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Heat budget analysis of Pendrell Sound Buckingham, William Richard 1976

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A HEAT BUDGET ANALYSIS OF PENDRELL SOUND by WILLIAM RICHARD BUCKINGHAM B.Sc.(Hon), Acadia U n i v e r s i t y , 19.73 Cert, of Applied Science, Acadia U n i v e r s i t y , 1973 A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF SCIENCE i n THE DEPARTMENT OF PHYSICS and THE INSTITUTE OF OCEANOGRAPHY We accept t h i s thesis as conforming to the required standard Dr. M. Miyake Dr. D.M. Farmer (D.O.E.) Dr. R.W. Burling THE UNIVERSITY OF BRITISH COLUMBIA -'. December,, 1976 (c) William Richard Buckingham In presenting th i s thes is in pa r t i a l fu l f i lment of the requirements for an advanced degree at the Univers i ty of B r i t i s h Columbia, I agree that the L ibrary shal l make it f ree ly ava i l ab le for reference and study. I further agree that permission for extensive copying of th is thesis for scho lar ly purposes may be granted by the Head of my Department or by his representat ives. It is understood that copying or pub l i cat ion of th is thesis for f inanc ia l gain sha l l not be allowed without my writ ten permission. Department of FtfrSiCS-The Univers i ty of B r i t i s h Columbia 2075 Wesbrook Place Vancouver, Canada V6T 1W5 Date ^ ^ T ~ . / , ( i i ABSTRACT A f i e l d program c o n s i s t i n g of a heat budget study was c a r r i e d out i n Pendrell Sound during the summer of 1974 by the Department of the Environment ( Coastal Zone Oceanography Group ) i n an attempt to resolve the mechanism involved i n creating the warm water favourable to oyster spawning. The temperature - s a l i n i t y structure was measured at various locations along the channel and meteorological parameters relevant to heat exchange were observed. The r e s u l t s show that advection i s the most important mechanism with regards to the heat budget of the en t i r e i n l e t , accounting f o r 80% of the increase i n heat content during a nine day warming period that was observed. i i i TABLE OF CONTENTS Page ABSTRACT i i LIST OF TABLES v LIST OF FIGURES v i ACKNOWLEDGEMENTS v i i PART I INSTRUMENTATION AND OBSERVATIONS Chapter 1 INTRODUCTION 1 1.1 Physical Description 1 1.2 Relevance of a Physical Study of Pendrell Sound to the Oyster Industry 3 1.3 Heat Budget Theory 5 2 INSTRUMENTATION AND DATA 8 2.1 Historical Data 8 2.2 Data Collection * 9 2.3 Heat Budget Terms . . . 12 2.4 Temperature versus Depth Profiles 18 2.5 Thermistor Chain Data 22 2.6 Anemometer Data 26 2.7 Current Meter Data 26 PART II DISCUSSION AND ANALYSIS 3 HEAT BUDGET OF PENDRELL SOUND 32 3.1 Description of the Temperature Structure of Pendrell Sound 32 3.2 Integrated Heat Equation of Pendrell Sound . . . 34 iv Chapter Page 4 EVALUATION OF THE HEAT BUDGET TERMS 38 4.1 Rate of Change of Heat Content 38 4.2 Local Heating Processes 39 4.3 Advection of Heat 40 4.3(a) Evaluation . . . . . 41 4.3(b) Wind-driven Currents 43 4.3(c) Density-driven Currents 43 4.4 Horizontal Turbulent Diffusion 47 4.5 Redistribution of Heat 48 4.6 Conclusions and Discussion 50 5 SUMMARY AND DISCUSSION 53 5.1 Why Pendrell Sound is a Unique System 53 5.2 Possible Future Quantitative Analysis 54 6 IMPLICATIONS FOR BIOLOGICAL PROCESSES 55 APPENDIX - TEMPERATURE VERSUS DEPTH DATA 57 REFERENCES 62 V LIST OF TABLES Table Page I Daily Values of the Heat Budget Terms 17 II Estimated Magnitudes of the Integrated Heat Equation Terms 51 III Temperature versus Depth Data '57 v i LIST OF FIGURES Figure Page 1 Northern section of the Straight of Georgia showing the l o c a t i o n of Pendrell Sound 2 2 Longitudinal depth p r o f i l e of Pendrell Sound . . . . 4 3 Location of hydrographic stations i n Pendrell Sound . . 10 4 Plots of heat budget terms versus time 14 5 Time series of temperature versus depth p r o f i l e s . . . 19 6 Temperature versus depth p r o f i l e s during warming period 21 7 Temperature versus time for various depths 23 8 Rate of Keating as a function of depth 25 9 Wind vectors versus time 27 10 Current vectors versus time and temperature at s i x meters depth versus time 29 11 Schematic sketch of Pendrell Sound 33 12 Density sections of July 26, 1967 44 13 Plot of v e r t i c a l shear versus time between two meters and ten meters depth 49 v i i ACKNOWLEDGEMENTS The production of t h i s thesis would have been impossible without the assistance of several people. F i r s t l y , I would l i k e to express my gratitude to Dr. Miyake, my supervisor, for providing guidance and sup-port throughout the study. I would also l i k e to thank Dr. Farmer of the Department of the Environment who suggested the problem and provided funding, t e c h n i c a l assistance, and constructive c r i t i c i s m . Many thanks for t e c h n i c a l and moral support must also go to Angus, Rube, Cactus, T.U., Shroeder Rabbit, Lome Ranger, Rasma, B i l l , Grace, Terry Two-Beer, Del, Sus, C o l i n , and Clinton. Thanks a bunch, gang! During my f i r s t year of study at the I n s t i t u t e of Oceanography, I was personally supported by a National Research Council Postgraduate Scholarship. Support during the subsequent years came from the Depart-ment of the Environment ( Coastal Oceanography Group ). PART I INSTRUMENTATION AND OBSERVATIONS 1 CHAPTER 1 INTRODUCTION The following t r e a t i s e describes a heat budget study that was ca r r i e d out i n Pendrell Sound during the summer of 1974 i n an attempt to resolve the mechanism involved i n the creation of warm water favour-able to oyster spawning i n t h i s i n l e t . The temperature structure was measured at various locations along the channel and meteorological par-ameters relevant to heat exchange were observed. The period of study coincided with the period of oyster spawning and spat c o l l e c t i o n i n thi s i n l e t . The r e l a t i v e importance of l o c a l heating and advection i s assessed. 1.1 Physical Description Pendrell Sound i s a deep f j o r d - l i k e i n l e t about s i x miles long and one mile wide which cuts very deeply into East Redonda Island i n the northeast corner of the S t r a i t of Georgia ( F i g . 1 ). This i n l e t i s s i g n i f i c a n t p h y s i c a l l y i n that i t contains some of the warmest sur-face water i n the whole of the Straight of Georgia with summer surface temperatures occasionally reaching 26°C. At the head of the i n l e t , a neck of low land approximately one h a l f mile wide separates i t from Pryce Channel. The rest of the i n l e t i s mostly surrounded by steep h i l l s which r i s e to 5000 feet within a mile or so of the shore. The Figure 1 Northern s e c t i o n of the Straight of Georgia showing the l o c a t i o n of Pendrell Sound 3 shores themselves are i n most cases nearly v e r t i c a l and there i s very l i t t l e beach area. Except for seepage-type runoff, there i s no s i g n i -f i c a n t fresh water drainage into the i n l e t . The l o n g i t u d i n a l section of the i n l e t i n Figure 2 shows the abs ence of a s i l l at the mouth and only a p a r t i a l s i l l of approximately 120 meters depth midway along the i n l e t . 1.2 Relevance of a Physical Study of Pendrell Sound to the Oyster Industry The P a c i f i c oyster industry i n B r i t i s h Columbia i s based on the p r i n c i p l e of bringing seed oysters from external sources to the growing area. B r i t i s h Columbia and the west coast of North America generally make use of two independent sources of oyster seed, one l o c a l and one Japanese. With respect to the l o c a l sources, Pendrell Sound i s the main breeding area f o r P a c i f i c oysters i n B r i t i s h Columbia. The oysters spawn and are i n a free f l o a t i n g stage for varying periods of time during June to the end of August before they s e t t l e on c o l l e c t o r s i n s t a l l e d by the oyster industry. Pendrell Sound i s unique since i t has been consistent-l y an area where successful spawning and recruitment of oysters has oc-cured. One of the s i g n i f i c a n t factors i n the i n l e t , r e l a t i v e to oyster breeding, i s the maintenance of high water temperatures at the surface during July and August. Water temperature appears to be the main l i m i t -ing factor i n breeding success. It may not have a d i r e c t e f f e c t on l a r -vae, but i t may have an e f f e c t on the production of l a r v a l food. Another l i m i t i n g factor i s the range of s a l i n i t i e s that the larvae are exposed to. The r e l a t i v e l y low s a l i n i t y i n Pendrell Sound may be one of the . 2 3 4 5 6 7 8 9 STATION Figure 2 Longitudinal depth p r o f i l e of Pendrell Sound 5 factors involved i n the high l e v e l of breeding success. The amount of oyster larvae c o l l e c t e d varied from year to year with the l a s t s i x years being somewhat e r r a t i c and 1973 being a complete f a i l u r e and a severe economic loss to the industry. In 1973 a good spawning did occur but the larvae disappeared from the system without s e t t i n g . This loss of larvae must be associated with environmental fa c t o r s , among which water movements are considered to be the most s i g n i f i c a n t , since they may e i t h e r d i r e c t l y transport the larvae or modify t h e i r accepted t r a v e l patterns. Water movements may also concentrate or disperse food or-ganisms and pollutants d i r e c t l y , and control production of food nec-essary for growth and s u r v i v a l . 1.3 Heat Budget Theory The primary objectives of t h i s study were to resolve the mech-anism involved i n the creation of the unusually warm surface water and to determine i f there i s any large scale advection into and out of Pendrell Sound. A d i r e c t approach for studying t h i s type of water movement i s to set an array of current meters at d i f f e r e n t depths and locations i n the i n l e t . However, t h i s method requires a very large number of current meters i n order to achieve useful r e s u l t s and also there i s usually a good deal of d i f f i c u l t y i n assessing information from the meters. It was decided that a new approach should be attempted i n study-ing Pendrell Sound. A heat budget analysis of the i n l e t was used to determine, i n d i r e c t l y , the advection into and out of the i n l e t . Heat 6 budget studies themselves are by no means new, but they have i n the past usually been confined to s p e c i f i c cases and large scale features to minimize the e f f e c t of terms that could not be evaluated. Schmidt ( 1915 ) f i r s t attempted to use a thermal energy budget to obtain est-imates of annual evaporation from oceans. Richardson ( 1931 ) deter-mined the evaporation from C a l i f o r n i a lakes using the heat budget ap-proach. He took time i n t e r v a l s when the change i n a i r temperature was small and assumed a correspondingly n e g l i g i b l e change i n energy storage. Sverdrup ( 1940 ) used a heat budget to study a region o f f the Bay of Biscay which was without d i s t i n c t currents, thus considering advection to be n e g l i g i b l e . He also studied a portion of the Kuroshio where the advected energy was assumed constant throughout the year and was deter-mined from the energy budget by f i r s t assuming that evaporation was n e g l i g i b l e during the early summer. Anderson ( 1954 ) ca r r i e d out an energy budget i n v e s t i g a t i o n at Lake Hefner to determine the u t i l i t y of the energy budget as a method f or computing evaporation from natural bodies of water. Tabata ( 1958 ) applied the. heat budget to the coast-a l waters of B r i t i s h Columbia near T r i p l e Island and, using monthly mean c a l c u l a t i o n s , determined the importance of the advective processes i n that area. In the present study, the i n l e t i s e f f e c t i v e l y an i s o l a t e d body of water connected with the rest of the Straight of Georgia by only a narrow mouth. As the advective e f f e c t s that were being looked for were presumed to have been of a l o c a l nature and occuring over a r e l a t i v e l y short time span, the data were c o l l e c t e d over short i n t e r v a l s , both i n space and i n time. The majority of the heat budget c a l c u l a t i o n s were based on three-hourly averages. 7 The v a r i a t i o n i n time of the temperature of a body of water depends on energy exchange processes occuring at the a i r - s e a bound-ary and advective processes occuring below the sea surface. Solar r a d i a t i o n , e f f e c t i v e back r a d i a t i o n , evaporation ( and condensation ), and conduction of sensible heat are included i n the energy processes. The advective processes are d i r e c t l y concerned with transport of water and occur due to external forces such as winds, t i d e s , and density differences of water masses. The water becomes warmer or cooler de-pending on whether there i s a net transfer of heat into or out of the water i n the area. The c a l c u l a t i o n s of the net rate of heat flow into or out of a water body are re f e r r e d to as heat budget studies. In the case of Pendrell Sound, the heat transfer across the a i r -sea boundary was d i r e c t l y measureable through various methods, leaving the advective processes as the only unknowns i n the heat budget. Thus i t could be determined whether or not transport of water into and out of the i n l e t was an important factor i n i t s thermal structure. 8 CHAPTER 2 INSTRUMENTATION AND DATA 2.1 H i s t o r i c a l Data The e a r l i e r oceanographic data c o l l e c t e d i n Pendrell Sound by Dr. Quayle ( 1974 ) and Dr. Bourne and t h e i r a s s i s t a n t s seem to i n d i -cate the following: 1. During June to September, s a l i n i t i e s can vary between 11'•%, and 29/%> i n the surface la y e r s . S a l i n i t i e s can vary about 5%° i n three to f i v e days. Marked s a l i n i t y s t r a t i f i c a t i o n p e r s i s t s from June to September. The surface layer as defined by t h i s sharp s a l i n i t y s t r a t -i f i c a t i o n i s usually around two to f i v e meters deep but can be deeper at times. 2. During June to September the temperature i n the surface l a y -er can change about 6°C i n three to f i v e days. Marked temperature s t r a t i f i c a t i o n p e r s i s t s from June to September. The surface layer as defined by t h i s sharp temperature s t r a t i f i c a t i o n i s s i m i l a r to that as defined by the s a l i n i t y ( i e . two to f i v e meters ). 3. The l o n g i t u d i n a l d i s t r i b u t i o n of properties i n the upper twenty meters indicates that the iso-halines slope upwards from the mouth to the head with the lower surface s a l i n i t i e s at the mouth and higher temperatures and s a l i n i t i e s at the head. 4. Surface to one meter water movement has very l i t t l e i n d i c a t i o n 9 of d e f i n i t e t i d a l movement. The water movement near Station 3 ( see F i g . 3 ) shows d e f i n i t e eastward movement i n observations taken i n July to September i n two years. The surface water can also move sev-e r a l miles per day and at times can move i n a c i r c l e of less than one mile i n diameter f or periods of four to f i v e days. 5. Surface drogue measurements show that drogues can d r i f t around i n the i n l e t for days while at other times they can move the whole length of the i n l e t i n one day. A d r i f t drogue experiment done i n the summer of 1974 ( Landry 1976 ) indicated a tendency f or counterclockwise c i r c u l a t i o n i n the region near the head. 2.2 Data C o l l e c t i o n The center of operations f o r the data c o l l e c t i o n was the F i s h -eries Research Board barge, the " V e l e l l a " . This barge was anchored i n the upper reaches of the i n l e t as shown i n Figure 3, and housed the p h y s i c i s t s , b i o l o g i s t s , and technicians involved with working on t h i s proj ect. Thirteen hydrographic stations were designated throughout the length of the i n l e t and can be seen i n Figure 3 as a numbered sequence s t a r t i n g with Station 1 near the head down to Station 9 near the mouth. Four transverse s t a t i o n s , 31, 32, 91, and 92 were also included as shown. These stations were the s i t e s of bathythermograph recordings which were made d a i l y both at dawn and at sunset. The temperature versus depth recordings were made from the government launch "Squamish" using a Figure 3 Location of hydrographic stations i n Pendrell Sound winched electronic bathythermograph ( WEBT ) which was designed and constructed by government laboratories in Victoria and Patricia Bay. This instrument was lowered on a conducting cable by means of a winch mounted near the stern of the Squamish. The signals from the thermis-tor and pressure transducer in the WEBT were run up the conducting cable to an x-y recorder situated i n the cabin portion of the launch. The WEBT measurements were taken to a depth of f i f t y meters with sup-plementary readings to two hundred meters. The information recorded on the x-y plotter was digitized, corrected with appropriate calibra - r tion formulae, and re-plotted in corrected form with the use of a Hew-lett-Packard calculator, digitizer, and x-y plotter. Some of this data reduction was done on the barge and the rest was completed at Patricia Bay after completion of the experiment. A net radiometer ( with integrator ) was located at the barge to measure net radiation ( incoming radiation less reflected and back radiation ). The radio-meter sensor was mounted on a thirty foot boom close to the surface of the water in order to ensure that no extraneous measurements were taken due to the proximity of the barge. A dew point meter was used at the barge to determine the humidity every three hours. A sling psychro-meter was also used every three hours for back-up humidity determin- -ation. Surface water temperatures were measured at the barge every three hours. An actinograph and an hygrothermograph were mounted on the barge for additional back-up data. Both Aanderaa and Lambrecht anemometers were mounted on the barge and atop geodyne buoys which were moored at Station 1 and at Station 9. Measurements were recorded from the Aanderaa anemometers every ten minutes. Two thermistor chains were placed at both Station 1 and Station 9 and also at the barge. In 12 each case, one of the chains was f i f t y meters i n length with therm-i s t o r s every f i v e meters and one chain ten meters i n length with therm-i s t o r s every meter. Measurements from a l l thermistors were recorded on Aanderaa data-loggers every ten minutes. A l i m i t e d number of STD measurements were taken i n the v i c i n i t y of Station four. Four Aanderaa current meters were moored i n the i n l e t , two at each of the Stations ECUR and WCUR ( see Figure 3 ) at two meters and ten meters depth. Measurements from these current meters were also recorded on Aanderaa data-loggers every ten minutes. 2.3 Heat Budget Terms In the discussion of the heat budget, the energy exchange terms s h a l l be defined as follows: - net r a d i a t i o n , i e . , short-wave r a d i a t i o n of the sun and sky, both d i r e c t and d i f f u s e , less the r e f l e c t e d r a d i a t i o n from the sea, less the e f f e c t i v e back r a d i a t i o n ( long-wave r a d i a t i o n from the sea surface less that from the atmosphere ). - latent heat due to evaporation ( and condensation ) - conduction of sensible heat between the atmosphere and the sea. - the amount of heat used l o c a l l y f o r changing the temperature of sea water ( heat storage ). Q -Q +Q +Q, - the net amount of heat brought i n or out of the i n l e t e r xe h by transport of water G-advective e f f e c t s ). The units for these exchange processes may be conveniently chosen as gram-calories per square centimeter per day ( langleys/day ). i 13 The f l u x of t o t a l r a d i a t i v e energy was measured at the barge with the use of an i n t e g r a t i n g net radiometer. As the i n l e t covers a r e l a t i v e l y small area, i t was assumed that the difference i n net r a d i a t i o n from one part of the i n l e t to another would be n e g l i g i b l e . A plot of versus time can be seen i n Figure 4(d). The diurnal cycle of incoming s o l a r r a d i a t i o n i s c l e a r from the diagram with a loss of radiant energy at night. The cloudy or overcast days are e a s i l y distinguished i n the middle of the diagram as the amplitude of Q at t h i s time i s d r a s t i c a l l y attenuated during the daylight hours. Q and Q, e h The f l u x of la t e n t heat across the a i r - s e a boundary was c a l -culated using the formula: Q = LC l u U q e q where L = latent heat of vaporization ( 2.46 x 1 0 ^ ergs/gm.) C = 1.5 x 10~ 3 ( Pond et a l , 1974 ) q |u| = wind speed i n meters per second as obtained from the anemometers at Stations one and nine and at the barge. Aq = the difference between the absolute humidities at the sea surface and i n the a i r . The f l u x of sensible heat across the a i r - s e a boundary was c a l -culated using the formula: (X = p C C J u l AT H h a^'. p t ' 14 Q- Q r+Q„+Q h e r 6 n - 2 0 0 0 J "-v AUG. 10 AUG.30 (b) Qh o. -100 -• 3 0 0 n (C) Qe o • i — i — i — i i — i -300-J 1000-1 (d) Qr o -I000-. 2000-1 (e) Qft o e -2000 AUG.IO AUG. 15 AUG.20 AUG. 25 AUG. 30 TIME (days) 5 n HUM. (g/m3) - 5 —' „ . ATEMP 5" 1 (g) SEA AIR o-' (°C) -5 - J WIND (h) SPEED (m/sec) o-- i 1 r Figure 4 Plots of heat budget terms versus time ( Q i n langleys/day ) 15 where p = a i r density ( 1.25 x 10 gm./cm ) (1!^ = s p e c i f i c heat of a i r at constant pressure ( 10^ergs/gm C = 1.5 x 10~ 3 ( Pond et a l , 1974 ) |u| = wind speed AT = sea-air temperature difference Both these terms are plotted against time i n Figure 4(b) and Figure 4(c). The magnitude of these terms appears to be r e l a t i v e l y small i n the period from around August 11 to August 22. Upon inspec-ti o n of the plots of humidity and temperature differences and wind speed ( from which and are calculated ) i n Figures 4 ( f ) , (g) , and (h), i t i s c l e a r that t h i s attenuation was due to a decrease i n the wind speed during t h i s time. The plot of temperature difference be-tween the surface water and the a i r c l e a r l y displays the diurnal cycle of the warming of the a i r during the day and cooling at night. From August 9 to August 27, the water was, on average, warmer than the a i r whereas a f t e r August 27, the water became colder than the a i r , caus-ing conduction of heat into the water instead ofifouf 6 f . f i t . TEMPERATURE The rate of change of heat content of the water was calculated from the temperature versus depth pro-f i l e s which were obtained from the WEBT measurements. The diagram on the l e f t shows two temperature traces at times t^ and t ^ . The shaded area represents the change i n heat content from time t.j to time t^. The rate of change of heat content of a column of water 16 of unit c r o s s - s e c t i o n a l area and of depth z can be calculated as: z z % = IF /pcP T d z 88 ^ P / f d z where p = density of water C = s p e c i f i c heat of water P T = temperature of the water. Because the temperature traces were evaluated i n a d i g i t i z e d fashion, the actual c a l c u l a t i o n was of the form: Z(AT.Az) % = p C p — A t — This term was p l o t t e d against time and can be seen i n Figure 4(e). The values p l o t t e d are d a i l y means of the rate of change of heat content. It i s clear from t h i s diagram that from August 12 to Aug-ust 22, the water i n the i n l e t was increasing i n heat content, while from August 22 to August 30, the heat content was decreasing. Q - Q + Q + Q, v 9 v e v h Assuming zero error i n the measurement of the above terms, the t o t a l of Q - Q + Q + Q, represents the rate of increase of heat con-6 r e h tent i n the i n l e t due to advective e f f e c t s . If the t o t a l were zero, then i t would i n d i c a t e that the rate of change of heat content was balanced by the net heat transfer across the a i r - s e a boundary due to r a d i a t i o n , evaporation, and conduction. This t o t a l i s plotted against time i n Figure 4(a) and a table of d a i l y values of a l l these terms i s given i n Table I along with averages and comparative r e s u l t s of 17 TABLE I DAILY VALUES OF HEAT BUDGET TERMS IN AUGUST 1974 ( i n langleys per day ) Date % August 9 -722 332 238 40 10 242 308 118 25 11 -399 198 79 21 12 -1733 252 60 16 13 352 300 43 10 14 805 . 19 40 12 15 1444 173 35 12 16 1172 293 27 6 17 1178 308 52 8 18 889 52 42 13 19 1159 123 38 9 20 1953 96 35 8 21 1529 256 84 15 22 -360 37 48 13 23 -1166 151 51 10 24 -167 63 40 19 25 -180 277 41 11 26 -689 268 64 11 27 -1779 279 81 1 28 -1554 264 125 -33 29 -802 257 100 -20 30 32 217 34 -3 MEAN 55 206 67 9 Grand monthly means for August during the years 1947-1954, from Tabata's ( 1958 ) T r i p l e Island study 300 26 -9 18 Tabata ( 1958 ) for h i s 1947 to 1954 study of the region around T r i p l e Island near Dixon Entrance, which i s approximately 400 kilometers north of Pendrell Sound. From Figure 4(a) i t can be seen that from August 13 to-August 22 there was a rather large continuously p o s i t i v e advective term. This means that the heat content of the water was increasing more than i t would have due to r a d i a t i o n and turbulent heat f l u x across the a i r - s e a boundary. It i s clear from examining the r e l a t i v e magni-tudes of the heat budget terms ( note the difference i n scales i n F i g -ure 4 ) that the advection term i s by f a r the most important and i n f l u -e n t i a l source of heat exchange. It was estimated that Q_, the largest term of the four, and also l i k e l y to have the largest error, was mea-sured with an accuracy of approximately + 15%. The reason f o r such a large error estimate was due to the d i f f i c u l t i e s involved with the s p a t i a l and temporal a l i a s i n g of the water temperature measurements i n the top several meters of the i n l e t r e s u l t i n g from the o s c i l l a t i o n s of a semi-diurnal i n t e r n a l t i d e near the thermocline. Even at the lower extreme of t h i s error estimate, the advection term i s s t i l l the largest heat source term. In the period from August 22 to August 30 there was a large continuously negative term. This coincides with a negative rate of change of heat content or, i n other words, heat l o s s . 2.4 Temperature versus Depth P r o f i l e s Figure 5 shows a time progression of temperature p r o f i l e s obtain-ed with the WEBT at Stations 1 ( head ), 3, and 9 ( mouth ). The F i g -ure includes morning and evening p r o f i l e s f o r each day. Table III i n the Appendix displays these p r o f i l e s i n d i g i t i z e d form. The p r o f i l e s STATION I (HEAD) T E M P E R A T U R E ( ° C ) am pm AUG 10 AUG 15 AUG 20 AUG 25 AUG 30 STATION 3 T E M P E R A T U R E ( ° C ) AUG 10 AUG IS AUG 20 AUG 25 AUG 30 STATION 9 (MOUTH) T E M P E R A T U R E ( ° C ) Figure 5 Time series of temperature versus depth profiles 20 around the time of August 10 show a very sharp thermocline with a large v e r t i c a l temperature gradient between two and f i v e meters. As time progresses, one can see that the abruptness of the thermocline becomes less and less with the least mean gradient occuring around August 22. A f t e r this time the reverse s i t u a t i o n occurs, with the thermocline becoming sharper and sharper. One can also note that the depth of the "upper l a y e r " doesn't appear to increase s i g n i f i c a n t l y throughout this t o t a l time period. The timing of the d e t e r i o r a t i o n of the sharpness of the thermocline coincides with the period of the large p o s i t i v e advective term i n Figure 4(a), while the reforming of the thermocline coincides with the period when the advection term was negative. Comparing Stations 1, 3, and 9, i t i s evident that these temperature changes occured nearly simultaneously throughout the len-gth of the i n l e t . It was found that there was l i t t l e v a r i a t i o n i n the temperature structure i n the transverse d i r e c t i o n of the i n l e t . To examine the temperature change a l i t t l e more c l o s e l y , three temperature versus depth p r o f i l e s which occured during the "warming" period of August 13 to August 22 were overlayed. Figure 6 shows three temperature p r o f i l e s , corresponding to three d i f f e r e n t times, for three d i f f e r e n t s t a t i o n s . It can be seen from these pl o t s that there was l i t t l e change i n temperature at depths of around f i f t y meters and also l i t t l e change i n the f i r s t few meters near the surface. The most dramatic temperature change occured i n the middle section, from about f i v e meters to f o r t y meters depth. The heat content increase during t h i s time period, then, must have been due mainly to the increase i n temperature of t h i s middle section. It should also be noted that the maintainence of a constant thickness of the upper layer ( two to three STATION TWO (HEAD) STATION FIVE STATION NINE (MOUTH) Figure 6 Temperature versus depth p r o f i l e s during warming period 22 meters from the surface ) i s c l e a r l y displayed here. 2.5 Thermistor Chain Data Approximately continuous (ten minute i n t e r v a l s ) time seri e s records of temperature were obtained from the thermistor chains i n -s t a l l e d i n the water at the head and mouth of the i n l e t ( Stations 1 and 9 ) and at the barge. Figure 7 shows these records at the head and at the mouth of the i n l e t . The top temperature trace corresponds to one meter depth, and the rest are at f i v e meter i n t e r v a l s from the f i r s t . The outstanding feature here i s the warming of the water as indicated from the s i x meter trace through to the thirty-one meter trace from August 13 to August 22. A f t e r t h i s time the temperatures l e v e l l e d o f f for a few days and then decreased. From looking at the plots for both Station 1 and Station 9 i t i s again evident that these temperature changes occured almost simultaneously throughout the length of the i n l e t and that the timing of these events coincides with the timing of the advective term i n the heat budget. It has been c a l c u l -ated that the r a d i a t i v e input during the heating period from August 13 to August 22 can account for approximately only 17% of the t o t a l heat content increase i n the i n l e t . This i l l u s t r a t e s the r e l a t i v e import-ance of heat exchange due to advective processes. From Figure 7 i t can be seen that the surface temperatures remained r e l a t i v e l y constant with higher temperatures at the head than at the mouth. The temperatures around t h i r t y - f i v e to f i f t y meters also remained f a i r l y constant with higher temperatures at the mouth than at the head. There i s an i n d i c a t i o n of semi-diurnal i n t e r n a l t i d a l o s c i l l a t i o n s at STATION I ( HEAD) AUG 10 STATION 9 (MOUTH ) AUG 15 AUG 20 TIME ( DAYS ) AUG 25 25n o o AUG 10 AUG 15 AUG 20 TIME (DAYS) AUG 25 Figure 7 Temperature versus time f or various depths ho 24 the s i x meter depth around August 10 which move deeper as the thermo-c l i n e descended with time. As these i n t e r n a l o s c i l l a t i o n s move deep-er, they appear i n the figu r e to be attenuated, but i n f a c t , this i s only a manifestation of the smaller v e r t i c a l temperature gradient at this depth. By superimposing the thermistor chain plots from the head, the barge, and the mouth of the i n l e t , there was an i n d i c a t i o n of these o s c i l l a t i o n s propagating from the head to the mouth i n approximately two to four hours. This would give a phase speed on the order of eighty centimeters per second which compares to a phase speed estimate of f i f t y centimeters per second using the STD measurements. The heat content at the mouth was found to be greater than at the head when the temper-atures were increasing but.the reverse s i t u a t i o n was true when the temperatures were decreasing. In order to determine the v e r t i c a l v a r i a t i o n of the rate of heating during the period of increasing heat content, average c a l -culations of the change i n temperature per time were made from the thermistor chain data. These c a l c u l a t i o n s were made f o r each therm-i s t o r depth both at the head of the i n l e t and at the mouth during two four-day periods. A curve was plotted through these points and the r e s u l t s are as shown i n Eigure 8. The areas enclosed by the curves and the depth axis indicate the amount of energy put into the water per day. During the f i r s t period ( August 13 to August 17 ), the majority of heat content increase took place between two meters and eighteen meters, with the maximum heating at eight meters, while during the second period ( August 18 to August 22 ), th i s heating took place s l i g h t l y deeper, between f i v e meters and twenty-two meters, with the maximum heating at twelve meters. The rate of heating ( as Figure 8 Rate of heating as a function of depth 26 a function of depth ) due to solar r a d i a t i o n was also calculated and p l o t t e d on the same plots as above i n order to estimate the c o n t r i -bution of i n s o l a t i o n to the t o t a l rate of heating i n the water column. The dif f e r e n c e i n the two s o l a r heating plots was due to the d i f f e r -ence i n solar r a d i a t i o n and also the d i f f e r e n t e x t i n c t i o n c o e f f i c i e n t s that were measured during these periods, the f i r s t being .002 c e n t i -meters ^, and the second being .0013 centimeters ^. 2.6 Anemometer Data Time series records of wind speed and d i r e c t i o n were obtained from anemometers located at the head ( Station 1 ), at the mouth ( Sta-t i o n 9 ), and at the barge. The r e s u l t s are shown i n Figure 9 by means of a time seri e s of vectors. Each vector indicates an hourly av-erage of wind speed and d i r e c t i o n with those directed toward the top of the page i n d i c a t i n g a wind blowing up-inlet and v i c e versa. During the warming period of August 13 to August 22, there were l i g h t winds blowing down i n l e t from the head and strong winds blowing consistent-l y up i n l e t from the mouth. The cooling period i n the i n l e t coincides exactly with the r e v e r s a l of the strong winds at the mouth from the up i n l e t to the down i n l e t d i r e c t i o n beginning on August 27, and also with an increase i n speed of the down i n l e t wind at the head. 2.7 Current Meter Data Time s e r i e s records of current speed and d i r e c t i o n were obtained from currentbmeters located at Stations ECUR and WCUR at both two and 2 8 ten meters depth. The records f o r the east side of the i n l e t at ten meters depth were almost i d e n t i c a l to those of the west side. The two meter current meter on the west side malfunctioned a l o t of the time, but the r e s u l t s that were obtained seemed to i n d i c a t e a pattern not r a d i c a l l y d i f f e r e n t from i t s counterpart on the east side except that a few times they recorded flows i n opposite d i r e c t i o n s . Figure 10 shows four-day records for the two and ten meter current meters at Station ECUR ( on the east side of the i n l e t ). The vector type of display i s the same as the preceding anemometer p l o t s , except that i n t h i s case each vector indicates a ten minute average of speed. The currents at the ten meter depth appear to be consistently much strong-er than the currents at the two meter depth and occasionally the two currents flowed i n opposite d i r e c t i o n s . This means that the region between two meters and ten meters depth was an area of f a i r l y strong v e r t i c a l shear. Also shown i n Figure 10, i n between the two current meter p l o t s , i s a plot of temperature versus time for the thermistor at s i x meters depth at Station 1 ( taken from Figure 7 ). Rattray ( 1960 ) shows how i n t e r n a l tides can be generated by the surface tide encountering a sloping shore, such as the shore at the head of Pendrell Sound. In t h i s case, the i n t e r n a l wave w i l l propagate from the head to the mouth and cause currents i n the upper layer i n the form of divergences from the crests and convergences toward the troughs. Thus, the fluctuations of the current i n the upper layer are ninety degrees out of phase with the o s c i l l a t i o n s of the i n t e r n a l t i d e . Comparing the temperature pl o t ( Figure 10 ) with the surface current p l o t , the two appear to be i n phase, but i n f a c t , the two positions of measurement ( temperature at STATION ECUR ( 2 meters depth ) — i — AUG 14 I I AUG 15 ( D A Y S ) I I AUG 16 T r — AUG 13 TIME 17-j o 16 -0 15 -14 -ec z> 13 -»-< 12 -Ul a. 1 1 -2 Ul 10-ui -<== (E or O - 5 0 — 1 STATION ONE ( 6 meters depth) -I T— AUG 13 T 1 i 1 1 1 r AUG 14 I AUG 15 T I M E ( D A Y S ) STATION ECUR ( 10 meters depth) T 1 r AUG 13 T 1 1 AUG 14 T I M E 1 i r AUG 15 ( D A Y S ) 1 AUG 16 — i r AUG 16 Figure 10 Current vectors versus time and temperature at s i x meters depth versus time 30 Station 1 and current at Station ECUR ) were estimated to be approx-imately one quarter of a wavelength ( of the i n t e r n a l t i d e ) apart. Thus, the temperature fluctuations were lagging the current f l u c t u a -tions by approximately ninety degrees, as expected. 31 PART II DISCUSSION AND ANALYSIS This i s a des c r i p t i v e study of some of the phys i c a l properties of Pendrell Sound and how these properties change with respect to time and space. A d e t a i l e d quantitative analysis i s beyond the scope of the measurements that were obtained, but a d e s c r i p t i o n of the mech-anisms involved i n the phys i c a l system of Pendrell Sound i s discussed i n the following chapters. 32 CHAPTER 3 HEAT BUDGET OF PENDRELL SOUND 3.1 Description of the Temperature Structure of Pendrell Sound It i s useful to discuss the thermal structure of Pendrell Sound i n terms of three d i f f e r e n t l a y e r s . Figure 11 i s a schematic sketch of a l o n g i t u d i n a l section of the i n l e t showing these three lay e r s . As can be seen from t h i s f i g u r e , the coordinate system for the follow-ing analysis has i t s o r i g i n at the a i r - s e a i n t e r f a c e at the mouth of the i n l e t . Also i n the f i g u r e , two temperature versus depth p r o f i l e s at times t^ and are superimposed to i l l u s t r a t e the v e r t i c a l change i n temperature during the period when the heat content was increasing within the i n l e t . Since the i n l e t i s r e l a t i v e l y narrow i n width com-pared to i t s length, and since the transverse temperature gradients were very small, the analysis i s two-dimensional only, with x increas-ing from the mouth of the i n l e t ( x = 0 ) to the head K x = L ) and with z increasing from the surface ( z = 0 ) downward. Upper Layer ( z = 0 t o z = H ) The upper layer i s considered to be v e r t i c a l l y homogeneous with a small h o r i z o n t a l temperature gradient with increasing temperature i n the p o s i t i v e x d i r e c t i o n ( i e . - warmer at the head than at the mouth ). During the warming period i n the i n l e t from August 13 to August 22, the Figure 11 Schematic sketch of Pendrell Sound co CO 34 temperature i n , t h i s upper layer stayed almost constant ( s l i g h t decrease with time when averaged over a d a i l y cycle, and the depth of the layer stayed shallow with time at a depth of two to three meters. Middle Layer ( z = H t o z = D ) The middle layer was the only layer whose temperature changed appreciably with time during the warming period. In the bottom part of t h i s layer there was a small negative h o r i z o n t a l temperature grad-ient with the warmer temperatures occuring at the mouth and the cooler temperatures at the head ( AT on the order of one degree C ). The depth z = D was taken to be f i f t y meters. Bottom Layer ( z = D t o z = B ) Below the depth z = D = 50 meters, the temperature did not change appreciably with time. In the following a n a l y s i s , h o r i z o n t a l v e l o c i t i e s w i l l be denoted by u(x,z,t) and v e r t i c a l v e l o c i t i e s by w(x,z,t). Transverse v e l o c i t i e s were considered to be of i n s i g n i f i c a n t importance to the thermal struc-ture of the i n l e t , since the transverse temperature gradients were n e g l i g i b l e and also since the i n l e t i s so narrow compared to i t s length. 3.2 Integrated Heat Equation of Pendrell Sound The conservation of heat equation for an incompressible f l u i d can be written as follows: 35 where T = temperature n = molecular kinematic d i f f u s i v i t y q = heat source s p = density of the water C = s p e c i f i c heat of the water at constant pressure P The absorption of solar r a d i a t i o n incident on the sea surface i s a function of depth that depends on the wavelength of the r a d i a t i o n and the t u r b i d i t y of the water ( Jerlov, 1968 ) . Although the absorption within the range of wavelengths that are incident on the sea surface varies with each wavelength, an average e x t i n c t i o n c o e f f i c i e n t y, can be defined such that the rate of solar heating, q^, at some depth z = Z Q can be expressed as: q r ( z Q ) = x Q r e _ Y Z0 ( Denman, 1972 ) where Q = net r a d i a t i o n incident on the surface, r Thus, the heat source term i n the heat equation can be written: — Y Z q = YQ e s r The two dimensional conservation of heat equation, expressed i n turb-ulent form, i s , then: 9(pC T) 3(pC T) 3(pC T) 3(pC u'T') 3(pC w'T') P_ + u £_ + w _ E_ + _^  2 + P. = P c n v 2 T + YQ. 3t 3x 3z 3x 3z p 1 where T = mean temperature u = mean ho r i z o n t a l v e l o c i t y w = mean v e r t i c a l v e l o c i t y T' = f l u c t u a t i o n about the mean temperature u' = f l u c t u a t i o n about the mean ho r i z o n t a l v e l o c i t y 36 w' = fluctuation about the mean ver t ica l velocity and overbars indicate ensemble averaging. Assuming molecular diffusion plays a negligible role , the term pC^r|V2T may be discarded. If we let n represent horizontal eddy di f fus iv i ty , then, by analogy to eddy viscosity, —TZTJ- - 3T U'T' * -n — eH 3x which implies, 3(pC u'T') • . P o r dT i * ~ 3x" l p C p V 1* ' rl This gives the turbulent heat equation in the form: 3(pC T) 3(pC T) 3(pC T) 3(pC w'T') a 2_ + u -2- + w 2_ + E = 3_ (PC N — } + YQ E 3t 3x 3z 3z 3x 1 M p e „ 3x 1 r v r H -1 -3 Each term in this equation has the units of calories day meter . The term w'T' represents the ver t ica l t rbulent diffusion of heat. At the air-sea boundary, -pC w'T' (0) = Q + p e h where 0 and Q, are the turbulent fluxes of latent and sensible heat, " e h respectively, across the air-sea interface. At some depth d, where mixing entrainment ceases, pC w'T'(d) = 0 P So, the ver t i ca l turbulent diffusion may be represented in the form: -pC w'T'(z) = F(Q + Q ) p e n where F is unity at z = 0 and diminishes to zero at z = d. The exact form of the function F does not enter into the integrated equations, but the redistribution of the turbulent flux down into the water co l -umn is an essential mechanism. Integration of the ver t i ca l turbulence 37 term from the surface ( z = 0 ) to z = D = 50 meters, which i s ass-umed to be much deeper than z = d ( the l e v e l at which entrainment ceases ), and throughout the length ( L ) of the i n l e t , then, gives: LD LD L ( p C D W ' T ' ) d z d x ='-HJk ( F ( Q e + V M z d x = / ( Q e + V d x 00 P 00 0 So, int e g r a t i o n of the enti r e turbulent heat equation throughout the length of the i n l e t and over the depth of f i f t y meters gives: LD LD LD // ~ (pC T)dzdx + / / — (pC uT)dzdx + // - r - (pC wT)dzdx 00 d t p 00 P 00 P 0 © © LD LD L = H h { p C „ n e S } d z d x + / M r e _ Y Z d z d x - /(Q + V d x 00 x P H 00 0 © © © with each term now having the units of c a l o r i e s day ^ ( unit width ) ^ . Each of the above terms can be i d e n t i f i e d as follows: (T) Rate of change of heat content (T) Horizontal advective heat transfer (^ T) V e r t i c a l advective heat transfer (T) Horizontal turbulent d i f f u s i o n of heat ^ i ) Solar heating ( jT) Turbulent heat fluxes. This, then, i s the integrated heat equation of Pendrell Sound. In the following sections, the magnitude of each of these terms w i l l be estimated during the warming period of August 13 to August 22 i n order to determine which processes are the most important to the ther-mal structure of the i n l e t . 38 CHAPTER 4 EVALUATION OF THE HEAT BUDGET TERMS 4.1 Rate of Change of Heat Content LD a ^ : 00 r " u The rate of change of heat content, as calculated from the temp-erature versus depth p r o f i l e s , i s plotted as a function of time i n Figure 4(e) . In evaluating the average magnitude of t h i s term during the warming period of August 13 to August 22, the length of the i n l e t 3 ( L ) was taken as 9.5 x 10 meters and the depth of i n t e g r a t i o n ( D ) was taken as 50 meters, since below t h i s depth there was only a n e g l i -g i b l e amount of temperature change. The volume (per unit width ) of LD 3 i n t e g r a t i o n , JJ dzdx, was approximated as ( 9.5 x 10 m ) x ( 5 0 m ) . 00 The value of pC was taken to be constant at 1.0 calories/-cm 3;./ °C. P ? 3T The value of J -s— dz for a unit c r o s s - s e c t i o n a l area was calculated 0 for various positions along the i n l e t $tf©-f.eexamp3)e.J.ngas. shown i n . FigU'reg 8'er)'.od and the r e s u l t was averaged over the length of the i n l e t . The rate of increase of thermal energy ( per unit width ) i n the i n l e t during the period of August 13 to August 22 was calculated to be: 1.0 ^fi^l x l 0 e -Hi x 9.5 x 1 03 (m) x ( cm3 C ) ( mJ) 9 (days) ' " ' ' - ' ' pG length (L) j hr d z P % 3t 1.03 x 10 1 1 - f ^ day .m 39 This represents the t o t a l rate of change of heat content per unit width i n the i n l e t due to a l l heat sources, or an average temperature r i s e i n the top f i f t y meters of 0.22 °C/day 4.2 Local Heating Processes LD L (5)&(6) ffrfQe Y Z dzdx - /(Q + Q )dx 00 0 These terms represent the heat transferred between the atmos-phere and the i n l e t due to r a d i a t i v e heat fluxes and turbulent fluxes of sensible and latent heat. These three fluxes are p l o t t e d as func-tions of time i n Figures 4(b), ( c ) , and (d). Assuming that the i n c i d -ent r a d i a t i o n and the turbulent heat fluxes occur uniformly over the length of the i n l e t , the i n t e g r a l s (5) and (6) can be evaluated as follows: L D - L J/yQ e Y Z dzdx - J(Q + Q )dx = LQ {1-e Y } - L(Q + Q ) 00 0 The term e y D had a maximum value of 0.002 ( corresponding to a coef-f i c i e n t of e x t i n c t i o n of 0.0013 centimeters ^ ) during the warming per-iod. In other words, the amount of s o l a r r a d i a t i o n absorbed below f i f t y meters depth was.only 0.2% of the t o t a l amount of r a d i a t i o n ab-sorbed and can therefore be regarded as being n e g l i g i b l e , and so: L Q rU - e" Y D} - L(Q e+ Q h) - LQ^ - L(Q £+ Qh> Thus, the t o t a l rate of thermal input ( per meter width ) throughout the i n l e t due to r a d i a t i o n during the nine day warming period from August 13 to August 22 was ( using the observed value of ) : 40 9.5 x 103(m) x 1705 ( c a l o r i e s ) ( c m Z ) x 1 Qu(cm 2) 9 days (m^ ) 1.80 x 10*° C a ^ ° r l e S day m length (L) The rate of heat loss due to latent and sensible heat exchanges at the sea surface during the same time period was ( using observed values of Q e and Q h ) 9.5 x 103(m) x 402.1 l£^4pk.89M^ (cmcro) ) -. (cm^ ) 9 days 9 ' days x .10 it (cm 2) (m2 ) 5.21 x 10 g c a l • day m 'length (E) So the t o t a l rate of heating due to the l o c a l heating processes i s the rate of heat gain due to r a d i a t i v e e f f e c t s less the rate of heat loss due to the latent and sensible heat fluxes: L(Q r- Qe- Q h) 1.28 x 10 10 c a l o r i e s day m If t h i s heat input were evenly d i s t r i b u t e d throughout the top f i f t y meters of the i n l e t , the average temperature would r i s e at a rate of 0.03 °C/day Comparing the rate of heating due to l o c a l processes with the t o t a l rate of change of heat content, i t can be seen that the l o c a l heating can account for only 13% of the t o t a l heating that occurred throughout the length and depth of the i n l e t from August 13 to August 22. 41 4.3(a) Evaluation Since the l o c a l heating processes accounted for less than 15% of the t o t a l heat that was put into the top f i f t y meters of the i n l e t during the warming period, then advection must therefore account f o r 85% of the heat put into the i n l e t . V e r t i c a l advection wi t h i n the i n l e t causes heat to be r e d i s t r i b u t e d i n the v e r t i c a l d i r e c t i o n and can account f o r heat exchanges between the upper and middle l a y e r s . However, when integrated throughout the depth of the water column, i t i s clear that t h i s term cannot be a heat source or sink f o r the i n l e t , since heat must come from outside the i n l e t v i a ho r i z o n t a l advection through the mouth or v i a r a d i a t i o n and ai r - s e a ex-change-. Thus, i n the case under consideration, the advection of heat into the i n l e t can be s p e c i f i e d by: LD r, LD ' H 3x" ( p C n u T > d z d x = " // h (PC T)dzdx + L(Q - Q - Q ) 00 P 00 d P If we now consider the heat balance i n the upper layer only ( i t w i l l be shown l a t e r that h o r i z o n t a l d i f f u s i o n i s n e g l i g i b l e ) , we have: Following the method used i n section 3.2, the v e r t i c a l turbulence term may be expressed as: 42 Thus, the heat equation integrates to: r, LH H L L f - //(pC T)dzdx - / pC (uT) dz + / PC (wT) dx + J pC (w'T') dx d t o o p o p o p o p = LQ {1 - e" Y H} - L{Q + Q, } r e h Using < > to denote a s p a t i a l average from x=0 to x=L, we now have: r, LH 4~ /J(pC T)dzdx - pC H(uT) V : + pC L{<wT> „ + <w'T'> u} dt ^ p p x=0 p z=H z=H = LQ {1 - e" Y H} - L{Q + Q, } r e h This leads to: „ LH, . , • ..-pC {-H(uT.) . + L<wT> „-+L<w'T'> „} = - -r-' j f CpC T)dzdx p x=0 z=H z=H dt J JQ p + L { Q r ( l - e" H ) - Q e- Qh} The l e f t hand side of this equation represents the t o t a l rate of heat f l u x out of the surface layer due to (i) flow through the end at the mouth ( i i ) flow through the bottom ( z = H ) ( i i i ) mixing through the bottom ( z = H ) This net rate of heat loss may be determined by evaluating the r i g h t hand side of t h i s equation ( taking H = 2.5 m ): 9 LH g _^ _^ - -jjj-jj //(pC T)dzdx = + 2.6 x 10 c a l m day ( calculated from the ther-00 P mistor chain data ) LQ (1 - e" Y H) = + 5.0 x 10 9 c a l m"1 day" 1 -L(Q + Q, ) = - 5.2 x 10 9 c a l m _ 1 day" 1 e h 9 -1 -1 The sum of these terms i s + 2.4 x 10 c a l m day Comparing any of these values with the t o t a l change of heat content i n the whole i n l e t ( l O ^ c a l m 1 day 1) shows that the surface layer appears to play only quite a small part. 43 4.3(b) Wind Driven Currents The mountainous t e r r a i n bordering Pendrell Sound confines the wind to the i n l e t ' s l o n g i t u d i n a l axis. The topography, i n turn, constrains the surface waters to move i n the same d i r e c t i o n as the wind s t r e s s . Since the i n l e t has a s o l i d boundary at the head, then, when up - i n l e t winds blow, a pressure gradient develops i n the water along the i n l e t i n opposition to the wind s t r e s s . Thus, up-inlet winds force outside surface water into the i n l e t and the continuity condition ensures that the deeper water i s forced down and out of the i n l e t . This replacement of deeper, cooler water with the warmer surface water tends to increase the heat content within the i n l e t . Conversely, down-inlet winds move the warm surface layer out of the i n l e t , causing up-welling of cooler water i n the i n l e t to replace i t . This decreases the heat content within the i n l e t . 4.3(c) Density Driven Currents Causes of Density Gradients There often e x i s t s a h o r i z o n t a l density gradient (see Figure 12(a)) such that the water j u s t below the pycnocline outside the i n l e t tends to be more dense, than water at the same depth i n s i d e Pendrell Sound. The solar heating inside and outside the i n l e t must be e s s e n t i a l l y the same due to t h e i r close proximity to each other, but the surface layer outside i s more exposed to higher v e l o c i t y winds. Thus there i s more mix-ing with the cooler and more s a l i n e water below and the outside water be-comes more dense than the ins i d e water at a given l e v e l near the surface. Also, the outside water i s more exposed to a larger scale of advection than the water ins i d e the i n l e t which i s more trapped. The outside upper water therefore has les s chance of accumulating l o c a l heating e f f e c t s and i s also cooled more by g l a c i a l runoff. 44 Figure 12 Density sections of July 26, 1967 ( values of a shown ) (a) afternoon (b) morning 45 E f f e c t of the Density Gradient Water tends to move i n the d i r e c t i o n of decreasing pressure and along isopycnal surfaces. The l a t e r a l boundary r e s t r i c t i o n s of the i n l e t i n h i b i t ^ a f u l l geostrophic flow. I f we assume that surface slope i s i n s i g n i f i c a n t ( which i s probably i n l i k e l y ), then with the near-surface water outside the i n l e t being denser than i t s counterpart i n s i d e , the r e s u l t i n g pressure gradient w i l l drive a density current i n t o the i n l e t and under the warm surface layer ( along the isopycnals ). From previous temperature and s a l i n i t y data ( Quayle 1974 ), which included measurements outside the i n l e t , a l o n g i t u d i n a l s e c t i o n of isopycnals was drawn ( Figure 12(a) ). From t h i s section, dynamic heights f o r a s t a t i o n between Marylebone Point and Horace Point and Station 7 i n Pendrell Sound were calculated and the resultant density current v e l o c i t i e s a f t e r a period of one day ( s t a r t i n g from r e s t ) were determined. Assuming the water to be i n v i s c i d and that the flow 3u i s uniform with respect to x ( i e . -r— = 0 ), then the Navier Stokes ox equation becomes: 3u 3t 1 3p p 3x where u = v e l o c i t y i n the x d i r e c t i o n P = pressure t = time This i s the same as 3u 3t 1 3x 1 P where g r a v i t a t i o n a l p o t e n t i a l ( df = gdz ) and thus, 3*(p r) 3u 3t - (AD(p r) - AD(p)} '46 where = reference pressure P AD = geopotential anomaly = f6dp 0 where 6 = s p e c i f i c volume anomaly. But at p = p r , 3u(p r) 3$(p r) 3t 3x and so, 3u(p) = 3_ 3t 3x {AD(p r) - AD(p)} The f i n i t e d ifference form of t h i s r e l a t i o n was used to calculate the v e l o c i t i e s r e l a t i v e to the v e l o c i t y at twenty meters depth between the Marylebone Point - Horace Point Station and Station 7, a f t e r a period of one day : The maximum v e l o c i t i e s , as determined by t h i s method, were at a depth of between two to four meters and a rate of = 85 cm/sec. This v e l o c i t y i s c l e a r l y f ar too large. This i s probably due to the fact that the density values used for t h i s c a l c u l a t i o n were obtained at one point i n time rather than averaged over several series of measurements. Thus, the slope of the isopycnals -" may- <- >b'e v" due to the passing of an i n t e r n a l wave. Indeed, from measurements taken l a t e r on the same day ( Figure 12(b)), one can see a very d i f f e r e n t configuration of the i s o -pycnals. In order to obtain an accurate estimate of the density cur-rent, a time series observation of s a l i n i t y and temperature i n s i d e and and outside the i n l e t would have to be made i n order to be able to f i l t e r out the i n t e r n a l wave o s c i l l a t i o n s that are superimposed on the density f i e l d . Au = At 47 4.4 Horizontal Turbulent D i f f u s i o n (4) //pC | - {n |£'} dzdx W J J p 3x e H 9x Horizontal turbulent d i f f u s i o n can act as a heat source ( or sink ) by d i f f u s i n g heat i n a turbulent fashion h o r i z o n a t a l l y into or out of the i n l e t . Using time averaged temperature values, as determined from the thermistor chain data.:at Stations 1, 9, and at the barge, the magni-. • 2 3 T -9 0 2 tude of -—j was estimated to be of the order 10 C/m . Thus, i n 3x order for the h o r i z o n t a l d i f f u s i o n term to be s i g n i f i c a n t i n the heat equation, the c o e f f i c i e n t of h o r i z o n t a l eddy d i f f u s i o n , r\ , would eH 6 2 have to be of the order 10 cm /second. However, by applying a method of Bowden (1964 ) to Pendrell Sound, values for n were obtained i n eH 3 4 2 the range of 10 to 10 cm /second. Also, i n t h e i r study of wake d i f -fusion i n Saanich I n l e t , which would be expected to have a larger coef-f i c i e n t of h o r i z o n t a l turbulent d i f f u s i o n than Pendrell Sound because 2 2 of i t s greater s i z e , Farmer and Lemon ( 1975 ) a r r i v e d at 5 x 10 cm /sec for the ambient value of n i n the i n l e t . C l e a r l y , then, h o r i z o n t a l 6H d i f f u s i o n can be considered n e g l i g i b l e i n the heat equation of Pendrell Sound. 48 4.5 R e d i s t r i b u t i o n of Heat V e r t i c a l and h o r i z o n t a l turbulent d i f f u s i o n increase the mixing of incoming and outgoing water and help to r e d i s t r i b u t e heat through-out the i n l e t . The v e r t i c a l turbulence was driven mostly by the shear between the upper and middle layers ( see Figure 13 ) and by wind mix-ing. The shear i s due to t i d a l currents, the wind-driven upper layer, the subsurface density currents, and the i n t e r n a l waves. To determine the extent of turbulence between the upper and the middle laye r s , bulk —sAzAo Richardson numbers i(i R. = ,—r? ) were calculated from current meter l p(Au)'i o data at two and ten meters depth and from s a l i n i t y and temperature pro-f i l e s . The bulk Richardson number i s , of course, only a very crude es-timate of turbulence or'lackaof if s t p r o d u c t i o n ) and the numerical values obtained are an upper l i m i t , since Au i s dependent on the distance, Az, between the current meters. Depending on the v e l o c i t y p r o f i l e , i t i s possible f or Az to be decreased without Au decreasing, which would re-su l t i n a smaller bulk Richardson number. The values of R. ranged o from 7.0 to 10.5, i n d i c a t i n g a very stable s i t u a t i o n . When R. >> 1, o s u f f i c i e n t k i n e t i c energy i s j u s t not a v a i l a b l e i n the mean motion to change a smooth shear flow having roughly s i m i l a r p r o f i l e s of v e l o c i t y and density, to a s t e p - l i k e structure ( Turner 1973 ). A l o c a l Richard-son number was also calculated at the thermocline following the method of P h i l l i p s ( 1969 ) which uses the Brunt-Vaisala frequency, and the frequency, wave number, and amplitude of the i n t e r n a l t i d e . Values for t h i s were of the order of 2.0, which also indicates that v e r t i c a l turbulence was very strongly damped. So, i n the case of Pendrell Sound, Figure 13 Plot of v e r t i c a l shear versus time between two meters and ten meters depth 4N 50 the e f f e c t of the mean shear on the v e r t i c a l turbulent d i f f u s i o n term can be considered to have been small. Wind mixing helped to keep the upper layer v e r t i c a l l y homogeneous, but since the region of the therm-ocli n e was very stable, the wind mixing e f f e c t was not able to increase the depth of the surface layer and thus contribute s i g n i f i c a n t l y to the v e r t i c a l d i f f u s i o n of heat into the middle layer, mining below the surface layer kept i >•/.surface j t • -o-v deeper due to -JHCL.' .-•"„ "i:5on from p o v f . E f f e c t of the Internal Tide The i n t e r n a l t i d e that was observed i n Pendrell Sound derived i t s energy from the v e r t i c a l displacement of s t r a t i f i e d layers of water as the surface t i d e moved the water over the sloping bottom at the head of the i n l e t . The water, thus displaced, would tend to f a l l back to i t s l e v e l of neutral buoyancy and i n so doing cause o s c i l l a t i o n s which travel!down the i n l e t to the mouth. The i n t e r n a l t i d e , t r a v e l l i n g mouthward, caused v e r t i c a l shear between the upper and middle layers due to convergence and divergence of water with the passing of the troughs and cre s t s . This shearing migb.t.-.enhance vthe.iho.fiizorital and v e r t i c a l mixing both above and below the pycnocline. There are also b i o l o g i c a l e f f e c t s associated with the i n t e r n a l t i d e , as w i l l be discussed i n Chapter 6. 4.6 Conclusions and Dlscu'ssiomj; mate Table II displays the integrated heat equation of Pendrell Sound TABLE II ESTIMATED MAGNITUDES OF THE INTEGRATED HEAT EQUATION TERMS LD . // | - (pC T)dzdx oo 9 t P = LD „ ^ (pC uT)dzdx 00 P + L{Q - Q - Q, } r e h RESIDUAL TERM rate of change of heat content t o t a l heat f l u x i n through mouth rate of heat from across the surface 1.03 x 1 0 U 9.02 x 10 1 0 1.28 x 10 1 0 c a l . day ^ m ^ c a l . day * m ^ c a l . day ^ m ^" + 0.22 °C day" 1 +0.19 °C d a y - 1 + 0.03 °C day" 1 52 and the estimated magnitude of each term. In order f or the heat equa-t i o n to balance, the h o r i z o n t a l advection term for the whole i n l e t , LD 3 1 Q - / / — (pC uT)dzdx, must have been i n the neighbourhood of 9 x 10 00 8 x p calories/day. Thus, the most important mechanisms causing the increase i n heat content i n Pendrell Sound were the wind driven surface current coming into the i n l e t and d i s p l a c i n g the cooler deeper water, and the density driven subsurface current bringing correspondingly ( by depth ) warmer water into the middle layer. The determination of the v e r t i c a l p r o f i l e of net v e l o c i t y i n the middle layer i s a task which i s beyond the scope of the measurements that were taken during t h i s study. For the most of t h i s layer, the ho r i z o n t a l termperature gradient i s negative, i n d i c a t i n g warmer water at the mouth than at the head. From the heat budget, i t i s clear that some of t h i s water must have been advected into the i n l e t i n order to heat i t , but, by conservation of mass, the net mass transport from the bottom of the upper layer to the bottom of the i n l e t must have been out of the i n l e t to compensate for the incoming upper la y e r . This means that the incoming water i n the middle layer must have had a larger (negative) h o r i z o n t a l temperature gradient than the outgoing water to account for the increasing heat content i n t h i s layer. I t i s impossible to say with any c e r t a i n t y where the water i s coming i n and where i t i s going out from t h i s study and, indeed, much of the outgoing water may have l e f t the i n l e t below the depth z = D = f i f t y meters. 53 CHAPTER 5 SUMMARY AND DISCUSSION 5.2 Why Pendrell Sound i s a Unique System The e x t r a o r d i n a r i l y warm surface waters i n Pendrell Sound are due to a number of f a c t o r s . Unlike most i n l e t s , Pendrell Sound i s a "negative" or "inverse" i n l e t ( Pri t c h a r d 1952 ) with no appreciable fresh run-off. This means that there i s no cooling e f f e c t i n the surface layer from run-off and also that the surface layer i s not constantly being advected out of the i n l e t as i s usually the case i n an i n l e t with fresh water run-o f f . The i n l e t i s also very protected and there are predominantly up-i n l e t winds blowing from the mouth, d r i v i n g warm currents between the sur-face and about ten meters depth into the i n l e t and f o r c i n g cooler, deep-er water out of the i n l e t . The upper water at the head of the i n l e t remains r e l a t i v e l y undisturbed, as the incoming surface water w i l l tend to remain at i t s own density l e v e l and w i l l s l i d e under the les s dense surface water at the head, and i s heated by l o c a l heating processes. The incoming water warms the middle layer which then r e s u l t s i n decreas-ed heat losses from the upper layer to the middle layer. When the wind s h i f t s from i t s predominantly up - i n l e t d i r e c t i o n at the mouth to a down-inlet d i r e c t i o n , then the upper water i s ad-vected out of the i n l e t and i t i s replaced by the cooler deeper water. This was the case during the period from August 24 to August 30. 54-5.2 Possible Future Quantitative Analysis In order to make a reasonable estimate of the magnitude of the density driven currents, an accurate time series of the density f i e l d is needed. This means that salinity as well as temperature profiles would have to be taken along the length of the inlet and out into the surrounding waters. It would be best i f this could be accomplished with self recording thermistor and conductivity c e l l chains so that simultaneous measurements could be compared throughout the area of study. Transverse salinity and temperature sections should also be measured to determine transverse pressure gradients due to the Coriolis force acting on the incoming and outgoing water. A more accurate det-ermination of the amount of mixing occurring between the upper and the middle layers would be desirable. Also, i t would be of value to set a larger array of current meters in order to better correlate the water movements as determined indirectly by the heat budget method and direct measurements of the currents. 55 CHAPTER 6 IMPLICATIONS FOR BIOLOGICAL PROCESSES The most important p h y s i c a l factor for the oyster industry i s the temperature of the surface layer of water i n Pendrell Sound, par-t i c u l a r l y at the head where desirable mooring locations are situated. Consistent up-inlet winds and s o l a r heating are favourable to the main-tenance of a warm surface layer. The longer period of time that up-i n l e t winds blow, the warmer the middle layer w i l l become and the l e s s dramatic the temperature change when the wind changes d i r e c t i o n and the middle layer water replaces the surface water. The wind speed and d i r e c t i o n at the mouth of the i n l e t , rather than at the head, i s the most i n d i c a t i v e of the surface layer movement within the major part of the i n l e t since i t i s usually the strongest i n terms of speed and covers a much longer fetch than the l i g h t wind at the head which blows almost always down-inlet during t h i s time of year. When the wind blows strongly down-inlet for any length of time, the surface water i s advected out of the i n l e t and the temperatures i n the upper layer decrease due to the cooler "replacement" water from below. If the oyster larvae are not advected out of the i n l e t at t h i s time, they may not be able to survive the reduced temperature of t h e i r environ-ment. The semi-diurnal i n t e r n a l t i d e observed i n the i n l e t w i l l also have some e f f e c t on the larvae. Kamykow'ski ( 1974 ) related the patch-iness of phytoplankton to i n t e r n a l t i d e s . He found that the r a d i a t i o n 56 f i e l d a v a i l a b l e to each organism was s i g n i f i c a n t l y affected by the v e r t i c a l water movement of a semi-diurnal i n t e r n a l t i d e and that the r e s u l t i n g d i f f e r e n c e i n s p e c t r a l d i s t r i b u t i o n of the r a d i a t i o n a f f e c t -ed phytoplankton growth. 57 APPENDIX TABLE III TEMPERATURE DATA 1974 ( In degrees C ) STATION 1 Depth (m) Aug. 8 Aug. 9 Aug. 10 Aug. 11 Aug. 12 Aug. 13 pm am pm am pm am pm am pm am pm 0 22.3 21.1 22.3 21.0 22.0 20.9 22.0 20.8 21.6 21.0 22.7 1 22.3 21.1 22.3 21.0 22.0 21.1 21.6 20.8 21.6 21.1 22.7 2 22.0 2113322.2 21.4 22.0 21.1 21.6 20.8 21.6 21.1 22.5 3 21.5 19.2 21.0 17.5 22.1 21.2 21.0 17.0 21.1 15.8 19.8 4 20.8 17.0 17.9 15.3 21.8 19.5 20.9 14.2 19.0 13.5 17.9 5 17.5 14.5 15.9 13.6 20.4 14.6 16.0 12.5 15.1 12.0 16.0 10 12.5 11.2 11.9 11.0 11.3 10.5 11.0 10.2 10.6 10.1 10.8 15 10.3 c9v6':10^2: 9~/8-10.;2. 957^79.9 >-'984 . 9,f 8 9.3 9.6 20 9.6 9.3 9.6 9.4 9.6 9.3 "9.3 9.0 9.4 8.9 9.3 30 9.0 8.8 9.0 9.0 9.1 8.8 8.8 8.6 8.9 8.5 9.0 40 8.5 8.5 8.6 8.5 8.6 8.4 8.5 8.5 8.7 8.5 8.8 50 8.5 8.3 8.4 8.4 8.5 8.3 8.4 8.4 8.5 8.4 8.6 Depth (m) Aug. 14 Aug. 15 Aug. 16 Aug. 17 Aug. 18 Aug. 19 am pm am pm am pm am pm am pm am pm 0 21. 7 21.6 21.0 21.7 20.8 22744217.2 22.7 21.7 21.4 20.7 21.1 1 21.7 21.7 21.0 21.7 20.9 22.2 21.3 22.6 21.7 21.4 20.7 21.0 2 21.7 21.6 20.5 21.4 20.0 21.5 20.9 22.5 21.6 21.4 20.7 21.0 3 18.8 19.9 17.3 20.1 18.1 20.0 17.5 21.2 21.5 19.7 19.0 18.4 4 15.5 16.9 15.5 17.2 16.4 18.2 15.9 19.9 18.2 16.6 16.4 17.0 5 13.5 15.0 13.6 16.1 15.3 17.0 15.5 17.6 16.9 16.0 16.1 16.6 10 10.5 11.5 11.2 12.6 11.8 14.6 12.9 14.6 13.4 14.4 14.0 14.7 15 9.8 10.1 10.0 10.6 10.5 11.3 10.5 12.6 11.0 11.5 12.1 13,0 20 9.2 9.6 9.5 10.0 9.7 10.0 9.9 10.3 10.3 10.3 10.5 11.3 30 8.8 8.9 8.9 9.2 9.0 9.3 9.0 9.3 9.6 9.3 9.7 9.7 40 8.6 8.6 8.7 8.9 8.6 8.8 8.8 9.0 9.2 9.1 9.0 9.0 50 8.4 8.5 8.5 8.6 8.5 8.7 8.5 8.6 8.8 8.8 8.6 8.7 58 STATION 1 (continued) Depth (m) Aug. 20 Aug. 21 Aug. 22 Aug. 23 Aug. 24 Aug. 25 am pm am pm am pm am pm am' pm am pm 0 19.9 20.4 19.7 21.3 20.3 19.6 18.7 19.8 19.3 19.9 18.8 20.7 1 19.9 20.4 19.7 21.3 20.4 19.7 19.0 19.0 19.4 19.6 18.9 20.2 2 19.9 20.3 19.5 20.6 20.4 19.1 18.4 18.4 19.5 19.0 19.0 19.3 3 20.0 18.8 19.2 19.9 20.2 18.2 17.8 18.3 19.0 18.4 18.8 18.2 4 18.6 18.1 18.1 18.6 19.1 17.8 17.5 17.7 18.5 17.7 18.5 17.8 5 17.1 17.5 17.6 18.0 18.2 17.5 17.3 17.6 18.2 17.3 17.7 17.4 10 15.2 15.8 15.8 16.5 16.5 15.9 16.3 14.9 15.6 15.2 15.6 15.5 15 13.2 14.2 14.0 14.6 14.6 13.1 13.7 13.2 13.8 13.8 14.1 13.8 20 11.7 12.2 12.2 12.6 12.6 12.0 12.0; 11.5 11.6 11.4 11.8 11.4 30 9.8 10.0 10.3 10.0 9.9 9.6 9.6 9.5 9.7 9.7 9.9 9.8 40 9.3 9.4 9.5 9.4 9.2 9.0 9.0 8.9 9.2 9.2 9.2 9.3 50 8.8 9.1 9.1 9.0 8.8 8.8 8.8 8.8 9.0 9.1 8.8 9.1 Depth (m) Aug. 26 Aug. 27 Aug. "2.8 Aug. 29 Aug. 30 am pm am pm am pm am pm am pm 0 19.3 23.0 19.9 22.3 20.6 24.3 20.9 22.9 21.2 24.7 1 19.4 21.0 20.0 21.7 20.7 22.4 21.0 21.5 20.8 21.6 2 19.6 20.1 20.0 20.5 20.0 21.2 18.8 21.0 19.0 20.6 3 19.5 18.5 18.9 19.0 18.4 20.1 17.3 19.3 17.1 18.5 4 18.5 17.9 18.3 18.0 16.9 19.0 16.6 18.0 16.6 17.3 5 17.9 17.3 17.5 17.5 16.1 17.0 15.7 17.0 16.0 16.8 10 15.8 15.5 14.9 15.3 12.6 13.5 12.5 12.0 12.-1 12.3 15 13.8 12.9 12.0 11.8 1:1.2 II. l.ia.2 10. i: 10.9 11.0 20 1-1.5 10.9 10.7 10.5 10.3 10.4 10.2 10.1 10.1 10.4 30 9.9 9.4 9.4 9.6 9.3 9.5 9;'4 9.4 9.3 9.4 40 8.8 9.1 8.8 9.2 9.0 9.0 9.0 9.0 9.0 9.1 50 8.6 8.8 8.6 8.9 8.8 8.8 8.8 8.8 8.7 8.7 STATION 3 Depth (m) Aug. 8 Aug. 9 Aug. 10 Aug. 11 Aug. 12 Aug. 13 aia pm am pm am pm am pm am pm am pm 0 '22'.o 22.6-21.3 23.3 21.3 20.4 20.1 21.2 20.2 21.1 20.4 21.4 1 22.6 21.5 23.0 21.5 21.4 20.5 21.0 20.4 21.1 20.4 21.4 2 21.8 21.6 22.7 21.4 22.0 20.8 21.0 20.7 21.2 20.6 21.4 3 21.7 20.0 22.0 20.5 21.9 21.0 21.2 16.7 21.2 18.0 20.1 4 20.0 15.9 19.0 16.9 21.3 20.0 20.7 14.4 17.3 14.3 16.5 5 17.5 19.0 15.9 19.4 19.0 15.8 16.7 13.4 14.2 13.2 15.1 10 11.8 10.5 11.1 10.6 11.3 11.0 11.4 10.6 10.6 10.3 10.9 15;, 9.8 9.6 10.0 9.8 10.0 10.0 10.1 9.7 9.7 9.6 9.8 20. 9.4 9.4 9.7 9.5 9.6 9.5 9.6 9.3 9.4 9.3 9.4 30 8.9 8.9 9.3 9.1 9.1 9.0 9.0 8.7 8.9 8.8 8.9 40 8.7 8.5 8.9 8.8 8.7 8.6 8.6 8.5 8.5 8.5 8.7 50 8.3 8.3 8.4 8.5 8.4 8.3 8.3 8.3 8.4 8.4 8.5 39 STATION 3 (continued) Depth (m) Aug. 14 Aug. 15 Aug. 16 Aug. 17 Aug. 18 Aug. 19 am pm am pm am pm am pm am pm am pm 0 21.1 21.0 20.3 21.3 20.1 21.9 20.2 21.4 20.5 20.5 19.9 20.6 1 21.1 21.0 20.4 21.0 20.1 20.8 20.2 21.4 20.5 20.5 19.9 20.5 2 20.5 21.0 20.0 20.5 20.1 20.7 20.2 21.0 20.5 20.5 20.0 20.3 3 17.9 18.8 17.3 18.6 17.2 18.4 18.0 19.0 20.5 18.5 18.8 17.8 4 16.0 16.6 15.5 16.9 15.7 16.5 16.1 17.1 17.0 16.9 16.4 16.5 5 14.2 16.0 14.8 15.7 15.6 15.7 15.6 16.5 15.8 15.9 15:7 16.2 10 10.7 11.9 11.3 13.1 12.3 13.5 13.1 14.0 13.9 14.0 14.0 14.7 15 -9.7 10.1 10.2 10.9 10.5 11.7 10.8 11.9 11.4 12.1 12.1 12.7 20 9.3 9.5 9.6 9.3 9.7 10.2 10.2 10.3 10.5 10.6 10.6 11.3 30 8.8 8.9 9.0 9.1 9.2 9.3 9.3 9.4 9.4 9.5 9.4 9.5 40 8.5 8.6 8.6 8.9 8.8 8.8 8.8 8.9 8.9 9.0 9.0 9.1 50 8.4 8.4 8.4 8.5 8.5 8,5 8.5 8.6 8.8 8.8 8.8 8.8 Depth (m) Aug. 20 Aug. 21 Aug. 22 Aug. 23 Aug. 24 Aug. 25 am pm am pm am pm am pm am pm am pm 0 19.3 20.0 19.4 20.2 19.6 19.6 18.8 19.5 19.0 19.2 18.6 20.8 1 19.3. 20.0 19.4 20.2 1996619.6 18.9. 19.3 19.1 19.5 18.6 20.0 2 19.3 19.9 19.5 20.0 19.618.5 18^7 18.1 18.7 18.9 18.7 19.3 3 18.6 18.6 18.8 19.3 18.9 17.8 18.6 17.8 18.3 18.5 18.7 18.6 4 17.2 18.0 18.2 18.3 17.9 17.5 18.1 17.6 17.8 17.6 18.3 18.0 5 16.7 17.0 17.2 18.2 17.6 17.3 17.8 17.2 17.5 17.2 17.9 17.4 10 15.2 15.2 15.5 16.0 16.5 15.9 16.0 15.3 16.0 15.3 15.9 15.3 15 13.2 14.0 14.2 14.5 14.5 13.5 14.1 12.9 13.8 13.2 14.2 13.0 20 11.8 12.0 12.2 12.4 12.5 12.2 12.2 11.5 11.7 11.2 11.7 11.2 30 9.7 9.8 9.9 9.8 9.9 9.5 9.6 9.5 9.7 9.6 9.7 9.7 40 9.2 9.3 9.3 9.4 9.3 9.0 9.0 9.0 9.1 9.1 9.2 9.1 50 8.8 8.8 9.0 9.1 8.9 8.8 8.8 8.8 8.9 8.8 8.8 8.7 Depth (m) Aug. 26 Aug. 27 Aug. 28 Aug. 29 Aug. 30 am pm am pm am pm am pm am pm 0 19.1 20.5 19.5 21.4 19^9922.6 19.9 22.4 19.8 22.7 1 19.2 20.3 20.3 21.0 19.9 21.0 19.9 21.0 19.9 22.8 2 19.4 20.1 20.0 20.4 19.6 20.4 18.5 19.8 18.9 21.0 3 19.4 18.9 19.8 19.2 18.0 19.3 17.2 18.8 17.8 19.1 4 18.9 17.8 18.3 18.0 17.0 18.0 16.3 17.2 16.9 17.5 5 18.3 17.4 17.3 17.2 16.3 17.0 15.6 16.5 15.9 16.8 10 15.6 15.2 14.6 14.4 13.0 13.5 12.7 12.9 12.3 12.6 15 13.6 12.6 11.9 11.8 11.2 11.1 11.0 10.9 10.8 10.9 20 11.4 10.9 10.6 10.4 10.3 10.2 10.1 10.1 10.0 10.0 30 9.8 9.5 9.4 9.2 9.2 9.3 9/3 9.2 9.1 9.2 40 9.3 9.0 9.0 8.8 8.8 8.9 8.9 8.8 8.8 8.8 50 8.9 8.6 8.5 8.4 8.4 8.5 8.4 8.4 8.4 8.4 60 STATION 9 Depth (m) Aug. 8 Aug. 9 Aug. 10 Aug. 11 Aug. 12 Aug. 13 am pm am pm am pm am pm am pm am pm 0 19.6 20.3 20.8 19.5 18.8 18.2 19.8 19.8 20.8 19.8 19.2 1 19.7 20.3 20.8 19.5 18.8 18.8 19.8 19.9 20.8 19.8 19.1 2 20.0 19.7 19.9 19.4 18.9 18.7 19.8 20.7 19.0 20.3 17.5 3 18.6 17.6 17.5 18.5 19.0 19.2 17.0 17.8 15.5 16.0 15.3 4 16.5 15.5 16.5 16.2 16.5 14.6 14.1 14.6 14.0 13.9 13.7 5 14.8 13.2 15.5 13.6 14.1 12.3 13.0 13.0 13.0 12.5 12.8 10 10.9 10.5 10.8 11.0 11.1 10.7 10.8 10.4 10.5 10.5 10.9 15 9.8 9.8 10.2 10.0 10.0 10.0 10.2 9.8 9.8' 9.8 10.0 20 9.5 9.5 9.8 9.6 9.6 9.6 9.7 9.5 9.5 9.6 9.6 30 9.4 9.3 9.5 9.5 9.4 9.4 9.4 9.3 9.3 9.4 9.4 40 9.2 9.2 9.4 9.3 9.1 9.2 9.2 9.1 9.1 9.3 9.3 50 8.9 8.9 9.2 9.2 9.0 9.1 9.2 9.0 9.1 9.3 9.2 Depth (m) Aug. 14 Aug. 15 Aug. 16 Aug. 17 Aug. 18 Aug. 19 am pm am pm am pm am pm am pm am pm 0 20.0 19.0 18.4 19.3 18.9 20.0 19.0 20.2 19.4 19.3 18.7 19.6 1 20.0 19.0 18.7 19.3 18.9 20.0 19.1 20.2 19.4 19.3 18.8 19.6 2 19.3 16.5 18.8 19.3 18.2 19.5 17.7 20.2 17.9 19.4 18.9 19.6 3 17.3 14.8 16.4 17.2 15.6 16.9 16.7 18.3 16.8 17.9 17.6 18.4 4 15.0 14.1 15.1 16.3 15.3 15.8 15.8 16.6 15.8 16.5 17.1 17.2 5 14.2 11.5 14.3 14.8 14.9 15.1 15.3 16.1 15.5 15.7 16.3 16.2 10 11.1 10.4 11.4 12.6 13.0 12.9 13.7 13.3 1316 13.3 14.2 14.2 15 V- 10.0 9.9 10.4 10.5 11.3 11.5 11.4 11.4 11.6 11.6 12.5 12.8 202.' 9.4 9.6 9.9 10.0 10.3 10.3 10.3 10.3 10.4 10.8 11.1 11.3 30 ::: 9.3 9.5 9.5 9.6 9.5 9.7 9 . 7 9 . 7 9.-6 9.8 9.8 9.8 40 40 9.2 9.5 9.4 9.5 9.4 9.5 9.4 9.4 9.2 9.4 9,5 9.4 50 50 9.1 9.4 9.3 9.4 9.3 9.2 9.2 9.0 9.0 9.1 9.2 9.1 Depth (m) Aug. 20 Aug. 21 Aug. 22 Aug. 23 Aug. 24 Aug. 25 am pm am pm am pm am pm am pm am pm 0 18.7 18.4 18.3 18.8 19.0 19.4 18.8 19.2 18.1 19.1 17.7 19.2 1 18.7 18.4 18.3 18.8 19.0 19.5 18.9 19.2 18.2 19.3 18.1 19.3 2 18.4 18.5 18.3 18.8 19.0 19.5 18.8 18.7 18.0 19.2 18.2 19.0 3 17.5 18.3 17.7 18.4 17.9 18.9 18.4 17.8 17.8 18.0 17.6 18.5 4 16.8 17.5 17.5 18.0 17.3 17.9 17.4 17.3 17.4 17.6 17.3 17.7 5 16.4 17.0 17.2 17.6 16.9 17.5 16.9 17.0 17.3 17.1 17.0 17.3 10 15.1 15.1 15.6 15.9 16.0 15.7 15.8 15.7 15.6 15.4 15.2 14.8 15 13.9 13.5 14.1 14.0 13.8 13.4 13.9 13.6 13.6 12.9 13.7 12.6 20 11.8 11.6 12.3 12.2 12.0 11.9 12.0 11.5 11.8 11.4 11.9 10.9 30 9.8 9.8 10.1 10.2 10.1 9.7 ^9v9 9.8 10.1 10.0 10.3 9.9 40 9.4 9.5 9.6 9.6 9.5 9.3 *9.'3 9.3 9.5 9.4 9.4 9.3 50 9.0 9.0 9.3 9.4 9.3 9.2 9.2 9.1 9.3 9.3 9.3 9.0 STATION 9 (continued) Depth (m) Aug. 26 am pm 0 18.5 20.2 1 18.5 19.8 2 18.7 19.7 3 18.1 19.1 4 17.6 17.9 5 17.4 17.3 10 15. 1 14.3 15 13.5 11.9 20 11.1 10.5 30 9.8 9.5 40 9.2 9.0 50 9.1 9.0 Aug. 27 Aug. 28 am pm am pm 18.0 21.1 19.8 22.0 19.3 20.5 20.0 21.3 18.5 20.3 19.8 20.7 17.9 19.0 18.9 18.6 17.2 17.9 17.8 16.9 16.6 16.8 17.0 15.9 14.6 13.7 14.0 13.2 11.5 11.1 11.2 11.0 10.5 10.2 10.3 10.3 9.6 9.4 9.5 9.6 9.2 9.0 9.1 9.2 8.9 9.0 9.0 8.9 Aug. 29 Aug. 30 am pm am pm 19.9 22.2 21.9 20.0 20.2 21.7 21.8 20.2 20.3 20.5 20.5 20.6 19.9 17.9 19.1 19.0 16.9 16.6 17.4 16.9 16.5 15.6 16.1 16.4 12.5 12.4 12.8 12.8 Hl'.O 10.9 10.8 11.1 10.3 10.3 10.2 10.2 9.6 9.7 9.6 9.6 9.1 9.0 9.0 9.0 8.9 8.9 8.9 8.9 62 REFERENCES Anderson, E.R. (1954). Energy-Budget Studies. Water Loss Investiga-tio n s : Lake Hefner Studies. Tech. Rept. U.S. Geological Survey Professional Paper, 269, pp. 71-117. Bowden, K.F. (1965). Horizontal Mixing i n the Sea Due to a Shearing Current. Journal of F l u i d Mechanics, Vol. 2_1, pp. 83-95. Denman, K.LL (1972). The Response of the Upper Ocean to Meteorological Forcing. Doctoral D i s s e r t a t i o n , Department of Physics and Ocean-ography, Un i v e r s i t y of B r i t i s h Columbia. Farmer, D. and Lemon, D. (1975). Dispersion of Dyed Sea-Water Discharg-ed From Moving Vessels i n Coastal Waters. Unpublished Manuscript. Je r l o v , N.G. (1968). O p t i c a l Oceanography. E l s e v i e r Publishing Co., London. Kamykowski, D. (1974). Possible.Interactions Between Phytoplankton and Semidiurnal Internal Tides. Journal of Marine Research, Vol. 32(1), pp. 67-89. Landry, L.P. (1976). Radar Tracking of D r i f t Drogues i n Pendrell Sound and Port Melon, June and September 1974. Unpublished Manuscript. P h i l l i p s , O.M. (1969). The Dynamics of the Upper Ocean'. Cambridge Univ e r s i t y Press. Pond, S. , Efesfels,, D%Br..„ andqiEiauison^. C J>PC$s(<i$9J fy-., ?A^Norte- on Bulk Aero-dynamic. CoeMecien-tstsf or2 StenTsib'lTe- 'Heat- and'-Moisture1 Fluxes. B'oundary^-La'y.eK Me'te^ Sciences, Vol. H ) , pp . C01--9 i 7 ./"" " Pritchard, D.W. (1952). Estuarine Hydrography. Advan. Geophy. , Vol. 1_, pp. 243-280. Quayle, D.B. (1974). Data Report. Pendrell Sound Oyster Breeding 1950-1970. F i s h e r i e s Research Board of Canada, Manuscript Report Series 1291. - 63 Rattray, M. (1960). On the Coastal Generation of Internal Tides. T e l l u s , Vol. 12^(1), pp. 54-62. Richardson, B. (1931). Evaporation as a Function of Insolation. Amer-ican Society of C i v i l Engineers, Transactions, Vol. 95_, pp. 996-1011. Schmidt, W. (1915). Strahlung und Verdunstung i n Freien Wasserflachen; ein Beitrage zum-Warmehaushalt des Weltmeers und zum Wasserhaus-ha l t der Erde. Annalen der Hydrographie und Maritimen Meteor-ologie, Vol. 43, pp. 111-124, 169-178. Sverdrup, H.U. 1(1940). On the Annual and Diurnal V a r i a t i o n of the Eva-poration from the Oceans. Journal of Marine, Research, V o l . 3^2), pp. 93-104. Tabata, S. (1958). Heat Budget of the Water i n the V i c i n i t y of T r i p l e Island, B r i t i s h Columbia. Journal of the F i s h e r i e s Research Board of Canada, Vol. 15_(3) , pp. 429-451. Turner, J.S. (1973). Buoyancy E f f e c t s i n F l u i d s . Cambridge University Press. 

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