time variation of atmospheric pressure and circulation associated with temperature changes during...

\PERGAMON Journal of Atmospheric and Solar!Terrestrial Physics 59 "0887# 0618Ð0626

0253Ð5715:88:, ! see front matter Þ 0888 Elsevier Science Ltd[ All rights reservedPII] S 0 2 5 3 Ð 5 7 1 5 " 8 7 # 9 9 0 4 9 Ð 2

Time variation of atmospheric pressure and circulationassociated with temperature changes during Solar Proton

EventsM[I[ Pudovkin�\ A[L[ Morozova

Institute of Physics\ University of St[ Petersburg\ St[ Petersburg\ Petrodvorets\ 087893\ Russia

Received 08 March 0887^ received in revised form 16 November 0887^ accepted 29 November 0887

Abstract

A decrease of the direct solar radiation at the Earth|s surface and associated variations of the altitudinal temperaturepro_le observed during Solar Proton Events "SPE# discussed by Pudovkin and Babushkina "0881b#\ Pudovkin andVeretenenko "0883# are believed to be caused by the appearance of a layer which partially re~ects solar radiation "by upto 09)# at an altitude of about 8 km[ This layer is associated with the cirrus cloud that can be nucleated by SolarCosmic Ray "SCR# particles "see Tinsley and Deen\ 0880^ Tinsley and Heelis\ 0882#[ The calculated variations of thealtitudinal pro_le of the air temperature in the high latitude atmosphere "Sodankyla\ Finland\ 8 ¼ 56> N# after the SPE\caused by the appearance of this layer\ are in good agreement with experimental data[

The variations of the temperature pro_le "=DT= ¾ 1Ð2 K at z ³ 09 km# in the high latitude atmosphere during the SPEmay produce a time variation of the meridional pressure pro_le\ which in turn might cause a change of the zonalcirculation[ The expected changes of pressure at the Earth|s surface\ the heights of constant pressure levels and the zonalcirculation are shown to be similar to those observed\ but which are smaller in magnitude[ These quantitative di}erencescan be associated with the oversimpli_cation of the atmospheric model that we used[ Þ 0888 Elsevier Science Ltd[ Allrights reserved[

0[ Introduction

The in~uence of energetic cosmic ray ~ux variationson the state of the lower atmosphere at middle and highlatitudes is a problem which attracts the attentions ofmore and more geophysicists[ Such particles havesu.cient energy to penetrate into the stratosphere andin~uence various physical!chemical processes there[

However\ the mechanism whereby cosmic rays in~u!ence the vorticity\ thermal regime and pressure in thelower atmosphere is not yet clear[ Tinsley et al[ "0878#\Tinsley "0889#\ Tinsley and Deen "0880# and Tinsley andHeelis "0882# supposed that variations of the GalacticCosmic Ray "GCR# intensity might result in changes ofthe rate of ion production and:or global electrical circuit\which in turn might cause the release of the latent heat

� Corresponding author[ Fax] ¦6!701!317!6139^ e!mail]pudovkinÝsnoopy[phys[spbu[ru

associated with the changed rate of ice nucleation inclouds[

At the same time\ Pudovkin and Babushkina "0881b#\Pudovkin and Veretenenko "0883#\ Pudovkin et al["0886#\ and Starkov and Roldugin "0883# have shownthat the variations of the intensity of galactic cosmicrays are associated with a variation "up to 09)# of thetransparency of the atmosphere and of its cloudiness"Veretenenko and Pudovkin\ 0884\ 0885#[ In particular\Forbush decreases of the GCR intensity are followed byan increase of the solar radiation "Pudovkin and Babu!shkina\ 0881b^ Starkov and Roldugin\ 0883^ Pudovkinand Veretenenko\ 0883#[ The bursts of Solar Cosmic Rays"SCR# during Solar Proton Events "SPE# cause a decreaseof the solar radiation intensity "Pudovkin et al[\ 0886#[The changes of the solar radiation intensity in the loweratmosphere have to produce some variations of the alti!tudinal temperature pro_le\ and certain variations of theT"z# pro_le are really observed in connection with cosmicray ~ux disturbances "see curves in Fig[ 2 and Pudovkinet al[\ 0884\ 0885#[

M[I[ Pudovkin\ A[L[ Morozova:Journal of Atmospheric and Solar!Terrestrial Physics 59 "0887# 0618Ð06260629

From the analysis of those pro_les\ Pudovkin andDementeeva "0886# and Pudovkin and Morozova "0886#have arrived at the conclusion that the decrease of thedirect solar radiation at the Earth|s surface "and associ!ated variations of the altitudinal temperature pro_le#observed during SPEs are caused by the appearance inthe atmosphere at an altitude of about 8 km of a layer\partially re~ecting the solar radiation "by up to 09)#[The existence of such a layer is con_rmed by the datapresented by Veretenenko and Pudovkin "0884\ 0885#[According to their data\ the SPE results in variations ofthe high!level cloudiness "8 × 44> N#\ mainly of the cirrustype[ The calculated variations of the altitudinal pro_leof the air temperature in the high latitude atmosphereafter a SPE caused by the appearance of this layer are ingood agreement with the experimental data[

The variations of the temperature pro_le in the highlatitude atmosphere during the SPE may produce a timevariation of the meridional pressure pro_le\ which in turnmight cause a change of the zonal circulation[ Exper!imental con_rmation of this was obtained by Pudovkinet al[ "0884\ 0885#\ Pudovkin and Babushkina "0881a#and Pudovkin and Veretenenko "0881\ 0883\ and 0885#[The main result is the intensi_cation of the zonal cir!culation in the middle and high!latitude troposphere afterthe SPE "see Figs 6 and 7#[ This variation of wind velocityis associated with an increase of the pressure gradient "adecrease of the high!latitude pressure\ "see Fig[ 4# and anincrease of the middle!latitude pressure\ "Pudovkin et al[\0884\ 0885#[

The aim of this paper is to examine whether the cal!culated variations of the temperature pro_le during aSPE may cause the observed changes in the latitude!altitude pressure distribution and in the atmospheric vor!ticity[

1[ Model

Time variations of atmospheric temperature at highlatitudes during solar proton events were calculated asdescribed by Pudovkin and Dementeeva "0886# andPudovkin and Morozova "0886#[ To estimate theexpected SPE e}ect on the dynamics of the lower atmo!sphere at middle and high latitudes\ we consider a simpletwo!dimensional model of the atmosphere where all vari!ables change only with latitude "8#\ height "z# and time"t#[ In this case we can estimate the SPE e}ect for theparameters averaged over latitude circles[ At each pointof the Earth|s surface we use the standard Cartesiancoordinate system with the X!axis directed along the lati!tude circle to the East\ the Y!axis directed along themeridian to the North\ and the Z!axis directed upwards[Then the evolution of the atmospheric parameters isdescribed by the following equations "Tverskoy\ 0851^Houghton\ 0866#]

p � RrT "0#

1r

1t¦ div "rVł # � 9 "1#

1"rVł _#1t

¦"div "rVł _Vł _## � −9p−1rðvł \Vł _Ł−rðał\Vł _Ł

"2#

Concerning the motion along the Z!axis\ we suppose itto be so slow that at any moment the atmosphere maybe considered to be in hydrostatic equilibrium\ so that]

1p1z

� −`r "3#

where p is the pressure\ T is the temperature and r is thedensity of the air\ Vł is the velocity of the circulation\ vłis the angular velocity of the Earth "v � 6[2×09−4 s#\ ałis the angular velocity of the zonal motion of the atmo!sphere "a � Vx:"Re cos 8##\ R is the universal gas constantfor a dry air "R � 1[76×095 erg:g grad#\ Re is the radiusof the Earth "Re � 5[3×092 km#\ ` is the acceleration dueto gravity "` � 8[7 m:s1#[

Equation "0# is the equation of state\ eqn "1# is thecontinuity equation and eqns "2# and "3# are the equationsof motion[ In our case the vector eqn "2# may be writtenas two scalar equations]

1

1t"rVx#¦

0Re cos 8

1

18"rVxVy cos 8#

� r01v¦Vx

Re cos 81Vy sin 8 "2a#

1

1t"rVy#¦

0Re cos 8

1

18"rV1

y cos 8#

� −r 01v¦Vx

Re cos 81Vx sin 8−0Re

1p18

"2b#

The system of eqns "0#Ð"3# permits one to obtain thetemporal and spatial variations of the pressure and den!sity of the air\ and the velocity of the zonal and meridionalcirculation in the lower atmosphere for given boundaryconditions[

To describe the zonal circulation of the atmosphere\we shall use the Blinova index A]

A � 092 a

v� 092 Vx

Rev cos 8[ "4#

Here a is the angular velocity of the atmosphere\ v is theangular velocity of the Earth|s rotation\ and Vx is thezonal velocity "velocity along a latitude circle# at latitude8[ The Blinova index is a measure of the ratio of theangular velocity of the atmosphere to that of the Earth|srotation[

The SPE e}ect in the lower atmosphere is relatively

M[I[ Pudovkin\ A[L[ Morozova:Journal of Atmospheric and Solar!Terrestrial Physics 59 "0887# 0618Ð0626 0620

small "DT ¼ 1 K#\ and the temperature\ pressure andvelocity distributions with height and latitude in the realatmosphere are determined by many changeable factors[Thus\ the SPE e}ect in the variation of the atmosphericpressure and zonal circulation revealed by Pudovkin etal[ "0884#\ Pudovkin and Babushkina "0881a#\ Pudovkinand Veretenenko "0881\ 0883\ 0885# and Veretenenkoand Pudovkin "0882# used the superposed epoch methodto show the di}erence between the mean pro_les of thepressure or index of circulation on a certain day after theonset of the SPE and those on a {quiet day|\ a day or twobefore the beginning of the event[ We also calculate thechanges of the atmospheric parameters from the {quiteday| values[

Thus\ _rst of all\ we obtain initial stationary pro_lesp"8\ z#\ r"8\ z#\ Vx"8\ z#\ and Vy"8\ z# under conditionstypical for a northern middle and high latitude atmo!sphere[ Further on we use these pro_les as {quite day|values[

1[0[ Initial conditions

The initial conditions are modeled by system of equa!tions\ eqns "0#Ð"3# for steady!state conditions "1:1t � 9#and incompressible air " dr: dt � 9#[ In this case eqn "1#can be written as

div Vł 00

Re cos 8

1

18"Vy cos 8# � 9 "1a#

Thus\ the value Vy cos 8 is a constant on 8]

Vy cos 8 � C �Const =8

At the North Pole cos 8 � 9[ Since Vy � � at 8 � 89> Nthen

Vy � 9 "5#

at the North Pole and at all other latitudes[ In this situ!ation eqn "2# may be written as

F

G

j

J

G

f

1

1t"rVx# � 9

9 � −r 01v¦Vx

Re cos 81Vx sin 8−0Re

1p18

"2a#

So\ in the case of the steady!state motion of incom!pressible air

Vx � vRe cos 8 &−0¦X0−1p18

0

r sin 8 cos 8v1R1e ' "6#

The initial stationary daily mean "latitude averaged#altitudinal temperature pro_les were obtained as inPudovkin and Morozova "0886# in accordance with thelatitudinal distribution of the solar ~ux during the cold

period "OctoberÐMarch#[ For example\ in Fig[ 0 theinitial temperature pro_le for 8 � 69> N is presented by asolid line^ the experimental quiet day pro_le "Sodankyla\Finland\ 8 � 56> N\ winter season# is shown by a dashedline "Pudovkin and Dementeeva\ 0886^ Pudovkin andMorozova\ 0886#[ The pressure and density of the air inthe stationary situation were calculated from eqns "0# and"3# with the de_ned temperature pro_le T"8\z# and givenatmospheric pressure at the Earth|s surface "Houghton\0866^ Tverskoy\ 0851#[

For example\ the calculated initial stationary lati!tudinal pro_les of atmospheric pressure at three heights"9\ 4 and 8 km# are presented in Fig[ 1 as solid lines\ withthe experimental standard latitude pro_les of pressure atthe same altitudes "Houghton\ 0886# shown by dashedlines[ As is seen in Fig[ 1\ in our calculations the pressuredistribution at the Earth|s surface from 8 � 39> N to8 � 79> N is in general agreement with the experimentaldata[ At other heights the pressure was calculated accord!ing to distribution of temperature "eqns "0# and "3##[

1[1[ SPE effect

Now\ having obtained the initial "{quite day|# height!latitude pro_les of the pressure pq"8\z#\ density rq"8\z#and velocity Vł q"8\z# of the air\ we can calculate disturbedpro_les of these parameters "Eqns "0#Ð"3# for non steady!state conditions# and estimate their departures from thepq"8\z#\ rq"8\z# and Vł q"8\z# pro_les during the SPE[ Theboundary conditions may be written as follows]

1[1[0[ TemperatureThe SPE e}ect in the lower atmosphere is modeled by

the introduction at latitudes 8 × 44> N of a layer re~ect!ing the short!wave solar radiation with a re~ectioncoe.cient dSR � 9[0 "Pudovkin and Dementeeva\ 0886^Pudovkin and Morozova\ 0886#[ For winter time "Octo!berÐMarch# this layer will only a}ect the atmosphereat 8 ³ 66> N[ We shall assume the temperature of theatmosphere to change in the latitude band 44>N ¾ 8 ¾ 66> N and not to change at other latitudes[ Thevariations of the temperature in the latitude band 44>N ¾ 8 ¾ 66> N are the same given by Pudovkin andMorozova "0886# and shown in Fig[ 2[

1[1[1[ Pressure\ density and velocityEquations "0#Ð"3# were numerically solved with the

boundary conditions "7# and "8#]

8 � 29> N]8p"z\t# � pq"z#

r"z\t# � rq"z#

Vł "z\t# � Vł q"z\t#n8�29> N

"7#

8 � 89> N]8p"z\t# � pq"z#

r"z\t# � rq"z#

Vł "z\t# � Vł q"z\t#n8�89> N

"8#


Fig[ 0[ Initial altitudinal temperature pro_les for 8 � 69> N] model*solid line\ and experiment "Sodankyla\ Finland#*dashed line[

Fig[ 1[ Initial latitudinal pro_les of atmospheric pressure at the Earth|s surface "a#\ z � 4 km "b#\ and z � 8 km "c#] model*solid lines\standard atmosphere model*dashed lines[


Fig[ 2[ Variations of altitudinal temperature pro_les at 44> N ¾ 8 ¾ 66> N associated with SPEs "Pudovkin and Morozova\ 0886#] dayzero*solid line\ day 0*dashed line\ day 1*dotted line\ day 2*dashÐdotted line\ day 3*dashÐtwo!dotted line\ day 4*small dottedline\ day 09*bold solid line[ Experimental data "Pudovkin et al[\ 0884#] day zero*line with open circles and day 2*line with blackcircles[

2[ Discussion

2[0[ Pressure variations

First we consider the variations of the atmosphericpressure at the Earth|s surface[ The in~uence of the SPEthat precedes the Forbush decreases of the GCR intensityon the surface pressure was considered by Pudovkin andBabushkina "0881a# and Pudovkin and Veretenenko"0881#[ On the _rst and second days after the event onsetthe surface pressure in the latitude band 44> N¾ 8 ¾ 79>N decreases approximately by 0 mbar "0 hPa#[ Then\ thepressure begins to grow\ and on third day exceeds the{quite| value by 0 mbar[ These are the experimental data[We assume that the last e}ect is connected with the For!bush*decrease in the intensity of the GCR[ The resultsof the SPE e}ect simulation for the Earth|s surface pres!sure are presented in Fig[ 3[ One can see that there arethree stages in the variations of the surface pressureassociated with the SPE[ On the day zero a growth of thepressure at latitudes 8 × 49> N is observed "9[4 mbar#\and a decrease at lower latitudes "9[14 mbar#[ Apparently\this is an in~uence of the {e}ect of the zeroth day| inthe variation of the temperature height!latitudinal pro_le"Fig[ 2# "Pudovkin and Morozova\ 0886#[ Then\ on the_rst day after the SPE onset\ the surface pressuredecreases at high latitudes "0[9 mbar# and grows at middlelatitudes "9[4 mbar#[ The last stage is characterized bythe growth of the surface pressure at latitudes 8 × 49> N"1[4 mbar# and decrease at the latitude 8 ³ 49> N "0[14mbar#[ One can see that the model pressure variations are

in a good agreement with those observed\ but somewhatsmaller in magnitude[

These surface pressure variations can be associatedwith the changes of the air temperature at high latitudesand a re!distribution of the air mass in the non!tropicaltroposphere[ The growth of the surface pressure at highlatitudes "and decrease at middle latitudes# decreases thepressure gradient "see Fig[ 3# as well as the zonal windvelocity at the Earth|s surface[

Variations of the atmospheric pressure at other heightsare described through variations of the heights of con!stant pressure levels "Pudovkin et al[\ 0884\ 0885#[ Modeland experimental variations of the pressure level heightsfor four pressure levels "8 � 69> N# are presented in Fig[4[ One can see that the character of the model changesof the pressure level heights are similar to the exper!imental ones but rather smaller in magnitude "note thedi}erences between the {model| and {experimental| scalesin Fig[ 4#[ These quantitative di}erences can be associatedwith two facts[ First\ the calculated temperature variationis smaller than that observed[ Secondly\ the atmosphericmodel is a simple one[ The decrease of the height ofconstant pressure levels in the high!latitude tropospherecauses an intensi_cation of the zonal wind velocity atthese altitudes[

2[1[ Zonal wind velocity variations

The variations of the meridional pro_le of pressureresult in changes of the zonal circulation of the atmo!sphere[ To describe the calculated zonal wind velocity


Fig[ 3[ Variations of the latitudinal pro_le of the Earth|s pressure "mbar# associated with the SPE] day zero*thin solid line\ day 0*dashed line\ day 1*dotted line\ day 2*dashÐdotted line\ day 3*dashÐtwo!dotted line\ day 4*bold solid line[

Fig[ 4[ Time variations of the pressure level heights during the SPE for p � 0999 mbar "a#\ p � 699 mbar "b#\ p � 499 mbar "c# andp � 299 mbar "d#] model*solid lines and left scales] observations*lines with black circles and right scales "Pudovkin et al[\ 0884#[

"Vx# variations and to compare it with that observed weuse the Blinova index A "eqn "4## associated with Vx[Figures 5Ð7 present the variation of the Blinova index"DA# after the SPE at the di}erent levels[

The model variation of the Blinova index "zonal windvelocity# at the Earth|s surface calculated for 09> latitudebands is shown in Fig[ 5[ Correspondingly to the timevariations of the pressure "Fig[ 3#\ during the SPEs theBlinova index "zonal wind velocity# decreases at all lati!tudes\ and then grows\ and then decreases again "accord!ingly with variations of the meridional pressure gradient#[

At the level z � 4[4 km "p ¼ 499 mbar#*see Fig[ 6*the time variations of the Blinova index calculated for09> latitude bands are simpler[ On day zero the zonalwind velocity and the Blinova index decrease "DA ¼ 9[4#\and then "days 0Ð4# grow monotonically[ In Fig[ 7 themodel and observed time variations of the Blinova indexat the level z � 4[4 km for latitudes 8 � 59Ð69> N and8 � 49Ð59> N are presented[ The character of the modelvariations of this circulation index are similar to thoseobserved but are up to three times smaller[ The inten!si_cation of the zonal circulation "growth of the Blinova


Fig[ 5[ Variations of the latitudinal pro_les of the Blinova index "DA# at the Earth|s surface associated with the SPE] day zero*thinsolid line\ day 0*dashed line\ day 1*dotted line\ day 2*dashÐdotted line\ day 3*dashÐtwo!dotted line\ day 4*bold solid line[

Fig[ 6[ Variations of the latitudinal pro_le of the Blinova index "DA# at z � 4[4 km associated with the SPE[ Model] day zero*thinsolid line\ day 0*dashed line\ day 1*dotted line\ day 4*bold solid line[ Observations "Pudovkin and Babushkina\ 0881a#] the samelines as for model data\ but with black circles[

index# is associated with the increase of the pressuregradient at heights z × 2 km "see Fig[ 4#[

3[ Conclusions

The results of our previous analysis show that thevariation of the high latitude troposphere transparencyobserved during Solar Proton Events may be caused by

the appearance at the height z � 7Ð8 km of an opticallyactive layer*cirrus cloud[ The model calculation of the~ux variations of radiative energy and temperature!height distribution associated with this e}ect show goodagreement with the experimental data[ These results leadus to a model of the air pressure and wind velocity vari!ations in the middle and high!latitude troposphere causedby the variations of the height!latitude temperaturepro_le[


Fig[ 7[ Time variations of the Blinova index "DA# at z � 4[4 km at 8 � 59> N "solid line# and 8 � 69> N "dashed line# compared withthe observations*bold line "Pudovkin and Veretenenko\ 0885#[

The model temperature variations associated with theSolar Proton Events cause a decrease of the atmosphericpressure and an intensi_cation of the zonal circulation atz × 2 km[ This fact is in good agreement with the data[

The results of our simulation of such a solar protone}ect on the troposphere may be considered as con!_rmation of the e}ectiveness of the radiative mechanismof the in~uence of solar activity "for example\ Solar Pro!ton Events# on weather[

Acknowledgements

This work was supported by the ISF\ grant no[ 426!p[

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time variation of atmospheric pressure and circulation associated with temperature changes during...

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