Statistical properties of flux closure induced by solar wind dynamic pressure fronts

Transcription

1 JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 114,, doi: /2008ja013813, 2009 Sttisticl properties of flux closure induced by solr wind dynmic pressure fronts B. Hubert, 1 C. Blockx, 1 S. E. Miln, 2 nd S. W. H. Cowley 2 Received 10 October 2008; revised 8 My 2009; ccepted 14 My 2009; published 10 July [1] We present sttisticl study of flux closure intervls induced by solr wind dynmic pressure fronts. We consider tht dynmic pressure front reches the Erth when dyside suburorl proton flsh is observed in the SI2 chnnel of the IMAGE-FUV experiment. This prgmtic criterion selects both wek nd strong pressure fronts. It is found tht the preconditioning of the mgnetosphere prior to the pressure pulse rrivl minly governs the mgnetospheric response to wek solr wind dynmic pressure front. This preconditioning includes the mount of open mgnetic flux vilble in the mgnetosphere prior to the pressure front rrivl nd the size of the mgnetospheric cvity. However, in the cse of strong pressure pulse, the mgnetospheric response is more sensitive to the solr wind properties chrcterizing the dynmic pressure front. The pressure jump is not the only one importnt, but lso the vrition of the solr wind velocity nd IMF mgnitude. In overll terms, we find tht strong dynmic pressure front is typiclly chrcterized by dynmic pressure increse lrger thn 2.8 np tht tkes plce on timescles of the order of few minutes. Cittion: Hubert, B., C. Blockx, S. E. Miln, nd S. W. H. Cowley (2009), Sttisticl properties of flux closure induced by solr wind dynmic pressure fronts, J. Geophys. Res., 114,, doi: /2008ja Introduction 1 Lbortory for Plnetry nd Atmospheric Physics, Astrophysics nd Geophysics Institute, University of Liège, Liège, Belgium. 2 Rdio nd Spce Plsm Physics Group, Deprtment of Physics nd Astronomy, University of Leicester, Leicester, UK. Copyright 2009 by the Americn Geophysicl Union /09/2008JA [2] The solr wind is the plsm outflow from the solr tmosphere. It crries the interplnetry mgnetic field (IMF), which is frozen in the solr plsm. When the solr wind reches the Erth, the geomgnetic field nd the IMF cn interconnect, nd crete open mgnetic flux, tht consists of mgnetic field lines tht originte in the interior of the plnet nd close through the interplnetry medium. The solr wind reches the plnet t velocity lrger thn the chrcteristic wve speed (the speed of mgnetosonic wves), so tht bow shock envelopes the mgnetic environment of the plnet, t typicl stndoff distnce of 15 Erth rdii (R E ) upstrem from the plnet in the subsolr region. The pressure exerted by the solr wind on the Erth s mgnetosphere compresses it on the dyside, nd gives it n elongted shpe, creting the mgnetotil on the nightside. Newly opened field lines, creted on the dyside, re convected ntisunwrd towrd the mgnetotil where they eventully undergo nother reconnection process tht closes them gin, thus reconfiguring the mgnetic topology bck to more dipolr pttern, relesing the energy tht regulrly powers the substorm expnsion phse. Occsionlly, the Sun releses burst of mteril, creting discontinuity in the solr wind, tht trnsltes to n incresed dynmic pressure, either cused by the incresed plsm density or to n enhnced velocity (or both), the most spectculr of which is the coronl mss ejection (CME), i.e., n explosive process tht releses lrge quntities of solr mteril into spce. When solr wind pressure front reches the Erth, it compresses the mgnetosphere, nd sometimes triggers substorm expnsion phse, during which lrge mount of open flux is closed in the mgnetotil. [3] Boudouridis et l. [2003, 2004] showed tht the interction of the mgnetosphere with solr wind dynmic pressure pulse results in shrp reduction in the polr cp size, cler signture of flux closure, especilly when pressure pulse hits the mgnetosphere fter n intervl of southwrd IMF, i.e., fter the mgnetosphere hs been loded with open flux by mgnetic reconnection on the dyside. Brittncher et l. [2000] observed n urorl intensifiction triggered by CME which develops from the dyside ovl nd propgtes towrd the nightside. Meurnt et l. [2003, 2003b, 2004] showed tht solr wind dynmic pressure pulses cn trigger n enhncement of urorl ctivity, in greement with Boudouridis et l. [2003]. They showed tht this enhncement is stronger for southwrd IMF conditions. For the set of events studied by Meurnt et l. [2004], the preconditioning of the mgnetosphere ws found to be less importnt thn the properties of the solr wind during the pressure pulse. In prticulr, they found tht the urorl response is stronger for lrger IMF intensity nd solr wind speed. It ws lso shown tht the propgtion of the urorl brightening from the dyside to the nightside occurred sooner for the proton uror thn for the electron uror [Meurnt et l., 2003, 2003b]. Moreover, compres- 1of16

2 sion of the dyside mgnetosphere first results in the formtion of dyside suburorl proton flsh [Hubert et l., 2003]. It ws lso shown tht the compression of the mgnetotil by solr wind dynmic pressure pulse cn lso directly stimulte mgnetic flux closure becuse it cretes the conditions necessry for mgnetic reconnection in the til [Hubert et l., 2006b] s the pressure disturbnce propgtes ll the wy down to the plsm sheet. Meurnt et l. [2005] showed tht pressure pulse-induced nd isolted substorms lrgely shre the sme properties, the pulse being the trigger tht initites the reconfigurtion of the unstble mgnetosphere. [4] We hve developed method tht combines ground bsed dt from the Super Dul Aurorl Rdr Network (SuperDARN) nd globl imges of the proton uror from the Spectrogrphic Imger t nm (SI12) onbord the Imger for Mgnetosphere to Auror Globl Explortion (IMAGE) stellite [Mende et l., 2000, 2000b] in order to estimte the mgnetospheric open flux nd the opening nd closure rtes of mgnetic flux [Hubert et l., 2006]. These rtes re expressed s voltges ccording to Frdy s lw. [5] In the present study, we nlyze the reltion between the properties of solr wind pressure pulses nd the mgnetospheric response in terms of open flux storge nd closure. In prticulr, we serch for correltions between the properties of the solr wind nd the opening nd closure of mgnetic flux. The configurtion of the geomgnetic field is lso considered using geosynchronous dt from the GOES stellites. The role of preconditioning of the mgnetospheric system is considered s well. Throughout the text, we will interchngebly use the terms (solr wind) dynmic pressure front or pulse, pressure front or pulse, or simply front or pulse to designte solr wind dynmic pressure pulse. 2. Dt Avilbility nd Selection [6] As lredy outlined in the introduction, the mount of open flux is estimted using dt from the SI12 instrument of the FUV experiment onbord the IMAGE stellite [Hubert et l., 2006]. This instrument produces globl imges of the Doppler shifted Lymn- emission, which is solely cused by the precipittion of urorl protons, nd is used here to estimte the loction of the open/closed field line boundry (ocb) t ionospheric ltitude, s well s its motion. The SuperDARN rdr network mesures the ionospheric convection, nd llows the reconstruction of the ionospheric electric field [Ruohoniemi nd Bker, 1998; Cowley nd Lockwood, 1992]. The SI12 dt re used in combintion with the SuperDARN rdr dt to estimte the opening nd closure voltges tht chrcterise the vritions of the mount of open flux. The solr wind dt re from the ACE stellite. We found 68 cses of pressure pulses over the period from June 2000 to Februry 2002, for which ACE, SI12 nd SuperDARN dt were vilble. Insted of identifying the pressure pulses from criterion bsed on vritions of the solr wind dynmic pressure, we identified dynmic pressure pulses from more prgmtic stndpoint. It hs been shown tht, when solr wind pressure pulse reches the Erth, it compresses the dyside mgnetosphere in such mnner tht it stimultes the precipittion of protons long closed field lines tht mp to the dyside ionosphere t mgnetic ltitudes lower thn tht of the urorl ovl, creting dyside suburorl proton flsh [Hubert et l., 2003; Fuselier et l., 2004]. We serched the SI12 dt set for dyside suburorl proton flsh signtures, nd we checked posteriori tht there ws ctully n increse of the solr wind dynmic pressure in the ACE solr wind dt, when vilble. This prgmtic pproch lso hs the dvntge of reducing the uncertinty in the time of propgtion of the solr wind feture from the ACE loction to the Erth s mgnetosphere, especilly if we consider tht shock wve (or ny disturbnce) propgtes within the medium in ddition to being dvected long with the plsm motion. Moreover, in the cse of wek pressure pulses, we cn be sure tht the solr wind pressure front did ctully interct with the mgnetosphere. For these wek pressure pulses, the identifiction of the pressure increse responsible for the proton flsh ws sometimes more difficult, nd there remins some uncertinty in few cses. The method of selection of pressure pulse events led us to select more thn 85 cses of dynmic pressure fronts. Some of them hd to be excluded becuse of filure of our open/ closed boundry identifiction softwre, especilly when the viewing conditions were not good enough or when the proton uror ws too dim, leving us with 68 cses. [7] The durtion of the intervl tht we investigte fter the rrivl of prticulr pressure front is gin determined from prgmtic stndpoint: the interction of the pressure front with the mgnetosphere generlly stimultes n intensifiction of the flux closure voltge (sometimes minor). The end of the intervl tht we consider is chosen to be the time t which the closure voltge returns to vlue close to its initil level prior to the front rrivl (i.e., within 10 kv), with mximum durtion limited to 35 minutes. In exceptionl cses when the intensifiction of the closure voltge is so wek tht it remins under 10 kv, durtion of 20 min is chosen. As n exmple, Figure 1 shows the solr wind properties, the open flux, the opening nd closure voltges, nd the net reconnection voltge obtined on 4 November As the nightside (dyside) reconnection voltge represents decrese (n increse) of the open flux, we choose to express the nightside flux closure (dyside flux opening) rte s negtive (positive, respectively) voltge, so tht the net voltge, i.e., the sum of the opening nd closure voltges, represents the time derivtive of the open flux. A shrp dynmic pressure front ws observed by the ACE stellite shortly fter 0130 UT. This front reched the Erth nd triggered dyside suburorl proton flsh detected by the SI12 instrument t 0224 UT (verticl dotted line). The open mgnetic flux deduced from the SI12 observtions prior to the dynmic pressure pulse rrivl ws rther low (0.46 GWb), sitution comptible with the northwrd IMF orienttion. The closure voltge estimted from the SI12 nd SuperDARN observtions intensified fter the dynmic pressure pulse rrived t the plnet nd reched 125 kv. The closure voltge returned to prepulse vlues fter 35 min. Note tht, s time smoothing hs to be pplied to correctly estimte the reconnection voltges, in n bsolute sense, our resolution is not the cdence of imge cquisition of the FUV-SI12 instrument (i.e., 2 min) but only min. This results in smering of the pulse signture in the closure voltge curve, so tht the striking time coincidence between the very shrp signture in the slope of V cl nd the pressure front rrivl 2of16

3 Figure 1. Dynmic pressure front recorded on 4 November The top shows () the open mgnetic flux deduced from ionospheric nd urorl observtions, (b) the net reconnection voltge, (c) the flux opening rte, nd (d) the flux closure rte. The bottom shows solr wind dt from observtions of the ACE stellite s (e) density, (f) velocity, (g) dynmic pressure, nd (h) IMF B z component. A suitble time shift is pplied to ccount for the propgtion of the solr wind from the ACE loction to the plnet. cn be considered incidentl: lthough the pressure pulse rrivl generlly initites n intensifiction of the flux closure, the signture in the closure voltge curve is generlly not tht shrp right t the time of the rrivl of the solr wind dynmic pressure pulse. [8] Severl quntities cn be determined tht, potentilly, cn revel the nture of the interction between interplnetry shocks (dynmic pressure fronts in this study) nd the mgnetosphere. The mount of open flux itself is of course considered, but its vritions cn lso be importnt: the net vrition of the open flux, its mximum rte of chnge during the whole event nd during the interction of the mgnetosphere with the rmp of the solr wind pressure front, nd its initil vlue re ll physicl quntities to be studied s well. A similr study of the flux closure rte cn lso be undertken: its verge, initil, nd mximl vlues must be considered (mximum in terms of its bsolute vlue, i.e., the miniml vlue of the closure voltge, which is negtive number). The net intensifiction nd rte of chnge of the closure voltge hs lso to be considered. In ddition, the time integrl of the closure voltge is lso computed. It represents the totl mount of open flux tht goes through closure during the intervl, wheres the vrition of the mount of open flux during the intervl includes flux opening contribution from the dyside reconnection site. [9] The solr wind dt cn lso be used to determine severl prmeters tht cn, possibly, ply n importnt role in the interction between solr wind dynmic pressure pulses nd the mgnetosphere. The most nturl prmeter to be considered is obviously the solr wind dynmic pressure itself (P dyn ). Previous studies mentioned in section 1 bove [Meurnt et l., 2003, 2003b, 2004] hve however shown tht this my not be the most importnt prmeter. We will nevertheless consider this prmeter, s well s its vrition (mximum vlue, pressure jump, rte of chnge etc) for correltion with the mgnetospheric response expressed in terms of open flux, closure voltge etc. The second nturl prmeter is the solr wind velocity (v sw ), tht hs lredy been pointed out s key prmeter governing the mgnetospheric response to solr wind pressure pulse. The solr wind density (n sw ) is lso considered, but these three solr wind properties re not independent, s P dyn = n sw mv 2 sw. The interplnetry mgnetic field (IMF: B sw ) hs lso to be studied, not only its mgnitude, but lso the vlue of ech component, nd their vritions. The solr wind properties cn be combined ccording to the model of Petrinec nd Russell [1993, 1996], to estimte the size of the mgnetospheric cvity: the rdius of the mgnetopuse R M (i.e., the distnce between the dyside nose of the mgnetopuse nd the plnet), the rdius t x GSM =0ndits cross section my be importnt, s well s the vritions of these quntities. The stndoff distnce of the bow shock R B cn lso be treted in similr mnner. [10] We lso consider the mgnetospheric response in terms of its signture t geosynchronous ltitude. More specificlly, the elevtion ngle of the mgnetic field is studied on the nightside using dt from the GOES-8 stellite. These dt re vilble only for subset of events, so tht less ccurte results my be obtined. [11] We nticipte the next sections by summrizing in Tble 1 the quntities tht will be ctully discussed in this pper nd their definition. In this study, the time intervl reported in Tble 1 is tht of the pressure pulse-induced flux closure. More vribles nd correltion pirs were considered initilly, but we will focus on the ones we found to be the most interesting. Severl vribles specificlly del with 3of16

4 Tble 1. List of Symbols Used in This Study Symbol Definition n sw v sw v sw,init v sw,mx Dv sw Dv sw j rmp P dyn DP dyn P dyn,mx dpdyn B mx z,mx(min) DjBj db j j rmp R M R M,mx R B F F init F finl DF V cl V cl nd V cl V cl,min V cl,init DV cl F cl V op F op e e init e min de min De rmp Solr wind numeric density Solr wind bulk velocity Initil vlue of v sw, i.e., prior the dynmic pressure pulse rrivl Mximum vlue reched by v sw fter the dynmic pressure pulse rrivl Vrition of v sw ssocited with the pressure pulse: Dv sw = v sw,mx v sw,init Vrition of v sw over the rmp of the solr wind dynmic pressure pulse Solr wind dynmic pressure Vrition of P dyn (pressure jump) Mximum vlue of P dyn over given time intervl Mximum vlue of the time derivtive of P dyn over given time intervl Mximum (minimum, respectively) vlue of B z over given time intervl Vrition of the IMF intensity over given time intervl Averge rte of chnge of the IMF intensity during the rmp of the solr wind dynmic pressure pulse Rdius of the mgnetopuse, i.e., stndoff distnce of the mgnetopuse Mximum vlue of R M over given time intervl Rdius of the bow shock, i.e., stndoff distnce of the bow shock Open mgnetic flux Initil vlue of F prior to the solr wind dynmic pressure pulse rrivl Finl vlue of F t the end of the pulse-induced flux closure intervl F finl F init Mgnetic flux closure voltge ( negtive number) Averge nd medin vlues (respectively) of V cl over given time intervl. Minimum vlue of V cl during given time intervl V cl initil vlue, i.e., prior to the solr wind dynmic pressure pulse rrivl V cl,min V cl,init : intensifiction of V cl during the dynmic pressure pulse-induced flux closure intervl Amount of open flux closed during given time intervl; F cl = Rt1 V cl Mgnetic flux opening voltge t0 Amount of open flux creted during given time intervl; F op = Rt1 V op Elevtion ngle of the geomgnetic field t geosynchronous ltitude from the GOES-8 mesurements Initil vlue of e, i.e., prior to the dynmic pressure pulse rrivl Minimum vlue of e over given time intervl Minimum vlue of the time derivtive of e over given time intervl Vrition of e during the rmp of the solr wind dynmic pressure pulse t0 the rmp of the dynmic pressure front. The front rmp is determined s follows: the time derivtive of the solr wind pressure is computed using Svitzky-Goly filtering [Svitzky nd Goly, 1964], nd the time intervl of incresing dynmic pressure round the time of mximum derivtive is considered s the rmp of the pressure front. This concept is however bit loosely defined in the cse of very wek pressure pulse. The Svitzky-Goly smoothing filter cn be used to smooth noisy signl. The filter is defined s weighted moving verge with weighting given s polynomil of certin degree. The returned coefficients, when pplied to signl, perform polynomil lestsqures fit within the filter window. This polynomil is designed to preserve higher moments within the dt nd reduce the bis introduced by the filter, nd the derivtives of the smoothed signl cn be obtined. 3. Sttisticl Anlysis [12] The vribles discussed in section 2 hve been serched for correltion. A set of 68 solr wind dynmic pressure pulse events hs been identified in the SI12, SuperDARN nd ACE dt sets, nd treted to estimte the open flux, reconnection voltges, dynmic pressure etc of these intervls. The method outlined bove is pplied to determine the durtion of ech pulse intervl. Correltions re serched for between the geomgnetic quntities (open flux, voltges, elevtion ngle etc, nd their vritions) nd solr wind properties. The correltion is studied using both Fisher s test nd the Student s test. The significnce level of the correltions re obtin in the sense of bilterl tests, nd the criticl level of confidence is such tht the estimted Person correltion coefficient equls one of the limit of the test intervl tht brckets correltion cses undistinguishble from ffiffiffiffiffiffi the cse r = 0. For the Student s test, the quntity ^r p p ffiffiffiffiffiffiffi n 2 (^r being the estimted correltion coefficient) 1 ^r 2 is known to follow t n 2 distribution function under the r = 0 hypothesis, which llows bilterl testing. In the cse of the Fisher s test, the quntity z = 1 2 ln 1þ^r 1 ^r is clculted, which is known to follow Gussin distribution N 1 2 ln 1þr 1 r, pffiffiffiffiffiffi 1 n 3 which gin llows us to perform bilterl testing under the r = 0 hypothesis. Whtever the test used, the (criticl) level of confidence tells us how confident we should feel tht the estimted correltion coefficient differs from zero, wheres the squre of the correltion coefficient (lso clled the coefficient of determintion) tells us wht frction of the vrince of the dt set could be explined by the dependence of both dt on ech other. From mthemticl stndpoint, the Fisher s test is known to be inefficient for smll size smples (less thn 25 dt pirs), wheres the Student s test is lwys vlid. Clerly, both tests give different significnce levels for given smple, but both significnce levels tend to the sme limit s the smple size is incresed. Obviously, if n tends to infinity, one is supposed to rech bsolute certinty nd the significnce level is lwys 1, whtever the test used. (In the following prgrphs, we will use the symbol r insted of ^r.) In our study, both tests give very similr results. More thn of16

5 study, we will essentilly present the most significnt correltions. The criticl level of confidence cn be estimted ccording to Fisher s or Student s test. We will lwys quote the worst of these two. For every vrible, outliers re systemticlly eliminted: dt points such tht jx i mj >3s re rejected, with m the verge vlue of the ensemble {x i }, nd s the stndrd devition of the smple. One cn consider tht this is rther conservtive choice tht tends to reduce the inferred correltions, becuse in collection of sets of 68 dt points, n verge of 0.18 points per smple would fll outside of the jx i mj >3s intervl, ssuming Gussin distribution of the dt, so tht one cn expect tht dt point representtive of the nturl distribution my be found outside of the selected intervl in 20% of the cses. [13] Figure 2 shows the distribution function of severl properties of the solr wind for our set of events. The dotted lines show the distribution function nd smoothing is pplied to produce the solid lines. The verge (m) nd stndrd devition (s) of the smple re lso given. The bin size used to construct distribution function is 10 s/ñ with ñ the number of points of the smple found in 2s wide intervl centered on m. The dynmic pressure increse cross the pressure front is shown in the top. It clerly ppers tht most of the fronts included in this study were rther wek: the medin of the distribution is 3 np. This lso ppers in the solr wind density increse cross the pressure pulse (middle) with medin vlue of 9.15 cm 3 nd most probble vlue of 4 cm 3. The vrition of the solr wind speed cross the dynmic pressure discontinuity (bottom) is generlly positive, lthough the most probble vlue is 0 km/s. Indeed, s the dynmic pressure is Figure 2. Sttisticl distribution function (dotted lines) nd smoothed sttisticl distribution function (solid lines) of () the solr wind dynmic pressure vrition, (b) the solr wind density vrition, nd (c) the solr wind velocity vrition for the selected set of solr wind dynmic pressure pulses. The verge nd stndrd devition of the smple is indicted for ech vrible. pirs of vribles were considered. A very lrge number of these pirs were found to be (linerly) correlted under level of confidence of 0.9. Clerly, much higher levels of confidence must be used to identify the correltion. The criticl level of confidence ws determined for ech pir of vribles (i.e., the level of confidence under which the correltion coefficient of the considered pir of vribles is equl to the threshold vlue tht discrimintes between correlted nd uncorrelted vribles, i.e., between nonzero nd zero correltion coefficient). From mthemticl stndpoint, it is impossible to define n bsolute threshold tht discrimintes once nd for ll between correlted nd uncorrelted smples of pired vribles. Only hypothesis test cn be crried out nd the significnce of correltion must be expressed in terms of level of confidence. The significnce is however not the finl word, s low correltion cn be sttisticlly significnt, nd the squre of the correltion coefficient cn be used s mesure of the prt of the vritions in the dt set tht cn be explined by the dependence between the correlted vribles. In this Figure 3. Finl open flux s function of the initil open flux. The dt point overplotted with n sterisk is n outlier. The solid line indictes the lest bsolute devition liner fit through the dt points (excluding the outlier), nd the dshed line is the regression line. The dotted line is the bisectrix. 5of16

6 Tble 2. Correltion Coefficients (r) nd Levels of Confidence () for F finl With F init, B z mx, DP dyn, nd P dyn,mx F finl r F init >0.999 B z,mx DP dyn P dyn,mx is the worst of the Fisher s nd the Student s tests. proportionl to the squre of the velocity, smll increse of the velocity will produce lrge increse of the dynmic pressure ( 10% increse of the velocity produces 20% increse of the dynmic pressure). [14] Considering the net open flux budget, the vlue of the open flux t the end of the pressure pulse-induced flux closure (F finl ) is, first of ll, correlted with the open flux vilble prior to the pressure front rrivl (F init ) (Figure 3 nd Tble 2). The correltion coefficient is r = 0.807, nd the correltion hypothesis must be ccepted with confidence level better thn = (ccording to both Fisher s nd Student s tests). (Throughout this pper, we will denote correltion coefficient with the symbol r, nd level of confidence with the symbol.) This correltion cn ccount for r 2 = 0.65 (65%) of the observed vrince, so tht much lrger correltions must not be expected with other prmeters, nd F init is considered here s one of the independent vribles. Indeed, the vlue of F init results from the pst history of the solr wind mgnetosphere interction nd represents preconditioning of the system. As my be expected, the finl open flux lso correltes with the IMF B z. The F finl nd B z,mx (generlly positive) re nticorrelted (ccounting for 17% of the vrince only) (Tble 2). This cn be esily understood: when the IMF is northwrd, very little open flux cn be creted on the dyside, nd the open flux is then lower. The reltion between the IMF B z component nd the cretion of open flux is lredy well known, so we will not dwell on this subject. The finl mount of open flux lso nticorreltes with the mximum vlue of P dyn, P dyn,mx nd with the pressure jump (DP dyn ). Strong compression of the til thus fvors lower vlues of F finl, but the mount of open flux itself depends more on the pst history of the mgnetosphere through F init, both correltions with P dyn,mx nd DP dyn being ble to ccount for 9% of the vrince only. [15] The vrition of the open flux (DF), which results from the blnce between flux opening on the dyside nd flux closure in the til, nd the mount of flux closed during the event (i.e., F cl = Rt 1 t 0 V cl with V cl the closure voltge nd [t 0,t 1 ] the considered time intervl) my be quntities much more representtive of the mgnetosphere pressure front interction rther thn the mount of open flux itself. However, the best correltion for both quntities is found with F init s well (Figure 4 nd Tble 3) explining 16 17% of the vrince. Indeed, DF = F finl F init nd F finl lredy correltes with F init. Also, F cl represents the mount of open flux tht goes through reconnection nd, if the mount of open flux newly creted on the dyside during Figure 4. Open flux vrition (DF) s function of the () initil open flux F init nd (b) mximum mgnetopuse rdius R M,mx expressed in erth rdii. Totl mount of mgnetic flux closed F cl s function of the (c) initil open flux F init nd (d) mximum mgnetopuse rdius R M,mx. Dt points overplotted with n sterisk or plus re outliers. The solid lines re the lest bsolute devition liner fits through the dt points (excluding the outliers), nd the dshed lines re the regression lines. 6of16

7 Tble 3. Correltion Coefficients (r) nd Levels of Confidence () for F cl nd DF With F init, R M,mx, nd F op F cl DF r r F init R M,mx F op is the worst of the Fisher s nd the Student s tests. the considered intervl is not too lrge, F cl cnnot be lrger thn F init. However, this correltion nevertheless suggests tht, s the mgnetosphere ccumultes open flux, its bility to close flux in the til under the stimultion of pressure pulse is incresed (DF nd F cl re negtive numbers). The importnce of mgnetospheric preconditioning lso ppers in the correltion of DF nd F cl with the mximum vlue of the mgnetopuse rdius (the stndoff distnce of the mgnetopuse) R M,mx computed on the bsis of solr wind dt using the model of Petrinec nd Russell [1993, 1996], both being ble to explin 10% of the vrince. Similr correltions re lso found with the stndoff distnce of the bow shock R B,mx nd with the initil vlues of R M nd R B : R M,init nd R B,init, with slightly lower confidence. [16] These correltions suggest tht the mgnetospheric preconditioning is not limited to the ccumulted open flux, but lso includes the cross section of the mgnetospheric cvity exposed to the solr wind flow, the stndoff distnce being considered here s rough proxy describing the shpe of the mgnetosphere. In the model of Petrinec nd Russell [1993, 1996], the stndoff distnce of the mgnetopuse is complicted nonliner function of both B z nd P dyn, nd one my wonder if the correltion with the mgnetopuse rdius does not stem from correltion with P dyn, especilly with its initil vlue, or with its vrition cross the dynmic pressure front. In our smple, which includes wek pulses, we found tht the dynmic pressure does not seem to strongly drive the flux closure process, s we will show below. It cn lso be noted tht F op, the mount of open flux creted on the dyside during the pressure pulse-induced flux closure intervl, nd F cl do not well correlte with ech other (Tble 3), suggesting tht til reconnection closes ccumulted open flux rther thn newly opened flux. Neither is significnt correltion found between F op nd DF. This supports the importnce of the loding-unloding prdigm, in which open mgnetic flux nd energy re ccumulted in the til before intense flux closure cn begin, compred with the direct driving of the mgnetosphere by the solr wind [Blockx et l., 2009, nd references therein] in which new mgnetic energy is supplied through the til mgnetopuse nd is nerly immeditely vilble for dissiptive processes. Indeed, the trnsport of mgnetic flux from the dyside mgnetopuse to the nightside reconnection site cn tke of the order of one hour. It is no surprise, however, tht F op is well correlted with B z,min (r = 0.437, = 0.999) s southwrd IMF (i.e., negtive Figure 5. () Averge closure voltge V cl s function of the initil open flux F init nd (b) the mximum mgnetopuse rdius R M,mx expressed in erth rdii, (c) medin closure voltge V cl versus the initil open flux F init nd (d) mximum mgnetopuse rdius R M,mx. Dt points overplotted with n sterisk or plus symbol re outliers. The solid lines re the lest bsolute devition liner fits through the dt points (excluding the outliers), nd the dshed lines re the regression lines. 7of16

8 Tble 4. Correltion Coefficients (r) nd Levels of Confidence () for V cl nd DF With F init, R M,mx, nd R B,mx V cl r r F init > R M,mx R B,mx is the worst of the Fisher s nd the Student s tests. IMF B z ) is condition tht strongly stimultes mgnetic reconnection on the dyside. [17] The vlue of the flux closure voltge itself bsiclly correltes with F init (Figure 5 nd Tble 4): the verge reconnection voltge V cl hs its best correltion with F init (r 2 21%). V cl then correltes with R M,mx nd R B,mx (r 2 17%). The medin voltge computed during the considered time intervl, V cl, hs its best correltion with F init, then with R M,mx nd R B,mx possibly representing 16 17% of the vrince. (Note tht R M,mx nd R B,mx re not independent on ech other). Slightly lower correltions re gin found with R M,init nd R B,init (Figure 5 nd Tble 4). These correltions show tht the preconditioning of the mgnetosphere is importnt for the process of flux closure itself. These results do not relly differ from those presented for F cl, s in principle, F cl = V cl Dt, with Dt the durtion of the pressure pulse-induced flux closure intervl. (Note tht, in our study, F cl is not exctly equl to V cl Dt becuse F cl is obtined from numericl integrtion, wheres V cl is the simple rithmetic verge of the discrete series of closure voltge vlues. This choice ws mde to ese the comprison between V cl nd V cl, wheres F cl hs to be compred with DF.) [18] The minimum vlue reched by the closure voltge V cl,min represents the mximum rte of flux closure, becuse V cl is negtive number. This quntity best correltes with R M,mx nd R B,mx (r 2 17%) (Tble 5). Similr correltions re found with R M,init nd R B,init, which, nturlly, re close to R M,mx nd R B,mx, respectively. Solr wind properties correlte slightly better with V cl,min thn F init. The vrition of the IMF intensity DjBj correltes with V cl,min s well s its verge rte of chnge during the dynmic pressure front rmp db j j nd the rmp vrition of the solr wind velocity cross the rmp of the pressure pulse Dv sw j rmp. These lst correltion coefficients remin wek. (All these correltions cn ccount for 10 12% of the vrince). The solr wind dynmic pressure does not V cl Tble 6. Correltion Coefficients (r) nd Levels of Confidence () fordv cl With DjBj, Dv sw j rmp, nd F op DV cl r DjBj Dv sw j rmp F op is the worst of the Fisher s nd the Student s tests. seem to ply significnt role so fr in the nlysis of the smple of dynmic pressure pulse-induced flux closure presented here (lthough the dynmic pressure nd the solr wind velocity re dependnt quntities). [19] The only potentil-relted prmeter tht we find to be well correlted with one of the solr wind properties is the intensifiction of the closure voltge DV cl = V cl,mx V cl,init, the difference between the mximum nd initil closure voltge s determined on the bsis of SI12 nd SuperDARN observtions. DV cl correltes best with DjBj nd with Dv sw j rmp (Tble 6). These correltions cn represent only 9 12% of the observed vrinces. The level of confidence of these correltions is somewht lower thn the vlues presented bove, tht hd levels of confidence reching An increse in the modulus of B, s well s n increse of the velocity implies n increse of the electric field of the solr wind, which is the cross product of the velocity nd mgnetic field (we exclude here the improb- Tble 5. Correltion Coefficients (r) nd Levels of Confidence () for V cl,min With F init, R M,mx, R B,mx, DjBj, db j j,nddv sw j rmp rmp V cl,min r F init R M,mx R B,mx DjBj db j j rmp Dv sw j rmp is the worst of the Fisher s nd the Student s tests. Figure 6. () Closure voltge intensifiction nd (b) mount of open flux closed versus the solr wind dynmic pressure increse. The dotted verticl lines indicte threshold of 2.8 np, the solid nd dshed lines re the lest bsolute devition fits nd regression lines, respectively, through the dt subset stisfying DP dyn >2.8nP. 8of16

9 Tble 7. Correltion Coefficients (r) nd Levels of Confidence () for DP dyn With DV cl nd F cl for the Full Dt Set (Upper Lines) nd for the Subset of Dt for Which DP dyn > 2.8 np (Lower Lines) DP dyn r Full dt set DV cl F cl DP dyn > 2.8 np DV cl F cl is the worst of the Fisher s nd the Student s tests. ble sitution in which the increse of B v would only tke plce long the component prllel to ~v ~B, respectively ). One cn here wonder if possible penetrtion of the interplnetry electric field into the mgnetosphere cn significntly influence the process of mgnetic reconnection. This might be supported by the fct tht the best correltion of DV cl is found with F op which, in principle, is proportionl to the electric field in the solr wind, wheres we hve seen bove tht the mgnetosphere essentilly closes prt of the ccumulted open flux rther thn the newly opened flux. [20] Inspection of the correltions found between the solr wind properties nd the quntities representtive of the closure process suggests tht the pressure fronts of our dt set rther hd the effect of inititing the flux closure process, which ws controlled by the properties of the mgnetosphere. Indeed, the flux closure is not strongly correlted with the pressure jump. To first pproximtion it does not depend on the properties of the solr wind pressure front, but rther on the initil stte of the mgnetosphere. Clerly, if independent prmeters hd to be selected s the min vribles tht control the compression-induced flux closure process, one could select F init nd R M,mx in the first plce, possibly supplemented by DjBj nd Dv sw j rmp. The dynmic pressure discontinuity is rther presented here s trigger tht fvors the growth of some instbility of the mgnetosphere nd, more specificlly, of the plsm sheet, tht eventully ends in relxtion of the whole system through flux closure, tht reconfigures the field of the mgnetotil. Figure 6 shows the lck of correltion (Tble 7) between the dynmic pressure increse DP dyn nd the closure voltge intensifiction DV cl (Figure 6) nd the closed flux F cl (Figure 6b). The dispersion of the full dt set is such tht no significnt correltion cn be found. However, Figure 6 lso suggests tht subset could be isolted for DP dyn > 2.8 np (the method used to determine this threshold is explined in the next section: it corresponds to n optiml correltion). The dotted verticl lines in Figures 6 nd 6b isolte this subset, nd the solid lines re the lest bsolute devition fits through the dt. For the subset, higher correltion coefficients re found for DV cl nd F cl with DP dyn (Tble 7), representing nerly 25% of the vrince. This suggests on sttisticl grounds tht sufficiently strong solr wind dynmic pressure pulse cn directly influence the flux closure process. Indeed, previous study of Hubert et l. [2006b] showed tht strong compression of the til cn ctively stimulte the flux closure process in the plsm sheet. Considering the distribution function of DP dyn in Figure 2, it clerly ppers tht most of the pressure fronts included in our dt set were wek ones, nd one could wonder if wek nd strong pressure pulses hve the sme impct on the mgnetosphere. Indeed, it my seem surprising tht the defining prmeter of n interplnetry pressure front does not influence t ll the response of the mgnetosphere to pressure pulse. 4. Subset Sttistics [21] As the properties of the solr wind pressure fronts in our dt set do not pper to significntly influence the mgnetospheric response expressed in terms of flux closure, we conducted n nlysis imed t identifying subsets in the dt set for which better correltion is found between the flux closure-relted prmeters nd the solr wind-relted prmeters. The qulity of the correltion is not determined by the vlue of the correltion coefficient itself, but rther by the level of confidence in the correltion, which combines the correltion coefficient nd the number of observtions vilble in the (sub)smple. Outliers re rejected from the nlysis by pplying the sme procedure to the subset of dt s tht described bove for the full dt set. [22] It hs been possible to find thresholds on vrious dynmic pressure-relted prmeters tht isolte subsets of Figure 7. Closure voltge vrition DV cl (top), minimum closure voltge V cl,min (middle), nd totl mount of flux closed F cl (bottom) s function of the solr wind dynmic pressure increse DP dyn for the subset of events for which DP dyn > 2.8 np. Outliers were not plotted. The solid lines represent the lest bsolute devition fits through the dt. 9of16

10 Tble 9. Subset Thresholds nd Correltions for dpdyn Tble 8. Subset Thresholds nd Correltions for DP dyn mx DP dyn Threshold (np) r dpdyn DV mx Threshold (np/s) r cl V cl,min DV cl F cl V cl,min V cl F cl V cl V cl DF V cl The correltion coefficient r nd level of confidence of the Student s DF test re obtined between DP dyn nd the quntities listed in column 1 restricting the dt set to events for which DP dyn is lrger thn the vlue listed in the column lbeled Threshold. These thresholds isolte the subset of events presenting the highest correltion level of confidence for ech pir of vribles. events for which correltion is found with the vribles describing the response of the mgnetosphere in terms of flux closure. We propose to use these thresholds to quntify wht cn be considered s strong solr wind dynmic pressure pulse, i.e., pulse tht cuses mgnetospheric response sensitive to the dynmic pressure itself. All things considered, identifying dynmic pressure fronts implicitly ssumes tht dynmic pressure vritions cn be clssified into two ctegories: modest vritions on the one hnd, nd pulses on the other, without proposing well defined criterion llowing us to discriminte between them. In our dt set selection, we chose to clssify dynmic pressure vritions s fronts if they produce dyside suburorl proton flsh, to be detected in the SI12 imges. This criterion mkes sense becuse the dyside suburorl proton flsh is nturl signture indicting sudden compression of the dyside mgnetosphere by the solr wind. Nothing Figure 8. () Closure voltge vrition DV cl nd (b) totl mount of flux closed F cl s function of the mximum solr wind dynmic pressure reched in ech event P dyn,mx for the subset of events for which P dyn,mx > 5.97 np. Outliers re not plotted. The solid lines represent the lest bsolute devition fits through the dt, nd the dshed lines re the regression lines. 10 of 16 The correltion coefficient r nd level of confidence of the Student s test re obtined between dpdyn nd the quntities listed in column 1 mx restricting the dt set to events for which dpdyn is lrger thn the vlue mx listed in the column lbeled Threshold. These thresholds isolte the subset of events presenting the highest correltion level of confidence for ech pir of vribles. gurntees, however, tht this dyside-bsed criterion llows us to fully pprecite the nture of dynmic pressure vrition in terms of the nightside response of the mgnetosphere to dynmic pressure front. [23] Pressure fronts presenting solr wind dynmic pressure increse DP dyn lrger thn 2.8 np form subset for which DP dyn nd DV cl correlte well, so tht their interdependence could ccount for 25% of the vrince of the subsmple (Figure 7 nd Tble 8). This clerly expresses rection of the mgnetosphere in response to the dynmic pressure increse in terms of n intensifiction of the flux closure rte. The sme threshold vlue of 2.8 np ws found when serching for the best possible correltion between DP dyn nd V cl,min but the correltion coefficient ws found to be rther low, s well s the level of confidence. Finding the sme threshold for these two prmeters is not surprising, s they re not independent of ech other. It nevertheless suggest tht, for strong pressure fronts, the solr wind dynmic pressure prtly controls the process of flux closure in the til by compressing it, s explined by Hubert et l. [2006b]. Vrible F cl is found to hve better correltion with DP dyn for threshold of 2.8 np s well, the correltion ccounting for 12% of the vrince, while V cl nd V cl re both found to better correlte with DP dyn for threshold of 3 np. The threshold for correltion with DF is 2.8 np s well, but the correltion coefficient is very low. A resonble threshold to discriminte between strong nd wek pressure pulses bsed on the dynmic pressure increse cross the dynmic pressure jump could therefore be chosen s np. This vlue of the pressure increse cn be compred with the typicl vlue of the solr wind dynmic pressure, i.e., 3 np [Feldmn et l., 1977]. Not surprisingly, threshold could lso be found for the mximum rte of chnge of the dynmic pressure dp dyn (Tble 9). A mx mximum level of confidence on correltion is found for this prmeter with DV cl (r 2 34%), F cl (r 2 24%), V cl (r 2 14%) nd V cl,min (r 2 22%) for threshold dp vlue of dyn > np/s, wheres mx threshold of np/s gives mximum level of confidence for correltion with V cl (r 2 12%) nd DF (r 2 6%, this vlue being rther low). A typicl threshold could be chosen on the bsis of these results, but the dynmic pressure growth hs lso to lst for sufficiently long time to produce significnt pressure increse.

11 Tble 10. Subset Thresholds nd Correltions for P mx P mx Threshold (np) r DV cl V cl,min F cl V cl V cl The correltion coefficient r nd level of confidence of the Student s test re obtined between P mx nd the quntities listed in column 1 restricting the dt set to events for which P mx is lrger thn the vlue listed in the column lbeled Threshold. These thresholds isolte the subset of events presenting the highest correltion level of confidence for ech pir of vribles. [24] The closure voltge intensifiction DV cl nd the totl mount of flux closed F cl re lso found to be well correlted with the mximum dynmic pressure reched during the pressure pulse-induced flux closure intervl P mx (Figure 8 nd Tble 10), restricting the dt set to events with P mx > 5.97 np (r 2 28%; r 2 11% respectively). Figure 9. () Closure voltge vrition DV cl, (b) minimum closure voltge V cl,min, nd (c) totl mount of flux closed F cl s function of the solr wind velocity vrition during the rmp of the solr wind dynmic pressure pulse for the subset of events for which Dv SW,rmp > 11.3 km/s. Outliers re not plotted. The solid lines represent the lest bsolute devition fits through the dt, nd the dshed lines re the regression lines. Tble 11. Subset Thresholds nd Correltions for Dv SW j rmp With Dv SW j rmp Threshold (km/s) r DV cl V cl,min > F cl V cl > V cl > The correltion coefficient r nd level of confidence of the Student s test re obtined between Dv SW j rmp nd the quntities listed in column 1 restricting the dt set to events for which Dv SW j rmp is lrger thn the vlue listed in the column lbeled Threshold. These thresholds isolte the subset of events presenting the highest correltion level of confidence for ech pir of vribles. Mximum levels of confidence on correltion re found between P mx nd V cl,min, V cl nd V cl when restricting to P mx > 6.14 np, with poorer correltion however (r 2 12%; r 2 7%; r 2 7% respectively). A resonble threshold for strong pressure pulse could thus be chosen s P mx > 6 np, but the net chnge of dynmic pressure must nevertheless be considered s well, s shown bove, becuse the solr wind cn present intervls of stedy high dynmic pressure. Indeed, the dependence on P mx is not ble to ccount for much of the vrince of the studied subsets. [25] Vritions of the solr wind velocity re not only ssocited with vritions of the electric field in the solr wind, they re lso ble to produce strong vritions of the dynmic pressure. Both effects could influence the process of mgnetic flux closure in the til. Indeed, DV cl nd Dv sw j rmp, the vrition of the solr wind velocity during the rmp of the dynmic pressure front, re strongly correlted (r 2 34%) if the nlysis is restricted to events with Dv sw j rmp >11.3 km/s (Figure 9 nd Tble 11). The correltion is even better with the other vribles relted with the closure voltge, the correltion being ble to ccount for 53% of the vrince of V cl. It clerly ppers tht n increse of the solr wind velocity by more thn km/s during the rmp of the dynmic pressure front cuses stronger response of the mgnetosphere in terms of flux closure. [26] Very similr results re obtined concerning the vrition of the solr wind velocity cross the whole intervl considered (Dv sw = v sw,mx v sw,init ), but with threshold vlue of 8.6 km/s, i.e., roughly 25% lower thn the threshold obtined For Dv sw j rmp (Tble 12). This difference could however be becuse of the fct tht Dv sw Dv sw j rmp, which cn slightly modify the correltions. As this threshold is independent of the mnner in which the rmp is defined, it my finlly be more suitble threshold. One could rgue tht 12 km/s increse in the solr wind velocity cn tke plce progressively during long intervl, nd should not be considered pulse. Indeed, we could lso identify threshold vlues for the mximum rte of chnge of the solr wind velocity. All thresholds found were lrger thn 0.22 km/s 2. A more typicl vlue could be km/s 2 (Tble 13). [27] Considering the full dt set, it hs been found bove tht vrition of the IMF intensity influences the flux closure process in the til, from sttisticl stndpoint. Keeping the subset of events for which DjBj > 0.47 nt (Tble 14), one finds much better correltions for DV cl, 11 of 16

12 Tble 12. Subset Thresholds nd Correltions for Dv sw With Dv SW Threshold (km/s) r DV cl V cl,min F cl V cl V cl The correltion coefficient r nd level of confidence of the Student s test re obtined between Dv sw nd the quntities listed in column 1, restricting the dt set to events for which Dv sw is lrger thn the vlue listed in the column lbeled Threshold. The sme threshold vlue ws found to isolte the subset of events presenting the highest correltion level of confidence for ech pir of vribles. V cl,min, F cl, V cl nd V cl. Indeed, this nerly zero threshold vlue suggests tht, in fct, n increse of the IMF mgnitude fvors the process of dynmic pressure pulse-induced flux closure. Further studies should elucidte if this is specific to the pulse-induced flux closure, or if this is generl trend including flux closure intervls unrelted to dynmic pressure front. [28] The lst prgrphs indicte tht strong solr wind dynmic pressure pulses cn be defined, from the stndpoint of their impliction on the process of flux closure, s pressure fronts presenting the following chrcteristics: dynmic pressure increse of 3 np, nd/or dynmic pressure reching 6 np, nd/or velocity increse by some 10 km/s. Events combining these three properties should nturlly be expected to be very efficient t directly stimulting flux closure in the mgnetotil. In ddition, n increse of the IMF mgnitude is lso fctor tht fvors more intense closure voltge, but this is not necessrily specific to pressure pulse-induced flux closure intervls nd should be checked by further studies. [29] The predominnt importnce of vritions of the solr wind velocity cn be highlighted by full nlysis of the subset defined by DP dyn > 2.8 np. For this subset, the vrition of the solr wind velocity is found to be the onethtbestcorrelteswithdv cl,v cl,min,f cl,v cl ndv cl (Tble (Tble 15 nd Figure 10), the correltions explining between 30 nd 46% of the vritions. The correltion between the vrition of the solr wind velocity nd the prmeters describing the pressure pulse-induced flux closure is obvious. It must be noted tht the preconditioning by the ccumulted open flux prior to the pulse rrivl t Erth plys now minor role. Indeed, F init correltes with F cl with r = nd = only. All other correltions between F init nd the vribles listed here re poorer. Clerly, smll correltion remins, especilly with F cl, becuse the mount of vilble open flux limits the mount of flux tht cn go through closure, but for strong pressure Tble 13. Subset Thresholds nd Correltions for mx dvsw With Mx ( dvsw ) Threshold (km/s 2 ) r DV cl V cl,min F cl > V cl V cl The correltion coefficient r ndlevel of confidence of the Student s test re obtined between mx dvsw nd the quntities listed in column 1, restricting the dt set to events for which mx dvsw is lrger thn the vlue listed in the column lbeled Threshold. Tble 14. Subset Thresholds nd Correltions for DjBj DjBj Threshold (nt) r DV cl > V cl,min > F cl V cl V cl > The correltion coefficient r nd level of confidence of the Student s test re obtined between DjBj nd the quntities listed in column 1, restricting the dt set to events for which DjBj is lrger thn the vlue listed in the column lbeled Threshold. These thresholds isolte the subset of events presenting the highest correltion level of confidence for ech pir of vribles. pulses, this remins minor fctor compred with the solr wind properties. It must be noted tht DP dyn correltes significntly with DV cl (r = 0.483, 0.997), wheres no other voltge-relted prmeter correltes well with DP dyn. This suggests tht, for strong pressure fronts, the compression of the mgnetosphere leds to n intensifiction of mgnetic reconnection without determining the vlue of the reconnection rte itself. The other voltgerelted prmeters better correlte with prmeters relted with the solr wind velocity: Dv sw, s explined bove but lso Dv sw j rmp, dv sw mx etc. Another prmeter tht ppers in the correltion nlysis is the rdius of the mgnetopuse t x GSM = 0, i.e., t Erth loction (DR M E, not listed in Tble 1). Its ssocited correltion coefficients, rnging between 0.45 nd 0.56, re generlly lower thn those found for the velocity-relted prmeters. The mgnetospheric rdius cn be found t ny x GSM using proxy bsed on the solr wind properties [Petrinec nd Russell, 1993, 1996] nd is dependnt on the solr wind velocity, the interplnetry mgnetic field etc. DR M E cn be viewed s proxy for the compression of the mgnetosphere tht only depends on the solr wind properties, nd these correltions show gin the compression of the til fvors flux closure. If set of independent vribles tht contribute to determine the mgnetospheric response to strong solr wind dynmic pressure discontinuities hd to be selected, one could probbly choose Dv sw nd DP dyn in the first plce, possibly supplemented by DR M E, but it would not be necessry to include the mgnetospheric preconditioning, in contrst with the results found for the full dt set. 5. Correltions With Geosynchronous Dt [30] For restricted subset of events, the GOES-8 stellite ws locted in the midnight sector, which we consider here s 6 h MLT intervl centered on midnight MLT. We Tble 15. Correltion Coefficients Relting Dv SW nd Severl Prmeters Describing the Dynmic Pressure Pulse-Induced Flux Closure, Restricting the Anlysis to the Subset for Which DP dyn > 2.8 np With Dv SW r DV cl >0.999 V cl,min >0.999 F cl >0.999 V cl >0.999 V cl >0.999 The reported level of confidence ws computed pplying the Student s test. A correltion coefficient of is found pplying the Fisher s test. 12 of 16