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A frequency analysis of ten years of surface atmospheric data at ocean weathership ’Papa’ Fissel, D. B. 1975

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A FREQUENCY ANALYSIS OF TEH YEAHS OF SURFACE ATMOSPHERIC DATA AT OCEAN WE ATHERSHIE ' PAPA' (50 S 145W) by DAVID BRYAN FISSEI B. Sc . , University Of Brit ish Columbia, 1971 A THESIS SUBMITTED IN PARTIAL FUIFIILBEKT CI THE BEQUIREMENTS FOR THE DEGREE OF MASTER OF SCIENCE i r the Department of Physics and the Irstitute of Oceanography We accept this thesis as conforming tc the required standard THE UNIVERSITY OF BRITISH CCLUKBIA Apri l , 1975 In presenting th is thesis in par t ia l fu l f i lment of the r e q u i r e m e n t s f o r an advanced degree at the Univers i ty of B r i t i s h C o l u m b i a , I agree that the L ibrary shal l make it f ree ly ava i lab le for reference and s t u d y . I fur ther agree that permission for extensive copying of t h i s t h e s i s for scho la r ly purposes may be granted by the Head of my Depar tment o r by his representat ives . It is understood that copying or p u b l i c a t i o n o f th is thes is fo r f inanc ia l gain shal l not be allowed without my written permission. Department of pt-f m s<.c S  The Univers i ty of B r i t i s h Columbia Vancouver 8, Canada i. i i ABSTBACT The standard 3-hourly meteorological observations from Ocean Weather Station »Papa» (SON 145W) for the period 1958 to 196 7 are examined. Power spectra of the wind speed, air pressure, a i r temperature, absolute humidity* and sea temperature are computed. The wind speed spectra from the open ocean environment are compared with those found at ether ccean, coastal and land stations. The seasonal spectra of these quantities averaged over each of the ten years indicate that the character of the act ivity changes both with respect to the size and frequency of the variations during the course of the year. Spectra are also computed for 0 » D x , u » U y , U»£T and U»Aq which through the bulk transfer formulas are representative of momentum, sensible heat and latent heat fluxes. The rotary power spectrum of the vector wind and vector wind stress show that clockwise rotations of the wind and the wind stress contain more energy than the anti-clockwise rotations. Cross-spectral values are computed between the vector wind and scalar quantities. As well, the cross-spectra between some of the various scalar quantities were examined. The effect of using data commonly available over the cceans on the computation of the bulk fluxes i s examined. P. comparison of the monthly wind stress and latent heat flux computed from the data organized into the format of the Marine Climatic fltlas with the direct ly calculated values show good agreement between the two methods, The sensible heat flux deviates more seriously, part icular i ly in months of small fluxes. The effect on computing bulk fluxes from surface weather i i i chart data i s examined fcy computing these fluxes frcm vector averaged wind data. The use of this data format results in substantial reductions to the wind stress (magnitude reduced to one-half of the d i rec t l j calculated value for an averaging period of one month). The latent heat flux is reduced by a factor of 0.53 and the sensible heat flux by a factor of 0.62 for the monthly averaging period. i v TABLE OF CONTENTS ABSTRACT i i LIST OF TABLES . . v i i LIST OF FIGURES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . V i i i ACKNOWLEDGEMENTS xi Chapter 1 INTRODUCTION . . 1 Chapter 2 DAT A COLLECT ION 6 2.1 Collection Procedures . . . . . . . . . . . 6 2.2 Missing And Erroneous Data . . . . . . . . . . . . . . . . . . . . . . . . . . 7 2.3 Derived Quantities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ? Chapter 3 SPECTRAL ANALYSIS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 3.2 Cross-spectra 12 3.3 Rotary Spectra . . . . . . . . . . . . . . . . . . . . . . . 1 4 3.4 Spectral Display Methods . . . . . . . . . . . . 1 6 3.5 Spectral Smoothing . . . . . . . . . . 1 7 3.6 Two-yearly Spectra . . . . . . . . . . . . . . . . . . 1 9 3.7 Seasonal Spectra .20 Chapter 4 SPECTRAL RESULTS . . . . . . 2 3 1.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 3 4.2 Wind . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 4.3 Air Pressure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 8 4.4 Sea Surface Temperature . . . . . 4 3 4.5 Air Temperature . . . . 49 4.6 Absolute Humidity 53 4.7 Turbulent Fluxes 57 Chapter 5 CROSS-SPECTBAL BESULTS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69 5.1 Introduction 69 5.2 Air Pressure .70 5.3 Air Temperature . . . . . . . . . . a . . . . . . . . . . . . . . • » • » • » • » » . . 7 4 5.4 Absolute Humidity 78 5.5 Sea Temperature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83 5.6 Co-spectra Between Quantities Used To Compute Bulk Fluxes . . . . . . . . . . 9 0 Chapter 6 THE EFFECT OF DATA SHCOTHIBG CN WIBE STBESS COHPUTATIOHS 95 6.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95 6.2 Direct Wind Stress Computation ..97 6.3 Wind Stress From Climatic Atlases . . . . . . . . . . . . . . . . . 102 6.4 Wind Stress From Surface Weather Charts . . . . . . . . . . . 106 Chapter 7 THE EFFECT OF DATA SMOOTHING ON HEAT FLOXES . . . .111 7.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1 1 7.2 Direct Calculation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1 2 7.3 Climatic Atlas . . . . . . . . . . . . . . 1 1 5 7.4 Surface Weather Charts . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1 9 Chapter 8 SUMMARY 123 v i EIBLIOGRAPHY 129 APPENDIX I INCORRECT DATA .133 APPENDIX II MEANS AND POWER SPECTRAL INTEGRALS 135 v i i LIST OF TABLES Table Page I The energy of single harmonic spectral peaks found at periods of one day, one-half day and one-quarter day. 28 II A summary of the period and level (f*^) of the synoptic peak of the wind speed spectra as determined by various investigators. . . . . . . . . . . . . 30 III The energy of single harmonic spectral peaks of air pressure, a ir temperature, absolute humidity and sea surface temperature found at periods of one day, one-half day and one-third day. . . . . . . . . 42 IV The energy of single harmonic spectral peaks of quantities^ which are representative of the wind stress (U»U), the sensible heat flux, the latent heat flux and the total turbulent heat flux found at periods of one day, one-half day and one-quarter day. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61 V The data format used in wind roses presented in the Marine Climatic Atlases. . . . . . . . . . . . . . . . . . . . . 1 0 4 VI Comparison of the wind stress magnitude and direction as computed from the data organized into the format of the Marine Climatic Atlas ('MCA') with the value computed directly from the 3-hourly data ( 'Direct ' ) . 105 VII A comparison of the sensible and latent heat fluxes computed from the data organized into the format of the Harine Climatic Atlas ('MCA') with the value computed direct ly from the 3-hourly data ( 'Direct ' ) . 117 v i i i LIST OF FIGURES Figure Page 1. An example of the effect of f i l t e r ing to remove the annual variation. 22 2. The two-yearly wind speed spectrum for the period 1958 to 1967. 24 3. Wind speed spectra for each of the seasons averaged over the ten years, 1958 tc 1967. . . . . . . 26 4. The rotary autc-spectrurn of the wind computed from five two-yearly blocks covering the period 1958 to 1 967. 34 5. The seasonal rotary auto-spectra of the K i n d averaged over the ten years, 1958 to 1967. . . . . . . 37 6. The power spectrum of air pressure computed from five two-yearly data blocks covering the period, 1958 to 1967. 39 7. The seasonal power spectra of air pressure; each spectrum is averaged over the ten years, 195€ tc 1967. 40 8. The power spectrum of sea temperature computed from five two-yearly blocks covering the period, 1958 to 1967. , . 44 9. The seasonal power spectra of sea temperature; each spectrum is averaged over the ten years, 1958 to 1 967. . 46 10. The power spectrum of air temperature computed from five two-yearly data blocks covering the period, 1958 to 1967. 50 11. The seasonal power spectra of air temperature; each spectrum is averaged over the ten years, 1958 to 1 967. 51 12. The power spectrum of absolute humidity computed from five two-yearly data blocks covering the period, 1958 to 1967. 54 13. The seasonal pcwer spectra of absolute humidity; each spectrum is averaged over the ten years, 1958 to 1 967 55 IX 14. The rotary auto-spectrum of a quantity which is proportional to the wind stress, computed from five two-yearly blocks covering the period 1958 to 1967. 58 15. The seasonal rotary auto-spectra of |tt|u% a guantity which i s proportional to the wind stress, computed from five twc-yearly blocks covering the period, 1958 to 1967. 59 16. The power spectra of U£T (in ( C ° - m / s e c ) 2 , proportional to the sensible heat f lux) , U"Aq (in (gm/m 2-sec) 2 , proportional to the latent heat flux) and 1.2 OAT + 2.44UAg (proportional to the total turbulent heat flux) , computed from five two-yearly blocks covering the period, 1958 to 1967. 62 17. The seasonal power spectra of 0AT (proportional to the sensible heat f lux). Each spectrum is averaged over the ten years, 1958 to 1967. . . . . . . 65 18. The seasonal power spectra of OAq (proportional to the latent heat flux). Each spectrum is averaged ever the ten years, 1958 to 1967. . . . . . . 66 19. The seasonal spectra of 1.20AT + 2.44UAg (proportional to the total turbulent heat f lux) . 67 20. Graphs of phase, coherence and the transfer spectra between the wind and air pressure 71 21. Graphs of phase, coherence and the transfer spectra between the wind and air temperature. . . . 75 22. Graphs of phase, coherence and the transfer spectra between the a i r temperature and 0A.T (a quantity representative of the sensible heat flux) . 77 23. Graphs of phase, coherence and the transfer spectra between the a i r temperature and the absolute humidity. 79 24. Graphs of phase, coherence and the transfer spectra between the wind and absolute humidity. . 81 25. Graphs of phase, coherence and the transfer spectra between the absolute humidity and UAq (a guantity representative of the latent heat flux) 82 X 26. Graphs of phase, coherence ana the transfer spectra between the a i r temperature and the sea temperature. 84 27. Graphs of phase, coherence and the transfer spectra between the wind and sea temperature. . . . 86 28. Graphs of phase, coherence, and the transfer spectra between the sea temperature and a ir pressure 88 29. Graphs of phase, coherence and the transfer spectra between the sea temperature and 1.2*u*A_ + 2.44*UAq (a quantity representative of the total turbulent heat f lux) . 89 30. The co-spectrum between the wind speed and the east-west wind component and between the wind speed and the north-south wind component computed from five two-yearly blocks. . . . . . . . . . . . 91 31. The co-spectrum between the wind speed and the sea-air temperature difference and between the wind speed and the sea-air humidity difference from five two-yearly blocks. 93 32. The directly calculated wind stress for each year from 1958 tc 1967. 99 33. The directly calculated wind stress for each month. 101 34. The ratio of the wind stress magnitude computed from wind data that are vector averaged over a period, T to the directly calculated wind stress 109 35. The yearly averages of the directly calculated sensible and latent heat fluxes 113 36. The monthly averaged sensible and latent heat fluxes direct ly calculated from the 3-hourly data. . . 115 37. The monthly averaged sensible and latent heat fluxes computed from the data organized intc the Marine Climatic Atlas format 118 38. The ratio of the sensible and latent heat fluxes as computed from data that i s vector averaged over a period, T to the heat fluxes computed directly from the 3-hourly readings. 121 xi ACKNOWLEDGEMENTS I would l ike to thank Dr. Stephen Pond for suggesting this study and for providing expert guidance and support throughout. Also my thanks to Dr. Miyake and Dr. Burling fcr their helpful comments. The National Research Council of Canada and the Office of Naval Research have provided the computing expenses. Finally, I wish to thank the National Research Council of Canada and the Defense Research Board of Canada who have supported me personally in the course of this study, Chapter 1 INTRODUCTION The atmosphere and the ocean are intr icate ly coupled by a wide variety of physical phenomena. Such interactions take place over a very large range of time and spatial scales and i t is useful to classify the types of interactions according to the characteristic scale size over which each occurs. One can divide the entire time ( or spatial ) range into several general overlapping scale ranges (see Denman,1972 or Fiedler and Panofsky,1970). The smallest i s the. microscale over which turbulent transfers of momentum, heat and water vapour occur in the surface boundary layer. This scale ranges from periods of approximately one second up to about an hour. The mesescale ranges from several minutes to approximately two days. An intermediate scale called the svncjtic scale ranges from periods of a day to several weeks. This scale is associated with movement of cyclonic and anti-cyclonic pressure systems together with their fronts. Beyond the synoptic scale, phenomena of longer periods are said to belong to the seasonal and climatic scales. In this study, the periodicit ies of surface layer meteorological and oceanographic quantities at Ocean Weather Station Papa in the ti.E. Pacific are examined ty means of spectral analysis. This technique computes the contribution to the total variance at various frequencies. The analysis resolves periods ranging from 6 hours to two years. The cross-spectra between pairs of selected quantities were also computed. This analysis allows for the examination of the relationships 2 between pairs of quantities at various frequencies. Where possible, these spectral results are compared with previous results found by other investigators. Much wcrk has been done on the spectra of wind speed at land and coastal weather stations but similar results for an open ocean environment are very limited. The previous work on spectra of the other quantities (such as air pressure, temperature and humidity) i s even less extensive at both land and sea stations. The interactions between the atmosphere and the sea in mid-latitudes are known tc vary markedly with seasons. The winds are generally l ighter in summer than in winter, indicating that less momentum i s transported to the sea. Computations by Tabata(1965) of the total heat transports to the atmosphere at Ocean Station 'Papa' show that this varies frcm about 30 cal/cm2-day during late spring to 150 cal/cm2-day in the winter. In order to study such seasonal variations, spectra fcr each season averaged over the ten years of available data were computed. These spectra reveal changes in both the level of fluctuations and the frequencies of identifiable spectral features with the time of year. A recent development in spectral analysis has been the use of co-ordinate invariant rotary auto- and cross-spectra (Mooers,1973). The rotary auto-spectrum is computed from the components of a vector quantity. This analysis resolves the spectrum into separate contributions to the variance from the vectors rotating either in the clockwise or anti-clockwise directions. in a similar fashion, the rotary cross-spectrum i s computed to determine coherence and phase values between a 3 vector time series and a time series of another quantity (either scalar or vector). Transfers of momentum, sensible heat and water vapour take place in the turbulent boundary layers of the ocean and the atmosphere. Direct measurements of such transfers require equipment which is capable of resolving micrcscale guantities and is complicated and expensive. Therefore, the time and spatial distribution of direct measurements is and l ikely wil l remain very l imited. Attempts have been made to parameterize the fluxes of momentum, sensible heat and water vapour in terms of variables averaged over a period of an hour or so, that are more generally ->• available. The momentum flux (T ) can be written as (Boll,1965) . x =pcD|0|lT (1) where P is the a ir density, 0 i s the mean wind velocity over a period of about an hour measured at some reference height, and Gp i s the non-dimensional drag coefficient. Determinations of the wind stress or momentum flux with fa i r ly direct estimates, show that Cp=(1.3 to 1.5)x10 - 3 on average with a considerable amount of scatter and an uncertainty of the mean of 20 to 30 % (Pond et. a l . , 1974; Stewart, 1974). This coefficient may be a weak function of wind speed but as yet v ir tual ly no direct estimates have been made for winds greater than 15 m/sec so this dependence remains uncertain. Similar non-dimensional bulk transfer coefficients, C^ , and Cq for sensible heat (Hg) and latent heat (fi^ ) , respectively have been defined (Roll,1965): Hs=PCpCTuAT (2) H L . f L C q U A g ( 3 ) where U is the mean wind speed over an hour (this is equal to -> |U| within 2 to 3$), Cp is the specific heat c-f a i r at constant pressure, AT is the temperature difference between the sea surface and a reference height, L is the latent heat per unit mass and Ag is the absolute humidity difference between the sea surface and a reference height. Direct estimates cf Cj, and C„ are rather l imited, but those that are available indicate that both values are around 1.5 x 10 - 3 with a considerable amount of scatter (Pond et. a l . , 1974). Using equations (1), (2), and (3), values which are representative of fluxes cf momentum (I-|tt), sensible heat (UAT) and latent heat (U&q) were subjected to spectral analysis. Parameterizing the turbulent fluxes in terms of mean quantities measured over periods of an hour s t i l l leaves much to be desired when examining the large scale spatial distribution of these fluxes. This deficiency i s due to the very limited ava i labi l i ty of measurements of these mean quantities over the world's oceans. The only regular source of this kind of information comes from the ocean weatherships which are necessarily few and far between. In practice, then, one is forced to rely on data from two sources: Climatic atlases such as those published by the U. S. Navy Cceanographic Office and surface weather charts. The climatic atlases are based on meteorological measurements collected over many years from weatherships and ships-of-opportunity. The values obtained are compiled into tables for each month summarizing a l l observations of each quantity for various sections cf the ocean surface. As 5 an example, the compiled wind data is displayed in the form of wind roses (which are described in Chapter 6). Meteorological weather maps issued by weather offices display the mean pressure f ield and reported surface observations for various periods. From the pressure distr ibution, the geostrcphic wind can be computed and then extrapolated to the surface. For both of these data sources, the o r g a n i 2 a t i c n of the data necessitates a considerable amount of smoothing. When the parameterization formulas are applied to this smoothed data, the resulting fluxes wil l differ from those computed from the direct measurements of mean quantities. The extent of the differences are examined by appropriate smoothing of the 3-hourly measurements at Ocean Weather Station 'Papa' to make them more like data that are commonly available. Using these smoothed data, the fluxes are computed by means of the bulk parameterizations and compared with the fluxes computed directly from the unsmoothed data. One can then 'correct 1 the parameterization coefficients to get better estimates of the fluxes from the more readily available smoothed data. 6 Chapter 2 DATA COIIECTICN 2_.J Collsction Procedures The data used in this study were collected by the Canadian Meteorological Service(now the Atmospheric Environment Service) at Ocean Weather Station 'Papa' located at longitude 145W and latitude 50N approximately 900 miles west cf Vancouver Island. The station was established in 1950 as one of a worldwide network of weatherships manned by various countries. The measurement program includes upper air soundings and routine surface meteorological readings. Since 1952, the Pacific Oceanographic Group (now Ocean and Aquatic Affairs, Pacific fiegion) has been making oceanographic measurements at Station •Papa' as well. The data used in this study are from the years 1958 to 1967 inclusive. The station is manned alternately by two ships which each spend 42 days on station. During the period over which the data were collected, the two ships were the CCGS Stonetown and the CCGS St, Catherines. While on station, the ships are normally underway. They are considered to be 'on stat ion' i f they remain inside a ten mile square centered on the station's location. The data were obtained from the Atmospheric Environment Service on d ig i t a l magnetic tape in the international Meteorological format (80 column card images). These data, after some sorting and interpretation were transferred to another tape in a more suitable form for data processing. A description of the procedure used in writing the second data 7 tape and time series plots of selected quantities is found in Hertzman, Miyake and Pcnd(1974). The quantities taken from the data tape for use in this study (together with their original units) are wind speed, U, (in knots) , wind direction, 9, (compass degrees indicating the direction from which the wind blows), air pressure, P, (in mil l ibars ) , air temperature, ^ , (in ° C ) , wet-bulb temperature, , (in °C) , and sea temperature, T s , (in °C) , a l l being measured at three hourly intervals. The wind is measured from one of three anemometers at 22 m above sea level . The reading, taken from the anemometer with the best exposure, is a ten minute mean. The air pressure is measured with an aneroid barometer and corrected for height and temperature. The air and wet bulb temperature are measured from a ventilated shelter at a height of 17 m above sea leve l . The sea temperature is determined from a surface water sample drawn with a bucket. 2_j_2 Missing And Erroneous Data The data record is very nearly complete. Cf the 175,296 possible samples (for 6 quantities recorded every 3 hours for ten years) only 1427, or 0.82% of the tota l , are missing or obviously incorrect. The worst case in the analysis that follows is for the seasonal spectra of the ten winters. Here 1.5% of the values used are missing or incorrect. Of these 1427 values, 1404 are , a result of the ship leaving i t s station and thus missing readings. The remaining 23 are apparently erroneous values. Examples of such errors are sea temperatures that suddenly plunge to 0.0 °C, wet-bulb temperatures that exceed the a ir temperature by 0.5 C° or more and wind directions 8 that are greater than 3 6 0 ° . A complete l i s t i n g of the missing and erroneous data is given in Appendix I. In addition to the missing or incorrect data values discussed above, examination of the sea temperature time series plots revealed regular intervals of increased diurnal variations for the f i r s t five years of the data. Because the period of the increased act ivi ty is very nearly equal tc the time that one ship is on station, i t i s thought that this effect i s due to observers on one of the weatherships inadvertantly leaving the surface water sample bucket on deck for some time before taking the temperature. A special correction for the spectra cf sea surface temperature wil l be discussed later. In the time series subjected tc spectral analysis, the missing and erroneous data values were replaced. The replacement values were simply determined by means cf linear interpolation between the last correct value tefore the incorrect data and the f i r s t correct value following the incorrect data. This correction procedure wi l l have l i t t l e effect on the spectral contributions cf periods longer than the period of replaced data but wi l l reduce contributions at periods less than that of the replaced data. However, since the data replaced is a very small fraction of the total data, this effect is expected to be negligible. 9 2.JL Derived Quantities From the basic quantities several other surface quantities were derived and used in the analysis. The east-west and north-south components of the wind were computed taking sinds directed to the east (westerly winds) and winds directed to the north (southerly winds) as being positive. The temperature difference between the sea and the air was computed taking AT=Tg-Ta so that positive values of AT should correspond to upward heat fluxes. The absolute humidity (q&) (with units of gm/m3) was calculated from the values of wet-bulb temperature (T ), air temperature (Ta) and air pressure (P). The vapour pressure of water (e) is given by €=^-[ 0.00066 (o C)-i ]P (T a-Tw) (4) where e w i s the saturation vapour pressure at T^  (CRC Handbook of Physics and Chemistry, 51st Edit ion, p. E-39). The absolute humidity of a saturated atmosphere (g) depends cnly cn the absolute temperature to a very good approximation: q=Ci exp (-C2/T) (5) where 0^6.4038 x 10s and C2=-5107.4 are determined by a least squares f i t to tabulated values given in the CBC Handbook of Physics and Chemistry. Applying the equation of state of an ideal gas, (g a=e/(RT a), where R i s the gas constant) to equation (4) : where the temperatures are in absolute degrees, pressure i s in millibars and the humidity i s in gm/m3. The atmosphere at the sea surface i s taken to be saturated sc that eguaticn (5) may be applied for the absolute humidity at the sea surface (q s ) : 10 g_=0.98Ciexp(-C2/T s) (7) where the factor of 0.98 accounts for the lowering cf vapour pressure due to the presence of sea salts at the surface. Equations (6) and (7) are used to compute the absolute humidity difference, Ag=q -q , so that positive values of A q correspond S ct to an upward water vapour flux. 11 Chapter 3 SPECTBAL ANALYSIS J i l - - - - - - - - - - - -To study the cycles and periodicit ies of a time varying quantity, some means of separating the fluctuations cf various frequencies must be employed. One can do this by elimination of unwanted frequencies, either visually or by using analog or d ig i ta l f i l ter ing techniques. Another method is to make a least squares f i t between the original time series signal and an osci l lat ing signal of some well known freguency. Such methods are useful for determining the strength cf a well known periodicity but are inadequate to provide an overview of the periodicit ies that are present. Spectral analysis, rather than eliminating frequencies, resolves the signal into i t s frequency components. A time series consisting of N equally spaced samples X(j) , j = 0 , 1 , 2 , . , . N - 1 can be represented by a frequency series A(k) by means of the discrete Fourier transform: - N -Jl A(k)= IX (j) exp (2rr i jk/N) k=0, 1 ,2 , . . .N-1 (8) j=9 where i=/= _1 (Jenkins and Watts, 1968). This expression can be written as A(k)=N(a(k) + i » b ( k ) ) where a (k) and fc (k) are the Fourier cosine and sine coefficients: a (k)=[ NlX(j)cos (2tt jk/N) ]/N (9) j=0 N-1 t(k)=[ EX (j)sin fa jk/N) ]/N (10) These values are computed using the fast Fourier transform (FFT) 12 algorithm developed by Cooley and Tukey(1965). In this study, a version of the FFT algorithm devised by Singleton (1968) is used. The values of a(k) and b(k) are defined over frequencies ranging from the fundamental freguency of the record Af= (1/N£t) to the flyquist freguency %=(1/2At) where At is the sampling period. A sample power spectrum has the property that _ %+Af/2 XMj) - (X ( j ) ) 2 = / <$> (f)df (11) Af/2 X X One can show (Jenkins and Watts,1968) that for a discrete time series of f in i te length (f ) x x ( f)=[a2 ( f ) +b*(f)]/2Af (12) Thus from a time series of N equally spaced points, N/2 discrete values (called harmonics) of ^ (f) wi l l be computed. Physically, each value of ^;X(f) represents the contribution to the variance per unit frequency over the frequency range from mAf-Af/2 to mAf+Af/2, for f=mAf. It has been tradit ional in discussing spectral results to term the power spectral values •energy densities' and the contribution to the variance (<J>df), as the spectral 'energy'. 3^ 2 Cross-spectra Spectral analysis can be applied to simultaneous time series of two guantities to analyse their relationship at various frequencies. For two guantities X (j), Y ( j ) » j=0,1,2, . . . . .N-1, one has a co-spectrum such that _ __ fN+Af/2 XY - XY = / * v v (f) df (13) Af/2 XJ where <J> i s computed from the Fourier coefficients a^Jf) , b (f), and a v(f) , b v(f) , of the time series X(t), Y (t) 13 respectively: <j> = (a a + b b ) /2&f . (14) xy ,x y x y ' ' u Similar i ly , the quadrature spectrum has the property that ft - XY = / Q (f) df (15) A f xy where the indicates the Y time series is shifted 90 degrees in phase at a l l freguencies. In terms of the Fourier coefficients, Q = (a b - a b )/ (2&f) (16) xy x y y x A study of the relationship between the two signals at various freguencies is made easier when some non-dimensional quantities are examined. The correlation, p (f) p(f)= A 1^2 (17) v xx yyJ is the normalized cospectrum between the two signals. The coherence, Y x y , i s defined as 1/2 Yk. = I * * y + V .• (18) X ^ » ^ xx* ^ yy / • This quantity ranges from 0 to 1 where a large value indicates that similar osci l lat ions were occuring in the two signals. (Y 2 represents the fraction of the.power spectrum of one signal xy that i s related to or predictive from the power spectrum cf the other s ignal) . In the discussion of the coherence estimates, some cr i t e r i a must be used to decide whether the two quantities being studied are s ignif icantly coherent. Such a c r i t e r i a can be found using the probability distribution for the coherence estimates as given by Groves and Hannan (1968) . The cumulative probability distribution of the coherence squared estimate Y ^ 2 for two randomly related signals ( i .e . a true coherence of 0) is 14 P (Y2 )=1 - {1-Y 2 f _ l (19) whare M i s the number of harmonics used in computing the estimate. That value of coherence at which there i s a 95% probability that a truly random coherence value w i l l f a l l below is, from (19) : 1 Y = [ 1- (O.OSV^1 ] (20) This w i l l be called the 95% significance level and i s plotted on tha coherence graphs. This level decreases with increasing freguency, as a result of the band averaging scheme employed which increases the amount of smoothing of spectral estimates with increasing freguency. For the purposes of our discussion of the coherence results, coherence estimates that f a l l below the 80% significance level are called poor, estimates that f a l l between the 80% and 95% significance levels are called f a i r , estimates between the 95% and 99% significance levels are called good and estimates above the 99% significance level are called very good. The phase F x y between the two signals at particular freguencies can be estimated by means of the formula: F x y=arctan(-Q x y /d> x y). (21) This definition is chosen so that the phase i s positive when signal Y leads signal X and negative for the opposite case. -3.3 Rotary Spectra The spectral theory described above applies to two scalar signals. This analysis can be generalized to apply to a vector signal and a scalar signal (or indeed another vector signal although this generalization has not been reguired in this investigation) following the method described by Fil lsbury {1972) 15 and Wooers (1973) . This technique, kncwn as rctary spectral analysis, offers two advantages over scalar spectral analysis. It resolves contributions to the variance and ccvariance from two oppositely rotating vectors at frequencies ranging from the fundamental to the Nyquist frequency. The frequencies range from -f^ through -Af/2 and from Af/2 to f^  ; the positive and negative freguencies being associated with anti-clcckwise and clockwise rotations, respectively. In addition, the derived spectral quantities are independent of the coordinate system. ->• Let the vector time series P be represented by the time series of i t s two components, X (j) and Y(j) , j=1,2...N. The scalar time series i s S(j) , j=1,2...K. For each of these time series, the fast Fourier transform is used tc compute their res-pective Fourier coefficients. These Fourier coefficients are then used to compute the power spectra of each time series ^ , and | s , as well as the co-spectral and guad-spectra 1 values cb d) , Q , Q , Q by means equations (14) and (16). The a^s;.- .^ys xs ys xy 1 * computational formula for the rotary (vector) pcwer spectrum i s < M f ) = ( <$> + (}> )/2 + C , f>0 (22) p xx yy ' ' xy < M f ) = ( <J> + (J) )/2 - Q , f<0 (23) p xx yy " -.xy where the factor cf 2 in the denominator results from computing a two-sided rather the ordinary one-sided spectra. The rotary power spectrum has the property that _F<t> (f )df=X2+f2- (X)2-(Y) 2 (24) f N This integral represents the total kinetic energy per unit mass -y i f P i s a velocity as i s the case here. The coherence sguared i s computed as 16 X z { f ) = (^xs+Qys)3- +W ys-Qxs) f < 0 (26) and the phase between the two signals i s given by F^c (f) = arctanr "^y q 1, £>0 (27) ps u v x s -yy S F* (f)=arctanl"-'"<i>ya+Qyfi 1, f<0 (28) P s L *xs+Qys J Both the coherence and phase values defined above, are co-or-dinate independent. Jiii Spectral Display Methods A useful means of displaying the information in the rotary coherence sguared i s to use the transfer spectrum. The transfer spectrum is defined as the product of the coherence squared and the rotary power spectrum. These values indicate the amount of energy in one signal which is coherent with that of the other signal for each frequency band. Such a technique avoids misin-terpreting cases of high coherence sguared values at freguencies where there i s very l i t t l e energy in either signal. Due to the large number of data points used for calculating the spectral values, the freguency range is correspondingly large. In some of the spectra to be discussed, the frequency range i s more than three decades. This wide range makes neces-sary the use of a logarithmic scale for frequency in the spec-t ra l plots. in order to display the relative contributions to total variance at different frequencies, the ordinate of the spectral plots is f 0(f) using the relation / f<J> (f)d(lcg f ) = f (K f ) /2 .303 ) df ; (29) 17 The use of graphs with f<J>(f) plotted against log f ensures that equal areas under the plotted curve contribute equal amounts tc the variance of the quantities being analysed. 3_.5 Spectra 1 Smoothing The random error of a spectral estimate computed from the Fourier coefficients at a single frequency ( i . e . with two degrees of freedom) ••is as great as the quantity being estimated" (Bendat and Piersol , 1971). In order tc reduce this error, some form of smoothing must be done. Smoothing can be done over spectral estimates made from independent records (ensemble smoothing) or smoothing can be done by averaging spectral estimates over a range of frequencies from within a single record (freguency smoothing). In this study, both means of smoothing are used following a scheme described by Garrett(1970). Smoothing by frequency i s done over a varying number of estimates in such a way that each smoothed estimate i s nearly equally spaced on the logarithmic plots. For example, the f i r s t four estimates are computed from single frequency points (no frequency smoothing), the next estimate is averaged from 2 points, then 3 points and so on up tc several hundred points per estimate. The number of points used for smoothing is chosen so that about 8 smoothed spectral estimates are produced for each decade of frequencies. While this band averaging scheme is well suited tc broad band (continuum) processes, i t tends to obscure narrow band (line) processes at higher frequencies. For example, a natural forcing frequency at the ocean surface i s the diurnal frequency 18 (period of one day) due to the daily cycle of solar radiation. The band containing the diurnal frequency in the spectral plots, is computed from 176 harmonics, just one of which is the diurnal frequency. Thus a significant peak may occur at cne day, but its contribution to the band may not be large enough to raise the spectral level of the band significantly above the others. To avoid missing significant line spectral peaks, single power spectral values were examined at natural frequencies at which line spectral responses might occur: the diurnal, semi-diurnal (12 hours) and their overtones (8 hours, 6 hours) and the iner-t i a l frequency (18 hours at 50 N). The total time series record was subdivided into N blocks and the frequency smoothed spectral estimates were computed for each block. These estimates were then ensembled averaged in order to provide further smoothing and to provide an emperical estimate of the s t a t i s t i c a l var i ab i l i ty . The mean, "| and the standard deviation between the estimates cr are computed for each frequency band. The spectral graphs that are presented plot fg<!> against log(f) , where f g i s the geometric mean of the endpoint frequencies of the particular frequency band. The geometric mean is used rather than the arithmetic mean because then fg.Alnif i s more nearly equal to <J>.-nA;f. The error bars shewn on the graphs are the approximate 95% confidence intervals of the mean, computed as +2a/ {\M- 1 ") . 19 3_.6 Two-y.early. Spectra The basic spectra used in this study, tc provide a survey of the periodicit ies present in each quantity, were computed from blocks of 5832 samples. Each block then covers a total period of just under two years (an ordinary two year period would contain 5840 3-hourly measurements while a two year period including one leap year contains 5848 such measurements), The number of samples, 5832, was chosen to use the fast Eourier transform algorithm ef f ic ient ly . The computational time re-quired by the fast Fourier transform increases rapidly with the size of the largest prime factor of the number cf samples. 5832 was chosen since i t s largest prime factor i s only 3 and i t comes very close to providing block lengths cf two years. Because the block length is not exactly two years, the strong annual spec-tra l peak found in many of the quantities spectra wil l have some energy 'leakage* tc adjacent freguencies. A simple calculation shows that for the rectangular window used in this study, the leakage to side lobes is extremely small, being less than 0.01% of the annual energy. The spectra produced resolve periods ran-ging from two years to 6 hours. The confidence intervals for each averaged spectral estimate are based on 5 individual spec-tra l estimates. While s t r i c t l y speaking, small sample statis-t ics should be used for computing the confidence intervals, i t i s fe l t that Gaussian s ta t i s t ics provide representative values of the scatter about the mean. 20 2JL1 Seasonal Spectra A special set of spectra of the various quantities were computed for blocks of 728 samples or a period of 91 days. Each block i s one 'season'. Because the available data began on Jan. 1, 1958 and ended on Dec. 31, 1967, the 'seasons' analysed were shifted from the natural seasons in order to use as much of the data as possible. For example, the f i r s t day of winter for our purposes was taken to be Jan. 1 rather than Tec. 21. In addition, the season size of 728 samples, chosen for eff icient use of the FFT algorithm, makes up a year which is 8 samples less than a complete non-leap year and 16 samples less than a complete leap year. This choice also necessitates slight adjus-tments. In non-leap years, the f i r s t four and last four records are not used. In a leap year, the f i r s t eight and last eight data records are not used. The spectral results for, each season were averaged over the ten years so that an average spectrum and its approximate 95% confidence intervals for each of the four seasons was produced. Before the seasonal spectra were computed, the data was processed by the computer to effectively high pass f i l t e r i t . This f i l t e r ing was done to remove the annual cycle from the sig-nals. Otherwise, a large trend would be present in the time series making up the seasons which could produce large, f i c t i -tious spectral values at the low frequencies. The high pass f i l t e r ing was achieved by Fourier transforming each individual 'year' (2916 samples), zeroing the f i r s t three harmonics of the transform values (corresponding to periods of one year, one-half year and one-third year) and then inverse Fourier transforming 21 these values back into a time series, an example of the effect of this procedure is i l lustrated in Figure 1. As discussed pre-viously, sideband leakage from the strong annual peak is pre-sent, but i s very small (less than 0.01%) and the dominant lea-kage would appear in the next two harmonics which are also set to zero. S U R F A C E O B S E R V A T I O N S AT S T A T I O N P A P f l UNFILTERED o c\i' id ID Q - O U J CM c r i n FILTERED o . CD o _ i o F ' H ' R ' H J J ' R ' S Figure 1: An example of the effect of f i l t e r ing to remove the annual variat ion. The graph displays the sea temperature of 1962 before and after f i l t e r i n g . Chapter 4 SPECTRAL RESOLTS i i i l Introduction For each physical quantity, the power spectra are displayed and the important p e r i o d i c i t i e s are described. These spectra are compared to the spectra computed by other investigators. The l i t e r a t u r e contains a sizeable number of spectra of wind speed and a smaller number of spectra of wind components, air pressure and a i r temperature. Spectra of absolute humidity and sea temperature are very rare. When discussing spectral re-s u l t s , i t i s often useful to know the average of the analysed guantity and the cumulative i n t e g r a l of the spectrum. These values are given i n Appendix II for the two-yearly spectra and the seasonal spectra. 4.2.2 wind The most s t r i k i n g feature of the wind speed spectrum (see Figure 2) i s the broad synoptic peak at 3.1 days, a re s u l t of the passage of cyclones, anti-cyclones and their f r o n t a l sys-tems. The peak which includes contributions from a wide range of scales (having i t s half-power points at periods of 10 days and 1.3 days) emphasizes the i r r e g u l a r nature of the passage of synoptic scale scale disturbances. The synoptic peak accounts for most of the t o t a l variance of the wind speed (28.3 m 2/sec 2) for the periods resolved. The wind speed spectrum shows l i t t l e v a r i a t i o n at periods longer than one month with the exception of an important annual cycle. The annual cycle, seen as a peak at one year and a secondary peak at one-half year, due to some d i s -o a i n . CM 3K 3K a . i n H-OJ a. a _j r o ' HIND SPEED f '-4 -3.0 -2.0 LOG10(FREQUENCY) -1.0 0.0 FREO IN CYCLES/OGY 1.0 Figure 2: The two-yearly wind speed spectrum for the period 1958 to 1967. The vert ica l error bars represent approximate 95% confidence intervals of the mean of each spectral estimate. 25 tortion, has a tota l variance of 3.9 m 2/sec 2. This corresponds to an average annual range (2*/2[ variance ] ) of 5.7 m/sec. At the high freguency end of the spectrum, the graph shows a steady decline to periods of about 9 hours and then an i n -crease out to the Nyguist period of 6 hours. This upturn at the smallest periods i s believed due to variance at smaller scales between 6 hours and the 10 minute averaging period being aliased back into the spectrum at lower frequencies. Eecause in our plots, the spectrum is multiplied by freguency, the contribu-tions due to aliasing are more apparent at small periods than at large periods (for a discussion of this effect see Oort and Taylor, 1969) . In order to correct the aliased spectrum, one must assume a frequency distribution of the spectrum at higher freguencies. Because the effect of aliasing appears small, this correction was not fe l t to be necessary. It seems clear from inspection of the graph, that a correction for aliasing would leave the spectrum declining out to the Nyquist period. Such a decline in the spectral levels i s consistent with the existence of a 'spectral gap'; a minimum of spectral levels in the mesos-cale separating spectral peaks in the synoptic scale and micros-cale (Fiedler and Panofsky,1970). Important changes in the wind speed spectra occur between one season and another. Figure 3 shows the wind speed spectra calculated separately, for the four seasons with each season's spectrum being averaged over the ten years. Differences are found in both the level and the period of the synoptic peak. The peak i s largest in the f a l l (ftf>=10.3 m2/sec2) declining through the winter (9.71 m2/sec2) and spring (6.36 m2/sec2) to WIND SPEED 26 r \ i _ o — 1 +--WINTER + O H rvi o o IU to —I as: t— O u a , to o - 1 SPRING •++++ • —1 SUMMER c \ i _ c o H o r -3 FALL i i r -2 -1 0 L0G10(FREQUENCY) Figure 3: Wind speed spectra for each of the seasons a v » r a g * d over the ten years, 1958 to 1967. The vert ica l error tar-s represent approximate 953E confidence intervals cf the mean 27 the lowest level in summer (5.48 m 2/sec 2). The period at which the peak occurs shows a similar variation being smallest in f a l l (2.5 days) increasing through winter and spring and being lar-gest in summer (4.4 days). These results i l lus trate the general seasonal pattern of synoptic disturbances which occur more fre-quently and with greater intensity in the f a l l and winter than in the spring and summer. It i s interesting to note that the largest change in the spectra i s between the adjacent summer and f a l l seasons with more gradual changes taking place over the rest of the year. In the spring and f a l l , there is some evi-dence of act ivity at longer periods (20 to 45 days) tut in both cases the peaks are not s t a t i s t i ca l ly s ignif icant. Figure 2 shows no peak at the diurnal or semi-diurnal periods but a closer examination of single harmonics cf the spe-ctra l values reveals some act iv i ty . The largest energy is found in a semi-diurnal peak with a contribution to the variance of 0.022 m2/sec2 corresponding to an average range of 0.46 m/sec. At the diurnal period a small peak is found but i t is not signi-ficant. A significant peak does appear at a period of one-guar-ter day, the f i r s t overtone of the semi-diurnal period, with a contribution to the variance of 0.016 m 2/sec 2 . No energy is found at periods of one-third of a day or the iner t i a l period. Examination of single harmonics of the seasonal spectra reveal similar results. No peak is found at the diurnal period for any of the seasons while each season does exhibit a semi-diurnal peak. The energy of the semi-diurnal peak, after corre-ction for the spectral background leve l , i s found in Table I. The background correction is made by subtracting the average of 2i TABLE I The energy of single harmonic spectral peaks fcurc at periods cf cne cay, ere-ha If day and c n e - g « a r t e r day. The annual values are computed from the spectra determined ircm data Hecks cf tve years. A ' - 1 indicates that E C peak was found. Cf one day, one-half day and one-guarter day. The annual values are cenpeted •S.p.* is the computed standard deviation of the energy estimates. Quantity Clock-wise u Anti-clock-wise 0 Pericd <aays) 1.0 S.D. 0.5 S. E. 0. 25 <; r 1.0 0.5 S.D. 0. 25 -+ 1.0 0. 5 0. 25 S.D. Energ y Annuall Winter 0.009 + .016 0.022 4.019 0.016 + .004 0.045 + .029 H 0.004 + .002 0.027 + .051 0.018 + .020 0.026 + .043 Spring! Sunirerj F a l l m/sec) 2 0.016 + .029 0.046 + .036 C.C24 + .026 C.CC6 +.010 -f— C.C4S + .063 C.C3 8 +.076 C.C18 +.013 0.C51 +.081 ™l L tha spectral levels of the four adjacent harmonics. In f a l l , the semi-diurnal variation i s the largest with an energy of 0.038 ffiVsec2 (an average range of 0.55 m/sec) while the spring has the lowest energy of 0.016 m 2/sec 2 (an average range of 0,36 m/sec) . Several spectra of wind speed in the surface layer have bean published. Oort and Taylor (1969) presented the wind speed spectrum for Caribou, Maine, a station with a continental c l i -mate. Van der Hoven (1957) has computed the wind speed spectrum at Brookhaven, New York on Long Island. Wind spectra at sta-tions on the Oregon coast are found in Frye et. al,(1972) and Burt et, al.(1974) while Hwang (1970) presents a wind spectrum on the tropical Pacific island of Palmyra. At stations over the open ocean, wind speed spectra have been computed by Eyshev and Ivanov (1969 ) , Millard (197 1) and Dorman (1974). A summary of the results of these investigators together with the important data parameters, i s found in.Table II. When comparing these results, differences in the experiments of the various investigators must be considered. Millard(1971), Burt et. a l . (1974), Frye et. a l . (1972) , Hwang (1970) and Van der Hoven (1957) used data that did not cover a complete year. Thus their spectra i s biased due to the seasonal var iab i l i ty of the wind speed spectra. In addi-t ion, different methods of computing and smoothing were used. However, for comparison of a broad band feature l ike the synop-tic peak these differences are not c r i t i c a l . Furthermore, the number of locations available for comparison i s very limited so that any discussion of regional patterns must be regarded as tentative. •Table I I A summary of the pericd and level (f»<j>) cf the synoptic peak of the wind speed spectra as determined by various investigators. Z is the height cf the anemometer and U is the mean wind speed cf the data analyzed. In cases where these values were net available, a ' - » i s shown. Investigators |Lccat ion I z I o Data Period | Synoptic I I (tn) I m/£ ec | Period j (days) | Level j (m/sec) 2 Van der Hoven{1957) | 4ON 73 W | 108 ! A ug. 1955 To Feb. 1956 I 4 | 5 Oort and Taylor (1969) | 47N 68W | 11 ! " i Jan. 1949 Tc Dec. 1958 I 3.9 1 3 Byshev and Ivanov (1969) |5 3N | 44N 36W 41 W j " j " i Jan. 1 961 tc Dec. 1963 I 6.4 1 5 | 8S | 16S 14« 6« ! - i - i July 1957 tc July 1958 I 12 1 1 Hwang (1970) | 6N 162W I 2 i - ! Mar. 1 967 to May 1967 I 5.9 i 1. 1 Millard (1971) |30N 70W I - I 5 .7 | Apr. 1967 tc June 1967 I 4 I 6 Frye et. a l . (1972) | 45N 125W | 20 ! July 1970 Tc Aug. 1970 I 2 I 5 I 3.5 I 1.5 Burt et. a l . (1974) | 45N 125W | 10 | 11. 8 I Aug t 1970 | 3.0 I 7.5 Dorman(1974) | 30N 140w | 25 I 6. 2 I Jan. 1951 tc Dec. 1970 I 8 | 2.9 This Study | 50N 145W | 22 | 10. 1 I Jan. 1958 tc Dec. 1967 | 3 I 8.2 31 The p e r i o d of the s y n o p t i c peaks range from atout 12 days at the Ascension (8S 14W) and S t . Helena (16S 6w) I s l a n d s to the period of 3 days found a t S t a t i o n 'Papa* (50N 145W) i n t h i s study and o f f the Oregon coast (45N 125W) reported by Burt at. a l . (1974). An i n t e r m e d i a t e value of 8 days i s r e p o r t e d by Dorman (1974) at S t a t i o n N (30N 140W) l o c a t e d near the northern l i m i t of the Trade Wind b e l t i n the P a c i f i c Ocean. These r e -s u l t s suggest, as might be expected, a g e n e r a l p a t t e r n of i n -c r e a s i n g frequency of s y n o p t i c a c t i v i t y with i n c r e a s i n g l a t i -tude . A comparison of the v a r i o u s s p e c t r a a l s o r e v e a l large zonal v a r i a t i o n s i n the p e r i o d . S t a t i o n 'Papa'(50N 145W) and the Oregon coast (45N 125W) both have a p e r i c d of abcut 3 days while at C a r i b o u , Maine (47N 68W) , Cort and T a y l o r r e p o r t a peak p e r i c d of 3.9 days. Van der Hoven (1957) f i n d s a peak period of appro-ximately 4 days a t Brookhaven, New York(41N 73W) . Further t o the east, Byshev and Ivanov(1969) found a p e r i c d of 6.4 days f o r the s y n o p t i c peaks at S t a t i o n C (53N 36W) and S t a t i o n D (44N 41W) . A s i m i l a r v a r i a t i o n i s seen at a l a t i t u d e of about 30N, with M i l l a r d (1971) r e p o r t i n g a p e r i c d of 4 days at 30N 70W compared to a period of 8 days r e p o r t e d by Dorman(1974) at 30N 140W. (In f a c t , t h i s comparison understates the d i f f e r e n c e , s i n c e M i l l a r d ' s r e s u l t s are f o r A p r i l and May, when the peak p e r i o d i s probably higher than the y e a r l y v a l u e ) . These zonal v a r i a t i o n s i n d i c a t e the importance of the l o c a l environment i n determining time v a r i a t i o n s of the s u r f a c e boundary l a y e r . . The i n t e n s i t y of the s y n o p t i c peak e x h i b i t s l a r g e r e g i o n a l v a r i a t i o n s . J u s t as the p e r i c d of the s y n o p t i c peak decreased 32 with increasing latitude, the intensity shows a corresponding increase. At low latitudes the peak level is low (f<}>~1.0 m2/sec2.) at the Ascension and St. Helena Islands, (Byshev and Ivanov, 1969) and i t increases at higher latitudes (f<j>=8.2 m2/sec2 at Station 'Papa'). Pronounced zonal variations exist as well with the f <i> of Station 'Papa* compared against fcj)=3.0 m 2/sec 2 at Caribou, Maine (Oort and Taylor, 1969) and f<J>=5 m2/sec2 at Stations C and D (Byshev and Ivanov, 1969). The zonal variation of both synoptic peak pericd and intensity appear to be related to more localized effects. One such effect could be the presence of topographic features of synoptic scale size in the v ic in i ty of the observation station. For example, at land stations the presence of surface features such as moun-tain ranges, may reduce the intensity and frequency of synoptic scale disturbances, in contrast to the open ocean with i t s very long fetches. Another factor may be the position of the station in relation to anomalous meteorological regions such as areas associated with freguent cyclogenesis or frequent blocking pat-terns. The act ivity found at the diurnal and semi-diurnal freguen-cies differ considerably between ocean stations and land and coastal stations. At 'Papa' there i s no significant diurnal peak and the semi-diurnal peak i s very small. Millard (1971) found a similar result over the open Atlantic ocean while Dorman's (1974) results show very small diurnal and semi-diurnal peaks, with the diurnal peak being the larger of the two. In contrast, Oort and Taylor's (1969) spectra at Caribou and five other land stations, show a large diurnal wind speed variation 33 and a very much smaller semi-diurnal peak. At coastal stations, a large diurnal peak and smaller semi-diurnal peak is found. Over land, Blackadar (1959) has explained the diurnal varia-b i l i ty of the wind as a result of the diurnal change in s t a b i l i -ty. During the daylight hours, as the surface layer is heated i t becomes less stable, allowing more convective mixing with the layer above. The two layers become more strongly coupled with a resulting increase in wind speed in the surface layer. At night cooling of the surface layer due to radiative losses, makes i t more stable and reduces i t s coupling with the layer above, de-creasing the surface layer wind speed. Frye et. a l . (1972) argue that along a coast, the diurnal wind variation is due to the land-sea temperature difference producing a sea breeze during the day and a weaker land breeze at night. Over the open ocean, neither of these mechanisms are very powerful and thus the diur-nal wind variation i s small. The semi-diurnal peak, though small, appears to be s i g n i f i -cant indicating that at least sometimes the wind speed has two maxima and minima each day. One possible explanation i s that this periodic motion i s associated with the well known semi-diurnal variation of a ir pressure (Butler, 1962) which is found in the spectral analysis of air pressure. Figure 4 shows the rotary wind spectrum. The synoptic peak dominates both the anti-clockwise and clockwise spectra with each having the peak occuring at a period of 3 days. The levels of the peaks d i f fer : the clockwise peak has f$=18.4 (m/sec)2 compared to f <p= 13 .5 (m/sec) 2 for the anti-clockwise peak. This result can be explained by the general pattern of synoptic wea-ROTARY WIND CLOCKWISE o . as -< r—\ o UJ IT) Q_ to 5K flNTI-CLOCKyiSE - 4 I t T -1 -1 -2 -3 LOG 10(FREQUENCY* -4 -3 FREQ IN CYCLES/DAY F i g u r e 4: The r o t a r y auto-spectrum of the wind computed from f i v e two-yearly b l o c k s c o v e r i n g the p e r i c d 1958 to 1967. The v e r t i c a l e r r o r bars represent approximate 95$ confidence i n t e r v a l s of the mean, 35 ther system movements in the N E. Pacif ic . The mcst common storm track is to the north of Station 'Papa' over the Gulf of Alaska (see U. S Navy, Marine Climatic Atlases). Eastward moving weather systems, whether cyclonic or anti-cyclonic, when passing to the north of the observation station, cause the ob-served wind to rotate in a clockwise manner. Consider, for example, the passage of an eastward moving cyclonic system to the north of the observation station (the most common situation at Station 'Papa'). As i t passes by, this would cause the ob-served wind to change from southwesterly to westerly to northwe-sterly in direction. That i s , the wind rotates in a clockwise sense. Weather systems moving to the south of Station 'Papa', make greater contributions to the anti-clockwise spectrum. Of course, the situation is complicated by such events as the pas-sage of storm fronts with their abrupt changes in wind direc-tion. Nevertheless, the computed rotary spectrum appears to differentiate between the passage of weather systems to the north and south of the observation station and is consistent with the known pattern of pressure system movements. A comparison of the wind speed spectrum (figure 2) with the rotary wind spectrum (figure 4) i s revealing. In both spectra, the dominant synoptic peak is found to occur at the same period. However, the important annual peak found in the wind speed spec-trum i s much less pronounced in the rotary spectrum, with no such peak for clockwise rotations and a relatively small peak for anti-clockwise rotations. This difference is due to the long period variation of the wind direction. Wind roses com-piled from the data show that the wind tends to be from the 36 south in winter and generally from the west in summer. The variation of the wind direction over a period of a year i s not a uniform rotation but rather an irregular shift . This type of variation in wind direction probably causes the spectral energy of the annual wind speed to be found at shorter periods in the rotary wind spectrum. Indeed, the rotary spectrum shows a less regular rise from a pericd of one year to the synoptic peak than does the wind speed spectrum. The seasonal rotary wind spectra are displayed in figure 5. The synoptic peak for both the clockwise and anti-clcckwise spe-ctra follows the same pattern of the wind speed spectra: higher levels and a shorter period of the peak in f a l l and winter in comparison with spring and summer. The relative contributions of the clockwise and anti-clockwise synoptic peaks does not vary appreciably with season. An examination of single harmonic spectral values indicates no significant diurnal peak but a significant semi-diurnal peak (see Table I). The semi-diurnal peak is found only in the cloc-kwise part of the rotary spectrum, with an energy of 0.045 (m/sec)2. This result agrees with the findings of Kuhlbrodt and Reger in the Trade Wind zone (discussed by Boll,1965) who re-ported a semi-diurnal wind variation from the mean wind which rotated in a clockwise sense during the course of the day. The clockwise semi-diurnal peak i s reduced in size in winter and remains relat ively constant through the remainder of the year. No significant peak was found in any of the rotary wind spectra at a period of one-third of a day or at the iner t i a l freguency. A small peak was found in the the anti-clockwise spectra at one-ROTARY WIND CLOCKWISE HNTI-CLOCKWJSE 37 WINTER [ I i I i 1 r 1 0 -3 -2 -3 -2 - 1 0 LOG 10(FREQUENCY") FREQ IN CYCLES/DRY Figure 5: The seasonal rotary auto-spectra of the wind average over the ten years, 1958 to 1967. The vert ica l error bar represent approximate 95* confidence intervals of the mean. 38 quarter of a day. Rotary wind spectra at other locations are uncommon, Dorman(1974) has computed rotary wind spectra for Station N (30H 140W) in the Pacif ic , a location even further away frcm the main storm track. His results show good qualitative agreement with those of this study. The spectral levels are lower due tc the smaller amount of synoptic act iv i ty in that area. The clockwise rotational spectral peak i s larger than the anti-clcckwise peak as in this study, while the difference in the levels of the two spectra i s even more pronounced. 4_j_3 Air Pressure The spectrum of atmospheric pressure (see figure 6) l ike the wind speed spectrum, i s dominated by a broad, somewhat i r re-gular peak at intermediate periods. However, this peak ranges over longer periods than that of the wind speed, having i t s half-power points at periods of 70 days and 3 days. The highest spectral level is found at 17 days where f4> = 55.8 (mbar) 2 . The spectrum also reveals a large annual periodicity in the air pressure by the presence of a peak at one year and a smaller peak at a period of one-half year. The annual peak has a total variance of 30.8 (mbar)2 corresponding to an annual range cf 16 mbar (about a mean of 1012 mbar). The spectrum at the shortest periods i s notable for i t s very low levels. There i s no evi-dence of any aliasing at these periods. Important changes take place in the pressure spectrum bet-ween one season and another. The seasonal pressure spectra (see Figure 7) show pronounced changes in the spectral levels with large values in f a l l and winter, intermediate values in spring RIR PRESSURE c CO o CD CM GQ o rr •• I— CM CJ> UJ Q_ CO O . O CM + '-4.0 -3.0 -2.0 LOG10(FREQUENCY) -1.0 0.0 FREQ IN CYCLES/DAY i.O F i g u r e 6: The power spectrum of a i r pressure computed from f i v e two-yearly data b l o c k s c o v e r i n g the p e r i o d , 1953 to 1967. The v e r t i c a l e r r o r bars r e p r e s e n t approximate 95% confidence i n t e r v a l s of the mean. 4 0 AIR PRESSURE o to o . o WINTER ru O O ' ID O —I SPRING az tQ cc I— C J Q_ i n 5K to o . o o o ' ID SUMMER FfiLL + -f-o r -3.0 -2.0 -1.0 0.0 L0G10(FREQUENCY) 1.0 Figure 7: The seas o n a l power s p e c t r a of a i r p r e s s u r e ; each spectrum i s averaged over the ten years, 1958 to 1967. The v e r t i c a l e r r o r bars r e p r e s e n t approximate 95% c o n f i d e n c e i n t e r v a l s of the mean. 41 and small values in summer. The seasonal variations of the period of the peaks are more complicated. In f a l l , a single peak i s found at 17 days. This peak is also present in winter together with a large contribution from periods around 45 days. In spring the 17 day peak is accompanied by a peak at 9.2 days while the longer pericd variations are markedly reduced. In summer, while a l l spectral levels are greatly reduced, the rela-tive contribution from longer periods (say periods greater than 20 days) i s larger than in spring. An examination of the single harmonic spectral values of the air pressure reveals a sharp semi-diurnal peak with a variance of 0.037 (mbar) 2 corresponding to an average range of 0.55 mbar. , Smaller variations (see Table III) are found at periods of one day and one-third of a day. These variations are larger in f a l l and winter at the one-half and one-third of a day periods but the diurnal variations are larger in spring and sum-mer . The air pressure spectral results are generally consistent with the results of other investigators. Boden(1965) has com-puted the annual and semi-annual pressure osci l lat ions for sta-tions on the Pacific coast of North America. The annual varia-tion found at Station 'Papa* agrees well with the annual varia-tion found at Prince Rupert, B.C. and Alaskan coastal stations but i t i s considerably larger than that found at Victor ia , B.C. and Washington and Oregon stations. Air pressure spectra covering the synoptic and seasonal scales have been computed by Dorman (1974) for Ocean Station N (30N 140W) and by Byshev and Ivanov(1969) for Ocean Stations C and D located at 53N 36W and 42 TABLE III The energy of single harmonic spectral peaks of a i r pressure, air temperature, absolute humidity and sea surface temperature found at periods of one day, one-half day and one-third day. 1 T Quantity (units) h— y +  Air T (CO) 2 Air P (mbar) 2 h Air q (gm/m3) 2 V— +-Sea T (CO) 2 Period 1.0 10.0118 S. D. |+.0086 0.5 |0.037 S. D. j+.0035 0.333 |0.0040 s . p. |+.0008 1.0 |0.0446 s. p. |+.0240 0. 5 |0.0047 s . p . I +.0012 + 1.0 10.0014 S. D. |+.0011 0 .5 1 0 . 0 0 0 1 S.D. | + . 0 0 0 1 1.0 j m 10.0020 S. D. I+.0011 0. 5 I0.0002 S. D. 1+.0002 Energy T T T 1 Annual' Sinter| Spring! Summer! F a l l 0.044 + .018 0.0064 +.0068 0.0281 +.0290 0.0043 +.0017 ' 0.0006 +.0008 0.0003 +.0002 0.034 + .022 0.035 + .008 |0.019 I+.017 I I0.030 1+.007 0.0014 |0.0017 J 0.0070 +.0013 I+.0012 I+.0052 0.0862 |0.0692 |0.0169 +.0378 I+.0245 I+.Q244 0.0040 |0.0068 |0.0055 +.0020 I+.0035 I+.0029 + -\ + ^ 0.0027 |0.0016 |0.0003 +.0029 I+.Q023 I+.0013 I 0.0045 J 0.0027 +.0024 I+.0016 r + 0.043 + .017 0.0007 +.0006 1 j 43 44N 41W, respectively. Both of these a ir pressure spectra reveal a broad peak similar to that found at Station 'Papa' (17 days) with the period of the peak being 16 days at Station N and about 12 days at Stations C and D. While the periods of the peaks were in reasonably good agreement, the levels differed considerably. At 'Papa' the peak level was f<}>=56 (mbar) 2 com-pared to 9 (mbar)2 at Station N and about 8 (mbar)2 at Stations C and D. This reflects at least in part, the difference in the level of synoptic act iv i ty between these locations. The semi-diurnal and diurnal variation of air pressure has been reported at many locations (Butler,1962) including Station N (Dorman,1974), San Diego (Gossard,1960) Bermuda (Wunsch,1972) and Palmyra Island (Hwang,1970). As expected the size of the variation found at 'Papa' i s smaller than that found at the more southerly locations cited above. 4^ 4 Sea Surface Temperature The spectrum of sea temperature is shown in Figure 8. As previously mentioned (see Chapter 2), the sea temperature was erroneously measured over the f i r s t five years on one of the two weatherships. The effect of this error on the spectrum was exa-mined by comparing the spectrum computed from a l l ten years with the spectrum computed from only the last five years of data. At the diurnal period, the ten year spectral value is more than twice the corresponding value computed from the last five years. However, at other periods, while the smoothed spectral estimates differ by as much as 40% for individual estimates, the dif-ferences are within the 95% confidence interval computed from the separate spectral estimates of each data block. Thus, the 4 4 i n ru »: o t o U J o O U J o i n o -4-146 4 213 SEH TEMPERATURE o I - 4 I i 1 r ~3 -2 -1 0 LOG!0(FREQUENCY) FREQ IN CYCLES/DAY F i g u r e 8: The power spectrum o f sea t e m p e r a t u r e computed from f i v e t w o - y e a r l y b l o c k s c o v e r i n g the p e r i o d , 1958 t o 1967 and f o r comp a r i s o n , the power spectrum computed by a v e r a g i n g the s e a s o n a l e s t i m a t e s (as a dashed l i n e ) . k c o r r e c t i o n i s made t o the spectrum a t t h e p e r i o d of one day t o compensate f o r er r o n e o u s sea t e m p e r a t u r e measurements o£ the f i r s t f i v e y e a r s . The v e r t i c a l e r r o r b a r s r e p r e s e n t a p p r o x i m a t e 95$ c o n f i d e n c e i n t e r v a l s o f the mean. 45 two yearly and seasonal temperature spectra are computed from a l l ten years of data but corrected at the diurnal period to agree with the diurnal spectral value computed from the last five years of data. The single harmonic spectral values dis-cussed below are computed from the last five years of data as well. The two-yearly sea temperature spectrum i s dominated by the annual cycle with peaks at the annual and semi-annual periods. Over 95% of the total energy of the spectrum i s contributed at these periods. The annual period has an energy of 7.50 ( C ° ) 2 corresponding to an average range of 7.9 C° while the semi-annual period has an energy of 0.56 ( C ° ) 2 corresponding to a range of 2.2 C ° . (The mean sea temperature i s 8.46 OC). with tha exception of the diurnal peak, the remainder of the spectrum is featureless, declining steadily with decreasing periods. The data from which each seasonal spectrum was computed, was dig i ta l ly f i l tered to remove the large annual variation (as explained in chapter 3), However, at the frequencies resolved and displayed on the seasonal spectra (Figure 9), this f i l t e r ing should have l i t t l e effect. To test th i s , the seasonal spectral values were averaged and the results are plotted as a dashed line in Figure 8. as expected, the agreement i s good except at the lowest seasonal frequency band. This discrepency i s due to the fact that the lowest band includes contributions from periods of 182 days to 105 days, which were zeroed by the f i l -tering. The seasonal spectra of sea temperature (see Figure 9), in contrast to the wind and air pressure spectra, have their lar-SEA TEMPERATURE 4 6 1 0 . WINTER to CO SUMMER 0 0 , o _ l o T 1 FALL 44 1-4-4--3.0 -2.0 -1.0 0.0 10G10(FREQUENCY! 1.0 Figure 9: The seasonal power spectra of sea temperature; each spectrum i s averaged over the ten years, 1958 to 1967. A correction is made to the spectra at the period of one day to compensate for erroneous sea temperature measurements of the f i r s t five years. The vert ica l error bars represent approximate 95% confidence intervals of the mean. 47 gest s p e c t r a l values i n summer and the s m a l l e s t s p e c t r a l values i n winter. The l a r g e s t changes i n the seasonal s p e c t r a occur a t periods ranging from 10 to 100 days. In s p r i n g the l a r g e s t values are found at p e r i o d s of 12 to 30 days, while the other seasons show the l a r g e s t s p e c t r a l values at longer p e r i o d s . In a l l cases, the 95% c o n f i d e n c e i n t e r v a l s are l a r g e i n d i c a t i n g a c l a r g e year to year v a r i a b i l i t y and the f a c t that the l o n g e s t period s p e c t r a l e s t i m a t e s have the l e a s t amount of smoothing. The s i n g l e harmonic s p e c t r a l values of the l a s t f i v e years were examined. They show a sharp peak at a p e r i o d of one day and a weaker peak at one-half day. No s i g n i f i c a n t peaks were found a t o n e - t h i r d or one-quarter of a day. The d i u r n a l peak has an energy of 0.0020 (CO) 2 corresponding to an average d a i l y range of 0.13 C° (see T a b l e I I I ) . The s e m i - d i u r n a l peak has an energy of 0.00015 (C°) 2 corresponding to a range of 0.04 C°. The d i u r n a l v a r i a b i l i t y of sea temperature a l s o shews a marked seasonal v a r i a b i l i t y . The energy i s l a r g e s t i n s p r i n g and de-creases by more than an order of magnitude to i t s lowest value i n w i n t e r . I t i s not s u r p r i s i n g t h a t the g r e a t e s t d i u r n a l v a r i a t i o n occurs i n s p r i n g s i n c e t h i s season, which f o r the pur-poses of the a n a l y s i s i n c l u d e s a l l of June, has the g r e a t e s t amount of s o l a r i n s o l a t i o n . In a d d i t i o n , downwards heat t r a n s -port i s reduced a t t h i s time of year due to the presence of a shallow seasonal t h e r m o c l i n e (see Tabata,1961). The combination of more heat i n p u t on a d a i l y c y c l e , together with l e s s t r a n s -port of heat away from the s u r f a c e r e s u l t s i n t h i s l a r g e d i u r n a l v a r i a t i o n . In winter, the s i t u a t i o n i s r e v e r s e d , and the r e s u l t i s a very s m a l l d i u r n a l v a r i a t i o n . 48 Other sea temperature s p e c t r a can be compared with the above r e s u l t s . Dorman (1974) has computed seasonal s p e c t r a a t Ocean S t a t i o n N (30N 1408). The summer spectrum agrees well with t h a t found at S t a t i o n 'Papa' while the winter spectrum shows more a c t i v i t y at periods of 2 to 10 days. Sea temperature o s c i l l a t i o n s with p e r i o d s of 25 to 45 days have been reported by Koizumi at Ocean S t a t i o n ' E x t r a ' (39N 153E), l o c a t e d o f f the coast of Japan ( R o l l , 1965). These o s c i l l a t i o n s were r e l a t e d to meandering ocean c u r r e n t s . G i l l ( 1974) has computed a s u r f a c e temperature spectrum f o r Ocean Weather S t a t i c n E (35N 48W) which shows a peak a t a p e r i o d of approximately o n e - f i f t h of a year (70 days) b e l i e v e d t o be r e l a t e d t o mid-ccean eddies. The lack of any e q u i v a l e n t s p e c t r a l f e a t u r e s at 'Papa' i s perhaps due to the great d i s t a n c e s e p a r a t i n g S t a t i o n 'Papa' from any int e n s e ocean c u r r e n t s . Both Koizumi and Dorman have s t u d i e d the d i u r n a l v a r i a t i o n of sea temperature. Koizumi f i n d s an average annual range of 0.28 co while Dorman determined a range of 0.13 C° very c l o s e t o the range found at 'Papa'. Koizumi and Dorman both f i n d . a change i n the d i u r n a l v a r i a t i o n with season. In both cases, the d i u r n a l v a r i a t i o n i s l a r g e s t i n summer and s m a l l e s t i n winter. However, at 'Papa' the r e l a t i v e change i s l a r g e r , r e f l e c t i n g i t s more n o r t h e r l y p o s i t i o n with more pronounced seasons. Denman(1972) has developed a model of the upper l a y e r of the ocean which was t e s t e d f o r the months cf May and June a t S t a t i o n 'Papa'. His model, using a constant wind speed of 8 m/sec, pre-d i c t s a d i u r n a l sea temperature range cf 0.18 Co. T h i s r e s u l t i s very c l o s e to the s p r i n g value found i n t h i s a n a l y s i s of 0.19 49 CO. 4 i5 Air Temperature The air temperature spectrum (see Figure 10), l ike the sea temperature spectrum, i s dominated by the annual and semi-annual variations. The annual peak has an energy of 8.29 ( C ° ) 2 while the semi-annual peak has an energy of 0.79 (C 0 ) 2 , which together account for 84% of the total energy. The corresponding average air temperature ranges are 8.3 C° for the annual period and 2.6 C° for the semi-annual period (as compared to the mean air tem-perature of 8.2 °C) . At periods between the semi-annual and diurnal, the a i r and sea temperature spectra differ considerably. The sea tempera-ture spectrum decreases uniformly from the semi-annual peak while the air temperature spectrum reveals a very broad, uneven peak between periods of 2 days and 60 days with spectral levels that are an order of magnitude larger than the corresponding sea temperature spectrum. This broad region of increased act iv i ty seems to be associated with the passage of different air masses. At the shortest periods, the spectrum increases. This result indicates that there are air temperature variations of periods less than one-quarter day which are aliased back to longer periods. The seasonal spectra (see Figure 11) reveal a striking dif-ference between the high spectral levels of f a l l and winter in contrast to the low spectral levels of spring and summer. In addition, i t appears that a 'gap' may exist in the f a l l and winter spectra at periods of about 12 days separating the spec-tra into a synoptic peak centered at about 6 days and a longer 5 0 AIR TEMPERRTURE i n . o It. o CM l_J IS)<\1. U J • DC O . O I 16!1 2!8 '-4.0 — , 1 -3 0 -2 0 LOG10(FREQUENCY) -1.0 0.0 FRE0 IN CYCLES/DRY 1.0 F i g u r e 10: The power spectrum of a i r t e m p e r a t u r e computed from f i v e t w o - y e a r l y data b l o c k s c o v e r i n g the p e r i c d , 1958 t c 1967. The v e r t i c a l e r r o r b a r s r e p r e s e n t a p p r o x i m a t e 95 3 c o n f i d e n c e i n t e r v a l s of the mean. filR TEMPERATURE 51 I D . O O . O WINTER 3K O - J SPRING --H-+ to a rr in li-es . o SUMMER + t o . O - J FALL - I -++ °-3.0 - ] 1 — -2.0 -1.0 L0G10(FREQUENCY) 0.0 —1 1.0 Figure 11: The seasonal power spectra of air temperature; each spectrum i s averaged over the ten years, 1958 tc 1967. The vert ica l error bars represent approximate 95% confidence intervals of the mean. 52 period peak centered at about 23 days. Both the two-year and seasonal spectra show a pronounced diurnal peak. An examination of the single harmonic spectral values (see Table III) reveal a significant but much smaller semi-diurnal peak as well. The diurnal peak energy is 0.045 ( C O ) 2 corresponding to an average daily temperature range of 0.64 C O , The semi-diurnal peak energy i s only 0.0047 ( C ° ) 2 cor-responding to an average range of 0,20 C ° . As might be ex-pected, the largest diurnal variations are found in spring and summer when the solar insolation i s the greatest. The annual and diurnal variations of air temperature over the sea are well known and have been studied by a number of in-vestigators. Boll (1965) provides a useful summary cf these re-sults . The diurnal and annual a i r temperature ranges found at Station 'Papa' are in good agreement with the findings of ethers at similar latitudes. Studies of periodicit ies of the air temperature at periods between one day and one year are much less common. Powalchuk and Panof sky (1968) have computed the spectra at a number of sta-tions in North America in winter. They find a peak occuring at each station with periods of the peak ranging from 4 days to 20 days. The peaks with longest periods are for stations on the western side of North America in maritime climates. Byshev and Ivanov( 1969) have computed the a ir temperature spectrum over the ocean. At stations of approximately the same latitude as Station 'Papa', their spectral results show a broad peak cen-tered at about 11 days. Dorman (1974) for Station N (30N 140W) further to the south, found a peak in winter at periods of 6 to 53 11 days. The behavior of the a ir temperature spectra at Station •Papa1 i s generally consistent with these results over synoptic periods, but additional energy i s found at longer periods (15-60 days). Absolute Humidity, The absolute humidity spectrum (see Figure 12) reveals the largest variations at the annual and semi-annual periods. The annual variation amounts to an energy of 2.28 (gm/m3) 2 corres-ponding to an average annual range of 4.4 gm/m3. The semi-annual variation has an energy of 0.36 (gm/m3)2 corresponding to a range of 1.7 gm/m3 (the mean absolute humidity i s 7.35 gm/m3). The absolute humidity spectrum features a broad well defined synoptic peak at 5.5 days with half power points at 1.5 days and 48 days. The increase in spectral values at the shortest periods i s an indication of shorter period variations being aliased back to longer periods. Figure 13 reveals important seasonal variations in the ab-solute humidity spectrum. The spectral levels are largest in f a l l and lowest in spring, in each of the seasons a synoptic peak is found, with the peak value at periods ranging from 3,8 days (fall) to 6,8 days (summer). The longer pericd act iv i ty appears to be more variable. In winter, and to a lesser extent, in spring and f a l l , a peak is found at periods of 17 to 23 days. In summer, the longer period act iv i ty i s greatly reduced. An examination of the single harmonics (see Table III) shows a sharp peak at a period of one day and a weak peak at a period of half a day. The diurnal peak has an energy of 0.0014 (gm/m3)2 corresponding to an average daily range of 0.11 gm/m3 5 4 ABSOLUTE HUMIDITY 4l4 1.4 o CM — o SK -v.t\). SZ • IS) D (X t— O UJ to—'• O . O '-4.0 -3.0 T -2.0 LOG10(FREQUENCY) -1.0 0.0 FREQ IN CYCLES/DAY 1.0 F i g u r e 12: The power spectrum of from f i v e t w o - y e a r l y data b l o c k s 1967. The v e r t i c a l e r r o r b a r s con f i d e n c e a b s o l u t e h u m i d i t y computed c o v e r i n g t h e p e r i o d , 1958 t o r e p r e s e n t a p p r o x i m a t e 95% ABSOLUTE HUMIDITY 55 Q. O WINTER ~K4-^-1 SPRING o o * 2 o _ D 2 O — EE CE 1— t_J UJ o D_ in _ o . o SUMMER O FftLL -l-H 1-°-3.0 — i 1 r -2.0 -i.o o.o L0G10[FREQUENCY) —I 1.0 Figure 13: The seasonal power spectra of absolute humidity; each spectrum i s averaged over the ten years, 1958 to 1967. The vert ical error bars represent 9'5 7, confidence intervals of the raea n. 56 while the semi-diurnal peak has an energy cf 0.0001 (gm/m3)2 corresponding to a range of 0.03 gm/m3. As might be expected, the diurnal variation is largest in spring and summer when the increased solar radiation evaporates mere water at the sea sur-face. The single harmonic spectral values show no peak at the semi-diurnal period because of the reduced freguency resolution. The semi-diurnal peak, which was only marginally defined with the resolution of a two-year time series, is lost in the back-ground with time series of 91 days length. It i s interesting to compare the spectra of the a ir tem-perature and absolute humidity. While both spectra are dominated by the annual peak, they show considerable differences at shorter periods. The absolute humidity spectrum shows a well defined peak, at 5.5 days while the air temperature spectrum shows no single peak but somewhat increased levels between 2 days and 60 days. The relative contribution from these periods to the total variance i s much larger for humidity than tempera-ture. Such differences in the spectra, suggest that consi-derable differences exist in the moisture and temperature fields and their interactions with the ocean, on synoptic and seasonal scales. Spectra of humidity are very rare indeed. Dorman (1974) has presented a spectrum of dew point temperature for Ocean Station N (140W 30N). Because dew point temperature is a deterministic and approximately linear function of absolute humidity (over the rather narrow range of temperature and humidities encountered), the relative energy found at various frequencies can be meaning-ful ly compared. Dorman's results reveal the same features found at 'Papa*. He finds a large annual variation and a much smaller diurnal variation. In addition, he finds a synoptic peak at about 5.8 days for each of the seasons. iL2 Turbulent Fluxes The spectra of quantities which are representative of the turbulent fluxes of momentum, sensible heat flux and latent heat flux are computed. Figure 14 i s a plot of the rotary spectrum of the vector time series (DD x,UO y), proportional through the bulk aerodynamic parameterization (equation 1) to the wind stress (also called the momentum flux). The rotary wind stress spectrum is similar to the rotary wind spectrum with both clock-wise and anti-clockwise rotations having a synoptic peak at 3 days. The clockwise rotations dominate the wind stress rotary spectrum to a greater extent than the wind rotary spectrum. The seasonal wind stress spectra (see Figure 15) show very marked differences. The spectral levels in f a l l are four to five times greater than in summer as a result of the increased storm act ivi ty . These levels decrease from f a l l through winter and spring to the lowest levels in summer. The spectra also reveal that a greater proportion of the f a l l and winter spectral energy is found at shorter periods than i s the case for spring and summer. The relative contributions from the clcckwise and anti-clockwise spectra to the total rotary spectrum over a l l periods remains remarkably constant for a l l seasons. However, changes are found between the clockwise and anti-clockwise con-tributions at individual frequency bands. The most noticeable of these changes is found in summer when the clockwise spectrum has a broad peak over periods from 1.5 to 9 days while the anti-ROTARY WIND STRESS CLOCKWISE 1 o in o o . 3 —^  Q . CJtQ to ft 5K li-ra C3_| in ~ i 1 — ' r -1 -2 -3 LQG10(FREQUENCY) PNTI-CL0CKV1SE ± -4 -3 -2 FREQ IN CYCLES/DflY -2 T 0 Fi g u r e 14: The r o t a r y auto-spectrum of |U|U, a q u a n t i t y which i s p r o p o r t i o n a l to the wind s t r e s s , computed frcm f i v e two-y e a r l y b l o c k s c o v e r i n g the p e r i o d 1958 to 1967, The v e r t i c a l e r r o r bars r e p r e s e n t <£% confidence i n t e r v a l s of the mean. ROTARY WIND STRESS CLOCKWISE ANTI-CL0CKW3SE 59 4 + Q CO WINTER .+++ D CO rr?.....L-SPRING Iff. o JSC o —1 w CO o cc I— B o_ CO SLIMMER + 1.0 T 44 FfiLL •++ — r 0.0 —1 1.0 1.0 0.0 -2.0 ^3.0 -2.0 -1.0 LOG10(FREQUENCY) FRE3 IN CYCLES/DAY F i g u r e 15: The s e a s o n a l r o t a r y a u t o - s p e c t r a o f JUIU, which i s p r o p o r t i o n a l t o t h e wind s t r e s s , computed t w o - y e a r l y b l o c k s c o v e r i n g the p e r i o d , 1958 t c v e r t i c a l e r r o r bars r e p r e s e n t a p p r o x i m a t e 95% i n t e r v a l s of the mean. a q u a n t i t y from f i v e 1967. The c o n f i d e n c e 60 clockwise spectrum has a rather sharp peak at 6.8 days. This deviation from the dominant f a l l and winter spectra could be the result of a change in the pattern of the passage of synoptic disturbances over the N. E. Pacific between summer and winter. Further study is required to test this hypothesis. An examination of the single harmonic spectral values (see Table IV) reveals a very sharp semi-diurnal peak in the clock-wise spectrum. This peak has an energy of 10.8 (m/sec)* which amounts to an average range of 9.5 (m/sec)2. No peaks are found at periods of one day, one-third of a day, one-guarter of a day, or the i n e r t i a l period. The anti-clockwise spectral values show no peaks other than a very small one at one-half day. Two-yearly spectra of quantities that are representative of turbulent heat transports are displayed in Figure 16. Figure 16 contains three plots: a plot of the spectrum of UAT which by equation (2) is proportional to the sensible heat flux, a plot of the spectrum of UAq which by equation (3) i s proportional to the latent heat flux and a plot of the spectrum of 1.20 AT + 2.440 Aq which i s proportional to the total turbulent heat transport (taking p=1.2 x 10~3 gm/cm3, L=2440 joules/gm, Qp=1.00 j o u l e s / g m - ° C and CT=Cq in equations (2) and (3)). Each plot in Figure 16 is scaled in such a way that equal displace-ments from the horizontal axis represent equal contributions to the variance of the total heat flux. Each spectrum has the same general features: relat ively small but significant annual and semi-annual peaks and a broad synoptic peak that contains most of the energy. The synoptic peak has i t s highest levels at periods of 7 and 4 days for each of the quantities. 61 T J J I J IV The energy cf s i n g l e ha rncn i c s p e c t r a l peaks of g u a n t i t i e s which are r e p r e s e n t a t i v e of the wind s t r e s s |0«t3), the s e t s i b l e beat f l u x , the l a t e n t heat f l v x and the t o t a l t u r b u l e n t heat f l u x found at pe r i o d s of one day, o n e - h a l f eay anc c r e - c u a i t e r day. Cuantity (units) Clock-wise UU (it/sec) 4 A n t i -c l o c k -wise UU (m/sec) A S e n s i b l e Heat (cal/cm 2/day) 2 1 l a t e n t Heat (cal/cm 2/day) 2 P e r i o d 1.0 0.5 S. I. 1.0 0.5 S.D, 1.0 S.D 0.5 S.I 4 1.0 0.5 S. t. C.25 S. I. Energy Annual! Winter| Spring | Summer! F a l l 10.83 • 8. 27 -I 4 -0.558 + 0.911 34.4 + 18.5 5. 15 + 1.09 1.78 + 2. 10 C.201 +0.197 4.07 13. 18 30.0 + 27.7 6. 11 +3.11 T o t a l | 1.0 | 42.4 | 50.9 | 62.1 | 23.4 j -Heat | S.D. 1+14.2 1+54.1 I+48.4 |+39. 1 | (cal/cm 2/day) 2 | j | ~ j ~ j | 0.5 | 5.63 | 8. 10 | 1.36 | 11.4 | 9.45 S.E. |+4.27 |+15.5 |+4.01 1+12.8 1+25.5 8.58 10.19 4 5.5 + 19.7 1.88 +2.54 4  2.84 +7.279 7.42 10.60 35.7 + 20. 1 5.90 + 3.97 4.34 + 5. 16 4 14. 64 30.26 4 29.2 • 36.0 8.76 • 8.79 j 4.05 • 24.6 2. 18 + 7.22 I 1 t J 62 -o * IX. SENSIBLE HEAT Q. C3 LATENT HEBT + + + o O O - , CO o o-<£> O LL o. CP CM . , T07RL HEAT FLUX ++ + -4.0 -3 .0 -2 .0 LOG10(FREQUENCY) -1 .0 FREQ IN CYCLES/DRY 0.0 i .O F i g u r e 16: The power s p e c t r a o f UAT ( i n (°C-ni/sec) p r o p o r t i o n a l t o t h e s e n s i b l e heat f l u x ) , UAq ( i n [gm/mz-sec) z, p r o p o r t i o n a l t o the l a t e n t heat f l u x ) and 1.2U4T + 2^44UAq ( p r o p o r t i o n a l t o the t o t a l t u r b u l e n t heat f l u x ) , computed from f i v e t w o - y e a r l y b l o c k s c o v e r i n g t h e p e r i o d , 1958 t c 1967. The v e r t i c a l e r r o r b a r s r e p r e s e n t a p p r o x i m a t e 95!? c o n f i d e n c e i n t e r v a l s of the mean. 63 It is clear from Figure 16 that the auto-spectral values cf the total heat flux represent considerable} more heat transfer variations than the the sum of the sensible and latent heat flux auto-spectral values at a l l periods greater than one day. This is a result of the high correlation between U«AT and U«Ag varia-tions. Over periods from two days to two years, the correlation between U»AT and D»^q is 0.7 or greater. On the plots in Figure 16, the semi-annual peaks are larger than the annual peaks because in the log f plots the bandwidth is narrower at the semi-annual pericd. However, the contribu-tion to the variance from the semi-annual period is less than that from the annual period. The annual variation cf the latent heat flux, as computed from the spectral values of U^q using Cq=1.5x10~3, has an average range of 103 cal/cm2-day while the semi-annual energy peak corresponds to a range cf 86.4 cal/cmz-day indicating large annual and semi-annual variations about the average of 88.9 cal/cm 2-day.- These values are considerably larger that the cor-responding values for the sensible heat flux (annual range of 46 cal/cm2-day and a semi-annual range of 32 cal/cm 2-day). The average sensible heat transfer was 11,7 cal/ci^-day. The total turbulent heat transfer has an annual range cf 147 cal/cm2-day and a semi-annual range of 105 cal/cut2-day about a mean cf 100 cal/cm 2-day. That the semi-annual variations are a large frac-tion of the annual variations i s a reflection of the preserce cf a secondary maximum in these heat fluxes in March in addition to the maximum heat transport which occurs in the f a l l . An inspection of the single harmonic values (see Table IV) 64 shows a very sharp diurnal peak in the UAT spectrum. This peak has an energy of 2.27 (CO-m/sec)2 corresponding to an average daily range of the sensible heat flux of 16.9 cal/cra2-day. A smaller semi-diurnal peak i s found as well. The seasonal varia-tion of the diurnal peak is rather small with the largest diur-nal variation occuring in spring (a sensible heat range of 19.5 cal/cm2-day) and the smallest diurnal variation in f a l l (a range of 15.6 cal/cm 2-day). The UAq spectrum shows no diurnal peak and only a very small semi-diurnal peak. Thus, there exists no daily cycle in latent heat transport similar to that cf sensible heat transport. The spectrum of the total heat flux shows a prominent diurnal peak and a smaller semi-diurnal peak. The average diurnal range i s 18.9 cal/cm2-day, very nearly egual to that of the sensible heat flux, which suggests the variation is largely due to the daily sensible heat cycle. Large changes in the spectra of turbulent heat fluxes (see Figures 17, 18, and 19) are found with the seasons. The sen-sible heat flux spectra show the largest differences in spectral levels with the summer spectral values being an order cf magni-tude less than those of f a l l and winter. The relative contribu-tions from various frequencies show less pronounced changes. In a l l spectra, a peak is found at periods of 3 to 4 days. A longer period peak of marginal significance at about 23 days i s prominent in f a l l and i s present in a l l the seasonal spectra except that of summer. The seasonal spectra of the latent heat flux also show marked changes with the seasons but not to the same extent as the sensible heat flux. Unlike the case of sensible heat flux, SENSIBLE HERT 65 CM K 3K m n i o o C3 . CM o r o. rvi o r tx O D_ VP 5*; o - J o r -3.0 WINTER -L.+ -t++. SPRING -+-T , : — SUMMER -+-H—H -* 1—H FALL + ++ - H -— I 1 -2.0 -1.0 L0G10(FREQUENCY) 0.0 1.0 Figure 17: The seasonal power spectra of UAT (proportional to the sensible heat f lux) . Each spectrum is averaged over the ten years, 1958 to 1967. The vert ical error bars represent approximate 957c confidence intervals of the mean. 66 LATENT HEAT to cr cc v-D_ in o . o WINTER o _ J o r r o O tn i OJ 21 SPRING SUMMER o r -™f4" o o FRLL + o _ i o r -3.0 - 2 . 0 - 1 . 0 0 . 0 L0G30(FREQUENCY! 1.0 F i g u r e 18: The s e a s o n a l power s p e c t r a of UAq ( p r o p o r t i o n a l t o the l a t e n t heat f l u x ) . Each spectrum i s averaged ever the t e n y e a r s , 1958 to 1967. The v e r t i c a l e r r o r b a r s r e p r e s e n t approximate 95% c o n f i d e n c e i n t e r v a l s of the toean. TOTAL HEAT FLUX 67 WINTER o" r « SPRING - k I Q LU ->! D_ i n ac U --+—4 SUMMER -S 0 + FALL -2.0 -1.0 0.0 L0G20(FREQUENCY) 1.0 Figure 19: The seasonal spectra of 1.2UAT + 2.miUAq (proportional to the total turbulent heat f lux) . Each spectrum is averaged over the ten years, 1958 to 1967. The ver t ica l error bars represent approximate 95% confidence intervals cf the mean. 68 the summer spectrum of latent heat i s much the same as the spring spectrum. Both these seasons have spectral levels about one-third of those of f a l l and winter. The period of the synop-tic peak shifts with the seasons, being shortest in f a l l (2.9 days), at an intermediate value in winter and spring (3.8 days) and longest in summer (6.8 days). A longer pericd peak is found in f a l l and winter at about 23 days. The seasonal spectra of the total turbulent heat flux i s very similar in character to that of latent heat flux since over the periods resolved, the total heat flux is dominated by the contributions of the latent heat flux. 69 Chapter 5 CROSS-SPECTRAL BESULTS 5A1 Introduction Cross-spectral analysis provides information on the relate-dness of pairs of quantities over the periods resolved. Because the number of basic measured quantities plus the number of quan-t i t i e s which may be derived from these (wind stress, sensible heat f lux, latent heat flux, total turbulent heat flux) is rela-t ively large, there are many possible pairs cf quantities that could be subjected to cross-spectral analysis. Cue to time and space l imitations, i t i s not possible tc present an analysis of each of these pairs. In this study, cross-spectral analysis is used to examine the relationship of each cf the basic surface scalar quantities (air pressure, air temperature, absolute humi-dity and sea temperature) with those factors which are capable of modifying the surface scalar quantities. Such factors (which are available from the data) are the wind and the parameterized turbulent heat fluxes. In addition, the relationships between some of the pairs of scalar quantities are also examined. The cross-spectral results are displayed by means of four graphs for each pair of quantities studied. These are plots of phase, coherence, the transfer spectrum of the f i r s t quantity and the transfer spectrum of the second quantity (see Chapter 3 for the definitions of these cross-spectral values). On the coherence plot, the dashed l ine represents those coherence values below which there i s a 95% probability that a randomly coherent signal w i l l f a l l . The computed coherence estimates 70 which l i e above this line are described as 'gccd' and 'very good1 while those below the dashed line are described as ' f a i r * and 'poor' (as described in Chapter 3). It should be noted that for the shorter periods, the number of degrees of freedom are so large that i t is possible to find s t a t i s t i ca l significance in coherence estimates that are small (say less than 0.3). Such small coherence estimates, though s ta t i s t i ca l ly significant are of l i t t l e value in attempting to predict the behavior of one quantity from that of another quantity. The transfer spectral values, (fraction of spectral energy of one quantity that is coherent with the other quantity) shown as dashed l ines , are plotted beneath the auto-spectral values for the same quantity. 5^ 2 air Pressure A study of the cross-spectra between wind and air pressure provides some insight into the dynamics of the surface atmos-pheric layer over the ocean. The rotary cross-spectra between vector wind and air pressure as well as the cross-spectrum bet-ween wind speed and air pressure are computed (see Figure 20). A discussion of the coherence relationship between wind and air pressure can be conveniently divided into three parts accor-ding to the scale ranges resolved: the climatic/seasonal scales, the longer synoptic scales and the shorter synoptic scales. The mesoscale i s unimportant since pressure fluctuations at these periods are very small. Over climatic/seasonal scales, the co-herence spectra show generally poor levels of coherence. One exception to this statement is found at the annual cycle in the wind speed-pressure coherence spectrum where the coherence of 0.91 i s very good. The two quantities, as one would expect are 71 CLCCKVJSE RNTI-CLOCKWISE PHASE CD. 1 8-co_) PHASE ru LT I r [L in o I r ~~\ r COHERENCE o COHERENCE ROTARY WIND ru. TRANSFER SPECTRUM -in V[ND SPEED TRANSFER SPECTRUM (0 (M 3K )K CK en o _ ca XL •&• >c II o CN 1 1 . 2 -3 -4 -3 -2 -1 LQG10CFRE3) FREQ IN CYCIES/OAY AIR PRESSURE o TRANSFER SPECTRUM ° flfR PRESSURE TRANSFER SPECTRUM 1 1 T -4 -3 -2 -1 0 1 LQG1Q(FREQI FREQ IN CYCLES/DAY Figure 20: Graphs of phase, coherence and the transfer spectra between the wind and a i r pressure. The cross-spectral guantities are displayed for both the vector wind (as rotary spectra) and the wind speed. 72 very nearly 180 degrees out of phase. Due tc the effect of wind direction changes, the annual cycle found in the wind rotary auto-spectra is greatly reduced and as a result , there is a smaller annual peak in the rotary coherence spectra. The most significant levels of wind-pressure coherence are found at the shorter synoptic scales (periods ranging from one to ten days). Over this range of periods, a prominent peak of s t a t i s t i ca l ly very good coherence appears in the clockwise co-herence spectrum (peak level of 0.70) and anti-clcckwise co-herence spectrum (peak level of 0.57) as well as the wind speed-pressure coherence spectrum (peak level of 0.47). The higher coherences found for the clockwise and anti-clockwise rotating wind in comparison with those of the wind speed, emphasize the importance of cyclonic and anti-cyclonic pressure systems in determining the wind f ie ld over the shorter synoptic scales. A passing cyclone or anti-cyclone should be characterized by a rotation of the wind vector in association with the pressure change. The wind speed would also be expected to change with the pressure, but with a more complicated response. A simple model can be used to i l lus trate this point. Con-sider the passage of an eastward-moving low pressure cyclonic system with i t s center s l ightly to the north of the observation station. The air pressure w i l l go through one-ha If a cycle during the passage of the system (from intermediate to low to intermediate values). Neglecting the effect of frontal discon-t inuit ies and other complications of pressure system airflows, the wind vector w i l l rotate from pointing very nearly due north to pointing very nearly due south in a clockwise sense. Thus, 73 the half-cycle change in a ir pressure i s clearly coherent with the 180 degree clockwise rotation of the wind. However, the wind speed of a typical middle latitude depression (see Mcintosh and Thorn, p. 150) wi l l f i r s t increase and then decrease as the low pressure center approaches and then increase and decrease again after the center passes by. Clearly, the response cf the wind speed should be less coherent with air pressure than the response of the rotating clockwise wind component for these at-mospheric pressure systems. A marked difference i s found in the coherence results at longer synoptic periods (greater than 10 days) in comparison with the coherence results at the shorter synoptic periods. At these longer periods, the rotary coherence levels are considera-bly lower. These results suggest that, at the longer synoptic periods, the variation of the wind can no longer be thought of as a relat ively simple response to travell ing atmospheric c i rcu-lation systems. Instead, the relation between the wind and air pressure appears to be considerably more complicated at such scales. Interestingly, the coherence between the wind speed and air pressure remains much the same at the longer periods as that found at shorter synoptic periods. Also, the phase difference between wind speed and air pressure remains f a i r ly constant (being nearly out of phase) throughout the synoptic scale. 74 5j_3 Air Temgerature The cross-spectral results (see Figure 21) show a s i g n i f i -cant amount of coupling between the air temperature and the wind over a wide range of scales. The most significant levels of coherence are found at synoptic scales. The clockwise rotary coherence ranges from 0.4 to 0.7 over periods cf 1.5 tc 35 days while the anti-clockwise rotary coherence levels are somewhat lower, ranging from 0.25 to 0.6 over the same interval of periods. These results suggest that the air temperature has a greater response to clockwise rotations of the wind than anti-clockwise rotations. This di f ferential response of air temperature, on synoptic scales, i s understandable in terms of the passage of synoptic circulation systems over the North Pacific Ocean. Synoptic pressure disturbances travell ing eastward to the north of Station 'Papa1 (resulting in a clockwise wind rotation at 'Papa') are more l ike ly to be associated with cold airmasses than pressure systems passing to the south (anti-clockwise wind rotations) due to the difference in latitude. It would seem that these cold airmasses produce more coherent changes in the air temperature than the relat ively warmer pressure systems pas-sing to the south. When the wind direction i s excluded from the analysis by computing the wind speed-air temperature cross-spectrum, the coherence levels are found to be much lower but s t i l l generally significant. At synoptic scales, the coherence spectrum shows a peak from 1.3 to 3.5 days but with coherence levels of only 0.20. This region of s t a t i s t i ca l ly very good coherence i s se-CLOCKVISE 8-1 ANTI-CLOCKWISE PHASE o CO. PHASE o COHERENCE i n o i r COHERENCE ~l 1 1 1 1 ROTARY WIND N TRANSFER SPECTRUM ~* AIR TEMPERATURE ^ _ TRANSFER SPECTRUM c co in i r -2 -3 -4 -3 -2 -1 LOG 10IFREQ) FREQ IN CYCLES/DAY WIND SPEEO TRANSFER SPECTRUM AIR TEMPERATURE TRANSFER SPECTRUM — i 1 T - n 1 -4 - 3 - 2 - 1 0 1 LQG10(FREQ) FREQ IN CYCLES/OAY Figure 2 1 : Graphs of phase, coherence and the transfer spectra between the wind and air temperature. The cress-spectral guantities are displayed for both the vector wind (as rotary spectra) and the wind speed. The annual and semi-annual peaks cf the air temperature auto-spectra are off-scale. 76 parated from the fair to good coherence found at longer periods by a region of poor coherence found at 6.5 to 11 days. The phase at the synoptic peak ranges from -30 degrees to 30 de-grees, indicating that the a ir temperature is nearly in phase with the wind speed. At periods longer than the synoptic scale, the coupling between air temperature and the wind remains at significant le-vels. The clockwise coherence i s very good out to periods of about 200 days and remains fa ir and good at the periods cf one year and two years, respectively. The anti-clockwise coherence exhibits a somewhat different behavior: i t remains good cut to periods of 64 days but for longer periods (with the exception of a peak of very good coherence at 100 days) i t declines to poor coherence levels . The wind speed-temperature coherence is generally good at the longer periods with two sharp peaks at the annual and semi-annual cycles. The annual coherence i s , of course, extremely good with a value of 0.99. Air temperature leads wind speed by 125 degrees over the annual cycle. We have seen that changes in the air temperature are signi-ficantly coherent with wind rotations. Such changes in the air temperature are due to advection of different airmasses past the observation point. The effect of more localized modifications i s examined by computing the cross-spectrum between the a ir tem-perature and U AT ( a quantity which through the bulk aerodynamic parameterization, equation (2), is representative -of the upward turbulent transport of sensible heat). The cross-spectral re-sults, displayed in Figure 22, show a very significant and high level of coherence between these quantities at a l l scales less G UJ £-j Win' (_> • to. SPECTRUM -4 - 2 - 1 LOGIO(FREQ) FREO JN CYCLES/DRY Figure 22: Graphs of phase, coherence and the transfer spectra between the air temperature and UAT (a guantity representative of the sensible heat f lux) . The annual and semi-annual peaks of the air temperature auto-spectra are off-scale. 78 than or equal to one-half year. At periods longer than one-half year, the coherence levels are poor, with the exception of very good coherence at the annual cycle. Over the synoptic and mesoscale periods, the phase between the two signals i s very uniform, remaining within 10 degrees of being exactly out of phase. Over these scales, then, an i n -crease in temperature is accompanied by a decrease in UA T and a decrease in temperature is accompanied by an increase in U«AT. The high coherence found here suggests that the fluctuations in the air temperature may be used to predict the corresponding fluctuations in U«AT. While the coherence levels for air tem-perature with U AT are large (0.7 to 0.9) the coherence levels of air temperature with the sensible heat flux may be lower because of the scatter found in experimental comparisons cf direct mea-surements of sensible heat and the calculated value of sensible heat through equation (2) (see for example, Pond et, al.(1971)). 5.4 Absolute Humidity The absolute humidity is an airmass characteristic, which l ike air temperature, is modified by means cf turbulent ex-changes with surrounding parcels of a i r . It i s further related to air temperature since the air temperature determines the upper l imit (saturation value) of absolute humidity. As one would expect, then, the air temperature-absolute humidity cross-spectrum, displayed in Figure 23 indicates a strong correlation over most scales, as seen from the high coherence levels and small phase values. For periods less than 3 days, the coupling declines sharply although the coherence between the signals does remain s t a t i s t i ca l ly s ignif icant. D aa-PHASE o. CO o tn-i o CD. COHERENCE Figure 23: Graphs of phase, coherence and the transfer spectra between the air temperature and the absolute humidity. The annual and semi-annual peaks of both the a ir temperature and absolute humidity auto-spectra are off-scale. 80 The absolute humidity-wind cross-spectrum (see Figure 24) i s remarkably similar to the air temperature-wind cross-spectrum previously discussed. Both cross-spectra show that the most significant coherence levels occur at synoptic periods and that the clockwise wind rotations are more coherent with air tempera-ture and absolute humidity than anti-clockwise wind rotations or the wind's speed. The major difference between the two cross-spectra are to be found at shorter periods. Over periods ran-ging from 4 days to 0.5 days, the absolute humidity i s more co-herent with the rotary wind and wind speed than air temperature. The largest change is found for the case of the clockwise rota-ting wind. Such differences between temperature and humidity in relation to the wind as well as the reduced temperature-humidity coherence suggest that over the smaller synoptic period, pro-cesses other than the wind are important. Apparently one mani-festation of such processes is to reduce the wind-air tempera-ture coherence. One possible process which would have a dif-ferent effect on temperature than humidity would be heat trans-fers by long wave radiation. The cross-spectrum between absolute humidity and UAg (a quantity which is representative of the turbulent water vapour transfer by means of equation (3)) was computed. The cross-spe-ctra l results, displayed in Figure 25, show very similar fea-tures to the air temperature-UAT spectral results previously discussed. The absolute humidity variations dominate U«&q changes but not to the same extent as temperature variations dominate the U»AT changes. Over a considerable part of the re-solved periods (periods less than 100 days) the coherence i s Figure 24: Graphs of phase, coherence ana the transfer spectra between the wind and absolute humidity. The cress-spectral quantities are displayed for both the vector wind (as rotary spectra) and the wind speed. The annual and seni-arnual peaks of the absolute humidity auto-spectrum are off-scale. o 00-CD O I O CD. PHASE to o COHERENCE IT) 8 ^ . ABSOLUTE HUMIDITY TRRNSFER SPECTRUM Jptn U --4 UXDELTR 0 TRANSFER SPECTRUM -3 - 2 - 3 0 LQGJO(FREQJ FREQ IN C Y C L E S / D R Y Figure 25: Graphs of phase,coherence and the transfer spectra between the absolute humidity and U4q (a quantity representative of the latent heat flux) . The annual and semi-annual peaks of the absolute humidity auto-spectrum are cff-scale. 83 s ta t i s t i ca l ly very good, ranging from 0.90 tc 0.65 and the phase remains within 20 degrees of the signals being exactly out of phase. While i t must be remembered that the correlation between water vapour (or latent heat) transfer and OAg is not perfect, the results suggest a strong inverse relationship between abso-lute humidity and water vapour transfer. 5_.5 Sea Temperature The cross-spectral results of sea temperature with various surface meteorological guantities can be used tc study the coup-ling between the ocean and the atmosphere. As previously men-tioned in Chapter 2, the sea temperature recorded over the f i r s t five years contain some apparently erroneous values. The major effect of these errors on the spectrum is to distort the diurnal spectral estimate (as discussed in Chapter 4). For the cross-spectral results that follow, a l l ten years cf the data were used in computing them. As a check on their r e l i ab i l ty , the same cross-spectra were computed using only the last five years of the data. The same general features were found in both sets of cross-spectra. The cross-spectrum between the sea temperature and the air temperature i s shown in Figure 26. It shows s ta t i s t i ca l ly very good levels of coherence at a l l periods but the levels are rather small to make a good predictor except at pericds longer than 100 days. The highest coherence i s found at the annual and semi-annual cycles and the coherence levels generally decline with decreasing periods. Over the synoptic scales, the co-herence ranges from 0.3 to 0.5 and seems to vary about a f a i r ly constant l eve l . The phase difference between the air and sea o 03-PHRSE o. CO o CD-I o CO. COHERENCE to o SER TEMPERATURE TRANSFER SPECTRUM in ru-0"-o •—<* sk AIR TEMPERATURE TRANSFER SPECTRUM t I • • I I - 4 1 — : 1 1 r -3 - 2 - 1 0 L0G3Q(FREQ) FREQ IN CYCLES/DAY Figure 26: Graphs of phase, coherence and the transfer spectra between the air temperature and the sea temperature. The annual and semi-annual peaks of both the sea and air temperature auto-spectra are offscale. 85 temperature i s small, being less than 40 degrees over most periods. The air temperature generally leads the sea tempera-ture. The wind-sea temperature cross-spectra are displayed in Figure 27. The rotary cross-spectrum shows s ta t i s t i ca l ly good to very good coherence levels over a l l periods. However the coherence levels are too low to be useful as a predictor. The clockwise coherence levels are somewhat higher than the anti-clockwise coherence levels, part icular i ly at synoptic periods. Apparently this difference i s a reflection of the difference between synoptic disturbances passing to the north (resulting in clockwise wind rotations) and those passing to the south (resul-ting in anti-clockwise wind rotations). Previously, we have seen that disturbances passing to the north are more strongly coupled to the air temperature, apparently because they or i -ginate at higher latitudes and therefore have more pronounced airmass temperature differences from the air they replace. One would then expect that the sea temperature wi l l be modified to a greater extent by such synoptic disturbances as well, resulting in higher coherence levels. The cross-spectrum between the wind speed and the sea tem-perature shows s t a t i s t i ca l ly very good levels of coherence over periods ranging from one year to one day. These levels are generally larger than those for the rotary wind at the longer synoptic and seasonal/climatic scales. The coherence decreases steadily with decreasing period. The phase plot indicates that except for the very longest and the very shortest periods re-solved, the sea temperature leads the wind speed by 90 to 135 36 CLOCKWISE ANTI-CLOCKWISE p PHRSE 0 PHASE *"1 r-1_ ^1 Figure 27: Graphs of phase, coherence and the transfer spectra between the wind and sea temperature. The cress-spectral guantities are displayed for both the vector wind (as rotary spectra) and the wind speed. The annual and semi-annual peaks af the sea temperature auto-spectrum are off-scale. 87 degrees. It is instructive to compare the cross-spectral results for the wind and the sea temperature with these cf the wind and the air temperature. The wind speed i s more coherent with the sea temperature than the air temperature while the rotary wind com-ponents are more coherent with the air temperature than the sea temperature for periods greater than 3 days. This result i n d i -cates a greater degree of coupling of the wind speed with sea temperature than air temperature on such scales. Ocean-atmos-pheric coupling processes which could account for the high degree of coupling with the wind speed include turbulent heat exchanges and wind driving of the ocean's upper layer, both of which are related to the wind speed. S imi lar i ly , the lower co-herence of sea temperature with the rotary wind shows that the sea temperature i s less . directly related to the passage of syno-ptic scale pressure disturbances. The relatedness of the sea temperature with a i r pressure i s examined by computing their cross-spectral values (see Figure 28). The major features of the coherence.spectrum are very good coherence levels at the. annual, period (0.92) and at shorter synoptic periods (ranging from 2 tc 7 days). Over the longer synoptic periods and the seasonal/climatic periods, the co-herence shows marked variations about the 95% significance level . At periods between 65 days and the annual period, the coherence is only fair to poor. A bulge in the spectrum to levels of s t a t i s t i ca l ly good and very good coherence is found between 10 and 30 day periods. The phase spectrum indicates that air pressure leads the sea temperature over most periods. PHASE K 8 -3K AIR PRESSURE r-i TRANSFER SPECTRUM j i j u t , I ' — i —T ; r -3 -2 -1 LGGIO(FREQ) FREO IN CYCLES/DAY - 4 Figure 28: Graphs of phase, coherence, and the transfer spectra between the sea temperature and air pressure. The annual and semi-annual peaks of the sea temperature auto-spectrum are off-PHASE in COHERENCE in CM'"* -3 C ° to ^ in g o . 3K SEA TEMPERATURE TRANSFER SPECTRUM T T o CD-CO O O • to U -TOTAL HEAT FLUX TRANSFER SPECTRUM -4 T -3 -2 -1 0 L0G10(FREQ) FREQ IN CYCLES/DAY Figure 29: Graphs of phase, coherence and the transfer spectra between the sea temperature and 1.2*U4T + 2.44*UAg (a quantity representative of the total turbulent heat f lux) . The annual and semi-annual peaks of the sea temperature auto-spectrum are off-scale. 90 The cross-spectrum between sea temperature and the total turbulent heat flux (see Figure 29) reveals generally very good coherence levels over most periods. However, the coherence is only large enough to be of practical use for predictive purposes at the longest periods. The phase difference between the two quantities ranges from 90 to 180 degrees, with the sea tempera-ture leading. Over periods from one year to one day, a compari-son of Figure 29 with Figures 22 and 25 shows that the sea temperature-heat flux coherence levels are considerably lower at periods less than 100 days, than the a ir temperature-liA T or the absolute humidity-Uag levels . 5.6 Co-sp_ectra Between Quantities Used To Commute Bulk Fluxes The bulk parameteri2a t i o n formula for momentum flux (or wind stress) i s a relationship which allows east-west and north-south components of the wind stress to be computed from the pro-duct of the wind speed and the east-west and north-south wind components ( 0 » D x , U « 0 y ) . S imi lar i ly , the sensible and latent heat fluxes are determined from the products, DAT and UAq, res-pectively (equations (2) and (3)). To assess at which scales important contributions are made to these products (and hence to the fluxes), the co-spectra between each quantity were computed for each of the products. The co-spectrum <J> resolves the contributions to the.co-variance XY due to in-phase osci l lat ions from various periods. In the co-spectral plots following, f$ i s plotted to produce xy the correct weighting for a logarithmic freguency scale. The co-spectra between the wind speed and each wind com-ponent are displayed in Figure 30. The contributions to the 91 i n - I 3C CO —j on a. CM • cn i E3 CJ 5K _ WIND, E-V SPEED M/SEC WIND COMPONENT M/SEC - r 0 r -A -3 -2 10510(F) : 1 - 3 F IN CYCLES/DAT en-i CM H I— cn i a o E 7 H 7-1 co J i VINO SPEED M/SEC N-S WIND COMPONENT M/SEC + -4 —r--3 1 — -2 LOGIOCF) 1 -I F IN CYCLES/OflY 0 Figure 30: The co-spectrum between the wind speed and the east-west wind component and between the wind speed and the north-south wind component computed from five two-yearly blocks. The vertical error bars represent approximate 95X confidence intervals of the mean co-spectral estimate. 92 covariance (as computed from the area under the graph of cc-spe-ctra l values) from a l l periods resolved by the co-spectral ana-lys i s i s 14.9 (m/sec) 2 for the U«U co-spectra and 3.1 (m/sec) 2 for the U«0 co-spectra. To put these values into perspective, i t should be noted that the contribution to covariance from the product of the long-term averages ( U - ^ and U'Oy.) are 41.5 (m/sec)2 and 14.4 (m/sec)2, respectively. The 0»U co-spectral values are always positive and show peak levels at periods of about seven days with a marked decline at the shorter periods. The contributions to the covariance from periods of 2 days to 6 hours amounts to only 12% of the total spectral covariance and less than 3% of the total co-variance (u•ux=/4>yyx+U•ux ). S imi lar i ly , the u - u y cc-spectral levels are generally* positive with the highest levels found at periods of about 4 days. As with the east-west case, the north-south covariance has relat ively small contributions from periods less than 2 days. These results suggest that when computing the long-term wind stress, using the bulk aerodynamic parameteriza-t ion, one must have measurements at intervals separated by no more than 2 or 3 days to obtain reliable wind stress estimates. The co-spectra of the wind speed with the sea-air tempera-ture difference (U«AT ) and of the wind speed with the sea-air humidity difference (U»Ag) are displayed in Figure 3 1. Both co-spectra follow the same pattern: relatively large positive con-tributions from the annual and semi-annual cycles, while at shorter periods between 7 days and 2 days, relatively large ne-gative co-spectral levels are found. These negative cospectral values are not unexpected since strong winds cause increased VINO SPEED SEfl-fllR TEMP M/SEC DEG C 1 T -2 - J LCSlOCn F IN CTCLES/DflY VINO SPEED SEfl-filR HUMIDITY M/SEC -2 -1 LOS10CFJ F IN CYCLES/DflY Figure 31: The co-spectrum between the wind speed and the sea-air temperature difference and between the wind speed and the sea-air humidity difference from five two-yearly blocks. The vert ical error bars represent approximate 95% confidence intervals of the mean co-spectral estimate. 94 mixing of the surface layers of both the atmosphere and the ocean which decreases air-sea temperature and humidity dif-ferences. In relation to the total co-variance of the wind speed and sea-air humidity difference (U*Aq), the annual and semi-annual variation accounts for only 4.7% of the total and the shorter period variation account for only 3.8%. In addition, because of their opposite signs, these two variations part ial ly cancel one another out. Clearly, the long term latent heat transfer can be determined adequately from long-term averages of the wind speed and the sea-air humidity difference. In terms of the total covariance of the wind speed and the sea-air temperature difference, contributions from the annual cycle and the shorter periods (2 to 7 days) are more important. The annual and semi-annual cycle peaks accounts for 24% of the total covariance (U«AT) while the shorter periods account for . approximately 12%. Thus, in computing the long term sensible heat flux by means of the bulk aerodynamic parameterization, i t is important to include the effects of these periods by choosing a suff iciently small sampling interval . 95 Chapter 6 THE EFFECT OF DATA SMOOTHING OS WIND STRESS COMPUTATIONS J L L I l £ i £ £ £ u c t i o n In this chapter a study is made of the effect cf using the smoothed data that are readily available over the oceans on the computation of wind stress (or momentum flux) by means of the bulk parameterization formula (equation ( 1 ) ) . The two sources of wind f ie ld data which are available over the entire ocean for long periods are wind roses (as compiled in climatic atlases) or mean pressure maps from surface weather charts (from which the wind can be computed geostrophically and then corrected for the f r ic t iona l effect of the surface). Both of these data sources are organized in such a way that the wind data are inherently averaged or smoothed. The effect that this smoothing has on the computed wind stress is examined by smoothing the basic 3-hourly wind data at Station 'Papa' in a similar fashion and then app-lying the equation (1) to this smoothed data. The resulting value of wind stress i s then compared with the estimate of wind stress made by applying the bulk parameterization formula direc-tly to the 3-hourly data. Two previous studies of this kind have been made by Malkus(1962) and Frye(1972). Malkus computed the wind stress by various means at two locations: one in the tropical Atlantic and the other at Weather Station ' C (53N 36W) in the North Atlantic. However, the data used at both locations covered a period of less than a month. Wind roses are generally compiled from many years of data for each month cf the year. The stress 96 magnitude calculated from the wind roses agreed with the direct calculation to within 25%. The stress magnitude computed from the vector averaged wind (which is similar tc what can be com-puted from surface pressure maps) showed good agreement with the direct calculation at the tropical location. However at the more northerly location, i t was low by a factor greater than 2 as a result of the much greater var iabi l i ty cf the wind direc-tion in the latitudes of the westerlies. Frye(1972) studied the effect that the averaging distance (or period) used in obtaining the mean wind speed has on the computed wind stress at an Oregon coastal location. Because his basic data did not include complete wind direction measurements, he chose a data run where the wind was consistently blowing from the north. His results showed that the wind stress steadily decreased with the size of the averaging pericd. At a period of about a week, this change was approximately 20%. Because the drag coefficient, may be a weak function of the wind speed, two different drag coefficients were used. These include a constant drag coefficient (Pcnd et. al. ,1974): CD=1.5x10-3 (30) and a linear drag coefficient (Deacon and Webb,1962): CD= (1 . 0 + 0 . 0 7 » U ) x 1 0 - 3 (31) where 0 i s the mean wind speed in m/sec. More recent measure-ments indicate that the weighting factor of 0.07 used in the linear drag coefficient i s too large. However, i t useful for this study in that i t provides an upper bound of the possible effects of the non-constant drag coefficient. The drag coefficient may depend on the atmospheric s t ab i l i -97 ty as well (Roll,1965). This effect may be important in coastal regions, but i t i s not l ike ly to be important over the open ocean, where the air-sea temperature difference ^T) i s r e l a t i -vely small. At Station »Papa* , the absolute value cf A T exceeds 2 Co in fewer than 10% of the observations. Furthermore, large values of AT often coincide with low wind speed values (Figure 31) , so that the effect of non-neutral s tabi l i ty i s limited to periods when the contributions to the wind stress are small. Since the examination of the effect of smoothing in this study i s limited to one location, the conclusions must be consi-dered tentative. It would be desirable to apply the same analy-sis at other locations to see how the effects vary geographical-ly. , The effect of smoothing over spatial scales also needs to be e xamined. 6±2 Direct Wind Stress Commutation In order to determine the effects of smoothing cn the wind stress computation, the wind stress i s f i r s t computed direct ly from the 3-hourly observations (i .e. no data smoothing). The directly calculated values w i l l be compared in later sections with the wind stress computed from smoothed data. In addition, the direct ly calculated values are useful to i l lus trate the var iabi l i ty of the wind stress over monthly and yearly periods. The direct calculation of the wind stress was made by com-puting both wind stress components for each three-hourly mea-surement and averaging these over the data record used: x x - J | £ n j n J « ^ j ^ ± ;x y = y D ( U . ^\*)\ (32) N N where W i s the number of data points, , x^ are the east-west 98 and north-south stress components, respectively and IL , V\ are the east-west and north-south wind components. The density P i s 1,25x10-3 gm/cm3 (based on Table F-9, Handbook of Chemistry and Physics, 51st edition using an a i r temperature of 8,2 ° C , abso-lute humidity of 7.4 gm/m3 and air pressure of 1010 mbar). The wind stress was computed using both the constant (equation (30)) and linear (equation (31)) drag coefficients. The stress was calculated from 2916 observations for each year (out of a total cf 2920 observations in an ordinary year and 2928 observations in a leap year). The observations were centered on the year. The monthly wind stresses were computed from the same number of observations with each 'month' consis-ting of 243 observations. In months or years which include mis-sing or erroneous data (see Appendix I), the incorrect data i s not used and the stress computation was based on the reduced number of good observations. The wind stress for each of the ten years, 1958 to 1967 inclusive, i s displayed in Figure 32. The results are displayed -as the magnitude of the wind stress (in dynes/cm2) and the dire-ction of the wind stress (as an angle in degrees clcckwise from north). The magnitude cf the stress has sizeable variations between different years. These variations are relat ively large in comparison with the long term wind stress mean but are small in comparison with the fluctuations of the wind stress at smal-ler scales. The direction of the wind stress has smaller year to year variations, ranging in size from 60 to 90 degrees east-ward of north in direction. The direct ly calculated stresses computed using the linear 99 YEARLY WIND STRESS to »-ru U J O 2 re 3E in CONSTANT C D 58 1 59 1 GO 1 Gl 1 G2 1 63 ' 64 1 65 1 66 1 67 CD. CD g i s -to U J U J oc to UJ a U J i CJD 58 1 59 1 60 1 61 1 62 1 63 1 64 1 65 1 66 ' 67 Figure 32: The directly calculated wind stress fcr each year from 1958 to 1967. The wind stress computed using the constant drag coefficient i s plotted as a solid l ine while the dashed line represents the wind stress computed using the linear drag coefficient. 100 drag coefficient are somewhat larger in magnitude but have nearly the same direction. The the ratio of the magnitude i n -crease over the constant drag coefficient case ranges from 1.32 (1962) to 1.50 (1 959) . A large seasonal variation is found in the wind stress ca l -culated for each month and averaged over each of the ten years (see Figure 33). The magnitude of the wind stress i s largest in the f a l l and smallest in the summer. The larger error bars shown on the graph indicate the large year to year differences in the wind stress magnitude for each month. As an example cf this variation, consider the month.of Febuary which in 1958 and 1962 was the month of the lowest wind stress for each year and which in 1967 was the month of the greatest wind stress. The monthly wind stress direction displayed in Figure 31 i s computed as the mean of the ten direction values available for each month. The graph indicates that for a l l months, the stress direction is generally northward (0°) to south eastward ( 1 3 5 ° ) . The monthly wind stresses computed using the linear drag coefficient show larger magnitudes. The relative size of the increase i s related to the mean wind speed of each month. In f a l l and winter, when the mean wind i s larger, the increase in the magnitude i s approximately 50% while in summer when the mean wind i s smaller, the increase i s 25 to 30%. The difference in wind stress direction as a result of using the linear drag coef-ficient is small, being less than 5 degrees for each month. cycn z: a. UJ C3 MONTHLY WIND STRESS LINEAR C D y 101 CONSTANT C D j 1 F 1 H ' fl ' H ' J Figure 33: The direct ly calculated wind stress for each month. The vert ica l error bars represent the 95% confidence intervals of the mean computed from the separate estimates for each of the ten years, 1958 to 1967. The sol id l ine represents the wind stress computed using the constant drag coefficient while the dashed line represents the wind stress computed using the linear drag coefficient. 102 6^ 3 Wind Stress From Climatic Atlases The impetus for studies of the wind stress f ie ld ever the ocean was provided by Sverdrup(1947) who related the strength cf ocean currents to the cur l of the wind stress. Shortly after the appearance of this pioneering work, the Scripps Institute of Oceanography computed the wind stress f i e ld over the North Pacific (1948) and the North Atlantic (1950). Hidaka(1 958) later extended the computations to cover the Indian and Southern Hemisphere Oceans. The basic data used in these computations were wind roses tabulated from many years of observations. For the North Paci f ic , Indian and Southern Hemisphere Cceans, these wind roses provided only the frequency of winds blowing in a given direc-t ion . The wind data for the Atlantic Ocean gave the wind speed distribution in each direction, as well, but in rather coarse groups. With the publication of the Marine Climatic Atlas of the World, volumes I-VIII (1955 to 1.969) , a better data set for wind stress computations became available. Using this atlas, Hellerman( 1967) recomputed the wind stress f i e ld over the world's oceans, although the drag coefficient as a function of wind speed that he used was probably not the best choice in the light of more recent measurements. In order to assess the effect of this data format on the wind stress computation, the data were sorted and tabulated in the format of the Marine Climatic Atlas wind roses for each month from a l l ten years of data. The intervals cf the wind speed distribution of each direction and of the overall wind 103 speed distribution are given in Table V. As in the Marine Climatic Atlas, the wind speed distribution values were rounded off to the nearest single percentage cf the total number of data points used in constructing the wind rose. The symbol *+ ' used in the Marine Climatic Atlas to represent percentages which are non-zero but less than one-half of one percent was taken to be 1/4 of one percent for the purposes of calculation. Twelve directions were used rather than the eight of the Atlas because the original data were provided in 36 directions. Sorting the data into eight directions wculd result in some bias as some of the eight directions would have contributions from five of the original 36 measured directions while others would have contributions from only four of the measured directions. (For a discussion of this effect see Lea and Helvej(1971)). The wind stress was computed for each of the twelve direc-tions following the method of Hellerman (1965). The computation was made using two different drag coefficients (equations (31) and (32)). Wind stresses were then added vectcria l ly tc obtain the east-west and north-south components* From the components, the magnitude and direction were computed and are used in disp-laying the results. The wind stresses, as computed from the data crgani2ed in the wind rose format, are given in Table VI. The corresponding directly calculated values are also given for comparison. The results show that the two magnitudes differ by amounts ranging from less than 1% to as much as 14% for the case of the constant drag coefficient. The average of the monthly absolute percent differences i s 5.6%. The difference between the magnitudes cal-1 04 TABLE V The data format used in wind roses presentee i t the KaiiEe Climatic Atlases. F i r s t , the speed distribution that i s used to group the wind data in each separated d irect icr i s presented. Then, the speed distribution for a l l wine read ir.es iecardless cf direction is presented. lor lach Eirect icn: |Interna1 | Beacfcitj Binimum | numbers J Speed !_ J I (knots) i 1 1 2-3 | 3.5 i 2 1 4-5 | 10.5 I 3 | 5-6 | 21.5 | 4 | 8-12 } 33.5 Overall Speed Distribution,: - T : T — 1 Interval j Feaufcrtj Minimum | | Members ] Speed | _ \ {_ (knots) | 1 I 0-1 | 0.0 | 2 I 2 | 3.5 | 3 I 3 | 6.5 | 4 I 4 I 10.5 | 5 I 5 | 16.5 | 6 i 6 I 21.5 | 7 I 7 I 27.5 | 8 I 8 | 2 3.5 | 9 ! 9 l 40.5 | . j . J J 105 TABLE VI Comparison of the wind stress magnitude arc direction as computed frcn the data organised into the format of the Marine Climatic Atlas (»KCA«) with the value ccnputec cirectly frcn the 2-hourly data ( 'Direct 1 ) . The results are given for the both the constant and linear forms of the drag cce f i i c ient . The stress magnitude has units of dynes/cms-day and the direction is in degrees clockwise from Korth. Ccnstant D rag Coefficient Magnitude I SDiff -1 4 -Eirectici Direct) HCA 1.111 U3.ua | 43.09 62.U3 | 59.61 99.30 | 97.23 91.78 | 68.66 69.89 | 65.18 63.49 j 66.15 6U.98 | 61.90 73.63 | 73.3 5 60.47 | 53.55 75.31 | 77.96 83.3 5 | 63.71 62.70 | 65.25 I 1.1 | 72.45 | 71.74 { C.71 Linear Magnitude JOS SssiiisisiJi; | Month F 4-Oan. Feb. Mar. Apr. May June July Aug. Sept Oct. Nov. Dec. 1 | Year Direct| 1.53 0 1.877 1.701 1.418 1.017 0.77 9 0. 781 1. 183 1.421 2.862 2.919 1.584 4 1.550 | MCA | *Dif f 1.552 1.708 1 .891 1.501 1.200 0.828 0. 872 1. 147 1.3 32 2.842 2.831 1.759 1.4 -9.0 11.2 5.9 18.0 6. 3 11.7 -3.0 -6.3 -0.7 -3.0 11.0 Cirecticr — r . Direct | 47.09 63.40 95.37 90.73 71.52 65.06 64.30 73,01 61.75 74.85 82.01 65.51 MCA • T -I 4-1.571 { 1.4\ 72.73 \ 46.74 60.7 6 98.58 88. 8C 65.46 61.66 60.70 72.66 53. 36 77.55 62.56 66.97 72. 5 C | Dif f . ] 4 -0.35 | -2.64 | 3. 21 -1.93 -6.06 2.80 | -3.60 | -0.35 | -6.37 | 2.70 | C.95 | 1.46 | C 2 3 | 106 culated over a l l the seasons i s only 1.1%. The difference in direction i s less than 6 degrees for each month. The correspon-ding differences for the case of the linear drag coefficient are s l ightly larger. These results demonstrate that the effect of organizing the data into the wind rose format of the Marine Climatic Atlas has a rather small effect on the computed wind stress. JLLH Wi_nd_ Stress From Surface Weather Charts Other sources of wind data over the oceans are the surface air pressure charts issued by various meteorological agencies. Such charts display the mean pressure f ie ld over various periods, often five days, one month or a season. By assuming that the pressure gradient i s balanced by the Coriolis force, the geostrophic wind i s calculated. At the earth's surface, the geostrophic wind must be corrected for the f r i c t iona l effect of the surface. While the relation between the geostrophic wind and the observed surface wind i s not well established, i t is thought that over the open ocean, this correction i s . relat ively small, amounting to a magnitude reduction of 0,7 and a rotation of less than 10 degrees (Flohn, 1969). The geostrophic wind computed from the pressure gradient is a vector quantity. Averaging the pressure f ie ld results in a vector averaging of the resultant geostrophic wind ( i .e . each wind component is averaged). To estimate the effect of using a vector averaged wind in the computation of the wind stress, the observed 3-hourly surface wind observations were vector averaged over various periods. The resultant wind was then used in the bulk transfer formula to determine the wind stress. The wind 107 stress computed from the vector averaged Hind was then compared with the directly calculated wind stress. The comparison scheme described above wi l l only be sensi-tive to the effect that the vector averaging of wind values has on the computed wind stress. Any variations of the resultant wind from other effects over the averaging periods investigated, wil l not be detected by this analysis. Other effects which may result in variations include a possible non-uniform surface cor-rection to the geostrophic wind and the breakdown of the assumed geostrophic balance in certain situations (e.g. during the pas-sage of a storm front), The vector averaging was done separately on each of the 5 blocks of 5832 wind components (each block includes very close to two years of the data). Each data block was divided into 5832 groups of one data sample, 2916 groups of two data samples, 1458 groups of four data samples, 729 groups of eight data samples, and so on up to one group of 5832 samples. The average of both wind components was computed from the individual components in each group. From these averaged wind components, (0 ± l v\ ), i=1,2, . . . L where L i s the number of groups, the wind stress was determined by applying the bulk aerodynamic parameterization: x (T) = p C D y | [ )zY*(\fV±) }A (34) where T i s the averaging period (T=729/L in days). The density, p was assumed to be constant and the calculations were made for both the constant and linear form of the drag coefficients. Because i t was convenient in such a computation scheme to 108 have complete data blocks, the small amount of missing and er-roneous wind data was replaced by wind data taken frcm the pre-vious two yearly data block sampled at the same time cf the year. For example, the two readings of missing wind data on Dec. 23, 1961 were replaced by wind data measurements made on Dec. 23, 1959. The results are displayed in Figure 34, which plots the ratio of the computed stress magnitude from the vector averaged data to the computed stress magnitude from the 3-hcurls data, | T ( T ) | / | T (1/8) | . Also plotted in Figure 34 i s the difference between the wind stress directions, 0< (T)-9;(1/8), computed from the vector averaged values and directly from the 3-hourly va-lues, respectively. The vert ica l error bars represent approxi-mate 95% confidence intervals of the mean computed from the five two-yearly data blocks. The magnitude of the wind stress decreases markedly with the vector averaging period. At a period of one mcnth, the com-puted magnitude i s reduced by more than one-half for the case of the constant drag coefficient. At the same averaging period, for the case of the linear drag coefficient the magnitude is reduced to less than one-third of the directly calculated value. The greater reduction for the case of the linear^ drag coeffi-cient can be partly attributed to the use of the vector mean wind speed in determining the drag coefficient. For longer averaging periods, the value of the drag coefficient i s reduced which results in a further reduction to the computed wind stress. The relat ively small size of the 95% confidence inter-vals indicates that the wind stress reduction with averaging 109 CO a a CM a T(T)/X(l/8) C O N S T A N T C , L I N E A R C D - 4 o.i i 1 1.0 10 PERIOD m IN Dflrs 100 1000 GCT) - eci/8) Figure 34: The rat io of the wind stress magnitude computed from wind data that are vector averaged over a pericd, T to the directly calculated wind stress. The lower plot represents the difference between the direction of the directly calculated wind stress and the direction of the wind stress computed from the vector averaged data. The vert ica l error bars represent approximate 95% confidence intervals of the mean. 110 period i s much the same for each two-yearly data block. The effect of vector averaging on the direction cf the wind stress i s much smaller. Figure 34 shows that the agreement bet-ween the direction computed from the vector averaged values i s generally within 3 degrees of the direction computed directly over a l l averaging periods studied. These results demonstrate that the effect of vector avera-ging the wind data (which is similar to the use cf mean pressure maps for computing the geostrophic wind) i s to reduce considera-bly the magnitude of the computed wind stress ever averaging periods of a few days or longer. However, the effect on the stress direction is quite small and averaged data cf this type seems to provide a good estimate of the direction the wind stress. These conclusions must be considered tentative as they are based on measurements at one location only. To test the results, the same kind of test should be made on wind data from other locations. I l l Chapter 7 THE EFFECT OF DATA SMOOTHING ON HEAT FLUXES Z2.I introduction When turbulent fluxes of sensible heat and latent heat are needed over large oceanic regions, the only data which are avai-lable are inherently smoothed. The effect of this data smoo-thing on the computation of the turbulent heat fluxes through bulk aerodynamic parameterizations is examined in this chapter. The bulk transfer formulas for the sensible heat flux and latent heat flux can be written as Hg = pCp Gj UAT (2) Hj-^ LCqUAq (3) respectively where U i s the mean wind in m/sec, AT is the sea-air temperature differences in ° C , and ag is the sea-air humidi-ty difference in gm/m3. The non-dimensional coefficients Gj. and C Qare taken to be 1.5x10~3, the heat of vapourization per unit mass, L=2.46x10*0 ergs/gm, the specific heat at constant pres-sure, Cp=1.Q0x107 ergs/gm- C and the density of air , p=1.25x10 - 3 gm/cm3 (based on the average temperature of 8 . 2 °C and average absolute humidity cf 7.4 gm/m3). The basic data set needed for the calculation of the heat fluxes are values of U, A T and Ag. Two sources of data avai-lable over large oceanic regions are marine climatic atlases and surface weather charts. The wind data format cf these sources was described in Chapter 6. From the climatic atlas, the wind roses used to display the wind data, allow an accurate determination of the mean wind 112 speed. Climatic atlases also provide the distribution of air temperature, sea temperature and wet-bulb temperature from which AT and Ag may be determined. Alternatively, surface weather charts may be used to obtain the wind information. However, the value determined from this data source corresponds to vector averaged mean wind rather than the mean wind speed (see Chapter 6) used in equations (2) and (3). In addition, surface weather charts may not contain tem-perature or humidity data so these would have to be obtained from other sources. 7.2 Direct Calculation In order to compare the effects of data smoothing on the computation of heat fluxes, the fluxes were computed direct ly from the 3-hourly data. These direct ly calculated heat fluxes sarva as standards for comparison purposes. They are also useful for displaying the year to year and monthly variations. The data were organized into ten yearly blocks, with each block consisting of 2916 3-hourly readings (out of a possible 2928 readings for a leap year and 2920 readings for a non-leap year). Each block was divided into 12 'months*, each being made up of 243 data readings. In those months which had 2 or more incorrect readings, the heat fluxes were computed from the re-duced number of only valid readings. When only a single reading was missing (often the slowly varying sea temperature), linear interpolation was used to replace the reading. The yearly averages of each heat flux are displayed in Figura 35. The latent heat flux has a mean value of 89.2 cal/cm2-day while the sensible heat flux averages 11.6 cal/cm 2-113 Figure 35: The yearly averages of the direct ly calculated sensible and latent heat fluxes. 1 1 4 day. (These values of mean heat fluxes differ s l ightly from the values computed from the spectral analysis as given in Appendix II because the missing and incorrect data were handled differently) . Clearly the sensible heat flux is considerably smaller than the latent heat flux as indicated by the Bcwen's ratio (HQ/H^) which ranges from 0 . 0 5 ( 1 9 5 8 ) to 0 . 18 ( 1 9 6 6 ) about the overall mean value of 0 . 1 3 . From Figure 3 5 , i t appears that over the ten year pericd, 1 9 5 8 to 1 9 6 7 , the sensible heat flux was gradually increasing. However, the latent heat flux does not show any similar long term trend. A very pronounced seasonal variation i s found in both the sensible and latent heat fluxes (see Figure 3 6 ) . The largest heat fluxes occur in the f a l l while the smallest heat fluxes are found in the summer months. A secondary peak in March i s found on average, in both the sensible and latent heat fluxes. The monthly latent heat flux is positive for each month ( i . e . transfering heat from the ocean into the atmosphere) but the monthly sensible heat flux i s generally negative during the months of May through August. 7^3 Climatic Atlas In order to estimate the effect of the smoothing of data presented in the format of the Marine Climatic Atlas, the data were organized into a similar format and from these data, the turbulent heat fluxes were computed. Marine atlases present the wind data in the form of monthly wind roses (as discussed in Chapter 6) from which the mean monthly wind speed can be accura-tely determined. These atlases also provide the mean values of the air temperature, sea temperature and wet-bulb temperature 115 Figure 36: The monthly averaged sensible and latent heat fluxes directly calculated from the 3-hourly data. The ver t i ca l error bars represent approximate 95% confidence intervals of the mean computed from the separate monthly averages for each of the ten years. 116 from which one can determine the mean monthly sea-air tempera-ture difference and sea-air humidity difference. The data were organized into 120 separate months with each •month' consisting of 243 readings (as described in section 7.2)• In those months with two or more incorrect or missing data values, these values were not included. In months which had only one missing or incorrect'value, the bad value was rep-laced by means of linear interpolation. The data fcr each dif-ferent month were then grouped together ( i .e . data from the ten Januarys, the ten Febuarys and so on, were grouped together). From the data in these monthly groupings, the average wind speed and the average sea-air temperature and humidity differences were computed. These were then used in the bulk parameteriza-tion formulae (eguations (2) and (3)) to compute the heat fluxes. The latent heat flux computed from the data in the climatic atlas format shows generally good agreement with the directly calculated heat flux (see Table VII and Figure 37). The average of the monthly absolute percentage difference between the two methods i s 5.5%. The agreement is better for months cf large latent heat fluxes than for months of smaller latent heat fluxes. When the heat fluxes are averaged over the year, the difference i s 2.5%. The use of the climatic atlas data format results in grea-ter deviations of sensible heat flux values. The agreement is poor in months of small sensible heat fluxes; in the months of Febuary and May through August (|H |<12.5 cal/cm2-day) the abso-s lute percent differences exceeds 25%. However in each month of 117 TABLE VII A comparison of the sensible and latent heat fluxes computed from the data organized into the format of the Marine Climatic Atlas ('MCA*) with the value computed directly from the 3-hourly data ( 'Direct ' ) . Both heat fluxes have units of cal/cm 2-day. Sensible Heat Flux Month| Direct I Jan. \ 1 3 . 7 | 1 4 . 8 | 8 . 0 I Feb. | 8 . 4 1 | 1 2 . 3 | 4 6 . 3 I Mar. | 2 5 . 1 | 2 4 . 5 I - 2 . 4 1 Apr. | 1 2 . 3 | 1 3 . 2 I 7 . 3 1 May. j - 6 . 0 9 | - 3 . 5 4 | - 4 1 . 9 | June | - 9 . 0 1 | - 6 . 6 4 | - 2 6 . 3 1 July | - 7 . 3 1 | - 5 . 0 6 | - 3 0 . 8 1 Aug. | - 5 . 7 9 | - 3 . 01 | - 4 8 . 0 1 Sep. | - 0 . 7 4 6 | 2 . 61 | - 4 5 0 . | Oct. | 3 4 . 2 | 3 4 . 3 I - 0 . 3 I Nov. | 4 3 . 9 | 4 5 . 6 I 3 . 9 | Dec. | | Year | 3 0 . 5 | 3 0 . 4 I - 0 . 3 11-6 | 1 3 . 3 | 1 4 . 5 MCA | XDiff• | 4 Latent Heat Flux Month| Direct | MCA %Diff. | I Jan. | 85.2 | 87 . 0 | Feb. | 82.5 | 82.9 | Mar. | 102.3 | 102.4 I Apr. | 91.3 | 91.3 I May | 49. 1 | 51.8 I Ju ne | 30.0 | 36.2 I July | 28.3 | 31.6 | Aug. | 54.9 | 60.4 I Sep. | 86.2 | 94.6 I Oct. j 179.3 | 173.3 I Nov. | 169.5 | 173.4 | Dec. | 111.6 I 111.3 — — • | — | Year | 89.2 | 11- . i - i , 1 . | 91.4 -+-I 2. 1 0.5 0.1 0.0 5.5 20.7 11.7 10.0 9.7 -3.3 2.3 -0.3 2.5 —i l i s CM MARINE CLIMATIC ATLAS DIRECT CALCULATION , . j ' F ' K ' f l ' K ' j ' j ' f l ' S ' f l ' N ' O ' Figure 37: The monthly averaged sensible and latent heat fluxes computed from the data organized into the Marine Climatic Atlases format. For comparison, the corresponding d irect ly calculated values are presented. 119 larger sensible heat fluxes, (JH |>12.5 cal/ctn z-day) the abso-lute percent difference i s less than 8.0%. Averaged over a l l the months, the difference is 14.5%. For the purposes of computing the turbulent heat exchanges ovsr the entire year, the data organized in the Marine Climatic Atlas format can be used with a reasonable degree of accuracy. However, for the spring and summer months when the heat fluxes are comparitively small, the difference between the heat fluxes computed directly and those computed from the marine climatic format may ba unacceptabley high for some purposes. 7^ 4 Surface Weather Charts The turbulent heat fluxes may be computed using wind data derived from surface weather charts. From the isobars provided on mean surface weather charts, the geostrophic wind may be de-termined. Knowing the geostrophic wind and correcting for the effects of surface f r i c t i o n , the surface wind i s derived. As described in section 6.4, the effect of using pressure maps averaged over long periods, i s that of vector averaging the shorter term wind observations. In order to simulate this averaging effect, the wind components, vector averaged over various periods were used to compute the magnitude of the wind. Often surface weather charts do not provide sufficient informa-tion to compute the sea-air temperature and humidity dif-ferences. Therefore, additional sources of data, such as clima-tic atlases, may be needed to compute the turbulent heat fluxes. The averaged heat fluxes were computed for each of the five two-yearly data blocks. As described in section 6.4, two or more missing or incorrect data readings are replaced by readings 120 taken from the previous two-yearly data block at the same time of year. For example, the missing data beginning on Dec, 3, 1967 was replaced by data beginning on Dec. 3,1965. Single i n -correct or missing readings are replaced by l inear i ly interpo-lated values. The effects of the surface weather chart smoo-thing are displayed in Figure 38. For each heat flux, Figure 38 displays the ratio of the heat flux computed from mean values averaged over a period, T, to the heat flux computed directly from the 3-hourly measurements. The vert ica l error bars repre-sent the approximate 95% confidence intervals of the mean of the ratio at each period, computed from the five separate data blocks. The effect of using the surface weather chart data format is to markedly reduce the heat fluxes over averaging periods longer than one day. For example, at a period of one month, the sensible heat flux i s reduced to 0.62 of the direct ly calculated value and the latent heat flux is reduced to 0.53 cf the direct-ly calculated value. At periods of approximately one year or more, the ratio between the heat fluxes computed by the two me-thods appears to become nearly constant. The reduction of the heat fluxes is less than that found for the magnitude cf the wind stress. This difference i s due to the wind stress being proportional to the square cf the wind while the heat fluxes are proportional to the wind i t s e l f . If C =C =C and C i s a linear function of the wind speed rather D T q D than a constant, the effects would be larger as in the case for wind stress although perhaps not so marked. Nevertheless, the reduction in the fluxes i s considerable and some correction is . , , , j 0 .1 1.0 10 100 woo PERIOD (T) IN DAYS F i g u r e 38: The r a t i o of the s e n s i b l e and l a t e n t heat f l u x e s as computed from data t h a t i s v e c t o r averaged over a p e r i o d , T to the heat f l u x e s computed d i r e c t l y from the 3-hourly r e a d i n g s . The v e r t i c a l e r r o r bars represent the approximate 955? con f i d e n c e i n t e r v a l s of the mean of the r a t i o ' s as computed from the f i v e two-yearly data b l o c k s . 122 needed i f surface weather charts of averaging periods of a few days or more are to be used to compute these fluxes. 123 Chapter 8 SUHFIARY The s u r f a c e l a y e r cf the atmosphere over the cpen ocean and the i n t e r a c t i o n between the ocean and the atmosphere were s t u -died by examining a ten year r e c o r d of 3-hourly surface meteoro-l o g i c a l g u a n t i t i e s a t Ocean Weather S t a t i o n •Papa' (50N 145W). To determine the important p e r i o d i c i t i e s cf each q u a n t i t y , the power spectrum was computed from data blocks of two years d u r a t i o n . Separate s p e c t r a were computed f o r each season as w e l l . The spectrum of the wind speed i s dominated by a c t i v i t y of s y n o p t i c s c a l e s . A peak l e v e l i n the f«$ spectrum of 8.2 (m/sec) 2 occurs at a p e r i o d of 3 days. The annual peak i s prominent while there i s no s i g n i f i c a n t d i u r n a l peak. A s m a l l but s i g n i f i c a n t amount of a c t i v i t y i s present at the semi-diur-n a l p e r i o d . Seasonal changes are found i n the behavior cf the wind speed. The wind speed s p e c t r a of the f a l l and winter f e a -ture a l a r g e r amplitude s y n o p t i c peak centered on s h o r t e r p e r i o d s as compared to the s y n o p t i c peak of the s p r i n g and sum-mer. A comparison with the wind speed s p e c t r a determined by other i n v e s t i g a t o r s at v a r i o u s l o c a t i o n s , r e v e a l s t h a t Ocean Weather S t a t i o n •Papa' i s c h a r a c t e r i z e d by higher l e v e l s cf ac-t i v i t y o c c u r r i n g at g e n e r a l l y s h o r t e r periods. An examination of the v e c t o r wind was made by computing the r o t a r y power spectrum. Both the clockwise and a n t i - c l o c k w i s e part of the spectrum are dominated by a broad s y n o p t i c peak at 3 days. The c l o c k w i s e s i d e has higher s y n o p t i c l e v e l s , a r e s u l t of the p r e v a i l i n g p a t t e r n of the movement of s y n c p t i c d i s t u r -124 bances to the north of Station 'Papa'. The rotary spectrum shows no significant annual or diurnal ac t iv i ty . A small but significant semi-diurnal peak is found only in the clockwise part of the spectrum. The synoptic peak has a dist inct seasonal variation occurring with higher levels and at shorter periods in f a l l and winter as compared to spring and summer. The air pressure spectrum i s dominated by a broad uneven peak over periods ranging from 3 to 70 days. The spectrum re-veals a sizeable annual variation. A much smaller semi-diurnal variation i s also present. As with the wind, the spectral levels are largest in the f a l l and winter, smaller in the spring and smallest in the summer. The spectra of sea temperature, air temperature and abso-lute humidity are a l l dominated by large annual and semi-annual peaks. The average annual range of sea temperature is 7.9 C° while the range of the semi-annual cycle is 2.2 C ° . The average annual and semi-annual ranges of air temperature are 8.3 C° and 2.6 C ° , respectively. The average annual and semi-annual ranges of absolute humidity are 4.4 gm/m3 and 1.7 gm/m3, respectively. Both the sea and a ir temperature have significant diurnal variations. The absolute humidity has a smaller diurnal varia-tion which is only marginally significant. The average diurnal range of the air temperature is 0.64 C° and that of the sea tem-perature is 0.13 C ° . Both the sea and air temperature have the largest diurnal variation in spring which includes the period of greatest solar insolation. From the spectrum of sea surface temperature, i t appears that there is very l i t t l e act iv i ty between periods of one day 125 and one year. However, the a i r temperature spectrum shows a very hroad, uneven peak between periods of 2 days and 60 days. The spectral levels over this range of periods increase in f a l l and winter and are reduced in spring and sunnier. The absolute humidity spectrum reveals a broad but well defined synoptic peak (over periods from about 1.5 days to 48 days) with a peak level at 5.5 days. These synoptic spectral levels are largest in the f a l l and smallest in the spring. The rotary power spectrum of the time series (U»U X ,0»Uy) , proportional through the bulk aerodynamic parameterization: to the wind stress, has the same general characteristics as the rotary power spectra of the wind. The spectra cf U»AT (repre-sentative of sensible heat flux) and 0«Aq (representative of latent heat flux) each show a strong annual peak and a broad synoptic peak that accounts for most of the quantities' variance. The synoptic peak shows that the largest variations are found between periods cf 4 to 7 days. The sensible heat flux has a sizeable diurnal variation with an average daily range of 16.9 cal/cm2-day (as compared to the mean sensible heat flux of 11.7 cal/cm 2-day). The latent heat flux has no diurnal cycle. The spectral levels of both the sensible and latent heat fluxes show the greatest var iabi l i ty taking place in the f a l l and the least in the spring and summer. ft rotary cross-spectral analysis cf the relatedness of the vector wind with the scalar quantities of air pressure, air tem-perature, absolute humidity and sea temperature reveals general-ly significant coherence levels over synoptic periods. While the coherence i s s t a t i s t i ca l ly s ignificant, the ccherences de-126 termined are generally too low to be useful for predictive pur-poses. In each of the rotary cross-spectra, the synoptic co-herence is larger for clockwise wind rotations than those of the anti-clockwise wind. The cross-spectra between the scalar quantities and the wind speed were also computed. The coherence levels found at synoptic periods were lower than the rotary coherence levels for each scalar quantity except the sea temperature which at periods of 3 days or more showed generally higher coherence. This result suggests that while the wind rotation i s important in determining air mass characteristics, i t i s much less important in the coupling of the wind f ie ld to ocean water mass charac-ter i s t ics at a fixed point. The coherence spectrum between the air temperature and ab-solute humidity shows high coherence levels (greater than 0.8) from periods of two years to 3 days. At periods shorter than 3 days, the coherence declines rapidly. The co-spectrum of the east-west wind component with the wind speed and the north-south wind component with the wind speed are representative of contributions to each of the wind stress components over the periods resolved. These values ind i -cate that wind measurements at intervals of 3 days or less are required to accurately estimate the wind stress (within 55?) . The co-spectrum of the wind speed with the sea-air humidity difference, representative of contributions to the latent heat flux, show that contributions from the periods resolved are small. Long-term averages of the wind speed and sea-air humidi-ty difference are adequate to compute the latent heat flux. In v127 •' contrast, the co-spectrum of the sea-air temperature difference and the wind speed indicates that measurements at intervals of 3 days or less are required for a rel iable estimate (within 5%) of the sensible heat flux. The effect of data smoothing inherent in the data format of the Marine Climatic Atlas was examined. The wind stress magni-tude computed from the data organized into this format, differs by 1 to 14% from the corresponding directly calculated wind stress for each month (taking the drag coefficient, CD=1.5x10-3) with an average absolute percentage difference of 5.6%. The difference in the stress direction i s less than 7 degrees for each month. When a drag coefficient that depends l inear i ly on the wind speed i s used ( 1 0 3 ( ^ = 1.0+0. 07«u", U in m/sec) , the dif-ferences are s l ight ly larger. The effect of the data smoothing of the Marine Climatic Atlas on the computation of latent heat flux i s also small. The average of the monthly absolute percentage difference between the two methods i s 5.5%. For the sensible heat flux, the effect of this data format i s larger, exceeding a 25% difference in months of small sensible heat fluxes (less than 12.5 cal/cm 2-day) and averaging just under 8% difference in months of larger sensible heat flux. An alternative method of computing turbulent fluxes over large oceanic regions is to use averaged surface weather charts. These are equivalent to vector averaging the wind data. The wind stress computed from vector averaged wind data over various periods i s displayed in Figure 34. The magnitude of the wind stress, for an averaging period of a month, i s reduced to less (128^ than one-half of the direct ly calculated value for the case of the constant drag coefficient. For the linear drag coefficient, the wind stress magnitude is reduced to less than one-third of the directly calculated value. The effect of vector averaging on the wind stress direction i s much smaller, with the methods giving the same results within 3 degrees, for a l l averaging periods. The effect of using the surface weather chart data format on the turbulent heat fluxes i s also large. For an averaging period of one month, the sensible heat flux i s reduced to 0.62 of the directly calculated value while the latent heat flux i s reduced to 0.53 of the direct ly calculated value. The results of the study of effects of data smoothing on the computation of bulk fluxes, must be regarded as tentative as they are made with data from only one location. Similar studies are needed for other locations. 129 BIBLIOGRAPHY Blackman, R. B. and J.W. Tukey (1958). The Measurement of Power S £ e c t r a . Dover Publications: New York, N.Y, Bendat, Julius S. and Allan G. Pierscl (1971). Random Data. Wiley-interscience, New York. Blackadar, A.K. (1959). Periodic wind variations. Mineral Industries, 28(4). College of Mineral Industries, The Pennsylvania State University, pp.1-5. Burt, W., H. Crew, N. Plutchak and J. Dumcn (1974). Diurnal variations of winds over an upwelling region off Oregon. Boundary-Layer Meteorology, 6, pp. 35-45. Butler, S. (1962). Atmospheric tides. Scienti f ic American, 207 (6) , pp. 48-59. Byshev, V.I . and Yu. A. Ivanov (1969). The time spectra of some characteristics of the atmosphere above the ocean. Izvestia, Atmsopheric and Oceanic Physics, 5(1), pp. 17-28. Cooley, J.W. and J.W. Tukey (1965). An algorithm for the machine calculation of complex Fourier series. Mathematics of Computation, J 9 , pp. 297-301. Deacon, E.L. (1969). Physical processes near the surface of the earth. In General Climatology, ed. by H. Flchn, Flsevier, Amsterdam, pp. 39-104. Deacon, E.L. , and E. K. Webb (1962). Small scale interactions. In The Sea Vol. I, ed. by M. H i l l , Interscience Publishers, New York. pp. 43-87. Denman, K. L. (1972). The response of the upper ocean to meteorological forcing. Ph.D. Thesis, Institute of Oceanography, University of Bri t i sh Columbia. 117 pp. Dorman, C.E. (1974). Analysis of meteorological and oceanographic data from Ocean Station Vessel N (30N 140W). Ph. D. Thesis, Oregon State University. 136 pp. Fiedler, F. and H. A. Panofsky (1970). Atmospheric scales and spectral gaps. Bullet in of the American Meteorological Society, 51(12), pp. 1114-1119. Flohn, H. (1969). Climate and weather. McGraw-Hill, New York. 253 pages. Frye, D.E. , S. Pond and W.P. E l l i o t t ( 1972). Note on the kinetic energy spectrum of coastal winds. Monthly Weather Review, IP_0(9), pp. 671-672. 130 Garrett, J . (1970). Field observations of frequency domain s tat i s t ics and nonlinear effects in wind-generated ocean waves. Ph. D. Thesis, Institute of Oceanography, University of Brit ish Columbia. 176 pp. G i l l , A. (1974). Mid-ocean eddies in ocean weather ship records. Mode Hot Line News, No. 49, pp. 3-10. Gossard, E .E . (1960). Spectra of atmospheric scalars. Journal of Geophysical Research, 65(10), pp. 3339- 3351 . Groves, G.W. and E . J . Hannan (1968). Time series regression of sea level on weather. Reviews of Geophysics, 6(2), pp. 129-174. Hertzman, o. , M. Miyake and S. Pond (1974). Ten years of meteorological data at Ocean Station Papa. Manuscript Report No. 29, Institute of Oceanography, University of Brit ish Columbia. 46 pp. Hellerman S., (1965). Computations of wind stress fields over the Atlantic Ocean. Monthly Weather Review, 93(4), pp. 239-244. Hellerman S., (1967). An updated estimate of the wind stress on the world ocean. Monthly Weather Review, 95(9), pp. 607-626. Hess, G.D. and R.H. Clarke (1973). Time spectra and cross-spectra of kinetic energy in the planetary boundary layer. Quarterly Journal of the Royal Meteorological Society, 99, pp. 130-153. Hidaka, K. (1958). Computation of the wind stresses over the oceans. Record of Oceanographic Works of Japan, 4, pp. 77-123. Jenkins, J.M. and D.G. Watts (1968). Spectral Analysis. Holden-Day, San Francisco. 325 pp. Kolesnikova, V.N. and A.S. Monin (1965). Spectra of meteorological f i e ld fluctuations. Izv. , atmospheric and Oceanic Physics, J,, pp. 653-669. Lea, D.A. , and Helvey (1971). Directional bias in wind roses due to mixed compass formats. Journal of Applied Meteorology, 10(5) , pp. 1 037-1039. Malkus, J.S. (1962). Large-scale interactions. In The Sea Vol. I ed. By M. H i l l , Interscience Publishers, New York, pp. 88-294. 131 Millard, R.C. (1971). Wind measurements from buoys; a sampling scheme. Journal of Geophysical Research, 76(24), pp. 5819-5828. Mooers, C. N.K. (1973). A technigue for the cross spectrum analysis of pairs of complex-valued time series, with emphasis on properties of polarized components and rotational invarients. Deep-Sea Research, 20, pp. 1129-1141. Oort, A.H. and A. Taylor (1969). On the kinetic energy spectrum near the ground. Monthly Weather Review, 97(9), pp. 623-636. Panofsky, H.A. (1969). Spectra of atmospheric variables in the boundary layer. Radio Science, 4(12), pp. 1101-1109. Pillsbury, R.D. (1972). A description of hydrography, winds and currents during upwelling season near Newport, Oregon, Ph. D. Thesis, Oregon State University. 163 pp. Polowchak, Van M., and H.A. Panofsky (1968). The spectrum of daily temperatures as a climatic indicator. Monthly Weather Review, 96(9), pp. 595-600. Pond, S., G.T. Phelps, J .E, Paguin, G. McEean and R.W. Stewart (1971). Measurements of the turbulent fluxes of momentum, moisture and sensible heat over the ocean. Journal of the Atmospheric Sciences, 28, pp. 901-917. Pond, S. , D. B. Fissel and C.A. Paulson (1974). A note cn bulk aerodynamic coefficients for sensible heat and moisture fluxes. Boundary-Layer Meteorology, 6, pp. 333-339. Roden, G.I. (1963). On sea l eve l , temperature, and sa l ini ty variations in the Central Tropical Pacif ic and cn Pacific Ocean Islands. Journal of Geophysical Research, 68(2), pp. 455-472. Roden, G.I . (1965). On atmospheric pressure osci l lat ions along the Pacific coast of North America, 1873-1963. Journal of the Atmospheric Sciences, 22, pp. 280-295. Rol l , H.V. (1965). Physics of the Marine AtmcsjDhere. Academic Press Inc., New Y o r k T 426~pp. ~ ~ Scripps Institute of Oceanography, University of California (1948). The f ie ld of mean wind stress over the North Pacific Ocean. Oceancgraphic Report No. 14. 132 Scripps Institute of Oceanography, University cf California (1951). The mean wind stress over the Atlantic Ocean. Oceanographic Report No. 21. Singleton, Richard C. (1969). An algorithm for computing the mixed radix Fast Fourier Transform. IEEE Transactions on Audio and Electroacoustics, V7(2), pp. 93- 103. Stewart, R. W. (1974). The air-sea momentum exchange, Boundary-Layer Meteorology, 6(1/2), pp. 151-167. Sverdrup, H.U. (1947). Hind driven currents in a baroclinic ocean; with application to the equatorial currents of the Eastern Pac i f ic . Proceedings of the National Academy of Sciences. 33(11), pp. 318-326. Tabata, S. (1961). Temporal changes of s a l in i ty , temperature and dissolved oxygen content of the water at Station "p" in the Northeast Pacif ic Ocean, and some of the determining factors. Journal of the Fisheries Research Board of Canada. 18 (6) : pp. 1073-1 124. Tabata, Susumu (1965). Var iab i l i ty of oceanographic conditions at Ocean Station 'P» in the Northeast Pacific Ocean. Transactions of the Royal Society of Canada, 3, Series 4, Section 3, pp. 367-418. U. S. Navy, Chief of Naval Operations (1955 to 1969). Marine climatic atlas of the world. Vol. I to VIII. Washington, D.C. NAVAER 50-1C-528. Van der Hoven, I. (1957). Power spectrum of horizontal wind speed in the frequency range from .0807 tc 900 cycles/hour. Journal of Meteorology, 1.4, pp. 160-164. Wunsch, C. (1972). Bermuda sea level in relation to tides, weather and baroclinic fluctuations. Reviews of Geophysics and Space Physics, 10(1), pp. 1-49. APPENDIX I INCORRECT DATA The following table provides a l i s t ing of the times missing(M) or erroneous(E) data samples. T T - T •T T -Year | Starting | Number of |9 IP ' T a JT |T J | time | readings I | -+- - j -+— +—+—4 1958 J 0000 Jan. 1 | 1 I | M 1 M | M 1 M | j 2100 Feb. 19 J 1 I I E ) 1 1 1 I 0900 Oct. 28J 1 I I 1 1 IE | I 0900 Nov. 11 1 |E I E I 1 1 1 1959 J 1200 Bar. 25J 1 | E j | j | | | | 2100 Sept, 10 j 1 j j j IB | 1 j 0600 Oct. 19 | 1 } E | J | 1 1 1 I 1500 Nov. 14| 2 | H I M 1 M |M |M | 1960 j 2100 Jan. 301 4 j j | 1 IB | | 0000 Feb. 7 | 3 | I | 1 IB | j 1200 N O V . 15| 1 J | 1 1 IB | I 1200 Dec. 18 J 2 I H | M | M |H |M | 1961 j 1200 Mar. 31 6 I n I w | M | W |H |M J | 1500 June 26 1 2 l a I M | M | M 1 H 1 M 1 | 0000 July 15 | 1 j J | IB | | j 0900 Sept. 15 j 5 | H | H | H 1 M | M J M | I 1200 Dec. 23 I 2 J M | M | » |M |H |M | 1962 J 0900 Jan. 21 2 I » I H |H | H |K |M 1 j 0000 Feb. 11 2 I H I M | M ) M 1 H | H | j 1800 Apr. 13 | 2 |M | M |H |M |M | W | | 1200 Oct. 41 1 j j j 1 IB | t 1500 Oct. 261 1 I 1 IB | 1963 | 1500 Feb. 271 1 I | j IB 1 | j 2100 Nov, 151 1 I 1 | 1 IB | I 0300 Nov. 24 | 1 j 1 IB | 1964 J 2100 Hay 6 S 1 | I 1 IB 1 | 0900 Oct. 6| 43 I a I I'l | M I M 1 M | M | I 1500 Oct. 12J 1 I 1 E 1 1 1 .... A . L J . . - j . _-L . . j . -JL L 1 Year | Starting |Number of | I | | | | time | readings I 6 I o • T a | T S | ^_ _ +— -+— {__ H—+— +—-1 1965 | 1200 Jan. 2| 52 I H I M | M I M in I M | | 0000 Jan. 9| 1 I " I M I | I w I | 0000 July : 226 | 1 I |E I j j J 1966 | 0900 Jan. 29| 1 | | I | |E | | 0900 Oct. , 15| 1 | H | H | M I n I | 1200 Oct. 15| 1 | H I M I I I M | 1967 | 1500 Jan. 11| 61 t H I M |M | M | M I M | | 0600 Jan. 19| 1 | M | M | | | M | | 0900 Dec. 3| 48 I « I H | M |H |M I M I | 1200 Dec. 9| 1 I M I n | j I « I 135 • APPENDIX II MEANS AND POWER SPECTRAL INTEGRALS when i n t e r p r e t i n g power s p e c t r a l r e s u l t s , i t i s u s e f u l to know the averages of the q u a n t i t y and the cumulative i n t e g r a l of the spectrum. These values are presented below f o r the two-yearly s p e c t r a and f o r the sea s o n a l s p e c t r a of each q u a n t i t y . Q u antity O v e r a l l | Winter| Spring|Summer | F a l l Average | Wind Speed | (m/sec) I 1 0 . 2 | 1 1 . 5 I 8 . 7 2 | 8 . 2 4 1 2 . 3 | | East-west Wind |. (m/sec) | 4 . 0 6 | 3 . 38 | 3 . 52 i 3 . 9 5 | 5 . 3 4 | | North-south Wind | (m/sec) | 1 . 40 1. 54 | 0 . 96 | 1 .69 1 . 4 1 | | A i r Pressure | (mbar) | 1 0 1 2 . 2 | 1 0 0 8 . 2 I 1 0 1 6 . 6 | 1 0 1 7 . 5 1 1 0 0 6 . 6 | | Sea Temperature 1 ( ° c ) | 8 . 4 6 5 . 65 I 7 . 1 9 | 1 2 . 5 8 . 5 4 | 1 A i r Temperature 1 (°C) | 8 . 1 8 | 5 . 25 | 7 . 18 | 1 2 . 5 | 7 . 7 8 | | Absolute Humidity j (gm/m3) I 7 . 35 5 . 9 1 | 6 . 85 | 9 . 8 2 | 6 . 8 2 | 1 (u«-u x ) | (m/sec) 2 1 5 6 . 4 ! 5 3 . 8 1 4 2 . 1 | 4 3 . 5 | 8 5 . 6 | 1 ( u - u y ) | (m/sec) 2 | 1 7 . 5 2 0 . 2 1 9 . 3 8 | 1 9 . 1 I 2 1 . 2 | | S e n s i b l e Heat Flux | (cal/cm 2-day) l 1 1 . 7 1 6 . 2 1 - 0 . 9 3 | - 4 . 59 | 3 6 . 3 | | L a t e n t Heat Flux | (cal/cm 2-day) | 8 8 . 9 i i 8 9 . 6 1 5 6 . 8 | .._.. ± 5 6 . 5 | 1 5 3 . 2 | 136 Quantity Wind Speed (m/sec)2 Clockwise U (m/sec) 2 Anti-Clockwise U (m/sec) 2 Pressure (mbar) Sea Temperature ( C O ) 2 Air Temperature ( C O ) 2 Absolute Humidity (gm/m3) 2 Clockwise U«U (m/sec) * Anti-clockwise U»U (m/sec)* Sensible Heat Flux (cal/cm2-day) 2 Latent Heat Flux (cal/cm2-day) 2 Overallj Winterj SpringjSummer j F a l l + + 19.4 Integral 28.3 63.0 50.5 176. 8.46 10.7 3.94 18200 13200 4130 14300 28. 1 75.8 60.0 194. 0. 106 1.83 1.11 23400 16900 5020 12400 43.? 34.8 87. 1 0. 179 0.949 0.726 9290 7130 1500 5130 16.9 36.7 28.2 70.6 0.248 0.837 1.28 7300 5060 952 6870 31.4 80.7 61.8 175. 0. 172 2. 19 1.72 28900 19500 6850 22100 

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