UBC Theses and Dissertations

UBC Theses Logo

UBC Theses and Dissertations

Atmospheric blocking in the northern hemisphere Knox, John Lewis 1981

Your browser doesn't seem to have a PDF viewer, please download the PDF to view this item.

Item Metadata

Download

Media
831-UBC_1981_A1 K66.pdf [ 13.88MB ]
Metadata
JSON: 831-1.0095459.json
JSON-LD: 831-1.0095459-ld.json
RDF/XML (Pretty): 831-1.0095459-rdf.xml
RDF/JSON: 831-1.0095459-rdf.json
Turtle: 831-1.0095459-turtle.txt
N-Triples: 831-1.0095459-rdf-ntriples.txt
Original Record: 831-1.0095459-source.json
Full Text
831-1.0095459-fulltext.txt
Citation
831-1.0095459.ris

Full Text

ATMOSPHERIC BLOCKING IN THE NORTHERN HEMISPHERE by JOHN LEWIS KNOX B.A., U n i v e r s i t y of Toronto, 1939 M.A., U n i v e r s i t y 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 requirements  this thesis f o r an  of  British  it  freely available  agree that for  understood for  Library  shall  for reference  and  study.  I  for extensive  that  h i s or copying  f i n a n c i a l gain  be  her or  shall  publication  not  be  Date  DE-6  (2/79)  of  Columbia  make  further this  thesis  head o f  this  It  my  is  thesis  a l l o w e d w i t h o u t my  of  The U n i v e r s i t y o f B r i t i s h 2075 Wesbrook P l a c e V a n c o u v e r , Canada V6T 1W5  the  representatives.  permission.  Department  copying of  g r a n t e d by  the  University  the  p u r p o s e s may by  the  I agree that  permission  department or  f u l f i l m e n t of  advanced degree at  Columbia,  scholarly  in partial  written  ii  ABSTRACT  Blocking i s generally understood as the obstruction on a large scale of the normal west - to - east motion of mid-latitude systems.  pressure  I t i s a p e r s i s t e n t phenomenon l a s t i n g from one t o several  weeks and the r e s u l t i n g prolonged weather regimes may have serious economic and s o c i a l consequences.  The recent Northern Hemisphere winters,  s t a r t i n g 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 r e l a t e d t o prolonged episodes of large s c a l e blocking. the i n t e n t of t h i s study i s to i n v e s t i g a t e the s t a t i s t i c s and c e r t a i n diagnostics of blocking i n the Northern Hemisphere.  The f i r s t of  the three primary objectives i s to present and i n t e r p r e t the s p a t i a l 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 r e l a t i n g the blocking anticyclone to i t s associated p o s i t i v e anomaly of 5-day mean 500MB height. 'blocking signatures.  1  Anomalies meeting the c r i t e r i a are c a l l e d  We present the seasonal  of these signatures by longitude and by area.  frequency of occurrence The r e s u l t s are i n good  agreement with published studies f o r the oceans, but they a l s o reveal a high frequency of blocking signatures over the Northeastern Archipelago.  Canadian  This r e s u l t , dubbed the 'Baffin Island Paradox' i s f u r t h e r  investigated and r a t i o n a l i z e d . A catalogue  has been prepared which i d e n t i f i e s the date, centre  l o c a t i o n 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 e p i sodes.  iii  The s e c o n d o b j e c t i v e incidence of blocking, feature  i s to investigate  in either  fields  latitude  the genesis  a r e found  high  stage,  o f 5 - d a y mean g e o p o t e n t i a l .  o f s i g n i f i c a n t l y low k u r t o s i s  r e g i o n s where  regions with  t h e d e v e l o p i n g o r the mature  non-Gaussian d i s t r i b u t i o n s  winter,  whether  During  i n certain mid-  and a m p l i f i c a t i o n o f b l o c k i n g  ridges  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  regions  i n higher  interrupt  latitude  the smaller f l u c t u a t i o n s  The f i n a l first  at  objective  s i x harmonics  characteristics lated  Results  500MB  agreement w i t h  height  around  f o r the northern  that there are spectral  signatures  occur.  variance  blocking,  latitude  zone a r e e m p h a s i z e d .  f o r t h e oceans  regimes  harmonics  the higher  contributions The is  ( 1 5 t o 25%)  'Baffin  found t h a t  retrograding  where  (waves  five  Island Paradox'  and s i x ) o f t e n  one t o f o u r .  During make  there i s such  significant  variance.  i s also studied  i n the m a j o r i t y o f cases B a f f i n blocks.  associated  zonal flow  v a r i a n c e o f 500MB h e i g h t .  to the total  North A t l a n t i c  It is  90% o f t h e s p a t i a l  f o r by wave c o m p o n e n t s  When t h e 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 of spatial  centred  are i n general  patterns  a t 6 0 ° N , more t h a n  i s accounted  a marked r e d u c t i o n  zones  (1980).  we f o u n d t h a t ,  o f 500MB h e i g h t  and s p a t i a l  Harmonics a r e c a l c u -  During the s t r o n g l y a m p l i f i e d meridional flow w i t h major  height.  d i s t i n c t i v e to the regions  Our r e s u l t s  those o f Austin  often  between t h e  and t h e temporal  blocking episodes.  of daily  anticyclones  episodes  the normal g e o p o t e n t i a l  o f t h e l o n g wave p a t t e r n  from p r o f i l e s  blocking  about  blocking  i s t o examine t h e a s s o c i a t i o n  of concurrent  40°N a n d 6 0 ° N .  found  where mature  using harmonics.  blocks originate  from  It  iv  F i n a l l y , f u l l latitude zonal harmonic analyses (15 N to pole, waves U  1 to 4) are presented for three case studies of major blocking - (a) land-North A t l a n t i c ,  (b)  P a c i f i c Ocean-Alaska, and  (c)  Green-  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  ii  TABLE OF CONTENTS  v  LIST OF TABLES  xii  LIST OF FIGURES  xi i i  LIST OF SYMBOLS  xx  ACKNOWLEDGEMENT  xxiv  CHAPTER 1  2.  INTRODUCTION  1  1.1  NATURE AND IMPORTANCE OF BLOCKING  1  1.2  PURPOSE AND SCOPE OF THIS STUDY  8  THE PHENOMENON OF BLOCKING  12  2.1  INTRODUCTION  12  2.2  WHAT IS BLOCKING?  14  2.3  A TYPICAL MAJOR BLOCKING EPISODE  15  THE MOTION OF BLOCKING ANTICYCLONES  18  2.4.1  Progression  26  2.4.2  Retrogression  26  • 2.4  2.5  CONSERVATION OF POTENTIAL VORTICITY A H e u r i s t i c 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 REAL-TIME BLOCKING EPISODE  2.10  THE EFFECT OF BLOCKING ON THE CIRCULATION OF THE STRATOSPHERE  47  CONCLUDING REMARKS  51  2.11 3  4  1  1  47  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  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 4.5  4.6  Sequel to the P i l o t Study  71  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  ANOMALY CENTRES  75  4.6.1  Location of Centres  75  4.6.2  Preparation of Master Catalogue  76  vii  CHAPTER  Page 4.7  5  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  I n t e r p r e t a t i o n of C r i t e r i o n  88  4.7.3  Blocking Signature Catalogue  89  DISTRIBUTION OF SIGNATURES AND SEQUENCES  91  5.1  INTRODUCTION  91  5.2  DISTRIBUTION OF BLOCKING SIGNATURES  91  5.3  5.4  5.2.1  Area! D i s t r i b u t i o n  5.2.2  Longitudinal D i s t r i b u t i o n  »  91 100  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 B a f f i n Island Paradox  123  5.3.7  Secular V a r i a t i o n of Blocking Signatures  127  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  6.5  6.6  6.4.1  Normals and Standard Deviation  6.4.2  Accuracy of Normal and Variance Fields  6.4.3  Interpretation of Standard Deviation Fields  STATISTICAL MOMENTS - PART II 6.5.1  Skewness  6.5.2  Kurtosis  6.5.3  Comparison of CS and CK F i e l d s with other Results  6.5.4  S i t e - S p e c i f i c Frequency  Distributions  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 7  Page 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  S e l e c t i o n of Representative  f o r Analyses and Display of Results  172  7.3.3  The Hovmoller Diagram  173  7.3.4  Zonal Harmonic Analysis of the 500MB Height F i e l d Temporal V a r i a t i o n of the Zonal Harmonics at Selected Latitudes Computation and Presentation of Zonal  7.3.5 7.3.6  7.3.7 7.4  177 179  Indices of U, V and U/V  182  Concluding  184  Remarks  PRESENTATION OF RESULTS 7.4.1  8  Latitudes  186  Spectral A t t r i b u t e s of Blocking by Region of Occurrence  186  7.4.2  Interpretations of Major Blocking Episodes  192  7.4.3  B a f f i n Island Blocking  197  7.4.4  Zonal Harmonics of Blocking  204  7.5 SUMMARY RESULTS AND CONCLUSIONS  '  216 218  X  Paoe 224  REFERENCES APPENDICES:  ARRANGEMENT AND PURPOSE  230  APPENDIX : I Conventions adopted i n t h i s Thesis regarding terms with possibly ambiguous meaning, and regarding abbreviations  231  APPENDIX I I  232  II - 1  The Motion of Planetary Waves  232  II - 2  The Response of Large-Scale Waves to Advection of Relative and Planetary Vorticity  234  APPENDIX I I I  A n a l y t i c a l Discussion of the Anomaly F i e l d  240  APPENDIX IV  APPENDIX  237  IV - 1  Development o f a F i l t e r Function which I l l u s t r a t e s the E f f e c t of a 5-Day Average  240  IV - 2  Guidelines f o r I d e n t i f i c a t i o n of a Blocking Episode  242  IV - 3  Procedure f o r Determination of Blocking Signature C r i t e r i a  243 245  V V  1  Smoothing of Area! Frequency Isopleths  245  V  2  Nomenclature  245  V  3  Test of Blocking Signatures and Sequences  247  V  4  Retrograde A t l a n t i c Blocking as Revealed by a Blocking Signature Sequence  249  V  5  Frequency D i s t r i b u t i o n s f o r S t a r t i n g and Ending Signatures during SUMMER, FALL and WINTER 251  V  6  Program f o r Computing and P l o t t i n g Histograms of Blocking Signature Frequency per 10° Longitude 258  xi  Page APPENDIX  VI VI - 1  VI - 2  VI - 3  260 Conversion of the Thickness of the Thickness of the (1000MB - 500MB) Layer i n t o i t s Mean Temperature  260  Transformation of the MSL Pressure i n t o Geopotential Height of the lOOOMB Surface  263  Computation of Normal and Standard Deviation Fields  265  VI - 4  Computation of C o e f f i c i e n t of Skewness  266  VI - 5  Computation of C o e f f i c i e n t of Kurtosis  266  APPENDIX VII  267  VII - 1  Hovmoller Diagrams  267  VII - 2  Zonal Harmonics ( f u l l l a t i t u d e ) f o r 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 A f f e c t i n g B a f f i n Island  125  6.1  Range of C o e f f i c i e n t s of Skewness and Kurtosis outside of which the D i s t r i b u t i o n i s S i g n i f i c a n t l y D i f f e r e n t from Normal Average (by geographical category) of Harmonic Data f o r Cases Listed i n Section 7.4.1  154 189  Standard Deviation and D i s t r i b u t i o n of Power f o r Representative Days December 30, 1962 to January 14, 1963  193  Harmonics a t 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  Discrete Harmonic Data f o r WI to W6 by Latitude f o r North A t l a n t i c Block December 23, 1978  209  Discrete Harmonic Data f o r WI to W6 by Latitude f o r Alaska Block January 4, 1979  214  lOOOMB - 500MB Thickness (dams) vs Mean Temperature (oc or ° A )  262  The West-to-East Speed of a Trough or Ridge Using the Hovmoller Diagram  267  7.1 7.2  7.3  7.4 7.5  VI-1 VII-1  XI  11  LIST OF FIGURES Figure 1.1 1.2  Page Normal 500MB height, standard deviation f o r WINTER  2  Contours and isotherms on the 500MB surface, 0300 GMT, February 20, 1948  5  1.3  Mean 700MB contours f o r Winter 1976-77  7  2.1  Normal height of the 1000MB surface f o r WINTER Normal height of the 500MB surface f o r  16  WINTER  17  2.3(a)  Evolution from zonal flow to amplifying wave  19  2.3(b)  Mature blocking anticyclone centred Northern Scotland P o s i t i o n s of f r o n t s during two 10-day periods:  20  2.2  2.4  (i) (ii) 2.5  preceding the formation f o l l o w i n g the establishment of the c u t - o f f high  21  Schematic representation of the v e r t i c a l s t r u c t u r e of a high-level anticyclone  22  Meridional motion with a n t i c y c l o n i c and c y c l o n i c branches and the implied v e r t i c a l s t r e t c h i n g or shrinking  29  Schematic diagram showing the changes from the normal " s i n u s o i d a l " a i r movement i n the upper troposphere, r e s u l t i n g from convergence above a s i n k i n g cold a i r mass i n 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 stability criterion  34  2.10  Normal 500MB contours i n January, Southern Hemisphere  38  2.6  2.7  XIV  Figure 2.11 2.12 2.13 2.14  Page Normal 500MB contours in J u l y , Southern  Hemisphere  39  Normal 500MB contours in January, Northern  Hemisphere  Normal 500MB contours in J u l y , Northern  Hemisphere  41 ,  42  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 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 l u s t r a t i n g simulation at 500MB of a blocking episode using 1967 11-level GFDL GCM .  48  Seasonal mean 30MB geopotential height and temperature f i e l d s for Summer and Winter Northern Hemisphere Seasons  49  3.1(a)  S p l i t j e t 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 j e t  60  3.6  5-day mean. 700MB height and anomaly for  2.18  December 10-14, 1968 and December 17-21, 1968 3.7  Same as Figure 3.6 except for December 24-28, 1968  63 64  Figure 4.0  F i l t e r i n g function f o r 5-day averaging  4.1  NMC Octagonal  4.2  Sample page of Master Catalogue  4.3(a)  Threshold f o r Blocking Signatures - WINTER  4.3(b)  Threshold f o r Blocking Signatures - SUMMER  4.4  Standard deviation of 5-day mean 500MB height f o r WINTER  4.5  Standard d e v i a t i o n o f 5-day mean 500MB height f o r SUMMER  4.6  Normal height of 500MB surface f o r WINTER  4.7  Normal height of 500MB surface, f o r SUMMER  4.8  Sample page of BLOCKING SIGNATURE CATALOGUE  5.1  Frequency of occurrence of Blocking Signatures f o r ALL SEASONS  5.2  As i n Figure 5.1 except f o r WINTER  5.3  As i n Figure 5.1 except f o r SPRING  5.4  As i n Figure 5.1 except f o r SUMMER  5.5  As i n Figure 5.1 except f o r FALL  5.6  Frequency of occurrence of Blocking Signatures by longitude - ALL SEASONS  5.7  As i n Figure 5.6 except f o r WINTER  5.8  As i n Figure 5.6 except f o r SPRING  5.9.  As i n Figure 5.6 except f o r SUMMER  5.10  As i n Figure 5.6 except f o r FALL  5.11  Sample page of BLOCKING SIGNATURE SEQUENCE CATALOGUE  Grid  xv i  Figure 5.12(a)  Page Frequency d i s t r i b u t i o n of Signature Sequence durations  116  5.12(b)  Frequency d i s t r i b u t i o n of Blocking Durations  117  5.13  Total ( i . e . , annual) frequency by longitude of i n i t i a t i o n of a l l signature sequences  119  of termination of a l l signature sequences  120  5.15  As in Figure 5.13 except for SPRING  121  5.16 5.17  122  5.18(a)  As-'in Figure 5.14 except for SPRING Example of blocking Hudson Bay-Baffin IslandDavis S t r a i t Long-period variations in index numbers,  5.18(b)  Annual frequency of blocking highs A t l a n t i c  5.14  Total ( i . e . , annual) frequency by.longitude  Nd, and sunspot numbers, N  126 129  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 5.20(b)  Duration (days/year) of blocking  6.1  Normal height of the lOOOMB surface for  •  132a 132a  WINTER  140  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  6.2  6.6  Normal height of the 500MB surface for  height for WINTER  145  height for WINTER  146  Standard deviation of 5-day average lOOOMB  Standard deviation of 5-day average 1000MB - 500MB thickness f o r WINTER Schematics:  Skewness and Kurtosis  Skewness of 5-day average 500MB height f o r WINTER Bering Sea WINTER Frequency of 500MB extremum Bering Sea WINTER Frequency of 500MB height As i n Figure 6.10(a) except f o r Northeast Canadian Archipelago As i n Figure 6.10(b) except f o r Northeast Canadian Archipelago As i n Figure 6.9 except for-SUMMER Kurtosis of 5-day average height f o r WINTER As i n Figure 6.10(a) except f o r Northeast Atlantic As i n Figure 6.10(b) except f o r Northeast Atlantic Hovmoller Diagram of 500MB height p r o f i l e 50ON - 70ON, December 1, 1962 t o March 31, 1963 Same as Figure 7.1 except f o r 30°N - 50°N Second Harmonic of the normal 500MB height f o r WINTER Hovmoller diagram of Second Harmonic of 500MB height 50°N - 70°N f o r December 1, 1962 to March 31, 1963 Amplitude, phase vs time, f o r Second Harmonic at 60°N, December 1, 1962 to March 31, 1963 Comparison between U , 50°N - 70°N and U , 30ON - 50°N t  z  t  xv i i i  Figure 7.7  Page Phase of harmonics for NORMAL 500MB heights WINTER'  188  7.8  As in Figure 7.4 except for Third Harmonic  194  7.9 7.10  As in Figure 7.5 except for Wave Number three Change with time of the r a t i o R of zonal (U) to meridional (V) components at 60°N, December 1, 1962 to March 31, 1963  195 196  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 l d on December 23, 1978 during a major episode of blocking over the North A t l a n t i c 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  F i r s t harmonic (Wl) of the 500MB height f i e l d on January 4, 1979 during a major episode of blocking, Alaska and Southwest along the west coast of B r i t i s h Columbia  211  7.18  As in Figure 7.17 except for the second  7.19  As in Figure 7.17 except for the third  11-1 III-1 IV-1  harmonic (W2)  212  harmonic (W3)  213  Planetary and r e l a t i v e v o r t i c i t y advection  235  Orthogonal cross-sections xOz and y ' O ' z ' through a maximum of Z Pentad Calendar  239  244  xix  Page  Figure V-l  V-2  Smoothing function used i n the construction of frequency f i e l d s Figures 5.1 to 5.5, inclusive  246  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  250  V-3  As i n Figure 5.13 except f o r SUMMER  V-4  As i n Figure 5.14 except f o r SUMMER  253  V-5  As i n Figure 5.13 except f o r FALL  254  V-6  As i n Figure 5.14 except f o r FALL  255  V-7  As i n Figure 5.13 except f o r WINTER  V-8  As i n Figure 5.14 except f o r WINTER  257  Hovmbller Diagram of 500MB height p r o f i l e 50ON - 70°N, November 1, 1978 to February 28, 1979  268  Same as i n Figure VII-1 except f o r 30°N - 50ON  269  VI1-1  VI1-2 VI1-3  252  256  F i r s t harmonic (WI) of the normal 500MB height f i e l d f o r WINTER  271  VII-4  As i n VI1-3 except f o r second harmonic (W2)  272  VII-5  As i n VII-3 except f o r t h i r d harmonic (W3)  VII-6  As i n VII-3 except f o r fourth harmonic (W4)  273 274  XX  LIST OF SYMBOLS Symbols are usually defined on f i r s t i n t r o d u c t i o n i n the t e x t ; 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 i n which i t i s used. Symbol A  Units Usually Used  Meaning Anomaly of geopotential height  (dam)  (Z - Z) yy  A (.I,J) k  Anomaly of Z f o r pentad (yy,k)  (dam)  at ( I , J ) ^A^  Magnitude of an Anomaly Centre  (dam)  for pentad (yy,k) A  Amplitude of nth Harmonic (Wn)  (dam)  c  Phase speed of a wave  (m s 1)  CS  C o e f f i c i e n t of Skewness E y^/a^  ( - )  CK  C o e f f i c i e n t of Kurtosis = y ^ a  ( - )  n  -  4  Decametre (1 dam = 10 m)  (dam)  f  C o r i o l i s parameter = 2ftsin<j>  (s~^)  g  Acceleration of g r a v i t y = 9.81 m s"^  (m s~^)  gph  Geopotential height  h  Scale height = 29.3T = height of an  (dam)  isothermal atmosphere with temperature = T  (km)  XXI  Symbol I  Meaning  '  Units Usually Used  Abscissa, NMC Octagonal Grid Fig. 4.1  J  ( - )  Ordinate, NMC Octagonal Grid Fig 4.1  ( - )  k  Wave number i n zonal (x) d i r e c t i o n  ( - )  L  Wave length ( l i n e a r )  (km)  m  Wave number i n meridional (y) direction  PE  ( - )  Pentad, one of the 73 5-day i n t e r v a l s s p e c i f i e d i n Fig. IV - 1  PE  y y  n Q  H  k  -The K  t n  pentad i n year (19)yy  ( - ) ( - )  Wave number  (- )  Sensible heat f l u x  (W m ) -2  Gas constant f o r dry a i r = 2.87 x 1 0 m 2  R  t  2  s " K' 2  1  (K m s" ) _ 1  2  Ratio (U /V ) of zonal to t  t  meridional average of wind at time t S  n  ( - )  % of t o t a l variance of Z ( A ) around a l a t i t u d e contributed by Wn  ( - )  SEQ  Sequence of Blocking Signatures  ( - )  SIG  Blocking Signature  ( - )  T  Temperature ( K )  ( - )  u  x-component of v e l o c i t y eastward  (m s ^)  2  Symbol  Units Usually Used  Meaning  U  Background zonal current  (m s ^)  U^  Zonal average a t time t of the algebraic x-component of v e l o c i t y = [u ]  (m s" )  v  y-component of v e l o c i t y poleward  (m s l )  V  Horizontal v e l o c i t y vector  ( - )  1  t  -  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  yy  Z-|  Z  y y  2  ^ ( I J J )  k  (I,J)  (dam)  5-day mean height f o r pentad  (yy,k)  of 1000MB surface at ( I , J )  (dam)  5-day mean height of 500MB surface  (dam)  Z (I,J)  Normal height at ( I , J ) f o r pentad k  (dam)  Z (I,J)  Normal height at ( I , J ) f o r WINTER  (dam)  B  Poleward v a r i a t i o n of the  k  W N  C o r i o l i s parameter =  r,  df  —1 -1 (rrf s~ )  V e r t i c a l component of r e l a t i v e vorticity  (s ^)  Symbol  Meaning  Units  Usually Used  9  Potential temperature^  (K)  ?  Mean [zonal average of e)  (K)  X  Longitude.  ( - )  Positive eastward  Phase speed of wave k (radians/day)  (s""') 3  3  y  4 0  -r  m  Third moment about mean  (m )  Fourth moment about mean Standard deviation  (m^) (m)  Mean temperature of an a i r column lOOOMB surface to MSL  $  (K) 2  Geopotential (energy)  (m  s  Latitude  ( - )  -2  )  Latitude of an Anomaly Centre  < > j n y  Pentad (yy,k)  ( - )  Phase angle of Wn  ( - )  Phase s h i f t of Wn  ( - ) 2  Streamfunction  (m  s  Angular frequency wave number n  (s ^)  Angular speed of rotation of the Earth  Except in Chapter 7 where e designates Latitude  (s" ) 1  -1  )  xx iv  ACKNOWLEDGEMENT I wish to express my sincere appreciation for encouragement and assistance received from the University of B r i t i s h Columbia during the course of this work. Professor J . E .  I am p a r t i c u l a r l y grateful to my supervisor,  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, a l s o , to the other members of my Committee, Profes-  sors R.W.  B u r l i n g , M. Church, T.R. Oke, and L. de Sobrino, for construc-  t i v e reviews of the f i n a l  draft.  Valuable data-processing assistance was provided by Dr. D.G. Steyn (graphics), Mike Patterson (centre searches) and Peter Madderom (Fourier decomposition).  I am p a r t i c u l a r l y 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, s i t y of Washington.  Univer-  Dr. Harry Edmon screened erroneous data from the  o r i g i n a l analyses (500MB, MSL) and provided 5-day means for the 33 year period.  Our thanks, a l s o , 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. T r e i d l and co-authors who made  available a comprehensive set of recently completed data concerning Blocking in the Northern Hemisphere.  XXV  Financial assistance was received from the U n i v e r s i t y of B r i t i s h Columbia through an H.R. MacMillan Family Fellowship. I s i n c e r e l y wish to thank Irene Hull f o r typing the f i n a l manuscript. And thank you, Mary Knox, f o r typing the d r a f t and f o r your patient support and encouragement throughout t h i s protracted venture.  1  CHAPTER 1 1.  INTRODUCTION  1.1  Nature and importance of blocking There are patterns of f l u i d flow which evoke analogous connotations.  One r e f l e c t s , for example, on the sinuous bends and cut-offs of meandering r i v e r s , the shedding of vortices by large-scale ocean currents, orographic lee waves and their r o t o r s , and, much farther a f i e l d , the gigantic red spot on the planet Jupiter.  These phenomena, generated by d i f f e r i n g physi-  cal processes operating on widely d i f f e r e n t time and space s c a l e s , 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 j e t streams.  It  i s 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 a i r data.  An inspection of the winter  season normal chart at the 500 m i l l i b a r level shows the circumpolar westerlies (Fig. 1.1a).  in a f a i r l y regular 3-wave pattern around the mid-latitudes The large departures from normal of day-to-day motion, par-  t i c u l a r l y in the mid- and high l a t i t u d e s , are synthesized by the f i e l d of standard deviation (Fig.  1.1b).  S i g n i f i c a n t contributors to these depar-  tures are, of course, the short-wave  10 km) troughs and ridges a s s o c i -  ated with the transient b a r o c l i n i c systems in their developing stage but their t o t a l i t y accounts for a minor portion of the total variance.  It  turns out that the "restlessness" of the atmosphere extends to f l u c t u a tions of longer periods [> 10 days) and often of larger dimensions  2 120E  100E  BOE  1BO  Fig.  1.1  500MB Winter Season (a) Normal g e o p o t e n t i a l h e i g h t contours (Knox) (b) Standard d e v i a t i o n o f t w i c e - d a i l y 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 l u i d does not operate this way and there i s constant interaction between them.  For example, on  daily 500MB analyses, we w i l l sometimes notice p a r a l l e l but separate short-wave systems with d i f f e r i n g  phase speeds.  The constructive or  destructive interference between members of these systems and, in turn, with long-wave components of the presiding c i r c u l a t i o n regime is a major determinant of the evolution of day-to-day weather. We should recognize, however, that zonal flow often does p e r s i s t 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 j e t stream which, in this s i t u a t i o n , exhibits gentle sinusoidal characterist i c s not far removed from the normal seasonal pattern. typical  This is the  "high index" scenario. Then, in a manner to be described in more detail in Chapter 2,  there is a s t r i k i n g change in j e t structure over one or more regions of the mid-latitudes.  C h a r a c t e r i s t i c a l l y the j e t s p l i t s into two branches,  the northernmost curving sharply to the l e f t and following the western flank of a ridge which i s 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 s p l i t  j e t usually bends to the right and can ultimately be found, with inter-  4  ruptions, along the southern flank of a succession of mid-troposphere l a t i t u d e cold lows.  low-  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.  I t i s shown i n F i g . 1.2. This process i s c a l l e d blocking and the term was coined to describe the obstruction of the normal west-to-east progress of migratory systems by that s a l i e n t development i n the mass f i e l d , the anticyclone.  aforementioned  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 ( r e t r o gression).  Of course, t r a n s i e n t systems continue to approach the blocked  area from the west, and t h e i r subsequent h i s t o r y i s not easy to generali z 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 o c c a s i o n a l l y intens i f y i n g when they pass east of the p r e - e x i s t i n g cold low. The blocking process i s important because i t i s the progenitor of s p e l l s of weather which, i n more extreme cases, can have serious consequences f o r 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 c l e a r weather (interrupted on occasion when fog or s t r a t u s may below the shallow, surface-based i n v e r s i o n ) . used advisedly.  persist  The word "favoured" i s  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 i n v a r i a b l y cause a high incidence of f o r e s t f i r e s .  The summer drought of 1976 over the United Kingdom was  a d i r e c t r e s u l t of blocking.  During the w i n t e r , p e r s i s t e n t a n t i c y c l o n i c  conditions w i l l cut o f f the normal accumulation of snow pack.  A recent  example was the e x t r a o r d i n a r i l y dry winter of 1976-77 over the Western  5  Fig.  1.2  Contours and isotherms on the 500MB s u r f a c e 0300 GMT, February 20, 1948.. (Berggren e t a l 1949)  6  C o r d i l l e r a of North America, and the consequent depletion of usually abundant sources of hydropower. teristically  Boundary layer inversions are charac-  reinforced during blocking high episodes, and this in turn  may increase the concentration of p o l l u t i o n over industrial areas to well above acceptable  levels. a  Problems of quite a d i f f e r e n t kind can arise in regions under the influence of the slow-rmoving troughs or cold lows flanking the a n t i cyclone.  The abundant p r e c i p i t a t i o n from the c y c l o n i c a l l y 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. most s t r i k i n g recent example was the winter of 1976-77 when a very  The  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 a r c t i c a i r into central and eastern North America, where record-setting low temperatures and disastrous fuel shortages brought hardship to m i l l i o n s . It  is c l e a r , therefore, that an understanding of the nature of  blocking and of i t s 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 t s t o t a l i t y ,  that there are those who w i l l  argue that the only useful approach i s exclusively by numerical modelling methods.  We do not agree.  There is s t i l l  a good deal to be learned  7  Fi  K-  1*3  M e a n 7 0 0 M B contours f o r w i n t e r 1 9 7 6 - 7 7 (December, January and February) l a b e l e d i n tens of f e e t . (Namias 1 9 7 8 )  8  about the climatology and diagnostics of blocking.  The next section w i l 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, i s  e a s i l y recognized, and the importance of i t s 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 c u l t y , well documented in the l i t e r a t u r e , of constructing an objective d e f i n i t i o n which would be generally acceptable.  Moreover, some  of the authors we shall refer to in Chapter 3 focussed t h e i r investigations on s p e c i f i c geographical regions and so there remains a need to synthesize their r e s u l t s . A premise of this t h e s i s , which was inferred during an i n i t i a l p i l o t 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 t e r i a for location and i n t e n s i t y , 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 w i l l be to present and interpret the spatial and temporal d i s t r i b u t i o n of 5-day positive anomaly centres over the Northern Hemisphere during the past 33 years.  The results w i l 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 r e l a t i n g positive anomaly centres to blocking anticyclones we needed sources l i s t i n g s p e c i f i c 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 t e r a t u r e  (e.g.,  Treidl et a l . , 1980a and 1980b) or from synoptic weather maps.  On the  other hand, an archive providing time, l o c a t i o n , and intensity of anomaly centres for the 33-year period of our study simply did not e x i s t .  There-  f o r e , 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  its  mature stage w i 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 l a t t e r structures are often associated with 5-day negative 500MB anomaly centres.  Therefore, i t was decided that for future research, the  locational h i s t o r i e s of negative anomaly centres should be included in the catalogue and, moreover, that their frequency d i s t r i b u t i o n s should be described. We also investigated whether regions with high incidence of blocking featured d i s t r i b u t i o n s of geopotential s i g n i f i c a n t l y d i f f e r e n t from Gaussian.  For this purpose calculations of skewness and kurtosis f i e l d s  at the 1000MB and 500MB levels were made for the Northern Hemisphere. The r a t i o n a l e , results and interpretation of this exercise w i 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 d a i l y atmospheric flow at 500MB during seven winters, each of which was notable for the occurrence of one or more major blocking episodes. (The f e a s i b i l i t y and computational techniques were developed during a p i l o t 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 l e v e l s , 500MB and 1000MB.  The record  consists of once d a i l y 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 g r i d - f i e l d s 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 i d e n t i f i c a t i o n and d i s t r i b u t i o n 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 i e l d s  (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 d a i l y 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 (a)  the frequency distributions of "blocking signatures",  investigate (b)  the  connection between blocking and hemispheric f i e l d s of s t a t i s t i c a l moments of geopotential height at selected l e v e l s , 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, w i l l prove to be useful for continuing research.  Also,  an attempt w i l l be made in Chapter 2 to interpret and synthesize relevant literature.  Some of the papers w i l l not necessarily be germane to our  11  s p e c i f i c o b j e c t i v e s , but i t i s intended that t h e i r review w i l l useful perspectives on a complex and challenging subject.  provide  12  CHAPTER 2 2. 2.1  THE PHENOMENON OF BLOCKING Introduction A treatment of the blocking phenomenon in i s o l a t i o n from i t s  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 d i s t r i b u t i o n s of the phenomenon of interest there would be no disadvantage in such a procedure.  However, while this is one of our important objectives  4 and 5) there w i l l be a need to interpret the s t a t i s t i c a l  (Chapters  results.  More-  over, our second primary objective is to investigate blocking in the context of those planetary and synoptic scale processes from which i t develops (Chapters 6 and 7). This chapter, therefore, w i l l present a number of results which we believe to be germane to those processes giving r i s e to the growth and decay of blocking, and to the motion of the associated wave-form.  In  a d d i t i o n , the respective roles of large scale topographic forcing and differential  heating w i l l be examined and an example of a successful  simulation of blocking w i l l be presented.  The climatology of blocking  w i l 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 appreciation 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 t e e n year period 1945-1959, compared with 30 papers for the subsequent f i f t e e n years 1960-1974. The i n i t i a l  spate of interest was not accidental.  The 1940 s 1  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, p a r t i c u l a r l y of papers concerning phenomenological aspects of blocking, is perhaps p a r t i a l l y 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.  A l s o , 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 A t l a n t i c .  In Great B r i t a i n 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 weste r l i e s from their normal position by large amplitude quasi-stationary long waves.  A l s o , there is a growing consensus that numerical models,  in spite of their remarkable development, have not r e a l l y been successful beyond 4 or 5 days, in regard to t h e i r a b 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 s t a t i s t i c s or in numerical simulation has produced over 20 papers in U.S., 2.2  Canadian and B r i t i s h journals alone, since 1975.  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 s c a l e , of the normal west-to-east progress of the migratory cyclones and a n t i cyclones.  It  is attended by pronounced meridional flow in the upper  l e v e l s , and, for a s i g n i f i c a n t period of i t s evolution, there is usually a closed anticyclonic c i r c u l a t i o n in the mid-troposphere (- 500MB) at high latitudes (mainly north of 50°N). a "warm cut-off high".  It  This is frequently referred to as  is not unusual for the complete blocking system  to include cold cyclonic c i r c u l a t i o n s at lower latitudes (south of 50°N), the so-called "cut-off cold lows". ("the  This anomalous c i r c u l a t i o n pattern  block") t y p i c a l l y moves very slowly (^ 400km per day) and persists  for one week or longer.  Frequently the warm anticyclone to the north  w i l 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 c i r c u l a t i o n and, in their normal p o s i t i o n , do not interrupt the westerlies.  Nevertheless we should note  that a block is often characterized, in i t s i n i t i a l  stages, by the north-  15  ward amplification of a sub-tropical r i d g e , accompanied by a s h i f t i n g of the polar j e t stream to more northerly l a t i t u d e s .  The blocking system  does not usually materialize, under our d e f i n i t i o n , until the formation of the higher latitude cut-off warm high.  However, because of the con-,  tinuous nature of the process, i t w i 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,  F i g . 2.1, gives way on average to zonal flow at 500MB, F i g . 2.2.  This is  a direct consequence of b a r o c l i n i c i t y 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 a i r mass. Again, we must note a q u a l i f i c a t i o n .  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 p a r a l l e l of l a t i t u d e .  The  500MB dai1y flow patterns show marked deviations from the regular westerly current shown on F i g . 2.2 and occasionally one w i l l observe, p a r t i c u l a r l y above the western portions of the 1000MB anticyclone, closed highs which c l e a r l y 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 l a s s i c paper,  Berggren et a l . (1949) presented an aero-  logical analysis of a remarkable break-down in zonal flow which occurred  16  120E  Fifi*  2.1  JOOE  BOE  Normal h e i g h t of the 1000MB s u r f a c e f o r WINTER (December 1 t o February 28). Contours l a b e l l e d i n decametres (dams). I n t e r v a l = 3 dams.  17  120E  2.2  IOOE  BOE  N o r m a l h e i g h t o f t h e 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 d e c a m e t r e s l e s s 5 0 0 . I n t e r v a l = 6 dams.  18  over the North A t l a n t i c and Western Europe, February 8th to 20th, 1948. Fig. 2.3(a) and (b)  show the evolution at the 500MB l e v e l , from zonal  flow (February 8th and 12th) to a mature blocking system (February 18th and 20th).  The s t r i k i n g e f f e c t 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  (ii)  shows the positions during the 10-day period after the blocking high had formed. The c h a r a c t e r i s t i c v e r t i c a l  structure of a blocking system is  i l l u s t r a t e d in F i g . 2.5 which shows the cross-section XY (Fig. Greenland to the Black Sea, February 18, 1948.  2.4a)  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 i n i t i a t i n g factors  large scale orography, longitudinally dependent d i f f e r e n t i a l  (e.g.,  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 t e d .  We  19  16 FEB. 1948  F i g . 2.3(a)  0 3 0 0 CCT  E v o l u t i o n from z o n a l flow February 8 through February 12 to a m p l i f y i n g wave on February 16. (Berggren et a l 1949)  20  500  mb  500 mb  Fig.  2.3(b)  18 FEB. 1948  (  20 FEB  1948  0 3 0 0 GCT  0 3 0 0 GCT  Mature b l o c k i n g a n t i c y c l o n e c e n t r e d n o r t h e r n Scotland February 18 has r e t r o g r a d e d toward I c e l a n d February 20. Deep c o l d low c e n t r e d over Germany now dominates Western Europe. Y f i s p r o j e c t i o n of v e r t i c a l c r o s s - s e c t i o n shown i n F i g . 2.5.. (Berggren et a l 1 9 4 9 )  Fig.  2.4  (Berggen  Positions periods:  et  a l  o f f r o n t s d u r i n g two t e n - d a y 1 . p r e c e d i n g the formation; 2. f o l l o w i n g the e s t a b l i s h m e n t of the c u t - o f f h i g h shown i n F i g . 2.3(b).  1949)  22  Fig.  2.5  Schematic r e p r e s e n t a t i o n of the v e r t i c a l structure of a h i g h - l e v e l anti-cyclone adapted to the case shown i n F i g . 2.3(h) (February 18). The c o l d dome i s i n d i c a t e d by heavy double l i n e s . The tropopause i s i n d i c a t e d by a heavy broken l i n e , and the a x i s of the h i g h b y a dash-dot l i n e . The slope of the i s o b a r i c s u r f a c e s 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 l u s t r a t e  westward  moving blocking waves which they described as a "retardation of the zonal c i r c u l a t i o n which appears f i r s t over western Europe and the eastern A t l a n t i c and subsequently retrogresses further westward affecting p a r t i c u l a r l y 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 nondivergence.  The results are developed in Appendix II  and may be summarized  as follows: Rossby (.1939) assumed a homogeneous incompressible f l u i d on an approximation to the rotating Earth ( the g-plane) and a uniform nondivergent flow.  From these conditions he deduced the p r i n c i p l e of con-  servation of v o r t i c i t y :  ? + f = constant  Where t, = the r e l a t i v e v o r t i c i t y flow and  (due to the configuration of the  relative  field)  f = the planetary v o r t i c i t y  (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: (2.1)  24  Where c = phase speed g = df/dy = (2Pxos<|>)a"^ L = wave length -5 n = angular speed of rotation of the earth (= 7.29x10  -1 rad.S  )  tj> = l a t i t u d e . 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. westward r e l a t i v e  Also the formula indicates that Rossby waves propagate to the mean zonal flow with a speed which increases  with the wave length.  There w i l l be a c r i t i c a l wave length L  a given U and <j>, w i l l make c = 0. r e l a t i v e to the earth.  If  L > l_ the wave w i l l c  c  which, for  retrograde  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 s i n u s o i d a l , i t can be shown, Haurwitz that the phase speed toward the east is c = U r + nT ?  3  (1940a)  (2.2)  ?  Where k = the wave number in the zonal direction m = the wave number in the meridional d i r e c t i o n . The expressions for c in equations (2.1)  and (2.2) were developed  for an extremely s i m p l i f i e d model, and the success with which they can be applied to the real atmosphere w i l l depend on a number of factors. example, best results are obtained at levels of small divergence  For (e.g.,  600MB, 500MB) and for latitude zones within which the maximum wind is l o 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  vorticity  advection tends to move the v o r t i c i t y pattern and hence the wave-form downstream.  On the other hand advection of planetary v o r t i c i t y tends to  move the wave-form upwind.  The resultant motion w i l l be determined by the  size of these opposing f a c t o r s .  Blocking anticyclones occur in high  latitudes and, at 60°N, 6 is decreased to half i t s value at the Equator. However, as we shall note in Chapter 7, the main wave components of blocks have small wave numbers.  The factor &/k  c  on balance, tends to increase  with latitude for very long waves (k small) and this may decrease c to a stage where i t s sign becomes negative unless the <; advection can compensate'. Blocking anticyclones, at least over the oceans, are quasi-barotropic near the core and the r e l a t i v e v o r t i c i t y advection is very small there.  Consequently the planetary v o r t i c i t y advection w i l l dominate.  This  accounts for t h e i r very slow movement and not infrequent retrogression. Sometimes the retrograde motion of blocking waves is "discontinuous". By this we mean that while the i n 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 e f f e c t is equivalent to a westward propagating blocking wave. A physical process which may contribute to this phenomenon, upstream energy d i s p e r s i o n , 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 w i l l be interference, which, i t turns out,  26  creates a pattern of wave groups.  These groups move with a velocity G,  quite d i f f e r e n t 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)  G therefore exceeds not only the individual wave speed  but also the basic current U, downstream.  and so energy dispersion sweeps rapidly  This effect is observed from time to time in the real atmos-  phere, where, following some point of energy i n t e n s i f i c a t i o n ( e . g . , west P a c i f i c cyclogenesis) the amplification influence moves rapidly  eastward  (30° longitude per day is not uncommon) and acts successively on downwind 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 d i f f e r e n -  t i a l into the model (unlike the Rossby model of uniform density).  He  examined energy propagation through dispersive waves in an "incompress i b l e atmosphere with a uniform north-south density gradient and with f i n i t e depth".  He found that the group velocity depended on a c r i t i c a l  27  wave length L G > c > 0.  c  such that i f the predominating wave length L < L  This does not d i f f e r from the uniform density case.  other hand, i f L is s l i g h t l y > L  c  then c > 0 and G < 0.  c  then On the  This corres-  ponds to upstream propagation of energy opposite to wave v e l o c i t y .  More-  over, by examining the subsequent dispersion of a s o l i t a r y wave (whose wave length L > l_ ) c  a t , respectively, 0 ° , 40°N, 70°N i t turned out that  only the wave at 70°N maintained i t s 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 v o r t i c i t y , energy dispersion) which appear to be factors in the motion (and, in the case of d i s p e r s i o n , 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 w i l l be useful for interpretation. 2.5  Conservation of potential v o r t i c i t y .  A h e u r i s t i c discussion of i t s  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 i r masses during meridional displacement.  In r e a l i t y ,  of course, the processes are very comp-  l i c a t e d , but, as always, i t i s best to proceed at f i r s t with the simpler concepts. We shall assume the p r i n c i p l e of the conservation of potential v o r t i c i t y defined by the relationship (Rossby, 1940)  28  ** ' ' = constant Ap  Where x, = r e l a t i v e v o r t i c i t y and Ap is the pressure depth of a small  air  column. Consider now the case of three a i r columns A, B and C embedded in an a i r current i n i t i a l l y uniform a t , say, 60 N and being displaced equatorward, F i g . 2.6(a).  The subsequent stream flow with an anticyclonic  branch to the right of the flow and a cyclonic branch to the l e f t  is  postulated such that when the columns arrive at their primed positions they have acquired v o r t i c i t i e s  typical of those found in the real atmos-  phere. Column B whose r e l a t i v e v o r t i c i t y <; remains zero, must shrink because f decreases. markedly.  Column A whose x, decreases w i l l shrink even more  The change.in column C w i 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 w i l l most frequently be characterized by shrinking a i r columns depicted i d e a l l y by the current AA'. trajectory  The  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  a t , say, 30°N with a configuration shown in F i g . 2.6(b). tion is reversed.  Here the s i t u a -  An a i r column E experiences strong stretching as  it  curves c y c l o n i c a l l y and column G experiences shrinking. Warm, deep anticyclones are t y p i c a l l y characterized, on their western and northern flanks by a i r columns conserving t h e i r absolute v o r t i c i t y r, + f.  On the western periphery the a i r columns may stretch  29  F i g 2.6  Fig.  2.7  M e r i d i o n a l motion w i t h w i t h a n t i c y c l o n i c and c y c l o n i c branches and the i m p l i e d v e r t i c a l s t r e t c h i n g or s h r i n k i n g . Along heavy s t r e a m l i n e s , a b s o l u t e 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 o p p o s i t e change i n r e l a t i v e v o r t i c i t y by c u r v a t u r e . (After P e t t e r s s e n , 1956)  Schematic diagram showing the changes from the normal " s i n u s o i d a l " a i r movement i n the upper t r o p o s p h e r e , r e s u l t i n g from.convergence above a s i n k i n g c o l d - a i r mass.in the trough. ( A f t e r Palmen and N a g l e r , 1949)  30  s l i g h t l y , 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 configuration 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  undisturbed current XY in the upper troposphere, F i g . 2.7.  relatively  If an intense  cold outbreak takes place in the lower troposphere (say an anticyclone centred at A*), then i t s strong low level divergence and subsidence, and southward displacement, w i l l be dynamically associated with strong convergence and stretching in the upper tropospheric trough.  This w i l l  increase  the v o r t i c i t y  in the trough and deform the current from i t s i n i t i a l  sinus-  oidal shape.  The resulting more meridional orientation of the current  east of the trough w i l l be consistent with an accentuated downstream ridge.  Moreover, the a i r stream, in i t s progress to higher l a t i t u d e s ,  bends a n t i c y c l o n i c a l l y in order to conserve absolute v o r t i c i t y .  Contin-  uation of this process may ultimately culminate in a closed anticyclone. 2.6  The index cycle Namias [1950) showed that blocking over the A t l a n t i c between 50°N  and 70°N, appeared to be a necessary (though not s u f f i c i e n t )  condition  for the southward s h i f t of the zonal wind maximum into the sub-tropics. This is the culminating stage of the "index c y c l e " , a cycle through which the polar vortex, i n i t i a l l y thens and becomes unstable.  confined to high l a t i t u d e , expands, strengThis results in the formation of large  amplitude ridges and troughs and, ultimately, cut-off warm highs in higher latitudes and cold lows in lower l a t i t u d e s , F i g . 2.8.  When the processes  which generate these eddies terminate, the warm highs gradually weaken  31  F i g . 2.8  Schematic r e p r e s e n t a t i o n o f successive c i r c u l a t i o n patterns a l o f t d u r i n g an index c y c l e . ( 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 c e l l s eventually dissipate marking the end of the  c y c l e , which on average takes about six weeks. 2.7  Baroclinic  instability  Why does the expanding circumpolar vortex ultimately become unstable, to form large amplitude troughs and ridges?  The answer l i e s in the process  of baroclinic i n s t a b i l i t y which is the major mechanism for energy transformation in the extra-tropical l a t i t u d e s .  The key to the process was  developed by Charney (1947) and Eady (1949).  Charney, using a 2-level  b a r o c l i n i c model of a compressible atmosphere, showed how b a r o c l i n i c i n s t a b i l i t y is dependent on v e r t i c a l wind shear, lapse r a t e ,  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 i k e l y 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 t s development  was, other factors being equal, less l i k e l y because in that portion of the wave spectrum the g-effect^$ = factor. and L„  2  became s i g n i f i c a n t as a s t a b i l i z i n g  In essence their results defined 2 wave length thresholds L ^ c  for development to take place, 1 <L c  L c  2  l  > 1 >L c-, 1 > L C  2  stable unstable stable  Here 1 = the actual wave length and L c  trum.  l  is at the shorter end of the spec-  33  Fig. 2.9 shows how the respective wave length cut-offs are dependent on the mean v e r t i c a l  stability—,  on the mean v e r t i c a l wind shear (which  arises from the mean N-S temperature gradient — ), and on latitude ( i m p l i c i t 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 o f . i n t e r e s t to enquire of those circumstances which govern the value of L ^. c  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 t a b i l i t y L^ c  and L ^ are s i g n i f i c a n t l y changed. c  criteria  In f a c t , 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 P a c i f i c Ocean to determine i f the real atmosphere supported H a l t i n e r ' s results.  theoretical  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 d i s t i n c t modal position at about 170°W and that i t was quasistationary, 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 c a l was sensible heat transfer  from ocean to atmosphere.  winters in which blocking predominated they found  factor  For autumns and  anomalously large  under the trough in the western P a c i f i c and anomalously small under the ridge.  Fig.  2.9  Baroclinic stability criterion. L i s the zonal p e r t u r b a t i o n wavelength, h i s t h e v e r t i c a l s c a l e height, g i s the a c c e l e r a t i o n of g r a v i t y , 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 comb i n e d theory (see f o r example P h i l l i p s , 1954). h =  where  from Smagorinsky  T... = l a y e r mean temperature between p^ and pg (1972)  ^  35  In the absence of sensible heat transfer (or some other nonuniform lower boundary condition such as orography or f r i c t i o n ) , baroc l i n i c a l l y unstable long-waves are not possible in 2-level models except at u n r e a l i s t i c a l l y 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 i k e l y 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. statistical  They therefore concluded that  their  results on blocking (which also included seasonal and year-  to-year v a r i a b i l i t y )  are a l l  in agreement with H a l t i n e r ' s  theory.  Diehl (1977) also hypothesized that blocking-ridge formation originates from the r e a l i z a t i o n of b a r o c l i n i c i n s t a b i l i t y operating in the long wave length part of the macro-wave spectrum (7000-9000km). 2-level b a r o c l i n i c model with an i n i t i a l  Using a  steady state current character-  i s t i c of the real troposphere, he tested i t s response to a simple perturbation:  In (i)  (i)  for adiabatic f r i c t i o n l e s s  flow,  (ii)  for flow subject to surface heat exchange,  (iii)  for flow subject to surface f r i c t i o n only, and  Civ)  for flow subject to both surface heat exchange and f r i c t i o n .  his results agreed with those of the aforementioned c l a s s i c a l  papers and, in ( i i ) ,  with those of Haltiner.  In (iv)  he found that the  inclusion of both f r i c t i o n and sensible heating from the surface,  still  36  further cut o f f the shortwave end of the spectrum and made b a r o c l i n i c i n s t a b i l i t y realizable further into the long-wave portion.  Moreover,  these unstable long waves could be stationary, progressive or retrogressive depending on the zonal current.  They had growth times and wave  lengths comparable to the dimensions of North P a c i f i c blocks reported by White and Clark.  Diehl therefore concluded that blocking ridges could  develop from the r e a l i z a t i o n of a b a r o c l i n i c a l l y unstable long wave. also emphasized the limitations of his study. (used by a l l the foregoing investigators)  He  Linear perturbation theory  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 2.8  surface heating.  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 p r i n c i p l e of the conservation of potential  vorticity  for a small a i r column embedded in a westerly current flowing across Ap  a mountain barrier with a N-S o r i e n t a t i o n , i t can readily be demonstrated that the a i r column w i l l be deflected southward with anticyclonic  curvature  at f i r s t , and subsequently execute a series of dampened downstream o s c i l l a tions.  If we v i s u a l i z e this process operating across mountain barriers on  the scale o f , say, the Rocky Mountain C o r d i l l e r a i t is reasonable to expect that within the complex of o s c i l l a t i o n s so generated, some w i l l be found on the long-wave scale.  37  An easterly current flowing over a mountain barrier ( e . g . ,  the  Greenland massif) w i l l turn southward with cyclonic curvature prior to reaching the b a r r i e r , recurve a n t i c y c l o n i c a l l y as i t passes the crest and resume i t s previous undisturbed flow without executing further o s c i l l a tions . Thus north-south oriented mountain barriers generate anticyclonic v o r t i c i t y within uniform westerly and easterly currents but the downstream response i s 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 c i r c u l a r in area! aspect, w i l l constrain westerly  (and easterly)  air  streams to flow around as well as over the b a r r i e r , while the generally E-W oriented Alpine-Caucasian chain w i l l have a s i g n i f i c a n t influence on meridional a i r stream components. To further add to the complexity of orographic e f f e c t s , the Rocky Mountain C o r d i l l e r a and the Himalayan - NE Siberia Mountains act as containment barriers to.the vast low level winter a i r masses generated primarily by boundary layer radiative processes. Some evidence of the impact of large-scale topography on global a i r currents can be obtained by a comparison of mean 500MB flow for the two hemispheres for corresponding seasons. Southern Hemisphere winter,  The normal charts for the  F i g . 2.10, and summer, Fig. 2.11, show a  f a i r l y uniform circumpolar flow between latitudes 40°S and 6 0 ° S , a zone of prevailing westerlies almost e n t i r e l y uninterrupted by s i g n i f i c a n t mountain b a r r i e r s .  These charts support the not unreasonable assumption that  i f the earth's surface were f r a c t i o n a l l y uniform, and thermally uniform by  38  F i g . 2,10  Mean 500MB contours (80-m i n t e r v a l ) i n January (summer), Southern Hemisphere. ( A f t e r T a l j a a r d et a l . , 1969).  39  F i g . 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 corresponding seasons in the Northern Hemisphere, Fig. 2.12 and F i g . 2.13, show substantial longitudinal v a r i a t i o n .  This is p a r t i c u l a r l y 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 amplitude 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  c i r c u l a t i o n models (GCMs) of the atmosphere.  In a recent experiment with  the GCM at the Geophysical Fluid Dynamics Laboratory (GFDL), Princeton, N.J.,  Lau (1980) c l e a r l y 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 e x i s tence. It was run for 10 successive winters (December, January, (a)  with Mountains  (M)  (b)  without Mountains  (NM)  February)  and the mean flows were calculated for the 1000MB and 300MB l e v e l s , respectively (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 a n t i c y c l o n i c i t y is evident j u s t east of the Himalayas, and much stronger patterns are located immediately upstream of the Rocky Mountains (the centre is over B.C.) (centred near Iceland).  It  and east of Greenland  is also of interest to note the downstream  41  F i g . 2.12  Mean 500MB c o n t o u r s i n J a n u a r y ( w i n t e r ) , N o r t h e r n Hemisphere. Redrawn a t 80-m i n t e r v a l s from I . Jacobs (1958). Light and h e a v i e r s t i p p l i n g show r e g i o n s where e l e v a t i o n s a r e above 1.5 km and 5 km (smoothed o v e r 5°latitude-longitude t e s s e r a ) , from B e r k o f s k y and B e r t o n i (1955). (Palmen and Newton, 1969)  42  F i g . 2.13  Mean 500MB contours i n J u l y (summer), Northern Hemisphere. (Redrawn from I. Jacobs, 1958). (Palmen and Newton,  1969)  43  F i g . 2.14  I l l u s t r a t i n g e f f e c t o f Northern Hemisphere major mountain systems on stream flow a t 300MB u s i n g GFDL General C i r c u l a t i o n Model f o r 10 w i n t e r seasons. i> equals d i f f e r e n c e 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 A t l a n t i c and P a c i f i c sub-tropical a n t i cyclones are strengthened, and the cyclonic v o r t i c i t y of the E. and E. North America troughs is increased.  Asiatic  The Himalayan plateau with i t s  rounded configuration appears to exercise a somewhat d i f f e r e n t  influence  both in i t s v i c i n i t y and downstream, from barriers with a predominant N-S component. Since the longitudinally dependent large scale d i f f e r e n t i a 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 i m p l i c a t i o n , the real .atmosphere. We would l i k e to be able to report on a similar experiment with regard to the e f f e c t of longitudinally dependent d i f f e r e n t i a 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 o s c i l l a t i o n s produced by orographic forcing and d i f f e r e n t i a l  heating, respectively.  This w i l 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 s i g n i f i c a n t 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 mountain systems rather than the thermodynamic influence of the surface temperature d i s t r i b u t i o n is the ultimate determinant of the wave characteri s t i c s of the mean flow in the upper troposphere.  46  F i g . 2.16  The mean h e i g h t o f the 500MB s u r f a c e as a f u n c t i o n o f l o n g i t u d e . I n summer the f i g u r e r e p r e s e n t s c o n d i t i o n s i n the l a t i t u d e b e l t 45°N - 50°N, i n w i n t e r 35°N - 40*1. The p r o f i l e s have been computed from the h e m i s p h e r i c a l mean c h a r t s p u b l i s h e d 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 l a s t  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 i k e the real  atmosphere in developing systems with magnitudes and characteristics of the synoptic and long waves.  Hence, the output for s p e c i f i c sequences  of days is looked at from time to time. Apparently one of the f a i l i n g s of GCMs is t h e i r i n a b i l i t y to simulate blocking with the frequency, persistence and- intensity charact e r i s t i c s that are in fact observed.  However, a few successful cases  have been reported and Mahlman (1979) presented the results of a simul a t i o n (by the 1967 GFDL 11-level model) of an east A t l a n t i c blocking a n t i cyclone.  F i g . 2.17 ('Jan. 22') shows the stream flow when the block was  f i r s t initiated.  Note that the overall structure includes a robust a n t i -  cyclone at 35°N, 30°W, the typical up-stream s p l i t j e t , cyclone at 25°N, 40°W.  and a low latitude  This system d r i f t e d 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 characterist i c s of the day-to-day GFDL simulations are not being reported in the 1iterature. 2.10  The effect of blocking on the c i r c u l a t i o n of the stratosphere Fig. 2.18(a) shows the summer mean stratospheric c i r c u l a t i o n at  30MB, a remarkably uniform (almost c i r c u l a r )  slack easterly  circulation  which is thermally consistent with the temperature f i e l d between the warm pole and cold equator.  J A N 22  Fig.  2.17  I l l u s t r a t i n g s i m u l a t i o n a t 500MB o f a b l o c k i n g e o i s o d e u s i n g 1967 1 1 - l e y e l GFDL GCM. Note b l o c k i n g a n t i c y c l o n e at"35°N 30°W, c y c l o n e a t 25 N 40°W and upstream s p l i t j e t . L a u ( l 9 8 0 ) .  00  Fig.  2.18  Seasonal mean 30MB g e o p o t e n t i a l h e i g h t ( 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 ( t o p ) and w i n t e r (bottom) Northern Hemisphere seasons ( A f t e r Hare, 1968).  50  Fig. 2.18(b) shows a dramatic reversal in the motion and temperature f i e l d s 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 t s absence in summer is explained by the manner in which the primary long waves in the s t r a t o s phere are generated.  They do not develop ' i n s i t u " but "appear to be  oproduced by the v e r t i c a l  propagation of planetary waves forced in the  troposphere by orography and land-sea contrasts.  [These, in turn,] can  only propagate v e r t i c a l l y 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 anticycloni c a 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 s u f f i c i e n t condition for a major mid-winter warming.  If  the blocking event is i n i t i a t e d by  constructive interference between wave numbers 1 and 2 then a subsequent  51  warming w i l l r e s u l t .  If  the dominant i n i t i a t i o n wave components are  then a major warming w i 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. of absolute v o r t i c i t y "  The "conservation  p r i n c i p l e was invoked to discuss i n e r t i a 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 midlatitudes.  Moreover, i t is conceivable that the growth of a blocking  anticyclone is the outcome of b a r o c l i n i c i n s t a b i l i t y at the long-wave part of the spectrum. Numerical simulation's using a general c i r c u l a t i o n model disclosed the e f f e c t of the Northern Hemisphere's topography on the low level and upper troposphere c i r c u l a t i o n .  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. F i n a l l y there was a b r i e f discussion of the relationship between blocking and sudden warmings in the polar vortex of the winter s t r a t o s 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 i t e r a t u r e review and w i l l refer to relevant papers as the dissertation is further developed.  52  CHAPTER 3 3. 3.1  ANOMALY FIELDS AND IMPLICATIONS FOR IDENTIFICATION OF BLOCKING Introduction The l i t e r a t u r e includes a number of comprehensive investigations  the climatology of blocking, and the i d e n t i f i c a t i o n c r i t e r i a quite  into  naturally  r e f l e c t those aspects of the phenomenon considered important by the respective authors.  Rex (1950a, 1950b), for example, perceived the s p l i t t i n g  of the j e t stream into two branches of comparable mass-transport characteri s t i c s to be essential to the blocking process and indeed recorded the location of the s p l i t as his "block p o s i t i o n " .  He further stipulated  that, for the process to qualify as a blocking episode, the observed double j e t 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 r e s t r i c t i v e  in his c r i t e r i a .  His exper-  ience as a synoptician gave him an appreciation of the variety of configurations of the pressure f i e l d 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 concentration of westerlies".  But to identify episodes he resorted to pattern  recognition at the 500MB level using, for guidance, six patterns of the more frequent occurrences.  typical  Of the s i x , two examples appeared to  predominate: (a)  The " s p l i t - j e t " ,  comparable to the Rex configuration  (b)  The "meridional", known in North America as the "fi-block"  These are i l l u s t r a t e d schematically in Fig. 3.1. are variants from, or combinations of (a)  and (b).  The other four patterns  53  Fig.  331(b)  Omega B l o c k  54  T r e i d l et a l . (1980a) stipulated that: (a)  Closed isopleths must be present simultaneously in the surface  and 500MB charts. (b)  The westerly current must s p l i t into two branches.  (c)  The minimum duration must be f i v e days.  The last-named authors applied these c r i t e r i a to the 33-year period 1945-1977, i n c l u s i v e .  Over 12,000 days of 500MB analyses of the Northern  Hemisphere were i n d i v i d u a l l y examined and the corresponding MSL analyses were used for supplementary information.  Adjuncts to this study have been  made available by the senior author. The c r i t e r i a used in these three papers did not exclude the need for subjective judgment. to the l e t t e r ,  Often cases were counted where, in p r i n c i p l e i f not  they appeared to q u a l i f y .  was amenable to machine processing.  Moreover, none of the methods  Each required the extremely demanding  procedure of inspecting hundreds, and in the case of T r e i d l et a l . , thousands, of synoptic weather maps and manually recording the relevant data. There was the ever-present p o s s i b i l i t y that cases woul*d inadvertently be overlooked and, p a r t i c u l a r l y over a long period of record, the accumulation of such omissions could become s i g n i f i c a n t . 3.2  Anomaly f i e l d s As indicated in Chapter 1, one of the goals of this thesis is to  investigate the climatology of blocking by using objective adaptable to machine processing large data sets.  criteria  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 l d and those other f i e l d s from which i t was derived.  55  We assume an i n f i n i t e 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 l d be Z = -a^y  (3.1)  (which implies a uniform West to East flow) and l e t the "instantaneous" height f i e l d be Z = - ^ y + a^sin lex sin my  (3.2)  By "instantaneous" we mean for a designated calendar day and time. we shall later use the 5-day interval  Since  (pentad) for a time u n i t , the term  "instantaneous" w i l l also be understood in the sense of " f o r a designated pentad". The expression for Z in (3.2)  describes a composite f i e l d which is  the resultant of a uniform zonal W-E flow, and also a c e l l u l a r defined by wave numbers k and m.  One measure for assessing which of these  two components (zonal or c e l l u l a r ) . w i l l  a  predominate is  2  -ma As explained in Appendix III,  structure  3  i f the r a t i o > 1, no centres of maximum or  minimum w i l l appear, whereas, as the r a t i o decreases from 1 to 0 the c e l l u l a r structure is increasingly amplified over the pattern domain. The Anomaly f i e l d , by d e f i n i t i o n , is Z - Z = (a-, - a )y 9  + 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 | in the mid-troposphere 2  Thereforea  l " 2 -ma  a  a  3  v.  2  -ma  3  Consequently an anomaly f i e l d w i l l usually have a larger number of maximum and minimum centres per given domain than either the "normal" or the "instantaneous" f i e l d s . As an example, Fig. 3.2 shows the anomaly f i e l d 1-1  arising from  subtracting a hypothetical "normal" f i e l d 1 = -4y from an "instantaneous" field  1 = -4y + 2sin\3x'sin y  Note that for this case the r a t i o  a  1 ". 2 -ma a  3  =0  Hence the anomaly f i e l d has zero zonal component and is markedly c e l l u l a r . Although the example is highly idealized the p r i n c i p l e is general and i l l u s t r a t e d 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 i g n i f i c a n t difference in orientation of the respective trough ridge patterns, NW - SW in the case of F i g . 3.3 and NW - SE in Fig. 3.4. A d i f f l u e n t j e t schematic is shown in F i g . 3.5. the anomalies (drawn by graphical subtraction)  A l l three figures show how have a d i s t i n c t i v e  cellular  structure with c l e a r l y i d e n t i f i e d 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 c r i t e r i o n to be met on an "instantaneous" chart to q u a l i f y as a possible blocking high.  The analysis of constant pressure charts in the  57  Y  Fig.  3.2  A n a l y t i c a l example o f Anomaly Normal F i e l d Instant F i e l d Anomaly F i e l d  Z =  -4y  Field  Z = -4y + 2 s i n 3x s i n y Z - Z = 2 s i n 3x s i n y  VJ1  00  j F i g . 3.4  A m p l i f y i n g Wave, NW-SE..tilt. Legend as i n F i g . 3.3.  P o s i t i v e Anomaly Centre i s NW  of  "H".  o Fig*  3 . 5  Diffluent  Jet.  Legend  a s i n  Pig.  3.3  i  61  mid-troposphere i s conventionally carried out by drawing contours at a 6 dam i n t e r v a l .  It w i l l be appreciated that the application of a "closed  contour c r i t e r i o n " w i l 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  difficulty.  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. respective Z and Z f i e l d s .  The amount of displacement w i l l vary with the A robust closed blocking anticyclone with a , •  centre, say, 30 dams above normal, w i l l usually have an associated anomaly centre located within one or two degrees of l a t i t u d e .  On the other hand  meridionally oriented ridges, e . g . , Figs. 3.3 or 3.4, may feature an anomaly centre some f i v e to ten degrees north of the reference (x-axis)  of the wave form.  latitude  If the anomaly is large ( c r i t e r i a w i l l be  developed in the next chapter)  i t is very l i k e l y that the ridge i s in an  amplifying stage and that the subsequent instantaneous chart w i l l an eddy ( i . e . , the blocking anticyclone)  reveal  at the northern extremity.  If  this does occur the anomaly centre w i l l usually be within 1 to 5 degrees latitude of the anticyclone. There may also be a longitudinal displacement of the anomaly r e l a t i v e to the location of the blocking anticyclone.  The sign and  amount of the s h i f t w i l l depend on the orientation .of the axes of the respective Z and Z f i e l d wave forms.  F i g . 3.3 shows that a positive  (NE-SW) t i l t w i l l displace the anomaly centre east of the ridge i n t e r section I with the x-axis, while F i g . 3.4 shows that a negative (NW-SE) t i l t w i l l result in a westward displacement.  62  Most of these displacements are greatest for daily f i e l d s 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 l u s t r a t e s 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 a c t i v i t y 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 s p l i t in the westerlies over the P a c i f i c Ocean near 40°N,  180°W, December 17-21, is synchronous with amplification of the subtropical 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 o f f 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 p o s i t i o n s , respectively) 500km (Iceland-Greenland  position on December 24-28).  to a maximum of  F i g . 3.6  (A) nean 700MB c o n t o u r s and (B) d e p a r t u r e from normal o f 700KB h e i g h t ( b o t h i n decametres) f o r December 10-14, 1968 and December 17-21, 1968 . (Green, 1968).  64  Pig.  3.7  Same a s P i g . 3.6 e x c e p t ( A ) and ( B ) f o r December 24-28, 1968. ( G r e e n , 1968).  65  3.4  Summary A review of selected studies from the 1iterature'has revealed a  considerable d i v e r s i t y in c r i t e r i a by which to judge the occurrence or otherwise of a blocking episode.  Moreover, the actual i d e n t i f i c a t i o n 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 a r i s e , has disclosed a strong propensity for c e l l u l a r structure of the Z - Z f i e l d which, in turn, implies centres of maxima and minima.  The positive centres were  closely i d e n t i f i e d with amplified anticyclones or ridges and the r e l a t i v e 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 amplif i e d feature ( e . g . , the wave crest) of the Z-field which has e f f e c t i v e l y become part of the blocking process. In the next chapter we shall f i r s t present the rationale for a p p l 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  w i l 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. 4.1  THE BLOCKING SIGNATURE Introduction So far our attention has been primarily focussed on certain  spatial  properties of two-dimensional f i e l d s of geopotential and, in p a r t i c u l a r on the use of the anomaly for the i d e n t i f i c a t i o n and measurement of s i g n i f icant features.  However, before proceeding with the empirical  tests  referred to in Chapter 3, there i s an important question to be addressed with regard to the data base. daily values of geopotential  The data available consists of twiceat  each point of a 381 km grid over the North-  ern Hemisphere for 33 years of record.  For s t a t i s t i c a l  investigations  into blocking did we r e a l l y 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 phenomenon being studied.  F i r s t , we did not want to include the high frequency  short-wave transient features conventionally referred to as synopticscale systems.  Second, a s i g n i f i c a n t 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 t r a c t able. 4.2  Considerations for a Time F i l t e r 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 l a t t e r 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  where T = time scale  ^ lO^s.  = 1 day It would therefore take the order of four days for a complete wave (L ^ 4x 10^m) to pass a reference point.  C l e a r l y , then, a simple 5-day  average f i l t e r w i l l provide a derived set of data which w i l 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 t y p i c a l l y c ranges between -5 and +5 m s""'.  If,  for example, k = 4 at 60°N (L = 5 x 10 m) and the speed 6  is 2.5 m s"^, then i t w i 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 l a t t e r as the quarter wave length centred about the crest. six days.)  It w i l l pass a reference point in about  The 5-day average w i l l not l i k e l y result in a serious attenua-  tion of the wave's features and therefore the blocking anticyclone w i l l still 4.3  be readily i d e n t i f i a b l e . The Response to a Five-Day Average F i l t e r The above discussion is h e u r i s t i c .  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). Figure 4.0, i s :  The f i l t e r i n g function,  68  A2  2(1 - cos 5ky )  k  k  (5ky )  V  Where  k  2  k = wave number A A y w  k  k  k  k  = amplitude = amplitude of the time averaged wave = phase speed (radians of longitude day"^) = angular frequency (day ^) = ky -  k  We tested this f i l t e r on harmonics of c h a r a c t e r i s t i c large amplitude long waves associated with blocking (k = 1 to 4, y  k  = 0 to 5 degrees  day~l) and also on those associated with transient b a r o c l i n i c waves in the mid-latitudes (k = 8 to 14, y were passed with l i t t l e attenuated.  k  > 5 degree day ^).  The former group  -  loss of amplitude while the l a t t e r were completely  The suppressed daily fluctuations caused by the b a r o c l i n i c  motions are then regarded as ' n o i s e , but only because of the choice of 1  our time scale.  We must remain aware of the continuous spectrum between  the wave length thresholds for i n s t a b i l i t y (Chapter 2) and also of the. crucial role of the short-wave eddies during energy exchange processes with the larger systems. Statistical  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, w i l l have time and space characteristics  69  Pig. 4.0  A t t e n u a t i o n of squared a m p l i t u d e s o f harmonic waves r e s u l t i n g from f i v e - d a y a v e r a g i n g , as a f u n c t i o n of a n g u l a r f r e q u e n c y (co^) i n r a d i a n s p e r day o r p e r i o d (TV) i n days. F o r 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. this is true.  In the case of major blocking episodes  But an inspection of d a i l y 500MB weather maps w i l l disclose  a surprising number of configurations ( p a r t i c u l a r l y over the continents) which have the c h a r a c t e r i s t i c s of blocking highs ( s p l i t upstream flow, barotropic core structure) of a b a r o c l i n i c system.  but a wavelength closer in magnitude to that  They do move slowly but, because they have smaller  dimensions than major blocks, the contiguous 5-day averages w i l l sometimes attenuate these cases so that they f a l l below our threshold of recognition. We shall attempt to design c r i t e r i a which w i l l minimize the number of times this happens. On balance we conclude that the 5-day average is an e f f e c t i v e 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 i m p l i c i t hypothesis  that positive anomalies of the 5-day mean 700MB or 500MB height may turn out to be useful i d e n t i f i e r s of blocking occurrence.  This was  tested for the 700MB level  We compared  in a p i l o t study (Knox, 1979).  samples of positive anomalies of 5-day averaged 700MB height f i e l d s  (of  the kind i l l u s t r a t e d 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 e d either by the author or from sources in the l i t e r a t u r e such as Rex (1950), Treidl et a l . (1980a), etc.  This approach sidestepped the  issue of common c r i t e r i a 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 a v a i l a b i l i t y 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 Northern Hemisphere during the sixteen year period 1947-1963, i n c l u s i v e .  It was  then possible by cross-comparison to develop a set of "associative"  criteria  against which a 700MB positive anomaly centre could be compared, to determine i f ,  in f a c t , i t was associated with an observed blocking episode.  The  c r i t e r i a 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 t e r i a . results to be developed.  This derived quantity has a central role in the The purpose of this Chapter i s to develop c r i -  t e r i a 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 P i l o t Study Although the results were encouraging, there were limitations to the  p i l o t study which were important to overcome in the subsequent investigation: (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 r e l a t i v e l y (c)  coarse.  the issue of "what is an actual observed blocking episode?"  needed to be c l a r i f i e d . (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 i s e n t i r e l y inappropriate in the v i c i n i t y 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 representative of the mid-troposphere.  (We considered the 300MB level but were  concerned with complications a r i s i n g from the frequent winter season lowering of the tropopause below 300MB.  Moreover, we preferred a longer  data base than is available at that l e v e l . )  A 33-year (1946-1978) set  of analyses of the daily 500MB> height f i e l d 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' 4.5  Processing the Data Base  4.5.1  The Data Base  investigation.  A 33-year record of 500MB grid point data for the Northern Hemisphere was obtained from the National Center for Atmospheric Research (NCAR), Boulder, Colorado.  This record includes d a i l y values (00GMT),  of 500MB heights at each of 1,977 points on the NMC Octagonal G r i d , 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 i s from January 1, 1946 to February 28, 1979 which ensures data for 33 complete winters. 24 x 10 4.5.2  The entire data set consists of  values of 500MB height expressed to the nearest tenth of a metre.  Pentad Averages A pentad is a specified period of f i v e consecutive days, and the  pentad calendar we shall use w i l l be found in Fig.. IV.-. 1. The conventions  4.1  NMC Octagonal G r i d . There are 1977 data p o i n t s i n the octagon. The Pole p o i n t 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) w i l l contain six days. We shall designate a pentad as:  yy  D r  P t  Where  K  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 F i g . 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 i e l d s per annum, or a total of approximately 2,400 f i e l d s 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)  = is  £ yy=i  yy  z n,J) K  75  This operation was carried out to compute 73 sets of normal 500MB heights corresponding respectively to each pentad.  Each s e t , in e f f e c t ,  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 f o r year y y , pentad K,  grid point I,J,  is  y y  A (I,J) = Z (I,J) K  y y  K  - Z (I,J) K  and this operation was carried out to produce approximately 2,400 anomaly f i e l d s f o r the 33-year period of record. 4.6  Anomaly Centres  4.6.1  Location of centres The anomaly f i e l d s , f o r reasons explained in Chapter 3, feature a  c e l l u l a r pattern of positive and negative i s o p l e t h s , and the next step was to locate the centres of the c e l l s .  Each of the 2,400 f i e l d s of A ^ ( I , J )  was searched f o r maxima and minima.  (Negative anomaly centres were not  yy  required f o r this i n v e s t i g a t i o n , but they were located and l i s t e d f o r use in a future study of cold lows and troughs.)  Trivial  centres were exclud-  ed by the requirement that to q u a l i f y , the centre's anomaly value must be greater than 5 dams or less than -5 dams. A l l centres were located to the nearest grid point (I,J) their positions are accurate to within ±1.7° l a t i t u d e .  so that  This resolution  was a decided improvement over the ±5.0° latitude of the data used f o r the p i l o t study.  76  4.6.2  Preparation of the Master Catalogue Since our objective was to determine c r i t e r i a for the "blocking  signature" (section 4.2) we needed a convenient source of positive anomaly information.  Therefore the anomaly centres were l i s t e d according to year,  pentad of occurrence, location and value (dams).  In e f f e c t , a Master  Catalogue was created which provided, in compact format, s a l i e n t information concerning the anomalous features of over 2,400 contiguous 500MB 5-day average height f i e l d s during the 33 years of record. The (I,J)  g r i d , though best for the centre search, and indeed for  a l l our data processing programs, was inconvenient for geographical l o c a tion.  Hence a l l anomaly centre positions were converted to latitude and  longitude for the Catalogue.  A sample page is i l l u s t r a t e d in F i g . 4.2.  For an " i n t e r n a l " consistency check we acquired a sequence of operational 500MB 5-day average height and anomaly analyses from the National Weather Service.  U.S.  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 limits 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  Criteria  The e a r l i e r P i l o t Study, Section 4.4, indicated the f e a s i b i l i t y of developing c r i t e r i a for the purpose of testing whether a single positive anomaly is l i k e l y associated with a concurrent blocking anticyclone.  A  positive anomaly which so q u a l i f i e d would be c a l l e d a "blocking signature" and of course one would expect to f i n d a sequence of blocking signatures  PENTAD 66 1968 MAXIMA MINIMA LA LO OM LA LO DM 38 91W 6 27 18W -14 28 44W 9 57 31W -26 31 132W 6 48 146W -6 3 0 147W 6 7 0 102W -29 43 2E 16 58 176W -13 79 10E 11 44 177E -14 75 176E 8 34 24E -14 58 37E 14 6 0 86E -27 47 135E 16 41 125E 16 PENTAD MAXIMA LA LO 26 135W 28 22W 6 1 73W 25 SW 53 153W 82 53W 52 51E 39 38E 24 37E 43 142E  7 1  1968  MINIMA DM LA LO DM 5 38 1 12W-24 7 42 59W - 13 3 1 27 16 1W -9 10 53 7W -28 28 75 100E -36 12 30 37E 5 14 3 1 159E -6 7 7 10  3 1969 PENTAD MINIMA MAXIMA LA LO DM LA LO DM 38 72W - 1 9 31 33W 11 48 128W -33 68 89W 39 31 154W - 11 51 160W 24 48 14W - 2 7 85 145E 29 72 10E -9 55 34E 7 55 166E -11 54 153E -7 66 73E - 1 9 48 142E -14 3 0 103E -5  F  1  fi'  4.2  PENTAD 67 1968 MAXIMA MINIMA LA LO DM LA LO DM 36 80W 12 30 107W -16 45 80W 12 53 51W, -25 23 141W 7 64 88W -16 66 17W 27 43 17W -14 38 162W 11 65 WOW -24 54 16E 19 34 27E -9 80 55E 8 61 100E -33 33 60E 6 26 79E -7 28 125E 6 20 76E -6 26 115E 6  PENTAD 68  1968  MAXIMA MINIMA LA LO DM LA LO DM 38 57W 10 44 93W -16 21 133W 5 56 1 12W -8 39 128W 1 1 48 32W -28 61 10E 26 56 152W -16 51 180 17 77 136W -16 43 142E 17 3 1 26E -7 35 32E -7 29 168E -5 56 68E -40  PENTAD 72 MAXIMA LA LO DM LA 2 1 129W 5 36 28 22W 8 45 61 50W 18 28 41 2W 19 68 60 156W 36 79 49 WOE 19 33 57 51E 27 68 58 83 31 61 28  1968 MINIMA LO DM 45W -20 131W - 17 15W 7 89W -6 80W -6 163W -11 1E -7 4E -9 100E -7 26E -16 107E -23 75E - 10  PENTAD 73 1968 MAXIMA MINIMA LA LO DM LA LO DM 32 70W 5 5 1 53W - 16 30 53W 5 '32 26W -10 20 127W 5 50 1 18W-26 71 69W 32 40 154W -15 64 24W 38 48 15E -25 6 0 176E 31 30 176W -7 67 139E 27 162E 26 -9 70 78E 36 46 145E -18 47 91E -23 21 72E -10  4 PENTAD MAXIMA LA LO DM LA 45 76W 18 36 31 6W 12 33 56 152W 21 50 74 37E 34 54 34 176E 9 55 35 152E 10 34 55 56 52  1969  PENTAD 5 MAXIMA LA LO DM LA 22 1 1 1W6 43 51 70W 25 46 53 153W 29 32 72 27W 23 78 44 1E 21 80 75 55E 19 55 35 160E 10 22 35 143E 12 52 30 66E 7  MINIMA LO DM 45W -23 142W -22 125W -25 1W -17 166E -21 24E -12 145E -23 1 18E-24 78E -28  Sample page o f M a s t e r p o s i t i v e and negative  1969 MINIMA LO DM 38W -23 125W -22 146W -28 28E 15 145E -17 166E -23 29E -22 78E -30  PENTAD 69 MAXIMA LA LO DM LA 37 107W 12 43 32 44W 9 49 75 156W 6 34 64 2E 22 78 43 142E 25 26 72 52 58 27  1968 MINIMA DM LO 63W -23 139W -25 4W -16 62W - 14 178E - 10 137E -30 44E -22 81E -16 162E -8  PENTAD 1 MAXIMA MINIMA LA LO DM LA 37 120W 18 45 55 35W 28 32 58W 70 56 30 54 4E 14 27 57 177E 4 1 35 75 1 14E 30 45 62 60E 35 39 24  PENTAD 6 1969 MAXIMA MINIMA LA LO DM LA LO DM 53 51W 38 26 65W -1 1 44 157W 29 31 37W -12 75 125W 1 1 46 125W -32 39 6E 12 67 8W -5 37 163E 17 60 176E -23 61 100E -6 22 178W -7 . 37 140E 19 71 1 1 -15 1E 56 42E -6 41 35E -13 18 169E -5 16 30E -2 1 47 86E -18 20 97E -6 14 93E -7  PENTAD 70 1968 MAXIMA MINIMA LA LO DM LA LO DM 25 1 17W 5 33 77W -8 48 56W 17 45 138W -25 33 30W 9 54 27W -23 54 9 1W 13 56 152W - 15 70 102W 14 22 5E -9 6 1 17E 12 39 14E - 13 45 167E 23 80 145E -37 54 1 1 1E12 66 73E -25 25 40E 6 59 64E -26 45 42E -15 3 11 3 1 -8 E PENTAD 2 1969 MAXIMA MINIMA LA LO DM LA LO DM 31 1 18W 11 44 89W -17 19 134W 7 28 22W -14 72 43W 35 52 136W -16 51 170W 38 62 130W -16 64 18E 18 48 14W -25 77 156E 17 24 164W -15 29 129E 6 29 32E -10 60 8 6 E -11 44 153E -6 37 50E -6 45 6 8 E -13 PENTAD 7 1969 MAXIMA MINIMA LA LO DM LA DM LO 27 89W 6 33 120W -6 80W 30 6 33 40W -15 52 46W 21 26 135W -5 61 80W 6 35 28W - 16 70 102W 5 56 138W -23 41 178W 37 77 24W - 18 80 145E 9 61 10E -20 75 55E 8 64 178W -14 33 31E 10 59 46E - 18 64 134E -16 19 172E -9 65 100E -21  Catalogue, i n d i c a t i n g p o s i t i o n and i n t e n s i t y A n o m a l y C e n t r e s o f 5 - d a y m e a n 500MB h e i g h t .  of  \  78  associated with an amplified block of substantial duration (> 10 days). The p i l o t study also indicated that the c r i t e r i a would be functions 'of the time of the year, anomaly magnitude and l a t i t u d e .  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 f a c t , 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 i t e r a t u r e discloses an extremely  broad range of c r i t e r i a 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 r e s u l t s . on major blocking episodes.  The one area of agreement is  The objective of this study i s , so far as  is p o s s i b l e , to design a threshold such that the set of qualifying positive anomalies (signatures)  w i l l r e f l e c t the f u 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 T r e i d l guidelines (Appendix IV - 2B) used to prepare his Catalogue were s u f f i c i e n t 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 t e s t i n g , occurred within the duration of a blocking episode l i s t e d in his Catalogue, i t q u a l i f i e d as a blocking signature. However, i t was not necessary for a l l the T r e i d l c r i t e 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 s i g n i f i c a n t number of  relatively  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 t e d . if,  Therefore  corresponding to the Master Catalogue-selective positive anomaly, the  Treidl Catalogue did not l i s t a block, we then went d i r e c t l y to the 5-day sequence of Daily 500MB analyses and, over the region concerned, applied the following guidelines: (i)  (see also Appendix IV - 2A).  During the pentad of the positive anomaly being tested, an  anticyclonic centre must be observed on at least 3 out of the 5 consecutive daily analyses. (ii)  The anticyclonic structure w i l l c l e a r l y have disrupted  the pre-existing zonal flow. (iii) If  The anticyclone centre must be N of 45°N.  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 T r e i d l guidelines were considered s u f f i c i e n t , while ours were considered necessary and s u f f i c i e n t .  In e f f e c t 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 e s s e n t i a l l y our own, as set out in f u 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 l a t i t u d e .  The plot  also i d e n t i f i e d whether or not, during that pentad, a blocking episode was in progress in the region of the anomaly being tested by: (i)  Occurrence  #  (ii)  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:  4.7.1.4  WINTER  318  SUMMER  384  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 atmospheric continuum one uses formal s t a t i s t i c a l  techniques.  of the This  a n a l y s i s , however, is concerned, not with elements of the continuum, but with s p a t i a l l y isolated derivatives  (anomaly maxima and centres of anti-  F i g . 4,3(a)  Threshold f o r B l o c k i n g Signatures, WINTER. 3.18 p o s i t i v e - anomaly c e n t r e s are t e s t e d f o r a s s o c i a t i o n w i t h a b l o c k i n g episode.. ( F o r d e t a i l s see Appendix IV, S e c t i o n s 2 and 3 ) .  Legend  •  Anomaly was found to be a s s o c i a t e d w i t h a contemporaneous b l o c k i n g episode.  O  No b l o c k i n g episode  observed.  Cases t e s t e d were from f o l l o w i n g years: 1947, 1948, 1951, 1953, 1954, 1955, 1956, 1958, 1961, 1965, 1966, 1968, 1970, 1971, 1972, 1973, 1974, 1975. Not shown i n F i g u r e i s one o u t l i e r a t 57°N w i t h a c e n t r e value o f 55 dams. This occurred December 17 - 21 (PE 71) i n 1955 and was a s s o c i a t e d with a strong 11 day b l o c k i n g h i g h over the m i d - P a c i f i c Ocean.  A  NOM  35  Dams  S UMM ER 3  30|  2 5  25  O 2 0 o  I 5  o o o  o  k  20  o  • o  o  10  0  o  O  O O  oo  I 5  oo o o ° o o_ o ooo oo ° po o o ooo°cP# • Q  °  oo oo  o*  I oo  ooo  o  o  • o  o  0  o oo  o  o  45  F i g 4-3  50  (b)  5 5  60  6 5  70  7 5  80  85  9 0  As i n F i g . 4.3(a) except f o r SUMMER. The p l o t i s f o r 384 p o s i t i v e anomalies which occurred i n June, J u l y and August f o r the y e a r s 1949, 1950, 1951, 1964, 1965, 1969, 1970, 1971 and 1972.  -L A T  CO  no  83  cyclones).  Moreover, we have used quasi-subjective guidelines to deter-  mine the dichotomous f i e l d s 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 t e r i a were: WINTER  (  y y  A  SUMMER  (  y y  A  K  K  - 15)( <f» yy  - 10)( (j> yy  K  K  - 49) > 16  (1)  - 53) > 9  (2)  Where yy = year, pentad number = K, anomaly magnitude = ^ A ^ and anomaly latitude = It  i s 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 i n e q u a l i t i e s (1)  and (2)  have no obvious physical explanation, but we assumed that the difference was related to the annual c y c l e . 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 t e d to a plot of 73 maximum standard deviations of 500MB 5-day mean height for the Northern Hemisphere.)  84  120E  'Fig. 4.4  100E  80E  Standard d e v i a t i o n o f 5-day mean 500MB h e i g h t f o r WINTER (December 1 to February 28). Contour i n t e r v a l = 2 dams.  fflg.  4.5  Standard d e v i a t i o n o f 5-day mean 5.00MB h e i g h t f o r SUMMER (June 1 to August 31). Contour i n t e r v a l = 2 dams.  86  J OOE  120E  Fig.  4.6  80E  Normal h e i g h t of the 5 0 0 M B s u r f a c e f o r WINTER (December 1 to February 28). Contours l a b e l l e d i n decametres l e s s 5 0 0 . I n t e r v a l = 6 dams. 585  dam  contour  87  120E  F 1  fi-  4  '7.  JOOE  BO£  Normal h e i g h t of jfche 50OMB s u r f a c e f o r SUMMER (June 1 to August 31). Contours 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. 591 dam  contour  88  The generalized c r i t e r i o n i s :  ( \ y  Where  A $ Q K  K  K  K  - A )( <D K  yy  K  - •*) K  >Q  (3)  K  = 12.5 + 2.5 cos (0.08607K - 0.2582) = 51.0 - 2.0 cos (0.08607K - 0.2582) = 12.5 + 3.5 cos (0.08607K - 0.2582) = 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 C r i t e r i o n (3) on SPRING and FALL data.  These  are the seasons when the rate of change of a l l c r i t e r i o n factors are greatest.  We proceeded as before and drew curves of separation for the respec-  t i v e seasons (not shown).  Again they approximated hyperbolas which turned  out to be reasonably close to the analytical  curves in c r i t e r i o n (3)  mid-spring (K = 21) and mid-fall (K = 57), respectively.  for  The results  were s u f f i c i e n t l y encouraging that we decided the Criterion could be used for the entire year. 4.7.2  Interpretation Criterion (3)  of Criterion t e 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 e f f e c t 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 s h i f t north of i t s normal p o s i t i o n , or some combination of these two events. 4.7.3  Blocking Signature Catalogue The Master Catalogue described in 4.6 i d e n t i f i e s 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 i n g only those positive anomalies which q u a l i f i e d as Blocking Signatures. application of Criterion (3) logue.  This was done by  to each positive centre in the Master Cata-  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 l u s t r a t e d in F i g . 4.8.  By scanning across the pentads one can discern sequences of varying 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  2 1971 LO DM 16E 23  PE LA 61 57  3 197 1 LO DM 170W 34 23E 35  PE LA 68  4 197 1 LO DM 80W 25  PE LA  PE 12 1971 LA LO DM 71 10E 25 74 86E 28  PE LA 61 71 59  13 1971 LO DM 20W 26 47E 27 154E 25  PE 14 1971 LA LO DM 67 7 1W 28 56 22W 20 61 130E 22 64 92E 22  PE LA 78 67  PE 21 1971 LA LO DM 3W 24 57 90 100E 14  PE 22 1971 LA LO DM 51W 22 53 68 80W 2 1 8 1 53W 22  PE LA 62 74  LO DM 57W 19 94W 34  PE 24 1971 LA LO DM 67 89W 23 67 172E 28  PE 25 1971 LA LO DM 6 1 100E 16  PE 26 1971 LA LO DM 61 17E 13  PE 27 1971 LA LO DM  PE 31 1971 LA LO DM 67 19E 20 59 136E 15  PE 32 1971 LA LO DM 6 1 30W 29 73 143W 18  PE LA 62 75  LO DM 57W 27  PE 34 1971 LA LO DM 81 107W 18 60 86E 13  PE 35 1971 LA LO DM 76 136W 19 81 37E 16 64 92E 14  PE LA 71  PE 37 1971 LA LO DM 84 125W 14 75 170W 15 75 10E 11  PE LA 76 54 57 76  PE 41 1971 LA LO DM 73 143W 11 53W 14 81 64 145E 12 57 59E 18  PE 42 1971 LA LO DM 54 133W 17 57 23E 16  PE 13 1971 LA LO DM 57 23E 13  PE 44 1971 LA LO DM 7 1 100E 14  PE 45 1971 LA LO DM 56 152W 15  PE 46 1971 LA LO DM 56 22W 13  PE 51 1971 LA LO DM 53W 19 65 64 2E 25 55E 19 59  PE 52 1971 LA LO DM 54 56W 15 59 1 1W 18 67 179W 14 56 68E 21  PE 53 1971 LA LO DM 53 141W 23  PE 54 1971 LA LO DM 62 123E 13  PE 55 1971 LA LO DM 61 73W 13 66 151E 17  PE 61 1971 LA LO DM 57 10E 2 1  PE 62 1971 LA LO DM  PE 63 1971 LA LO DM 59 35W 3 1 60 114E 18  PE 64 1971 LA LO DM 57 80W 16 51 24W 24  PE 65 1971 LA LO DM 61 50W 17 57 113E 26  PE 71 1971 LO DM LA 51 165W 40 64 100E 23  PE 72 1971 LA LO DM 53 159W 34 8 1 73E 30  PE LA 64 G1  1 197 1 LO DM 80W 3 1 30W 16  PE 11 1971 LA LO DM 8 1 37E 28  PE LA 54  ***  PE 73 1971 LA LO DM 62 13W 38 82 100E 17  Fig.  5 1971 LO DM  ++**  4«8  LO DM 62W 21 82E 29  PE LA 61 71 56 54 61  6 1971 LO DM 40W 18 69W 19 172E 38 55E 26 107E 19  PE 7 1971 LA LO DM 70 102W 16 56 22W 32 61 150E 32 58 73E 29  PE 8 1971 LA LO DM 56 138W 21 53 1W 31 70 122E 37  PE 9 197 1 LA LO DM 78 118E 33  PE 10 1971 LA LO DM 8 1 73E 19  PE LA 81  16 1971 LO DM 107W 32  PE 17 1971 LA LO DM 74 156W 34  PE 18 1971 LA LO DM 78 172E 27  PE 19 1971 LA LO DM 67 1E 15 7 1 153E 20  PE LA 79 63  PE 28 1971 LA LO DM 74 125W 12  PE 29 1971 LA LO DM 78 28E 18  PE LA LO DM 62 33E 17 61  38 1971 LO DM 136W 16 164W 17 10E 20 134E 17  PE 39 1971 LA LO DM 56 22W 24 53 159W 23 79 145E 24  PE LA 63 70  PE 47 1971 LA LO DM 60 4W 18  PE 48 1971 LA LO DM 57 86W 14 7 1 153E 15  PE 49 1971 LA LO DM 74 145E 23  PE LA 53 76  PE 56 1971 LA LO DM 68 80W 14 56 8W 19  PE 57 1971 LA LO DM  PE 58 1971 LA LO DM * + •* *  PE 59 1971 LA LO DM * ++*  PE 60 197 1 LA LO DM 60 4W 21  PE 66 1971 LA LO DM 63 96W 18 54 27W 24 56 68E 22  PE 67 1971 LA LO DM 65 163E 25 61 40E 23  PE 68 1971 LA LO DM 57 4E 20 69 145E 18  PE 69 1971 LA LO DM 5 1 12W 37  PE LA  LO  DM  LO  26E 18  LO DM 46W 21  LO DM 1W 19 134E 14  <  LO DM ***  Sample page from B l o c k i n g S i g n a t u r e C a t a l o g u e . Q u a l i f y i n g p o s i t i v e Anomaly C e n t r e s l i s t e d by  p e n t a d , l o c a t i o n and i n t e n s i t y  (DM = dams).  DM  O  91  CHAPTER 5 5.  DISTRIBUTION OF SIGNATURES AND SEQUENCES  5.1  Introduction We r e c a l l that a Blocking Signature is a positive anomaly of  500MB 5-day mean height which, for a s p e c i f i c year (yy) meets C r i t e r i o n (3),  and pentad (K)  viz:  (  y y  A  K  - A )( <|, yy  K  K  -  +K  )  >Q  K  Where the signature magnitude = A ^ y y  the signature latitude  = <j> yy  K  and the threshold values A^, <j>^, Q^ are sinusoidal functions of K (Section 4.4.3). One purpose of this chapter w i l l be to present and interpret the frequency d i s t r i b u t i o n of Blocking Signatures for the Northern Hemisphere.  Later (Section 5.3),  i t w i l l be shown how the Signature Catalogue  can be modified to reveal the beginning and ending of Sequences of Signatures.  We shall' then present and interpret the frequency d i s t r i b u t i o n of  these sequences. 5.2  Distribution of Blocking Signatures  5.2.1  Area! Distribution A l l blocking signatures, having now been i d e n t i f i e d and recorded,  were counted according to their (I,J)  location.  Isopleths of equal f r e -  quency were drawn over the two-dimensional grid and the resulting area!  92  d i s t r i b u t i o n is presented by TOTAL, Fig. 5.1.  (A s l i g h t 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 P a c i f i c Ocean and SW Alaska, and  (ii)  the NE A t l a n t i c and NW Europe (Rex, 1950).  However, i t also reveals areas of comparable blocking signature frequency over (iii)  NE Canada (including Baffin  Island)  (iv)  the portion of the high A r c t i c (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 i c i n i t y of the mean 500MB trough, would have been a surprise had we not already noted a similar pattern in the 700MB P i l o t Study.  What  little  comment we have seen concerning blocking in this region has been somewhat controversial.  For example, Sumner (1959) stated that  blocks are almost non-existent over North America".  "well-developed  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". paradox in Section 5.3.6.  We shall return to address the  9>  FREQ 5 - D A Y MEAN  500 MB  BLOCKING SIGS  TOTAL-SMOOTHED  120E  IOOE  -V  BOE  +  +  140E  -V  +  . 60E  +  <BE  160E-  7^ 180.  •20 £  160 V  DO  140V  A"  -20 w  3O0V  PERIOD  OF  RECORD  1946  -  1978  Fig.  5.1  INCL  sow .  INTERVALS NMC G R I D  WEIGHTS •  Frequency o f occurrence o f B l o c k i n g S i g n a t u r e s w i t h i n s q u a r e s o f 381 km x 381 km ( e x a c t a t 6 0 N) f o r a l l seasons (1946 t o 1978). o  94  Turning now to the high A r c t i c , l e t us examine the d i s t r i b u t i o n of blocking signatures not only by YEAR (Fig. 5.2 - 5.5).  5.1)  but also by SEASON (Figs.  In a l l of these frequency d i s t r i b u t i o n s the closed isopleths  in that region are explained, in part at l e a s t , by the not unusual observation (from daily 500MB analyses)  of warm anticyclones, removed from the  mainstream of the westerlies, d r i f t i n g slowly around the Pole.  They no  longer block the zonal flow in the usual sense. Namias (1958) has suggested that, "one of the more s i g n i f i c a n t differences [between synoptic-scale phenomena of A r c t i c and Temperate latitudes] appears to be that the Polar Basin i t s e l f is either a sort of t r a n s i t area or a sink for cyclones and anticyclones which develop e l s e 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 c e l l s over extreme northern Greenland (80° - 85°N) which have evolved from the meridional extension of warm A t l a n t i c ridges.  It  is also not unusual to find a second c e l l  further  west (120° - 180°W),, either concurrently or subsequently, with a probable genesis over Yukon-Alaska, d r i f t i n g into the 75° - 80°N zone. cause the normal 500MB c i r c u l a t i o n (Figs.  Now, be-  4.6 and 4.7) features a Pole-  centred low, the signature centres corresponding to these c e l l s w i l l , reasons explained in Chapter 3, be very close to the Pole.  for  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 s t r i k i n g seasonal variation from a minimum in WINTER to a, maximum in SUMMER. as follows:  The results are summarized  ;  95  FREQ 5-DRY MEAN  500  BLOCKING SIGS  WINTER-SMOOTHED  120E  JOOE  * ^  PERIOD  OF RECORD  1946  1978  -  Fig.  INCL  MB  BOE  + +  /  INTERVALS N M C  G  R  ^  5 . 2 A s i n F i g . 5 . 1 e x c e p t f o r WINTER  WEIGHT=4 •  96  FREQ 5 - D R Y MERN  500 MB  BLOCKING S I G S  SPRING-SMOOTHED  BOE  120E  180  :~20E  160 V  60 W  PERIOD  OF  RECORD  1946 -  1978  Fig 5.5  INCL  60 U  INTERVALS NMC GRID  As i n F i g . 5.1 except f o r SPRING  WEIGHTS •  97  FREQ 5 - D R Y BLOCKING  500 MB  MERN  SIGS  SUMMER-SMOOTHED  120E  P E R I O D OF 1946  -  Fig.  INTERVRL=1  RECORD  1978  5.4  NMC GRID  INCL  As i n F i g u r e  5.1  e x c e p t f o r SuTMER  WEIGHT=4 •  98  FREQ 5 - D R Y MERN  500 MB  BLOCKING  FRLL-SMOOTHED  SIGS 120E  180  160 V  60W  P E R I O D OF 1946 -  RECORD  1978  Fig.  INCL  5.5 As i n P i g .  INTERVALS NMC G R I D  5.1 e x c e p t f o r  PALL  WEIGHTS •  99  TABLE  5.1  Blocking Signatures North of 75°N Winter  154  Spring  217  Summer  245  Fall  170  Total  786  1946 - 1978  Although the physical reasons for the increase in blocking f r e quency in the SPRING and SUMMER are n o t ' c l e a r , we can speculate on a number of contributing factors.  For example, by summer the westerlies  have shifted at least 5 degrees north of t h e i r winter p o s i t i o n , and we may therefore i n f e r that blocking action w i l l have a corresponding displacement. This w i l l increase the p o s s i b i l i t y of anticyclones migrating into the Arctic.  Moreover, the normal pressure around the Pole i s . h i g h e r and the  circumpolar c i r c u l a t i o n less vigorous.  Therefore, whatever the o r i g i n a l  cause of these high latitude warm anticyclones, once they do d r i f t over the Polar Basin they are less l i k e l y 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 l u s t r a t e d more c l e a r l y 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 F i g . 5.6 and the strong longitudinal dependence described in the previous section is s t r i k i n g l y evident. The seasonal variations are shown in Figs. 5.7 to 5.10.  In  WINTER, F i g . 5.7, the low frequency of signatures in Zone 3 (E S i b e r i a , W P a c i f i c ) is not surprising for that zone is centred near the axis of the normal 500MB east A s i a t i c trough (Fig. 4.6) and also in an area of relatively  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 T r e i d l 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 thermallyforced b a r o c l i n i c a l l y unstable waves meeting the c r i t e r i a of F i g . 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 P a c i f i c Ocean between 20° and 50°N, while the topographic forcing agency is the Rocky Mountain C o r d i l l e r a . Fig. 5.8, SPRING, and F i g . 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 A t l a n t i c 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 i n t e r p o l a t i o n , which avoids repeated and expensive coordinate system transformations on very large data s e t s , w i l l be found in Appendix V.  TOTAL EUROPE  -j  0  i  1  1  30E Fig.  1  W.SIBERIA  1  1  60E 5.6  1  r  1  90 E  1  i  ,—i  1  120E  i  i  1  150E  i  5  4  ALASKA E .PACIFIC  E.SIBERIA V.PACIFIC  1  180  1  1  1  1  i  CANADA  I  1  1  1  1  150 V 120 V 90 W  1  GREENLAND N.ATLANTIC  1  1  60W  i  i  i  i  30 V  i  EUROPE  1  0  1  1  i  30E  i  Frequency of occurrence of B l o c k i n g S i g n a t u r e s f o r each 10 degrees o f l o n g i t u d e counted from southernmost l a t i t u d e o f occurrence to 75°N. F o r ALL SEASONS (1946 t o 1978).  i  !  60E  1  EUROPE  i  0  i  r  30E  WINTER  2 W.SIBERIA  'eOE'  '9UE'  Fig.  E.SIBERIA V.PACIFIC  .4  ALASKA E .PACIFIC  5 CANADA  GREENLAND N.ATLANTIC  ' 120E 'l50E " 180 " 'l50W ' 3 20W ' 90W' '60W' 5.7  As i n F i g .  5.6 e x c e p t f o r WINTER  '30W'>  EUROPE  '  6'  '30E'  '60E  EUROPE  30E  W.SIBERIA  60E  90E  120E F i g . 5.8  E.SIBERIA W.PACIFIC  150E  SPRING d I  180  ALASKA E .PACIFIC  150W  As i n P i g . 5.6  GREENLAND N.ATLANTIC  CANADfl  320W 90W  60W  except f o r SPRING  30V  0  I  EUROPE  30E  '60E  §  SUMMER W .SIBERIA E.SIBERIA W.PACIFIC  EUROPE  0  30E  60E  90E Fig.  120E 5.9  150E  180  As i n F i g .  4  5  ALASKA E.PACIFIC  CANADA  150V  90W  5.6  120V  1  GREENLAND N.ATLANTIC  60W  e x c e p t f o r SUMMER  30V  EUROPE  0  30E  60E  FALL  V. SIBERIA  EUROPE  0  30E  3 l 4 E. SIBERIA ALASKA W.PACIFIC . E.PACIFIC  60E  90E Fig.  120E 5.10  150E  180  As i n F i g .  150W 5.6  120W  90W  ]  GREENLAND N.ATLANTIC  CANADA  60W  except f o r F A L L  30V  EUROPE  0  30E  60E  &  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, signature maximum at 80°W.  1948) and this is reflected by the blocking  Over Zone 4 (Alaska and the E. P a c i f i c ) we  observe, not an eastward d r i f t as in the case of the A t l a n t i c , but a westward d r 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 substantial heating in the lower troposphere, greatly enhanced by the nature of the t e r r a i n , w i l l (from hydrostatic considerations) increase the 500MB gph and therefore the positive anomaly.  The blocking anticyclones  centred over Alaska w i l l usually have signature centres located between 70°  and 75°N, and between 140° and 180°W.  These contribute to the  SUMMER d i s t r i b u t i o n in Zone 4. By FALL (Fig. 5.10)  the blocking signatures in that area have  declined, partly because the thermal e f f e c t over Alaska is in reverse. It  now becomes a source region for cold a i r masses, hence signatures over  the Alaska-Yukon area are rare (Fig.  5.5).  Moreover, under appropriate  synoptic conditions, cold a i r is deployed over the r e l a t i v e l y  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 d i s p o s i t i o n , 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 i c i n i t y of the Ural Mountains. Serebreny et a l . maximum?  This result is supported by Baur (1958),  (1961) and Knox (1979).  What is the reason for this  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) flow.  indicate the dominance of Wave component 3 on the mean  As discussed in Chapter 2, the' f i r s t two waves starting from the  west P a c i f i c trough are primarily the result of topographic forcing combined with longitudinally dependent heating. factors for the third wave.  We cannot invoke these  (The low p r o f i l e of the Urals does not pro-  vide a s i g n i f i c a n t orography and the thermal forcing does not e x i s t . ) Its  presence was explained ( B o l i n ,  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 i c i n i t y of 60°E and i t i s reasonable to assume that the Ural Mountain blocking anticyclones make a s i g n i f i c a n t contribution, just as do their oceanic counterparts, to variance maxima at 160°W and 20°W, respectively. F i n a l l y , to compare the seasonal frequency of blocking signatures south of 75°N, we present Table 5.2 (which complements Table TABLE 5.2 Blocking Signatures South of 75°N Winter  1055  Spring  1278  Summer  1186  Fall  1089  TOTAL  4608  1946 - 1978  5.1).  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 It  5.2.1). is well to re-emphasize the d i s t i n c t i o n between a blocking s i g -  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 w i l l correspond to a sequence of signatures. we shall describe a proposal to objectively  In Section  5.3  identify these sequences, to  catalogue their attributes and calculate t h e i r frequencies. 5.3  Blocking Signature Sequences  5.3.1  Rationale and Technique The Blocking Signature Catalogue (Fig. 4.8)  positive anomaly centres whose trajectories  reveals sequences of  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 l u s t r a t e d by F i g . 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 respective trajectories were geographically well separated.  109  The signatures moved with speeds c h a r a c t e r i s t i c of blocking a n t i cyclones (1 to 5 m s""*).  Could we use this fact as a data processing  c r i t e r i o n 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 i k e l y occurred in the Northern Hemisphere during the 33-year period. To determine the c r i t e r i o n 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 1905 km) per 5 days, which is equivalent to a speed of 4.4 m s"^  (or  at  60°N. If we designate a sequence of n successive signatures (a-j, Or>, o-g> . . .  . . . a ) as S ( a ) then the c r i t e r i o n for n  n  member is that the distance from  to  w i l l be referred to as Criterion (4).  +  +  -| to be a  -| * 5 grid lengths.  This  Therefore, to determine i f a signa-  ture in pentad K had a successor, C r i t e r i o n (4) was applied to the distance between  and each signature l i s t e d in pentad K + 1.  Either there was no  successor, in which case the sequence was terminated, or one was determined and the process was repeated with the signatures in K + 2.  Occasion-  a l l y (usually with cases in the high A r c t i c ) , two signatures q u a l i f i e d , 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 i n g a l l such sequences over the 33-year period.  A sample page from  the resulting Blocking Signature-Sequence Catalogue is shown in F i g . 5.11.  5-DAY MEAN BLOCKING SIGNATURE PE LA 67 *57 PE LA 51  1 1955 PE 2 1955 PE LO DM LA LO DM LA 8W 38* *G3 57W 4 1 S3 51E 19* *54 133W 23* *75 *57 1 13E 21* *55 11 1955 LO DM 53W 37*  PE 21 1955 LA LO DM 69 69E 15* •53 7W 21  PE 31 1955 LA LO DM 68 1E 22* •58 80W 19 58  SEQUENCES 3 1955 PE 4 1955 LO DM LA LO DM 57W 31 57 67W 23* 94W 21* *58 100E 27* 7GE 20 60 86E 26  PE 12 1955 PE 13 1955 LA LO DM LA LO DM •58 170W 39* *6' 20W 21 •78 82E 24 78 82t 26 *64 134E 24* PE 22 1955 LA LO DM 63  PE 23 1955 LA LO DM *75 80W 28 13W 23* *63 77E 28  PE 32 1955 LA LO DM *90 19* 58 74W 30  73E 17*  1955  PE 14 1955 LA LO DM 58 17W 19 78 82E 18* PE 24 1955 LA LO DM 64 88W 17* 69 69E 19*  PE 33 1955 PE LA LO DM LA •63 123E 13 66 59 101W 19* *6 1 *58 73E 14* *61 *69  PE 42 1955 LA LO DM 60 4W 22  PE 43 1955 LA LO DM 55 14W 16  PE 44 1955 LA LO DM 55 14W 20  67 172E  72 WOW  7 1 179E  PE 51 1955 LA LO DM *82 37E 17 *56 28E 15  PE 52 1955 PE 53 1955 LA LO DM LA LO DM 80 55E 23* *78 62W 21* 59 46E 18 60 55E 22  PE 61 1955 LA LO DM 59 59W 37 *61 177W 27 *58 73E 22*  PE 62 1955 LA LO DM 58 53W 30 66 163E 30*  PE 71 1955 LA LO DM *74 53W 26 57 177E 55  PE 72 1955 PE 73 1955 LA LO DM LA LO DM 68 80W 27* *64 66E 17 51 175W 41* *59 136E 26*  15  5 1955 LO DM  PE LA  6 1955 LO DM  * ** +  56  82E 21*  PE LA *61 *79  7 1955 LO DM 80W 24* 1OOE 21  PE LA  8 1955 LO DM  80 145E  18  PE 15 1955 PE 16 1955 PE 17 1955 PE 18 1955 LA LO DM LA LO DM LA LO DM LA LO DM 57 31W 32* *70 58W 37 59 59W 19 64 24W 20* *83 100E 28 86 100E 30 85 145E 20* *64 66E 20* *72 117W 24* •57 93W 18 PE 25 1955 LA LO DM * ** *  34 1955 PE 35 1955 LO DM LA LO DM 127E 14 67 82E 18 20W 12* *61 80W 20* WOW 12* *59 116W 13 145E 14*  PE 41 1955 LA LO DM 60 4W 23 *69 139W 16* *57 157W 15  11  PE LA  ****-NO SIGNATURES RECORDED  PE 26 1955 LA LO DM * * *• +  PE 36 1955 LA LO DM 75 100E 11 59  PE 27 1955 LA LO DM *58 53W 23  PE 37 1955 PE 38 1955 LA LO DM LA LO DM 85 145E 17* *60 4W 19  101W 13*  PE 46 1955 PE 47 1955 LA LO DM LA LO DM 59 31E 15 56 28E 15 *6 1 130E 14* *54 4E 17* *67 28E 16*  PE 48 1955 LA LO DM 60 24E 17*  PE 54 1955 LA LO DM  PE 55 1955 LA LO DM  74  69  PE 56 1955 PE 57 1955 LA LO DM LA LO DM + 68 89W 15 67 62W 23 60 86E 17* *58 37E 20* *58 73E 17*  PE 58 1955 LA LO DM 60 66W 44  37E  22  PE 63 1955 PE 64 1955 LA LO DM LA LO DM 63 57W 19* *59 1 1W 25  69E  16  PE 65 1955 PE 66 1955 LA LO DM LA LO DM 56 8W 31 59 26W 30* *54 179E 27* *65 80W 19*  F i g . 5.11  PE 67 1955 LA LO DM * * * *  PE LA  19 1955 LO DM  58  PE LA 59  10 1955 LO DM 44W 36  PE 20 1955 LA LO DM *75 55E 19  86W 18'  PE 28 1955 PE 29 1955 PE 30 1955 LA LO DM LA LO DM LA LO DM 64 46W 13* *59 136E 22* •67 8W 17 *56 98W 16* *60 35W 13* *59 64E 16 69 69E 13 64 84E 30  PE 45 1955 LA LO DM 65 10E 18  13*  PE 9 1955 LA LO DM •62 30W 42 79 100E 19*  PE 68 1955 LA LO DM *75 WOW 20  PE 39 1955 LA LO DM 6 1 10E 22 *60 94W 13  PE 40 1955 LA LO DM 56 8W 15 56 98W 15  PE 49 1955 LA LO DM  PE 50 1955 LA LO DM *64 134E 16  PE 59 1955 LA LO DM 60 35W 15 •56 82E 16*  PE 60 1955 LA LO DM 64 46W 23  * +- * *  PE 69 1955 PE 70 1955 LA LO DM LA LO DM 86 80W 25 85 145E 19* *64 72W 24* *56 152W 33  Sample page from B l o c k i n g S i g n a t u r e Sequence C a t a l o g u e . *• i n d i c a t e s b e g i n n i n g and end of a sequence. Component s i g n a t u r e s remain on same row.  11,1  Note that the beginning and end of a sequence is indicated by an asterisk (*)  and that i t s component signatures always occupy the same row. Example 1.  The entry l i s t e d for pentad 50 (September 3 to 7,  1955), a positive anomaly centred at 64°N 134°E, magnitude 16 dams, represents a single signature sequence.  (An inspection of the daily 500MB  analyses discloses a short-lived but well-defined blocking anticyclone over eastern S i b e r i a . ) Example 2.  The entry l i s t e d 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 A t l a n t i c (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 i m i -  tations of our basic u n i t , the 5-day average 500MB height anomaly, have already been discussed in Chapter 4 and these carry over into the signature-sequences.  On the other hand, the trajectory  tests suggested that,  p a r t i c u l a r l y 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  criteria"  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 i e l d s .  Any test of the c r i t e r i a 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) Criterion (4)  (What determines a qualifying signature?) or  (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? those used during the development of C r i t e r i o n (3)  They were  in the f i r s t place,  that is to say, the necessary and s u f f i c i e n t conditions (Appendix IV - 2) which, in our judgment, must obtain for a block to occur. The results are summarized in Table 5.3.  It w i 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 t s duration (column 3) but also the number of. times i t s component signatures actually concurred with the blocking episode (Column 6).  The rationale  was that, p a r t i c u l a r l y during long sequences, there would be interruptions 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 # of SEQ's tested (including those N of 75N)  SEQ  1  SEQ  ALL  n  2 # of SEQ's within which one or more blocking episodes occurred  3 % of SEQ's which were related to one or more associated blocking episodes. (Col. 2 * Col. 1) x 100  4 # of SIG's contained in SEQ's l i s t e d in Col. 1  5 # of SIG's within the SEQ's of Col. 2 which were concurrent with blocking episode  6 % of SIG's which were concurrent with a r e lated blocking episode (Col. 5^ Col. 4) x 100  21  13  62  21  13  62  26  25  96  109  90  83  47  38  81  130  103  79  114  It w i l l be noted that a total  of 47 signature-sequences (SEQ's) were  l i s t e d 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 (SEQ 's where n ^ 1). n  The success r a t i o of the SEQ^s was 62% and of the SEQ 's 96%. n  The success r a t i o of SEQ-j signatures was, of course, 62% while of SEQ natures i t was 83%.  This difference is not surprising because the  n  sig-  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 s u f f i c i e n t amplitude to produce a single qualifying anomaly. Of the total of 130 signatures l i s t e d , 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 w i 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 ident i f y i n g a blocking episode, and to have an understanding of the l i m i t a tions of using 5-day averages for the s p e c i f i c a t i o n of events in a continuum.  Subject to those reservations, the Signature-Sequence Catalogue  can be used to advantage (a)  for quick i d e n t i f i c a t i o n of probable periods of blocking  (b)  for a wide variety of frequency studies, the results of  which w i l l be closely connected with corresponding frequency studies of blocking. 5.3.4  Signature-Sequence  Frequency by Duration  The number of signature-sequences ( a l l during the 33 years of record is 1,868.  durations) which occurred  Of these, 994 were 2 pentads or  115  longer, and the remaining 874 had a duration of only one pentad. complete d i s t r i b u t i o n is shown in F i g . 5.12(a). ated north of-75°N were not :  The  (SEQ's which were i n i t i -  counted.)  As a matter of interest the 16-pentad ' o u t l i e r ' was  initiated  July 20th, 1976 at 56°N 22°W and terminated October 7th, 1976 at 72°N 10°E (PE 41 to PE 56, i n c l u s i v e ) .  This extraordinarily long sequence was  immediately preceded by one which also resided in the E. A t l a n t i c - 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 d i s t r i b u t i o n of durations of those blocks which they i d e n t i f i e d 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  r e l a t i v e s i m i l a r i t y 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 d i s t r i b u t i o n by  season and year of the frequency of occurrence of Blocking Signatures. Although these diagrams c l e a r l y .revealed areas of high and low blocking frequency, they could not be used to distinguish between areas where Signature-Sequences were i n i t i a t e d 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.  11i6  TOTRL  Fig.  5  5.12(a)  (5  "7  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 d u r a t i o n 16 pentads.  I  8  l— 9  DURATION (PENTADS;  10  I).  12  13  117  80 75 70  Fig.  5.12(b)  Frequency D i s t r i b u t i o n Blocking durations. 1945 - 1977 ( T r e i d l et a l  of  1980)  wmm  .1  0  10  A  15  20  25  30 DAYS  35  40  m i  45  50  55  118  Fig. 5.13 presents the frequency d i s t r i b u t i o n of the i n 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 d i s t r i b u t i o n of the f i n a l positions.  (It  should be  noted that some signatures d r i f t e d north of 75°N in which case their  final  position was noted and they were included in the d i s t r i b u t i o n of Fig. 5.14.) It would appear (Fig. 5.13)  that blocking sequences have a pre-  ferred longitudinal band of i n i t i a t i o n in the East A t l a n t i c and that subsequently CFig. 5.14)  they are more l i k e l y to retrograde or progress than  to remain quasi-stationary.  This is consistent with the results of Rex  (1950) and T r e i d l 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 r e f l e c t s a propensity for blocks i d e n t i f i e d 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 l a t i t u d i n a l d i s t r i b u t i o n . The results of Namias (1958) suggest that many of these terminations over NE Siberia and the A r c t i c Ocean r e f l e c t 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 s i t e of maximum i n i t i a t i o n , and Central Siberia one of maximum termination.  Again, this r e f l e c t s the predominance of progressive motion for  blocks over this part of the Eurasian continent.  Moving to the  Pacific  TOTAL EUROPE  0  '30E' Pig.  V.SIBERIA  '60E  120E  3 E.SIBERIA W.PACIFIC  150E  180'  STARTING .SIGS 4  ALASKA E.PACIFIC  'l50W  1  I  5  CANADR  ' I20V  5 . 1 3 T o t a l ( i . e . a n n u a l ) / f r e q u e n c y by all signature-sequences.  90W  1  GREENLAND N.ATLANTIC  60W  30W  EUROPE  30E  0  longitude of i n i t i a t i o n  of  SOF  1  EUROPE  30E  TOTAL  2  V.SIBERIA  SOE  F i g . 5.14  ~i—i—i—i—1~  90E  120E  ENDING  150E  180  SIGS  4 • ALASKA E.PACIFIC  3 E.SIBERIA V.PACIFIC  -i  r  1  1  150V  1-  I  5 CANADA  120V  90W  1  T o t a l ( i . e . annual) frequency.by a l l signature-sequences.  6 GREENLAND N.ATLANTIC  60W  30V  -i  ]  EUROPE  1  0  r-  30E  l o n g i t u d e of t e r m i n a t i o n o f  60E  SPRING V.SIBERIA  EUROPE  r O  3 E.SIBERIA V.PACIFIC  STARTING SIGS  ALASKA E.PACIFIC  ; ,,,,, i 30E  60E  90E  120E  150E  F i g . 5.15  180  ; 150V  J20W  As i n F i g . 5.13  S GREENLAND N.ATLANTIC  5  CANADA  1 EUROPE  1,,,,, 90W  f o r SPRING  60W  30W  > 0  30E  60E  2  EUROPE  V.SIBERIA  SPRING 3 E.SIBERIA W.PACIFIC  ENDING S'IGS d  ALASKA E .PACIFIC  GREENLAND N.ATLANTIC  CANADA  EUROPE  a  UJ  0  30E  60E  90E  120E  150E  F i g . 5.16  180  J50V 120W 90W  As i n F i g . 5.14  SOW  f o r SPRING  30W  0  30E  60E  g  123  and Alaska, there is a d i s t i n c t 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. It  Retrogression appears to predominate.  is well known that blocking highs centred in the v i c i n i t y 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 d y 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 d i s t r i b u t i o n s .  The excess of  terminations over i n i t i a t i o n s suggests that not only do blocks develop ' i n 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 w i l l be found in Appendix V (Figs. 5.3.6  V - 3 to V - 8).  The Baffin Island Paradox In the familiar 3-wave pattern of the normal 500MB WINTER c i r c u -  lation (Fig. 4.6), we note a primary trough extending from the Canadian Archipelago southward to the St. 70°W meridian.  Its  Lawrence Valley with i t s axis along the  intensity naturally diminishes with the approach of  SUMMER (Fig. 4.7) but i t s normal seasonal location remains e s s e n t i a l l y 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 t s deep quasi-permanent core?  There is certainly no  p a r a l l e l for this paradox in the case of that other primary feature, the A s i a t i c trough, where the incidence of signatures is much lower 5.1).  (Fig.  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 S t r a i t ( e . g . , Namias, 1958) but to our knowledge the question has not been addressed e x p l i c i t l y .  The d i f f e r i n g 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 activity",  the counts of occurrences over Canada were low.  In an attempt to resolve the paradox we l i s t e d a l l Blocking Sequences which contained at least one Signature in the area 60°N to 75°N and 6 0 % ' t o 9 0 % for the period July 1955 to June 1956. cases.  There were 15  We then examined the corresponding d a i l y 500MB analyses with par-  t i c u l a r care and found that during 12 cases the Sequence was in fact concurrent with an observed blocking episode.  On the other hand, T r e i d l ' s  Catalogue l i s t s only f i v e cases for that area during the same period. The difference in results arises almost e n t i r e l y 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 r e s t r i c t i v e and therefore reject cases which we would include. The l i s t i n g of these 12 cases and associated comments are presented 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 S t r a i t . See Dec....9,. 500MB A n a l y s i s , F i g . 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 S t r a i t (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 i n i t i a t e d over the Barents Sea and terminated over Davis S t r a 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  SYNOPTIC  NORTHERN 500  M8  WEATHER  MAP  HEMISPHERE 1500 GMT !iaa_£l«i«$uait  DEC  e 1399  i....  i  J,.  F l f i  null  -  5  ,  1  7  f f c  i a  ?Q^  c i l ^ ? B a y - B a f f i n I s l a n d - D a v i s S t r a i t d u r i n g Pentad 500MB a n a l y s i s i s f o r c e n t r e day o f p e n t a d . See T a b l e 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 o f Commerce)  0 f  u  d  s  o  n  r\3  CTl  127  December 13th.  Note how the Baffin Low has bifurcated.  The o r i g i n a l  centre, which was in i t s normal position on December 4th, has r e t r o 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 a n t i -  cyclone lacks the unmistakable robust structure of the major ocean blocks, but the general c i r c u l a t i o n features over the U.S.  and Canada, p a r t i c u -  l a r l y the s p l i t j e t over B r i t i s h Columbia, are clear indicators of a s i g n i f i c a n t blocking episode. Further evidence of the high incidence of winter blocking in the vicinity  of the normal 500MB Baffin Low is provided by the d i s t r i b u t i o n of  the c o e f f i c i e n t 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 t s usual p o s i t i o n , a s u f f i c i e n t number of large positive anomalies occur to skew the d i s t r i b u t i o n markedly so that the mode is well to the l e f t of the mean.  Interpretation  of the spatial d i s t r i b u t i o n of  the higher moments w i l l be discussed in Chapter 6. 5.3.7  Secular Variation of Blocking Signatures In view of the range of c r i t e r i a 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 interannual v a r i a b i l i t y .  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 i n t e r e s t , among European c l i m a t o l o g i s t s .  particularly  128  Prior to the a v a i l a b i l i t y  of Northern Hemisphere upper a i r data,  blocking was i d e n t i f i e d by the application of plausible c r i t e r i a 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 r e s u l t s , but in the case of the continents, p a r t i c u l a r l y during the winter season (because of the masking by A r c t i c a i r masses) i t was d i f f i c u l t and at times imposs i b l e to determine i f blocking was, in f a c t , in progress. Elliott  Nevertheless  and Smith did use the daily analyses of MSL pressure for the  months of January and February, 1900 - 1938 to assess the secular v a r i a tion of blocking over nearly three-quarters of the hemisphere (from 140°E eastward to 4 0 ° E ) .  They found that the year-to-year extent of blocking  in the three sectors, the P a c i f i c and A t l a n t i c 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 F i g . 5.18(a).  The promising in-phase relationship early  the period becomes out-of-phase later in the record.  in  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 -  c a l l y sound conclusions. Brezowsky et a l . (1951) examined the secular variation of A t l a n t i c and European blocking from 1881 to 1950 (for a l l months) using a c i r c u l a tion c l a s s i f i c a t i o n technique,and their curve of overlapping 10 year means shows an interesting quasi-periodicity (Fig.  5.18b).  These authors  also looked for the p o s s i b i l i t y of a relationship with solar The result was inconclusive.  The sample is s t i l l  too small not only  temporally but, in our opinion, s p a t i a l l y , for meaningful conclusions.  activity.  statistical  129  F i g . 5.18(a)  Long-period v a r i a t i o n i n index numbers, N , and sunspot numbers, N, f o r the January-February seasons of the 20 even y e a r s : 1900-1938. ( E l l i o t t et a l . , 1949). d  IBSO  Fig.  ~i$x>  5.18(b)  •  m>  "f92o  *uo  'wo  igso  Annual frequency of b l o c k i n g h i g h s , 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 c u l t y [ i f  not impossibility) of  i n t e r p r e t a t i o n , 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.  F i g . 5.19 presents, in e f f e c t ,  three  frequency d i s t r i b u t i o n s : (a)  The top curve is the total duration in pentads per year of  al1 i d e n t i f i e d 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 a i r data over Siberia and northern China was v i r t u a l l y  non-existent.  Hence the accu-  racy of 500MB analyses over these areas f a l l s well short of the standard for the remainder of the hemisphere.  Interpretation  of F i g . 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 r e l a t i v e l y  short duration) are r e l a t i v e l y  uniform from year to year.  (Compare unstippled areas.) (b)  The sequences containing two or more signatures  related to blocks with average or above average persistence) provide the major component of inter-annual (c)  (usually appear to  variation.  There is a suggestion of a complex quasi-periodicity with a  time scale of the order of a decade.  Of p a r t i c u l a r note is the 15-year  fluctuation with crests at 1953 and 1968. for interpretations of s t a t i s t i c a l  Again, the sample is too small  significance.  Fig.  5.19  D u r a t i o n 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 u n s t i p p l e d . Two-signature and ^ 3-signature f r e q u e n c i e s 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, i n c l u s i v e .  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 r e l a t i v e to a longer period average over the Strait-Greenland area".  Baffinland-Davis  (The "longer period" referred to one which began  in the 1930's with the construction of 700MB contours from MSL analyses using a s t a t i s t i c a l - d i f f e r e n t i a l  analysis  technique.)  Namias' astute observation is in agreement with Lamb (1972) who also noted the higher average pressure and incidence of blocking a n t i cyclones over Greenland in the 1950's.  Now there is a strong teleconnec-  tion between positive anomalies centred in the Davis S t r a i t 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 r e l a t i v e  already discussed.  sense for reasons  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. subsequent decline in the early 1970 s is much more marked in (b) 1  in (a).  The than  Both curves are consistent with an abrupt recovery in 1976,  1 2 5H  2 jioo-j  Mean  >  ~98  V)  Q < UJ  7 54  OL  5 04  _ l  1 — I — I — •  50  55  60  •  65  (b)  375H  70  •  1  1  1  >  75  1  1  L.  -I  L.  80  oc < UJ  2504  Mean  ~24 5 <  1 21^"*^—*——*—  * -* *——• *  1  *  1  ' -* * i  ,t  —• •  » »—f  t  « « i  . . .  «  t  «- . » ,  46 48 50 52 54 56 58 60 62 64 66 68 70 72 74 76 78 F i g . 5.20 (a) D u r a t i o n (Pentads/year) o f a l l sequences > 2 s i g n a t u r e s ( S E Q ' s ) . (b) D u r a t i o n (Days/year) o f b l o c k i n g , r e p o r t e d by T r e i d l e t a l (1980). n  80~  133  but agreement is not good in 1977, or from 1946 to 1952, i n c l u s i v e .  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 geographical d i s t r i b u t i o n 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 p r e c i s e l y , the Foxe Basin) which is subject to a much higher frequency of blocking than these investigations would indicate.  The paradox was r a t i o n a l i z e d .  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. C r i t e r i a for identifying a blocking signature-sequence were used to prepare a Catalogue l i s t i n g t h e i r attributes Initiation,  (Time and Location of  Termination, Component Signatures and Intensity).  A test  of these sequences showed a strong relationship with actual blocking events, with a 96% success r a t i o for sequences  2 pentads duration  and 62% for those of only one pentad duration. A comparison between the i n i t i a l  and f i n a l 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 s t a t i s t i c a l conclusions due to the size of the sample (33 years) r e l a t i v e to the time scale (order of 1 decade) of the fluctuations of i n t e r e s t .  It  is l i k e l y that these fluctuations are part  of the natural v a r i a b i l i t y 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 s t a t i s t i c s 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 p r i n c i p l e that a blocking episode w i l l feature some c h a r a c t e r i s t i c extremum in the mid-troposphere such as the centre of the anticyclone or the centre of the associated positive anomaly. Unfortunately, in r e s t r i c t i n g the data to an investigation of extrema, one pays the price of a severe reduction in sample s i z e . Consider, for example, a proposal to investigate the frequency d i s t r i b u t i o n (spatial  and temporal) of a l l s i g n i f i c a n t positive and negative  anomalies on 5-day average 500MB charts over the Northern Hemisphere during the past 33 years. subject of this thesis.  This would be a more general study than the 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 negative anomalies (Fig. 4.2) discloses that there are about 20 anomaly centres per pentad. orders of magnitude.  The data sample, therefore, has been reduced by two 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 i z e , there is an e f f e c t i v e reduction of three orders of magnitude from the o r i g i n a l set of data. It  is c l e a r , 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 i s t r i b u 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 i n f o r mation on the nature of low frequency atmospheric v a r i a b i l i t y  and, in  p a r t i c u l a r , of the blocking process. 6.2  Purpose and Objectives So far we have confined this investigation to the 500MB l e v e l .  However, i t is clear from previous discussions of the v e r t i c a l  charac-  t e r i s t i c s of blocking anticyclones that additional information from lower troposphere pressure levels is needed to better define the thermal structure.  This is p a r t i c u l a r l y 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 i e l d s of Standard Deviation at these for evidence of the influence of blocking on the v a r i a b i l i t y  levels  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 i g n i f i c a n t l y from Gaussian in certain regions. The non-dimensional c o e f f i c i e n t s of the 3rd and 4th s t a t i s t i c a l moments, skewness and k u r t o s i s , provide a measure of such departures.  Our objec-  t i v e , therefore, w i l l be to investigate hemispheric f i e l d s of these parameters at the 500MB l e v e l . We shall not necessarily confine a'ttention exclusively to 'continuum' data.  If  the evidence so warrants, we shall investigate areas of  s i g n i f i c a n t skewness and kurtosis by using the Master Catalogue (Fig. to prepare positive and negative anomaly frequency d i s t r i b u t i o n s .  4.2)  This  may a s s i s t with the interpretation of non-Gaussian d i s t r i b u t i o n s of lowfrequency 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 described 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 Where Z  -  3(p  I °°' <"•" 10  p = MSL pressure 1 Q  = gph of 1000MB surface  Thus isobars drawn at 4MB intervals on a MSL pressure analysis can be converted to 1000MB contours by r e l a b e l l i n g with a 3 dam i n t e r v a l . 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 a r c t i c air) to 7.1 dams (warm tropical a i r ) per 8MBs of pressure. We therefore chose the method used by the B r i t i s h Meteorological O f f i c e , described by Moffitt and R a t c l i f f e  (1972).  The p r i n c i p l e i s that  empirical relationships between lOOOMB and 500MB thickness and surface temperature can be used to provide an approximation f o r the l a t t e r .  The  algorithm i s presented in Appendix VI - 1 and 2, i n c l u s i v e . 6.3.2  (lOOOMB - 500MB) Thickness Five-day averages of the 500MB gph f o r 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 i e l d s of (lOOOMB - 500MB) thickness. 6.3.3  Seasonal 0  Stratification  In this Chapter, our continuum s t a t i s t i c s w i l l be calculated by  Season and the resulting spatial d i s t r i b u t i o n w i l l be displayed geographically.  The nomenclature w i l l follow Chapter 4.  WINTER  WN  (PE  to P E ) + ( P E  SPRING  SP  (PE  SUMMER  SU  ( P E ™ to PE  FALL  FA  (PE  1  ]2  13  50  to PE ) 31  49)  to P E ) 67  68  to P E ) 73  139  6.4 6.4.1  Statistical  Moments Part I  -Normals and Standard Deviation A l l s t a t i s t i c a 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 w i l l be found in Appendix VI - 3. Normals and Standard Deviation f i e l d s for 1000MB and 500MB surfaces and for (1000MB - 500MB) thickness have been prepared for each season and are available from the author.  Those relevant to the discus-  sion w i 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.) d  The Normal Charts  of the 1000MB and 500MB f i e l d s for the Winter .Figures 6.1 and 6.2, and Summer Figures 6.3 and 6.4, are in very good agreement with corresponding f i e l d s 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 i t e r a t u r e 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 i e l d s calculated by M o f f i t t and  F i g . 6.1  Normal h e i g h t 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). I n t e r v a l = 3 dams.  141  1'20E  Fig.  6.2  BOE  ]00E  N o r m a l h e i g h t o f the 5 0 0 M B s u r f a c e f o r WINTER (December 1 to February 28). Contours 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 dams. 535 d  i  a  m  s  contour  142  120E  Fig.  6.3  100E  As i n F i g .  6.1  BOE  except f o r  SUMMER  Fig.  6.4  As  in  Fig.  6.2  except  for  SUMMER  144  Ratcliffe pectively.  (1972) for the mid-season months of A p r i l and October, resSimilar checks with other a t l a s e s , e . g . , Lahey et a l .  (1958)  and Crutcher et a l . (1970) reinforce confidence in our baseline Normal fields. In the case of Standard Deviation, we are not aware of any other source where such f i e l d s have been computed for 5-day average gph. note that our 500MB Standard Deviation f i e l d for Winter (Fig.  We  6.5)  corresponds closely with the low pass f i e l d of Blackmon (1976).  It was  also encouraging to note that our 1000MB Standard Deviation f i e l d for Winter (Fig. 6.6) was in good agreement with the low pass f i l t e r e d Standard Deviation f i e l d of sea level pressure in F i g . 2(a) Blackmon et a l . (1977).  of the paper by  F i n a l l y , our results appeared to be consistent  with Standard Deviation f i e l d s computed by Moffitt and R a t c l i f f e  (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 P a c i f i c  (160°W),  E A t l a n t i c (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 s i g n i f i c a n t contribution to the variation of gph North of latitude 50°. For a l l seasons there is a close correspondence between the geographic v a r i a b i l i t y  of the 1000MB and 500MB gph f i e l d s over the oceans,  but they d i f f e r s i g n i f i c a n t l y over the continents, p a r t i c u l a r l y WINTER (Figs. 6.5 and 6.6).  in  Consider, for example, North America and  1 4 5  i2oc  F i g . 6.5  joor.  Boe  Standard d e v i a t i o n of 5-day average 500MB h e i g h t f o r WINTER (December 1 to February 28).  — — — —  Contours ( I n t e r v a l = 2 dams) Intermediate (1 dam i n t e r v a l ) contours 10 dam contour  146  120E  F i g . 6.6  )00E  BOE  Standard d e v i a t i o n of 5-day average 1000MB h e i g h t f o r WINTER (December 1 to February 28). Contour i n t e r v a l = 1 dam.  147  the North A t l a n t i c .  At 1000MB an axis of minimum variance extends from  the Canadian p r a i r i e s to the Northwest T e r r i t o r i e s and there is a well defined maximum centre over the North A t l a n t i c (60°N 20°W).  These f e a -  tures are found in approximately the same locations at 500MB but, at that l e v e l , there is a second area of maximum variance over Northeastern Canada centred on Baffin Island with an intensity almost equal to the A t l a n t i c centre (16 dams).  This r e l a t i v e difference in the variance  pattern between the 1000MB and 500MB levels is related to the thickness f i e l d (Fig. 6.7) which also shows a maximum of v a r i a b i l i t y eastern Canada.  over North-  Sawyer (1970) showed that there is a very high c o r r e l a -  tion between 500MB gph and 1000MB - 500MB thickness for fluctuations north of 50°N and with a period of » 15 days. correlation exceeds 0.90.  In Northeastern Canada the  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 d i s t r i b u t i o n s of negative anomalies (though not the subject of this thesis) were prepared and, indeed, the WINTER d i s t r i b u t i o n of anomalies ^ -20 dams shows a strong concentration over Baffin Island and Northern Hudson Bay. the Baffin Island Paradox (Section 5.3.6).  This sheds more l i g h t on 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 ' i n s i t u ' anomaly is moder-  ately to strongly positive the pre-existing trough is usually s p l i t by a  148  7.  120E  F i g . 6.7  100E  BOE  Standard d e v i a t i o n of 5-day average 1000MB - 500MB t h i c k n e s s 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 ' i n s i t u ' anomaly is large negative, there i s , usually near the normal l o c a t i o n , 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 i k -  ing annual pattern depicted in F i g .  5.1.)  We could not find a counterpart to the behaviour of the Northeastern Canadian trough in other parts of the hemisphere.  The East Asian  trough does show the 500MB and thickness f i e l d s 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 b a r o c l i n i c trough has e s s e n t i a l l y 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 corresponding r e l a t i v e maxima of thickness variance. gph and 1000MB - 500MB thickness i s s t i l l  The correlation between 500MB 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 d i s t r i b u t i o n of the 3rd and 4th moments of these r e s pective variates may throw additional l i g h t on the difference in behaviour of the longer period fluctuations over continent and ocean.  150  6.5  Statistical  Moments Part  II  For reasons already given we decided to examine the extent to which the temporal d i s t r i b u t i o n 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 i e l d s of the 3rd and 4th moments about the mean or, more s p e c i f i c a l l y , the non-dimensional c o e f f i c i e n t s of skewness and kurtosis, 6.5.1  respectively.  Skewness Skewness is the measure of the departure of a frequency d i s t r i b u -  tion from symmetry.  It  is zero for a Gaussian d i s t r i b u t i o n , usually  " p o s i t i v e " i f the mode l i e s to the l e f t of the mean so that the f r e quencies f a l l  off sharply to the l e f t and usually "negative" i f the mode  l i e s to the right of the mean (Fig. 6.8).  Skewed distributions of atmos-  pheric variables are not uncommon p a r t i c u l a r l y in the case of discrete events such as amount of r a i n f a l l . Skewness is measured in an absolute sense by the third moment about the mean  "3"  ft-F—  and the r e l a t i v e asymmetry, which takes account of the size of the Standard Deviation (= a), is given by the non-dimensional c o e f f i c i e n t  There are other measures of skewness but this has general acceptance in the meteorological  literature.  POSITIVE S K E W N E S S  /j  LOW  HIGH  KURTOSIS  KURTOSIS  C K < 3-0  Fig.  6.8  Schematics:  Skewness and  Kurtosis  152  The standard error of skewness is given by S.E.  - (6/n)  4  Where n = number of s t a t i s t i c a l l y  independent observations (Brooks and  Carruthers, 1953). One of the problems in the s t a t i s t i c a l  treatment of parameters of  the atmospheric continuum is that consecutive observations at conventional time intervals  (hourly, d a i l y , etc.)  longer the time interval  are not independent.  the less the dependence.  However, the  To explore the r e l a -  t i o n s h i p , Madden (1976) estimated c h a r a c t e r i s t i c intervals for e f f e c t i v e l y independent sample values for Northern Hemisphere sea level pressure.  He found that for January the intervals ranged from two days over  the Southern U.S.A. to eight days over the Eastern North A t l a n t i c .  For  July they ranged from less than two days west of the Great Lakes to greater than f i v e 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 f e r s i g n i f i c a n t l y at 500MB. By season, for a given grid-point we had 18 x 33 = 600 observations averaged over contiguous 5-day i n t e r v a l s .  As an ensemble they are  probably considerably less interdependent than daily values.  In view of  Madden s results i t is reasonable to i n f e r that our sample contained the 1  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 s i g n i f i c a n t l y d i f f e r e n t from Gaussian at the 95% level of confidence. The CS computation is outlined in Appendix VI - 4.  Values of the  skewness c o e f f i c i e n t s were computed by season for the 500MB and 1000MB levels and 1000MB - 500MB thickness. the author.  These charts are available from  We shall discuss the interpretation of those of immediate  interest in section 6.6. 6.5.2  Kurtosis A d i s t r i b u t i o n may be symmetrical and at the same time s i g n 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 o f a preponderance of large positive and negative deviations. this  The fourth moment is an absolute measure of  feature  "4  - £ —R  and kurtosis is the term given to the r e l a t i v e measure, the non-dimensional coefficient  For a Gaussian d i s t r i b u t i o n  CK = 3  For a Peaked (Leptokurtic) d i s t r i b u t i o n  CK > 3  For a Blunted (Platykurtic) d i s t r i b u t i o n  CK < 3  These are shown schematically in Fig. 6.8.  TABLE 6.1  Range of c o e f f i c i e n t s of skewness and kurtosis outside of which the d i s t r i b u t i o n is s i g n i f i c a n t l y d i f f e r e n t (at the 95% confidence level) from a Gaussian d i s t r i b u t i o n , 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 d i s t r i b u t i o n 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 s i g n i f i c a n t l y  different  from Gaussian at the 95% l e v e l . Calculation of the CK f i e l d s is detailed in Appendix VI - 5. Charts showing the spatial d i s t r i b u t i o n of s i g n i f i c a n t kurtosis for 1000MB and 500MB, by season, are available from the author.  Interpre-  tation w i l l follow in Section 6.6. 6.5.3  Comparison of CS and CK Fields with Other Results The Skewness and Kurtosis f i e l d s were consistent with those pub-  lished by M o f f i t t and R a t c l i f f e  (1972) and White (1980).  These authors  used d a i l y data rather than 5-day averages, and M o f f i t t and R a t c l i f f e calculated monthly instead of seasonal s t a t i s t i c s .  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  S i t e - s p e c i f i c Frequency Distributions To a s s i s t with the interpretation of the Skewness and Kurtosis  f i e l d s we shall present frequency d i s t r i b u t i o n s for s i t e s of regions of i n t e r e s t . d i f f e r e n t ways. age height (the  representative  These d i s t r i b u t i o n s w i l l be prepared in two  One histogram w i l l show frequency vs 500MB 5-day aver'continuum').  The other w i l l show frequency vs 500MB  5^-day average height anomaly (the  'extremum').  156  The 'continuum' histograms were obtained from White 0 980) and M o f f i t t and R a t c l i f f e  (1972).  They are for point locations chosen for  their proximity to the centre of the area of i n t e r e s t . 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 s u f f i c i e n t size to be s t a t i s t i c a l l y  significant.  Both types of histogram w i l l be used to i l l u s t r a t e the interpretation of CS and CK f i e l d s in the next Section. 6.6  Interpretation  of Distribution of Skewness and Kurtosis in the  Northern Hemisphere 6.6.1 6.6.1.1  Skewness WINTER - POSITIVE In WINTER (Fig. 6.9) positive skewness is c h a r a c t e r i s t i c 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 d e t a i l . (a)  Bering Sea  The large positive skewness of the 'continuum' d i s t r i b u t i o n at 55°N 175°E is c l e a r l y indicated by comparison of the histogram in Fig. 6.10(b) with the superimposed normal curve for the same mean and  157  120E  F i g . 6.9  ]00E  BOE  Skeyness o f 5-day average 500MB h e i g h t f o r WINTER (December 1 to February 28). Contours l a b e l l e d CS x 100. I n t e r v a l = 10. Areas below l e v e l of s i g n i f i c a n c e (Table 6.1) n o t contoured.  158 BERING  SEA  WINTER  (°)  EXTREMUM  Continuum  f  (5-day  22  88N  20 18+,  16 14  S t a t i s t i cs mean 5 0 0 m b * 1T5W  Z  =  523 dams  O  =  15  CS  =  +0-81*  CK  =  3-40  12 10 8 - 6 4 64 -40  (b)  -30  cases  -20  CONTINUUM  f  -10  TJ  2  5 0 cases 10  20  Continuum (_t_w i c e - d a i l y S 5N 175E Z  a  O =  4 0 0 k-  50  40  30  60  Z-2 (dams)  Statistics 500mb)  52 3 d a m s 16  C S  = +.0 7 0 *  CK  =  r  3-32  300  200H 100h-  (dams)  Pig. 6.10(a) (b)  Frequency of 500MB Extremum occurring within 9-point g r i d centred on 58K 175V (Knox). Frequency of 500MB height at 55N 175E f o r Winter. Curve shows Gaussian d i s t r i b u t i o n with same mean and variance. (Adapted from White,. 1980). * . i n d i c a t e s s i g n i f i c a n t at 95$ l e v e l .  159  variance.  The upper panel, F i g . 6.10(a), shows the s t r i k i n g difference  between the d i s t r i b u t i o n 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 d i s t r i b u t i o n on the right hand side of Fig. 6.10(a) t e l l s us that the Bering Sea not infrequently becomes the s i t e of large positive anomalies. of these are blocking signatures (Fig.  The majority  5.2).  We may reasonably conclude that the p o s i t i v e l y skewed d i s t r i b u tion is partly attributable to the frequency of blocking episodes. (b)  The Northeast Canadian Archipelago  To i l l u s t r a t e the continuum d i s t r i b u t i o n for the Northeast Canadian Archipelago we used a histogram for 80°N 100°W (Fig. 6.11(b)). tion i s about 750 km NW of the centre of maximum CS.  That l o c a -  Nevertheless, i t .  is within the area of interest and does confirm the strong positive skewness c h a r a c t e r i s t i c of the region.  The upper panel Fig. 6.11(a) for an  area centred on 71°N 69°W shows an anomaly frequency d i s t r i b u t i o n somewhat s i m i l a r 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 t s normal position and increases or decreases in i n t e n s i t y .  On occasion, however (as described in Section  5.3.6), the region is subject to a regime of a very d i f f e r e n t type.  The  160  NE  CANADIAN  ARCHIPELAGO  WINTER Continuum  (a)  (5-day  EXTREMUM  71 N Z  a  22  CS  20  |CK  18  statistics  mean  5 0 0 mb)  69 W -  506 dams  s  1 5 "  =  +0-6 0  s  3-2 0  *  16  62 cases  75 cases - 40  (b)  -30  -20  ib  -10  20  30  40  50  Continuum  CONTINUUM  (twice 80N Z  60  Z-Z (d am6  statistics  daily  5 0 0 mb)  100W t  a=  504 i  dams 5  ..  cs = +o-63 * C K =  470  Fig.  6.11(a) (b)  480  490  500  510  520  530  540  As i n F i g . 6.10(a) e x c e p t f o r 71N 69W Frequency January.  550  560  (Knox).  o f 500MB h e i g h t a t 80N 100W f o r ( A d a p t e d from M o f f i t t and R a t c l i f f e ,  # = significant  a t 95$ l e v e l .  570 dams  1972)  161  associated positive anomaly is well above the winter blocking signature threshold (16 dams) as indicated by F i g . 6.11(a).  C l e a r l y , these are  episodes which contribute to the s t r i k i n g blocking signature maximum of Fig. 5.2.  Again we conclude, as in the case of the Bering Sea,  that  the positive skewness c h a r a c t e r i s t i c of the d i s t r i b u t i o n 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 a n t 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 d i s t r i b u t i o n to t a 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 t is i n i t i a t e d by an upstream s p l i t j e t (Fig. 6.6.1.3  if  3.3(a)).  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 A t l a n t i c .  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 c h a r a c t e r i s t i c of the other seasons has disappeared e n t i r e l y . 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  Fig.  6.12  100E  BOE  A s i n F i g . 6.9 e x c e p t f o r SUMMER  163  frequency centre is located about 10 degrees longitude west of i t s 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 s i g n i f i c a n t 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 r e l a -  tionship between blocking in high latitudes and p o s i t i v e l y skewed d i s t r i b u tions in Winter, Spring and Fall are strongly modified in Summer.  Further  investigation w i l l be reserved for future research. Negative skewness in SUMMER remains large in sub-tropical but there is a d i s t i n c t northward s h i f t in pattern.  latitudes  This is consistent with  the seasonal northward migration of the sub-tropical anticyclone and the mid-latitude westerlies. Around the 20°N p a r a l l e l , regions of positive skewness become d i s 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 A s i a t i c Summer monsoon. The positive skewness in a l l these regions is probably attributable anomalous events in the Intertropical  Convergence Zone.  to  Though not  d i r e c t l y connected with the subject of this t h e s i s , i t should warrant further investigation. 6.6.2  Kurtosis In WINTER (Fig. 6.13) s i g n i f i c a n t l y high kurtosis ( i . e . , ^ 3.5)  occurs over the A r c t i c regions immediately to the north of Canada and also over wide swaths of the sub-tropical oceans. s i g n i f i c a n t l y low kurtosis ( i . e . , < 2.6)  On the other hand,  extends from the mid- to east  164  120E  F i g 6.13  3 00E  BOE  K u r t o s i s of 5-day average 500MB h e i g h t f o r WIN-TEH (December 1 to February 28). Contours l a b e l l e d CK x 1.00. I n t e r v a l = 20. Areas below l e v e l o f s i g n i f i c a n c e (Table 6 . 1 ) n o t contoured.  165  P a c i f i c Ocean along the 40°N to 50°N latitude zone, and also from the central A t l a n t i c 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 A t l a n t i c . Fig. 6.14(b), for 52.5°N 25°W, c l e a r l y shows a platykurtic d i s t r i b u t i o n for continuum data.  The d i s t r i b u t i o n for frequency extrema (Fig.  is for an area centred at 57°N 22°W.  6.14(a))  It reinforces the inference that  over area 'A' the atmospheric regimes can be c l a s s i f i e d into two-sub-sets each with a d i f f e r e n t mean of 500MB gph. 1  The interpretation in terms of  blocking w i l l be reserved for the next section.  The Eastern A t l a n t i c -  Scandinavia low kurtosis persists throughout SPRING, SUMMER and FALL (not shown).  Over the P a c i f i c 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 d i s t r i b u t i o n s of  skewness and kurtosis to avoid complications introduced by the oceancontinent temperature reversal. As indicated e a r l i e r the low kurtosis over the eastern halves of the mid-latitude oceans indicates that the 500MB height population cons i s t s of two sub-sets which have frequency distributions with d i f f e r e n t means.  Is i t possible that the distributions arise from two types of  regime, one of which includes the ensemble of nascent or maturing blocking 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 l a t i t u d e s .  166  !  NORTHEAST  ATLANTIC  WINTER  (a)  EXTREMUM  Continuum (5-day  f '  5  4 20-  a= -  C S =  18'  C K -  16.  500  mb )  22W  7N z  Statistics  mean 5 34  dams  16  -  +0-2 I 2-40*  I A I 2 10 8  - 6 69  5 0 -40  (b)  cases  -20  -30  CONTINUUM  -10  4 2-\  4 4 cases I0  20  30  40  50  Continuum Statistics (t wi c e - d a i I y 5 0 0 m b) 5 2-5N 25 W z  = 545  dams  0=19 C S - -0-1 C K =  gig.  6.14(a) (b)  (dams)  0  2-2 3 *  As i n F i g . 6.10(a) e x c e p t f o r 57N 22W  (Knox).  As i n P i g . 6.10(b) e x c e p t f o r 52.5N 25W f o r W i n t e r ( a d a p t e d f r o m White, 1980).  167  In the case of the Northeast A t l a n t i c , i f the blocking is r e t r o 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 w i l l p e r s i s t over the  dinavia region.  Iceland-Scan-  The strong p o s i t i v e l y skewed d i s t r i b u t i o n over this  area (Fig. 6.9) may be attributed to the r e l a t i v e frequency of these events.  If progressive, the blocking wave w i l l proceed across the northern  Eurasian continent.  The d i s t r i b u t i o n 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 P a c i f i c 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 r e t r o grading from Alaska, or less frequently, progressing from S i b e r i a . What seems to emerge from this analysis is the impression that blocking systems evolve in a manner somewhat analogous to unstable baroc l i n i c cyclones.  The i n i t i a t i o n of both processes begins well south of  the termination.  The f i n a l stage of the typical b a r o c l i n i c cycle is the  cold cyclonic vortex in the high latitude with, of course, higher gph to the south.  The f i n a l 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 b a r o c l i n i c waves.  It would appear then that  blocking may be i n i t i a t e d by the r e a l i z a t i o n of b a r o c l i n i c  instability  168  in the long-wave part of the spectrum (Fig. 2.9).  This view has already  been given some theoretical j u s t i f i c a t i o n by a number of authors quoted in Chapter 2.  The subsequent response to the amplifying wave in terms  of large scale v o r t i c i t y r e d i s t r i b u t i o n results in the  characteristic  quasi-barotropic structure of the blocking system components. It would appear, then, that the blocking phenomenon i s r e a l l y a manifestation of long-wave a m p l i f i c a t i o n , and that a climatologicaldiagnostic 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 c o n f i g -  urations as s p a t i a l l y isolated anomalies of the large scale mass d i s t r i b u t i o n in the troposphere. uration space  1  Their features were described in ' c o n f i g -  Ci-e., as they appear on conventional synoptic analyses)  using for reference the NMC I,J  grid.  This afforded the most convenient  method of i d e n t i f i c a t i o n for h e u r i s t i c diagnostics and also for obtaining the s t a t i s t i c a l  results presented in Chapters 5 and 6.  Sometimes, however, additional insights into attributes of physical systems ( e . g . , the 500MB height f i e l d ) may be obtained by s p e c i f i c a t i o n in terms of functions related to characteristic responses of the atmosphere (e-g-> o s c i l l a t i o n s ) .  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. number space'.  We therefore decided to investigate blocking in 'wave  To do so i t was necessary to specify the 500MB height  f i e l d 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  a n a l y s i s , is well-known and the application to our s p e c i f i c problem w i l 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 d i s t i n c t i v e to the region in which they occurred. For example, were the spectral attributes of Northeast P a c i f i c - Alaska blocks c h a r a c t e r i s t i c a l l y  d i f f e r e n t , on average, from those which reside  in the North A t l a n t i c - Greenland area?  If  so, was there a connection  between these attributes and those of the normal 500MB height d i s t r i b u t i o n for the winter season?  A s i m i l a r i n v e s t i g a t i o n , 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  ' B a f f i n Island Paradox  1  by an interpretation of the spectral  arising out of the results of 7.2.1, above.  statistics  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 t h i r d 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 w i l l be in progress. The interruption is characterized by a sudden increase in the zonal  171  westerlies, a condition which, at any given l a t i t u d e , is  relatively  transitory (^-a few days). 7.2.4  Our fourth and f i n a l objective was to i l l u s t r a t e how zonal har-  monics from 20°N to the Pole could be related to s a l i e n t 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 i t e r a t u r e (for example, Namias (1975) and the Monthly Weather Review issues referenced in the bibliography). Although our d e f i n i t i o n 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 a v a i l a b l e .  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 l o t study of the harmonic  analysis of 1977-78 daily data revealed that there were a s i g n i f i c a n t number of occasions when the genesis and dissolution of long-wave components occurred quite rapidly (one to three days).  We therefore chose  to use d a i l y 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 A r c t i c .  Therefore, i t was decided to compute the above values of  Z(x,e,t) for every 5° p a r a l l e l of Latitude from 25°N to 85°N. arrays constitute our working data.  It  These  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 c l e a r l y necessary to select representative (or zones).  latitudes  The choice of the northern latitudes was based on F i g .  5.2  which shows the areal frequency d i s t r i b u t i o n 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 i k e l y to indicate the blocking anticyclone evolution and i t s 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 f l a n k -  ing cold lows are usually centred between 30°N and 50°N.  Therefore, we  selected Z(x,t) around 4 0 ° N / o r mean values for 30°N to 50°N, to approximate s a l i e n t features of the southern structure. Since e a r l i e r p i l o t 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 ' n o i s e .  As i t turned out the difference  1  for a l l practical purposes was not appreciable.  Some results w i l l be  displayed based on data from cross-zonal averaging while others w i l l use discrete l a t i t u d e s , and the plots w i l l be i d e n t i f i e d 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). tion of Z ( x , e , t ) n  by longitude (abscissa)  specified p a r a l l e l of latitude e  n  It depicts the v a r i a -  and time (ordinate) around a  (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. height Z(x,t) are drawn at an interval labeled with values of (Z - 500).  Isopleths of 500MB  of 10 dams and, for brevity,  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 h e i g h t p r o f i l e averaged a c r o s s the zone 50°N - 70°N. Ridges are shaded. P o s i t i o n s ( x , t ) of B l o c k i n g Signatures marked • . I s o p l e t h s l a b e l l e d Z - 500. Contour I n t e r v a l = 1 0 dams.  175  The large amplitude long-wave patterns o s c i l l a t i n g about their mean winter position are c l e a r l y evident.  Westward (retrograde)  motion,  indicated by the downward t i l t to the l e f t of the isopleth axes, is not uncommon, p a r t i c u l a r l y in the 50°N to 70°N zone where planetary  vorticity  advection may be the determining f a c t o r . The smaller amplitude transient troughs and ridges, usually associated with synoptic scale waves, are p a r t i c u l a r l y evident in the 30°N to 50°N zone (Fig. 7.2), a region of maximum b a r o c l i n i c a c t i v i t y the winter season.  during  Their eastward progress, reflected by the downward  t i l t to the right of the axes, i s also apparent. Blocking signatures, marked • , have been superimposed on F i g . 7.1. The close correspondence between t h e i r motion and the long wave ' r i d g e ' axes would appear to confirm the choice of the 50°N to 70°N zone for harmonic analysis of blocking episodes. Hovmoller diagrams of 500MB height have been prepared for each of the selected winters; those for 1978-79 w i l l be found in Appendix Fig.-1 and-2.  VII,  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  p r o f i l e 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 information such as daily or 5-day mean 500MB Analyses.  176 HOVMOLLER 500MB RVG(30N-50N) DEC 1.1962-MRR 3 J J 9 6 3  F i g . 7.2  Same as F i g . 7.1 except f o r 30°N - 50°N and without b l o c k i n g s i g n a t u r e l o c a t i o n s .  177  7.3.4  Zonal Harmonic Analysis of the 500MB Height Field (a)  One-dimension  We shall summarize here, following B o v i l l e and Kwizak (1959) the discrete Fourier series method for calculating the f i r s t six harmonics of the instantaneous d i s t r i b u t i o n of 500MB height around a s p e c i f i c 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 i  o  +  2 ^_ -j  (a  n  cos n X. + b i n  sin n x.) + R I  72 Where* a  = -AIL  o  2  72  2 r~j  136  *n  Z(X,)  -'V  c  o  s  n  X  i  72  2 —  436  n  Z(X.) = mean of Z(x.) = Z i I  i = 1  Z- (vX",-)/ sin n x. v  i = 1  i'  i  35 Residual =  2 n=7  (a n  cos n X. + b i n  We used the reformulation: 6  ZCx .) = A + n  Q  2  A cos (n X. - <j,) +R n  n  sin n X.) i  178  Where A  = Amplitude =  and < > j = Phase angle = tan" n  b/a n n  y  72  The Variance  =  a  2  2  [ZUJ - if  =  72  For brevity, the harmonics (A ,<(» ) w i l l be designated as W . p  Now a  is proportional to the eddy ( i . e . , wave) kinetic energy  of the c i r c u l a t i o n and i t can be shown that  (Godson, 1959)  The percentage of the total variance contributed by W w i l l be designated S  and therefore  Values of A , a, A , *  and S  were determined for each day at  every f i v e degree latitude and also f o r 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. tent with Eliasen (1958) and Barrett  These results are e n t i r e l y consis(1958).  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 i n t e r polation to prepare, for a selected calendar day the two-dimensional representation of W  n>  Analyses showing the spatial d i s t r i b u t i o n of A  n  were constructed for December 23, 1978 and January 4, 1979 and the results w i l l be discussed in Section 7.4. (ii)  Normal Harmonics  One of our objectives was to compare the phase of harmonics during blocking episodes with those for the normal WINTER d i s t r i b u t i o n 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 w i 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.)  Normal Charts W-j to W^ w i l l be found in Appendix VII, VII  The complete set of Figs. VII  - 3 to  - 6, i n c l u s i v e .  7.3.5  Temporal Variations of the Zonal Harmonics at Selected (a)  Latitudes  Zonal P r o f i l e 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 F i g . 7.4 showing the temporal variation of the p r o f i l e of  180  120E  Fig-  7.3  100E  80E  Second harmonic (W2) o f the normal 500MB h e i g h t f i e l d f o r WINTER (December 1 to February 2 8 ) . Contours l a b e l l e d i n decametres. I n t e r v a l = 1 dam.  181  F i g . 7.4  Time-Longitude (Hovmoller) diagram of Second Harmonic of 500 MB h e i g h t p r o f i l e averaged a c r o s s the zone 50 N - 70 N. Contour I n t e r v a l = 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 time for selected latitudes and wave numbers of i n t e r e s t . the variation with time of the amplitude  and phase ^  n  and < > ( against  F i g . 7.5 shows of the second  harmonic W around latitude 60°N for 1962-63. 2  7.3.6  Computation and Presentation of Zonal Indices of U, V and U/V The evolution of the expanding circumpolar vortex was b r i e f l y d i s -  cussed in Section 2.6 and i t was noted that the blocking phenomenon is frequently associated with a southward s h i 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 p a r a l l e l  (or  zonal band) of l a t i t u d e " 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 a t 60°N as a f u n c t i o n of time. amplitude i n dams phase angle i n degrees  CO  longitude  184  i  l» |dx -  f "  t  Jo  [|v |] t  | v | = absolute value of the N - S  component measured  t  every 5° longitude  R  t  V t v  is the zonal average of u^  Vj. is the zonal average of |v^.| and R  may be interpreted as an indicator of the degree of predominance  t  of zonal over meridional around a s p e c i f i c 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. II  t  It is evident that the  maxima for the northern zone tend to coincide with  southern zone and vice versa. statistical  This observation is consistent with the  result of a strong correlation between  and u" minima at 40°N (Panofsky and B r i e r , t  minima for the  1968).  maxima at 60°N That study also found  a s i g n i f i c a n t lag correlation indicating that zonal maxima at 60°N precede 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^ w i 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 w i l l be presented in the next Section.  F i g . 7.6  Comparison between U  50°N - 70°F  t  and TJ  t  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 P a c i f i c - Alaska  (180W - 120W)  5  42  Baffin - Hudson Bay  (100W - 60W)  4  26  Northeast A t l a n t i c - Greenland (60W - 0)  6  42  Western Europe  5  39  5  43  (0 - 60E)  Double Blocking ( A t l a n t i c - P a c i f i c )  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 s i g n i f i c a n t concurrent blocking elsewhere in the Northern Hemisphere.  This usually had the e f f e c t of reducing the duration of  e l i g i b l e cases to f i v e to eight days. Some winters ( e . g . ,  1962-63, 1978-79) featured pronounced regimes  of concurrent major blocking, usually over NE P a c i f i c - Alaska and NE A t l a n t i c - 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 reasonable to assume the c i r c u l a t i o n 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 i g i b l e 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 r e l a t i v e l y weak meridional flow V. three day duration was selected. are  A sample of 12 cases each of two (At 60°N predominantly zonal regimes  transitory.) In order to compare the phases of category harmonics with those  for the "normal" 500MB height d i s t r i b u t i o n , the l a t t e r 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 i n t e r -  ference is greatest between Wl and W2 over Western Europe ( 2 0 ° E ) W3 and W4 over NE A t l a n t i c (20°W) and at 50°N between W2 and W3 over NE P a c i f i c  (140°W).  Moreover, the trough line of Wl crosses the NE P a c i f i c 60°N at 160°W.  intersecting  Therefore, i f Wl, on. any given occasion, is near normal  phase, i t w i l l interfere destructively with any tendency for ridging over the NE P a c i f i c Ocean. The parameters a, A^, <j> and S n  day of each case.  n  at 60°N were abstracted for each  (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.  i  80  140  100  60 W E S T  F i g . 7.7  20  20  6 0  100  140  180  L O N G  E A S T  Phase of Harmonics 1 to 4 f o r Normal 500MB h e i g h t - WINTER (December, January and February).  00 00  TABLE 7.1 Mean Spectral Attributes of WINTER Blocking Episodes 60°N 500MB CATEGORY  a  A  m  m  l  l  •l  S  degs  %  2  <J> /2  S  m  degs  %  A  2  2  A  3  m  (|)3/3  S  degs  %  m  deg  3  A  4  V  4  S  4  %  *  S  m  deg  %  m  deg  %  A  5  5  A  6  S  6  22  81  -155 + '25 59  43  -140 - 20 +100  17  15  - 17  2  -  -  -  -  -  -  23 (±15)  57  -  19  50  -  15  47  -  13  45  -  12  32  -  6  -72  14  121  -141  34  102  -139  24  83  -179  16  51  -  6  29  -  2  117  -89  41  77  - 24  18  71  - 22  15  58  - 89  10  48  -  7  36  -  4  169  162  - 1  96  -. 8  16  99' - 12  17  86  -  9  13  53  •-  5  41  -  3  (±35)  46 (±21)  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  NORMAL (Winter)  75  50  +20  ZONAL  92  62  -  PACIFIC BLOCKING  147  78  BAFFIN BLOCKING  129  NE ATLANTIC BLOCKING  190  Standard Deviation  (SD)  As expected, the SD of the hemispheric c i r c u l a t i o n during the blocking episodes is much larger than 'normal' (usually more than twofold).  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 P a c i f i c and Alaska The primary components were  (34%)  and W^ (24%) which  interfere  constructively at an average position of 140°W, close to t h e i r normal phase.  W-j at 72°W is c l e a r l y not contributing to the blocking structure  and is 90 degrees removed from i t s normal phase location.  W^ (16%)  phased at 179 W reinforces W^ and W^, and tends to s h i 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 A t l a n t i c Blocking. n  3  Blocking over the NE A t l a n t i c - 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 W are 20 to 30 degrees west of normal. 9  191  Blocking over Western Europe Clearly W-j and  are the dominant components, interfering con-  s t r u c t i v e l y at 20°E which is very close to normal phase for both.  Also  ^3 ( f 3/^~^2°E) contributes s i g n i f i c a n t l y . <  >  Double Blocking (E P a c i f i c - Alaska; NE A t l a n t i c - 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 W phase positions at 60°N. 2  W  3  (S  3  = 23%, <f> /3=7°E, 127°E, H 3 ° W ) 3  provides s i g n i f i c a n t 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%. A l s o , because wave components moved r a p i d l y , <|> values have no meaning n  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 components are more than double t h e i r normal value.  The contributions to the  mean blocking structures from the wave component ridges may be r e l a t i v e l y assessed as follows:  192  U  !  W  2  W  3  W  4  NE P a c i f i c - Alaska  Small  Large  Large  Moderate  Baffin - Hudson Bay  Large  Small  Smal 1  Moderate  NE A t l a n t i c - Greenland  Large  Smal 1  Smal 1  Smal 1  W Europe  Large  Large  Moderate  Smal 1  Double  Nil  Very Large  Moderate  Small  The position r e l a t i v e to normal of the dominant wave component ridges w i l 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 w i l l be well removed from i t s normal longitude.  On the  other hand, NE P a c i f i c , N A t l a n t i c 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 A t l a n t i c and found s i g n i f i c a n t spectral differences. As far as we are aware, blocking over the North-Eastern Canadian Archipelago (including Baffin Island) has never been e x p l 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 January 9 to February 4, 1963).  (e.g.,  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-  t i v e episodes. The winter of 1962-63 provided a set of remarkable examples. two dominant harmonics of the persistent regimes were c l e a r l y but on three occasions  The  and W^,  collapsed, W,, l o s t s i g n i f i c a n t 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:  F i g . 7.8, show-  ing the time-longitude variation of W^; by F i g . 7.9, showing the corresponding plot of Amplitude vs time; and by F i g . 7.10, showing the change with time of R = U/V. 8, 1962), 0  2  The interruptions are i d e n t i f i e d by 0^ (December  (January 7, 1963), 0  1963) and 0^ (March 27, 1963).  3  (February 7-12, 1963), 0  4  (March 15,  The most s t r i k i n g of these f i v e 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 r e d i s t r i b u t i o n of power among the harmonics during the t r a n s i t i o n 0  2  is i l l u s t r a t e d 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  Fig. 7.3  500MB  flVG(50N-70N)  DEC J . .1962-MRR 3] , .1 963  As i n P i g . 7 . 4 except f o r T h i r d Harmonic. Minima of amplitude a t O-j, O2, O3, O4, O5  60N  F i g . 7.9  WINTER 6 2 / 6 3  A s i n F i g . 7.5  WRVE 3  e x c e p t f o r wave number 3.  =g  F i g . 7.10  Change with time of the r a t i o R of z o n a l (U) to m e r i d i o n a l (V) components a t 60°'1T, December 1 , 1962 to March 31 , 1963.  197  The inception of strong zonal flow implies enhanced b a r o c l i n i c i t y and therefore an increase in available potential energy.  Moreover,  1 c) fl because the N-S thermal gradient - - - r - is increasing, so too is the 2  8 ay  range of wave lengths over which i n s t a b i l i t y may occur (Fig.  2.9).  The  ensuing r e a l i z a t i o n of b a r o c l i n i c i n s t a b i l i t y in the form of deepening extra-tropical cyclones results in the conversion of available energy into eddy kinetic energy.  potential  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 b a r o c l i n i c systems which are the mature stage of " f r e e " or "transient" unstable waves that originated in lower l a t i t u d e s .  Table 7.2 also shows that the energy transfer to the  longer wave components  and  representing the "forced" o s c i l l a t i o n s ,  was swift (< 2 days) and ushered in a protracted double (and later blocking regime from January 9 to February 4.  triple)  This is c l e a r l y shown on  the Hovmoller Diagram of Fig. 7.1 (50°N to 70°N), and the  full-latitude  extent of the long-wave pattern is confirmed by F i g . 7.2 (30°N to 50°N). The extraordinary rate at which these massive energy transfers occur i s 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 c u l t problem for medium range forecasting (Baumhefner and Downey, 7.4.3  1978; Somerville, 1980).  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 A t l a n t i c 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 A t l a n t i c Block.  Is retrogression of  Baffin blocks a predominant c h a r a c t e r i s t i c or are they as l i k e l y 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 i k e l y 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 s i g n i f i c a n t spectral attributes are l i s t e d in Table 7.3. retrograde North A t l a n t i c blocking wave is c l e a r l y evident through  A  199  F i g . 7.11  Sequence o f 5-day mean 700MB c h a r t s : ( a) 19-25 Dec 1978 N. A t l a n t i c - Greenland B l o c k l b ) 26-50 Dec 1978 B a f f i n I. B l o c k e s t a b l i s h e d ( c ) 2-6 J a n 1979 A l a s k a - West Coast B l o c k , (Taubensee, 1979, Wagner, 1979). ;  200  TABLE 7.3 Harmonics at 60°N associated with retrograde blocking from the N. A t l a n t i c to NE Canada and subsequent blocking Gulf of Alaska  Location  Date  a  S  1978-79 Atlantic  4>/2 2  S  2  *3  / 3  S  3  0  - 19  31  3  10  - 21  19  3  14  - 19  19  Dec. 21  167  + 1  47  22  183  - 7  55  23  179  -12  53  24  152  -22  88  —  2  25  125  -28  84  —  3  26  107  -34  65  22  16  •.  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  1  196  -92  65  •  —  1  - 21  17  2  150  -85  58  •  —  3  - 12  20  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  Baffin  Jan.  Alaska  l  —  -  •• —  •-  —  , - —  .-.  2 2  '  4  —  —  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 P a c i f i c  (- 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 t s  normal longitude. The general c h a r a c t e r i s t i c s of this sequence have been observed synoptically many times ( e . g . , Namias, 1975) but we are not aware of reference in the l i t e r a t u r e to day-to-day harmonic analyses.  (The  zonal harmonic graphics for December 23, 1978 and January 4, 1979 w i 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, p a r t i c u l a r l y at 70°N, is quickly noted from a comparison of amplitude-time p l o t s , e . g . , F i g . 7.12 (1949-50) vs F i g . 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 P a c i f i c and Wl and W2 over the NE A t l a n t i c .  These ridges o s c i l l a t e slowly about their  70N  F i g . 7.12  WINTER  49/50  WRVE 1  Amplitude and phase angle of wave number 1 a t 70°N as a f u n c t i o n 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 r e -  quency Baffin Blocking, e . g . , 1978-79, F i g . V I I -  1, feature a repeat-  ing pattern of retrograding blocking waves i n i t i a t e d over the N A t l a n t i c , subsequently crossing northern Canada and usually weakening or terminating west of Hudson Bay.  A subsequent amplification of the long-wave  pattern over the NE P a c i f i c and Alaska is associated with a readjustment 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 i n t e r -  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 A t l a n t i c .  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 t s normal l o c a t i o n .  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 temporal 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 F i g . 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 w i l l be part of our research  subsequent to this d i s s e r t a t i o n . However, discrete one-dimensional analyses, even though over representative zones, do not provide an integrated visual perception of the harmonies of a blocking system. dimensional zonal harmonic analysis.  To achieve this requires a twoThe purpose of this s e c t i o n , there-  f o r e , w i l l be to present and discuss the results of this kind of analysis applied to instantaneous ( i ; e . , 1200Z) 500MB height f i e l d s 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 l u s t r a t e 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 t r a n s i t i o n period p a r t i c u l a r l y as they apply to the southern structure of the blocking systems. (a)  A t l a n t i c - Greenland Block, December 23, 1978  The f i r s t three zonal harmonics of the 500MB height f i e l d on December 23, 1978 are displayed in Figs. 7.14 to 7.16,  respectively.  The corresponding d i g i t a l data are presented in Table 7.4 as well as those for components 4, 5 and 6-.  206  120E  Fig. 7.H  100E  80E  F i r s t harmonic (W1) o f the 500MB h e i g h t f i e l d on December 2 3 , 1978 d u r i n g a major episode o f b l o c k i n g over the North A t l a n t i c and Greenland. Contours i n dams. I n t e r v a l = 3 dams.  Pig.  7.15  A s i n P i g . 7.14  except 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 WAVE 1 LAT  WAVE 2  500MB  December 2.3, 1978  WAVE 3  AVG  SD  A  S  A  S  A  m  m  m  %  m  %  m  *  WAVE 4  WAVE 5  S  A  S  A  %  m  %  m  *  85  5108  156  220  - 30  99  18  27  1  6  -108  0  0  27  0  1  80  5112  237  332  - 27  98  38  16  1  34  -126  1  2  - 90  0  6  -  75  5130  239  321  - 21  90  69  -20  4  81  -115  6  5  - 96  0  70  5140  221  270  - 17  75  103  -37  11  115  - 95  14  14  -126  65  5160  196  224  - 14  66  105  -32  14  113  - 83  17  20  60  5193  179  185  - 12  53  94  - 5  14  109  - 58  19  55  5252  163  106  -  3  21  98  30  18  125  - 42  50  5346  144  25  85  2  118  44  33  126  45  5470  132  62  159  11  116  55  38  40  5586  115  50  -177  9  101  66  35  5679  96  29  -128  5  62  30  5753  74  18  - 91  3  25  5810  59  3  - 66  0  WAVE 6 S  A  S  %  m  %  174  0  1  52  0  7  0  2  - 54  0  9  - 37  0  5  - 55  0  0  19  -130  0  2  64  0  168  1  42  -149  2  10  133  0  65  110  7  51  -160  4  26  -177  1  30  98  107  18  41  -169  3  58  -175  6  - 46  38  68  102  11  19  152  1  66  177  11  110  - 68  35  31  81  3  24  117  2  44  178  6  39  92  -105  32  12  95  1  27  152  3  37  -167  5  69  21  88  -144  42  6  114  0  38  150  8  21  -138  2  13  44  2  71  -180  46  16  - 22  3  44  143  18  25  - 54  6  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 consistent with the results of Section 7.4.1.  are  A p r o f i l e 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 r e f l e c t i o n  of the observed low geopotential height over the mid-Atlantic (Fig. (a)  and ( b ) ) a  tude blocking.  7.11  condition which is t y p i c a l l y associated with high l a t i 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 r e f l e c t i o n of the deep low over the A r c t i c 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 l a t t e r components that replicates much of the deep low in the Newfoundland 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 l d on January 4, 1979 are displayed in Figs. 7.17 to 7.19, respectively.  The  corresponding d i g i t a 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 t r a n s i t i o n 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 v o r t i c i t y 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 t s maximum progressed slowly eastward to mainland Alaska.  Note that i t ,  too,  211  120E  F i g . 7.17  100E  BOE  F i r s t harmonic (W1) of the 500MB h e i g h t f i e l d on January 4, 1979 d u r i n g a major episode of b l o c k i n g A l a s k a and Southward along West Coast of B.C. Contours i n dams. I n t e r v a l = 3 dams.  Fig.  7.18  As  i n Figure  7.17  except  f o r second harmonic  (W2)  F i g . 7.19  As i n F i g . 7.17 except f o r t h i r d harmonic (W3).  TABLE 7.5 A l a s k a Block Zonal Harmonics WAVE 2  WAVE 1 LAT  500MB  January 4, 1979  WAVE 3  AVG  SD  A  S  A  S  A  m  m  m  %  m  %  m  4>  WAVE 4  WAVE 6  WAVE 5  S  A  S  A  S  A  S  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  no  - 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 b i - c e l l u l a r structure in the meridional (N - S) plane, and that the eastward motion of the southern c e l l s (centred in the 40°N - 50°N zone)  was so much greater r e l a t i v e 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 ' i n s i t u '  (140°W -  150°W). (c)  Alaska - NE P a c i f i c 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 t s 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 = 153°W, S  and W3  (4.3/3 = 152°W, S  2  2  2  = 44%) = 18%)  account for the blocking ridge from Alaska southward, p a r a l l e l i n g the West Coast of B r i t i s h Columbia.  The block occurred in conjunction with  an intense low level A r c t i c a i r mass which stretched from the Yukon to Colorado and brought record-breaking cold to the mid-west.  The f r i g i d  outflow to coastal B r i t i s h 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. the latitude zone 30°N - 40°N across the central P a c i f i c Ocean. we find reinforcing minima with WI playing the dominant r o l e .  7.18)  in  Here The  constructive interference accounts for the mean E - W oriented trough (Fig.  7.11(c)), a typical concomitant of NE Pacific-Alaska blocking.  the lower latitudes there is a s h i f t of power to higher wave numbers, e . g . , Sf. = 13% at 40°N and, moreover, 14% of the total variance  is  In  216  unaccounted f o r .  At these l a t i t u d e s , : i n Winter, additional harmonics  (up to W12) must be calculated in order to include the e f f e c t of intense b a r o c l i n i c a c t i v i t y 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 p a r t i c u l a r l y  apt  phrase, "spectral signature", for harmonic d i s t r i b u t i o n s 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, i s 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 c i r c u l a t i o n of the Northern Hemisphere reveals a wave component structure associated not only with the higher latitude anticyclone but also with the lower latitude cyclonic a c t i v i t y which, plays an important role in maintaining the blocking system. Van Mieghem (1961)  stated:  Average spectral d i s t r i b u t i o n s of general c i r c u l a t i o n parameters should be computed for d i f f e r e n t world weather types (strong zonal c i r c u l a t i o n , zonal c i r c u lation with strong e c c e n t r i c i t y , strong meridional c i r c u l a t i o n , blocking flow patterns, . . . ) and for t r a n s i t i o n periods between world weather types.  We f u l l y 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 l e v e l s .  Data locations were the 1977 grid points of the  National Meteorological Centre octagonal g r i d .  Three different method-  ologies were employed which required the computation respectively (i)  U.S.  of:  Anomaly Centres of 5-day mean 500MB height (date, l o c a tion and magnitude)  (ii)  S t a t i s t i c a l Moments (zero to four) of the frequency distributions of the 5-day mean 500MB, 1000MB, and lOOOMB - 500MB thickness at each grid point  (iii)  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.  C r i t e r i a were developed based on season, magnitude of the  positive anomaly centre and l a t i t u d e , which determined with a high degree of probability the existence or otherwise of a blocking a n t i cyclone.  Qualifying anomalies were called "blocking signatures."  A  Catalogue was prepared which i d e n t i f i e d 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 d i s t r i b u t i o n by season of blocking signature  frequency in the Northern Hemisphere is consistent with published i n v e s t i gations of blocking over the P a c i f i c and A t l a n t i c Oceans and Western Europe.  However, our results also reveal an area over the Northeastern  Canadian Archipelago (including Baffin Island and Davis S t r a i t ) with a much higher frequency of blocking signatures than previous would indicate.  investigations  The test of an independent sample of blocking signatures  by comparison with corresponding d a i l y 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." c r i t e r i a were developed to identify these sequences.  Displacement  A Catalogue was  prepared l i s t i n g t h e i r attributes including dates of i n i t i a t i o n , termination and component signature data. 4.  A statistical  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. draw a s t a t i s t i c a l l y  However, i t was not possible to  valid conclusion due to the size of the sample  (33 years) r e l a t i v e to the fluctuation period (^ one decade).  220  STATISTICAL MOMENTS 1.  The geographical d i s t r i b u t i o n of the s t a t i s t i c a l  moments of the  geopotential height continuum were useful in an interpretive sense. Normal and Standard Deviation f i e l d s 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 i e l d s (500MB) showed strong, well-defined positive areas  in the higher latitudes for WINTER, SPRING and FALL. with some (but not a l l )  These i d e n t i f i e d  areas of blocking signature maxima.  Site-  s p e c i f i c 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 i e l d s (500MB) showed s i g n i f i c a n t l y low values in WINTER  over the eastern P a c i f i c , the eastern A t l a n t i c and western Europe.  These  are the regions where ridges begin their northward a m p l i f i c a t i o n , sometimes (but not always) terminating in a blocking anticyclone in higher latitudes.  S i t e - s p e c i f i c histograms reinforce the l i k e l i h o o d of the low  kurtosis areas indicating bi-modal d i s t r i b u t i o n s .  Presumably the sub-set  with the higher mean would r e f l e c t the incidence of ridge a m p l i f i c a t i o n . ZONAL HARMONICS 1.  The zonal harmonics (WI  to W6) of the 500MB height p r o f i l e at  40°N and 6 0 ^ , respectively, were computed for each day of seven winters  221  and t h e i r flanking months ( i . e . , November to March, i n c l u s i v e ) . of zonal (U) 2.  and meridional (V)  Indices  components of flow were also computed.  It was found that the spatial harmonics of blocking episodes were  d i s t i n c t i v e to the region in which they occurred.  For example, W2 and  W3 predominate during blocking over Alaska and the eastern P a c i f i c .  In  other words, the blocking anticyclone has a spectral signature associated with i t s regional location. 3.  (Our results confirm those of Austin, 1980.)  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 s t r i k i n g l y unambiguous, at quasi-periodic intervals 40 days) and transitory-(-v. a few days).  (30 to  The behaviour .of the harmonics  during the resumption of blocking suggested that ' f o r c e d '  oscillation  components (W2 and W3 in this case) amplify from eddy k i n e t i c energy derived from ' f r e e '  o s c i l l a t i o n components whose previous amplification  derived from major b a r o c l i n i c development.  This example supports a  long-standing hypothesis that blocking may be a response to rapid deepening of baroclinic waves. 4.  Zonal harmonic analysis of the two-dimensional 500MB c i r c u l a t i o n  of the Northern Hemisphere during typical major blocking episodes reveals wave structures in both higher and lower latitudes with charact e r i s t i c s of motion and growth, associated with the total blocking system.  This study emphasized the higher latitudes (50°N to 70°N),  s i t e of the majority of blocking anticyclone centres when they reach the mature stage.  The f u l l zonal analysis of case studies suggest that  it  222  would be profitable to investigate the ensemble characteristics of the lower.latitude 5.  (30°N to 50°N) harmonics.  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 A t l a n t i c blocking (with a westward s h i f t of phase).  The  majority of Baffin blocks arise from retrograding North A t l a n t i c blocking 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 c h a r a c t e r i s t i c of the winter's blocking regimes.  Those with low frequency Baffin blocking featured  large amplitude ridges o s c i l l a t i n g slowly about their mean winter l o c a tion.  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 t r a i n .  This frequently resulted in  the inverted c e l l u l a r pattern of Fig. 3.4 and a 5 to 10 degree latitude southward displacement of the Baffin Low from i t s Normal l o c a t i o n . GENERAL 1.  The 5-day mean was an e f f e c t i v e f i l t e r for screening out the  higher frequency fluctuations occasioned by mobile synoptic-scale systems  223  and r e t a i n i n g , 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 l d of daily height, F i g . 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 circumpolar 500MB gph p r o f i l e s and > 80% of lower latitude 3.  (60°N)  (40°N).  The value of GCM diagnostics was i l l u s t r a t e d in Chapter 2 where an  example demonstrated the great influence on the general c i c u l a t i o n 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 v i t a l 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 i n a l l y , we believe that the three avenue approach to our i n v e s t i -  gation of blocking, namely, Anomaly Frequency, Continuum S t a t i s t i c s  and  Zonal Harmonics has achieved our objectives and yielded a number of s i g n i f i c a n t results concerning the nature of blocking in the Northern Hemisphere.  224  REFERENCES  American Meteorological Society (a): Abstracts. Rigby, M., Editor.  Meteorological and Geoastrophysical  American Meteorological Society (b), 1974-1979: Weather and Circulation of (Month, Year), Monthly Weather Review, Vol. 102-107 i n c l u s i v e . Austin, J . F . , 1980: The Blocking of Middle Latitude Westerly Winds by Planetary Waves. Quarterly Journal of the Royal Meteorological Society, 106, 327-350. B a r r e t t , E.W., 1958: Some Applications of Harmonic Analysis to the Study of the General C i r c u l a t i o n . Ph.D. Thesis, Department of Meteorology, University of Chicago, 209 pp. Baumhefner, D.P. and P. Downey, 1978: Forecast Intercomparisons from Three Numerical Weather Prediction Models. Monthly Weather Review, 106, 1245-1279. Baur, F., 1958: The Seasonal and Geographic Distribution of Blocking Highs on the Northern Hemisphere to the North of the 50th P a r a l l e l in the Period of 1949-1957. Idoja>£s, 62(2), 73-82. Berggren, R., B. Bolin and C.-G. Rossby, 1949: An Aerological Study of Zonal Motion, i t s Perturbation and Break-down. T e l l us, 1, 14-37. Berkofsky, L. and E.A. Bertoni, 1955: Mean Topographic Charts for the Entire Earth. B u l l e t i n of the American Meteorological Society, 36, 350-354. Blackmon, M.L,, 1976: A Climatological Spectral Study of the Geopotent i a l Height of the Northern Hemisphere. Journal of the Atmospheric Sciences, 33, 1607-1623. Blackmon, M.L., J.M. Wallace, N.-C. Lau and S.L. Mullen, 1977: An Observational Study of the Northern Hemisphere Wintertime C i r c u l a tion. Journal of the Atmospheric Sciences, 34, 1040-1053. B o l i n , B., 1950: On the Influence of the Earth's Orography on the General Character of the Westerlies. T e l l u s , 2, 184-195. B o v i l l e , B.W., and M. Kwizak, 1959: Fourier Analysis Applied to Hemispheric Waves of the Atmosphere. CIR-3155 TEC-292, Atmospheric Environment Service, Downsview, Ontario, Canada, 21 pp. Brezowsky, H., H. Flohn and P. Hess, 1951: Some Remarks on the Climatology of Blocking Action. T e l l u s , 3, 191-194.  225  Brooks, C.E.P., and N. Carruthers, 1953: Handbook of S t a t i s t i c a l Methods in Meteorology. Her Majesty's Stationery O f f i c e , London, England, 412 pp. Charney, J . , 1947: Dynamics of the Long Waves in a B a r o c l i n i c Westerly Current. Journal of Meteorology, 4, 135-162. Crutcher, H.L., and J.M. Meserve, 1970: Selected Level Heights, Temperatures, and Dew-Points for the Northern Hemisphere. NAVAIR 50-1C-52, U.S. Govt. Printing O f f i c e , Washington, D.C. D i e h l , L.W., 1977: Dynamics of Baroclinic Waves and Blocking Ridge Development. M.Sc. Thesis, Department of Geography, University of A l b e r t a , 106 pp. Eady, E.T.,  1949:  Long Waves and Cyclone Waves.  T e l l us, 1 , 35-52.  Egger, J . , 1980: Blocking and Stratospheric Warming. Phys. (Germany), 53, 172-80.  Contrib. Atmos.  E l i a s e n , E., 1958: A Study of the Long Atmospheric Waves on the Basis of Zonal Harmonic Analysis. T e l l u s , 10, 206-215. E l l i o t t , R.D., and D.B. Smith, 1949: A Study of the Effects of Large Blocking Highs on the General Circulation in the Northern Hemisphere Westerlies. Journal of Meteorology, 6, 67-85. Godson, W.L., 1959: The Application of Fourier Analysis to Meteorological Data. ' CIR-3168 TEC-295, Atmospheric Environment Service, Downsview, Ontario, Canada, 25 pp. Graham, R.D., 1955: An Empirical Study of Planetary Waves by Means of Harmonic Analysis. Journal of Meteorology, 12, 298-307. Green, R.A., 1969: The Weather and Circulation of December 1968. Monthly Weather Review, 97, 281-286. Haltiner, G.J. and F.L. Martin, 1957: McGraw-Hill, 470 pp.  Dynamical and Physical  Meteorology.  H a l t i n e r , G.J., 1967: The Effect of Sensible Heat Exchange on the Dynamics of B a r o c l i n i c Waves. T e l l u s , 19, 183-198. Haney, R.L., 1961: Behaviour of the Principal Harmonics of Selected 5-day Mean 500MB Charts. Monthly Weather Review, 89, 391-396. Hare, F.K., 1968: The A r c t i c . Quarterly Journal of the Royal Meteorological Society, 94, 439-459. Haurwitz, B., 1940a: The Motion of Atmospheric Disturbances. of Marine Research, 3, 35-50.  Journal  226  Headquarters, A i r Weather Service, 1946-1948: Northern Hemisphere H i s t o r i c a l Weather Maps Sea Level and 500 M i l l i b a r . A i r Weather Service, Washington, D.C. Holton, J . R . , 1979: An Introduction to Dynamic Meteorology. Academic Press, New York, 391 pp. Hovmoller, E.,  1949:  2nd Ed.  The Trough-and-Ridge Diagram, T e l l u s , 1, 62-66.  Jenne, R.L., 1970: The NMC Octagonal G r i d , National Centre for Atmospheric Research, Boulder, Colorado. . Jenne, R.L., 1975: Data sets for Meteorological Research, NCAR-TN/ IA-111 Atmospheric Technology D i v i s i o n , National Centre for Atmospheric Research, Boulder, Colorado. Johnson, C.B., 1948: Anticyclogenesis in Eastern Canada during Spring. B u l l e t i n of the American Meteorological Society, 29, 47-55. Johnson, K., 1978: An Observational Study of Planetary Waves during a Stratospheric Warming. Proceedings of the Twelfth Stanstead Seminar, Dept. of Meteorology, McGill University, Montreal. Knox, J . L . , 1979: Blocking Frequency in the Northern Hemisphere. Unpublished paper presented to the Annual Congress of Canadian Meteorological and Oceanographic Society, May, 1979. (Mimeo, 27 pp). Knox, J . L . , 1981: Master Catalogue of 5-Day Mean 500MB Height Anomaly Centres for the~Northern Hemisphere 1946-1978 (to be published). Labitzke, K., 1978: On the Different Behaviour of the Zonal Harmonic Height Waves 1 and 2 During the Winters 1970/71 and 1971/72. Monthly Weather Review, 106, 1704-1713. Lahey, J . F . , R.A. Bryson, E.W. Wahl, L.H. Horn, and V.D. Henderson, 1958: Atlas of 500MB Wind Characteristics for the Northern Hemisphere. University of Wisconsin Press, Madison, Wisconsin. Lamb, H.H., 1972: Climate: London, 613 pp. Lau, N . - C , 1980:  Present, Past and Future, V o l . 1, Methuen,  Personal Communication.  Madden, R.A., 1976: Estimates of the Natural V a r i a b i l i t y of Timeaveraged Sea-level Pressure. Monthly Weather Review, 104, 942-952. Mahlman, J . D . , 1979: Structure and Interpretation of Blocking A n t i cyclones as Simulated in a GFDL General Circulation Model. 1979 Stanstead Seminar, Sponsored by McGill University, Montreal, P.Q., Canada.  227  M o f f i t t , B.J., and R.A.S. R a t c l i f f e , 1972: Northern Hemisphere Monthly Mean 500 M i l l i b a r and 100-500 M i l l i b a r thickness Charts and some Derived S t a t i s t i c s (1951-1966). Geophysical Memoirs, Vol. 16, Meteorological O f f i c e , London, England, 61 pp. Namias, J . , 1950: The Index Cycle and i t s Role in the General C i r c u l a t i o n . Journal of Meteorology, 7, 130-139. Namias, J . , 1958: Synoptic and CIimatological Problems Associated with the General Circulation of the A r c t i c . Transactions American Geophysical Union, 39(1), 45-51. Namias, J . , 1975: Short Period Climatic Variations. University of C a l i f o r n i a , San Diego. 648 pp.  Vol. I and  II.  Namias, J . , 1978: Multiple Causes of the North American Abnormal Winter 1976-77. Monthly Weather Review, 106, 279-295. Namias, J . , and P.F. Clapp, 1944: Studies of the Motion and Development of Long Waves in the Westerlies. Journal of Meteorology, 1, 55-77. Namias, J . , and P.F. Clapp, 1951: Observational Studies of General culation Patterns. Compendium of Meteorology, Meteorological Society, 551-567.  Cir-  O'Connor, J . F , 1964: Hemispheric Distribution of 5-day Mean 700MB Circulation Centres. 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 M i l l i b a r s . ESSA Technical Report WB 10, 103 pp. National Meteorological Centre, S i l v e r 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. B r i e r , 1968: Some Applications of to Meteorology. The Pennsylvania State University.  Statistics  Perry, J . D . , 1979: Address to S p e c i a l i s t Group on Dynamical Problems, Atmospheric Blocking: Meeting - September 1979. Weather, 35, 148-152.  228  Petterssen, S., 1956: H i l l , 428 pp.  Weather Analysis and Forecasting, Vol. I,  McGraw-  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 i t s Effect upon Regional Climate (I): An Aerological Study of Blocking. T e l l u s , 2, 196-211. Rex, D.F., 1950b: Blocking Action in the Middle Troposphere and i t s Effect upon Regional Climate, II: The climatology of Blocking. T e l l u s , 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, Supplement, 68-87. Sawyer, J . S . , 1970: Observational Characteristics of Atmospheric Fluctuations 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 P r e d i c t a b i l i t y of Ultralong Waves. Journal of the Atmospheric Sciences, 37, 11411156. 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. T a l j a a r d , 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 r e i d l , R.A., E.C. Birch and P. Sajecki, Hemisphere: A Climatological Study. (1980).  1980a: Blocking in the Northern Submitted to ATMOSPHERE-OCEAN  T r e i d 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, V o l . 82-101, i n c l u s i v e .  U.S.  Department of Commerce, 1949-1956: Daily Series Synoptic Weather Maps, Northern Hemisphere Sea Level and 500 M i l l i b a r Charts, U.S. Weather Bureau, Washington, D.C.  Van Mieghem, J . , 1961: Zonal Harmonic Analysis of the Northern Hemisphere Geostrophic Wind F i e l d . Union Geodisique et Ge"ophysique Internationale, Monographie 8, P a r i s , 57 pp. Wagner, A . J . , 1979: Weather and Circulation of January 1979. Weather Review, 107, 499-506.  Monthly  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 A c t i v i t y over the Central North P a c i f i c . Journal of Atmospheric Science, 32, 489-502. Woffinden, C M . , 1960: 236-240.  Blocking Action.  Meteorological Magazine, 89,  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. Normal Harmonics for 500MB - Winter, Figs. VII  -  The  - 3 to 6, i n c l u s i v e ,  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 v a r i a b l e , taken over a s u f f i c i e n t period of time that i t can be accepted as a mean for climatological purposes. Thus, the Normal d i s t r i b u t i o n of 500MB height for the Winter. GAUSSIAN Because of the above use of the word "normal," the Gaussian, w i l l be used to refer to a d i s t r i b u t i o n which is  alternative, statistically  normal. HEIGHT (of a constant pressure surface) Abbreviation for "geopotential height" (gph).  The geopotential  $ of unit mass of a i r at geometric height z is equal to the work required to raise the mass to that height from sea l e v e l .  The "geopotential height" I is the height of a given level in the atmosphere in units proportional to the geopotential energy of unit mass at that l e v e l .  I and z are interchangeable for most meteorological purposes.  232  APPENDIX 11 - 1.  II  The Motion of Planetary Waves. Assume a homogeneous incompressible f l u i d on a rotating sphere and  a uniform non-divergent zonal flow.  If  the flow is perturbed, the iner-  t i a l response of the f l u i d to the varying C o r i o l i s Force w i l l generate a planetary (or Rossby) wave. The equations of motion are:  £  +  f u  = -fi  (II  -2)  where $ = geopotential. For horizontal non-divergent motion:  7T 3x Therefore  +  ^dy = 0  f = planetary v o r t i c i t y Therefore  i.e.,  (u , 1  (II  - 4)  = ^- -  dX  dy  = 2osin<j> J  ? + f = constant  the absolute v o r t i c i t y If  - 3) •  ^p- (t, + f) = 0  where t, = r e l a t i v e v o r t i c i t y  and  (II  is conserved.  the zonal flow has a mean speed U and the perturbation  v') u = U + u'  v = v'  is  233  Now, define a stream function  such that  3y  and from (II  3x  - 4)  <£ i>'* ^-° +U  2  +  (II -5)  This wave equation w i l l be s a t i s f i e d by $ =  A e  i k ( x  if c = U -  If m = 0  "  9  c t )  B  c o s my  (II  9  - 6)  (no wave component along meridians)  then c = U -  4- ll - ( =  k  2  B  2  ^  )  (II  - 7)  Thus a l l planetary waves move west r e l a t i v e to the zonal flow and the longer the wave length the greater the retrogressive speed. A wave w i l l become stationary r e l a t i v e to the surface i f  L = 2TT  234  II  - 2.  The Response of Large-scale Waves to Advection of Relative and Planetary  Vorticity.  To i s o l a t e the p r i n c i p l e under discussion we assume an incompress i b l e non-divergent barotropic atmosphere, and that the f i e l d of geopotential height at 500MB is described by the wave form $ = F(.t)  sin kx sin ly 2  where the wave numbers k and 1 are defined as k = -r^ L  x  2  1 = j^L  y  Then, following Hoi ton (1979) i t can be shown that  v (|f) . - I k • l >ff 2  2  But  at  Therefore  V $ = -fV 2  o g  2  • v(^- V $ + f) 2  TQ  | | = K'V • v(c +f)  (I.I  g  - 8)  where K is a positive constant 1 2  x, = j- v $ is the r e l a t i v e 9  o  f is the planetary  . .  vorticity  vorticity  ||- is the local tendency.  In Fig. II  - 1 there is depicted at time t a schematic of the  - f i e l d , of the associated c - f i e l d , and of the f - f i e l d .  235  Y (North)  Fig,  Schematic"500MB height and v o r t i c i t y f i e l d s showing regions of planetary and r e l a t i v e v o r t i c i t y advectioni Wave form of 4> —  —  —  Lines of constant planetary v o r t i c i t y * Lines of constant r e l a t i v e  ( Adapted from Holton,  vorticity,  1979i)  236  East of the ridge l i n e and west of the trough l i n e , e . g . , at 4-  point P, V? > 0 along the flow so that V • Vc > 0. g  Therefore this  term contributes to an increase, of $ with time. A l s o , at P, vf = where j is a unit vector pointing north, and — > 0.  But the y-component of Vg < 0 and therefore  Hence this term contributes to a decrease of $ with time.  • vf < 0.  Thus the advec-  tion of r e l a t i v e v o r t i c i t y over P w i l l cause an increase of $ and tend to make the ridge progressive, while advection of planetary  vorticity  w i 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 r e l a t i v e vort i c i t y isopleths p a r a l l e l to the stream flow and therefore v o r t i c i t y advection is small, at least near the core.  relative  On the other  hand, the planetary e f f e c t is large and hence they often retrograde.  237  APPENDIX III  - 1.  III  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 —"=-ka cos kx sin my = 0 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 i x x at one of these values, say, x = i\/2k and consider the variation of 1 in the z ' y ' plane: gZ  —  Therefore y = 1 (i)  If  (ii)  If  a  2  = - a + ma-cos my = 0 9  cos  _ 1  (l||)  = 0, then y = iT/2m, 2ir/2m,  = ma^, then y = 0, a-n/m,  . .  . nTr/2m, . . .  . . . mr/m, . . .  and therefore the number of maxima and minima i s reduced by one half.  238  (iii)  If a  > ma , then cos"  c. 0  0  o  -'(—)• m a^  is indeterminate and there can be no maxima or minima. The functions 1, 1 and therefore 1-1 assigning values to a-|,  a^, k and m.  may be varied at w i l l by  Patterns can be made even more 3  r e a l i s t i c i f the linear term -a^y  is replaced by a cubic -a^y .  This  w i l l determine a parabolic N-S p r o f i l e for the "instantaneous" zonal wind because  If - - v  2  To simulate phase s h i f t with latitude the function sin my may be generalized to  sin [my + <j>(y)].  239  t Max I  *--" 2k  Fig.  3 ft  '2 k  5Ti,  2k  Orthogonal c r o s s - s e c t i o n s xOz and y'O'z' through a maximum of Z(x,y).  240  APPENDIX IV IV - 1.  To Develop a F i l t e r Function Which I l l u s t r a t e s the Effect of the 5-day Average Let geopotential height p r o f i l e around a given latitude be  Z(.x,t) Resolve into harmonics Z ( x , t ) = A c o s ( k x - <o t)dt k  where  k  k  k  = wave number  X  = longitude  A^ = amplitude oj  k  = angular frequency (day""'')  Assume that wave components move with constant speed which w i l l be w  k  ^ - , that they maintain constant amplitude A^, and that the i n i t i a l angle i s zero: Let averaging interval = T days Then the time mean of Z ( x , t ) b  is  T Therefore Z. = -  o  cos(kx - a ) | , t ) d ( k x  - oi. t )  phase  = -— J ^ s i n  kA cos ou^T - cos kA sin oo^T - sin kxj  [ ssin i w.T cos kA + (1 - cos co.T)sin kA  ^  L  CO.J  Now, l e t the amplitude of Z  Then, A^ =  A 0)i  A  Let y  k  j^sin^T + (1 - cos o ^ T )  j  T  = A  k  A  (l  - cos u > T ) k  2  1/2  2(1 - cos o> T)  k 2  k  = phase speed (in rads long, day" ) 1  k  Then y. = k  k  A l s o , l e t the averaging interval A2 2(1 - cos 5 k y Then R. = j-? = — k V (5ky ) k  k  where R  k  be 5 days,  k)  L  2  i s the response function.  Examples If  k = 1 and .  If.k  = O.OS/^ay"  v  = 4 and p  k  1  = O.OS/^ay"  1  R. = 0.99 R  R  = 0.78  J  1/2  242  (A phase speed of .087  day "  typical  long wave speed).  If  k =  8 and y  If  k = 12 and  k  U | <  is equivalent to 5 degree day" , a f a i r l y  = 0.174 day" r  = 0.174 day" r  1  1  R  = 0.01  R  = 0.03  R  k  Thus wave components in the 'long-wave'  category moving at  characteristic  speeds (0 to 5 degree longitude day" ) w i l l be passed at between 80% and 1  100% of the original amplitude.  Components with speeds c h a r a c t e r i s t i c  of mobile b a r o c l i n i c waves in the mid-latitudes w i l l be almost e n t i r e l y attenuated. The f i l t e r function is shown in F i g . 4.0. IV - 2. A.  Guidelines for I d e n t i f i c a t i o n . o f  a Blocking Episode  Necessary and S u f f i c i e n t (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 l a s s i f i c a t i o n s (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 f i v e consecutive daily 500MB analyses. 4. The centre of the anticyclone must be north of 45°N. B.  S u f f i c i e n t (Treidl et a l , 1980a) " 1 . Closed isopleths must be present simultaneously in the surface and 500MB charts, s p l i t t i n g the westerly current a l o f t 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 f i v e days." IV - 3. A.  Procedure for Determination of Blocking Signature C r i t e r i 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 if,  in f a c t , a blocking episode was in progress at the time of and  in the region of a s p e c i f i c l i s t e d 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 contemporaneous block and O i f i t was not. E.  Draw a curve separating the  F.  The results for WINTER and SUMMER are shown in Figs. 4.3(a) and 4.3(b),  respectively.  # 's from the O  's.  244  PENTAD CALENDAR  PE  SUMMER  SPRING  WINTER  PE  Jun05  -  Jun09  50  Sep03  33  JunlO  -  Junl4  51  Sep08  -  Sepl2  Marl 2 - Marl6  34  Junl5  Junl9  52  Sepl3  Marl 7 - Mar21  35  Jun20  Jun24  53  Sepl8  -  Sepl7  16  Dec26  17  Mar22 - Mar26  36  Jun25  Jun29  54  Sep23  -  Sep27  Dec31  18  Mar27 - Mar31  37  Jun30  -  Jul04  55  Sep28  0ct02  Jan05  19  AprOl - Apr05  38  Jul05  Jul09  56  0ct03  JanlO  20  Apr06 - AprlO  39  JullO  Jull4  57  Oct08  Janl 5  21  April - Aprl5  40  Jul 15  -  -  Jul 19  58  0ctl3  0ctl7  Jan20  22  Aprl6 - Apr20  41  Jul20  -  Jul24  59  0ctl8  -  Jan25  23  Apr21 - Apr25  42  Jul25  Jul29  60  0ct23  0ct27  Jan30  24  Apr26 - Apr30  43  Jul30  Aug03  61  0ct28  Feb04  25  May 01 - May05  44  Aug08  62  Nov02  Feb09  26  May06 - MaylO  45  Aug 13 63  Nov07  Febl4  27  May 11 - May15  46  Aug 18 64  Novl2  Febl9  28  May! 6 - May20  47  Aug23  65  Novl7  Feb24  29  May21 - May25  48  Aug28  66  Nov22  MarOl  30  May26 - May30  49  Aug04 Aug09 Aug 14 Aug! 9 Aug24 Aug29 -  -  Sep02  67  Nov27  31  May 31 - Jun04  PE  Interval  PE  Dec 06  13  Mar02 - Mar06  32  Dec 11 14  Mar07 - Marll  Dec! 6  15  Dec21  Dec02  69  Dec07  70  Decl2  -  71  Dec! 7  -  72  Dec22  73  Dec27  1  JanOl  2  Jan06  3  Janll  4  Janl6  -  5  Jan21  -  6  Jan26  7  Jan31  8  Feb05  9  FeblO  10  Febl5  11  Feb20  -  12  Feb25  -  -  Total  Season  Note:  Interval  Interval  Interval  68  FALL  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 •  For Leap Year PE 12 contains 6 days. Fig. IV - 1.  The Pentad Calendar  Sep07  -  Sep22  0ct07 0ctl2 0ct22 NovOl Nov06 Novll Novl6 Nov21 Nov26 DecOl  245  APPENDIX V V - 1.  Smoothing of Areal Frequency  Figs. 5.1 to 5.5,  Isopleths  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 i s o -  pleths that this procedure introduced an a r t i f i c i a l certain grid-points.  'clustering'  at  That is to say, there was a frequency gradient  between adjacent grid points which was u n j u s t i f i e d by the spacing of upper a i r stations. Therefore the f i e l d was s l i g h t l y smoothed as in F i g . V - 1  F  Where  C  F  c  =  I  ( 4 F  C  +  F  A  +  F  B  +  F  D  +  F  E  )  = I n i t i a l Frequency at point C  F^ = Frequency at Point A Fg = Frequency at Point B Fp = Frequency at Point D F  V-2.  £  = Frequency at Point E  Nomenclature  Master Catalogue  The Catalogue identifying a l l  positive  and negative Anomaly Centres of 500MB 5-day average height f i e l d s .  (Fig.  4.2).  246  D  'C •  E  • B  A  1_ 8"  Fig.  V-1  ( 4 F,  +  +  Smootliing f u n c t i o n u s e d i n t h e construction of frequency f i e l d s F i g . 5.1 t o 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 s a t i s f i e d C r i t e r i o n (3). Blocking Signature Sequence Catalogue  4.8)  The Catalogue which sorts the Signatures into Sequences using Criterion (Fig.  SIG  (Fig.  (4).  5.11)  Any positive anomaly l i s t e d in the Blocking Signature Catalogue  SEQ  Any Sequence l i s t e d in the Blocking Signature Sequence Catalogue  SEQ.J  Sequence consisting of only 1 SIG  SEQ  Sequence consisting of more than 1 SIG  n  K.BLK  A blocking episode i d e n t i f i e d from daily analyses by KNOX guidelines, APPENDIX IV - 2  T.BLK  A blocking episode i d e n t i f i e d 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 d a i l y analyses. PREDICTOR  Identification  of SIG and SEQ from Catalogue and relevant  data V - 3. 1.  Test of Blocking Signatures and Sequences  This is a test of Blocking Signatures and Sequences to determine: (a)  The success r a t i o for SIG components of SEQ's.  they related to a 5-day period of a blocking episode?  How often are  248  (b) 2.  The success r a t i o for SEQ's with respect to blocking episodes.  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 C r i t e r i o n  5.  (3).  Go to the Blocking Signature Sequence Catalogue and, for that period, L i s t each SEQ on a Master Sheet by  6.  (a)  PE number of each component SIG  (b)  Starting date and location  (c)  Ending date and location  (d)  Maximum amplitude reached (dams)  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)  7.  Yes  •  No  O  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 i d e n t i f i c a t i o n , occurrence north or south of 75°N.  9.  Count a l l SIG's which occurred in period corresponding to SEQ-j, SEQ  n  and SEQ.  Let number = N , N and N. 1  10.  Success r a t i o SIG's = '  11.  Proceed as in 10. for SEQ's.  12.  For results see Table III  K  V - 4.  B  N  L K S  of the main text.  Retrograde A t l a n t i c Blocking as Revealed by a Blocking Signature Sequence Fig. V - 2 i l l u s t r a t e s how a blocking signature sequence i d e n t i -  f i e d the wave of blocking which retrogressed from Scandinavia to Baffin Island December 16-31, 1976. The motion of individual daily 500MB a n t i cyclone centres (shown as 12-hour displacement vectors) was e r r a t i c . 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 GreenlandIceland (December 19-28) and the third over Baffin Island-Davis (December 29-31).  Strait  The adjustment in the mass f i e l d , December 19-20,  was a s t r i k i n g example of "discontinuous retrogression."  Note how the  seat of blocking a c t i v i t y 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 i s associated with the westward signature motion. The Hovmoller (time-longitude) diagram f o r 500MB gph, 50-70°N (not shown), c l e a r l y confirms the retrograde motion.  250  P i g . V-2  I d e n t i f i c a t i o n of a r e t r o g r a d i n g North A t l a n t i c B l o c k by a B l o c k i n g Signature Sequence. P e r i o d was .  1200Z Dec.  16 to 1200Z Dec.  51,  1976.  •12 - hour displacement of 500MB a n t i c y c l o n e centre. (Canadian M e t e o r o l o g i c a l C e n t r e ) . Simultaneous c e n t r e - p a i r along  ridge  line.  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 27-31 Note d i s c o n t i n u o u s r e t r o g r e s s i o n which December 1 9 t h and 2 0 t h .  occurred  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 EUROPE  "1  0  1  1  1  1  30E  SUMMER  2 V.SIBERIA  1  1  1  60E  1  1  P  90E  1  STARTING  3 i 4 E.SIBERIA ALASKA V. ACIEIC , E.PACIFIC  1  I  SIGS  5 CANADA  P  1  1  1  1  1  1  1  1  120E 150E 180  P i g . V-3  1  1  i  p  1  1  1  1  150V 120W •' 90W  1  1  1  6 ! 1 GREENLAND EUROPE N.ATLANTIC  I  1  1  1  1  1  SOW 30W  As i n P i g . 5.13 except f o r SUMMER  1  1  0  1  1  1  p  1 !  30E 60E  SUMMER EUROPE  ~i  0  i  I  I  P  30E  V.SIBERIA  I  i  i  60E  I  I  I  90E  I  ENDING  3 E.SIBERIA V.PACIFIC  I  1  1  I  P  1  ALASKA E.PACIFIC  1  1  120E 150E 180 F i g . V-4  SIGS  4  1  1  1  1  1  1  6 GREENLAND N.ATLANTIC  5  I  CANADA  1  1  1  1  150W 120V 90W  1  1  I  60W  As i n F i g . 5.14 except f o r SUMMER  1  1  1  30W  1  ]  EUROPE  p  0  1  1  i  r — — r  30E 60E  FALL EUROPE  W.SIBERIA  E.SIBERIA V.PACIFIC  STARTING  I  4  ALASKA E.PACIFIC  1  SIGS  5  CANADA  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 P i g . V-5  A s i n P i g . 5.13 e x c e p t f o r P A L L  EUROPE  FALL  2 W . S I B E R I A  3 E.SIBERIA V.PACIFIC  ENDING  SIGS I  4 A L A S K A E  . P A C I F I C  !  5 C A N A D A  GREENLAND N.ATLANTIC  .1  EUROPE  a UJ  °0 ' '30E' '60E ' '90E' ' 120E 'l50E ' 180 ' 'l50V ' 120V '9oY '60W' '30W' ' 6 ' 'SOE' '60E Pig.  V-6  As i n P i g . 5.14 except f o r PALL  2 W.SJBERIR  EUROPE  WINTER  STARTING  SIGS  3 1 4 I 5 E.5I5ER[fl ALASKA CANADA W.PACIFIC , E.PACIFIC  ]  GREENLAND N.ATLANTIC  1  EUROPE  a  LU on  u_  °0  30E  60E  90E  120E 150E 180  F i g . V-7  150W 120W 90W  60W  As i n P i g . 5.13 except f o r WINTER  30W  0  ' 30F." '60E  2 V. SIBERIA  1  EUROPE  WINTER 3 E.SIBERIA V.PACIFIC  ENDING  SIGS  4 ALASKA E .PACIFIC  1  I  5 CANADA  GREENLAND  EUROPE  N.ATLANTIC  a  LU  cc  0  30E  60E  90E  120E 150E 180  P i g . V-8  I50W  I2QW 90W  As i n P i g . 5.14 except f o r WINTER  60W  30W  0  30E  60E $  258  V - 6.  Program for Computing and Plotting Histograms of Blocking Signature Frequency per 10° Longitude.  Reference:  Chapter 5,  Section 5.2.2. On the next page is l i s t e d the computer algorithm for preparing longitudinal histograms of Blocking Signature Frequency from data read from the I,J  grid.  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( 1 9 8 0 ) . L E N REAL A B S C ( 4 3 ) , M I D ( 3 6 ) R E A D ( 5 , 1 0 1 ) NDIV C* 1 C  SET  UP  ABSCISSA  VECTOR USED BY  PLT  5  IN A GRID IN NMC FORMAT, AND THE HISTOGRAM FOR THAT GRID.  OF  (X,Y)  25 30 40 C* C*  £ * * + * * * + * * * * * + + * + ++ + + + * * * * + * * * + + + **•* + * +  * *  DO 65 J=1 .51 DO 6 0 I=N1,N2 K = K+ 1 V A L = I D A T A ( K ) / ( 1 0 0 . 0 * F L O A T ( N D I V ) * *2) IF(VAL.EO.0.0) GOTO 60 ++ +++++*+*++ ++ D I V I D E EACH GRID BLOCK INTO * ' N D I V BY ' N D I V SUBUNITS * TO ACCURATELY ASSIGN PORTION * OF DATA VALUE TO LONG. BAND. * DO 50 11=1,NDIV DO 5 0 J J = 1 . N D I V X= I +II/FL0AT(NDIV)-24.55 Y=J+JJ/FL0AT(NDIV)-26.55 R2=X**2+Y**2  + R2 ) )  * *  GOTO 15 EL0N=90.0 I F ( Y . L T . O . O ) GOTO 25 I F ( X . L T . O . O ) GOTO 20 GOTO 40 ELON=18O.O-EL0N GOTO 4 0 I F ( X . L T . O . O ) GOTO 30 EL0N=36O.0-EL0N GOTO 40 ELON=180.0+ELON RLO=15 O+ELON IF(RLO.GE.360.0) RL0=RL0-360.0  10 15 20  * *  *  I F ( R L A . G T . 7 5 ) GOTO 50 I F ( X . E O . 0 . 0 ) GOTO 10 ELON=RADDEG*ATAN(ABSf Y/X ) ) -  DO 5 1 = 1 . 3 6 MID(I)=0.0 CALL R E A D ( I DATA . L E N . 0 , L N U M , 8 , & 9 9 ) K=LEN/2-1977 INT= 1 N1 = 15 N2 = 33  C * STEP THROUGH THE DATA P O I N T S , C+ T A L L Y I N G VALUES INTO THE CORRECT C * LONGITUDE ZONE.  C* C* C* C*  LATITUDE  RLA=RADDEG*ARSIN((ZK2-R2)/(ZK2  *  DO 1 1 = 1 , 4 3 ABSC(I)=I*0.2-0.1 ABSC(43)=8.4  READ PLOT  COMPUTE  C+ IF L A T > 7 5 N , IGNORE POINT C * OTHERWISE, COMPUTE LONG.  RADDEG=57.2958 ZK2=973.71202 DO 70 L = 1 . 5 (^*****+ C* C*  C*  50 60  65 C* 70 99 100 101  T A L L Y VALUE APPROPRIATE  INTO THE LONG. BAND.  * *  LB=RLO/10.0+1 MID(LB)=MID(LB)+VAL CONTINUE CONTINUE I F ( ( d . E Q . 15).OR. ( J . E O . 3 7 ) ) N1=N1-INT N2=N2+INT CONTINUE WRITE(6.100)(MID(I).1=1,36) CALL  PLT  TO PLOT  I NT = INT-1  THE HISTOGRAM.  CALL P L T ( M I D . L . A B S C ) CONTINUE C A L L PLOTND STOP FORMAT(' ' . 1 8 F 6 . 1 , / , ' FORMAT(14) END  '.18F6.1)  *  260  APPENDIX VI VI - 1.  Conversion of the Thickness of the 1000MB - 500MB Layer into i t s Mean Temperature It  can be shown from the hydrostatic equation and the equation of  state that for dry a i r the thickness of a layer is proportional to i t s 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 v i r t u a l temperature' (T ).  This  is the mean temperature of a layer of dry a i r with the same density as the moist a i r layer.  Now T  v  > T, but reference to Table 72 of L i s t  (1966) w i l l show that the difference is quite small ( 0 . 0 2 ° to 0.50°C) for the range of mean temperatures of the lOOOMB - 500MB layer usually encountered in the mid- and high l a t i t u d e s .  Consequently i t w i l l be s u f f i -  c i e n t l y 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 t h i c k -  ness f i e l d i s , in e f f e c t , a f i e l d 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 a i r = 287JK" kg  T  y  = virtual  temperature at pressure p  g = acceleration of gravity As explained above this may be written:  1  - I  R  p If p-j = 1000MB and p then Z  5 0 Q  -  Z  1 0 0 0  Tin  lhf= 4  =—  2  2  = 500MB  = 20.27T  Thus for any value of (2gQg -  ^-jQOO^  1  N  M  E  ^  R  E  S  7 _ | 500 - 1000 ] " \ 20.27 / Z  Z  1  Even more convenient relationships can be derived which w i l l make possible the d i r e c t r e l a b e l l i n g of conventional 1000MB - 500MB thickness contours drawn at 6 dam intervals in terms of isotherms of (or K ) with integral values at 3° i n t e r v a l s . We have: (a)  0.5 (ZgQQ -  e  - 9 - ' 500 ' Z  dams - 4.0 dams = T degrees K  2-|QQQ)  Z  1000  =  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° i n t e r v a l s .  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.  version table is as follows: TABLE VI - 1 Thickness (dams)  T(°C)  T(K)  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  1000 - 500MB  •  The con-  263  VI - 2. Transformation of the MSL Pressure into Geopotential Height of the 1000MB Surface The transformation algorithm i s generated as follows:  Where  Let height o f 500MB surface  = Z  Let height of lOOOMB surface  = h-,  Let MSL pressure  = p.(I,J)  K  2  ,(I,J)  .(I,J)  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 , Z-j 2  and p. Z-| i s 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 i s also temperature dependent, s i g n i f i c a n t l y 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  v e r t i c a l extent Z  2  ~ ^]  thickness) is proportional to the mean temperature of AB = T^. Z  2  - Z  ]  * 2.027 T  (called In f a c t :  M  What we want, however, is not T^ but T , the mean temperature of the a i r column BC.  C l e a r l y , there must be a strong positive correlation  between T^ and T .  The following empirical relationships (Moffitt and  R a t c l i f f e , 1972) gave good results when tested over a wide range of t h i c k nesses for MSL pressure deviations from 1000MB, of up to 30MB. (i)  If Z  T  (ii)  m  2  - Z  1  < 478.00 dams,  = (0.93 x 478 - 223) K.  If 541.50 dams **• Z T  m  =  [0.93 x (Z  2  2  - 1, > 478.00 dams,  - Z^  - 223] K  (iii)  If Z - Z-, > 5 4 1 . 5 0 dams. 2  x  m  = [0.52 x (Z - Z^ - 1] K 2  To compute Z-j at this stage, the f i r s t approximation i s : 3( p.(.I,J) - 1000)  ]/  K  These values of Z-j are used in ( i ) , ( i i ) or ( i i i ) , applies.  whichever  This w i l l provide the f i e l d of T .  The second and f i n a l approximation f o r the 1000MB height i s : (P Z  l  =  1000)x 342  m  The f i e l d of Z-, .(I,J) provides the 1000MB height data set. K  VI - 3 .  Computation of Normal and Standard Deviation Fields  The Normal geopotential height at (I.,J) f o r the i th pentad i s (Z)  (I,J)  wA  2 %  N  K.  (I,J)  ^K=l  Where N = period of record and Z-j represents the 5-day average of gph f o r pentad i . The Normals f o r the respective seasons are: 12  73  2 (W(I,J) 'T8 i=i  2 =68  =  (z ) i  u  ( I  '  0)  31  ( Sp)'(I,J) Z  19  2  i=13  a.)  1  ,0)  and so on.  266  For the Seasonal Standard Deviations at (I,J) we used:  2  2 WN  C,J) etc • VI - 4.  s  18N  HA  +  etc.  Computation of Coefficient of Skewness  S p e c i f i c a l l y for WINTER at ( I , J ) : (1,0)  A program was written to calculate values of C S ^ , CS^p, CS<.y and C S  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 ' p l o t contour' routine yielded spatial d i s t r i b u t i o n s of areas of s i g n i f i c a n t skewness, either positive or negative. VI - 5. 0  Computation of Coefficient of Kurtosis  S p e c i f i c a l l y for WINTER at ( I . J ) :  CK. 'WN  A procedure similar to that for calculating f i e l d s of skewness was followed.  267  APPENDIX VII  - 1.  VII  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 meridX through R.  Then the zonal speed c  in degrees of longitude per day  (for  the r e l a t i v e axis scales of the diagrams  Days  used in this thesis)  is  c = 5 tan a The following tabulation is provided for convenience of the user. TABLE VII Contour Axis with Meridian a (degs.)  - 1 Zonal Speed of trough or ridge 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  F i g VII-1  Same as F i g . 7.1 except f o r November'1, 1978 to February 28, 1979. Note episodes of A t l a n t i c B l o c k i n g A f o l l o w e d by P a c i f i c - A l a s k a B l o c k i n g P. (See S e c t i o n 7.4.3).  269 HOVMOLLER 500MB RVG(30N-50N) NOV 1.1978-FEB 28.1979 DEGREES  0  F i g . VII-2  180  0  Hovmoller Diagram f o r 30°N - 50°N November 1, 1978 to December 28, 1979(See S e c t i o n 7.4.3).  270  VII  - 2.  Zonal Harmonics for the Normal 500MB Height Field - WINTER  The following f i g u r e s , VII  - 3 to VII  - 6, i n c l u s i v e , show the  Zonal Harmonics in the Northern Hemisphere for Waves 1 to 4, respectively.  (See Section 7.3.4(b) of the Text.)  271  120E  F i g . VII-3-  100E  SOE  F i r s t harmonic (W1) o f t h e normal 500MB h e i g h t f i e l d f o r WINTER (December 1 t o F e b r u a r y 2 8 ) . Contours l a b e l l e d i n decametres. I n t e r v a l = 1 dam.  F i g . VII-&-  As i n F i g u r e VII-3 , . except f o r second harmonic (W2).  Fig.  VII-5-  A s i n F i g . VII-3- , harmonic (W3).  except f o r t h i r d  274  12DE  Fig. VII-6  100E  As i n F i g . VII-3 > harmonic (W4).  BOE  except f o r f o u r t h  

Cite

Citation Scheme:

        

Citations by CSL (citeproc-js)

Usage Statistics

Share

Embed

Customize your widget with the following options, then copy and paste the code below into the HTML of your page to embed this item in your website.
                        
                            <div id="ubcOpenCollectionsWidgetDisplay">
                            <script id="ubcOpenCollectionsWidget"
                            src="{[{embed.src}]}"
                            data-item="{[{embed.item}]}"
                            data-collection="{[{embed.collection}]}"
                            data-metadata="{[{embed.showMetadata}]}"
                            data-width="{[{embed.width}]}"
                            async >
                            </script>
                            </div>
                        
                    
IIIF logo Our image viewer uses the IIIF 2.0 standard. To load this item in other compatible viewers, use this url:
http://iiif.library.ubc.ca/presentation/dsp.831.1-0095459/manifest

Comment

Related Items