and the Western North Pacific National Research Institute for Earth Science and Disaster Prevention, Tsukuba, Ibaraki, Japan and Takio Murakami

Size: px
Start display at page:

Download "and the Western North Pacific National Research Institute for Earth Science and Disaster Prevention, Tsukuba, Ibaraki, Japan and Takio Murakami"

Transcription

1 Journl of the Meteorologicl Society of Jpn, Vol. 76, No. 4, pp , Biu ner Jpn nd Its Reltion to Summer Monsoons over Southest Asi nd the Western North Pcific By Ryuichi Kwmurl Ntionl Reserch Institute for Erth Science nd Disster Prevention, Tsukub, Ibrki, Jpn nd Tkio Murkmi Deprtment of Meteorology, School of Ocen nd Erth Science nd Technology, University of Hwii, Honolulu, USA (Mnuscript received 11 September 1997, in revised form 20 My 1998) Abstrct The slowly evolving nnul cycle (signified s "L-mode" ) ws defined by the sum of the first three sinusoids in series of climtologicl pentd men dt of infrred equivlent blck body temperture, 850hP wind, temperture, geopotentil height nd specific humidity, while the rpidly vrying nnul cycle (denoted by "S-mode") ws determined by dding up the remining sinusoids. During erly summer, the L-mode exhibited blocking-type configurtion with ridge over the Kmchtk-Okhotsk region, wheres trough stretched estwrd from northern Chin (center of continentl het low) to Jpn nd beyond. The estblishment of loclly independent L-mode nticyclonic cell over the Se of Okhotsk enhnced low-level esterly nomlies from the vicinity of the Aleutin islnds through northern Jpn. The L-mode esterly nomlies merged with southwesterly nomlies long the southestern periphery of continentl-scle het low, thus generting pronounced cyclonic sher zone round Jpn ccompnied by low-level moisture convergence. This L-mode lower tropospheric trough in intrinsiclly ssocition with the est-west temperture grdient between Est Asi nd the western North Pcific plys vitl role in the formtion of Biu system in erly summer. The L-mode southwesterlies long the est cost of Chin, which re ttributed to the prominence of the continentl-scle het low, served s bridge tht links the monsoon westerlies of tropicl origin with the westerly jet of mid-ltitude origin. This resulted in producing low-level westerly duct extending from the South Chin Se to the centrl North Pcific. At the Biu onset phse (mid-june), the S-mode onset cyclone of convective origin developed over the South Chin Se, nd concurrently the S-mode onset nticyclone orgnized to the northest of the onset cyclone. The consolidted effect of these onset vortexes mplified in the vicinity of the low-level westerly duct ws to cuse the northwrd dvection of wrm nd moist ir from the tropics to southern Jpn. By mid-july, the Asin continentl het low reched its pek nd the summer monsoon over Southest Asi becme fully estblished. At the Biu withdrwl phse (lte July), the continentl het low begn to decy becuse of lnd surfce cooling; nevertheless, the L-mode Pcific High still developed northwrd nd ws most intense t the beginning of August. As the est-west temperture grdient between the ocen nd continent decresed, the L-mode lower tropospheric trough ner Jpn dissipted, wheres L-mode WNPM (summer monsoon over the western North Pcific) trough previled in the subtropics. The withdrwl of Biu ws lso chrcterized by the dominnce of S-mode disturbnces s well s the Biu onset. 1 Corresponding uthor: Ryuichi Kwmur, Ntionl Reserch Institute for Erth Science nd Disster Prevention, 3-1 Tennodi, Tsukub, Ibrki , Jpn. E-mil: kwmur@ess.bosi.go.jp

2 620 Journl of the Meteorologicl Society of Jpn Vol. 76, No. 4 It is thus nticipted tht the sesonl evolution of L-mode circultion field, ssocited with continentocen therml contrst, strongly regultes the ctivities of S-mode perturbtions in nd round the lowlevel westerly duct. It seems likely tht the westerly duct served s wve guide for the brotropic Rossby wve dispersion of the S-mode disturbncebncencencerbnces. The presence of horizontlly shered L-mode flow my lso contribute substntilly to the development nd persistence of S-mode vortexes vi in situ brotropic interction process between the two modes. At ny rte, the combined contribution of the L-mode flow nd S-mode disturbnces is to mke such locl climtologicl events s the onset nd withdrwl of Biu so rpid nd drmtic. 1. Introduction It hs long been known tht Biu (in Jpnese) or Meiyu (in Chinese) is of midltitude frontl chrcter combined with tropicl convective nture. Ninomiy nd Murkmi (1987) hd ccess to most literture pertining to Biu published before the mid-1980s, while To nd Chen (1987) surveyed reserch ctivities on Meiyu during the sme period. The Biu onset round erly June coincides nerly with the onset of summer monsoon over the northern By of Bengl (Murkmi, 1958). Flohn nd Oeckel (1956) were the first to note tht lrge mounts of moisture re trnsported by the previling low-level southwesterlies, from the By of Bengl through southern Chin to Jpn nd beyond. Ninomiy (1978, 1980), Kto (1989), nd Kodm (1993) hve ll indicted results similr to those of Flohn nd Oeckel (1956). Hence, strong ssocition of Biu with the Southest Asin monsoon (signified s "SEAM"; see Appendix) is implied. In the mentime, Murkmi (1959), Sito (1966), Kurshim (1968), nd Askur (1971) hve ll confirmed tht the equtoril western North Pcific is lso n importnt moisture source region. As the Biu dvnces from its erly to lter stge, the moisture trnsport due to the southesterly trde flowing round the Pcific high becomes incresingly importnt. Recently, Murkmi nd Mtsumoto (1994), nd Wng nd Xu (1997) climed ner simultneous occurrence of the Biu onset with the monsoon onset over the tropicl western North Pcific (denoted s "WNPM"). Nkzw (1992) nd Tnk (1992) pointed out tht the sesonl phse lock of intrsesonl oscilltion cn be seen in the Asin summer monsoon system, nd tht such phse-locked convective ctivities in the tropics significntly ffect the Biu onset nd withdrwl. Subsequently, Ued et l. (1995) postulted possible ssocition of the Biu withdrwl with enhnced lrge-scle convection in the WNPM domin. These studies re strong evidence for climtologicl linkge between Biu nd WNPM. The trnsient (not climtologicl) chrcter of Biu hs lso ttrcted the ttention of mny investigtors. Ninomiy nd Murki (1986) mentioned tht intrsesonl vritions seen in the ctivity of Biu is intimtely relted to ctive convection over the South Chin Se. Nitt (1987), Hung nd Li (1987), nd Kurihr nd Tsuyuki (1987) demonstrted occurrence of summertime extrtropicl wve trin in ssocition with nomlous convection round the Philippines. Kwmur et l. (1996) showed tht during borel summer, midltitude intrsesonl oscilltion (ISO), which displys brotropic wve trin structure long gret circle trversing the North Pcific, emerges s prt of the Rossby wve dispersion out of the equtoril convective forcing nd influences upon the trnsient spects of Biu in individul yers. Despite the efforts of mny theoreticl s well s synoptic meteorologists cited here, the questions of why Biu commences on the specific clendr time of the yer, nd lso how nd why Biu is relted to SEAM nd/or WNPM, hve not been nswered stisfctorily. The present study is sequel to the Kwmur et l.'s (1996) pper, but pys specil ttention to the climtologicl spects of Biu. As is well known, Biu occurs during n erly prt of the summer nd, s such, its timescle is shorter thn the seson (90 dys or less). It is then possible to ctegorize Biu s n intrsesonl climtologicl event. In comprison, the SEAM nd WNPM monsoons cn be regrded s n intesesonl climtologicl event since they both lst longer thn four to five months. Without doubt, the monsoons re of therml origin regulted by the nnul cycle of the sun (i.e., nnul nd/or semi-nnul cycles). Mny of meteorologicl vribles over the monsoon domin exhibit winter-summer symmetry in intensity s well s in phse. Such winter-summer symmetric nnul cycle cn be pproximted, with sufficient ccurcy, by the sum of the first (1 yer), second (1/2 yer) nd third (1/3 yer) hrmonics. Due to this reson, in the present study we define the L- mode by consolidting the first three sinusoids. The remining sinusoids describe the rpidly evolving intrsesonl climtologicl vribility nd re denoted s the "S-mode." Included in the S-mode vribility re Biu, nd the onset/withdrwl of SEAM nd WNPM, whose timescles re of course shorter thn the seson. The spce scle lso turns out to be different; nmely, the L-mode is of plnetry-scle while the S-mode is of synoptic-scle. We nticipte tht the S-mode is responsible for bringing bout rpid nd loclized climte over the Asin continentwestern North Pcific domin. How the L- nd S- modes jointly contribute to the life cycle of Biu, SEAM nd WNPM will be detile

3 August 1998 R. Kwmur nd T. Murkmi 621 nd 4. Section 5 documents the counterclockwise progression of L-mode during borel summer. A concluding summry of the results nd discussion re found in Section Dt nd nlysis procedures Dtsets used in the present study include: (1) infrred equivlent blckbody temperture (TBB) with sptil resolution of 1x1 obtined by the Jpnese Geosttionry Meteorologicl Stellite for the period of , nd (2) u, v, T, z nd q extrcted from the ECMWF (Europen Centre for Medium-Rnge Wether Forecsts) routine nlysis with sptil resolution of 2.5x2.5 for the period of The ECMWF dt ssimiltion system remined prcticlly unchnged during this period, thus providing dtsets of nerly uniform qulity. The climtologicl dily men vlue is first computed by verging over the entire 9-yer period. Owing to the reltively short smple size, the climtologicl dily men vlue thus evluted is subjected to some sttisticl noises cused by dy-tody synoptic events occurring in individul yers. To eliminte such undesirble noises, low-pss time filter is then pplied to series of climtologicl dt (signified s A2) s follows: AZ=wkA2k, i=1 to 365. (1) Here, A represents ny of vribles (TBB, u, v, T, z nd q). In Eq. (1), Ai is ssumed to be cyclic t i=1 nd 365, nd the weights wk, re the sme s those used by Kwmur et l. (1996). The response is pproximtely 0.2 for 10-dy period nd zero for noises with periods of less thn 8 dys. To further eliminte unnecessry noises, we compute (1-2-1) weighted men of three consecutive Ai dt. These smoothed pentd men dt t every other pentd re herefter designted s "(A)Z", i=1, 73. Hence, (A) describes the climtologicl nnul cycle, which is identicl from yer to yer. As the next step, we performed hrmonic nlysis to the time series of (A) s follows: (A)=A(0)+A(l)+A(s), (2) where A(0) is the climtologicl nnul men; A(l) represents the sum of the first three hrmonics, wheres A(s) denotes the sum of remining sinusoids. Hence, A(l) defines slowly evolving nnul cycle with periods longer thn 120 dys. A(s) indictes rpidly vrying nnul cycle with periods shorter thn 90 dys. Murkmi nd Mtsumoto (1994) determined the norml onset (withdrwl) dte of Biu t 35N, 135E to be round Pentd 31 (40), which mens tht Biu lsts only for bout 45 dys. By contrst, the time-scle of both SEAM nd WNPM is much longer nd exceeds 120 dys (see their Fig. 2). Both A(l) nd A(s) re eqully importnt when describing the evolution of monsoons (including Biu). Figure 1 shows the time series of 850hP reltive vorticity ((l), divergence D(l) nd moisture flux convergence DQ(l) (dshed lines), verged over the Biu domin (30-40N, E). Also shown re the time series of ((s), D(s) nd DQ(s) (full lines) t 850hP over the sme domin. (DQ) indictes the net convergence of climtologicl pentd men moisture flux {(qu), (qv)j s follows: DQdcqu)+dqvcos)dMK} Kn,cosc8Acosc (3) where M represents the Biu domin. Hence, note tht [(qu), (qv)] is not identicl to [(q) (u), (q) (v)]. As in Eq. (2), (DQ) is then prtitioned into three components BAIU (30-40N, Fig. 1. Time series of 850 hp reltive vorticity ((unit is 10-6s-1), divergence D (unit is 10-7s-1) nd moisture flux convergence DQ (unit is 10-5gkg-1s-1) verged over the BAIU domin (30-40N, E). L-nd S-modes re denoted by dshed nd full lines, respectively. Note tht the strting pentd is Pentd 19 (April 1-5). Also shown re the onset phse (Pentd 33) nd withdrwl phse (Pentd 41). s E) (DQ) = DQ(0) + DQ(l) + DQ(s). (4) Both DQ(l) nd DQ(s) exhibit distinct sesonl chrcter. By definition, DQ(l) nd DQ(s) in Fig. 1 re plotted s the deprture (nomly) from the nnul men. For brevity, the term "nomly" will rrely be used when referring either to L-or S-mode vribles. Likewise, the term "850hP" is herefter omitted becuse most of figures re for the 850hP level. This level is most suited for representing the low-level monsoon flow.

4 622 Journl of the Meteorologicl Society of Jpn Vol. 76, No. 4 h c d Fig. 2. () Climtologicl pentd men (TBB) t Pentd 31 (My 31-June 6). Contour intervl is 5 K, nd shding indictes regions of less thn 265 K. (b) As in () but for Pentd 33 (June 10-14). (c) As in () but for Pentd 35 (June 20-24). (d) Difference in (TBB) between Pentd 31 nd 35. Contour intervl is 2K, nd shding indictes negtive vlues. Between lte April (Pentd 24) nd lte July (Pentd 42), C(l) is positive (cyclonic) with its pek round mid-june (Pentd 34), mid-june is lso the time of minimum D(l) (convergence) nd mximum DQ(l) (moisture sink). These re fvorble conditions for the Biu to begin round Pentd 34. An ctul onset dte cn be determined from n inspection of the time series of c(s), D(s) nd DQ(s). For instnce, the onset cn be defined s the first pentd when ((s) becomes positive, while the withdrwl is determined by the lst pentd before ((s) returns to negtive. Following this definition, the onset (withdrwl) pentd is Pentd 33 (41). Our definition is consistent with previous studies (e.g., Tnk, 1992; Murkmi nd Mtsumoto, 1994, Wng nd Xu, 1997). Actully, the onset (withdrwl) dte slightly differs when different vribles used. In the time series of D(s), the onset is chrcterized by step-like shift from divergent to convergent t Pentd 32 to 33, while the withdrwl occurring s step-like shift from convergent to divergent t Pentd 40 to 41. Since DQ(s) is nerly out of phse with D(s), the onset (withdrwl) dte s defined by DQ(s) is identicl to tht determined from D(s). The onset (withdrwl) dte is not only sensitive to vrible used, but lso vries significntly from one prt to nother in nd round the Biu domin. In this study, we hve defined the onset (withdrwl) pentd of Biu from n ll-inclusive synoptic inspection of the pentd men mps for (TBB), TBB(l) nd TBB (s), s will be elborted in the following sections. 3. Biu onset 3.1 Synoptic spects How nd when the Biu begins over Jpn cn be clerly seen in Figs. 2 to 2c, which show the pentd men (TBB) from Pentd 31 (My 31-June 4) to Pentd 35 (June 20-24). At Pentd 31, n illorgnized bnd of (TBB) less thn 265K stretches off the southern cost of Jpn. This cloud bnd becomes more clerly estblished s it shifts northwrd nd reches Jpn by Pentd 33. Between Pentd 33 nd 35, the cloud bnd further intensifies s indicted by decrese in (TBB) down to below 260 K. Hence, Pentd 33 (June 10-14) cn be defined s the onset pentd of Biu in Jpn. South of the Biu cloud bnd is the Pcific dry zone with (TBB) greter thn 265K. In ssocition with the northwrd migrtion of the Pcific dry zone, erly summer rins ner Tiwn terminte before Pentd 33. The intertropicl convergence zone (ITCZ) stretches long bout 5-10N cross the equtoril Pcific. In the vicinity of the Philippines, which lie t the western end of ITCZ, (TBB) shrply decreses from Pentd 33 to 35. This implies the onset of WNPM sometime between Pentd 33 nd 35, i.e.,

5 August 1998 R. Kwmur nd T. Murkmi 623 C d Fig. 3. () Climtologicl pentd men 850hP wind t Pentd 33 (onset). Unit is 10m (b) As in () but for 850hP geopotentil height. Contour intervl is 10m, nd shding indictes regions of less thn 1430m. (c) As in () but for 850hP temperture. Contour intervl is 2K, nd shding denotes regions of greter thn 294K. (d) As in () but for 850hP specific humidity. Contour intervl is 1gkg-1, nd shding indictes regions of greter thn 13gkg-1. nerly concurrent with or slightly behind the Biu onset. Further to the west over the By of Bengl is intense convection of SEAM, which commences s erly s Pentd 27 (not shown). SEAM tends to extend northwrd s well s westwrd, hence cusing the monsoon onset over southern Indi t Pentd 33. The reltive mgnitude of the Biu onset s compred to the WNPM nd/or SEAM onset cn be mesured by the difference in (TBB) between Pentd 31 nd 35, this difference being signified s 4 (TBB) in Fig. 2d. There re three seprte negtive d(tbb) zones of intense convection. First, the minimum d (TBB) center of less thn -20 K over centrl Indi reflects the monsoon onset there. Second, the onset of WNPM clerly stnds out s mrked negtive d(tbb) zone over the tropicl western Pcific with minimum of below -20 K. Third, the commencement of Biu is chrcterized by WSW-ENE oriented bnd of wekly negtive 4 (TBB) of -4 to -6K from centrl Chin to Jpn. The Biu onset is thus much less pronounced thn the WNPM/SEAM onset in terms of 4(TBB) mgnitude. It should be noted, however, tht the Biu onset is n importnt nd unique climtologicl event ner Jpn. Figure 3 shows the mjor circultion systems t Pentd 33, which my directly or indirectly influence the Biu onset. To begin with, the Biu system is ccompnied by prominent meridionl grdient in both (T) nd (q) cross Jpn, indicting the frontl chrcter of Biu. (T) is highest over Irn nd Pkistn, while (q) is lrgest over northern Indo-Chin. Thus, the equivlent potentil temperture reches its mximum between bout 20 nd 30N, with distinct north-south grdient over the equtoril Arbin Se nd the By of Bengl. There exists remrkble meridionl grdient in (z) over the Arbin Se nd the By of Bengl. These key SEAM res re dominted by monsoon westerlies in excess of 10ms-1. After reching the South Chin Se, the monsoon westerlies turn cycloniclly nd shift towrd southern Chin nd Jpn s southwesterlies. These southwesterlies correspond to wht is generlly referred to s the low-level jet (To nd Chen, 1987). A dominnt het low is centered over Mongoli t round 50N, 115E (Fig. 3b). The Aleutin Low is permnent feture through the yer, lthough substntilly wekening from winter to summer. Equtorwrd of the Aleutin Low is the Pcific High, which moves northwrd nd intensifies s winter dvnces to summer. The trde winds previling to the south of the Pcific High merge with the SEAM westerlies ner the Philippines. This confluence zone, which ws previously locted over the South Chin Se prior to Pentd

6 624 Journl of the Meteorologicl Society of Jpn Vol. 76, No. 4 b c d Fig. 4. () Difference in climtologicl pentd men 850hP wind between Pentd 31 nd 35. Unit is 6ms-1. The letters C nd A denote cyclonic nd nticyclonic circultion nomlies, respectively. (b) As in () but for 850hP geopotentil height. Contour intervl is 5m, nd shding indictes negtive vlues. (c) As in () but for 850hP temperture. Contour intervl is 1K, nd shding denotes negtive vlues. (d) As in () but for 850hP specific humidity. Contour intervl is 1gkg-1, nd shding indictes negtive vlues. 30, grdully shifts estwrd into the western Pcific round E, where WNPM becomes fully estblished by Pentd 46 (August 14-18). Which of the circultion systems mentioned here is closely linked to the Biu onset? This question cn be nswered by exmining Figs. 4 to 4d, which show the differences in [(u), (v)], (z), (T) nd (q), respectively, between Pentd 31 nd 35. An immedite indiction is tht the Biu onset is prt of plnetry-scle circultion chnges occurring not only over the Asin continent but lso over the western Pcific. Note tht the symbols "A" nd "C" denote nticyclonic nd cyclonic circultion chnges, respectively. Except for the ner-equtoril regions, o[(u), (v)] is in pproximte geostrophic blnce with d (z). Of prticulr interest is the presence of pronounced "C" circultion cell centered in between the Alti Mountins nd the Tibetn Plteu, where dry wether persists. The "C" cell in question my correspond to het low. On the other side of the Tibetn Plteu is trin of three "C" cells t (25N, 85E), (20N, 110E), nd (16N, 130E), respectively. These "C" cells re embedded within the convectively ctivted SEAM nd WNPM domin (see Fig. 2d) nd, thus, they re of convective origin. When these four "C" cells re combined together, they tend to form continentl-scle cyclonic circultion encircling the whole Asin continent (Fig. 4) with monsoon westerlies equtorwrd of the convection-induced three "C" cells nd extrtropicl southesterlies (northesterlies) to the est (west) of the continentl cloud-free "C" cell. In Fig. 4, note the presence of wve trin structure with two cyclonic "C" cells nd two nticyclonic "A" cells ligned long the longitudes E from 10N to 50N. Whether this wve trin relly indictes the Rossby-wve dispersion emnting out of the convection-induced "C" cell is not yet known. However, it is more importnt tht this wve trin contributes, to gret extent, to the Biu onset. In prticulr, distinct cyclonic "C" cell ner Jpn indictes the development of Biu. This "C" cell is sndwiched between two nticyclonic "A" cells, one t 25N, 140E nd the other t 50N, 145E. Polewrd (equtorwrd) of the Biu front re northesterly (southwesterly) winds tht crry cold (wrm) ir from the Okhotsk Se (the tropicl western Pcific), s suggested in Figs. 3c nd 4. This results in prominent meridionl LX(T) grdient cross Jpn (Fig. 4c), which stnds in shrp contrst with rpid dissiption of meridionl temperture grdient over northern Chin (Kto, 1985; 1987). It is interesting, likewise, tht o(t) is positive but very smll in the vicinity of the Se of Jpn. As seen in

7 August 1998 R. Kwmur nd T. Murkmi 625 b C d e f Fig. 5. Sptil ptterns of 850hP geoptentil height z(l) t Pentd 27 (), Pentd 31(c) nd Pentd 35(e). Contour intervl is 5m, nd shding indictes negtive vlues. Sptil ptterns of 850hP wind [u(l), v(l)] t Pentd 27 (b), Pentd 31 (d) nd Pentd 35 (f). Unit is 6ms-l. Fig. 4d, moist Ll (q) tongue lso fvors Biu ctivities. Yet nother feture of interest in Fig. 4c is distinct negtive Lt(T) cell over centrl Indi, where the monsoon rins just begin. It is well known mong Indin meteorologists tht the temperture quickly flls fter the commencement of monsoon rins. Likewise, one should not overlook the dominnce of n nticyclonic "A" cell over the northestern Pcific (Fig. 4b), which stnds in shrp contrst to the continentl "C" cell. 3.2 Contribution o f L-mode to the Biu onset As emphsized erlier, the Biu onset is ssocited with rpid intensifiction of the het low over the Asin continent. This cn be more firmly substntited by tking look t Fig. 5. At Pentd 27 (My 11-15), z(1) is lowest to the leewrd of the Tibetn Plteu. At the southestern periphery of the het low re prominent southwesterly {u(l), v(l)] winds in intimte ssocition with n ocen-to-continent z(l) grdient. These southwesterlies over southern Chin re expected to be strongest t round 850hP becuse of the presence of continent-to-ocen T (l) grdient t nd below tht level (figure not shown). Nmely, they correspond to the so-clled low-level jet t 850hP (To nd Chen,1987). The low-level jet ws initilly formed round Pentd 20 (erly April) due to wrming up of the surfce T(l) over Judo-Chin (Tin nd Ysunri, 1998). This is followed by rpid increse in the surfce T(l) in the Mongoli-estern Siberi region, fcilitting the birth of the continentl het low slightly fter Pentd 23. By Pentd 35 (Fig. 5e), the het low becomes fully estblished nd domintes lmost ll of Est Asi. Circling round the periphery of the het low re the continentl-scle cyclonic flows; nmely, westerlies (esterlies) long the southern (northern) periphery, nd southerlies (northerlies) long the estern (western) periphery. By contrst, during the winter hlf, Est Asi is dominted by continentl-scle nticyclonic circultion with northerly cold outbreks emnting out of the Siberin High nd the esterly trde winds sweeping over the By of Bengl nd Arbin Se

8 626 Journl of the Meteorologicl Society of Jpn Vol. 76, No. 4 b c d Fig. 6. () Difference in TBB(l) between Pentd 31 nd 35. Contour intervl is 2K, nd shding denotes negtive vlues. (b) As in () but for 850hP wind [u(l), v(l)]. Unit is 3ms-1. (c) As in () but for 850hP geopotentil height z(l). Contour intervl is 5m, nd shding indictes negtive vlues. (d) As in () but for 850hP temperture T(l). Contour intervl is 1K, nd shding indictes negtive vlues. (figure not presented). Let us now turn our ttention to wht is occurring over the extrtropicl western Pcific. In contrst with the Asin continent, z(l) is positive nd nticyclonic, reflecting the sesonl wekening of the Aleutin Low, the sesonl northwrd migrtion of the Pcific High, nd the enhncement of locl nticyclonic cell in the vicinity of the Se of Okhotsk, which is customrily termed s the "Okhotsk High" by Jpnese meteorologists (e.g., Kto, 1995). The previling [u(l), v(l)] wind there is esterly to southesterly (Fig. 5, right). Of interest is the southesterly {u(l), v(l)] wind polewrd of Jpn, which progressively intensifies from Pentd 27 to 35 due to the increse in the continent-ocen therml contrst. The southesterly [u(l), v(l)] wind of extrtropicl Pcific origin merges with the southwesterly [u(1), v(l)] wind of tropicl monsoon origin, so tht n est-west oriented L-mode trough is formed in the vicinity of Jpn. As indicted in Fig. 1, this L-mode trough is initited round mid-april, grdully intensifies, nd reches its pek by mid-june. Differences in TBB(l), [u(l), v(l)], z(l) nd T(l) between Pentd 35 nd 31, s shown in Figs. 6 to 6d, re direct mnifesttions of the degree to which the L-mode contributes to the Biu onset. These Figures should be compred with Figs. 2d, 4, 4b nd 4c, which re for differences in the originl pentd men (TBB), [(u), (v)], (z) nd (T), respectively. First, comprison between Fig. 6 nd Fig. 2d revels tht the L-mode contributes little to the onset of Biu, since dtbb(l) is not negtive but positive ner Jpn. Around 13N, 130E, QTBB(l) mounts to -8 K, which ccounts for bout 50 % of lrge negtive 4(TBB) in tht vicinity. dtbb(l) over centrl Indi mounts to -14 K or less, being bout 70 % of 4(TBB). This implies tht 4TBB(l) component is more dominnt over the Indin subcontinent. The role of L-mode becomes less importnt s one pproches the western Pcific. In the vicinity of Jpn, no distinctive indictions of the Biu frontl structure in the dt(l) field re seen in Fig. 6d. However, evidence will be presented lter tht the L-mode plys n importnt role during the onset phse of Biu. Of prticulr interest in Fig. 6c is tht dz(l) exhibits distinct ocen-continent contrst in extrtropicl regions polewrd of bout 25N. In comprison, dt(l) in Fig. 6d increses rnonotoniclly with incresing ltitude without ny pprent ocencontinent contrst. This puzzling problem cn be explined by tking look t the ot(l) field t 1000hP level (figure not shown). As expected, the 1000hP dt(l) is two to three times s high over the Asin continent s tht over the western Pcific. The higher surfce temperture fvors

9 August 1998 R. Kwmur nd T. Murkmi 627 Fig. 7. Time-longitude section of geostrophic meridionl wind t 25N, estimted t surfce level. Contour intervl is 1ms-1, nd dshed lines denote northerly wind. the development of the het low over the Asin continent, thus resulting in significnt continentocen contrst in dz(l). Over the Est Chin Se (25-35N, E), n est-west /z(l) grdient nd the southerly Lv(l) flow re pproximtely in geostrophic blnce (see Fig. 6b nd 6c). The geostrophic meridionl wind vg evolves quite regulrly with seson, s illustrted in Fig. 7, which shows the longitude-month section of vg long 25N computed from the climtologicl monthly men surfce pressure prepred by Sdler et l. (1987). The Siberin High is governing pressure system in borel winter with northerly vg penetrting deep into the Pcific. Conversely, the continentl het low is dominnt pressure system in borel summer, with southerly vg ll the wy from 120E to Thus, the western North Pcific clerly stnds out s one of the importnt monsoon domins, since the lterntion of vg from northerly in winter to southerly in summer stisfies the monsoon criterion introduced by Khromov (1957). April is the month of lterntion from northerly to southerly vg. Between 120 nd 140E, the southerly vg shrply increses during erly June, which coincides with the Biu onset phse. The Biu termintes when the southerly vg becomes strongest, exceeding 6ms-1 ner E in mid-july. During August, mrked zone of strong vg tends to expnd estwrd to round 140E where WNPM is t its pek phse. Fig. 8. Time series of lower tropospheric reltive vorticity ((unit is 10-6s-1), divergence D (unit is 107s-1) nd moisture flux convergence DQ (unit is 10-5gkg-1s-1) verged over the northern hlf of Est Asi (35-55N, E). L- nd S-modes re denoted by dshed nd full lines, respectively. These fetures support tht the continentl het low, which is ccompnied by southerlies long its estern periphery, hs n influentil effect on the life cycle of Biu s well s WNPM (e.g., Kto, 1989; Kodm, 1993). Incidentlly, SEAM lso becomes fully estblished in mid-july when the southerly vg becomes most pronounced in terms of monsoonl winds. Such coincidence is not fortuitous but suggests tht SEAM is lso regulted, in some wy, by the continentl het low. An exct life cycle of the continentl het low is demonstrted by the dshed line in the top pnel of Fig. 8, which shows the evolution of ((l) verged over the northern hlf of Est Asi (35-55N, E). The re-verged ((l) vries very slowly with seson nd becomes cyclonic for bout five months from mid-april to mid-september with its mximum in mid-july. We consider tht the L- mode vorticity (l) is direct mnifesttion of the continentl het low tht evolves with the sesonl migrtion of the sun. By contrst, the S-mode vorticity ((s), s shown by the full line in Fig. 8 (top), exhibits frequent shifts between cyclonic nd nticyclonic, nd hence contributes little to the sesonl dependence of the continentl het low. 3.3 Contribution o f S-mode to the Biu onset Our primry objective with this subsection is to detil the structurl fetures of S-mode nd, if possible, to clrify how the S-mode contributes to the Biu onset. To fcilitte further investigtion, we computed differences in vrious S-mode vribles between Pentd 31 (pre-onset) nd Pentd 35 (post-

10 628 Journl of the Meteorologicl Society of Jpn Vol. 76, No. 4 b b C c Fig. 9. () Difference in TBB (s) between Pentd 31 nd 35. Contour intervl is 2K, nd shding denotes negtive vlues. (b) As in () but for 850hP wind [u(s), v(s)]. Unit is 5ms-1. The letters C nd A denote cyclonic nd nticyclonic circultion cells. (c) As in () but for 850hP reltive vorticity ((s), divergence D(s). Note tht o((s) nd 4D(s) re plotted in vector form with cyclonic (nticyclonic) ((s) pointing estwrd (westwrd) nd divergent (convergent) dd(s) directed northwrd (southwrd). Units re 1.5x105 s-1nd 3x106s-1 for ((s) nd LW(s), respectively. onset), s shown in Figs. 9 nd 10. Note tht o((s) nd 4D(s) in Fig. 9c re plotted in vector form with cyclonic (nticyclonic) o((s) pointing estwrd (westwrd) nd divergent (convergent) 4D(s) directed northwrd (southwrd). The Biu onset over nd round Jpn cn be clerly seen in Fig. 9, with dtbb (s) s low s -6K Fig. 10. () Difference in 850hP geopotentil height z(s) between Pentd 31 nd 35. Contour intervl is 5m, nd shding denotes negtive vlues. (b) As in () but for 850hP temperture T(s). Contour intervl is 0.5K. (c) As in () but for 850hP specific humidity q(s). Contour intervl is 0.3gkg-1. or less. An immedite indiction is dominnt role of S-mode on enhncement of convective rins during the Biu onset phse. One of the importnt roles of S-mode is to estblish distinct S-mode trough extending northestwrd from southern Chin, vi the Est Chin Se, to northern Jpn nd beyond (see Figs. 9b nd 10). As mtter of course, the newly estblished S-mode trough is ssocited with prominent cyclonic ((s) nd convergent D(s) in Fig. 9c. Another spect of S-mode is its cpbility to produce front-type structure in the temperture nd moisture fields round Jpn. As suggested in Figs. 9b nd 3c, the southwesterly {Lu(s), dv(s)] flow equtorwrd of the S-mode trough cuses the northwrd dvection of wrm nd moist ir from the trop-

11 August 1998 R. Kwmur nd T. Murkmi 629 b c d Fig. 11. () Sptil pttern of 850hP wind [u(l), v(l)] t Pentd 33. Unit is 6ms-l. (b) As in () but for bsic flow [u(0)+u(l),v(0)+v(l)], which mens the sum of the L-mode flow nd the nnul men flow. Unit is 10ms-1. (c) Sptil pttern of 850hP wind [u(s), v(s)] t Pentd 31. Unit is 3 ms-1. The letters C nd A denote S-mode cyclonic nd nticyclonic circultion cells, respectively. (d) As in (c) but for Pentd 35. icl Pcific to southern Jpn, wheres the northesterly counterprt polewrd of the trough crries cold nd dry ir from the Se of Okhotsk to northern Jpn, resulting in strong meridionl grdient in both dt (s) nd dq(s) cross Jpn (Figs. lob nd loc). It is lso seen tht Meiyu is estblished round estern Chin. We should note here tht the intensifiction of the Okhotsk High is less cler t the onset phse of Biu in terms of S-mode ctivity. This feture is in contrst with the L-mode Okhotsk High enhnced t the sme phse (see Fig. 6c). The S-mode is lso n importnt contributor to the onset of WNPM. In the vicinity of the Philippines, the mgnitude of 4TBB(s) is greter thn 12 K (sign omitted), which is bout twice s lrge s tht ner Jpn. The [Lu(s), Lv(s)] pttern in Fig. 9b displys wve trin structure encompssing not only the SEAM, WNPM nd Biu domins, but lso the higher ltitude regions of the North Pcific. Obviously, the S-mode ctivity is insignificnt over mjority of the Asin continent, including the Indin subcontinent. Fig. 9b lso shows tht the S-mode ctivities in the tropicl centrl Pcific estwrd of the dteline between the equtor nd 30N re reltively quiet. 3.4 Combined contribution of L- nd S-modes to the Biu onset The L-mode is primrily responsible for inititing the Asin continentl het low before the Biu onset. By Pentd 33 (Fig. ll), the Asin het low becomes pprecibly strong nd ssocited {u(l), v(l)] flows disply prominent cyclonic (nticyclonic) sher inside (outside) of the het low. To define the bsic flow, we dd the L-mode flow to the nnul men flow. The consolidted bsic flow, i. e., [u(0)+u(l), v(0)+v(l)j, t Pentd 33 is shown in Fig. 11b. The consolidted winds re southwesterly long the est cost of Chin, while they re westerly over the Arbin Se-By of Bengl region. This is due to the dominnce of the L-mode flow over the nnul men flow. The reverse is true t the mid-ltitude North Pcific, where the consolidted winds re westerly due to greter contribution of the nnul men westerly jet. The most importnt indiction in Fig. 11b is tht the southwesterlies long the est cost of Chin, which re cused by the continentl-scle het low, serve s bridge (or duct) tht connects the monsoonl westerlies of tropicl origin with the westerly jet of midltitude origin.

12 630 Journl of the Meteorologicl Society of Jpn Vol. 76, No. 4 It is possible tht the Biu onset ner Jpn occurs s prt of the Rossby wve dispersion of S- mode perturbtions occurring within the shered bsic flow. The low-level westerly duct ppers to fcilitte time-clustering nd prtilly spceoverlpping development of S-mode disturbnces. As seen in Figs. 11c nd lid, the S-mode disturbnces including C1(s) nd A1(s) cells re well orgnized in nd round the wesssterly duct extending from South Chin Se to the extrtropicl centrl North Pcific. This feture is similr to wht is commonly known s Rossby wve dispersion vi the westerly duct. Actully, Kwmur et l. (1996) showed tht convection-induced intrsesonl disturbnces in the vicinity of the Philippines hve brotropic component through the interction between the men monsoon flow nd disturbnces, nd the brotropic component effectively serves s n origin of the brotropic Rossby wve dispersion. If the sesonl phse lock of convection-induced disturbnces round the Philippines is prominent, geogrphiclly fixed extrtropicl wvetrins re expected to occur frequently on prticulr clender dtes, since the westerly duct is lso geogrphiclly fixed by the sesonl evolution of L-mode. This mechnism seems to resonbly explin why the S-mode onset nticyclone is orgnized just to the northest of the onset cyclone of convective origin. Furthermore, Tsuyuki nd Kurihr (1989) postulted possibility tht sttionry Rossby wves propgting polewrd from the subtropics excite geogrphiclly fixed brotropic unstble modes in the extrtropics. Their proposed ide my lso be responsible for the formtion of S-mode wvetrin structures. Kwmur et l. (1996) lso postulted tht in situ brotropic instbility is likely to be triggered by Rossby-wve dispersion emnting out of loclized convection just est of the Philippines. The presence of horizontlly shered bsic flow is expected to be prerequisite for in situ brotropic development of S-mode disturbnces. Actully, the convection-induced C1(s) cell becme most intense in the cyclonic sher zone inside the het low t Pentd 35, but considerbly wekened by Pentd 37 s it moved northwrd wy from the westerly duct (not shown). Conversely, the A1(s) cell, which ws generted just to the est of C1(s) round Pentd 35, moved west-northwestwrd nd becme very intense nticyclone s it intruded into the nticyclonic sher zone of the westerly duct. The consolidted effect of intensified C1(s) nd A1(s) cells is to mke the Biu onset so quick in climtologicl sense. Thus, n importnce of the in situ brotropic interction between S- nd L-mode upon the Biu onset my be implied. We emphsize tht the role of L-mode is to consolidte the westerly duct nd to set stge for ctivities of S-mode disturbnces. The C1(s) nd A1(s) re the most influentil S-type disturbnces tht mke the Biu onset so drmtic. For brevity, we will herefter cll them "onset cyclone" nd "onset nticyclone," respectively. The onset nticyclone A1(s) stys ctive until Pentd 41 nd exerts crucil influence on the Biu withdrwl. 4. Biu withdrwl 4.1 Contribution of L-mode to the Biu withdrwl Evolution of L-mode before, during nd fter the Biu withdrwl will be investigted by using the z(l) nd [u(l), v(l)] mps t every four pentds from Pentd 37 to 45, s shown in Figs. 12 to 12f, respectively. In the vicinity of Jpn, the L-mode lower tropospheric trough, which hs persisted throughout the Biu seson (see, for exmple, Fig. 5c), tends to weken nd dissipte before the Biu withdrwl (see Fig. 12). At lmost the sme time, the loclly independent L-mode nticyclonic cell over the Se of Okhotsk loses its identity. Judging from chnges in the z(l) configurtion, the Asin het low ppers to be deepest sometime between Pentd 37 nd 41. Actully, z(l) becomes minimum (less thn -60m) to the leewrd of the northestern Tibetn Plteu t Pentd 40 (figure not shown). After Pentd 40 (mid-july), the L-mode Asin het low begins to weken in close ssocition with lnd-surfce cooling. While wekening, the northestern periphery of the L-mode het low exhibits tendency to move southwrd s if it is pushed by the westwrdextending L-mode Pcific ridge. By contrst, the L-mode Pcific High still develops northwrd nd reches its pek round Pentd 43. The L-mode ppers to rotte counterclockwise. Associted with the development of nother L- mode lower tropospheric trough re widespred southerly flows over the tropicl Pcific ll the wy from 120 to 170E long bout 25N, congruous with wht we hve lredy found in Fig. 7. Also note in Figs. 12b, 12d, nd 12f tht the enhnced het trough, which will be herefter signified s the "L-mode WNPM trough," seems to ccelerte the cross-equtoril southerly flows over the mritime continent. These cross-equtoril southerlies, which represent the low-level brnch of locl Hdley circultions, converge into the L-mode WNPM trough fter ccelerting the southwesterly [u(l), v(l)] flows to its south. This my imply tht the L-mode WNPM trough is further reinforced by the locl Hdley circultion. Through these intercting processes, WNPM becomes most ctive t Pentd 46 (e.g., Tnk, 1992; Murkmi nd Mtsumoto, 1994; Wng nd Xu, 1997), i, e., bout one month lter thn the Biu withdrwl. Figure 13 shows chnges in 1000hP T(l) from Pentd 37 to 47. We hve delibertely chosen such long pentd difference to show up the chnges in ner-surfce temperture in conspicuous mn-

13 August 1998 R. Kwmur nd T. Murkmi 631 b C d e f Fig. 12. Sptil ptterns of 850hP geoptentil height z(l) t Pentd 37(), Pentd 41(c) nd Pentd 45(e). Contour intervl is 5m, nd shding indictes negtive vlues. Sptil ptterns of 850hP wind [u(l), v(l)] t Pentd 37b), Pentd 41(d) nd Pentd 45 (f). Unit is 6m ner. As expected, d 1000hP T(l) is negtive over the mjority of the Asin continent, which reflects the cooling-off of ner-surfce temperture due to low het cpcity of the continent. Conversely, hP T(l) is positive over the North Pcific region, suggesting tht the ner-surfce temperture is still incresing up to Pentd 47 (August 19-23) due to lrge het cpcity of the ocen. A remrkble bnd of high d 1000hP T(l) in excess of 3C stretches zonlly from northern Jpn to the centrl North Pcific long bout 40N, reflecting n increse in solr rdition under high TBB res. An inspection of Fig. 13 lso shows tht the northsouth grdient of 41000hP T(1) between the equtor nd 30N is directed polewrd over Southest Asi. Consequently, it is only nturl tht SEAM tends to dissipte from Pentd 37 to 47. Yet WNPM still continues intensifying during the sme period. One my rgue tht higher SST ctivtes convection nd then leds to mturing WNPM. This my be true, but d 1000hP T(l) is only bout 0.5C or less, nd even slightly negtive over the western WNPM domin (0-20N, E). It does not Fig. 13. Difference in 1000hP temperture T(l) between Pentd 37 nd 47. Contour intervl is 0.5K, nd shding indictes negtive vlues. seem tht the higher SST lone is cpble of development of the plnetry-scle monsoon system. We emphsize here tht the decrese in the est-west therml contrst between Est Asi nd the western North Pcific brings bout the dissiption of L- mode nticyclonic circultions over the WNPM do-

14 632 Journl of the Meteorologicl Society of Jpn Vol. 76, No. 4 b c d Fig. 14. Sptil ptterns of TBB(s) t Pentd 39(), Pentd 41(b) nd Pentd 43(c). Contour intervl is 2K, nd shding indictes negtive vlues. (d) Difference in TBB(s) between Pentd 39 nd 43. min, eventully fvoring intense convection in the wrm pool region of the western Pcific. Once the plnetry-scle monsoon circultion is estblished, widespred convection occurs throughout the monsoon domin. 4.2 Contribution o f S-mode to the Biu withdrwl The TBB(s) mps t every two pentds from Pentd 39 to 43, together with the 4TBB(s) field, re shown in Figs. 14 to 14d, respectively. These re to be compred with the corresponding S-mode wind ptterns s shown in Figs. 15 to 15d. First of ll, the A2(s) nticyclone in Fig. 15 is newly born cell developed just prior to Pentd 39, wheres A1(s) ws generted mny pentds erlier, even before Pentd 35, nd served s Biu onset nticyclone (see Fig. lid). At Pentd 39, sndwiched between the A1(s) cell nd C2(s) cell re strong westerly to southwesterly [u(s), v(s)] winds (Fig. 15) nd ssocited convection (Fig. 14), congruous with continued Biu-type wet wether. By Pentd 41, the A1(s) nticyclone previls round Jpn nd suppresses convection. As such, the A1(s) cell is the one tht cuses the Biu to withdrw from Jpn. In this respect, we now chnge its nme from the "onset" to "withdrwl" nticyclone. Although negtive TBB(s) res were lredy routed from Jpn, C2(s) is still responsible for reltively wek convection over northern Kore nd off the est cost of Hokkido t Pentd 41 (see Fig. 14b). A rin-belt is thus mintined in the vicinity of northern Chin, s exemplified in Mtsumoto (1985). Of prticulr interest is tht, t the sme time with the Biu withdrwl from Jpn, new cyclonic cell C3(s) is generted over the WNPM domin (Fig. 15b), ccompnied by scttered wek convection (Fig. 14b). Two pentds lter by Pentd 43, WNPM mtures due to rpid intensifiction of the C3(s) cyclone in ssocition with much intense convection. The development of convection-induced C3(s), which is relted to the northwestwrd migrtion of A1(s) from Pentd 39 to 43, is lso responsible for the Biu withdrwl, especilly over Kore nd the northestern prt of Jpn. It should be noted tht the withdrwl of Biu is chrcterized by the dominnce of S-mode disturbnces s well s the Biu onset. 5. Counterclockwise progression of z(l) nomlies during borel summer In Section 2, z(l) ws defined s n nomly reltive to the nnul men. In Figs. 12, 12c nd 12e, one notes distinct dipole configurtion in 850hP z(l) with negtive (cyclonic) nomly over Est Asi while positive (nticyclonic) nomly exists over the western North Pcific. This dipole is thermlly regulted by temperture contrst between continent nd ocen. Thus, the continentl het low (nomly) remins centered over northern Chin throughout summer (see lso Figs. 5, 5c nd 5e). Likewise, the L-mode nticyclone (nomly) lso persists ner the Kmchtk-Aleutin region during

15 August 1998 R. Kwmur nd T. Murkmi 633 b c d Fig. 15. As in Fig. 14, but for 850hP wind [u(s), v(s)j. Unit is 3m but for 5ms-1 in (d). The letters C nd A denote S-mode cyclonic nd nticyclonic circultion cells, respectively. the whole summer. Generlly speking, convections t ny loclity re ctivted (depressed) to bove (below) norml during the cyclonic (nticyclonic) phse of z(l) nomlies. It is, therefore, importnt to determine the phse (pentd) t which z(l) becomes minimum (or mximum) t every grid point over the entire Est Asi-North Pcific domin. The minimum (or mximum) z(l) phse thus determined differs substntilly from one geogrphicl loction to nother, nd tends to exhibit counterclockwise progression. It is this counterclockwise propgting z(l) phse tht regultes locl convective ctivities over the Est Asi-western North Pcific domin. On "tril nd error" bsis, it turns out tht the counterclockwise z(l) phse shift is most clerly defined over the domin enclosed by 110E (west), 20N (south), 180E (est) nd 40N (north), respectively. Figure 16 plots 850hP z(l) long these selected boundries during the borel summer of My to October. The hevy full line in Fig. 16 trces the phse of minimum z(l) long 110E. More specificlly, the minimum z(l) phse t (40N, 110E) occurs on Pentd 38 (July 5-9) with z(l) vlue of -60m, while the minimum z(l) phse t (20N, 110E) is encountered bout three pentds fter t Pentd 41 (July 20-24) with z(l) vlue of -43 m. Therefore, the pek summer phse of minimum z(l) is systemticlly displced southwrd cross Chin with n verge phse speed of -1.3m s-1. As mentioned erlier in Figs. 12 nd 12c, the continentl het low itself remins centered ner (40N, 105E) between Pentd 38 nd 41. Similrly, the hevy full line in Fig. 16b trces the phse of minimum (cyclonic) z(l) lon 20N. Evidently, the phse progression is estwrd (counterclockwise) with n pproximte speed of +1.2m At Pentd 46 (August 14-18), the mjor prt of WNPM from 125 to bout 150E experiences the minimum z(l) phse, reflecting the mture phse of WNPM convective ctivities. This minimum z(l) phse is brought bout by n estwrd penetrtion of the continentl het low into the tropicl western Pcific, s substntited in Figs. 12c nd 12e. The mplitude of z(l) nomlies long 20N monotoniclly decreses s one pproches estwrd to the dteline (see Fig. 16b). Undoubtedly, this is due to wekening of therml forcing over the open ocen. Although very wek, cyclonic z(l) nomlies lso occur ner (20-27N, 180E) t Pentd 55 (September 28-October 2) in Fig. 16c. Hence, Pentd 55 corresponds to the pek summer phse over the equtoril centrl Pcific, which is bout three months lgging behind the pek summer phse over northern Chin (40N, 110E). A phse difference between continent nd ocen depends sensitively on longitude nd ltitude, rnging from less thn one month to s long s three months. Figure 16 lso shows commencement of the winter phse over northern Chin s erly s the beginning

16 634 Journl of the Meteorologicl Society of Jpn Vol. 76, No. 4 b C d Fig. 16. () Time-ltitude section of 850hP geopotentil height z(s) t 110E. Contour intervl is 5 m, nd shding denotes nigtive vlues. (b) As in () but for time-longitude section t 20N. (c) As in () but for 180E. (d) As in () but for time-longitude section t 40N. The hevy solid nd dshed lines denote the L-mode trough nd ridge, respectively. of September, s confirmed by chnges from negtive to positive z(l) t (40N, 110E). At this loction, z(l) becomes mximum in excess of +40m by Pentd 59 (October 18-22), s shown in Fig. 16d. Let us next trce the summertime mximum (nticyclonic) z(l) phse long 180E (Fig. 16c) nd 40N (Fig. 16d), respectively. It should be noted here tht the hevy dshed lines in Figs. 16c nd 16d do not indicte n ctul displcement of the summertime Pcific High (nomly). An inspection of Fig. 16c indictes tht the pek summertime nticyclonic z(l) phse t (20N, 180E) occurs round Pentd 38 (July 5-9). This is followed by regulr northwrd progression of the pek summer-time nticyclonic z(l) phse from 20 to 40N long 180E, n pproximte phse speed being +0.9ms-1. The counterclockwise phse progression is then completed by westwrd shift (-0.9 ms-1) of the pek summertime nticyclonic z(l) phse from 180 to 110E long 40N (Fig. 16d). This westwrd migrtion of mximum z(l) phse is directly, or indirectly, relted to the westwrd extension of the Pcific ridge system over to Jpn nd beyond (see Figs. 12, 12c nd 12e). Associted with the westwrd progression of nticyclonic z(l) nomlies is the termintion of convective ctivities ner Jpn by Pentd 41 (July 20-24). The Biu withdrwl occurs more thn five pentds prior to the mture phse of WNPM. During erly summer, z(l) nomlies behve differently from those in mid- to lte-summer. More specificlly, the counterclockwise progression of z(l) nomlies tends to occur over much higher ltitude region of Est Asi nd the North Pcific. This sttement cn be justified by n inspection of Figs. 5, 5c nd 5e. An nticyclonic z(l) cell, locted off the est cost of the Kmchtk Peninsul t Pentd 27, grdully drifts westwrd with its western edge covering the vstness of estern Siberi by Pentd 35. Further south over Jpn is contrsted with n estwrd extension of the continentl het low between Pentd 27 nd 35. At Pentd 31 (Biu onset phse), the z(l) nomly exhibits feture similr to tht of "blocking" with deep est-west extended trough ner Jpn s ginst substntilly strong nticyclonic cell over Kmchtk. In this section, evidence hs been provided tht

17 August 1998 R. Kwmur nd T. Murkmi 635 Fig. 17. Schemtic digrms of lower tropospheric L-mode flow nd S-mode disturbnces previling t the Biu onset (mid-june) nd withdrwl (lte July) phses. The letters C nd A denote L-mode (or S-mode) cyclonic nd nticyclonic circultion cells, respectively. Shding indictes intense convection ssocited with the two modes. The wvy lines denote the L-mode lower tropospheric trough round Jpn seen t the onset phse, nd the L-mode WNPM trough t the withdrwl phse. The dshed lines denote the border between the climtologicl low-level westerlies nd esterlies. the L-mode, which follows the sesonl chnge in solr rdition, strongly regultes the climtologicl phse shift of convective ctivities over the Biu domin. The L-mode is lso the mjor regultor for the dry-to-wet phse shift over the WNPM region. As emphsized in Sections 3 nd 4, nother importnt effect of L-mode is to control S-mode ctivities. Finlly, the consolidted contribution of L- nd 5- mode is to mke such locl climtologicl events s the onset nd withdrwl of Biu nd WNPM so rpid nd drmtic. 6. Concluding remrks nd discussion In this study much of the needed documenttion of the Biu onset nd withdrwl hs been rchived by prtitioning the climtologicl pentd men dt into L- nd S-components. The L-mode defines slowly evolving nnul cycle expressed by the sum of one, one hlf nd one third yerly sinusoids, while the S-mode signifies rpidly vrying nnul cycle obtined by summing up the remining trnsient sinusoids. The sesonl mrch of solr rdition strongly influences the evolution of the L-mode during borel summer. There exists significnt phse difference in the L-mode response from one ltitude to nother between different longitudes of the Asin continent nd the western North Pcific. Some of the mjor results re schemticlly summrized in Fig. 17. At the Biu onset phse (mid-june), the continentlscle het low becomes well estblished nd domintes over lmost ll of Est Asi. Associted with this is the enhncement of SEAM, s suggested by intense convection over the regions from the By of Bengl to the South Chin Se (Fig. 17). An L- mode nticyclone previling over the North Pcific implies the sesonl wekening of the Aleutin Low nd the sesonl northwrd development of the Pcific High. Another loclly independent L-mode nticyclonic cell in the vicinity of the Se of Okhotsk, which corresponds to the development of the "climtologicl" Okhotsk High, enhnces L-mode esterlies from the Aleutin islnds through northern Jpn. The L-mode esterlies merge with southwesterlies long the est cost of Chin, hence generting pronounced cyclonic sher zone just round Jpn ccompnied by low-level moisture convergence. This L-mode lower tropospheric trough, intrinsiclly ssocited with the est-west temperture grdient between the Asin continent nd the western North Pcific Ocen, plys vitl role in the formtion of the Biu system s bckground field. The L-mode southwesterly flow long the south-

18 636 Journl of the Meteorologicl Society of Jpn Vol. 76, No. 4 estern periphery of the Asin continentl het low cts s bridge between the SEAM westerlies nd mid-ltitude westerlies dominting over the North Pcific, which produces low-level westerly duct extending from the South Chin Se to the centrl North Pcific. In the vicinity of the westerly duct, S-mode disturbnces tend to be generted nd enhnced. As shown in Fig. 17b, s soon s the S-mode onset cyclone of convective origin is estblished over the South Chin Se, the S-mode onset nticyclone is orgnized to the northest of the onset cyclone. These onset vortexes cuse the northwrd dvection of wrm nd moist ir from the tropics to southern Jpn. Another S-mode cyclonic cell locted est of northern Jpn, which trnsports cold nd dry ir from the Se of Okhotsk to northern Jpn, plys n influentil role in producing strong meridionl grdient in both temperture nd moisture fields cross Jpn. These fetures imply tht the S-mode disturbnces previling long the westerly duct contribute gret del to the occurrence of the Biu onset. At the withdrwl phse (lte July), the Asin continentl het low begins to decy in reltion to surfce cooling of the continent, but the L-mode Pcific High still develops northwrd nd reches its pek round Pentd 43. As the est-west therml contrst between the ocen nd continent decreses, the L-mode lower tropospheric trough round Jpn dissiptes, while the L-mode WNPM trough domintes in the wrm pool region of the western Pcific (see Fig. 17c). The estblishment of the L-mode WNPM trough mkes it possible to trigger S-mode convective perturbtions over the subtropicl western Pcific, such s the S-mode withdrwl cyclone south of Jpn. A couple of S-mode vortexes mplified in nd round low-level westerly duct; i. e., the withdrwl nticyclone just over Jpn nd the withdrwl convective vortex, re crucilly responsible for rpid withdrwl of Biu (Fig. 17d). As cn be seen in these two phses of Biu, the S-mode disturbnces over the western North Pcific region re strongly regulted by the sesonl evolution of L-mode circultions in ssocition with continent-ocen therml contrst. Very interestingly, the S-mode onset cyclone nd onset nticyclone re mplified in L-mode cyclonic nd nticyclonic sher zones, respectively. Another S-mode cyclonic cell just est of northern Jpn seen t the onset phse is lso enhnced in L-mode cyclonic sher zone. These S-mode perturbtions could thus be enhnced vi in situ brotropic interction between the two modes. One wekness in this study is mere qulittive description on the S-L brotropic interction. To remedy this deficiency, our pln clls for n ppliction of the enstrophy eqution introduced by Kwmur et l. (1996). The S-L brotropic interction is expressed by correltion between vorticity fluxes due to S-mode perturbtions nd the grdient of bsolute vorticity in the L-mode flow, s well s in the nnul men flow. Here, cution must be exercised when evluting the correltion, such tht products of ny S nd L vribles become pproximtely zero by choosing n optimum spn of time integrtion. As lredy stted in previous sections, it is lso possible tht the westerly duct served s wve guide for the Rossby wve dispersion of the S-mode perturbtions. Much work needs to be done before we completely understnd these possible mechnisms. No remrkble S-mode nticyclonic cells over the Se of Okhotsk re intensified t the onset phse of Biu. We do not hve ny evidence tht the Okhotsk High contributes significntly to the occurrence of Biu onset in terms of S-mode ctivities. However, the prominence of individul Okhotsk Highs is supposed to prtilly enhnce the Biu front system, especilly over northern Jpn. Actully, there is cse in which n S-mode nticyclonic cell is intensified to the west of the Se of Okhotsk round Pentd 36 fter the onset (not shown). It is thus inferred tht round the onset phse, the Okhotsk High tends to develop more rndomly thn S-mode disturbnces of convective origin over the subtropicl western Pcific. An importnt question still remins unnswered. Why do the S-mode disturbnces recur t the sme plce over the Est Asi-western Pcific domin every yer on the sme clendr dte? Our specultion is tht the slowly evolving, plnetry-scle L-mode is strongly regulted by the nnul cycle of solr rdition, so tht it excites regionl-scle S-mode perturbtions ccording to the clendr dte. This specultion requires further clrifiction. Jpn experiences the second riny seson ("Syurin" in Jpnese) round September. As lredy indicted in Fig. 1, ((l) in the vicinity of Jpn becomes negtive (nticyclonic) t the beginning of August nd it continues until winter, which mens the bsence of L-mode lower tropospheric trough, such s the L-mode Biu trough, during Syurin. This my be why the Syurin front system is not sttionry s compred to the Biu. The bsence of L-mode trough during Syurin is primrily ttributed to the dissiption of the Asin continentl het low due to lnd-surfce cooling. Acknowledgments We re grteful to Dr. K. Kto, Dr. J. Mtsumoto nd two nonymous reviewers for their helpful comments, which led to n improved mnuscript. This reserch ws prtilly supported by the JACCS progrm of the Jpn Science nd Technology Agency.

Journal of the Meteorological Society of Japan, Vol. 75, No. 6, pp ,

Journal of the Meteorological Society of Japan, Vol. 75, No. 6, pp , Journl of the Meteorologicl Society of Jpn, Vol. 75, No. 6, pp. 1109-1123, 1997 1109 Internnul nd Interdecdl Vritions of the Western North Pcific Monsoon nd Biu Rinfll nd their Reltionship to the ENSO

More information

Vorticity. curvature: shear: fluid elements moving in a straight line but at different speeds. t 1 t 2. ATM60, Shu-Hua Chen

Vorticity. curvature: shear: fluid elements moving in a straight line but at different speeds. t 1 t 2. ATM60, Shu-Hua Chen Vorticity We hve previously discussed the ngulr velocity s mesure of rottion of body. This is suitble quntity for body tht retins its shpe but fluid cn distort nd we must consider two components to rottion:

More information

Synoptic Meteorology I: Finite Differences September Partial Derivatives (or, Why Do We Care About Finite Differences?

Synoptic Meteorology I: Finite Differences September Partial Derivatives (or, Why Do We Care About Finite Differences? Synoptic Meteorology I: Finite Differences 16-18 September 2014 Prtil Derivtives (or, Why Do We Cre About Finite Differences?) With the exception of the idel gs lw, the equtions tht govern the evolution

More information

Entropy ISSN

Entropy ISSN Entropy 006, 8[], 50-6 50 Entropy ISSN 099-4300 www.mdpi.org/entropy/ ENTROPY GENERATION IN PRESSURE GRADIENT ASSISTED COUETTE FLOW WITH DIFFERENT THERMAL BOUNDARY CONDITIONS Abdul Aziz Deprtment of Mechnicl

More information

ESCI 343 Atmospheric Dynamics II Lesson 14 Inertial/slantwise Instability

ESCI 343 Atmospheric Dynamics II Lesson 14 Inertial/slantwise Instability ESCI 343 Atmospheric Dynmics II Lesson 14 Inertil/slntwise Instbility Reference: An Introduction to Dynmic Meteorology (3 rd edition), J.R. Holton Atmosphere-Ocen Dynmics, A.E. Gill Mesoscle Meteorology

More information

Physics 201 Lab 3: Measurement of Earth s local gravitational field I Data Acquisition and Preliminary Analysis Dr. Timothy C. Black Summer I, 2018

Physics 201 Lab 3: Measurement of Earth s local gravitational field I Data Acquisition and Preliminary Analysis Dr. Timothy C. Black Summer I, 2018 Physics 201 Lb 3: Mesurement of Erth s locl grvittionl field I Dt Acquisition nd Preliminry Anlysis Dr. Timothy C. Blck Summer I, 2018 Theoreticl Discussion Grvity is one of the four known fundmentl forces.

More information

Math 8 Winter 2015 Applications of Integration

Math 8 Winter 2015 Applications of Integration Mth 8 Winter 205 Applictions of Integrtion Here re few importnt pplictions of integrtion. The pplictions you my see on n exm in this course include only the Net Chnge Theorem (which is relly just the Fundmentl

More information

SUPPLEMENTARY INFORMATION

SUPPLEMENTARY INFORMATION doi:10.1038/nture11097 Supplementl Text Supplementry Figure 8 shows the zonl nnul men ensemle men temperture trends for the CAM individul forcing experiments. Both lck cron (BC) nd tropospheric ozone (TO3)

More information

SUMMER KNOWHOW STUDY AND LEARNING CENTRE

SUMMER KNOWHOW STUDY AND LEARNING CENTRE SUMMER KNOWHOW STUDY AND LEARNING CENTRE Indices & Logrithms 2 Contents Indices.2 Frctionl Indices.4 Logrithms 6 Exponentil equtions. Simplifying Surds 13 Opertions on Surds..16 Scientific Nottion..18

More information

DIRECT CURRENT CIRCUITS

DIRECT CURRENT CIRCUITS DRECT CURRENT CUTS ELECTRC POWER Consider the circuit shown in the Figure where bttery is connected to resistor R. A positive chrge dq will gin potentil energy s it moves from point to point b through

More information

Minimum Energy State of Plasmas with an Internal Transport Barrier

Minimum Energy State of Plasmas with an Internal Transport Barrier Minimum Energy Stte of Plsms with n Internl Trnsport Brrier T. Tmno ), I. Ktnum ), Y. Skmoto ) ) Formerly, Plsm Reserch Center, University of Tsukub, Tsukub, Ibrki, Jpn ) Plsm Reserch Center, University

More information

Math 1B, lecture 4: Error bounds for numerical methods

Math 1B, lecture 4: Error bounds for numerical methods Mth B, lecture 4: Error bounds for numericl methods Nthn Pflueger 4 September 0 Introduction The five numericl methods descried in the previous lecture ll operte by the sme principle: they pproximte the

More information

4 The dynamical FRW universe

4 The dynamical FRW universe 4 The dynmicl FRW universe 4.1 The Einstein equtions Einstein s equtions G µν = T µν (7) relte the expnsion rte (t) to energy distribution in the universe. On the left hnd side is the Einstein tensor which

More information

Lecture 13 - Linking E, ϕ, and ρ

Lecture 13 - Linking E, ϕ, and ρ Lecture 13 - Linking E, ϕ, nd ρ A Puzzle... Inner-Surfce Chrge Density A positive point chrge q is locted off-center inside neutrl conducting sphericl shell. We know from Guss s lw tht the totl chrge on

More information

Interactions between the tropical ISO and midlatitude low-frequency flow

Interactions between the tropical ISO and midlatitude low-frequency flow Clim Dyn (2008) 31:375 388 DOI 10.1007/s00382-007-0272-7 Interctions between the tropicl ISO nd midltitude low-frequency flow Lin-Lin Pn Æ Tim Li Received: 3 October 2006 / Accepted: 2 My 2007 / Published

More information

200 points 5 Problems on 4 Pages and 20 Multiple Choice/Short Answer Questions on 5 pages 1 hour, 48 minutes

200 points 5 Problems on 4 Pages and 20 Multiple Choice/Short Answer Questions on 5 pages 1 hour, 48 minutes PHYSICS 132 Smple Finl 200 points 5 Problems on 4 Pges nd 20 Multiple Choice/Short Answer Questions on 5 pges 1 hour, 48 minutes Student Nme: Recittion Instructor (circle one): nme1 nme2 nme3 nme4 Write

More information

1 Which of the following summarises the change in wave characteristics on going from infra-red to ultraviolet in the electromagnetic spectrum?

1 Which of the following summarises the change in wave characteristics on going from infra-red to ultraviolet in the electromagnetic spectrum? Which of the following summrises the chnge in wve chrcteristics on going from infr-red to ultrviolet in the electromgnetic spectrum? frequency speed (in vcuum) decreses decreses decreses remins constnt

More information

APPROXIMATE INTEGRATION

APPROXIMATE INTEGRATION APPROXIMATE INTEGRATION. Introduction We hve seen tht there re functions whose nti-derivtives cnnot be expressed in closed form. For these resons ny definite integrl involving these integrnds cnnot be

More information

Supplementary Material for Wave-pinning and cell polarity from a bistable reaction-diffusion system

Supplementary Material for Wave-pinning and cell polarity from a bistable reaction-diffusion system Supplementry Mteril for Wve-pinning nd cell polrity from bistble rection-diffusion system Yoichiro Mori, Alendr Jilkine nd Leh Edelstein-Keshet Model Comprisons We concentrte here the three systems to

More information

Exam 1 Solutions (1) C, D, A, B (2) C, A, D, B (3) C, B, D, A (4) A, C, D, B (5) D, C, A, B

Exam 1 Solutions (1) C, D, A, B (2) C, A, D, B (3) C, B, D, A (4) A, C, D, B (5) D, C, A, B PHY 249, Fll 216 Exm 1 Solutions nswer 1 is correct for ll problems. 1. Two uniformly chrged spheres, nd B, re plced t lrge distnce from ech other, with their centers on the x xis. The chrge on sphere

More information

SEASONAL VARIATI0,NS OF THE RELATIONSHIP BETWEEN SOME ENSO PARAMETERS AND INDIAN RAINFALL

SEASONAL VARIATI0,NS OF THE RELATIONSHIP BETWEEN SOME ENSO PARAMETERS AND INDIAN RAINFALL INTERNATIONAL JOURNAL OF CLIMATOLOGY, VOL. 16, 923-933 (1996) 551.521.1 l(4) SEASONAL VARIATI0,NS OF THE RELATIONSHIP BETWEEN SOME ENSO PARAMETERS AND INDIAN RAINFALL K. D. PRASAD nd S. V SINGH' Indin

More information

Operations with Polynomials

Operations with Polynomials 38 Chpter P Prerequisites P.4 Opertions with Polynomils Wht you should lern: How to identify the leding coefficients nd degrees of polynomils How to dd nd subtrct polynomils How to multiply polynomils

More information

Physics 9 Fall 2011 Homework 2 - Solutions Friday September 2, 2011

Physics 9 Fall 2011 Homework 2 - Solutions Friday September 2, 2011 Physics 9 Fll 0 Homework - s Fridy September, 0 Mke sure your nme is on your homework, nd plese box your finl nswer. Becuse we will be giving prtil credit, be sure to ttempt ll the problems, even if you

More information

ECO 317 Economics of Uncertainty Fall Term 2007 Notes for lectures 4. Stochastic Dominance

ECO 317 Economics of Uncertainty Fall Term 2007 Notes for lectures 4. Stochastic Dominance Generl structure ECO 37 Economics of Uncertinty Fll Term 007 Notes for lectures 4. Stochstic Dominnce Here we suppose tht the consequences re welth mounts denoted by W, which cn tke on ny vlue between

More information

New Expansion and Infinite Series

New Expansion and Infinite Series Interntionl Mthemticl Forum, Vol. 9, 204, no. 22, 06-073 HIKARI Ltd, www.m-hikri.com http://dx.doi.org/0.2988/imf.204.4502 New Expnsion nd Infinite Series Diyun Zhng College of Computer Nnjing University

More information

P 3 (x) = f(0) + f (0)x + f (0) 2. x 2 + f (0) . In the problem set, you are asked to show, in general, the n th order term is a n = f (n) (0)

P 3 (x) = f(0) + f (0)x + f (0) 2. x 2 + f (0) . In the problem set, you are asked to show, in general, the n th order term is a n = f (n) (0) 1 Tylor polynomils In Section 3.5, we discussed how to pproximte function f(x) round point in terms of its first derivtive f (x) evluted t, tht is using the liner pproximtion f() + f ()(x ). We clled this

More information

Chapter 4 Contravariance, Covariance, and Spacetime Diagrams

Chapter 4 Contravariance, Covariance, and Spacetime Diagrams Chpter 4 Contrvrince, Covrince, nd Spcetime Digrms 4. The Components of Vector in Skewed Coordintes We hve seen in Chpter 3; figure 3.9, tht in order to show inertil motion tht is consistent with the Lorentz

More information

We partition C into n small arcs by forming a partition of [a, b] by picking s i as follows: a = s 0 < s 1 < < s n = b.

We partition C into n small arcs by forming a partition of [a, b] by picking s i as follows: a = s 0 < s 1 < < s n = b. Mth 255 - Vector lculus II Notes 4.2 Pth nd Line Integrls We begin with discussion of pth integrls (the book clls them sclr line integrls). We will do this for function of two vribles, but these ides cn

More information

A027 Uncertainties in Local Anisotropy Estimation from Multi-offset VSP Data

A027 Uncertainties in Local Anisotropy Estimation from Multi-offset VSP Data A07 Uncertinties in Locl Anisotropy Estimtion from Multi-offset VSP Dt M. Asghrzdeh* (Curtin University), A. Bon (Curtin University), R. Pevzner (Curtin University), M. Urosevic (Curtin University) & B.

More information

Credibility Hypothesis Testing of Fuzzy Triangular Distributions

Credibility Hypothesis Testing of Fuzzy Triangular Distributions 666663 Journl of Uncertin Systems Vol.9, No., pp.6-74, 5 Online t: www.jus.org.uk Credibility Hypothesis Testing of Fuzzy Tringulr Distributions S. Smpth, B. Rmy Received April 3; Revised 4 April 4 Abstrct

More information

Heat flux and total heat

Heat flux and total heat Het flux nd totl het John McCun Mrch 14, 2017 1 Introduction Yesterdy (if I remember correctly) Ms. Prsd sked me question bout the condition of insulted boundry for the 1D het eqution, nd (bsed on glnce

More information

The State of the Far East Seas during the 1997/98 El Niño Event

The State of the Far East Seas during the 1997/98 El Niño Event The Stte of the Fr Est Ses during the 1997/98 El Niño Event A.S. Krovnin, 1 G. P. Vnyushin, 1 M. Yu. Kruzhlov, 1 G.V. Khen, 2 M.A. Bogdnov, 1 E.I. Ustinov, 2 V.V. Mslennikov, 1 A.M. Orlov 1 B.N. Kotenev,

More information

Properties of Integrals, Indefinite Integrals. Goals: Definition of the Definite Integral Integral Calculations using Antiderivatives

Properties of Integrals, Indefinite Integrals. Goals: Definition of the Definite Integral Integral Calculations using Antiderivatives Block #6: Properties of Integrls, Indefinite Integrls Gols: Definition of the Definite Integrl Integrl Clcultions using Antiderivtives Properties of Integrls The Indefinite Integrl 1 Riemnn Sums - 1 Riemnn

More information

Consequently, the temperature must be the same at each point in the cross section at x. Let:

Consequently, the temperature must be the same at each point in the cross section at x. Let: HW 2 Comments: L1-3. Derive the het eqution for n inhomogeneous rod where the therml coefficients used in the derivtion of the het eqution for homogeneous rod now become functions of position x in the

More information

The Properties of Stars

The Properties of Stars 10/11/010 The Properties of Strs sses Using Newton s Lw of Grvity to Determine the ss of Celestil ody ny two prticles in the universe ttrct ech other with force tht is directly proportionl to the product

More information

Conservation Law. Chapter Goal. 5.2 Theory

Conservation Law. Chapter Goal. 5.2 Theory Chpter 5 Conservtion Lw 5.1 Gol Our long term gol is to understnd how mny mthemticl models re derived. We study how certin quntity chnges with time in given region (sptil domin). We first derive the very

More information

p-adic Egyptian Fractions

p-adic Egyptian Fractions p-adic Egyptin Frctions Contents 1 Introduction 1 2 Trditionl Egyptin Frctions nd Greedy Algorithm 2 3 Set-up 3 4 p-greedy Algorithm 5 5 p-egyptin Trditionl 10 6 Conclusion 1 Introduction An Egyptin frction

More information

The Regulated and Riemann Integrals

The Regulated and Riemann Integrals Chpter 1 The Regulted nd Riemnn Integrls 1.1 Introduction We will consider severl different pproches to defining the definite integrl f(x) dx of function f(x). These definitions will ll ssign the sme vlue

More information

Recitation 3: More Applications of the Derivative

Recitation 3: More Applications of the Derivative Mth 1c TA: Pdric Brtlett Recittion 3: More Applictions of the Derivtive Week 3 Cltech 2012 1 Rndom Question Question 1 A grph consists of the following: A set V of vertices. A set E of edges where ech

More information

The heat budget of the atmosphere and the greenhouse effect

The heat budget of the atmosphere and the greenhouse effect The het budget of the tmosphere nd the greenhouse effect 1. Solr rdition 1.1 Solr constnt The rdition coming from the sun is clled solr rdition (shortwve rdition). Most of the solr rdition is visible light

More information

Numerical Integration

Numerical Integration Chpter 5 Numericl Integrtion Numericl integrtion is the study of how the numericl vlue of n integrl cn be found. Methods of function pproximtion discussed in Chpter??, i.e., function pproximtion vi the

More information

Week 10: Line Integrals

Week 10: Line Integrals Week 10: Line Integrls Introduction In this finl week we return to prmetrised curves nd consider integrtion long such curves. We lredy sw this in Week 2 when we integrted long curve to find its length.

More information

DECAMETER RADIO EMISSION OF THE SUN: RECENT OBSERVATIONS

DECAMETER RADIO EMISSION OF THE SUN: RECENT OBSERVATIONS DECAMETER RADIO EMISSION OF THE SUN: RECENT OBSERVATIONS V. N. Melnik *,H.O.Rucker, A. A. Konovlenko, V. V. Dorovskyy, E. P. Abrnin, nd A. Leccheux Abstrct We present n overview of the recent results in

More information

Kepler's Three LAWS. Universal Gravitation Chapter 12. Heliocentric Model. Geocentric Model. Other Models. Johannes Kepler

Kepler's Three LAWS. Universal Gravitation Chapter 12. Heliocentric Model. Geocentric Model. Other Models. Johannes Kepler Universl Grvittion Chpter 1 Johnnes Kepler Johnnes Kepler ws Germn mthemticin, stronomer nd strologer, nd key figure in the 17th century Scientific revolution. He is best known for his lws of plnetry motion,

More information

7.2 The Definite Integral

7.2 The Definite Integral 7.2 The Definite Integrl the definite integrl In the previous section, it ws found tht if function f is continuous nd nonnegtive, then the re under the grph of f on [, b] is given by F (b) F (), where

More information

Review of Calculus, cont d

Review of Calculus, cont d Jim Lmbers MAT 460 Fll Semester 2009-10 Lecture 3 Notes These notes correspond to Section 1.1 in the text. Review of Clculus, cont d Riemnn Sums nd the Definite Integrl There re mny cses in which some

More information

UNIFORM CONVERGENCE. Contents 1. Uniform Convergence 1 2. Properties of uniform convergence 3

UNIFORM CONVERGENCE. Contents 1. Uniform Convergence 1 2. Properties of uniform convergence 3 UNIFORM CONVERGENCE Contents 1. Uniform Convergence 1 2. Properties of uniform convergence 3 Suppose f n : Ω R or f n : Ω C is sequence of rel or complex functions, nd f n f s n in some sense. Furthermore,

More information

Riemann Sums and Riemann Integrals

Riemann Sums and Riemann Integrals Riemnn Sums nd Riemnn Integrls Jmes K. Peterson Deprtment of Biologicl Sciences nd Deprtment of Mthemticl Sciences Clemson University August 26, 203 Outline Riemnn Sums Riemnn Integrls Properties Abstrct

More information

Acceptance Sampling by Attributes

Acceptance Sampling by Attributes Introduction Acceptnce Smpling by Attributes Acceptnce smpling is concerned with inspection nd decision mking regrding products. Three spects of smpling re importnt: o Involves rndom smpling of n entire

More information

Duality # Second iteration for HW problem. Recall our LP example problem we have been working on, in equality form, is given below.

Duality # Second iteration for HW problem. Recall our LP example problem we have been working on, in equality form, is given below. Dulity #. Second itertion for HW problem Recll our LP emple problem we hve been working on, in equlity form, is given below.,,,, 8 m F which, when written in slightly different form, is 8 F Recll tht we

More information

Math 360: A primitive integral and elementary functions

Math 360: A primitive integral and elementary functions Mth 360: A primitive integrl nd elementry functions D. DeTurck University of Pennsylvni October 16, 2017 D. DeTurck Mth 360 001 2017C: Integrl/functions 1 / 32 Setup for the integrl prtitions Definition:

More information

Rel Gses 1. Gses (N, CO ) which don t obey gs lws or gs eqution P=RT t ll pressure nd tempertures re clled rel gses.. Rel gses obey gs lws t extremely low pressure nd high temperture. Rel gses devited

More information

A REVIEW OF CALCULUS CONCEPTS FOR JDEP 384H. Thomas Shores Department of Mathematics University of Nebraska Spring 2007

A REVIEW OF CALCULUS CONCEPTS FOR JDEP 384H. Thomas Shores Department of Mathematics University of Nebraska Spring 2007 A REVIEW OF CALCULUS CONCEPTS FOR JDEP 384H Thoms Shores Deprtment of Mthemtics University of Nebrsk Spring 2007 Contents Rtes of Chnge nd Derivtives 1 Dierentils 4 Are nd Integrls 5 Multivrite Clculus

More information

Riemann Sums and Riemann Integrals

Riemann Sums and Riemann Integrals Riemnn Sums nd Riemnn Integrls Jmes K. Peterson Deprtment of Biologicl Sciences nd Deprtment of Mthemticl Sciences Clemson University August 26, 2013 Outline 1 Riemnn Sums 2 Riemnn Integrls 3 Properties

More information

Basic model for traffic interweave

Basic model for traffic interweave Journl of Physics: Conference Series PAPER OPEN ACCESS Bsic model for trffic interweve To cite this rticle: Ding-wei Hung 25 J. Phys.: Conf. Ser. 633 227 Relted content - Bsic sciences gonize in Turkey!

More information

Data Assimilation. Alan O Neill Data Assimilation Research Centre University of Reading

Data Assimilation. Alan O Neill Data Assimilation Research Centre University of Reading Dt Assimiltion Aln O Neill Dt Assimiltion Reserch Centre University of Reding Contents Motivtion Univrite sclr dt ssimiltion Multivrite vector dt ssimiltion Optiml Interpoltion BLUE 3d-Vritionl Method

More information

The impact of wind on air temperature distribution in Athens and in Santorini

The impact of wind on air temperature distribution in Athens and in Santorini Interntionl Conference Pssive nd Low Energy Cooling 133 The impct of wind on ir temperture distribution in Athens nd in Sntorini I. Livd, K. Nichou nd M. Sntmouris Lbortory of Meteorology, Section of Applied

More information

P5.25 NUMERICAL SIMULATIONS OF HEAVY RAINFALL DURING THE MESOSCALE ALPINE PROGRAM (MAP)

P5.25 NUMERICAL SIMULATIONS OF HEAVY RAINFALL DURING THE MESOSCALE ALPINE PROGRAM (MAP) P5.25 NUMERICAL SIMULATIONS OF HEAVY RAINFALL DURING THE MESOSCALE ALPINE PROGRAM (MAP) Jmes A. Thurmn, Y.-L Lin*, nd J.J Chrney North Crolin Stte University, Rleigh, North Crolin 1. Introduction To ssess

More information

Driving Cycle Construction of City Road for Hybrid Bus Based on Markov Process Deng Pan1, a, Fengchun Sun1,b*, Hongwen He1, c, Jiankun Peng1, d

Driving Cycle Construction of City Road for Hybrid Bus Based on Markov Process Deng Pan1, a, Fengchun Sun1,b*, Hongwen He1, c, Jiankun Peng1, d Interntionl Industril Informtics nd Computer Engineering Conference (IIICEC 15) Driving Cycle Construction of City Rod for Hybrid Bus Bsed on Mrkov Process Deng Pn1,, Fengchun Sun1,b*, Hongwen He1, c,

More information

Factors affecting the phonation threshold pressure and frequency

Factors affecting the phonation threshold pressure and frequency 3SC Fctors ffecting the phontion threshold pressure nd frequency Zhoyn Zhng School of Medicine, University of Cliforni Los Angeles, CA, USA My, 9 57 th ASA Meeting, Portlnd, Oregon Acknowledgment: Reserch

More information

NUMERICAL INTEGRATION. The inverse process to differentiation in calculus is integration. Mathematically, integration is represented by.

NUMERICAL INTEGRATION. The inverse process to differentiation in calculus is integration. Mathematically, integration is represented by. NUMERICAL INTEGRATION 1 Introduction The inverse process to differentition in clculus is integrtion. Mthemticlly, integrtion is represented by f(x) dx which stnds for the integrl of the function f(x) with

More information

8 Laplace s Method and Local Limit Theorems

8 Laplace s Method and Local Limit Theorems 8 Lplce s Method nd Locl Limit Theorems 8. Fourier Anlysis in Higher DImensions Most of the theorems of Fourier nlysis tht we hve proved hve nturl generliztions to higher dimensions, nd these cn be proved

More information

Shear Degradation and Possible viscoelastic properties of High Molecular Weight Oil Drag Reducer Polymers

Shear Degradation and Possible viscoelastic properties of High Molecular Weight Oil Drag Reducer Polymers ANNUAL TRANSACTIONS OF THE NORDIC RHEOLOGY SOCIETY, VOL. 3, 2005 Sher Degrdtion nd Possible viscoelstic properties of High Moleculr Weight Oil Drg Reducer Polymers A.A. Hmoud, C. Elissen, C. Idsøe nd T.

More information

Density of Energy Stored in the Electric Field

Density of Energy Stored in the Electric Field Density of Energy Stored in the Electric Field Deprtment of Physics, Cornell University c Tomás A. Aris October 14, 01 Figure 1: Digrm of Crtesin vortices from René Descrtes Principi philosophie, published

More information

Shear and torsion interaction of hollow core slabs

Shear and torsion interaction of hollow core slabs Competitive nd Sustinble Growth Contrct Nº G6RD-CT--6 Sher nd torsion interction of hollow core slbs HOLCOTORS Technicl Report, Rev. Anlyses of hollow core floors December The content of the present publiction

More information

ADVANCEMENT OF THE CLOSELY COUPLED PROBES POTENTIAL DROP TECHNIQUE FOR NDE OF SURFACE CRACKS

ADVANCEMENT OF THE CLOSELY COUPLED PROBES POTENTIAL DROP TECHNIQUE FOR NDE OF SURFACE CRACKS ADVANCEMENT OF THE CLOSELY COUPLED PROBES POTENTIAL DROP TECHNIQUE FOR NDE OF SURFACE CRACKS F. Tkeo 1 nd M. Sk 1 Hchinohe Ntionl College of Technology, Hchinohe, Jpn; Tohoku University, Sendi, Jpn Abstrct:

More information

Summary of equations chapters 7. To make current flow you have to push on the charges. For most materials:

Summary of equations chapters 7. To make current flow you have to push on the charges. For most materials: Summry of equtions chpters 7. To mke current flow you hve to push on the chrges. For most mterils: J E E [] The resistivity is prmeter tht vries more thn 4 orders of mgnitude between silver (.6E-8 Ohm.m)

More information

Conservation Law. Chapter Goal. 6.2 Theory

Conservation Law. Chapter Goal. 6.2 Theory Chpter 6 Conservtion Lw 6.1 Gol Our long term gol is to unerstn how mthemticl moels re erive. Here, we will stuy how certin quntity chnges with time in given region (sptil omin). We then first erive the

More information

CS667 Lecture 6: Monte Carlo Integration 02/10/05

CS667 Lecture 6: Monte Carlo Integration 02/10/05 CS667 Lecture 6: Monte Crlo Integrtion 02/10/05 Venkt Krishnrj Lecturer: Steve Mrschner 1 Ide The min ide of Monte Crlo Integrtion is tht we cn estimte the vlue of n integrl by looking t lrge number of

More information

energy exchange charts ol the North Atlantic ocean

energy exchange charts ol the North Atlantic ocean energy exchnge chrts ol the North Atlntic ocen Abstrct Chrts of clculted energy exchnge cross the surfce of the North Atlntic Ocen hve been constructed. Wind nd temperture observtions obtined from 8 million

More information

NOT TO SCALE. We can make use of the small angle approximations: if θ á 1 (and is expressed in RADIANS), then

NOT TO SCALE. We can make use of the small angle approximations: if θ á 1 (and is expressed in RADIANS), then 3. Stellr Prllx y terrestril stndrds, the strs re extremely distnt: the nerest, Proxim Centuri, is 4.24 light yers (~ 10 13 km) wy. This mens tht their prllx is extremely smll. Prllx is the pprent shifting

More information

PHYSICS ASSIGNMENT-9

PHYSICS ASSIGNMENT-9 MPS/PHY-XII-11/A9 PHYSICS ASSIGNMENT-9 *********************************************************************************************************** 1. A wire kept long the north-south direction is llowed

More information

1B40 Practical Skills

1B40 Practical Skills B40 Prcticl Skills Comining uncertinties from severl quntities error propgtion We usully encounter situtions where the result of n experiment is given in terms of two (or more) quntities. We then need

More information

Thermal Diffusivity. Paul Hughes. Department of Physics and Astronomy The University of Manchester Manchester M13 9PL. Second Year Laboratory Report

Thermal Diffusivity. Paul Hughes. Department of Physics and Astronomy The University of Manchester Manchester M13 9PL. Second Year Laboratory Report Therml iffusivity Pul Hughes eprtment of Physics nd Astronomy The University of nchester nchester 3 9PL Second Yer Lbortory Report Nov 4 Abstrct We investigted the therml diffusivity of cylindricl block

More information

Unit #9 : Definite Integral Properties; Fundamental Theorem of Calculus

Unit #9 : Definite Integral Properties; Fundamental Theorem of Calculus Unit #9 : Definite Integrl Properties; Fundmentl Theorem of Clculus Gols: Identify properties of definite integrls Define odd nd even functions, nd reltionship to integrl vlues Introduce the Fundmentl

More information

Jack Simons, Henry Eyring Scientist and Professor Chemistry Department University of Utah

Jack Simons, Henry Eyring Scientist and Professor Chemistry Department University of Utah 1. Born-Oppenheimer pprox.- energy surfces 2. Men-field (Hrtree-Fock) theory- orbitls 3. Pros nd cons of HF- RHF, UHF 4. Beyond HF- why? 5. First, one usully does HF-how? 6. Bsis sets nd nottions 7. MPn,

More information

Math 42 Chapter 7 Practice Problems Set B

Math 42 Chapter 7 Practice Problems Set B Mth 42 Chpter 7 Prctice Problems Set B 1. Which of the following functions is solution of the differentil eqution dy dx = 4xy? () y = e 4x (c) y = e 2x2 (e) y = e 2x (g) y = 4e2x2 (b) y = 4x (d) y = 4x

More information

#6A&B Magnetic Field Mapping

#6A&B Magnetic Field Mapping #6A& Mgnetic Field Mpping Gol y performing this lb experiment, you will: 1. use mgnetic field mesurement technique bsed on Frdy s Lw (see the previous experiment),. study the mgnetic fields generted by

More information

( dg. ) 2 dt. + dt. dt j + dh. + dt. r(t) dt. Comparing this equation with the one listed above for the length of see that

( dg. ) 2 dt. + dt. dt j + dh. + dt. r(t) dt. Comparing this equation with the one listed above for the length of see that Arc Length of Curves in Three Dimensionl Spce If the vector function r(t) f(t) i + g(t) j + h(t) k trces out the curve C s t vries, we cn mesure distnces long C using formul nerly identicl to one tht we

More information

Definition of Continuity: The function f(x) is continuous at x = a if f(a) exists and lim

Definition of Continuity: The function f(x) is continuous at x = a if f(a) exists and lim Mth 9 Course Summry/Study Guide Fll, 2005 [1] Limits Definition of Limit: We sy tht L is the limit of f(x) s x pproches if f(x) gets closer nd closer to L s x gets closer nd closer to. We write lim f(x)

More information

Math Calculus with Analytic Geometry II

Math Calculus with Analytic Geometry II orem of definite Mth 5.0 with Anlytic Geometry II Jnury 4, 0 orem of definite If < b then b f (x) dx = ( under f bove x-xis) ( bove f under x-xis) Exmple 8 0 3 9 x dx = π 3 4 = 9π 4 orem of definite Problem

More information

3.2.2 Kinetics. Maxwell Boltzmann distribution. 128 minutes. 128 marks. Page 1 of 12

3.2.2 Kinetics. Maxwell Boltzmann distribution. 128 minutes. 128 marks. Page 1 of 12 3.. Kinetics Mxwell Boltzmnn distribution 8 minutes 8 mrks Pge of M. () M On the energy xis E mp t the mximum of the originl pek M The limits for the horizontl position of E mp re defined s bove the word

More information

On the Linear Stability of Compound Capillary Jets

On the Linear Stability of Compound Capillary Jets ILASS Americs, th Annul Conference on Liquid Atomiztion nd Spry Systems, Chicgo, IL, My 7 On the Liner Stbility of Compound Cpillry Jets Mksud (Mx) Ismilov, Stephen D Heister School of Aeronutics nd Astronutics,

More information

The Wave Equation I. MA 436 Kurt Bryan

The Wave Equation I. MA 436 Kurt Bryan 1 Introduction The Wve Eqution I MA 436 Kurt Bryn Consider string stretching long the x xis, of indeterminte (or even infinite!) length. We wnt to derive n eqution which models the motion of the string

More information

Predict Global Earth Temperature using Linier Regression

Predict Global Earth Temperature using Linier Regression Predict Globl Erth Temperture using Linier Regression Edwin Swndi Sijbt (23516012) Progrm Studi Mgister Informtik Sekolh Teknik Elektro dn Informtik ITB Jl. Gnesh 10 Bndung 40132, Indonesi 23516012@std.stei.itb.c.id

More information

This document is downloaded from DR-NTU, Nanyang Technological University Library, Singapore.

This document is downloaded from DR-NTU, Nanyang Technological University Library, Singapore. This document is downloded from DR-NTU, Nnyng Technologicl University Librry, ingpore. Title Isentropic zonl verge formlism nd the ner-surfce circultion( Conference proceedings ) Author(s) Koh, Tieh Yong;

More information

Numerical integration

Numerical integration 2 Numericl integrtion This is pge i Printer: Opque this 2. Introduction Numericl integrtion is problem tht is prt of mny problems in the economics nd econometrics literture. The orgniztion of this chpter

More information

25 Which of the following summarises the change in wave characteristics on going from infra-red to ultraviolet in the electromagnetic spectrum?

25 Which of the following summarises the change in wave characteristics on going from infra-red to ultraviolet in the electromagnetic spectrum? PhysicsndMthsTutor.com 25 Which of the following summrises the chnge in wve chrcteristics on going from infr-red to ultrviolet in the electromgnetic spectrum? 972//M/J/2 frequency speed (in vcuum) decreses

More information

ARITHMETIC OPERATIONS. The real numbers have the following properties: a b c ab ac

ARITHMETIC OPERATIONS. The real numbers have the following properties: a b c ab ac REVIEW OF ALGEBRA Here we review the bsic rules nd procedures of lgebr tht you need to know in order to be successful in clculus. ARITHMETIC OPERATIONS The rel numbers hve the following properties: b b

More information

1 Probability Density Functions

1 Probability Density Functions Lis Yn CS 9 Continuous Distributions Lecture Notes #9 July 6, 28 Bsed on chpter by Chris Piech So fr, ll rndom vribles we hve seen hve been discrete. In ll the cses we hve seen in CS 9, this ment tht our

More information

THERMAL EXPANSION COEFFICIENT OF WATER FOR VOLUMETRIC CALIBRATION

THERMAL EXPANSION COEFFICIENT OF WATER FOR VOLUMETRIC CALIBRATION XX IMEKO World Congress Metrology for Green Growth September 9,, Busn, Republic of Kore THERMAL EXPANSION COEFFICIENT OF WATER FOR OLUMETRIC CALIBRATION Nieves Medin Hed of Mss Division, CEM, Spin, mnmedin@mityc.es

More information

A Brief Review on Akkar, Sandikkaya and Bommer (ASB13) GMPE

A Brief Review on Akkar, Sandikkaya and Bommer (ASB13) GMPE Southwestern U.S. Ground Motion Chrcteriztion Senior Seismic Hzrd Anlysis Committee Level 3 Workshop #2 October 22-24, 2013 A Brief Review on Akkr, Sndikky nd Bommer (ASB13 GMPE Sinn Akkr Deprtment of

More information

First Law of Thermodynamics. Control Mass (Closed System) Conservation of Mass. Conservation of Energy

First Law of Thermodynamics. Control Mass (Closed System) Conservation of Mass. Conservation of Energy First w of hermodynmics Reding Problems 3-3-7 3-0, 3-5, 3-05 5-5- 5-8, 5-5, 5-9, 5-37, 5-0, 5-, 5-63, 5-7, 5-8, 5-09 6-6-5 6-, 6-5, 6-60, 6-80, 6-9, 6-, 6-68, 6-73 Control Mss (Closed System) In this section

More information

A5682: Introduction to Cosmology Course Notes. 4. Cosmic Dynamics: The Friedmann Equation. = GM s

A5682: Introduction to Cosmology Course Notes. 4. Cosmic Dynamics: The Friedmann Equation. = GM s 4. Cosmic Dynmics: The Friedmnn Eqution Reding: Chpter 4 Newtonin Derivtion of the Friedmnn Eqution Consider n isolted sphere of rdius R s nd mss M s, in uniform, isotropic expnsion (Hubble flow). The

More information

Tests for the Ratio of Two Poisson Rates

Tests for the Ratio of Two Poisson Rates Chpter 437 Tests for the Rtio of Two Poisson Rtes Introduction The Poisson probbility lw gives the probbility distribution of the number of events occurring in specified intervl of time or spce. The Poisson

More information

Lecture 3 Gaussian Probability Distribution

Lecture 3 Gaussian Probability Distribution Introduction Lecture 3 Gussin Probbility Distribution Gussin probbility distribution is perhps the most used distribution in ll of science. lso clled bell shped curve or norml distribution Unlike the binomil

More information

A New Grey-rough Set Model Based on Interval-Valued Grey Sets

A New Grey-rough Set Model Based on Interval-Valued Grey Sets Proceedings of the 009 IEEE Interntionl Conference on Systems Mn nd Cybernetics Sn ntonio TX US - October 009 New Grey-rough Set Model sed on Intervl-Vlued Grey Sets Wu Shunxing Deprtment of utomtion Ximen

More information

State space systems analysis (continued) Stability. A. Definitions A system is said to be Asymptotically Stable (AS) when it satisfies

State space systems analysis (continued) Stability. A. Definitions A system is said to be Asymptotically Stable (AS) when it satisfies Stte spce systems nlysis (continued) Stbility A. Definitions A system is sid to be Asymptoticlly Stble (AS) when it stisfies ut () = 0, t > 0 lim xt () 0. t A system is AS if nd only if the impulse response

More information

MATHS NOTES. SUBJECT: Maths LEVEL: Higher TEACHER: Aidan Roantree. The Institute of Education Topics Covered: Powers and Logs

MATHS NOTES. SUBJECT: Maths LEVEL: Higher TEACHER: Aidan Roantree. The Institute of Education Topics Covered: Powers and Logs MATHS NOTES The Institute of Eduction 06 SUBJECT: Mths LEVEL: Higher TEACHER: Aidn Rontree Topics Covered: Powers nd Logs About Aidn: Aidn is our senior Mths techer t the Institute, where he hs been teching

More information

5.7 Improper Integrals

5.7 Improper Integrals 458 pplictions of definite integrls 5.7 Improper Integrls In Section 5.4, we computed the work required to lift pylod of mss m from the surfce of moon of mss nd rdius R to height H bove the surfce of the

More information