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On the geographic variability of oceanic mesoscale motions 1986

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ON THE GEOGRAPHIC VARIABILITY OF OCEANIC MESOSCALE MOTIONS by KEITH ALEC THOMSON B.Sc.,.Royal Roads M i l i t a r y College, 1977 • A THESIS SUBMITTED IN PARTIAL FULFILMENT OF . THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY i n THE FACULTY OF GRADUATE STUDIES . Oceanography Department We accept t h i s t h e s i s as conforming to the required standard THE UNIVERSITY OF BRITISH COLUMBIA June 1986 ©Keith Alec Thomson, 1986 In presenting t h i s thesis i n p a r t i a l f u l f i l m e n t of the requirements f o r an advanced degree at the University of B r i t i s h Columbia, I agree that the Library s h a l l make i t f r e e l y available for reference and study. I further agree that permission for extensive copying of t h i s t h e s i s for scholarly purposes may be granted by the Head of my Department or by h i s or her representatives. I t i s understood that copying or p u b l i c a t i o n of t h i s thesis for f i n a n c i a l gain s h a l l not be allowed without my written permission. Department of Oceanography The University of B r i t i s h Columbia 6270 University Boulevard Vancouver, B.C. Canada V6T 1W5 Date: June 26, 1986 i i ABSTRACT Quasi-synoptic expendable bathythermograph data were acquired, from the Canadian Armed Forces, the United States Navy and the United States National Oceanographic Data Center, f o r the P a c i f i c and A t l a n t i c Oceans. On the basis of these data and the r e s u l t s of previous studies using c l i m a t o l o g i c a l data, s i x geographic regions were defined: the high-energy regions of the Northwest A t l a n t i c and Northwest P a c i f i c , and the low-energy regions of the Northeast A t l a n t i c , Northeast P a c i f i c , South A t l a n t i c and South P a c i f i c . S p a t i a l s e r i e s of two varia b l e s , representative of the upper layer (400 m) mesoscale v a r i a b i l i t y , were obtained for each section - the mid- thermocline temperature and the geopotential anomaly (0 - 4000 kPa). The central moments and the wavenumber spectra of each variable were estimated for the s i x geographic regions, the combined high-energy areas and the combined low-energy areas. In the high-energy regions and the Northeast A t l a n t i c , i t was found that the temperature between 350 and 400 m i s representative of the temperature v a r i a b i l i t y due to the b a r o c l i n i c eddy f i e l d , whereas, the temperature between 150 and 200 m i s more representative of the eddy v a r i a b i l i t y i n most of the low-energy regions. The standard deviations of temperature, i n the high- and low-energy regions, are 1.40 and 0.54°C, respectively. The standard deviations of the geopotential anomaly are 0.67 and 0.26 m^/s^, re s p e c t i v e l y . The high-energy regions have dominant s p e c t r a l wavelengths i n the geopotential anomaly f i e l d s of 300 and 155 km, with corresponding b a r o c l i n i c surface v e l o c i t y scales of 9.6 and 17.5 cm/s. The low-energy regions have dominant wavelengths of 300 and 170 km with v e l o c i t y scales of 4.5 and 5.5 cm/s, respectively. In general, the high-energy regions have a greater portion of t h e i r s pectral variance concentrated i n the higher wavenumbers ( i . e . 280 to 100 km wavelengths), than the low-energy regions. The eddy k i n e t i c energies per unit mass for the high- and low-energy regions were estimated at 250 and 36 cm^/s^, respectively. The geographic v a r i a b i l i t y of the governing dynamics was i n f e r r e d by evaluating the quasigeostrophic s c a l i n g parameters ( i . e . the Rossby number (Ro), the Burger number (B) and the s p h e r i c i t y parameter (3*)) and the Rossby wave steepness parameter (M). Also, the properties of free l i n e a r dispersive Rossby waves were c a l c u l a t e d with the observed wavelengths and the s p e c t r a l power-laws of the temperature spectra were compared with several models of i i i nonlinear geophysical turbulence. I t was found that Ro<<1, B = 0(1) and 3*<<1, which i s consistent with the s c a l i n g f o r quasigeostrophy. The dynamics i n f e r r e d from these analyses exhibit a d i s t i n c t geographic v a r i a b i l i t y . Motions with wavelengths greater than 200 km i n a l l regions are consistent with linear/nonlinear Rossby wave theory. Mesoscale perturbations i n the high-energy regions are, of course, more nonlinear than the corresponding length scales i n the low-energy regions. Motions, with wavelengths les s than 200 km i n the high-energy regions, are consistent with quasigeostrophic turbulence theory, more s p e c i f i c a l l y , with Charney's (1971) model of three-dimensional quasigeostrophic turbulence. Motions with wavelengths less than 200 km i n the low-energy regions have dynamics that are intermediate between linear/nonlinear Rossby wave theory, and quasigeostrophic turbulence theory. i v TABLE OF CONTENTS Page A b s t r a c t i i T a b l e o f C o n t e n t s i v L i s t o f Symbols v L i s t o f A b b r e v i a t i o n s v i L i s t o f T a b l e s v i i i L i s t o f F i g u r e s x i Acknowledgements x i v Ch a p t e r I - I n t r o d u c t i o n 1 C h a p t e r I I - Data S e t 5 A. Data C o l l e c t i o n 5 B. Data P r o c e s s i n g 11 Ch a p t e r I I I - D e s c r i p t i v e A n a l y s e s 22 A. G e o g r a p h i c R e g i o n s 22 B. G e o g r a p h i c V a r i a b i l i t y o f t h e Thermal S t r u c t u r e 24 C h a p t e r IV - S t a t i s t i c a l A n a l y s e s 58 A. S p a t i a l S e r i e s 59 B. C e n t r a l Moments 60 C. S e a s o n a l V a r i a b i l i t y 74 D. H o r i z o n t a l A n i s o t r o p y 77 E. Wavenumber S p e c t r a 79 Ch a p t e r V - D y n a m i c a l I n f e r e n c e s 100 A. Q u a s i g e o s t r o p h i c S c a l i n g P arameters 100 B. L i n e a r Rossby Waves 108 C. N o n l i n e a r G e o p h y s i c a l T u r b u l e n c e 113 D. Summary o f t h e I n f e r r e d Dynamics 118 Ch a p t e r V I - C o n c l u s i o n s 121 R e f e r e n c e s 126 LIST OF SYMBOLS a n i s o t r o p y f a c t o r B u r g e r number group v e l o c i t y phase v e l o c i t y g e o p o t e n t i a l anomaly p e r t u r b a t i o n , 0 - 4000 kPa wavenumber s p e c t r u m C o r i o l i s p a r a m eter a t a g i v e n l a t i t u d e g r a v i t a t i o n a l a c c e l e r a t i o n z o n a l wavenumber, p o s i t i v e t o t h e e a s t h o r i z o n t a l wavenumber, = k ^ + l 2 k u r t o s i s m e r i d i o n a l wavenumber, p o s i t i v e t o t h e n o r t h l e n g t h s c a l e , A = 2TTL Rossby wave s t e e p n e s s p a r a m e t e r o b t a i n e d w i t h U Rossby wave s t e e p n e s s p a r a m e t e r o b t a i n e d w i t h U* B r u n t - V a i s a l a f r e q u e n c y number o f o b s e r v a t i o n s number o f i n d e p e n d e n t o b s e r v a t i o n s s p e c t r a l power-law exponent i n t e r m i t t e n c y f a c t o r r a d i u s o f t h e e a r t h , R = 6371 km Rossby number i n t e r n a l Rossby d e f o r m a t i o n r a d i u s s t a n d a r d d e v i a t i o n m i d - t h e r m o c l i n e t e m p e r a t u r e p e r t u r b a t i o n , v e r t i c a l l y - a v e r a g e d f r o m 150 t o 200 m o r from 350 t o 400 m b a r o c l i n i c (0-400m) v e l o c i t y s c a l e upper bound o f t h e t r u e v e l o c i t y s c a l e skewness m e r i d i o n a l g r a d i e n t o f t h e C o r i o l i s p arameter a t a g i v e n l a t i t u d e s p h e r i c i t y p a r a m e t e r l a t i t u d e w a v e l e n g t h , A = 2 nL v i LIST OP ABBREVIATIONS Geographic Regions NWA N o r t h w e s t A t l a n t i c , a h i g h - e n e r g y r e g i o n NWP N o r t h w e s t P a c i f i c , a h i g h - e n e r g y r e g i o n NEA N o r t h e a s t A t l a n t i c , a low-energy r e g i o n SA S o u t h A t l a n t i c , a low-energy r e g i o n NEP N o r t h e a s t P a c i f i c , a low-renergy r e g i o n SP S o u t h P a c i f i c , a low-energy r e g i o n HIGH c o m p o s i t e h i g h - e n e r g y r e g i o n c o n s i s t i n g o f t h e NWA and NWP r e g i o n s LOW c o m p o s i t e low-energy r e g i o n c o n s i s t i n g o f t h e NEA, SA, NEP and SP r e g i o n s NPSF N o r t h P a c i f i c S u b t r o p i c a l F r o n t , a s u b r e g i o n o f t h e NEP i n t h e v i c i n i t y o f t h e s u b t r o p i c a l f r o n t NPEC N o r t h P a c i f i c E q u a t o r i a l C u r r e n t , a s u b r e g i o n o f t h e NEP i n t h e v i c i n i t y o f t h e e q u a t o r i a l c u r r e n t Data Sources and Instruments CAF C a n a d i a n Armed F o r c e s USN U n i t e d S t a t e s Navy N0DC N a t i o n a l O c e a n o g r a p h i c Data C e n t e r ( U n i t e d S t a t e s ) XBT e x p e n d a b l e bathythermograph SXBT s h i p - l a u n c h e d expendable b a t h y t h e r m o g r a p h AXBT a i r - l a u n c h e d expendable b a t h y t h e r m o g r a p h Oceanographic Parameters T-S t e m p e r a t u r e - s a l i n i t y S-Z s a l i n i t y - d e p t h v i i T-Z t e m p e r a t u r e - d e p t h SSS sea s u r f a c e s a l i n i t y EKE eddy k i n e t i c energy EPE eddy p o t e n t i a l energy Quasigeostrophic Dynamics LRW l i n e a r Rossby wave NRW n o n l i n e a r Rossby wave QGT q u a s i g e o s t r o p h i c t u r b u l e n c e Miscellaneous UBC U n i v e r s i t y o f B r i t i s h C o l umbia RRMC R o y a l Roads M i l i t a r y C o l l e g e RMS root-mean-square ACF a u t o c o r r e l a t i o n f u n c t i o n v i i i LIST OF TABLES T a b l e I I - 1 RMS d i f f e r e n c e s between b u c k e t SSS and i n f e r r e d SSS f o r t h e CAF t r a n s - o c e a n i c s e c t i o n s . T a b l e IV-1 D e c o r r e l a t i o n s c a l e s o b t a i n e d f r o m t h e f i r s t - z e r o c r o s s i n g s o f t h e a v e r a g e d a u t o c o r r e l a t i o n f u n c t i o n s f o r t h e s e c t i o n s i n each g e o g r a p h i c r e g i o n . T a b l e I V - 2 Sample s t a n d a r d d e v i a t i o n , skewness, k u r t o s i s and i n t e r m i t t e n c y o f T f o r t h e g e o g r a p h i c r e g i o n s f r o m t h e s e c t i o n s . T a b l e IV-3 Sample s t a n d a r d d e v i a t i o n , skewness, k u r t o s i s and i n t e r m i t t e n c y o f D f o r t h e g e o g r a p h i c r e g i o n s f r o m t h e s e c t i o n s . T a b l e IV - 4 Sample s t a n d a r d d e v i a t i o n , skewness, k u r t o s i s and i n t e r m i t t e n c y o f T f o r t h e g e o g r a p h i c r e g i o n s , t h e NPSF and t h e NPEC fr o m t h e s u r v e y s . T a b l e IV-5 Sample s t a n d a r d d e v i a t i o n , skewness, k u r t o s i s and i n t e r m i t t e n c y o f D f o r t h e g e o g r a p h i c r e g i o n s , t h e NPSF and t h e NPEC fr o m t h e s u r v e y s . T a b l e IV-6 Summary o f t h e number o f s e c t i o n s by g e o g r a p h i c r e g i o n and q u a r t e r o f t h e y e a r . T a b l e IV-7 Summary o f t h e s t a t i s t i c s o f T and D f o r t h e NEP i n each q u a r t e r o f t h e y e a r . T a b l e IV-8 I s o t r o p i c d e c o r r e l a t i o n s c a l e s o b t a i n e d f r o m t h e f i r s t - z e r o c r o s s i n g s o f t h e r e g i o n a l l y - a v e r a g e d a u t o c o r r e l a t i o n f u n c t i o n s o f t h e s u r v e y s . T a b l e IV-9 The a n i s o t r o p y f a c t o r , A g = L M / L Z , i s t h e r a t i o o f t h e m e r i d i o n a l d e c o r r e l a t i o n l e n g t h s c a l e ( L ^ ) from t h e a v e r a g e d m e r i d i o n a l a u t o c o r r e l a t i o n f u n c t i o n o f t h e s u r v e y s , t o t h e z o n a l d e c o r r e l a t i o n l e n g t h s c a l e (1*2) f r o m t h e a v e r a g e d z o n a l a u t o c o r r e l a t i o n f u n c t i o n . Page 81 T a b l e IV-10 V a r i a n c e o f T and D w i t h 95% c o n f i d e n c e l i m i t s o b t a i n e d by i n t e g r a t i n g t h e s p e c t r a between w a v e l e n g t h s o f 1000 and 100 km. 86 T a b l e IV-11 Peak w a v e l e n g t h s o f t h e T s p e c t r a . 89 T a b l e IV-12 Peak w a v e l e n g t h s o f t h e D s p e c t r a . 92 T a b l e IV-13 Tw o - d i m e n s i o n a l i s o t r o p i c eddy k i n e t i c e nergy e s t i m a t e s o f t h e g e o g r a p h i c r e g i o n s . 95 T a b l e IV-14 C o n t r i b u t i o n o f each b a n d w i d t h o f t h e D s p e c t r a t o t h e t w o - d i m e n s i o n a l i s o t r o p i c eddy k i n e t i c e n e r g y . 97 T a b l e IV-15 L e n g t h and v e l o c i t y s c a l e s o f t h e b a r o c l i n i c m e s o s c a l e eddy v a r i a b i l i t y . 99 T a b l e V-1 Summary o f t h e Rossby number ( R o ) , t h e B u r g e r number (B) and t h e s p h e r i c i t y p a r a m e t e r ( g * ) f o r t h e g e o g r a p h i c r e g i o n s . 104 T a b l e V-2 Summary o f t h e Rossby wave s t e e p n e s s parameter and t h e i n f e r r e d dynamics f r o m i t s v a l u e . 105 T a b l e V-3 F r e q u e n c i e s ( w , 1 / s ) , p e r i o d s (T, y r ) , phase v e l o c i t i e s (Cp, m/s), and group v e l o c i t i e s ( C g , m/s) o f t h e f r e e b a r o c l i n i c Rossby waves o f t h e o b s e r v e d q u a s i - s y n o p t i c l e n g t h s c a l e s i n t h e NEP. 111 T a b l e V-4 Summary o f t h e p r o p e r t i e s o f t h e l i n e a r f i r s t - m o d e b a r o c l i n i c Rossby waves w i t h t h e o b s e r v e d w a v e l e n g t h s . 112 X Page T a b l e V-5 Summary of t h e s p e c t r a l power-law exponents o f t h e m i d - t h e r m o c l i n e t e m p e r a t u r e . 117 T a b l e V-6 Summary o f t h e i n f e r r e d dynamics. 119 x i LIST OF FIGURES F i g u r e I I - 1 L o c a t i o n s o f t h e XBT d a t a used i n t h i s i n v e s t i g a t i o n . F i g u r e I I - 2 Anr example o f t h e XBT s p a t i a l s e r i e s p r o d u c e d f o r each c r u i s e t o check f o r d i g i t i z a t i o n e r r o r s . F i g u r e I I - 3 Map o f t h e P a c i f i c and A t l a n t i c Oceans showing t h e T-S and S-Z c u r v e s used t o i n f e r s a l i n i t y . F i g u r e I I - 4 P l o t s o f t h e i n f e r r e d SSS and t h e b u c k e t SSS f o r each o f t h e CAF s i n g l e - s h i p s e c t i o n s . F i g u r e I I I - 1 G l o b a l mesoscale v a r i a b i l i t y f r o m c o l l i n e a r SEASAT a l t i m e t e r ground t r a c k s . F i g u r e I I I - 2 The s i x g e o g r a p h i c r e g i o n s as d e f i n e d f o r t h i s i n v e s t i g a t i o n a r e shown w i t h t h e XBT d a t a s e t . F i g u r e I I I - 3 Eddy k i n e t i c energy ( c m 2 / s 2 ) o b t a i n e d f r o m t h e N0DC h i s t o r i c a l s h i p d r i f t f i l e . F i g u r e -1.11-4 S t a n d a r d d e v i a t i o n o f t e m p e r a t u r e a t 260 m base d on a v a r i a b l e g r i d a n a l y s i s o f t h e NODC XBT f i l e n o r t h o f 10°S. F i g u r e I I I - 5 S u r f a c e c u r r e n t s o f t h e A t l a n t i c and P a c i f i c Oceans. F i g u r e I I I - 6 SXBT s e c t i o n (PE-071082) c o l l e c t e d by t h e HMCS P r e s e r v e r , i n O c t o b e r 1982 a c r o s s t h e N o r t h A t l a n t i c . F i g u r e I I I - 7 Temperature (°C) s e c t i o n (72-001276) o b t a i n e d f r o m t h e USN m u l t i s h i p s u r v e y a t 33°N i n t h e NWA. F i g u r e I I I - 8 Maps o f te m p e r a t u r e (°C) v e r t i c a l l y - a v e r a g e d f r o m 150 t o 200 m i n t h e NWA, f r o m m u l t i s h i p s u r v e y s c o l l e c t e d by t h e CAF. x i i F i g u r e I I I - 9 Temperature (°C) s e c t i o n s f r o m t h e USN m u l t i s h i p s u r v e y s i n t h e NWP. P a 9 e 36 F i g u r e 111-10 Temperature (°C) s e c t i o n (SY-051081) c o l l e c t e d by t h e HMCS Saguenay (CAF) a c r o s s t h e N o r t h A t l a n t i c i n October 1981. 38 F i g u r e III-.11 Map of v e r t i c a l l y - a v e r a g e d t e m p e r a t u r e (°C) fro m 150 t o 200 m i n t h e NEA o b t a i n e d by t h e CAF, O c t o b e r 1982 (ME-041082). F i g u r e 111-12 Temperature (°C) s e c t i o n s f r o m t h e NODC i n t h e SA. F i g u r e 111-13 Temperature (°C) s e c t i o n (QE-251182) c o l l e c t e d by t h e HMCS Q u ' A p p e l l e (CAF) i n t h e NEP, fro m H a w a i i t o Vancouver I s l a n d i n November 1982. 38 40 42 F i g u r e 111-14 Temperature (°C) s e c t i o n c o l l e c t e d by t h e HMCS Qu ' A p p e l l e (CAF) fr o m Samoa t o H a w a i i i n t h e c e n t r a l e q u a t o r i a l P a c i f i c , November 1982. 42 F i g u r e I I I - 1 5 CAF m u l t i s h i p s u r v e y s o f v e r t i c a l l y - a v e r a g e d t e m p e r a t u r e (°C) fro m 150 t o 200 m t a k e n i n t h e v i c i n i t y o f t h e N o r t h P a c i f i c S u b t r o p i c a l F r o n t between F e b r u a r y 1980 and May 1982. 44 F i g u r e 111-16 D e t a i l e d t e m p e r a t u r e (°C) s e c t i o n s o f t h e a n t i c y c l o n i c eddy f o u n d i n t h e March 1980 CAF m u l t i s h i p s u r v e y (GU-270380) i n t h e NEP. 46 F i g u r e I I I - 1 7 USN AXBT s u r v e y s o f v e r t i c a l l y - a v e r a g e d t e m p e r a t u r e (°C) f r o m 150 t o 200 m t a k e n i n t h e v i c i n i t y o f t h e N o r t h P a c i f i c S u b t r o p i c a l F r o n t between December 1979 and F e b r u a r y 1980. 47 F i g u r e I I I - 1 8 USN AXBT s u r v e y s o f v e r t i c a l l y - a v e r a g e d t e m p e r a t u r e (°C) f r o m 150 t o 200 m t a k e n i n t h e N o r t h P a c i f i c E q u a t o r i a l C u r r e n t s o u t h o f H a w a i i , between J a n u a r y 1981 and A p r i l 1981. 50 x i i i F i g u r e 111-19 CAF SXBT s u r v e y (QE-141182) o f v e r t i c a l l y - a v e r a g e d t e m p e r a t u r e (°C) from 100 t o 150 m t a k e n a c r o s s t h e N o r t h P a c i f i c E q u a t o r i a l C o u n t e r c u r r e n t , November 1982. Page 53 F i g u r e 111-20 USN AXBT s u r v e y (AA-16081) o f v e r t i c a l l y - a v e r a g e d t e m p e r a t u r e (°C) f r o m 150 t o 200 m t a k e n n o r t h o f H a w a i i , 16 J a n u a r y 1981. 54 F i g u r e 111-21 CAF SXBT s u r v e y f r o m New Z e a l a n d t o Samoa, November 1982. . 55 F i g u r e 111-22 Temperature (°C) s e c t i o n (24-230483) o b t a i n e d f r o m t h e NODC i n t h e e a s t e r n SP. 57 F i g u r e IV-1 Examples o f t h e s p a t i a l s e r i e s o f T and D f o r t r a n s - o c e a n i c s e c t i o n s i n t h e NWP and NEP. 61 F i g u r e IV-2 Sample p l o t s o f t h e a v e r a g e d i s o t r o p i c , m e r i d i o n a l and z o n a l a u t o c o r r e l a t i o n f u n c t i o n s f o r t h e NWP and NEP. 78 F i g u r e IV-3 Examples of t h e n o r m a l i z e d v a r i a n c e - c o n s e r v i n g s p e c t r a . 84 F i g u r e IV-4 Examples o f t h e v a r i a n c e - c o n s e r v i n g s p e c t r a w i t h c o n f i d e n c e l i m i t s . 85 F i g u r e IV-5 N o r m a l i z e d v a r i a n c e - c o n s e r v i n g s p e c t r a o f T. 88 F i g u r e IV-6 N o r m a l i z e d v a r i a n c e - c o n s e r v i n g s p e c t r a o f D. 91 F i g u r e V-1 The dominant l e n g t h (L) and v e l o c i t y (U) s c a l e s p l o t t e d i n r e l a t i o n t o t h e i s o p l e t h s o f t h e Rossby wave s t e e p n e s s p a r a m e t e r (M). 107 F i g u r e V-2 Sample p l o t s o f t h e l o g - l o g s p e c t r a l r e p r e s e n t a t i o n s . 116 x i v ACKNOWLEDGEMENTS F i n a n c i a l support was received from a number of sources and i s g r a t e f u l l y acknowledged. These include: a research a s s i s t a n t s h i p (1981-85) from a contract with the Defence Research Establishment-Pacific held by W.J. Emery (UBC) and D.P. Krauel (RRMC), several teaching assistantships (1981-85) from the Department of Oceanography, UBC, a research assistantship (1985-86) from a Natural Science and Engineering Research Council Strategic Grant held by L.A. Mysak (UBC), K. Groot (PBS) and K. Hamilton ( M c G i l l ) , and part-time employment and typing services f o r the production of t h i s t h e s i s (1985-86) from Dobrocky Seatech Ltd., Sidney, B.C.. The ship-of-opportunity program could not have been successfully completed without the cooperation and assistance of the Defence Research Establishment- P a c i f i c , the o f f i c e r s and crews of the nineteen Canadian Armed Forces vessels that p a r t i c i p a t e d , P. Nowlan (UBC) and N. Sutherland (RRMC). R. Thomson kind l y provided access to the UBC computing system from Sidney, B.C. The guidance from my research supervisor, W. J . Emery, and my supervisory committee, c o n s i s t i n g of D.P. Krauel, P.H. LeBlond and S. Pond, i s g r a t e f u l l y acknowledged. A s p e c i a l acknowledgement i s extended to L.A. Mysak f o r h i s encouragement and support over the l a s t two years. I am grateful to M. Bowman fo r h i s review of the thesis and short tenure on the supervisory committee. B e n e f i c i a l discussions were held with A. Bennett, A. Blaskovich, D. Dunbar, J . Harper, G. L o u t t i t , P. Greisman and G. Swaters. The courier and hostelry services of A. Weaver, the heroic typing e x p l o i t s of D. Duncan and the substantial contributions of time and e f f o r t by my Mom and Dad to proofreading t h i s t h e s i s were very much appreciated. A very s p e c i a l thanks i s due to Joanne, Keith and Elizabeth f o r t h e i r i n s p i r a t i o n and support during my studies at UBC and f o r l i v i n g i n poverty with a tyrant f o r the l a s t year (or so). 1 I . INTRODUCTION The purpose o f t h i s i n v e s t i g a t i o n i s t o d e t e r m i n e t h e g e o g r a p h i c v a r i a b i l i t y o f the s y n o p t i c s t a t i s t i c s and dynamics of t h e o c e a n i c mesoscale ( i . e . 100 t o 1000 km w a v e l e n g t h s ) from q u a s i - s y n o p t i c expendable bathythermograph (XBT) s u r v e y s . A d a t a s e t was c o m p i l e d o f q u a s i - s y n o p t i c s i n g l e - s h i p t r a n s - o c e a n i c XBT s e c t i o n s and m u l t i s h i p / A X B T s u r v e y s , o b t a i n e d f r o m t h e Canadian Armed F o r c e s , t h e U n i t e d S t a t e s Navy and t h e N a t i o n a l Oceanographic Data C e n t e r . These d a t a were s o r t e d i n t o s i x g e o g r a p h i c r e g i o n s i n t h e P a c i f i c and A t l a n t i c Oceans. The g e o g r a p h i c v a r i a b i l i t y o f t h e d e s c r i p t i v e f i e l d s and wavenumber s t a t i s t i c s w i l l be d i s c u s s e d and t h e g o v e r n i n g dynamics w i l l be i n f e r r e d from s e v e r a l d y n a m i c a l models. I t i s h y p o t h e s i z e d t h a t t h e dominant l e n g t h and v e l o c i t y s c a l e s o f t h e b a r o c l i n i c m o t i o n s e x h i b i t a g e o g r a p h i c v a r i a b i l i t y s i m i l a r t o t h a t w h i c h has been demonstrated f o r t h e i n t e n s i t y o f t h e m e s o s c a l e p e r t u r b a t i o n s u s i n g c l i m a t o l o g i c a l d a t a s e t s , and t h a t t h e s e s c a l e s r e f l e c t a g e o g r a p h i c v a r i a b i l i t y o f t h e g o v e r n i n g m e s o s c a l e dynamics. The e x i s t e n c e o f dynamic f e a t u r e s o f mesoscale d i m e n s i o n s , i n t h e form o f d i s t u r b a n c e s o r d i s c r e t e e d d i e s i n t h e mean f l o w , has been known s i n c e a t l e a s t 1936 when I s e l i n n o t e d a s t r o n g i s o l a t e d eddy n o r t h of t h e G u l f Stream. The b e g i n n i n g s o f c o n c e n t r a t e d i n v e s t i g a t i o n s i n t o t r a n s i e n t ocean c u r r e n t s came i n t h e 1950s w i t h a s e r i e s o f c r u i s e s l e d by F u g l i s t e r , t o map t h e i n s t a n t a n e o u s f o r m o f t h e G u l f Stream and t h e r i n g s o f c u r r e n t thrown o f f t o t h e n o r t h and s o u t h . Swallow's f l o a t s i n t h e same decade c l e a r l y showed deep d i s c r e t e e d d i e s w i t h depths o f up t o 4000 m and c u r r e n t s e x c e e d i n g 10 cm/s ( R h i n e s , 1977). E x t e n s i v e work has s i n c e been done t o i n v e s t i g a t e t h i s mesoscale v a r i a b i l i t y u s i n g a w i d e v a r i e t y o f d a t a b a s e s . C l a s s i c a l h y d r o g r a p h i c s u r v e y s i n t h e N o r t h P a c i f i c (Roden, 1977) have shown w a v e l i k e d i s t u r b a n c e s w i t h w a v e l e n g t h s between 400 and 600 km i n t h e r e g i o n o f 20° t o 50°N, w h i c h were shown t o be c o n s i s t e n t w i t h s e v e r a l i d e a l i z e d models o f f r e e l i n e a r Rossby waves. H i s t o r i c a l h y d r o g r a p h i c and XBT d a t a have been u s e d t o d e t e r m i n e t h e d i s t r i b u t i o n , number and movement o f t h e G u l f Stream R i n g s i n t h e S a r g a s s o Sea w i t h r e s p e c t t o t h e g e n e r a l c i r c u l a t i o n ( P a r k e r , 1971; L a i and R i c h a r d s o n , 1977; Ebbesmeyer and T a f t , 1979). S a t e l l i t e - t r a c k e d buoys have been a b l e t o t r a c e t h e e v o l u t i o n o f s e v e r a l G u l f Stream Rings q u i t e s u c c e s s f u l l y 2 ( R i c h a r d s o n , 1979). S e v e r a l i n v e s t i g a t o r s have a n a l y s e d l o n g t i m e s e r i e s o f h y d r o g r a p h i c and XBT d a t a a t Ocean Weather s t a t i o n s (White and W a l k e r , 1974; Emery and Magaard, 1976). Remote-sensing t e c h n i q u e s have been employed t o s t u d y t h e v a r i a b i l i t y o f t h e sea s u r f a c e t e m p e r a t u r e f i e l d ( S a u n d e r s , 1972b; H o l l o d a y and O ' B r i e n , 1975; Deschamps e t a l . , 1981; Van Woert, 1982). V a l u a b l e d e s c r i p t i o n s o f t h e g e o g r a p h i c i n h o m o g e n e i t y o f t h e mesoscale v a r i a b i l i t y have been p r o v i d e d by u t i l i z i n g t h e h i s t o r i c a l s h i p d r i f t d a t a f i l e ( W y r t k i et_ a l . , 1976), t h e h i s t o r i c a l h y d r o g r a p h i c d a t a f i l e ( L u t j e h a r m s and B a k e r , 1980), t h e h i s t o r i c a l XBT d a t a f i l e ( D a n t z l e r , 1977; Emery, 1983a) and s a t e l l i t e a l t i m e t r y f rom SEASAT (Cheney e t a l . , 1983; Fu, 1983) and GOES-3 ( R o b i n s o n e t a l . , 1983). I n t h e l a s t decade, t h e c a p a b i l i t y o f XBTs t o o b t a i n q u a s i - s y n o p t i c c o v e rage o f l a r g e r e g i o n s o f t h e ocean has been demonstrated. Saunders (1971) o b s e r v e d t h e e v o l u t i o n o f an i s o l a t e d eddy n o r t h o f t h e G u l f Stream w i t h AXBTs. B e r n s t e i n and White (1974) d e t e r m i n e d a dominant w a v e l e n g t h o f 600 km w i t h s e v e r a l s e t s o f XBTs i n t h e N o r t h P a c i f i c s u b t r o p i c a l g y r e . The same i n v e s t i g a t o r s ( 1 977), w i t h a d i f f e r e n t s e t o f XBT d a t a i n t h e m i d - l a t i t u d e N o r t h P a c i f i c , o b s e r v e d an o r d e r o f magnitude d e c r e a s e i n t h e e n e r g y d i s t r i b u t i o n a t 500 t o 1000 km w a v e l e n g t h s e a s t o f 170°W. S i m i l a r i n v e s t i g a t i o n s were c o n d u c t e d i n t h e Newfoundland B a s i n ( S c h m i t z , 1981) and a d j a c e n t t o South A f r i c a ( L u t j e h a r m s , 1981). S h i p - o f - o p p o r t u n i t y programs u s i n g XBTs have been, and a r e c o n t i n u i n g t o , y i e l d s u b s t a n t i a l amounts o f d a t a o v e r space and t i m e (White and B e r n s t e i n , 1979). POLYGON ( K o s h l y a k o v and Grachev, 1973), MODE (MODE Group, 1975 and 1978) and POLYMODE ( R o b i n s o n , 1982) have c o n t r i b u t e d s i g n i f i c a n t l y t o t h e knowledge o f m e s o s c a l e dynamics, w i t h i n t e n s e s u r v e y s of s p e c i f i c r e g i o n s o f t h e ocean. A p i c t u r e o f t h e d i v e r s i t y o f t h e q u a s i g e o s t r o p h i c dynamics has emerged. A t one extreme, t h e m o t i o n s can be r e p r e s e n t e d as l i n e a r wave p r o c e s s e s . A t t h e o t h e r extreme, t h e m o t i o n s can be c o m p l e t e l y n o n l i n e a r and t u r b u l e n t . The p o t e n t i a l o f q u a s i - s y n o p t i c XBT d a t a f o r e x a m i n i n g m e s o s c a l e s t a t i s t i c s and dynamics has n o t as y e t been e x p l o i t e d . S i m i l a r l y , t h e i r u s e f o r d e t e r m i n i n g t h e g e o g r a p h i c v a r i a b i l i t y has o n l y been t o u c h e d on. I t i s t h e i n t e n t o f t h i s i n v e s t i g a t i o n t o use q u a s i - s y n o p t i c XBT s u r v e y s t o make a s t a t e m e n t about t h e g e o g r a p h i c v a r i a b i l i t y o f t h e s t a t i s t i c s and t h e dynamics o f t h e o c e a n i c mesoscale m o t i o n s . The t h e s i s c o m p r i s e s s i x c h a p t e r s . C h a p t e r 3 I I d e s c r i b e s t h e c o l l e c t i o n and p r o c e s s i n g o f t h e q u a s i - s y n o p t i c XBT d a t a s e t . The d e s c r i p t i v e a n a l y s e s a r e i n C h a p t e r I I I . G e o g r a p h i c r e g i o n s w i t h d i f f e r e n t l e n g t h s c a l e s and a m p l i t u d e s of the mesoscale s t r u c t u r e a r e d e l i n e a t e d and t h e d e s c r i p t i v e c h a r a c t e r i s t i c s o f t h e eddy v a r i a b i l i t y i n each r e g i o n a r e examined w i t h t y p i c a l t e m p e r a t u r e s e c t i o n s and maps. C h a p t e r IV c o n t a i n s t h e s t a t i s t i c a l a n a l y s e s . Two v a r i a b l e s a r e used t o r e p r e s e n t t h e mesoscale v a r i a b i l i t y - t h e m i d - t h e r m o c l i n e t e m p e r a t u r e and t h e g e o p o t e n t i a l anomaly (0 - 400 m). The c e n t r a l moments and t h e wavenumber s p e c t r a o f t h e s e v a r i a b l e s a r e u sed t o d i s c u s s t h e g e o g r a p h i c v a r i a b i l i t y o f t h e m e s o s c a l e eddy f i e l d . The s e a s o n a l v a r i a b i l i t y o f t h e mesoscale f i e l d s a r e examined f o r t h e N o r t h e a s t P a c i f i c , t h e r e g i o n w i t h t h e most even d i s t r i b u t i o n o f s u r v e y s over t h e f o u r q u a r t e r s o f t h e y e a r . The g e o s t r o p h i c v e l o c i t y s p e c t r a a r e o b t a i n e d from t h e g e o p o t e n t i a l anomaly s p e c t r a and t h e eddy k i n e t i c e n e r g i e s a r e e s t i m a t e d . The dominant l e n g t h and v e l o c i t y s c a l e s f o r each r e g i o n a r e d e t e r m i n e d from t h e wavenumber s p e c t r a . I n C h a p t e r V, t h e a p p l i c a b i l i t y o f q u a s i g e o s t r o p h i c dynamics i s i n f e r r e d by e v a l u a t i n g t h e q u a s i g e o s t r o p h i c s c a l i n g p a r a m e t e r s and t h e Rossby wave s t e e p n e s s p a r a m e t e r . The p r o p e r t i e s o f f r e e l i n e a r b a r o c l i n i c Rossby waves a r e examined and t h e wavenumber s p e c t r a a r e compared w i t h s e v e r a l models o f n o n l i n e a r g e o p h y s i c a l t u r b u l e n c e . The c o n c l u s i o n s , i n C h a p t e r V I , summarize t h e g e o g r a p h i c v a r i a b i l i t y o f t h e s t a t i s t i c s and t h e i n f e r r e d dynamics. I t i s i m p o r t a n t t o d e f i n e s e v e r a l key terms u s e d t h r o u g h o u t t h e t h e s i s . The o c e a n i c m e s o s c a l e i s a high-wavenumber band ( i . e . 100 t o 1000 km w a v e l e n g t h s ) o f v a r i a b i l i t y compared t o t h e l a r g e - s c a l e mean f l o w o f the ocean c u r r e n t s , w h i c h i s comparable t o t h e i n t e r n a l Rossby d e f o r m a t i o n r a d i u s . Due t o t h e s t a t i s t i c a l methods employed i n t h i s s t u d y , a c o n v e n i e n t r e p r e s e n t a t i o n o f l e n g t h s c a l e s i s t h e w a v e l e n g t h ( B e r n s t e i n and W h i t e , 1977). The w a v e l e n g t h ( A ) o f a f e a t u r e i s r e l a t e d t o i t s l e n g t h s c a l e ( L ) by t h e r e l a t i o n (Emery e t a l . 1982), X = 2TTL. The term "eddy" a p p l i e s t o t h e d e s c r i p t i o n o f a l l m e s o s c a l e p e r t u r b a t i o n s . I t i n c l u d e s i n d i v i d u a l c l o s e d c i r c u l a t i o n c e l l s and s p a c e / t i m e v e l o c i t y o r p r o p e r t y f l u c t u a t i o n s c a u s e d by a wide v a r i e t y o f c i r c u l a t i o n f e a t u r e s (Emery, 1983b). The t e r m "eddy" has no c o n n o t a t i o n s o f o r i g i n , d y n a m i c a l b e h a v i o r o r r o t a t i o n a l m o t i o n . A " d i s c r e t e eddy" o r " i s o l a t e d eddy" i s u s e d t o s i g n i f y i n d i v i d u a l c l o s e d c i r c u l a t i o n f e a t u r e s w i t h a r o t a t i o n a l m o t i o n . The t e r m expendable b a t h y t h e r m o g r a p h (XBT) i n c l u d e s b o t h a i r - l a u n c h e d (AXBT) and s h i p - l a u n c h e d (SXBT) p r o b e s . T h i s t e r m does n o t i n c l u d e m e c h a n i c a l b a t h y t h e r m o g r a p h s (MBT). A l i s t o f t h e symbols and a l i s t o f t h e a b b r e v i a t i o n s used r e g u l a r l y t h r o u g h o u t t h e t h e s i s can be f o u n d i m m e d i a t e l y a f t e r t h e T a b l e o f C o n t e n t s . 5 II. THE DATA SET The c o l l e c t i o n and p r o c e s s i n g o f t h e q u a s i - s y n o p t i c XBT d a t a s e t i s d e s c r i b e d i n t h i s c h a p t e r . I n o r d e r t o examine t h e m e s o s c a l e s t r u c t u r e o v e r a l a r g e p o r t i o n o f t h e P a c i f i c and A t l a n t i c Oceans, 83 s e t s o f XBT d a t a were o b t a i n e d . These d a t a c o m p r i s e o v e r 10,000 i n d i v i d u a l XBTs a c q u i r e d from t h e Ca n a d i a n Armed F o r c e s (CAF), t h e U n i t e d S t a t e s Navy (USN), and t h e U n i t e d S t a t e s N a t i o n a l O c e a n o g r a p h i c Data C e n t e r (NODC). These t e m p e r a t u r e - d e p t h (T-Z) p r o f i l e s were f i l t e r e d s u b j e c t i v e l y t o d e l e t e q u e s t i o n a b l e d a t a ; s a l i n i t y was i n f e r r e d u s i n g h i s t o r i c a l t e m p e r a t u r e - s a l i n i t y (T-S) and s a l i n i t y - d e p t h (S-Z) c u r v e s ; and s e v e r a l o c e a n o g r a p h i c v a r i a b l e s were c a l c u l a t e d f o r t h e a n a l y s e s o f t h e m e s o s c a l e eddy v a r i a b i l i t y . A. DATA COLLECTION The XBT d a t a s e t , o b t a i n e d from t h e CAF, USN and NODC, p r o v i d e s a r e a s o n a b l e c o v e r a g e o f t h e P a c i f i c and A t l a n t i c . F i g u r e I I - 1 shows t h e l o c a t i o n s o f t h e s e d a t a pn a M e r c a t o r p r o j e c t i o n o f t h e ocea n s . The CAF d a t a were p r o c u r e d by managing and i m p l e m e n t i n g a s h i p - o f - o p p o r t u n i t y program w i t h t h e C a n a d i a n Navy, w h i l e t h e USN and NODC d a t a were a c q u i r e d f r o m a r c h i v e d f i l e s . The C a n a d i a n Armed F o r c e s Data CAF d e s t r o y e r squadrons were used i n a s h i p - o f - o p p o r t u n i t y program f r o m F e b r u a r y 1980 t o June 1983 t o c o l l e c t q u a s i - s y n o p t i c SXBT d a t a . These d a t a were o b t a i n e d on a c o n t r a c t from t h e Defence R e s e a r c h E s t a b l i s h m e n t - P a c i f i c t o W.J. Emery and D.P. K r a u e l . E l e v e n c r u i s e s were c o n d u c t e d , r e s u l t i n g i n t e n t r a n s - o c e a n i c s i n g l e - s h i p s e c t i o n s and n i n e m u l t i s h i p s u r v e y s i n t h e P a c i f i c and N o r t h A t l a n t i c Oceans- Data were c o l l e c t e d on t h e r e t u r n passage o f CAF d e s t r o y e r squadrons f r o m o v e r s e a s deployments when t h e c o u r s e was, f o r t h e most p a r t , d i r e c t l y t o Canada. On each c r u i s e , SXBTs and sea s u r f a c e s a l i n i t i e s (SSSs) were t a k e n h o u r l y f r o m one o f t h e s h i p s f o r t h e e n t i r e voyage. The squadrons g e n e r a l l y c r u i s e d a t speeds o f 13 k n o t s , r e s u l t i n g i n a h i g h s a m p l i n g d e n s i t y o f one SXBT and SSS p e r 25 km o v e r r a n g e s o f about 4000 km. Depending on o p e r a t i o n a l and Figure II-1 Locations of the XBT data used In this investigation. a. A l l of the XBT data. b. CAF data. Figure II-1 Continued. c. USN data. d. NODC data. 8 t r a i n i n g r e q u i r e m e n t s , m u l t i s h i p s u r v e y s were c o n d u c t e d . The coverage o f t h e s e s u r v e y s v a r i e d f r o m 40 t o 180 km i n w i d t h and 600 t o 1300 km i n l e n g t h w i t h t h r e e o r f o u r s h i p s . Each of Canada's f o u r d e s t r o y e r squadrons p a r t i c i p a t e d i n t h i s o b s e r v a t i o n a l program - a t o t a l o f 19 d i f f e r e n t d e s t r o y e r s and s u p p l y s h i p s . An on-board s c i e n t i s t , t e c h n i c i a n o r s t u d e n t from t h e U n i v e r s i t y o f B r i t i s h Columbia (UBC) o r R o y a l Roads M i l i t a r y C o l l e g e m o n i t o r e d and a s s i s t e d w i t h t h e c o l l e c t i o n o f t h e data on each c r u i s e . They were r e s p o n s i b l e f o r o n - s i t e q u a l i t y c o n t r o l and c o o r d i n a t i o n o f t h e m u l t i s h i p s u r v e y s . The S i p p i c a n XBT system i s w i d e l y used, so t h e d e t a i l s w i l l n o t be d i s c u s s e d h e r e . Most o f t h e CAF s h i p s had SXBT systems c o n s i s t i n g o f S i p p i c a n MK2A-1 s t r i p - c h a r t r e c o r d e r s and deck-mounted l a u n c h e r s . A MK2A-1 s t r i p - c h a r t r e c o r d e r and h a n d - h e l d l a u n c h e r were u s e d on t h e s h i p s w i t h o u t s y s t e m s . The T-4 p r o b e s (460 m) were p r o v i d e d by t h e CAF's s u p p l y system. The r e p o r t e d a c c u r a c y of t h e T-4 probe i s +_0.2°C and 5 m o r +2% w h i c h e v e r i s g r e a t e r (Anderson, 1979; S i p p i c a n , 1975). The SXBTs were t a k e n e v e r y hour and f a u l t y o r s u s p e c t SXBTs were i m m e d i a t e l y r e p e a t e d . As a r u l e o f thumb, no more t h a n two p r o b e s were u s e d on each s t a t i o n . The XBT systems were t e s t e d p r i o r t o each c r u i s e u s i n g t h e X B T e s t e r Model A-4 f o r t e m p e r a t u r e c a l i b r a t i o n , s e r v o - a m p l i f i e r g a i n , l a u n c h e r i n s t a l l a t i o n r e s i s t a n c e and s e r v o r e s p o n s e . The c a l i b r a t i o n was s u b s e q u e n t l y checked e v e r y s i x h o u r s . The t e m p e r a t u r e p r o f i l e s were v i s u a l l y i n s p e c t e d f o r f a i l u r e s and s u s p e c t t r a c e s (Department o f t h e Navy, 1978) upon r e t u r n i n g f r o m each c r u i s e . The good T-Z t r a c e s were d i g i t i z e d a t t h e i n f l e c t i o n p o i n t s , such t h a t l i n e a r i n t e r p o l a t i o n w o u l d p r o v i d e r e a s o n a b l e t e m p e r a t u r e s f o r a l l d e p t h s . The d i g i t i z e d v a l u e s were c o r r e c t e d f o r t h e n o n l i n e a r i t y o f t h e t r a c e due t o t h e f a l l r a t e (depth) and t h e s e r v o - a m p l i f i e r r e s p o n s e ( t e m p e r a t u r e ) a c c o r d i n g t o S i p p i c a n ' s XBT s y s t e m l i n e a r i t y e q u a t i o n s ( S i p p i c a n , 1970). These o p e r a t i o n s were p e r f o r m e d on a D a t a t i z e r DTR-3036 (GTO C o r p o r a t i o n ) and LSI-11/23 m i n i c o m p u t e r . The d a t a were t r a n s f e r r e d t o UBC's Amdahl V8 mainframe computer. SSS was o b t a i n e d f r o m b u c k e t samples t a k e n i m m e d i a t e l y a f t e r each SXBT. The samples were r e t a i n e d i n 4 oz g l a s s sample b o t t l e s and r e t u r n e d t o UBC f o r a n a l y s i s . The c o n d u c t i v i t y r a t i o s were measured u s i n g a G u i l d l i n e A u t o s a l 9 Model 8400 s a l i n o m e t e r . The s a l i n i t i e s were e s t i m a t e d u s i n g t h e P r a c t i c a l S a l i n i t y S c a l e , 1978 (Pond and P i c k a r d , 1983). The G u i l d l i n e A u t o s a l s a l i n o m e t e r has a m a n u f a c t u r e r ' s r e p o r t e d a c c u r a c y o f +^.003 x 10~3 e q u i v a l e n t s a l i n i t y . The s a l i n i t i e s o f t h e f i r s t two c r u i s e s , i n t h e N o r t h e a s t P a c i f i c , were o r i g i n a l l y e s t i m a t e d u s i n g t h e 1966 UNESCO t a b l e s . A l t h o u g h t h e d i f f e r e n c e s between t h e s e two methods of e s t i m a t i n g s a l i n i t y i s l e s s t h a n .003 x 1 0 - 3 , o v e r t h e o b s e r v e d range o f s a l i n i t y (32 t o 36 x 1 0 ~ 3 ) , t h e c o r r e c t i o n s were made. Thus, SSSs used i n t h i s i n v e s t i g a t i o n have been e s t i m a t e d from, o r c o r r e c t e d t o , t h e P r a c t i c a l S a l i n i t y S c a l e , 1978. The n a v i g a t i o n a l methods employed v a r i e d d e p e n d i n g on t h e v e s s e l and t h e l o c a t i o n , i n o r d e r t o o b t a i n t h e b e s t p o s s i b l e a b s o l u t e and r e l a t i v e f i x . Radar f i x e s on p o i n t s o f l a n d , s a t e l l i t e n a v i g a t i o n , Loran-C and Omega were used. When p o s s i b l e , d u r i n g m u l t i s h i p s u r v e y s , r a d a r f i x e s were t a k e n on a d j a c e n t s h i p s . O v e r a l l , t h e a b s o l u t e n a v i g a t i o n was c o n s i d e r e d t o be much b e t t e r t h a n + 5 km. The CAF d a t a were f o r m a t t e d and a r c h i v e d f o r f u r t h e r p r o c e s s i n g a l o n g w i t h t h e USN and NODC d a t a . A d e t a i l e d d a t a r e p o r t o f t h e CAF d a t a was p r e p a r e d (Thomson e t a l . , 1984b). The U n i t e d S t a t e s Navy Data The USN d a t a u s e d i n t h i s i n v e s t i g a t i o n were c o l l e c t e d i n t h r e e s e p a r a t e programs and o b t a i n e d f r o m a r c h i v e d d a t a f i l e s . Data f r o m s i x t r a n s - o c e a n i c m u l t i s h i p SXBT s u r v e y s , c o n d u c t e d i n t h e N o r t h P a c i f i c and N o r t h A t l a n t i c by W i l s o n and Dugan ( 1 9 7 8 ) , were a c q u i r e d . These d a t a were p r e v i o u s l y u s e d t o i n v e s t i g a t e v a r i o u s a s p e c t s o f t h e mesoscale eddy v a r i a b i l i t y (Emery et^ a l . , 1979; Emery et_ a l . , 1980; H a r r i s o n et^ a l . , 1983). A l s o , two d a t a s e t s f r o m AXBT s u r v e y s c o n d u c t e d by t h e USN, were p r o c u r e d . The f i r s t s e t i s f r o m e i g h t s u r v e y s n o r t h e a s t o f H a w a i i i n t h e r e g i o n o f t h e s u b t r o p i c a l f r o n t , c o l l e c t e d by M i y a k i ( M i y a k i , 1981). The second s e t i s fr o m a s e r i e s o f f i v e s u r v e y s o b t a i n e d from t h e U n i t e d S t a t e s N a v a l . R e s e a r c h L a b o r a t o r y i n Washington, D.C. (Emery, p e r s o n n a l c ommunication) - one s u r v e y on t h e s u b t r o p i c a l f r o n t n o r t h e a s t o f H a w a i i and f o u r s u r v e y s i n t h e N o r t h P a c i f i c E q u a t o r i a l C u r r e n t s o u t h o f H a w a i i . These two d a t a s e t s o f AXBT s u r v e y s have n o t been p u b l i s h e d , n o r have t h e y been u s e d t o s t u d y t h e eddy v a r i a b i l i t y o f t h e s e r e g i o n s . 10 Model 8400 s a l i n o m e t e r . The s a l i n i t i e s were e s t i m a t e d u s i n g t h e P r a c t i c a l S a l i n i t y S c a l e , 1978 (Pond and P i c k a r d , 1983). The G u i l d l i n e A u t o s a l s a l i n o m e t e r has a m a n u f a c t u r e r ' s r e p o r t e d a c c u r a c y o f _+. 003 x 1 0 - 3 e q u i v a l e n t s a l i n i t y . The s a l i n i t i e s o f t h e f i r s t two c r u i s e s , i n t h e N o r t h e a s t P a c i f i c , were o r i g i n a l l y e s t i m a t e d u s i n g t h e 1966 UNESCO t a b l e s . A l t h o u g h t h e d i f f e r e n c e s between t h e s e two methods of e s t i m a t i n g s a l i n i t y i s l e s s t h a n .003 x 1 0 ~ 3 , o v e r t h e o b s e r v e d range o f s a l i n i t y (32 t o 36 x 1 0 ~ 3 ) , t h e c o r r e c t i o n s were made. Thus, SSSs used i n t h i s i n v e s t i g a t i o n have been e s t i m a t e d from, o r c o r r e c t e d t o , t h e P r a c t i c a l S a l i n i t y S c a l e , 1978. The n a v i g a t i o n a l methods employed v a r i e d d e p e n d i n g on t h e v e s s e l and t h e l o c a t i o n , i n o r d e r t o o b t a i n t h e b e s t p o s s i b l e a b s o l u t e and r e l a t i v e f i x . Radar f i x e s on p o i n t s o f l a n d , s a t e l l i t e n a v i g a t i o n , Loran-C and Omega were u s e d . When p o s s i b l e , d u r i n g m u l t i s h i p s u r v e y s , r a d a r f i x e s were t a k e n on a d j a c e n t s h i p s . O v e r a l l , t h e a b s o l u t e n a v i g a t i o n was c o n s i d e r e d t o be much b e t t e r t h a n + 5 km. The CAF d a t a were f o r m a t t e d and a r c h i v e d f o r f u r t h e r p r o c e s s i n g a l o n g w i t h t h e USN and NODC d a t a . A d e t a i l e d d a t a r e p o r t o f t h e CAF d a t a was p r e p a r e d (Thomson e t a l . , 1984b). The U n i t e d S t a t e s Navy Data The USN d a t a u s e d i n t h i s i n v e s t i g a t i o n were c o l l e c t e d i n t h r e e s e p a r a t e programs and o b t a i n e d f r o m a r c h i v e d d a t a f i l e s . Data f r o m s i x t r a n s - o c e a n i c m u l t i s h i p SXBT s u r v e y s , c o n d u c t e d i n t h e N o r t h P a c i f i c and N o r t h A t l a n t i c by W i l s o n and Dugan ( 1 9 7 8 ) , were a c q u i r e d . These d a t a were p r e v i o u s l y u s e d t o i n v e s t i g a t e v a r i o u s a s p e c t s o f t h e me s o s c a l e eddy v a r i a b i l i t y (Emery e t a l . , 1979; Emery et^ a l . , 1980; H a r r i s o n et_ a l . , 1983). A l s o , two d a t a s e t s f r o m AXBT s u r v e y s c o n d u c t e d by t h e USN, were p r o c u r e d . The f i r s t s e t i s fr o m e i g h t s u r v e y s n o r t h e a s t o f H a w a i i i n t h e r e g i o n o f t h e s u b t r o p i c a l f r o n t , c o l l e c t e d by M i y a k i ( M i y a k i , 1981). The second s e t i s f r o m a s e r i e s of f i v e s u r v e y s o b t a i n e d f r o m t h e U n i t e d S t a t e s N a t i o n a l R e s e a r c h L a b o r a t o r y i n Washington, D.C. (Emery, p e r s o n n a l communication) - one s u r v e y on t h e s u b t r o p i c a l f r o n t n o r t h e a s t o f H a w a i i and f o u r s u r v e y s i n t h e N o r t h P a c i f i c E q u a t o r i a l C u r r e n t s o u t h o f H a w a i i . These two d a t a s e t s o f AXBT s u r v e y s have n o t been p u b l i s h e d , n o r have t h e y been u s e d t o s t u d y t h e eddy v a r i a b i l i t y o f t h e s e r e g i o n s . 11 The N a t i o n a l O c e a n o g r a p h i c Data C e n t e r Data The NODC XBT (1984) g e o g r a p h i c f i l e (NODC, 1984) was s e a r c h e d f o r q u a s i - s y n o p t i c s e c t i o n s . I n i t i a l l y t h e f i l e was s o r t e d by c r u i s e d e s i g n a t i o n number and c o n s e c u t i v e XBT number. A l l c r u i s e s w i t h more th a n 25 XBTs, i n w a t e r deeper t h a n 500 m, were removed f o r f u r t h e r e x a m i n a t i o n . T h i s y i e l d e d 486 c r u i s e s . The f o l l o w i n g c r i t e r i a were used t o i d e n t i f y 53 s i n g l e - s h i p c r u i s e s w i t h a q u a s i - s y n o p t i c q u a l i t y comparable t o t h e CAF and USN d a t a : a. c r u i s e p a t h s must be r e a s o n a b l y s t r a i g h t t r a n s e c t s a c r o s s o c e a n i c r e g i o n s o f i n t e r e s t ; b. t h e XBT s p a c i n g must be l e s s t h a n 200 km ( A l t h o u g h t h i s does n o t p r o v i d e t h e same high-wavenumber r e s o l u t i o n as t h e CAF and USN d a t a , i t p r o v i d e s a more e f f i c i e n t r a t i o o f number o f samples t o i n d e p e n d e n t o b s e r v a t i o n s ) ; c t h e t i m e between XBT c a s t s must be l e s s t h a n 6 h o u r s ; and d. t h e c r u i s e t r a c k s must be a t l e a s t 1000 km i n l e n g t h . B. DATA PROCESSING The d a t a s e t was p r o c e s s e d t o o b t a i n s e v e r a l o c e a n o g r a p h i c v a r i a b l e s f o r t h e subsequent d e s c r i p t i v e and s t a t i s t i c a l a n a l y s e s . T h i s p r o c e s s i n g i n c l u d e d a v i s u a l e x a m i n a t i o n o f t h e d i g i t i z e d T-Z d a t a , t h e i n f e r e n c e o f s a l i n i t y f r o m T-S and S-Z c u r v e s and t h e c a l c u l a t i o n o f s e v e r a l o c e a n o g r a p h i c v a r i a b l e s . XBT T r a c e s S p a t i a l s e r i e s o f XBTs were produced f o r e a c h c r u i s e and v i s u a l l y i n s p e c t e d t o check f o r f a u l t y o r s u s p e c t XBTs and d i g i t i z a t i o n e r r o r s . F i g u r e I I - 2 , as an example, i s t h e SXBT s p a t i a l s e r i e s o f t h e HMCS P r o v i d e r , f r o m H a w a i i t o Vancouver I s l a n d i n March 1980. Temperature was l i n e a r l y i n t e r p o l a t e d t o 10 m i n c r e m e n t s o f d e p t h f o r each t r a c e and t h e d a t a f r o m t h e t h r e e s o u r c e s were c o n v e r t e d t o a common f o r m a t .  13 S a l i n i t y I n f e r e n c e S a l i n i t y was i n f e r r e d f o r each XBT t o e s t i m a t e d e n s i t y f i e l d s and c a l c u l a t e g e o p o t e n t i a l a n o m a l i e s . Mean T-S and S-Z c u r v e s f r o m Emery and Dewar (1982) and P i c k a r d and Emery (1982) were used t o i n f e r s a l i n i t y . The a c c u r a c y o f i n f e r r i n g s a l i n i t y f i e l d s by t h i s method was examined by comparing t h e b u c k e t SSS f r o m t h e CAF d a t a and t h e i n f e r r e d SSS. Emery and Dewar computed mean T-S and S-Z c u r v e s f o r a l l 5° s q u a r e s i n t h e P a c i f i c and A t l a n t i c , n o r t h o f 10°S, u s i n g NODC's h y d r o g r a p h i c (1978) f i l e . H y d r o c a s t s made i n w a t e r s h a l l o w e r t h a n 500 m were n o t used, so t h e s e c u r v e s r e p r e s e n t t h e o c e a n i c w a t e r s beyond t h e c o n t i n e n t a l s h e l f - b r e a k . F o l l o w i n g t h e method p r o p o s e d by t h e s e i n v e s t i g a t o r s , s a l i n i t y was i n f e r r e d u s i n g t h e T-S c u r v e s , e x c e p t i n t h e r e g i o n s n o r t h o f 40°N i n t h e P a c i f i c and n o r t h w e s t o f 50°N, 45°W i n t h e A t l a n t i c . I n t h e s e two a r e a s , Emery and Dewar f o u n d t h a t t h e root-mean-square (RMS) e r r o r , between t h e dynamic h e i g h t u s i n g t h e i n f e r r e d s a l i n i t y and t h e dynamic h e i g h t u s i n g t h e measured s a l i n i t y , was l e s s w i t h t h e S-Z c u r v e s t h a n w i t h t h e T-S c u r v e s . S-Z c u r v e s were, t h e r e f o r e , u s e d t o i n f e r s a l i n i t y i n t h e s e two r e g i o n s . Mean T-S c u r v e s f o r t h e Southwest P a c i f i c , t h e S o u t h e a s t P a c i f i c , t h e P a c i f i c S u b - A n t a r c t i c and t h e South A t l a n t i c were o b t a i n e d f r o m P i c k a r d and Emery (1982), f o r use s o u t h o f 10°S. The mean T-S c u r v e s f r o m P i c k a r d and Emery (1982) a r e h e u r i s t i c and t h e r e f o r e n o t p r e c i s e . T h e i r use i s c o n s i d e r e d t o be s u b s t a n t i a l l y b e t t e r t h a n u s i n g a mean s a l i n i t y and i s c o n s i s t e n t w i t h t h e method used t o i n f e r s a l i n i t y n o r t h of 10°S. F i g u r e I I - 3 p r e s e n t s a map o f t h e P a c i f i c and A t l a n t i c showing s p e c i f i c a l l y i n w h i c h r e g i o n s t h e above T-S and S-Z c u r v e s were u s e d t o i n f e r s a l i n i t y . S a l i n i t y was i n f e r r e d f o r each T-Z p r o f i l e u s i n g a w e i g h t e d average o f t h e a p p r o p r i a t e c u r v e s o f t h e f o u r c l o s e s t 5° s q u a r e s . The T-S o r S-Z c u r v e s were w e i g h t e d by t h e i n v e r s e o f t h e square o f t h e d i s t a n c e from t h e c e n t e r o f e a c h s q u a r e t o t h e XBT. I t was f o u n d t h a t i n f e r r i n g s a l i n i t y s o l e l y on t h e b a s i s o f t h e c u r v e o f t h e 5° square c o n t a i n i n g t h e XBT c r e a t e d f a l s e s a l i n i t y and d e n s i t y f e a t u r e s i n t h e r e g i o n s o f o c e a n i c f r o n t s . The use of a w e i g h t e d a v e r a g e o f t h e f o u r c l o s e s t s quares s o l v e d t h i s p r o b l e m . As a check on t h e a c c u r a c y of e m p l o y i n g mean c u r v e s f o r i n f e r r i n g s a l i n i t y , p l o t s o f t h e i n f e r r e d SSS and t h e b u c k e t SSS f o r each o f t h e CAF c r u i s e s (where w a t e r samples were c o l l e c t e d ) were c r e a t e d ( F i g u r e I I - 4 ) . These p l o t s show Figure II-3 Map of the P a c i f i c and A t l a n t i c Oceans showing the T-S and S-Z curves used to i n f e r s a l i n i t y . In the regions denoted ED, the mean curves from Emery and Dewar (1982) f o r each 5° square were used. The temperature-salinity and the s a l i n i t y - d e p t h curves were used i n the areas l a b e l l e d TS and SZ, r e s p e c t i v e l y . South of 10*S, the temperature-salinity curves obtained from Pickard and Ki&ery (1982) were: West South P a c i f i c Central (WSPC), East South P a c i f i c Central (ESPC), P a c i f i c Sub-Antarctic (PSA) and South A t l a n t i c Central (SAC). 15 A. HMCS PROVIDER. 2-13 FEBRUARY 1980. 01 BUCKET SAMPLE - SOLID INFERREO SSS - DASHED TTCO w8 26 N — H - 30 N H— 1—h 34N -+J— 38N -f—' h 42 N RANGE : ONE TICK = 300 KM B.HMCS PROVIDER. 26 MARCH - 2 APRIL 1980 cn TT 8 W BUCKET SAMPLE - SOLIO INFERREO SSS - DASHEO f- -+- 27 N — H - 31N H L—4- 35 N -i 1 — h 39 N -i 1 — h 43N 47 N — H - RANGE : ONE TICK = 300 KM GHMCS PROVIDER. 1-7 MAY 1981 cn T BUCKET SAMPLE - SOLID . INFERRED SSS - DASHED . J r r cn 25N. 29N i — — i — - J - H 1—1—y— RANGE : ONE TICK = 300 KM 33 N H— i 1- 37 N 41N H — ' H 45N Figure I I - 4 Plots of the inferred SSS and the backet SSS for each of the CAF single-ship sections, where water samples were collected. For each cruise the two SSSs are plotted as a function of along-track range. The small ticks on the central axis are the SXBT positions where SSS has been inferred. 16 Q HMCS SASKATCHEWAN. 17-24 NOVEMBER 1981. cn rr <n<n co cn cn fcncn BUCKET SAMPLE - SOL10 INFERRED SSS - 0ASHED cn 25 N H—1 r- 29N H — ' r- 33 N 37N H f- 41 N H '—I- 45 N — H — RANGE : ONE TICK 300 KM E.HMCS TERRA NOVA. 11-12 MAY 1982, cn T T •q-tn BUCKET SAMPLE - SOLID INFERRED SSS - DASHED 29 N H '—(- RANGE : ONE TICK = 300 KM E HMCS QITAPPELLE. 2-7 NOVEMBER 1982. t n r r BUCKET SAMPLE - SOLID INFERRED SSS - DASHED CM n 36 S H— H- 32 S —H- 28 S •+- -+- 24S — H — 20 S —H- 16S H — J — H RANGE : ONE TICK = 300 KM Figure II-4 Continued. 17 QHMCS QU'APPELLE. 9-18 NOVEMBER 1982. 03 CO BUCKET SAMPLE - SOLID . INFERRED SSS - DASHED 14S 12S 10S 8 S 6 S 4 S 2 S 0 2 N 4 N 6 N 8 N ION 12N 14N 16N 18N I H 1—I—1 H P H H 1 —I— 1 H H '—I—' H H — — H — RANGE : ONE TICK = 300 KM Figure II-4 Continued. I, HMCS PRESERVER. 1-7 OCTOBER 1982. A/ BUCKET SAMPLE INFERRED SSS - 1 1 1 - SOLID DASHED 1 1 . . . i . i \-r-i—i 60 1 1 r V 54 W n 48 V 42 V " I T 1 1 1 36 V t 1 1 1 30 W 24 V 18 V 12 V 6 RANGE i ONE TICK = 300 KM. J.HMCS PRQTECTEUR. 22-29 JUNE 1983. 00 h 1 r H 1—i 1 1 1 1—I h 1 1 1 1 1 , 1 1— 61 W 55 V 49 V 43 W 37 V 31 V 25 V 19 V 13 W 1 tf RANGE : ONE TICK = 300 KM Figure II-4 Continued. 19 v e r y r e a s o n a b l e agreement between t h e measured and i n f e r r e d SSS. N o t a b l e e x c e p t i o n s were t h e w e s t e r n boundary c u r r e n t r e g i o n s i n t h e t h r e e A t l a n t i c s e c t i o n s ( F i g u r e s I I - 4 h - j ) and t h e e q u a t o r i a l P a c i f i c ( F i g u r e I I - 4 g ) . T a b l e I I - 1 l i s t s t h e RMS d i f f e r e n c e f o r each c r u i s e . The s e c t i o n s i n t h e n o r t h e a s t e r n and s o u t h w e s t e r n P a c i f i c a l l have RMS d i f f e r e n c e s no h i g h e r t h a n 0.20 x 1 0 ~ 3 . The s e c t i o n a c r o s s t h e c e n t r a l e q u a t o r i a l P a c i f i c ( F i g u r e 11-4- g) has an RMS d i f f e r e n c e of 1.07 x 10~ 3. The i n f e r r e d SSS e x h i b i t s t h e g e n e r a l m e r i d i o n a l SSS c h a r a c t e r i s t i c s of t h i s r e g i o n ( P i c k a r d and Emery, 1982: F i g u r e 4.9) w i t h a minimum a t about 10°N i n c r e a s i n g t o w a r d t h e n o r t h and s o u t h s u b t r o p i c a l r e g i o n s . The a n o m a l o u s l y low b u c k e t SSSs, a c r o s s t h e N o r t h P a c i f i c E q u a t o r i a l C o u n t e r c u r r e n t , a r e due t o t h e i n c r e a s e d p r e c i p i t a t i o n i n t h i s c e n t r a l e q u a t o r i a l r e g i o n d u r i n g t h e 1982-83 E l Nino - S o u t h e r n O s c i l l a t i o n (ENSO) e v e n t (Rasmusson et_ a l . , 1983). The t h r e e N o r t h A t l a n t i c s e c t i o n s ( F i g u r e s I I - 4 h - j ) have h i g h RMS d i f f e r e n c e s due t o d i f f i c u l t i e s a s s o c i a t e d w i t h i n f e r r i n g s a l i n i t y i n t h e r e g i o n s o f t h e w e s t e r n boundary c u r r e n t s (Emery and Dewar, 1982). To t h e e a s t of t h e s e r e g i o n s , t h e b u c k e t and i n f e r r e d SSS show a v e r y r e a s o n a b l e agreement. The d i f f e r e n c e s i n t h e w e s t e r n boundary c u r r e n t r e g i o n s a r i s e from a p p l y i n g mean T-S c u r v e s t o T-Z p r o f i l e s t a k e n a c r o s s a f r o n t s e p a r a t i n g w a t e r masses o f v e r y d i f f e r e n t T-S c h a r a c t e r i s t i c s . The a n o m a l o u s l y low s a l i n i t y v a l u e s i n t h e e q u a t o r i a l s e c t i o n w i l l n o t p r o t r u d e much deeper t h a n t h e m i x e d - l a y e r d e p t h o f about 60 m, so t h e T-S c u r v e s s h o u l d p r o v i d e r e a s o n a b l e s a l i n i t y e s t i m a t e s f o r most o f t h e w a t e r column. I n t h e w e s t e r n boundary c u r r e n t r e g i o n s , p a r t i c u l a r l y where t h e d a t a f o r t h i s i n v e s t i g a t i o n were o b t a i n e d , t h e T-S c u r v e s o f Emery and Dewar (1982) a r e d o minated by t h e c o n t r i b u t i o n f r o m o f f s h o r e o c e a n i c w a t e r s r a t h e r t h a n t h e l e s s s a l i n e c o n t i n e n t a l s h e l f and s l o p e w a t e r s . Thus, t h e eddy v a r i a b i l i t y d e t e r m i n e d from t h e g e o p o t e n t i a l anomaly due t o c o l d - c o r e r i n g s w i l l be u n d e r e s t i m a t e d , w h i c h i s much p r e f e r a b l e t o o v e r e s t i m a t i n g t h e eddy v a r i a b i l i t y . F o r t h e above r e a s o n s , t h e method o f i n f e r r i n g s a l i n i t y f r o m mean T-S c u r v e s i n t h e s e r e g i o n s i s c o n s i d e r e d more a p p r o p r i a t e and u s e f u l t h a n u s i n g a mean s a l i n i t y f o r t h e p u r p o s e s o f t h i s i n v e s t i g a t i o n . O c e a n o g r a p h i c V a r i a b l e s F u r t h e r p r o c e s s i n g o f t h e measured t e m p e r a t u r e and i n f e r r e d s a l i n i t y p r o f i l e s were r e q u i r e d f o r each XBT i n p r e p a r a t i o n f o r t h e d e s c r i p t i v e and 20 Table II-1 RMS diff e r e n c e s between backet SSS and Inferre d SSS f o r the CAF trans—oceanic sections shown In Figure II—A. S h i p Date Ocean RMS D i f f e r e n c e ( x 1 0 ~ 3 ) a. HMCS P r o v i d e r Feb 80 N o r t h e a s t P a c i f i c 0.17 b. HMCS P r o v i d e r Apr 80 N o r t h e a s t P a c i f i c 0.18 c. HMCS P r o v i d e r May 81 N o r t h e a s t P a c i f i c 0.15 d. HMCS Saskatchewan Nov 81 N o r t h e a s t P a c i f i c 0.20 e. HMCS T e r r a Nova May 82 N o r t h e a s t P a c i f i c 0.13 f . HMCS Q u ' A p p e l l e Nov 82 Southwest P a c i f i c 0.15 g. HMCS Q u ' A p p e l l e Nov 82 E q u a t o r i a l P a c i f i c 1.07 h. HMCS Saguenay O c t 81 N o r t h A t l a n t i c 1.22 1. HMCS P r e s e r v e r Oct 82 N o r t h A t l a n t i c 0.93 j . HMCS P r o t e c t e u r J u n 83 N o r t h A t l a n t i c 0.54 21 s t a t i s t i c a l a n a l y s e s . As w i l l be d i s c u s s e d i n C h a p t e r s I I I and IV, t e m p e r a t u r e w i l l be used t o examine t h e m e s o s c a l e v a r i a b i l i t y i n t h e m i d - t h e r m o c l i n e and t h e g e o p o t e n t i a l anomaly w i l l be u s e d t o examine t h e b a r o c l i n i c eddy v a r i a b i l i t y i n t h e upper l a y e r (400 m) o f t h e ocean. The m i d - t h e r m o c l i n e t e m p e r a t u r e was c a l c u l a t e d as v e r t i c a l a v e r a g e s o f t h e measured t e m p e r a t u r e o v e r two 50 m segments o f t h e w a t e r column ( i . e . 150 t o 200 m and 350 t o 400 m). The a p p l i c a b i l i t y o f t h e s e t e m p e r a t u r e v a r i a b l e s f o r d e s c r i b i n g t h e mesoscale v a r i a b i l i t y o f t h e ocean w i l l be d i s c u s s e d i n C h a p t e r IV. The g e o p o t e n t i a l anomaly f r o m 0 t o 4000 kPa ( i . e . 0 t o 400 db o r 0 t o 400 m) was c a l c u l a t e d as t h e i n t e g r a l o f t h e s p e c i f i c volume anomaly. T h i s r e q u i r e d t h e d e t e r m i n a t i o n o f t h e s i g m a - t p r o f i l e f r o m t h e measured t e m p e r a t u r e and i n f e r r e d s a l i n i t y . Sigma-t was o b t a i n e d f r o m t h e I n t e r n a t i o n a l E q u a t i o n o f S t a t e o f Sea Water, 1980 ( M i l l e r o and P o i s s o n , 1981) w i t h t h e g i v e n t e m p e r a t u r e and s a l i n i t y a t a t m o s p h e r i c p r e s s u r e . 22 I I I . DESCRIPTIVE ANALYSES The p u r p o s e o f t h e d e s c r i p t i v e a n a l y s e s i s t o q u a l i t a t i v e l y d i s c u s s t h e g e o g r a p h i c v a r i a b i l i t y o f t h e o b s e r v e d m e s o s c a l e s t r u c t u r e . G e o g r a p h i c r e g i o n s w i t h d i f f e r e n t s c a l e s and a m p l i t u d e s o f m e s o s c a l e s t r u c t u r e a r e d e f i n e d and t y p i c a l s e c t i o n s and maps o f each r e g i o n a r e u s e d t o examine t h e g e o g r a p h i c v a r i a b i l i t y o f t h e t h e r m a l s t r u c t u r e i n t h e q u a s i - s y n o p t i c XBT d a t a s e t . A. GEOGRAPHIC REGIONS G e o g r a p h i c r e g i o n s w i t h d i f f e r e n t h o r i z o n t a l s c a l e s and a m p l i t u d e s o f eddy v a r i a b i l i t y were d e f i n e d u s i n g t h e q u a s i - s y n o p t i c s e c t i o n s o f each c r u i s e , w i t h t h e a i d o f p r e v i o u s work u s i n g c l i m a t o l o g i c a l d a t a s e t s ( W y r t k i , 1975; Emery, 1983a; Cheney e t a l . , 1983). These i n v e s t i g a t o r s examined t h e g e o g r a p h i c v a r i a b i l i t y o f t h e mesosc a l e s t r u c t u r e w i t h t h e s t a n d a r d d e v i a t i o n s o f : dynamic h e i g h t from a r c h i v e d h y d r o g r a p h i c r e c o r d s , t e m p e r a t u r e and i n f e r r e d dynamic h e i g h t from a r c h i v e d XBT r e c o r d s , and s e a s u r f a c e a l t i m e t r y f r o m SEASAT. A l l t h r e e y i e l d e d s i m i l a r r e s u l t s , w i t h r e g i o n s o f h i g h m e s o s c a l e v a r i a b i l i t y n e ar t h e w e s t e r n boundary c u r r e n t s and low v a r i a b i l i t y i n t h e i n t e r i o r o f t h e ocean b a s i n s and i n t h e e a s t e r n boundary c u r r e n t s . Cheney e t a l . 's r e s u l t s , u s i n g t h e SEASAT a l t i m e t r y , were used t o d e f i n e a p p r o x i m a t e b o u n d a r i e s between r e g i o n s o f h i g h and low eddy v a r i a b i l i t y . These r e s u l t s were c o n s i d e r e d most a p p r o p r i a t e f o r t h i s p u r p o s e due t o t h e g l o b a l c o v e r a g e and even d i s t r i b u t i o n o f t h e SEASAT a l t i m e t r y d a t a . F i g u r e I I I - 1 , a d a p t e d f r o m Cheney e t a l . (1983), shows t h e g e o g r a p h i c v a r i a b i l i t y o f t h e eddy f i e l d w i t h t h e s t a n d a r d d e v i a t i o n o f t h e SEASAT a l t i m e t r y . S i x g e o g r a p h i c r e g i o n s were d e f i n e d u s i n g t h e SEASAT mesos c a l e v a r i a b i l i t y , t h e o b s e r v e d s t r u c t u r e i n t h e q u a s i - s y n o p t i c d a t a s e t and t h e g e o g r a p h i c d i s t r i b u t i o n o f t h e d a t a . The'se r e g i o n s were c l a s s i f i e d , i n a manner s i m i l a r t o t h a t o f Fu (1983), as a r e a s o f h i g h o r low eddy v a r i a b i l i t y . The 6 cm c o n t o u r i n F i g u r e I I I - 1 , was us e d as a g u i d e t o d e l i n e a t e t h e boundary between h i g h - and low-energy r e g i o n s . These g e o g r a p h i c r e g i o n s , c l a s s i f i e d by h i g h - and low-energy l e v e l s , a r e : Figure III-1 Global mesoscale v a r i a b i l i t y from c o l l i n e a r SEASAT altimeter ground tracks. The standard deviation of the altimetry i s contoured i n centimeters. The bold 6 cm contour separates regions of r e l a t i v e l y high and low eddy a c t i v i t y . 24 H i g h - e n e r g y R e g i o n s Low-energy Regions NWA - N o r t h w e s t A t l a n t i c NEA N o r t h e a s t A t l a n t i c NWP - N o r t h w e s t P a c i f i c SA South A t l a n t i c NEP N o r t h e a s t P a c i f i c SP S outh P a c i f i c Two c o m p o s i t e r e g i o n s were d e f i n e d t o r e p r e s e n t t h e combined h i g h - e n e r g y r e g i o n s and t h e combined low-energy r e g i o n s . The HIGH r e g i o n c o m p r i s e s t h e NWA and NWP r e g i o n s ( i . e . t h e h i g h - e n e r g y r e g i o n s ) . The LOW r e g i o n c o m p r i s e s t h e NEA, SA, NEP and SP r e g i o n s ( i . e . t h e low-energy r e g i o n s ) . The g e o g r a p h i c d i s t r i b u t i o n o f t h e q u a s i - s y n o p t i c XBT d a t a and t h e d e m a r c a t i o n o f t h e s i x g e o g r a p h i c r e g i o n s a r e shown i n F i g u r e I I I - 2 . The q u a s i - s y n o p t i c XBT d a t a , f r o m t h e s i n g l e - s h i p s e c t i o n s and t h e m u l t i s h i p / A X B T s u r v e y s , were b i n n e d i n t o t h e a p p r o p r i a t e g e o g r a p h i c r e g i o n s . I f a c r u i s e p a s s e d t h r o u g h b o t h h i g h - and low-energy r e g i o n s , i t was d i v i d e d where t h e s e c t i o n e x h i b i t e d a marked change i n t h e m e s o s c a l e e x p r e s s i o n . The r e s u l t i n g s i n g l e - s h i p s e c t i o n s were d i s c a r d e d i f t h e y h ad l e s s t h a n 25 XBTs o r were l e s s t h a n 1000 km i n l e n g t h . There a r e a t o t a l o f 95 t r a n s - o c e a n i c s i n g l e - s h i p s e c t i o n s ( h e r e a f t e r known as s e c t i o n s ) and 29 m u l t i s h i p / A X B T s u r v e y s ( h e r e a f t e r known as s u r v e y s ) . B. GEOGRAPHIC VARIABILITY OF THE THERMAL STRUCTURE The p u r p o s e o f t h i s s e c t i o n i s t o d e s c r i b e t h e g e o g r a p h i c v a r i a b i l i t y o f t h e b a r o c l i n i c eddy f i e l d as e x p r e s s e d i n t h e t e m p e r a t u r e s t r u c t u r e o f t h e XBT d a t a s e t . T y p i c a l t e m p e r a t u r e s e c t i o n s f r o m each g e o g r a p h i c r e g i o n a r e examined and compared t o t h e g e o g r a p h i c eddy v a r i a b i l i t y r e v e a l e d i n p r e v i o u s works by r e s e a r c h e r s u s i n g c l i m a t o l o g i c a l d a t a s e t s . I t i s c o n s i d e r e d i m p o r t a n t t o examine t h e q u a l i t a t i v e a s p e c t s o f t h e me s o s c a l e v a r i a b i l i t y i n e a c h r e g i o n and t o dem o n s t r a t e t h a t t h e eddy f i e l d s o b s e r v e d i n t h e q u a s i - s y n o p t i c XBT d a t a s e t a r e c o n s i s t e n t w i t h p r e v i o u s o b s e r v a t i o n s . T h r e e d i f f e r e n t c l i m a t o l o g i c a l d a t a s e t s have been u s e d , by o t h e r i n v e s t i g a t o r s , t o examine t h e g l o b a l g e o g r a p h i c v a r i a b i l i t y o f t h e mesoscale Figure III-2 The s i x geographic regions as defined f o r t h i s i n v e s t i g a t i o n are shown with the XBT data set. The regions designated as high eddy energy areas are s t i p p l e d . 26 eddy f i e l d . The g l o b a l map o f t h e eddy k i n e t i c e n ergy computed from t h e h i s t o r i c a l s h i p d r i f t f i l e ( a dapted from W y r t k i et_ a l . , 1976) i s shown i n F i g u r e I I I - 3 . F i g u r e I I I - 1 p r e s e n t s t h e g e o g r a p h i c v a r i a b i l i t y o f t h e eddy f i e l d o b t a i n e d by Cheney e_t a l . (1983) u s i n g t h e s t a n d a r d d e v i a t i o n of SEASAT a l t i m e t r y . The s t a n d a r d d e v i a t i o n o f t e m p e r a t u r e a t 260 m, based on a v a r i a b l e g r i d a n a l y s i s o f t h e XBT f i l e f o r t h e N o r t h P a c i f i c and N o r t h A t l a n t i c , has been a d a p t e d from Emery (1983a) i n F i g u r e I I I - 4 . These t h r e e d i f f e r e n t s t u d i e s o f f e r v i e w s of t h e g e o g r a p h i c v a r i a b i l i t y o f t h e g l o b a l eddy f i e l d t h a t show r e g i o n s o f h i g h eddy a c t i v i t y n e ar t h e w e s t e r n boundary c u r r e n t s and low eddy a c t i v i t y i n t h e i n t e r i o r and e a s t e r n boundary c u r r e n t r e g i o n s . As p r e v i o u s l y d i s c u s s e d , t h e 6 cm c o n t o u r of the SEASAT a l t i m e t r y d e v i a t i o n map ( F i g u r e I I I - 1 ) has been u s e d as a g u i d e f o r d e l i n e a t i n g t h e h i g h - and low-energy r e g i o n s ( F i g u r e I I I - 2 ) . I n F i g u r e I I I - 1 , h i g h v a l u e s o f 12 and 9 cm a r e f o u n d i n t h e NWA and NWP, r e s p e c t i v e l y . Low v a l u e s o f 4 cm a r e f o u n d i n t h e NEA, w i t h low v a l u e s o f 3 cm i n t h e SA, NEP and SP. The s t a n d a r d d e v i a t i o n o f t h e a l t i m e t r y r e p r e s e n t s t h e eddy p o t e n t i a l energy (EPE) o f t h e b a r o t r o p i c s i g n a l . S i n c e o n l y a t o t a l o f 24 days o f d a t a were used ( i n A u g u s t o f 1978), t h e e n e r g i e s a t p e r i o d s l o n g e r t h a n 24 days were i n a d e q u a t e l y sampled. Fu (1983) d e t e r m i n e d t h e t r a n s f e r f u n c t i o n o f t h i s 24-day f i l t e r and f o u n d t h a t t h e b u l k o f t h e m e s o s c a l e energy a t p e r i o d s f r o m 50 t o 150 days was s e v e r e l y s u p p r e s s e d . The eddy k i n e t i c energy (EKE) map ( F i g u r e I I I - 3 ) , as d e t e r m i n e d f r o m s h i p d r i f t d a t a by W y r t k i et^ a l . (1976), r e p r e s e n t s t h e b a r o t r o p i c s i g n a l . . Highl- and low-energy r e g i o n s , s i m i l a r t o t h o s e o f F i g u r e I I I - 1 , can be d e f i n e d u s i n g t h e 600 c m 2 / s 2 c o n t o u r . The EKE has maximum v a l u e s o f o v e r 2000 c m 2 / s 2 i n t h e NWA and o v e r 1000 c m 2 / s 2 i n t h e NWP. Minimum v a l u e s of about 300 c m 2 / s 2 o c c u r i n t h e SA and SP. The s h i p d r i f t d a t a were n o t c o r r e c t e d f o r d r i f t due t o t h e w i n d a c t i n g on t h e v e s s e l s , t h u s o v e r e s t i m a t i n g t h e EKE. T h i s o v e r e s t i m a t e and t h e s e a s o n a l s i g n a l o f t h e w i n d s and c u r r e n t s e x p l a i n s t h e d i s t i n c t d i f f e r e n c e between F i g u r e I I I - 1 and I I I - 3 i n t h e e q u a t o r i a l r e g i o n s o f b o t h t h e P a c i f i c and A t l a n t i c Oceans. F i g u r e I I I - 1 shows d e v i a t i o n s of SEASAT a l t i m e t r y o f 5 cm i n t h e e q u a t o r i a l r e g i o n s , w h i c h a r e about o n e - h a l f o f t h e maximum v a l u e s i n t h e h i g h - e n e r g y r e g i o n s . F i g u r e I I I - 3 has e q u a t o r i a l v a l u e s o f a b o u t 1000 c m 2 / s 2 w h i c h a r e e q u a l t o t h e maximum v a l u e s i n t h e NWA. The SEASAT a l t i m e t r y i m p l i e s a r a t i o o f o n e - q u a r t e r f o r t h e eddy k i n e t i c e n e r g i e s i n t h e e q u a t o r i a l r e g i o n s compared t o t h e w e s t e r n boundary c u r r e n t r e g i o n s . 27 Figure III-4 Standard deviation of temperature a t 260 m based on a v a r i a b l e g r i d analysis of the NODC XBT f i l e north of 10°S. 28 The s h i p d r i f t d a t a p r o v i d e eddy k i n e t i c e n e r g i e s two t o f o u r t i m e s g r e a t e r f o r t h e e q u a t o r i a l r e g i o n s , t h a n t h e r e l a t i v e c o m p a r i s o n o f t h e SEASAT EKEs. The r e l a t i v e l y h i g h e r eddy e n e r g i e s r e p o r t e d by W y r t k i et_ a l . (1976) i n t h e e q u a t o r i a l r e g i o n s a r e due t o t h e s e a s o n a l v a r i a b i l i t y o f t h e e q u a t o r i a l c u r r e n t and t r a d e w i n d s y s t e m s , and t h e h i g h - f r e q u e n c y ( i . e . p e r i o d s on t h e o r d e r o f days and weeks) s i g n a l o f t h e w i n d s . The s i g n i f i c a n t s e a s o n a l v a r i a b i l i t y o f t h e m e r i d i o n a l p o s i t i o n and magnitude o f t h e s e c u r r e n t s and winds ( W y r t k i e t a l . , 1981) w i l l i n d u c e an " a p p a r e n t " eddy s i g n a l i n t o t h e s h i p d r i f t d a t a t h a t w i l l n o t be a p p a r e n t i n . t h e 24-day r e c o r d o f the SEASAT a l t i m e t r y d a t a . I t s h o u l d be n o t e d , t h a t t h e h i g h - e n e r g y r e g i o n s a s s o c i a t e d w i t h t h e w e s t e r n boundary c u r r e n t s , as d e l i n e a t e d w i t h t h e s h i p d r i f t d a t a ( F i g u r e I I I - 3 ) , a r e s p a t i a l l y s m a l l e r t h a n t h e h i g h - e n e r g y r e g i o n s d e l i n e a t e d w i t h t h e SEASAT a l t i m e t r y ( F i g u r e I I I - 1 ) . The s t a n d a r d d e v i a t i o n o f t e m p e r a t u r e a t 260 m f o r t h e N o r t h P a c i f i c and N o r t h A t l a n t i c ( F i g u r e I I I - 4 ) r e p r e s e n t s t h e m i d - t h e r m o c l i n e t e m p e r a t u r e v a r i a b i l i t y w h i c h c a n be r e l a t e d t o t h e b a r o c l i n i c m e s o s c a l e a c t i v i t y (Emery, 1983a). The t e m p e r a t u r e v a r i a b i l i t y c o r r e s p o n d s t o t h e EPE o f t h e b a r o c l i n i c s i g n a l a t 260 m. The h i g h - and low-energy a r e a s i n F i g u r e I I I - 2 can be a p p r o x i m a t e d by t h e 1.0°C c o n t o u r o f F i g u r e I I I - 4 . The NWA and NWP have maximum s t a n d a r d d e v i a t i o n s o f o v e r 3.0 and 4.0°C, r e s p e c t i v e l y , w h i l e t h e NEA and NEP have minimum v a l u e s l e s s t h a n 0.5°C. The t e m p e r a t u r e d e v i a t i o n map shows h i g h v a l u e s i n t h e e q u a t o r i a l r e g i o n s w h i c h a r e r e l a t i v e l y s m a l l e r t h a n t h o s e o f t h e s h i p d r i f t d a t a ( F i g u r e I I I - 3 ) , b u t r e l a t i v e l y g r e a t e r t h a n t h o s e o f t h e SEASAT a l t i m e t r y ( F i g u r e I I I - 4 ) . T h i s i s c o n s i s t e n t w i t h t h e l i m i t a t i o n s o f each d a t a s e t f o r e x a m i n i n g t h e eddy v a r i a b i l i t y on a g l o b a l s c a l e . The EKEs o f W y r t k i e t a l . (1976) a r e o v e r e s t i m a t e d due t o the w i n d s . The SEASAT a l t i m e t r y w i l l u n d e r e s t i m a t e t h e eddy v a r i a b i l i t y due t o t h e s h o r t d a t a r e c o r d o f 24 days. The t e m p e r a t u r e v a r i a b i l i t y w i l l n o t be b i a s e d by e i t h e r t h e s u r f a c e w i n d s n o r t h e l e n g t h o f t h e d a t a r e c o r d , however, i t w i l l m i s s an i m p o r t a n t p a r t o f t h e b a r o t r o p i c v a r i a b i l i t y . I n summary, t h e s h i p d r i f t d a t a , t h e SEASAT a l t i m e t r y , and t h e te m p e r a t u r e d e v i a t i o n s a r e t h r e e d i f f e r e n t r e p r e s e n t a t i o n s o f t h e g l o b a l eddy v a r i a b i l i t y . W y r t k i e t a l . (1976) e s t i m a t e d t h e EKEs w i t h t h e s h i p d r i f t d a t a . The SEASAT a l t i m e t r y (Cheney e_t a l . , 1983) r e p r e s e n t s t h e EPE o f t h e b a r o t r o p i c eddy v a r i a b i l i t y , and t h e t e m p e r a t u r e d e v i a t i o n s (Emery, 1983a) c o r r e s p o n d t o t h e EPE o f t h e b a r o c l i n i c s i g n a l . The l i m i t a t i o n s o f each have been d i s c u s s e d . 29 The t e m p e r a t u r e d e v i a t i o n maps of Emery (1983a) a r e t h e most a p p r o p r i a t e f o r c o m p a r i s o n w i t h t h e r e s u l t s o f t h i s i n v e s t i g a t i o n , w i t h the e x c e p t i o n t h a t t h e s e maps p r o v i d e no coverage s o u t h o f 10°S. The f o l l o w i n g d i s c u s s i o n w i l l examine t y p i c a l q u a s i - s y n o p t i c s e c t i o n s and maps o f t h e te m p e r a t u r e s t r u c t u r e f o r e a ch g e o g r a p h i c r e g i o n and compare them w i t h r e s u l t s o f t h e above a n a l y s e s . N o r t h w e s t A t l a n t i c The N o r t h w e s t A t l a n t i c r e g i o n , d e f i n e d i n F i g u r e I I I - 2 , i s a r e g i o n o f h i g h eddy a c t i v i t y . The i n t e n s i t y o f t h e eddy f i e l d i n c r e a s e s as one approaches t h e G u l f S tream ( F i g u r e I I I - 5 ) . The mean c i r c u l a t i o n o f t h e r e g i o n i s dominated by t h e G u l f Stream System ( F o f o n o f f , 1981), c o n s i s t i n g o f t h e F l o r i d a C u r r e n t , t h e G u l f S t r e a m and t h e N o r t h A t l a n t i c D r i f t . C h a r a c t e r i s t i c mesoscale f e a t u r e s i n c l u d e G u l f Stream meanders and t h e r e s u l t i n g warm- and c o l d - c o r e r i n g s i n t h e c o n t i n e n t a l s l o p e w a t e r s and S a r g a s s o Sea, r e s p e c t i v e l y . A p p r o x i m a t e l y t e n c o l d - c o r e r i n g s c o - e x i s t i n t h e S a r g a s s o Sea a t a s i n g l e t i m e ( R i c h a r d s o n , 1983). F i v e t o e i g h t c o l d - c o r e r i n g s f o r m p e r y e a r w i t h d i a m e t e r s o f a p p r o x i m a t e l y 200 km and r a i s e d i s o t h e r m s i n t h e i r c e n t e r s o f up t o 600 m. The warm-core a n t i c y c l o n i c r i n g s form i n a t r i a n g u l a r r e g i o n bounded by t h e c o n t i n e n t a l s l o p e on t h e n o r t h and t h e G u l f Stream on t h e s o u t h ( S a u n d e r s , 1971). The l a r g e s t r i n g s , 200 t o 300 km i n d i a m e t e r form t o t h e e a s t o f Georges Bank, however s m a l l e r r i n g s (100 km) f o r m t o t h e west. T y p i c a l l y , f i v e warm r i n g s f o r m p e r y e a r w i t h a v e r a g e d i a m e t e r s s m a l l e r t h a n t h a t o f t h e c o l d r i n g s ( L a i and R i c h a r d s o n , 1977). A p p r o x i m a t e l y t h r e e warm-core r i n g s e x i s t a t a s i n g l e t i m e ( R i c h a r d s o n , 1983). T w e n t y - t h r e e s e c t i o n s were o b t a i n e d f o r t h e NWA. The SXBT d a t a c o l l e c t e d by t h e HMCS P r e s e r v e r a c r o s s t h e N o r t h A t l a n t i c i n O c t o b e r 1982 ( F i g u r e I I I - 6 ) e x h i b i t t h e s a l i e n t mesoscale f e a t u r e s o f t h e NWA. F i g u r e I I I - 6 a shows t h e SXBT l o c a t i o n s . The G u l f Stream, a warm-core r i n g , a c o l d - c o r e r i n g and s e v e r a l s m a l l e r c o l d e d d i e s i n t h e S a r g a s s o Sea can be c l e a r l y seen i n F i g u r e I I I - 6 b . The G u l f Stream a t 55°W s e p a r a t e s a warm r i n g a t 57°W and a c o l d r i n g a t 51°W. The warm r i n g has a w i d t h o f 350 km w i t h a d e p r e s s i o n o f t h e 10°C i s o t h e r m o f about 200 m. The c o l d r i n g has a w i d t h o f 450 km w i t h an e l e v a t i o n o f t h e 14°C i s o t h e r m o f about 300 m. Between 47°W and 32°W ( F i g u r e I I I - 6 b ) t h e r e a r e t h r e e s m a l l e r e d d i e s w i t h w i d t h s o f 250 t o 300 km. The upward d e f l e c t i o n s o f t h e 15°C i s o t h e r m a r e 200 m and 175 m f o r t h e e d d i e s a t 45°W and 60N 140E 170E 16QU 130U 100U 70U 40U 30N 2 ° C BON 30N 30S flOE 140E 170E 160U 130U 100U- 70U 40U 10U 1 60S 20E 0 - Oyashio NECC - North Equatorial Countercurrent LC - Labrador Current K - Kuroahio EOC Equatorial Undercurrent NAD - North A t l a n t i c D r i f t KE - Kuroshio Extension SEC South Equatorial Current GS - Gulf Stream AS — Alaskan Stream EAC East Australian Current FC - F l o r i d a Current NFC - North P a c i f i c Current PC Peru Current BC - B r a z i l Current CC - C a l i f o r n i a Current AACC - Antarctic Circumpolar Current BEC — Benguela Current NBC - North Equatorial Current Ul o Figure III-5 Surface currents of the P a c i f i c and A t l a n t i c Oceans. 31 O N E S Q U A D R O N . 1-7 O C T O B E R 1982. 6 Q F 7 0 U 6 0 U SOU 40U 3 0 U 2 0 U 10U — J 1 _ — r r ? *a*i»»atgflB*'-*" * r'""*— A. SON 5 0 N 5 0 N 4 0 N 4 0 N 301 1 3 0 N 6 0 U 5QU 4 0 U HMCS PRESERVER. 1-7 OCTOBER 1 9 8 2 . 3 0 U 2 0 U 10U r / • .'\,-' , 1 ,> / SST - SOLID LINE r V SSS - DRSHEO 60 V 54 W 43 V 42 V RRNGE i ONE TICK = 300 KM 36 V 30 W 24 V 18 V 12 V 6 W Figure III-6 SXBT section (PE-071082) collected by the HMCS Preserver, i n October 1982 across the North Atlantic. a. SXBT locations. b. Temperature (*C) section. 32 41°W, r e s p e c t i v e l y . The eddy a t 34"W has a 275 m d e f l e c t i o n o f t h e 14°C i s o t h e r m . A f u r t h e r sample s e c t i o n , o b t a i n e d from t h e USN m u l t i s h i p s u r v e y i n December 1976 ( F i g u r e I I I - 7 ) ( e a s t o f the G u l f Stream r i n g c o n c e n t r a t i o n s ) a t 33°N, shows t h r e e c o l d e d d i e s a t 52°W, 38°W and 32°W. These e d d i e s have w i d t h s of 450, 400 and 350 km, r e s p e c t i v e l y , w i t h v e r t i c a l d e f l e c t i o n s o f t h e 17°C i s o t h e r m o f 200 m. S i x s u r v e y s were o b t a i n e d f o r t h e NWA r e g i o n . Four o f t h e s e a r e t h e m u l t i s h i p USN s u r v e y s examined by Emery e_t a l . (1980) f o r the f r a c t i o n o f v e r t i c a l i s o t h e r m d e f l e c t i o n s a s s o c i a t e d w i t h c l o s e d e d d i e s . Seventeen c l o s e d e d d i e s were i d e n t i f i e d west of 30°W w i t h mean d i a m e t e r s o f 150 km. These i n v e s t i g a t o r s n o t e d t h a t about o n e - h a l f o f t h e e d d i e s were G u l f Stream r i n g s . I n d i v i d u a l maps o f t h e s e s u r v e y s w i l l n ot be examined h e r e i n l i g h t o f t h i s d e t a i l e d work. I t w i l l s u f f i c e t o say t h a t t h e i n d i v i d u a l s e c t i o n s o b t a i n e d from t h e s e s u r v e y s , and t h e s u r v e y s as a whole, e x h i b i t t h e c h a r a c t e r i s t i c m e s o s c a l e s t r u c t u r e o f t h e NWA. The two m u l t i s h i p s u r v e y s c o l l e c t e d by t h e CAF, s o u t h e a s t o f Newfoundland, a r e i n F i g u r e I I I - 8 . B o t h s u r v e y s show t h e s t r o n g s u b s u r f a c e t h e r m a l f r o n t o f t h e L a b r a d o r C u r r e n t m e e t i n g t h e N o r t h A t l a n t i c D r i f t . I n t h e O c t o b e r 1981 s u r v e y ( F i g u r e I I I - 8 a ) , t h e f r o n t has a n o r t h e a s t - s o u t h w e s t a l i g n m e n t . W i t h a s u r v e y w i d t h o f 110 km, i t i s n o t s u r p r i s i n g t h a t no c l o s e d e d d i e s c a n be i d e n t i f i e d . The f r o n t r e t a i n s i t s g e n e r a l n o r t h e a s t - s o u t h w e s t a l i g n m e n t i n t h e June 1983 s u r v e y ( F i g u r e I I I - 8 b ) , w i t h t h e a d d i t i o n o f an e a s t w a r d c o l d w a t e r e x c u r s i o n o f about 150 km. There a r e a l s o a l t e r n a t i n g n e a r - m e r i d i o n a l bands o f warm and c o l d w a t e r t o t h e e a s t o f t h e f r o n t . A g a i n , t h e l i m i t e d w i d t h o f t h e s u r v e y (200 km) does n o t p e r m i t t h e h o r i z o n t a l s t r u c t u r e o f t h e s e f e a t u r e s t o be r e s o l v e d any f u r t h e r . N o r t h w e s t P a c i f i c The N o r t h w e s t P a c i f i c ( F i g u r e I I I - 2 ) i s a r e g i o n o f h i g h eddy a c t i v i t y w h i c h i n c l u d e s t h e K u r o s h i o , t h e K u r o s h i o E x t e n s i o n , t h e Oy a s h i o and t h e w e s t e r n p o r t i o n t h e N o r t h P a c i f i c C u r r e n t . B o t h t h e K u r o s h i o and t h e O y a s h i o meander and shed warm- and c o l d - c o r e r i n g s s i m i l a r t o t h e G u l f Stream. Recent i n v e s t i g a t i o n s o f h i s t o r i c a l d a t a i n t h e r e g i o n ( R i c h a r d s o n , 1983) documented t h e c o e x i s t a n c e o f 13 c o l d r i n g s and two warm r i n g s i n t h e summer o f 1939, and s u g g e s t e d t h a t t h e c o l d r i n g s form a t t h r e e o r f o u r s p e c i f i c s i t e s . A s y n o p t i c  34 LONGITUDE WEST 50 48 46 44 42 40 38 36 34 8-1 1 L_ 1 I I L_ I I I ' I l l I I 32 cc o LU D - -3 SO 48 FIVE SON. 2 5 - 2 7 JUN 83, TEMP: 15Q-2QQ t l . 1 I I I T I I I I 40 38 36 34 32 Figure III-8 Maps of temperature (°C) ve r t i c a l l y - a v e r a g e d from 150 to 200 m i n the NWA, from multiship surveys c o l l e c t e d by the CAF. a. Survey PE-071081, October 1981. b. Survey FR-270683, June 1983. 35 s t u d y r e p o r t e d by Cheney (1977) i d e n t i f i e d t h r e e warm and two c o l d r i n g s . One o f t h e r i n g s had a d i a m e t e r o f 250 km. K i t a n o (1975) examined 154 warm-core r i n g s from t h e K u r o s h i o and t h e O y a s h i o and f o u n d an a v e r a g e d i a m e t e r o f 140 km. The XBT d a t a s e t o b t a i n e d f o r t h e NWP c o m p r i s e s two m u l t i s h i p s u r v e y s c o n d u c t e d by t h e USN ( W i l s o n and Dugan, 1978) and two s e c t i o n s a c q u i r e d f r o m t h e NODC. F i g u r e I I I - 9 shows two sample t e m p e r a t u r e s e c t i o n s i n t h e r e g i o n (one f r o m each o f t h e USN s u r v e y s ) , e a s t w a r d o f t h e c o n c e n t r a t i o n s o f K u r o s h i o and O y a s h i o r i n g s . S e c t i o n 54-000575 ( F i g u r e I I I - 9 a ) was t a k e n a t 37.5°N, n o r t h o f t h e mean K u r o s h i o a x i s ( W i l s o n and Dugan, 1978). Three c o l d e d d i e s can be i d e n t i f i e d a t 165°E, 172°E and 178°E (pres u m a b l y f r o m t h e O y a s h i o ) , and one warm eddy a t 170°E (presumably f r o m t h e K u r o s h i o ) . These f e a t u r e s have w i d t h s o f 180, 250, 180 and 250 km, r e s p e c t i v e l y , w i t h d i s p l a c e m e n t s o f t h e 11°C i s o t h e r m o f 170, 350, 200 and 300 m. S e c t i o n 40-001175 was t a k e n s o u t h o f t h e mean K u r o s h i o a x i s a t 31.5°N. Three c o l d e d d i e s a r e d i s c e r n a b l e a t 163°E, 172°E and 176°E, w i t h w i d t h s o f 180, 200 and 280 km, r e s p e c t i v e l y . The d e f l e c t i o n s o f t h e 14°C i s o t h e r m f o r t h e s e f e a t u r e s a r e 220, 170 and 140 m, r e s p e c t i v e l y . Emery e t a l . (1980) examined t h e s e two USN s u r v e y s f o r t h e f r a c t i o n o f v e r t i c a l i s o t h e r m d e f l e c t i o n s a s s o c i a t e d w i t h c l o s e d e d d i e s . A g a i n , t h e i n d i v i d u a l maps o f t h e s e s u r v e y s w i l l n o t be examined h e r e . A t o t a l o f f i v e c l o s e d e d d i e s were i d e n t i f i e d . N o r t h e a s t A t l a n t i c The N o r t h e a s t A t l a n t i c i s a r e g i o n o f low eddy a c t i v i t y r e l a t i v e t o t h e w e s t e r n boundary c u r r e n t r e g i o n s . G e n e r a l l y , t h e mean c i r c u l a t i o n i s weak. The N o r t h A t l a n t i c D r i f t c r o s s e s t h e m i d - A t l a n t i c r i d g e f r o m t h e west i n two b r a n c h e s ( S a u n d e r s , 1982) n o r t h o f 45°N and a t 35°N ( n o r t h and s o u t h o f t h e A z o r e s ) w h i c h t u r n n o r t h and s o u t h , r e s p e c t i v e l y . G o u l d (1983) i d e n t i f i e s f o u r d i s t i n c t a r e a s where m e s o s c a l e f e a t u r e s can be fo u n d . I n t h e f i r s t a r e a , p e r t u r b a t i o n s o f t h e s o u t h e r n edge o f t h e p o l a r f r o n t a r e m a n i f e s t e d i n l a r g e i s o t h e r m d i s p l a c e m e n t s n o r t h w e s t o f a l i n e f r o m 40°N 30°W t o 50°N 20°W. The meanderings o f t h e p o l a r f r o n t ( G o u l d , 1983) have t y p i c a l r a d i i on t h e o r d e r o f 100 t o 150 km w i t h l a r g e g e o p o t e n t i a l anomaly V 01 co cn I H H H I VO 10 S S T 2 0 4 0 0 D E P T H ( M E T E R S ) 3 0 0 2 0 0 100 4 0 0 3 0 0 2 0 0 D E P T H ( M E T E R S ) 10 2 0 S S T cn ft n P CD 10 S S T 2 0 4 0 0 D E P T H ( M E T E R S ) 3 0 0 2 0 0 100 co CO CO o r~ 3 0 0 2 0 0 100 D E P T H ( M E T E R S ) 10 2 0 S S T 9C 37 f l u c t u a t i o n s . Howe and T a i t (1967) examined a c o l d eddy n e a r 53°N and 19°W, c o n f i n e d t o t h e upper 500 m. T h i s f e a t u r e was e l o n g a t e d i n a n o r t h - s o u t h d i r e c t i o n and measured a p p r o x i m a t e l y 200 km by 100 km. I t was s p e c u l a t e d t h a t t h i s was a p i n c h e d o f f meander of t h e N o r t h A t l a n t i c D r i f t . The second a r e a i s above and t o t h e e a s t of. t h e m i d - A t l a n t i c r i d g e , j u s t s o uthwest o f the A z o r e s . I n t e n s e l e n s e s o f M e d i t e r r a n e a n w a t e r have been r e p o r t e d w i t h d i a m e t e r s o f about 50 km. These e d d i e s a r e fo u n d a t dept h s between 700 and 1200 m and have no t h e r m o h a l i n e s i g n a t u r e above 500 m. G o u l d (1983) a l s o r e p o r t e d a c y c l o n i c eddy a t 33°N 32°W w i t h a d i a m e t e r o f 100 km. I t was o b s e r v e d s e p a r a t i n g from a f r o n t a l f e a t u r e i n t h e summer o f 1981. The t h i r d a r e a i s i n t h e z o n a l band o f 30°N t o 40°N between 12°W and 20°W. The eddy v a r i a b i l i t y i s r a t h e r p o o r l y d e f i n e d , b u t G o u l d s u g g e s t s t h a t i t may r e f l e c t t h e i n f l u e n c e o f t h e M e d i t e r r a n e a n o u t f l o w . A f o u r t h a r e a , e a s t o f a l i n e f r o m t h e UK t o t h e A z o r e s , appears t o have v e r y l i t t l e m e s o s c a l e a c t i v i t y . The XBT d a t a s e t o b t a i n e d f o r t h e NEA c o n s i s t s o f 16 s e c t i o n s and f o u r s u r v e y s . F i g u r e I I I - 6 b and F i g u r e 111-10 a r e t h e t r a n s - o c e a n i c s e c t i o n s f o r t h e CAF c r u i s e s i n O c t o b e r 1982 and O c t o b e r 1981, r e s p e c t i v e l y . B o t h s e c t i o n s i l l u s t r a t e t h e r e d u c e d mesoscale a c t i v i t y o f t h e NEA, e a s t o f about 30°W. F i g u r e I I I - 6 b a l s o p r o v i d e s a r e a l i z a t i o n o f t h e m e s o s c a l e s t r u c t u r e i n two o f t h e f o u r a r e a s o b s e r v e d above. Between 32°W and 20°W, t h e t e m p e r a t u r e s t r u c t u r e has numerous p e r t u r b a t i o n s between 100 t o 200 km i n w i d t h , w i t h i s o t h e r m d e f l e c t i o n s o f about 100 m, c h a r a c t e r i s t i c o f t h e a r e a n o r t h w e s t o f t h e A z o r e s . E a s t o f 20°W, t h e s t r u c t u r e i s r e l a t i v e l y q u i e s c e n t . The CAF s u r v e y c o n d u c t e d n o r t h w e s t o f t h e A z o r e s ( F i g u r e 111-11) shows a warm eddy a t 30°W w i t h a d i a m e t e r o f 100 km. From t h e t e m p e r a t u r e s e c t i o n i n F i g u r e I I I - 6 , t h e eddy can be seen t o be c o n f i n e d t o t h e up p e r 500 m o f t h e w a t e r column and have a maximum i s o t h e r m (14°C) d e f l e c t i o n o f about 40 m. Three o f t h e N o r t h A t l a n t i c USN s u r v e y s e x t e n d s u f f i c i e n t l y e a s t w a r d t o be i n c l u d e d i n an e x a m i n a t i o n o f t h e NEA. S u r v e y 64-000776 i s n o r t h o f t h e A z o r e s , w h i l e 93-000577 and 21-001077 a r e s o u t h o f t h e A z o r e s . West o f 35°W Emery et^ a l . (1980) f o u n d no c l o s e d e d d i e s , a l t h o u g h v e r t i c a l i s o t h e r m d e f l e c t i o n s s i m i l a r t o t h o s e o f F i g u r e I I I - 6 b can be f o u n d i n a l l t h e s e c t i o n s t a k e n f r o m t h e s e s u r v e y s . 38 HMCS SAQUENAY. 2-8 OCTOBER 1981, 1 * SST - SOLID L INE SSS - DASHED 1 i i i i i i i i i i in i II n u n i n mi n i I II III III 111 1111,1 58 V 52 V 46 V 40 V RRNGE : ONE T ICK = 300 KM 3 4 W 28 V 22 V 16 V 10 V Figure III-10 Temperature (°C) section (SY-051081) collected by the HMCS Saguenay (CAF) across the North Atlantic i n October 1981. 33 9- o Q ZD cn- 31 I LONGITUDE WEST 29 27 25 23 _ J I I _ ! I I L_ * 4 • • • • - .•14. 1 4 , w1-4 14 1 I I ~ \ r • * 13 33 31 29 27 25 ONE SON. 3-4 OCT 82. TEMP: 150-200 M. 23 -5 •cn Figure 111-11 Map of vertically-averaged temperature (°C) from 150 to 200 m i n the NBA obtained by the CAF, October 1982 (MK-041082). 39 South A t l a n t i c The S o u t h A t l a n t i c r e g i o n , d e f i n e d i n F i g u r e I I I - 2 , has r e l a t i v e l y l i t t l e m e s o s c a l e eddy a c t i v i t y . I t i s a low i n t h e maps of b o t h t h e eddy k i n e t i c energy ( F i g u r e I I I - 3 ) and t h e s t a n d a r d d e v i a t i o n o f SEASAT a l t i m e t r y ( F i g u r e I I I - 1 ) . The r e g i o n i s bounded by t h e South A t l a n t i c E q u a t o r i a l C u r r e n t , t h e B r a z i l C u r r e n t , t h e A n t a r c t i c C i r c u m p o l a r C u r r e n t and t h e Ben g u e l a C u r r e n t . There have been v i r t u a l l y no o b s e r v a t i o n a l s t u d i e s o f t h e eddy v a r i a b i l i t y o f t h e r e g i o n . The d a t a s e t a c q u i r e d f o r t h e SA c o n s i s t s o f two z o n a l s e c t i o n s from NODC ( F i g u r e 111-12). The s t a t i o n s p a c i n g s a r e about 100 km, so e d d i e s s m a l l e r t h a n 200 km i n w i d t h c a n n o t be r e s o l v e d . S e c t i o n 40-190283 was t a k e n i n F e b r u a r y 1983 a t 24° S. S e v e r a l m e s o s c a l e f e a t u r e s a r e d i s c e r n a b l e : a warm eddy a t 27°W, a c o l d eddy a t 20°W and an eddy a t 5°W, w i t h a c o l d c o r e above 200 m and a warm c o r e below 200 m. The f e a t u r e s have w i d t h s o f 400, 400 and 200 km, r e s p e c t i v e l y , w i t h v e r t i c a l d e f l e c t i o n s o f t h e 15°C i s o t h e r m o f 25, 25 and 50 m. S e c t i o n 04-310383, t a k e n a t 12°S, has c o l d e d d i e s a t 34°W and 2°E. T h e i r w i d t h s a r e 300 and 500 km, r e s p e c t i v e l y , w i t h d e f l e c t i o n s o f t h e 12° i s o t h e r m o f 40 and 75 m. N o r t h e a s t P a c i f i c The N o r t h e a s t P a c i f i c r e g i o n has been d e f i n e d as t h e low eddy a c t i v i t y r e g i o n o f t h e s u b t r o p i c a l and s u b p o l a r g y r e s , bounded i n t h e n o r t h by t h e A l a s k a n Stream and i n t h e s o u t h by t h e N o r t h E q u a t o r i a l C o u n t e r c u r r e n t . B e r n s t e i n (1983) p r o v i d e d a r e v i e w o f t h e eddy v a r i a b i l i t y o f t h e NEP and d e s c r i b e d a g e n e r a l i n c r e a s e i n t h e mesos c a l e a c t i v i t y as one p r o c e e d e d t o w a r d t h e t r o p i c s . T h i s i s c o n s i s t e n t w i t h t h e z o n a l band of h i g h e r eddy a c t i v i t y shown i n t h e d e v i a t i o n s o f SEASAT a l t i m e t r y ( F i g u r e I I I - 1 ) between 5°N and 25°N. Royer ( 1 9 7 8 ) , i n a m e r i d i o n a l h y d r o g r a p h i c s e c t i o n , f o u n d t h e e d d i e s t o be few i n number and weak between 54°N and 34°N. T h e i r t y p i c a l a m p l i t u d e s were 5 dyn-cm w i t h w i d t h s o f about 40 km. Between 34°N and 22°N t h e eddies,.were more numerous w i t h t y p i c a l a m p l i t u d e s o f 10 t o 15 dyn-cm and w i d t h s o f 150 t o 200 km. Roden (1980) f o u n d e d d i e s n o r t h and s o u t h o f t h e s u b t r o p i c a l f r o n t , n o r t h o f H a w a i i a t 30°N. B e r n s t e i n and White (1974) a n a l y s e d a d a t a s e t n e a r H a w a i i s o u t h o f t h e s u b t r o p i c a l f r o n t a t 25°N. E d d i e s a p p e a r e d r e g u l a r l y i n t h e d a t a w i t h average i s o t h e r m p e r t u r b a t i o n s o f about 40 m and d i a m e t e r s o f 40 Figure III-12 Temperature (•C) sections from the NODC i n the SA. a. Section 40-190283, February 1983. b. Section 04-310383, March 1983. 41 200 km- The H a w a i i t o T a h i t i S h u t t l e E x p e r i m e n t ( W y r t k i e t a l . 1981; W y r t k i , 1982) i d e n t i f i e d two t y p e s o f e d d i e s d r i f t i n g westward w i t h t h e N o r t h E q u a t o r i a l C u r r e n t . The f i r s t t y p e appeared a t 158°W near 20°N, s o u t h of Oahu, on n i n e o f t h e 26 s e c t i o n s and was e x t e n s i v e l y s t u d i e d by P a t z e r t (1969). These c o l d e d d i e s were formed t o t h e west o f t h e i s l a n d o f H a w a i i and had w i d t h s on t h e o r d e r o f 200 km w i t h v e r t i c a l d i s p l a c e m e n t s o f t h e 14°C i s o t h e r m o f about 60 m. The second t y p e appeared i n t h e N o r t h E q u a t o r i a l C u r r e n t between 14°N and 19°N. There were c o l d e d d i e s p r e s e n t i n t h e m e r i d i o n a l s e c t i o n s between 150°W and 158°W, 50% o f t h e t i m e . These e d d i e s ranged i n w i d t h from 150 t o 350 km w i t h p e r t u r b a t i o n s i n t h e 14°C i s o t h e r m o f 40 t o 65 m i n a m p l i t u d e . W y r t k i f o u n d no o b v i o u s r e l a t i o n s h i p between eddy d i a m e t e r s and a m p l i t u d e s . I m m e d i a t e l y s o u t h , i s t h e N o r t h E q u a t o r i a l C o u n t e r c u r r e n t , a s t r o n g s e a s o n a l l y v a r y i n g e a s t w a r d c u r r e n t . L e g e c k i s (1977) d i s c o v e r e d meanders o c c u r r i n g when t h e c u r r e n t f l o w i s s t r o n g e s t , i n September t o J a n u a r y , w i t h z o n a l w a v e l e n g t h s o f 1000 km and n o r t h - s o u t h a m p l i t u d e s o f 100 km. The d a t a o b t a i n e d f o r t h e NEP c o n s i s t o f 37 s e c t i o n s ( s i x f r o m t h e CAF and 32 f r o m t h e NODC), and 16 s u r v e y s . F i g u r e 111-13 i s a t y p i c a l s e c t i o n t a k e n by t h e CAF ( f r o m H a w a i i t o Vancouver I s l a n d ) t h a t i l l u s t r a t e s t h e d i f f e r e n c e i n t h e m e s o s c a l e s t r u c t u r e on e i t h e r s i d e o f t h e N o r t h P a c i f i c S u b t r o p i c a l F r o n t a t 35°N. C l i m a t o l o g i c a l l y , t h e s u b t r o p i c a l f r o n t i s d e f i n e d as t h e n o r t h e r n l i m i t o f t h e N o r t h P a c i f i c C e n t r a l Water, w h i c h has w i n t e r t i m e t e m p e r a t u r e s g r e a t e r t h a n 18°C and s a l i n i t i e s g r e a t e r t h a n 34.8 x 10~3. Sou t h o f t h e f r o n t , t h r e e c o l d e d d i e s can be i d e n t i f i e d a t 22°N, 25°N and 34°N. T h e i r w i d t h s a r e 200, 350 and 150 km, r e s p e c t i v e l y , w i t h v e r t i c a l d i s p l a c e m e n t s o f t h e 11°C i s o t h e r m o f 30 m. N o r t h o f 35°N, t h e t h e r m a l s t r u c t u r e i s r e l a t i v e l y q u i e s c e n t . The SXBT s e c t i o n c o l l e c t e d by t h e CAF i n November 1982 ( F i g u r e 111-14) e x h i b i t s t h e t e m p e r a t u r e p a t t e r n c h a r a c t e r i s t i c o f t h e P a c i f i c e q u a t o r i a l c u r r e n t s y s t e m a t 165°W. The 14°C i s o t h e r m i s i n t h e lo w e r p o r t i o n o f t h e t h e r m o c l i n e and r e f l e c t s t h e g e o s t r o p h i c s l o p e a s s o c i a t e d w i t h t h e N o r t h E q u a t o r i a l C u r r e n t (NEC) n o r t h o f 9°N, t h e N o r t h E q u a t o r i a l C o u n t e r c u r r e n t (NECC) between 4° and 9°N, and t h e South E q u a t o r i a l C u r r e n t (SEC) s o u t h o f 4°N. Imbedded i n t h e SEC, t h e E q u a t o r i a l U n d e r c u r r e n t (EUC) i s marked by a s p r e a d i n g o f t h e i s o t h e r m s a t 175 m between 2°S and 2°N. The South E q u a t o r i a l C o u n t e r c u r r e n t (SECC), a l s o imbedded i n t h e SEC, i s a r e l a t i v e l y weak e a s t w a r d f l o w i n g c u r r e n t between 11°S and 8°S. A c o l d eddy can be i d e n t i f i e d i n t h e NEC 42 HMCS Q U ' A P P E L L E . 25 NOVEMBER - 2 DECEMBER 1 9 8 2 . RRNGE : ONE TICK = 300 KM Figure III-13 Temperature (°C) section (QE-251182) c o l l e c t e d by the HMCS Qu'Appelle (CAF) i n the NEP, from Hawaii to Vancouver Island i n November 1982. HMCS Q U ' A P P E L L E . 9 - 1 8 NOVEMBER 1982. RANGE i ONE T ICK = 300 KM Figure III-14 Temperature (°C) section c o l l e c t e d by the HMCS Qu'Appelle (CAF) from Samoa to Hawaii i n the c e n t r a l equatorial P a c i f i c , November, 1982. Only the portion of t h i s section north of 4*N has been retained (QE-151182) f o r the XBT data set summarized i n Table A-4. 43 i n F i g u r e I I I - 1 4 w i t h c h a r a c t e r i s t i c s v e r y s i m i l a r t o eddy "A" d i s c u s s e d by W y r t k i ( 1 9 8 2 ) . I t has a w i d t h o f 350 km and a 25 m v e r t i c a l d e f l e c t i o n o f t h e 14°C i s o t h e r m . I n t h e H a w a i i t o T a h i t i S h u t t l e E x p e r i m e n t , two s e c t i o n s a l m o s t s i m u l t a n e o u s l y i n t e r s e c t e d eddy "A". I t s w i d t h was 350 km and t h e d e f l e c t i o n s o f t h e 14°C i s o t h e r m were 27 m and 50 m a t 150°W and 153°W, r e s p e c t i v e l y . P r e s u m a b l y , t h e s e c t i o n i n F i g u r e I I I - 1 4 c u t t h r o u g h t h e s i d e o f a l a r g e r a m p l i t u d e eddy. The XBT s u r v e y s i n t h e NEP a r e i n the v i c i n i t y o f t h e s u b t r o p i c a l f r o n t n o r t h o f H a w a i i and i n t h e NEC and NECC s o u t h o f H a w a i i . F i g u r e I I I - 1 5 shows t h e s u b s u r f a c e t e m p e r a t u r e maps of t h e f o u r CAF m u l t i s h i p s u r v e y s c o n d u c t e d a c r o s s t h e f r o n t between F e b r u a r y 1980 and May 1982. W i t h t h e n o t a b l e e x c e p t i o n o f t h e March 1980 s u r v e y , no c l o s e d e d d i e s c o u l d be d e f i n e d due t o t h e narrow w i d t h o f t h e s u r v e y s . I n March 1980 ( F i g u r e I I I - 1 5 b ) , an a n t i c y l o n i c eddy i s c l e a r l y d e f i n e d by t h e 17°C i s o t h e r m a t 28.5°N 153°W, s o u t h o f t h e f r o n t . The a l o n g - t r a c k and c r o s s - t r a c k t e m p e r a t u r e s e c t i o n s t h r o u g h t h e eddy a r e shown i n F i g u r e 111-16. I t has a v e r t i c a l d e f l e c t i o n o f the 17°C i s o t h e r m o f about 60 m and a d i a m e t e r o f 130 km w h i c h i s c o n s i s t e n t w i t h t h e l o c a l i n t e r n a l Rossby d e f o r m a t i o n r a d i u s (Emery e t a l . , 1984) o f 45.5 km. A t i m e s e r i e s o f s i x AXBT s u r v e y s was c o l l e c t e d by t h e USN a c r o s s t h e s u b t r o p i c a l f r o n t n o r t h o f H a w a i i . The t e m p e r a t u r e maps i n F i g u r e II.I-17 show an a c t i v e f r o n t a l regime. Between 18 December 1979 t o 25 J a n u a r y 1980, a meander fo r m s . The n o r t h w a r d d i s p l a c e m e n t o f t h e tongue o f warm wa t e r has an a m p l i t u d e o f about 100 km. On 7 F e b r u a r y 1980, t h i s f e a t u r e i s r e p l a c e d by a " t r o u g h " o f c o l d w a t e r o f t h e same a m p l i t u d e . S o u t h o f H a w a i i a s e r i e s o f f o u r USN AXBT s u r v e y s shows a n o t h e r a c t i v e eddy f i e l d i n t h e N o r t h E q u a t o r i a l C u r r e n t ( F i g u r e 111-18). On 30 J a n u a r y 1981, a c y c l o n i c eddy i s c l e a r l y d e f i n e d a t 15°N 156°W w i t h a d i a m e t e r o f about 200 km. Two weeks l a t e r ( F i g u r e I I I - 1 8 b ) t h e f e a t u r e has moved westward a t a speed o f 10 cm/s t o t h e edge o f t h e s u r v e y a r e a . A n o t h e r c y c l o n i c eddy (150 km d i a m e t e r ) has appeared a t 15°N 155°W. The 13 March 1981 s u r v e y ( F i g u r e I I I - 1 8 c ) i s on average about 3°C warmer t h a n a month e a r i i e r . T h i s i s a s i g n a t u r e o f t h e a n n u a l weakening o f , and t h e so u t h w a r d d i s p l a c e m e n t o f , t h e t r o p i c a l t r o u g h t h a t s e p a r a t e s t h e NEC and NECC, s o u t h o f t h e s u r v e y a r e a . The s u r v e y o f 16 A p r i l 1981 ( F i g u r e I I I - 1 8 d ) i s a g a i n , warmer t h a n t h e s u r v e y o f a month e a r l i e r . A c o l d eddy can be seen a t 14°N 155°W w i t h a di a m e t e r o f LONGITUDE WEST TUO SON, 27-28 MRR 80, TEflP: 150-200 fl. Figure III-15 CAF multiship surveys of vertically-averaged temperature (°C) from 150 to 200 m taken i n the v i c i n i t y of the North P a c i f i c Subtropical Front between February 1980 and Hay 1982. a. Survey PR-110280, February 1980. b. Survey GU-270380, March 1980. 157 LONGITUDE WEST 155 153 151 149 • • • • • • • X 1 6 •18 • * * • • 17. c . o • cn oo • (M •CM (M CM CM 157 155 153 151 149 TWO SON, 1-2 MAY 81. TEMP: 150-200 M. 156 CD - cn o • cn • CM - Q ZD y— i — i t— cr CM • in CM- LONGITUDE WEST 154 T T 152 150 . 14- • 14 . ' 14 w £ 15 y ) / . / • • j ^ y a ^7*16 • fr 17 D. i r 152 • on cn • CM • CM in • (M 156 154  150 TUO SON, 11-12 HAY 82. TEMP: 150-200 M. Figure 111-15 Continued. c. Survey PR-010581, May 1981. d. Survey TA—110582, May 1982. RANGE : ONE TICK = 50 KM Figure 111-16 Detailed temperature (°C) sections of the a n t i c y c l o n i c eddy found i n the March 1980 CAF multiship survey (GD-270380) i n the HEP (Figure III-15b). a. Along-track section (southwest to northeast). b. Cross-track section (northwest to southeast). Figure III-17 USN AXBT surveys of vertically-averaged temperature C O from 150 to 200 m taken i n the v i c i n i t y of the North P a c i f i c Subtropical Front between December 1979 and February 1980. a. Section BB-181279, 18 December 1979. b. Section CC-211279, 21 December 1979.  H M M I M> a n • • o ft co to A a o o ft ft H- H- ft 0 0 • D P ?? o to o o 0 0 0 3 o o VC 0 3 0 0 O o • m 0 1 T ] Ln LRTITUDE NORTH 30 32 J I L LATITUDE NORTH 30 32 6 f r A. B. Figure 111-18 USN AXBT surveys of v e r t i c a l l y - a v e r a g e d temperature (°C) from 150 to 200 m taken i n the North P a c i f i c E q u a t o r i a l Current south of Hawaii, between January 1981 and A p r i l 1981. a. Section BB-300181, 30 January 1981. b. Section CC-110281, 11 February 1981. Figure III-1.8 Continued. c. Section DD-120381, 12 March 1981. d. Section EE-150481, 15 A p r i l 1981. 52 a p p r o x i m a t e l y 150 km. The i n t e n s i f i e d m e r i d i o n a l t e m p e r a t u r e g r a d i e n t n o r t h o f 14°N i s a s i g n a t u r e o f an i n c r e a s e d westward f l o w , d u r i n g a p e r i o d o f t h e a n n u a l c y c l e o f t h e NEC when th e f l o w i s g e n e r a l l y a b a t i n g . The p r e s e n c e o f t h e c o l d eddy d u r i n g t h i s warming t r e n d may a c c o u n t f o r t h e anomalous t h e r m a l g r a d i e n t s . The CAF c o n d u c t e d a m u l t i s h i p s u r v e y a c r o s s t h e NECC/NEC boundary a t 9°N 164°W i n November 1982 ( F i g u r e 111-19). The f l o w i s z o n a l and t h e m e r i d i o n a l t e m p e r a t u r e g r a d i e n t o f t h e NECC dominates t h e s u r v e y . There i s no d i s c e r n i b l e eddy v a r i a b i l i t y . N o r t h of H a w a i i , b u t s o u t h of t h e s u b t r o p i c a l f r o n t , t h e USN c o l l e c t e d an a d d i t i o n a l AXBT s u r v e y i n J a n u a r y 1981 ( F i g u r e 111-20). A l a r g e and d i s t i n c t s o u t h w a r d d i s p l a c e m e n t o f t h e 18°C i s o t h e r m w i t h a c o l d 17°C c o r e can be o b s e r v e d a t 25°N 155°W. T h i s f e a t u r e has a m e r i d i o n a l s i z e o f 240 km and a z o n a l w i d t h o f 120 km, w h i c h i s c o n s i s t e n t w i t h t h e l o c a l i n t e r n a l d e f o r m a t i o n r a d i u s o f 53 km (Emery e t a l . , 1984). South P a c i f i c The South P a c i f i c r e g i o n , d e f i n e d i n F i g u r e I I I - 2 , i s an a r e a o f low eddy a c t i v i t y t o t h e n o r t h and e a s t o f New Z e a l a n d , bounded by t h e S o u t h E q u a t o r i a l C u r r e n t , t h e A n t a r c t i c C i r c u m p o l a r C u r r e n t , and t h e P e r u C u r r e n t . The extreme • p a u c i t y o f d a t a i n t h i s r e g i o n makes i t p e r h a p s t h e l e a s t - s u r v e y e d p a r t o f t h e g l o b a l ocean ( B e n n e t t , 1983). The " S c o r p i o " e x p e d i t i o n (Stommel e t a l . , 1973) s u b s t a n t i a l l y added t o t h e e x i s t i n g d a t a w i t h i t s two t r a n s - P a c i f i c t r a n s e c t s a t 28°S and 43°S, however, t h e s t a t i o n s p a c i n g e a s t of New Z e a l a n d c o u l d n o t r e s o l v e m e s o s c a l e e d d i e s . P a t z e r t and B e r n s t e i n (1976) r e p o r t e d on t h e eddy v a r i a b i l i t y o b s e r v e d i n two m e s o s c a l e r e s o l v i n g XBT s e c t i o n s t a k e n i n t h e c e n t r a l South P a c i f i c R e g i o n . Only one m e s o s c a l e f e a t u r e , w i t h a w i d t h o f 200 km, was i d e n t i f i e d . The maps o f W y r t k i e t a l . ( F i g u r e I I I - 3 ) and Cheney e t a l . ( F i g u r e I I I - 1 ) b o t h show low eddy l e v e l s i n t h e r e g i o n and i n c r e a s i n g eddy a c t i v i t y w i t h p r o x i m i t y t o t h e A n t a r c t i c C i r c u m p o l a r C u r r e n t . The XBT d a t a o b t a i n e d f o r t h e SP c o n s i s t o f n i n e s e c t i o n s and one s u r v e y . F i g u r e 111-21 shows a h i g h r e s o l u t i o n SXBT c r u i s e by t h e CAF f r o m New Z e a l a n d t o Samoa i n November 1982. The t h e r m a l s i g n a t u r e o f t h e S o u t h S u b t r o p i c a l C o u n t e r c u r r e n t ( T a b a t a , 1975) i s a p p a r e n t a t 24°S ( F i g u r e I I I - 2 1 a ) . T h i s 53 LONGITUDE WEST .167 165 163 161 n i ^ I i i i r v " 167 165 163 161 FOUR SON, 1 4 - 1 5 NOV 8 2 , TEMP : 100-150 M. Figure III-19 CAF SXBT survey (QB-141182) of vertically-averaged temperature (°C) from 100 to 150 m taken across the North P a c i f i c E q u a t o r i a l Countercurrent, November 1982. LONGITUDE WEST 158 156 154 158 156 154 Figure 111-20 USH AXBT survey (AA-16081) of vertically-averaged temperature (•C) from 150 to 200 m taken north of Hawaii, 16 January 1981. HMCS QU'APPELLE. 2-7 NOVEMBER 1982. in to (MT CT i n _ t n en «• 3~ SST - SOLID LINE SSS - DASHED rf<n . t n t n RANGE : ONE TICK = 300 KM CM • 177 to CM • ZD O CO LU CM - Q ZD CE o cn - CM cn- E R S T 179 180 W E S T 178 T 176 .-<19r . "^-18^r • • • * • • • • « • * • .18 / • • ' . " T o •• 17 • . • / •' 17 ' 3/ CD 177 179 180 178 176 FOUR SON, 3-4 NOV 82. TEMP: 150-200 M. Figure 111-21 CAF SXBT survey from New Zealand to Samoa, November 1982. a. Temperature section C O , QE-021182. b. Map of vertically-averaged temperature (°C) from 150 to 200 m, QE-031182. 56 s u b s u r f a c e t h e r m a l f r o n t a p p e a r s t o be a permanent f e a t u r e t h a t was a l s o p r e s e n t i n a l l f i v e SXBT s e c t i o n s r e p o r t e d by Denham e_t aJU (1981) f r o m New Z e a l a n d t o F i j i . The a m p l i t u d e and h o r i z o n t a l s c a l e o f t h e t h e r m a l eddy s t r u c t u r e e x h i b i t marked i n c r e a s e s s o u t h o f t h e f r o n t . F i g u r e I I I - 2 1 a shows a warm eddy a t 27.5°S w i t h a w i d t h o f about 400 km and a 150 m d e f l e c t i o n o f t h e 16°C i s o t h e r m . The m u l t i s h i p s u r v e y c o l l e c t e d by t h e CAF on t h i s c r u i s e ( F i g u r e I I I - 2 1 b ) was t o o narrow (180 km) t o c l o s e t h e f e a t u r e . S e c t i o n 24-230483 ( F i g u r e 111-22), t a k e n i n t h e n o r t h e a s t c o r n e r o f t h e SP r e g i o n , was o b t a i n e d f r o m NODC. I t i s r e l a t i v e l y q u i e s c e n t , a l t h o u g h t h r e e e d d i e s can be seen: a warm eddy a t 106°W, a c o l d eddy a t 93°W and a warm sub- t h e r m o c l i n e eddy a t 85°W. These f e a t u r e s have w i d t h s o f 300, 250 and 400 km, r e s p e c t i v e l y , w i t h d i s p l a c e m e n t s o f t h e 11°C i s o t h e r m o f 25, 30 and 60 m. 57 Figure 111-22 Temperature (°C) section (24-230483) obtained from the NODC the eastern SP. 58 IV. STATISTICAL ANALYSES The purpose o f t h i s c h a p t e r i s t o q u a n t i f y t h e g e o g r a p h i c v a r i a b i l i t y o f t h e q u a s i - s y n o p t i c mesoscale s t r u c t u r e i n t h e upper 400 m o f t h e ocean. S t a t i s t i c a l a n a l y s e s were used t o compress t h e numerous o b s e r v a t i o n s i n t o c o n c i s e s t a t e m e n t s about what " u s u a l l y " happens i n t h e g e o g r a p h i c r e g i o n s , and how t h e r e g i o n s d i f f e r from each o t h e r . The m i d - t h e r m o c l i n e t e m p e r a t u r e and t h e g e o p o t e n t i a l anomaly were u s e d t o r e p r e s e n t t h e m e s o s c a l e eddy v a r i a b i l i t y . A s u f f i c i e n t number of o b s e r v a t i o n s must be a v a i l a b l e t o o b t a i n sample s t a t i s t i c s w h i c h e s t i m a t e t h e p o p u l a t i o n s t a t i s t i c s w i t h r e a s o n a b l y s m a l l u n c e r t a i n t i e s . Each s e c t i o n and s u r v e y must be c o n s i d e r e d r e l a t i v e l y s m a l l , i n l i g h t o f t h e few mesoscale p e r t u r b a t i o n s p e r c r u i s e and t h e r e l a t i v e l y l a r g e d e c o r r e l a t i o n s c a l e s (on t h e o r d e r o f t h e i n t e r n a l Rossby d e f o r m a t i o n r a d i u s ) . To i n c r e a s e t h e degrees o f freedom, and t h e r e f o r e d e c r e a s e t h e e r r o r b a r s , sample s t a t i s t i c s were o b t a i n e d u s i n g p o o l e d e s t i m a t e s o f t h e s t a t i s t i c s i n e a ch g e o g r a p h i c r e g i o n . T h i s r e q u i r e d t h e a s s u m p t i o n t h a t t h e t e m p e r a t u r e f i e l d and t h e b a r o c l i n i c eddy f i e l d were e r g o d i c , s t a t i o n a r y , random p r o c e s s e s and t h a t each XBT s e c t i o n o r s u r v e y was an i n d e p e n d a n t r e a l i z a t i o n . The d a t a were p r o c e s s e d i n t h r e e ways t o s u b s t a n t i a t e t h e s e a s s u m p t i o n s . F i r s t , as d i s c u s s e d i n C h a p t e r I I I , t h e g e o g r a p h i c r e g i o n s were d e f i n e d on t h e b a s i s o f t h e v a r i a n c e o f t h e eddy f i e l d . O n ly c r u i s e s i n t h e same g e o g r a p h i c r e g i o n o r i n g e o g r a p h i c r e g i o n s w i t h s i m i l a r m e s o s c a l e v a r i a n c e s were "averaged". Second, t h e l a r g e - s c a l e c u r r e n t systems ( t r e n d s ) were removed f r o m each s e c t i o n o r s u r v e y t o o b t a i n t h e p e r t u r b a t i o n v a r i a b l e s ( i . e . mean e q u a l t o z e r o ) , o f t h e m i d - t h e r m o c l i n e t e m p e r a t u r e and t h e g e o p o t e n t i a l anomaly, w i t h near-normal f r e q u e n c y d i s t r i b u t i o n s . T h i r d , t h e s e c t i o n s and s u r v e y s u s e d were s e p a r a t e d i n space by a t l e a s t t h e l o c a l i n t e r n a l Rossby r a d i u s , and s e p a r a t e d i n t i m e by p e r i o d s o f weeks t o y e a r s . I n t h i s c h a p t e r , a q u a n t i t a t i v e r e p r e s e n t a t i o n o f t h e m e s o s c a l e v a r i a b i l i t y w i l l be o b t a i n e d by computing t h e c e n t r a l moments o f t h e f r e q u e n c y d i s t r i b u t i o n s and t h e wavenumber s p e c t r a o f t h e m i d - t h e r m o c l i n e t e m p e r a t u r e and t h e g e o p o t e n t i a l anomaly f o r each g e o g r a p h i c r e g i o n . The s t a n d a r d d e v i a t i o n , skewness, k u r t o s i s and i n t e r m i t t e n c y o f t h e f r e q u e n c y d i s t r i b u t i o n s of each s e c t i o n and s u r v e y w i l l be used. The s e a s o n a l v a r i a b i l i t y o f t h e mesoscale s t a t i s t i c s i n t h e NEP r e g i o n w i l l be examined. I s o t r o p i c , m e r i d i o n a l and z o n a l 59 autocorrelation functions w i l l be employed to discuss the assumption of isotropy. Wavenumber spectra w i l l be used to i d e n t i f y spectral bandwidths of d i s t i n c t i v e wavenumber ranges, and the dominant length scales of v a r i a b i l i t y . V e l o c i t y spectra w i l l be computed using the geostrophic r e l a t i o n to obtain k i n e t i c energy estimates and the geostrophic v e l o c i t y scales for each region. A. SPATIAL SERIES S p a t i a l series and maps of the mid-thermocline temperature and geopotential anomaly, used to represent the upper-layer v a r i a b i l i t y , were required f or the s t a t i s t i c a l analyses. This involved the c a l c u l a t i o n of several quantities f o r each XBT and the removal of the low-wavenumber signal of the "l a r g e - s c a l e " c i r c u l a t i o n . The r e s u l t i n g perturbation variables are signatures of the r e l a t i v e l y high-wavenumber mesoscale eddy f i e l d s . Three quantities were calculated for each XBT i n the sections and surveys: the vertically-averaged temperature between 150 and 200 m, the vertically-averaged temperature between 350 and 400 m, and the geopotential anomaly between the surface and 4000 kPa ( i . e . 0-400 db or 0-400 m). The temperature was averaged over two 50 m depth i n t e r v a l s to represent the mid-thermocline temperatures. The temperatures were averaged over a p o r t i o n of the water column ( i . e . 50 m) to reduce the high-wavenumber noise that might be induced by instrument error. No one depth can be adequately used to examine the v a r i a b i l i t y of the thermocline on a global scale (Emery, 1983a). Examinations of the mean thermal structure of the geographic regions (Stommel et a l . 1960; Defant, 1981; Emery and Dewar, 1982; Thomson et a l . 1984b), and the standard deviations of the temperatures at 150 to 200 m and 350 to 400 m revealed the most appropriate depth i n t e r v a l f o r each region. In the NWA, NWP and NEA, the temperature between 350 and 400 m were used to represent the mid-thermocline v a r i a b i l i t y , whereas, the temperature between 150 and 200 m were used i n the SA, NEP and SP. The signature of the upper-layer b a r o c l i n i c eddy f i e l d i n the XBT data set was characterized by the geopotential anomaly (0-4000kPa). The perturbation variables of the mid-thermocline temperature (T) and the geopotential anomaly (D) were obtained f o r each section by removing a 1000 km running mean. A running mean of t h i s s i z e was chosen to take out the low-wavenumber signal of the large-scale mean c i r c u l a t i o n systems and r e t a i n 60 t h e f u l l a m p l i t u d e o f t h e m e s o s c a l e f e a t u r e s . B e r n s t e i n and White (1974) o b s e r v e d dominant w a v e l e n g t h s o f 600 t o 400 km i n t h e N o r t h P a c i f i c , so an a v e r a g i n g i n t e r v a l o f a g r e a t e r s c a l e was r e q u i r e d . D e t r e n d i n g t h e s e c t i o n s w i t h l e a s t - s q u a r e s - f i t p o l y n o m i a l s was c o n s i d e r e d a t some l e n g t h , but r e j e c t e d i n f a v o u r of the r u n n i n g mean. Running means of 500, 750, 1000, and 1250 km were a p p l i e d t o t y p i c a l s p a t i a l s e r i e s i n d i f f e r e n t g e o g r a p h i c r e g i o n s . The 1000 km r u n n i n g mean was c o n s i d e r e d t h e most a p p r o p r i a t e . F i g u r e IV-1 shows examples of t h e s p a t i a l s e r i e s o b t a i n e d f o r s e c t i o n s i n t h e NWP and NEP. The p e r t u r b a t i o n v a r i a b l e s f o r each s u r v e y were d e t e r m i n e d by removing t h e m e r i d i o n a l and z o n a l l i n e a r t r e n d s . T h i s was c o n s i d e r e d more a p p r o p r i a t e t h a n t h e l a r g e r u n n i n g mean due t o t h e r e l a t i v e l y s m a l l d i m e n s i o n s o f t h e s u r v e y s ( e x c e p t t h e USN m u l t i s h i p s u r v e y s ) . The r e m o v a l o f t h e z o n a l l i n e a r t r e n d of t h e USN m u l t i s h i p s u r v e y s was s t i l l c o n s i d e r e d adequate, s i n c e t h e s e s u r v e y s were c o n f i n e d t o t h e i n t e r i o r of t h e s u b t r o p i c a l o r s u b p o l a r g y r e s and d i d n o t c r o s s major f r o n t a l systems (e. g . G u l f Stream o r K u r o s h i o ) . B. CENTRAL MOMENTS The mesoscale v a r i a b i l i t y r e p r e s e n t e d by T and D may be q u a n t i t a t i v e l y examined w i t h t h e c e n t r a l moments o f t h e i r sample p r o b a b i l i t y d e n s i t y f u n c t i o n s : t h e s t a n d a r d d e v i a t i o n , skewness and k u r t o s i s . These s t a t i s t i c s were c a l c u l a t e d f o r each s e c t i o n and s u r v e y , and p o o l e d s t a t i s t i c s were o b t a i n e d f o r each g e o g r a p h i c r e g i o n . The g e o g r a p h i c v a r i a b i l i t y o f t h e t e m p e r a t u r e f i e l d and t h e b a r o c l i n i c eddy f i e l d w i l l be d i s c u s s e d . A few comments must f i r s t be made about t h e use o f t h e s t a n d a r d d e v i a t i o n , skewness and k u r t o s i s f o r d e s c r i b i n g t h e mesoscale eddy f i e l d . The sample s t a n d a r d d e v i a t i o n , S, w i l l p r o v i d e a c o n v e n i e n t measure o f t h e average a m p l i t u d e o f t h e f l u c t u a t i o n s . The s t a n d a r d d e v i a t i o n o f t h e l a r g e - s c a l e f l o w has been commonly u s e d by o c e a n o g r a p h e r s t o q u a n t i f y t h e i n t e n s i t y and g e o g r a p h i c v a r i a b i l i t y o f t h e m e s o s c a l e eddy f i e l d ( W y r t k i , 1975; D a n t z l e r , 1976; Ebbesmeyer and T a f t , 1979; Emery e_t a l . , 1980; Emery, 1983a). The s t a n d a r d d e v i a t i o n s o f T ( S T ) o b t a i n e d f r o m t h i s q u a s i - s y n o p t i c d a t a s e t may be d i r e c t l y compared t o t h e r e s u l t s o f Emery (1983a) u s i n g c l i m a t o l o g i c a l d a t a ( F i g u r e I I I - 4 ) . The sample s t a n d a r d d e v i a t i o n was o b t a i n e d f o r each s e c t i o n and s u r v e y by t h e r e l a t i o n : 61 Figure IV-1 Examples of the spatial series of the mid-thermocline temperature perturbations (T) and the geopotential anomaly perturbations (D) for trans-oceanic sections i n the NWP and NEP. 62 ( ( ^ x j ) / ( n - l ) ) 1 / 2 (4.1) where x^ i s T o r D and n i s t h e number o f o b s e r v a t i o n s . Skewness i s a measure of d e p a r t u r e o f t h e f r e q u e n c y d i s t r i b u t i o n f r o m symmetry. I t i s t h e t h i r d c e n t r a l moment n o r m a l i z e d by t h e s t a n d a r d d e v i a t i o n . A c o n v e n i e n t e s t i m a t e o f skewness i s : W = (Z n x j ) / ( n - l ) ( 4 . 2 ) . 7 ". I f t h e mode l i e s t o t h e l e f t o f t h e mean, so t h a t t h e f r e q u e n c i e s f a l l o f f s h a r p l y t o t h e l e f t , t h e skewness i s p o s i t i v e . T h i s i n d i c a t e s t h a t more v a l u e s a r e n e g a t i v e and c o n s e q u e n t l y t h e f r e q u e n c y d i s t r i b u t i o n has a number o f extreme p o s i t i v e v a l u e s . A p o s i t i v e skewness o f T o r D w o u l d s u g g e s t t h a t t h e m e s o s c a l e eddy f i e l d c o n s i s t s o f a number o f warm e d d i e s i n a r e l a t i v e l y q u i e s c e n t , c o l d background. The skewness o f t h e p o p u l a t i o n i s c o n s i d e r e d t o be s i g n i f i c a n t l y (95% c o n f i d e n c e l e v e l ) n o n z e r o i f t h e a b s o l u t e v a l u e o f W i s g r e a t e r t h a n 1 . 9 6 ( 6 / n ^ ) ( B r o o k s and C a r r u t h e r s , 1953), where n^ i s t h e number o f ind e p e n d e n t o b s e r v a t i o n s . K u r t o s i s i s a measure of t h e d i s p r o p o r t i o n a l i t y o f t h e number o f o b s e r v a t i o n s i n t h e i n t e r m e d i a t e range between t h e mean and extreme v a l u e s . I t i s t h e f o u r t h c e n t r a l moment n o r m a l i z e d by t h e s t a n d a r d d e v i a t i o n . A u s e f u l f o r m o f k u r t o s i s i s g i v e n by (Brooks and C a r r u t h e r s , 1953): K = ( ( ^ x j ) / ( n - l ) ) -3 (4.3) I f K i s p o s i t i v e t h e f r e q u e n c y d i s t r i b u t i o n i s termed " l e p t o k u r t i c " and i t w i l l have a r e l a t i v e l y s m a l l number o f o b s e r v a t i o n s i n t h e i n t e r m e d i a t e ranges and a r e l a t i v e l y l a r g e number o f o b s e r v a t i o n s n e a r t h e mean; i f K i s n e g a t i v e t h e f r e q u e n c y d i s t r i b u t i o n i s termed " p l a t y k u r t i c " , w i t h a l a r g e p r o p o r t i o n o f v a l u e s i n t h e i n t e r m e d i a t e r a n g e s and a r e l a t i v e l y s m a l l number o f o b s e r v a t i o n s n e a r t h e mean; and i f K i s z e r o t h e d i s t r i b u t i o n i s " i s o k u r t i c " , as i s a G a u s s i a n d i s t r i b u t i o n . The a c c e p t a n c e r e g i o n s f o r t e s t i n g t h e n u l l h y p o t h e s i s t h a t K=0, a t t h e 0.05 l e v e l o f s i g n i f i c a n c e , a r e g i v e n by Brooks and C a r r u t h e r s 63 (1953). The k u r t o s i s o f a p o p u l a t i o n s h o u l d n o t be e s t i m a t e d f r o m a sample o f l e s s t h a n 100 i n d e p e n d e n t o b s e r v a t i o n s . I n t h e c l a s s i c a l s t u d i e s o f t u r b u l e n c e ( H i n z e , 1975), K i s known as t h e f l a t n e s s f a c t o r and may be c o n s i d e r e d a measure f o r t h e degree o f i n t e r m i t t e n c y . T u r b u l e n c e i n v e s t i g a t o r s have d e f i n e d an i n t e r m i t t e n c y f a c t o r , Q, as t h e f r a c t i o n of t h e r e c o r d l e n g t h o v e r w h i c h t u r b u l e n c e o c c u r s . On t h e a s s u m p t i o n t h a t t h e v a r i a b l e c o n c e r n e d i s n o r m a l l y d i s t r i b u t e d d u r i n g t h e t u r b u l e n t s t a t e , and i s z e r o d u r i n g t h e n o n t u r b u l e n t s t a t e , t h e r e l a t i o n Q(K+3)=3 was s u g g e s t e d ( H i n z e , 1975). The i n t e r m i t t e n c y o f t h e m e s o s c a l e eddy f i e l d may t h u s be q u a n t i f i e d by e s t i m a t i n g K and u s i n g t h e above r e l a t i o n . I n summary, t h e s t a n d a r d d e v i a t i o n i s a measure o f t h e average a m p l i t u d e o f t h e f l u c t u a t i o n s o f t h e v a r i a b l e ; t h e skewness i s a measure o f t h e symmetry o f t h e s a m p l i n g d e n s i t y d i s t r i b u t i o n ; and t h e k u r t o s i s i s a measure o f t h e r e l a t i v e number of v a l u e s near t h e mean. Where K i s s i g n i f i c a n t l y d i f f e r e n t f r o m z e r o , t h e i n t e r m i t t e n c y f a c t o r , Q, may be o b t a i n e d . Q i s t h e f r a c t i o n o f t h e sample where m e s o s c a l e p e r t u r b a t i o n s o c c u r . Thus, f o r g i v e n s t a t i s t i c s , i t may be s a i d t h a t t h e a v e r a g e a m p l i t u d e o f t h e mesoscale p e r t u r b a t i o n s i s S, t h a t t h e s e p e r t u r b a t i o n s o c c u r i n Q x 100% o f t h e r e g i o n and t h a t t h e p e r t u r b a t i o n s a r e p r e d o m i n a n t l y c o l d (W<0) o r warm (W>0) e d d i e s . C e n t r a l Moments o f t h e S e c t i o n s The sample s t a t i s t i c s o f T and D were c a l c u l a t e d f o r each o f t h e 95 s e c t i o n s . The numbers o f i n d e p e n d e n t o b s e r v a t i o n s (n^) p e r s e c t i o n were d e t e r m i n e d f r o m t h e a u t o c o r r e l a t i o n f u n c t i o n (ACF) o f each v a r i a b l e . S p a t i a l s c a l e s may be i n f e r r e d f r o m z e r o - c r o s s i n g s o f t h e ACF, s i n c e t h e ACF o f a f i e l d h a v i n g a dominant w a v e l e n g t h s h o u l d c r o s s z e r o a t t h e q u a r t e r - w a v e l e n g t h p o i n t (MODE Group, 1978). T h i s d e c o r r e l a t i o n s c a l e may be d i v i d e d i n t o t h e l e n g t h o f t h e s p a t i a l s e r i e s t o o b t a i n nj_. The number o f i n d e p e n d e n t o b s e r v a t i o n s may n o t , o f c o u r s e , e x c e e d t h e a c t u a l number o f o b s e r v a t i o n s . The ACF o f each v a r i a b l e was d e t e r m i n e d f o r each g e o g r a p h i c r e g i o n by a v e r a g i n g t h e ACFs o f a l l t h e s e c t i o n s i n t h e r e g i o n . T a b l e IV-1 p r e s e n t s t h e d e c o r r e l a t i o n s c a l e s o b t a i n e d from t h e f i r s t - z e r o c r o s s i n g s o f each v a r i a b l e i n each r e g i o n . These d e c o r r e l a t i o n s c a l e s were u s e d t o d e t e r m i n e t h e numbers o f i n d e p e n d e n t o b s e r v a t i o n s . 64 Table IV—1 Decorrelation scales obtained from the f i r s t - z e r o crossings of the averaged autocorrelation functions f o r the sections i n each geographic region. R e g i o n D e c o r r e l a t i o n S c a l e s (km) T D NWA 59 63 NWP 72 76 NEA 54 52 SA 95 102 NEP 78 83 SP 81 77 HIGH LOW 66 76 66 76 6 5 I n o r d e r t o examine t h e g e o g r a p h i c v a r i a b i l i t y o f t h e v a r i a b l e s , " p o o l e d " s t a t i s t i c s were c a l c u l a t e d f o r each r e g i o n . The p o o l e d e s t i m a t e o f t h e sample s t a n d a r d d e v i a t i o n s (Sp) i s o b t a i n e d f r o m t h e r e l a t i o n ( W a l p o l e , 1974), S 2 = d t n . - D S ^ / d n -j) (4.4) where j i s t h e number of i n d i v i d u a l sample s t a n d a r d d e v i a t i o n s , S^. The p o o l e d e s t i m a t e s o f skewness (Wp) and k u r t o s i s (Kp) a r e , K P  = ^ ^ v i ) s i ( K i + 3 ) ) / ( E K - j ) / s o 4 ) - 3 <4-6> I n t h e f o l l o w i n g d i s c u s s i o n on t h e g e o g r a p h i c v a r i a b i l i t y o f t h e m e s o s c a l e s t a t i s t i c s , t h e s i g n i f i c a n c e o f t h e p o o l e d e s t i m a t e s , w i t h r e s p e c t t o t h e p o p u l a t i o n s t a t i s t i c o f each r e g i o n , i s i m p o r t a n t . The methods u s e d t o d e t e r m i n e whether o r n o t W and K o f t h e p o p u l a t i o n a r e no n z e r o have been d e t a i l e d a l r e a d y . The 95% c o n f i d e n c e i n t e r v a l f o r t h e v a r i a n c e o f a p o p u l a t i o n ( a 2 ) i s : ( ( n r j ) / x 2 0 2 5 ) S2 < a 2 < ( ( n r j ) / x 2 9 7 5 ) ) S2 ( 4 - 7 ) 2 2 where x Q 2 5 a n a - X 9 7 5 a r e t h e v a l u e s o f a c h i - s q u a r e d i s t r i b u t i o n w i t h n ^ - j d e g r e e s o f freedom, l e a v i n g a r e a s o f .0 25 and .975, r e s p e c t i v e l y t o t h e r i g h t . 2 F o r ( n ^ - j ) > 3 0 , a normal d i s t r i b u t i o n i s q u i t e a c c u r a t e , and t h u s x v a l u e s may be computed by t h e f o r m u l a s ( S e l b y , 1965): 0.5 (1.96 + (2(n..-j)-l) 1 / 2) 2 C 2 9 7 5 = 0.5 (-1.96 + ( 2 ( n j , - j ) - l ) 1 / 2 ) 2 (4.8) 66 i . M i d - t h e r m o c l i n e Temperature S t a t i s t i c s The sample s t a t i s t i c s o f T a r e l i s t e d i n T a b l e I V - 2 . The s t a n d a r d d e v i a t i o n s o f t h e NWA and NWP a r e n o t s i g n i f i c a n t l y d i f f e r e n t . The S T v a l u e s i n t h e low-energy r e g i o n s a r e a l l e q u a l w i t h i n t h e 95% c o n f i d e n c e l i m i t s . The HIGH r e g i o n has a s t a n d a r d d e v i a t i o n o f 1.40°C w i t h a 95% c o n f i d e n c e i n t e r v a l o f 1.35 t o 1.46°C f r o m 1184 inde p e n d e n t o b s e r v a t i o n s . The LOW r e g i o n has a v a l u e o f 0.54°C w i t h a 95% c o n f i d e n c e i n t e r v a l o f 0.52 t o 0.56°C fr o m 2223 i n d e p e n d e n t o b s e r v a t i o n s . The g e o g r a p h i c v a r i a b i l i t y and t h e v a l u e s o f S T a r e v e r y c o n s i s t e n t w i t h t h e c l i m a t o l o g i c a l r e s u l t s o f Emery (1983a) shown i n F i g u r e I I I - 4 . The b o u n d a r i e s between t h e h i g h - e n e r g y r e g i o n s and t h e low-energy r e g i o n s a r e a p p r o x i m a t e l y d e l i n e a t e d by t h e 1.0°C c o n t o u r o f t h e s t a n d a r d d e v i a t i o n o f t h e 260 m t e m p e r a t u r e . The h i g h - and low-energy r e g i o n s can a l s o be a p p r o x i m a t e l y d e l i n e a t e d by t h e 1.0°C c o n t o u r i n a s i m i l a r map o f t h e s t a n d a r d d e v i a t i o n o f t e m p e r a t u r e a t 460 m (Emery, 1983a). The NWA, NWP and HIGH r e g i o n s have S T v a l u e s g r e a t e r t h a n 1.0°C; t h e NEA, SA, NEP, SP and LOW r e g i o n s have S T v a l u e s l e s s t h a n 1.0°C. The a m p l i t u d e s o f t h e m e s o s c a l e v a r i a b i l i t y as r e f l e c t e d i n t h e s t a n d a r d d e v i a t i o n s o f t h e m i d - t h e r m o c l i n e t e m p e r a t u r e s o f t h e q u a s i - s y n o p t i c d a t a and t h e c l i m a t o l o g i c a l d a t a a r e v e r y c o n s i s t e n t . The HIGH and LOW r e g i o n s have Q T v a l u e s o f 0.45 and 0.49, r e s p e c t i v e l y . These s t a t i s t i c s s u g g e s t t h a t p e r t u r b a t i o n s o f T g r e a t e r t h a n 1.40°C o c c u r i n about 45% o f t h e HIGH r e g i o n , w h i l e p e r t u r b a t i o n s o f 0.54°C o c c u r i n about 49% o f t h e LOW r e g i o n . The skewness o f t h e HIGH r e g i o n (W T<0) s u g g e s t s t h a t t h e p e r t u r b a t i o n s a r e p r e d o m i n a n t l y c o l d e d d i e s , whereas, t h e skewness o f t h e LOW r e g i o n (W T>0) s u g g e s t s t h a t t h e y a r e warm e d d i e s . The r a t i o o f t h e s t a n d a r d d e v i a t i o n o f t h e m i d - t h e r m o c l i n e t e m p e r a t u r e o f t h e HIGH r e g i o n t o t h e LOW r e g i o n i s 2.59. The 95% c o n f i d e n c e l i m i t s o f t h i s r a t i o , o b t a i n e d u s i n g t h e F d i s t r i b u t i o n ( S e l b y , 1965), a r e 2.16 and 3.09. Thus t h e average a m p l i t u d e o f t h e m i d - t h e r m o c l i n e t e m p e r a t u r e p e r t u r b a t i o n s i n t h e h i g h - e n e r g y r e g i o n s i s 2.5 t i m e s t h a t o f t h e low-energy r e g i o n s . i i . G e o p o t e n t i a l Anomaly (0-4000 kPa) S t a t i s t i c s The sample s t a t i s t i c s o f t h e g e o p o t e n t i a l anomaly (0-4000 kPa) p e r t u r b a t i o n s a r e l i s t e d i n T a b l e I V - 3 . The NWA and t h e NWP have s i g n i f i c a n t l y Table IV-2 Sample standard deviation, skewness, kurtosis and intermittency of the mid-thermocline temperature (T) for the geogxaphic regions from the sections. w and K values that are significantly nonzero are underlined. Q i s shown only when K i s significantly nonzero. R e g i o n n i S T 95% C o n f i d e n c e wT Rj, Q T CO L i m i t s CO NWA. 901 1.43 1.37 - 1.50 -0.66 3.96 0.43 NWP 283 1.30 1.20 - 1.40 0.13 1.63 0.63 NEA 503 0.51 0 . 4 8 - 0 . 5 4 0.04 3.89 0.44 SA 88 0.48 0.42 - 0.54 0.14 -0.22 NEP 1354 0.57 0.55 - 0.59 0.17 3.55 0.46 SP 278 0.56 0.51 - 0.60 0.12 1.69 0.74 HIGH 1184 1.40 1.35 - 1.46 -0.51 3.60 0.45 LOW 2223 0.54 0.52 - 0.56 0.11 3.16 0.49 CM Table IV-3 Sample standard deviation, skewness, kurto s i s and intermittency of the geopotential anomaly (D) f o r the geographic regions from the sections. W and K values that are s i g n i f i c a n t l y nonzero are underlined. Q i s shown only when K i s s i g n i f i c a n t l y nonzero. R e g i o n n^ S D 95% C o n f i d e n c e WD K D Q D ( m 2 / s 2 ) L i m i t s ( m 2 / s 2 ) NWA 854 0.69 0.66 - 0.72 0.12 3.63 0 .45 NWP 271 0.58 0.54 - 0.63 -0.05 1 .44 0.68 NEA 517 0.21 0.19 - 0.22 0.25 1.73 0 .63 SA 85 0.20 0.18 - 0.23 -0.01 0.88 - NEP 1330 0.26 0.25 - 0.27 0.21 3 .44 0 .47 SP 279 0.32 0.30 - 0.35 0.63 4.50 0.40 HIGH 1125 0.67 0.64 - 0.69 0.10 3 . 4 4 0 > 4 7 LOW 2211 0.26 0.25 - 0.27 ^ 0 . 3 3 4.10 0 i 4 2 69 d i f f e r e n t S Q v a l u e s . The low-energy r e g i o n s a l l have s t a n d a r d d e v i a t i o n s t h a t a r e s i g n i f i c a n t l y l o w e r t h a n t h e h i g h - e n e r g y r e g i o n s and a r e g e n e r a l l y n o t s i g n i f i c a n t l y d i f f e r e n t f r o m each o t h e r . The HIGH r e g i o n has a s t a n d a r d d e v i a t i o n o f 0.67 m 2/s 2 w i t h a 95% c o n f i d e n c e i n t e r v a l o f 0.64 t o 0.69 m 2/s 2 f r o m 1125 ind e p e n d e n t o b s e r v a t i o n s . The LOW r e g i o n has a s t a n d a r d d e v i a t i o n o f 0.26 m 2/s 2 w i t h a 95% c o n f i d e n c e i n t e r v a l o f 0.25 t o 0.27 m 2/s 2 f r o m 2211 ind e p e n d e n t o b s e r v a t i o n s . The skewness o f t h e HIGH r e g i o n i s n o t s i g n i f i c a n t l y d i f f e r e n t f r o m z e r o , whereas, t h e skewness o f t h e LOW r e g i o n i s s i g n i f i c a n t l y p o s i t i v e . The HIGH and t h e LOW r e g i o n s have i n t e r m i t t e n c i e s o f 0.47 and 0.42, r e s p e c t i v e l y . These s t a t i s t i c s s u g g e s t t h a t g e o p o t e n t i a l anomaly p e r t u r b a t i o n s g r e a t e r t h a n 0.67 m 2/s 2 may be f o u n d i n about 47% of t h e HIGH r e g i o n , t h a t p e r t u r b a t i o n s g r e a t e r t h a n 0.26 m 2/s 2 may be f o u n d i n about 42% o f t h e LOW r e g i o n and t h a t t h e LOW r e g i o n has m e s o s c a l e p e r t u r b a t i o n s t h a t a r e p r e d o m i n a n t l y warm e d d i e s . The r a t i o o f t h e s t a n d a r d d e v i a t i o n s o f t h e HIGH r e g i o n t o t h e LOW r e g i o n i s 2.58 w i t h 95% c o n f i d e n c e l i m i t s o f 2.15 and 3.08. Thus, t h e average a m p l i t u d e o f t h e g e o p o t e n t i a l anomaly p e r t u r b a t i o n s (0-4000 kPa) i n t h e h i g h - e n e r g y r e g i o n s i s about 2.5 t i m e s t h a t o f t h e low-energy r e g i o n s . C e n t r a l Moments o f t h e Surve y s The c e n t r a l moments o f t h e m i d - t h e r m o c l i n e t e m p e r a t u r e and t h e g e o p o t e n t i a l anomaly were c a l c u l a t e d f o r each o f t h e 29 s u r v e y s . P o o l e d e s t i m a t e s o f each s t a t i s t i c were d e t e r m i n e d f o r t h e g e o g r a p h i c r e g i o n s . I n t h e NEP, two s u b r e g i o n s were a l s o examined: t h e N o r t h P a c i f i c S u b t r o p i c a l F r o n t (NPSF), and t h e N o r t h P a c i f i c E q u a t o r i a l C u r r e n t (NPEC). These s t a t i s t i c s w i l l be d i s c u s s e d and compared w i t h t h o s e o f t h e t r a n s - o c e a n i c s e c t i o n s . The number o f in d e p e n d e n t o b s e r v a t i o n s , n^, was d e t e r m i n e d by d i v i d i n g t h e square o f t h e d e c o r r e l a t i o n s c a l e ( T a b l e I V - 1 , from t h e f i r s t - z e r o c r o s s i n g s o f t h e a v e r a g e d ACFs o f t h e s e c t i o n s ) o f t h e a p p r o p r i a t e r e g i o n i n t o t h e a r e a o f each s u r v e y . i . M i d - t h e r m o c l i n e Temperature S t a t i s t i c s The sample s t a t i s t i c s o f T fr o m t h e s u r v e y s a r e shown i n T a b l e I V -4. The s t a n d a r d d e v i a t i o n s o f t h e NWA and NWP a r e s i g n i f i c a n t l y d i f f e r e n t . The S T Table IV-4 Sample standard deviation, skewness, kurtosis and intermittency of the mid-thermocline temperature (T) for the geographic regions, the NPSF and the NPEC from the surveys. W and K values that are significantly nonzero are underlined. Q i s shown only when K i s significantly nonzero. R e g i o n No. o f n̂ ^ S T 95% C o n f i d e n c e w T Krp Q T Surveys C O L i m i t s (°C) NWA 6 494 1.71 1.61 - 1.81 -0 .59 1.89 0.61 NWP 2 230 1 .42 1.30 - 1 .54 0 .47 1 .06 • 0 .74 NEA 4 466 0.66 0.62 - 0.70 0.63 1.41 0 .68 NEP 16 236 1.11 1.02 - 1 .20 0 .37 0 .86 0 .78 NPSF 10 129 0.91 0.81 - 1.02 0 .24 0 .44 - NPEC 4 68 1 .39 1.19 - 1 .60 0 .36 0 .20 - SP 1 16 0.46 0.34 - 0.71 0 .04 - 0 . 4 8 _ 71 of t h e NEP i s s i g n i f i c a n t l y l a r g e r t h a n t h e o t h e r two low-energy r e g i o n s . The NPEC has a S T o f 1.39°C w h i c h i s s i g n i f i c a n t l y l a r g e r t h a n t h a t o f t h e NPSF. Compared t o t h e S T v a l u e s o f t h e s e c t i o n s i n each r e g i o n , t h e S T o f t h e s u r v e y s a r e s i g n i f i c a n t l y h i g h e r ( e x c e p t i n t h e S P ) , p a r t i c u l a r l y t h a t o f t h e NEP w h i c h i s a l m o s t t w i c e as l a r g e . The skewness of T i s s i g n i f i c a n t l y n o nzero i n t h e NWA, NWP, t h e NEA and t h e NEP. The s i g n s o f WT from t h e s e c t i o n s f o r t h e s e r e g i o n s a r e t h e same f o r t h e NWA and NEP. The v a l u e s o f Q T compare r e a s o n a b l y w e l l w i t h t h o s e o b t a i n e d f r o m t h e s e c t i o n s , w i t h t h e e x c e p t i o n o f t h e NEP. Q T o f t h e s u r v e y s , f o r t h e NEP, i s l a r g e r by a f a c t o r o f 1.7. These s t a t i s t i c s a r e c o n s i s t e n t w i t h t h o s e o f t h e s e c t i o n s . The i n t e r m i t t e n c i e s Q T a r e somewhat l a r g e r t h a n t h e c o r r e s p o n d i n g s t a t i s t i c s o f t h e s e c t i o n s . i i . G e o p o t e n t i a l Anomaly (0-4000 kPa) S t a t i s t i c s The sample s t a t i s t i c s o f t h e g e o p o t e n t i a l anomaly o b t a i n e d f r o m t h e s u r v e y s a r e shown i n T a b l e I V - 5 . I n t h e h i g h - e n e r g y r e g i o n s , t h e NWA and t h e NWP have S D v a l u e s t h a t a r e e q u a l w i t h i n t h e 95% c o n f i d e n c e l i m i t s . The NEA, t h e NEP and t h e SP have v a l u e s o f S D t h a t a r e , g e n e r a l l y , e q u i v a l e n t w i t h i n t h e 95% c o n f i d e n c e l i m i t s . The NPEC has a s t a n d a r d d e v i a t i o n w h i c h i s s i g n i f i c a n t l y l a r g e r t h a n t h e v a l u e o f t h e NPSF. The s t a n d a r d d e v i a t i o n s f r o m t h e s u r v e y s a r e e q u a l t o t h o s e f r o m t h e s e c t i o n s w i t h i n t h e 95% c o n f i d e n c e l i m i t s i n t h e NWA, t h e NWP and t h e SP. The NEA and t h e NEP have s i g n i f i c a n t l y h i g h e r S D v a l u e s from t h e s u r v e y s t h a n from t h e s e c t i o n s . The skewness i s s i g n i f i c a n t i n t h e NWP, t h e NEA, t h e NPSF and t h e NPEC. The NWP and t h e NEA v a l u e s , o n l y , a r e c o n s i s t e n t w i t h t h o s e from t h e s e c t i o n s . The i n t e r m i t t e n c e s a r e a l l w i t h i n 0.10 o f t h e c o r r e s p o n d i n g Q D from t h e s e c t i o n s , e x c e p t f o r t h e NWA w h i c h has a h i g h e r Q D f r o m t h e s u r v e y s t h a n t h e s e c t i o n s . The NPSF has a Q D o f 0.61 compared t o t h e NEP Q D o f 0.37. Summary o f t h e C e n t r a l Moments The g e o g r a p h i c v a r i a b i l i t y o f t h e m e s o s c a l e t e m p e r a t u r e f i e l d and b a r o c l i n i c eddy f i e l d have been d i s c u s s e d w i t h t h e p o o l e d e s t i m a t e s o f t h e c e n t r a l moments o f t h e s e c t i o n s and s u r v e y s . The p r i m a r y r e s u l t s can be summarized as f o l l o w s : Table IV-5 Sample standard deviation, skewness, kurtosis and intermittency of the geopotential anomaly (D) for the geographic regions, the NPSF and the NPEC from the surveys. W and K values that are significantly nonzero are underlined. Q i s shown only when K i s significantly nonzero. Region No. o f n.̂  S D 95% C o n f i d e n c e WD K D QQ Surveys (m 2/s 2) L i m i t s (m 2/s 2) NWA 6 432 0.71 0.67 - 0.76 0.21 1 .76 0 .63 NWP 2 207 0.63 0.59 - 0.71 0.52 1 .04 0 .74 NEA 4 502 0 .32 0.30 - 0.34 0.99 2.42 0.55 NEP 16 206 0.46 0.42 - 0.50 -0.06 5.11 0 .37 NPSF 10 112 0 .32 0.28 - 0.35 0.53 1 .91 0.61 NPEC 4 60 0.53 0.45 - 0.61 -1 .09 6.75 - SP 1 17 0.46 0.34 - 0.70 0 .26 -0 .70 73 a. The b a r o c l i n i c m e s o s c a l e eddy f i e l d i n t h e h i g h - and low-energy r e g i o n s can be q u a n t i t a t i v e l y compared u s i n g t h e c e n t r a l moments of t h e HIGH and LOW r e g i o n s - The HIGH r e g i o n has g e o p o t e n t i a l anomaly p e r t u r b a t i o n s w i t h a v e r a g e a m p l i t u d e s o f 0.67 m 2/s 2, and t h e LOW r e g i o n has p e r t u r b a t i o n s w i t h average a m p l i t u d e s o f 0.26 m 2/s 2. The average a m p l i t u d e s o f t h e g e o p o t e n t i a l anomaly p e r t u r b a t i o n s a r e 2.58 t i m e s g r e a t e r i n the HIGH ' r e g i o n t h a n i n t h e LOW r e g i o n . The p o s i t i v e skewness o f t h e LOW r e g i o n s u g g e s t s t h a t t h e b a r o c l i n i c eddy f i e l d c o n s i s t s , p r e d o m i n a n t l y , o f warm e d d i e s . The skewness of the HIGH r e g i o n i s n o t s i g n i f i c a n t l y d i f f e r e n t f r o m z e r o . The i n t e r m i t t e n c i e s a r e t h e same and i n d i c a t e t h a t t h e mesoscale p e r t u r b a t i o n s o c c u r o v e r about 45% o f each r e g i o n . b. The g e o g r a p h i c v a r i a b i l i t y o f t h e m e s o s c a l e eddy f i e l d can a l s o be examined w i t h t h e m i d - t h e r m o c l i n e t e m p e r a t u r e s t a t i s t i c s . The HIGH and LOW r e g i o n s have s t a n d a r d d e v i a t i o n s of 1.40 and 0.54°C, r e s p e c t i v e l y . The r a t i o o f t h e s t a n d a r d d e v i a t i o n o f t h e HIGH r e g i o n t o t h e LOW r e g i o n i s 2.59, w h i c h i s t h e same as t h a t f o r the g e o p o t e n t i a l anomaly o f t h e two r e g i o n s . The p o s i t i v e skewness o f t h e t e m p e r a t u r e i n t h e LOW r e g i o n i s c o n s i s t e n t w i t h t h a t d i s c u s s e d above. The n e g a t i v e skewness i n t h e HIGH r e g i o n s u g g e s t s t h a t t h e b a r o c l i n i c eddy f i e l d c o n s i s t s o f p r e d o m i n a n t l y c o l d e d d i e s , as opposed t o t h e f i e l d o f warm e d d i e s i n t h e low-e n e r g y r e g i o n s . c. The s t a n d a r d d e v i a t i o n s and i n t e r m i t t e n c i e s o f t h e s u r v e y s a r e , f o r t h e most p a r t , g r e a t e r t h a n t h e c o r r e s p o n d i n g s t a t i s t i c s o f t h e s e c t i o n s . I n t h e NEP, t h i s i s a r e s u l t o f s a m p l i n g s u b r e g i o n s o f r e l a t i v e l y h i g h eddy a c t i v i t y ( i . e . t h e NPSF and NPEC). I n t h e NWA, NWP and NEA, t h i s i s a r e s u l t o f d e t r e n d i n g t h e s u r v e y s w i t h a l i n e a r t r e n d , r a t h e r t h a n a 1000 km r u n n i n g mean. d. The NPSF and NPEC, as s u b r e g i o n s o f t h e NEP, have meso s c a l e s t a t i s t i c s c h a r a c t e r i s t i c o f t h e low-energy r e g i o n s . The s t a n d a r d d e v i a t i o n s o f t e m p e r a t u r e and g e o p o t e n t i a l anomaly i n t h e two s u b r e g i o n s a r e g r e a t e r t h a n t h e c o r r e s p o n d i n g s t a t i s t i c s o f t h e NEP fr o m t h e s e c t i o n s . The s t a n d a r d d e v i a t i o n s o f t h e m i d - t h e r m o c l i n e t e m p e r a t u r e and b a r o c l i n i c eddy f i e l d s a r e g r e a t e r i n t h e NPEC t h a n t h e NPSF. The skewness o f D i n the NPSF i s p o s i t i v e . T h i s i s c o n s i s t e n t w i t h t h e NEP s t a t i s t i c s . The NPEC has a n e g a t i v e WD. T h i s i s c o n s i s t e n t w i t h t h e f i e l d o f c o l d e d d i e s t h a t was f o u n d i n t h e AXBT s u r v e y s d i s c u s s e d i n C h a p t e r I I I . 74 C. SEASONAL VARIABILITY OF THE STATISTICS The s e a s o n a l v a r i a b i l i t y of t h e m e s o s c a l e s t a t i s t i c s o f t h e NEP w i l l be examined i n t h i s s e c t i o n . The d i s t r i b u t i o n o f t h e q u a s i - s y n o p t i c XBT d a t a s e t , i n t h e f o u r q u a r t e r s of t h e y e a r ( T a b l e I V - 6 ) , shows some s e a s o n a l b i a s e s . I n p a r t i c u l a r , t h e h i g h - e n e r g y r e g i o n s have no s e c t i o n s i n t h e f i r s t q u a r t e r and o v e r 60% o f t h e s e c t i o n s i n t h e l a s t q u a r t e r . Each low-energy r e g i o n , g e n e r a l l y , has a good d i s t r i b u t i o n o f d a t a t h r o u g h o u t t h e y e a r ( w i t h t h e o b v i o u s e x c e p t i o n o f t h e SA) . When t h e low-energy r e g i o n s a r e c o n s i d e r e d as a whole, t h e r e i s a r e a s o n a b l y even d i s t r i b u t i o n o f d a t a t h r o u g h o u t t h e y e a r . The e f f e c t t h a t t h e s e s e a s o n a l b i a s e s w i l l have on t h e r e s u l t s i s n o t c l e a r . The NEP i s t h e g e o g r a p h i c r e g i o n w i t h t h e most even d i s t r i b u t i o n of s e c t i o n s o v e r t h e f o u r q u a r t e r s o f t h e y e a r . The v a r i a b i l i t y o f t h e p o o l e d s t a t i s t i c a l e s t i m a t e s o f t h e NEP f o r t h e f o u r q u a r t e r s o f t h e y e a r w i l l be u s e d t o i n v e s t i g a t e t h e p o t e n t i a l f o r t h e s e a s o n a l b i a s i n g o f t h e r e g i o n a l s t a t i s t i c s due t o t h e uneven d i s t r i b u t i o n of t h e s e c t i o n s o v e r t h e y e a r . The q u a r t e r l y - p o o l e d s t a t i s t i c s o f t h e NEP a r e summarized i n T a b l e I V - 7 . The s t a n d a r d d e v i a t i o n , skewness and i n t e r m i t t e n c y f a c t o r have s e a s o n a l v a r i a t i o n s f o r b o t h T and D. The s t a n d a r d d e v i a t i o n s o f T and D a r e l a r g e s t i n t h e f i r s t two q u a r t e r s o f t h e y e a r and s m a l l e s t i n t h e l a s t two q u a r t e r s o f t h e y e a r . The q u a r t e r l y - p o o l e d skewness o f each v a r i a b l e i s c o n s i s t e n t w i t h t h e c o r r e s p o n d i n g r e g i o n a l l y - p o o l e d skewness w i t h one e x c e p t i o n . WD i n t h e f o u r t h q u a r t e r i s n e g a t i v e r a t h e r t h a n p o s i t i v e . The i n t e r m i t t e n c i e s o f T and D e x h i b i t s i m i l a r s e a s o n a l v a r i a t i o n s w i t h t h e l a r g e s t i n t e r m i t t e n c i e s i n f i r s t and t h i r d q u a r t e r s and t h e s m a l l e s t i n t e r m i t t e n c i e s i n t h e second and f o u r t h q u a r t e r s . I n summary, i t has been seen t h a t i n t h e NEP t h e s t a n d a r d d e v i a t i o n , skewness and i n t e r m i t t e n c y e x h i b i t a s e a s o n a l v a r i a b i l i t y . T h i s s u g g e s t s t h a t t h e m e s o s c a l e s t a t i s t i c s o b t a i n e d f r o m t h e q u a s i - s y n o p t i c XBT d a t a s e t may be s e a s o n a l l y b i a s e d f o r t h e NWA, NWP, HIGH, NEA, SA and SP ( i . e . a l l t h e r e g i o n s e x c e p t t h e NEP and LOW) due t o t h e uneven d i s t r i b u t i o n o f t h e s e c t i o n s o v e r t h e y e a r . These r e g i o n s w i l l have s e a s o n a l l y - b i a s e d s t a t i s t i c s o n l y , of c o u r s e , where t h e s t a t i s t i c s have s e a s o n a l s i g n a l s . To t h e a u t h o r ' s knowledge, t h e s e a s o n a l v a r i a b i l i t y o f t h e m e s o s c a l e eddy f i e l d has been r e p o r t e d o n l y i n a s u b r e g i o n 75 Table IV-6 Summary of the number of sections by geographic region and quarter of the year. G e o g r a p h i c Q u a r t e r o f t h e Year R e g i o n 1 2 3 4 Tota: HIGH NWA o 4 4 15 23 NWP rj 4 0_ 4 8 T o t a l 0 8 4 19 31 LOW NEA 1 4 4 7 16 SA 2 0 0 0 2 NEP 8 5 10 14 37 SP 3 1 0 5 9 T o t a l 14 10 14 26 64 Table IV-7 Summary of the s t a t i s t i c s of T and D from the sections f o r the NEP by quarter of the year- W and K values that are s i g n i f i c a n t l y nonzero are underlined. Q i s shown only when K i s s i g n i f i c a n t l y nonzero. The T standard deviations have u n i t s of °C . The D standard deviations have units of (m/s) 2. V a r i a b l e Q u a r t e r No. o f nL s 95% C o n f i d e n c e W K S e c t i o n s L i m i t s T D 1 8 294 0.68 0.63 - 0.73 0.09 1.17 0.72 2 5 205 0.65 0.59 - 0.71 0.59 4.43 0.40 3 10 407 0.42 0.39 - 0.44 0 .45 2.04 0.60 4 14 448 0.58 0.54 - 0.61 -0.12 4.05 0 .43 1 8 285 0.29 0.26 - 0.31 0.34 2.40 0.56 2 5 202 0.32 0 .29 - 0.35 0.42 3.90 0.44 3 10 402 0.22 0.20 - 0.23 0.45 1.29 0.70 4 14 441 0.25 0 .23 - 0.26 -0 .30 3.20 0.48 77 o f t h e NEA. D i c k s o n e t a l . (1982) f o u n d a s i g n i f i c a n t s e a s o n a l s i g n a l o f t h e eddy k i n e t i c energy e s t i m a t e s a t a number o f s i t e s i n t h e N o r t h e a s t A t l a n t i c , n o r t h o f t h e A z o r e s (35°N t o 60°N). The N o r t h E a s t A t l a n t i c Dynamics Study (NEADS) c o l l e c t e d t w o - y e a r - l o n g c u r r e n t r e c o r d s a t depths between 200 and 4000 m. The a m p l i t u d e o f t h e s i g n a l was l a r g e enough t h a t t h e r e c o r d s were dominated by t h e w i n t e r maxima. T h i s e f f e c t was seen from 200 t o 4000 m a t a l l t h e s i t e s w i t h s i g n i f i c a n t bottom s l o p e s o r roughness. The p a u c i t y o f t h e d a t a a v a i l a b l e w i l l n o t p e r m i t a more comprehensive e x a m i n a t i o n o f t h e i s s u e . T h i s a n a l y s i s may be us e d t o h i g h l i g h t t h e p o t e n t i a l o f t h e b i a s i n g o f t h e r e s u l t s due t o s e a s o n a l s i g n a l s o f t h e mesoscale eddy f i e l d , however t h e b i a s i n g cannot be q u a n t i t a t i v e l y o r even q u a l i t a t i v e l y d e t e r m i n e d . D. HORIZONTAL ANISOTROPY An a n i s o t r o p y f a c t o r , A s has been e v a l u a t e d u s i n g t h e averaged a u t o c o r r e l a t i o n f u n c t i o n s o f t h e s u r v e y s t o p a r a m e t e r i z e t h e h o r i z o n t a l a n i s o t r o p y o f t h e m e s o s c a l e eddy f i e l d s . The a n i s t r o p y f a c t o r i s o b t a i n e d f r o m t h e r e l a t i o n , A s = L M / L Z , where L M and L z a r e t h e m e r i d i o n a l and z o n a l d e c o r r e l a t i o n s c a l e s o b t a i n e d f r o m t h e f i r s t z e r o - c r o s s i n g s o f t h e a v e r a g e d m e r i d i o n a l and z o n a l a u t o c o r r e l a t i o n f u n c t i o n s , r e s p e c t i v e l y . The a n i s o t r o p y f a c t o r i s i m p o r t a n t , t o e v a l u a t e t h e a s s u m p t i o n o f i s o t r o p y t h a t has been w i d e l y u s e d i n t h i s and o t h e r s t u d i e s . Where t h e m e s o s c a l e eddy f i e l d s a r e n o t i s o t r o p i c , A s w i l l p r o v i d e a measure o f t h a t a n i s o t r o p y . The a v e r a g e d i s o t r o p i c , m e r i d i o n a l and z o n a l a u t o c o r r e l a t i o n f u n c t i o n s (ACFs) were c a l c u l a t e d from t h e s u r v e y s i n each g e o g r a p h i c r e g i o n . The ACFs o f each s u r v e y were c a l c u l a t e d by b i n n i n g t h e p e r t u r b a t i o n v a r i a b l e s o f each p a i r o f XBTs i n t o 20 km wide b i n s . F o r t h e i s o t r o p i c ACF, t h e XBT p a i r s were b i n n e d a c c o r d i n g t o t h e r h u m b l i n e d i s t a n c e between them. The m e r i d i o n a l and z o n a l ACFs where c a l c u l a t e d by b i n n i n g t h e XBT p a i r s by t h e i r m e r i d i o n a l and z o n a l s e p a r a t i o n , r e s p e c t i v e l y , w i t h i n 20 km wide swaths. Due t o t h e l i m i t e d m e r i d i o n a l o r z o n a l e x t e n t o f some o f t h e s u r v e y s , t h e m e r i d i o n a l and z o n a l ACFs a r e somewhat n o i s y . The averaged ACFs were o b t a i n e d by a v e r a g i n g t h e a p p r o p r i a t e i n d i v i d u a l ACFs w i t h i n t h e g e o g r a p h i c r e g i o n s . As an example, p l o t s o f t h e ACFs f o r t h e NWP and t h e NEP a r e shown i n F i g u r e I V - 2 . 78 NWP NEP Figure IV-2 Sample p l o t s of the averaged i s o t r o p i c , meridional and zonal autocorrelation functions f o r the NWP and NEP. The p l o t s on the l e f t are the i s o t r o p i c ACFs with 95% confidence l i m i t s (dashed l i n e s ) . The p l o t s on the r i g h t are the i s o t r o p i c ACFs ( s o l i d l i n e ) , meridional ACFs (long-dashed l i n e ) and the zonal ACFs (short-dashed l i n e ) . 79 The i s o t r o p i c d e c o r r e l a t i o n s c a l e s o b t a i n e d f r o m t h e f i r s t - z e r o c r o s s i n g s o f t h e r e g i o n a l l y - a v e r a g e d ACFs of t h e s u r v e y s a r e summarized i n T a b l e I V - 8 . The g e o g r a p h i c v a r i a b i l i t y of t h e s e d e c o r r e l a t i o n s c a l e s , t h a t can be d e f i n e d t o t h e 95% c o n f i d e n c e l i m i t s ( i . e . t h e s c a l e s t h a t a r e u n d e r l i n e d i n T a b l e I V - 8 ) , e x h i b i t t h e same g e n e r a l g e o g r a p h i c v a r i a b i l i t y as t h e d e c o r r e l a t i o n s c a l e s from t h e s e c t i o n s ( T a b l e I V - 1 ) . These d e c o r r e l a t i o n s c a l e s a r e about t w i c e as l a r g e as t h o s e of the s e c t i o n s because t h e l a r g e - s c a l e s i g n a l was d e t r e n d e d w i t h a l i n e a r f i t f o r t h e s u r v e y s and a 1000 km r u n n i n g mean f o r t h e s e c t i o n s . The 95% c o n f i d e n c e l i m i t s o f t h e s c a l e s i n T a b l e IV-8 may be d e t e r m i n e d f r o m t h e f i r s t - z e r o c r o s s i n g s o f t h e 95% c o n f i d e n c e l i m i t s o f t h e ACFs. The d e c o r r e l a t i o n s c a l e cannot be u n i q u e l y d e t e r m i n e d a t t h e 95% c o n f i d e n c e l e v e l where th e upper 95% c o n f i d e n c e l i m i t does not c r o s s z e r o . The c o n f i d e n c e l i m i t s a r e wide and a r e n o t shown. I t i s s u f f i c i e n t t o say t h a t , w i t h o u t a s i n g l e e x c e p t i o n , t h e i s o t r o p i c d e c o r r e l a t i o n s c a l e s a r e n o t s i g n i f i c a n t l y d i f f e r e n t from each o t h e r . The a n i s o t r o p y f a c t o r and the m e r i d i o n a l and z o n a l d e c o r r e l a t i o n l e n g t h s c a l e s a r e summarized by g e o g r a p h i c r e g i o n i n T a b l e I V - 9 . The 95% c o n f i d e n c e l i m i t s o f 1^ and L z may be d e t e r m i n e d i n t h e same manner as t h e i s o t r o p i c d e c o r r e l a t i o n s c a l e s w i t h t h e 95% e r r o r b a r s ( n o t shown). L^j and L z a r e nowhere s i g n i f i c a n t l y d i f f e r e n t from each o t h e r , t h u s , A s i s not d i f f e r e n t f r o m one. There i s no s i g n i f i c a n t i n d i c a t i o n f r o m t h e s e r e s u l t s t h a t t h e m e s o s c a l e eddy f i e l d s a r e a n i s o t r o p i c and t h e r e f o r e t h e a s s u m p t i o n o f i s o t r o p y , f o r t h e m e s o s c a l e eddy f i e l d s examined i n t h i s i n v e s t i g a t i o n , appears t o be q u i t e r e a s o n a b l e . K. WAVENUMBER SPECTRA The p u r p o s e o f t h i s s e c t i o n i s t o examine t h e g e o g r a p h i c v a r i a b i l i t y o f t h e wavenumber s p e c t r a o f t h e m i d - t h e r m o c l i n e t e m p e r a t u r e and t h e g e o p o t e n t i a l anomaly p e r t u r b a t i o n s . T h i s s e c t i o n i s d i v i d e d i n t o s u b s e c t i o n s d i s c u s s i n g t h e methods u s e d t o e s t i m a t e t h e s p e c t r a , t h e t o t a l s p e c t r a l v a r i a n c e , t h e d i s t r i b u t i o n o f v a r i a n c e i n wavenumber s p a c e , t h e dominant w a v e l e n g t h s , t h e eddy k i n e t i c e n e r g y , and t h e b a r o c l i n i c l e n g t h and v e l o c i t y s c a l e s . T h i s e x a m i n a t i o n o f t h e wavenumber s p e c t r a w i l l be r e s t r i c t e d t o t h e range o f 10~3 t o 10~ 2 c y c l e s / k m ( i . e . 1000 t o 100 km w a v e l e n g t h s ) s i m i l a r t o t h e SEASAT a l t i m e t r y a n a l y s i s o f Fu (1983). The m e s o s c a l e s i g n a l s a r e e i t h e r 80 Table IV-8 Isotropic decorrelation scales obtained from the f i r s t - z e r o crossings of the regionally-averaged autocorrelation functions of the surveys- The decorrelation scales that can be defined to the 95% confidence l e v e l are underlined- R e g i o n D e c o r r e l a t i o n S c a l e s (km) T D NWA 147 145 NWP 135 150 NEA 146 130 NEP 191 200 NPSF 150 143 NPEC 122 104 SP 115 >180 81 Table IV-9 The anisotropy factor, Ag = L M / L Z , i s the ratio of the meridional decorrelation length scale ( 1 ^ ) from the averaged meridional autocorrelation function of the the surveys to the zonal decorrelation length scale ( L Z ) from the averaged zonal autocorrelation function. The units of L J J and L Z are kilometers. R e g i o n T D A s L M L z A s L M L z NWA 0.34 85 250 0.55 123 224 NWP 1-10 152 138 1.08 153 142 NEA — >160 149 — >160 140 NEP 0.73 210 289 2.76 387 140 NPSF 0.75 119 159 0.86 111 129 NPEC — 89 >320 — 85 >320 SP 1-01 117 116 — 110 >180 82 s u f f i c i e n t l y s m a l l o r s u f f i c i e n t l y a t t e n u a t e d by t h e h i g h - p a s s f i l t e r t o be u n i m p o r t a n t a t wavenumbers l e s s t h a n 10 -3 c y c l e s / k m . The average s a m p l i n g i n t e r v a l s o f t h e s p a t i a l s e r i e s i n t h e g e o g r a p h i c r e g i o n s v a r y c o n s i d e r a b l y f r o m 100 t o 35 km. T h i s c r e a t e s a wide range of N y q u i s t wavenumbers t h a t a r e g e n e r a l l y ( w i t h t h e e x c e p t i o n o f t h e SA and t h e SP) g r e a t e r t h a n 1 0 - 2 c y c l e s / k m . As w i l l be s e e n , t h e g e o p h y s i c a l s i g n a l s a t wavenumbers h i g h e r t h a n 1 0 - 2 c y c l e s / k m * c o n t a i n r e l a t i v e l y s m a l l amounts o f t h e v a r i a n c e compared t o t h e 10 -3 t o 1 0 - 2 c y c l e s / k m r a n g e . The use o f t h i s wavenumber range a l s o f a c i l i t a t e s t h e c o m p a r i s o n of t h e s p e c t r a between t h e g e o g r a p h i c r e g i o n s and w i t h t h e r e s u l t s o f Fu (1983). E s t i m a t i o n o f the S p e c t r a The g e o g r a p h i c v a r i a b i l i t y o f t h e v a r i a n c e i n wavenumber space w i l l be examined u s i n g n o r m a l i z e d v a r i a n c e - c o n s e r v i n g s p e c t r a l p l o t s , and t h e dominant w a v e l e n g t h s w i l l be i d e n t i f i e d u s i n g v a r i a n c e - c o n s e r v i n g s p e c t r a l p l o t s w i t h e r r o r b a r s . The s p e c t r a o f each g e o g r a p h i c r e g i o n were o b t a i n e d by a v e r a g i n g t h e s p e c t r a o f t h e i n d i v i d u a l t r a n s - o c e a n i c s e c t i o n s . The raw s p e c t r a l e s t i m a t e s o f each s e c t i o n were c a l c u l a t e d u s i n g a F o u r i e r t r a n s f o r m s u b r o u t i n e a v a i l a b l e i n t h e UBC Computing C e n t r e s o f t w a r e l i b r a r y (Moore, 1981). T h i s s u b r o u t i n e r e q u i r e s no p a d d i n g o r t r u n c a t i n g o f t h e d a t a . The raw e s t i m a t e s o f t h e s e c t i o n s were b i n n e d i n t o wavenumber b i n s w i t h w i d t h s o f 3.9 x 10~3 c y c l e s / k m and averaged, t o o b t a i n r e g i o n a l raw s p e c t r a l e s t i m a t e s between 1.95 x 10 -4 and 2.5 x 1 0 - 2 c y c l e s / k m - Smoothed s p e c t r a l e s t i m a t e s were computed w i t h a D a n i e l l ( b o x c a r ) window o v e r f i v e a d j o i n i n g s p e c t r a l e s t i m a t e s . V a r i a n c e - c o n s e r v i n g p l o t s o f t h e s p e c t r a where p r o d u c e d by m u l t i p l y i n g t h e smoothed s p e c t r a l e s t i m a t e s by t h e i r c o r r e s p o n d i n g wavenumbers and p l o t t i n g t h e r e s u l t s on a l o g a r i t h m i c wavenumber s c a l e . The a r e a under any wavenumber band o f t h i s p l o t i s e q u a l t o t h e v a r i a n c e w i t h i n t h a t wavenumber band t i m e s 2.3. ( I f t h e s e p l o t s were p r o d u c e d on a n a t u r a l l o g a r i t h m i c wavenumber s c a l e , t h e a r e a under t h e c u r v e w o u l d be e q u a l t o t h e v a r i a n c e . ) N o r m a l i z e d v a r i a n c e - c o n s e r v i n g p l o t s o f t h e s p e c t r a were p r o d u c e d f o r t h e wavenumber range 10"-* t o 1 0 - 2 c y c l e s / k m by d i v i d i n g t h e v a r i a n c e - c o n s e r v i n g s p e c t r a by t h e t o t a l v a r i a n c e w i t h i n t h i s wavenumber r a n g e . The a r e a under t h e c u r v e o f a 83 n o r m a l i z e d v a r i a n c e - c o n s e r v i n g p l o t between 10"3 and 1 0 - 2 c y c l e s / k m on a n a t u r a l l o g a r i t h m i c wavenumber s c a l e i s e q u a l t o one. The s p e c t r a have been p l o t t e d on a l o g a r i t h m i c wavenumber s c a l e t o t h e base t e n t o f a c i l i t a t e i n t e r p r e t a t i o n . Examples of t h e n o r m a l i z e d v a r i a n c e - c o n s e r v i n g s p e c t r a a r e shown i n F i g u r e I V - 3 . These s p e c t r a w i l l be u s e d t o d i s c u s s t h e g e o g r a p h i c v a r i a b i l i t y o f t h e d i s t r i b u t i o n of t h e v a r i a n c e o f each v a r i a b l e between t h e w a v e l e n g t h s o f 1000 and 100 km. Two d i f f e r e n t s e t s of e r r o r b a r s were p r o d u c e d f o r each v a r i a n c e - c o n s e r v i n g s p ectrum. An example i s shown i n F i g u r e I V - 4 . N i n e t y - f i v e p e r c e n t and e i g h t y p e r c e n t c o n f i d e n c e i n t e r v a l s were d e t e r m i n e d u s i n g t h e s t a n d a r d e r r o r o f each s p e c t r a l e s t i m a t e . The 95% c o n f i d e n c e i n t e r v a l s were c a l c u l a t e d w i t h t h e r e l a t i o n + C > 0 2 5 S s / ( n s ) 1 / 2 ? where S s i s t h e sample s t a n d a r d d e v i a t i o n o f t h e smoothed s p e c t r a l e s t i m a t e and n s i s t h e number o f s p e c t r a l e s t i m a t e s . F o r n s > 30, C.025 = 1*960, t h e v a l u e o f t h e s t a n d a r d normal d i s t r i b u t i o n l e a v i n g an a r e a o f .025 t o t h e r i g h t . F o r n g < 30» ' c . 0 2 5 was o b t a i n e d from t h e S t u d e n t - t d i s t r i b u t i o n w i t h n s-1 degrees o f freedom. The 80% c o n f i d e n c e i n t e r v a l s were c a l c u l a t e d w i t h t h e same r e l a t i o n u s i n g C > 0 v These e r r o r b a r s , a c c o u n t f o r t h e u n c e r t a i n t y o f t h e s p e c t r a l e s t i m a t e s due t o t h e c o m p u t a t i o n a l p r o c e d u r e and t h e u n c e r t a i n t y due t o t h e i n s t r u m e n t n o i s e and g e o p h y s i c a l s i g n a l . S p e c t r a l V a r i a n c e The s p e c t r a l v a r i a n c e o f T and D, between w a v e l e n g t h s o f 1000 and 100 km, was o b t a i n e d by i n t e g r a t i n g t h e v a r i a n c e - c o n s e r v i n g s p e c t r a . The SA and SP r e g i o n s were i n t e g r a t e d up t o t h e i r N y q u i s t wavenumbers a t about t h e 200 km w a v e l e n g t h , so t h e i r v a r i a n c e s a r e n o t d i r e c t l y comparable t o t h e o t h e r r e g i o n s . The v a r i a n c e e s t i m a t e s w i t h 95% c o n f i d e n c e l i m i t s a r e summarized i n T a b l e IV-10. The s p e c t r a l v a r i a n c e s i n t h i s wavenumber band, n a t u r a l l y , e x h i b i t t h e same p a t t e r n s of g e o g r a p h i c v a r i a b i l i t y as t h e r e g i o n a l l y - p o o l e d e s t i m a t e s o f t h e s t a n d a r d d e v i a t i o n s o f t h e s p a t i a l s e r i e s . I n t h e HIGH r e g i o n , t h e v a r i a n c e s o f T and D a r e 1.018°C 2 and 0.237 ( m / s ) 4 , r e s p e c t i v e l y . I n t h e LOW r e g i o n t h e s e v a r i a n c e s a r e 0.169°C 2 and 0.040 ( m / s ) 4 . The v a r i a n c e o f each v a r i a b l e i s s i g n i f i c a n t l y h i g h e r i n t h e HIGH r e g i o n compared t o t h e LOW r e g i o n . 84 WAVELENGTH - KM 104 103 io 2 io 1 WAVELENGTH - KM [O4 . 103 102 IO1 IO'4 3 5 IO"3 3 5 IO"2 3 5 IO"1 K - CYCLES/KM • IO-4 3 5 10-3 3 5 IO"2 3 5 IO'1 K - CYCLES/KM Figure XV-3 Examples of the normalized variance-conserving spectra. These two spectra represent the variance of the geopotential anomaly perturbations, D, as a function of wavenumber f o r the HIGH and LOW regions. The variance-conserving spectra were normalized by the t o t a l variance between wavenumbers of 10"^ and 1 0 - 2 cycles/km. These spectra are used to compare the sp e c t r a l shapes between geographic regions. 85 W A V E L E N G T H - K M 104 103 IO2 10' • l u i i M i i in1 1 1 1 1 i in1 1 1 1 1 i 10- 3 5 10-3 3 5 10-* • 3 5 10" K - C Y C L E S / K M W A V E L E N G T H - K M IO4 103 102 10' IO-4 3 5 IO"3 3 5 IO"2 3 5 10" K - C Y C L E S / K M W A V E L E N G T H - K M N colO4 IO3 102 10' IO-4 3 5 IO"3 3 5 IO"2 3 5 10"' K - C Y C L E S / K M W A V E L E N G T H - K M c£l04 103 10* 10' [ T | 1 | I | l l l l j 1 | I 11 III IO-4 3 5 IO"3 3 5 IO"2 3 5 10"' K - C Y C L E S / K M Figure IV - 4 Examples of the variance-conserving spectra with confidence l i m i t s . This f i g u r e presents the spectra of the geopotential anomaly perturbations f o r the HIGH and LOW regions with two d i f f e r e n t sets of erro r bars. The spectra on the l e f t side have 95% confidence i n t e r v a l s obtained with the standard e r r o r of the spec t r a l estimates of the sections. The spectra on the r i g h t s i d e have 80% confidence i n t e r v a l s obtained i n the same manner. These spectra are used t o i d e n t i f y d i s t i n c t peak wavenumbers and the confidence with which they are defined. 86 Table IV-10 Variance of T and D with 95% confidence l i m i t s obtained by i n t e g r a t i n g the spectra between wavelengths of 1000 and 100 km. The SA and SP variances have a s t e r i s k s since these regions have average Nyquist wavenumbers les s than 1 0 - 2 cycles Am- The variances of these regions were obtained by i n t e g r a t i n g the spectra from 10~3 cycles/km to the Nyquist wavenumber (at approximately a 200 km wavelength). T D R e g i o n V a r i a n c e 95% C o n f i d e n c e V a r i a n c e 95% C o n f i d e n c e (»C 2) L i m i t s (°C 2) ( m 4 / s 4 ) L i m i t s ( m 4 / s 4 ) NWA 1.014 0.665 - 1.426 0.239 0.142 - 0.336 NWP 1.015 0.580 - 1.378 0.219 0.131 - 0.307 NEA 0.107 0.041 - 0.173 0.017 0.010 - 0.027 SA 0.096* 0.077 - 0.121 0.016* 0.011 - 0.023 NEP 0.194 0.149 - 0.246 0.045 0.036 - 0.056 SP 0.131* 0.092 - 0.170 0.035* 0.017 - 0.049 HIGH 1.018 0.732 - 1.304 0.237 0 . 1 6 8 - 0 . 3 2 1 LOW 0.169 0.139 - 0.211 0.040 0.031 - 0.049 87 I n t e r p r e t a t i o n of t h e S p e c t r a The g e o g r a p h i c v a r i a b i l i t y o f t h e wavenumber s p e c t r a and t h e dominant w a v e l e n g t h s of t h e wavenumber s p e c t r a w i l l be d i s c u s s e d w i t h t h e n o r m a l i z e d v a r i a n c e - c o n s e r v i n g p l o t s of each v a r i a b l e as d e p i c t e d on maps showing t h e g e o g r a p h i c r e g i o n s t h a t t h e s p e c t r a r e p r e s e n t ( e . g . F i g u r e I V - 5 ) . T h i s p r o d u c t has been d e s i g n e d t o f a c i l i t a t e t h e g e o g r a p h i c c o m p a r i s o n s o f t h e s p e c t r a l shapes. The dominant w a v e l e n g t h s of v a r i a t i o n o f each v a r i a b l e a r e summarized by g e o g r a p h i c r e g i o n i n t a b l e s (e.g. T a b l e I V - 1 1 ) . T h i s p r o d u c t l i s t s t h e peak w a v e l e n g t h s , t h e c o n f i d e n c e l e v e l s , t h e b a n d w i d t h s and t h e p e r c e n t a g e o f v a r i a n c e (between 1 0 - 3 and 10~ 2 cyclesAm) t h a t i s a c c o u n t e d f o r by t h e wavenumber bands. The dominant w a v e l e n g t h s and c o n f i d e n c e i n t e r v a l s were d e t e r m i n e d from v a r i a n c e - c o n s e r v i n g s p e c t r a w i t h e r r o r b a r s . The w a v e l e n g t h bands were d e f i n e d by t h e h a l f - p o w e r p o i n t s o f t h e s p e c t r a l peaks o r t h e t r o u g h s between a d j a c e n t bands. The p e r c e n t a g e o f t h e v a r i a n c e , t h a t each w a v e l e n g t h band c o n t r i b u t e s t o t h e t o t a l v a r i a n c e between 1000 and 100 km, was d e t e r m i n e d from n o r m a l i z e d v a r i a n c e - c o n s e r v i n g s p e c t r a . i . S p e c t r a o f t h e M i d - t h e r m o c l i n e Temperature The n o r m a l i z e d v a r i a n c e - c o n s e r v i n g s p e c t r a o f T a r e shown i n F i g u r e I V - 5 . The dominant w a v e l e n g t h s a r e t a b u l a t e d i n T a b l e I V - 1 1 . The s p e c t r u m o f t h e NWA has two dominant w a v e l e n g t h s and t h e s p e c t r u m o f t h e NWP has t h r e e dominant w a v e l e n g t h s w h i c h a r e d i s t i n c t t o a t l e a s t t h e 80% c o n f i d e n c e l e v e l . The low-energy r e g i o n s have one dominant w a v e l e n g t h each ( e x c e p t f o r t h e NEP) w h i c h a r e d i s t i n c t t o a t l e a s t t h e 80% c o n f i d e n c e l e v e l . The NEP has two dominant w a v e l e n g t h s , b o t h d i s t i n c t t o t h e 95% c o n f i d e n c e l e v e l . The T spec t r u m o f t h e HIGH r e g i o n has peak w a v e l e n g t h s a t 340 km, d i s t i n c t t o t h e 95% c o n f i d e n c e l e v e l s , and a t 195 km, d i s t i n c t t o t h e 80% c o n f i d e n c e l e v e l s . The LOW r e g i o n has peak w a v e l e n g t h s o f 320 and 170 km, b o t h d i s t i n c t t o t h e 95% c o n f i d e n c e l e v e l s . The d i f f e r e n c e i n t h e d i s t r i b u t i o n o f t h e v a r i a n c e between t h e s e two s p e c t r a i s c h a r a c t e r i s t i c o f t h e d i f f e r e n c e s between t h e s p e c t r a l shapes of t h e h i g h - and low-energy r e g i o n s . A l t h o u g h t h e dominant w a v e l e n g t h s a r e comparable, t h e HIGH r e g i o n has a s m a l l e r p e r c e n t a g e o f i t s v a r i a n c e i n t h e l a r g e r w a v e l e n g t h band and t w i c e t h e p e r c e n t a g e o f i t s v a r i a n c e i n t h e s h o r t e r w a v e l e n g t h band t h a n t h e LOW r e g i o n . 00 CO Figure IV-5 Normalized variance-conserving spectra of the mid-thermocline temperatures on a map showing the regions that the spectra represent. The s t i p p l e d areas are the high-energy regions. The spectra are p l o t t e d between wavenumbers of 1 0 - 3 and 1 0 - 2 cycles/km. 89 Table IV-11 Peak wavelengths of the temperature spectra. The peaks are d i s t i n c t to the confidence l i m i t s shown. The wavelength band indicates the range between the half-power points. The percent variance i s the contribution to the t o t a l variance between wavelengths of 1000 and 100 km. The t o t a l variances of the SA and SP were determined between 1000 and 200 km. R e g i o n Peak Wavelength C o n f i d e n c e Wavelength P e r c e n t o f (km) L e v e l Band (km) V a r i a n c e NWA 285 95% 560 - 220 53 165 80% 220 - 120 35 NWP 340 95% 590 - 245 58 180 80% 245 - 160 18 145 80% 160 - 120 13 NEA • 220 95% 320 - 130 63 SA 395 80% 600 - 300 73 250 ~ 300 - 210 18 NEP 320 95% 600 - 200 70 170 95% 200 - 110 13 SP 395 80% 600 - 220 81 HIGH 340 95% 600 - 220 53 195 80% 220 - 130 30 LOW 320 95% 700 - 195 70 170 95% 195 - 120 15 90 i i . S p e c t r a o f t h e G e o p o t e n t i a l Anomaly (0-4000 kPa) The n o r m a l i z e d v a r i a n c e - c o n s e r v i n g s p e c t r a o f D a r e shown i n F i g u r e I V - 6 . The dominant w a v e l e n g t h s a r e t a b u l a t e d i n T a b l e IV-12. The NWA has two dominant w a v e l e n g t h s . The l o n g e s t w a v e l e n g t h i s d i s t i n c t t o t h e 95% c o n f i d e n c e l e v e l and t h e s h o r t e r w a v e l e n g t h i s not d i s t i n c t t o t h e 80% c o n f i d e n c e l e v e l . The NWP has t h r e e peak w a v e l e n g t h s , a l l d i s t i n c t t o a t l e a s t t h e 80% c o n f i d e n c e l e v e l . The NEA has t h r e e dominant w a v e l e n g t h s . The SA and t h e NEP have two dominant w a v e l e n g t h s each and t h e SP has one dominant w a v e l e n g t h . The l o n g e r w a v e l e n g t h s o f t h e NEA, SA and NEP are d i s t i n c t t o t h e 95% c o n f i d e n c e l e v e l . The o t h e r w a v e l e n g t h s a r e n o t d i s t i n c t a t t h e 80% c o n f i d e n c e l e v e l . The s p e c t r a l shapes o f t h e HIGH and LOW r e g i o n s a r e , of c o u r s e , s i m i l a r t o t h o s e o f t h e m i d - t h e r m o c l i n e t e m p e r a t u r e s p e c t r a . The r e s p e c t i v e s p e c t r a l peaks i n t h e HIGH r e g i o n o c c u r a t 300 km, d i s t i n c t t o t h e 95% c o n f i d e n c e l e v e l , and a t 155 km. The 155 km peak i s n o t d i s t i n c t t o t h e 80% c o n f i d e n c e l e v e l . The D s p e c t r u m i n t h e LOW r e g i o n has peak w a v e l e n g t h s a t 300 km, d i s t i n c t t o t h e 95% c o n f i d e n c e l e v e l , and a t 170 km. The l a t t e r s p e c t r a l peak i s n o t d i s t i n c t t o t h e 80% c o n f i d e n c e l e v e l . i i i . Summary o f t h e Wavenumber S p e c t r a The g e o g r a p h i c v a r i a b i l i t y o f b o t h t h e wavenumber s p e c t r a and t h e dominant w a v e l e n g t h s o f t h e m e s o s c a l e t e m p e r a t u r e and b a r o c l i n i c eddy f i e l d s can be summarized as f o l l o w s : a. The dominant w a v e l e n g t h s o f v a r i a b i l i t y o f t h e T and D v a r i a b l e s have been i d e n t i f i e d w i t h c o n f i d e n c e l e v e l s a t w h i c h t h e y a r e d i s t i n c t ( T a b l e s IV-11 and I V - 1 2 ) . The dominant w a v e l e n g t h s a r e between 400 and 100 km. There a r e no s i g n i f i c a n t s c a l e s e p a r a t i o n s between t h e dominant l e n g t h s c a l e s o f t h e h i g h - e n e r g y r e g i o n s and t h e low-energy r e g i o n s . The v a r i a n c e s o f t h e h i g h - e n e r g y r e g i o n s a r e , however, s i g n i f i c a n t l y h i g h e r t h a n t h e v a r i a n c e s o f t h e low-energy r e g i o n f o r a g i v e n v a r i a b l e . b. I n a l l r e g i o n s , t h e l o n g e r w a v e l e n g t h bands c o n t a i n t h e g r e a t e s t p e r c e n t a g e o f t h e m e s o s c a l e eddy v a r i a n c e s . A l t h o u g h t h e dominant wavelengths a r e g e n e r a l l y c o m p a r a b l e between t h e h i g h - and low-energy r e g i o n s , t h e Figure IV-6 Normalized variance-conserving spectra of the geopotential anomaly on a map showing the regions that the spectra represent. The stippled areas are the high-energy regions. The spectra are plotted between wavenumbers of 10"^ and 10~ 2 cycles/km. 92 Table I V - 1 2 Peak wavelengths of the geopotential anomaly spectra. The peaks are d i s t i n c t to the confidence l i m i t s shown. The bandwidths are between the half-power points of the peaks. The percent variance i s the contribution to the t o t a l variance between wavelengths of 1 0 0 0 and 1 0 0 km. The t o t a l variances of the SA and SP were determined between 1 0 0 0 and 2 0 0 km. Region Peak Wavelength Confidence Wavelength Percent of (km) Level Band (km) Variance NWA 285 95% 600 - 220 55 155 — 220 - 120 35 NWP 395 95% 600 - 240 55 195 80% 240 - 155 20 145 95% 155 - 130 •' 10 NEA 205 95% 340 - 190 33 160 — 190 - 130 23 115 — 130 - 100 10 SA 510 95% 680 - 320 63 245 — 320 - 220 15 NEP 320 95% 620 - 190 71 170 — 190 - 120 16 SP 300 — 500 - 220 73 HIGH 300 95% 620 - 220 60 155 ~ 220 - 120 30 LOW 300 95% 690 - 190 73 170 — 190 - 120 15 93 h i g h - e n e r g y r e g i o n s , compared t o t h e low-energy r e g i o n s have s m a l l e r p e r c e n t a g e s o f t h e i r v a r i a n c e s i n t h e l o n g e r w a v e l e n g t h s and about t w i c e t h e p e r c e n t a g e s of v a r i a n c e s i n the s h o r t e r w a v e l e n g t h bands. c The NEA r e g i o n i s an anomalous r e g i o n . The dominant w a v e l e n g t h s a r e n o t i c e a b l y s h o r t e r t h a n t h o s e o f t h e o t h e r g e o g r a p h i c r e g i o n s . The anomalous n a t u r e of t h e NEA i s perhaps due t o some s e t of c h a r a c t e r i s t i c f o r c i n g mechanisms i n t h e r e g i o n . Eddy K i n e t i c Energy E s t i m a t e s G e o s t r o p h i c v e l o c i t y s p e c t r a have been used t o e s t i m a t e t h e g e o s t r o p h i c eddy k i n e t i c energy i n t h e wavenumber range 10~3 t o 1 0 ~ 2 c y c l e s / k m and t h e p o r t i o n s o f t h i s EKE a t t r i b u t a b l e t o t h e wavenumber bands o f each peak i n t h e g e o p o t e n t i a l anomaly s p e c t r a . The n o r m a l i z e d v a r i a n c e - c o n s e r v i n g s p e c t r a o f t h e g e o s t r o p h i c v e l o c i t y were o b t a i n e d from t h e g e o p o t e n t i a l anomaly s p e c t r a w i t h t h e g e o s t r o p h i c r e l a t i o n . The wavenumber bands c o r r e s p o n d v e r y c l o s e l y t o t h o s e o f t h e D s p e c t r a . The t o t a l eddy k i n e t i c energy p e r u n i t mass was c a l c u l a t e d f o r t h e wavenumber band 10~3 t o 1 0 - 2 c y c l e s / k m by i n t e g r a t i n g t h e s e v a r i a n c e - c o n s e r v i n g s p e c t r a . The 95% c o n f i d e n c e l i m i t s on t h e s e EKE e s t i m a t e s were d e t e r m i n e d by i n t e g r a t i n g t h e r e s p e c t i v e c u r v e s d e f i n e d by t h e l o w e r bound of t h e 95% c o n f i d e n c e l i m i t s and t h e upper bound o f t h e 95% c o n f i d e n c e l i m i t s . The EKEs o b t a i n e d from t h e i n t e g r a t i o n o f t h e g e o s t r o p h i c v e l o c i t y s p e c t r a p r o v i d e o n l y t h a t p o r t i o n o f t h e k i n e t i c energy due t o one o f t h e two o r t h o g o n a l h o r i z o n t a l components o f t h e p e r t u r b a t i o n v e l o c i t i e s . They must t h e r e f o r e be termed t h e o n e - d i m e n s i o n a l EKE. The t w o - d i m e n s i o n a l i s o t r o p i c EKE has been e s t i m a t e d as two t i m e s t h e o n e - d i m e n s i o n a l eddy k i n e t i c e n e r g y . Under t h e p r e s e n t a s s u m p t i o n t h a t t h e p e r t u r b a t i o n v a r i a b l e s i n e a c h g e o g r a p h i c r e g i o n a r e e r g o d i c , s t a t i o n a r y , random p r o c e s s e s , t h e a u t o c o v a r i a n c e f u n c t i o n i s r o t a t i o n a l l y i n v a r i a n t . The v e l o c i t y s p e c t r a o f t h e two o r t h o g o n a l components o f t h e p e r t u r b a t i o n v e l o c i t i e s w i l l , t h u s , be s i m i l a r and t h e i r c o n t r i b u t i o n s t o t h e t w o - d i m e n s i o n a l i s o t r o p i c eddy k i n e t i c energy w i l l be a p p r o x i m a t e l y t h e same. T h i s i s a d m i t t e d l y a s i m p l i s t i c , and by no means r i g o r o u s argument, b u t i t w i l l p r o v i d e an e s t i m a t e o f t h e t w o - d i m e n s i o n a l i s o t r o p i c eddy k i n e t i c energy f o r comparison w i t h t h e e s t i m a t e s o f W y r t k i et^ a l . (1976) and Fu (1983). 94 The t w o - d i m e n s i o n a l EKE e s t i m a t e s f o r t h e w a v e l e n g t h bands between 1000 and 100 km a r e summarized i n T a b l e IV-13. The t w o - d i m e n s i o n a l EKEs o f t h e h i g h - e n e r g y r e g i o n s a r e 258 and 236 c m 2 / s 2 , r e s p e c t i v e l y , i n t h e NWA and t h e NWP. These e s t i m a t e s a r e not s i g n i f i c a n t l y d i f f e r e n t . I n t h e low-energy r e g i o n s , t h e NEA, SA, NEP and SP have t w o - d i m e n s i o n a l EKEs of 18, 20, 40 and 24 c m 2 / s 2 r e s p e c t i v e l y . The NEP has about t w i c e t h e eddy k i n e t i c energy o f t h e NEA, a s i g n i f i c a n t d i f f e r e n c e . The SA and SP c a n n o t be d i r e c t l y compared t o t h e NEA and NEP s i n c e t h e i r k i n e t i c e n e r g i e s were e s t i m a t e d o v e r a s m a l l e r wavenumber range. The eddy k i n e t i c e n e r g i e s o f t h e SA and t h e SP a r e , however, n o t s i g n f i c a n t l y d i f f e r e n t from each o t h e r . The HIGH r e g i o n has a t w o - d i m e n s i o n a l i s o t r o p i c EKE o f 250 c m 2 / s 2 w i t h 95% c o n f i d e n c e l i m i t s o f 222 t o 306 c m 2 / s 2 . The LOW r e g i o n has a v a l u e of 36 c m 2 / s 2 w i t h 95% c o n f i d e n c e l i m i t s o f 32 t o 40 c m 2 / s 2 . The HIGH r e g i o n has about s e v e n t i m e s t h e g e o s t r o p h i c eddy k i n e t i c energy o f t h e LOW r e g i o n i n w a v e l e n g t h s between 1000 and 100 km. T w o - d i m e n s i o n a l i s o t r o p i c eddy k i n e t i c e n e r g i e s were e s t i m a t e d by Fu (1983) u s i n g SEASAT a l t i m e t r y d a t a . He r e p o r t e d EKEs o f 290 c m 2 / s 2 f o r t h e h i g h - e n e r g y r e g i o n s and 50 c m 2 / s 2 f o r t h e low-energy r e g i o n s . The e s t i m a t e d EKE o f t h e HIGH r e g i o n u s i n g t h e q u a s i - s y n o p t i c XBT d a t a s e t i s n o t s i g n i f i c a n t l y d i f f e r e n t from t h e r e s u l t s o f Fu. I n t h e LOW r e g i o n , Fu's r e s u l t s a r e s i g n i f i c a n t l y g r e a t e r t h a n t h o s e o f t h e XBT d a t a s e t by a f a c t o r o f 1.25. The EKEs e s t i m a t e d by Fu a r e t h o s e a s s o c i a t e d w i t h t h e b a r o t r o p i c s i g n a l s w i t h p e r i o d s l e s s t h a n 24 days. The EKEs e s t i m a t e d i n t h i s i n v e s t i g a t i o n a r e t h o s e a s s o c i a t e d w i t h t h e b a r o c l i n i c s i g n a l s i n t h e upper 400 m o f t h e ocean. The l a t t e r EKEs w i l l m i s s an i m p o r t a n t p a r t o f t h e b a r o t r o p i c s i g n a l b ecause t h e l e v e l o f no m o t i on ( i . e . t h e d e p t h a t w h i c h t h e b a r o t r o p i c s i g n a l i s compensated by t h e b a r o c l i n i c s i g n a l ) i s g e n e r a l l y c o n s i d e r e d t o be on t h e o r d e r o f 1000 m, not t h e 400 m used i n t h i s i n v e s t i g a t i o n . D e s p i t e t h e s e u n d e r e s t i m a t e s , t h e EKEs from t h e q u a s i - s y n o p t i c XBT d a t a s e t compare v e r y w e l l w i t h t h o s e o f Fu, s i n c e t h e y do n o t f i l t e r any f r e q u e n c y band o u t o f t h e 1000 t o 100 km w a v e l e n g t h band. The eddy k i n e t i c e n e r g i e s r e p o r t e d by Fu and e s t i m a t e d i n t h i s i n v e s t i g a t i o n a r e l e s s t h a n t h o s e o f W y r t k i e t a l . (1976) by a f a c t o r o f 5. T h i s can be e x p l a i n e d by t h e f a c t t h a t t h e EKEs o f Fu and t h i s i n v e s t i g a t i o n a r e u n d e r e s t i m a t e d (as d i s c u s s e d a b o v e ) , and t h e EKEs o f W y r t k i e t a l . a r e o v e r e s t i m a t e d due t o t h e w i n d d r i f t o f t h e s h i p s . 95 Table IV-13 Two-dimensional i s o t r o p i c eddy k i n e c t i c energy estimates of the geographic regions. The SA and SP were integrated up to the Nyquist wavenumber ( i . e . about 200 km). Region T w o - d i m e n s i o n a l I s o t r o p i c Eddy 95% C o n f i d e n c e K i n e t i c Energy ( c m 2 / s 2 ) L i m i t s ( c m 2 / s 2 ) NWA 258 201 - 315 NWP 236 209 - 330 NEA 18 1 4 - 2 1 SA 20 1 5 - 3 1 NEP 40 3 3 - 4 5 SP 24 2 1 - 3 0 HIGH 250 222 - 306 LOW 36 3 2 - 4 0 96 The c o n t r i b u t i o n of each dominant b a n d w i d t h o f t h e g e o p o t e n t i a l anomaly- s p e c t r a t o t h e t o t a l t w o - d i m e n s i o n a l i s o t r o p i c eddy k i n e t i c energy i s shown i n T a b l e IV-14. I n t h e h i g h - e n e r g y r e g i o n s , t h e d i s t r i b u t i o n s o f t h e EKEs i n wavenumber space a r e v e r y comparable, w i t h t h e e x c e p t i o n t h a t t h e energy of t h e NWP i n t h e band o f 240 t o 130 km i s d i v i d e d between two d i s t i n c t wavenumber bands. I n t h e low-energy r e g i o n s , a l t h o u g h t h e t o t a l EKE o f t h e SA and SP c a n n o t be d i r e c t l y compared t o t h e o t h e r r e g i o n s , t h e g e o g r a p h i c v a r i a b i l i t y o f t h e eddy k i n e t i c e n e r g i e s w i t h i n i n d i v i d u a l wavenumber bands may be compared. W i t h t h e e x c e p t i o n o f t h e NEA, t h e low-energy r e g i o n s have eddy k i n e t i c e n e r g i e s o f about 20 c m 2 / s 2 a t w a v e l e n g t h s g r e a t e r t h a n 200 km. The NEA has o n e - q u a r t e r o f t h e EKE of t h e o t h e r low-energy r e g i o n s a t w a v e l e n g t h s g r e a t e r t h a n 200 km. The NEA has about h a l f t h e eddy k i n e t i c energy of t h e NEP a t w a v e l e n g t h s l e s s t h a n 200 km. The HIGH r e g i o n has an EKE of 65 c m 2 / s 2 a t w a v e l e n g t h s l a r g e r t h a n 200 km, whereas t h e LOW r e g i o n has 14 c m 2 / s 2 . I n w a v e l e n g t h s s h o r t e r t h a n 200 km, t h e EKEs o f t h e HIGH and LOW r e g i o n a r e 185 and 17 c m 2 / s 2 , r e s p e c t i v e l y . B o t h t h e HIGH and LOW r e g i o n s have more o f t h e i r eddy k i n e t i c e n e r g i e s i n t h e s h o r t e r w a v e l e n g t h s . B a r o c l i n i c L e n g t h and V e l o c i t y S c a l e s The dominant l e n g t h s c a l e s o f v a r i a b i l i t y o f t h e b a r o c l i n i c m e s o s c a l e eddy f i e l d s and t h e c o r r e s p o n d i n g v e l o c i t y s c a l e s were o b t a i n e d f r o m t h e wavenumber s p e c t r a . The g e o g r a p h i c v a r i a b i l i t y o f t h e s e s c a l e s w i l l be d i s c u s s e d and t h e r e s u l t s w i l l be used i n t h e d y n a m i c a l a n a l y s e s o f C h a p t e r V. The v a r i a b i l i t y o f t h e b a r o c l i n i c m e s o s c a l e eddy f i e l d i n t h e upper l e v e l o f t h e ocean may be b e s t r e p r e s e n t e d by t h e g e o p o t e n t i a l anomaly ( i . e . t h e D s p e c t r a ) . The dominant l e n g t h s c a l e s were t a k e n as t h e peak w a v e l e n g t h s o f t h e D s p e c t r a ( T a b l e IV-12) d i v i d e d by 2 TT. The v e l o c i t y s c a l e s were t a k e n as t h e s q u a r e - r o o t o f t h e v a l u e s of t h e v a r i a n c e - c o n s e r v i n g g e o s t r o p h i c v e l o c i t y s p e c t r a a t t h e c o r r e s p o n d i n g w a v e l e n g t h s . The v e l o c i t y s c a l e s c o r r e s p o n d t o t h e b a r o c l i n i c s i g n a l i n t h e upper 400 m o f t h e w a t e r column. An i m p o r t a n t p o r t i o n o f t h e b a r o t r o p i c s i g n a l has most c e r t a i n l y been m i s s e d , t h e r e f o r e , t h e s e v e l o c i t y s c a l e s a r e u n d e r e s t i m a t e s o f t h e t r u e v e l o c i t y p e r t u r b a t i o n s . The t r u e v e l o c i t y s c a l e s may be a p p r o x i m a t e d by c o n s i d e r i n g t h e f a c t t h a t t h e EKEs r e p o r t e d by W y r t k i et_ a l . (1976) a r e a f a c t o r o f f i v e g r e a t e r t h a n t h e 97 Table IV-14 Contribution of each bandwidth of the geopotential anomaly spectra to the two—dimensional i s o t r o p i c eddy k i n e t i c energy. Region Peak Wavelength Confidence Wavelength P e r c e n t of Eddy Eddy K i n e t i c Energy (km) L e v e l Band (km) K i n e t i c Energy (cm 2/s 2) NWA 285 95% 600 - 220 20 52 155 — 220 - 120 55 142 NWP 395 95% 600 - 240 29 68 195 80% 240 - 155 31 73 145 95% 155 - 130 34 80 NEA 205 95% 340 - 190 29 5 160 -- 190 - 130 40 7 115 — 130 - 100 23 4 SA 510 95% 680 - 320 47 9 245 -- 320 - 220 47 9 NEP 320 95% 620 - 190 45 18 170 — 190 - 120 48 19 SP 300 — 500 - 220 91 22 HIGH 300 95% 620 - 220 26 65 155 — 220 - 120 74 185 LOW 300 95% 690 - 190 40 14 170 — 190 - 120 48 17 98 EKEs e s t i m a t e d i n t h i s c h a p t e r . The e s t i m a t e s o f W y r t k i e t a l . a r e c o n s i d e r e d h i g h , t h e r e f o r e , an upper bound t o t h e t r u e v e l o c i t y p e r t u r b a t i o n s o f t h e o b s e r v e d b a r o c l i n i c l e n g t h s c a l e s may be e s t i m a t e d by s i m p l y m u l t i p l y i n g t h e b a r o c l i n i c v e l o c i t y s c a l e , U, by ( 5 ) V 2 t o o b t a i n U*. The dominant l e n g t h and v e l o c i t y s c a l e s a r e summarized i n T a b l e I V - 1 5 . These l e n g t h s c a l e s e x h i b i t a g e o g r a p h i c v a r i a b i l i t y w h i c h i s , of c o u r s e s i m i l a r t o t h a t o f t h e d e c o r r e l a t i o n s c a l e s o f t h e g e o p o t e n t i a l anomaly i n T a b l e I V - 1 . The d e c o r r e l a t i o n s c a l e s were s a i d t o r e f l e c t t h e s i z e o f t h e l a r g e s t dominant p e r t u r b a t i o n s . The d e c o r r e l a t i o n s c a l e s o f T a b l e IV-1 may be compared w i t h t h e l e n g t h s c a l e s o f T a b l e IV-15 a f t e r m u l t i p l y i n g them by 0.64 ( i . e . d e c o r r e l a t i o n s c a l e x (4/2TT) = l e n g t h s c a l e ) . The D d e c o r r e l a t i o n s c a l e s a r e t h e same s i z e o r s l i g h t l y s m a l l e r t h a n t h e l a r g e s t dominant s c a l e s o f T a b l e IV-15. Comparable d e c o r r e l a t i o n s c a l e s between t h e HIGH and LOW r e g i o n s w o u l d be e x p e c t e d f r o m an e x a m i n a t i o n o f t h e dominant l e n g t h s c a l e s o f t h e two r e g i o n s . The d e c o r r e l a t i o n s c a l e o f t h e HIGH r e g i o n i s s i g n i f i c a n t l y l a r g e r , however, as a r e s u l t o f t h e HIGH r e g i o n h a v i n g a l a r g e r p e r c e n t a g e o f i t s v a r i a n c e i n t h e s h o r t e r l e n g t h s c a l e s ( T a b l e I V - 1 2 ) . 99 Table IV-15 Length sc a l e s (L) and v e l o c i t y scales (U) of the b a r o c l i n i c mesoscale eddy v a r i a b i l i t y * The length scales were obtained from the peak wavelengths of D spectra (L= A/2 TT ). The bold length scales are d i s t i n c t to the 95% confidence l i m i t s of the D spectra, and the underlined lengthscale i s d i s t i n c t to the 80% confidence l i m i t s . The other length scales are not d i s t i n c t to the 80% confidence l i m i t s . The v e l o c i t y scales (U) were obtained from the geostrophic v e l o c i t y spectra. The upper bound of the true v e l o c i t y perturbations (D*) were obtained by m u l t i p l y i n g D by ( 5 ) V 2 , since Wyrtki et a l . *s (1976) EKEs are a f a c t o r of f i v e greater than the EKEs reported i n t h i s chapter, and are considered an overestimate of the true EKEs. R e g i o n L U U* (km) (cm/s) (cm/s) NWA 45 10.2 22.8 25 18.1 40.5 NWP 63 8.9 19.9 31 14.5 32.4 23 18.6 41.6 NEA 33 3.8 8.5 26 4.6 10.2 25 4.8 10.7 SA 81 4.0 8.9 39 5.6 12.5 NEP 51 4.6 10.3 27 5.5 12.3 SP 48 6.3 14.1 HIGH 48 9.6 21.5 25 17.5 39.1 LOW 48 4.5 10.1 27 5.5 12.3 100 V. DYNAMICAL INFERENCES The p u r p o s e o f t h i s c h a p t e r i s t o examine t h e g e o g r a p h i c v a r i a b i l i t y o f t h e me s o s c a l e dynamics u s i n g t h e p r e c e d i n g s t a t i s t i c a l r e s u l t s . Q u a s i g e o s t r o p h y i s a t y p e o f d y n a m i c a l b a l a n c e w i t h c e r t a i n c h a r a c t e r i s t i c l e n g t h , v e l o c i t y and t i m e s c a l e s , w h i c h i n c l u d e s l i n e a r Rossby waves, n o n l i n e a r Rossby waves and q u a s i g e o s t r o p h i c t u r b u l e n c e . The r e s u l t s o f MODE-I (Richman e t a^L., 1977; MODE Group, 1978) have shown t h a t l i n e a r dynamics do n o t appear t o be a p p l i c a b l e i n t h e v i c i n i t y o f t h e G u l f Stream, b u t have l e d i n v e s t i g a t o r s t o su g g e s t t h a t t h e somewhat weaker m o t i o n s t o t h e e a s t may be l i n e a r . T h i s h y p o t h e s i z e d i n h o m o g e n e i t y o f t h e dynamics i s c o n s i s t e n t w i t h t h e de m o n s t r a t e d s p a t i a l i n h o m o g e n e i t y o f t h e eddy k i n e t i c energy and dominant h o r i z o n t a l l e n g t h and v e l o c i t y s c a l e s . R h i n e s (1977) s u g g e s t e d t h a t t h e r e i s nev e r l i k e l y t o be enough d a t a t o make t h e s t a b i l i t y o f s t a t i s t i c a l e s t i m a t e s o f m e s o s c a l e p r o p e r t i e s r e a l l y s a t i s f a c t o r y and t h a t , " i t seems t o be more u s e f u l t o i n v e n t c r u d e d y n a m i c a l t e s t s w h i c h w i t h s t a n d t h e p a u c i t y o f d a t a , r a t h e r t h a n make a m o n o l i t h i c d r i v e t o d e t e r m i n e t h e f u l l frequency-wavenumber s p e c t r u m o f t h e e d d i e s " . The r e l e v a n t q u a s i g e o s t r o p h i c dynamics w i l l be i n f e r r e d w i t h t h e s t a t i s t i c a l r e s u l t s o f Ch a p t e r I V , and t h e g e o g r a p h i c v a r i a b i l i t y o f t h e dynamics w i l l be d i s c u s s e d . The n o n d i m e n s i o n a l q u a s i g e o s t r o p h i c s c a l i n g p a r a m e t e r s w i l l be e v a l u a t e d u s i n g t h e dominant h o r i z o n t a l l e n g t h and v e l o c i t y s c a l e s . The p r o p e r t i e s o f f r e e l i n e a r b a r o c l i n i c Rossby waves w i l l be examined f o r each g e o g r a p h i c r e g i o n and t h e wavenumber s p e c t r a w i l l be compared w i t h s e v e r a l models o f n o n l i n e a r g e o p h y s i c a l t u r b u l e n c e . A. Quasigeostrophic Scaling Parameters The q u a s i g e o s t r o p h i c e q u a t i o n s f o r s t r a t i f i e d f l u i d s may be d e r i v e d u s i n g s y s t e m a t i c s c a l i n g arguments. The s c a l i n g a n a l y s i s i s a consequence o f an e x p l i c i t c h o i c e t o d e s c r i b e a p a r t i c u l a r c l a s s o f m o t i o n s . The n o n l i n e a r p o t e n t i a l v o r t i c i t y e q u a t i o n f o r a s t r a t i f i e d f l u i d on a B - p l a n e o f c o n s t a n t d e p t h , i n n o n d i m e n s i o n a l f orm, i s ( L e B l o n d and Mysak, 1978), 101 where 3t 3x 3y 3y 3x ' h . 2 , 2 DC J J 3x 3y (5.1) i s t h e s t r e a m f u n c t i o n , Ro i s t h e Rossby number, B i s t h e B u r g e r number and B * i s t h e s p h e r i c i t y p a r a m e t e r . I n o r d e r t o o b t a i n t h i s q u a s i g e o s t r o p h i c p o t e n t i a l v o r t i c i t y e q u a t i o n from the s c a l e d i n v i s c i d h y d r o s t a t i c e q u a t i o n s f o r a r o t a t i n g s t r a t i f i e d f l u i d , i t i s r e q u i r e d t h a t Ro<<1, B = 0(1) and g*<<1. These t h r e e n o n d i m e n s i o n a l q u a s i g e o s t r o p h i c s c a l i n g p a r a m e t e r s a r e : Ro = U / ( f Q L ) , B = ( N H ) 2 / ( f 0 L ) 2 = ( r i / L ) 2 and 6* = - 6 . 0 L / f 0 # where U i s t h e v e l o c i t y s c a l e , L i s t h e h o r i z o n t a l l e n g t h s c a l e , f Q i s t h e C o r i o l i s p a r a m e t e r a t a g i v e n l a t i t u d e , 6 Q i s t h e m e r i d i o n a l g r a d i e n t o f f Q a t a g i v e n l a t i t u d e , N i s t h e B r u n t - V a i s a l a f r e q u e n c y , H i s t h e wa t e r depth and r ^ i s t h e i n t e r n a l Rossby d e f o r m a t i o n r a d i u s . The Rossby number i s t h e r a t i o o f t h e i n e r t i a l t o t h e C o r i o l i s f o r c e s . When Ro<<1, t h e C o r i o l i s f o r c e s dominate o v e r t h e i n e r t i a l f o r c e s . The B u r g e r number i s a measure o f t h e s t r a t i f i c a t i o n . As s t r a t i f i c a t i o n i n c r e a s e s , m o t i o n p a r a l l e l t o t h e l o c a l d i r e c t i o n o f g r a v i t y i s i n h i b i t e d and t h e m o t i o n s become n e a r l y h o r i z o n t a l . The B u r g e r number can a l s o be w r i t t e n as . t h e s q u a r e o f t h e r a t i o o f t h e i n t e r n a l d e f o r m a t i o n r a d i u s and t h e h o r i z o n t a l l e n g t h s c a l e . The c o n d i t i o n B = 0(1) i m p l i e s t h a t t h e m o t i o n s under c o n s i d e r a t i o n a r e on t h e o r d e r o f r ^ ( P e d l o s k y , 1979). The s p h e r i c i t y p a r a meter i s a measure o f t h e change o f t h e C o r i o l i s p a r a m e t e r o v e r t h e m e r i d i o n a l S c a l e o f t h e m o t i o n (Charney and F l i e r l , 1981). The c o n d i t i o n 6*<<1 i s a r e q u i r e m e n t f o r t h e use o f t h e B-plane. An e x a m i n a t i o n o f t h e s e p a r a m e t e r s , as e v a l u a t e d w i t h t h e h o r i z o n t a l l e n g t h and v e l o c i t y s c a l e s f r o m C h a p t e r IV, w i l l r e v e a l t h e a p p l i c a b i l i t y o f t h e q u a s i g e o s t r o p h i c e q u a t i o n s t o t h e o b s e r v e d m e s o s c a l e v a r i a b i l i t y . E q u a t i o n (5.1) i s a c o n s e r v a t i o n s t a t e m e n t f o r t h e q u a s i g e o s t r o p h i c a p p r o x i m a t i o n t o t h e p o t e n t i a l v o r t i c i t y w h i c h i s a l i n e a r c o m b i n a t i o n o f t h r e e t e r m s . The f i r s t two terms a r e due t o t h e r e l a t i v e m o t i o n . The f i r s t i s t h e r e l a t i v e v o r t i c i t y and t h e second i s t h e c o n t r i b u t i o n t o t h e p o t e n t i a l v o r t i c i t y due t o t h e s l o p i n g i s o p y c n a l s i n t h e w a t e r column. 102 The B u r g e r number, B = ( r ^ / L ) 2 , i s a measure o f t h e r e l a t i v e i m p o r t a n c e o f t h e f i r s t term t o t h e second term. The Rossby d e f o r m a t i o n r a d i u s i s t h e s c a l e f o r w h i c h t h e s l o p i n g i s o p y c n a l s ( v o r t e x - t u b e s t r e t c h i n g ) and t h e r e l a t i v e v o r t i c i t y make e q u a l c o n t r i b u t i o n s t o t h e p o t e n t i a l v o r t i c i t y ( P e d l o s k y , 1979). When L i s l e s s than r ^ , t h e r e i s a n e g l i g i b l e c o n t r i b u t i o n t o t h e p o t e n t i a l v o r t i c i t y by t h e v o r t e x - t u b e s t r e t c h i n g . The t h i r d t erm i n (5.1) i s t h e ambient p o t e n t i a l v o r t i c i t y . The Rossby wave s t e e p n e s s p a r a m e t e r , M = R o / B * , i s a measure o f t h e r e l a t i v e i m p o r t a n c e o f t h e f i r s t t erm ( t h e i n e r t i a l term) t o t h e t h i r d t e r m ( the wave phase d i s p e r s i o n ) . Q u a s i g e o s t r o p h i c motions may be w a v e l i k e o r t u r b u l e n t . More s p e c i f i c a l l y , t h e y may be governed by l i n e a r Rossby wave (LRW) t h e o r y , n o n l i n e a r Rossby wave (NRW) t h e o r y o r q u a s i g e o s t r o p h i c t u r b u l e n c e (QGT) t h e o r y . The c r i t i c a l p a r a m eter f o r d i s t i n g u i s h i n g t h e s e r e g i m e s i s t h e Rossby wave s t e e p n e s s p a r a m e t e r . W a v e l i k e ( l i n e a r ) r e g i m e s o c c u r where M<1 and t u r b u l e n t ( n o n l i n e a r ) regimes o c c u r where M>1. LRW t h e o r y i s v a l i d where M<1, t h a t i s , t h e wave phase d i s p e r s i o n o f t h e 6 - e f f e c t i s g r e a t e r t h a n t h e i n e r t i a l e f f e c t s (wave s t e e p e n i n g ) . NRW t h e o r y i s v a l i d where M = 0 ( 1 ) , and t h e phase d i s p e r s i o n b a l a n c e s t h e wave s t e e p e n i n g e f f e c t s . R h i n e s (1977) d e m o n s t r a t e d t h a t t h e s t r o n g n o n l i n e a r i n t e r a c t i o n s i n v o l v e d i n QGT o c c u r o n l y when t h e i n e r t i a l e f f e c t s a r e much s t r o n g e r t h a n t h e wave phase d i s p e r s i o n , t h a t i s , M>>1. Charney and F l i e r 1 (1981) s u g g e s t e d t h a t i n t h e oceans M = 0 ( 1 ) , b u t t h a t i t v a r i e s f r o m one o c e a n i c r e g i o n t o a n o t h e r . I n t h i s i n v e s t i g a t i o n , t h e Rossby wave s t e e p n e s s parameter has been e v a l u a t e d and t h e g e o g r a p h i c v a r i a b i l i t y o f t h e c h a r a c t e r o f t h e q u a s i g e o s t r o p h i c m o t i o n s w i l l be d i s c u s s e d . Kang and Magaard (1980) have shown t h a t t h e l i n e a r i z e d wave e q u a t i o n s can s t i l l be used where M = 0(1) f o r s i n g l e p l a n e waves. The LRW and NRW r e g i m e s , t h e r e f o r e , cannot be d i s t i n g u i s h e d w i t h t h e Rossby wave s t e e p n e s s p a r a m e t e r . The f o l l o w i n g r egimes can be i d e n t i f i e d : (1) where M < 0 ( 1 0 ) , LRW and NRW t h e o r i e s a r e a p p l i c a b l e , and (2) where M > 0 ( 1 0 0 ) , QGT t h e o r y i s a p p l i c a b l e . The i n t e r m e d i a t e r e g i o n , where M = 0 ( 1 0 ) , i s a t u r b u l e n t regime t h a t does n o t have t h e s t r o n g n o n l i n e a r i n t e r a c t i o n s r e q u i r e d f o r QGT, b u t does have i n e r t i a l terms l a r g e enough t o p r e c l u d e LRW and NRW t h e o r i e s . 103 The e v a l u a t i o n o f t h e q u a s i g e o s t r o p h i c s c a l i n g p a r a m e t e r s i s summarized i n T a b l e V-1. The h o r i z o n t a l l e n g t h and v e l o c i t y s c a l e s were o b t a i n e d from t h e wavenumber s p e c t r a as summarized i n T a b l e I V - 1 5 . The average median l a t i t u d e o f each g e o g r a p h i c r e g i o n was c a l c u l a t e d from t h e s e c t i o n s . The C o r i o l i s p a r a m e t e r was c a l c u l a t e d as f Q = 2 £2 s i n 0 , where £2 = 7.29 x 1 0 - 5 r a d / s ( i . e . t h e a n g u l a r r a t e o f r o t a t i o n o f t h e e a r t h ) and 0 i s t h e average median l a t i t u d e , and g 0 = 20, cos 0 / R , where R = 6371 km ( i . e . r a d i u s o f t h e e a r t h ) . The i n t e r n a l Rossby d e f o r m a t i o n r a d i i , r^_, f o r t h e r e g i o n s i n the n o r t h e r n h emisphere were o b t a i n e d from t h e r e s u l t s o f Emery e t a l . (1984). S p a t i a l a v e r a g e s o f r ^ were c a l c u l a t e d w i t h t h e a p p r o p r i a t e 5° s q u a r e v a l u e s . I n t h e SA and SP, t h e r j _ were d e t e r m i n e d from t h e q u a s i - s y n o p t i c s e c t i o n s , assuming a t w o - l a y e r f l u i d , by t h e r e l a t i o n ( L e B l o n d and Mysak, 1978) 2 r ± = g(P 2"P 1) H 1H 2 — 2 (5.2) f Q P 2(H L + H 2 ) where and Pi a r e t h e t h i c k n e s s and d e n s i t y o f t h e upper l a y e r , H 2 and P2 a r e t h e same q u a n t i t i e s i n t h e l o w e r l a y e r and g i s g r a v i t y . The v a l u e s o f Ro, B and $* i n T a b l e V-1 a r e everywhere c o n s i s t e n t w i t h q u a s i g e o s t r o p h i c t h e o r y . The Rossby number does n o t e x c e e d a v a l u e of 8.3 x 1 0 ~ 2 . I t i s everywhere much l e s s t h a n one, i n d i c a t i n g t h e dominance o f t h e C o r i o l i s f o r c e s o v e r t h e i n e r t i a l f o r c e s r e q u i r e d f o r q u a s i g e o s t r o p h y . I f t h e u pper bound o f t h e v e l o c i t y s c a l e , U*, i s u s e d , Ro i s s t i l l much l e s s t h a n one. The B u r g e r number i s everywhere on t h e o r d e r o f one i n d i c a t i n g t h a t t h e o b s e r v e d b a r o c l i n i c l e n g t h s c a l e s a r e on t h e o r d e r o f t h e a v e r a g e r e g i o n a l i n t e r n a l Rossby r a d i i . The v a l u e s o f B i n T a b l e V-1 v a r y f r o m 3.0 x 1 0 - 1 t o 3.8. The HIGH r e g i o n and t h e LOW r e g i o n b o t h have one l e n g t h s c a l e t h a t i s g r e a t e r t h a n r ^ and one l e n g t h s c a l e t h a t i s s m a l l e r . The s p h e r i c i t y p a r a m e t e r i s everywhere much l e s s t h a n one. I t s v a l u e v a r i e s from 4.5 x 1 0 - 3 t o 4.0 x 10~ 2 . The changes i n t h e C o r i o l i s p a r a m e t e r o v e r t h e dominant s c a l e s o f v a r i a b i l i t y a r e s m a l l , and t h u s t h e 3 - p l a n e i s a v a l i d a p p r o x i m a t i o n . The v a l u e s o f t h e Rossby wave s t e e p n e s s p a r a m e t e r c a l c u l a t e d from t h e dominant l e n g t h and v e l o c i t y s c a l e s ( T a b l e I V - 1 5 ) a r e l i s t e d i n T a b l e V-2. M was c a l c u l a t e d u s i n g t h e b a r o c l i n i c v e l o c i t y s c a l e , U, and i s c o n s i d e r e d t o be Table V-1 Summary of the Rossby number (Ro), the Burger number (B) and the sphericity parameter ( B*) for ene geographic regions. The input parameters consist of the length scale (I#=» X/2 ir) , the velocity scale (0) , the average median latitude, the Coriolis parameter ( f Q ) , the meridional gradient of f 0 ( 8 0) and the internal Rossby radius ( r ^ ) . Region L (m) U (m/s) Average Median Latitude (rad/s) Bo (rad/(ms) r i (m) R 0-U/(f 0L) B - U j / L ) 2 6 - 8 0 L / f 0 NWA 4.54x10* 2.47x104 1.02x10 _ 1 1.81x10 - 1 37.3" 8.84x10 - 5 1.82x10 - 1 1 2.49x10* 2.5x10-2 8.3x10-2 3.0x10"1 1.0 9.3x10 - 3 5.1x10 - 3 NWP 6.29x104 3.10x104 2.31x10* 8.9x10 - 2 1.45X-10"1 . 1.86x10"1 33.3° 8 . 0 0 X 1 0 " 5 1.91x10 - 1 1 3.67x10* 1.7x10-2 5.8x10-2 1.0x10 - 1 3 .4x10 _ 1 1 .4 2.5 1.5x10-2 7.4x10 - 3 5.5x10 - 3 NEA 3.26x10* 2.55x10* 2.47x10* 3.8x10"2 4.6x10 - 2 4.8x10-2 41.6° 9.68x10"5 1.71x10" 1 1 2 . 4 0 x 1 0 * 1.2x10-2 1.9x10-2 2 .0x10-2 5 . 4 X 1 0 - 1 8.9x10 - 1 9 . 4 X 1 0 - 1 5.7x10 - 3 4.5x10 - 3 4 . 4 x 1 0 " 3 SA 8.12x10* 3.90x10* 4.0x10-2 5.6x10-2 17.8* 4.38x10"5 2.18x10 - 1 1 4.90x10* 1.1x10-2 3 .3x10-2 3.6x10 _ 1 1.6 4.0x10-2 1.9x10-2 NEP 5.09x10* 2.71x10* 4.6x10-2 5.5x10-2 33. T 8.08x10 - 5 1.90x10 - 1 1 5.27x10* 1.1x10-2 2.5x10-2 1.1 3.8 1.2x10-2 6.4x10 - 3 SP 4.77x10* 6.3x10"2 27.7° 6.78X10"5 2.03X10"11 3.31x10* 1 .9x10-2 4.8x10-1 1.4x10-2 HIGH 4.77x10* 2.47x10* 9.6x10-2 1.75x10"1 36.3° 8 . 6 3 X 1 0 - 5 1.84x10" 1 1 3.08x10* 2 .3x10-2 8.2x10-2 4.2x10 - 1 1 .6 1.0x10-2 5.3x10"3 LOW 4.77x10* 2.71x10* 4.5x10"2 5.5x10-2 34.3° 8.21x10 - 5 1.89x10 - 1 1 3.97x10* 1.1x10-2 2 .5x10-2 6.9x10 - 1 2.1 1.1x10-2 6.2x10 - 3 o lb 105 Table V—2 Summary of the Rossby wave steepness parameter and the inferred dynamics from i t s value, for each geographic region. M and M* were determined from U and O*, respectively. The true Rossby wave steepness parameter of the observed length scales w i l l be between M and M*. The inferred dynamics include: linear Rossby wave (LRW) theory, nonlinear Rossby wave (NRW) theory and quasigeostrophic turbulence (QGT) theory. Region X M M* I n f e r r e d (km) Dynamics NWA 285 2.7 6.1 LRW/NRW 155 16.3 36.4 QGT NWP 395 1.1 2.5 LRW/NRW 195 7.8 17.4 145 18.2 40.7 QGT NEA 205 2.1 4.7 LRW/NRW 160 4.2 9.4 -115 4.5 10.0 - SA 510 0.3 0.7 LRW/NRW 245 1.7 3.8 LRW/NRW NEP 320 0.9 2.0 LRW/NRW 170 3.9 8.7 - SP 300 1.4 3.1 LRW/NRW HIGH 300 2.3 5.1 LRW/NRW 155 15.5 34.7 QGT LOW 300 1.0 2.2 LRW/NRW 170 4.0 8.9 - 106 u n d e r e s t i m a t e d . M* i s c a l c u l a t e d u s i n g t h e e s t i m a t e d upper l i m i t o f t h e v e l o c i t y s c a l e , U*, and i s c o n s i d e r e d t o be o v e r e s t i m a t e d . The t r u e Rossby wave s t e e p n e s s p a r a m e t e r f o r t h e o b s e r v e d w a v e l e n g t h s w i l l be between M and M*. The dynamics i n f e r r e d from t h e s e v a l u e s o f M and M* a r e t a b u l a t e d f o r each w a v e l e n g t h . I n b o t h t h e h i g h - and low-energy r e g i o n s , t h e l o n g e r dominant w a v e l e n g t h s (>200 km) a r e c o n s i s t e n t w i t h l i n e a r and n o n l i n e a r Rossby wave t h e o r i e s . The s h o r t e r w a v e l e n g t h s (-<200 km) i n t h e low-energy r e g i o n s , have s c a l e s c o n s i s t e n t w i t h g o v e r n i n g dynamics i n t e r m e d i a t e between LRW/NRW and QGT t h e o r i e s . I n t h e h i g h - e n e r g y r e g i o n s , t h e s c a l e s o f t h e s h o r t e r w a v e l e n g t h s a r e c o n s i s t e n t w i t h q u a s i g e o s t r o p h i c t u r b u l e n c e t h e o r y , w i t h t h e e x c e p t i o n o f t h e 195 km w a v e l e n g t h i n t h e NWP, w h i c h has s c a l e s c o n s i s t e n t w i t h dynamics i n t e r m e d i a t e between LRW/NRW and QGT t h e o r i e s . The magnitudes o f t h e Rossby wave s t e e p n e s s p a r a m e t e r , M, fro m T a b l e V-2 have been i l l u s t r a t e d i n F i g u r e V-1 as f u n c t i o n s o f t h e l e n g t h (L) and v e l o c i t y (U) s c a l e s . The x - a x i s i s t h e l e n g t h s c a l e i n k i l o m e t e r s on a l o g a r i t h m i c s c a l e and t h e y - a x i s i s t h e v e l o c i t y s c a l e i n cm/s on a l o g a r i t h m i c s c a l e . I s o p l e t h s o f t h e s t e e p n e s s parameter a r e shown f o r v a l u e s o f 0.1, 1.0, 10 and 100, assuming a l a t i t u d e o f 35°. Due t o t h e r e l a t i o n , U = M 3 0 L 2 , t h e s e i s o p l e t h s have a s l o p e o f two. The magnitude o f M, o b v i o u s l y , i n c r e a s e s as a l o g a r i t h m i c s c a l e f r o m t h e bottom r i g h t t o t h e t o p l e f t c o r n e r , p e r p e n d i c u l a r t o t h e i s o p l e t h s . Each p a i r o f l e n g t h and v e l o c i t y s c a l e s has been p l o t t e d and l a b e l l e d w i t h t h e a p p r o p r i a t e g e o g r a p h i c r e g i o n . The s o l i d c i r c l e s i n d i c a t e l e n g t h s c a l e s t h a t a r e d i s t i n c t t o t h e 95% c o n f i d e n c e l e v e l , t h e a s t e r i s k i n d i c a t e s a l e n g t h s c a l e d i s t i n c t t o t h e 80% c o n f i d e n c e l e v e l and t h e empty c i r c l e s r e p r e s e n t l e n g t h s c a l e s t h a t c o u l d n o t be d e f i n e d t o t h e 80% c o n f i d e n c e l e v e l . L i n e s have been drawn t o j o i n t h e l e n g t h s c a l e s w i t h i n t h e same r e g i o n . The upper l i m i t o f t h e v e l o c i t y s c a l e s , U*, has n o t been p l o t t e d , t o a v o i d c o n f u s i o n . T h i s graph p r o v i d e s an i l l u m i n a t i n g p i c t u r e o f many o f t h e mes o s c a l e eddy p r o p e r t i e s d i s c u s s e d e a r l i e r . The EKEs, o f c o u r s e , a r e g r e a t e r f o r h i g h e r v e l o c i t y s c a l e s . Thus, t h e p o i n t s w i t h t h e l a r g e s t k i n e t i c e n e r g i e s a r e h i g h e r up on t h e graphs I t i s c l e a r l y seen f r o m t h e n e g a t i v e s l o p e o f t h e l i n e s o f eac h g e o g r a p h i c r e g i o n t h a t t h e s h o r t e s t s c a l e s c o n t a i n t h e most k i n e t i c e n e r g y . An i n f e r e n c e may be made about t h e d i s t r i b u t i o n o f t h e v a r i a n c e o f t h e g e o p o t e n t i a l anomaly i n each g e o g r a p h i c r e g i o n f r o m t h e s l o p e o f t h e r e g i o n a l l i n e s . The v e l o c i t y s c a l e s were d e t e r m i n e d f r o m t h e g e o s t r o p h i c r e l a t i o n and 107 X Q_ < UJ o z I in I _ i 0- CL < (Jj 00 Z 4 - L T" T 0 P; (KM) I 0 0 100 00 o 7" M = I 0 0 / / / / / / / / / / / / / / / N W P L (KM) Figure V-1 The dominant: length (L) and velocity (0) scales plotted in relation to the isopleths of the Rossby wave steepness parameter (M). M<1 suggests a wavelike (linear) regime and M>1 suggests a more turbulent (nonlinear) regime. The solid circles Indicate dominant length scales that are distinct to the 95% confidence level, the asterisk indicates a length scale distinct to the 80% confidence level and the empty circles indicate scales not distinct to the 80% confidence level. The scales within each region are connected by lines. The line with a slope of -1 is the slope of the regional line that would be expected i f the variance of D within a region was constant for a l l wavenumbers. 108 t h u s a r e p r o p o r t i o n a l t o ( f 0 L ) - ^ S D . The C o r i o l i s p a r a m e t e r i s assumed t o be c o n s t a n t f o r each r e g i o n . F o r a c o n s t a n t v a r i a n c e , (SQ 2), a t a l l w a v e l e n g t h s w i t h i n a r e g i o n , t h e r e g i o n a l l i n e p l o t t e d i n F i g u r e V-1 would have a -1 s l o p e . A l l o f t h e r e g i o n a l l i n e s have n e g a t i v e s l o p e s w i t h magnitudes l e s s t h a n one, r e f l e c t i n g t h e f a c t t h a t t h e s p e c t r a l peaks on t h e D v a r i a n c e - c o n s e r v i n g p l o t s a r e s m a l l e r f o r t h e s h o r t e r l e n g t h s c a l e s i n each r e g i o n . The r e g i o n a l l i n e s o f t h e h i g h - e n e r g y r e g i o n s have n e g a t i v e s l o p e s w i t h g r e a t e r magnitudes t h a n t h e low-energy r e g i o n s . T h i s i l l u s t r a t e s t h e f a c t t h a t t h e d i f f e r e n c e s between t h e magnitudes o f t h e D s p e c t r a l peaks i n each h i g h - e n e r g y r e g i o n a r e s m a l l e r t h a n t h e d i f f e r e n c e s i n each low-energy r e g i o n . Thus, f o r s i m i l a r wavenumber b a n d w i d t h s , each h i g h - e n e r g y r e g i o n has D v a r i a n c e s a t t h e dominant l e n g t h s c a l e s t h a t a r e more comparable i n magnitude t h a n t h e D v a r i a n c e s o f t h e dominant l e n g t h s c a l e s i n each l o w - e n e r g y r e g i o n . The e x c e p t i o n t o t h i s g e n e r a l i z a t i o n i s t h e NEA r e g i o n w h i c h has a r e g i o n a l l i n e w i t h a s l o p e s i m i l a r t o t h e h i g h - e n e r g y r e g i o n s . I t can a l s o be c l e a r l y seen, t h a t t h e h i g h - e n e r g y r e g i o n s a r e more n o n l i n e a r t h a n t h e low-energy r e g i o n s . T hat i s , t h e y have l a r g e r v a l u e s o f M. T h i s c o m p a r i s o n , however, must be made between c o r r e s p o n d i n g l e n g t h s c a l e s . I n o r d e r o f i n c r e a s i n g n o n l i n e a r i t y , t h e s c a l e s may be g e n e r a l l y l i s t e d a s : 1) l o n g w a v e l e n g t h s (>280 km) i n t h e low-energy r e g i o n s , 2) l o n g w a v e l e n g t h s i n t h e h i g h - e n e r g y r e g i o n s , 3) s h o r t w a v e l e n g t h s (<280 km) i n t h e l o w - e n e r g y r e g i o n s and 4) s h o r t w a v e l e n g t h s i n t h e h i g h - e n e r g y r e g i o n s . B. Linear Rossby Waves I t i s o f i n t e r e s t t o examine t h e p r o p e r t i e s o f t h e f r e e l i n e a r b a r o c l i n i c Rossby waves w i t h w a v e l e n g t h s as d i s c e r n e d f r o m t h e wavenumber s p e c t r a . I n a manner s i m i l a r t o t h a t o f Roden (1977), t h e c o r r e s p o n d i n g f r e q u e n c i e s , group v e l o c i t i e s and phase v e l o c i t i e s o f t h e dominant l e n g t h s c a l e s i n each g e o g r a p h i c r e g i o n were d e t e r m i n e d . The g e o g r a p h i c v a r i a b i l i t y o f t h e s e p r o p e r t i e s w i l l be d i s c u s s e d and compared t o t h e r e s u l t s o f o t h e r i n v e s t i g a t o r s . 109 The d i s p e r s i o n r e l a t i o n f o r f r e e l i n e a r f i r s t - m o d e b a r o c l i n i c Rossby waves i s ( L e B l o n d and Mysak, 1978), a) = - fcyc/(k2 + l 2 + r / * 2 ) (5.3) where u i s t h e f r e q u e n c y , k and 1 a r e t h e z o n a l and m e r i d i o n a l wavenumbers such t h a t t h e h o r i z o n t a l wavenumber i s k H = ( k 2 + l 2 p / 2 and 3Q i s t h e m e r i d i o n a l g r a d i e n t o f t h e C o r i o l i s p a r a m e t e r a t a g i v e n l a t i t u d e . The e a s t w a r d and n o r t h w a r d components o f t h e group v e l o c i t y a r e , c g x = B o ( k 2 - l 2 - r i " 2 ) / ( k 2 + l 2 + r i _ 2 ) 2 2 2 -2 2 ( 5 ' 4 ) C g y = 20Qkl/(k +r+ri ) The e a s t w a r d and n o r t h w a r d components of t h e phase v e l o c i t y a r e , • C p x = - 0 o k 2 / ( ( k 2 + l 2 ) ( k 2 + l 2 + r i ' 2 ) ) (5-5) C p y = - e o k l / ( ( k 2 + l 2 ) ( k 2 + l 2 + r . " 2 ) ) F o r a g i v e n l a t i t u d e t h e f i r s t b a r o c l i n i c mode w i l l have an upper c u t - o f f f r e q u e n c y o f OJ C = 8 Q r ^ / 2 . The f r e q u e n c i e s , group v e l o c i t i e s , phase v e l o c i t i e s and c u t - o f f f r e q u e n c i e s were d e t e r m i n e d f o r t h e dominant w a v e l e n g t h s o f t h e g e o g r a p h i c r e g i o n s a t d i f f e r e n t l a t i t u d e s . F o r each w a v e l e n g t h , t h e p r o p e r t i e s o f t h e m e r i d i o n a l waves (k = 0, 1 = 2TT/X, where X i s the w a v e l e n g t h ) , t h e o b l i q u e waves (-k = 1, k H = 2 T/ X) and t h e z o n a l waves (k = -2TI/X, l = o) were c a l c u l a t e d w i t h t h e above r e l a t i o n s . By c o n v e n t i o n , k<0 t o o b t a i n co>0. Z o n a l bands w i t h 5° m e r i d i o n a l w i d t h s were examined i n each g e o g r a p h i c r e g i o n . Z o n a l averages o f t h e i n t e r n a l Rossby d e f o r m a t i o n r a d i u s ( r ^ ) were o b t a i n e d f r o m Emery et_ a l . ( 1 9 8 4 ) . I n v e s t i g a t i o n s i n t o t h e e x i s t e n c e o f l i n e a r Rossby waves, t h e i r p r o p a g a t i o n c h a r a c t e r i s t i c s and g e n e r a t i o n mechanisms have been p r e d o m i n a n t l y i n t h e N o r t h e a s t P a c i f i c Ocean ( B e r n s t e i n and W h i t e , 1974; Emery and Magaard, 1976; W h i t e , 1977; Kang and Magaard, 1980; P r i c e and Magaard, 1980; W h i t e and Saur, 1981; W h i t e , 1982; P r i c e and Magaard, 1983; Mysak, 1983; W h i t e , 1985; Cummins 110 e t . a l . , 1986). Kang and Magaard (1980) d e m o n s t r a t e d , i n a r e g i o n n o r t h o f H a w a i i , t h a t t h e Rossby waves have n e g l i g i b l e energy e x c e p t a t a n n u a l f r e q u e n c i e s . F o r t h e most p a r t , i n v e s t i g a t o r s have c o n c e n t r a t e d on t h e c h a r a c t e r i s t i c s o f t h e a n n u a l Rossby wave. Kang and Magaard (1 9 8 0 ) , i n t h e r e g i o n 30°-40°N, 130°W-160°E, o b s e r v e d a n n u a l Rossby waves o f random phase. These waves had n o r t h w e s t w a r d phase v e l o c i t i e s , 300 km w a v e l e n g t h s , phase speeds of 2 cm/s and RMS p a r t i c l e v e l o c i t i e s o f . 2 t o 7 cm/s. T h i s i n v e s t i g a t i o n was bas e d on a 40-month XBT d a t a s e t . G e n e r a t i o n mechanisms were o n l y p r o p o s e d . Mysak (1983) s u g g e s t e d t h a t t h e i n t e n s e and l o c a l i z e d e a s t e r n boundary c u r r e n t f l u c t u a t i o n s , west o f Vancouver I s l a n d , c o u l d p r o v i d e t h e main s o u r c e o f v o r t i c i t y o f t h e s e waves. The t h e o r y p r e d i c t e d w a v e l e n g t h s o f 300 km, and phase and group speeds on t h e o r d e r o f 1 cm/s i n t h e NEP due t o t h i s g e n e r a t i o n mechanism. Cummins e t a l . (1986) examined t h e g e n e r a t i o n o f a n n u a l Rossby waves i n t h e N o r t h P a c i f i c by t h e w i n d s t r e s s o v e r t h e Whole r e g i o n . T h i s model p r e d i c t s s i m i l a r w a v e l e n g t h s and d i r e c t i o n a l p r o p e r t i e s as Kang and Magaard (1980) and Mysak (1983), and RMS c u r r e n t speeds o f 3 t o 6 cm/s. The w a v e l e n g t h s o b s e r v e d i n t h e q u a s i - s y n o p t i c XBT d a t a s e t , i n t h e NEP, a r e 320 and 170 km w i t h v e l o c i t y p e r t u r b a t i o n s c a l e s o f 4.6 and 5.5 cm/s, r e s p e c t i v e l y . The p r o p e r t i e s o f t h e d i s p e r s i v e b a r o c l i n i c Rossby waves w i t h t h e above w a v e l e n g t h s a r e shown i n T a b l e V-3. The 320 km w a v e l e n g t h w i t h i t s 4.6 cm/s v e l o c i t y s c a l e i s i n v e r y good agreement w i t h t h e o b s e r v a t i o n s o f Kang and Magaard (1980), t h e t h e o r y of-Mysak (1983) and t h e model o f Cummins e t a l . (1986). The 170 km w a v e l e n g t h , however, has a s h o r t e r w a v e l e n g t h and s m a l l e r phase v e l o c i t i e s t h a n t h o s e p r e d i c t e d i n t h e above models. These w a v e l e n g t h s a r e n o t comparable t o t h o s e o b t a i n e d by White and h i s c o - i n v e s t i g a t o r s u s i n g n o n d i s p e r s i v e models. T h e i r p r e d i c t e d w a v e l e n g t h s were g e n e r a l l y about 1000 km. There a r e no o b s e r v a t i o n s o r models o f LRWs, o f t h e q u a l i t y o f t h o s e i n t h e NEP, t h a t may be compared w i t h t h e o b s e r v e d l e n g t h and v e l o c i t y s c a l e s i n t h e o t h e r g e o g r a p h i c r e g i o n s . T a b l e V-4 summarizes t h e p r o p e r t i e s o f l i n e a r b a r o c l i n i c Rossby waves o b t a i n e d f r o m 5.3 t o 5.5 f o r t h e s i x g e o g r a p h i c r e g i o n s . I t w i l l be assumed t h a t t h e LRW t h e o r y i s c o n s i s t e n t w i t h t h e o b s e r v e d s c a l e s o f m o t i o n i f a l l o f t h r e e c r i t e r i a a r e met. F i r s t , a n e a r - a n n u a l p e r i o d i s r e q u i r e d . Kang and Magaard (1980) f o u n d t h a t t h e r e was n e g l i g i b l e energy a t o t h e r t h a n t h e a n n u a l p e r i o d s . I t i s r e a s o n a b l e t o e x p e c t t h e a n n u a l p e r i o d t o be dominant i n t h e o t h e r g e o g r a p h i c r e g i o n s on t h e b a s i s 111 BAROCLINIC ROSSBY WAVES - NEP Wavelength = 320 km Latitude Be X 106 • X 10* c, x ia dir i2 rectlon • x 10s T C_ x direction C_ x 102 direction 7.5 12.5 17. 5 22.5 27.5 32.5 37.5 42.5 47.S 52. 5 57.5 L39. 2 86. 6 66. 9 53 44.4 36. 2 31.2 25. 2 20 17. 1 _ 1.58 .97 . 73 .56 .45 . 35 .28 .21 .15 .12 - Meridional W a v e 3 , , k=0 0 0 0 0 0 0 0 0 0 0 _ 5.19 4.31 3.58 2.85 2.27 1.68 1.29 .86 .54 .37 -270 270 270 270 270 270 270 270 270 270 - Oblique Waves, k = l .72 .6 .5 .4 .32 .23 .13 .12 .07 .05 . 3 .3 .4 .5 .6 .9 1.1 1.7 2.7 3.9 _ 3.67 3.04 2.53 2.02 1.61 1.19 .91 .61 .38 .26 _ 315 . 315 315 315 315 315 315 315 315 315 -4.62 3. 39 2. 62 2.02 1.62 1. 25 . 1 .71 .47 .33 _ 188 199 210 223 233 243 249 256 261 264 - Zonal Waves, 1=0 u x 10s T Cp X 10* direction C_ x 102 direction 1.02 .85 .7 .56 .45 .33 .25 .17 .11 .07 -.2 .2 .3 .4 .4 .6 .3 1.2 1.9 2.8 -5. 19 4. 31 3. 58 2.85 2. 27 1. 68 1.29 .86 .54 .37 -270 270 270 270 270 270 270 270 270 270 3.96 2.09 .95 .11 . 31 .55 .58 .52 .39 .29 -90 90 90 90 270 270 270 270 270 270 - Wavelength = 170 km Latitude 7.5 12.5 17.5 22.5 27.5 32.5 37.5 42.5 47.5 52.5 57.5 r. 139.2 86.6 66.9 53 44.4 36. 2 31.2 25.2 20 17.1 Me x 10s 1.58 .97 .73 .56 .45 .35 .28 .21 .15 .12 Meridional Waves, k=0 a x 10s 0 0 0 0 0 0. 0 0 0 0 - C_ x 10* 1-6 1.49 1.37 1.23 1.08 .91 .76 .57 .4 .29 direction 270 270 270 270 270 270 270 270 270 270 Oblique Waves, k=l • X 10* .42 .39 .36 .32 .28 .24 .2 .15 .1 .08 -T .5 .5 .6 .6 .7 .8 1 1.3 1.9 2.6 -Cp X 10* direction 1.13 1.05 .97 .86 . 76 . 64 .54 .41 .28 .21 -315 315 315 315 315 315 315 315 315 315 -C_ x 101 direction 1.54 1.36 1.2 1.01 .84 .67 .54 .41 .29 .22 -182 186 189 19S 200 209 217 229 241 248 - Zonal Waves, 1=0 a x 10s .59 .55 .51 .45 .4 .34 .28 .21 .15 .11 T .3 .4 .4 .4 .5 .6 .7 .9 1.3 1.9 Cp X 10* direction 1.6 1.49 1.37 1.23 1.08 .91 .76 .57 .4 .29 270 270 270 270 270 270 270 270 270 270 X 10* direction 1.48 1.23 .99 .72 .5 .26 .11 .04 .12 .12 90 90 90 90 •90 90 90 270 270 270 Table V - 3 Frequencies (u, 1/s), periods (T, y r ) , phase v e l o c i t i e s (Cp, m/s), and group v e l o c i t i e s (Cg, m/s) of the free b a r o c l i n i c Rossby waves of the observed quasi-synoptic length scales at the appropriate l a t i t u d e s i n the NEP. The d i r e c t i o n s are i n degrees clockwise from north. The Internal Rossby radius ( r ^ , km) and the upper cut-off frequency ( u c, 1/s) of the first-mode b a r o c l i n i c Rossby wave i s als o given f o r each l a t i t u d e . 112 Table V-4 Summary of the properties of the l i n e a r first-mode b a r o c l i n i c Rossby waves. X i s the wavelength. U i s the b a r o c l i n i c v e l o c i t y s c a l e obtained from the data s e t . U* i s the estimated upper l i m i t of the true v e l o c i t y perturbations obtained using Wyrtki et a l . ' s (1976) EKEs. Cp i s the phase speed. The only dynamics which may be i n f e r r e d from these properties i s the l i n e a r Rossby wave (LRW) theory. R e g i o n X P e r i o d C p U/C p U*/C p I n f e r r e d (km) ( y r ) (cm/s) Dynamics NWA 285 0.5 - 6.4 0.14 - 1.97 9.7 21.7 155 0.5 - 4.0 0.12 - 0.93 34.5 77.1 NWP 395 0.5 - 1.8 0.70 - 2.77 5.1 11.4 195 0.5 - 1.3 0.48 - 1.34 15.9 35.6 145 0.5 - 1.3 0.36 - 0.86 30.5 68.2 NEA 205 0.5 - 13.0 0.05 - 1.28 5.7 12.7 160 0.5 - 10.5 0.05 - 0.93 9.4 21.0 115 0.7 - 8.1 0.04 - 0.56 16.0 35.8 SA 510 0.3 - 1.0 1.64 - 5.68 1.1 2.5 LRW 245 0.3 - 0.7 1.06 - 2.48 3.2 7.2 LRW NEP 320 0 . 2 - 3 . 9 0 . 2 6 - 5 . 1 9 1.7 3.8 LRW 170 0.3 - 2.6 0.21 - 1.60 6.1 13.6 SP 300 0.3 - 2.8 0.34 - 3.28 3.5 7.9 113 o f t h e i r r e s u l t s . A l s o , t h e p r o p o s e d g e n e r a t i o n mechanisms of t h e LRW f i e l d i n t h e NEP, f o r t h e most p a r t , have a n n u a l p e r i o d s . S i m i l a r mechanisms a r e l i k e l y t o be v o r t i c i t y s o u r c e s f o r t h e LRW f i e l d i n t h e o t h e r r e g i o n s , and t h u s c r e a t e a r e s o n a n c e a t t h e a n n u a l p e r i o d . Second, i t i s r e q u i r e d t h a t t h e phase speed o f t h e LRWs be on t h e o r d e r o f one. T h i s w i l l be c o n s i s t e n t w i t h t h e i n v e s t i g a t i o n s i n t h e NEP. T h i r d , i t i s r e q u i r e d t h a t t h e v e l o c i t y p e r t u r b a t i o n s , U and U*, n o t be much g r e a t e r t h a n t h e phase speeds. Where t h i s o c c u r s , t h e i n e r t i a l e f f e c t s w i l l be more i m p o r t a n t t h a n t h e wave phase d i s p e r s i o n . Kang and Magaard (1980), as p r e v i o u s l y d i s c u s s e d , d e m o n s t r a t e d t h a t t h e p a r t i c l e v e l o c i t i e s may be on t h e o r d e r o f t h e phase speed f o r s i n g l e p l a n e waves and t h e n o n l i n e a r terms w i l l c a n c e l . Thus, t h e t e r m s , U/Cp and U*/Cp, may be used as a n a l o g s t o t h e Rossby wave s t e e p n e s s p a r a m e t e r . I t i s r e q u i r e d t h a t e i t h e r o f t h e s e terms be on t h e o r d e r . o f one f o r LRW t h e o r y t o be v a l i d . o • An e x a m i n a t i o n o f t h e LRW p r o p e r t i e s , i n T a b l e V-4, shows t h a t t h e o b s e r v e d l e n g t h s c a l e s have, f o r t h e most p a r t , n e a r - a n n u a l p e r i o d s and phase speeds on t h e o r d e r o f one. Only a few w a v e l e n g t h s , however, have U/Cp o r U*/Cp on t h e o r d e r o f , o r l e s s t h a n , one. The r e g i o n s w h i c h can be s a i d t o have l e n g t h and v e l o c i t y s c a l e s c o n s i s t e n t w i t h LRW t h e o r y ( a c c o r d i n g t o t h e above c r i t e r i a ) a r e t h e SA and t h e NEP. That i s , LRW t h e o r y i s c o n s i s t e n t w i t h t h e o b s e r v e d l e n g t h and v e l o c i t y s c a l e s o n l y f o r w a v e l e n g t h s l o n g e r t h a n 200 km i n t h e low-energy r e g i o n s . C. Nonlinear Geophysical Turbulence A number o f models o f n o n l i n e a r t u r b u l e n c e e x i s t t h a t use d i m e n s i o n a l i t y t o d e t e r m i n e t h e t h e o r e t i c a l decay c o e f f i c i e n t s o f t h e t e m p e r a t u r e and v e l o c i t y s p e c t r a i n an i n e r t i a l wavenumber range. That i s , t h e t h e o r y p r e d i c t s a s p e c t r a l shape o f t h e fo r m k~P i n t h e wavenumber ranges between t h e s o u r c e s and s i n k s o f energy, where k i s t h e wavenumber and p i s t h e power-law exponent. The c o n s i s t e n c y o f t h e t e m p e r a t u r e s p e c t r a , o f t h e q u a s i - s y n o p t i c XBT d a t a s e t , w i t h t h e e x i s t i n g models o f n o n l i n e a r t u r b u l e n c e w i l l be examined u s i n g t h e s l o p e s o f t h e s p e c t r a between t h e l o n g e s t dominant w a v e l e n g t h s and t h e N y q u i s t wavenumbers. S i n c e t h e D and g e o s t r o p h i c v e l o c i t y s p e c t r a a r e dependent on t h e t e m p e r a t u r e s p e c t r a , t h e y w i l l p r o v i d e no new i n f o r m a t i o n f o r t h i s a n a l y s i s . 114 Ozmidov (1965) d e p i c t e d t h e energy d i s t r i b u t i o n o v e r t h e f u l l wavenumber spectrum o f m o t i o n s ( i . e . wavelengths o f 10,000 km t o 1 cm) i n t h e ocean i n a c c o r d a n c e w i t h t h e 5/3 "Kolmogorov Spectrum Law". The b a s i c f e a t u r e s o f t h i s i d e a l i z e d model a r e t h e i n f l u x of e x t e r n a l e nergy o v e r l o c a l i z e d wavenumber bands, s e p a r a t e d by i n e r t i a l subranges o f c a s c a d i n g energy from low t o h i g h wavenumbers. W y r t k i (1967) examined t h e s p e c t r u m o f ocean t u r b u l e n c e between 40-•'•and 1000 km w a v e l e n g t h s u s i n g t h e MBT d a t a from t h e s i x t e e n "Townsend C r o m w e l l " c r u i s e s o f 1964-66. The r e s u l t s were c o n s i s t e n t w i t h Ozmidov's model, w i t h a peak i n t h e spectrum n e a r 200 km l i k e l y r e p r e s e n t a t i v e o f an energy i n f l u x f r o m l a r g e e d d i e s . T h i s t h r e e - d i m e n s i o n a l i s o t r o p i c model, d e v e l o p e d by Kolmogorov, p r e d i c t s power-law exponents o f 5/3 f o r b o t h t h e t e m p e r a t u r e and v e l o c i t y s p e c t r a i n t h e i n e r t i a l s ubranges. Temperature i s assumed t o be a p a s s i v e t r a c e r . S e v e r a l o t h e r models o f t u r b u l e n c e have been d e v e l o p e d , a l t h o u g h none a r e s u f f i c i e n t l y r e a l i s t i c t o be d i r e c t l y a p p l i c a b l e t o t h e o b s e r v e d m e s o s c a l e v a r i a b i l i t y . I n t h e g e o p h y s i c a l c o n t e x t , i t may be e x p e c t e d t h a t any t h e o r y w i l l be a p p l i c a b l e o n l y t o a c e r t a i n range o f s c a l e s . The K o l m o g o r o v - t y p e t u r b u l e n c e has o n l y been v e r i f i e d f o r s m a l l - s c a l e p r o c e s s e s . A t somewhat l a r g e r s c a l e s , t h e s t r a t i f i c a t i o n must e x e r c i s e an i m p o r t a n t r o l e and P h i l l i p s ' (1966) t h e o r y may be a p p r o p r i a t e . P h i l l i p s ' t h e o r y p r e d i c t s a K o l m o g o r o v - t y p e t u r b u l e n c e a t wavenumbers h i g h e r t h a n a c r i t i c a l buoyancy wavenumber where t h e t u r b u l e n c e i s t h r e e - d i m e n s i o n a l . A t l o w e r wavenumbers, t h e t u r b u l e n c e i s a n i s o t r o p i c when c o m p a r i n g t h e h o r i z o n t a l s c a l e s t o t h e v e r t i c a l s c a l e , due t o t h e s t r a t i f i c a t i o n . The power-law exponents a r e t h r e e and one f o r t h e v e l o c i t y and t e m p e r a t u r e s p e c t r a , r e s p e c t i v e l y . A t s c a l e s where t h e e a r t h ' s r o t a t i o n i s a dominant f a c t o r , K r a i c h n a n (1967) and Charney (1971) p r o p o s e d t w o - d i m e n s i o n a l and t h r e e - d i m e n s i o n a l models o f q u a s i g e o s t o p h i c t u r b u l e n c e , r e s p e c t i v e l y . K r a i c h n a n p o s t u l a t e d two i n e r t i a l s ubranges f o r t h e t w o - d i m e n s i o n a l t u r b u l e n c e . Energy i s i n j e c t e d a t a g i v e n wavenumber and i s t r a n s f e r r e d u n i f o r m l y t o l o w e r wavenumbers, w h i l e e n s t r o p h y ( i . e . mean-squared v o r t i c i t y ) i s t r a n s f e r r e d u n i f o r m l y t o h i g h e r wavenumbers. The t r a n s f e r s o f e n e r g y , i n t h e second r a n g e , and e n s t r o p h y i n t h e f i r s t range, a r e z e r o . By s i m i l a r i t y arguments, t h e v e l o c i t y and t e m p e r a t u r e s p e c t r a have power-law exponents o f 5/3 i n t h e e n e r g y - c a s c a d e r a n g e , w h i l e i n t h e e n s t r o p h y c a s c a d e range t h e v e l o c i t y and t e m p e r a t u r e s p e c t r a have power-laws o f t h r e e and one, r e s p e c t i v e l y . Charney d e v e l o p e d a t h r e e - d i m e n s i o n a l model t h a t a c c o u n t s f o r t h e b a r o c l i n i c n a t u r e o f t h e atmosphere (and ocean) w i t h t h e c o n s e r v a t i o n o f a p s e u d o - p o t e n t i a l 115 v o r t i c i t y . T h i s i s a c o m b i n a t i o n of the c o n s e r v a t i o n o f p o t e n t i a l v o r t i c i t y and p o t e n t i a l t e m p e r a t u r e . T h i s t h e o r y p r e d i c t s a k - 3 law a t wavenumbers h i g h e r t h a n t h e e x c i t a t i o n wavenumber f o r b o t h t h e h o r i z o n t a l v e l o c i t y and t e m p e r a t u r e s p e c t r a . Temperature i s a p a s s i v e t r a c e r i n b o t h o f t h e s e t h e o r i e s . Examples o f t h e l o g - l o g r e p r e s e n t a t i o n s o f t h e s p e c t r a i n C h a p t e r IV a r e shown i n F i g u r e V-2, w i t h t h e t e m p e r a t u r e s p e c t r a shown f o r t h e HIGH and LOW r e g i o n s . The power-law exponents where d e t e r m i n e d i n t h e wavenumber range from t h e p eaks o f t h e l o g - l o g s p e c t r a t o t h e r e g i o n a l N y q u i s t wavenumbers. F o r s p e c t r a w i t h dominant w a v e l e n g t h s a t s c a l e s s m a l l e r t h a n t h e peak wavenumber, t h i s wavenumber range c a n n o t be c o n s i d e r e d a t r u e i n e r t i a l s ubrange, however, t h e s l o p e s o b t a i n e d may s t i l l be o f use. The s l o p e s were d e t e r m i n e d w i t h a l e a s t - s q u a r e s l i n e a r r e g r e s s i o n o f t h e a v e r a g e smoothed s p e c t r a l e s t i m a t e s ( Z a r , 1974). The 95% c o n f i d e n c e i n t e r v a l s o f t h e s l o p e s were c a l c u l a t e d u s i n g t h e upper and l o w e r 95% c o n f i d e n c e l i m i t s o f t h e s p e c t r a l e s t i m a t e s . The s p e c t r a l power-law exponents o f t h e t e m p e r a t u r e s a r e summarized i n T a b l e V-5. The h i g h - and low-energy r e g i o n s have power-law exponents t h a t a r e g e n e r a l l y between two and t h r e e . The exponents o f t h e SA and t h e SP r e g i o n s have l a r g e e r r o r b a r s as a r e s u l t o f t h e s h o r t wavenumber range (due t o t h e low N y q u i s t wavenumbers) u s e d i n t h e r e g r e s s i o n and must be c o n s i d e r e d n e x t t o u s e l e s s . F o r t h e most p a r t , t h e power-law exponents o f each v a r i a b l e a r e n o t s i g n i f i c a n t l y d i f f e r e n t between r e g i o n s . The power-law exponents o f t h e HIGH and LOW r e g i o n s p r o v i d e a g r e a t e r c o n t r a s t t h a n t h e i n d i v i d u a l g e o g r a p h i c r e g i o n s . The t e m p e r a t u r e v a r i a n c e a s s o c i a t e d w i t h t h e b a r o c l i n i c eddy f i e l d i n t h e HIGH r e g i o n has a c h a r a c t e r i s t i c power-law exponent o f 3.01 w i t h 95% c o n f i d e n c e l i m i t s o f 2.85 t o 3.17 ( i . e . about 3.0) between w a v e l e n g t h s o f 300 t o 54 km. I n t h e LOW r e g i o n , t h e t e m p e r a t u r e v a r i a n c e has a c h a r a c t e r i s t i c power-law exponent o f 2.47 w i t h 95% c o n f i d e n c e l i m i t s o f 2.29 and 2.65 ( i . e . about 2.5) between w a v e l e n g t h s o f 300 t o 91 km. The c h a r a c t e r i s t i c power-law exponent o f t h e LOW r e g i o n i s s i g n i f i c a n t l y l e s s t h a n t h a t o f t h e HIGH r e g i o n . These r e s u l t s show t h a t , i n t h e HIGH r e g i o n , t h e t e m p e r a t u r e s p e c t r u m i s p r o p o r t i o n a l t o t h e -3.0 power. T h i s i s c o n s i s t e n t w i t h Charney's (1971) t h r e e - d i m e n s i o n a l g e o p h y s i c a l t u r b u l e n c e model. T h i s i m p l i e s t h a t t h e energy 116 W A V E L E N G T H - KM IO 4 1 0 3 1 0 2 1 0 ' Inn i i i i Inn i t i i Inn i i i i I I l | i 111ii| I | i 11 I | I 1 1 1 l l | IO"4 3 5 IO"3 3 5 IO"2 3 5 IO"1 K - C Y C L E S / K M W A V E L E N G T H - KM 10" 103 IO 2 10' l l l l l I I I I Inn i i i i Inn i i i i I -1 I | I | IIW| I | I 11 I | I 11 10-4 3 5 10-3 3 5 10-2 3 5 I O ' 1 K - C Y C L E S / K M Figure V-2 Sample p l o t s of the l o g - l o g s p e c t r a l representations. These spectra depict the mid-thermocline temperature v a r i a b i l i t y i n the HIGH and LOW regions. 117 Table V-5 Summary of the s p e c t r a l power-law exponents of the mid-thermocline temperature. The slopes of the log—log spectra (-p) were obtained over the wavelength bands as shown. The r e l a t i o n E(k) =» k -P describes the slopes of the spectra In the applicable wavenumber range where E i s the temperature spectrum, k i s the wavenumber and p i s the power-law exponent. R e g i o n p 95% C o n f i d e n c e Wavelength I n t e r v a l Band (km) NWA 2.85 2.62 - 3.08 285 - 70 NWP 3.07 2.84 - 3.30 395 - 54 NEA 2.61 2.16 - 3.06 205 - 91 SA 2.70 1.10 - 4.33 510 - 210 NEP 2.40 2.19 - 2.61 320 - 88 SP 2.37 -2.50 - 7.24 300 - 220 HIGH 3.01 2.85 - 3.17 300 - 54 LOW 2.47 2.29 - 2.65 300 - 91 118 o f t h e m e s o s c a l e p e r t u r b a t i o n s i s i n p u t i n t o t h e h i g h - e n e r g y r e g i o n s a t w a v e l e n g t h s of about 300 km, cascades t o s l i g h t l y l o w e r wavenumbers and p r o p a g a t e s away as l i n e a r / n o n l i n e a r Rossby waves. E n s t r o p h y , however, cascades t o h i g h e r wavenumbers o v e r a w a v e l e n g t h band o f 300 t o 54 km w i t h no energy t r a n s f e r . The e n t h u s i a s m w i t h w h i c h one a c c e p t s t h e s e r e s u l t s and t h e i r p h y s i c a l i n t e r p r e t a t i o n must be tempered by t h e f a c t t h a t Charney's model assumes t h a t t e m p e r a t u r e i s a p a s s i v e t r a c e r , and t h i s i s c l e a r l y not the case f o r o c e a n i c m e s o s c a l e m o t i o n s . I n t h e LOW r e g i o n , t h e t e m p e r a t u r e spectrum has a s l o p e o f -2.5. T h i s i s not c o n s i s t e n t w i t h any o f t h e models of n o n l i n e a r g e o p h y s i c a l t u r b u l e n c e . The low-energy r e g i o n o f t h e NEA has a power-law exponent o f t h r e e , s i m i l a r t o t h a t o f t h e h i g h - e n e r g y r e g i o n s , however, t h e r e g i o n a l Rossby wave s t e e p n e s s p a r a meter ( T a b l e V-2) i s not l a r g e enough t o p e r m i t q u a s i g e o s t r o p h i c t u r b u l e n c e . A d i s t i n c t g e o g r a p h i c v a r i a b i l i t y o f t h e c o n s i s t e n c y of t h e n o n l i n e a r g e o p h y s i c a l t u r b u l e n c e models has been i d e n t i f i e d . Charney's t h r e e - d i m e n s i o n a l model of q u a s i g e o s t r o p h i c t u r b u l e n c e i s c o n s i s t e n t w i t h t h e s p e c t r a l s l o p e s of t h e t e m p e r a t u r e s p e c t r a i n t h e h i g h - e n e r g y r e g i o n s ( i . e . t h e w e s t e r n boundary c u r r e n t r e g i o n s ) , b u t n o t i n t h e low-energy r e g i o n s ( i . e . t h e ocean i n t e r i o r and e a s t e r n boundary c u r r e n t r e g i o n s ) . There a r e no e x i s t i n g models of g e o p h y s i c a l t u r b u l e n c e t h a t a r e c o n s i s t e n t w i t h t h e r e p o r t e d power-law exponents between 2.0 and 3.0 i n t h e low-energy r e g i o n s . The s p e c t r a do n o t p r o v i d e e v i d e n c e f o r a -5/3 power-law c h a r a c t e r i s t i c o f t h e t h r e e - d i m e n s i o n a l K olmogorov-type t u r b u l e n c e . N e i t h e r do t h e y s u g g e s t t h a t K r a i c h n a n ' s model o f t w o - d i m e n s i o n a l q u a s i g e o s t r o p h i c t u r b u l e n c e i s a p p r o p r i a t e . D. Summary o f t h e I n f e r r e d Dynamics The dynamics i n f e r r e d from t h e Rossby wave s t e e p n e s s p a r a m e t e r , t h e LRW t h e o r y and t h e g e o p h y s i c a l t u r b u l e n c e models a r e summarized i n T a b l e V-6. The r e s u l t s a r e i d e n t i c a l t o t h o s e i n f e r r e d f r o m t h e Rossby wave stee p n e s s p a r a m e t e r ( T a b l e V - 2 ) . The l i n e a r Rossby wave a n a l y s i s p r o v i d e d more c o n f i d e n c e i n t h e a p p l i c a b i l i t y o f LRW t h e o r y t o w a v e l e n g t h s l e s s t h a n 200 km i n t h e low-energy r e g i o n s , w h i l e t h e a n a l y s i s o f t h e s p e c t r a l power-laws p r o v i d e d a d d i t i o n a l e v i d e n c e f o r t h e v a l i d i t y o f QGT t h e o r y i n t h e h i g h - e n e r g y r e g i o n s . The l a t t e r , a l s o , i d e n t i f i e d t h e s p e c i f i c g e o p h y s i c a l t u r b u l e n c e model t h a t i s c o n s i s t e n t w i t h t h e s p e c t r a l s l o p e s o f t h e t e m p e r a t u r e i n t h e 119 T a b l e V-6 Summary o f t h e i n f e r r e d dynamics o f t h e dominant wavelengths ( A ) . The i n f e r r e d dynamics a r e : l i n e a r Rossby wave (LRW) t h e o r y , n o n l i n e a r Rossby wave (NRW) t h e o r y and g u a s i g e o s t r o p i c t u r b u l e n c e (QGT) t h e o r y . The b o l d wavelengths a r e d i s t i n c t t o t h e 95% c o n f i d e n c e l e v e l , t h e u n d e r l i n e d wavelength i s d i s t i n c t t o t h e 80% c o n f i d e n c e l e v e l and t h e o t h e r wavelengths a r e n o t d i s t i n c t t o t h e 80% c o n f i d e n c e l e v e l . Region X I n f e r r e d (km) Dynamics NWA 285 LRW/NRW 155 QGT NWP 395 LRW/NRW 195 145 QGT NEA 205 LRW/NRW 160 - 115 - SA 510 LRW/NRW 245 LRW/NRW NEP 320 LRW/NRW 170 SP 300 LRW/NRW HIGH 300 LRW/NRW 155 QGT LOW 300 LRW/NRW 170 120 h i g h - e n e r g y r e g i o n s - Charney's (1971) t h r e e - d i m e n s i o n a l q u a s i g e o s t r o p h i c t u r b u l e n c e model. The dominant w a v e l e n g t h s o f t h e b a r o c l i n i c eddy f i e l d t h a t a r e d i s t i n c t t o t h e 95% c o n f i d e n c e l e v e l and t h e i r r e s p e c t i v e i n f e r r e d dynamics, i n T a b l e V-6, a r e i n b o l d s c r i p t . These a r e t h e most s i g n i f i c a n t r e s u l t s . These dominant w a v e l e n g t h s a r e a l l g r e a t e r t h a n 200 km and a r e c o n s i s t e n t w i t h LRW and NRW t h e o r i e s . The one e x c e p t i o n t o t h i s s t a t e m e n t i s t h e 145 km w a v e l e n g t h i n t h e NWP, w h i c h i s c o n s i s t e n t w i t h QGT t h e o r y . The HIGH and LOW r e g i o n s have dominant w a v e l e n g t h s o f 300 km t h a t a r e c o n s i s t e n t w i t h t h e dynamics o f LRWs and NRWs. The HIGH energy r e g i o n i s , o f c o u r s e , more n o n l i n e a r , b u t one must examine t h e s h o r t e r and l e s s e r s i g n i f i c a n t w a v e l e n g t h s i n o r d e r t o f i n d t h e s t r o n g n o n l i n e a r i n t e r a c t i o n s r e q u i r e d f o r QGT. 121 V I . CONCLUSIONS The g e o g r a p h i c v a r i a b i l i t y o f t h e m e s o s c a l e s t a t i s t i c s and t h e i n f e r r e d dynamics has been examined w i t h a q u a s i - s y n o p t i c expendable b a t h y t h e r m o g r a p h (XBT) d a t a s e t . Over 10,000 XBT p r o f i l e s were o b t a i n e d from t h e Canadian Armed F o r c e s , t h e U n i t e d S t a t e s Navy and t h e N a t i o n a l O ceanographic Data C e n t e r i n 95 s i n g l e - s h i p t r a n s - o c e a n i c s e c t i o n s and 29 m u l t i s h i p / A X B T s u r v e y s . Mean t e m p e r a t u r e - s a l i n i t y and s a l i n i t y - d e p t h c u r v e s were used t o i n f e r t h e g e o p o t e n t i a l anomaly f r o m t h e t e m p e r a t u r e p r o f i l e s f o r use i n t h e s t a t i s t i c a l and d y n a m i c a l a n a l y s e s . The d e s c r i p t i v e a n a l y s e s q u a l i t a t i v e l y d i s c u s s e d t h e g e o g r a p h i c v a r i a b i l i t y o f t h e o b s e r v e d q u a s i - s y n o p t i c t e m p e r a t u r e s t r u c t u r e . G e o g r a p h i c r e g i o n s w i t h d i f f e r e n t h o r i z o n t a l l e n g t h s c a l e s and a m p l i t u d e s o f eddy v a r i a b i l i t y were d e f i n e d w i t h t h e a i d o f p r e v i o u s work u s i n g c l i m a t o l o g i c a l d a t a s e t s . S i x g e o g r a p h i c r e g i o n s were d e l i n e a t e d and c l a s s i f i e d as h i g h - o r low-energy a r e a s . The h i g h - e n e r g y r e g i o n s a r e t h e N o r t h w e s t A t l a n t i c (NWA) and t h e N o r t h w e s t P a c i f i c (NWP). The low-energy r e g i o n s a r e t h e N o r t h e a s t A t l a n t i c (NEA), t h e South A t l a n t i c ( S A ) , t h e N o r t h e a s t P a c i f i c (NEP) and t h e South P a c i f i c ( S P ) . Two c o m p o s i t e r e g i o n s were a l s o d e f i n e d . The HIGH r e g i o n c o m p r i s e d t h e h i g h - e n e r g y r e g i o n s , and t h e LOW r e g i o n c o m p r i s e d t h e low-energy r e g i o n s . T y p i c a l t e m p e r a t u r e s e c t i o n s from each g e o g r a p h i c r e g i o n were examined and compared t o o b s e r v a t i o n s o f t h e m e s o s c a l e v a r i a b i l i t y f r o m o t h e r s o u r c e s . T h i s i n v e s t i g a t i o n f o u n d t h e q u a s i - s y n o p t i c d a t a s e t t o e x h i b i t mesoscale p r o p e r t i e s v e r y s i m i l a r t o t h o s e r e p o r t e d i n t h e l i t e r a t u r e , and t h u s t h e d a t a s e t was c o n f i d e n t l y a c c e p t e d as b e i n g r e p r e s e n t a t i v e o f t h e eddy v a r i a b i l i t y i n t h e r e g i o n s under e x a m i n a t i o n . S e v e r a l s t a t i s t i c a l a n a l y s e s were u s e d t o q u a n t i f y t h e q u a s i - s y n o p t i c m e s o s c a l e s t r u c t u r e i n t h e upper 400 m o f t h e ocean. The m i d - t h e r m o c l i n e t e m p e r a t u r e and t h e g e o p o t e n t i a l anomaly (0-4000 kPa) were u s e d t o r e p r e s e n t t h e m e s o s c a l e v a r i a b i l i t y . P e r t u r b a t i o n v a r i a b l e s were o b t a i n e d by r e m o v i n g t h e low-rwavenumber s i g n a l from t h e s e c t i o n s w i t h a 1000 km r u n n i n g mean, and f r o m t h e s u r v e y s w i t h z o n a l and m e r i d i o n a l l i n e a r t r e n d s . The g e o g r a p h i c v a r i a b i l i t y o f t h e s t a n d a r d d e v i a t i o n s , skewness, k u r t o s i s and i n t e r m i t t e n c i e s o f t h e t e m p e r a t u r e and t h e g e o p o t e n t i a l anaomaly f o r t h e 122 s e c t i o n s and t h e s u r v e y s were d i s c u s s e d . The s t a t i s t i c s o f t h e s e c t i o n s and t h e s u r v e y s a r e comparable. The HIGH r e g i o n has g e o p o t e n t i a l anomaly p e r t u r b a t i o n s w i t h a v e r a g e a m p l i t u d e s o f 0.67 m 2/s 2, and t h e LOW r e g i o n has av e r a g e a m p l i t u d e s o f 0.26 m 2/s 2. The r a t i o o f t h e s e a m p l i t u d e s i s 2.58. The p o s i t i v e skewness of t h e LOW r e g i o n s u g g e s t s t h a t t h e b a r o c l i n i c eddy f i e l d c o n s i s t s o f p r e d o m i n a n t l y warm e d d i e s . The skewness o f t h e HIGH r e g i o n i s n o t s i g n i f i c a n t l y d i f f e r e n t " from z e r o . The i n t e r m i t t e n c i e s a r e t h e same and i n d i c a t e t h a t t h e mesos c a l e p e r t u r b a t i o n s o c c u r o v e r about 45% of t h e two r e g i o n s . The s t a n d a r d d e v i a t i o n o f t h e t e m p e r a t u r e i s 1.40°C i n t h e HIGH r e g i o n and 0.54°C i n t h e LOW r e g i o n . The p o s i t i v e skewness o f t e m p e r a t u r e i n t h e LOW r e g i o n i s c o n s i s t e n t w i t h t h e f i e l d o f warm e d d i e s s u g g e s t e d above. The n e g a t i v e skewness of t h e t e m p e r a t u r e i n t h e HIGH r e g i o n s u g g e s t s t h a t t h e b a r o c l i n i c eddy f i e l d c o n s i s t s p r e d o m i n a n t l y o f c o l d e d d i e s , as opposed t o t h e f i e l d o f warm e d d i e s i n t h e LOW r e g i o n . The N o r t h P a c i f i c S u b t r o p i c a l F r o n t (NPSF) and t h e N o r t h P a c i f i c E q u a t o r i a l C u r r e n t (NPEC) a r e s u b r e g i o n s o f t h e NEP. The s t a n d a r d d e v i a t i o n s o f t h e s e two r e g i o n s a r e h i g h e r t h a n t h e c o r r e s p o n d i n g s t a t i s t i c s o f t h e NEP, s i n c e t h e s a m p l i n g s u b r e g i o n s a r e i n r e l a t i v e l y h i g h eddy a c t i v i t y a r e a s o f t h e NEP. The NPEC has t h e l a r g e s t m i d - t h e r m o c l i n e t e m p e r a t u r e and g e o p o t e n t i a l anomaly p e r t u r b a t i o n s . The p o s i t i v e skewness o f t h e b a r o c l i n i c eddy f i e l d i n t h e NPSF i s c o n s i s t e n t w i t h t h e NEP s t a t i s t i c s . The NPEC has a n e g a t i v e skewness. T h i s i s n o t c o n s i s t e n t w i t h t h e NEP, however, i t i s c o n s i s t e n t w i t h t h e f i e l d o f c o l d e d d i e s d i s c u s s e d i n t h e d e s c r i p t i v e a n a l y s i s o f t h e f o u r s u r v e y s o f t h e a r e a . The s e a s o n a l v a r i a b i l i t y o f t h e NEP r e g i o n and t h e i s o t r o p y o f t h e m e s o s c a l e eddy f i e l d were i n v e s t i g a t e d i n some d e t a i l - The s t a n d a r d d e v i a t i o n s , skewness, k u r t o s i s and i n t e r m i t t e n c i e s were c a l c u l a t e d f o r q u a r t e r l y s u b s e t s o f s e c t i o n s . S i g n i f i c a n t s e a s o n a l s i g n a l s were a p p a r e n t . There may be a s e a s o n a l v a r i a b i l i t y i n t h e m e s o s c a l e eddy f i e l d s s i m i l a r t o t h a t d i s c u s s e d by G o u l d (1983) i n t h e NEA, and t h e r e g i o n s t h a t a r e u n e v e n l y sampled o v e r t h e seasons ( i . e . a l l b u t t h e NEP and LOW r e g i o n s ) may have s e a s o n a l b i a s e s . Q u a n t i f y i n g t h e s e a s o n a l v a r i a b i l i t y i s beyond t h e a b i l i t y o f t h i s d a t a s e t . The a s s u m p t i o n o f h o r i z o n t a l i s o t r o p y was e v a l u a t e d w i t h an a n i s o t r o p y f a c t o r d e t e r m i n e d f r o m t h e s u r v e y s . The a n i s o t r o p y f a c t o r , A s , was d e t e r m i n e d by t h e r e l a t i o n , A s = L M / L Z . L M and L z a r e t h e m e r i d i o n a l and z o n a l d e c o r r e l a t i o n s c a l e s , r e s p e c t i v e l y , o b t a i n e d f r o m t h e 123 m e r i d i o n a l l y and z o n a l l y a v eraged a u t o c o r r e l a t i o n f u n c t i o n s o f t h e s u r v e y s . The r e g i o n a l a n i s o t r o p y f a c t o r s a r e n o t s i g n i f i c a n t l y d i f f e r e n t from one. W i t h no e v i d e n c e t o t h e c o n t r a r y , the a s s u m p t i o n o f i s o t r o p y was c o n s i d e r e d r e a s o n a b l e f o r t h e s p a t i a l s c a l e s of m o t i o n b e i n g examined. Wavenumber s p e c t r a were used t o examine t h e d i s t r i b u t i o n of v a r i a n c e i n wavenumber space''' between wave l e n g t h s of 1000 t o 100 km. The dominant w a v e l e n g t h s o f t h e m i d - t h e r m o c l i n e t e m p e r a t u r e and g e o p o t e n t i a l anomaly s p e c t r a a r e between 100 and 400 km. There i s no s i g n i f i c a n t s c a l e s e p a r a t i o n between t h e dominant l e n g t h s c a l e s o f t h e h i g h - and low-energy r e g i o n s . I n t h e HIGH r e g i o n , t h e g e o p o t e n t i a l anomaly s p e c t r u m has peak w a v e l e n g t h s of 300 and 155 km, w i t h t h e r e s p e c t i v e wavenumber bands c o n t a i n i n g 60 and 30% o f t h e v a r i a n c e . The LOW r e g i o n has s p e c t r a l p eaks a t 300 and 170 km c o n t a i n i n g 73 and 15% o f t h e v a r i a n c e , r e s p e c t i v e l y . The low-energy r e g i o n s have a g r e a t e r p o r t i o n o f t h e i r t o t a l v a r i a n c e i n t h e l o n g e r w a v e l e n g t h s . The t w o - d i m e n s i o n a l i s o t r o p i c eddy k i n e t i c e n e r g i e s (EKEs) were e s t i m a t e d f o r each g e o g r a p h i c r e g i o n and wavenumber band. The eddy k i n e t i c e n e r g i e s p e r u n i t mass f o r t h e HIGH and LOW r e g i o n s a r e 250 and 36 c m 2 / s 2 , r e s p e c t i v e l y . The HIGH r e g i o n has about seven t i m e s t h e b a r o c l i n i c eddy k i n e t i c energy o f t h e LOW r e g i o n i n w a v e l e n g t h s between 1000 and 100 km. These EKEs a r e s i m i l a r t o t h o s e r e p o r t e d by F u (1983) w i t h SEASAT a l t i m e t r y d a t a , b u t a r e l e s s t h a n t h o s e o f W y r t k i et_ a l . (1976) by a f a c t o r o f f i v e . T h i s i s c o n s i s t e n t w i t h t h e u n d e r s t a n d i n g t h a t : t h e b a r o c l i n i c (0-400 m) EKEs o f t h e q u a s i - s y n o p t i c XBT d a t a s e t a r e u n d e r e s t i m a t e s , s i n c e t h e y w i l l m i s s a s i g n i f i c a n t p o r t i o n o f t h e b a r o t r o p i c s i g n a l ; t h a t t h e EKEs o f t h e SEASAT a l t i m e t r y ( F u , 1983) a r e u n d e r e s t i m a t e s , s i n c e t h e y w i l l m i s s a s i g n i f i c a n t p o r t i o n o f t h e m e s o s c a l e s i g n a l due t o t h e 24-day s a m p l i n g window; and t h a t t h e EKEs o f t h e s h i p d r i f t d a t a ( W y r t k i e t a l . , 1976) a r e o v e r e s t i m a t e s due t o t h e winds a c t i n g on t h e v e s s e l s . The r e l e v a n c e o f q u a s i g e o s t r o p h i c dynamics was i n f e r r e d u s i n g s e v e r a l d y n a m i c a l t e s t s w i t h t h e wavenumber s t a t i s t i c s . The q u a s i g e o s t r o p h i c s c a l i n g p a r a m e t e r s ( i . e . t h e Rossby number ( R o ) , t h e B u r g e r number (B) and t h e s p h e r i c i t y p a r a m e t e r ( (3*)) were e v a l u a t e d u s i n g t h e dominant l e n g t h and v e l o c i t y s c a l e s of each g e o g r a p h i c r e g i o n . F o r a l l r e g i o n s and l e n g t h s c a l e s , i t was f o u n d t h a t R Q<<1, B = 0(1) and (5*<<1, c o n s i s t e n t w i t h t h e q u a s i g e o s t r o p h i c s c a l i n g . The Rossby wave s t e e p n e s s p a r a m e t e r , 124 M = U/( 3 0t>2), was c a l c u l a t e d t o i n v e s t i g a t e whether t h e b a r o c l i n i c eddy f i e l d s a r e w a v e l i k e ( l i n e a r ) o r t u r b u l e n t ( n o n l i n e a r ) . The f r e q u e n c i e s , phase v e l o c i t i e s and group v e l o c i t i e s were c a l c u l a t e d u s i n g f r e e l i n e a r d i s p e r s i v e b a r o c l i n i c Rossby wave t h e o r y and t h e o b s e r v e d w a v e l e n g t h s . These r e s u l t s were compared w i t h t h e e x t e n s i v e work, by o t h e r i n v e s t i g a t o r s , i n t h e NEP. The c o n s i s t e n c y o f t h e t e m p e r a t u r e s p e c t r a w i t h t h e e x i s t i n g models o f g e o p h y s i c a l t u r b u l e n c e Was examined w i t h t h e s l o p e s o f t h e n e a r - i n e r t i a l s p e c t r a l s u b r a n g e s . The r e s u l t s o f t h e s e d y n a m i c a l t e s t s i m p l y a g e o g r a p h i c v a r i a b i l i t y o f t h e dynamics g o v e r n i n g t h e o b s e r v e d b a r o c l i n i c eddy f i e l d s . F o r a l l t h e g e o g r a p h i c r e g i o n s , t h e w a v e l e n g t h s g r e a t e r t h a n 200 km a r e c o n s i s t e n t w i t h l i n e a r Rossby wave t h e o r y o r n o n l i n e a r Rossby wave t h e o r y . The a p p l i c a b i l i t y o f t h e s e two t h e o r i e s cannot be d i s t i n g u i s h e d w i t h t h e s e s i m p l e d y n a m i c a l t e s t s . The m o t i o n s i n t h e h i g h - e n e r g y r e g i o n s are,, o f c o u r s e , more n o n l i n e a r t h a n t h e m o t i o n s i n t h e low-energy r e g i o n s w i t h c o r r e s p o n d i n g s c a l e s . I n t h e h i g h - e n e r g y r e g i o n s , t h e p e r t u r b a t i o n s w i t h w a v e l e n g t h s l e s s t h a n 200 km a r e c o n s i s t e n t w i t h q u a s i g e o s t r o p h i c t u r b u l e n c e t h e o r y , i n p a r t i c u l a r , Charney's (1971) model o f t h r e e - d i m e n s i o n a l q u a s i g e o s t r o p h i c t u r b u l e n c e . The m o t i o n s w i t h w a v e l e n g t h s l e s s t h a n 200 km i n t h e low-energy r e g i o n s have s c a l e s t h a t a r e i n t e r m e d i a t e between t h o s e e x p e c t e d o f l i n e a r / n o n l i n e a r Rossby wave t h e o r i e s , and q u a s i g e o s t r o p h i c t u r b u l e n c e t h e o r i e s . T h i s i n v e s t i g a t i o n has examined t h e g e o g r a p h i c v a r i a b i l i t y o f t h e p r o p e r t i e s o f t h e m e s o s c a l e motions i n t h e ocean w i t h a q u a s i - s y n o p t i c XBT d a t a s e t . An i n h o m o g e n e i t y o f t h e mesoscale s t a t i s t i c s i s demonstrated t h a t i s comparable t o t h e r e s u l t s o f p r e v i o u s i n v e s t i g a t o r s . The wavenumber s t a t i s t i c s o f t h e q u a s i - s y n o p t i c d a t a p r o v i d e d e s t i m a t e s o f t h e dominant l e n g t h and v e l o c i t y s c a l e s . From t h e s e s c a l e s o f m o t i o n , an inho m o g e n e i t y i n t h e g o v e r n i n g dynamics o f t h e mesos c a l e p e r t u r b a t i o n s i n t h e ocean has been i n f e r r e d . The s t r e n g t h o f t h e q u a s i - s y n o p t i c d a t a l i e s i n t h e a b i l i t y t o d e t e r m i n e t h e l e n g t h and v e l o c i t y s c a l e s o f v a r i a b i l i t y f r o m w h i c h s i m p l e d y n a m i c a l models may be d i s c u s s e d . Recommendations F o r F u t u r e Work The r e s u l t s o f t h i s work have emphasized t h e v a l u e o f q u a s i - s y n o p t i c d a t a s e t s f o r r e s o l v i n g t h e l e n g t h and v e l o c i t y s c a l e s i n t h e ocean. The d a t a s e t 125 employed h e r e i s by no means t h e complete c o l l e c t i o n o f t h e q u a s i - s y n o p t i c d a t a t h a t may be u s e d f o r t h e e x a m i n a t i o n o f t h e m e s o s c a l e v a r i a b i l i t y . There i s a p o t e n t i a l t o examine t h e c h a r a c t e r i s t i c s o f t h e m e s o s c a l e i n a s i m i l a r manner, b u t i n more d e t a i l , i n s e v e r a l r e g i o n s of t h e ocean w i t h a v a i l a b l e d a t a s e t s (most n o t a b l y t h e Northwest A t l a n t i c and t h e N o r t h e a s t P a c i f i c ) . T h i s i n v e s t i g a t i o n h i g h l i g h t s t h e r e q u i r e m e n t f o r f u r t h e r work i n f o u r a r e a s . F i r s t , t h e s e a s o n a l s i g n a l o f the s y n o p t i c m e s o s c a l e v a r i a b i l i t y must be examined. The p o s s i b i l i t y o f s i g n i f i c a n t s e a s o n a l s i g n a l s o f t h e m e s o s c a l e v a r i a b i l i t y was i d e n t i f i e d i n t h i s s t u d y , b u t c o u l d n o t be q u a n t i f i e d . Two, t h e h o r i z o n t a l a n i s o t r o p y of t h e s e s c a l e s o f m o t i o n s has n o t been a d e q u a t e l y r e s o l v e d . I n v e s t i g a t o r s have i d e n t i f i e d i n d i v i d u a l f e a t u r e s i n most r e g i o n s o f t h e ocean w i t h a n i s o t r o p i c c h a r a c t e r i s t i c s , b u t t h e r e i s no s t a t i s t i c a l l y s i g n i f i c a n t e v i d e n c e t h a t mesoscale m o t i o n s a r e , oh a v e r a g e , a n i s o t r o p i c o v e r l a r g e r e g i o n s o f t h e ocean. Three, t h e d e t r e n d i n g scheme u s e d h e r e t o remove t h e low-wavenumber s i g n a l of t h e l a r g e - s c a l e mean f l o w c a n n o t be c o n s i d e r e d i d e a l . I t would be much p r e f e r a b l e t o use a t i m e s e r i e s o f q u a s i - s y n o p t i c s e c t i o n s a l o n g a r e p e a t e d t r a n s e c t . I n t h i s manner t h e mean f l o w may be removed by a v e r a g i n g . F o u r t h , i t w o u l d be v a l u a b l e t o o b t a i n t h e wavenumber s p e c t r a o f t h e measured v e l o c i t i e s i n c o n j u n c t i o n w i t h t h e measured t e m p e r a t u r e s . A t t h i s d a t e , however, t h e r e a r e no q u a s i - s y n o p t i c v e l o c i t y and t e m p e r a t u r e d a t a s e t s a v a i l a b l e f o r e x a m i n i n g t h e m e s o s c a l e . The i n s t r u m e n t s r e q u i r e d a r e v e r y new and e x p e n s i v e . An a c o u s t i c d o p p l e r c u r r e n t p r o f i l e r (ADCP) w i t h XBTs, o r expendable c u r r e n t p r o f i l e r s (XCPs) w o u l d be c a p a b l e o f o b t a i n i n g t h e r e q u i r e d d a t a s e t s . 126 REFERENCES Anderson, E.R., 1979. Expendable B a t h y t h e r m o g r a p h (XBT) A c c u r a c y S t u d i e s . N a v a l Ocean Systems C e n t e r , San D i e g o , p. 143. Andrews, J . C and P. S c u l l y - P o w e r s , 1976. 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