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UBC Theses and Dissertations

Atmospheric blocking in the northern hemisphere Knox, John Lewis 1981

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ATMOSPHERIC BLOCKING IN THE NORTHERN HEMISPHERE by JOHN LEWIS KNOX B.A., University of Toronto, 1939 M.A., University of Toronto, 1948 A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY in THE FACULTY OF GRADUATE STUDIES Department of Geography We accept t h i s thesis as conforming to the required standard THE UNIVERSITY OF BRITISH COLUMBIA June, 1981 © John Lewis Knox, 1981 In p r e s e n t i n g t h i s t h e s i s 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 U n i v e r s i t y o f B r i t i s h Columbia, I agree t h a t the L i b r a r y s h a l l make i t f r e e l y a v a i l a b l e f o r r e f e r e n c e and study. I f u r t h e r agree t h a t p e r m i s s i o n f o r e x t e n s i v e copying o f t h i s t h e s i s f o r s c h o l a r l y purposes may be granted by the head o f my department o r by h i s o r her r e p r e s e n t a t i v e s . I t i s understood t h a t c o p y i n g or p u b l i c a t i o n o f t h i s t h e s i s f o r f i n a n c i a l g a i n s h a l l not be a llowed without my w r i t t e n p e r m i s s i o n . Department o f The U n i v e r s i t y of B r i t i s h Columbia 2075 Wesbrook P l a c e Vancouver, Canada V6T 1W5 Date DE-6 (2/79) i i ABSTRACT Blocking i s generally understood as the obstruction on a large scale of the normal west - to - east motion of mid-latitude pressure systems. I t is a persistent phenomenon lasting from one to several weeks and the resulting prolonged weather regimes may have serious economic and social consequences. The recent Northern Hemisphere winters, starting with 1976-77, featured unusually large c i r c u l a t i o n anomalies, many of which can be d i r e c t l y related to prolonged episodes of large scale blocking. the intent of this study i s to investigate the s t a t i s t i c s and certain diagnostics of blocking in the Northern Hemisphere. The f i r s t of the three primary objectives i s to present and interpret the spatial and temporal d i s t r i b u t i o n of.blocking during the past 33 years. We develop objective i d e n t i f i c a t i o n c r i t e r i a , adaptable to machine processing methods, by relating the blocking anticyclone to i t s associated positive anomaly of 5-day mean 500MB height. Anomalies meeting the c r i t e r i a are called 'blocking signatures. 1 We present the seasonal frequency of occurrence of these signatures by longitude and by area. The results are in good agreement with published studies for the oceans, but they also reveal a high frequency of blocking signatures over the Northeastern Canadian Archipelago. This r e s u l t , dubbed the 'Baffin Island Paradox' i s further investigated and rationalized. A catalogue has been prepared which i d e n t i f i e s the date, centre location and magnitude of every blocking signature which occurred from January 1, 1946 to December 31, 1978. A supplementary Catalogue i d e n t i -f i e s sequences of these signatures corresponding to actual blocking epi-sodes. i i i The s e c o n d o b j e c t i v e i s t o i n v e s t i g a t e w h e t h e r r e g i o n s w i t h h i g h i n c i d e n c e o f b l o c k i n g , i n e i t h e r t h e d e v e l o p i n g o r t h e m a t u r e s t a g e , f e a t u r e n o n - G a u s s i a n d i s t r i b u t i o n s o f 5 -day mean g e o p o t e n t i a l . D u r i n g w i n t e r , f i e l d s o f s i g n i f i c a n t l y low k u r t o s i s a r e f o u n d i n c e r t a i n m i d -l a t i t u d e r e g i o n s where t h e g e n e s i s and a m p l i f i c a t i o n o f b l o c k i n g r i d g e s are-frequently o b s e r v e d . F i e l d s o f s i g n i f i c a n t l y p o s i t i v e skewness a r e found i n h i g h e r l a t i t u d e r e g i o n s where ma tu re b l o c k i n g e p i s o d e s o f t e n i n t e r r u p t t he s m a l l e r f l u c t u a t i o n s a b o u t t he normal g e o p o t e n t i a l h e i g h t . The f i n a l o b j e c t i v e i s t o examine t h e a s s o c i a t i o n between t h e f i r s t s i x h a r m o n i c s o f t he l o n g wave p a t t e r n and t h e t e m p o r a l and s p a t i a l c h a r a c t e r i s t i c s o f c o n c u r r e n t b l o c k i n g e p i s o d e s . H a r m o n i c s a r e c a l c u -l a t e d f rom p r o f i l e s o f d a i l y 500MB h e i g h t a r o u n d l a t i t u d e zones c e n t r e d a t 40°N and 6 0 ° N . R e s u l t s f o r t h e n o r t h e r n zone a r e e m p h a s i z e d . I t i s found t h a t t h e r e a r e s p e c t r a l s i g n a t u r e s d i s t i n c t i v e t o t h e r e g i o n s where b l o c k i n g a n t i c y c l o n e s o c c u r . Our r e s u l t s f o r t he oceans a r e i n g e n e r a l agreement w i t h t h o s e o f A u s t i n ( 1 9 8 0 ) . D u r i n g t he s t r o n g l y a m p l i f i e d m e r i d i o n a l f l o w p a t t e r n s a s s o c i a t e d w i t h ma jo r b l o c k i n g , we f o u n d t h a t , a t 6 0 ° N , more t h a n 90% o f t h e s p a t i a l v a r i a n c e o f 500MB h e i g h t i s a c c o u n t e d f o r by wave components one t o f o u r . When t he m e r i d i o n a l r e g i m e g i v e s way t o p r e d o m i n a n t l y z o n a l f l o w t h e r e i s a marked r e d u c t i o n o f s p a t i a l v a r i a n c e o f 500MB h e i g h t . D u r i n g s u c h r e g i m e s t h e h i g h e r h a r m o n i c s (waves f i v e and s i x ) o f t e n make s i g n i f i c a n t c o n t r i b u t i o n s (15 t o 25%) t o t h e t o t a l v a r i a n c e . The ' B a f f i n I s l a n d P a r a d o x ' i s a l s o s t u d i e d u s i n g h a r m o n i c s . I t i s f o u n d t h a t i n t h e m a j o r i t y o f c a s e s B a f f i n b l o c k s o r i g i n a t e f rom r e t r o g r a d i n g N o r t h A t l a n t i c b l o c k s . iv F inal ly , fu l l latitude zonal harmonic analyses (15UN to pole, waves 1 to 4) are presented for three case studies of major blocking - (a) Green-land-North At lant ic , (b) Pacif ic Ocean-Alaska, and (c) Double Blocking. The harmonics often reveal two wave structures, one in the higher and other in the lower latitudes. The motion and growth characteristics of the two structures can be interpreted in terms of well-known features of total blocking systems. V TABLE OF CONTENTS Page ABSTRACT i i TABLE OF CONTENTS v LIST OF TABLES x i i LIST OF FIGURES xi i i LIST OF SYMBOLS xx ACKNOWLEDGEMENT xxiv CHAPTER 1 INTRODUCTION 1 1.1 NATURE AND IMPORTANCE OF BLOCKING 1 1.2 PURPOSE AND SCOPE OF THIS STUDY 8 2. THE PHENOMENON OF BLOCKING 12 2.1 INTRODUCTION 12 2.2 WHAT IS BLOCKING? 14 2.3 A TYPICAL MAJOR BLOCKING EPISODE 15 • 2.4 THE MOTION OF BLOCKING ANTICYCLONES 18 2.4.1 Progression 26 2.4.2 Retrogression 26 2.5 CONSERVATION OF POTENTIAL VORTICITY A Heuristic Discussion of i t s Relationship to blocking 27 2.6 THE INDEX CYCLE 30 2.7 BAROCLINIC INSTABILITY 32 2.8 TOPOGRAPHIC FORCING 36 vi CHAPTER Page 2.9 SIMULATION OF A 1 REAL-TIME1 BLOCKING EPISODE 47 2.10 THE EFFECT OF BLOCKING ON THE CIRCULATION OF THE STRATOSPHERE 47 2.11 CONCLUDING REMARKS 51 3 ANOMALY FIELDS AND IMPLICATIONS FOR IDENTIFICATION OF BLOCKING 52 3.1 INTRODUCTION 52 3.2 ANOMALY FIELDS 54 3.3 A CASE STUDY 62 3.4 SUMMARY 65 4 THE BLOCKING SIGNATURE 66 4.1 INTRODUCTION 66 4.2 CONSIDERATIONS FOR A TIME FILTER 66 4.3 THE RESPONSE TO A FIVE-DAY AVERAGE FILTER 67 4.4 PURPOSE 70 4.4.1 Sequel to the P i l o t Study 71 4.5 PROCESSING THE DATA BASE 72 4.5.1 The Data 72 4.5.2 Pentad Averages 72 4.5.3 Pentad Normals 74 4.5.4 Pentad Anomalies 75 4.6 ANOMALY CENTRES 75 4.6.1 Location of Centres 75 4.6.2 Preparation of Master Catalogue 76 v i i CHAPTER Page 4.7 BLOCKING SIGNATURES 76 4.7.1 Development of Signature C r i t e r i a 76 4.7.1.1 Data Sources 78 4.7.1.2 Blocking Episode Guidelines 78 4.7.1.3 Procedure 80 4.7.1.4 Results 80 4.7.2 Interpretation of Criterion 88 4.7.3 Blocking Signature Catalogue 89 5 DISTRIBUTION OF SIGNATURES AND SEQUENCES 91 5.1 INTRODUCTION 91 5.2 DISTRIBUTION OF BLOCKING SIGNATURES 91 5.2.1 Area! Distribution » 91 5.2.2 Longitudinal Distribution 100 5.3 BLOCKING SIGNATURE SEQUENCES 108 5.3.1 Rationale and Technique 108 5.3.2 Signature-Sequence Catalogue 109 5.3.3 Test on Independent Data ' 111 5.3.4 Signature-Sequence Frequency by Duration 114 5.3.5 Signature-Sequence Frequency by Longitude 115 5.3.6 The Baffin Island Paradox 123 5.3.7 Secular Variation of Blocking Signatures 127 5.4 SUMMARY 133 6 CONNECTIONS BETWEEN BLOCKING AND THE STATISTICAL MOMENTS OF.THE.FIVE-DAY MEAN HEIGHT FIELDS IN THE LOWER TROPOSPHERE 6.1 RATIONALE 6.2 PURPOSE AND OBJECTIVES 6.3 PREPARATION OF THE WORKING DATA BASE 6.3.1 Conversion from MSL Pressure to lOOOMB Height 6.3.2 (lOOOMB - 500MB) Thickness 6.3.3 Seasonal S t r a t i f i c a t i o n 6.4 • STATISTICAL MOMENTS - PART I 6.4.1 Normals and Standard Deviation 6.4.2 Accuracy of Normal and Variance Fields 6.4.3 Interpretation of Standard Deviation Fields 6.5 STATISTICAL MOMENTS - PART II 6.5.1 Skewness 6.5.2 Kurtosis 6.5.3 Comparison of CS and CK Fields with other Results 6.5.4 Site - S p e c i f i c Frequency Distributions 6.6 INTERPRETATION OF DISTRIBUTIONS OF SKEWNESS AND KURTOSIS IN THE NORTHERN HEMISPHERE 6.6.1 Skewness 6.6.1.1 WINTER - POSITIVE 6.6.1.2 WINTER - NEGATIVE 6.6.1.3 SPRING, SUMMER, FALL 6.6.2 Kurtosis 6.6.3 Further Discussion ix CHAPTER Page 7 HARMONIC ANALYSIS OF THE 500MB HEIGHT'DURING BLOCKING EPISODES IN WINTER 169 7.1 RATIONALE 169 7.2 OBJECTIVES 170 7.2.1 F i r s t Objective 170 7.2.2 Second Objective 170 7.2.3 Third Objective 170 7.2.4 Fourth Objective 171 7.3 METHODOLOGY AND TECHNIQUES 171 7.3.1 Data Base 171 7.3.2 Selection of Representative Latitudes for Analyses and Display of Results 172 7.3.3 The Hovmoller Diagram 173 7.3.4 Zonal Harmonic Analysis of the 500MB Height Field 177 7.3.5 Temporal Variation of the Zonal Harmonics at Selected Latitudes 179 7.3.6 Computation and Presentation of Zonal Indices of U, V and U/V 182 7.3.7 Concluding Remarks 184 7.4 PRESENTATION OF RESULTS 186 7.4.1 Spectral Attributes of Blocking by Region of Occurrence 186 7.4.2 Interpretations of Major Blocking Episodes 192 7.4.3 Baffin Island Blocking 197 7.4.4 Zonal Harmonics of Blocking 204 7.5 SUMMARY ' 216 8 RESULTS AND CONCLUSIONS 218 X REFERENCES Paoe 224 APPENDICES: ARRANGEMENT AND PURPOSE 230 APPENDIX : I Conventions adopted in this Thesis regarding terms with possibly ambiguous meaning, and regarding abbreviations 231 APPENDIX II II - 1 II - 2 The Motion of Planetary Waves The Response of Large-Scale Waves to Advection of Relative and Planetary V o r t i c i t y 232 232 234 APPENDIX III Analytical Discussion of the Anomaly Fiel d 237 APPENDIX IV IV - 1 IV - 2 IV - 3 Development of a F i l t e r Function which I l l u s t r a t e s the Effect of a 5-Day Average Guidelines for Id e n t i f i c a t i o n of a Blocking Episode Procedure for Determination of Blocking Signature C r i t e r i a 240 240 242 243 APPENDIX V V V V V V V 1 2 3 4 5 6 Smoothing of Area! Frequency Isopleths Nomenclature Test of Blocking Signatures and Sequences Retrograde A t l a n t i c Blocking as Revealed by a Blocking Signature Sequence 245 245 245 247 249 Frequency Distributions for Starting and Ending Signatures during SUMMER, FALL and WINTER 251 Program for Computing and Plotting Histograms of Blocking Signature Frequency per 10° Longitude 258 x i Page APPENDIX VI 260 VI - 1 Conversion of the Thickness of the Thickness of the (1000MB - 500MB) Layer into i t s Mean Temperature 260 VI - 2 Transformation of the MSL Pressure into Geopotential Height of the lOOOMB Surface 263 VI - 3 Computation of Normal and Standard Deviation Fields 265 VI - 4 Computation of Coefficient of Skewness 266 VI - 5 Computation of Coefficient of Kurtosis 266 APPENDIX VII 267 VII - 1 Hovmoller Diagrams 267 VII - 2 Zonal Harmonics ( f u l l latitude) for Normal 500MB WINTER Waves 1 to 4 270 xi i LIST OF TABLES Table Page 5.1 Blocking Signatures North of 75°N 1946-1978 99 5.2 Blocking Signatures South of 75°N 1946-1978 107 5.3 Results of the Test of Catalogue Sequences on the Independent Data 113 5.4 Twelve Cases of Blocking Affecting Baffin Island 125 6.1 Range of Coefficients of Skewness and Kurtosis outside of which the Distribution i s S i g n i f i c a n t l y Different from Normal 154 7.1 Average (by geographical category) of Harmonic Data for Cases Listed in Section 7.4.1 189 7.2 Standard Deviation and Distribution of Power for Representative Days December 30, 1962 to January 14, 1963 193 7.3 Harmonics at 60°N associated with retrograde Blocking from the North A t l a n t i c to Northeast Canada and Subsequent Blocking Gulf of Alaska 200 7.4 Discrete Harmonic Data for WI to W6 by Latitude for North A t l a n t i c Block December 23, 1978 209 7.5 Discrete Harmonic Data for WI to W6 by Latitude for Alaska Block January 4, 1979 214 VI-1 lOOOMB - 500MB Thickness (dams) vs Mean Temperature (oc or °A) 262 VII-1 The West-to-East Speed of a Trough or Ridge Using the Hovmoller Diagram 267 X I 1 1 LIST OF FIGURES Figure Page 1.1 Normal 500MB height, standard deviation for WINTER 2 1.2 Contours and isotherms on the 500MB surface, 0300 GMT, February 20, 1948 5 1.3 Mean 700MB contours for Winter 1976-77 7 2.1 Normal height of the 1000MB surface for WINTER 16 2.2 Normal height of the 500MB surface for WINTER 17 2.3(a) Evolution from zonal flow to amplifying wave 19 2.3(b) Mature blocking anticyclone centred Northern Scotland 20 2.4 Positions of fronts during two 10-day periods: ( i ) preceding the formation ( i i ) following the establishment of the cut-off high 21 2.5 Schematic representation of the v e r t i c a l structure of a high-level anticyclone 22 2.6 Meridional motion with anticyclonic and cyclonic branches and the implied v e r t i c a l stretching or shrinking 29 2.7 Schematic diagram showing the changes from the normal "sinusoidal" a i r movement in the upper  troposphere, resulting from convergence above a sinking cold a i r mass in the trough 29 2.8 Schematic representation of successive c i r c u -l a t i o n patterns a l o f t during an index cycle 31 2.9 Baroclinic s t a b i l i t y c r i t e r i o n 34 2.10 Normal 500MB contours in January, Southern Hemisphere 38 X I V Figure Page 2.11 Normal 500MB contours in July, Southern Hemisphere 39 2.12 Normal 500MB contours in January, Northern Hemisphere 41 2.13 Normal 500MB contours in July, Northern Hemisphere , 42 2.14 I l lustrating effect of Northern Hemisphere major mountain systems on stream flow at 300MB using GFDL General Circulation Model for ten Winter seasons 43 2.15 As in Figure 2.14 except at..lOOOMB 44 2.16 The mean height of the 500MB surface as a function of longitude 46 2.17 I l lustrating simulation at 500MB of a blocking episode using 1967 11-level GFDL GCM . 48 2.18 Seasonal mean 30MB geopotential height and temperature f ie lds for Summer and Winter Northern Hemisphere Seasons 49 3.1(a) Spl i t jet block 53 3.1(b) Omega block 53 3.2 Analytical example of Anomaly Field 57 3.3 Amplifying wave, NE-SW t i l t 58 3.4 Amplifying wave, NW-SE t i l t 59 3.5 Diffluent jet 60 3.6 5-day mean. 700MB height and anomaly for December 10-14, 1968 and December 17-21, 1968 63 3.7 Same as Figure 3.6 except for December 24-28, 1968 64 Figure 4.0 F i l t e r i n g function for 5-day averaging 4.1 NMC Octagonal Grid 4.2 Sample page of Master Catalogue 4.3(a) Threshold for Blocking Signatures - WINTER 4.3(b) Threshold for Blocking Signatures - SUMMER 4.4 Standard deviation of 5-day mean 500MB height for WINTER 4.5 Standard deviation of 5-day mean 500MB height for SUMMER 4.6 Normal height of 500MB surface for WINTER 4.7 Normal height of 500MB surface, for SUMMER 4.8 Sample page of BLOCKING SIGNATURE CATALOGUE 5.1 Frequency of occurrence of Blocking Signatures for ALL SEASONS 5.2 As in Figure 5.1 except for WINTER 5.3 As in Figure 5.1 except for SPRING 5.4 As in Figure 5.1 except for SUMMER 5.5 As in Figure 5.1 except for FALL 5.6 Frequency of occurrence of Blocking Signatures by longitude - ALL SEASONS 5.7 As i n Figure 5.6 except for WINTER 5.8 As in Figure 5.6 except for SPRING 5.9. As in Figure 5.6 except for SUMMER 5.10 As in Figure 5.6 except for FALL 5.11 Sample page of BLOCKING SIGNATURE SEQUENCE CATALOGUE xv i Figure Page 5.12(a) Frequency distribution of Signature Sequence durations 116 5.12(b) Frequency distribution of Blocking Durations 117 5.13 Total ( i . e . , annual) frequency by longitude of in i t ia t ion of a l l signature sequences 119 5.14 Total ( i . e . , annual) frequency by.longitude of termination of a l l signature sequences 120 5.15 As in Figure 5.13 except for SPRING 121 5.16 As-'in Figure 5.14 except for SPRING 122 5.17 Example of blocking Hudson Bay-Baffin Island-Davis Strait 126 5.18(a) Long-period variations in index numbers, Nd, and sunspot numbers, N 129 5.18(b) Annual frequency of blocking highs Atlantic and Europe 129 5.19 Duration in pentads per year 131 5.20(a) Total duration (pentads/year) of a l l sequences > two signatures • 132a 5.20(b) Duration (days/year) of blocking 132a 6.1 Normal height of the lOOOMB surface for WINTER 140 6.2 Normal height of the 500MB surface for WINTER 141 6.3 As in Figure 6.1 except for SUMMER 142 6.4 As in Figure 6.2 except for SUMMER 143 6.5 Standard deviation of 5-day average 500MB height for WINTER 145 6.6 Standard deviation of 5-day average lOOOMB height for WINTER 146 Standard deviation of 5-day average 1000MB - 500MB thickness for WINTER Schematics: Skewness and Kurtosis Skewness of 5-day average 500MB height for WINTER Bering Sea WINTER Frequency of 500MB extremum Bering Sea WINTER Frequency of 500MB height As in Figure 6.10(a) except for Northeast Canadian Archipelago As in Figure 6.10(b) except for Northeast Canadian Archipelago As in Figure 6.9 except for-SUMMER Kurtosis of 5-day average height for WINTER As in Figure 6.10(a) except for Northeast A t l a n t i c As in Figure 6.10(b) except for Northeast A t l a n t i c Hovmoller Diagram of 500MB height p r o f i l e 50ON - 70ON, December 1, 1962 to March 31, 1963 Same as Figure 7.1 except for 30°N - 50°N Second Harmonic of the normal 500MB height for WINTER Hovmoller diagram of Second Harmonic of 500MB height 50°N - 70°N for December 1, 1962 to March 31, 1963 Amplitude, phase vs time, for Second Harmonic at 60°N, December 1, 1962 to March 31, 1963 Comparison between U t, 50°N - 70°N and U t, 30ON - 50°N z xv i i i Figure Page 7.7 Phase of harmonics for NORMAL 500MB heights -WINTER' 188 7.8 As in Figure 7.4 except for Third Harmonic 194 7.9 As in Figure 7.5 except for Wave Number three 195 7.10 Change with time of the rat io R of zonal (U) to meridional (V) components at 60°N, December 1, 1962 to March 31, 1963 196 7.11 Sequence of 5-day mean 700MB Charts 199 7.12 Amplitude and phase angle of wave number 1 at 70°N as a function of time, December 1, 1949 to March 31, 1950 202 7.13 As in Figure 7.12 except for November 1, 1978 to February 28, 1979 203 7.14 .First Harmonic (W.l) of the 500MB height f i e ld on December 23, 1978 during a major episode of blocking over the North Atlantic and Greenland 206 7.15 As in Figure 7.14 except for second harmonic (W2) 207 7.16 As in Figure 7.14 except for third Harmonic (W3) 208 7.17 First harmonic (Wl) of the 500MB height f i e ld on January 4, 1979 during a major episode of blocking, Alaska and Southwest along the west coast of Br i t ish Columbia 211 7.18 As in Figure 7.17 except for the second harmonic (W2) 212 7.19 As in Figure 7.17 except for the third harmonic (W3) 213 11-1 Planetary and relative vort ic i ty advection 235 III-1 Orthogonal cross-sections xOz and y 'O ' z ' through a maximum of Z 239 IV-1 Pentad Calendar 244 Figure xix Page V-l Smoothing function used in the construction of frequency f i e l d s Figures 5.1 to 5.5, inclusive 246 V-2 Iden t i f i c a t i o n of a Retrograding North A t l a n t i c Block by a Blocking Signature Sequence 250 V-3 As in Figure 5.13 except for SUMMER 252 V-4 As in Figure 5.14 except for SUMMER 253 V-5 As in Figure 5.13 except for FALL 254 V-6 As in Figure 5.14 except for FALL 255 V-7 As in Figure 5.13 except for WINTER 256 V-8 As in Figure 5.14 except for WINTER 257 VI1-1 Hovmbller Diagram of 500MB height p r o f i l e 50ON - 70°N, November 1, 1978 to February 28, 1979 268 VI1-2 Same as in Figure VII-1 except for 30°N - 50ON 269 VI1-3 F i r s t harmonic (WI) of the normal 500MB height f i e l d for WINTER 271 VII-4 As in VI1-3 except for second harmonic (W2) 272 VII-5 As i n VII-3 except for th i r d harmonic (W3) 273 VII-6 As in VII-3 except for fourth harmonic (W4) 274 XX LIST OF SYMBOLS Symbols are usually defined on f i r s t introduction in the text; for ease of reference they are summarized here. In a few cases the symbolism.is not unique but i t w i l l be obvious from the context in which i t i s used. Units Symbol Meaning Usually Used A Anomaly of geopotential height (dam) (Z - Z) y yA k(.I,J) Anomaly of Z for pentad (yy,k) (dam) at (I,J) ^A^ Magnitude of an Anomaly Centre (dam) for pentad (yy,k) A n Amplitude of nth Harmonic (Wn) (dam) c Phase speed of a wave (m s -1) CS Coefficient of Skewness E y^/a^ ( - ) CK Coefficient of Kurtosis = y ^ a 4 ( - ) Decametre (1 dam = 10 m) (dam) f C o r i o l i s parameter = 2ftsin<j> (s~^) g Acceleration of gravity = 9.81 m s"^ (m s~^) gph Geopotential height (dam) h Scale height = 29.3T = height of an isothermal atmosphere with temperature = T (km) X X I Units Symbol Meaning ' Usually Used I Abscissa, NMC Octagonal Grid Fig. 4.1 ( - ) J Ordinate, NMC Octagonal Grid Fig 4.1 ( - ) k Wave number in zonal (x) direction ( - ) L Wave length (linear) (km) m Wave number in meridional (y) direction ( - ) PE Pentad, one of the 73 5-day intervals specified in Fig. IV - 1 ( - ) y y P E k -The K t n pentad in year (19)yy ( - ) n Wave number ( - ) QH Sensible heat fl u x (W m-2) Gas constant f o r dry a i r = 2.87 x 10 2 m2 s" 2 K'1 ( K _ 1 m 2 s " 2 ) Rt Ratio (U t/V t) of zonal to meridional average of wind at time t ( - ) S n % of total variance of Z ( A ) around a latitude contributed by Wn ( - ) SEQ Sequence of Blocking Signatures ( - ) SIG Blocking Signature ( - ) T Temperature ( K ) ( - ) u x-component of velocity eastward (m s ^ ) Units Symbol Meaning Usually Used U Background zonal current (m s ^ ) U^ Zonal average at time t of the algebraic x-component of velocity = [u t] (m s" 1) v y-component of velocity poleward (m s - l ) V Horizontal velocity vector ( - ) Zonal average of the absolute y-component = [|v^|] (m s~^) Wn nth Harmonic (or wave number) ( - ) x,y Eastward and poleward distance, respectively (km) z Upward distance (m) Z Height (above MSL) of a constant pressure surface (dam) y yZ-| ^ ( I J J ) 5-day mean height for pentad (yy,k) of 1000MB surface at (I,J) (dam) y y Z 2 k ( I , J ) 5-day mean height of 500MB surface (dam) Z k(I,J) Normal height at (I,J) for pentad k (dam) Z W N ( I , J ) Normal height at (I,J) for WINTER (dam) B Poleward variation of the df —1 -1 Co r i o l i s parameter = (rrf s~ ) r, Vertical component of r e l a t i v e v o r t i c i t y (s ^ ) Units Symbol Meaning Usually Used 9 Potential temperature^ (K) ? Mean [zonal average of e) (K) X Longitude. Positive eastward ( - ) Phase speed of wave k (radians/day) (s""') y 3 4 0 3 Third moment about mean (m ) Fourth moment about mean (m )^ Standard deviation (m) - r m Mean temperature of an air column lOOOMB surface to MSL (K) 2 -2 $ Geopotential (energy) (m s ) Latitude ( - ) Latitude of an Anomaly Centre Pentad (yy,k) ( - ) <j> Phase angle of Wn ( - ) y n Phase shi f t of Wn ( - ) 2 -1 Streamfunction (m s ) Angular frequency wave number n (s )^ Angular speed of rotation of the Earth (s" 1 ) Except in Chapter 7 where e designates Latitude xx iv ACKNOWLEDGEMENT I wish to express my sincere appreciation for encouragement and assistance received from the University of Br i t ish Columbia during the course of this work. I am particularly grateful to my supervisor, Professor J .E . Hay, for his continuing support, prompt review of draughts, and for ensuring that I remained focussed on the goals we set out to achieve. My thanks, also, to the other members of my Committee, Profes-sors R.W. Burling, M. Church, T.R. Oke, and L. de Sobrino, for construc-tive reviews of the f inal draft. Valuable data-processing assistance was provided by Dr. D.G. Steyn (graphics), Mike Patterson (centre searches) and Peter Madderom (Fourier decomposition). I am part icularly indebted to Mark Roseberry who carried out the considerable computer programming required for Chapters 5, 6 and 7. The accuracy of bur data base has been enhanced in no small measure through the assistance of the Department of Atmospheric Sciences, Univer-sity of Washington. Dr. Harry Edmon screened erroneous data from the original analyses (500MB, MSL) and provided 5-day means for the 33 year period. Our thanks, also, to Professors J.M. Wallace, J.R. Holton and D.L. Hartmann and to Dr. G.H. White for sharing their knowledge and insights on topics related to this thesis. Some support has been received from the Atmospheric Environment Service of Canada. We thank Dr. R.A. Treidl and co-authors who made available a comprehensive set of recently completed data concerning Blocking in the Northern Hemisphere. X X V Financial assistance was received from the University of B r i t i s h Columbia through an H.R. MacMillan Family Fellowship. I sincerely wish to thank Irene Hull for typing the f i n a l manu-sc r i p t . And thank you, Mary Knox, for typing the draft and for your patient support and encouragement throughout this protracted venture. 1 CHAPTER 1 1. INTRODUCTION 1.1 Nature and importance of blocking There are patterns of f lu id flow which evoke analogous connotations. One ref lects , for example, on the sinuous bends and cut-offs of meandering r ivers, the shedding of vortices by large-scale ocean currents, orographic lee waves and their rotors, and, much farther a f i e ld , the gigantic red spot on the planet Jupiter. These phenomena, generated by differ ing physi-cal processes operating on widely different time and space scales, a l l exhibit regularity of form and temporal persistence. To our group of analogies we might have added the great deformations observed from time to time in the Earth-girdling jet streams. It is to certain characteristics of these phenomena that this thesis is addressed. The structure of the normal horizontal motion of the Earth's atmosphere is now well known, at least over the Northern Hemisphere, thanks to a substantial record of upper air data. An inspection of the winter season normal chart at the 500 mil l ibar level shows the circumpolar westerlies in a f a i r l y regular 3-wave pattern around the mid-latitudes (Fig. 1.1a). The large departures from normal of day-to-day motion, par-t icu lar ly in the mid- and high lat itudes, are synthesized by the f i e ld of standard deviation (Fig. 1.1b). Significant contributors to these depar-tures are, of course, the short-wave 10 km) troughs and ridges associ-ated with the transient baroclinic systems in their developing stage but their tota l i ty accounts for a minor portion of the total variance. It turns out that the "restlessness" of the atmosphere extends to f luctua-tions of longer periods [> 10 days) and often of larger dimensions 2 120E 100E BOE 1BO F i g . 1.1 500MB Winter Season (a) Normal geopotential height contours (Knox) (b) Standard deviation of twice-daily 500MB gph. (Lau, N-C from White, 1980). 3 lo\m). It is the mode, motion, growth and decay of these fluctuations that accounts for most of the variance (Blackmon et a l . , 1977). It would be convenient i f these wave categories could be treated in watertight divisions but the atmospheric f lu id does not operate this way and there is constant interaction between them. For example, on daily 500MB analyses, we wil l sometimes notice parallel but separate short-wave systems with dif fer ing phase speeds. The constructive or destructive interference between members of these systems and, in turn, with long-wave components of the presiding circulation regime is a major determinant of the evolution of day-to-day weather. We should recognize, however, that zonal flow often does persist over the greater part of the mid-latitudes, "steering" the families of baroclinic cyclones and anticyclones .along the polar front in a sequence which may last for several days, or even weeks. In the upper troposphere (300MB) the kinetic energy of the flow is concentrated along the jet stream which, in this s i tuat ion, exhibits gentle sinusoidal characteris-t ics not far removed from the normal seasonal pattern. This is the typical "high index" scenario. Then, in a manner to be described in more detail in Chapter 2, there is a str iking change in jet structure over one or more regions of the mid-latitudes. Characteristically the jet spl i ts into two branches, the northernmost curving sharply to the le f t and following the western flank of a ridge which is now amplifying in the downstream area occupied previously by the zonal current. The northern portion of this ridge usually develops into a closed anticyclone which, during major episodes, may grow to a diameter of about 2000km. The southern branch of the sp l i t jet usually bends to the right and can ultimately be found, with inter-4 ruptions, along the southern flank of a succession of mid-troposphere low-latitude cold lows. A c l a s s i c example of the mature stage of the foregoing evolution occurred over the eastern North A t l a n t i c on February 20, 1948. It i s shown in Fig. 1.2. This process i s called blocking and the term was coined to des-cribe the obstruction of the normal west-to-east progress of migratory systems by that salient development in the mass f i e l d , the aforementioned anticyclone. This deep robust eddy i s warm, almost thermally symmetric near the core, and capped by a high cold tropopause. I t t y p i c a l l y remains quasistationary or moves slowly eastward (progression) or westward (retro-gression). Of course, transient systems continue to approach the blocked area from the west, and the i r subsequent history i s not easy to general-iz e ; some w i l l be diverted to the north steered by the northern branch of the j e t ; others w i l l move along the southern branch occasionally inten-s i f y i n g when they pass east of the pre-existing cold low. The blocking process i s important because i t i s the progenitor of spells of weather which, in more extreme cases, can have serious consequences for many sectors of the economy. The area dominated by the slow-moving anticyclone w i l l be favoured by several days or even weeks of clear weather (interrupted on occasion when fog or stratus may persist below the shallow, surface-based inversion). The word "favoured" i s used advisedly. Prolonged episodes during the growing season w i l l dras-t i c a l l y lower grain-crop y i e l d s , and invariably cause a high incidence of forest f i r e s . The summer drought of 1976 over the United Kingdom was a direct result of blocking. During the winter, persistent anticyclonic conditions w i l l cut o f f the normal accumulation of snow pack. A recent example was the extraordinarily dry winter of 1976-77 over the Western 5 F i g . 1.2 Contours and isotherms on the 500MB surface 0300 GMT, February 20, 1948.. (Berggren et a l 1949) 6 Cordil lera of North America, and the consequent depletion of usually abundant sources of hydropower. Boundary layer inversions are charac-te r i s t i ca l l y reinforced during blocking high episodes, and this in turn may increase the concentration of pollution over industrial areas to well above acceptable levels. a Problems of quite a different kind can arise in regions under the influence of the slow-rmoving troughs or cold lows flanking the ant i -cyclone. The abundant precipitation from the cyclonically active sectors can produce a variety of impacts including blizzards in normally milder climates and serious local flooding. Events of this kind were experi-enced in southern Europe in February 1956. During that month an intensely active cyclonic complex, cradled by a blocking high to the north, persisted over southern Europe and the Mediterranean. The persistent meridional flow associated with strong blocking invariably results in large temperature anomalies over vast regions. The most striking recent example was the winter of 1976-77 when a very large amplitude 500MB ridge persisted off the west coast of North America and an intense downstream trough extended along the 75°W meridian (Fig. 1.3). This configuration resulted in repeated and prolonged deployment of arct ic a i r into central and eastern North America, where record-setting low temperatures and disastrous fuel shortages brought hardship to mil l ions. It is c lear, therefore, that an understanding of the nature of blocking and of i ts causative processes should be one of the central goals of meteorology. It is a complex problem, so intimately wedded to the atmospheric system in i ts to ta l i t y , that there are those who wil l argue that the only useful approach is exclusively by numerical modelling methods. We do not agree. There is s t i l l a good deal to be learned 7 F iK- 1*3 Mean 700MB contours f o r winter 1976-77 (December, January and February) labeled i n tens of feet. (Namias 1978) 8 about the climatology and diagnostics of blocking. The next section wil l outline the contribution in these areas that this thesis hopes to make. 1.2 Purpose and scope of this study While atmospheric blocking, at least during major episodes, is easily recognized, and the importance of i ts relationship to macro-scale weather and short-term climate is beyond dispute, the phenomenon has been an awkward one for frequency of occurrence studies. There i s , for example, the d i f f i cu l t y , well documented in the l i terature, of constructing an objective definit ion which would be generally acceptable. Moreover, some of the authors we shall refer to in Chapter 3 focussed their investiga-tions on specif ic geographical regions and so there remains a need to synthesize their results. A premise of this thesis, which was inferred during an i n i t i a l p i lot study (Knox, 1979) is that 5-day positive anomaly centres at appropriate levels of the troposphere (e .g. , 700MB, 500MB) which meet certain c r i te r ia for location and intensity, have a close relationship with the actual location and intensity of a blocking anticyclone. These anomaly centres then serve as "blocking signatures" and so the f i r s t of  our primary objectives wil l be to present and interpret the spatial and  temporal distribution of 5-day positive anomaly centres over the Northern  Hemisphere during the past 33 years. The results wil l then be compared with those of numerous studies of blocking frequency extant in the l i t e r a -ture. To test this premise relating positive anomaly centres to blocking anticyclones we needed sources l i s t ing specif ic details of the respective sets of events. In so far as blocking anticyclones were concerned, data 9 concerning their centres were obtainable from the l i terature (e .g . , Treidl et a l . , 1980a and 1980b) or from synoptic weather maps. On the other hand, an archive providing time, location, and intensity of anomaly centres for the 33-year period of our study simply did not exist. There-fore, i t was necessary to produce a catalogue providing this information. The preparation and use of this reference is explained in Chapter 4. As indicated in section 1.1, a complete blocking system at i ts mature stage wi l l feature not only a strongly anomalous mid- or high latitude warm ridge (or closed anticyclone) at 500MB but also anomalous cold troughs (or closed cyclones) at low or mid-latitudes. It turns out that the latter structures are often associated with 5-day negative 500MB anomaly centres. Therefore, i t was decided that for future research, the locational histories of negative anomaly centres should be included in the catalogue and, moreover, that their frequency distributions should be described. We also investigated whether regions with high incidence of block-ing featured distributions of geopotential s ignif icant ly different from Gaussian. For this purpose calculations of skewness and kurtosis f ie lds  at the 1000MB and 500MB levels were made for the Northern Hemisphere. The rationale, results and interpretation of this exercise wi l l be found in Chapter 6. Blocking is a manifestation of amplifying large scale waves, so we chose as the third primary objective of our study harmonic analysis of  the dai ly atmospheric flow at 500MB during seven winters, each of which  was notable for the occurrence of one or more major blocking episodes. (The feas ib i l i t y and computational techniques were developed during a p i lot study of 1977-78, 1978-79 data, Appendix VII). The results of 10 the 7-winter investigation are reported in Chapter 7. Our data base is for two levels, 500MB and 1000MB. The record consists of once daily geopotential height values, January 1, 1946 to February 28, 1979, for each of 1977 points on a 381 km grid (true at 60°N). This data set (obtained from the National Centre for Atmospheric Research, U.S.A.) provides a sequence of over 12,000 grid-fields for each pressure level for the Northern Hemisphere from the pole to about 15°N (Jenne, 1975). Those parts of the thesis (Chapters 4 and 5) which are concerned with identif icat ion and distr ibution of "blocking signatures" use a derived set of data consisting of contiguous 5-day means ( i . e . , 73 per annum) for the period of record. The skewness and kurtosis f ie lds (Chapter 6) were also calculated from 5-day means. On the other hand, the harmonic components of the long waves (Chapter 7) were computed from daily values of 500MB gph. Pilot-study material, background theory and mathematical techniques are contained in the Appendices. In summary, the main purposes of this thesis are to investigate (a) the frequency distributions of "blocking signatures", (b) the connection between blocking and hemispheric f ie lds of s ta t is t i ca l moments of geopotential height at selected levels, and (c) the behaviour of the Northern Hemisphere long-wave components during the evolution of blocking episodes. It is hoped that certain by-products of the study, such as the catalogues, wi l l prove to be useful for continuing research. Also, an attempt wil l be made in Chapter 2 to interpret and synthesize relevant l i terature. Some of the papers wi l l not necessarily be germane to our 11 s p e c i f i c objectives, but i t i s intended that th e i r review w i l l provide useful perspectives on a complex and challenging subject. 12 CHAPTER 2 2. THE PHENOMENON OF BLOCKING 2.1 Introduction A treatment of the blocking phenomenon in isolat ion from its ante-cedent processes would be somewhat analogous to investigating the i n c i -dence of occluded cyclones outside of the context of baroclinic waves. If the sole purpose were to prepare temporal and spatial distributions of the phenomenon of interest there would be no disadvantage in such a pro-cedure. However, while this is one of our important objectives (Chapters 4 and 5) there wil l be a need to interpret the s tat is t ica l results. More-over, our second primary objective is to investigate blocking in the con-text of those planetary and synoptic scale processes from which i t devel-ops (Chapters 6 and 7). This chapter, therefore, wi l l present a number of results which we believe to be germane to those processes giving rise to the growth and decay of blocking, and to the motion of the associated wave-form. In addition, the respective roles of large scale topographic forcing and dif ferent ia l heating wil l be examined and an example of a successful simulation of blocking wi l l be presented. The climatology of blocking wil l be treated in Chapters 3, 4 and 5. Since a knowledge of the 3-dimensional structure of the atmosphere over a substantial portion of the hemisphere is necessary for an appreci-ation of the nature of a blocking system, i t is not surprising that rather few papers on the subject were written prior to 1946. It is also evident that interest in the subject has waxed and waned down through the years. For example, from the Meteorological and Geophysical Abstracts (AMS(a)) 13 and other sources, we have located a total of 61 papers for the f i f teen year period 1945-1959, compared with 30 papers for the subsequent f i f teen years 1960-1974. The in i t i a l spate of interest was not accidental. The 19401s featured the introduction and development of long-wave theory pioneered by C G . Rossby. The blocking phenomenon was a natural candidate for the extension of his ideas. Moreover, many of the pronounced departures from normal weather during the 1940's and 1950's (e .g. , the winters of 1946-47 and 1955-56) were engendered by large-scale blocking. The reduction in output from 1960-1974, part icularly of papers concerning phenomenological aspects of blocking, is perhaps part ia l ly attributable to the remarkable development during that era of numerical methods in large-scale prediction and simulation. The progress along these lines probably generated an attitude that the onset of blocking episodes would soon be successfully predicted. Also, there appears to have been a modest decrease in blocking frequency during that period (Chapter 5) although 1962-63 was a notable exception. Since 1975, however, there has been a resurgence of interest on both sides of the Atlantic. In Great Britain this was stimulated by events such as the west European drought during the summer of 1976, and in North America by the persistent cold over the eastern half of the continent during the winter of 1976-77. Both of these climate anomalies were a direct result of a protracted diversion of the mid-latitude west-er l ies from their normal position by large amplitude quasi-stationary long waves. Also, there is a growing consensus that numerical models, in spite of their remarkable development, have not real ly been successful beyond 4 or 5 days, in regard to their ab i l i t y to simulate and predict 14 the rather abrupt way in which the real atmosphere switches from one long-wave mode to another (Somerville, 1980). In any event, the resurgence of interest in blocking, either in the areas of synoptic diagnostics and stat is t ics or in numerical simulation has produced over 20 papers in U.S., Canadian and Br i t ish journals alone, since 1975. 2.2 What is blocking? The blocking phenomenon, in the sense in which i t is understood for the purposes of this paper, is the obstruction, on a large scale, of the normal west-to-east progress of the migratory cyclones and ant i -cyclones. It is attended by pronounced meridional flow in the upper levels, and, for a s ignif icant period of i ts evolution, there is usually a closed anticyclonic circulation in the mid-troposphere (- 500MB) at high latitudes (mainly north of 50°N). This is frequently referred to as a "warm cut-off high". It is not unusual for the complete blocking system to include cold cyclonic circulations at lower latitudes (south of 50°N), the so-called "cut-off cold lows". This anomalous circulation pattern ("the block") typical ly moves very slowly (^  400km per day) and persists for one week or longer. Frequently the warm anticyclone to the north wil l move in a direction opposite to that of the cyclonic systems to the south. There are atmospheric structures which possess some but not a l l of the attributes of blocking systems. The sub-tropical anticyclones -deep, warm, persistent and slow-moving - do not qualify as blocking highs. They are quasi-permanent features of the circulation and, in their normal posit ion, do not interrupt the westerlies. Nevertheless we should note that a block is often characterized, in i ts i n i t i a l stages, by the north-15 ward amplification of a sub-tropical ridge, accompanied by a shift ing of the polar jet stream to more northerly latitudes. The blocking system does not usually materialize, under our def in i t ion, until the formation of the higher latitude cut-off warm high. However, because of the con-, tinuous nature of the process, i t wi l l be appreciated that there must perforce be grey areas, and subjective judgment must be evoked to decide when and where the block has occurred. Although the winter season anticyclones over the continents (e .g. , the Siberian high) are persistent and slow-moving, they also do not qualify as blocking highs. Their rotational configuration at 1000MB, Fig. 2.1, gives way on average to zonal flow at 500MB, Fig. 2.2. This is a direct consequence of barocl inicity and of the hydrostatic balance equation. These anticyclones are shallow structures, rarely extending to more than 4km at their deepest point. The main contribution to the high pressure at MSL (or high gph at 1000MB) is from the density of the cold air mass. Again, we must note a qual i f icat ion. The mean winter Siberian anticyclone covers a vast area stretching from the Caspian Sea to Korea (almost 90° long) and from the 30th to the 60th parallel of latitude. The 500MB dai1y flow patterns show marked deviations from the regular westerly current shown on Fig. 2.2 and occasionally one wil l observe, particularly above the western portions of the 1000MB anticyclone, closed highs which clearly block the normal mid-tropospheric flow. Usually there is no ambig-uity regarding what is the block and where i t is located. 2.3 A typical major blocking episode In a c lassic paper, Berggren et a l . (1949) presented an aero-logical analysis of a remarkable break-down in zonal flow which occurred 16 120E JOOE BOE F i f i * 2 . 1 Normal height of the 1000MB surface f o r WINTER (December 1 to February 28). Contours l a b e l l e d i n decametres (dams). Interval = 3 dams. 17 120E IOOE BOE 2.2 Normal h e i g h t o f the 500MB s u r f a c e f o r WINTER (December 1 t o F e b r u a r y 2 8 ) . C o n t o u r s l a b e l l e d i n decametres l e s s 500. I n t e r v a l = 6 dams. 18 over the North Atlantic and Western Europe, February 8th to 20th, 1948. Fig. 2.3(a) and (b) show the evolution at the 500MB leve l , from zonal flow (February 8th and 12th) to a mature blocking system (February 18th and 20th). The str iking effect of this transformation of mid-troposphere flow on the motion of frontal systems (located at sea level) is shown in Fig. 2.4. Panel (i) shows the positions (once a day) of the fronts at sea level before the cut-off high began to develop, while Panel ( i i ) shows the positions during the 10-day period after the blocking high had formed. The characteristic vertical structure of a blocking system is i l lustrated in Fig. 2.5 which shows the cross-section XY (Fig. 2.4a) Greenland to the Black Sea, February 18, 1948. The warm deep anticyclone over the U.K. and Scandinavia, capped by a cold and elevated (250MB) tropopause, contrasts markedly with the cold trough over the USSR, capped by a warm and depressed (400MB) tropopause. 2.4 The motion of blocking anticyclones The blocking phenomenon can be investigated in terms of: (a) Boundary conditions which may be in i t ia t ing factors (e .g . , large scale orography, longitudinally dependent dif ferent ia l heating, etc.) (b) Internal dynamics of the atmosphere (c) Motion of blocking components (d) Factors which maintain the anticyclone While this thesis does not intend to examine the theory of blocking in any depth, we shall discuss, from time to time, the above processes though not necessarily in the order in which they have been l i s ted . We 19 16 FEB. 1948 0300 CCT F i g . 2.3(a) Evolution from zonal flow February 8 through February 12 to amplifying wave on February 16. (Berggren et a l 1949) 20 500 mb 18 FEB. 1948 0300 GCT 500 mb ( 20 FEB 1948 0300 GCT F i g . 2.3(b) Mature blocking anticyclone centred northern Scotland February 18 has retrograded toward Iceland February 20. Deep cold low centred over Germany now dominates Western Europe. Y f i s projection of v e r t i c a l cross-section shown i n F i g . 2.5.. (Berggren et a l 1 9 4 9 ) F i g . 2.4 P o s i t i o n s of fronts during two t e n - d a y p e r i o d s : 1 . preceding the formation; 2. following the establishment of the cut-off high shown i n Fig. 2.3(b). ( B e r g g e n e t a l 1949) 22 Fi g . 2.5 Schematic representation of the v e r t i c a l structure of a high-level anti-cyclone adapted to the case shown i n F i g . 2.3(h) (February 18). The cold dome i s indicated by heavy double l i n e s . The tropopause i s indicated by a heavy broken l i n e , and the axis of the high by a dash-dot l i n e . The slope of the i s o b a r i c surfaces has been exaggerated. (Berggren et a l 1949). 23 shall begin with an interesting feature of the motion of certain types of blocking - retrogression. Namias and CIapp (1944) used case studies to i l lustrate westward moving blocking waves which they described as a "retardation of the zonal circulation which appears f i r s t over western Europe and the eastern Atlantic and subsequently retrogresses further westward affecting particularly North America". Why do blocking waves sometimes retrograde? Some insight into the mechanisms can be obtained from the theory of planetary waves and from the tendency equation for change of geopotential at the level of non-divergence. The results are developed in Appendix II and may be summarized as follows: Rossby (.1939) assumed a homogeneous incompressible f lu id on an approximation to the rotating Earth ( the g-plane) and a uniform non-divergent flow. From these conditions he deduced the principle of con-servation of vort ic i ty : ? + f = constant Where t, = the relative vort ic i ty (due to the configuration of the relative and f = the planetary vort ic i ty (due to the spin of the earth). For a uniform background zonal current U on which is superimposed a sinusoidal transverse velocity perturbation of wave length L he derived the well-known formula: flow f ie ld) (2.1) 24 Where c = phase speed g = df/dy = (2Pxos<|>)a"^  L = wave length -5 -1 n = angular speed of rotation of the earth (= 7.29x10 rad.S ) tj> = latitude. It turns out that for typical observed values of U and c the computed values of L are of the same order of magnitude as the long waves observed in the atmosphere. Also the formula indicates that Rossby waves propagate westward relative to the mean zonal flow with a speed which increases with the wave length. There wil l be a c r i t i ca l wave length L c which, for a given U and <j>, wi l l make c = 0. If L > l_ c the wave wi l l retrograde  relative to the earth. In Chapter 7 we shall note numerous occasions when this happened during seven winters selected for analysis. Equation (.2.1) assumes that the wave structure is independent of latitude which, of course, is never the case. If we postulate the variation of the flow with <j> is also sinusoidal, i t can be shown, Haurwitz (1940a) that the phase speed toward the east is c = U - ? 3 ? (2.2) r + nT Where k = the wave number in the zonal direction m = the wave number in the meridional direction. The expressions for c in equations (2.1) and (2.2) were developed for an extremely simplif ied model, and the success with which they can be applied to the real atmosphere wi l l depend on a number of factors. For example, best results are obtained at levels of small divergence (e .g . , 600MB, 500MB) and for latitude zones within which the maximum wind is lo -cated [Petterssen, 1956). The formula tends to give excessive (westward) values of c for small k (1,2,3), i . e . , large L, and works best for wave 25 numbers 4 to 8. As demonstrated by equation (8) Appendix II, relative vort ic i ty advection tends to move the vort ic i ty pattern and hence the wave-form downstream. On the other hand advection of planetary vort ic i ty tends to move the wave-form upwind. The resultant motion wil l be determined by the size of these opposing factors. Blocking anticyclones occur in high latitudes and, at 60°N, 6 is decreased to half i ts value at the Equator. However, as we shall note in Chapter 7, the main wave components of blocks have small wave numbers. The factor &/kc on balance, tends to increase with latitude for very long waves (k small) and this may decrease c to a stage where i ts sign becomes negative unless the <; advection can compensate'. Blocking anticyclones, at least over the oceans, are quasi-baro-tropic near the core and the relative vort ic i ty advection is very small there. Consequently the planetary vort ic i ty advection wil l dominate. This accounts for their very slow movement and not infrequent retrogression. Sometimes the retrograde motion of blocking waves is "discontinuous". By this we mean that while the in i t i a l anticyclone may be quasi-stationary Cor moving slowly eastward) and weakening, there is anticyclogenesis immediately upstream and the newly formed anticyclone to the west of the original becomes the new blocking centre. This process may be repeated several times so that the resultant effect is equivalent to a westward propagating blocking wave. A physical process which may contribute to this phenomenon, upstream energy dispersion, was discussed by Yeh (1949). His work was based on the fact that, because the phase speed of synoptic and planetary waves is wave length dependent, they must be dispersive (unlike sound waves) and over a spectrum of such waves there wi l l be interference, which, i t turns out, 26 creates a pattern of wave groups. These groups move with a velocity G, quite different from that of an individual wave: G - c - L £ 2.4.1 Progression Now in the case of Rossby Waves in a non-divergent barotropic  atmosphere the group velocity is (assuming m = 0) but also the basic current U, and so energy dispersion sweeps rapidly  downstream. This effect is observed from time to time in the real atmos-phere, where, following some point of energy intensif icat ion (e .g. , west Pacif ic cyclogenesis) the amplification influence moves rapidly eastward waves, Haltiner and Martin (1957). It is conceivable that amplification of some downstream ridges, ultimately resulting in blocking anticyclones, is a result in part of this progressive energy dispersion mechanism. 2.4.2 Retrogression Returning now to Yeh's paper, he introduced a temperature dif feren-t i a l into the model (unlike the Rossby model of uniform density). He examined energy propagation through dispersive waves in an "incompres-sible atmosphere with a uniform north-south density gradient and with f in i te depth". He found that the group velocity depended on a c r i t i ca l G therefore exceeds not only the individual wave speed (30° longitude per day is not uncommon) and acts successively on downwind 27 wave length L c such that i f the predominating wave length L < L c then G > c > 0. This does not d i f fer from the uniform density case. On the other hand, i f L is s l ight ly > L c then c > 0 and G < 0. This corres-ponds to upstream propagation of energy opposite to wave velocity. More-over, by examining the subsequent dispersion of a sol i tary wave (whose wave length L > l_c) at, respectively, 0 ° , 40°N, 70°N i t turned out that only the wave at 70°N maintained its amplitude for a time interval com-parable to that for blocks in the real atmosphere. We have devoted considerable space to the consideration of two of the mechanisms (advection of vor t ic i ty , energy dispersion) which appear to be factors in the motion (and, in the case of dispersion, growth) of blocking anticyclones. In Chapter 7 we shall examine characteristics of the motion and growth of wave components of actual blocking cases. It is hoped that the background theory just reviewed wi l l be useful for interpretation. 2.5 Conservation of potential vort ic i ty . A heuristic discussion of i ts  relationship to blocking Since warm blocking anticyclones are deep structures compared with the cold anticyclones confined to the lower troposphere, i t may be useful to consider the reasons for changes in depth of a ir masses during merid-ional displacement. In rea l i ty , of course, the processes are very comp-l icated, but, as always, i t is best to proceed at f i r s t with the simpler concepts. We shall assume the principle of the conservation of potential vort ic i ty defined by the relationship (Rossby, 1940) 28 ** ' ' = constant Ap Where x, = relative vort ic i ty and Ap is the pressure depth of a small air column. Consider now the case of three air columns A, B and C embedded in an a i r current i n i t i a l l y uniform at, say, 60 N and being displaced equatorward, Fig. 2.6(a). The subsequent stream flow with an anticyclonic branch to the right of the flow and a cyclonic branch to the lef t is postulated such that when the columns arrive at their primed positions they have acquired vort ic i t ies typical of those found in the real atmos- phere. Column B whose relative vort ic i ty <; remains zero, must shrink because f decreases. Column A whose x, decreases wil l shrink even more markedly. The change.in column C wi l l depend on the extent to which increasing x, counters decreasing f, and in the real atmosphere, t, is usually dominant and there is stretching. Cold low level anticyclones wi l l most frequently be characterized by shrinking air columns depicted ideally by the current AA'. The trajectory CC corresponds to what is observed with cold lows. Now consider an i n i t i a l l y uniform poleward-bound current starting at, say, 30°N with a configuration shown in Fig. 2.6(b). Here the s i tua-tion is reversed. An air column E experiences strong stretching as i t curves cyclonical ly and column G experiences shrinking. Warm, deep anticyclones are typical ly characterized, on their western and northern flanks by air columns conserving their absolute vort ic i ty r, + f. On the western periphery the air columns may stretch 29 F i g 2.6 Meridional motion with with anticyclonic and cyclonic branches and the implied v e r t i c a l stretching or shrinking. Along heavy streamlines, absolute v o r t i c i t y i s conserved, the change of c o r i o l i s parameter being'compensated by an opposite change i n r e l a t i v e v o r t i c i t y by curvature. (After Petterssen, 1956) F i g . 2.7 Schematic diagram showing the changes from the normal "sinusoidal" a i r move-ment i n the upper troposphere, r e s u l -t i n g from.convergence above a sinking c o l d - a i r mass.in the trough. ( A f t e r Palmen and Nagler, 1949) 30 s l ight ly , but to conserve ^ A p as f increases i t is necessary for t, to decrease through most of this region. These heuristic considerations suggest how a sinusoidal configura-tion in the upper troposphere may amplify in the manner sometimes observed during the formation of blocking systems. Consider an i n i t i a l relat ively undisturbed current XY in the upper troposphere, Fig. 2.7. If an intense cold outbreak takes place in the lower troposphere (say an anticyclone centred at A*), then i ts strong low level divergence and subsidence, and southward displacement, wi l l be dynamically associated with strong conver-gence and stretching in the upper tropospheric trough. This wil l increase the vort ic i ty in the trough and deform the current from i ts i n i t i a l sinus-oidal shape. The resulting more meridional orientation of the current east of the trough wi l l be consistent with an accentuated downstream ridge. Moreover, the air stream, in i ts progress to higher lat i tudes, bends anticyclonically in order to conserve absolute vort ic i ty . Contin-uation of this process may ultimately culminate in a closed anticyclone. 2.6 The index cycle Namias [1950) showed that blocking over the Atlantic between 50°N and 70°N, appeared to be a necessary (though not suff icient) condition for the southward shi f t of the zonal wind maximum into the sub-tropics. This is the culminating stage of the "index cycle" , a cycle through which the polar vortex, i n i t i a l l y confined to high latitude, expands, streng-thens and becomes unstable. This results in the formation of large amplitude ridges and troughs and, ultimately, cut-off warm highs in higher latitudes and cold lows in lower lat itudes, Fig. 2.8. When the processes which generate these eddies terminate, the warm highs gradually weaken 31 F i g . 2.8 Schematic representation of successive c i r c u l a t i o n patterns a l o f t during an index cycle. ( A f t e r Namias and Clapp, 1951). 32 by radiative cooling and the cold lows weaken by low latitude low level heat exchanges. These cel ls eventually dissipate marking the end of the cycle, which on average takes about six weeks. 2.7 Baroclinic instabi l i ty Why does the expanding circumpolar vortex ultimately become unstable, to form large amplitude troughs and ridges? The answer l ies in the process of baroclinic instabi l i ty which is the major mechanism for energy trans-formation in the extra-tropical latitudes. The key to the process was developed by Charney (1947) and Eady (1949). Charney, using a 2-level baroclinic model of a compressible atmosphere, showed how baroclinic instabi l i ty is dependent on vertical wind shear, lapse rate, latitude and wave length. Both writers agreed that given the observed mean state of the atmosphere in the mid-latitudes, the wave lengths most l ikely to be associated with development were in the synoptic scale range (-v 10 km). If the wave length was in the planetary range lO^km) i ts development was, other factors being equal, less l ikely because in that portion of the wave spectrum the g-effect^$ = became signif icant as a stabi l iz ing factor. In essence their results defined 2 wave length thresholds Lc^ and L„ for development to take place, 2 1 < L stable c l L > 1 > L unstable c 2 c-, 1 > L stable C2 Here 1 = the actual wave length and L is at the shorter end of the spec-c l trum. 33 Fig. 2.9 shows how the respective wave length cut-offs are dependent on the mean vertical s t a b i l i t y — , on the mean vertical wind shear (which arises from the mean N-S temperature gradient — ), and on latitude ( implicit in the f and B terms). Now, blocking waves do appear to be generated, at least in part, by the growth of planetary waves, so i t is of. interest to enquire of those circumstances which govern the value of Lc^. It turns out (Haltiner, 1967) that i f certain non-uniform lower boundary conditions are introduced into the two-level baroclinic model (e .g. , Haltiner introduced a sensible heat source to the lower boundary), the resulting wave length s tab i l i ty c r i te r ia Lc^ and Lc^ are s ignif icant ly changed. In fact , there are combinations of prescribed non-uniform boundary conditions which can increase to - 7xl0^km which corresponds to k = 4 at 45° latitude and k = 3 near 60°N. White and Clark ("1975) investigated blocking over the North Pacif ic Ocean to determine i f the real atmosphere supported Haltiner's theoretical results. They calculated height "anomalies from 700MB charts averaged by month over the period 1950-1970 (240 charts). From these patterns they prepared "composite" charts of predominately blocking and non-blocking months, respectively. They found that in autumn and winter the blocking ridge had a dist inct modal position at about 170°W and that i t was quasi-stationary, with a modal wave length = 7000km which they noted was the width of the mid-latitude ocean. In spring and summer the modal location was unidentifiable and therefore they hypothesized that a c r i t i ca l factor was sensible heat transfer from ocean to atmosphere. For autumns and winters in which blocking predominated they found anomalously large under the trough in the western Pacif ic and anomalously small under the ridge. F i g . 2.9 B a r o c l i n i c s t a b i l i t y c r i t e r i o n . L i s the zonal perturbation wavelength, h i s the v e r t i c a l scale height, g i s the acceleration of gravity, f i s the G o r i o l i s parameter and 0 = d f / d y ; the dashed curved l i n e i s the com-bined theory (see f o r example P h i l l i p s , 1954). h = where T... = layer mean temperature between p^ and pg ^ from Smagorinsky (1972) 35 In the absence of sensible heat transfer (or some other non-uniform lower boundary condition such as orography or f r i c t i on ) , baro-c l in i ca l l y unstable long-waves are not possible in 2-level models except at unreal ist ica l ly high values of the thermal wind (Charney's and Eady's results indicated that mobile synoptic scale waves L = 3 x 10 km were more l ikely to be unstable under normal thermal wind values). However, White and Clark noted that Haltiner had found that for these normal winter values of the background mid-tropospheric thermal wind, the otherwise  stable stationary long wave became unstable when a sensible heat transfer  source was introduced into his model. Moreover, the wave length was 7000-8000km with a growth time of about two weeks and i t could be either quasi-stationary or retrogressive. They therefore concluded that their s tat is t ica l results on blocking (which also included seasonal and year-to-year var iabi l i ty ) are a l l in agreement with Haltiner's theory. Diehl (1977) also hypothesized that blocking-ridge formation originates from the real ization of baroclinic instabi l i ty operating in the long wave length part of the macro-wave spectrum (7000-9000km). Using a 2-level baroclinic model with an i n i t i a l steady state current character-i s t i c of the real troposphere, he tested i ts response to a simple pertur-bation: (i) for adiabatic f r ict ionless flow, ( i i ) for flow subject to surface heat exchange, ( i i i ) for flow subject to surface f r i c t ion only, and Civ) for flow subject to both surface heat exchange and f r i c t ion . In (i) his results agreed with those of the aforementioned classical papers and, in ( i i ) , with those of Haltiner. In (iv) he found that the inclusion of both f r ic t ion and sensible heating from the surface, s t i l l 36 further cut off the shortwave end of the spectrum and made baroclinic instabi l i ty realizable further into the long-wave portion. Moreover, these unstable long waves could be stationary, progressive or retrogres-sive depending on the zonal current. They had growth times and wave lengths comparable to the dimensions of North Pacif ic blocks reported by White and Clark. Diehl therefore concluded that blocking ridges could develop from the realization of a barocl inical ly unstable long wave. He also emphasized the limitations of his study. Linear perturbation theory (used by a l l the foregoing investigators) cannot explain the sustenance without further amplification of blocking highs. Moreover, his model did not include latent heat release, orographic effects of large-scale differential surface heating. 2.8 Topographic forcing In Chapter 5 we shall examine histograms of blocking frequency vs longitude around the Northern Hemisphere. 'The results quoted in the following discussion of topographic forcing should provide a context within which to judge the importance of this factor in the formation of blocking anticyclones. Using the principle of the conservation of potential vort ic i ty for a small a i r column embedded in a westerly current flowing across Ap a mountain barrier with a N-S orientation, i t can readily be demonstrated that the a i r column wi l l be deflected southward with anticyclonic curvature at f i r s t , and subsequently execute a series of dampened downstream osc i l l a -tions. If we visualize this process operating across mountain barriers on the scale of, say, the Rocky Mountain Cordil lera i t is reasonable to expect that within the complex of osci l lat ions so generated, some wi l l be found on the long-wave scale. 37 An easterly current flowing over a mountain barrier (e .g. , the Greenland massif) wil l turn southward with cyclonic curvature prior to  reaching the barrier, recurve anticyclonical ly as i t passes the crest and resume i ts previous undisturbed flow without executing further o s c i l l a -tions . Thus north-south oriented mountain barriers generate anticyclonic vort ic i ty within uniform westerly and easterly currents but the downstream response is periodic in the former case and zero in the latter . Clearly the orientation and shape of the large scale topography must be considered for determining the resultant flow. The Himalayan plateau for example, with less of a N-S extent than the Rockies, and more circular in area! aspect, wi l l constrain westerly (and easterly) a ir streams to flow around as well as over the barrier, while the generally E-W oriented Alpine-Caucasian chain wil l have a signif icant influence on meridional a ir stream components. To further add to the complexity of orographic effects , the Rocky Mountain Cordil lera and the Himalayan - NE Siberia Mountains act as con-tainment barriers to.the vast low level winter air masses generated primarily by boundary layer radiative processes. Some evidence of the impact of large-scale topography on global a ir currents can be obtained by a comparison of mean 500MB flow for the two hemispheres for corresponding seasons. The normal charts for the Southern Hemisphere winter, Fig. 2.10, and summer, Fig. 2.11, show a fa i r l y uniform circumpolar flow between latitudes 40°S and 60°S, a zone of prevailing westerlies almost entirely uninterrupted by signif icant moun-tain barriers. These charts support the not unreasonable assumption that i f the earth's surface were fract ional ly uniform, and thermally uniform by 38 Fig. 2,10 Mean 500MB contours (80-m i n t e r v a l ) i n January (summer), Southern Hemisphere. (After Taljaard et a l . , 1969). 39 Fig. 2 .11 40 longitude, the long period mean flow would have no meridional component. On the other hand, normal charts of 500MB flow for the correspond-ing seasons in the Northern Hemisphere, Fig. 2.12 and Fig. 2.13, show substantial longitudinal variation. This is particularly noticeable for the winter when a strong 3-wave component is evident, with pronounced mean troughs located near 140°E and 80°W and a third of diminished ampli-tude near 40°E. These departures from purely zonal flow are caused by the extent to which large-scale topography and longitudinally dependent heating are distributed over the Northern Hemisphere. The question is how to assess the respective influences of these major factors. For this purpose investigators have turned to general circulation models (GCMs) of the atmosphere. In a recent experiment with the GCM at the Geophysical Fluid Dynamics Laboratory (GFDL), Princeton, N.J., Lau (1980) clearly demonstrated the climatological influence of the earth's major mountain complexes during the winter season. The model used is one of the most successful simulators of the real atmosphere in exis-tence. It was run for 10 successive winters (December, January, February) (a) with Mountains (M) (b) without Mountains (NM) and the mean flows were calculated for the 1000MB and 300MB levels, res-pectively (not shown). The NM flow was then subtracted from the M flow and the difference patterns (M-NM) are shown by Figs. 2.14 and 2.15. At 300MB a weak pattern of anticyclonicity is evident just east of the Himalayas, and much stronger patterns are located immediately upstream of the Rocky Mountains (the centre is over B.C.) and east of Greenland (centred near Iceland). It is also of interest to note the downstream 41 F i g . 2.12 Mean 500MB contours i n January ( w i n t e r ) , Northern Hemisphere. Redrawn at 80-m i n t e r v a l s from I. Jacobs (1958). L i g h t and h e a v i e r s t i p p l i n g show regions where e l e v a t i o n s are above 1.5 km and 5 km (smoothed over 5°latitude-longitude t e s s e r a ) , from Berkofsky and B e r t o n i (1955). (Palmen and Newton, 1969) 42 Fig. 2.13 Mean 500MB contours i n July (summer), Northern Hemisphere. (Redrawn from I. Jacobs, 1958). (Palmen and Newton, 1969) 43 Fig. 2.14 I l l u s t r a t i n g e f f e c t of Northern Hemisphere major mountain systems on stream flow at 300MB using GFDL General C i r c u l a t i o n Model f o r 10 winter seasons. i> equals difference between "with mountain" (M) and "without mountain" (NM.) runs. Lau (1980). 44 45 resonant effects of orography on the quasi-permanent centres of action. The western lobes of both the Atlantic and Pacif ic sub-tropical ant i -cyclones are strengthened, and the cyclonic vort ic i ty of the E. Asiat ic and E. North America troughs is increased. The Himalayan plateau with i ts rounded configuration appears to exercise a somewhat different influence both in its v ic in i ty and downstream, from barriers with a predominant N-S component. Since the longitudinally dependent large scale dif ferent ia l sur-face heating remained the same during both experiments (M) and (NM), the conclusion is that large scale orography exercises a major influence on the mean flow of the GCM and, by implication, the real .atmosphere. We would l ike to be able to report on a similar experiment with regard to the effect of longitudinally dependent dif ferent ia l heating but to our knowledge i t has yet to be carried out on the latest GCM. Therefore, the comparative effects of the two major factors on the mean atmospheric flow are yet to be assessed. Also we should be aware that strong non-linear interaction is to be expected between osci l lat ions produced by orographic forcing and differential heating, respectively. This wil l greatly add to the complexity of the problem. It is interesting to note a point remarked upon by several writers, e .g . , Bolin (1950), that the mid- and upper tropospheric flow shows a signif icant relationship between wave location and topography in summer as well as in winter (Fig. 2.16). This lends weight to the existing consensus (Smagorinsky, 1972) that the dynamic forcing of the large moun-tain systems rather than the thermodynamic influence of the surface temp-erature distribution is the ultimate determinant of the wave character-i s t i cs of the mean flow in the upper troposphere. 46 F i g . 2.16 The mean height of the 500MB surface as a function of long-itude . In summer the figure represents conditions i n the la t i t u d e b e l t 45°N - 50°N, i n winter 35°N - 40*1. The p r o f i l e s have been computed from the hemispherical mean charts published by Sherhag (1948). 47 2.9 Simulation of a "real-time" blocking episode The results of running a GCM (of the type described in the last section) are not continuously examined at GFDL in terms of their day-to-day output. However, i t is important that the model behave l ike the real atmosphere in developing systems with magnitudes and characteristics of the synoptic and long waves. Hence, the output for specif ic sequences of days is looked at from time to time. Apparently one of the fa i l ings of GCMs is their inab i l i ty to simulate blocking with the frequency, persistence and- intensity charac-ter is t ics that are in fact observed. However, a few successful cases have been reported and Mahlman (1979) presented the results of a simu-lation (by the 1967 GFDL 11-level model) of an east Atlantic blocking ant i -cyclone. Fig. 2.17 ('Jan. 22') shows the stream flow when the block was f i r s t in i t ia ted. Note that the overall structure includes a robust ant i -cyclone at 35°N, 30°W, the typical up-stream sp l i t j e t , and a low latitude cyclone at 25°N, 40°W. This system drifted slowly eastward at a speed of about 5m s~^  (- lOkts) and persisted for about nine days. Note, however, that the latitude of the "blocking anticyclone" was well south of what is normally observed. Hopefully the more recent models are show-ing greater success but, unfortunately, the phenomenological characteris-t ics of the day-to-day GFDL simulations are not being reported in the 1iterature. 2.10 The effect of blocking on the circulation of the stratosphere Fig. 2.18(a) shows the summer mean stratospheric circulation at 30MB, a remarkably uniform (almost circular) slack easterly circulation which is thermally consistent with the temperature f i e ld between the warm pole and cold equator. J A N 22 F i g . 2.17 I l l u s t r a t i n g simulation at 500MB of a b l o c k i n g eoisode using 1967 11-leyel GFDL GCM. Note blocking a n t i c y c l o n e at"35°N 30°W, cyclone at 25 N 40°W and upstream s p l i t j e t . Lau(l980). 00 F i g . 2.18 Seasonal mean 30MB geopotential height ( s o l i d l i n e s , km) and temperatures (dashed l i n e s , °C) f i e l d s f o r summer (top) and winter (bottom) Northern Hemi-sphere seasons (After Hare, 1968). 50 Fig. 2.18(b) shows a dramatic reversal in the motion and temperature f ie lds for the winter season. The mean flow in the mid- and high latitudes is characterized by fast "polar night" westerlies in a pattern made strongly asymmetric by the prevailing Aleutian anticyclone. This asymmetric feature in winter and i ts absence in summer is explained by the manner in which the primary long waves in the stratos-phere are generated. They do not develop ' in situ" but "appear to be oproduced by the vertical propagation of planetary waves forced in the troposphere by orography and land-sea contrasts. [These, in turn,] can only propagate vert ica l ly when the stratospheric winds are westerly" (Holton, 1979). Consequently, the summer mean vortex is almost completely undisturbed, but the winter vortex is highly distorted (often anticyclon-ica l l y over the Aleutian area) by upward propagating waves. Every two or three years (e .g . , 1976-77, 1978-79) tropospheric planetary zonal wave numbers 1 or 2 become anomalously large and their upward propagation into the stratosphere results in a deceleration of the mean zonal winds. The subsequent sequence of events culminates in a rapid breakdown of the polar night j e t , a sudden large scale warming (as much as 40°C in a few days has been observed) and the creation of a circum-polar easterly current. These stratospheric warmings have been investigated by Labitzke (1978), Johnson (1978) and Quiroz (1979) and theoretical treatments have been developed by Tung (1977) and Egger (1979). The consensus seems to be that strong blocking is a necessary but not suff ic ient condition for a major mid-winter warming. If the blocking event is in i t iated by constructive interference between wave numbers 1 and 2 then a subsequent 51 warming wi l l result. If the dominant in i t ia t ion wave components are then a major warming wi l l not occur. 2.11 Concluding remarks In this Chapter we have attempted to explain what is meant by "blocking" and have described a typical major episode. The "conservation of absolute vort ic i ty" principle was invoked to discuss inert ia l res-ponses of an idealized atmosphere to an internal perturbation or external forcing. Some of these responses could be related to the motion and development of high latitude anticyclones. Blocking is frequently observed during that part of the index cycle where meridional flow becomes strongly established in the mid-latitudes. Moreover, i t is conceivable that the growth of a blocking anticyclone is the outcome of baroclinic instabi l i ty at the long-wave part of the spectrum. Numerical simulation's using a general circulation model disclosed the effect of the Northern Hemisphere's topography on the low level and upper troposphere c irculat ion. It was also noted that characteristics of blocking episodes as they occur from day-to-day in the real atmosphere are not being well simulated by the models. Finally there was a brief discussion of the relationship between blocking and sudden warmings in the polar vortex of the winter stratos-phere. It is hoped that this chapter has provided a useful background from which to draw interpretations of data to be subsequently presented. We have deliberately avoided a l iterature review and wi l l refer to relevant papers as the dissertation is further developed. 52 CHAPTER 3 3. ANOMALY FIELDS AND IMPLICATIONS FOR IDENTIFICATION OF BLOCKING 3.1 Introduction The l iterature includes a number of comprehensive investigations into the climatology of blocking, and the identif icat ion cr i te r ia quite naturally ref lect those aspects of the phenomenon considered important by the respec-tive authors. Rex (1950a, 1950b), for example, perceived the sp l i t t ing of the jet stream into two branches of comparable mass-transport character-i s t i cs to be essential to the blocking process and indeed recorded the location of the sp l i t as his "block posit ion". He further stipulated that, for the process to qualify as a blocking episode, the observed double jet system must extend over at least 45 degrees of longitude and the pattern must maintain recognizable continuity for at least ten days. Sumner (.1954, 1959) was less restr ict ive in his c r i t e r i a . His exper-ience as a synoptician gave him an appreciation of the variety of configur-ations of the pressure f i e ld which can occur even within the context of a predominant atmospheric mode such as blocking. He described the essential characteristics of blocking as a "rather sharp diminution of zonal flow within the band occupied elsewhere and previously by the main concentra-tion of westerlies". But to identify episodes he resorted to pattern  recognition at the 500MB level using, for guidance, six patterns typical of the more frequent occurrences. Of the s ix , two examples appeared to predominate: (a) The " sp l i t- je t " , comparable to the Rex configuration (b) The "meridional", known in North America as the "fi-block" These are i l lustrated schematically in Fig. 3.1. The other four patterns are variants from, or combinations of (a) and (b). 53 F i g . 331 (b ) Omega B l o c k 54 Treidl et a l . (1980a) stipulated that: (a) Closed isopleths must be present simultaneously in the surface and 500MB charts. (b) The westerly current must sp l i t into two branches. (c) The minimum duration must be five days. The last-named authors applied these c r i te r ia to the 33-year period 1945-1977, inclusive. Over 12,000 days of 500MB analyses of the Northern Hemisphere were individually examined and the corresponding MSL analyses were used for supplementary information. Adjuncts to this study have been made available by the senior author. The cr i te r ia used in these three papers did not exclude the need for subjective judgment. Often cases were counted where, in principle i f not to the le t ter , they appeared to qualify. Moreover, none of the methods was amenable to machine processing. Each required the extremely demanding procedure of inspecting hundreds, and in the case of Treidl et a l . , thou-sands, of synoptic weather maps and manually recording the relevant data. There was the ever-present poss ib i l i ty that cases woul*d inadvertently be overlooked and, particularly over a long period of record, the accumula-tion of such omissions could become signif icant. 3.2 Anomaly f ie lds As indicated in Chapter 1, one of the goals of this thesis is to investigate the climatology of blocking by using objective c r i te r ia adaptable to machine processing large data sets. Since the block appears to be a strongly anomalous feature of the height f i e l d , i t seemed natural to consider the relationship between the geometry of the anomaly f i e ld and those other f ie lds from which i t was derived. 55 We assume an inf in i te plane, on which simple, idealized patterns are described with reference to a rectangular coordinate system where: x = longitude (+)ve to the East of the Greenwich meridian y = latitude (+)ve to the North Let the "normal" height f i e ld be Z = -a^y (3.1) (which implies a uniform West to East flow) and let the "instantaneous" height f i e ld be Z = -^y + a^sin lex sin my (3.2) By "instantaneous" we mean for a designated calendar day and time. Since we shall later use the 5-day interval (pentad) for a time unit, the term "instantaneous" wil l also be understood in the sense of "for a designated pentad". The expression for Z in (3.2) describes a composite f i e ld which is the resultant of a uniform zonal W-E flow, and also a ce l lu lar structure defined by wave numbers k and m. One measure for assessing which of these two components (zonal or ce l lu lar ) .wi l l predominate is a2 -ma3 As explained in Appendix III, i f the ratio > 1, no centres of maximum or minimum wil l appear, whereas, as the ratio decreases from 1 to 0 the cel lu lar structure is increasingly amplified over the pattern domain. The Anomaly f i e l d , by def in i t ion, is Z - Z = (a-, - a 9)y + a,sin kx sin my 56 Now, a-| and a 2 are both positive in the mid-latitudes and usually each is > |a-j - a 2 | in the mid-troposphere Therefore-a l " a2 a 2 -ma3 v. -ma3 Consequently an anomaly f i e ld wi l l usually have a larger number of maximum and minimum centres per given domain than either the "normal" or the "instantaneous" f ie lds . As an example, Fig. 3.2 shows the anomaly f i e ld 1-1 arising from subtracting a hypothetical "normal" f i e ld 1 = -4y from an "instantaneous" f i e ld 1 = -4y + 2sin\3x'sin y Note that for this case the ratio a1 ". a 2 -ma3 = 0 Hence the anomaly f i e ld has zero zonal component and is markedly ce l lu lar . Although the example is highly idealized the principle is general and i l lustrated by a series of schematics (Figs. 3.3., 3.4 and 3.5). Figures 3.3 and 3.4 are structures typical of the amplifying stage of the meridional type of blocking which often evolve into an omega pattern. There is a s ignif icant difference in orientation of the respective trough -ridge patterns, NW - SW in the case of Fig. 3.3 and NW - SE in Fig. 3.4. A diff luent jet schematic is shown in Fig. 3.5. Al l three figures show how the anomalies (drawn by graphical subtraction) have a dist inct ive cel lu lar structure with clearly identif ied centres. Several studies (e .g. , Treidl et a l . , 1980a) stipulate a closed anticyclonic 1 - contour of the 500MB surface in the mid- and high l a t i -tude as one cr i ter ion to be met on an "instantaneous" chart to qualify as a possible blocking high. The analysis of constant pressure charts in the 57 Y F i g . 3.2 A n a l y t i c a l example of Anomaly F i e l d Normal F i e l d Instant F i e l d Anomaly F i e l d Z Z = -4y Z = -4y + 2sin 3x s i n y - Z = 2sin 3x s i n y V J 1 00 j F i g . 3.4 Amplifying Wave, NW-SE..tilt. Positive Anomaly Centre i s NW of "H". Legend as i n Fig. 3.3. o F i g * 3 . 5 D i f f l u e n t J e t . L e g e n d a s i n P i g . 3 . 3 i 61 mid-troposphere is conventionally carried out by drawing contours at a 6 dam interval . It wi l l be appreciated that the application of a "closed contour cr i ter ion" wil l be influenced by the arbitrary choice of isopleth interval. On the other hand the nature of the geometry of the associated anomaly pattern to a large extent eliminates this d i f f i cu l t y . It is important to remind ourselves that anomaly centres do not exactly coincide with the centres of the associated lows and highs of the Z-field. Positive anomalies are displaced north of the high and negative anomalies south of the low. The amount of displacement wi l l vary with the respective Z and Z f i e lds . A robust closed blocking anticyclone with a , • centre, say, 30 dams above normal, wi l l usually have an associated anomaly centre located within one or two degrees of latitude. On the other hand meridionally oriented ridges, e .g . , Figs. 3.3 or 3.4, may feature an anomaly centre some five to ten degrees north of the reference latitude (x-axis) of the wave form. If the anomaly is large (cr i ter ia wil l be developed in the next chapter) i t is very l ikely that the ridge is in an amplifying stage and that the subsequent instantaneous chart wi l l reveal an eddy ( i . e . , the blocking anticyclone) at the northern extremity. If this does occur the anomaly centre wil l usually be within 1 to 5 degrees latitude of the anticyclone. There may also be a longitudinal displacement of the anomaly relative to the location of the blocking anticyclone. The sign and amount of the shif t wi l l depend on the orientation .of the axes of the respective Z and Z f ie ld wave forms. Fig. 3.3 shows that a positive (NE-SW) t i l t wi l l displace the anomaly centre east of the ridge inter-section I with the x-axis, while Fig. 3.4 shows that a negative (NW-SE) t i l t wil l result in a westward displacement. 62 Most of these displacements are greatest for daily f ie lds at the amplification and decay stages of the episodes. This is one of the reasons why we chose to use 5-day averages of Z for basic data units in Chapters 4, 5 and 6. 3.3 A Case Study The sequence of 700MB 5-day mean contours shown in Figs. 3.6 and 3.7 from Green (1968) i l lustrates the relationship between the position and strength of actual blocking episodes and the corresponding (+)ve anomaly. December 1968 was unusual in that i t featured the development of three geographically separated areas of blocking act iv i ty within the Western Hemisphere: (1) A progressive amplifying ridge over Western Canada December 10-14 (anomaly +8 dams) develops into a blocking high over Hudson Bay, December 17-21 (anomaly +23 dams), which by December 24-28 has progressed to 60°N, 25°W (anomaly +30 dams) southwest of Iceland. (2) A sp l i t in the westerlies over the Pacif ic Ocean near 40°N, 180°W, December 17-21, is synchronous with amplification of the sub-tropical high centred at 25°N, 135°W, and the subsequent establishment of a moderately strong blocking anticyclone over Alaska December 24-28 (anomaly +21 dams). (3) A blocking anticyclone centred near 55°N, 10°E (Denmark), December 10-14 (anomaly +14 dams), moves eastward and off the chart by December 17-21. In cases (1) and (2) the distance between the blocking anticyclone centre and the associated positive anomaly centre ranges from a minimum of 100km (Hudson Bay and Alaska positions, respectively) to a maximum of 500km (Iceland-Greenland position on December 24-28). F i g . 3.6 (A) nean 700MB contours and (B) departure from normal of 700KB height (both i n decametres) f o r December 10-14, 1968 and December 17-21, 1968 . (Green, 1968). 64 Pig. 3.7 Same as Pig. 3.6 e x c e p t ( A ) and ( B ) f o r December 24-28, 1968. (Green, 1968). 65 3.4 Summary A review of selected studies from the 1iterature'has revealed a considerable diversity in c r i te r ia by which to judge the occurrence or otherwise of a blocking episode. Moreover, the actual identif icat ion of an occurrence was carried out by subjective inspection of daily charts, a very time-consuming procedure for a large data set. An investigation into the relationship between height anomalies and the Z-field configurations from which they ar ise, has disclosed a strong propensity for ce l lu lar structure of the Z - Z f i e ld which, in turn, implies centres of maxima and minima. The positive centres were closely identif ied with amplified anticyclones or ridges and the relative locations depended on the orientation of the original Z structure. From examination of a case study, i t was clear that centres of strong positive anomalies in the mid- and high latitudes corresponded unambiguously to blocking anticyclones, or, more generally, to the ampli-f ied feature (e .g . , the wave crest) of the Z-field which has effectively become part of the blocking process. In the next chapter we shall f i r s t present the rationale for appl i -cation of an appropriate time f i l t e r to the data base. We shall then describe the results of empirical tests on positive anomalies. These wil l be designed to provide objective c r i t e r i a for frequency studies of blocking using machine processing methods. 66 CHAPTER 4 4. THE BLOCKING SIGNATURE 4.1 Introduction So far our attention has been primarily focussed on certain spatial properties of two-dimensional f ie lds of geopotential and, in particular on the use of the anomaly for the identi f icat ion and measurement of s ign i f -icant features. However, before proceeding with the empirical tests referred to in Chapter 3, there is an important question to be addressed with regard to the data base. The data available consists of twice-daily values of geopotential at each point of a 381 km grid over the North-ern Hemisphere for 33 years of record. For s ta t is t i ca l investigations into blocking did we really need a series of observations with a time interval as small as 12 hours? For two reasons i t seemed to be preferable to use a temporal resolution more related to the time scale of the phenom-enon being studied. F i rs t , we did not want to include the high frequency short-wave transient features conventionally referred to as synoptic-scale systems. Second, a signif icant reduction in the size of the enormous data base, without loss of the features of interest would reduce the computation time and make the task of cataloguing results more tract-able. 4.2 Considerations for a Time F i l ter One of the primary characteristics of major blocking systems is their association with large amplitude slow moving long waves. Therefore we required a technique which, when applied to the available data, would pass these features' and f i l t e r out the faster moving transients. Typical 67 of the latter category are the frontal waves of the lower troposphere. They are usually scaled (Hoiton, 1979) as: c 1 % 10 m where 1 = length scale - 1/4 L c ^ 10ms"^ where c = speed scale T ^ lO^s. where T = time scale = 1 day It would therefore take the order of four days for a complete wave (L ^ 4x 10^ m) to pass a reference point. Clearly, then, a simple 5-day average f i l t e r wi l l provide a derived set of data which wil l strongly suppress the features of transient synoptic-scale systems. The slow moving long waves are conventionally regarded as having wave numbers in the range k = 1 to 5 and typical ly c ranges between -5 and +5 m s""'. If, for example, k = 4 at 60°N (L = 5 x 106m) and the speed is 2.5 m s"^, then i t wi l l take the wave 23 days to pass a reference point. (If the amplitude is large and the wave is associated with a blocking anticyclone, we might regard the latter as the quarter wave length centred about the crest. It wi l l pass a reference point in about six days.) The 5-day average wi l l not l ikely result in a serious attenua-tion of the wave's features and therefore the blocking anticyclone wil l s t i l l be readily ident i f iable. 4.3 The Response to a Five-Day Average F i l te r The above discussion is heurist ic. In Appendix IV-1, we have developed an expression for the response of a longwave harmonic to a contiguous 5-day average following Barrett (1958). The f i l t e r ing function, Figure 4.0, i s : 68 Ak2 2(1 - cos 5kyk) V (5ky k ) 2 Where k = wave number A k = amplitude A k = amplitude of the time averaged wave y k = phase speed (radians of longitude day"^) wk = angular frequency (day-^) = ky k We tested this f i l t e r on harmonics of characteristic large ampli-tude long waves associated with blocking (k = 1 to 4, y k = 0 to 5 degrees day~l) and also on those associated with transient baroclinic waves in the mid-latitudes (k = 8 to 14, y k > 5 degree day -^). The former group were passed with l i t t l e loss of amplitude while the latter were completely attenuated. The suppressed daily fluctuations caused by the baroclinic motions are then regarded as 'no ise 1 , but only because of the choice of our time scale. We must remain aware of the continuous spectrum between the wave length thresholds for instab i l i ty (Chapter 2) and also of the. crucial role of the short-wave eddies during energy exchange processes with the larger systems. Stat ist ica l studies of the kind we envisage must be founded on the creation of categories relevant to the physical system. The atmosphere can be categorized using devices such as scaling and pattern recognition but we would be naive to expect these categories to bear a one-to-one relationship to individual large scale structures. For example, we have suggested that a blocking anticyclone, viewed as a component of an amplified long-wave structure, wi l l have time and space characteristics 69 P i g . 4 . 0 A t t e n u a t i o n of squared amplitudes of harmonic waves r e s u l t i n g from five-day averaging, as a f u n c t i o n of angular frequency (co^) i n radians per day or p e r i o d (TV) i n days. For d e t a i l s see Appendix IV. ( A f t e r B a r r e t t , 1958). 70 of the same order of magnitude. In the case of major blocking episodes this is true. But an inspection of daily 500MB weather maps wi l l disclose a surprising number of configurations (particularly over the continents) which have the characteristics of blocking highs (sp l i t upstream flow, barotropic core structure) but a wavelength closer in magnitude to that of a baroclinic system. They do move slowly but, because they have smaller dimensions than major blocks, the contiguous 5-day averages wil l sometimes attenuate these cases so that they fa l l below our threshold of recognition. We shall attempt to design cr i te r ia which wil l minimize the number of times this happens. On balance we conclude that the 5-day average is an effective low  pass f i l t e r and we shall therefore use i t for the purpose of this Chapter  and also 5 and 6. 4.4 Purpose In Section 3.3 (Anomaly Fields) there is the impl ic i t hypothesis that positive anomalies of the 5-day mean 700MB or 500MB height may turn out to be useful identi f iers of blocking occurrence. This was tested for the 700MB level in a p i lot study (Knox, 1979). We compared samples of positive anomalies of 5-day averaged 700MB height f ie lds (of the kind i l lustrated in Figs. 3.6 and 3.7) with actual blocking episodes observed on day-to-day mid-troposphere analyses. The episodes were iden-t i f i ed either by the author or from sources in the l i terature such as Rex (1950), Treidl et a l . (1980a), etc. This approach sidestepped the issue of common cr i te r ia by which to judge the occurrence of a blocking episode, an issue we shall attempt to resolve later in this Chapter. The reason we chose the 700MB level was because of the ava i l -ab i l i ty of a catalogue of 700MB 5-day average anomaly centres (O'Connor, 71 1966). This publication l i s t s the date, position and magnitude of each positive and negative 700MB anomaly centre that has occurred in the North-ern Hemisphere during the sixteen year period 1947-1963, inclusive. It was then possible by cross-comparison to develop a set of "associative" c r i te r ia against which a 700MB positive anomaly centre could be compared, to deter-mine i f , in fact , i t was associated with an observed blocking episode. The cr i te r ia turned out to be functions of time of year, anomaly magnitude and latitude. We coined the term BLOCKING SIGNATURE for a positive anomaly centre which met the c r i te r i a . This derived quantity has a central role in the results to be developed. The purpose of this Chapter is to develop c r i - ter ia for the blocking signature using a much longer record of data at a  more appropriate level in the troposphere. 4.4.1 Sequel to the Pi lot Study Although the results were encouraging, there were limitations to the p i lot study which were important to overcome in the subsequent investiga-t ion: (a) the data base needed to be updated from 1963 to the present. (b) the resolution of centre locations in the O'Connor Catalogue (±5 degree latitude and ±5 degree longitude) was relat ively coarse. (c) the issue of "what is an actual observed blocking episode?" needed to be c l a r i f i ed . (d) the somewhat "ad hoc" method we used to determine "blocking signature" needed to be replaced by a more objective systematic procedure. (e) the 700MB level is too close to boundary layer processes, and is entirely inappropriate in the v ic in i ty of the world's major mountain massifs. 72 (f) because of the enormous volume of information, i t was essen-t i a l for the technique to be amenable to automatic data processing. We selected the 500MB level (=5.5 km).. It is generally removed from turbulent and convective boundary layer processes, and is more representa-tive of the mid-troposphere. (We considered the 300MB level but were concerned with complications arising from the frequent winter season lowering of the tropopause below 300MB. Moreover, we preferred a longer data base than is available at that level.) A 33-year (1946-1978) set of analyses of the daily 500MB> height f i e ld over the Northern Hemisphere was available on magnetic tape. In the next sections we shall outline the procedures and present the results of the 500MB 'blocking signature' investigation. 4.5 Processing the Data Base 4.5.1 The Data Base A 33-year record of 500MB grid point data for the Northern Hemis-phere was obtained from the National Center for Atmospheric Research (NCAR), Boulder, Colorado. This record includes daily values (00GMT), of 500MB heights at each of 1,977 points on the NMC Octagonal Grid, which extends from 15°N to the pole (Jenne, 1970). The map projection is polar stereographic and the grid resolution is 381 km, true at 60°N (Fig. 4.1). The exact record is from January 1, 1946 to February 28, 1979 which ensures data for 33 complete winters. The entire data set consists of 24 x 10 values of 500MB height expressed to the nearest tenth of a metre. 4.5.2 Pentad Averages A pentad is a specified period of f ive consecutive days, and the pentad calendar we shall use wil l be found in Fig.. IV.-. 1. The conventions 4.1 NMC Octagonal Grid. There are 1977 data points i n the octagon. The Pole point i s I,J = 24,26. (Jenne, 1970). 74 adopted here are that Spring contains 19 pentads, while the other seasons have eighteen each, and that in the event of leap year, pentad number 12 (February 25 to March 1) wi l l contain six days. We shall designate a pentad as: y y D r P t K Where yy = year K = pentad number (1 to 73) The 5-day average height at grid point (I,J) for pentad K is n=l Where I = abscissa J = ordinate (see Fig. 4.1 for location of axes). The data were converted to contiguous 5-day averages, thus reducing the data-sets from 365 to 73 grid-point f ie lds per annum, or a total of approximately 2,400 f ields of 500MB 5-day mean height for the period of record. For the purposes of this Chapter the five-day average is the basic unit. 4.5.3 Pentad Normals Symbolically the normal height at (I,J) for pentad K is 33 httJ) = i s £ yyzKn,J) yy=i 75 This operation was carried out to compute 73 sets of normal 500MB  heights corresponding respectively to each pentad. Each set, in ef fect , consisted of the average of 33 x, 5~ 165 daily height values at each grid point. These normals provide the baselines from which to calculate the anomalies. 4.5.4 Pentad Anomalies The anomaly of the 5-day average 500MB height for year yy, pentad K, grid point I,J, is y y A K ( I , J ) = y y Z K ( I , J ) - Z K(I,J) and this operation was carried out to produce approximately 2,400 anomaly f ie lds for the 33-year period of record. 4.6 Anomaly Centres 4.6.1 Location of centres The anomaly f i e lds , for reasons explained in Chapter 3, feature a cel lu lar pattern of positive and negative isopleths, and the next step was to locate the centres of the ce l l s . Each of the 2,400 f ie lds of y yA^(I,J) was searched for maxima and minima. (Negative anomaly centres were not required for this investigation, but they were located and l isted for use in a future study of cold lows and troughs.) Tr iv ia l centres were exclud-ed by the requirement that to qual i fy, the centre's anomaly value must be greater than 5 dams or less than -5 dams. Al l centres were located to the nearest grid point (I,J) so that their positions are accurate to within ±1.7° latitude. This resolution was a decided improvement over the ±5.0° latitude of the data used for the pi lot study. 76 4.6.2 Preparation of the Master Catalogue Since our objective was to determine c r i te r ia for the "blocking signature" (section 4.2) we needed a convenient source of positive anomaly information. Therefore the anomaly centres were l isted according to year, pentad of occurrence, location and value (dams). In effect , a Master Catalogue was created which provided, in compact format, sal ient informa-tion concerning the anomalous features of over 2,400 contiguous 500MB 5-day average height f ie lds during the 33 years of record. The (I,J) gr id , though best for the centre search, and indeed for a l l our data processing programs, was inconvenient for geographical loca-t ion. Hence a l l anomaly centre positions were converted to latitude and longitude for the Catalogue. A sample page is i l lustrated in Fig. 4.2. For an " internal" consistency check we acquired a sequence of operational 500MB 5-day average height and anomaly analyses from the U.S. National Weather Service. The positive and negative anomaly centres were compared for position and magnitude with those of our catalogue and the mean differences were 150 km and 1.5 dams which are within our l imits of resolution. We therefore concluded that the catalogue is an accurate source of 500MB anomaly data. 4.7 Blocking Signatures 4.7.1 Development of Signature Cr i ter ia The earl ier P i lot Study, Section 4.4, indicated the feas ib i l i t y of developing c r i te r ia for the purpose of testing whether a single positive anomaly is l ikely associated with a concurrent blocking anticyclone. A positive anomaly which so qual i f ied would be called a "blocking signature" and of course one would expect to find a sequence of blocking signatures PENTAD 66 MAXIMA LA LO OM LA 38 91W 6 27 28 44W 9 57 31 132W 6 48 30 147W 6 70 43 2E 16 58 79 10E 11 44 75 176E 8 34 58 37E 14 60 47 135E 16 41 125E 16 1968 MINIMA LO DM 18W -14 31W -26 146W -6 102W -29 176W -13 177E -14 24E -14 86E -27 PENTAD 67 MAXIMA LA LO DM LA 36 80W 12 30 45 80W 12 53 23 141W 7 64 66 17W 27 43 38 162W 11 65 54 16E 19 34 80 55E 8 61 33 60E 6 26 28 125E 6 20 26 115E 6 1968 MINIMA LO DM 107W -16 51W, -25 88W -16 17W -14 WOW -24 27E -9 100E -33 79E -7 76E -6 PENTAD 68 1968 PENTAD 69 1968 PENTAD 70 1968 MAXIMA MINIMA MAXIMA MINIMA MAXIMA MINIMA LA LO DM LA LO DM LA LO DM LA LO DM LA LO DM LA LO DM 38 57W 10 44 93W -16 37 107W 12 43 63W -23 25 1 17W 5 33 77W -8 21 133W 5 56 1 12W -8 32 44W 9 49 139W -25 48 56W 17 45 138W -25 39 128W 1 1 48 32W -28 75 156W 6 34 4W -16 33 30W 9 54 27W -23 61 10E 26 56 152W -16 64 2E 22 78 62W - 14 54 9 1W 13 56 152W - 15 51 180 17 77 136W -16 43 142E 25 26 178E - 10 70 102W 14 22 5E -9 43 142E 17 3 1 26E -7 72 137E -30 6 1 17E 12 39 14E - 13 35 32E -7 52 44E -22 45 167E 23 80 145E -37 29 168E -5 58 81E -16 54 1 1 1E 12 66 73E -25 56 68E -40 27 162E -8 25 40E 6 59 45 3 1 64E 42E 1 3 1 E -26 -15 -8 PENTAD 7 1 1968 PENTAD 72 1968 PENTAD 73 1968 PENTAD 1 MAXIMA MINIMA MAXIMA MINIMA MAXIMA MINIMA MAXIMA LA LO DM LA LO DM LA LO DM LA LO DM LA LO DM LA LO DM LA LO DM LA 26 135W 5 38 1 12W -24 2 1 129W 5 36 45W -20 32 70W 5 5 1 53W - 16 37 120W 18 45 28 22W 7 42 59W - 13 28 22W 8 45 131W - 17 30 53W 5 '32 26W -10 55 35W 28 32 6 1 73W 3 1 27 16 1W -9 61 50W 18 28 15W 7 20 127W 5 50 1 18W -26 70 58W 30 56 25 SW 10 53 7W -28 41 2W 19 68 89W -6 71 69W 32 40 154W -15 54 4E 14 27 53 153W 28 75 100E -36 60 156W 36 79 80W -6 64 24W 38 48 15E -25 57 177E 4 1 35 82 53W 12 30 37E 5 49 WOE 19 33 163W -11 60 176E 31 30 176W -7 75 1 14E 30 45 52 51E 14 3 1 159E -6 57 51E 27 68 1E -7 67 139E 26 27 162E -9 62 60E 35 39 39 38E 7 58 4E -9 70 78E 36 46 145E -18 24 24 37E 7 83 100E -7 47 91E -23 43 142E 10 31 61 28 26E 107E 75E -16 -23 - 10 21 72E -10 MINIMA PENTAD MAXIMA LA LO DM 31 1 18W 11 19 134W 7 72 43W 35 51 170W 38 64 18E 18 77 156E 17 29 129E 6 2 1969 MINIMA LA LO DM 44 89W -17 28 22W -14 52 136W -16 62 130W -16 48 14W -25 24 164W -15 29 32E -10 60 86E -11 44 153E -6 37 50E -6 45 68E -13 PENTAD MAXIMA LA LO DM 31 33W 11 68 89W 39 51 160W 24 85 145E 29 55 34E 7 54 153E -7 3 1969 MINIMA LA LO DM 38 72W -19 48 128W -33 31 154W - 11 48 14W -27 72 10E -9 55 166E -11 66 73E -19 48 142E -14 30 103E -5 PENTAD MAXIMA LA LO DM 45 76W 18 31 6W 12 56 152W 21 74 37E 34 34 176E 9 35 152E 10 4 1969 PENTAD 5 1969 PENTAD 6 1969 PENTAD 7 1969 MINIMA MAXIMA MINIMA MAXIMA MINIMA MAXIMA MINIMA LA LO DM LA LO DM LA LO DM LA LO DM LA LO DM LA LO DM LA LO DM 36 45W -23 22 1 1 1W 6 43 38W -23 53 51W 38 26 65W -1 1 27 89W 6 33 120W -6 33 142W -22 51 70W 25 46 125W -22 44 157W 29 31 37W -12 30 80W 6 33 40W -15 50 125W -25 53 153W 29 32 146W -28 75 125W 1 1 46 125W -32 52 46W 21 26 135W -5 54 1W -17 72 27W 23 78 28E 15 39 6E 12 67 8W -5 61 80W 6 35 28W - 16 55 166E -21 44 1E 21 80 145E -17 37 163E 17 60 176E -23 70 102W 5 56 138W -23 34 24E -12 75 55E 19 55 166E -23 61 100E -6 22 178W -7 41 178W 37 77 24W - 18 55 145E -23 35 160E 10 22 29E -22 . 37 140E 19 71 1 1 1E -15 80 145E 9 61 10E -20 56 1 18E -24 35 143E 12 52 78E -30 56 42E -6 75 55E 8 64 178W -14 52 78E -28 30 66E 7 41 35E -13 33 31E 10 59 46E - 18 18 169E -5 64 134E -16 16 30E -2 1 19 172E -9 47 86E -18 65 100E -21 20 97E -6 14 93E -7 F 1 f i ' 4 . 2 S a m p l e p a g e o f M a s t e r C a t a l o g u e , i n d i c a t i n g p o s i t i o n a n d i n t e n s i t y o f p o s i t i v e a n d n e g a t i v e A n o m a l y C e n t r e s o f 5 - d a y m e a n 5 0 0 M B h e i g h t . \ 78 associated with an amplified block of substantial duration (> 10 days). The p i lot study also indicated that the c r i te r ia would be func-tions 'of the time of the year, anomaly magnitude and latitude. These were the attributes selected from the Master Catalogue when testing for the anomaly's association with a blocking anticyclone. 4.7.1.1 Data Sources To determine i f , in fact , a block was in progress we used the following sources of information: (a) Daily Series, Synoptic Weather Maps, Northern Hemisphere Sea Level and 500MB Charts (Air Weather Service, 1946-1948; U.S. Depart-ment of Commerce, 1949-1956). (b) A Catalogue of Northern Hemisphere Blocking Situations for the Period 1945-1977 (Treidl et a l . , 1980b). (c) Monthly Weather Review (U.S. Department of Commerce, 1954-1973; American Meteorological Society, 1974-1979). The source for the positive anomaly attributes was, of course, the Master Catalogue (Knox, 1981). 4.7.1.2 Blocking Episode Guidelines As indicated in Section 3.2, the l iterature discloses an extremely broad range of c r i te r ia which authors have used to judge the occurrence or otherwise of a blocking episode, and this has been reflected in the published frequency of occurrence results. The one area of agreement is on major blocking episodes. The objective of this study i s , so far as is possible, to design a threshold such that the set of qualifying positive anomalies (signatures) wi l l ref lect the fu l l spectrum of blocking episodes - minor, moderate or major. 79 The f i r s t step was to establish guidelines by which to judge the occurrence or otherwise of blocking on the daily analyses. We decided that the Treidl guidelines (Appendix IV - 2B) used to prepare his Catalogue were suff ic ient for a block to be judged to have occurred. Therefore i f the 5-day l i f e of our Master Catalogue positive anomaly, selected for testing, occurred within the duration of a blocking episode l isted in his Catalogue, i t qualif ied as a blocking signature. However, i t was not necessary for a l l the Treidl c r i te r i a to be met for a block to have occurred. For example, during an inspection of a large sample of daily 500MB analyses we found a signif icant number of relat ively short-lived (3 to 7 days) occasions when the pre-existing zonal flow was interrupted by a blocking anticyclone, which were not l i s ted . Therefore i f , corresponding to the Master Catalogue-selective positive anomaly, the Treidl Catalogue did not l i s t a block, we then went direct ly to the 5-day sequence of Daily 500MB analyses and, over the region concerned, applied the following guidelines: (see also Appendix IV - 2A). (i) During the pentad of the positive anomaly being tested, an anticyclonic centre must be observed on at least 3 out of the 5 consecu-tive daily analyses. ( i i ) The anticyclonic structure wil l clearly have disrupted the pre-existing zonal flow. ( i i i ) The anticyclone centre must be N of 45°N. If these guidelines were met we decided a block was in progress. For assistance with marginal cases there was frequent recourse to the Monthly Weather Review (1951-1979), which presents the four 5-day average 700MB height analyses most representative of the month under review. 80 In summary, the Treidl guidelines were considered suf f i c ient , while ours were considered necessary and suff ic ient . In effect this means that the guidelines used in this investigation for judging the occurrence  or otherwise of an actual blocking episode on daily 500MB analyses are  essential ly our own, as set out in fu l l in Appendix IV - 2. It is important to keep this in mind when comparing the results of this thesis with other studies. 4.7.1.3 Procedure We selected a large sample of positive anomalies from the Master Catalogue and plotted centre value (dams) against latitude. The plot also identif ied whether or not, during that pentad, a blocking episode was in progress in the region of the anomaly being tested by: (i) Occurrence # ( i i ) Non-occurrence O (Further details of the procedure are provided in Appendix IV - 3). The WINTER and SUMMER seasons were examined f i r s t and the number of anomalies were: WINTER 318 SUMMER 384 4.7.1.4 Results The results are presented in Figs. 4.3(a) and 4.3(b). Note that the separation curves are approximate hyperbolas. Usually to analyze the relationship between two variates of the atmospheric continuum one uses formal s ta t is t i ca l techniques. This analysis, however, is concerned, not with elements of the continuum, but with spatial ly isolated derivatives (anomaly maxima and centres of anti-F i g . 4,3(a) Threshold f o r Blocking Signatures, WINTER. 3.18 positive- anomaly centres are tested f o r association with a blocking episode.. (For d e t a i l s see Appendix IV, Sections 2 and 3). Anomaly was found to be associated with a contemporaneous blocking episode. No blocking episode observed. Cases tested were from following years: 1947, 1948, 1951, 1953, 1954, 1955, 1956, 1958, 1961, 1965, 1966, 1968, 1970, 1971, 1972, 1973, 1974, 1975. Not shown i n Figure i s one o u t l i e r at 57°N with a centre value of 55 dams. This occurred December 17 - 21 (PE 71) i n 1955 and was associated with a strong 11 day blocking high over the mid-Pacific Ocean. Legend • O A N O M D a m s 3 0 | 2 5 2 0 I 5 10 O o o o o o o ooQ oo o o ° o o _ o ooo oo ° k O po o o ooo°cP# • O ° oo O o o I oo o S UMM ER • o o o* o o • o o o o o o o o o o 4 5 5 0 5 5 6 0 6 5 7 0 7 5 8 0 8 5 3 5 3 0 2 5 2 0 I 5 0 9 0 -L A T F i g 4-3 (b) As i n F i g . 4.3(a) except f o r SUMMER. The plot i s f o r 384 posit i v e anomalies which occurred i n June, July and August f o r the years 1949, 1950, 1951, 1964, 1965, 1969, 1970, 1971 and 1972. CO no 83 cyclones). Moreover, we have used quasi-subjective guidelines to deter-mine the dichotomous f ields in Fig. 4.3. Under these circumstances we decided to estimate the separation curves by eye. For the anomaly to qualify as a "blocking signature", the c r i te r i a were: WINTER ( y y A K - 15)( y y<f» K - 49) > 16 (1) SUMMER ( y y A K - 10)(yy(j>K - 53) > 9 (2) Where yy = year, pentad number = K, anomaly magnitude = ^ A ^ and anomaly latitude = It is noted that the anomaly magnitude threshold values of 15 dams (winter) and 10 dams (summer) are close to the mid-latitude maxima of the seasonal standard deviation at 60°N (Figs. 4.4 and 4.5). This is not sur-prising considering the amplification associated with blocking. The anomaly latitude threshold values of 49°N (winter) and 53°N (summer) are consistent with the northward displacement of the E-W axis of the sub-tropical anticyclones (Figs. 4.6 and 4.7). The values 16 and 9 on the R.H.S. of inequalities (1) and (2) have no obvious physical explanation, but we assumed that the difference was related to the annual cycle. It was decided to generalize (1) and (2) into a single inequality which would take account of the nearly sinusoidal annual cycle. (To determine the phase angle parameter a sinusoid was f i t ted to a plot of 73 maximum standard deviations of 500MB 5-day mean height for the Northern Hemisphere.) 84 120E 100E 80E 'Fig. 4.4 Standard deviation of 5-day mean 500MB height f o r WINTER (December 1 to February 28). Contour i n t e r v a l = 2 dams. fflg. 4.5 Standard deviation of 5-day mean 5.00MB height f o r SUMMER (June 1 to August 31). Contour i n t e r v a l = 2 dams. 86 120E J OOE 80E F i g . 4 . 6 Normal height of the 5 0 0 M B surface f o r WINTER (December 1 to February 28). Contours l a b e l l e d i n decametres le s s 5 0 0 . Interval = 6 dams. 585 dam contour 87 120E JOOE BO£ F 1 f i - 4 '7. Normal height of jfche 50OMB surface f o r SUMMER (June 1 to August 31). Contours l a b e l l e d i n decametres less 500. Interval = 6 dams. 591 dam contour 88 The generalized criterion is : ( y \ - A K)( y y<D K - •*K) > Q K (3) Where A K = 12.5 + 2.5 cos (0.08607K - 0.2582) $ K = 51.0 - 2.0 cos (0.08607K - 0.2582) Q K = 12.5 + 3.5 cos (0.08607K - 0.2582) K = Pentad number (1 to 73) This expression provides for a within season change of anomaly magnitude and latitude threshold for a corresponding change to Q^. The hyperbolic threshold changes in 73 discrete steps through the course of a year. It was decided to test Criterion (3) on SPRING and FALL data. These are the seasons when the rate of change of a l l cr i ter ion factors are great-est. We proceeded as before and drew curves of separation for the respec-tive seasons (not shown). Again they approximated hyperbolas which turned out to be reasonably close to the analytical curves in cr i ter ion (3) for mid-spring (K = 21) and mid-fall (K = 57), respectively. The results were suff ic ient ly encouraging that we decided the Criterion could be used for the entire year. 4.7.2 Interpretation of Criterion Criterion (3) te l l s us that blocking episodes, in the main, are associated with a signature threshold which is proportional to the product of the latitude and magnitude of the anomaly centre. Therefore, in order to qualify as a signature near the cut-off southern latitude (4^) the 89 anomaly magnitude must be much larger than the cut-off value A K . This has the desirable effect of screening out those positive anomalies, say, near 50°N, which are attributable either to amplification of the sub-tropical anticyclone, or to a temporary shi f t north of i ts normal posit ion, or some combination of these two events. 4.7.3 Blocking Signature Catalogue The Master Catalogue described in 4.6 identif ies al]_ 500MB pentad anomalies, positive and negative, that occurred from 1946 to 1978. Our next requirement was to prepare a catalogue l i s t ing only those positive anomalies which qualif ied as Blocking Signatures. This was done by application of Criterion (3) to each positive centre in the Master Cata-logue. The resulting Blocking Signature Catalogue provides a compact inventory of a l l blocking signatures that occurred during the 33 years of record. A sample page is i l lustrated in Fig. 4.8. By scanning across the pentads one can discern sequences of vary-ing length which contain geographically proximate signatures and which therefore are probably with observed blocking episodes of corresponding duration. In Chapter V we shall describe a modification of this Cata-logue designed to conveniently identify these sequences of blocking signatures. 5-DAY MEAN BLOCKING SIGNATURES 197 1 NONE RECORDED PE LA 64 G 1 PE LA 8 1 1 197 1 LO DM 80W 3 1 30W 16 11 1971 LO DM 37E 28 PE LA 54 2 1971 LO DM 16E 23 PE 12 1971 LA LO DM 71 10E 25 74 86E 28 PE 21 1971 PE 22 1971 PE LA LO DM LA LO DM LA 57 3W 24 53 51W 22 62 90 100E 14 68 80W 2 1 74 8 1 53W 22 PE 31 1971 PE 32 1971 PE LA LO DM LA LO DM LA 67 19E 20 6 1 30W 29 62 59 136E 15 73 143W 18 75 PE 41 1971 PE 42 1971 PE LA LO DM LA LO DM LA 73 143W 11 54 133W 17 57 81 53W 14 57 23E 16 64 145E 12 57 59E 18 PE 51 1971 PE 52 1971 PE LA LO DM LA LO DM LA 65 53W 19 54 56W 15 53 64 2E 25 59 1 1W 18 59 55E 19 67 179W 14 56 68E 21 PE 61 1971 PE 62 1971 PE LA LO DM LA LO DM LA 57 10E 2 1 * * * 59 60 PE 71 1971 PE 72 1971 PE LA LO DM LA LO DM LA 51 165W 40 53 159W 34 62 64 100E 23 8 1 73E 30 82 LO DM 57W 19 94W 34 LO DM 57W 27 13 1971 LO DM 23E 13 53 1971 LO DM 141W 23 63 1971 LO DM 35W 3 1 114E 18 73 1971 LO DM 13W 38 100E 17 PE 24 1971 LA LO DM 67 89W 23 67 172E 28 PE 34 1971 LA LO DM 81 107W 18 86E 13 60 PE 44 1971 LA LO DM 7 1 100E 14 PE 54 1971 LA LO DM 62 123E 13 PE 64 1971 LA LO DM 57 80W 16 51 24W 24 PE 3 197 1 PE 4 197 1 PE LA LO DM LA LO DM LA 6 1 170W 34 68 80W 25 57 23E 35 PE 13 1971 PE 14 1971 PE LA LO DM LA LO DM LA 6 1 20W 26 67 7 1W 28 78 7 1 47E 27 56 22W 20 67 59 154E 25 61 130E 22 64 92E 22 5 1971 LO DM + + * * Fig. PE LA 6 1 7 1 LO DM 62W 21 82E 29 PE 25 1971 LA LO DM 6 1 100E 16 PE 45 1971 LA LO DM 56 152W 15 PE 55 1971 LA LO DM 61 73W 13 66 151E 17 PE 65 1971 LA LO DM 61 50W 17 57 113E 26 6 1971 LO DM 40W 18 69W 19 56 172E 38 54 55E 26 6 1 107E 19 PE 16 1971 LA LO DM 81 107W 32 PE 26 1971 LA LO DM 61 17E 13 PE 35 1971 PE LA LO DM LA 76 136W 19 7 1 81 37E 16 64 92E 14 LO DM PE 46 1971 LA LO DM 56 22W 13 PE 56 1971 LA LO DM 68 80W 14 56 8W 19 PE 66 1971 LA LO DM 63 96W 18 54 27W 24 56 68E 22 PE 7 1971 LA LO DM 70 102W 16 56 22W 32 61 150E 32 73E 29 58 PE 17 1971 LA LO DM 74 156W 34 PE 27 1971 LA LO DM PE 37 1971 LA LO DM 84 125W 14 75 170W 15 75 10E 11 PE 47 1971 LA LO DM 60 4W 18 PE 57 1971 LA LO DM PE 67 1971 LA LO DM 65 163E 25 61 40E 23 PE 8 1971 PE 9 197 1 PE LA LO DM LA LO DM LA 56 138W 21 78 118E 33 8 1 53 1W 31 70 122E 37 PE 18 1971 PE 19 1971 PE LA LO DM LA LO DM LA 78 172E 27 67 1E 15 79 7 1 153E 20 63 PE 28 1971 PE 29 1971 PE LA LO DM LA LO DM LA 74 125W 12 78 28E 18 62 6 1 PE 38 1971 PE 39 1971 PE LA LO DM LA LO DM LA 76 136W 16 56 22W 24 63 54 164W 17 53 159W 23 70 57 10E 20 79 145E 24 76 134E 17 PE 48 1971 PE 49 1971 PE LA LO DM LA LO DM LA 57 86W 14 74 145E 23 53 7 1 153E 15 76 PE 58 1971 PE 59 1971 PE LA LO DM LA LO DM LA * + •* * * + + * 60 PE 68 1971 PE 69 1971 PE LA LO DM LA LO DM LA 57 4E 20 5 1 12W 37 69 145E 18 10 1971 LO DM 73E 19 LO DM 26E 18 LO DM 33E 17 LO DM 46W 21 LO DM 1W 19 134E 14 60 197 1 LO DM 4W 21 LO < * * * DM 4«8 Sample page from B l o c k i n g Signature Catalogue. Q u a l i f y i n g positive Anomaly Centres l i s t e d by pentad, location and i n t e n s i t y (DM = dams). O 91 CHAPTER 5 5. DISTRIBUTION OF SIGNATURES AND SEQUENCES 5.1 Introduction We recall that a Blocking Signature is a positive anomaly of 500MB 5-day mean height which, for a specif ic year (yy) and pentad (K) meets Criterion (3), v iz : ( y y A K - A K)( y y<|, K - + K) > Q K Where the signature magnitude = y y A ^ the signature latitude = yy<j>K and the threshold values A^, <j>^ , Q^ are sinusoidal functions of K (Section 4.4.3). One purpose of this chapter wil l be to present and interpret the frequency distr ibution of Blocking Signatures for the Northern Hemis-phere. Later (Section 5.3), i t wi l l be shown how the Signature Catalogue can be modified to reveal the beginning and ending of Sequences of Signa-tures. We shall' then present and interpret the frequency distribution of these sequences. 5.2 Distribution of Blocking Signatures 5.2.1 Area! Distribution Al l blocking signatures, having now been identif ied and recorded, were counted according to their (I,J) location. Isopleths of equal f re -quency were drawn over the two-dimensional grid and the resulting area! 92 distribution is presented by TOTAL, Fig. 5.1. (A sl ight smoothing routine was introduced as explained in Appendix V - 1.) An isopleth numbered 'n ' means that i t encloses an area within which a blocking signature centre occurred at least n times per 381 km grid per 33 years. The TOTAL (Annual) Fig. 5.1, confirms the well-known propensity for blocking over (i) the NE Pacif ic Ocean and SW Alaska, and ( i i ) the NE Atlantic and NW Europe (Rex, 1950). However, i t also reveals areas of comparable blocking signature frequency over ( i i i ) NE Canada (including Baffin Island) (iv) the portion of the high Arctic (N of 75°N) clockwise from 90°W to about 40°E (v) a vast reach of the Soviet Union extending from 40°E to 100°E. The intensity of the Baffin Island frequency maximum, located in the v ic in i ty of the mean 500MB trough, would have been a surprise had we not already noted a similar pattern in the 700MB Pi lot Study. What l i t t l e comment we have seen concerning blocking in this region has been somewhat controversial. For example, Sumner (1959) stated that "well-developed blocks are almost non-existent over North America". On the other hand, Woffinden (1960) responded to the contrary, with convincing evidence from his own paper, and those of Namias and Clapp (1944) and others, that in this area "some form of blocking 'wave' or 'impulse' [often] proceeded upstream against the westerly current". We shall return to address the paradox in Section 5.3.6. FREQ 5 - D A Y MEAN B L O C K I N G S I G S 120E 9 > 500 MB TOTAL-SMOOTHED 140E IOOE -V + + -V + + BOE . 60E 160E-7^  180. 160 V 140V A " <BE •20 £ DO -20 w 3O0V sow . P E R I O D OF RECORD 1 9 4 6 - 1 9 7 8 I N C L I N T E R V A L S W E I G H T S NMC GRID • F i g . 5 . 1 Frequency o f o c c u r r e n c e o f B l o c k i n g S i g n a t u r e s o w i t h i n s quares o f 381 km x 381 km ( e x a c t a t 60 N) f o r a l l seasons (1946 t o 1978). 94 Turning now to the high Arct ic , let us examine the distribution of blocking signatures not only by YEAR (Fig. 5.1) but also by SEASON (Figs. 5.2 - 5.5). In a l l of these frequency distributions the closed isopleths in that region are explained, in part at least, by the not unusual observa-tion (from daily 500MB analyses) of warm anticyclones, removed from the mainstream of the westerlies, dr i f t ing slowly around the Pole. They no longer block the zonal flow in the usual sense. Namias (1958) has suggested that, "one of the more signif icant differences [between synoptic-scale phenomena of Arctic and Temperate latitudes] appears to be that the Polar Basin i t s e l f is either a sort of transit area or a sink for cyclones and anticyclones which develop else-where" . In the case of blocking anticyclones, Figs. 5.3 (SPRING) and 5.4 (SUMMER) suggest that the Basin acts as a sink. During these seasons we sometimes observe high pressure cel ls over extreme northern Greenland (80° - 85°N) which have evolved from the meridional extension of warm Atlantic ridges. It is also not unusual to find a second cel l further west (120° - 180°W),, either concurrently or subsequently, with a probable genesis over Yukon-Alaska, dr i f t ing into the 75° - 80°N zone. Now, be-cause the normal 500MB circulation (Figs. 4.6 and 4.7) features a Pole-centred low, the signature centres corresponding to these cel ls w i l l , for reasons explained in Chapter 3, be very close to the Pole. This accounts for the clustering of signatures at the Pole in Fig. 5.4. For reasons discussed above we decided to do a frequency analysis on signatures north of 75°N, and found a striking seasonal variation from a minimum in WINTER to a, maximum in SUMMER. The results are summarized as follows: ; 95 FREQ 5-DRY MEAN 500 MB BLOCKING SIGS WINTER-SMOOTHED 120E JOOE BOE * ^ + + / P E R I O D OF RECORD I N T E R V A L S WEIGHT=4 1 9 4 6 - 1 9 7 8 I N C L N M C G R ^ • F i g . 5 . 2 As i n F i g . 5 .1 e x c e p t f o r WINTER 96 FREQ 5 - D R Y MERN B L O C K I N G S I G S 120E 500 MB S P R I N G - S M O O T H E D BOE 180 :~20E 160 V 60 W 60 U P E R I O D OF RECORD 1 9 4 6 - 1 9 7 8 I N C L I N T E R V A L S W E I G H T S NMC GRID • F i g 5 . 5 As i n Fi g . 5.1 except f o r SPRING 97 FREQ 5 - D R Y MERN B L O C K I N G S I G S 120E 500 MB SUMMER-SMOOTHED P E R I O D OF RECORD 1 9 4 6 - 1 9 7 8 I N C L INTERVRL=1 WEIGHT=4 NMC GRID • F i g . 5.4 As i n F i g u r e 5.1 except f o r SuTMER 98 FREQ 5 - D R Y MERN B L O C K I N G S I G S 120E 500 MB F R L L - S M O O T H E D 180 160 V 60W P E R I O D OF RECORD 1 9 4 6 - 1 9 7 8 I N C L I N T E R V A L S W E I G H T S NMC G R I D • F i g . 5.5 As i n P i g . 5.1 except f o r PALL 99 TABLE 5.1 Blocking Signatures North of 75°N 1946 - 1978 Winter 154 Spring 217 Summer 245 Fall 170 Total 786 Although the physical reasons for the increase in blocking f re -quency in the SPRING and SUMMER are not 'c lear, we can speculate on a number of contributing factors. For example, by summer the westerlies have shifted at least 5 degrees north of their winter posit ion, and we may therefore infer that blocking action wi l l have a corresponding displacement. This wil l increase the possibi l i ty of anticyclones migrating into the Arct ic . Moreover, the normal pressure around the Pole is.higher and the circumpolar circulation less vigorous. Therefore, whatever the original cause of these high latitude warm anticyclones, once they do dr i f t over the Polar Basin they are less l ikely to be displaced. South of 75°N the increase in blocking signature frequency from WINTER to SPRING is immediately evident from Figs. 5.2 and 5.3, and the higher incidence of observed SPRING blocking episodes has been noted many times CRex, 1950; Sumner, 1959). There are also longitudinal seasonal displacements of frequency maxima (and minima) but these are perhaps i l lustrated more clearly by histograms presented in the next sub-section. 100 5.2.2 Longitudinal Distributions Blocking signatures were counted for every 10 degrees of longitude from the southernmost latitude of'occurrence to 75°NJ The resulting histogram (TOTAL) is shown in Fig. 5.6 and the strong longitudinal depen-dence described in the previous section is str ikingly evident. The seasonal variations are shown in Figs. 5.7 to 5.10. In WINTER, Fig. 5.7, the low frequency of signatures in Zone 3 (E S iberia, W Pacific) is not surprising for that zone is centred near the axis of the normal 500MB east Asiatic trough (Fig. 4.6) and also in an area of relat ively low standard deviation (Fig. 4.4). Continuing eastward into Zone 4, we note the unmistakably higher frequency from 180°W to 140°W, a result which is consistent with Rex (1950) and Treidl et a l . (1980a). From the discussion in Chapter 2 i t seems reasonable to suggst that this high frequency area may be attributed to complex interaction between, on the one hand thermally-forced barocl inical ly unstable waves meeting the c r i te r ia of Fig. 2.8 and, on the other, topographically-forced planetary waves. The primary seat of the thermal forcing is located in the western half of the Pacif ic Ocean between 20° and 50°N, while the topographic forcing agency is the Rocky Mountain Cordi l lera. Fig. 5.8, SPRING, and Fig. 5.9, SUMMER, indicate that, during the reversal of the ocean-continent thermal contrast, there is an eastward d r i f t of the high frequency signatures in the northeast Atlantic which For a l l computations we retained our data on the I,J, grid system. However, for this exercise a problem arose concerning a bias introduced when counting grid point centres into the 10° poleward converging sectors. A computer algorithm for interpolation, which avoids repeated and expen-sive coordinate system transformations on very large data sets, wi l l be found in Appendix V. EUROPE W.SIBERIA TOTAL E.SIBERIA V.PACIFIC 4 ALASKA E .PACIFIC 5 CANADA GREENLAND N.ATLANTIC 1 EUROPE -j i 1 1 1 1 1 1 r 1 1 i ,—i 1 i i 1 i 1 1 1 1 1 i I 1 1 1 1 1 1 i i i i i 1 1 1 i i i ! 0 30E 60E 90 E 120E 150E 180 150 V 120 V 90 W 60W 30 V 0 30E 60E F i g . 5.6 Frequency of occurrence of Blocking Signatures f o r each 10 degrees of longitude counted from southernmost l a t i t u d e of occurrence to 75°N. For ALL SEASONS (1946 to 1978). 1 EUROPE 2 W . S I B E R I A WINTER E.SIBERIA V.PACIFIC .4 ALASKA E .PACIFIC 5 CANADA GREENLAND N.ATLANTIC EUROPE 0 30E 'eOE' ' 9 U E ' ' 120E 'l50E " 180 " 'l50W ' 3 20W ' 90W' '60W' '30W'> ' 6 ' '30E' '60E i i r F i g . 5.7 As i n F i g . 5.6 except f o r WINTER EUROPE W.SIBERIA SPRING E.SIBERIA W.PACIFIC I d ALASKA E .PACIFIC CANADfl GREENLAND N.ATLANTIC I EUROPE 30E 60E 90E 120E 150E 180 150W 320W 90W 60W 30V 0 30E '60E § F i g . 5.8 As i n Pig. 5.6 except f o r SPRING SUMMER EUROPE W .SIBERIA E.SIBERIA W.PACIFIC 4 ALASKA E.PACIFIC 5 CANADA GREENLAND N.ATLANTIC 1 EUROPE 0 30E 60E 90E 120E 150E 180 150V 120V 90W 60W 30V 0 30E 60E F i g . 5 . 9 A s i n F i g . 5 . 6 e x c e p t f o r SUMMER EUROPE V. SIBERIA F A L L 3 l 4 E. SIBERIA ALASKA W.PACIFIC . E.PACIFIC CANADA GREENLAND N.ATLANTIC ] EUROPE 0 30E 60E 90E 120E 150E 180 150W 120W 90W 60W 30V 0 30E 60E & F i g . 5.10 As i n F i g . 5.6 except f o r FALL 106 culminates by SUMMER, with a well-defined maximum centred on the Greenwich meridian. Over Canada, the phenomenon of persistent Hudson Bay highs in SPRING is well-known (Johnson, 1948) and this is reflected by the blocking signature maximum at 80°W. Over Zone 4 (Alaska and the E. Pacific) we observe, not an eastward dr i f t as in the case of the At lant ic , but a westward dr i f t from WINTER through SPRING to SUMMER by which time the maximum is located at 170°W. This motion is not inconsistent with the thermal contrast reversal theory when we consider the summer heating of the vast Alaskan land mass. If the disposition of the planetary waves favours anticyclonic conditions at the surface over Alaska, the sub-stantial heating in the lower troposphere, greatly enhanced by the nature of the terra in, wil l (from hydrostatic considerations) increase the 500MB gph and therefore the positive anomaly. The blocking anticyclones centred over Alaska wi l l usually have signature centres located between 70° and 75°N, and between 140° and 180°W. These contribute to the SUMMER distribution in Zone 4. By FALL (Fig. 5.10) the blocking signatures in that area have declined, partly because the thermal effect over Alaska is in reverse. It now becomes a source region for cold air masses, hence signatures over the Alaska-Yukon area are rare (Fig. 5.5). Moreover, under appropriate synoptic conditions, cold air is deployed over the relat ively warmer Gulf of Alaska, and the large diabatic heating contributes to vigorous cyclogenesis in that area during FALL and WINTER. Blocking can s t i l l occur (Fig. 5.10 shows a concentration of signatures 135° - 145°W between Latitude 50° and 60°N) provided there is a favourable long wave disposit ion, but there is no reinforcement from the thermal regime over the adjoining continent. 107 One feature common to a l l seasons is the maximum at 60°E in the v ic in i ty of the Ural Mountains. This result is supported by Baur (1958), Serebreny et a l . (1961) and Knox (1979). What is the reason for this maximum? The normal WINTER 500MB flow (Fig. 4.6) and the three centres of maximum Standard Deviation located downstream from the respective troughs (Fig. 4.4) indicate the dominance of Wave component 3 on the mean flow. As discussed in Chapter 2, the' f i r s t two waves starting from the west Pacif ic trough are primarily the result of topographic forcing com-bined with longitudinally dependent heating. We cannot invoke these factors for the third wave. (The low prof i le of the Urals does not pro-vide a signif icant orography and the thermal forcing does not exist. ) Its presence was explained (Bolin, 1950) as a resonant response, required to produce a dynamically stable circumpolar system. The associated axis of maximum standard deviation is located, for each season, in the v ic in i ty of 60°E and i t is reasonable to assume that the Ural Mountain blocking anticyclones make a signif icant contribution, just as do their oceanic counterparts, to variance maxima at 160°W and 20°W, respectively. F inal ly , to compare the seasonal frequency of blocking signatures south of 75°N, we present Table 5.2 (which complements Table 5.1). TABLE 5.2 Blocking Signatures South of 75°N 1946 - 1978 Winter 1055 Spring 1278 Summer 1186 Fall 1089 TOTAL 4608 108 Adding to this total the 786 counted North of 75 N we have a grand total of 5,394 signatures, or an average of 2.24 per individual pentad. Baur (1958), in a study of Northern Hemisphere blocking from 1949 to 1957, found a comparable rate of 2.8 blocks. The higher incidence of blocking in SPRING (.20 per cent greater than in WINTER or FALL) has already been noted (See 5.2.1). It is well to re-emphasize the dist inction between a blocking s ig -nature and the actual blocking episode observed on the daily 500MB analyses. We shall find that an episode, i f a short one, say, 3 to 7 days, has a better than even chance of being matched by a single blocking signature. But episodes may be longer, with durations from 10 to - 50 days, in which case they wil l correspond to a sequence of signatures. In Section 5.3 we shall describe a proposal to objectively identify these sequences, to catalogue their attributes and calculate their frequencies. 5.3 Blocking Signature Sequences 5.3.1 Rationale and Technique The Blocking Signature Catalogue (Fig. 4.8) reveals sequences of positive anomaly centres whose trajectories could often be related to the ensemble behaviour of anticyclone centres on the daily 500MB analyses. (An example is discussed in Appendix V - 4, and i l lustrated by Fig. V - 2.) Exceptions understandably occurred during the i n i t i a l and terminal stages of an episode but, especially for ^ 10-day episodes, there was a very close correspondence. Moreover, in the event of concurrent blocking (the Catalogue indicates that anywhere from zero to four episodes may be in progress around the hemisphere during a specified pentad), the respec-tive trajectories were geographically well separated. 109 The signatures moved with speeds characteristic of blocking ant i -cyclones (1 to 5 m s""*). Could we use this fact as a data processing cr iter ion for grouping the signatures into their respective sequences? If so, i t might then be possible to prepare a catalogue of these sequen-ces which would enable a user to quickly identify where, when and with what intensity real blocking episodes l ike ly occurred in the Northern Hemisphere during the 33-year period. To determine the cr i ter ion threshold we made a large number of . manual comparisons of signature motions during these episodes. The results indicated that the maximum displacement was * 5 Grid Points (or 1905 km) per 5 days, which is equivalent to a speed of 4.4 m s"^  at 60°N. If we designate a sequence of n successive signatures (a-j, Or>, o-g> . . . . . . a n) as S(a n) then the criterion for + -| to be a member is that the distance from to + -| * 5 grid lengths. This wil l be referred to as Criterion (4). Therefore, to determine i f a signa-ture in pentad K had a successor, Criterion (4) was applied to the distance between and each signature l isted in pentad K + 1. Either there was no successor, in which case the sequence was terminated, or one was determ-ined and the process was repeated with the signatures in K + 2. Occasion-a l ly (usually with cases in the high Arc t i c ) , two signatures qual i f ied, in which case the one providing the smaller displacement was selected. 5.3.2 Signature-Sequence Catalogue A computer program was written for the purpose of identifying and l i s t ing a l l such sequences over the 33-year period. A sample page from the resulting Blocking Signature-Sequence Catalogue is shown in Fig. 5.11. 5-DAY MEAN BLOCKING SIGNATURE SEQUENCES 1955 ****-NO SIGNATURES RECORDED PE 1 1955 PE 2 1955 PE 3 1955 PE 4 1955 PE 5 1955 PE 6 1955 PE 7 1955 PE 8 1955 PE 9 1955 LA LO DM LA LO DM LA LO DM LA LO DM LA LO DM LA LO DM LA LO DM LA LO DM LA LO DM 67 8W 38* *G3 57W 4 1 S3 57W 31 57 67W 23* * * * + *61 80W 24* •62 30W 42 *57 51E 19* *54 133W 23* *75 94W 21* *58 100E 27* *79 1OOE 21 80 145E 18 79 100E 19* *57 1 13E 21* *55 7GE 20 60 86E 26 56 82E 21* PE 11 1955 LA LO DM 51 53W 37* PE 21 1955 LA LO DM 69 69E 15* •53 7W 21 PE LA 68 •58 31 1955 LO DM 1E 80W 22* 19 58 73E 17* PE 41 1955 LA LO DM 60 4W 23 *69 139W 16* *57 157W 15 PE 51 1955 LA LO DM *82 37E 17 *56 28E 15 PE 61 1955 LA LO DM 59 59W 37 *61 177W 27 *58 73E 22* PE 71 1955 LA LO DM *74 53W 26 57 177E 55 PE 12 1955 LA LO DM •58 170W 39* •78 82E 24 PE 13 1955 LA LO DM *6' 20W 21 78 82t 26 *64 134E 24* PE 14 1955 LA LO DM 58 17W 19 78 82E 18* PE 15 1955 LA LO DM 57 31W 32* PE 16 1955 LA LO DM *70 58W 37 *83 100E 28 *64 66E 20* PE 17 1955 LA LO DM 59 59W 19 86 100E 30 *72 117W 24* PE 18 1955 LA LO DM 64 24W 20* 85 145E 20* •57 93W 18 PE 19 1955 LA LO DM 58 86W 18' PE 10 1955 LA LO DM 59 44W 36 PE 20 1955 LA LO DM *75 55E 19 PE 22 1955 PE 23 1955 PE 24 1955 PE 25 1955 PE 26 1955 PE 27 1955 PE 28 1955 PE 29 1955 PE 30 1955 LA LO DM LA LO DM LA LO DM LA LO DM LA LO DM LA LO DM LA LO DM LA LO DM LA LO DM *75 80W 28 64 88W 17* * * * * * * *• + *58 53W 23 64 46W 13* *59 136E 22* •67 8W 17 63 13W 23* *63 77E 28 69 69E 19* *56 98W 16* *60 35W 13* *59 64E 16 69 69E 13 64 84E 30 PE 32 1955 PE 33 1955 PE 34 1955 PE 35 1955 PE 36 1955 PE 37 1955 PE 38 1955 PE 39 1955 PE 40 1955 LA LO DM LA LO DM LA LO DM LA LO DM LA LO DM LA LO DM LA LO DM LA LO DM LA LO DM *90 19* •63 123E 13 66 127E 14 67 82E 18 75 100E 11 85 145E 17* *60 4W 19 6 1 10E 22 56 8W 15 58 74W 30 59 101W 19* *6 1 20W 12* *61 80W 20* *60 94W 13 56 98W 15 *58 73E 14* *61 WOW 12* *59 116W 13 59 101W 13* *69 145E 14* PE 42 1955 PE 43 1955 PE 44 1955 PE 45 1955 PE 46 1955 PE 47 1955 PE 48 1955 PE 49 1955 PE 50 1955 LA LO DM LA LO DM LA LO DM LA LO DM LA LO DM LA LO DM LA LO DM LA LO DM LA LO DM 60 4W 22 55 14W 16 55 14W 20 65 10E 18 59 31E 15 56 28E 15 60 24E 17* * +- * * *64 134E 16 *6 1 130E 14* *54 4E 17* 67 172E 11 72 WOW 15 7 1 179E 13* *67 28E 16* PE 52 1955 PE 53 1955 PE 54 1955 PE 55 1955 PE 56 1955 PE 57 1955 PE 58 1955 PE 59 1955 PE 60 1955 LA LO DM LA LO DM LA LO DM LA LO DM LA LO DM LA LO DM LA LO DM LA LO DM LA LO DM 80 55E 23* *78 62W 21* + 68 89W 15 67 62W 23 60 66W 44 60 35W 15 64 46W 23 59 46E 18 60 55E 22 74 37E 22 69 69E 16 60 86E 17* *58 37E 20* •56 82E 16* *58 73E 17* PE 62 1955 PE 63 1955 PE 64 1955 PE 65 1955 PE 66 1955 PE 67 1955 PE 68 1955 PE 69 1955 PE 70 1955 LA LO DM LA LO DM LA LO DM LA LO DM LA LO DM LA LO DM LA LO DM LA LO DM LA LO DM 58 53W 30 63 57W 19* *59 1 1W 25 56 8W 31 59 26W 30* * * * * *75 WOW 20 86 80W 25 85 145E 19* 66 163E 30* *54 179E 27* *65 80W 19* *64 72W 24* *56 152W 33 PE 72 1955 LA LO DM 68 80W 27* 51 175W 41* PE 73 1955 LA LO DM *64 66E 17 *59 136E 26* F i g . 5.11 Sample page from B l o c k i n g Signature Sequence  Catalogue. *• i n d i c a t e s beginning and end of a sequence. Component signatures remain on same row. 11,1 Note that the beginning and end of a sequence is indicated by an asterisk (*) and that i ts component signatures always occupy the same row. Example 1. The entry l isted for pentad 50 (September 3 to 7, 1955), a positive anomaly centred at 64°N 134°E, magnitude 16 dams, rep-resents a single signature sequence. (An inspection of the daily 500MB analyses discloses a short-lived but well-defined blocking anticyclone over eastern Siberia.) Example 2. The entry l isted for pentad 64 (November 12 to 16, 1955) 59°N 11°W is the starting signature of a 3-member sequence which ends with pentad 66 (November 22 to 26) at 59°N 26°W. This corresponded to a well-defined 14-day block over the eastern Atlantic (Treidl et a l . , 1980b). 5.3.3 Test on Independent Data Of course we did not expect that a l l signature sequences would identify blocks with the same precision as these two examples. The l im i -tations of our basic unit , the 5-day average 500MB height anomaly, have already been discussed in Chapter 4 and these carry over into the signa-ture-sequences. On the other hand, the trajectory tests suggested that, part icularly in the case of the more protracted blocks, there would be a high rate of correspondence. It is also important to remember that the "objective c r i te r ia " developed so far are the result of empirical analyses on what at best may be termed quasi-objective data. These were the data concerning blocking systems extracted by individuals from analyses of daily 500MB height f ie lds . Any test of the c r i te r ia must inevitably be made on data obtained in a similar manner. 112 For the test we chose a sample of data which had not been used to calculate Criterion (3) (What determines a qualifying signature?) or Criterion (4) (What determines a qualifying sequence?). We carried out a tedious but, we believe, ultimately rewarding examination of twelve months of daily analyses of 500MB height for January, February, December 1952 June to November 1955 March to June 1956. The procedure (Appendix V - 3) was to compare each catalogued sequence which occurred during this period with the contemporaneous daily analyses and to determine the frequency with which a geographically related blocking episode occurred. What were the guidelines for judging the occurrence of an actual blocking episode during this test? They were those used during the development of Criterion (3) in the f i r s t place, that is to say, the necessary and suff ic ient conditions (Appendix IV - 2) which, in our judgment, must obtain for a block to occur. The results are summarized in Table 5.3. It wi l l be noted that, not only have we compared the number of times a sequence was related to one or more associated blocking episodes which occurred within i ts dura-tion (column 3) but also the number of. times i ts component signatures  actually concurred with the blocking episode (Column 6). The rationale was that, particularly during long sequences, there would be interrup-tions of blocking occurrence, and a more appropriate measure of the success of the Catalogue would be the percentage of the component signatures which- were concurrent with blocking. TABLE 5.3 Results of the Test of Catalogue Sequences on the Independent Data Months of January, February and December 1952, June - November 1955, and March - June 1956. Col. 1 2 3 4 5 6 # of SEQ's tested (including those N of 75N) # of SEQ's within which one or more blocking episodes occurred % of SEQ's which were related to one or more associated blocking episodes. (Col. 2* Col. 1) x 100 # of SIG's contained in SEQ's l is ted in Col. 1 # of SIG's within the SEQ's of Col. 2 which were concurrent with block-ing episode % of SIG's which were concurrent with a re-lated block-ing episode (Col. 5^ Col. 4) x 100 SEQ1 21 13 62 21 13 62 SEQn 26 25 96 109 90 83 ALL 47 38 81 130 103 79 114 It wi l l be noted that a total of 47 signature-sequences (SEQ's) were l isted in the Catalogue for the test period. Of these, 21 were one-pentad duration (SEQ-j's) and the remaining 26 were two or more (SEQn's where n ^ 1). The success ratio of the SEQ^s was 62% and of the SEQ n's 96%. The success ratio of SEQ-j signatures was, of course, 62% while of SEQn s ig -natures i t was 83%. This difference is not surprising because the latter are associated with the more persistent blocking episodes, often with large equally persistent positive anomalies. The former are sometimes associated with transient ridges of suff ic ient amplitude to produce a single qualifying anomaly. Of the total of 130 signatures l i s ted , 103, or nearly 80% were concurrent with an ongoing related block. Now, since we have no reason to believe the test period was unrepresentative, we conclude that the Signature-Sequence Catalogue wi l l provide a useful and convenient source of information for investigations into the nature of blocking. It is important for the user to be aware of the author's guidelines for iden-t i fy ing a blocking episode, and to have an understanding of the l imita-tions of using 5-day averages for the specification of events in a con-tinuum. Subject to those reservations, the Signature-Sequence Catalogue can be used to advantage (a) for quick identif icat ion of probable periods of blocking (b) for a wide variety of frequency studies, the results of which wi l l be closely connected with corresponding frequency studies of blocking. 5.3.4 Signature-Sequence Frequency by Duration The number of signature-sequences (al l durations) which occurred during the 33 years of record is 1,868. Of these, 994 were 2 pentads or 115 longer, and the remaining 874 had a duration of only one pentad. The complete distribution is shown in Fig. 5.12(a). (SEQ's which were i n i t i -ated north of-75°N were :not counted.) As a matter of interest the 16-pentad 'out l ier ' was in i t iated July 20th, 1976 at 56°N 22°W and terminated October 7th, 1976 at 72°N 10°E (PE 41 to PE 56, inclusive). This extraordinarily long sequence was immediately preceded by one which also resided in the E. Atlantic - N.W. Europe region. It began June 25th at 54°N 4°E and ended July 19th at 74°N 37°E, and was associated with the blocking episode which resulted in an exceptional heat wave over England and neighboring countries. Figure 5.12(b) from Treidl et a l . (1980a) represents the frequency distribution of durations of those blocks which they identif ied over the northern Hemisphere 1945 to 1977. Treidl does not ascribe any s t a t i s t i -cal significance to the 'spikes' at 12 and 19 days, respectively. The relative s imi lar i ty between Figs. 5.12(a) and 5.12(b) does confirm, in a climatological sense, a strong relationship between Signature Sequence Duration and Observed Blocking Duration. 5.3.5 Signature-Sequence Frequencies by Longitude In section 5.2 we presented areal and longitudinal distribution by season and year of the frequency of occurrence of Blocking Signatures. Although these diagrams clearly .revealed areas of high and low blocking frequency, they could not be used to distinguish between areas where Signature-Sequences were ini t iated and those where they terminated. We now have the means to do so and a program was written to identify and count a l l sequences which Ca) started in a 10° longitude sector (b) ended in a 10° longitude sector. TOTRL 11i6 Fig. 5 .12(a) Frequency d i s t r i b u t i o n of Signature-Sequence durations. One o u t l i e r of duration 16 pentads. 5 (5 "7 DURATION I l— 8 9 (PENTADS; 10 I ) . 12 13 117 8 0 75 70 0 wmm Fig. 5.12(b) Frequency D i s t r i b u t i o n of Blocking durations. 1945 - 1977 ( T r e i d l et a l 1980) .1 A m i 10 15 20 25 3 0 35 4 0 45 D A Y S 50 55 118 Fig. 5.13 presents the frequency distribution of the in i t i a l positions of a l l sequences which were started south of 75°N, while Fig. 5.14 presents the corresponding distribution of the f inal positions. (It should be noted that some signatures drifted north of 75°N in which case their f inal position was noted and they were included in the distribution of Fig. 5.14.) It would appear (Fig. 5.13) that blocking sequences have a pre-ferred longitudinal band of in i t ia t ion in the East Atlantic and that sub-sequently CFig. 5.14) they are more l ikely to retrograde or progress than to remain quasi-stationary. This is consistent with the results of Rex (1950) and Treidl et a l . (1980a). In the 30 degree sector centred on the Urals (60°E) starting signatures outnumber ending ones, whereas the reverse is the case from 90°E to 110°E (central Siberia). Personal obser-vation of a large number of 500MB Northern Hemisphere analyses confirms that this reflects a propensity for blocks identif ied in the Ural Mountain area to progress and terminate before reaching the east Asian coast. Proceeding s t i l l further east to 130° - 150°E the excess of ENDS over STARTS can only be surmised in the absence of a latitudinal distr ibut ion. The results of Namias (1958) suggest that many of these terminations over NE Siberia and the Arctic Ocean ref lect warm anticyclones that retrograde from the Aleutians. A comparison of Figs. 5.13 and 5.14 indicates that some could have even have retrograded from mainland Alaska. The most revealing of the comparisons by season is SPRING (Figs. 5.15 and 5.16). For example, western Russia (30°E to 40°E) appears to be a site of maximum in i t i a t i on , and Central Siberia one of maximum termina-t ion. Again, this reflects the predominance of progressive motion for blocks over this part of the Eurasian continent. Moving to the Pacif ic EUROPE V.SIBERIA TOTAL 3 E.SIBERIA W.PACIFIC S T A R T I N G . S I G S 4 I 5 ALASKA 1 CANADR E.PACIFIC GREENLAND N.ATLANTIC 1 EUROPE 0 '30E' '60E 120E 150E 180' 'l50W ' I20V 90W 60W 30W 0 30E SOF P i g . 5 . 1 3 T o t a l ( i . e . annual)/frequency by l o n g i t u d e of i n i t i a t i o n of a l l signature-sequences. 1 EUROPE 2 V.SIBERIA TOTAL 3 E.SIBERIA V.PACIFIC ENDING S I G S 4 • I 5 ALASKA 1 CANADA E.PACIFIC 6 GREENLAND N.ATLANTIC ] EUROPE ~i—i—i—i—1~ -i r 1 1 1-30E SOE 90E 120E 150E 180 150V 120V 90W 60W 30V -i 1 r-0 30E 60E F i g . 5.14 Total ( i . e . annual) frequency.by longitude of termination o f a l l signature-sequences. EUROPE V.SIBERIA SPRING 3 E.SIBERIA V.PACIFIC S T A R T I N G ALASKA E.PACIFIC S I G S 5 CANADA S GREENLAND N.ATLANTIC 1 EUROPE r ; ,,,,, i ; 1 , , , , , > O 30E 60E 90E 120E 150E 180 1 5 0 V J 2 0 W 90W 60W 30W 0 30E 60E F i g . 5.15 As i n Fig. 5.13 f o r SPRING EUROPE 2 V.SIBERIA SPRING 3 E.SIBERIA W.PACIFIC ENDING d ALASKA E .PACIFIC S'IGS CANADA GREENLAND N.ATLANTIC EUROPE a UJ 0 30E 60E 90E 120E 150E 180 J50V 120W 90W SOW 30W 0 30E 60E g Fig. 5.16 As i n F i g . 5.14 f o r SPRING 123 and Alaska, there is a dist inct suggestion that blocking signatures i n i t i -ated in the maximum frequency sector 165°W to 135°W, progress or retrogress rather than remain quasi-stationary. Retrogression appears to predominate. It is well known that blocking highs centred in the v ic in i ty of 160°W create a synoptic situation favourable for cold lows originating in the Gulf of Alaska to track southeastward and to punctuate the otherwise i dy l l i c West Coast spring with periods of unsettled weather. Over Central Canada the maximum at 80°W was noted previously (Section 5.2.2) during the discussion of longitudinal signature distributions. The excess of terminations over in i t iat ions suggests that not only do blocks develop ' in s i t u ' , but that they are also 'imported' and we shall elaborate upon this in the next section. Frequency distributions for Starting and Ending Signatures during SUMMER, FALL and WINTER wil l be found in Appendix V (Figs. V - 3 to V - 8). 5.3.6 The Baffin Island Paradox In the familiar 3-wave pattern of the normal 500MB WINTER c i rcu-lation (Fig. 4.6), we note a primary trough extending from the Canadian Archipelago southward to the St. Lawrence Valley with i ts axis along the 70°W meridian. Its intensity naturally diminishes with the approach of SUMMER (Fig. 4.7) but i ts normal seasonal location remains essentially unchanged. Why, then, do we find for every season a maximum frequency of blocking signatures, not only in the location of the normal trough, , but centred near i ts deep quasi-permanent core? There is certainly no parallel for this paradox in the case of that other primary feature, the Asiatic trough, where the incidence of signatures is much lower (Fig. 5.1). 124 To what extent are these North-Eastern Canada signatures associated with blocking? There have been several studies of anomalous circulations featuring strong positive mid-troposphere height anomalies over Baffin Island and Davis Strait (e .g. , Namias, 1958) but to our knowledge the question has not been addressed exp l i c i t l y . The differ ing opinions of Sumner and Woffinden on the question of blocking frequency in that area have already been noted (5.2.1). Treidl et a l . (1980a) concluded that except for SPRING, which "showed an interesting flare-up in blocking ac t iv i ty " , the counts of occurrences over Canada were low. In an attempt to resolve the paradox we l isted a l l Blocking Sequ-ences which contained at least one Signature in the area 60°N to 75°N and 60% ' to 90% for the period July 1955 to June 1956. There were 15 cases. We then examined the corresponding daily 500MB analyses with par-t icular care and found that during 12 cases the Sequence was in fact concurrent with an observed blocking episode. On the other hand, Tre id l ' s Catalogue l i s t s only f ive cases for that area during the same period. The difference in results arises almost entirely from the difference between our respective guidelines for deciding whether a blocking episode has occurred on a series of daily analyses (Appendix IV - 2). His are more restr ict ive and therefore reject cases which we would include. The l i s t ing of these 12 cases and associated comments are pre-sented in Table 5.4. We are convinced that the blocking process in the generally accepted sense was operating on each occasion. As a typical example, consider the Blocking Signature for PE 69 (December 7-11, 1955 64% 72%) . The 500MB analysis for December 9 (Fig. 5.17) shows a warm blocking high over Western Hudson Bay and a blocking ridge extending eastward to southern Greenland. This condition persisted through to TABLE 5.4 Twelve Cases of Blocking Affecting Baffin Island (1955-56) No. PE Lat. Long. PE. Lat. Long. Max. (dams) Comments 1 53 78N 62W 53 78N 62W 21 Block over Ellesmere Island, developed from retrogression of high-latitude blocking over Scandinavia. Low normally over Baffin area displaced southward 2 66 65N 80W 66 65N 80W 19 Short term (5-day)Block over Hudson Bay during pentad 66 3 69 64N 72W 69 64N 72W 24 Block over Hudson Bay-Southern Baffin Island - Davis Strait . See Dec....9,. 500MB Analysis, Fig. 5.17 4 71 74N 53W 72 68N 80W 27 Block formed by discontinuous retrogression of a North Atlantic blocking wave 5 2 58N 80W 2 58N 80W 36 Associated with a warm Quebec-Labrador anticyclone 6 2 53N 51W 5 60N 66W. 47 Robust Blocking four pentads duration 7 4 64N 88W 6 60N 94W 38 Robust Blocking three pentads duration 8 10 67N 62W 11 67N 29W 31 A progressive case where the Anomaly was i n i t i a l l y over Davis Strait (PE10) and crossed Greenland to reinforce Atlantic blocking (PE11) 9 17 67N 98W 17 67N 98W 16 Small persistent blocking anticyclone over Northwest Territories 10 15 69N 41E 22 67N 62W 37 Striking example of steady retrogression March 12 -April 20 of a positive anomaly ini t iated over the Barents Sea and terminated over Davis Stra i t 11 32 64N 88W 32 64N 88W 13 Short term (5-day) omega-Block 12 34 71N 91W 36 70N "102W 30 Major blocking episode S Y N O P T I C W E A T H E R M A P N O R T H E R N HEMISPHERE 5 0 0 M8 1500 GMT !iaa_£l«i«$uait null DEC e 1399 i . . . . i J , . F l f i - 5 , 1 7 f c f i a ? Q ^ 0 f c i l ^ ? u d s o n B a y - B a f f i n Island-Davis S t r a i t during Pentad 500MB a n a l y s i s i s f o r centre day of pentad. See Table 5.4. — contours i n hundreds o f f e e t isotherms i n degrees C e l s i u s (US Department of Commerce) r\3 CTl 127 December 13th. Note how the Baffin Low has bifurcated. The original centre, which was in i ts normal position on December 4th, has retro-graded to Alaska while to the south we find a slow moving anomalous centre of low gph over Labrador. It is true that the Hudson Bay blocking ant i -cyclone lacks the unmistakable robust structure of the major ocean blocks, but the general circulation features over the U.S. and Canada, particu-lar ly the sp l i t jet over Br i t ish Columbia, are clear indicators of a signif icant blocking episode. Further evidence of the high incidence of winter blocking in the v ic in i ty of the normal 500MB Baffin Low is provided by the distribution of the coeff icient of skewness of 5-day average 500MB heights in that area (Fig. 6.9). The inference is that although the most numerous deviations from normal are caused by variations of intensity of the Baffin Low, more or less in i ts usual posit ion, a suff ic ient number of large positive anomalies occur to skew the distribution markedly so that the mode is well to the le f t of the mean. Interpretation of the spatial distribution of the higher moments wil l be discussed in Chapter 6. 5.3.7 Secular Variation of Blocking Signatures In view of the range of c r i te r ia used by authors, for defining blocking, and of the individual judgment required for marginal cases, one is inclined to be somewhat circumspect with regard to studies of inter-annual var iab i l i ty . Nevertheless, because of the profound impact of recurrent large scale blocking on the climate over vast regions of the globe, the subject has been one of considerable interest, part icularly among European climatologists. 128 Prior to the ava i lab i l i ty of Northern Hemisphere upper air data, blocking was identif ied by the application of plausible c r i te r ia to analyses of MSL pressure, e .g . , E l l i o t and Smith (1949). If one's interest was focussed on the oceans this gave reasonable results, but in the case of the continents, particularly during the winter season (because of the masking by Arctic a ir masses) i t was d i f f i cu l t and at times impos-sible to determine i f blocking was, in fact , in progress. Nevertheless E l l i o t t and Smith did use the daily analyses of MSL pressure for the months of January and February, 1900 - 1938 to assess the secular varia-tion of blocking over nearly three-quarters of the hemisphere (from 140°E eastward to 40°E) . They found that the year-to-year extent of blocking in the three sectors, the Pacif ic and Atlantic Oceans and the North American continent, were (not surprisingly) in phase and therefore used a combined index for a representation of the extent of blocking in a given year. The result of their study along with a graph of concurrent sun-spot numbers is shown in Fig. 5.18(a). The promising in-phase relationship early in the period becomes out-of-phase later in the record. Lag relationships were also explored and the authors suggested that the phase relationship was probably random. The sample i s , of course, too small for s t a t i s t i -cal ly sound conclusions. Brezowsky et a l . (1951) examined the secular variation of Atlantic and European blocking from 1881 to 1950 (for a l l months) using a c i rcu la -tion c lass i f icat ion technique,and their curve of overlapping 10 year means shows an interesting quasi-periodicity (Fig. 5.18b). These authors also looked for the poss ib i l i ty of a relationship with solar act iv i ty . The result was inconclusive. The sample is s t i l l too small not only temporally but, in our opinion, spat ia l ly , for meaningful s ta t is t i ca l conclusions. 129 F i g . 5.18(a) Long-period v a r i a t i o n i n index numbers, N d, and sunspot numbers, N, f o r the January-February seasons of the 20 even years: 1900-1938. ( E l l i o t t et a l . , 1949). IBSO ~i$x> • m> "f92o *uo 'wo igso F i g . 5.18(b) Annual frequency of blocking highs, A t l a n t i c and Europe; Overlapping 10-year means. (Brezowsky et a l . , 1951). 130 Notwithstanding the expected d i f f i cu l t y [ i f not impossibility) of interpretation, we thought i t would be useful to examine the annual  variation of blocking sequences for the Northern Hemisphere which originated south of 74°N from 1946 to 1978. Fig. 5.19 presents, in effect , three frequency distr ibutions: (a) The top curve is the total duration in pentads per year of al1 identif ied sequences. (b) The middle curve is the corresponding measure for a l l sequences containing two or more signatures. (c) The lower curve is for a l l sequences containing three or more signatures. For the years 1946 and 1947, i t should be noted that upper air data over Siberia and northern China was v i r tual ly non-existent. Hence the accu-racy of 500MB analyses over these areas fa l l s well short of the standard for the remainder of the hemisphere. Interpretation of Fig. 5.19 should therefore begin with 1948. The histograms reveal a number of interesting features: (a) The single signature-sequences (those associated with blocks of relat ively short duration) are relat ively uniform from year to year. (Compare unstippled areas.) (b) The sequences containing two or more signatures (usually related to blocks with average or above average persistence) appear to provide the major component of inter-annual variation. (c) There is a suggestion of a complex quasi-periodicity with a time scale of the order of a decade. Of particular note is the 15-year fluctuation with crests at 1953 and 1968. Again, the sample is too small for interpretations of s tat is t ica l significance. F i g . 5.19 Duration i n Pentads per year. Top curve f o r a l l Sequences. Middle curve f o r sequences ^ 2 Signatures. Lower curve f o r Sequences > 3 Signatures. (One-signature unstippled. Two-signature and ^ 3-signature frequencies d i f f e r e n t i a t e d by s t i p p l i n g ) . 132. (d) The frequency of blocking sequences was well above normal from 1951 to 1954, inclusive. This seems to be related to a statement by Namias (1958) when discussing the so-called 'normal' 700MB charts which were available at that time: "There are suggestions that the eight-year period 1948-1955 may have been abnormal in the sense that pressures were too high relative to a longer period average over the Baffinland-Davis Strait-Greenland area". (The "longer period" referred to one which began in the 1930's with the construction of 700MB contours from MSL analyses using a stat is t ica l-di f ferent ia l analysis technique.) Namias' astute observation is in agreement with Lamb (1972) who also noted the higher average pressure and incidence of blocking ant i -cyclones over Greenland in the 1950's. Now there is a strong teleconnec-tion between positive anomalies centred in the Davis Strait area between 60°N and 70°N and concurrent positive anomalies around the hemisphere centred north of 50°N (Namias, 1958; O'Connor, 1969). Hence i t is reas-onable to conclude that above normal pressure in that area, 1948 to 1955, is indeed related to the blocking frequency maximum 1951 to 1954. We thought i t would be of interest to compare the secular variation of blocking 1945 to 1977 as reported by Treidl et a l . and reproduced in Fig. 5.20(b), with our result for blocking signature sequences, Fig. 5.20 (a). These curves should be compared in a relative sense for reasons already discussed. In Fig. 5.20(b), much above normal blocking in the 1950's, with a strong peak 1953-1954, is reasonably consistent with Fig. 5.20(a). So, too, is the generally below normal blocking in the 1960's terminated by an abrupt reversal to above normal 1968-1969. The subsequent decline in the early 19701s is much more marked in (b) than in (a). Both curves are consistent with an abrupt recovery in 1976, 1 2 5H 2 jioo-j > V) Q < U J OL 7 54 5 04 _ l 1 — I — I — • 50 55 60 375H oc < U J < 2504 65 (b) M e a n ~98 • • 1 1 1 > 1 1 L. 70 75 -I L. 80 M e a n ~24 5 1 21^ "*^ —*——*— * -* *——• * 1 * 1 ' -* * i ,t —• • » »—f t « « i . . . « t « - . » , 46 4 8 50 52 54 56 58 60 62 64 66 68 70 72 74 76 78 80~ F i g . 5.20 (a) Duration (Pentads/year) of a l l sequences > 2 signatures (SEQ n's). (b) Duration (Days/year) of blocking, reported by T r e i d l et a l (1980). 133 but agreement is not good in 1977, or from 1946 to 1952, inclusive. The differences are no doubt mainly attributable to the respective guidelines and methodologies discussed in Chapter 4. 5.4 Summary In this Chapter we have applied an objective technique to 33 years of 5-day averages of 500MB height for the preparation of the geo-graphical distribution of blocking signature frequency in the Northern Hemisphere. The results are consistent with published investigations of frequency of actual blocking over the oceans, but they also reveal a large area, centred near Baffin Island (or, more precisely, the Foxe Basin) which is subject to a much higher frequency of blocking than these investigations would indicate. The paradox was rationalized. We% found a high incidence near the Pole in Spring and Summer in agreement with Perry (1979) and Treidl et a l . (1980a). There was also a high frequency of blocking signatures in a wide sector centred about 60°N, confirming the result of Baur (1958). Interseasonal comparisons of blocking frequency (highest in spring and summer, lowest in f a l l and winter) confirm previous studies. Cr i ter ia for identifying a blocking signature-sequence were used to prepare a Catalogue l i s t ing their attributes (Time and Location of In i t iat ion, Termination, Component Signatures and Intensity). A test of these sequences showed a strong relationship with actual blocking events, with a 96% success ratio for sequences 2 pentads duration and 62% for those of only one pentad duration. A comparison between the in i t i a l and f inal locations of the se-quence signatures revealed progressive and retrogressive tendencies dependent on the region of origin and'the time of year. 134 The interannual variation of blocking was placed on record but i t was not possible to draw stat is t ica l conclusions due to the size of the sample (33 years) relative to the time scale (order of 1 decade) of the fluctuations of interest. It is l ikely that these fluctuations are part of the natural var iabi l i ty of the prevailing climate regime (time scale order of 1 century). 135 CHAPTER 6 6. CONNECTIONS BETWEEN BLOCKING AND THE STATISTICAL MOMENTS OF THE 5-DAY MEAN HEIGHT FIELDS IN THE LOWER TROPOSPHERE 6.1 Rationale Nearly a l l the investigations into the stat is t ics of blocking are founded on the enumeration of episodes either subjectively from examination of sequences of synoptic analyses or (as in our case) by the application of objective analysis to a related parameter (e .g. , the blocking signature). Common to both these methods is the principle that a blocking episode wil l feature some characteristic extremum in the mid-troposphere such as the centre of the anticyclone or the centre of the associated positive anomaly. Unfortunately, in restr ict ing the data to an investigation of extrema, one pays the price of a severe reduction in sample size. Consider, for example, a proposal to investigate the frequency d is -tribution (spatial and temporal) of a l l s ignif icant positive and negative anomalies on 5-day average 500MB charts over the Northern Hemisphere during the past 33 years. This would be a more general study than the subject of this thesis. On a designated 5-day mean 500MB chart there are 1,977 data points or nearly 2,000 discrete values of gph. On the other hand, an examination of the Master Catalogue of positive and nega-tive anomalies (Fig. 4.2) discloses that there are about 20 anomaly centres per pentad. The data sample, therefore, has been reduced by two orders of magnitude. Moreover, i f we confine our attention (as this study does) to large positive anomalies north of a latitude threshold, we find there is s t i l l further reduction. Indeed the Blocking Signature Catalogue (Fig. 4.8) reveals an average of two per pentad. Thus, in terms 136 of sample s ize , there is an effective reduction of three orders of magni-tude from the original set of data. It is c lear, therefore, that for meaningful areal distributions of extreme values a very long record of data is required. Fortunately, the 33-year period did produce reasonably well defined spatial d is t r ibu-tions of blocking signatures (Figs. 5.2 to 5.5, inclusive) but i t is Obvious from the frequency isopleth labels that the number of occurrences per 381 km grid is very low. Consequently, i t seemed appropriate to return to the vastly greater original data set to determine whether i t would provide additional infor -mation on the nature of low frequency atmospheric var iabi l i ty and, in part icular, of the blocking process. 6.2 Purpose and Objectives So far we have confined this investigation to the 500MB level . However, i t is clear from previous discussions of the vertical charac-ter is t ics of blocking anticyclones that additional information from lower troposphere pressure levels is needed to better define the thermal struc-ture. This is part icularly important in winter over the continents. We decided, therefore, to compute seasonal normals and standard deviations of lOOOMB 5-day mean height and of 1000MB-500MB thickness. We shall examine Northern Hemisphere f ie lds of Standard Deviation at these levels for evidence of the influence of blocking on the var iabi l i ty of the atmos-phere. A second theme of this Chapter is that in view of the highly anomalous spatial and temporal characteristics of blocking, their total impact may in some way cause the distribution<of long term 500MB 5-day 137 mean height to depart s ignif icant ly from Gaussian in certain regions. The non-dimensional coefficients of the 3rd and 4th s ta t is t i ca l moments, skewness and kurtosis, provide a measure of such departures. Our objec-t ive , therefore, wi l l be to investigate hemispheric f ie lds of these param-eters at the 500MB level . We shall not necessarily confine a'ttention exclusively to 'con-tinuum' data. If the evidence so warrants, we shall investigate areas of signif icant skewness and kurtosis by using the Master Catalogue (Fig. 4.2) to prepare positive and negative anomaly frequency distr ibutions. This may assist with the interpretation of non-Gaussian distributions of low-frequency fluctuations and highlight the role of blocking. 6.3 Preparation of the Working Data Base 6.3.1 Conversion from sea level pressure to 1000MB gph We acquired from NCAR a 33-year set (1946-1978) of analyses of the daily sea level pressure for the Northern Hemisphere on magnetic tape. This was then converted into contiguous 5-day means in the manner des-cribed in Section 4.3.2. Subsequently, these were transformed into values of geopotential height of the concurrent 5-day mean 1000MB surface. A f i r s t approximation is ho - 3(p I  10°°' <"•" Where p = MSL pressure Z 1 Q = gph of 1000MB surface Thus isobars drawn at 4MB intervals on a MSL pressure analysis can be converted to 1000MB contours by relabell ing with a 3 dam interval. However, this approximation (6 dams per 8MB) assumes a uniform surface 138 temperature (- 0 °C ) , and the conversion factor should range from 5.5 dams (very cold arct ic air) to 7.1 dams (warm tropical air) per 8MBs of pres-sure. We therefore chose the method used by the Brit ish Meteorological Off ice, described by Moffitt and Ratcl i ffe (1972). The principle is that empirical relationships between lOOOMB and 500MB thickness and surface temperature can be used to provide an approximation for the latter. The algorithm is presented in Appendix VI - 1 and 2, inclusive. 6.3.2 (lOOOMB - 500MB) Thickness Five-day averages of the 500MB gph for the 33 year period over the Northern Hemisphere had already been computed (Section 4.3.2). Sub-traction of the lOOOMB gph from the 500MB gph immediately yielded the f ields of (lOOOMB - 500MB) thickness. 6.3.3 Seasonal Strat i f icat ion 0 In this Chapter, our continuum stat is t ics wil l be calculated by  Season and the resulting spatial distribution wil l be displayed geo-graphically. The nomenclature wi l l follow Chapter 4. WINTER WN (PE1 to PE ] 2 ) + (PE 6 8 to PE 7 3) SPRING SP (PE 1 3 to PE 3 1) SUMMER SU (PE™ to PE 49) FALL FA (PE 5 0 to PE 6 7) 139 6.4 Stat ist ical Moments Part I 6.4.1 -Normals and Standard Deviation Al l s tat is t ica l moments must be calculated from a baseline which is the mean of the variate. When the period of record reaches a duration (e .g. , 30 years) for which the mean may be conventionally accepted as representing the climatological average we shall refer to i t as the Normal (Appendix I). The details for computing the Normals and Standard Deviations wil l be found in Appendix VI - 3. Normals and Standard Deviation f ie lds for 1000MB and 500MB sur-faces and for (1000MB - 500MB) thickness have been prepared for each season and are available from the author. Those relevant to the discus-sion wi l l be displayed as figures within chapters. 6.4.2 Accuracy of Normal and Variance Fields If a population (33 years of record of daily gph) is divided into equal sub-sets (5-day means) then the average of the population equals the average of the sub-sets. Consequently our Normal Charts of 5-day mean gph are also Normals for daily mean gph. (The same does not hold true, of course, for the variance and higher moments.) The Normal Charts d of the 1000MB and 500MB f ields for the Winter .Figures 6.1 and 6.2, and Summer Figures 6.3 and 6.4, are in very good agreement with correspond-ing f ields calculated by Blackmon (1976) and Blackmon et a l . (1977). We were unable to find normal charts of gph for the Spring and Fall seasons in the l iterature and i t could well be that this is the f i r s t time they have been computed. Such charts have been prepared by calendar month, and our 500MB gph and 1000MB - 500MB thickness for Spring and Fall are consistent with corresponding f ields calculated by Moffitt and F i g . 6.1 Normal height of the 1000MB surface f o r WINTER (December 1 to February 28). Contours l a b e l l e d i n decametres (dams). Interval = 3 dams. 141 1'20E ]00E BOE F i g . 6 . 2 N o r m a l h e i g h t o f t h e 5 0 0 M B s u r f a c e f o r W I N T E R ( D e c e m b e r 1 t o F e b r u a r y 2 8 ) . C o n t o u r s l a b e l l e d i n d e c a m e t r e s l e s s 500 . I n t e r v a l = 6 d a m s . 535 d a m s c o n t o u r i 142 120E 100E BOE F i g . 6 . 3 As i n F i g . 6 . 1 except f o r SUMMER F i g . 6 . 4 A s i n F i g . 6 . 2 e x c e p t f o r S U M M E R 144 Ratcl i ffe (1972) for the mid-season months of April and October, res-pectively. Similar checks with other atlases, e .g . , Lahey et a l . (1958) and Crutcher et a l . (1970) reinforce confidence in our baseline Normal f ie lds . In the case of Standard Deviation, we are not aware of any other source where such f ie lds have been computed for 5-day average gph. We note that our 500MB Standard Deviation f i e ld for Winter (Fig. 6.5) corresponds closely with the low pass f i e ld of Blackmon (1976). It was also encouraging to note that our 1000MB Standard Deviation f i e ld for Winter (Fig. 6.6) was in good agreement with the low pass f i l tered Standard Deviation f i e ld of sea level pressure in Fig. 2(a) of the paper by Blackmon et a l . (1977). F inal ly , our results appeared to be consistent with Standard Deviation f ields computed by Moffitt and Ratcl i ffe (1972) after making allowance for the data base difference. 6.4.3 Interpretation of Standard Deviation Fields In Chapter 5 (Fig. 5.7 WINTER), we noted preferred longitudes for blocking signatures centred, in the mean, over the E Pacif ic (160°W), E Atlantic (30°W), Ural Mountains (60°E) and Baffin Island (70°W). These four locations correspond closely to the four Winter centres of maximum Standard Deviation at 500MB (Fig. 6.5) suggesting that large positive anomalies associated with blocking highs or ridges provide a signif icant contribution to the variation of gph North of latitude 50°. For a l l seasons there is a close correspondence between the geo-graphic var iabi l i ty of the 1000MB and 500MB gph f ie lds over the oceans, but they d i f fer s ignif icant ly over the continents, particularly in WINTER (Figs. 6.5 and 6.6). Consider, for example, North America and 1 4 5 i2oc j o o r . B o e F i g . 6.5 Standard deviation of 5-day average 500MB height f o r WINTER (December 1 to February 28). Contours (Interval = 2 dams) Intermediate (1 dam in t e r v a l ) contours — — — — 10 dam contour 146 120E )00E BOE F i g . 6.6 Standard deviation of 5-day average 1000MB height f o r WINTER (December 1 to February 28). Contour i n t e r v a l = 1 dam. 147 the North Atlantic. At 1000MB an axis of minimum variance extends from the Canadian prairies to the Northwest Territories and there is a well defined maximum centre over the North Atlantic (60°N 20°W). These fea-tures are found in approximately the same locations at 500MB but, at that leve l , there is a second area of maximum variance over Northeastern  Canada centred on Baffin Island with an intensity almost equal to the  Atlantic centre (16 dams). This relative difference in the variance pattern between the 1000MB and 500MB levels is related to the thickness f i e ld (Fig. 6.7) which also shows a maximum of var iabi l i ty over North-eastern Canada. Sawyer (1970) showed that there is a very high correla-tion between 500MB gph and 1000MB - 500MB thickness for fluctuations north of 50°N and with a period of » 15 days. In Northeastern Canada the correlation exceeds 0.90. What this implies is that not only is there a frequent occurrence of large fluctuations of 500MB gph and thickness in Northeastern Canada (because of the high Standard Deviations for both) but that they occur in tandem. Large amplitude fluctuations are caused by warm ridges (including blocking highs) and cold troughs (including cold lows). This area, centred on Baffin Island, must therefore not only be the seat of frequent large positive anomalies as we have already shown, but also of large negative anomalies. Now, as stated in Chapter 1, Section 1.2, the areal frequency distributions of negative anomalies (though not the subject of this thesis) were prepared and, indeed, the WINTER distribution of anomalies ^ -20 dams shows a strong concentration over Baffin Island and Northern Hudson Bay. This sheds more l ight on the Baffin Island Paradox (Section 5.3.6). That area, in spite of being located precisely under the Normal 500MB trough, is the seat of numerous fluctuations with periods £ 10 days. When the ' in s i tu ' anomaly is moder-ately to strongly positive the pre-existing trough is usually sp l i t by a .7 1 4 8 120E 100E BOE F i g . 6.7 Standard deviation of 5-day average 1000MB - 500MB thickness f o r WINTER. Contour i n t e r v a l = 1 dam. 149 blocking ridge (or high) as described in Section 5.3.6. On the other hand, when the ' in s i tu ' anomaly is large negative, there i s , usually near the normal location, an intense expanded cyclonic vortex dominating a vast area from Hudson Bay to Greenland. These large positive and nega-tive fluctuations in Northeastern Canada were also found to occur in the other three seasons. (In the case of blocking signatures see the s t r ik -ing annual pattern depicted in Fig. 5.1.) We could not find a counterpart to the behaviour of the North-eastern Canadian trough in other parts of the hemisphere. The East Asian trough does show the 500MB and thickness f ie lds fluctuating in tandem in WINTER, but the respective patterns of maximum variance reside at a lower latitude (30°N to 50°N) and are less intense. By SUMMER the reversal of the continent-ocean temperature regime is complete and the East Asian baroclinic trough has essential ly disappeared. Over the Oceans, well-defined areas of maximum Standard Deviation at 1000MB and 500MB are in near coincidence for a l l seasons, but i t is interesting to note that these areas are not the residence of correspond-ing relative maxima of thickness variance. The correlation between 500MB gph and 1000MB - 500MB thickness is s t i l l high (greater than 0.8 accord-ing to Sawyer) but in WINTER, for example (Figs. 6.5 and 6.7), the 500MB Standard Deviation of 16 dams at the maximum (centred at 57°N 28°W) is greater than the thickness Standard Deviation by a factor of two. An examination of the distribution of the 3rd and 4th moments of these res-pective variates may throw additional l ight on the difference in behaviour of the longer period fluctuations over continent and ocean. 150 6.5 Stat ist ica l Moments Part II For reasons already given we decided to examine the extent to which the temporal distribution of the 5-day average gph and thickness over the 33 years of record, and at each of the 1977 grid points, departed from Gaussian. We followed the methodology of White (1980) and calculated f ields of the 3rd and 4th moments about the mean or, more spec i f i ca l l y , the non-dimensional coefficients of skewness and kurtosis, respectively. 6.5.1 Skewness Skewness is the measure of the departure of a frequency d is t r ibu-tion from symmetry. It is zero for a Gaussian distr ibut ion, usually "positive" i f the mode l ies to the lef t of the mean so that the f re -quencies fa l l off sharply to the lef t and usually "negative" i f the mode l ies to the right of the mean (Fig. 6.8). Skewed distributions of atmos-pheric variables are not uncommon particularly in the case of discrete events such as amount of r a in f a l l . Skewness is measured in an absolute sense by the third moment about the mean " 3 " ft-F— and the relative asymmetry, which takes account of the size of the Standard Deviation (= a), is given by the non-dimensional coeff icient There are other measures of skewness but this has general acceptance in the meteorological l i terature. H I G H K U R T O S I S F i g . 6.8 Schematics: P O S I T I V E / j S K E W N E S S L O W K U R T O S I S C K < 3 - 0 Skewness and K u r t o s i s 152 The standard error of skewness is given by S.E. - (6/n)4 Where n = number of s ta t i s t i ca l l y independent observations (Brooks and Carruthers, 1953). One of the problems in the s tat is t ica l treatment of parameters of the atmospheric continuum is that consecutive observations at conventional time intervals (hourly, da i ly , etc.) are not independent. However, the longer the time interval the less the dependence. To explore the re la -t ionship, Madden (1976) estimated characteristic intervals for effec-t ively independent sample values for Northern Hemisphere sea level pres-sure. He found that for January the intervals ranged from two days over the Southern U.S.A. to eight days over the Eastern North Atlantic. For July they ranged from less than two days west of the Great Lakes to greater than five days in the mid-oceans. These results would apply to our 1000MB data and in agreement with White (1980) there is no apparent reason why they would d i f fer s ignif icant ly at 500MB. By season, for a given grid-point we had 18 x 33 = 600 observa-tions averaged over contiguous 5-day intervals. As an ensemble they are probably considerably less interdependent than daily values. In view of Madden1s results i t is reasonable to infer that our sample contained the equivalent of about 500 independent observations per season, so that the standard error of skewness was t S.E. = ( 4 ) ^ ±0.11 153 Turning now to Table 6.1, we concluded that i f the calculated Skewness Coefficient (CS) was outside the range ±0.22, i t would be signif icant ly different from Gaussian at the 95% level of confidence. The CS computation is outlined in Appendix VI - 4. Values of the skewness coefficients were computed by season for the 500MB and 1000MB levels and 1000MB - 500MB thickness. These charts are available from the author. We shall discuss the interpretation of those of immediate interest in section 6.6. 6.5.2 Kurtosis A distribution may be symmetrical and at the same time s ign i f i-cantly non-Gaussian. On the one hand i t might be sharply peaked at the centre because of an excess frequency of small deviations, and on the other i t might be blunted because of a preponderance of large positive and negative deviations. The fourth moment is an absolute measure of this feature "4 - £ —R and kurtosis is the term given to the relative measure, the non-dimensional coefficient For a Gaussian distribution CK = 3 For a Peaked (Leptokurtic) distribution CK > 3 For a Blunted (Platykurtic) distribution CK < 3 These are shown schematically in Fig. 6.8. TABLE 6.1 Range of coefficients of skewness and kurtosis outside  of which the distr ibution is s ignif icant ly different (at the 95% confidence level) from a Gaussian d is t r ibu-t ion, as a function of N, the number of independent events (adapted from Brooks and Carruthers, 1953 and White, 1980) N Skewness Kurtosis 100 ±.49 2.27 to 4.06 150 ±.40 2.38 to 3.88 200 ±.35 2.45 to 3.76 500 ±.22 2.62 to 3.48 1000 ±.16 2.72 to 3.33 2500 ±.10 2.82 to 3.20 155 A possible cause of platykurtosis could be that the population contains (perhaps as sub-sets) two atmospheric distributions with d i f f e r -ent means. Brooks and Carruthers (1953) give a number of examples. In extreme cases the distribution may become bimodal with two maxima, one on either side of the mean. From Table 6.1 we concluded that i f the Coefficient of Kurtosis was outside the range 2.6 to 3.5 i t would be signif icant ly different from Gaussian at the 95% level . Calculation of the CK f ields is detailed in Appendix VI - 5. Charts showing the spatial distr ibution of signif icant kurtosis for 1000MB and 500MB, by season, are available from the author. Interpre-tation wi l l follow in Section 6.6. 6.5.3 Comparison of CS and CK Fields with Other Results The Skewness and Kurtosis f ie lds were consistent with those pub-lished by Moffitt and Ratcl i ffe (1972) and White (1980). These authors used daily data rather than 5-day averages, and Moffitt and Ratcl iffe calculated monthly instead of seasonal s ta t i s t i cs . However, as was the case with Standard Deviation, the lower frequency fluctuations appear to dominate the third and fourth moments. Thus patterns of isopleths were similar with regard to gradient as well as shape. 6.5.4 Site-specif ic Frequency Distributions To assist with the interpretation of the Skewness and Kurtosis f ie lds we shall present frequency distributions for sites representative of regions of interest. These distributions wil l be prepared in two different ways. One histogram wi l l show frequency vs 500MB 5-day aver-age height (the 'continuum'). The other wil l show frequency vs 500MB 5^ -day average height anomaly (the 'extremum'). 156 The 'continuum' histograms were obtained from White 0 980) and Moffitt and Ratcl i ffe (1972). They are for point locations chosen for their proximity to the centre of the area of interest. The 'extremum' histograms were prepared from our Master Catalogue. For the grid-point centred upon the region of interest and the surrounding eight points, we manually recorded a l l anomaly centres > +5, +10, +15, . . . . . dams and < -5, -10, -15, dams This provided a sample of suff ic ient size to be s ta t i s t i ca l l y s ignif icant. Both types of histogram wi l l be used to i l lust rate the interpreta-tion of CS and CK f ields in the next Section. 6.6 Interpretation of Distribution of Skewness and Kurtosis in the  Northern Hemisphere 6.6.1 Skewness 6.6.1.1 WINTER - POSITIVE In WINTER (Fig. 6.9) positive skewness is characteristic of the high latitudes. There are three dominant areas centred respectively over the Bering Sea, the NE Canadian Archipelago and the NE Atlantic Ocean between Iceland and Scandinavia. We shall examine the two f i r s t-named areas in further deta i l . (a) Bering Sea The large positive skewness of the 'continuum' distribution at 55°N 175°E is clearly indicated by comparison of the histogram in Fig. 6.10(b) with the superimposed normal curve for the same mean and 157 120E ]00E BOE F i g . 6.9 Skeyness of 5-day average 500MB height f o r WINTER (December 1 to February 28). Contours l a b e l l e d CS x 100. Interval = 10. Areas below l e v e l of significance (Table 6.1) not contoured. 158 BERING S E A W I N T E R (°) EXTREMUM 6 4 c a s e s f 22 20 1 8 + , 16 14 12 10 8 - 6 4 2 TJ C o n t i n u u m S t a t i s t (5-day mean 5 0 0 m 8 8 N 1 T 5 W Z = 523 d a m s O = 15 C S = + 0 - 8 1 * C K = 3-40 i cs b * 5 0 c a s e s - 4 0 - 3 0 - 2 0 - 1 0 10 20 30 4 0 50 60 Z - 2 (dams) (b) CONTINUUM f 4 0 0 k-3 0 0 200H 1 0 0 h -C o n t i n u u m S t a t i s t i c s (_t_w i c e - d a i l y 5 0 0 m b ) S 5 N 1 7 5 E Z a 52 3 d a m s O = 16 C S = +.0 r 7 0 * C K = 3-32 (dams ) Pig. 6.10(a) Frequency of 500MB Extremum occurring within 9-point grid centred on 58K 175V (Knox). (b) Frequency of 500MB height at 55N 175E for Winter. Curve shows Gaussian distribution with same mean and variance. (Adapted from White,. 1980). * . indicates significant at 95$ level. 159 variance. The upper panel, Fig. 6.10(a), shows the striking difference between the distr ibution of positive and negative anomalies in the region centred on 58°N 175°W. The two panels are consistent with what is ob-served from mid-tropospheric analyses for the Bering Sea in Winter (O'Connor, 1964). At the 500MB level the large number of fluctuations clustered about a mode of 510-515 dams result from deep cyclones that usually have their genesis in the normal East Asian Coastal trough. However, although a cyclonic regime predominates, the distribution on the right hand side of Fig. 6.10(a) te l ls us that the Bering Sea not infrequently becomes the site of large positive anomalies. The majority of these are blocking signatures (Fig. 5.2). We may reasonably conclude that the positively skewed dist r ibu-tion is partly attributable to the frequency of blocking episodes. (b) The Northeast Canadian Archipelago To i l lust rate the continuum distribution for the Northeast Canadian Archipelago we used a histogram for 80°N 100°W (Fig. 6.11(b)). That loca-tion is about 750 km NW of the centre of maximum CS. Nevertheless, i t . is within the area of interest and does confirm the strong positive skew-ness characteristic of the region. The upper panel Fig. 6.11(a) for an area centred on 71°N 69°W shows an anomaly frequency distribution some-what similar to that for the Bering Sea. As previously noted, this area is the residence of the normal winter 500MB low. The gph fluctuates about the mean value of 506 dams as the Baffin Low gyrates about i ts normal position and increases or decreases in intensity. On occasion, however (as described in Section 5.3.6), the region is subject to a regime of a very different type. The 160 NE CANAD IAN A R C H I P E L A G O W I N T E R (a) EXTREMUM 22 2 0 18 16 75 c a s e s - 4 0 - 3 0 - 2 0 - 1 0 6 2 c a s e s ib 2 0 C o n t i n u u m s t a t i s t i c s ( 5 - d a y m e a n 5 0 0 mb) 71 N 6 9 W Z - 5 0 6 d a m s a s 1 5 " CS = + 0 - 6 0 * | C K s 3-2 0  3 0 4 0 5 0 6 0 Z - Z (d am6 (b) CONTINUUM C o n t i n u u m s t a t i s t i c s ( t w i c e d a i l y 5 0 0 mb) 8 0 N 1 0 0 W Z t 5 0 4 d a m s a = i 5 .. cs = +o-63 * C K = 4 7 0 4 8 0 4 9 0 5 0 0 5 1 0 5 2 0 5 3 0 5 4 0 5 5 0 5 6 0 5 7 0 d a m s F i g . 6.11(a) As i n F i g . 6.10(a) except f o r 71N 69W (Knox). (b) Frequency of 500MB height a t 80N 100W f o r January. (Adapted from M o f f i t t and R a t c l i f f e , 1972) # = s i g n i f i c a n t a t 95$ l e v e l . 161 associated positive anomaly is well above the winter blocking signature threshold (16 dams) as indicated by Fig. 6.11(a). Clearly, these are episodes which contribute to the striking blocking signature maximum of Fig. 5.2. Again we conclude, as in the case of the Bering Sea, that the positive skewness characteristic of the distribution of 500MB height over the Northeast Canadian Archipelago is attributable in part to the nature and frequency of blocking episodes. 6.6.1.2 WINTER - NEGATIVE Returning to Fig. 6.9, we note vast regions of negative skewness over the oceans between 20°N and 40°N. In this latitude zone, the southern half of which is the normal residence of the sub-tropical ant i -cyclone, the 500MB height fluctuates about a high mean value. However, slow-moving persistent cold troughs and lows do penetrate from time to time and the consequent large negative anomalies of 5-day average heights cause the distribution to ta i l to the l e f t . These lower latitude cold lows often are generated by the blocking process i t s e l f , especially i f i t is in i t iated by an upstream sp l i t jet (Fig. 3.3(a)). 6.6.1.3 SPRING, SUMMER, FALL In SPRING and FALL, not shown, the patterns of positive skewness are similar to WINTER, although there is noticeable weakening over the Northeast Atlantic. In SUMMER, however (Fig. 6.12), positive skewness has weakened everywhere except for the emergence of a maximum to the southeast of Greenland. Indeed, over the Northeast Canadian Archipelago the pattern characteristic of the other seasons has disappeared entirely. At f i r s t sight this is surprising because in SUMMER, Blocking Signature frequencies remain high (Fig. 5.4). Note, however, that the Signature 162 120E 100E BOE F i g . 6 . 1 2 As i n F i g . 6.9 except f o r SUMMER 163 frequency centre is located about 10 degrees longitude west of i ts WINTER position. Meanwhile, by SUMMER, the Baffin trough has moved about 10 degrees east (Fig. 6.4). We infer that the reversal of the ocean-continent thermal regime has played a signif icant role in changing the character of regime alternation over the Canadian Archipelago and also over the Bering Sea. We suggest that dynamic processes which seem to result in a re la -tionship between blocking in high latitudes and positively skewed dist r ibu-tions in Winter, Spring and Fall are strongly modified in Summer. Further investigation wil l be reserved for future research. Negative skewness in SUMMER remains large in sub-tropical latitudes but there is a dist inct northward shif t in pattern. This is consistent with the seasonal northward migration of the sub-tropical anticyclone and the mid-latitude westerlies. Around the 20°N para l l e l , regions of positive skewness become d is -cernible. Moreover, there is a remarkably well defined area centred near 25°N 100°E, which is approximately the location of the normal upper troposphere anticylone centre associated with the Asiatic Summer monsoon. The positive skewness in a l l these regions is probably attributable to anomalous events in the Intertropical Convergence Zone. Though not direct ly connected with the subject of this thesis, i t should warrant further investigation. 6.6.2 Kurtosis In WINTER (Fig. 6.13) s ignif icant ly high kurtosis ( i . e . , ^ 3.5) occurs over the Arctic regions immediately to the north of Canada and also over wide swaths of the sub-tropical oceans. On the other hand, s ignif icant ly low kurtosis ( i . e . , < 2.6) extends from the mid- to east 164 120E 3 00E BOE F i g 6 .13 Kurtosis of 5-day average 500MB height f o r WIN-TEH (December 1 to February 28). Contours l a b e l l e d CK x 1.00. Interval = 20. Areas below l e v e l of significance (Table 6 .1) not contoured. 165 Pacif ic Ocean along the 40°N to 50°N latitude zone, and also from the central Atlantic Ocean to Scandinavia and Northern Russia. To further examine the nature of these low kurtosis distributions we present histograms for two locations near 'A' over the Eastern At lant ic . Fig. 6.14(b), for 52.5°N 25°W, clearly shows a platykurtic distribution for continuum data. The distribution for frequency extrema (Fig. 6.14(a)) is for an area centred at 57°N 22°W. It reinforces the inference that over area 'A' the atmospheric regimes can be c lass i f ied into two-sub-sets each with 1a different mean of 500MB gph. The interpretation in terms of blocking wi l l be reserved for the next section. The Eastern Atlantic -Scandinavia low kurtosis persists throughout SPRING, SUMMER and FALL (not shown). Over the Pacif ic Ocean, however, each season shows a noticeable weakening from the winter pattern. 6.6.3 Further Discussion We shall confine this discussion to the WINTER distributions of skewness and kurtosis to avoid complications introduced by the ocean-continent temperature reversal. As indicated ear l ier the low kurtosis over the eastern halves of the mid-latitude oceans indicates that the 500MB height population con-sists of two sub-sets which have frequency distributions with different means. Is i t possible that the distributions arise from two types of regime, one of which includes the ensemble of nascent or maturing block-ing systems? We have noted from a large number of case studies that the birth and growth of the blocking wave appears to take place in regions of low kurtosis. The wave crest amplifies rapidly northward (often without appreciable change of phase) and culminates in a strong blocking anticyclone in the higher latitudes. ! 166 N O R T H E A S T A T L A N T I C W I N T E R (a) EXTREMUM 69 c a s e s f ' 4 20-18' 16. I A I 2 10 8 - 6 4 2-\ 5 0 -40 - 3 0 -20 -10 C o n t i n u u m S t a t i s t i c s (5-day m e a n 500 mb ) 5 7N 2 2 W z - 5 34 dams a = 16 -C S = +0-2 I C K - 2 - 4 0 * I 0 4 4 c a s e s 20 30 40 50 (dams) (b) CONTINUUM C o n t i n u u m S t a t i s t i c s (t wi ce-d a i I y 5 0 0 m b) 5 2-5N 25 W z = 545 d a m s 0 = 1 9 C S - -0-1 0 C K = 2-2 3 * g i g . 6.14(a) As i n F i g . 6.10(a) except f o r 57N 22W (Knox). (b) As i n P i g . 6.10(b) except f o r 52.5N 25W f o r Winter (adapted from White, 1980). 167 In the case of the Northeast At lant ic , i f the blocking is retro-grade, the blocking wave often moves into the Canadian Archipelago and the resulting positive anomaly of 500MB height is a factor in creating the large positive skewness observed in Winter distributions for that area. If i t is quasi-stationary i t wi l l persist over the Iceland-Scan-dinavia region. The strong positively skewed distribution over this area (Fig. 6.9) may be attributed to the relative frequency of these events. If progressive, the blocking wave wil l proceed across the northern Eurasian continent. The distribution of positive Coefficient of Skewness between 60°N and 70°N extending into northeastern Siberia is suggestive of the influence of this category. Turning now to the western hemisphere, the Bering Sea appears to be the graveyard, or the crossroads, for blocking anticyclones from three directions. We have already mentioned how northward amplification from the central and eastern Pacif ic Ocean brings warm blocking anticyclones into that region. From the discussion of Signature Sequences in Chapter 5, there is evidence that the Bering Sea also received blocks retro-grading from Alaska, or less frequently, progressing from Siberia. What seems to emerge from this analysis is the impression that blocking systems evolve in a manner somewhat analogous to unstable baro-c l i n i c cyclones. The in i t ia t ion of both processes begins well south of the termination. The f inal stage of the typical baroclinic cycle is the cold cyclonic vortex in the high latitude with, of course, higher gph to the south. The f inal stage of the typical blocking cycle is the reverse, a warm high latitude anticyclone and, frequently, low gph to the south. Moreover, the dimensions of blocking waves in the mid-troposphere are larger than synoptic scale baroclinic waves. It would appear then that blocking may be init iated by the real ization of baroclinic instabi l i ty 168 in the long-wave part of the spectrum (Fig. 2.9). This view has already been given some theoretical just i f i cat ion by a number of authors quoted in Chapter 2. The subsequent response to the amplifying wave in terms of large scale vort ic i ty redistribution results in the characteristic quasi-barotropic structure of the blocking system components. It would appear, then, that the blocking phenomenon is real ly a manifestation of long-wave amplif ication, and that a climatological-diagnostic study would hardly be complete without a treatment in that context. This we propose to do in the next chapter. 169 ' CHAPTER 7 7. HARMONIC ANALYSIS OF THE 500MB HEIGHT DURING BLOCKING EPISODES IN WINTER 7.1 Rationale So far in this dissertation we have perceived blocking config-urations as spatial ly isolated anomalies of the large scale mass d is -tribution in the troposphere. Their features were described in 'conf ig-uration space1 Ci-e., as they appear on conventional synoptic analyses) using for reference the NMC I,J gr id. This afforded the most convenient method of identif icat ion for heuristic diagnostics and also for obtain-ing the stat is t ica l results presented in Chapters 5 and 6. Sometimes, however, additional insights into attributes of physical systems (e .g . , the 500MB height f ie ld) may be obtained by specif ication in terms of functions related to characteristic responses of the atmosphere (e-g-> osc i l la t ions) . Some aspects of the large scale responses of the atmosphere to thermal and mechanical forcing were reviewed in Chapter 2. These are customarily described as the planetary and synoptic scale waves, the resultant of which provides the main features of the tropospheric motion systems. Moreover, whatever the generic causes, blocking seems ultimately to be a manifestation of such large scale interaction. We therefore decided to investigate blocking in 'wave number space'. To do so i t was necessary to specify the 500MB height f i e ld Z ( A , 0 , t ) i n terms of sinusoidal functions.^ The technique, harmonic In this Chapter e designates latitude and <f> is reserved for phase angle of the zonal harmonic. 170 analysis, is well-known and the application to our specif ic problem wil l be outlined in Section 7.3.3. 7.2 Objectives 7.2.1 Our f i r s t objective was to determine whether the spatial harmonics  of blocking episodes were dist inct ive to the region in which they occurred. For example, were the spectral attributes of Northeast Pacif ic - Alaska blocks characterist ical ly dif ferent, on average, from those which reside in the North Atlantic - Greenland area? If so, was there a connection between these attributes and those of the normal 500MB height distribution for the winter season? A similar investigation, which was conducted concurrently, has been reported by Austin (1980) and we shall compare results in Section 7.4.1. 7.2.2 The second objective was to pursue our investigations of the  'Baffin Island Paradox1 by an interpretation of the spectral s tat is t ics arising out of the results of 7.2.1, above. We also applied harmonic analysis to typical cases of retrogressive and progressive blocking in the Baffin area. The extent to which blocking waves crossing this region originated upstream or downstream was also determined. A count was made of progressive vs retrogressive blocking signatures during the past 33 winters. 7.2.3 The third objective was to examine the spectral circumstances  associated with interruptions to persistent regimes of large amplitude  waves. These are regimes, sometimes of several weeks duration, during part of which one or more major blocking episodes wil l be in progress. The interruption is characterized by a sudden increase in the zonal 171 westerlies, a condition which, at any given lat i tude, is relat ively transitory (^ -a few days). 7.2.4 Our fourth and f inal objective was to i l lust rate how zonal har- monics from 20°N to the Pole could be related to salient features of a  complete major blocking system, including the frequently occurring cyclonic structure south of the blocking anticyclone. 7.3 Methodology and Techniques 7.3.1 Data Base We confined our investigation primarily to the data of seven winters, namely: December 1, 1946 - February 28, 1947 90 days December 1, 1949 - February 28, 1950 90 days December 1, 1955 - February 29, 1956 91 days December 1, 1962 - February 28, 1963 90 days December 1, 1968 - February 28, 1969 90 days December 1, 1976 - February 28, 1977 90 days December 1, 1978 - February 28, 1979 90 days The occurrence of major blocking episodes during these winters and their profound impact on the short term climate has been well documented in the l iterature (for example, Namias (1975) and the Monthly Weather Review issues referenced in the bibliography). Although our definit ion of the WINTER season is December, January and February, we added November and March to the data base of each winter except 1978-79 for which March was not available. Data for these flanking 172 months would be necessary to determine the complete l i f e history of those blocks which happened to be already in progress on December 1st or those which had not terminated by the end of February. For the purpose of frequency analyses documented in Chapters 4, 5 and 6, we found that the 5-day average of 500MB height was a practical temporal resolution. On the other hand, a p i lot study of the harmonic analysis of 1977-78 daily data revealed that there were a signif icant number of occasions when the genesis and dissolution of long-wave com-ponents occurred quite rapidly (one to three days). We therefore chose to use daily data for the harmonic analyses of this chapter. The 1200Z 500MB geopotential height for each day of the seven winters (and flanking months) at each point of the NMC grid was extracted from the 33-year record described in Section 4.3.1. These heights were then interpolated to each 5-degree intersection of Latitude and Longitude. A typical major blocking system may extend from the sub-tropics to the Arct ic . Therefore, i t was decided to compute the above values of Z(x,e,t) for every 5° parallel of Latitude from 25°N to 85°N. These arrays constitute our working data. It is from them that subsequent derived data were computed, using techniques to be described in the following sections. 7.3.2 Selection of Representative Latitudes for Analyses and Display  of Results For the investigations into the change of Z(x,e,t) (and harmonics) with time, i t was clearly necessary to select representative latitudes (or zones). The choice of the northern latitudes was based on Fig. 5.2 which shows the areal frequency distribution of blocking signatures during the WINTER. The preference for the 50°N to 70°N zone is unmistak-173 able. Consequently, we decided that Z(x,t) at 60°N or, alternatively, averaged between 50°N and 70°N would be the data most l ike ly to indicate the blocking anticyclone evolution and i ts zonal component of motion. Moreover, from examination of a large number of total blocking system episodes (e.g. , Figs. 2.3 and 2.4) i t appeared that the associated flank-ing cold lows are usually centred between 30°N and 50°N. Therefore, we selected Z(x,t) around 40°N/or mean values for 30°N to 50°N, to approxi-mate salient features of the southern structure. Since ear l ier p i lot studies had shown that only the lower wave numbers (1 to 6) would be of consequence, we f e l t that the spatial smoothing of Z by latitude zone would be advantageous since i t would suppress higher wave number 'noise 1 . As i t turned out the difference for a l l practical purposes was not appreciable. Some results wil l be displayed based on data from cross-zonal averaging while others wi l l use discrete latitudes, and the plots wi l l be identif ied accordingly. 7.3.3 The HovmoTler Diagram To obtain a visual perspective of the day-to-day evolution of hemispheric 500MB height, we used a simple but effective diagram named after the Swedish meteorologist Hovmoller (1949). It depicts the varia-tion of Z(x ,e n ,t) by longitude (abscissa) and time (ordinate) around a specified parallel of latitude e n (or latitude zone). Figure 7.1 is an example, computed from data for the period December 1, 1962 to March 31, 1963. Note that in order to complete patterns which happened to be truncated by the Greenwich meridian (x = 0), the right hand boundary was extended to x = 30°E. Isopleths of 500MB height Z(x,t) are drawn at an interval of 10 dams and, for brevity, labeled with values of (Z - 500). Areas of high geopotential are shaded. 174 HOVMOLLER 500MB flVG(50N-70N) DEC 1.1962-MRR 3].1963 F i g . 7.1 Hovmoller Diagram of 500MB height p r o f i l e averaged across the zone 50°N - 70°N. Ridges are shaded. Positions (x,t) of Blocking Signatures marked • . Isopleths l a b e l l e d Z - 500. Contour Interval =10 dams. 175 The large amplitude long-wave patterns osci l lat ing about their mean winter position are clearly evident. Westward (retrograde) motion, indicated by the downward t i l t to the lef t of the isopleth axes, is not uncommon, particularly in the 50°N to 70°N zone where planetary vort ic i ty advection may be the determining factor. The smaller amplitude transient troughs and ridges, usually asso-ciated with synoptic scale waves, are particularly evident in the 30°N to 50°N zone (Fig. 7.2), a region of maximum baroclinic act iv i ty during the winter season. Their eastward progress, reflected by the downward t i l t to the right of the axes, is also apparent. Blocking signatures, marked •, have been superimposed on Fig. 7.1. The close correspondence between their motion and the long wave 'r idge' axes would appear to confirm the choice of the 50°N to 70°N zone for harm-onic analysis of blocking episodes. Hovmoller diagrams of 500MB height have been prepared for each of the selected winters; those for 1978-79 wil l be found in Appendix VII, Fig.-1 and-2. For convenient calculation of speed (W to E) of troughs and ridges, Table VII-1 has been provided. Notwithstanding the usefulness and convenience of the Hovmoller diagram as a compact source of information for diagnostic purposes, i t should be used with some reservation. It i s , after a l l , a one-dimensional profi le of two-dimensional patterns and cannot therefore indicate the N-S components of structure or motion. For case study diagnostics i t should i f possible be complemented by sources of data which provide this informa-tion such as daily or 5-day mean 500MB Analyses. 176 HOVMOLLER 500MB RVG(30N-50N) DEC 1.1962-MRR 3J J963 F i g . 7.2 Same as Fi g . 7.1 except f o r 30°N - 50°N and without blocking signature locations. 177 7.3.4 Zonal Harmonic Analysis of the 500MB Height Field (a) One-dimension We shall summarize here, following Boville and Kwizak (1959) the discrete Fourier series method for calculating the f i r s t six harmonics of the instantaneous distribution of 500MB height around a specif ic  latitude (or zone). Let Z(x.)' = 500MB height at longitude and divide the latitude into 72 equal intervals so that.x. = 0, 5 ° , 10°, etc. Then Z(X.) = a + 2 (a cos n X. + b sin n x.) + R i o ^_ -j n i n I Where* a 72 = -A- 2 Z(X.) = mean of Z(x.) = Z o IL i = 1 i I 72 1 2 Z(X,) *n 36 r~j - ' V c o s n X i 72 4 2 Z(X,) — - v " - / sin n x. n 36 i = 1 v i ' i 35 Residual = 2 (a cos n X. + b sin n X.) n=7 n i n i We used the reformulation: 6 ZCxn.) = AQ + 2 A n cos (n X. - <j,n) +R 178 Where A = Amplitude = and <j> = Phase angle = tan" b/a y n n n 72 2 [ZUJ - if The Variance = a = 2 72 For brevity, the harmonics (A ,<(» ) wi l l be designated as Wp. Now a is proportional to the eddy ( i . e . , wave) kinetic energy of the circulation and i t can be shown that Values of A , a, A , * and S were determined for each day at every five degree latitude and also for values of Z(x,t) averaged across the two zones (30°N - 50°N) and (50°N - 70°N), respectively. The results for latitudes 60°N and 40°N for the period December 28, 1962 to February 17, 1963 show that the f i r s t six components contribute on  average about 95% of the total variance for the zone 50°N to 70°N and about 85% for the zone 30°N to 50°N. These results are entirely consis-tent with Eliasen (1958) and Barrett (1958). (Godson, 1959) The percentage of the total variance contributed by W wi l l be designated S and therefore 179 (b) Two dimensions (i) Day-Specific Harmonics Since values of A^  and $ were available for every 5 degrees of latitude from 25°N to 85°N i t was a straightforward matter of inter-polation to prepare, for a selected calendar day the two-dimensional representation of Wn> Analyses showing the spatial distribution of A n were constructed for December 23, 1978 and January 4, 1979 and the results wi l l be discussed in Section 7.4. ( i i ) Normal Harmonics One of our objectives was to compare the phase of harmonics during blocking episodes with those for the normal WINTER distribution of 500MB height. Therefore, analyses were completed for the f i r s t four normal harmonics. (Wave 2 is displayed in Fig. 7.3.) These normals wi l l be used for baseline reference purposes during the presentation of results in Section 7.4. (Note that the contour interval for the Normal Charts is 1 dam, whereas for day-specific Charts, when amplitudes are much larger, the interval has been increased to 3 dams.) The complete set of Normal Charts W-j to W^  wi l l be found in Appendix VII, Figs. VII - 3 to VII - 6, inclusive. 7.3.5 Temporal Variations of the Zonal Harmonics at Selected Latitudes (a) Zonal Profi le of A (x,t) Hovmoller diagrams of the f i r s t four harmonics for the two l a t i -tude zones were constructed for each of the seven winters. An example is provided by Fig. 7.4 showing the temporal variation of the prof i le of 180 120E 100E 80E Fig- 7.3 Second harmonic (W2) of the normal 500MB height f i e l d f o r WINTER (December 1 to February 28). Contours l a b e l l e d i n decametres. Interval = 1 dam. 181 F i g . 7.4 Time-Longitude (Hovmoller) diagram of Second Harmonic of 500 MB height p r o f i l e averaged across the zone 50 N - 70 N. Contour Interval = 5 dams. 182 the second harmonic, to^, around the zone 50°N to 70°N for the winter of 1962-63. (b) Variation of Amplitude and Phase To focus exclusively on the change of amplitude and phase of the long-wave components we followed Haney (1961) and plotted A n and <(> against time for selected latitudes and wave numbers of interest. Fig. 7.5 shows the variation with time of the amplitude and phase ^ of the second harmonic W2 around latitude 60°N for 1962-63. 7.3.6 Computation and Presentation of Zonal Indices of U, V and U/V The evolution of the expanding circumpolar vortex was br ief ly d is -cussed in Section 2.6 and i t was noted that the blocking phenomenon is frequently associated with a southward shi f t of a zonal wind maximum into the sub-tropics. We therefore measured the following variables at selected latitudes (or latitude zones) and plotted them against time: For this study t = calendar day A = longitude (at increments of 5 degrees) [] = symbol for "average taken around a paral lel (or zonal band) of latitude" u^  = W - E algebraic component of geostrophic wind measured every 5° longitude F i g . 7.5 Amplitude and phase angle of wave number 2 at 60°N as a function of time. amplitude i n dams phase angle i n degrees longitude CO 184 R t is the zonal average of u^  Vj. is the zonal average of |v .^| and R t may be interpreted as an indicator of the degree of predominance of zonal over meridional around a specif ic latitude. The variation of U t for the 1962-63 winter for 50°N to 70°N and 30°N ,to 50°N, respectively, is shown in Fig. 7.6. It is evident that the IIt maxima for the northern zone tend to coincide with minima for the southern zone and vice versa. This observation is consistent with the s tat is t ica l result of a strong correlation between maxima at 60°N and u"t minima at 40°N (Panofsky and Br ier , 1968). That study also found a signif icant lag correlation indicating that zonal maxima at 60°N pre-cede those at 40°N, a result that f i t s the concept of a winter-time process of quasi-cyclical circumpolar vortex expansion. The variation of R^  wi l l be discussed in Section 7.4. 7.3.7 Concluding Remarks We now have the information base and analytical techniques re-quired to proceed with the four objectives outlined in Section 7.2. The results wi l l be presented in the next Section. i f " l » t | d x - [ | v t | ] Jo |v t | = absolute value of the N - S component measured every 5° longitude V v t F i g . 7.6 Comparison between U t 50°N - 70°F and TJt 30°N - 50°.N 186 7.4 Presentation of Results 7.4.1 Spectral Attributes of Blocking by Region of Occurrence Our f i r s t objective was to determine how the spatial harmonics of blocking were related to the region in which the episodes occurred. A sample of cases was selected from each of the following regions: Location Category No. of Cases No. of Days Eastern Pacif ic - Alaska (180W - 120W) 5 42 Baffin - Hudson Bay (100W - 60W) 4 26 Northeast Atlantic - Greenland (60W - 0) 6 42 Western Europe (0 - 60E) 5 39 Double Blocking (Atlantic-Pacific) 5 43 The cases were selected from the Blocking Signature Sequence Catalogue and confirmed by the daily Synoptic Analyses or the Monthly Weather Review. A case (except for Double Blocking) could only qualify provided there was no signif icant concurrent blocking elsewhere in the Northern  Hemisphere. This usually had the effect of reducing the duration of e l ig ib le cases to five to eight days. Some winters (e .g. , 1962-63, 1978-79) featured pronounced regimes  of concurrent major blocking, usually over NE Pacif ic - Alaska and NE Atlantic - Western Europe. These "Double Blocking" episodes were always associated with extremes of weather, often with serious social and economic consequences. We therefore created a "Double Blocking" category and selected a sample of cases in the manner described above. We also decided i t would be useful to compare the mean harmonics for the categories in the above tabulation (for which i t would be reason-able to assume the circulation at 60°N would have a strong meridional 187 component V) with those for situations of predominantly zonal flow. We therefore created a "Zonal" category and e l ig ib le cases were selected with reference to plots of U and R as described in Section 7.3.6. We looked for coincident maxima in U and R ensuring strong zonal flow and relat ively weak meridional flow V. A sample of 12 cases each of two -three day duration was selected. (At 60°N predominantly zonal regimes are transitory.) In order to compare the phases of category harmonics with those for the "normal" 500MB height d istr ibut ion, the latter were extracted from the plots of the zonal harmonics for normal wave components 1 to 4. These are shown in Fig. 7.7^ and a few comments would seem appro-priate. It is noted, for example, that at 60°N constructive ridge inter-ference is greatest between Wl and W2 over Western Europe (20°E) W3 and W4 over NE Atlantic (20°W) and at 50°N between W2 and W3 over NE Pacif ic (140°W). Moreover, the trough line of Wl crosses the NE Pacif ic intersecting 60°N at 160°W. Therefore, i f Wl, on. any given occasion, is near normal phase, i t wi l l interfere destructively with any tendency for ridging over the NE Pacif ic Ocean. The parameters a, A^, <j>n and S n at 60°N were abstracted for each day of each case. (All blocks were centred between 50°N and 70°N.) They were then averaged by category and the results are presented in Table 7.1 along with corresponding data for the normals. ^ Figure 7.7 is consistent with the results of Graham (1955) and Eliasen (1958) who presented normal harmonics for January. 8 0 140 1 0 0 6 0 2 0 W E S T i 20 E A S T 6 0 1 0 0 140 1 8 0 L O N G F i g . 7.7 Phase of Harmonics 1 to 4 f o r Normal 500MB height - WINTER (December, January and February). 00 00 TABLE 7.1 Mean Spectral Attributes of WINTER Blocking Episodes 60°N 500MB CATEGORY a A l •l S l A2 <J>2/2 S 2 A3 (|)3/3 S 3 A 4 V 4 S 4 A 5 * S 5 A 6 S 6 m m degs % m degs % m degs % m deg % m deg % m deg % NORMAL (Winter) 75 50 +20 22 81 -155 + '25 59 43 -140 - 20 +100 17 15 - 17 2 - - - - - -ZONAL 92 62 - 23 (±15) 57 - 19 50 - 15 47 - 13 45 - 12 32 - 6 PACIFIC BLOCKING 147 78 -72 14 121 -141 34 102 -139 24 83 -179 16 51 - 6 29 - 2 BAFFIN BLOCKING 129 117 -89 41 77 - 24 18 71 - 22 15 58 - 89 10 48 - 7 36 - 4 NE ATLANTIC BLOCKING 169 162 - 1 (±35) 46 (±21) 96 -. 8 16 99' - 12 17 86 - 9 13 53 •- 5 41 - 3 W EUROPEAN BLOCKING 171 143 +11 35 132 + 30 30 100 + 12 17 76 - 5 10 48 - 4 34 - 2 DOUBLE BLOCKING 202 111 +64 15 206 + 20 52 137 + 7 23 70 + 10 6 40 - 2 29 - 1 190 Standard Deviation (SD) As expected, the SD of the hemispheric circulation during the blocking episodes is much larger than 'normal' (usually more than two-fold) . It is least (129m) for blocking in the Baffin - Hudson Bay area, a result that is consistent with our remarks in Section 5.3.6, and, greatest (202m) for 'Double Blocking.' The Standard Deviation for the Zonal category (92m) was not far removed from the Normal (75m). Blocking over NE Pacif ic and Alaska The primary components were (34%) and W^  (24%) which interfere constructively at an average position of 140°W, close to their normal phase. W-j at 72°W is clearly not contributing to the blocking structure and is 90 degrees removed from its normal phase location. W^  (16%) phased at 179 W reinforces W^  and W ,^ and tends to shi f t the resultant maximum 500MB height about 10 - 20 degrees further west. This is con-sistent with the location of our blocking signature maximum,Figs. 5.2 and 5.7,. Blocking over Baffin Island (and Hudson Bay) We shall reserve detailed comment for Section 7.4.4 and simply note here that the S values are similar to those for Atlantic Blocking. n 3 Blocking over the NE Atlantic - Greenland The primary component is W^  (S-j = 46%, fy^ '= 1°W) and the balance is made up of more or less equal contributions from the other three components. Note that W^  and W^  are close to their normal phase (20°W) while W-, and W9 are 20 to 30 degrees west of normal. 191 Blocking over Western Europe Clearly W-j and are the dominant components, interfering con-structively at 20°E which is very close to normal phase for both. Also ^3 (<f>3/^~^2°E) contributes s ignif icant ly . Double Blocking (E Pacif ic - Alaska; NE Atlantic - W Europe) Because of the geometry of the prescribed configuration i t is not surprising that W^  ($2 = 52%) is the dominant component. It is interest-ing to note that the average phases (20°E,160°W) are almost precisely the normal W2 phase positions at 60°N. W3 (S 3 = 23%, <f>3/3=7°E, 127°E, H 3 ° W ) provides signif icant reinforcement but contributions from W^  (S-j = 15%, <|>1 = 64°E) and W^  (S^ = 6%) are inconsequential. Zonal Unlike the blocking categories there are no predominant components. The variance is shared across the spectrum and Wg and Wg account for 18%. Also, because wave components moved rapidly, <|>n values have no meaning and were omitted. Summary The average circumpolar harmonics at 60°N for blocking occurring in the 50°N - 70°N zone show that the amplitudes of the primary compo-nents are more than double their normal value. The contributions to the mean blocking structures from the wave component ridges may be relat ively assessed as follows: 192 U! W2 W3 W4 NE Pacif ic - Alaska Small Large Large Moderate Baffin - Hudson Bay Large Small Smal 1 Moderate NE Atlantic - Greenland Large Smal 1 Smal 1 Smal 1 W Europe Large Large Moderate Smal 1 Double Nil Very Large Moderate Small The position relative to normal of the dominant wave component ridges wil l depend on the blocking location category and, of course, on the history of motion. Clearly the large W-| component of the Baffin Island blocks wi l l be well removed from its normal longitude. On the other hand, NE Pac i f ic , N Atlantic and W Europe blocks are frequently a result of highly amplified wave components which are interfering constructively near their normal positions. These results are reasonably consistent with those of Austin C1980). The methodology differed in that rather than drawing con-clusions from individual cases we obtained our results from averages of categories. We also chose to separate W Europe blocks from those over the North Atlantic and found signif icant spectral differences. As far as we are aware, blocking over the North-Eastern Canadian Archipelago (including Baffin Island) has never been expl i c i t l y examined by harmonic analysis. We shall report on further results in Section 7.4.3. 7.4.2 Interruptions of Major Blocking Episodes During the course of this investigation we were struck by the nature of the interruptions to the otherwise persistent hemispheric regimes of large amplitude waves. Invariably these regimes were associated 193 with major blocking episodes, sometimes of several weeks duration (e .g. , January 9 to February 4, 1963). The interruption is characterized by rapid decrease of amplitude and the concurrent establishment, for a few days, of strong zonal flow. Each of the 14 'zonal ' cases summarized in the previous Section (Table 7.2) occurred during the peaks of interrup-tive episodes. The winter of 1962-63 provided a set of remarkable examples. The two dominant harmonics of the persistent regimes were clearly and W ,^ but on three occasions collapsed, W,, lost signif icant power and the ensuring strong zonal flow was marked by low amplitude harmonics with power more evenly distributed over the spectrum. The interruptions are consistently revealed by: Fig. 7.8, show-ing the time-longitude variation of W ;^ by Fig. 7.9, showing the corres-ponding plot of Amplitude vs time; and by Fig. 7.10, showing the change with time of R = U/V. The interruptions are identif ied by 0^  (December 8, 1962), 0 2 (January 7, 1963), 0 3 (February 7-12, 1963), 0 4 (March 15, 1963) and 0^  (March 27, 1963). The most striking of these five occasions were 0^, 0^ and 0^, because in each case they were flanked by long-wave regimes of unusual amplitude and persistence. The change of Standard Deviation and the redistribution of power among the harmonics during the transition 0 2 is i l lustrated in the f o l -lowing table: TABLE 7.2 Date a Cm-) s-,(%) S 2 S 3 S 4 S 5 S 6 R = U/V 30 Dec. 1962 137 4 34 33 17 9 1 0.6 7 Jan. 1963 76 3 10 1 31 13 35 2.1 9 Jan. 1963 144 10 27 44 10 0 7. 1.3 14 Jan. 1963 193 6 29 53 0 3 7 0.6 WAVE 3 500MB flVG(50N-70N) DEC J . .1962-MRR 3] , .1 963 F i g . 7 . 3 As i n Pig. 7 . 4 except f o r Third Harmonic. Minima of amplitude at O-j, O2, O3, O4, O5 60N WINTER 6 2 / 6 3 WRVE 3 F i g . 7.9 As i n F i g . 7.5 except f o r wave number 3. =g F i g . 7.10 Change with time of the r a t i o R of zonal (U) to meridional (V) components at 60°'1T, December 1 , 1962 to March 31 , 1963. 197 The inception of strong zonal flow implies enhanced barocl inicity and therefore an increase in available potential energy. Moreover, 1 c) fl because the N-S thermal gradient - --r 2- is increasing, so too is the 8 ay range of wave lengths over which instabi l i ty may occur (Fig. 2.9). The ensuing realization of baroclinic instabi l i ty in the form of deepening extra-tropical cyclones results in the conversion of available potential energy into eddy kinetic energy. Table 7.2 shows that, at one stage of the zonal flow of January 7, 1963, 35% of the eddy (or wave) energy was accounted for by the Wg component. This is a wave length which, at 60°N, is representative of the scale of baroclinic systems which are the mature stage of "free" or "transient" unstable waves that originated in lower latitudes. Table 7.2 also shows that the energy transfer to the longer wave components and representing the "forced" osc i l la t ions , was swift (< 2 days) and ushered in a protracted double (and later tr iple) blocking regime from January 9 to February 4. This is clearly shown on the Hovmoller Diagram of Fig. 7.1 (50°N to 70°N), and the ful l- lat i tude extent of the long-wave pattern is confirmed by Fig. 7.2 (30°N to 50°N). The extraordinary rate at which these massive energy transfers occur is not being accurately replicated by numerical models. Hence the onset of these persistent long-wave regimes and their subsequent evolution poses a d i f f i cu l t problem for medium range forecasting (Baumhefner and Downey, 1978; Somerville, 1980). 7.4.3 Baffin Island Blocking In Section 7.4.1 i t was noted from Table 7.1 that the Amplitude  Spectrum of Baffin blocking was nearly the same as for Atlantic blocking. The mean Phase Spectrum was, of course, shifted westward. If the samples 198 examined are representative, the implication is that the Baffin Block may be a later stage of a retrograding Atlantic Block. Is retrogression of Baffin blocks a predominant characteristic or are they as l ikely to be quasi-stationary or progressive? To answer this question we conducted a census,'from the Blocking Signature Sequence Catalogue, of a l l Sequences whose trajectories lay across the Canadian Archipelago, an area we defined with boundaries 60°N, 80°N and 50°W, 100°W. There were 61 Sequences and a total of 115 signatures for the 33 winters. The movement from one signature to the following was assessed as 'retrograde' or 'progressive.' If the sequence was only 1 pentad in duration, the motion was categorized 'indeterminate.' The count for the 33 winters was Retrogression 63 Progression 27 Indeterminate 25 Total 115 Clearly the most l ikely motion during a Baffin blocking episode is retrogression but at least 25% of the time there can be progression. What is the spectral history of a typical retrograding Baffin blocking episode? The sequence December 21, 1978 to January 6, 1979 is one such example. To provide a perspective of the synoptic evolution, Fig. 7.11 displays a panel of 5-day mean 700MB charts, Taubensee (1979) and Wagner [1979). The signif icant spectral attributes are l isted in Table 7.3. A retrograde North Atlantic blocking wave is clearly evident through 199 Fig. 7.11 Sequence of 5-day mean 700MB charts: (;a) 19-25 Dec 1978 N. A t l a n t i c - Greenland Block l b ) 26-50 Dec 1978 B a f f i n I. Block established (c) 2-6 Jan 1979 Alaska - West Coast Block , (Taubensee, 1979, Wagner, 1979). 200 TABLE 7.3 Harmonics at 60°N associated with retrograde blocking from the N. Atlantic to NE Canada and subsequent blocking Gulf of Alaska Location Date 1978-79 a S l 4>2/2 S 2 * 3 / 3 S 3 Atlantic Dec. 21 167 + 1 47 — 0 - 19 31 22 183 - 7 55 3 10 - 21 19 23 179 -12 53 - 3 14 - 19 19 24 152 -22 88 — 2 .-. 2 25 125 -28 84 — 3 2 26 107 -34 65 22 16 •. 4 Baffin 27 106 -54 47 8 15 - 45 25 28 117 -75 43 •• 4 - 35 27 29 136 -83 45 — 0 - 29 39 30 171 -90 52 •- — 2 - 28 34 31 203 -88 60 , - — 3 - 24 22 Jan. 1 196 -92 65 • — 1 - 21 17 2 150 -85 58 • — 3 - 12 20 Alaska 3 169 -69 25 -152 28 -142 17 4 189 -81 17 -152 44 -153 18 5 218 -82 15 -155 50 -149 12 6 234 -92 13 -157 69 ' — — 2 201 December 26, 1978, with the main power contributed by Wl which peaks at 88% on December 24. The process continues into a slowly retrograding Baffin block December 27 to January 1 following which there is a transfer of power to W2 (nearly 70% by January 6) and the W2 ridge is phased over the NE Pacif ic (- 155°W). This component combines with the residual Wl (now quasi-stationary at 90°W) to form the strongly amplified blocking ridge from Alaska south-eastward along the West Coast of North America (Fig. 7.11(c)). Meanwhile the Baffin trough has been restored to i ts normal longitude. The general characteristics of this sequence have been observed synoptically many times (e .g. , Namias, 1975) but we are not aware of reference in the l i terature to day-to-day harmonic analyses. (The zonal harmonic graphics for December 23, 1978 and January 4, 1979 wi l l be presented in Section 7.4.4.) There is a marked variation in Baffin blocking frequency even during the winters when hemisphere frequency of blocking is high. For example, during the winters of 1946-47, 1955-56, 1968-69 and 1978-79, we counted a total of 9 + 8 + 13+ 8= 38 signatures or 9.5 per winter, whereas for the winters of 1949-50, 1962-63, 1976-77 we counted 2 + 0 + 6 = 8 signatures or 2.7 per winter. The predominance of Wl during the high frequency winters, particularly at 70°N, is quickly noted from a comparison of amplitude-time plots , e .g . , Fig. 7.12 (1949-50) vs Fig. 7.13 (1978-79). Of the winters examined, those with low frequency Baffin Blocking seem to have large amplitude ridges which are the result of constructive interference between W2 and W3 over the Pacif ic and Wl and W2 over the NE Atlantic. These ridges osc i l late slowly about their 70N WINTER 4 9 / 5 0 WRVE 1 F i g . 7.12 Amplitude and phase angle of wave number 1 at 70°N as a function of time. December 1, 1949 to March 31, 1950. 70N WINTER 7 8 / 7 9 WRVE I 204 mean winter location (e .g. , Fig. 7.1). Those winters with high f re -quency Baffin Blocking, e .g . , 1978-79, Fig. VI I- 1, feature a repeat-ing pattern of retrograding blocking waves init iated over the N At lant ic , subsequently crossing northern Canada and usually weakening or terminat-ing west of Hudson Bay. A subsequent amplification of the long-wave pattern over the NE Pacif ic and Alaska is associated with a readjust-ment of the hemispheric wave mode and, ultimately, the primary power resides in the W2 and W3 components. There were two such cycles observed from December 1, 1978 to February 28, 1979 and a third in March (not shown). Baffin blocking may then be perceived as an inter-mediate stage of such a cycle. Summary Blocking over the eastern Canadian Archipelago is frequently the result of a retrograding blocking wave from the North Atlantic. It has a similar amplitude signature and WI usually contributes at least 50% of the variance, but, at 60°N the WI ridge is displaced 90 degrees or more west of i ts normal location. Examination of Hovmoller diagrams of Z(x,t) at 60°N and superimposed blocking locations suggests that Baffin Blocks, though frequent, are not as persistent or robust as oceanic episodes. 7.4.4 Zonal Harmonics of Blocking Systems - Two case studies -So far this Chapter has focussed on a one-dimensional harmonic analysis of 500MB height for the 50°N - 70°N zone, and related the tem-poral variation of the wave components to blocking episodes. This zone was chosen because the main target of interest was the blocking anti-205 cyclone. However, i f we wish to investigate the evolution of entire blocking systems (and this would include the flanking cold lows or troughs such as portrayed in the sequence of Fig. 1.2) then i t would be necessary to analyze the spatial and temporal variation of the harmonics in the 30°N - 50°N zone. Such analyses wil l be part of our research subsequent to this dissertation. However, discrete one-dimensional analyses, even though over representative zones, do not provide an integrated visual perception of the harmonies of a blocking system. To achieve this requires a two-dimensional zonal harmonic analysis. The purpose of this section, there-fore, wil l be to present and discuss the results of this kind of analysis applied to instantaneous ( i ; e . , 1200Z) 500MB height f ie lds during two geographically disparate blocking episodes. These situations were December 23, 1978 - a N Atlantic-Greenland block and January 4, 1979 -a NE Pacific-Alaska block. These dates are contained in the sequence which was presented in the previous section (Table 7.3 and Fig. 7.11) to i l lustrate an example of retrograde Baffin Island blocking. Here we shall emphasize the spatial characteristics of the zonal harmonics on the two dates, but we shall also comment on temporal aspects of the transition period particularly as they apply to the southern structure of the blocking systems. (a) Atlantic - Greenland Block, December 23, 1978 The f i r s t three zonal harmonics of the 500MB height f i e ld on December 23, 1978 are displayed in Figs. 7.14 to 7.16, respectively. The corresponding digi ta l data are presented in Table 7.4 as well as those for components 4, 5 and 6-. 206 120E 100E 80E F i g . 7.H F i r s t harmonic (W1) of the 500MB height f i e l d on December 2 3 , 1978 during a major episode of blocking over the North A t l a n t i c and Greenland. Contours i n dams. Interval = 3 dams. P i g . 7.15 As i n P i g . 7.14 e x c e p t f o r second harmonic (W2) F i g . 7.16 As i n F i g . 7.14 except f o r t h i r d harmonic (W3). TABLE 7.4 North Atlantic Block Zonal Harmonics 500MB December 2.3, 1978 WAVE 1 WAVE 2 WAVE 3 WAVE 4 WAVE 5 WAVE 6 LAT AVG SD A S A S A * S A S A * S A S m m m % m % m % m % m % m % 85 5108 156 220 - 30 99 18 27 1 6 -108 0 0 27 0 1 174 0 1 52 0 80 5112 237 332 - 27 98 38 16 1 34 -126 1 2 - 90 0 6 - 7 0 2 - 54 0 75 5130 239 321 - 21 90 69 -20 4 81 -115 6 5 - 96 0 9 - 37 0 5 - 55 0 70 5140 221 270 - 17 75 103 -37 11 115 - 95 14 14 -126 0 19 -130 0 2 64 0 65 5160 196 224 - 14 66 105 -32 14 113 - 83 17 20 168 1 42 -149 2 10 133 0 60 5193 179 185 - 12 53 94 - 5 14 109 - 58 19 65 110 7 51 -160 4 26 -177 1 55 5252 163 106 - 3 21 98 30 18 125 - 42 30 98 107 18 41 -169 3 58 -175 6 50 5346 144 25 85 2 118 44 33 126 - 46 38 68 102 11 19 152 1 66 177 11 45 5470 132 62 159 11 116 55 38 110 - 68 35 31 81 3 24 117 2 44 178 6 40 5586 115 50 -177 9 101 66 39 92 -105 32 12 95 1 27 152 3 37 -167 5 35 5679 96 29 -128 5 62 69 21 88 -144 42 6 114 0 38 150 8 21 -138 2 30 5753 74 18 - 91 3 13 44 2 71 -180 46 16 - 22 3 44 143 18 25 - 54 6 25 5810 59 3 - 66 0 30 -96 13 41 137 23 25 - 24 9 38 135 21 28 - 28 11 210 The phase and large amplitude of Wl in the higher latitudes are consistent with the results of Section 7.4.1. A prof i le along the 20°W meridian reveals an asymmetric wave structure cresting at 77°N (33 dams) and troughing at 4.5°N (-6 dams). The trough is a reflection of the observed low geopotential height over the mid-Atlantic (Fig. 7.11 (a) and ( b ) ) a condition which is typical ly associated with high l a t i -tude blocking. We also note a di-pole configuration across the North Pole from a maximum at 77°N 20°W to a minimum at 77°N 160°E (-30 dams). This minimum is a reflection of the deep low over the Arctic Ocean. North of 60°N, Wl accounts for between 50 and 100 percent of the hemispheric variance, while in the mid-latitudes (40°N - 50°N) W2 and W3 account for about 70 percent. It is the constructive interference of the latter components that replicates much of the deep low in the New-foundland area, Figs. 7.11(a) and (b). (b) Transition December 23, 1978 to January 4, 1979 The f i r s t four zonal harmonics of the 500MB height f i e ld on January 4, 1979 are displayed in Figs. 7.17 to 7.19, respectively. The corresponding digi ta l data are presented in Table 7.5. A number of features of the evolution of events in the 50°N to 70°N zone during this transition period were discussed in Section 7.4.3. It is also noted that the Wl di-pole configuration of Fig. 7.14 rotated clockwise about the N Pole. This high latitude retrogression was pre-sumably a result of strong planetary vort ic i ty advection. By January 4, 1979, the Wl maximum was located at 70°N 90°W. Meanwhile W2, i n i t i a l l y weak over Kamchatka, amplified as i ts maximum progressed slowly eastward to mainland Alaska. Note that i t , too, 211 120E 100E BOE F i g . 7.17 F i r s t harmonic (W1) of the 500MB height f i e l d on January 4, 1979 during a major episode of blocking Alaska and Southward along West Coast of B.C. Contours i n dams. Interval = 3 dams. F i g . 7.18 As i n F i g u r e 7.17 except f o r second harmonic (W2) F i g . 7.19 As i n Fig. 7.17 except f o r t h i r d harmonic (W3). TABLE 7.5 Alaska Block Zonal Harmonics 500MB January 4, 1979 WAVE 1 WAVE 2 WAVE 3 WAVE 4 WAVE 5 WAVE 6 LAT AVG SD A S A S A 4> S A S A S A S m m m % m % m X m % m % m % 85 5184 58 77 - 94 91 21 - 43 7 14 100 3 2 - 79 0 3 - 20 0 1 129 0 80 5140 122 160 - 83 86 46 - 6 7 44 90 6 13 - 71 1 7 - 73 0 0 - 98 0 75 5135 189 245 - 90 84 99 42 14 37 62 2 10 -128 0 6 - 42 0 6 - 49 0 70 5159 220 257 -100 68 168 51 29 28 - 44 1 37 142 1 20 116 0 11 - 27 0 65 5178 210 191 -103 41 206 52 48 65 - 87 5 57 170 4 32 100 1 16 45 0 60 5207 189 n o - 81 17 178 55 44 113 - 97 18 99 -162 14 54 59 4 26 77 1 55 5258 185 82 - 37 10 84 65 10 162 - 95 38 130 -157 25 80 54 9 30 81 1 50 5338 182 80 - 10 10 45 158 3 157 - 92 37 137 -157 28 77 64 9 45 50 3 45 5428 173 83 3 12 90 -165 14 132 - 92 29 109 -148 20 64 84 7 70 23 8 40 5521 160 100 0 20 97 -154 18 102 - 94 20 75 -128 11 42 92 4 82 9 13 35 5626 127 119 - 5 44 60 -144 11 48 - 98 7 51 -106 8 14 144 1 62 0 12 30 5726 86 95 - 12 61 30 -114 6 9 157 1 42 - 62 12 19 -114 3 26 - 7 5 25 5797 62 48 - 15 30 27 - 92 10 22 98 6 39 - 36 20 22 -114 6 9 -141 1 215 had a bi-cel lular structure in the meridional (N - S) plane, and that the eastward motion of the southern cel ls (centred in the 40°N - 50°N zone) was so much greater relative to the northern (60°N - 70°N) that the maxima and minima were almost in longitudinal opposition by January 4 (Fig. 7.18). Meanwhile Wave 3 amplified almost ' in s i tu ' (140°W -150°W). (c) Alaska - NE Pacif ic Block, January 4, 1979 During the 12-day period to January 4 there has been a major change in the resultant long-wave pattern (Fig. 7.11(c)). At 65°N, W2 has doubled i ts amplitude (10 to 20 dams) and has become the dominant harmonic (S 2 = 70% by January 6). Constructive interference at 60°N between W2 (<j>2/2 = 153°W, S 2 = 44%) and W3 (4.3/3 = 152°W, S 2 = 18%) account for the blocking ridge from Alaska southward, paral lel ing the West Coast of Br i t ish Columbia. The block occurred in conjunction with an intense low level Arctic a i r mass which stretched from the Yukon to Colorado and brought record-breaking cold to the mid-west. The f r ig id outflow to coastal Br i t ish Columbia froze ponds and rivers and for two weeks a common sight in Vancouver was skating on natural ice! Note, too, the structure of WI (Fig. 7.17) and W2 (Fig. 7.18) in the latitude zone 30°N - 40°N across the central Pacif ic Ocean. Here we find reinforcing minima with WI playing the dominant role. The constructive interference accounts for the mean E - W oriented trough (Fig. 7.11(c)), a typical concomitant of NE Pacific-Alaska blocking. In the lower latitudes there is a shi f t of power to higher wave numbers, e .g . , Sf. = 13% at 40°N and, moreover, 14% of the total variance is 216 unaccounted for. At these lat i tudes, : in Winter, additional harmonics (up to W12) must be calculated in order to include the effect of intense baroclinic act iv i ty on the variation of 500MB height (Van Mieghem, 1961). 7.5 Summary We have confirmed that the zonal harmonics of blocking episodes have characteristics related to the region of occurrence. Our results are consistent with those of Austin (1980) who used the particularly apt phrase, "spectral signature", for harmonic distributions peculiar to the blocking category. It was also noted that regimes of blocking (or, more generally, large amplitude quasi-stationary long waves) can be interrupted swiftly by strong zonal flow featuring a much reduced total wave variance. On such occasions the power, which formerly resided with the low wave number components, is spread more evenly across the spectrum. Baffin blocking, though a frequent occurrence, is less robust and persistent than blocking over the northern oceans. Its predominant motion is retrograde. Zonal harmonic analysis of the two-dimensional 500MB circulat ion of the Northern Hemisphere reveals a wave component structure associated not only with the higher latitude anticyclone but also with the lower latitude cyclonic act iv i ty which, plays an important role in maintaining the blocking system. Van Mieghem (1961) stated: Average spectral distributions of general circulation parameters should be computed for different world weather types (strong zonal c i rculat ion, zonal c i rcu-lation with strong eccentr ic i ty, strong meridional c i rculat ion, blocking flow patterns, . . . ) and for transition periods between world weather types. We fu l ly agree and hope that this Chapter contributes in some measure toward such a goal. 218 CHAPTER 8 RESULTS AND CONCLUSIONS The objective of this study was to investigate the climatology and certain diagnostics of blocking in the Northern Hemisphere. The data record was January 1, 1946 to February 28, 1979 at the 500MB and lOOOMB levels. Data locations were the 1977 grid points of the U.S. National Meteorological Centre octagonal grid. Three different method-ologies were employed which required the computation respectively of: (i) Anomaly Centres of 5-day mean 500MB height (date, loca-tion and magnitude) ( i i ) Stat ist ica l Moments (zero to four) of the frequency distributions of the 5-day mean 500MB, 1000MB, and lOOOMB - 500MB thickness at each grid point ( i i i ) Zonal Harmonics of daily 500MB height for each of seven winters. The main results and conclusions are as follows. ANOMALY CENTRES 1. The close relationship between a blocking anticyclone and the associated positive anomaly of 5-day mean 500MB height can be used to advantage for computation of blocking frequency using machine processing methods. Cr i ter ia were developed based on season, magnitude of the positive anomaly centre and lat itude, which determined with a high degree of probability the existence or otherwise of a blocking ant i -cyclone. Qualifying anomalies were called "blocking signatures." A Catalogue was prepared which identif ied by date, location and magnitude 219 every signature that had occurred in the Northern Hemisphere from January 1. 1946 to February 28, 1978. 2. Our geographical distribution by season of blocking signature frequency in the Northern Hemisphere is consistent with published invest i -gations of blocking over the Pacif ic and Atlantic Oceans and Western Europe. However, our results also reveal an area over the Northeastern Canadian Archipelago (including Baffin Island and Davis Strait) with a much higher frequency of blocking signatures than previous investigations would indicate. The test of an independent sample of blocking signatures by comparison with corresponding daily synoptic analyses confirmed that this was indeed a high frequency blocking region. However, these blocks are usually less robust and persistent (except possibly in the Spring) than occurrences over the oceans. 3. The trajectory of an actual blocking anticyclone is closely related to the corresponding "blocking signature sequence." Displacement c r i te r ia were developed to identify these sequences. A Catalogue was prepared l i s t ing their attributes including dates of i n i t i a t i on , termina-tion and component signature data. 4. A stat is t ica l analysis of within sequence displacements revealed motion tendencies dependent on the region of origin and time of year. 5. There was a marked interannual variation of signature sequences 2 pentads in duration ( i . e . , moderate to strong blocking episodes) which suggested a 10 to 15 year cycle. However, i t was not possible to draw a s ta t i s t i ca l l y valid conclusion due to the size of the sample (33 years) relative to the fluctuation period (^  one decade). 220 STATISTICAL MOMENTS 1. The geographical distribution of the s tat is t ica l moments of the geopotential height continuum were useful in an interpretive sense. Normal and Standard Deviation f ields for 5-day mean lOOOMB, 500MB and lOOOMB - 500MB thickness, revealed the difference in nature of the two maxima of Standard Deviation (WINTER) at 500MB, one over Baffin Island and the other southeast of Greenland. The former derives a larger , • contribution from variations caused by the incidence of cold lows or warm (mid-troposphere) blocking ridges. 2. Skewness f ields (500MB) showed strong, well-defined positive areas in the higher latitudes for WINTER, SPRING and FALL. These identif ied with some (but not a l l ) areas of blocking signature maxima. Site-specif ic histograms strongly suggested that the positive skewness was attributable in part to the occasional establishment of blocking regimes in areas of low normal geopotential height. 3. Kurtosis f ie lds (500MB) showed signif icant ly low values in WINTER over the eastern Pac i f ic , the eastern Atlantic and western Europe. These are the regions where ridges begin their northward amplif ication, some-times (but not always) terminating in a blocking anticyclone in higher latitudes. Site-specific histograms reinforce the l ikelihood of the low kurtosis areas indicating bi-modal distr ibutions. Presumably the sub-set with the higher mean would ref lect the incidence of ridge amplification. ZONAL HARMONICS 1. The zonal harmonics (WI to W6) of the 500MB height prof i le at 40°N and 6 0 ^ , respectively, were computed for each day of seven winters 221 and their flanking months ( i . e . , November to March, inclusive). Indices of zonal (U) and meridional (V) components of flow were also computed. 2. It was found that the spatial harmonics of blocking episodes were dist inctive to the region in which they occurred. For example, W2 and W3 predominate during blocking over Alaska and the eastern Pacif ic . In other words, the blocking anticyclone has a spectral signature associated with i ts regional location. (Our results confirm those of Austin, 1980.) 3. Regimes of blocking may be interrupted swiftly by strong zonal flow featuring a much reduced variance which is more evenly, spread across the long-wave spectrum. In a case study (1962-63) the interrup-tions were str ikingly unambiguous, at quasi-periodic intervals (30 to 40 days) and transitory-(-v. a few days). The behaviour .of the harmonics during the resumption of blocking suggested that 'forced' osc i l lat ion components (W2 and W3 in this case) amplify from eddy kinetic energy derived from 'free' osc i l la t ion components whose previous amplification derived from major baroclinic development. This example supports a long-standing hypothesis that blocking may be a response to rapid deep-ening of baroclinic waves. 4. Zonal harmonic analysis of the two-dimensional 500MB circulation of the Northern Hemisphere during typical major blocking episodes reveals wave structures in both higher and lower latitudes with charac-ter is t ics of motion and growth, associated with the total blocking system. This study emphasized the higher latitudes (50°N to 70°N), site of the majority of blocking anticyclone centres when they reach the mature stage. The fu l l zonal analysis of case studies suggest that i t 222 would be profitable to investigate the ensemble characteristics of the lower.latitude (30°N to 50°N) harmonics. 5. A recurring theme throughout this^study was the Baffin Island Paradox, the intriguing maximum of blocking signatures centred each season in the area of the Normal Baffin trough. The zonal harmonics of 61 episodes of Baffin blocking indicate that the amplitude spectrum was similar to Atlantic blocking (with a westward sh i f t of phase). The majority of Baffin blocks arise from retrograding North Atlantic block-ing waves. Their termination is often (but NOT invariably) followed by a re-adjustment of the zonal long-wave pattern featuring the development of an amplified blocking ridge from Alaska southeastward along the West Coast of North America. The seven winters studied were notable for major blocking episodes. Even so, there was a marked variation in Baffin blocking frequency. This appeared to be related to the predominant characteristic of the winter's blocking regimes. Those with low frequency Baffin blocking featured large amplitude ridges osci l lat ing slowly about their mean winter loca-t ion. Those with high frequency Baffin blocking featured several occa-sions of a retrograding amplified long wave train in the higher latitudes out of phase with the lower latitude train. This frequently resulted in the inverted cel lu lar pattern of Fig. 3.4 and a 5 to 10 degree latitude southward displacement of the Baffin Low from i ts Normal location. GENERAL 1. The 5-day mean was an effective f i l t e r for screening out the higher frequency fluctuations occasioned by mobile synoptic-scale systems 223 and retaining, without undue attenuation, the majority of the lower frequency phenomena of interest to this study. 2. Another recurring theme was the large proportion C- 80%) of the temporal variation of 500MB height accounted for by the low-frequency fluctuations. This is readily apparent from a comparison between the Standard Deviation f i e ld of daily height, Fig. 1.1(b), and of 5-day  mean height, Fig. 4.4. In the space domain the long-wave components (1 to 5) accounted for ^ 90% of the variance of higher latitude (60°N) circumpolar 500MB gph profi les and > 80% of lower latitude (40°N). 3. The value of GCM diagnostics was i l lustrated in Chapter 2 where an example demonstrated the great influence on the general ciculation of large scale mountain systems. The frequency and harmonic analyses of our study reinforce the widely-held hypothesis that the large scale orography of the Northern Hemisphere plays a vital role in the blocking process. 4. Our study has produced a number of spin-offs. The Master Cata-logue, an inventory of a l l positive and negative anomalies of 5-day mean 500MB height in the Northern Hemisphere for the past 33 years, and also the Blocking Signature Sequence Catalogue should be useful sources of information for research in such topics as large scale climatology and medium and long range weather prediction. 5. F inal ly, we believe that the three avenue approach to our invest i -gation of blocking, namely, Anomaly Frequency, Continuum Stat ist ics and Zonal Harmonics has achieved our objectives and yielded a number of s ig -nif icant results concerning the nature of blocking in the Northern Hemisphere. 224 REFERENCES American Meteorological Society (a): Meteorological and Geoastrophysical  Abstracts. Rigby, M., Editor. American Meteorological Society (b), 1974-1979: Weather and Circulation of (Month, Year), Monthly Weather Review, Vol. 102-107 inclusive. Austin, J . F . , 1980: The Blocking of Middle Latitude Westerly Winds by Planetary Waves. Quarterly Journal of the Royal Meteorological  Society, 106, 327-350. Barrett, E.W., 1958: Some Applications of Harmonic Analysis to the Study  of the General Circulation. Ph.D. Thesis, Department of Meteorology, University of Chicago, 209 pp. Baumhefner, D.P. and P. 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Monthly Weather Review, 92, 303-315. O'Connor, J . F . , 1966: Catalogue of 5-day Mean 700MB Height Anomaly Centres 1947-1963 and Suggested Applications. Technical Memorandum 37, 63 pp. National Meteorological Centre, Washington, D.C. O'Connor, J . F . , 1969: Hemispheric Teleconnections of Mean Circulation  Anomalies at 700 Mi l l ibars . ESSA Technical Report WB 10, 103 pp. National Meteorological Centre, Si lver Spring, Maryland. Palmen, E. and K.M. Nagler, 1949: The Formation and Structure of a Large-scale Disturbance in the Westerlies. Journal of Meteorology, 6, 227-242. Palmen, E. and C.W. Newton, 1969: Atmospheric Circulation Systems -Their Structure and Physical Interpretation. Academic Press, New York, 603 pp. Panofsky, H.A. and G.W. Brier, 1968: Some Applications of Stat ist ics  to Meteorology. The Pennsylvania State University. Perry, J .D . , 1979: Address to Special ist Group on Dynamical Problems, Atmospheric Blocking: Meeting - September 1979. Weather, 35, 148-152. 228 Petterssen, S., 1956: Weather Analysis and Forecasting, Vol. I, McGraw-H i l l , 428 pp. Quiroz, R.S., 1979: Tropospheric-Stratospheric Interaction in the Major • Warming Event of January-February 1979. Geophysical Research Letters, 6, 645-648. Rex, D.F., 1950a: Blocking Action in the Middle Troposphere and its Effect upon Regional Climate (I): An Aerological Study of Blocking. Tel lus, 2, 196-211. Rex, D.F., 1950b: Blocking Action in the Middle Troposphere and i ts Effect upon Regional Climate, II: The climatology of Blocking. Tel lus, 2, 275-301. Rossby, C.-G., 1939: Relations between Variations in the Intensity of the Zonal Circulation and the Displacements of the Semi-permanent Centres of Action. Journal of Marine Research, 2, 38-55. Rossby, C.-G., 1940: Planetary Flow Patterns in the Atmosphere. Quarterly Journal of the Royal Meteorological Society, 66, Supple-ment, 68-87. Sawyer, J . S . , 1970: Observational Characteristics of Atmospheric Fluc-tuations with Time Scale of a Month. Quarterly Journal of the Royal  Meteorological Society, 96, 610-625. Serebreny, S.M., E.J. Weigman and R.G. Hadfield, 1961: Jet Stream Climatology at 500MB North of 50°N. U.S. Navy Weather Research,  NWRF 20-00661-045, 138 pp. Smagorinsky, J . , 1972: The General Circulation of the Atmosphere. Meteorological Challenges: A History. Ed. D.P. Mclntyre. Information Canada,Ottawa, 338 pp. Somerville, R.C.J., 1980: Tropical Influences on the Predictabi l i ty of Ultralong Waves. Journal of the Atmospheric Sciences, 37, 1141-1156. Sumner, E.J., 1954: A Study of Blocking in the Atlantic-European Sector of the Northern Hemisphere. Quarterly Journal of the Royal  Meteorological Society, 80, 402-416. Sumner, E.J., 1959: Blocking Anticyclones in the Atlantic-European Sector of the Northern Hemisphere. Meteorological Magazine, 88, 300-311. Taljaard, J . J . , H. Van Loon, H.L. Crutcher and R.L. Jenne, 1969: Climate of the Upper A i r , Vol. I. Charts of Monthly Mean Pressure,  Temperature, Dew Point and Geopotential in the Southern Hemisphere. NAVAIR 50-IC-55. Off. Chief of Naval Ops., Washington, D.C. 229 Taubensee, R.E., 1979: Weather and Circulation of December 1978. Monthly Weather Review, 107, 354-360. T re id l , R.A., E.C. Birch and P. Sajecki, 1980a: Blocking in the Northern Hemisphere: A Climatological Study. Submitted to ATMOSPHERE-OCEAN (1980). T re id l , R.A., E.C. Birch and P. Sajecki, 1980b: A Catalogue of Northern  Hemisphere Blocking Situations for the Period 1945-1977. Atmospheric  Environment Service, Downsview, Ontario, Canada (to be published). Tung, K.K., 1977: Stationary Atmospheric Long Waves and the Phenomenon  of Blocking and Sudden Warming. Ph.D. Thesis, Harvard University, 222 pp. U.S. Department of Commerce, 1954-1973: Weather and Circulation of (Month, Year). Monthly Weather Review, Vol. 82-101, inclusive. U.S. Department of Commerce, 1949-1956: Daily Series Synoptic Weather  Maps, Northern Hemisphere Sea Level and 500 Mi l l ibar Charts, U.S. Weather Bureau, Washington, D.C. Van Mieghem, J . , 1961: Zonal Harmonic Analysis of the Northern Hemis- phere Geostrophic Wind Fie ld. Union Geodisique et Ge"ophysique Internationale, Monographie 8, Paris, 57 pp. Wagner, A. J . , 1979: Weather and Circulation of January 1979. Monthly  Weather Review, 107, 499-506. White, G.H., 1980: Skewness, Kurtosis and Extreme Values of Northern Hemisphere Geopotential Heights. Monthly Weather Review, 108, 387-401. White, W.B., and N.E. Clark, 1975: On the Development of Blocking Ridge Activity over the Central North Pac i f ic . Journal of Atmospheric  Science, 32, 489-502. Woffinden, C M . , 1960: Blocking Action. Meteorological Magazine, 89, 236-240. Yeh, T . - C , 1949: On Energy Dispersion in the Atmosphere, Journal of  Meteorology, 6, 1-16. 230 APPENDICES Arrangement and Purpose Appendices are numbered according to the Chapter to which they apply. Subsections and Figures number consecutively from the beginning of each Appendix. The material includes derivations of results presented in the text; procedural details for testing c r i t e r i a ; adjunct sets of diagrams; and other supporting documentation. The Hovmoller diagrams presented in Appendix VII - 1 (Figs. VII -1 and 2) are integral to Sections 7.3.3 and 7.4.3 of Chapter 7. The Normal Harmonics for 500MB - Winter, Figs. VII - 3 to 6, inclusive, provide a complete set WI to W4, of which W2 was presented as an example in Fig. 7.3. 231 APPENDIX I I - 1. Conventions adopted in this thesis regarding terms with  possible ambiguous meaning and regarding abbreviations. NORMAL The average value of a variable, taken over a suff ic ient period of time that i t can be accepted as a mean for climatological purposes. Thus, the Normal distribution of 500MB height for the Winter. GAUSSIAN Because of the above use of the word "normal," the alternative, Gaussian, wi l l be used to refer to a distribution which is s ta t i s t i ca l l y HEIGHT (of a constant pressure surface) Abbreviation for "geopotential height" (gph). The geopotential $ of unit mass of a ir at geometric height z is equal to the work required to raise the mass to that height from sea level. The "geopotential height" I is the height of a given level in the atmos-phere in units proportional to the geopotential energy of unit mass at that level . normal. I and z are interchangeable for most meteorological purposes. 232 APPENDIX II 11 - 1. The Motion of Planetary Waves. Assume a homogeneous incompressible f lu id on a rotating sphere and a uniform non-divergent zonal flow. If the flow is perturbed, the iner-t ia l response of the f lu id to the varying Coriol is Force wi l l generate a planetary (or Rossby) wave. The equations of motion are: £ + f u = - f i ( I I -2) where $ = geopotential. For horizontal non-divergent motion: 7T + ^ = 0 (II - 3) 3x dy • Therefore p^- (t, + f) = 0 where t, = relative vort ic i ty = ^ - -dX dy and f = planetary vort ic i ty = 2oJsin<j> Therefore ? + f = constant (II - 4) i . e . , the absolute vort ic i ty is conserved. If the zonal flow has a mean speed U and the perturbation is (u 1 , v') u = U + u' v = v' 233 Now, define a stream function such that 3y 3x and from (II - 4) <£+Ui>'2* + ^ -° (II -5) This wave equation wil l be sat isf ied by $ = A e i k ( x " c t ) c o s my i f c = U - 9 B 9 (II - 6) If m = 0 (no wave component along meridians) then c = U- 4-=ll - B ( ) (II - 7) k 2 2 ^ Thus a l l planetary waves move west relative to the zonal flow and the longer the wave length the greater the retrogressive speed. A wave wi l l become stationary relative to the surface i f L = 2TT 234 II - 2. The Response of Large-scale Waves to Advection of Relative and  Planetary Vort ic i ty. To isolate the principle under discussion we assume an incompres-sible non-divergent barotropic atmosphere, and that the f i e ld of geo-potential height at 500MB is described by the wave form $ = F(.t) sin kx sin ly 2 2 where the wave numbers k and 1 are defined as k = -r^  1 = j^-L x L y Then, following Hoi ton (1979) i t can be shown that v 2 ( | f ) . - I k 2 • l 2 >ff But V 2$ = - f V • v(^- V 2$ + f) at o g TQ Therefore | | = K'V • v(c g +f) (I.I - 8) where K is a positive constant 1 2 . . x, = j- v $ is the relative vort ic i ty 9 o f is the planetary vort ic i ty ||- is the local tendency. In Fig. II - 1 there is depicted at time t a schematic of the -f ie ld, of the associated c-f ie ld, and of the f- f i e ld . 235 Y (North) Fig, Schematic"500MB height and vorticity f i e l d s showing regions of planetary and relative vorticity advectioni Wave form of 4> — — — Lines of constant planetary vorticity* Lines of constant relative vorticity, ( Adapted from Holton, 1979i) 236 East of the ridge l ine and west of the trough l ine , e .g . , at 4-point P, V? > 0 along the flow so that V g • Vc > 0. Therefore this term contributes to an increase, of $ with time. Also, at P, vf = where j is a unit vector pointing north, and — > 0. But the y-component of Vg < 0 and therefore • vf < 0. Hence this term contributes to a decrease of $ with time. Thus the advec-tion of relative vort ic i ty over P wil l cause an increase of $ and tend to make the ridge progressive, while advection of planetary vort ic i ty wi l l tend to make the ridge retrograde. In the higher latitudes the large-scale pressure systems (warm blocking highs, cold quasi-stationary lows) tend to have relative vor-t i c i t y isopleths parallel to the stream flow and therefore relative vort ic i ty advection is small, at least near the core. On the other hand, the planetary effect is large and hence they often retrograde. 237 APPENDIX III III - 1. Analytic Discussion of the Anomaly Field Consider the f i e l d : I = -a^y + a^sin kx sin my At a maximum or minimum (e.g. , centre of high or low) 9Z —"=-ka0cos kx sin my = 0 oX o 9 ? and = -a^ + ma^sin kx cos my = 0 Figure III - 1 shows 2 orthogonal cross-sections xOz and y 'O ' z ' through a maximum. For any given value of y, i f — = 0, then O A x = 7r/2k, 3Tr/2k, . . . (2n+l)u/2k, . . . Now f ix x at one of these values, say, x = i\/2k and consider the variation of 1 in the z 'y ' plane: gZ — = -a 9 + ma-cos my = 0 Therefore y = 1 c o s _ 1 ( l | | ) (i) If a 2 = 0, then y = iT/2m, 2ir/2m, . . . nTr/2m, . . . ( i i ) If = ma^, then y = 0, a-n/m, . . . mr/m, . . . and therefore the number of maxima and minima is reduced by one half. 238 ( i i i ) If a 0 > ma 0, then cos" -'(—)• c. o m a^ is indeterminate and there can be no maxima or minima. The functions 1, 1 and therefore 1-1 may be varied at wil l by assigning values to a-|, a^, k and m. Patterns can be made even more 3 rea l i s t i c i f the linear term -a^y is replaced by a cubic -a^y . This wil l determine a parabolic N-S prof i le for the "instantaneous" zonal wind because If - - v 2 To simulate phase shi f t with latitude the function sin my may be generalized to sin [my + <j>(y)]. 239 Max t I * - - " 3 ft 2k '2 k 5Ti, 2k F i g . Orthogonal cross-sections xOz and y'O'z' through a maximum of Z(x,y). 240 APPENDIX IV IV - 1. To Develop a F i l ter Function Which I l lustrates the Effect of  the 5-day Average Let geopotential height prof i le around a given latitude be Z(.x,t) Resolve into harmonics Z k ( x , t ) = A k cos (kx - <okt)dt where k = wave number X = longitude A^ = amplitude oj k = angular frequency (day""'') Assume that wave components move with constant speed which wil l be w k ^- , that they maintain constant amplitude A^, and that the in i t i a l phase angle is zero: Let averaging interval = T days Then the time mean of Z b ( x , t ) is Therefore Z. = -o T cos (kx - a ) | , t )d(kx - oi. t ) = - — J ^ s i n kA cos ou^T - cos kA sin oo^T - sin kxj ^ [ s i CO.J L sin w.T cos kA + (1 - cos co.T)sin kA Now, let the amplitude of Z k = A k A Then, A^ = 0)i j j^sin^T + (1 - cos o ^T ) 2 J 1/2 T A (l - cos u> k T) 1 / 2 A k 2 2(1 - cos o>kT) Let y k = phase speed (in rads long, day" 1) Then y. = k k Also, let the averaging interval be 5 days, Ak2 2(1 - cos 5ky k ) Then R. = j-? = —  L k V (5ky k ) 2 where Rk is the response function. Examples If k = 1 and v . = O.OS/^ay" 1 R. = 0.99 If.k = 4 and p k = O.OS/^ay" 1 RR = 0.78 242 (A phase speed of .087 day " is equivalent to 5 degree day" , a fa i r l y typical long wave speed). If k = 8 and y k = 0.174 r day" 1 RR = 0.01 If k = 12 and U | < = 0.174 r day" 1 Rk = 0.03 Thus wave components in the 'long-wave' category moving at characteristic speeds (0 to 5 degree longitude day" 1) wil l be passed at between 80% and 100% of the original amplitude. Components with speeds characteristic of mobile baroclinic waves in the mid-latitudes wi l l be almost entirely attenuated. The f i l t e r function is shown in Fig. 4.0. IV - 2. Guidelines for Identif ication.of a Blocking Episode A. Necessary and Sufficient (This Study) 1. The 500MB analyses are used exclusively. 2. There must be a disruption in the pre-existing zonal flow by a pattern resembling one of Sumner's six c lassif icat ions (see 3.2). 3. During the 5-day period of the positive anomaly being tested, an anticyclonic centre must be observed on at least three of the five consecutive daily 500MB analyses. 4. The centre of the anticyclone must be north of 45°N. B. Suff icient (Treidl et a l , 1980a) "1. Closed isopleths must be present simultaneously in the surface and 500MB charts, sp l i t t ing the westerly current a loft into two branches. 243 2. The latitude belt where the high occurs extends northward from 35°N. 3. The minimum duration of the high must be five days." IV - 3. Procedure for Determination of Blocking Signature Cr i ter ia A. Select a large sample of positive anomalies from the Catalogue and l i s t year, pentad, position and magnitude in chronological order on a Master Sheet. B. From an information source (e .g. , published charts of daily 500MB height analyses for the Northern Hemisphere, or the Monthly Weather Review) and by applying the guidelines of Section 4.5.1.2, determine i f , in fact , a blocking episode was in progress at the time of and in the region of a specif ic l isted anomaly. Enter the particulars on a Master Sheet. C. Divide the cases into four seasonal sets. D. Plot: Anomaly Magnitude (dams) vs Anomaly Latitude (degrees) and mark the point • i f the anomaly was associated with a contem-poraneous block and O i f i t was not. E. Draw a curve separating the # 's from the O ' s . F. The results for WINTER and SUMMER are shown in Figs. 4.3(a) and 4.3(b), respectively. 244 PENTAD CALENDAR WINTER SPRING SUMMER FALL PE Interval PE Interval PE Interval PE Interval 68 Dec02 - Dec 06 13 Mar02 - Mar06 32 Jun05 - Jun09 50 Sep03 Sep07 69 Dec07 - Dec 11 14 Mar07 - Marll 33 JunlO - Junl4 51 Sep08 - Sepl2 70 Decl2 - Dec! 6 15 Marl 2 - Marl6 34 Junl5 - Junl9 52 Sepl3 - Sepl7 71 Dec! 7 - Dec21 16 Marl 7 - Mar21 35 Jun20 - Jun24 53 Sepl8 - Sep22 72 Dec22 - Dec26 17 Mar22 - Mar26 36 Jun25 - Jun29 54 Sep23 - Sep27 73 Dec27 - Dec31 18 Mar27 - Mar31 37 Jun30 - Jul04 55 Sep28 - 0ct02 1 JanOl - Jan05 19 AprOl - Apr05 38 Jul05 - Jul09 56 0ct03 - 0ct07 2 Jan06 - JanlO 20 Apr06 - AprlO 39 JullO - Jul l4 57 Oct08 - 0ctl2 3 Janll - Janl 5 21 April - Aprl5 40 Jul 15 - Jul 19 58 0ctl3 - 0ctl7 4 Janl6 - Jan20 22 Aprl6 - Apr20 41 Jul20 - Jul24 59 0ctl8 - 0ct22 5 Jan21 - Jan25 23 Apr21 - Apr25 42 Jul25 Jul29 60 0ct23 - 0ct27 6 Jan26 - Jan30 24 Apr26 - Apr30 43 Jul30 - Aug03 61 0ct28 - NovOl 7 Jan31 - Feb04 25 May 01 - May05 44 Aug04 - Aug08 62 Nov02 - Nov06 8 Feb05 - Feb09 26 May06 - MaylO 45 Aug09 - Aug 13 63 Nov07 - Novll 9 FeblO - Febl4 27 May 11 - May15 46 Aug 14 - Aug 18 64 Novl2 - Novl6 10 Febl5 - Febl9 28 May! 6 - May20 47 Aug! 9 - Aug23 65 Novl7 - Nov21 11 Feb20 - Feb24 29 May21 - May25 48 Aug24 - Aug28 66 Nov22 - Nov26 12 Feb25 - MarOl 30 May26 - May30 49 Aug29 - Sep02 67 Nov27 - DecOl 31 May 31 - Jun04 Season Total Pentads WINTER = PE 68 - PE 12 18 SPRING = PE 13 - PE 31 19 SUMMER = PE 32 - PE 49 18 FALL = PE 50 - PE 67 18 YEAR = PE 1 - PE 73 73 • Note: For Leap Year PE 12 contains 6 days. Fig. IV - 1. The Pentad Calendar 245 APPENDIX V V - 1. Smoothing of Areal Frequency Isopleths  Figs. 5.1 to 5.5, inclusive The positive anomaly centres, from which the blocking signatures were selected, were located by a search program to the nearest grid point I,J. It was obvious from a few t r i a l plots of the frequency iso-pleths that this procedure introduced an a r t i f i c i a l 'c luster ing' at certain grid-points. That is to say, there was a frequency gradient between adjacent grid points which was unjustified by the spacing of upper a i r stations. Therefore the f i e ld was s l ight ly smoothed as in Fig. V - 1 F C = I ( 4 F C + FA + FB + FD + F E ) Where F c = Ini t ia l Frequency at point C F^  = Frequency at Point A Fg = Frequency at Point B Fp = Frequency at Point D F £ = Frequency at Point E V - 2 . Nomenclature Master Catalogue The Catalogue identifying a l l positive and negative Anomaly Centres of 500MB 5-day average height f i e lds . (Fig. 4.2). 246 D E 'C • • B A 1_ 8" ( 4 F, + + F i g . V-1 Smootliing f u n c t i o n used i n the c o n s t r u c t i o n of frequency f i e l d s F i g . 5.1 to 5.5 i n c l u s i v e . 247 Blocking Signature Catalogue The Catalogue identifying a l l positive Anomaly Centres in the MASTER Catalogue which sat isf ied Criterion (3). (Fig. 4.8) Blocking Signature Sequence The Catalogue which sorts the Signatures Catalogue into Sequences using Criterion (4). (Fig. 5.11) SIG Any positive anomaly l isted in the Blocking Signature Catalogue SEQ Any Sequence l is ted in the Blocking Signature Sequence Catalogue SEQ.J Sequence consisting of only 1 SIG SEQn Sequence consisting of more than 1 SIG K.BLK A blocking episode identif ied from daily analyses by KNOX guidelines, APPENDIX IV - 2 T.BLK A blocking episode identif ied from daily analyses by TREIDL guidelines, APPENDIX IV - 2 PREDICTAND Identification of blocking episode (by unspecified source) by date, location and duration of actual block from daily analyses. PREDICTOR Identification of SIG and SEQ from Catalogue and relevant data V - 3. Test of Blocking Signatures and Sequences 1. This is a test of Blocking Signatures and Sequences to determine: (a) The success rat io for SIG components of SEQ's. How often are they related to a 5-day period of a blocking episode? 248 (b) The success ratio for SEQ's with respect to blocking episodes. 2. The independent data periods are June - November 1955, March - June 1956 and January, February and December 1952. 3. Let us designate the data related to the actual blocking episode as the PREDICTANDS and the data related to the SIGS and SIG. SEQ's as the PREDICTORS. Then the source of the PREDICTANDS was the Northern Hemisphere 500MB Daily Analyses and the source of the PREDICTORS was the Blocking Signature Sequence Catalogue. 4. The period chosen provides independent data because i t was not used to determine the threshold Criterion (3). 5. Go to the Blocking Signature Sequence Catalogue and, for that period, List each SEQ on a Master Sheet by (a) PE number of each component SIG (b) Starting date and location (c) Ending date and location (d) Maximum amplitude reached (dams) 6. For each SEQ examine corresponding 500MB daily height analyses and determine whether or not a related blocking anticyclone existed during each SIG pentad. Use guidelines in Appendix IV - 1, KNOX Enter (under K.BLK) Yes • No O 7. Consult an independent Catalogue of blocking in the Northern Hemisphere (we used Treidl et a l . , 1980b) and proceed as in 6. Enter (under T.BLK) Yes # No O 249 8. Enter comments concerning breaks in continuity of blocking episode during a SEQ, degree of confidence in block ident i f icat ion, occur-rence north or south of 75°N. 9. Count a l l SIG's which occurred in period corresponding to SEQ-j, SEQn and SEQ. Let number = N 1 , N and N. 10. Success ratio SIG's = K ' B N L K S 11. Proceed as in 10. for SEQ's. 12. For results see Table III of the main text. V - 4. Retrograde Atlantic Blocking as Revealed by a Blocking Signature  Sequence Fig. V - 2 i l lustrates how a blocking signature sequence ident i -f ied the wave of blocking which retrogressed from Scandinavia to Baffin Island December 16-31, 1976. The motion of individual daily 500MB ant i -cyclone centres (shown as 12-hour displacement vectors) was errat ic . Nevertheless, the vectors appear to be grouped in three areas, the f i r s t over Northern Scandinavia (December 16-20), the second over Greenland-Iceland (December 19-28) and the third over Baffin Island-Davis Strait (December 29-31). The adjustment in the mass f i e l d , December 19-20, was a striking example of "discontinuous retrogression." Note how the seat of blocking act iv i ty was transferred rapidly upstream from the Gulf of Finland to the East coast of Greenland. The vector clusters are reflected by Signatures A, B and C, respectively, and the retrograding blocking wave is associated with the westward signature motion. The Hovmoller (time-longitude) diagram for 500MB gph, 50-70°N (not shown), clearly confirms the retrograde motion. 250 Pig. V-2 I d e n t i f i c a t i o n of a retrograding North A t l a n t i c Block by a Blocking Signature Sequence. Period was 1200Z Dec. 16 to 1200Z Dec. 51, 1976. . •12 - hour displacement of 500MB anticyclone centre. (Canadian Meteorological Centre). Simultaneous centre-pair along ridge l i n e . 5 - day displacement of p o s i t i v e anomaly centres (blocking signatures) f o r : A Pentad 71 December 17 - 21 B Pentad 72 December 22 - 26 C: Pentad 73 December 2 7 - 3 1 Note discontinuous retrogression which occurred December 1 9 t h and 2 0 t h . 251 V - 5 . Frequency Distributions for Starting and Ending Signatures  during SUMMER, FALL and WINTER The following series of Figures (V - 3 to V - 8) taken together with Figs. 5.13 to 5.16 of the main text provide a complete set by season, and by year, of Frequency Distributions for Starting and Ending Signatures. (See Chapter 5.) 1 2 EUROPE V.SIBERIA SUMMER S T A R T I N G S I G S 3 i 4 I 5 I 6 ! 1 E.SIBERIA ALASKA 1 CANADA 1 GREENLAND EUROPE V.PACIEIC , E.PACIFIC N.ATLANTIC "1 1 1 1 1 1 1 1 1 1 P 1 1 1 1 1 1 1 1 1 1 1 i p 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 p 1 ! 0 30E 60E 90E 120E 150E 180 150V 120W '• 90W SOW 30W 0 30E 60E Pig. V-3 As i n Pig. 5.13 except f o r SUMMER EUROPE V.SIBERIA SUMMER 3 E.SIBERIA V.PACIFIC ENDING S I G S 4 I 5 ALASKA 1 CANADA E.PACIFIC 6 GREENLAND N.ATLANTIC ] EUROPE ~i i I I P I i i I I I I I 1 1 I P 1 1 1 1 1 1 1 1 1 1 1 1 1 1 I 1 1 1 1 p 1 1 i r — — r 0 30E 60E 90E 120E 150E 180 150W 120V 90W 60W 30W 0 30E 60E F i g . V-4 As i n Fig . 5.14 except f o r SUMMER F A L L EUROPE W.SIBERIA E.SIBERIA V.PACIFIC S T A R T I N G S I G S 4 I 5 ALASKA 1 CANADA E . P A C I F I C GREENLAND N.ATLANTIC EUROPE -I—i—i—i—i—i—i—i—i i i—i—i—i—i—i—i—i—1—i—i—i—i—i—i—i—i—i—i—i—!—i—i—i—i—i—i—i—i—i—p—i—I 0 30E 60E 90E 120E 150E 180 150W 120W 90W 60W 30W 0 30E 60E Pig. V-5 As i n Pig. 5.13 e x c e p t f o r PALL a U J EUROPE 2 W . S I B E R I A F A L L 3 E.SIBERIA V.PACIFIC ENDING S I G S 4 I 5 A L A S K A ! C A N A D A E . P A C I F I C GREENLAND N.ATLANTIC .1 EUROPE °0 ' '30E' '60E ' '90E' ' 120E 'l50E ' 180 ' 'l50V ' 120V '9oY '60W' '30W' ' 6 ' 'SOE' '60E Pig. V-6 As i n Pig. 5.14 except f o r PALL EUROPE 2 W.SJBERIR WINTER S T A R T I N G S I G S 3 1 4 I 5 E.5I5ER[fl ALASKA 1 CANADA W.PACIFIC , E.PACIFIC a LU on u_ GREENLAND N.ATLANTIC ] EUROPE °0 30E 60E 90E 120E 150E 180 150W 120W 90W 60W 30W 0 ' 30F." '60E F i g . V-7 As i n Pig. 5.13 except f o r WINTER 1 EUROPE 2 V. SIBERIA WINTER 3 E.SIBERIA V.PACIFIC ENDING S I G S 4 I 5 ALASKA 1 CANADA E .PACIFIC GREENLAND N.ATLANTIC EUROPE a LU cc 0 30E 60E 90E 120E 150E 180 I50W I2QW 90W 60W 30W 0 30E 60E $ Pig. V-8 As i n Pig. 5.14 except f o r WINTER 258 V - 6. Program for Computing and Plotting Histograms of Blocking Signa- ture Frequency per 10° Longitude. Reference: Chapter 5, Section 5.2.2. On the next page is l isted the computer algorithm for preparing longitudinal histograms of Blocking Signature Frequency from data read from the I,J gr id. This program has a general application and is designed to correct a bias which occurs when counting grid points into the 10° poleward converging sectors. It eliminates the requirement for repeated (and expensive) coordinate system transformations on large Hemispheric data sets. £ * * * + + #-** + + * * * * * * * + + + * + + * + *+ * * * * * + * * * + * * * * * * * * * * * + * * * C + PROCESS DATA GRIDS FROM UNIT 8 TO GENERATE * C* HISTOGRAMS BY LONGITUDE BAND. * INT EGE R * 2 I DATA( 1980) .LEN REAL ABSC(43) ,MID(36) READ(5 ,101) NDIV C* SET UP ABSCISSA VECTOR USED BY PLT * DO 1 1=1,43 1 ABSC ( I )= I *0 .2-0 .1 ABSC(43 )=8.4 C -RADDEG=57.2958 ZK2=973.71202 DO 70 L=1.5 (^*****+ C* READ IN A GRID IN NMC FORMAT, AND * C* PLOT THE HISTOGRAM FOR THAT GRID. * DO 5 1=1.36 5 M ID ( I )=0 .0 CALL READ(I DATA . LEN.0 ,LNUM,8 ,&99) K=LEN/2-1977 INT= 1 N1 = 15 N2 = 33 £ * * + * * * + * * * * * + + * + ++ + + + * * * * + *** + + + **•* + * + C* STEP THROUGH THE DATA POINTS, * C+ TALLYING VALUES INTO THE CORRECT * C* LONGITUDE ZONE. DO 65 J=1 .51 DO 60 I=N1,N2 K = K+ 1 VAL=IDATA(K)/( 100.0*FLOAT(NDI V ) * *2) I F ( V A L . E O . 0 . 0 ) GOTO 60 + + + + + + + * + * + + + + C* DIVIDE EACH GRID BLOCK INTO * C* ' N D I V BY ' N D I V SUBUNITS * C* TO ACCURATELY ASSIGN PORTION * C* OF DATA VALUE TO LONG. BAND. * DO 50 11=1,NDIV DO 50 JJ=1.NDIV X = I + I I /FL0AT(NDIV)-24.55 Y=J+J J/FL0AT(NDIV)-26.55 R2=X**2+Y**2 C* COMPUTE LATITUDE OF (X ,Y ) * RLA=RADDEG*ARSIN((ZK2-R2)/(ZK2 + R2 ) ) C+ IF LAT>75N, IGNORE POINT * C* OTHERWISE, COMPUTE LONG. * I F ( R LA .GT .75 ) GOTO 50 I F ( X . E O . 0 . 0 ) GOTO 10 ELON=RADDEG*ATAN(ABSf Y/X ) ) GOTO 15 10 EL0N=90.0 15 I F ( Y . L T . O . O ) GOTO 25 I F ( X . L T . O . O ) GOTO 20 GOTO 40 20 ELON=18O.O-EL0N GOTO 40 25 I F ( X . L T . O . O ) GOTO 30 EL0N=36O.0-EL0N GOTO 40 30 ELON=180.0+ELON 40 RLO=15 O+ELON I F ( R L O . G E . 3 6 0 . 0 ) RL0=RL0-360.0 C* TALLY VALUE INTO THE * C* APPROPRIATE LONG. BAND. * LB=RLO/10.0+1 MID(LB)=MID(LB)+VAL 50 CONTINUE 60 CONTINUE I F ( ( d . E Q . 15) .OR. ( J . E O . 3 7 ) ) I NT = INT-1 N1=N1-INT N2=N2+INT 65 CONTINUE WR ITE (6 .100 ) (M ID ( I ) . 1=1 ,36 ) C* CALL PLT TO PLOT THE HISTOGRAM. * CALL PLT (M ID .L .ABSC ) 70 CONTINUE 99 CALL PLOTND STOP 100 FORMAT(' ' . 1 8 F 6 . 1 , / , ' ' . 1 8 F 6 . 1 ) 101 FORMAT(14) END 260 APPENDIX VI VI - 1. Conversion of the Thickness of the 1000MB - 500MB Layer into  i ts Mean Temperature It can be shown from the hydrostatic equation and the equation of state that for dry air the thickness of a layer is proportional to i ts mean temperature (T). In the real atmosphere the presence of water vapour decreases the density and therefore increases the thickness which now becomes proportional to the 'mean virtual temperature' (T ). This is the mean temperature of a layer of dry air with the same density as the moist a ir layer. Now T v > T, but reference to Table 72 of List (1966) wil l show that the difference is quite small (0.02° to 0.50°C) for the range of mean temperatures of the lOOOMB - 500MB layer usually en-countered in the mid- and high latitudes. Consequently i t wi l l be s u f f i -ciently accurate for our purposes to assume T y = T. It follows that contours of constant thickness can readily be converted to isotherms of constant T. Hence the lOOOMB - 500MB thick-ness f i e ld i s , in effect , a f i e ld of mean temperature for the lower half of the troposphere. The conversion is readily derived from the hypsometric equation: Where Z 9 = gph at level 2 Z, = gph at level 1 R. = gas constant for dry air = 287JK" kg T y = virtual temperature at pressure p g = acceleration of gravity As explained above this may be written: 1 - I = — lhf=R4 T i n p 2 If p-j = 1000MB and p 2 = 500MB then Z 5 0 Q - Z 1 0 0 0 = 20.27T Thus for any value of (2gQg - ^ - j Q O O ^ 1 N M E ^ R E S 7 _ | Z500 - Z1000 ] 1 " \ 20.27 / Even more convenient relationships can be derived which wil l make possible the direct relabell ing of conventional 1000MB - 500MB thickness contours drawn at 6 dam intervals in terms of isotherms of (or K ) with integral values at 3° intervals. We have: (a) 0.5 (ZgQQ - 2 - | Q Q Q ) dams - 4.0 dams = T degrees K e - 9 - ' Z500 ' Z1000 = 5 4 6 d a m s Therefore T = (0.5)(546) - 5.0 = 269K and successive contours can be labelled as isotherms at 3° intervals. 262 (b) In the (.1000MB - 500MB) normal charts (available from the author) the contours are labelled in dams less 500. The following relationship obtains: 0 .5 (Z 5 0 Q - Z 1 0 0 0 - 500) - 27 = T degrees C e .g . , 0.5(546 - 500) - 27 = -4°C Again, since 6 dams corresponds to 3°C (or 3K) the thickness contours may quickly be relabelled as 3° interval isotherms. The con-version table is as follows: TABLE VI - 1 Thickness (dams) T( °C) T(K) 1000 - 500MB 492 -31 242 498 -28 245 • 504 -25 248 510 -22 251 516 -19 254 522 -16 257 528 -13 260 534 -10 263 540 - 7 266 546 - 4 269 552 - 1 272 558 + 2 275 564 + 5 278 570 + 8 281 576 +11 284 263 VI - 2. Transformation of the MSL Pressure into Geopotential Height of  the 1000MB Surface The transformation algorithm is generated as follows: Let height of 500MB surface = K Z 2 ,(I,J) Let height of lOOOMB surface = h-, .(I,J) Let MSL pressure = p.(I,J) Where K = year 1 = pentad number (I,J) = NMC coordinate 2 = 500MB index 1 = lOOOMB index For the time being we shall abbreviate these variables to Z 2 , Z-j and p. Z-| is the unknown but so closely related to p that: ^ e 3(p - 1000) d a m s is a reasonable f i r s t approximation. Z-j is also temperature dependent, s ignif icant ly so for substantial deviations of p from lOOOMB. 264 This is a West to East cross-section schematic showing topography of 500MB and 1000MB surfaces. Consider the a i r column AB. Its vertical extent Z 2 ~ ]^ (called thickness) is proportional to the mean temperature of AB = T^. In fact: Z 2 - Z ] * 2.027 T M What we want, however, is not T^ but T , the mean temperature of the air column BC. Clearly, there must be a strong positive correlation between T^ and T . The following empirical relationships (Moffitt and Ratc l i f fe , 1972) gave good results when tested over a wide range of thick-nesses for MSL pressure deviations from 1000MB, of up to 30MB. (i) If Z 2 - Z 1 < 478.00 dams, T = (0.93 x 478 - 223) K. m ( i i ) If 541.50 dams **• Z 2 - 1, > 478.00 dams, Tm = [0.93 x (Z 2 - Z^ - 223] K ( i i i ) If Z 2 - Z-, > 5 4 1 . 5 0 dams. x m = [ 0 . 5 2 x (Z 2 - Z^ - 1 ] K To compute Z-j at this stage, the f i r s t approximation is : ]/ 3(Kp.(.I,J) - 1000) These values of Z-j are used in ( i ) , ( i i ) or ( i i i ) , whichever applies. This wil l provide the f i e ld of T . The second and f inal approximation for the 1000MB height i s : (P - 1000)x Z l = m 342 The f ie ld of KZ-, .(I,J) provides the 1000MB height data set. VI - 3 . Computation of Normal and Standard Deviation Fields The Normal geopotential height at (I.,J) for the i th pentad is (Z) w A K. (I,J) N 2 % ^K=l (I,J) Where N = period of record and Z-j represents the 5-day average of gph for pentad i . The Normals for the respective seasons are: 73 (W(I,J) = ' T8 (ZSp)'(I,J) 19 12 2 i=i 31 2 a.) i=13 1 2 ( z i ) ( I =68 u ' 0) ,0 ) and so on. 266 For the Seasonal Standard Deviations at (I,J) we used: C,J) WN 18N HA 2 + 2 etc • s etc. VI - 4. Computation of Coefficient of Skewness Specif ical ly for WINTER at (I,J): (1,0) A program was written to calculate values of CS^ , CS^p, CS<.y and CS p L for each grid-point for the 1000MB, 500MB and thickness data and the results were printed out in a geographical format. Subsequently a 'plot contour' routine yielded spatial distributions of areas of s ig -nif icant skewness, either positive or negative. VI - 5. Computation of Coefficient of Kurtosis 0 Specif ical ly for WINTER at (I.J): A procedure similar to that for calculating f ields of skewness was followed. CK. 'WN 267 APPENDIX VII VII - 1. Hovmoller Diagrams and Computation of Zonal Speed of troughs  and ridges For rapid computation of zonal speed of troughs or ridges, let the contour axis RS make an angle a with the merid-X through R. Then the zonal speed c in degrees of longitude per day (for the relative axis scales of the diagrams used in this thesis) is c = 5 tan a The following tabulation is provided for convenience of the user. TABLE VII - 1 Days Contour Axis with Meridian Zonal Speed of trough or ridge a (degs.) Angular Speed Linear Speed (kmhr- 1) (Degs. Long, per Day) 40°N 60°N 80 28 101 66 70 14 49 32 60 9 31 20 50 6 21 14 40 4 15 10 30 3 10 7 20 2 6 4 10 1 3 2 268 HOVMOLLER 500MB RVG(50N-70N) NOV 1.1978-FEB 28.1979 Fig VII-1 Same as Fig. 7.1 except f o r November'1, 1978 to February 28, 1979. Note episodes of A t l a n t i c Blocking A followed by Pacific-Alaska Blocking P. (See Section 7.4.3). 269 HOVMOLLER 500MB RVG(30N-50N) NOV 1.1978-FEB 28.1979 DEGREES 0 180 0 Fig. VII-2 Hovmoller Diagram f o r 30°N - 50°N November 1, 1978 to December 28, 1979-(See Section 7.4.3). 270 VII - 2. Zonal Harmonics for the Normal 500MB Height Field - WINTER The following f igures, VII - 3 to VII - 6, inclusive, show the Zonal Harmonics in the Northern Hemisphere for Waves 1 to 4, respec-t ively. (See Section 7.3.4(b) of the Text.) 271 120E 100E SOE F i g . VII-3- F i r s t harmonic (W1) of the normal 500MB height f i e l d f o r WINTER (December 1 to February 28). Contours l a b e l l e d i n deca-metres. I n t e r v a l = 1 dam. F i g . VII-&- As i n Figure VII-3 , . except f o r second harmonic (W2). F i g . VII-5- As i n F i g . VII-3- , harmonic ( W 3 ) . e x c e p t f o r t h i r d 274 12DE 100E BOE F i g . VII- 6 As i n Fig. VII-3 > except f o r fourth harmonic (W4). 

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