A'J ABSTRACT OF TH Shenq - .ei in Analysis General by Ocean Models Circulation Redacted for Privacy Abstract aoproved: 'oung - June Han simulated stress wind Surface 192 1, and Stress Wind Science of July presented on Surface of Sinulated Circulations Master for the degree of Lee Atmospheric Sciences Title: THFSIS OF two-level OSU ov cieneral circulation model is analyzed in terms atmospheric It of its spatial aid temooral cnaracteristics, shown is that the main features of the annual mean field in Morthern are Eemisphere corresponlina deirees 20 to 10 observational too south of The oatterns in positions. the Southern Hemisphere, however, are dell simulated. The mean fields reveal a distinct seasonal variability monthly which the deoendent highly Is on Spectral latitude. and cross-soectral analysis of the 3-year time series Show that eastward travelina time synootic dominate the variability. disturbances scale The long oerlod disturbances are symmetric and have no oreferred directions of The ocean clrcuiations version of the OSU simulated six-layer by the oropaaation. barotropic ocean general circulation model using simulated wind stress are found to he larciely controlje1 by variabilities the of stress curl f1el. i1r the corresoni1ni nass The sesorl trarisDort are larqer than that of the circulation driven by observed wind stress due to the stroner variability of the curl field of the sj'iulated Planetary waves with westward wind stress, phase orooaaation and eastward constitute a najor cart rouo velocity are likely to ot t'e resoonse of a barotrooic 'odel to the fluctuatinq winds. SURPACE ItNO ANAIJYSIS 3 srss AND OCEAM CIRCUIJ&TIOMS SIMUEATED BY GENERAL CIRCULATIOi MODELS bY SKENG-EI LEE A THESIS submitted to Oreon State University in oartial fu1fi11ent of the requirenents for the degree of Master of Science Corn'nenCernent June 19R3 APPROVED: Redacted for Privacy Ass1stn'Pr&?essor of the Deortient of Atmoso!eric Sciences in chre of njor Redacted for Privacy (Acting for U. L. Gates) Chairin of the DepartTent of Atrnosoheric Redacted for Privacy Dean of Date thesis is resented Typed by Shu-Chinq Ru for July 1, 19R2 S,enc-Wei tee Sciences C KNOW L ED G M E 1 T xoress ny crt1tude to I woUli 11ce to for qtij'ance his Dr. Y.-J. Hr and assistance in this research, and to Dr. S. K. Esbensen for his valuable comments on some of the material. expert helo I also sincerely thank in most of the r. W. R. McKie for his comouter constructive review of the manuscript. oroqrarnmjncj and TABLE OF' CDNTE'!TS 1. INTRODUCTflN 2. DESCRIPTION oF' THE AGCM SIMULATED WIND STRESS FIELDS AND THE COMPARISON WITH OBSERVED FIELDS Calculation of surface wind stress in 2.1. the AGCM 3-year mean wind stress fIelds 2.2. Vectors 2.2.1 2.2.2 Zonal-corrponent MeridIonal-component 2.2.3 2.2.4 Curl Root mean square wind stress 2.2.5 Seasonal Variations 2.3. Vectors 2.3.1 Curl 2.3.2 I 5 7 11 12 15 18 25 28 32 32 43 SPECTRAL ANALYSIS OF' THE SIMULATED WIND STRESS Autosoectral analysis 3.1. Algorithm and method of calculatIon 3.1.1 Autospectra of simulated wind stress 3.1.2 Cross-soectral analysis 3.2. AlgorIthm and method of calculation 3.2.1 Cross-spectra of selected fields 3.2.2 51 51 51 BAROTROPIC OCEAN EXPERIMENT The ocean circulation driven by the 4.1. AGCM simulated wind stress Seasonal variation of simulated ocean 4,2. transport 80 5. SUMMARY 99 6. RIBIJIOGRAP4Y 3. 4. 56 67 67 71 82 103 (IST OF' F'IURF'S Daqe F'iqure 2.1. SchematIc representation of the OSfJ AGCM's vertical structure. 22. Annual mean observed wind stress vectorS, 13 2,3. 3-year mean A(C'-sImulated wind stress vectors. 14 2.4. Zonal-co,00nent of the 3-year mean AGCMsimulated wind stress. 16 2.5, Zonal-conoonent of the annual mean observed wind stress. 17 2.6. Zonal means of the simulated and observed zonal-conponent of the wind stress. 19 2.7. As is ft. 2.4 except for meridional component. 20 2.8. As 1r fI. 2.5 except for meridional component. 22 2.9. As in fiq, 2,6 except for meridional component. 24 2.10. 3-year mean ACM-simulate1 wind stress curl, 26 2.11. Annual mean observed wind stress curl. 27 2.12. Zonal means of the simulated and ohserved wind stress curl. 29 2.13. Root mean square observed wind stress over (a) 4ortr Pacific (b) Iorth Atlantic Oceans. (after Willebrand (1978)) 30 2.14. Root mean square simulated wind stress over qiobal oceans, 31 2,15. onthly variation of zonal mean of observed zonal-co'noonent of the wind stress. 33 & 2.16a. Mean observed wind stress vectors for January. 34 2.16b, As in fiq. 216a except for July. 35 2.17. As in fiq. 2.15 exceot for simulated wind stress. 37 2.lRa, Mean simulated Mind stress vectors for 2.18b. ti,ree Ja,uarles. 38 As in fii. 2.18a excert for Aoril, 39 2.lBc. As in fLi. 2.lRa exceot for July. 40 2.181. As in fi. 2.18a except for October. 41 2.19a. Mean observed Mind stress curl for January. 44 2.19b. As in fi. 2.19a except for July. 45 2.20a. Mean simulated Mind stress curl for 46 three Januartes. 2,20b. As in fi. 2.20a exceot for Aoril. 2.20c, As in fj. 2,20a exceot for July. 2.20d. As in fij. 2.20a exceot tor October. 3.1. 48 49 r.onqituiinal1y averaqeci autosoectra over the orth Pacific Jcen at 42J (J:34) 3.2. 47 57 LongItudinally averaged spectra of horizontal stress at 5 latitudes over the 'orth Pacific 59 Ocean. (1:55, J26). 3,3. Autospectra at (90, 10!') 3.4. Autospectra at 4 points over the South Pacific 61 Ocean. 63 3.5, Autospectra at (160, 42M) (1:69, J:34), 65 3.6. Longitudinally averaged autospectra of zonalcomoonent Mind stress for the summer and winter 3.7. 3.8. over the 'lorth Pacific Ocean at 4214. 66 Coherence nd ohase spectra of stress comoonents for two ooints at (170, 3014) and (160, 3014) with a east-west separation of 963 Km. 72 As in fii. 3.7 except for two ooints at (170, 3014) and (150, 3014) with an east-west seoaratton of 1926 Km. 3.9. 74 As in fIg. 3.7 except for two points at (160, 3014) and (160!, 3414) with an south-north seoaration of 445 (rn, 76 3.10. 3.11. 4.1. As in f1. 3.7 except for two points at (160!, 341) and (160!, 421) with ar south-north seoaration of 80 Km. 79 Coherence and onase spectra of zona]. comoonent wind stress for two points at (.175W, 581) and (175!, 58N) with an east-west separation of 589 Km. 79 Annual mean streamfunction of the mass transoort of the oceanic circulation driven b the ACCM simulated surface wind stress. 94 4.2. Streamfurictlon of the nass tranoort at day 90 of the oceanic circulation driven by observed surface wind stress. 4.3a. 4onthly mean streamfunction of the simulated transoort for January. 90 4.3b. As in fii. 4.3a exceot for April. 91 4.3c. As in f13. 4.3a exceot for July. 92 4.3d, As in fi. 4,3a exceot for Octooer. 93 4.4a. rirne-lonitude olot of the strearnfunction alona 344 (J32) for day 190-240 of the 4,4b. simulation. 97 As in fi. 4.4a exceot for day 300-360. 98 STRESS ANALYSIS DF SURFACE AIND AND OCEAN CIRCULATIONS SIMULATED BY GENERAL 1. CIRCULATION INTRODUCTION The ocean has long been Due Imoortant an as recognized climate. earth's the in cofrDonent '4ODEtS large the to coverage of the earth's surface and the high specific water, of ocean the acts as It heat and of with the atmosphere and the ooleard transoort of moisture yonder Hear and Oort (1973) energy by the ocean currents. transports oceanic the that comparable overall imoortance Thus, reservoir. exchange influences the climate through Its found heat a heat as are atmospheric least at of transports. it is necessary to take into account the hydrosphere as well as climate. the The ocean-atmosphere for atmosohere first model better exoeriment was done by modeling of the coupled using a UCflabe (1969) ho performed a series of controlled experiments to investigate the problem of ocean-atmosphere interaction. et al. (1975) carried out a subsequent experiment with realistic global qeogreohy and found the role of oceans. Later, Manabe further evidence of The Climatic Research Institute at DSIJ has recently been devotinq much effort to couol.e a ne 6-level ocean general circulation model (0GC) to the extstin 2-level atmosPheric oeneral circulation rnode1(PGCM). Schiesinqer and Gates (1981) examined the role of the ocean in the qiobal climate in a series of five simulations usini the OSU AGCM with different surface and Gates studied the oerformance of OSU -far conditions. maintenance of JGCM first by a hornoqeneous Nir1ddrIven ocean exoeriment (1982a), then by a baroclinic ocean exoer1nent In which the ocean is driven by thernohaline forclnq as well as wind third exoeriment which combined the forcin (1982b). OGCM with a mixed layer and sea-ice model is now in oroqress. The couoled AGCM-OGCM model will then be used In climate experiments. The main urpose of this study is to A examine the behavior of the AGCM simulated wind stress in the coupled model, is to be exoitcitly used hV the OGCM as one of the major forcinq fields from the 4h1ch overlyinci atmosohere. Surface wind stress is an important factor in the It reoresents the orincipal. mechanism for the dissipation of atmospheric kinetic enerqy (Gates, 1979). It also contributes to the ocean the major part of eneray for maintaininci the semi-oerrnanent currents Sverdrup (1947) and the corresoonding mass transoort. atmosphere-ocean system, 3 Showed that the mass transport for most of the ocean can be approximated from a knowledge of wind stress alone. Later, Bryan (1963) demonstrated, with a numerical model of a barotrooic ocean, the sensitivity of nass transoort to the wind stress field. Therefore, in order to get better simulation of the ocean current and the associated mass and energy transport, a reasonally good set of wind stress data is greatly in need. The first systematic comoutatlon of the was made by Scripps wind stress Institute of 3ceanography in 194R. iidaka (195R) later extended the comoltation to three malor Both computations used only the mean speed which, in each direction category of the wind rose to Hellerman (1965), would significantly according 10-30%, underestimate the wind stress magnitude by world oceans. (1967) revised Hidaka's calculation by utilizing wind roses with both direction ni speed frequencies, More recently, Han and Lee (191) cornoiled a new set of monthly mean stress data over the global ocean using The clirnatological monthly mean wind data. uDdated calculated stress data extended to high-latitude oceans and revealed many features which were not resolved in earlier Hellerrnan anal vses. Once the wind stress field is established, it is ri desirable its space-time variability Which might row to contribute to the strong variability as which Is treguently observed the In Several spectra of wind soeed at ocean. certain stations in the surface layer have been documented. are at stations on the Oregon coast (Erye et al., Examples 1972), on the troolcal Pacific island Pairnyra (Fiwang, at weathershio P on NE Pacific (Fissel, 197F), etc. 1970), ijlebrand (1978) analyzed wind of Including parameters, surface over Northern Jceans and found that eastwari stress, ropagatIna disturbances with period shorter than days 10 dominate the atmospheric variability. distributution In the following, the spatial of the 3-year mean wind stress and stress curl fields simulated by the OSU AcCM are reviewed. are seasonal Their These fields are comoared against the also discussed. observational fields whenever available. wi].l with deal space-time the simulated wind stress. spectral analysis variabilities are characteristics Results of shown. The next the In auto- model driven by those observed variabilities of the simulated also discussed. the cross- and OGCA with Streamfunction fields of ocean mass transoort are compared with same of the last chapter, the simulated wind stress is actually tested on the homogeneous stratification. chapter wind simulated stress. streanfunction by the Seasonal fields are S SIMU[ATD WIND STRESS DESCRIPTIO1 or THE AGC 2. FIELDS AMD THE CD!PARISDN WIT1 OBSERVED FIELDS this In by qenerated the chapter, the surface 0511 AGCM will be described in detail in terms of mean field and temporal variations. is a field stress wind The JSU AGCM primitive equation model for the troposohere. It is system with formulated in the 0 vertical coordinate a-defined as a-=( P-P1.) / (Ps-P1) where P is the pressure, PS surface structure divided and top is of the sletched in pressures P,the and model atmosohere. Fl.2.1. is level with a- = 1/2. with a- equals The interface between the layers The tropopause corresponds to 0 and the surface is always :iven by 0 = 1. boundary condition 0 earth's is At the center of each layer are the reference levels 1 and 3 1/4 and 3/4 resoectively, The vertical- atmosohere The into two layers with equal mass. the at da/dt = 0 is cr = The kinematic applied at surface and the too of the model atmosphere, the The primary dependent variables in the model are the horizontal velocity V, temoerature I', and specific humidity q for both layers, toqether with the surface pressure parameter Ps-P, ). The reader is referred to sates _et al, IF (= (1971), Upper teve% LeJeI2.°'2 - Level 3, 3/4 layer 1 2.1. Eatth surface reOte!tatt0n of tre OSU AGCM'S vertt1 structutP fter sateS et (1971)) 7 (1979) Gates and Schlesinger (1977), Schlesinger and Gates for detailed The horizontal, grid size and numerical methods, lonqitude of the model's ohysica]. aspects lescriotion A B-scheme grid structure is and 4jr latitude. adopted in which the horizontal velocity is oolnt carried at a that is stagaered one-halt grid length latitudinally and longitudinally from the coint variables where T, q, are carried. lrand the ge000tential 2.1 5'in J.s CalculatIon of Surtace 4tnd Stress in the AGCM wind Surface momentum) serves ? stress as turbulent flux of of the frictional force In the oart lower layer of the AGCM. (or It is parameterized by the bulk aerodynamic method = where P4CDV;VS (2.1.1) P4 is the surface air density, Vs' the effective - surface wind soeed and Vs the vector surface wind. The surface wind is extrapolated from the vector wind at level 3 and level 1 according to the formulae: Vs = o.7V4 = 0.7(4 V3 (2.1.2) and the effective wind soeed is given bY Vs ax (Vs I , 6 ) (2.1.3) R where G is the gustiness oaraneter (: 2 'n/sec). coefficient C drag Is qlvei, by Zs L2(1+3 5000) CD The overno water surfaces vnr[(I+o.o7(VsL2.5JxIO3 over water surfaces (2. 1.4) where Zs Is the surface elevation In meters. The drag coefficient has been evaluating surface the wind parameter uncertain an in It is knowh to be stress, affected by the surface Nind soeed and stability condition. The latter estimation shown was of monthly 1981). Reynold, The mean little very nave to wind stress effect (sbensen on and formulation of the drag coefficient over water surface In the ACCM Is suggested b Deacon and Webb (1962), and is linearly dependent on wind soeed, The numerical values of Cp over ocean for various wind soeeds are tabulated in Table 2.1. Also included in the 's used h table, as a comarison, are the C (1981) (hereafter referred to as HL) and Han and Lee illebrand (1978). HL took the values for the neutral stability condition from the CD table given by Bunker (1976). from the formulae olven by 4Illebrand calculated arratt (1977): -& = (0.75 +' ô.067 fVs 10 ,, (2.1.5) Three esti!nates of the cirg coeffic1ert (10 Table 2.1 ACM ind soeei (rfl/SQC) a a a ----------------- - fl ) arratt Buncer a ------------------- flea aaaaaaa o - 5 1.00 - 1.35 1.20 0.75 - 1.09 5 - 10 1.35 - 1.70 1.54 1.09 - 1.42 10 - 15 1.70 - 2.05 1.87 1.42 - 1.76 15 - 20 2.05 - 2.40 2.16 1.76 - 2.09 20 - 25 2.40 - 2.50 2.40 2.09 - 2.43 25 - 30 2.50 2.60 2.43 - 2.76 - 35 2.50 2.90 2.76 - 3.10 35 - 40 2.50 3.00 3.10 - 3.43 40 - 50 2.50 3.20 3.43 - 4.10 >50 2.50 3.40 30 a a fi a a a a a a a flaflaa a a a a a As can been see, for wind see1 lower than value bY Carratt's formulae other two are co,parable. TI/sec. the value in is 25 m/sec, the is the sna].lest whereas the For wind soeerl larger than 25 GCM was held constant while the other two continued increasir. SDeel >4.10 The large lifference at higher not inportant because Such speed Is rarely found near the surface. The source-sInk ter!ns in the governing equations (and hence the surface wind stress) are evaluated at every sixth to time step, that is, values once the ieendent variable. of using hour, every latest the The wind stress values were saved every six hours. Since the observed stress fields recently analyzed HI will, be heavily used as the verification of the (1981) AGCM's bY simulated stress, review briefly will e the algorithm and data source of their calculation, data The primary surface wind for used the stress calculation were obtained from the National Climatic Center . (MCC). These data are defined 3fl a 5X5 each for rid of the a subsouare MarSden 12 calendar months, and reoresent observed climatoloqical surface winds available up to 1974. The zonal and meridional comoonent of the wind at each grid oolnt, directjon-soeed soace, were computed for over average weighted a stress each of the 12 calendar months from the formulae: (2.1.6) / FCiUjCo5i)/flj = I-) where is the unnormaliZed frequency (probability of ii of wind soeed Uij occurrence) j!j is the observed wind In ; soeed category I and direction category 1; for direction 1; f) Is the air density, The NCC data set orovides In only wind mean the soeed and eight directions (11, NE, E,.,,IW) olus total standard deviation of the speed. of angle C,is the surface drag coefficient for the soeed category I and frequency the soeed for each ausstan A found distribution to Ive a lata-soarse areas, directionwas satisfactory estimation of the wind stress. Seciai care was taken high latitudes. mainly in stress field calculated geostrophically computed in the This involved a merairtg of the from the ICC data with the wind stress field, and a spatial smoothing which removed the possible discontinuity due to the merging. 2.2 3-YEAR MEAJ !IEfDS We will look at the mean fields of the vectors, zonal and meridional components, curl and root mean square of the simulated wind stress in this section. the averages sImulation. of the The mean fields are 6 hourly fields over three years of 12 2.2.1 Vectors annual Fig, 2.2 srows the zilobal distributions of the stress vector. observed mean the eastern oart of tne Hemisphere, and basins. the In 'Jorthern westerly stress turns c].occwiSe below SON the counterclocKwise southern ocean The main gyres are found in boundary 50M above westerlies the of at 3GM in both is The northern boundary, however, is at 55'J oceans. Pacific and equatorward and 35S of in countercloccwlse near Antarctica. clockwise the Southern the In stress Nesterly the Hemisphere, Atlantic. the in 6071 The oceans. both in The boundaries between westerlies and easterlies are at 30S and 70S. Fl;. 2.3 shows vectors. stress the In distribution north the of Pacific, simulated the wind stress is estwar1 almost everywhere exceot between 4071 and 2071. cyclonic gvre is found centered at (175E, 45N) whIch is about 15 degree south of the observed gyre. anticyclortic gyre defined and anticyclonic In the gyres are exceot that they are 20 and 10 degrees south of the corresoondinq those that are means observed The near Morth America Is not seen. north Atlantic, the cyclonic well The observed. This also that the westerly stress belt is 10 degree narrower. As shown in fig. 2.2, the annual mean observed stress is WI. a... / / . / /111? . 11/11/1/ a- ,,,pr, 4r,d,,,III.. 11 / / ',,-.-,.1 a,,, \ '. , I -a, S4 7SN f( ,I.I 1NJ'1.-? AI' //# ñ ,, ç.,...:, 5, ... ...-'- --- I I, ' U % t 1 / ". _. '11 / ' '--' *'' %%bt r \ '( a-I, . IW a. - /'. '/ ' , 1v,.---------.#'/I' (.#..r.__..,. -'r------ - a '' IS N jv1j1 / /1/ 1 / 'bI,1 1 iij{'........r. Ia- v I I - %%%'.*_%\ a.. a-/I 1''' 31S --'t1 -. I F''.'.\F/'-a--a--a--aF/ _r_ - I 3SS -----a.. 5$ a. "F - F..-- - 7.s ' - _.d - I 111 f.///i?a. a.. 4.1 Itt -'ass 9.5 4S 3U U( jg. 2.2. W 1151 1551 III li$II iaSw Nl * S Annual mean observed wind stress Vectors, (after (Ian and Lee (1981)). pa. ION -- '' r a '.' r--' "' ri 4à IJ . i ri '' I - I r-' ' I -_'.S% -' r- _ -- I L -- - v'r .'%_ //t/1 lit 7711 1.- v.I-1.va.a/I/171t4 I -. --r_ _ --.,i- ii l's. V., V..--' - I S 1 -e%%,_ -.."-- r- - IL N N L I.,'V5a. - JLN -- J-VJff.7. s it r_i._r*. JI_I.i - ION I -I.1- %'-'i i5I ?7711 777 -I.-I 1 - i I_1_-, --i-.-i-i,/.- -t - r" - -* -- In 1O$ _-It.-5.- -i-i_.,% -I----4 - .. rrj1.% - V.vrvV.V..,% - .////.#n% !.-/1Zt%.'.1 !V.',r U'I1i#I11 \na/ 311 5-n %'s' -.#' 1\ i J$.-JL i-4P/i..14.J f. r.rJJ_J- JV..1IN J*J$IJ.. - i?..L tiiJ t% UI 31$ tl -.ra.. -_5I-__JIr - - r ,*V**.e._. £ £ 't L t- 1t.'S%S, -%%%' ..-r - %.-_k-V1-* III - -.r - is- - a- % 11114 -wV..V. %,,Srir_)1mV..t1,.f1rJ tt It 71$ --- .J.r,.r J SIJ -'- - 70$ Us $ an P1g. in 2.3. au sin sis is. issu sasu asu MU SU S 3-year mean AGCM-simulated wind stress vectors. I- 15 southwesterly and weak northwesterly over the North Indian 3cean desoite the throuh November dominating !hile the simulated flel.-1 shows 4oril. northeastely strong fairly this from stress northeasterly 1omtnatini stress northwesterly and This will be discussed in a later area. oart of this Chaoter. me fairly over Jistrioutlon well the Southern They part of the ocean are clearly seen near 305. east degrees simulated of observed the northward stress qyres. 3lon is yres on the eastern The cyclonic simulated. Hernisohere tne are 1.0 Conseguentiv, the west coast nf continents is confined to a relatively narrow band. 2.2.2 Zonal component F'ig, 2.4 shows the global distribution North Indian 3cean. zonal the The region between component of the simulated wind stress, 20M and 30S is dominated b of westward stress except in the The oattern is similar to that of the observed field (fIg. 2.5). The magnitude Is smaller on the average, except for eastern Dart of te south Pacific where a center is found to have a value of 1.2 dyne cm2 , while the center at aporoximately the same location on the observed field is 1.0 dyne cm . South of 30S, the UN ?SN ?SN ..: -1-i-. .:::::.: I -..: I_ L SIN 2 3SHJ is 1I 1.5 3.5 4'i ___,. _-i:- 7" -1. 1I: 95 . - 7.5 I 31u I 9 3Sf tij. 2.4. 9.1 9Sf I tast I 19.1 I uS I lilu I hIM I I 1 1 NM flu 3SM I III Zonal-conponent of the 3-year mean A(CM-simulated wind. Contour interval is 0.2 dyne/cm2. The zero lines are dashed and negative values are stloled. a' SON 0N /)r \ 10$ 10$ Jkt3 . - 50$ 705 90$30W I 0 30E Fig. 2,5, SIE OlE uSE ISlE II 1SSU 1*IU OSU SIM SM I As in Fig.2.4 except for annual mean observed wind stress. 30$ iR eastward stress dominates most of the area with observed f1el, zonat the mean south-shift of the main qyres. fjq, 2.6. in oceans northern over distribution shown curve magnitude the but of This can be clearly sen stress is much smaller. eastward from the to similar The pattern is also fr1ca. of South the tb near center maximum a The reflects again the bounds Fhe north and south of positive area are 1R and 6 degres south of those of the observed field. at The maximum values of the centers located 30P4) and (53W, 30) are 0,5 and 0.7 dyne cm (165E, compared to 0.9 and 1.3 dyne cm2 for the observation. south-shift is also Illustrated by the phase difference stress In high latitude of Iorth f4emisohere Is relatively strong comoarel to the observation. value dyne cm -2 center the at dominating The 'between the two curves shown in fIg. 2.6. westward The of the Sea Berinq while no value over 0.4 dyne cm -2 The maximum is Is found 1.2 over that area In the observed field. 2.2.3 'erjdIonal component FIg. 2.7 shOws the meridional component (Tv) simulated stress. wind In the Positive values are found north of 15M over the Pacific the Atlantic. Morthern and of the Hemisohere, east of 170F and almost everywhere north of 15N over Jegat1ve values are mainly on the western 80 _____- ØeGER VEO ZØNM.. -CøMPENT S IPIULATEU Z04.JAL -CØMPØPIEN 70 30 w IC 10 -to -30. -50. -70. -90. i I I -2.0 Fig. 2.6. -1.5 -1.0 -0.6 0.0 0.5 1.0 1.5 I OYNE/CMN2 J MAGNITU Zonal means of the sirnlated (solid lines) nri observed (dashed lines) zonal-component of the wind stress. 2.0 74.J] .yJ r-J LL ) f \ ,.: ( (t uN ( :/ / : till a : __- -.----..--- . 4 f/V. SiS Sill / I ç /Y / 1,S.s , __7.. :( [l I Ut I 2.7. SIC 1 liii / o :. I SIC 1$. ISIW ils alu NM 31M S As Is F'Ig. 2.4 except for meridional component. 31C 21 long the east coasts of the Asian and The southern boundary nts). area positive absolute The olace. same south values observed the of The northern boundary, however, (fjq, 2.8), the deorees 15 is is are general in summer southwesterly generally oosltive due to the strong However, the simulated field has a negatIve value monsoon. is one of the largest negative values. dyne cm2 which Southern -0.4 The center has a value of everywhere in tnis region. the 154. of Jcean, the annual mean of observed t y Is Indian the about at s].iahtly laroer than observed in the region north In the of northward Hemisphere, stresses found are mainly over the eastern part of the ocean basins. In They are confined in a smaller area with a value larger than that of the observation. maximum found over the Pacific is The oth cases have a The contrast is small over the Atlantic. dyne cm2 maximum of 1.0 northward stress observation. the against 4 In . weaker much is maximum of the 0.5 observed 1.1 dyne cm Indian than dyne crn -2 instead field. However, because oriented. the of northward the stresses stress difference in this in Ocean, that is of the the compared The central oart of the Pacific between lOS and 30S is dominated stress dyne cm2 0.58 observed compared to the 0.90 dyne cri2 as by southward in the observed magnitude Is small area are mainly east-west High latitudes are dominated mainly by westward 50N 3SN 23e I" dY c .S.N KO/ ::(_ro.}. 1 VEx A / : (1 : p IØN 0. ' 1 SOS eu 1. s F1j. 2.8. As In rig, 2.5 except for merjjonaj component, 23 is almost zonai. The distribution of observed stress. with well defined centers located south southeast of Africa. -0.69 dyne cm2 zonal distribution. the -0.4 dyne cm over value means of both cases. cannot we see The simulated maqnitudes are much has Dnly a very small area smaller than the observations. a and The values at these centers can reach In tne simulated field, . Australia of -2 Fii. 2.9 shows the zonal. . As in tne zonal component, the that simulated wind stress field suffers phase difference in the north hemisphere and a maznitu1e difference in the Southern Hemisphere when compared to the observed field. The wind stress is calculated from the therefore surface wind, oositioning errors of the rain gyres in the the Northern Hemisohere must result directly from the errors in the A comoarison between AGCM simulated wind wind fields. and observed wind at the surface, 800mb 400mb (1977). occur C 0 = 1/4 ) was qiven by 3/4 ), C Schlesinoer and and Gates The maximum soeed of the simulated westerlies did equatorward to the observed positions at all levels. The difference is especially evident in July. However, the maximum soeed of simulated wind is larqer than the observed wind, stress This contradicts the fields, comparison between two wind This could be due to the exclusion of land ooints in the present study. Also, the comparisons made aqatost observational data trom different sources. were 90 - BSERVED MER!DI2NAL-CØMPØPEWT SIMULATED PIER IDIaNAL-CØMPØNENT 70 50 30 w o tO I_J -to -30 -50 -70 -90 -0.5 -0.4 -0.3 -0.2 -0. t MANTUDE Fjz. 2.9. 0.1 0.0 I 0.2 0.3 0.4 OYN'CM*M2 As in Fig. 2.6 except for meriiional component, Curl 2.2.4 crucial The curl of wind stress is in decldir liagnitude of nass transoort of the ocean by direction and currents. The relation between the transoort and the M=( ' 0 x\ Y " 212C0560 ,' fdpvdz current: ocean is net the (2.2.1) meridional transoort d is e1ual to or ireater than the 1eoth curl ('Jeative) (southward) Sverdrup transport. distribution of the oserve by t raiient becomes zero. which the horizontal oressure Positive curl Sverdruo (1947): was first derived b where M., the corresoonis northward to Ei. 2.11 shows the qiobal The annual mean stress curl. curl, is aooroxlnated as the circulation per area within 5X5 1eree boxes whose centers are the corners of 1ecree shows E't. 2.10 subscuares. distribution of the stnulated curl field. Hefflisohere, arsden the In the 5X5 olobal orthern values are found between 27N and SON oosltive (6O in Atlantic). The observed maximum centers alonc 60M are reoroduced about at magnitudes are smaller, of the the sane locations except the As expected from the distribution zona]. component of the stress, the zero lines also shift south to those of the observation. The northern zero geM 9ON 7SN 7IN EON SOH 30N 30,4 ION ION 10$ I'S 30$ 3e5 50$ SOS 70$ 70$ ,u 00$ 30 S 35L FIg, 2.10. H( 0O ia. ISSE 105 15aI ia.0 oe cow S 3$E Contour 3-year mean AGCM-slmu:Iated wind stress curl. . The zero lines are Interval Is 0.5 X 10 dyne/cm dashed and the negative values are stippled. 0' SON s. .--..-. d!Z3i- 70N SON :::IA ( (%s. t4(--_fl.I ,.".:.: . 30N 1d ION los ( (O.52s1 t,7J 'r0.c- 30S C) ( c SOS '.5 . . . los 9051 30W 0 30E 60E 90E 120E 150E 180 150W 120W 90W 60W 30W Fig. 2.11. 0 30E In Fig, 2.10 except for annual mean observed wind stress curl. (after ian and Lee (1981)) s p.J 28 line shifts iS leqrees, and the southern zero line shifts S Southern femIsohere, the oattern a'irees observations to In the narrower than that of 'he observed field, much be reilon This causes the negatIve ierees to the South. zutte well with the The in the area between the e'uator and SOS. observed centers over te Indian ocean are also seen on the simulated field, exceot the value over the Pacific Ocean is smaller io8 1.5 unit In tourtd ge cannot find the zonal distribution as observed the simulated described ooserved and curl, clearly are features The fIelds. We may here. illustrated notice that there seems to be a constant latitudinal between shift the zonal phase mean curves of the curl and the This zonal stress comoortent. variation in FIg. 2.12 shows the zona]. means of field. above of The distribution beyond 50S Is sbmewhat dyne cm3 ). noisy, the observed against (1.0 is because meridional the of the zonal wind stress is the dominant term of the curl's magnitude. 2.2,5 Root mean square The root mean square (rms) wind stress field gives the spatial distribution of the energy density. shows the rms observed surface wind stress over Fig, 2.13 the orth Pacific and Atlantic Oceans, as given bY Wlllebrartd (1978). He used four years of observational data up to 1976 to - Z2NAI.. MEAN ØBBERVED CUI..) ZØNAL MEAN &XMULATW CURtI .1.0 -0.5 0.5 0.0 MAGNITUDE 1.0 IIOMN-Ø DYNE.'CM3) ai means of te simulated (solid lines) and observed ished lines) wind stress curl. 2.0 calculate the surface wind stress and rms stress. _15 35 . (a) 25- (b) 20 4W 60W Eli. 2.13. mear souare observed wind stress over lant1c ice; ta) North Pacific (b) Jorth Root after value The tyoical. 0W 1llebrad (1978)) between Varies 1 and dyne cm2 3 Maxima are found southwest of the Aleutian islands near 45N in the Pacific and east of r4ewfounilanl The Atlantic. qlob-1. is ienerally less than found value bein oceans, the cornoticated. position The value structure the of 1 the 30N and dyne cm2 , with the minimum eivator. the found norther the In distribution The minimum center is here in between Is a lItte to e at the ft haopens to be a maximum in the observed This is due to the soutnard shift of the field, yre near 5O distrioution of rms simulated wind stress is ShoWn in fL, 2,14, 30S near cyclonic In cne North 'Pacific lcean as we mentioned in section 2.2.1. replaced The observed by the storm track semi-oeranent (laroe Aleutian rms value) 15 Low (small rms NH 711$ -I 5.1$ 31M2 / 111$ 0 C3. 1 rJJ_LL 0 - .-__ / \>\1JLJ -=:-. ..-'- ( 311 __-.J :. 791 k' I 5.1 ,2 I-.______ 3I r'1. 2.14. ss vu (J _____ LIU .3" ''--S..,--- sn c\?%'II , Tr us ui uas s s 3s I Ni Root ilean square sirnilateri wind stress over olohal oceans. rontour 1ntervl is 0.2 dyne/cm The lines of 1 dyne/cm are dashed. . 32 are In the Pacific, maxima value) in the simulated field. located in the Bering Sea and east of Janan with values 2.8 and 2.1 dyne Pacific is cm2 , larger value The respectively. the over that over the rktlantic where the than maximum value is found to be 1.8 dyne cm2 at locations in Morth Sea and east of New Fnqand, 2.3 Seasonal Variations 2.3.1 Vectors the First, we briefly zllscrlbe the seasonal chanae of observed wind stress field. of zonal stress strongly reveals deoenzJent a rhe study of the monthly mean with where a weak southern The almost all exceotlons semi-annual latitudes around semi-annual variation, with oredorninates, rrom mode for in the northern high latitudes variation 505 predominates maxima in are with the in soring and fall, the distributions of the monthly mean shown in figs. annual variations, and where distinct 603, and observed vector field for the 12 'nonths (only July 1.s on latitude as seen in fig. 2.15. annual variation is the oredoninant latitudes which variation seasonal January and 2.16a,o). we can clearly see the The most consoicuous one is associated sian monsoon as seen in the Indian Ocean and west Pacific Ocean. The northeasterly stress orevails during 33 2. CI, 12.SS 72.SN 32.5S 52.SN I .0 0. C -1.0 2. C 1.0 0.0 -t .0 32.SN 2. 0 52.5S t.0 D.0 -t.c 72.5S 2. 0 12.SN 1.0 0. -t.c J.Nt 1A1'R1 rig. 2.15. 'JIJL1 1øTtDc.0 JArJ 1JLtJL1 'øOt.0 Monthly variation of zonal mean of observel zonal-conponent of the wind stress. Units are iyne/cm' I I l- 1! d'I/i ,,,,, .w1I!l,Z--.-¼ 79N I/.d'// -'\t 1..- / / / / . --. : \ L.. rc /L ( O ' rOS i ....--../... j , ......, 34 3I SIN S's l's 3.5 31S 5.5 S's 1SS 71$ -+115 91$ 431u I 31E lIE 91C 5105 ISlE ill 151W 111W 91W 514J 30U trig. 2.16a. Mean observed wind stress vectors for January. (after Han and Lee (1981)) S 3S 71M - - ' 1.-.'tri .av k i - 1$ ri -"i \ 1 I 1 1 '' I ' ,, i*.,- //,--. F ? .W%\\ - Q 7 V------.-----.--.-.-.---ve / Fff 1N 1/IL!\ ,/1\--' -.----. tIs I ' t\-.- .' c J, J J/'/1\\\\ I -.-...-.-..---., 31S / -.-. /_____------_, -__, ... -.--.-.--.---.-.---.-.-. --- .--.- -----. '. - - -'- _ - .- - - -, ,s '. 1-.-.-.-.--.-.-....-..--.'- -i.. ---- --..-,--.-.-..-.--.-.-- '--",'. 'i 71$ , 7 -- .. '.*.,._..__._.'.,_.,_-._._, I ' \ '-.-..v'I / \ ...-, -r _----.-' - -_ -- -. 7.5 ,,_._._.-_.-_.__- __.-.-_-_\.' _._*_.___._.___.._._._ 91$ 1 1 3S S 35E $lC NE 1SE ISlE ill 151W 1IW 91W 51W 31W 6 31C F1, 2,16b, As In E1g, 2.16a except for July. 'I' 16 November through become southwesterly in their maximum until October. anti Atlantic reach southwesterlies rhe gay. its direction to rDverses intensity in July anti then qradually weaken Pacific The anticyclonie qvre in the North experience also time while the then pril, counteroerts dramatic fluctuations with the in Southern fe!n1sphere aooear to be semi-permanent. tine 2.17 shOws the Fig. variability of zonal stress at latitudes close to those in Fi7. simulated 2.15. As in the observed field, the annual variation is the dominant mode latitudes. most for the In interestin' the Hemisphere. The similar to that of the observation at most Is However, some distinct latitudes. found Southern the only at high latitudes in variability Semi-annual variation is found can inconsistences latitudes of both hemispheres. high It is to note that at 50N, the oattern is similar observed one be to except the sIan is completely reversed. This is due mainly to the southward shift of the westerly stress as described in the orevious section. FIgS. 2.18a-d show the distributions of the simulated In the vector fields of January, April, July, and October. Northern Hemisohere, variation occurs orevious section. the most consoicuous seasonal the Indian Ocean as mentioned In a over In the simulated field, the 37 2. C log 70N 30S 50N SOS 30N l.a 0. C -t 2.0 I .0 0. -t C 2. ---- 0.l -1 705 2.' ION I..' 0. - $ 0 J hN IAIL?t F13. 2,17. I IIhIl CJAI!1 1A$'R1 1J&1 'øc!:ro As in Fig. 2.15 exceot for si'nulated wind stress. 7IN .4 ".'' r SON r r L S'.'-.' r 441.4 I .4...-. / ITt'.. Il!flhItlt111Ii SON '.'VW/FII//7 IT 301$ - - - .'v".v......r.4v.- liii 1 1111 '-.'..'.s.*.- ' ...-.-- t . f.v .IiU4s'. 'I 11£ '' tLt'.'.'I W'. - -r-.-..r 1III,I1/...-"'" J /.-.-.-.-.. - .- - ___s I-. II::!1. vrvwI1 IL I ---v'/I II\'. I4Ir,----11t\_-I a'.... _, -- . - iS - ___t_4..t.__ _ - . --.--.--.-v'--.'.'. -'- - -- S -- --r'.".% S-_*.*.'. ' JrV1_'.* .- .- i.\ - - .\/ _'11._----'-_.__--.- .-.---.-.". /-i /I/I//I/.-..-.-r_.-\ -.-,- . _. \\\%\ 1-"..'. r+ --.-_rr__ _ .. L -----4---.--. Iit\'4".". -.-----.--". 7-. - ---- .-- -----1ss.. -S _.--__4'._ - ._1*-_-._-.v_.s.-.-.._ -------- Iv' ,a//v' '. /_ _ -i-I-.. £ I I/i'.-t . ..// 4 %- l..v/7 I 1Z I - s.-I 'IViLU.4b'.I U s- - - , -------. _i__.ii wjj u-v,.r.J-j._r, . 5 - /..'.'.'.'.-t -r - - - _'. r-._.-i - sq *_r_ __t- . '.'.'.q_ _ Li.I.1r.1I'....4'.,*p'b1j q-. sS -,.-.._i t7i'.tFeZLjj/#I iUI-'-u-.'...-.-..'.'. v'III. -- - q-r-,-_s-_sj,_r S 30E SU 9$L 1OE 15CC LU LIOU - 'b-'-- -- I F '..'.s 90$ 30W S -I tu 90W I I iOU 35U 1-90 C 3SE ri;. 2.18a. Mean simu1ate wind stress vectors for three Januaries. '5., ass rW ?SP4 %SS ..//,A %LU t V & AlL - / '. V1 j --1 ----I- 4I/'/r--' L TILL "'-'-' .e.S--- JJ -' -- 1 --V/,f--s - j- ---_ - r.. ' *.%% .'.-.-.-i-ve/r'\ '.%__ - vet s - T I r r t.L '- '- - J__-_--. 3Sf 5Sf fig. 9Sf S -t t __S5* - -av,.--------. ri-r tIP?_.-.-.-N--_. '' -f' f_i iseg 2.1gb, As in r__ _ 1 fig, $$e 2.18 -- - - -'_- t I-1 - , -t - - - -I - -- -. - ,-----_-- --,L .,SVL I /---w i-..%%'. frr 13$ rr' . .-i...._,% I---.__-ve.-L.-J-$_t I.A.IU $N.. -*---s ....v_/ - -I I t 70$ S -. e. .--%l/II%.% -rr/%'.W. --. % ri-1 F _ 1P.% S#/v .-.v-t-Ij.0 ----------_ __ -i,-,-w- -- -f - -*--- - - .s..% - - %.,_t_. - -- -. _r _i - r*..... _..J-JJ Ii... _1 - IJUL f.U_tJ - I *-___-_t S s _ J.-,.rf_ _ tI4r_ - --- -. ---- W --- ._.__-__-ø__J___l, -. I - ,VAIA / Ja..'.'.-J.. ... - ja-r.t,-. _.', I- \.---- Si.A.A.AVA.âV 1 --' #/IL\\\ 4V I I ." -' - - '.. T/ I I I 1 ..-.,--I.-s--p..-..,-...., / F /#-".. J rt,- L / /#.. Z/,m..-.--L t AL t -U - *'A / A 3sw -'% ''I r-' .I,% - I *J -ljrs,I_ss. L1. __ J. f. - ._l Ia..- J.;._.,.r..\fJ__ LL k tt '--- 756 155iJ IMU 90U $au 3.11 3$ exceot for April. 'ad 11$ r i r1'IiLr-' 71$ P P- h ii 51$ \ SIN ' -I 31$ -. -v'/ L/ Ills 11$ -.. .._.I_-, --I - v/ S. v4 _____ ,-, _._.1s..._------.-- I ------.-.-.-, -' --'--- I 7 S- - -. -* %%%%%\S% '%'.%% - i'- .S.%%%%.-. - - i-/ '"-'.'/,?f 1-' v'v -----_ _ 1 - - -- --- .j-.r-. ___________________________ , 71 7 11 '''-."/ .---t-r-. ----- '' - - -- r*-4 -N 11$ S. 4 A I.. - l's t//.vv///-'-'- ri 1.'I LI YI I ". _ 't I -.-.i.S.-'7%% r41 Li ''.'--------.%S.VbiI 714 r 71 % - *._-.F',-. I t'-.\ 1% 31S 71$ .3.' '-" S%--.5.' ?Z?l/r'-'. UI ri// L?!.Pfs'%%%'.i I'b'.'r- 1141 7 7.' 71$ 5,5 S 3S l's lIE ass Fig. 2.lSc. As 1155 in III *S$U 1ZSd 91$ 11$ Fig, 2.18a except for July. 31$ S 315 90N r--'-.%'%? I ?SN I '-' '-' r I 11 ... L1L . uN -- 1 L t1t,,,1\/-'._%' 'fl //-,?/II.-.S%% Ill 't'.II'--.-II'i11I'i %4i-e.'.''-'-/I 111 7 V.-. .'%.SS*'/ .aS-'V. V.V.V.r'r,, a* // V?I V. ISN jr - * 1I\//tt_J .a$t_ _ ---- .1 "..--- - -'-- --- - --- I-, - a* II1\. :1-- I * - *. - '' -'---- 'wa-V., P '.'- -' I 'S%t till 15$ %b%'.l.t ISS 's.',% I PP P 1 .-r'. -. - - W'-'71 71! rgs JI 3.5 ---- wV.v JI.t1I Z1tlII.'.% ass 'a I .-i,i/II lilt .' . 4/ 7.-V. LI l-,- -I--'-,- -w.-1 F t?-'--..'. _'- Is. V.rvV..r'.ts V.V.V./vs''. -- ---.- LF11iI -s1/V..1. V./F( 7 t%--V.' 7,?/V.rV.r.' \'-.'.V./?-.\ £1 -.7F I -.V.. L i. I %v.- '--- i, /£ 'a Z IF i 7S$ ----'.'. -WV.V.d//.%.%I £/'r1 e/V..'%.-1.\'t%t 5.5 7SS ass 35W 35E usc Fig. an ian issc is. ius 155W uu MU 2.18d. As in Fig. 2.18a except tor October. 35W I 35$ 42 stresses northeasterly winter in turn ra'ivally counterclockwise to northwesterlies as the season roes into summer, never but This observed field. vectors stress have to caused has observed those of the southwesterlies as found In the reach and area. this over stress observed the the icean, Atlantic the anticyclonic qyre is found only durinc3 its center near 231. ustralia, the nearly east of turn variation with time. little clockwise to become zonal of Zealand Mew in season summer the In the Indian Ocean and stresses cyclonic June. show ocean in northward in July. this northward flow, a distinct east The In the Southern Hemisohere, the anticyclonic gyres in the eastern Dart of very In micrates also yre cyclonlc 45N in winter to about 35N In summer.' from southward with field, found to be well shaoei throughout the year. never in The simulated anticyclonic 3O4 in July. at the yre charvies Its nositlon from ivre, which is the dominatino 'node In the is In The center of the cell Is found at 45N month to month. January, wind nean annual. almost 0000site direction to an flcean, the cyclonic Pacific toe cell January Because of is formed It lasts throuhout the southern winter and aradually fades as the northward stress turns back to zona]. aqain. stress field In the Southern accordance with the Northern Hemisphere. It Is obvious that the wind Hemisphere behaves more In observed field with time than In the 43 2.3.2 Curl By examing the monthly mean observed curl fields (only January 2.19a,b), one finds are shown In figs. July and again that the most dramatic seasonal variation occurs the monsoon Asian where a large negative value in area, the summer can change to a weak positive value in In the rteoative and the throughout year, remains values in direction of relatively weaker than Variation is found only in The magnitude. strength in transport during the year. the southern oceans, te'nooral fluctuation of are unchanged almost the maanitude does chanae from but season to season, indicating a variation not those in oattern the northern not but the but in curl stress the oceans. in the tine variations in te tropical ocean are snail, yet it is significant because of the raPid of winter. and Atlantic Dceans, the boundary between Pacific positive in response ocean to the wind stress due to the small Coriolis Parameter. Pigs. January 2.20a-d show the simulated curl July, and Dctober. In Aorll, fields the riorthern Hemisohere, the curl in January is generally positive changes for over to negative in Ocean and gradually summer. However, the negative compared to the observation, due to the model's failure in the Indian value remains small, SON I I I I I I I I I I 70N 50N 30N ç ..::'k(:: 4' \ E' 2 ' , () ." iON (4? á!4J% -m '-' 0.5 05 los '00 '05 30S 1.0 - 505 TOS 90S1 30W 0 30E 6O 90E 120E 150E 180 150W 120W 90W 60W 30W fl Contour Fig. 2.19a, Mean observed wind stress curl tor January. The zero lines are dyne/cm3 interval is 0.5 X 10 dashed and the negative values are stippled. (after Han and Lee (1981)) . 30E 90N .. ::::::::::::::::::::::' i:::: .:::::::i ,.çk 70N 50N-' A: ,°2: I:h:llii I 30N iON coE' .:.::Nao-:L,--- 3,'( .--. ) :.:O..: :..'.:: F 30S ' r'-'''::' __s_-_ 05 ' 50S i..... 0 0.5. -?: ' .1 .::('-- los 90S 30W 0 30E 60E 90E 120E 150E 180 150W 120W 90W 60W 30W Fj, 2.19b, As in Fig, 2.19a except for July. 0 30E iI nu C)1., ri1J42 3." , ) t.N 1J./, . . . . '(L 7 .. . r& O.... :.:.. . / ..: . "i: B.. I i 30w 0 3 SOC OBE 1205 I I ISSE 1$, 1SG I I2SU 9 Fig. 2.20a. Mean simulated wind stress curl for Also see Flq. 2.19a, three Januaries. Sw I I 31U 0 N 111d\I 10 3C S fleC I'S9 %O6 da3Xa M21 ?SSt I I O'2 'b1J 1St I U 3ST S IIfl qO 356 I I .eT. 359 I I S I 556 rec ç sei. sez. - . '. \ ?C.ce! \ :/ --... : set .. L p-' - we, - I L2EJ I I z/7 lit I ---.- -'- '\:-...- ..D so F ' c:i - NeC- 4NSS NIS N52-1 wee wee - 7SN 7SN 0'V:L., te,. gas j 35W 5 I I I 30E HE 95E 1 I 2eE ISU 180 I tHU I 125W I 90W L1KfSI -1N I 6I Fig. 2,20c. As in rig. 2.20a exceDt for July. 30W 0 35E SN PON 7N ;t4 30N 31N I SN ISM 1G5 tis 3,5 3.5 S's S's 7,5 755 - 915 I 31E $5 SIC 121C ISlE 18$ ISSU 125W 95U SSW 3U I t_9,S 35C Fig. 2.20d. As in Fig. 2.20a exceot for October. 0 50 tniian Ocean. Pacific the In to curl South the to from In the Southern Hemisohere, fields over the Atlantic and east oart of the Pacific ocean have little variation with Indian the summer as a result of the seasonal mlqratlon of the main iyre over the oceans. the over and Atlantic oceans, the oositive area shifts aout 10 deqrees winter monsoon siimrnr the simulatinri the strenqth of Ocean, Over time. the neative recilon oetween 105 and 305 in the January shifts about 15 learees to the north July in and the maximum value reaches -2.0 cooare1 to -1.0 in January. distinct. In the west Pacific Ocean, the variation Is also The sign of the curl is seasons channes from summer reversed almost everywhere as to (southern) This winter. results from the chare of flow Pattern due to the bulldina uo of the cyclonic cell east of Iew Zealand In winter. sjqnjflcant variation can be found at the southern Another tip of Africa, where the magnitude of the curl becomes very lare in winter. As in the observed fields, the time variability in the troolcal area is small both In magnitude and pattern. me large values near the northern and southern boundaries are statistically unstable due to the relatively short period of saroling, and hence they will be smoothed out when averages period of simulation, are taken over longer time 51 SPECTRAL A4ALYSIS OF SIMULATED WIND STRESS 3, In the last chaPter the spatial characteristics ot the simulated AGCM wind in terms of mean fields and stress, root mean square fields, have been reviewed. We will the temporal. characteristics of the wind stress by examine means of sPectral analysis of the 3-year time series. allows technique total variance at periods conoutation In this study, from 12 hours to one year are resolved in ranqing quantities selected This the contribution to the of frequencies. various The cross soectra between pairs the autospectral analysis. of are also calculated. This will the examination of the relationshto between oairs allo now quantities information at various about the of frequencies, and will also provide spatial scales and directional oroperties of disturbances. 3.1 Autosr'ectral analysis 3.1.1 Algorithm and method of calculation The raw time series consists of 4380 data points a uniform time interval of 6 hours. segments of six-month length calculated each. with It Is divided into ii The autospectrurn s for each seqment accordini to the definition In Jenicins and Watts (1968, hereafter referred to as JW). The 52 soectrl estimates are tnen averaqel over the it sementS. For a stochst1c orocess x(t), -t/2<1<T/2, The samole spectrum Cxx(f) lefinel for a continuous range of frequency ) can be exDressel as 2 C(f) = T (x(f)t (3.1.1) where X(f) is the Fourier trarsform of x(t) T/2 X(f)=+J-T/2 X(t)e 2ft dt (3.1.2) (3.1.1) then becomes 1/2 C(f) -- 12u'ft x(t)e J-T/2 , jztif' / x(t)e. dt 11/2 By deftninq a pair of new vartaoles u:t-t' vt', (3.1.3) b ec o me s T (3.1.4) Cx(f)=Jcxx(u)e_124u where cxx(u) is the samole auto-covariance function (ACP) and is comouted as 1 ° Cxx(U) = (T-1t41 t4 H (X('t)_)(xCt+tuI)_)dt OIU(T Jo (3.1.5) 53 Thus the sar'ole soèctrurn is the Fourier transform of the By taklnq the inverse transform of (3.1.4), we samole ACE. ciet °° (3.1.6) The sample soectrum Is able to tell how Power) distributed over frequencies. is the variance It Is lesired to produce a soectrum that has smaller variance than yet preserves the total oower. Cxx(f), spectrum the raw This can orocedure whIch Is commonly be achieved thrDuqh a smoothir done (or by introducinq a laci window on the ACE. The smoothed spectrum Is of the form C(f) du Cxx(U)e. du (3.1,7) satisfies some -a - here w(u) is the laci properties: - ..ztfu W(L4)C(U)e window w(0) (1) = 1, which basic (2) an even function, and (3) w(u)= 0 for fu> r, Jow t&ce the Inverse transform of (3.1.7) and let u=0 o) I C(f)4f W(0)ccx(0) i-co By use of prooerty (1), we qet Cxx(0)=jC*(f)dfCx(0)JCxx(f)df (3.1.8) hence the total cower (variance of the time series) remains invariant. oractice, In w(u)O for (UI> '4 can reclace orooerty (3) by we < T), and the ACF needs to be computed ('4 only uo to maximum lag '4. The behavior of the spectrum is largely controlled the selection of '4. If we choose a small the soectrum will be made small, look smoother. 'width C width spectral window, main the of and lobe eoual is the thus a smaller However, the variance of soectrum the 2/M) corresponding which imolles smoothing over a wide range of treguency, so that the (difference between The most commonly used lag windows spectrum) may be large. are Bartlett, Tuey (cosine), reader should refer to J (1972) for details or Parzen windows, Otnes and The nochson of the characteristics of these Parzen estimator the smallest variance, and tre Tulcey estimator has the Lowest bias. of (1968) and In general, for a given '4, the windows. has more bias estimator and the true soectrum the will means a larger base '4 of to '4 b the e choose Tucey preference of its inlow in this study because low-bias characteristic, The algebraic exoresslon for the Tuey window is W(u) = o.(IcoS) IIM to IuI>M (3.1.9) 55 and the corresponiinq sDectral window is can The variance of the sioothed soectrum (75M/T)% unsiioothed the of be reduced to In this Study, we soectru'n. choose M to be 25 days, theretore, the variance is reduced to about 10% of that of the raw sDectr']m. Equation (3.1.7) can be written in discrete form for a batch of discrete tyoc data f)= 2t{co)+ 2Z cc((tQW(K)cos(2lTfKAt)j (3 1.11) Ic* where t calculate is the of frequency, i.e. Then interval., r equals M/t. We only over the oosittve half of the ranqe Cxx(f) function, ttre 0<f<i/24t the value since Cxx(t) is an even is doubled as is necessary to preserve the transfori, relation between sample soectrum an sample ACF. In (3.1.11) cxx('c) is calculated as N-K (XtX)(Xt+KX) C,oc(p)= Of(N-1 (3.1.12) t=I where N = T/At, which is the total number of data oolnts; and the lag window (Tuey) is W()= K>L (3.1.13) si The confidence 95% interval estimated also Is by calculatinq the lower and uooer limits of the Interval: V (IO5) J1 ((I_0.95) where the is ) ' degrees estimator, spectra]. window. and is randoi the is of freedom (3.1.14) smoothed to 2.667N/L for Tukey equal distributed variable chi-squared, with probability the for as Taking the logarithm of . (3.1,14), we oet log C(f)* log log C(f)+tog5 ,ç(i_.95) 2. expressions The second parts in both hence frequency, confidence the scale, of olot the soectrum on logarithmic we if indeoendent are interval is constant for all frequencies and can be indicated by a single vertical bar, 3.1.2 Autospectra of the simulated wind stress fig. In 3.1 wind meridional longitudinally increase maximum the the of The SQectra have been and averaged over S points from 140E to 120W in order to statistical resolvable stability. frequencies The are (4ygujst frequency) which correspond to 365 zonal components over the 4orth Pacific stress are shown. ¶Jcean at 42 autosoectra the days and 12 hours respectively. minimum and 2Nt and Deriods of Fhe soectra are lower '57 I $ .0 -------'N:\ .5 0 U N a. 0..0 I I N 1 * U '3$ 2 -1. 0 0 -I. S p.- U '3$ a. ZØNAL CØMPØNENT U) -2. 0 (0 (0 PIERIOIØNIu.. COMPOt.4NT (3$ p.. 10 -2. S -3. 0 4 -3. 5 -3.0 -2.5 p p -2.0 -1.5 -2.0 LØG FREQUENCY F'ji. 3.1. -0.5 ICPO) 0.0 0.5 Conqitudinafly averaqed autospectra over the Morth Pacific Ocean at 42N (J34), The 95% confidence interval Is indicated br the vertical, bars, 1.0 )2 than 10 ('dyne/cm2 /pd vlrtuauv everywhere with a sharp drop at 0.28 cpd which corresooids to synootic scale of 3.6 iays. a The 'drop of power is almost linear with frequency on scale, log-log significant No The soectrum of observed frecuency. (Willebrand, oea is found at any wind stress at 1978) shows a much flatter shape with a sharp The power is mucr larger than that of the droo at 0.3 cod, This is stress, especially at high frequencies, simulated probably due to the inability meso-scale 43I simulating coarse-resolution model. Also, moving fast disturbances scale small or of 43N heopens by be to a the latitude of maximum ooserved rns stress in constrast to the minimum rms stress in simulated fields. soectrum The of the zona]. comoonent is larger than the meridional comoonent only for frequencies lower than 0.035 cod (28 days). is true for most latitudes in the North Pacific. the stress soectra for the observed This However, component zonal is larger for all freauencies. 3.2 displays the wind stress rig, at five different are similar except frequencies is at 62N where much more rapid. stress field (fig nultiole-center latitudes from 26 the magnitude in the The shaoes to 62N. decrease at high The structure of the rms 2.13) is reflected here. nature soectra rns field Due , judoe which latitude has the maximum averaged to the it is hard to enemy, but S9 2. C i.E N - a a. (I z N* * E U U 0.0 z a < -0_s I- LI U a. w J 30 LT 26 -J. 32 -J 34 01 Id LAT. 34 LAT 42 Ilb -l.5 -2. 0 3.0 -5-.-L5-L0 -.s FREOtJENCY F'i, 3.2. .s ICPO) tonq1tudina11.y averaced spectra of horilatitudes over the zontal stress 3t North Pacific Ocean. .0 it is clear that the northern latitudes have large energies than the southern latitudes. case in higher at iroos s3ectra rhe latitudes. lower the 2N are larger than those 3.2. the spectra at 54P4 and fIg. at Tnls Indeed Is frequencies have virtually no difference for all latitudes. rhe sPectra of selected oints over the North Atlantic Ocean reveals those on very similar shape and energy level with a about Pacific. the the soectrun over the North tnciian ocean exhibits owever, spectra illustrates 3.3 Pig. pattern. different a very over latituies same the a oolnt at (90E, iON), just east of Sri Lanka. of As exoected fron the rms stress field, the enerqy level very the 80th especially for the neridional component. low, Is Components show a significant Deak at the diurnal frequency day). (one troolcal the In atrnosohere, iependinq islands the lands, and atmosoheric geographical the on Parameters (Houze et al., 191). attributed to diurnal are Jver mechanisms possible variability is evident due to several location, Over variations many controlled by land-sea breeze the ooen oceans, they are day-night differences in the radiative the surrounding or near of heating profiles between the thick cloud covered the diurnal a area and clear air areas (McBride and Gray, 1980). may Atmospheric tide variability althouah also contribute to it Is relatively weak, the diurnal In the AGCM, 61 U 0 a. o N I. B 1. 0 0. S o. 0 - g I N I * \ r U 'S lii z -t. 0 >. 0 -1. S I- U Id a. ZNAL CØMPØNENT 'A -2. 'A U, Id ---MERIOINAL CØMPØNENT -2. : -3. -3. -3.0 -2.6 -2.0 -1.5 -1.0 LØG FREQUENCY Flcj. 3.3. Autosoectra -0.6 ICPDI 0.0 0.5 t (90E, iON) (I55, J:26), 1.0 62 characterlstics the cloud effect and the diurnally varying ocean point Is the existence of cloud. ootnt selected (l75, Pacific not does be the fowever, the effect because out ruled the is surrounded oy large land mass, besides, another point at 6S) such Show the a center strong of eguatorlal. peak at diurnal 'jg. 3,4 shows the soectra of horizontal stress frequency. 'iagnItude cannot contrast of land-sea over frequency diurnal at resoonsible for the peak echantsm The nost likely of solar radiation are included. four ooints in the South Pacific alon at The energy level increases with latitude except 175'. 385, at just east of New Zealand. lthouah the data period is only 3 years, it is oossible oeaks of longer nerlod C at least to resolve to the annual cycle) if there exists one. we still ror ourpose, this have to use a much narrower window, i.e., larger M, To averaae of avoid large cornouting tine, we first take the every four consecutive data to get a time series of one day interval. be 365 Then choose the maximum lag for Tukey window days. By doing this, the degrees of freedom is largely reduced, hence a wider 95% confidence expected. One point arid interval is in the west Pacific Ocean on 42N is selected for this analysis. iagnjtude to The soectra of both components are calculated. the stress n average over frequency bands of different lengths is done for every 63 2. 0 1. 1.0 0 - 0. LI N * 0.0 N * * I) -0.5 hi z a -1 0 I(-I hi a -*.s J. 10 -,J 14 U) U) U) lii LAT 545 LAT JBS LATE Z2S -.J 1$ --J 2 LA!. -2.0 -1.5 65 -2.0 -2.5 -3. 0-1-- -3.0 -2.5 -- I -0.5 -1.0 FREQUENCY 3.4. Autosoectra at 4 Pacific Ocean. 0.0 0.5 ICPO) ojnts over the South .0 64 Spectrum estimate In order to ootain equidistant spacing on a logarithmic scale and to eliminate the wiggles at 3.5, annual oeas are found s shown in fjg frequencies. cornoonent meridional The uncertainty. though co'nOonent, in the stress magnitude and Zonal great higher wIth not does exhibit a significant annual oe&c, however it has a neaK at and the behavior of this dynamics The cycle. half-year The arrival :ycle is stronger In fluctuation are riot clear. This reveals the magnitude than In the comoorients. stress Since 1978). wlllebrand, tne of nonstattonary criaracter wind simulated the field magnitude stress only positive quantity, the annual cycle is distinct Is C a when fluctuation of the comoonent stress is much stronger in one we the repeat verify To season than in another six months later. this, procedure used in obtaining the spectra jn tjg, 3.1, except that the soectra are not averaged over all the segments 11 months oerlod in but the over year. those containing the same six 'our winter o'ier 5 oojnts The summer for The energy level all for Those frequencies. soectra for the other two seasons (not shown here) are somewhat in between. over longitudinally. and summer are shown In fig. 3.6. Is higher in winter than In obtained Again, the spectra roughly reoresenting the four seasons. are averaged are spectra all seasons illebrand oointel out that averaging would distort the spectra shape in the oresence of nonstationarity. However, If all the other 65 2. 0 1.0 0. a 1) 0.0 N * * '.5 I- Li w Q. U, -STRESS MA(3NITLJDE -2. 0 ZØNAL CØMPNEMT U, U, MERLDIZNAL CØMPØNENT La I- -2.5 -3.0 -3.5-F -3.5 t- -3.0 -2.5 -2.0 -1.5 - -1.0 FREQUENCY Ft, 3,5. -0.5 0.0 0. (CPO) Autospectra at (160, 42M) (1=69, J=34). .0 6!, a. U t. S I. o 0. 0 a. U N 0. o \\ I N * 0. I U Id z -i. o 0 1. S I- U U a. SUiIMER 4 - 9 ---------WTNTER 10 - 3 (a -2. 0 Cl) (a Id IU) S -3. 0 -3. S -3.0 I -2.5 F1, 3.6. -2.0 -1.0 -0.5 LG FREQUENCY ICPO) -1.5 0.0 0.5 1.0 Longjtujna11y averaqed autospectra of zoh1-co'nporent 4ind stress for the swnmer 1nter over the 4orth Pacific 'Dcean and at 42M. such characteristics, the shaoe, remiln unchanied for as nd all seasons, as in the oresent analysis averaing the atmosphere, ouli and will justified e real the In increase the statistical stability. Cross-soectral analysis 3.2. 3.2.1 lqorithm and '4thod of calculation The sample cross soectrun is defined as C42f) = TXI*(f)X2(f) for two time wnere -r/2<t<T/2, conjugate. series and x1 (t) x2 Ct) astertsc the (3.2.1) In denotes ranoe the the comdex similar steps as in section 3.1., we qet B (T C12(f) = -121rIU (3.2.2) c,2(u)e I i-T where c12 (u) is the sample CrOSS covariance function (CCF') and is defined as Tf2-U (X1(t)- C42(u)= =-I 1)(X1(t.u)-Xa)ctt, (x1(t)_1)(X(kiu)- IUI >T 1)cjt,-TUO o = The inverse transform of (3.2.2) Is written as (QO C12(u) = I -r (3.2.3) 121rfU C42(f)e. (3.2.4) Since C12 (f) is a coolex function, it can be written as C12f) = R42(f) - (3.2.5) G12(f) where R12 (f) is an even function and G,. (f) is an odd The samPle amolttuie and ohase spectra are then function. defined as + G(f) A2'+) (3.2.6) tQr(-Gl2(f)/Rl2(f)) F12(f) = F'roni (3.2.4) and (3.2.5), we qet Ci2(u)JRiz(f)COS(2flft4)df +5 c2(f)si n(214u)4f (3.2.7) the first and second terms on the rtqht hand side reoresent the even oart respectively. r Cu) and odd oart q12 Cu) of the CCP, They can be obtained by definition the of CCF: 2(u) =(C;2(u)+Caa(_u))=JRia(-f)COs(21T-1u)f - g12(U) By takjn C12.(-i.0) JG12(f)sin(21rfu)df the inverse transform of the last two equations, we can calculate the value of R12 (f) and C12 U) as R12f) Jz(U)COS(21fU)dLA (3.2.9) G12(f) 912(u)Sin(2i$u)4U Thus the anolitude and phase soectrun can be obtained by estimates, introduce the la windo W(U)as a seibt1nq function, qet To (3.2.6). srnoothel a soectra]. we JT5(21rfu)d R12(f) (3.2.10) %(U)W(I.4)SIfl(2lTcU)dU G12(f) rd ohaSe Soectra are then The smoothed ampliturle by reolacinq (3.2.10). R It is and , in (3.2.6) 4ith often more convenient to I2 obtained inzi G12 in calculate the sauared coherency soectrum defined as (3.2.11) K12(f) = where C U) C22 (f) are the frequency soectra for series x1 Ct) and the previous section. time x1 (t) resoectively as descrIbed In discrete farm of the above equations for estirnatini the smoothed cross soectra are similar to those for autospectre, hence they are not described here. The JW showed that art estimator 112. U) which takes the inverse hyperbolic tanqent value of coherency 121 will have a variance which is controlled only by the s'noothlnq factor (variance ratio) of the inoosed window, and is relatively jncieoendent of frequency. qence, the confidence K interval can be reoresertted b a constant interval on the Y 7° will this The coherency soectra to he shown in scale. be in scale. Y The 5% sectinn interval is confidence a vertical, bar. calculated and illustrated b frequency certain (f) at a E'or squared coherency t, we have Y z U) .L arctanh J K,2 U)J 2 fttKaI(3212) 1- and the 100(1- c)% confidence interval, is /. Yz(f) ± 2 (1 --a-) 2 42T where + 7(1 - ) (3.2.13) is the range which in the 100(1- a chance that a random variable with normal distribution will is 1.96 for fall, the value of I/IT the is phase of 95%. for a specified w1ndo, and Is variance ratj O.75M/T for Tuky probability a window. The Interval confidence for soectral, estimates depends on the coherency estjmate and the deqrees of freedom of used a diaqram rovjded in J a certain frequency. represented b of soectra estimate, We to determine the interval, for Several Intervals are calculated and vertical bars at corresoondinq freauertcies. The raw ttie series are seqments the 12-month divided each. rhe Into cross S overlappinq soectra are n averaqe over all senments is made for squared coherency and phase soectrum, F'inallv, calculated for each sement. 71 and the confidence intervals are evaluated for Y estimator ohase spectrum. 3.2.2 Cross soectra of MInd stress components the perform to soectral analysis. cross the often hard to Interoret spectrum cross orovides one-field the cross The a certain oatr of quantities. for prsented are that soectra However, It Is that information series time There are many ootions for selecttnq two here are tn-noint, The "one-field" Is eithe.r tyoe of correlations. the zonal. or meridional co"oonent of wind stress. Ca) Two ooints of east-west seoaration Two ooints, at lonItuies 160E (t69) and hOE (1=71), on latitude are 30 shown are In coherences The east-west distance of 953 Km. differences They are separated b selected. fIg. 3,7, arid an phase The coherences for zonal stress are very high for lower frequencies. There Is a distinct peak at 0.28 cod (3.6 days) which corresoonds to the time synoptic scale. The overall coherence for meridional stress is low except between 0.16 cod (6.3 days) and 0,33 frequencies cod (3 days). The low coherence at htoh could be either due to noise of any kind or to the destructive interference amnonq different wavenumber in 72 'B' 2' 6' Id to I Q. -6 -12 -18 2.0 1.8 1.6 '.4 1.2 1.0 0.6 0.4 0.2 0.0 -4.0 -3.5 -3.0 -2.5 -2.0 -1.5 -1.0 LØG FREQUENCY rig. 3.7. -0.5 0.0 0.5 1.0 ICPO) Coherence and phase soectra of stress comoonent for two points at (170E, 30N) and (160E, 30N) with a east-west seoaration of 963 (rn. The Y is the inverse hyperbolic tanrlent of the coherence. See text for detail. 73 a process sucgested The latter was broad wavenumoer bandwidth, of tllebrand by of the disturbance from analysis his in ooservational data. If there is a net prooagation of one ootnt spatial occur. Otherwise, respect to another, to phase spectrum of symmetric is with that connectes the two ooints. The indicates the stress both co'noonents ohases The asymmetry. east-west chase difference will disturbance the line the a a nearly re for -190 about to It decreases periods longer than 15 days, zero The negative ohase value 0.53 cpd (1.5 days). degrees at means a lag of the first calculation) to the second point, hence indicating a net eastward oropagation, meridional The la at for the comonent indicating the association of smaller wavelength fluctuations. value this in distinct more is point (east ooint positive to The sudden increase higher frequencies is due to the use of a single branch Ot the multivalued arctan function in a comPuter and should be recognized as continuously decreasing, Fig. 3.8 shows the results above exceot doubled. the The between distance coherency estimates apoarently components are estimates. However, it of is lower same the the process as 3oints is two for both than the interesting to stress orevious note that .74 too. 120. 60. Iii (I) I 0. a. -60. -*20. -180. Itt I It tt ,ittj t1 I U 1.8 1.4 1.2 1.0 0.0 0.5 0.4 0.2 0.0 -4.0 -3.5 -3.0 -2.5 -2.0 -1.5 -1.0 L0G FREOUENCY Eig. 3.8, -0.5 0.0 0.5 1.0 ICPO) As. In F1Q, 3,1 except for two Points at (17O, 30N) and (1SOC,30N) with an east west seoaration of 1926 Km0 75 meridional stress is i1.rnoSt uncorrelated for the although most frequencies, cod 0.16 at peak the clearly still exists, but with lower coherence. (b) Two ooints with south-north seoaration seoaratei The same analysis for two points along 160E by a south-north distance of 445 Km are shown in fig. 3.9. when The stress components act differently found also ohertomena, (wjllebrand, 1973), can states which theory, entire the almost larger coherence for This in that points two the Period (4 days). for all are except at the difference is h the turbulence correlated at the synoptic Indicatina symmetric structure with are synootic The coherences from fins, of the generally low for higher frequencies scale of 3-5 jays. phase The slightly negative between oeriods of 6 days and 30 hours, Indicating a southward propagation. see zero The ortase dIfference Is essentially frequencies, comoonent atmosphere The meridional components respect to south-north wavenunber. zonal real loogituilnal correlation tme well hand. frequency the predicted he exceeds the lateral correlation. at with The meridional comoonent now has the case. orevious the comoarel e can 3.7 an 3.9 that no matter what orientation the calculation is based on, the zonal component is more 'red' than the meridional co'noonent. always 76 -so. ZNAL CI1PNENT -120. - MERrOZONAL COMPONENT -180. 2.0 i.EJ 1.6 '.4 1.2 I.0' 0.8 0.6 0.4 ZONAL. COr P4ENT - MERIOOP4.t.. CeI8NENT 0.2 0.0 is-. i-i -4.0 i-s -3.5 us -3.0 s-Ft-i $1) I it I( Iii, Iii., 1' -0.6 -1.0 -1.5 -2.0 -2.6 LØG FREQUENCY Pig. 3,9, 0.0 0.6 1.0 ICPOJ As in Pig, 3,7 excePt for two points at (l'6O, 30N) and (16O, 34N) with a southnorth separatIon of 445 cm. 77 F'lg. 3.10 Shows the results of the same orocess with fr both (890 distance doubled co'noonents decrease frequencies of The Km). Yet the frequencies of the zonal component. synoptic oertoi sane the soacing scale for 3.7, cornoonent, disturbances the at oeaI the By e firtd that for about between 2 ooints, the coherence is much zonal larger for the lower at the zonal comPonent still exists. in 3.10 with fig. comparing fjq, and comoonent higher at esoeclally rapidly, meridional the coherences is indicating larger spatial the in its east-west direction than in its south-north direction. In an attenot to resolve the signal of longer oeriods, we again modify the original time series as we dii in the 1/8 of autospectral analysis, eccept the size is reduced to its original size by tainq te average of 8 data in a two- 365 days of the window is chosen to The maximum la day oeriod. (or r:183). rwo points at 175W and 175E on 58I, seoarated by east-west distance of S89 The spectrum of frequencies K!n, are zonal stress is shown in fjq overall coherence is high. low be The most distinct oea corresponds to the 3.11. The at the annual cycle. phase is generally small, indicatina a symmetric of low frequency disturbances. selected. The structure 7 too. 120. 60. Ia ID I 0. a. A I -60. 1' -120. 'I PP4ENT ZONAL - PIERIOIONAL COIIPONENT - too. t-, il itt-It ill ttlll St ijii.iti ii 1111111 lIt i-I-I--i- 2.0 I.e 1.6 1.4 1.2 l.a 0.0 0.6 0.4 ZØNAL C0NENT - PREO10NAL. C2PNT 0.2 0.0 P.O -3.6 -3.0 -2.6 -2.0 -1.51 -1.0 LØG FREOUENCY Fig. 3.10. -0.6 0.0 0.6 1.0 ICPO) As in Fig. 3.7 exceot for two oolnts at (1'60E, 34fl artd (160F, 42w) with a southnorth separation of 90 Kt,i, 79 teo. 20. 60. U U) I 0. -50. - 20. - lea. 2.4 2.2 2.0 I.e 1.6 1.4 1.2 l.0 o.a 0.6 0.4 0.2 0.0 -4.0 -3.5 -3.0 -2.6 -2.0 -1.6 -1.0 LØG FREQUENCY 3.11. -0.6 0.0 0.5 1.0 ICPO) Coherence and ohase spectra of zonal comoorient wind stress for two points at (175w, 5N) arid (175E, 58) with a east west seoaration of 59 Km. RO ExPRIMEM'r BR3TR3PIC QCA 4, The large Scale ocean circulation Is primarily by atmospheric the atmosphere. stress and the exchange of heat with Certain processes in the earth's hvrologlc affect that cycle wind driven the such salinity, evaporation. as Imøortant an precipitation and river runoff nay also play In recent years, numerical modeling techniques have role. study become Increasingly useful for the ocean scale numerical modeling for the ocean those from for te orinciples of the basic The circulations. atmosphere. different much not are large these of primary However, difficulties exist due to currently limited knowledge about processes, process. In spite of the coarse-grid with reproduction of 'nany features, Indicating difficulties, ocean lobal of that some models observed the turbulent subgrld-scale the e.g. oceanic experiments ocean good show do large-scale the coarse-resolution model is capable of simulating some large-scale processes. The homogeneous wind-driven oceanic circulation has been shown to be successful in describing the general characteristics of the horizontal circulation. ocean, model the most striking feature Intensification of the circulation. is In the real. the western The pattern exists in each ocean although the basin differs in shape, topography, stratification and pattern stress. wind of that tre ocean circulation is governed by a set of suggest simple the factors which vary among ocean basins. of those The homogeneous model is able to expose constraints rorthermore, when the model elementary way. most the relatively are which constraints nowerful Vet independent in might This fails to Predict some feature well, the physical cause be related to the absence of stratification or to roughly any simolification made wind-driven model Of many including the roles friction, has factors In the in t000graphy, on the The model. h,mogeneous been extensively used to study the -effect, bottom works previous can general ocean effects, nonlinear good etc. circulation, bottom review of ocean circulation Is homogeneous given bY Welander (1975), although only analytical models are included. In this chapter, the barotrooic six-layer OCCM version euatton The OSU-OGCM is at global boundary each model OSIJ a model in which the ocean is vertically divided up to six layers of unequal mass depending depth the Is tested, in which the ocean is driven by the AGCM simulated surface wind stress. primitive of ocean point. extends from on the The horizontal domain of the 74r4 to 725. The northern follows the edges of the continental shelf of the composite landmass of the Morth and South America, !urope, The southern boundary follows the edge of frica and Asia. shelf continental the combined rAustralia with longitude Han streamfunction and Antarctica are Guinea, rid size is 5 degrees Gates and the of A descriotion of the governing GCM. Drocedures, and the numerical methods solution oy is given Zealani, 4ew 4 degrees in latitude which matches the and resolution of the OSU equations, Iew The horizontal treated as islands. in Antarctica. of mass (1982a). The annual transoort and the seasonal variabilities of the strearnfunction fields mean discussed. are are also comoared against those oenerated by the same They model using observed wind stress. The circulation driven by AGCM simulated wind stress 4.1. In this experiment, the density of sea water is as constant a throughout The heat and the integration. salinity fluxes prescribed at the uooer boundary tacen originally diffusivity cm 8 2 /sec and cm2 /sec X heat in , and 1 gm/cm salt. and topography bottom The zero. from the Gates vertical and is included, Ielson direction fixed eot are was and The (1975). given is as I horizontal direction is for momentum and 2 X 1O cm2 /sec for The reference fixed as that in the density is the specific heat of water is 1 cal/qm/deq C. R3 We will refer to the experiment with time-varying AGC stress Case as In Case A the OCCM used a new set of A. AGCM simulated wind stress data every from the rest, year. system streamfunction pattern is Starting hours. integrated for one simulated was mean annual The wind of shown in transport mass total jq. 4.2 fig. 4.1. shows the streamfunction of simulated mass transport of the exoeriment the observed annual mean wind stress hich in was used as the constant forcing (Han and 'ates, 192). will refer to We the latter exoeriment as Case B hereafter. The integration in Case B was carried out for 90 lays to obtain a steady state. The streamfunction fields shown in figs. 4.1 are similar quite term in Both many of the show the present model is relatively small compared to the lateral friction due to the diffusivity. 4.2 The nonlinear effect of the momentum familiar ocean gyres. advection general. In and Hence, the use laroc of mean circulation driven b varying forcing field should be very close to that the driven by constant mean forcing field. In clearly Northern the in both seen are different. 20 N which is Hemisphere, clockwise are ase A and Case 3, but the oositions The maximum transport is 10 qyres degrees found to be South to that of Case B. on The 9.14 SIN 4j-*l rj\ 5.14 (__ 3114 .3.14 Li 31$ JJ I ,II J I I -91$ - C.. 3U rig, 4.1. ICE E lasE I I I ISlE IC. 15511 iasis U I uu aIM I Arnu3l mean streamtunction of the mass transport ot the oceanic circulation driven by the AGCM simulated surface Contour interval is 4 Sv. The zero lines wind stress. are dashed and the nejative values are stippled. 3CC 90N 70N 50N (4 30N ION LJ!U1 'Os L I 30S 50S 70S 9051 30W I 0 Fig. 4.2. 30E 60E 90E120E 150E 180 150WI20W 90W 60W 30W 0 30E streamfunction of the mass tranport at day 90 of the oceanic circulation driven by observed surface wind stress. Also see Fig, 4.1. 'I' maximum only to the latitudes of boundary western the all the SUbtrOptca]. gyres intensify with associated currents that oredicts thenry linear curl, stress wind and subsequently return to the interior asbroad and relatively slow currents. positioning error figs 2.11. The circulation Is about transoort 30 Sv (1 Sv agreement reasonable tø12 cm3 /sec) in the with the oWever, 80th Cases, Case B. geostrophic observed could discrepancy thermohaline be transport due circulation to and Gates. 1982). underestimate tne the Gulf stream. The qreatl.y of the lack Sv, which internal of By viscous coarse-arid enhanced Is is comparable with the transoort of the observed florida Current (29 Sv), but still lower than the transport of 75 Sv in the vicinity of Cape Hateras. Pacific ocean, the circulation is 3 model the thermohaline including forcing (Han ani Gates, 1982b), the transoort 27 Ocean Atlantic and/or a nonlinear recirculatlon which cannot be simulated bV a to geostrophic observed the still but stream) is 12 Sv, which is smaller than the 15 Sv In (Gulf (Han clockwise the of The transoort in transport of 40 Sv. deiree 10 This Is smaller than In Case 8, Pacific ocean. in maximum the zonal mean curls as shown in the from exoect could we i1ence, north-south extent of the In the clockwise degrees comoarerl to 40 degrees in Case B. This is the result of te existence of a broad and strong counterclockwise subarctic qyre to the north. The transport reach could circulation in Case transport the while Sv 18 nd rather weaK. gyre in the Iorth Atlantic Ocean Is broad In is agreement with that of Case B, remarkable Antarctica present case. transport. of Differences are found only in the maqnituie The circulation observed In the Southern Hemisphere, the pattern The subarctic in less than 4 Sv, S same tre of Current is much weaker In the Circumpolar Drake the The total mass transoort throucib The Passage is less than 4 Sv comoarel to in Sv In Case B. difference results directly from the smaller curl value the AGCM simulated wind stress (fig. 2.12). It is hard to lack judge tne accuracy of the oresent estimate due to the of direct measurement magnitudes in numerical transport both studies. is mainly are much Han and cates barocljrticity and topography. hlch excludes the smaller cases affected baroclinic However, the transport. this of by other than found (1982b) effect joint the of the of In the barotropic experiment the effect, transoort is largely controlled by the value of eddy ditfusivity because the wind stress torque is mainly balanced friction a in the Antarctica region. bV the lateral The oresent model uses therefore greatly The clockwise subtropical gyres in the South Atlantic relatively large diffusivity and suppresses the transport, 98 and Pacific Oceans aree well with those In Case 8. South Both cases fail to simulate which return bouniarv flow of toe South Doleward the is Pacific Subtropical current oasses Australia Ocean Indian into flows and model the Instead, circulation. Australia. through a narrow channel between Irdo-Ch1na and The current, Australia East the total mass transoort through the channel is about latter Sv agrees In Case A cornoarel to 10 Sv In Case B. The with the observational estimate made b Godfrey and Goldlng (1981). In the South Indian Ocean transport Sv, less is circulation not correctly than maximum 28 Sv corresoonding the of The associated Aquihas current is in Case B. simulated. branching without the , the counterclockwise circulation is about 20 of which Case for It returns around the southern tl interior the to of Africa as is found in Case B and the observation. The tropical controlled, circulatIon therefore, it is inertially largely is poorly simulated due to the lack of inertial effect in the model. The only tiiscernable found in the eastern part of the tropical circulation Pacific. The maximu!n transoort is 9 Sv in Case about Sv 6 in Case is B. Both observational estimate of 40 Sv. are much A and is less than the 89 Seasonal Variation of the Simulated Dcean Trnsoort 4.2. seen s can be last the in cnaoter, ny cycle neriod atmospheric forcing on the ocean can be of However, most of the variance between hours and years. the forcing to atmospheric the can be with disturbances less is than one oerlod year, the the inertial traooed the simulated ocean barotropic model would be temporal (18 quite oeriod response can of penetrate to the ocean floor and is independent Hence, oeriods traoped near the ocean surface. strongly when the forcing period is away from and ocean Willebrand (1980) found the longer than one year, or close to the inertial hours), of field (wind stress) is explained in the ranze ot one day to 300 days. response imposed th depth. by the present significant due to response the characteristics of the AGCM sinulated wind stress field. Figs. 4.3a-d display the monthly mean stream functions of January, seasons. Aoril, July and representing four October In the Northern Hemisphere, the cyclonic yre in 5 degrees to the south of its winter position in the summer. This results from the south the shift Pacific in the shifts about curl field. The mean mass transport bV the associated Kuroshio current Is other months. However, larger in Ppril than in a more careful check of selected 7 sGl 30N 3$t4 10$ 1 GS 1$5 3*5 3.5 '$5 '.5 705 7.5 I I I 3$IJ 0 3$E Fig. 4.3a. 60 N( 1*SE I hOC I 15$ I ISSId I I IUIJ '.I '.44 3 I S 30E Monthly mean strearnfunction of the simulated transPort for The zero lines are Contour interval is 5 Sv. January. dashed and the negative values are stippled, 0 0 E-fl ::: N J rH r-')L.......... t'--., 'R <_ 105JS H H r1 L1.0 30$ pZ' c/,-' SOS I 705 -1 . (> : 1 I . gas la.s 1 30U S 3G SOC OQE Fig. 4.3b, ISOC IU ISOIJ iasw OSU OGU 3GW S AS in Fig,, 4.3a exceot for April, '0 7014 SM 3M ::: r 1014 Hi' las iss 30$ 305 30W 0 30E 60E 90& lilE 4.3c. 15$E As ir ISO 1SIU SOW 30W 0 30 F'Iq. 4.3a except for July, 0 90N get,' Ll:...:%FIJ - ?SH 70N 1 7 * (v'.. 3s$ GN -1 I 4c J1e5 I - I, -- I I 3gU a 30E GIE t'ig. I eE 4.,3d. JrL_1 ?SS t-. .s I iae ISSE IN IS$W ia.0 9W 61U As in Fig. 4,3a exceDt for October, 30M $ f 6' daily fields reveals a maximal transoort minimum and E'ebruary v rhe inrU3l ctoher. of 2() Sv in 1te i.n co!noarel to 24 Sv in Case variability is 40 Sv in Case B in which maximum and ,inimurn transoortoccir in January and Seotember, rasoe:tively. from winter to summer. The northward maSS transport by the and A minimum aqrees well in ohase with that of variability annual July. in value of 8 Sv is found in late Seote'noer but not The late in low in early July. relatively is Sv 30 of ulf Stream Current reaches a maximum January southward moves also yre The 4tlantic subtropical Case 8, but not in rranitude. seasonal variation The most interesttr the Ocean. Indian North in strenqth of the the Althouzth found is summer monsoon is not adequately simulated by the AGCM, the ocean's response observed. January reverses also maximum The with the a value annual circulation reverses qradually counterclockwise in current weak the clockwise The pronounced. winter to its summer. Its oattern rhe the In become associated Somali season with transoort occurs of 8 Sv (1.7 Sv In Case maximum northward transoort is about 24 Sv in aqrees well with that in Case 8. Is to direction direction southward variation ) July, as in and the which 95 the The subarctic circulation does not chanqe much in while it varies significantly with tine In Ocean Atlantic The naxImu the Pacific Ocean. wIth January In The agn1tude of about 20 Sv. averaged an occurs transport nass utnimum is found in su!nuer Tonths 1ith a iean value of less than 8 Sv. noves circulation counterclockwise subtropical the Heiisphere, Southern the In toward the eluator as January. the seasons change fron July (southern winter) to The annual variation tne of sinulatel transoort of the larer Brazil current is 12 Sv, which is simulated in Case B. than the 4 v The maxinu!n of 24 Sv occurs in August and the minimum is in January. In the Pacific Ocean, the transoort of the return flow just east of does Zealand 'Jew not change much in the monthly mean fields, however, very raojd fluctuation can be seen from response of the selected daily fields, indicating the rapid the model to and January intensifies progresses to July. weak A variation is fairly shifts westward as the season rhls is also observed in Case B. simulated transoort of the current field. forcing gyre occupying the western equatorial Pacific in clockwise little the the in magnitude. weak in Indian Ocean gyre The shows The Antactica circumpolar January. It gradually 96 intensifies until July, and then we&els very rapidly. along streamfunction the Westward increases the of order barotrooic found cm/sec. experiment similar velocity anolitule in (rouos of Willebrand part of amolitude with the wind stress of wave (1980), varying with characteristics In moving trains who did a wind stress forcing, the zonal simulated field but with a smaller ohase soeed (3-5 rn/sec). Therefore, the waves with westward eastward The rn/sec. also be identified with a oroup speed of the can 70-80 indicates This Increase is almost synchronous fluctuation (fig. 2.17). eastward 9-10 order increase seasonal isolines the of late October to late February as discussed from in this section. the tIlt orooagation virtually everywhere, with the ohase phase soeeds 34N CJ32) for t.o 60-lay oeriods of The simulation. the of Figs. 4.4a,b show the time-longitude sections rouo the velocity response fluctuating winds. are of a ohase propagation and liIely to constitute a main barotrooic model to the -. .-.. ......-. ... : _________J eae -III Fj, 4,4a. -1b Time-longitude plot of the strearutunction 1on 34N (J32) Contour interval is for day 180-240 of the simulation. 10 Sv. The zero lines are dashed and the neat1ve values The abscissa Is tre lonqitude (deqree) are stipoled. and the ordinate Is tne time (day). \ 7i Fig. 4,4b. -iii i _____ -iS. -141 -131 The heavy dashei As ir Fig. 4,4a except tor 1ay 300-360. lines correspond to an eastward group velocity of 75cm/sec. SUMMARY 5. OSU Surface wind stress, as simulated by the AGCM has been analyzed. 2-level The nalor findings are summarized as follows: Cl) the shifts 3-year mean vector fields reveal oosttlon qvres main the northern oceans comPared with the in observations. The cyclonic gyre In the approximately 15 deqrees Ocean is too far south compared with the about are to 20 degrees south of the 10 southern The distribution over the observed. Ocean Pacific The cyclonic and anticyclonic gyres over oberved oosltlon. Atlantic of oceans is, we1. simulated. (2) Magnitudes (3) bears generally fields, I.e. Hemisohere and stress are esoecially distinct emisphere. vertical The wind mean The difference is co!noonents fields. in the Southern 3-year than the obervations as revealed in the smaller generally the of component of the wind stress cur]. characteristics as the stress oositioning differences In the Morthern magnitude differences In the Southern the same Hemisphere. (4) The root mean square wind stress field shows that the maximum time variability occurs In the northern oceans near the northern boundary and western part of the oceans. (5) Seasonal variablity is strongly dependent on 100 Annual latitude. Semi-annual variation is found only at the latitudes high In The most distinct annual cycle 1emisohere. southern latitudes. most dominates variation simulated over Indian ocean monsoon area Is missing in the field. similar Autosoectral analysis of wind stress shows a (6) shaDe Soectral to the of that a frequency corresoondinq tO the synoptic time at frequency 4o slqntflcant oeak Is found at any scale. droos It sPectrum is oenerally white at low frequencies. sharoly The stress. observed for However, a distinct diurnal cycle extratropical latitudes. is found In the tropical area. The annual oea)c Is resolvable (2) than stress magnitude reveals The wIndow, spectral the The fluctuations are stronger field. comoonents, stress winter In which of the stress characteristics nonstationary the narrower a Is much more dominant in the peak In using ôy than in summer. (8) Cross-spectral disturbances oropaqating the variability Disturbances symmetric. as to shows analysis is the eastward the that synoptic time scale dominate of found In meridional the real direction 1.ow frequency disturbances are also atmosphere. are rather symmetric and have no preferred oropaaatiort directions. An exoeriment using a homoaeneouS ocean which Is 101 driven AGCM simulated wind stress has been carried Out bY version using a barotrooic of cCCM. six-layer OSIJ We found: (1) The oositions of the major circulations controlled bY the wind stress cur). field. are largely Thus, the annual. mean circulations in the Northern Hemisohere driven by AGCM wind stress reveal a southward shut comoared to simulated The that driven bY observed wind stress. the Southern aaree Hemisphere well. circulations in with that driven by observed wind stress. (2) The annual vari3bilities of most oceans the transoort mass in for the oresent study are larger than that of This is probably due to the the observed wind stress case. stronger seasonal variability of the simulated wind field. (3) the ohase Planetary waves with westward speed 9-10 of 70'80 cm/sec are rn/sec likely Drooagation at and eastward group velocity of the be to major part of the response of the barotrooic model to the fluctuating winds. The overall performance of the simulated is satisfactory. positioning error of the the However, main gyre in the northern oceans must be improved of its further important diagnostic variabilities effects study on of stress wind the the ocean soatla]. in transport and view A temporal of the wind stress curl. is needed due to its imoortance in modifying the ocean resoonse Reetmaa, 1978). 102 A cross-sectra1. arlvs1s beteer the ocean resoorse the atnosoher1c forc1r, e.q. lnd stress curl, should the the strearn'function also e done in order quantitatively unierstnd the resoonse of the model to forcing. rd to the t03 BIBtI3CRAPHY A nwnerical investiation of a nonlinear Bryan, K., 1963: J. Atmos. Set., 20, wind-driven ocean, model of a 594-606. 3unker, A. F., 1976: Comoutatlons of surface energy flux and annual air-sea Interaction cycles of the r4orth Mon. sea. Rev,, 104, 1122-1140. Atlantic Ocean. Deacon, . 1. and E. K, webb, 1962: Small scale interaction. 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