been visualized using DMI’s Metgraf system. These weather
maps containing information of mean sea level pressure (MSLP), 300 hPa winds, 500 hPa geopotential heights and relative vorticity along with 10 m. wind speeds and 850 hPa equivalent potential
temperatures are found in the appendix in 6 hour intervals. The most important maps are shown in
the case studies as well. Results from the TE1 run are not shown because of very small differences
between the perturbed runs, but will be mentioned regularly, especially when the small differences
compared with the TE2 run after all do occur.
5.2
Study of a winter cyclone, January 2005
On January 7th 00Z, a strong surface anticyclone is found across Southern France while an area of
low pressure dominates the Northeast Atlantic and the Norwegian Sea. Between these two systems
strong west-southwesterly flow with widespread average windspeeds above 17 m/s, at least over
open waters, dominates the Northern and Western parts of Europe. This flow is also recognized at
upper levels with a low-amplitude trough and ridge over The Atlantic Ocean west of The British
Isles and across Central Europe, respectively. The associated jet stream extends from The Atlantic
Ocean across Central Scandinavia into The Baltic States. Within this zonal upper level flow a jet
streak can be identified northwest of Great Britain with wind speeds exceeding 85 m/s in the jet core.
Figure 4: Mean sea level pressure (black lines, 4 hPa intervals) and 300 hPa winds (colour shading,
m/s) for TREF (left) and TE2 (right) on January 7th 2005, 12Z. Note the stronger jet streak across
the Northwestern Atlantic Ocean in TREF.
By 12Z the first signs of divergence between the reference run and the perturbed run appear
(figure 4). First of all, the Atlantic jet streak is weakened in the TE2 run (as in TE1), while it
persists with very strong winds in TREF. Maps showing the equivalent potential temperature (θe )
at 850 hPa reveal that θe in TE2 is substantially lower (<5◦ C) at the warm side of the frontal
zone extending approximately from Southern Norway across Northern England and Ireland into
the Atlantic basin than in TREF (figure 5). This could be due to a lack of latent heat release in the
14
frontal boundary causing a decreased gradient in the 300 hPa geopotential height field and thereby
a weaker jet.
Furthermore, the cyclone in the Norwegian Sea has slightly weakened in TE2 whereas it slightly
strengthened in TREF. Both of these observations indicate that the lack of release of latent heat
has a damping effect on developing extratropical dirsturbances.
Concerning the Atlantic basin, in the TREF run, a small wave seems to develop nearby the right
entrance region of the jet streak. As discussed in section 4, the right entrance region constitutes a
favourable environment for cyclone development.
Figure 5: 850 hPa equivalent potential temperature (colour shading, ◦ C) and mean sea level pressure
(black lines, 4 hPa intervals) for TREF (left) and TE2 (right) on January 7th 2005, 12Z
Figure 6: Mean sea level pressure (black lines, 4 hPa intervals) and 300 hPa winds (colour shading,
m/s) for TREF (left) and TE2 (right) on January 7th 2005, 18Z
On 18 hours things start to become very interesting. In TREF, a distinct area of low surface
pressure forms west of Ireland. This closed circulation (not directly recognizable on figure 6) with
15
a centre pressure of 992 hPa is situated downstream from an upper level trough and upstream
from a low-amplitude upper level ridge. At the same time an area of upper level positive vorticity
is found just to the west of the low, which with westerly winds is advected over the developing
surface cyclone (not shown). In TE2 the surface wave is still present, but the rate of development
is remarkably weaker, which may act as a consequence of less vorticty advection because of less
vorticity at the trough axis. TE1 shows a very high degree of similarity with TE2.
On January 8th 00Z, the reference run simulates strong development of the closed circulation
now centered over Northern Ireland (figure 7), approximately midway between the upper level
trough and ridge directly beneath the jet stream. Weak warm air advection dominates across most
parts of Europe while cold air flows southward over the Eastern Atlantic, amplifying the geopotential wave. θe maps show that diabatic heating due to latent heat release seems to contribute to the
strengthening of the ridge (section 4.3) since θe are remarkably higher in TREF, especially along
the fronts (not shown).
The difference of ridging between the two runs (TREF and TE2) can be hard to recognize on
500 hPa maps, but a look at 300 hPa winds shows a slightly stronger ridge in the unperturbed run.
This ridge also contributes to shortening of the entire wave with increasing curvature vorticity of
the trough west of The British Isles (not shown). All together the difference between TREF and
TE2 (and TE1) is quite evident.
Figure 7: Mean sea level pressure (black lines, 4 hPa intervals) and 300 hPa winds (colour shading,
m/s) for TREF (left) and TE2 (right) on January 8th 2005, 00Z
During the next six hours (figure 8), in TREF, the cyclone undergoes an impressive development
with a centre MSLP fall of 17 hPa! Maps of 500 hPa vorticity and wind (figure 9) indicates strong
vorticity advection from 24 to 30 hours as the cyclone moves towards the cyclonic shear side of the
jet and eventually becomes located near the left exit region of the jet streak. An extensive maximum in positive vorticity (mainly shear vorticity) is located across Northwestern England. Due
to the strong southwesterly flow (70-80 m/s in 300 hPa) vorticity advection may be very strong
in the western part of the North Sea southeast of the low. In combination with strong warm air
advection along the warm front NNE of the low pressure centre, the cyclone moves ENE towards
16
Figure 8: Mean sea level pressure (black lines, 4 hPa intervals) and 300 hPa winds (colour shading,
m/s) for TREF (left) and TE2 (right) on January 8th 2005, 06Z
Southwestern Norway during the next six hours.
Figure 9: 500 hPa geopotential heights (black lines, 80 m intervals), wind (black marks) and relative
vorticity (10−5 s−1 ) for TREF (left) and TE2 (right) on January 8th 2005, 06Z
It is also noticable that the cold front loses its connection with the centre of the storm at 30
hours (figure 10). The strongest gradient of θe is now found from Southeastern England across the
Channel region into the Atlantic Ocean while warmer air more og less erodes the cold front over
the Western North Sea. This development is in good agreement with the Shapiro-Keyser model of
rapidly developing cyclones (section 2.1.1 and figure 1) as well as the warm core structure on 42
and 48 hours (not shown).
At the same time (30 hours) in TE2, an area of strong positive vorticity is present as well, in
this run across Southern Ireland and The Irish Sea. In spite of that, the wave has not even yet
developed a closed surface circulation. Thus, it can be concluded that other forcing mechanisms
17
Figure 10: 850 hPa equivalent potential temperature (colour shading, ◦ C) and mean sea level pressure
(black lines, 4 hPa intervals) for TREF (left) and TE2 (right) on January 8th 2005, 06Z
than differential cyclonic vorticity advection have to play a vital role in the development process.
With starting-point near the left exit region of the jet streak, the cyclone continues to deepen
on its way over the North Sea. Just off the Norwegian coast at January 8th 12Z (figure 11), the
cyclone has peak intensity with a centre pressure of 949 hPa and surface winds exeeding hurricane
force (>32 m/s). The 500 hPa map shows an upper level low superimposed over the surface cyclone
inhibiting further development since both vorticity and temperature advection have now come to a
halt (not shown).
Figure 11: Mean sea level pressure (black lines, 4 hPa intervals) and 300 hPa winds (colour shading,
m/s) for TREF (left) and TE2 (right) on January 8th 2005, 12Z
In TE2, the wave does not develop, but even though no closed circulation appears until 48
hours, surface winds still reach storm force (>24 m/s). Despite that the overall difference between
the two runs is evident. It is therefore possible, that latent heat release plays a vital role in the
development of at least some extratropical winter storms.
18
Figure 12: Mean seal level pressure of the developing winter cyclone from TREF (blue) and TE2
(red) as a function of time
Figure 12 depicts the MSLP in the centre of the cyclone in TREF and TE2 as a function of
time. Since the cyclone, or just the wave, in TE2, does not develop a closed circulation until 48
hours, its ’centre pressure’ has been estimated manually from close-up surface maps (not shown).
Because the wave is not recognizable in TREF nor in TE2 until 12 hours, data from 0 and 6 hours
on this system are missing. The graph shows that the cyclone in the unperturbed run develops
extremely fast and reaches maximum intensity before the cyclone in TE2. In TREF, the mean sea
level centre pressure decreases from 998 hPa to 949 hPa in just 24 hours.
A similar result was obtained by Nielsen and Sass in 2003 concerning a powerful cyclone across
Denmark and Northern Germany in December 1999. They found that the difference in peak intensity running a perturbed and unperturbed model regarding latent heat release was 24 hPa. In this
study the difference exceeds 30 hPa.
5.3
Study of a summer cyclone, June 2009
Concerning this case, the effect of diabatic heating is even more evident regarding the analysis of
the model outcome.
At the time of the analysis the cyclone has already formed. The cyclone development is initiated a couple of days before the analysis, as it interfers with a jet streak (300 hPa) off the Atlantic
coast of France. On June 10th, 00Z, the jet core associated with the jet streak is located around
20◦ W and 46◦ N. At the same time the low pressure centre is situated at 46◦ N and 10◦ W directly
underneath the exit region of the jet streak. Due to vorticity advection in the left exit region, i.e.
to the north of the low pressure centre, and strong warm air advection to the east of the low, the
surface cyclone moves northeastwards17 .
17 For
confirmation and further information on this system before June 11th 00Z, see Nielsen (2009)
19
Figure 13: Mean sea level pressure (black lines, 2 hPa intervals) and 300 hPa winds (colour shading,
m/s) for TREF (left) and TE2 (right) on June 11th 2009, 06Z
On June 11th 00Z, the cyclone centre is located over Belgium slightly downstream from a largeamplitude upper level trough. This trough can be identified from both the 500 hPa maps and the
300 hPa wind pattern (not shown). East of the low, especially across Northern Germany, warm air
advection is present.
Figure 14: 500 hPa geopotential heights (black lines, 60 m intervals), wind (black marks) and
relative vorticity (10−5 s−1 ) for TREF (left) and TE2 (right) on June 11th 2009, 06Z. Note the
higher geopotential heights across the Netherlands and Northwestern Germany in TREF relative to
TE2.
At 06Z, the cylone in TREF slightly intensifies reaching a centre pressure of 1002 hPa, while
in TE2 the cyclone fills to 1006 hPa (figure 13). 500 hPa maps show that in TREF, the height of
the 500 hPa surface near the cyclone centre is larger than in TE2 (figure 14). In TREF, the 5520
m. isohypse crosses the Northwestern Netherlands while in TE2, it almost reaches Northwestern
20
Germany. This must be due to latent heating of the airmass close to the surface low.
Figure 15: 500 hPa geopotential heights (black lines, 60 m intervals), wind (black marks) and
relative vorticity (10−5 s−1 ) for TREF (left) and TE2 (right) on June 11th 2009, 18Z. Note the
western displayment of isohypses north of the surface cyclone in TREF compared with TE2.
This development pattern is assumed to dominate at 12 and 18 hours as well. At 18Z, though,
an indirect effect of diabatic heating seems to occur. Geopotential heights (in TREF) begin to rise
to the north of the cyclone due to diabatic heating (figure 15). Both the 5520 m. and the 5580
m. isohypse is remarkably displaced to the west in TREF compared with TE2 causing slightly
backing upper level winds across Northern Poland, the Central Baltic Sea and Southern Sweden.
As a result of rising geopotentials, the wave shortens and vorticity at the trough axis across the
Northern Czech Republic and Southern Poland increases. So far no remarkable differences appear
between TE2 and TE1 (not shown).
It is possible that the release of latent heat can be detected in the 850 hPa equivalent potentiel
temperature field as well. On 30 hours (figure 16), θe is lower (<4◦ ) in TREF than in TE2 over
and north of the surface low across the Eastern Baltic Sea and Northeastern Poland. This could
be due to the condensation decreasing the amount of water vapor in the troposphere since θe rises
whenever temperature rises and/or absolute humidity increases. Though, this cannot be concluded
with certainty without further investigations. The fact that the cyclone in TREF has developed
more rapidly than in TE2 could be an explanation as well, if the cold front and the warm front
have occluded closest to the cyclone centre, cutting off the warm airmass to the north.
From this point on the development of the cyclone passes more like a traditional mid-latitude
cyclone. The fact that both vorticity as well as upper level winds are stronger across Central Poland
(increasing positive differential vorticity advection over the Baltic Sea) in TREF than in TE2 (figure
15) suggests that upper level forcing now plays a greater role than before.
21
Figure 16: 850 hPa equivalent potential temperature (colour shading, ◦ C) and mean sea level pressure
(black lines, 2 hPa intervals) for TREF (left) and TE2 (right) on June 12th 2009, 06Z
Figure 17: Mean sea level pressure (black lines, 2 hPa intervals) and 300 hPa winds (colour shading,
m/s) for TREF on June 12th 2009, 06Z and TE2 on June 12th 2009, 18Z. At these times the cyclone
has peak intensity in the respective model runs
On June 12th 06Z, the cylone in TREF has peak intensity with a centre pressure of 997 hPa in
the Central Baltic Sea (figure 17). In TE2, the cyclone continues its slow development and on June
12th 18Z, it reaches its lowest centre pressure of 1004 hPa in the Eastern Baltic Sea. Regarding
TE1, the lowest MSLP occurs at the same time as in TE2 but at 1005 hPa. Moreover, contrary
to the evolution in TE2, TREF shows a surface cyclone with increasing pressure gradients when
moving towards the cyclone centre, at least on its southwestern side. In TE2, the pressure gradients
around the cyclone are more uniformly distributed.
This strong summer cyclone especially affected the area around the Central and Western Baltic
Sea, including Eastern Denmark and Southern Sweden. Near the town of Hillerød (Northern
Sealand, Denmark) 161.6 mm of precipitation fell in just 37 hours18 from the rain showers and
thunderstorms associated with this system.
18 See
Nielsen (2009)
22
Figure 18: Mean sea level pressure of the developing summer cyclone from TREF (blue) and TE2
(red) as a function of time
Figure 18 depicts the MSLP in the centre of the cyclone as a function of time. Like in the winter
case, the cyclone in the unperturbed run reaches peak intensity earlier than in TE2. Moreover it
seems like the direct effect of diabatic heating keeps the cyclone from weakening while the indirect
effect, creating a shorter wave and more vorticity at the trough axis, contributes to the most rapid
intensification. This happens in the 12 hour period from 18 to 30 hours.
6
Extratropical cyclones in future climate
Concerning extratropical cyclones it is interesting to investigate how these most likely will behave
in future climate. Earth’s temperature has increased during the last century, mainly because of
growing anthropogenic emissions of greenhouse gasses into the atmosphere. This global warming
has an affect on extratropical cyclogenesis through different mechanisms and the most important
ones are listed in the following.
The baroclinicity of the atmosphere, which is related to the horizontal and vertical temperature
distributions19 , constitutes the main mechanism in extratropical cyclogenesis. Today most global
climate models generally show a stronger near surface warming in the far northern regions in the
NH during the winter20 than in the equatorial regions. This results in a weaker meridional temperature gradient, i.e. the baroclinicity in the lower troposphere decreases, making the environment
less conducive for extratropical cyclone activity21 . Even though the poles are exposed to the greatest warming the temperature aloft is still increasing at a higher rate in the tropics, leading to an
increase in the upper tropospheric baroclinicity, which leads to a more favorable environment for
extratropical cyclogenesis.
19 Holton
(1992)
et al. (2002) fig. 1.1
21 Kaas et al. (2002)
20 Kaas
23
Static stability also have an important effect on cyclone development which has already been
discussed in section 3 and 4. Static stability depends on the atmospheric lapse rate and here the climate models show an increase at high latitudes in the NH, because of the increase in concentration
of greenhouse gasses. This results in a decrease in static stability tending to ease the interaction
between upper and lower level systems (section 4). Furthermore, static stability is proportional to
the horizontal scale of atmospheric waves in such way, that if static stability decreases the scale of
atmospheric waves and cyclones becomes smaller22 . Altogether meaning smaller and more intense
storms at high latitudes23 .
Regarding latent heat, a warmer climate would lead to increasing amounts of atmospheric water
vapor, thereby increasing the potential for significant latent heat release during cyclone formation,
especially in connection with lower static stability. Therefore, the isolated effect of a warmer climate
with respect to latent heat release is most likely to enhance extratropical cyclogensis.
7
Summary and conclusion
Two perturbed runs regarding the release of latent heat were succesfully executed using the HIRLAMT15 model. The case studies of both the winter cyclone and the summer cyclone made it likely,
that the release of latent heat is an extremely important forcing mechanism concerning extratropical
cyclone development.
During the investigation of the winter cyclone it was found that the difference in MSLP in the
centre of the cyclone at peak intensity was 32 hPa. In the unperturbed run (TREF) the cyclone
peaked at 949 hPa (at 36 hours) with a maximum deepening rate of 49 hPa/day from 12 to 36 hours,
whereas both of the perturbed runs (TE1 and TE2) simulated the cyclone with a peak intensity of
981 hPa. This was in good agreement with the Nielsen and Sass studies in 2003 of a strong 1999
winter cyclone. Because of the fact that the cyclone in TE1 and TE2 peaked at 48 hours, it cannot
be ruled out that the cyclone would continue its slow rate of development for some time beyond
the 48 hour time frame. Nevertheless, the effect of latent heat release on this cyclone was evident
and the indirect effect by this heating seemed to be the most important factor.
The indirect effect of latent heating altered the structure and evolution of the associated upper
level wave. It was found that latent heating on the warm side of the frontal boundary associated
with the developing cyclone had a frontogenetical effect causing increased upper level winds, supporting results obtained by Kuo et. al. in 1990. Furthermore, latent heating seemed to contribute
to the amplification and shortening of the wave resulting in enhanced vorticity advection downstream from the trough.
Concerning the summer cyclone, the examination of the unperturbed and the perturbed runs
revealed both the direct and the indirect effect of latent heating. The direct effect, especially recognizable during the first 12 to 18 hours due to latent heating near the cyclone centre, seemed to keep
the cyclone from weakening by forcing surface pressure falls. The indirect effect, amplifying and
shortening the wave (like in the winter case) contributed to the most rapid intensification from 18
to 30 hours decreasing the centre pressure from 1002 hPa to 997 hPa. It is also noticeable that, in
TREF, pressure gradients especially on the south side of the surface low decreased away from the
cyclone centre. This pattern was hardly recognizable in TE2 which points to the fact, that latent
22 See
e.g. Holton (1992)
et. al. (2002)
23 Kaas
24
heat release may contribute to an evolution, at least to a small degree, like the one of a tropical
cyclone.
As expected, the two perturbed runs showed only some small mutual differences, only really
noticable in the summer case. In TE1 and TE2 the summer cyclone peaked at 1005 and 1004 hPa,
respectively. This difference in minimum centre pressure seems to be due to the difference in the
type of perturbation between the two runs. The fact that the differences between TE1 and TE2,
regarding the winter case, are essentially non-existing owes to the relatively small surface moisture
fluxes during winter time, especially over land.
Since these case studies have shown that lower static stability through the release of latent heat
forces shorter waves, they also support studies indicating shorter geopotential waves and thereby
smaller and more intense low pressure systems in future climate.
8
Acknowledgement
Thanks to Claus Petersen, DMI, for technical assistance with running the experiments TE1 and
TE2.
9
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26