Science, Faculty of
Zoology, Department of
DSpace
UBCV
Buchanan, Douglas Bruce
Master of Science - MSc
University of British Columbia
Same of the philosophical aspects of modelling are discussed along with the importance of understanding primary marine food-web components. Howe Sound, a coastal embayment on the British Columbia coast, is examined as a base study area, and field sampling methods as well as laboratory techniques are summarized. The main body of the investigation involves the development of a mathematical description of phytoplankton population growth and distribution as a function of biological and physical circulation parameters in the sound. This is accomplished by dividing the sound into zones and modelling primary productivity as a result of certain key environmental forcing functions. Transport between zones is shown to affect spatial timing and distribution. Observed and predicted values of nutrients, temperature, extinction coefficients, zooplankton biomass, and phytoplankton productivity and biomass are compared as the model is refined. It is then used to simulate the effects of a delayed spring on productivity in Howe Sound, as well as to model growth in Indian /Arm, an adjacent embayment. Simulated annual productivity in Have Sound is 235, 316 and 384 gC‧m⁻²‧yr⁻¹ in the down inlet direction for the three model zones. With a delayed spring the values are reduced to 200, 308 and gC‧m⁻²‧yr⁻¹ and comparisons are made with observed data in Howe Sound in 1974 when poor spring weather conditions prevailed. In Indian Arm the model predicts a spatial productivity distribution of 318, 256 and 239 gC‧m⁻²‧yr⁻¹, values which agree with field observations of two workers. The general applicability of such models to complex ecosystems is discussed.
A MATHFJYS7ATICAL MODEL OF PRIMARY FOOD WEB ENERGETICS IN HOWE SOUND, BRITISH COLUMBIA. B.SC. UNIVERSITY OF BRITISH COLUMBIA, 1974 A THESIS SUBT4ITTED IN PARTIAL FUIFIIJMEMT OF THE REQUIREMENTS FOR THE DEGREE OF THE FACULTY OF GRADUATE STUDIES DEPARTMENT OF ZOOLOGY WE ACCEPT THIS THESIS AS CONFORMING TO THE REQUIRED STANDARD THE UNIVERSITY OF BRITISH COLUMBIA MAY 1976 (c) DOUGLAS BRUCE BUCHANAN, 1976. by DOUGLAS BRUCE BUCHANAN MASTER OF SCIENCE IN In presenting th i s thesis in pa r t i a l fu l f i lment of the requirements for an advanced degree at the Un ivers i ty of B r i t i s h Columbia, I agree that the L ibrary sha l l make it f ree l y ava i l ab le for reference and study. I fur ther agree that permission for extensive copying of th i s thes i s 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 ca t ion of th is thes is fo r f i nanc ia l gain sha l l not be allowed without my wr i t ten permission. Depa rtment The Univers i ty of B r i t i s h Columbia 2075 Wesbrook Place Vancouver, Canada V6T 1W5 i i 7 A B S T R A C T Same of the philosophical aspects of modelling are discussed along with the importance of understanding primary marine food-web components. Howe Sound, a coastal embayment on the British Columbia coast, i s ex-amined as a base study area, and f i e l d sampling methods as well as lab-oratory techniques are summarized. The main body of the investigation involves the development of a mathematical description of phytoplankton> population growth and distribution as a function of biological and phys-i c a l circulation parameters i n the sound. This i s accomplished by divid-ing the sound into zones and modelling primary productivity as a result of certain key environmental forcing functions. Transport between zones i s shewn to affect spatial timing and distribution. Observed and predicted values of nutrients, temperature, extinction coefficients, zooplankton bicmass, and phytoplankton productivity and biomass are compared as the model i s refined. It i s then used to simulate the effects of a delayed spring on productivity i n Howe Sound, as well as to model growth i n Indian /Arm, an adjacent embayment. Simulated annual productivity i n Have Sound i s 235, 316 and 384 -2 -1 gOm -yr xn the down i n l e t direction for the three model zones. With -2 - ^ l a delayed spring the values are reduced to 200, 308 and 381 gOm *yr' and comparisons are made with observed data i n Howe Sound i n 1974 when poor spring weather conditions prevailed. In Indian Arm the model predicts -2 -1 a spatial productivity distribution of 318, 256 and 239 gOm '-yr , values which agree with f i e l d observations of two workers. The general applica-b i l i t y of such models to complex ecosystems i s discussed. i i i TABLE OF (XNTENTS PAGE ABSTRACT i i LIST OF TABLES V LIST OF FIGURES v i MXmiJimBEMEmS i x I INTRODUCTION 1 I I ANALYSIS OF THE STUDY AREA 7 Description, Hydrography, Tides and Climate 7 S i m i l a r i t y t o other Fiords 10 Zones 11 I I I FIELD AND LABORATORY METHODS 13 Sampling Procedure 13 Physical and Chemical Parameters 13 1. Incident Radiation and Attenuation 13 2. Nutrients 14 3. C0 2 Alkalinity 14 4. Temperature 14 B i o l o g i c a l Parameters 15 1. Phytoplankton Stocks 15 2. Phytcplankton Production 15 3. Zooplankton Stock 16 C i r c u l a t i o n and Inter-zonal Transport 16 TV OBSERVED DATA ' 18 Physical and Chemical Parameters 18 1. Light Intensity and Attenuation 18 iv PAGE 2. Nutrients. 1 9 3. Temperature 20 Biological Parameters 20 1. Phytoplankton Stock and Productivity. 20 2. Zooplankton Stock 21 Circulation and Inter-zonal Transport 21 V MODEL DEVELOPMENT 23 Biological Submodel 23 Inter-zonal Transport Submodel 27 Complete System Model 29 Parameter Estimation 31 VT MODEL SIMULATIONS 42 VII DISCUSSION 48 VIII CONCLUSIONS 55 IX BIBLIOGRAPHY 57 X TABLES 61 XI FIGURES 69 APPENDIX I PROGRAM LISTING 149 APPENDIX II 152 V LIST OF TABLES TABLE PAGE I OBSERVED EXTINCTION COEFFICIENT AVERAGES AND STAND-ARD DEVIATIONS, HOWE SOUND, 1972 TO 1975 62 I I OBSERVED TOTAL NITRATE AVERAGES AND STANDARD DEVIA-TIONS, HOWE SOUND, 1972 TO 1975. 63 I I I OBSERVED TEMPERATURE AVERAGES AND STANDARD DEVIATIONS, HOVE SOUND, 1972 TO 1975- 64 IV OBSERVED CHLOROPHYLL OTNCTOTRATTON AVERAGES AND STANDARD DEVIATIONS, HOWE SOUND, 1972 TO 1975 65 V OBSERVED PRIMARY PRODUCTIVITY AVERAGES AND STANDARD DEVIATIONS, HOWE SOUND 1972 TO 1975 66 VI OBSERVED ZOOPLANKTON BIOMASS AVERAGES AND STANDARD DEVIA-TIONS, HOWE SOUND 1972 TO 1975. * 67 VII ABBREVIATIONS AND UNITS OF GRAPHICAL PARAMETERS 68 v i LIST CF FIGURES FIGURE PAGE 1. LOWER BRITISH COLUMBIA COASTLINE, HOWE SOUND, i „ 70 2. HOWE SOUND WITH BELL'S (1975) CURRENT METERING STATIONS HS - 3, HS - 4, AND HS - 5 72 3. AXIAL CROSS-SECTION THROUGH MAIN CHANNEL OF HOWE SOUND (FROM BELL, 1975) 74 4. HOWE SOUND SAMPLING STATIONS WITH EASTERN QiANNEL BROKEN UP INTO MODELLING ZONES 76 5. ANNUAL INCIDENT SOLAR RADIATION AND MATCH TO NORMAL DISTRIBUTION 78 6. OBSERVED DATA AVERAGES AND STANDARD DEVIATIONS, ZONE 1.80 7. OBSERVED DATA AVERAGES AND STANDARD DEVIATIONS, ZONE 2.80 8. OBSERVED DATA AVERAGES AND STANDARD DEVIATIONS, ZONE 3.80 9. PHOTOSYNTHETIC ACTION SPECTRUM, SKELETONEMA COSTATUM. 84 10. PHOTOSYNTHETIC ACTION SPECTRUM, DUNALIELLA TERTIOLECTA. 84 11. PHOTOSYNTHETIC ACTION SPECTRUM, AI4PHIDINIUM CARTEEI. 84 12. EXTINCTION COEFFICIENT AS A FUNCTION OF WAVELENGTH AT VARIOUS DISTANCES FROM KRAFT PULP MILL AT PORT MELLON IN HOWE SOUND 88 13. ANNUAL SQUAMISH RIVER DISCHARGE HYDROGRAPH AND MATCH TO NORMAL DISTRIBUTION... 90 14. CURRENT SPEED AND DIRECTION HS - 5, 3 m 92 15. CURRENT SPEED AND DIRECTIONs-HS - 5 , 5 m 92 16. CURRENT SPEED AND DIRECTION HS - 5, 10 m 92 17. CURRENT SPEED AND DIRECTION HS - 4, 3 m 92 18. CURRENT SPEED AND DIRECTION HS - 3 , 3 m 92 v i i FIGURE PAGE 19. CURRENT SPEED AND DIRECTION HS - 3 , 10 m 92 20. POLYNOMIAL REGRESSION P.P./P MAX VS 1 99 21. ORIGINAL ZONE 1 SMHATICN, PP^DICTED VS OBSERVED 101 22. ORIGINAL ZONE 2 S3MJIATION, PREDICTED VS. OBSERVED 101 23. ORIGITIAL ZONE 3 SMILATICN, PREDICTED VS OBSERVED 101 24. ZONE 1'SIMULATION, PREDICTED VS OBSERVED 105 25. ZONE 2 SIMULATION, PREDICTED VS OBSERVED 105 26. ZONE 3 SIMITATION, PREDICTED VS OBSERVED 105 27. ZONE 1 SIMULATION, PREDICTED VS OBSERVED 109 28. ZONE 2 SIMULATION, PREDICTED VS OBSERVED 109 29. ZONE 3 SIMULATION, PREDICTED VS OBSERVED 109 30. ZONE 1 SIMULATION, PREDICTED VS OBSERVED 113 31. ZONE 2 SIMULATION, PREDICTED VS OBSERVED 113 32. ZONE 3 SIMULATION, PREDICTED VS OBSERVED 113 33. ZONE 1 SINGULATION, PREDICTED VS OBSERVED 117 34. ZONE 2 SIMULATION, PREDICTED VS OBSERVED 117 35. ZONE 3 SIMULATION, PPvEDICTED VS OBSERVED 117 36. ZONE 1 SD^JLATION, PREDICTED VS OBSERVED 121 37. ZONE 2 SBfJIATION, PREDICTED VS OBSERVED 121 38. ZONE 3 SDftlLATION, PREDICTED VS OBSERVED 121 39. ZONE 1 SIMULATION, PREDICTED VS OBSERVED 125 40. ZONE 2 S1ICILATION, PREDICTED VS OBSERVED 125 41. ZONE 3 Sl>IUIATION, PREDICTED VS OBSERVED 125 42. ZONE] 1 SIMULATION, PREDICTED VS OBSERVED 129 43. ZONE 2 SIMULATION, PREDICTED VS OBSERVED 129 44. ZONE 3 SIMULATION, PREDICTED VS OBSERVED 129 viii FIGURE PAGE 45. ZONE 1 SBCILATION, PREDICTED VS OBSERVED* 133 46. ZONE 2 SIMULATION, PREDICTED VS OBSERVED. 133 47. ZONE 3 SIMULATION, PREDICTED VS OBSERVED 133 48. ZONE 1 SZMJLATION, PREDICTED VS OBSERVED 137 49. ZONE 2 SIMULATION, PREDICTED VS OBSERVED. 137 50. ZONE 3 SIMULATION, PREDICTED VS OBSERVED. 137 51. ZONE 1 SIMULATION, HOWE SOUND VS INDIAN ARM. 141 52. ZONE 2 SIMJLATION, HOWE SOUND VS INDIAN ARM. 141 53. ZONE 3 SMTLATION, HOWE SOUND VS INDIAN ARM 141 54. ZONE 1 SIMUIATION, HOWE SOUND VS THEORETICAL NORTHERLY FIORD. 145 55. ZONE 2 SIMULATION, HOVE SOUND VS THEORETICAL NORTHERLY FIORD. 145 56. ZONE 3 SIMUIATION, HOWE SOUND VS THEORETICAL NORTHERLY FIORD. 145 i x ACKNCHLEDGEMEOTS I would l i k e to sincerely thank my good f r i e n d Dr. John Stockner of P a c i f i c Environment I n s t i t u t e f o r many years of continuing support and good advice as the ideas f o r t h i s project have come to the fore. The mutual reinforcement of two d i f f e r e n t approaches and the rapport that has developed between us since I came to work f o r John w i l l con-tinue to benefit us both I am sure. I would also l i k e to extend deep-est thanks to my academic advisor Dr. Tim Parsons f o r whom I have great respect. Sincere and e a s i l y approachable, h i s guidance was w e l l heeded. Thanks should also go to my fellow laboratory workers; Ken Shortreed, Anne Cos t e l l a , and especially David C l i f f f o r a never ending supply of he l p f u l suggestions. 1 INTRODUCTION I t appears that a gradual development of large-scale and long-term resource planning i s taking place i n Canada and other countries. This has been fostered by the need f o r management decisions i n a system where change i s taking place at an accelerated pace. At the same time these changes inpose l i m i t s on long-term predictive powers, since system mechanisms may be affected. Relatively speaking, the oceans are a new f r o n t i e r on the time scale of man's study of h i s environment. However, t h e i r s i z e and irtportance make i t obvious that i t w i l l become increasingly important to plan f o r t h e i r future use on a long-range basis. In order to do t h i s properly, i t w i l l be necessary to learn as much as possible about the oceanographic mechanisms governing the complex dynamics of t h i s system. Mathematical modelling i s one of many approaches we can use i n these studies. This thesis considers some philosophical aspects and the develop-ment of a model of but one subsystem of the extensive spectrum of ocean dynamics. I t s ' value w i l l be demonstrated by the degree to which the hy-potheses about system dynamics i n i t i a t e d can be extended to describe larger and more important parts of the world oceans. In recent years, the use of mathematical models i n marine ecology has increased out of proportion to the understanding of the basic b i o l o g i c a l mechanisms studied. This i s the r e s u l t of excessive f a i t h i n mathematics and i t i s up to the modern research planner to insure adequate integration of empirical and th e o r e t i c a l sciences. In l i g h t of t h i s grim outlook, and because now more b i o l o g i s t s receive a basic mathematical t r a i n i n g , t h i s f a i t h i n mathematical magic i s d i m i n -2 ishing. As a r e s u l t , many former t h e o r e t i c a l modellers are turning to purely empirically based research. Empirical or " t a c t i c a l " models (Holling, 1966) , are p r a c t i c a l f o r certain types of resource management or for aid i n the digestion of large amounts of experimental data. They do not, however, lend to easy conceptualization of general ecological p r i n c i p l e s , nor do they claim to do so. On the other end 'of the spectrum of possible models, the strategic or general model i s c e r t a i n l y more conducive to the investigation of b i o -l o g i c a l mechanisms and to system response under perturbation. Regardless of diminishing f a i t h , there e x i s t s within the range of p o s s i b i l i t i e s , a mathematical model which i n some way w i l l benefit the study of any system, no matter the complexity. In f a c t , empirical and the o r e t i c a l approaches to systems analysis w i l l mutually reinforce, each providing insights f o r the other at higher degrees of model refinements. Models are used i n so many v/ays that i t i s not always clear which i s the model and which i s the mimic. Not only i s the physical world modelled by mathematical constructions, mathematical theory may be tested by the physical construction of the designed experiment. This reverse modelling i s e ssential to avoid an overabundance of questionable speculative models. The meaning of models and t h e i r results should also be considered, since every conception i s open to reinterpretation. The relationship between experience and models must be such that; " I t i s from experience that they derive t h e i r meaning, i t i s i n terms of experience that they f i n d expression, and i t i s by conforming to experience that they demonstrate t h e i r value1,1" (Stettam, 1971). As H. G. Wells once said; "the forceps of the mind are clumsy and pinch 3 the t r u t h a l i t t l e i n talcing hold of i t . " When building cohesive models, one learns by thinking, b u i l d i n g , testing and thinking again. This step by step process i s the true a r t of model construction, but i s seldom re-vealed or discussed i n the l i t e r a t u r e , where the emphasis i s on the f i n a l r e s u l t s . One problem which arises out of t h i s dynamic t e s t i n g , i s how the t e s t -ing i s a f f e c t i n g the true nature of the system. I t i s a basic physical p r i n c i p l e that whenever measurements of a phenomenon are imposed on a system, changes occur which bias these measurements. Sim p l i c i t y i s another important c h a r a c t e r i s t i c of models. The simple general model avoids many of the downfalls of a more complicated and spec-i f i c formulation. Also the economy of thought gained can compensate f o r incurred inaccuracies. The f i n a l q u a l i t y of models which must be examined i s a p p l i c a b i l i t y . I t i s unreasonable to ask i f a model accurately describes nature, since t h i s i s impossible. What i s important, i s whether the model i s accurate enough for the purpose of i t s ' construction. The application of mathematical formulation to problems does not necess-a r i l y y i e l d worthwhile r e s u l t s . This can only occur when the mathematical structure i s an adequate model of the true system structure. Mathematics i s the framework, but uninterpreted, i t i s void of empirical content. I t seems there i s only purpose, i n s p i r a t i o n and economy to guide one toward good mathematical modelling. For the modeller there i s no complete r e a l i t y , j u s t the hope of r e l i a b i l i t y . Primary productivity i n the oceans i s the basis of a highly complex organic food web. Therefore, t o t a l oceanic production, i n terms of b e n e f i c i a l 4 output, i s traceable to energy input at basic trophic l e v e l s . Phytoplankton, the main primary producers, have been studied f o r some time. They have a long f o s s i l h i s t o r y and are the forerunners of modern photosynthetic c e l l u l a r plants. The phytoplankters major inportance i s i n the ecology of the seas which cover 70% of the world's surface. They are the primary organic producers, and thus the fundamental part of the food web leading to f i s h i n the aquatic environment. To analyze even one l e v e l of t h i s web i s a d i f f i c u l t task, l e t alone the complex multi-variate r e l a t i o n -ships between l e v e l s . These system dynamics must be structured from the bottom up. Regier et al. (1974) define four basic modelling classes, depending on the intention of the user. Expository models can be used f o r problem iden-t i f i c a t i o n . S t a t i s t i c a l models are useful i n the analysis of data sets f o r the determination and i d e n t i f i c a t i o n of problem-relevant variables. Models may be developed f o r poorly understood systems to aid i n the research planning phase. The fourth class i s probably the most powerful. These are dynamic models incorporating causal mechanisms to simulate the processes a f f e c t i n g the state i n time. Each modelling class can be considered a systems analysis. Also, within each class there are numerous modelling variations to consider. Whether the model i s completely new, or a v a r i a t i o n on an o l d theme, what i s important i s that the use of a mathematical framework for dynamic des-c r i p t i o n i s synonymous with the application of a hypothesis to the problem. In using mathematics as a framework i n constructing a model of primary food web energetics, one i s c e r t a i n l y l i m i t e d to a more general solution to the problem. However, a mathematical description can be used for prediction purposes f o r future states or perturbation response. In addition, the range 5 of a p p l i c a b i l i t y i s widened. U n t i l recently, i n d i v i d u a l s c i e n t i s t s have concentrated s o l e l y on one of the t r a d i t i o n a l d i s c i p l i n e s . Because of the need to understand i n t e r -actions between the various d i s c i p l i n e s affecting multi-resourceinterests, workers are tending t o tackle problems with a m u l t i - d i s c i p l i n a r y outlook. The more objective s c i e n t i s t s w i l l be able to transcend d i s c i p l i n e s (trans-disc i p l i n a r y ) , not being anchored to any one f i e l d (Regier, et al. 1974). There are few models i n b i o l o g i c a l oceanography which consider non-b i o l o g i c a l interaction. Probably one of the f i r s t attempts to use physical c i r c u l a t i o n as an interacting term i n b i o l o g i c a l productivity was that of Riley (1956) who calculated organic productivity using observed non-conser-vative concentration gradients of oxygen and phosphorus along with calculated advection and d i f f u s i o n c o e f f i c i e n t s . Recently, Winter et al. (1975) devel-oped a model of primary productivity incorporating g r a v i t a t i o n a l c i r c u l a t i o n for Puget Sound i n the northwestern United States. The match with observed data was very good over the short time period investigated. This model also incorporates both b i o l o g i c a l and physical considerations i n an attempt to analyze the system more f u l l y . Interaction between the two d i s c i p l i n e s w i l l be an important factor i n an attempt to get" at the underlying oceanographic mechanisms. The predictive power of the model i s important, i f i t i s to be useful fo r long-term p o l i c y decisions and f o r perturbation response analysis. Extension of the model to the study of s i m i l a r systems i s a prerequisite of construction i f i t i s to gain a greater value through an increased range of a p p l i c a b i l i t y . The basic objective of t h i s thesis i s to formulate a mathematical des-c r i p t i o n of phytoplankton population growth and d i s t r i b u t i o n as a function 6 of b i o l o g i c a l and physical conditions i n Howe Sound, B r i t i s h Columbia. The underlying objective i s to gain seme insight into the complex oceano-graphic mechanisms governing the dynamics of the primary levels of the marine food web. 7 ANALYSIS OF THE STUDY AREA Description, Hydrocrraphy, Tides and Climate Howe Sound has long been thought of as a typical representative of the extensive system of fiords which constitutes the major portion of the British Columbia coastline between latitudes 48° and 59° N. Carter (1934) describes a fiord as a narrow arm of the sea bounded by steep noantain walls. They may extend far inland and quite often bend at sharp angles forming "reaches'.T However, though this may seem to f i t Howe Sound quite well, Carter considers i t a sound or large embayment rather than a true fiord up to the Anvil Island constriction. Past this constriction i t i s considered as a true fiord, since from Anvil Island to Squamish the sound is very narrow and reaches depths of close to 300 meters. Bancroft (1913) was one of the f i r s t to hypothesize the geological origin of the f i o r d system. Originally, the two theories of gl a c i a l erosion and tectonic activity were i n opposition, each with plausible reasons to account for the great depths of the threshold-separated basins. Now, i t i s believed that both have played a role i n the design. Tectonic activity in the early stages of the earths' geological history formed the geosyn-clines which later became the fiords. More recently, the scouring action of glaciers has helped to produce the deep U-shaped trendies. A temporary pause i n g l a c i a l recession i s believed to be the cause of the threshold s i l l which comes to within 70 meters of the surface at the Defense Islands constriction (Waldichuk, 1972). Because i t i s so close to Vancouver, Howe Sound i s heavily u t i l i z e d for recreation such as boating, fishing, and scuba diving. It has long been attractive to commercial users as well. Britannia Beach copper mine has a 8 h i s t o r y dating from the f i r s t of the century. There are pulp m i l l s at Woodfibre and Port Mellon and a c h l o r - a l k a l i plant has been i n operation at Squamish since the 1960's. Good fresh water a v a i l a b i l i t y and r e l a t i v e l y easy access to transportation by r a i l and sea maintain the d e s i r a b i l i t y of the area today (Waldichuk, 1972). The Squamish River and t r i b u t a r i e s have a good salmon run and the delta has been shown to be a major nursery area for^young salmonids as w e l l as an important waterfowl region. I t would seem from t h i s that a c o n f l i c t of interests f o r the use of t h i s system w i l l require a more thorough under-standing of i t s ' complex dynamics to a i d i n the proper analysis of various perturbations. Howe Sound i s an excellent area f o r a mathematical study of phytoplank-ton dynamics. Not only i s i t t y p i c a l of much of the B r i t i s h Columbia coast-l i n e physically and geologically, i t also supplies the researcher with many micro-environments to study the effects of various pollutants and other stresses. Howe Sound i s located near to the c i t y of Vancouver, centered at approximately l a t i t u d e 49° 30' N. and longitude 123° 15' W. (Figs. 1 & 2). The main channel, on which t h i s thesis concentrates, consists of Queen Charlotte and Montagu Channels, leading up to the head at the Squamish Delta. The t o t a l length of t h i s channel i s 45 kilometers. The inner basin i s approximately 18 km long and 280 m deep while the wider outer basin i s 27 km long and 230 m deep (Fig. 3). Hcwe Sound i s t y p i c a l of the estuarine f i o r d systems of the B r i t i s h Columbia coast. Fresh water, derived from the Squamish River discharge, flows along the surface i n a wedge, mixing with entrained saline water from 9 depth as i t moves seaward. This r i v e r water i s heavily laden with s i l t and has a profound e f f e c t on the biology of the system. A e r i a l photo-graphs can be used to examine the flow of the s i l t - l a d e n Squamish Paver waters and show an a x i a l flow which i s deflected at Watts" Point where Howe Sound takes a sharp bend (Waldichuk, 1972). The highest degree of s t r a t i f i c a t i o n i n the sound i s observed during the Squamish freshet and i f t h i s coincides with summer warming the high density gradients are further enhanced. During periods of lower runoff the s t r a t i f i c a t i o n decreases and there i s a uniform mixed zone of about ten meters. In winter when the surface waters become cold and dense, a turn-over of surface and deeper waters may occur. Currents i n Howe Sound are a r e s u l t of runoff, t i d e s , and winds. There i s a slow seaward motion at the surface due to runoff and volume i s conserved by a subsurface flow i n the deeper layers. These flows are included i n the model as the long-term inter-zonal transport mechanism. Tides i n the sound are t y p i c a l of the P a c i f i c Coast being of the mixed type with a large diurnal inequality between the magnitude and timing of the highs. The mean range i s 3.2 meters with a maximum of 5.0 meters. T i d a l currents .in and out of Have Sound respond to the r i s e and f a l l of the tides i n the S t r a i t of Georgia and are of r e l a t i v e l y short time periods associated with t i d a l p e r i o d i c i t y . Winds can also contribute to currents especially a f t e r a lengthy duration at high speeds. However, the thickness of the wind driven layer i s r e l a t i v e l y small and hence volumetric transport i s of l i t t l e e f f e c t . Have Sound has a moderate marine climate with cool and f a i r l y dry summers and cold wet winters. Because of adiabatic cooling of moist P a c i f i c 10 a i r r i s i n g up the steep slopes of the sound, the p r e c i p i t a t i o n i s almost double that of neaby N. Vancouver, (222 versus 113 cm-yr ^) on the average (Waldichuk, 1972). Also, because of the v a l l e y - e f f e c t of the steep sides of Howe Sound, there i s a tendency f o r cold a i r to sweep i n from the i n t e r i o r of B r i t i s h Columbia. Hence, the o r i g i n of the strong unpredictable "Squamish" winds. Another e f f e c t of the high mountainous sides i s a high incidence of cloud cover as w e l l as a certain shading e f f e c t . This l i m i t to solar i n -solation i s an important consideration i n a study of primary productivity. S i m i l a r i t y to Other Fiords As mentioned, one of the values of modelling ecosystem dynamics may be i n the useful extinsion of the r e s u l t to other systems. Have Sound i s very much l i k e Toba I n l e t having about the same dimensions and a s i m i l a r large volume of s i l t y runoff at the head. Many of the other fio r d s of the B r i t i s h Columbia coastline, such as Bute I n l e t , are s i m i l a r i n s i z e and shape as w e l l , but generally runoff volumes are smaller (see Pickard, 1961). Smaller runoff and varying degrees of s i l t load can be entered i n t o the model to simulate phytoplankton growth under these conditions and therefore, do not l i m i t the range of a p p l i c a b i l i t y of the model developed here. However, t i d a l and wind-driven currents may become r e l a t i v e l y more important i n t h i s case, and require a more comprehensive examination. Regardless of the many complex differences, c e r t a i n features of the B r i t i s h Columbia fio r d s may be generalized (Carter, 1934; Pickard, 1961). Plankton outbursts occur early i n the year but do not p e r s i s t . Nutrients brought down by r i v e r s are mixed i n t o the water column u n t i l u t i l i z e d . However, when these r i v e r s carry much s i l t , i n s o l a t i o n i s l i m i t e d 11 to the upper layers.. For this reason, and because of a greater influx of nutrients from the Strait of Georgia, production at the mouth of these fiords i s greater than at the head. The effects of changing the forcing functions on the s t a b i l i t y of the output w i l l demonstrate the r e l i a b i l i t y of the model for application to other similar and even dis-similar regions. Zones Because of large differences i n the variables affecting primary pro-ductivity over the whole of Howe Sound, the eastern channel was divided into three zones (Fig. 4). Phytoplankton growth i s simulated i n each zone and inter-zonal transport i s considered. The f i r s t zone i s bounded by the Squamish Delta at the northeastern corner of the sound and by the threshold s i l l at the Defense Islands con-striction. This area represents the zone of direct influence of the Squamish River and the physical barrier imposed by the s i l l i s the perfect cutoff point, due to i t s effect on the c y c l i c circulation i n zone one. The volume of the f i r s t region over the ten meter depth of interest of the model i s 0.214 cubic kilometers. Zone two extends from the s i l l to just north of Bowyer Island i n the middle of Montagu Channel. This region has the largest volume of interest, 0.439 cubic kilometers. This zone i s affected more indirectly by the out-flow of the Squamish River and sediment studies (e.g. Mathews and Murray, 1966) , have shown that i t i s out of the direct influence of the Fraser River via the Strait of Georgia as well. Zone three extends from the zone two boundary to the mouth of Howe Sound. This i s the most productive area, due to a continuous supply of ) 12 nutrients from the deep waters of the S t r a i t of Georgia. The productive volume of t h i s zone i s 0.293 cubic kilometers. Starting points and observed data averages f o r a l l zones are c a l -culated frcm observations made at various stations i n Howe Sound. Namely f i v e of the stations sampled as part of a survey of the area conducted by Dr. John Stockner of P a c i f i c Environment I n s t i t u t e . The author has been involved with f i e l d and laboratory aspects of t h i s program f o r the four years since i t s o r i g i n i n May 1972. In these calculations, data from pulp m i l l stations i s ignored, since these contribute such a small perturbation on r e l a t i v e scales. In f a c t , Stoclcner et al. (1975) have shown the t o t a l e f f e c t of both pulp m i l l s on areal production i n Have Sound i s i n s i g n i f i c a n t . Zone one values are calculated from the averages of data collected at Stations 9 and 10 over the four year-.study period. Zone two values come from the data of Stations 5 and 6, while Station 1 i s the basis f o r zone three observations (Fig. 4). Comparison of the observed data at these stations with the model simulation is the main te s t of model r e l i a b i l i t y . 13 FIELD AND LABORATORY METHODS Since May 1972, the Plankton Ecology section at Pacific Environment Institute in West Vancouver, has been conducting field research on phyto-plankton growth and distribution in Howe Sound. Originally this work was concentrated in the area of the Squamish River delta, since this region was being considered a possible superport site for the immediate future. Since then, the program has been extended to cover the entire sound by sampling 10 stations (Fig. 4). Sampling Procedure In Howe Sound, each station was sampled once per month. Water samples were collected from the surface, 0f 1,2,3,5,10, 20 and 30 meters in a six lit e r polyvinylchloride Van Corn bottle. The water was placed in various polyethylene and glass containers for tracer inoculation or laboratory analysis. During incubation, a temperature profile and a zooplankton haul are made, both to 50 meters. Light penetration is measured at the incubation site. Usually two or three stations were completed in one day. Physical and Chemical Parameters 1. Incident Radiation and Attenuation. The total incident solar radiation was measured with a Belfort pyrhel-iometer. The curves were digitized for integration and areal radiation cal-_o culated in gram calories-cm for the incubation period and for the f u l l 24 hour period. These values were used to extrapolate to productivity on a daily basis. Light attenuation with depth was measured with Montedoro-lAhitney and Interocean systems Underwater Illuminance meters. This was checked by 14 measuring water transparency at every incubation set using a standard 30 cm white Secchi disc. These data are used to regress the natural logarithm of light intensity (In I) against depth (z) to calculate the mean extinction coefficient (k) for the water column, where: I (z) = I (o) e (see Jerlov, 1963) (1) 2. Nutrients. Nutrient samples were taken from 1, 3, 5 and 20 m depths and frozen as soon as possible. These were analyzed by the DOE, Fisheries and Purine Service and Environmental Protection Service analytical laboratories using methods as outlined i n their manual (Fisheries/EPS, 1974). Nitrate has been shown to be the main limiting nutrient i n phytoplank-ton growth since N:P assimilation ratios are always about 16:1, while i n the summer the avail a b i l i t y ratio may drop to 1:1 (Steele and Baird, 1962). For this reason, the model w i l l be concerned with simulating observed nitrate values and other nutrients w i l l be ignored. This leads to the assumption that inucro-nutrient-vitamin factors are also i n sufficient supply relative to nitrate. 3. C0 2 Alkalinity. The total inorganic carbonate of the water i s an important term i n the 14 calculation of productivity from ."• CXX, uptake. These samples were collected in acid-rinsed 100 ml polyethylene bottles from 1, 3, 5 and 20 meters. The method of Strickland and Parsons (1972) was used to determine carbonate alkalinity with the use of an Orion d i g i t a l pH meter. 4. Temperature. Temperature was recorded as a function of depth using a bathythermograph. Surface temperatures were obtained with a bucket ttiermometer. 15 Biological Parameters 1. Phytoplankton Stocks. A 100 ml sample was obtained from 1,3,5 and 20 m to assess phyto-plankton species and volumes. These were preserved i n Lugol's solution and counted on a Wild M40 inverted microscope, after sedimentation. Volumes were computed from generalized geometric shapes. One l i t e r samples were obtained from the same depths and f i l t e r e d onto Whatman GF/C f i l t e r s for chlorophyll determinations. A small amount of MgCO-j was added to prevent f i l t e r acidification upon freezing. Hie samples were ground i n 90% acetone and the f i l t r a t e made up to 10 ml. Absoip'tion as a function of wavelength was measured using a Cary recording spectropho-tometer and the equation of Strickland and Parsons (1972) was used to c a l -culate chlorophyll a. 2. Phytoplankton Production. The standardization of measurements of primary production i s extremely important i f relative comparisons are to be valid ( J i t t s , 1961). The standard radioactive carbon-14 technique of Steemann-Nielsen (1952) was modified only slightly for this study. Two ligh t and one dark bottle are f i l l e d with water from each of the nine depths sampled. A l l are inoculated with 1 ml of 14 NaH CO-j stock solution having an activity of about 1 uCi per ml. The added activity must be checked since productivity i s proportional to the absorbed radioactivity as a portion of the available carbon~14. Following a 4 to 5 hour incubation, in situ, the phytoplankton were f i l t e r e d onto B.D.H. cellulose nitrate f i l t e r s (0.45 ym pore size). Activity was analyzed i n a Packard Tri-Carb Liquid S c i n t i l l a t i o n Spectrometer and the equation of Strick-land (1960) was used to calculate productivity. Depth profiles can easily be integrated using a linear extrapolation between points, giving area! production 16 for the water column. 3. Zooplankton Stock. Vertical zooplankton hauls were made from 100 m u n t i l the end of 1973 and thereafter from 50 m. A Scor-Unesco net was u t i l i z e d having a 57 cm mouth diameter and 350 uv bucket mesh. Samples were f i l t e r e d onto preweighed GF/C f i l t e r s and dried to a constant weight at 100°C, to determine the biomass 2 per m for the water column. ( i t should be acknowledged at this point that the author has been involved with the f i e l d and laboratory aspects of this program for only 16 months (4 summers). Much of the data for this thesis, i s a result of the continuing research of the Plankton Ecology section of Pacific Environment Institute. ) Circulation and Iriter-zonal Transport Although Howe Sound has been separated into three distinct zones, i t would not be proper modelling of the system to consider each separately. Instead, i t i s necessary to consider inter-zonal transport, whereby organisms enter a different environmental regime i n time. What i s d i f f i c u l t i s to accurately simulate the mechanisms by which this transport takes place. Bell(1975), set up an extensive program, using taut-line moored buoys for his current meters, at three stations i n Howe Sound (Fig. 2). Two types of current meters were used in the study. A Geodyne model A-850 was used at the shallow depths and the Aanderaa model 4 at a l l other depths. Bell's progressive vector diagrams (PVD's) were based on hourly averages and represent the theoretical displacement of the sampling point on a daily basis for fifteen day periods. The difference between the end point coordin-ates can be used to calculate current speed and direction during these periods. When there was an obvious directional switch during the period, i t was 17 broken up into two or three shorter ones. The main dr i v i n g force for the c i r c u l a t i o n patterns and therefore inter-^zonal transport i n the sound i s the Squamish River 1 In order to simulate t h i s flow an average discharge hydrograph was matched to a stand-ard d i s t r i b u t i o n . A portion of the flow volume was considered to be the input i n t o the productive volume of the adjacent zone. A smaller portion was considered to be transported up i n l e t i n subsurface flow. These transport rates were matched to the current data obtained by B e l l (1975). 18 OBSERVED DATA In order to properly t e s t the simulation model, i t must be shown to predict, withinyspecified l i m i t s , the magnitude, timing and d i s t r i -bution of phytoplankton production i n Howe Sound. Mean of the observed data f o r the main factors influencing production i n the sound w i l l be presented along with the standard deviations. Each monthly point has been recorded as the r e s u l t of averages of a l l data available f o r that month from four years of observation. Physical and Chemical Parameters 1. Light Intensity and Attenuation. Annual incident solar radiation as calculated from pyrheliometer curves i s presented i n Figure 5. As expected, maxima are i n June with -2 values of over 600 g-cal-cm . The curve appears symmetrical about t h i s maximum and has minimum values of less than 100 g- c a l -an i n December -January. Since l i g h t i s one of the main exogenous variables a f f e c t i n g the system, i t was necessary to approximate the in s o l a t i o n curve f o r use i n the model. This i s done with a normal d i s t r i b u t i o n and the f i t was good (Fig.. 5)-,! Using a d i s t r i b u t i o n l i k e t h i s instead of actual data gives the modeller the f l e x i b i l i t y to change i t s shape i n order t o simulate the response of the system to varying l i g h t curves. Regressed extinction c o e f f i c i e n t s f o r the water column are given i n Table I . The stations of interest i n each zone are analyzed, followed by the average value f o r that zone. The standard deviations are given f o r a l l values where data was s u f f i c i e n t . Extinction c o e f f i c i e n t s are extremely important since they determine the available l i g h t at depth. The model simulates these values as a function of part i c u l a t e matter derived from 19 Squamish and Fraser discharge and also incorporates phytoplankton s e l f -shading . As expected, extinction o f f l i g h t i s highest i n zone 1 (Table i , F i g . 6), since t h i s zone i s d i r e c t l y influenced by the heavily s i l t - l a d e n output of the Squamish River. Zone 2 (Fig. 7) shows a much less marked time v a r i a t i o n indicating only secondary effects of Squamish discharge. Zone 3 (Fig. 8) i s influenced more by the Fraser River s i l t and values are higher than zone 2, but the influence i s s t i l l not a d i r e c t one as i s the case i n zone 1. To simulate t h i s e f f e c t the model s i m p l i f i e s r e a l i t y with the assumption that the timing of the Fraser discharge i s s i m i l a r to that of the Squamish River. The standard deviation of each point i s plotted as an error bar to give the reader an idea of the magnitude of year to year v a r i a t i o n (error bars are plus or minus one standard deviation). The effects of l i g h t q u a l i t y can be important i n phytoplankton pro-duction as w e l l . However, as observed from the action spectra of three pure axenic cultures, t h i s factor i s more l i k e l y to a f f e c t the productive species, since d i f f e r e n t phytoplankters prefer d i f f e r e n t spectral ranges (Figs. 9, 10, 11), (Stockner and C o s t e l l a , i n press). Also, spectrophotometer analysis of samples from Howe Sound show a f a i r l y l i n e a r absorbtion of the v i s i b l e spectrum u n t i l i n close proximity to a k r a f t pulp m i l l (Fig. 12). 2. Nutrients. Nutrient patterns appear f a i r l y s i m i l a r i n a l l zones (Table I I , F i g s . 6, 7, 8). The values, which are averages of the top 5 m, f a l l o f f rapidly with the advent of the spring bloom. Replenishment i s minimal during the summer i n the inner zones due to a highly s t r a t i f i e d mixed layer, and increases during the autumn as surface cooling promotes a turnover with deeper waters. The main difference between zones i s the timing of the 20 i n i t i a l f a l l o f f . This i s a r e s u l t of a s l i g h t spring bloom delay i n down-inlet zones. 3. Temperature. Temperature data f o r zones 2 and 3 are s i m i l a r , following the incident l i g h t d i s t r i b u t i o n (Table T i l F i gs. 7 & 8). In the f a l l , cooling and i n -creased mixing promote the steady decrease of temperatures i n the surface layers. The main difference i n zone 1 (Fig. 6) i s the depression of the summer maximum due to increased output of cold r i v e r water at t h i s time. B i o l o g i c a l Parameters 1. Phytoplankton Stock and Productivity. Integral primary productivity and standing stock, as represented by clilorophyll a, are given i n Tables -IV and V, and displayed graphically i n Figures 6, 7 and 8. In zone 1, the spring blocm occurs very early i n the year, but does not p e r s i s t due to a high degree of l i g h t attenuation r e s u l t i n g from s i l t - l a d e n flushing during the Squamish River freshet. In zone 2, the advent of the spring bloom i s delayed s l i g h t l y . Here also the productivity declines i n the summer, but the reason- i s nutrient depletion i n the s t r a t i -f i e d surface layers, rather than lack of radiant energy. A very small f a l l peak i s the r e s u l t of increased mixing due to cooling during the l a t e summer and early f a l l . Zone 3 peak production i s delayed u n t i l about May and unlike the other stations p e r s i s t s at f a i r l y high levels during the summer. This i s due to increased t i d a l and other mixing with waters from the S t r a i t of Georgia, which continually supplies nutrients for assimilation. There i s an obvious f a l l peak i n zone 3, since the population levels remain high and can respond quickly to optimal conditions at t h i s time. 21 2. Zcoplarikton Stock. Because zooplankton have been obtained from ve r t i c a l hauls, their biomass i s an integral for the water column. In zones 2 and 3 (Table VI, Figs. 7 & 8) zooplankton stocks follow the phytoplankton peaks as expected i n this trophic relationship. The phase lag i s a good indicator of the response time of the zooplankton population. levels i n zone 1 also follow primary peaks (Fig. 6), but the magnitude i s much greater. This would be odd since the primary production i s lowest i n zone 1, however, i t i s be-lieved that these high levels are a result of large numbers of benthic amphipods being washed off of the Squamish Delta during the river freshet. Also large year to year variations make i t d i f f i c u l t to analyze secondary producer levels. Circulation and Inter-zonal Transport The main driving force behind inter-zonal transport i s considered to be the Squamish River. In order to model this force and to allow f l e x i b i l i t y i n i t s simulation, a normal distribution was matched to an average discharge hydrograph" (Fig. 13). To analyze inter-zonal transport, i t was assumed that a portion of this outflow could be used as down-inlet transport and a smaller portion as up-inlet transport. These portions were estimated from the current data of B e l l (1975), using speed and direction from progressive vector diagrams. At Station HS-5, rnorfch of the s i l l , the surface layer measurements (i.e. 3m and 5 m) indicate a net down-inlet flow averaging out at about 5 km per day (Figs. 14 & 15). A summer rraximum i s indicated for down-inlet, but current speeds are also high i n the winter. Since these maxima do not coincide with the discharge hydrograph, there must be some other driving force, such as winter storms. The 10 m pro f i l e shows regular 180° directional shifts (Fig. 16). 22 This would indicate that 10 m may be the depth of the t r a n s i t i o n zone from down-inlet to up~inlet transport. Surface current measurements at Be l l ' s HS-4 and HS-3 are s i m i l a r to those at HS-5 (Figs. 17 & 18) showing down-inlet flow. At HS-3, the 10 m currents seem to follow the runoff curve very c l o s e l y (Fig. 19). What i s obvious from these data (Figs. 14 to 19), i s that inter-zonal transport i s a very complex function of many parameters. Therefore, i n constructing a model where t h i s transport i s considered a function of runoff only, the system i s being greatly s i m p l i f i e d . This should lead to a greater ease of conceptualization i n an attempt to i n t e r r e l a t e b i o l o g i c a l and physical causitive factors i n a complicated natural system. A continued m u l t i - d i s c i p l i n a r y approach to t h i s problem would lead to the need f o r , and development of,, greater accuracy i n the b i o l o g i c a l and especially the physical sub-models. 23 MODEL DEVELOPMENT Models of phytoplankton production have been i n use f o r some time, as have models of physical c i r c u l a t i o n . Here, these w i l l be analyzed as separate submodels, but combined to form a more complete and comprehensive framework to describe oceanographic mechanisms i n Howe Sound. One of the f i r s t simple models of i n t e g r a l photosynthesis i n a column of water was that of T a i l i n g (1957) , showing a d i r e c t proportionality with the natural log of the incident radiation. This model was l a t e r generalized by Fee (1969) , who generated a family of production l i g h t curves to f i t any population. As t h i s thesis w i l l show, i t i s not the form of the r e l a t i o n -ships between the variables and productivity; rather, i t i s the complex interaction of the various l i m i t i n g factors which determine the true nature of the system. B i o l o g i c a l Submodel The f i r s t step i n model building i s to define the variable f i e l d . This f i e l d follows, with the symbol for each to the r i g h t : Exogenous variables. Incident areal solar i n s o l a t i o n I Average over the productive volume I Inorganic pa r t i c u l a t e matter S Extinction c o e f f i c i e n t k Nitrate concentration N Temperature T Zone number x Range X = 1, 2, or 3 24 Time t Range 0 £ t <_ 12 Endogenous variables. Integral chlorophyll a P Areal primary productivity dP/dt Integral zooplankton biomass Z Areal secondary productivity ;;dZ/dt A l l constants w i l l be expressed i n the form C i , and a l l variable constants i n the f o r m A i . As discussed, incident solar radiation i s simulated by a simple normal d i s t r i b u t i o n I(t) = C i exp (-.5 (t-A]_)/A 2) 2) / (2 TT A X ) ^ (2) where A-^ and A 2 are the time of maximum i n t e n s i t y and the spread of the curve, respectively. For most runs of the model these w i l l remain at, A-j_ = 5.5, A 2 = 3, values which gave good observed data match i n Figure 5. However, these can be varied to simulate other environments. Sakamoto (1966), showed that the extinction c o e f f i c i e n t of l i g h t was a function of absorption and self-shading by phytoplankters, extinction by inorganic p a r t i c u l a t e s , and extinction by dissolved substances as w e l l as pure water. He used the compensation depth and two known attenuation terms to calculate the t h i r d . For t h i s model dissolved e x t i n c t i o n i s assumed constant and a multiple regression used to determine the constants i n the formula for k i n r a ^ K (x,t) = C 3 S (x,t) + C 4 P (x,t) + C5 (3) -3 where C3 = 0.06 to 0.07, with S i n mg-m -2 C4 = 0.7, with P i n g-m C 5 = 0.2 n f 1 25 Now, i t i s possible to calculate average l i g h t a v a i l a b i l i t y over the 10 m productive layer: I (x,t) = 1 of10 I (t) e~ d" k ( x , t ) d d (4) 10 and upon integration T (x,t) = I (t) (1 - e ~ 1 0 k ( x , t ) ) (5) 10 k (x,t) These and other radiation calculations are summarized i n Parsons and Takahashi (1973). Temperature i n the surface layer i s a function of incident radiation and mixing of colder water from depth: dT (x,t) = C 6 I(t) - C 7 M(t) (6) dt where the mixing M i s a function of the breakdown of s t r a t i f i c a t i o n i n the early f a l l . Nutrient concentrations depend on uptake by phytoplankters and mixing input: dN (x,t) = -C 8 dP(x,t) + Cg M(t) (7) dt dt The most important functional relationship to be modelled i s the primary production. I t depends on chlorophyll concentrations, available l i g h t energy, n i t r a t e concentration, temperature and losses to higher trophic l e v e l s . Two p r o d u c t i v i t y - l i g h t functions are used i n the model. The f i r s t i s a polynomial equation obtained by regressing assimilation against average mixed layer l i g h t (Fig. 20): 26 g . = P ( X f t ) (1.4 I ( x , t ) - .014 I 2 ( x,t)) (8) Winter values only were used to avoid times where nutrient depletion may have been l i m i t i n g . To see the effects of changing t h i s function on the f i n a l output, i t was l a t e r changed to an asymptotic hyperbola of the form: dP (x,t) = P(x,t) C 1 0 I (x,t) dt r - ^ (9) C 1 ] : + 1 (x,t) Many p r o d u c t i v i t y - l i g h t functions are summarized i n Parsons and Takahashi (1973). Temperature dependence i s considered very l i m i t e d and a low powered exponential i s used: g | ( x , t ) = exp (.01 T (x,t)) (10) A standard Michaelis-Menten (see Caperon, 1967) hyperbola i s used to simulate n i t r a t e l i m i t a t i o n : dP (x,t) = N(x,t) dt (11) A 3 + N(x,t) (Parsons and Takahashi, 1973). -3 For most runs a ha l f l i m i t a t i o n concentration of A3 = 0.3 g*m was used. The complete primary productivity equation included a l l of the exogenous variables on which i t depends: dP (x,t) = C , , P(x,t) (1.4 I (x,t) - .014 T 2 ( x ,t)) • e ^ 0 1 - 1 ^ / ^ ) . _ N(Xft) _ C l 3_dZ_(x,t) (12) A3 + N(x,t) dt The secondary production i s , i n contrast, very simply modelled. No exogenous factors are considered, other than a constant mortality (natural plus grazing) of .046 days ^ (50% over the 15 day simulation 27 time interval). It i s assumed that the rate of increase of the zooplankton stock depends linearly on stock levels and available food: ^ = C 1 4 Z (x,t) P (x,t) • e - - 0 4 6 * (13) This system of differential equations describe system rates for the three zones at time t. The solution to these equations was discreet (e.g. May, 1973) , using relatively large time intervals (15 days). Limitations imposed by processing times for such a complex system of equations prevent the use of small interval discreet solutions or contin-uous solutions. However, this interval gives solutions which are quite adequate for the purposes of the model. The main detrimental effect w i l l be a slight distortion of population response times. It should be noted that P, Z, N, T, and S, also depend on inter-zonal transport, especially over the large time intervals sampled by the model. This means the system of di f f e r e n t i a l equations must be solved for a l l zones for each simulation, since populations w i l l be transported between adjacent zones. Inter-zonal Transport Submodel Circulation and transport processes i n Howe Sound are important factors affecting the timing and distribution of phytoplankton growth. The observed data have demonstrated the significance of the effects of Squamish River discharge on phytoplankton dynamics, especially i n zone 1. Winter et al. (1975) have shown, that i n order to properly simulate the dynamics of phyto-plankton blooms, physical circulation must be incorporated into the biological model. In this thesis, river discharge i s considered the main driving force for transport i n the fiord. In cubic feet per second, the discharge hydrograph 28 can be matched (Fig. 13) to a normal distribution: Vr ' (t) = 105 exp (-.5 ((t-A 4)/A 5) 2) / (2 IT K5)h (14) The values which gave the good observed data match in Figure 13, were A4 = 6.5 (mid-July) and Ac- = 1.8. These can easily be altered in order to simulate phytoplankton dynamics in a system with a different discharge distribution. Another use for demonstrating the flexibility would be to analyze the effect of any proposed port development which would alter the pattern of the Squamish Paver outflow. Runoff is converted into metric flow volume per 15 day period to correspond to the simulation time interval: Vr (t) =3.7 Vr'(t) x 10~5 (15) where Vr is the volume in cubic kilometers per 15 days. Down-inlet transport volume is a portion of Vr as is up-inlet transport. VD (t) = Ag Vr .(t) (16) VU (t) = A 7 Vr (t) (17) These portions can be varied to observe the effects on the result, but will be in the area of Ag = 0.9 and A 7 = 0.2. This is probably a reasonable estimate, since down-inlet flow must be large enough to conserve volume and up-inlet sub-surface flow is generally only a fraction of the surface flow. This inter-zonal transport is in agreement with the characteristic feature of estuarine circulation as proposed by Bowden and Gilligan (1971) for the Mersey estuary. Their analysis shows that the integral transport by the velocity profile U(z) over the surface layer depth zi in an estuary having ' depth cross section b(z), is equal to the average river discharge of the previous ten days minus the transport across the section of the lower layer: o/ Z 1 U(z) b(z) dz = R 1 Q - F (from Bowden andGGilligan, 1971) 29 I f these flow relationships are v a l i d , the e f f e c t on the concentration Bi(x,t) of variable i i n zone x having productive volume Vx i s simply: B i ( x , t + At) = C 1 4 (Bi(x,t) Vx + B i ( x - l , t ) VD(t) + Bi(x+l,t) W ( t ) ) : (18) Vx + VD(t) + W (t)) This relationship assumes a l i n e a r mixing of the t o t a l input and i n i t i a l amounts of variable i over the productive plus input volumes. The sinking rate f o r each variable i s 1 - C-^ and depends on the p a r t i c u l a r variable. When x = 1, down-inlet transport of concentration B i ( x - l , t ) i s the concen-t r a t i o n of that variable i n the Squamish River flow. In zone 3 when x = 3, up-inlet transport of concentration B i (x+l,t) i s the amount of variable i transported i n from the adjacent S t r a i t of Georgia. Complete System Model Using the transport processes described above, along with the system of d i f f e r e n t i a l equations which describe the b i o l o g i c a l processes i n the sound has allowed f o r a more complete model of the area considering factors from two d i s c i p l i n e s . The s t a r t i n g point f o r each of the exogenous system variables are calculated from the observed data, but the simulations are a r e s u l t s o l e l y of the mathematical framework herein developed to attempt to describe the dynamic oceanographic mechanisms governing the system. For program l i s t i n g see Appendix I. 30 FLOW CHART - ZONE X: BIOLOGICAL PHYSICAL TIME FUNCTION: t INCIDENT RADIATION: RIVER DISCHARGE: V R ZOOPLANKTON STOCK: Z : PHYTOLANKTON STOCK: P NUTRIENTS : NH TEMPERATURE : T-| PARTICULATES : S EXTINCTION COEFFICIENT: K MEAN PRODUCTIVITY ZONE INTENSITY: I TO ZONE X+1 FROM ZONE X-1 TO ZONE X ~ 1 FROM ZONE X + 1 PHYTOPLANKTON dP PRODUCTIVITY: d t ZOOPLANKTON dZ PRODUCTIVITY: d t DOWN-INLET FLOW: V D UP- INLET FLOW: Vu 31 The flow chart shows the many complex and i n t e r r e l a t e d factors governing phytoplankton growth and d i s t r i b u t i o n i n Howe Sound. The ca l c u l a t i o n sequence as depicted i n the flow chart i s d e f i n i t e l y important i n such a model, which uses d iscreet difference equations derived from continuous d i f f e r e n t i a l equations. Pate functions which feedback on certain of the d r i v i n g variables are also e a s i l y observed from t h i s diagram. Feedback i s an importantsbuilt-i n component which has a s t a b i l i z i n g e f f e c t on levels i n the natural system, and i s therefore necessary i n an accurate simulation of that system. In most models of marine primary productivity,' only the primary trophic l e v e l i s considered. This i s an oversimplification of the phytoplankton growth dynamics, since net growth over large time i n t e r v a l s depends on energy-biomass transfer to higher trophic l e v e l s . Considering other trophic levels i s another more i n d i r e c t form of feedback and i s an important factor affecting cycling of populations. Here, zooplankton levels are considered as a feedback on primary levels and the effects on population cycling and trophic response time i s examined. Feedback, cy c l i n g , response times and transfer e f f i c i e n c i e s are j u s t a few of the many complex factors a f f e c t i n g system dynamics i n nature. These factors are j u s t as important as the more d i r e c t environmental and physical factors influencing the system, when formulating a mathematical description of i t . Parameter Estimation This section of the thesis i s b a s i c a l l y concerned with analyzing the res u l t s of the simulations derived from various combinations of the parameters, d i r e c t and i n d i r e c t , a ffecting the model output. The main objective w i l l be to get at the important underlying mechanisms governing the processes within 32 the system. On each zone simulation of the annual variations i n nutrients, temp-erature, e x t i n c t i o n c o e f f i c i e n t , zooplankton biomass, phytoplankton pro-duction and chlorophyll concentration, the observed averages and standard deviations of these variables w i l l also be plotted. This w i l l f a c i l i t a t e easy comparisons of actual versus predicted values and serve as a means of testing the v a l i d i t y of the model. Also on each p l o t there w i l l be a set of parameters (forcing set)^ describing the di s t r i b u t i o n s of the main dr i v i n g functions and the s t a r t i n g points of certain variables; IM - month when the incident s o l a r l r a d i a t i o n d i s t r i b u t i o n i s at i t s maximum. ID - spreaeLlof incident solar radiation d i s t r i b u t i o n . RM - month when Squamish River discharge d i s t r i b u t i o n i s at i t s maximum. RD - spread of Squamish River discharge d i s t r i b u t i o n . CO - " . . i n i t i a l chlorophyll a concentration i n the productive volume. NO - i n i t i a l n i t r a t e concentration i n the productive volume. SI, S2, S3 - i n i t i a l inorganic p a r t i c u l a t e concentration i n the productive volume of the three zones. sZ - i n i t i a l zooplankton biomasss i n the productive volume. The effects of changing t h i s forcing set and of changing various model parameters w i l l be examined win the simulations. For the f i r s t runs of the model, the forcing set was that which gives the appropriate Howe Sound driving functions and s t a r t i n g points. The constants f o r the f i f t e e n day difference equations were chosen to give the proper magnitude' i n the units chosen (Table VTI). The o r i g i n a l zone 1 simulation i s only a f a i r match to the observed 33 data, even when the large standard deviations are considered with the observed values (Fig. 21). The annual v a r i a t i o n i n t o t a l n i t r a t e shows the expected dropoff with the early spring phytoplankton bloom and a gradual increase f o r the remainder of the year enhanced by increased mixing and reduced losses i n a zone which remains barren due to the large s i l t - l a d e n flushing volume of the Squamish Paver. The temperature d i s t r i b u t i o n i s w e l l out of phase with observed values. This i s because, i n zone 1, most of the heating by the sun i s occurring during the early part of the year, since, according to the model, the extinction c o e f f i c i e n t s are s i g n i f i c a n t l y lower at t h i s time. Also, the model assumes the water input from the r i v e r i s at a r e l a t i v e l y low temperature, which causes the temperature to be depressed i n July to August when runoff i s a maximum. I t i s obvious from these plots that the temperature function i s not an accurate description of the true system mechanism at t h i s point. The simulated extinc-t i o n c o e f f i c i e n t data follows the observed data, at least i n pattern. The st a r t i n g point which results from observed inorganic p a r t i c u l a t e i n zone 1 i n January appears to be a l i t t l e high, leading to the conclusion that the multiple regression of ext i n c t i o n c o e f f i c i e n t against particulates and chlorophyll may be misleading when chlorophyll values are very low. Also, with the large year to year variations i n observed attenuation (as indicated by the error bars), to match the o v e r a l l pattern ;is an achievement at t h i s stage of model development. The observed zooplankton values have a very large year to year v a r i a t i o n associated with them. In general they should follow the phytoplankton stocks with a c h a r a c t e r i s t i c response l a g , and indeed do so f o r both predicted and actual values. I t would appear from t h i s p l o t that the phase difference between the two trophic levels i s approximately too months. 34 Of main concern i n t h i s model are phytoplankton growth and standing stock. The zone 1 simulation "of productivity responds very quickly to optimal conditions i n the early spring. The magnitude of the bloom i s much greater than that measured i n the f i e l d , but drops o f f very rapidly. There i s no secondary peak i n t h i s zone because of the high degree of flushing i n the l a t e summer and autumn. The high degree to which the predicted chlorophyll d i s t r i b u t i o n correlates with observed values may indicate certain inaccuracies i n the f i e l d productivity data. Indeed, i f the short-term bloom was missed by monthly sampling, t h i s would explain the discrepancies between measured and predicted r e s u l t s . Also, as mentioned i n the introduction, whenever measurements are made on a system, these measurements may a f f e c t the system and bias the r e s u l t . Could i t be that the predicted values are a better representation of the true system dynamics than are the measured ones ? In zone 2 (Fig. 22), the simulated values indicate the advent of a sec-ondary bloom i n the l a t e autumn of the year. The predicted nutrient values drop o f f s l i g h t l y before the observed ones due to a very f a s t response of the system to optimal l i g h t and nutrient conditions. There i s also a s l i g h t dip i n September when the f a l l production peak occurs. The temperature d i s t r i b u t i o n i s again out of phase with observed values, since the model temperature function shows a decrease when the inter-zonal transport of colder water frcm zone 1 i s at a maximum. Extinction coe f f i c i e n t s match observed values very w e l l , except at the i n i t i a l s t a r t i n g point. Predicted zooplankton biomass levels are also a good match with measured data. They show the expected bimodal function associated with response to a double-peaking prey population. The magnitude of the predicted primary productivity and stock values i s s u bstantially larger than the observed data. Also, the model shows 35 an earlier spring bloom than that observed i n nature. In fact, the original zone 1 peak seems to be swept down-inlet, occuring later i n each successive _zone. The reason for this delay i n the real system w i l l be investigated as the model i s further refined. The zone 3 simulation again shows a rapid onset of the spring produc-t i v i t y peak (Fig. 23). This i s shown by the rapid dropoff of predicted nutrient values as well as by the primary productivity and standing stock curves. It would seem from this that the nutrient supply to zone 3 i s greater than that assumed by the model equations. Temperature i s again ahead of measured values, indicating the delay of solar heating following the onset of density s t r a t i f i c a t i o n . The extinction coefficients are of the right order of magnitude, but peak according to the ri^imum i n the Squamish River discharge. Observed values indicate that i n this zone at the mouth of Have Sound, extinction may depend more on self-shading by the persist-ently high phytoplankton population and on particulates derived from Fraser River outflow. Zooplankton predictions were i n agreement with observations and even though the observed December peak seemed unusual, i t made sense when the model substantiated the phase relationship between primary and secondary trophic levels. For an analysis of ecological transfer efficiency using these simulated data see Appendix II. For the next set of simulations (Figs. 24 to 26) certain changes were made i n the mathematical description of the system. The degree of solar heating was lowered i n a l l zones by 16% to improve the correlation between observed and predicted temperature values. This was achieved by changing constant Cg i n equation (6) from 0.006^to 0.005. Also, i n order to reduce the magnitude of phytoplankton g3?cwth and standing stock,-dP/dt was reduced by changing C-^ i n equation (12) from 0.145 to 0.140 (3.4%). As revealed 36 here, model refinement i s a step by step process. These changes seem to have very l i t t l e e f f e c t on the simulations (Figs. 24 to 26). The predicted temperature values are closer to the r i g h t order of magnitude, but are s t i l l s ubstantially out of phase with the observed values. The relationships between solar heating of the surface layer, s t r a t i f i c a t i o n , and discharge of cold r i v e r water are indeed complex. The reduction i n energetics e f f i c i e n c y of the phytoplankton population, lowers the peak values of the productivity and standing stock curves to a s l i g h t degree as expected. In addition i t i s apparent that there i s a widening of the i n i t i a l spring peak. This i s due to a reduced rate of nutrient depletion, delaying the onset of the more nutrient l i m i t e d summer growth. In the next set of model runs (Figs. 27 to 29) solar heating i s further decreased by 15%. In addition, the effects of an increase i n photo-i n h i b i t i o n are simulated by the model. This i s done by changing the square — 2 — 2 term i n polynomial equation (8) from -0.014 I (x,t) to -0.0175 I (x,t) . r>3agnitude compensation i s achieved by increasing dP/dt (equation 12). Temperature function phase i s s t i l l a problem, and the functional relationship must be changed. In zone 1 (Fig. 27), phytoplankton dynamics are s i m i l a r to previous simulations. As expected, photo-inliibition i s not important i n t h i s area, since l i g h t attenuation i s always high i n the heavily s i l t - l a d e n surface layer. However, i n zones 2 and 3 , the increase i n high i n t e n s i t y i n h i b i t i o n does play a s i g n i f i c a n t r o l e i n changing the system dynamics (Figs. 28 & 29). Autumnal bloom magnitudes are as high as vernal peaks, because of the early onset of photo-inhibition when the waters are clearest i n these zones. Adaptation to high i n s o l a t i o n levels i s not included i n the model, and may be one reason why carbon:chlorophyll r a t i o s vary so widely i n nature. 37 Even though the productivity peaks are s i m i l a r , the spring chlorophyll peak i s s t i l l higher than i t i s i n the f a l l . Zooplankton response lag i s responsible f o r increased grazing pressure on the autumnal phytoplankton maximum. The timing of the simulated blooms i n zones 2 and 3 i s s t i l l ahead of observed values. This i s a r e s u l t of e a r l i e r optimization of l i g h t con-dit i o n s as predicted by the polynomial dP/dt vs. I relationship compared with the true system. This points to using a d i f f e r e n t functional r e l a t i o n -ship to describe the true mechanism affecting timing i n the natural system. In the next zone simulations (Figs. 30 to 32), the temperature function i s changed to follow solar radiation d i r e c t l y , rather than on an i n t e g r a l heating basis. The polynomial relationship between dP/dt and I (equation 8), i s changed to an asymptotic hyperbola as i n equation (9), where photo-i n h i b i t i o n has a l i m i t i n g as opposed to a reducing e f f e c t . Also, the nutrient dynamics of the system are changed, such that losses due to pro-d u c t i v i t y are doubled, Cg i n equation (7). This i s p a r t i a l l y o f f s e t by st a r t i n g the turnover function, M(t), i n June instead of August, so that the mixing of nutrients i s higher by the f a l l . These changes should give some insig h t i n t o the dynamics which govern phytoplankton growth and d i s -t r i b u t i o n i n Howe Sound. In zone 1 (Fig. 30), the predicted nutrient values are i n good agreement with observed data. This would tend to support the revised nutrient dy-namics as one possible description of r e a l i t y . Temperature corresponding to the l i g h t i n t e n s i t y function seems to be a better match to the measured values. However, the phase -is s t i l l ahead, ind i c a t i n g a-.delay i n the relationship between temperature and l i g h t energy. Obviously, the best submodel would incorporate t h i s delay i n solar heating. Extinction of l i g h t with depth 38 i s similar to previous runs as i s the zooplankton biomass. The levels of the latter are lower due to lower phytoplankton population levels. Using the new hyperbolic light relationships causes a delay i n optimal conditions for the spring bloom u n t i l later i n the year. Productivity corresponds more accurately to the observed values i n pattern as well as in magnitude (Fig. 30). The slower rates of population change are ob-viously closer to reality where peaks are not as extreme. In zones 2 and 3 (Figs. 31 & 32), the new ligh t function causes successively later vernal peaking, corresponding to the theory that phyto-plankton standing stock i s transported down-inlet from the Squamish Paver in Howe Sound (Stockner and C l i f f , 1976). Magnitude i n these outer zones are closer to measured values of phytoplankton growth and standing stock as well. However, in zone 3, the predicted productivity does not persist through the summer as does observed growth (Fig. 32). From this, and from observing the slow dropoff of measured nutrient values, i t would seem evident that the input of nutrients into the productive volume of zone 3 i s greater than into the other two up-inlet zones. This input must be almost enough to offset the high rate of u t i l i z a t i o n during spring growth i n zone 3. For the f i f t h run.of the model, nutrient input from external sources into zone 3 i s increased by a factor of 2.5, i n an attempt to further refine the mathematical description. Also, losses to secondary producers are decreased by 50% i n a l l zones. The results of this run (Figs. 33 to 35), are similar i n zones 1 and 2 to the previous simulation. The main difference i s slightly higher phyto-plankton stocks due to reduced grazing pressure. However, this i s offset by corresponding higher zooplankton stocks which follow the primary levels. It i s interesting to note that such stabilizing factors occur i n even a simple 39 mathematical description of the system. In zone 3 (Fig. 35), differences are more noticeable. The high nutrient input and lower predation promote an earl i e r peaking i n primary production. Low summer values exist for only a short period and the advent of the f a l l bloom i s much more rapid. Chlorophyll values are very r e a l i s t i c , remaining f a i r l y high i n the summer and showing the expected bimodal dis-tribution for the mouth of the sound. Secondary productivity follows that of the primary producers for both predicted and measured values. The temperature dependence on light energy i s delayed 2 months to incorporate some integral solar heating into this submodel. In the next model run the effects of this change are simulated for the three zones (Figs. 36 to 38). M l show a very good match between predicted and observed temperatures. It i s this continual refinement that i s the true art of model building and the main benefit of this process i s that the modeller learns many details of the system dynamics during the construction of their description. Because of the delay i n temperature increases, there i s a very slight delay i n the advent of the spring bloom i n a l l zones. However, temperature effects are relatively unimportant i n the model, as evidenced by very l i t t l e change i n the pattern and magnitude of annual phytoplankton dynamics. In the seventh simulation set (Figs. 39 to.41), the temperature de-pendence on solar insolation i s lowered just slightly (15%), to bring the temperature description even closer to observed values. There are also some changes made to the extinction coefficient function. The dependence on self-shading i s increased. This i s done by changing C4 i n equation (3) from 0.7 to 4.0 and lowering C3 from 0.07 to 0.06. Also, i n i t i a l particulate concentrations are lowered as seen i n the forcing set (SI, S2, S3), such that 40 the starting points of the predicted light attenuation distributions comply more closely with measured quantities. In the f i r s t zone (Fig. 39), the changes in the extinction coefficient distribution are hardly noticeable, since the predicted values depend largely on the high levels of particulates which absorb and scatter light. There i s a small bump i n the curve coinciding with the spring chlorophyll peak, but this effect i s only short term as chlorophyll values f a l l right off i n zone 1. In zone 2 (Fig. 40), the light extinction i s a better match to observed levels. It can be seen that the i n i t i a l peak i s due to self-shading effects while the latter peak would be more a result of particulate turbidity. The zone 3 simulation (Fig. 41), shows the greatest benefit from this refinement. In the previous zone 3 simulation (Fig. 38), when self-shading had only a minimal effect, predicted extinction coefficients showed a peak corresponding to increased particulates from both Squamish and Fraser discharge which was out of phase with the observed peak. Increasing self-shading gives a more r e a l i s t i c description of light attenuation, with the i n i t i a l spring peak corresponding to the spring bloom and the late summer peak resulting from a combination from autumnal bloom chlorophyll levels and higher river-derived particulates. It can also be noted from this set of simulations, that the lower i n i t i a l particulates has the effect of promoting a slightly e a r l i e r start to the vernal bloom i n a l l zones. Up to this stage, the various sets of zone simulations have been the result of continually refining the model so that i t becomes a better description of the mechanisms governing system dynamics. Naturally, this process could be carried on, resulting i n better and better matches between predicted and 41 observed values. However, since the model description i s a combination of l o g i c a l l y and empirically derived relationships, and as previously mentioned, the observed values may not be t r u l y representative of the system, i t i s possible that the model may be as r e l i a b l e a description as the f i e l d data at t h i s stage i n i t s development. I t i s c l e a r l y superior i n that i t gives the s c i e n t i s t some insig h t i n t o the numerous relationships a f f e c t i n g levels of many of the variables w i t h i n the primary food-web system i n Howe Sound. 42 MODEL SLMUIATTONS Remaining model runs, w i l l t e s t effects of changes i n environirental forcing functions, while holding the relationships describing the i n t e r -actions between the system-state variables constant. In t h i s way, i t i s possible to study effects of environmental perturbations or to use the model to simulate phytoplankton dynamics i n other regions. In the f i r s t of these simulations, the Squamish River discharge function i s doubled. This could be the r e s u l t of a year of heavy r a i n f a l l or one of unusually high temperatures causing increased runoff i n the Squamish water-shed. I t has the e f f e c t of doubling inter-zonal transport and increasing nutrient inputs, especially i n zone 3. The e f f e c t i n the f i r s t zone are less notable '(Figl4'2). Nutrient values are a l i t t l e higher, probably due to the lower phytoplankton productivity and there i s a further depression of summer temperatures because of the increased input of cold r i v e r water. Extinction c o e f f i c i e n t s are only s l i g h t l y higher, ind i c a t i n g an asymptotic approach to maximum part i c u l a t e concentrations i n zone 1, even at the lower discharge volumes. Productivity i s lowered due to the reduction i n available l i g h t and the tendency for an increase i n winter values i s negated by the increased flushing of the productive volume. In zone 2 (Fig. 43), high inter-zonal transport promotes an e a r l i e r advent of the spring productivity peak, while higher extinction of l i g h t delays the autumnal bloom. Effects are s i m i l a r on phytoplankton growth i n zone 3 (Fig. 44), but again the main difference i s i n timing, while patterns and magnitudes remain v i r t u a l l y the same. As a re s u l t of the high transport values, input of subsurface nutrients i n t o zone 3 from the adjacent S t r a i t of Georgia i s quite large, causing a rapid increase i n available n i t r a t e when 43 productivity f a l l s of i n the winter. When the river discharge function i s halved as i n the next model run (Figs, 45 to 47), the effects are quite different. It i s warmer in zone 1 (Fig. 45), and the lower light attenuation results i n higher productivity predictions. Lower surface zone flushing and higher light penetration promote a winter optimum in growth conditions, indicating that this zone also would exhibit a bimodal productivity curve i f Squamish turbidity was ever reduced or discharge lowered by some natural or man-made perturbation i n this water-shed. There i s a further delay of growth in zones 2 and 3 (Figs. 46 and 47), as i t takes longer for the high productivity to be swept down the i n l e t . Extinction coefficients i n these zones depend greatly on self-shading and follow the pattern of the chlorophyll distribution. The lower values promote a more rapid onset of the f a l l blocm. Another environmental forcing function which can be changed in the model is the annual distribution of solar insolation. It was suggested that a delayed spring simulation,might be interesting, since occasionally, bad weather conditions may persist in Howe Sound u n t i l late spring. This i s done i n the next run of the model (Figs. 48 to 50), where the incident radiation i s -9 -1 set at a constant low winter value (100 gcal*cm "-day ) , u n t i l A p r i l when the normal distribution i s then used. The most drastic effects of this delay i n good weather are evident i n zone 1 (Fig. 48). Negation of the early optimum in light energy by persistently low values causes a definite lag i n the onset of the spring bloom. However, when the surface radiation does start to increase, the extinction coefficients are high, resulting i n a very low spring growth peak. Mien the curves are digitized and integrals calculated, the difference, i n annual areal productivity 44 between a delayed spring and a normal spring (Fig. 48) i s 17% (delayed -200 gC-m '-yr ; normal - 235 gCm "-yr ) , in zone 1. There i s a definite delay i n the advent of the vernal peak i n the two outer zones as well (Figs. 49 and 50). However, since ligh t attenuation i s s t i l l relatively low when the good weather begins i n May, these blooms attain normal maximum values. In zone 2 the peak i s delayed approximately two months by the poor weather, but the loss i n areal productivity i s only 3% -2 -1 -2 -1 (delayed - 308 gOm -yr ; normal - 316 gOm -yr ) . In zone 3, where normally the peak does not occur u n t i l May - June, the predicted values are delayed only a month. Areal productivity i s v i r t u a l l y the same on an annual -2 -1 -2 -1 basis, differing by 1% (delayed - 381 gOm -yr ; normal - 384 gC*m "yr ) in the outer zone. The model predictions of the effects of poor spring weather are i n agreement with observations made i n Howe Sound i n 1974 (Stockner and C l i f f , 1976). In this year, a delayed end to winter weather reduced- spring pro-ductivity near the Squamish River and caused a lag and widening of spring peaks i n the outer zones of the i n l e t . It would seem from this, that the model description does indeed closely simulate ithe real mechanisms governing the dynamics of phytoplankton timing and distribution i n B r i t i s h Columbia turbid coastal inlets. The next run of the model i s an attempt to simulate phytoplankton produc-t i v i t y i n an i n l e t similar to Indian Arm. This can be done easily with a few quick changes to various model functions. F i r s t , the i n l e t i s broken up into three zones of equal productive volume, since i n Indian Arm there i s no distinct zonal transition, as there i s i n Howe Sound. Nutrient entrainrrtent i s thought to be similar i n a l l zones, as opposed to increased t i d a l incursions i n the outer zone as simulated for Howe Sound. The Indian River i s the main circula-45 tion driving force i n the i n l e t . It has a discharge of only half that of the Squamish River and only half the turbidity, since there i s not the same high content of gl a c i a l flour. In this set, Howe Sound distributions are also plotted for comparative purposes. Zone 1 waters (Fig. 51), are certainly less opaque than i n Howe Sound because of the reduced discharge turbidity (Gilmartin, 1964). This allows for the occurrence of a f a l l peak i n phytoplankton growth, increasing the annual areal productivity i n zone 1 by 35%. In zone 2 (Fig. 52), the water remains clearer i n comparison to Have Sound. Havever, the difference i s small and the advantage of greater light a v a i l a b i l i t y i s negated by the reduced entrainment and inter-zonal transport of nutrients. As a result, annual productivity i n this zone i s actually slightly laver than i n zone 1 and also lower than the Howe Sound value for zone 2 (19% lower). A definite contrast i s evident between Howe Sound and Indian Arm in the zone 3 plot ( Fig. 53). Indian Arm waters are clear but lack sufficient nutrient input to maintain much phytoplankton gravth i n the summer. It seems - 2 - 1 that i n this i n l e t the highest production i s at the head (318 gC*m -yr ), -2 -] -2 decreasing ih._the down-inlet direction -through 256 gOm *yr " to 239 gCm • yr This i s a reversal of the Howe Sound trend and i s most certainly linked to the differences i n flushing and nutrient entrainment between the two systems. The v a l i d i t y of the simulated Indian Arm values i s corroborated by pro-ductivity measurements taken by Stockner and C l i f f (in preparation), who found similar patterns and magnitudes i n the area. Gilmartin (1964), also measured productivity i n Indian Arm. His result shaved a similar annual distribution -2 -1 with an areal integral for net photosynthesis of 450 gC*m '-yr . This i s -2 -1 certainly comparable to the simulated value (318 gC-m -yr ), since Gilmartin 46 measured only instanteous productivity and d i d not consider losses by grazing and sinking. The l a s t set of simulations i s a look at productivity i n a th e o r e t i c a l northern B r i t i s h Columbia f i o r d . This i s simulated by decreasing the spread of the solar i n s o l a t i o n d i s t r i b u t i o n , A 2 i n equation (2), from 3 to 2. A shorter summer r e s u l t s , as would be expected f o r the higher latitudes of t h i s province. Also, nutrient entrainment i n the outermost zone i s assumed to be only s l i g h t l y higher (1.5 times) than that of the upper zones. This i s a l o g i c a l conclusion, since not many B r i t i s h Columbia i n l e t s receive such continuous incursions of high nutrient water as Howe Sound does from t i d a l mixing with the S t r a i t of Georgia (e.g. Pickard, 1961). For a l l zones (Figs. 54 to 56), i t appears that productivity i s l i g h t -l imited. Greater transparency increases phytoplankton growth i n the down-i n l e t d i r e c t i o n s i m i l a r to Howe Sound, but available radiation drops o f f rapidly and there i s no f a l l bloom. Only i n the zone 3 simulation (Fig. 56), i s there some evidence of nutrient l i m i t a t i o n . However, t h i s i s only f o r a r e l a t i v e l y short period compared to the depleted summer shown by the Howe Sound nutrient d i s t r i b u t i o n . Again, the modelling description i s validated as i t conforms to patterns and magnitudes of the r e a l world. Both phytoplankton and zooplankton timing and d i s t r i b u t i o n are as might be expected i n a northern f i o r d , which was governed by the modified forcing functions of t h i s simulation. This i s the true v e r s a t i l i t y of a model which describes a few of the main complex oceano-graphic mechanisms governing the dynamics of a system. I t can be used to study other d i f f e r e n t systems merely by changing the environmental d r i v i n g forces. I t can also be used to calculate the effects of perturbations on growth and timing. Or, i t i s useful i n long-term predictions of system 47 behaviour. This l a t t e r i s becoming increasingly important i n a changing world as resource management decisions become more and more c r i t i c a l . 48 DISCUSSION The re s u l t s of numerous simulations have made i t possible to refine a model of primary food-web relations which involves physical c i r c u l a t i o n , as w e l l as b i o l o g i c a l phenomena at two trophic l e v e l s . Although t h i s r e -f i n i n g process i s not normally seen i n the l i t e r a t u r e , i t i s a valuable part of the development of concepts which leads the modeller-to an accurate description of the true ..system ..dynamics. Hie modeller has achieved h i s objective i f the simulated system i s a combination of functions which represent mechanisms and processes i n the r e a l world. The model has not only given ins i g h t i n t o the complex relations governing b i o l o g i c a l growth and population levels i n Howe Sound but also into'the mechanisms which determine the environmental forcing functions governing t h i s system. Rather than attempting to match observed data, the object of the simulations was to explain why these values were observed. Considering the complexity of the model description and the f a r greater complexity of the r e a l system, the good co r r e l a t i o n between predicted and measured quantities, indicates that the simulated system may indeed be a good model of the r e a l one. One int e r e s t i n g aspect of the model output was the difference i n timing of phytoplankton growth as a function of po s i t i o n i n Howe Sound. The observed values show an increasing delay i n the onset of the vernal bloom i n the down'-rinlet d i r e c t i o n . The model shows that t h i s i s a r e s u l t of down-inlet f l a v of higher chlorophyll values, driven by the Squamish discharge which i s the main force behind inter-zonal transport. Physical transport of system properties i s shown to be an important determinant of the levels of temper-ature, nutrients, particulates and zooplankton biomass as w e l l , i n the three 49 Howe Sound zones. I t i s obvious from t h i s , that i t would be a much less complete description of the system i f physical and b i o l o g i c a l submodels were considered separately! Temperature was one of the exogenous variables with a d i s t r i b u t i o n simulated by the model. In the f i r s t few runs, i t was assumed that temperature i n the water column would follow the solar radiation d i s -t r i b u t i o n . The magnitudes were about r i g h t , but there was a d e f i n i t e lag i n phase of the observed temperature values r e l a t i v e to the predicted values. This indicated that temperature i n the surface layer was a r e s u l t of i n t e g r a l solar heating, following the onset of s t r a t i f i c a t i o n i n the water column. Later,when t h i s delay was incorporated into the temperature sub-model, observed and predicted values agreed i n phase as w e l l as i n magnitude. In zone 1, nearest the Squamish River, a depression i n summer temperature values was observed. The simulation matched t h i s d i s t r i b u t i o n , and showed the lcwosummer values to be a re s u l t of large amounts of g l a c i a l -o r i g i n cold water during the r i v e r freshet period. Simulated l i g h t e x t i n ction c o e f f i c i e n t s were the r e s u l t of absorbence and scattering by inorganic particulates and by phytoplankton. I t was o r i g i n a l l y assumed that the attenuation of l i g h t was affected to a greater degree by particulate, concentration than by self-shading. This was adequate for zone 1 where particulates were high and chlorophyll values di d not p e r s i s t , but i n the outer zones t h i s description was not e n t i r e l y adequate. Mien self-shading was increased i n l a t e r model runs, zone 1 was not affected and the other zones showed a good cor r e l a t i o n with measured values. This showed that the early peak i n l i g h t e x t i n ction i n zones 2 and 3 was mainly a r e s u l t of self-shading during the spring bloom, while the l a t e r peak was due to a highly s i l t - l a d e n surface layer during r i v e r freshet, and, 50 to a lesser degree, to attenuation by f a l l peaks i n chlorophyll. Model predictions of annual nutrient d i s t r i b u t i o n are close l y linked to many factors. U t i l i z a t i o n of nutrients by phytoplankton depletes the productive volume, while replenishment i s a r e s u l t of entrainment, t i d a l mixing and water column turnover. In zone 1, a certain amount of nutrients are brought into the surface layer with the Squamish River flow. This model assumption i s corroborated by the steady increase i n observed and predicted n i t r a t e values following the short spring bloom i n t h i s area. In zone 3, the persistence of observed phytoplankton growth and the r e l a t i v e l y slow n i t r a t e depletion i n the spring indicated a much greater degree of nutrient input than i n the other zones. This fact was included i n the model by increasing entxainment and t i d a l mixing i n t h i s zone only. As a r e s u l t , nutrient depletion existed f o r a very short period i n the summer months, and phytoplankton stock levels remained high i n d i r e c t c o r r e l a t i o n with measured data. This agrees with Carter (1934), who noted persistent productivity at the mouths of B r i t i s h Columbia fio r d s and reasoned that i t was due to increased mixing with adjacent waters. Primary productivity has also been shown to be a complex function of many environmental deterrninants. Growth follows the available l i g h t energy i n the mixed layer, but may be lim i t e d by nutrient depletion following periods of population blooms. In zone 1, optimal growth conditions occur early i n the year when the water i s clear. However, productivity i s only short term here, and the Squamish freshet negates any substantial growth for the remainder of the year. In the outer zones, the spring peaks are followed by a barren, nutrient-poor summer, but when the breakdown of s t r a t i f i c a t i o n occurs i n the f a l l , nutrients are replenished and the water i s transparent enough that a secondary bloom can occur at t h i s time. Again the mathematical 51 framework used to formulate the mechanisms governing phytoplankton dynamics gives predicted results which correspond to actual f i e l d data. Net productivity, which depends on net assimilation and losses due to grazing and sjjnking, determines the annual d i s t r i b u t i o n of phytoplankton standing stocks. The model prediction of these levels agrees with observed responses, simulating patterns which follow the productivity curve with a cha r a c t e r i s t i c phase l a g of 15 days. Zooplankton population levels are linked to the amount of t h e i r prey, tiie primary producers. Since higher trophic levels are not considered, the secondary producer-population i s controlled by a constant grazing and natural mortality. This assumes an instantaneous response of these higher levels and may not be an accurate description of r e a l i t y . However, the feedback i s adequate i n the zooplankton stock submodel, since i t i s the primary-secondary grazing which has the most s i g n i f i c a n t e f f e c t on phytoplankton dynamics. As expected, zone 1 zooplankton populations have only one peak corresponding to the single primary productivity bloom. The year to year v a r i a t i o n of observed values i s very large here, and the model i s probably a better prediction of response to primary populations than i s the observed net haul data. In the outer zones the secondary producers e x h i b i t a bimodal annual d i s t r i b u t i o n as a r e s u l t of the two primary peaks. The many complex interrelationships of the model can best be seen i n the flow-chart presented e a r l i e r . I t i s obvious from t h i s and from the simula-t i o n runs that phytoplankton dynamics i n Howe Sound are a complex function of b i o l o g i c a l conditions, as w e l l as being s p a t i a l l y and temporally dependent on physical c i r c u l a t i o n . That the mathematical framework i s an accurate simulation of oceanographic mechanisms i n Howe Sound, i s exemplified by the degree to which the predictions agree with years of f i e l d observations. 52 Indeed, i t may be better than the measured data; at least i t i s more f l e x i b l e . F l e x i b i l i t y i s an important attr i b u t e of simulation models. I t i s fine to have a model which accurately matches observed values i n an isol a t e d system, but i t i s more valuable i f i t i s more universally applicable. The range of a p p l i c a b i l i t y of the model was tested by using i t to simulate phytoplankton growth and d i s t r i b u t i o n i n two other d i s s i m i l a r i n l e t s . Indian Arm was modelled by modifying productive volumes, r i v e r d i s -charge and t u r b i d i t y , and nutrient entrainment at the i n l e t mouth. Model output was very close to the patterns and magnitudes measured by s c i e n t i s t s who have worked i n t h i s area (e.g. Gilmartin, 1964; Stockner and C l i f f , unpublished data). The model was also used to 1.look at productivity i n a theor e t i c a l northern B r i t i s h Columbia f i o r d , by changing the solar i n s o l a t i o n function. Although no data were available f o r comparison, the simulated values were r e a l i s t i c . In f a c t , this, model could be used to analyze phyto-plankton dynamics i n any i n l e t system where environmental forcing functions and physical c i r c u l a t i o n could be described mathematically. Another important useage of models i s i n analyzing perturbation response. Simulations were performed using poor spring weather conditions to attempt to discover why spring productivity had been so low i n Howe Sound i n 1974. Model output was i n d i r e c t agreement with observations made i n that year, showing greatly reduced productivity i n zone l,,and d e f i n i t e delays i n the vernal bloom i n the two adjacent zones. Many d i f f e r e n t types of perturbations could be imposed on the model system. To analyze the effects of certain types of these i n advance would c e r t a i n l y be better than measuring them l a t e r . Modern management decisions require a look at long-term effects of perturbing a system. Even long-range trends i n the un-perturbed system 53 may be of int e r e s t . The type of model developed herein i s also adaptable to t h i s type of analysis. The end points of the f i r s t simulation become the st a r t i n g points f o r the next. There are certain l i m i t a t i o n s on the analysis when the modeller employs a more general strategic mathematical framework such as t h i s . The l o g i c a l development of general ecological p r i n c i p l e s aids i n the conceptualization of system processes, but i s inadequate f o r the digestion of large amounts of data. When interests are t a c t i c a l analysis of data trends, i t i s necessary to turn to more empirically based systems research. In contrast, i n t h i s t h e s i s , observed values have been used only f o r s t a r t i n g points, and t h e i r main value has been for comparison with the results of the mathematical description. The modeller has not asked what i s happening i n the system, rather, why does i t behave as i t does? Another problematic point i s i n the use of discreet time period difference equations to simulate changing states. Any population response time that i s much shorter than the simulation period w i l l be delayed f o r the duration of that i n t e r v a l . Fortunately, as evidenced by measured levels of primary and secondary populations, trophic response i s of a r e l a t i v e l y long-term timing. However, response to environmental changes may be faster than indicated by the model. This could be one reason why phytoplankton growth and standing stock do not quite reach low winter values u n t i l a f t e r the end of the simula-t i o n i n December. To correct t h i s problem, the simulations could be run using continuous d i f f e r e n t i a l equations or very small time i n t e r v a l difference equations. However, the gains may be negated by large increases i n turn-around time f o r i n d i v i d u a l simulations. This, l i k e any model, i s a s i m p l i -f i c a t i o n of nature. A complete description of the r e a l world i s an impossible task. The objective of t h i s thesis has been the development of a mathematical 54 description of oceanographic mechanisms governing primary productivity i n Howe Sound and other B r i t i s h Columbia i n l e t s . Naturally, only the major meclianisms have been simulated. However, model response, predictive power and range of a p p l i c a b i l i t y are very good for such a complex natural system. In a properly designed research program, the o r e t i c a l and empirical approaches to the investigation w i l l mutually reinforce, each providing insi g h t i n t o the refinement of the other. Empirical observations are required i n a proper th e o r e t i c a l evaluation f o r the development and testing of hypotheses. The t h e o r e t i c a l model w i l l give insight into areas which must be examined i n greater d e t a i l . Hence, the development of the most powerful t o o l of the modern research s c i e n t i s t ; the designed experiment. Both physical and b i o l o g i c a l d i s c i p l i n e s have been considered i n the mathematical model. The t r a n s i t i o n to a t r a n s - d i s c i p l i n a r y approach to ecological problems is, becoming an absolute necessity f o r the s c i e n t i f i c cormunity. Surely models such as t h i s which are developed on t h i s basis, are a more complete description of system dynamics than models which are anchored i n only one d i s c i p l i n e . The increased a p p l i c a b i l i t y and r e l i a b i l i t y i s a great advantage i n an environment where increasingly complex multiple use perturbations must be analyzed with greater accuracy and f o r longer periods. The application of mathematical modelling to ecosystem analysis i s a valuable t o o l f o r the assessment of system dynamics to a i d i n the understanding and management of world resources. 55 CONCLUSIONS A model has been developed and tested, for the purpose of describing the oceancgraphic mechanisms governing primary food?.web energetics i n Howe Sound, Bri t i s h Columbia. Certain other important aspects of the model have been examined, including perturbation response, range of applicability and long range predictive powers. A l l of these factors have;potential management implications, and they demonstrate the importance of the construction of such mathematical descriptions of complex ecosystems, i n a world where rapid changes make resource management decisions very d i f f i c u l t . Even though the model has been developed i n a theoretical, more general framework, i t i s not entirely void of empirical input. Observed data starting points and patterns were used i n the construction of the framework which describes system processes. However, there has been no attempt to simply match measured values, only to simulate the mechanisms which result i n such patterns. The main conclusions of the Jthesis are: 1. By comparing observed and mathematically simualted values of nutrients, temperature, extinction coefficients, zcoplankton bicmass, and phytoplankton productivity and biomass i t has been possible to develop and refine a mathematical framework describing primary food web dynamics i n Howe Sound, Br i t i s h Columbia. This has allowed some insight into the key under-lying mechanisms and processes governing the system. 2. Predicted patterns and magnitudes i n a l l Howe Sound zones were shown to closely model observed data. Simulated annual productivity i n the sound -2 -1 v/as 235, 316 and 384 gC^ m *yr i n the down-inlet direction for the three model zones. 56 3. The model was used to simulate the effects of a delayed spring and the results show a reduction i n annual productivity to 200, 308 and 381 -2 -1 gC-m -yr xn zones 1, 2 and 3, respectively. This was i n direct agreement with observations made when poor weather conditions prevailed i n Howe Sound in early 1974. 4. Productivity i n Indian Arm, an adjacent coastal embayment, was predicted using the model. Spatial magnitudes and patterns were i n good agreement with f i e l d data of two workers. Annual productivity was 318, 256 -2 -1 . and 239 gC*m *yr i n the three zones according to the model. 5. Changing the environmental forcing functions was shown to affect model output. River discharge was altered as an example of using the model to predict the effects of perturbations on the system. The distribution of solar radiation was changed to demonstrate the f l e x i b i l i t y of the model i n application to other systems with different environments. 6. The overall conclusion of the thesis i s that mathematical modelling i s a useful tool for the study of primary marine food web dynamics, for analyzing the effects of perturbations on the system and for increasing our f l e x i b i l i t y i n the management of the marine environment. 57 LX BIBLIOGRAPHY Bancroft, J . A. 1913. Geology of the coast and islands between the S t r a i t of Georgia and Queen Charlotte Sound, B r i t i s h Columbia. Canada Dept. Mines, Geol. Survey, Mem. 23. B e l l , W. H. 1975. The Howe Sound current metering program. P a c i f i c Marine Science Report 7 5 - 7 . Vols. I , I I , and I I I . Bowden, K. F., and R. M. G i l l i g a n . 1971. Characteristic features of estuarine c i r c u l a t i o n as represented i n the Mersey Estuary. Limnol. and Oceanogr. Vol. 16. No. 3. pp 490 - 502. Caperon, J . 1967. Population growth i n micro-organisms l i m i t e d by food supply. Ecology. Vol. 48. pp 715 - 722. Carter, N. M. 1934. Physiography and oceanography of some B r i t i s h Columbia f i o r d s . Proc. F i f t h Pac. S c i . Cong. 1933. 1: pp 721 - 733. C l i f f , D. D., and J . G. Stockner. 1973. Primary and secondary compon-ents of the food-web of the outer Squamish River estuary. Fish. Res. Board Can. Man. Rep. No. 1214. 45 p. . Fee, E. J . 1969. A numerical model for the estimation of photosynthetic production, integrated over time and depth, i n natural waters. Limnol. and Oceanogr. Vol. 14. No. 6. pp 906 - 911. Fisheries/E.P.S. Laboratory Manual. 1974. Dept. of Environment, Fish, and Mar. Serv. P a c i f i c Region. Gilmartin, M. 1964. The primary production of a B r i t i s h Columbia f i o r d . J. Fish. Res. Board Can. Vol. 21. No. 3. pp 505 - 538. Goodall, D. W. 1971. Building and t e s t i n g ecosystem models, In: Mathematical Models i n Ecology. J e f f e r s , J . N. R. (ed.) pp 173 - 194. Hoiling, C. S. 1966. The strategy of building models of complex ecological system. In: Systems Anlaysis i n Ecology. Watt, K.E.F. (ed.) pp 195 - 214. 58 J e f f e r s , J . N. R. 1971. The challenge of modern mathematics to the ecologistji In: Mathematical Models i n Ecology. J e f f e r s , J . N. R. (ed.) PP 1 " 11-Jerlov, N. G. 1968. Optical Oceanography. Elsevier Press, New York. 199 p. J i t t s , H. R. 1961. The standardization and comparison of measurements of primary production by the carbon - 14 technique. Proc. Gonf. Prim. Prod. Meas. at the Univ. of Hawaii. U. S. Atomic Energy Comm. M. Doty (ed.) pp 114 - 120. Mathews, W. H., and J . W. Murray. 1966. Recent sediments and t h e i r environment of deposition, S t r a i t of Georgia and Fraser River Delta. Prepared by Tenneco O i l and Minerals Ltd. Calgary, Alberta. May, R. M. 1973. S t a b i l i t y and complexity qf model ecosystems. Prince-ton University Press. 235 p. M u l l i n , M. M., P. R. Sloan, and R. W. Eppley. 1966. Relationship between carbon content, c e l l volume, and area i n phytoplankton. Limnol, and Oceanogri. Vol. 11: pp 307 - 311. Parsons, T. R., and M. Takahashi. 1973. B i o l o g i c a l Oceancgraphic Processes. Pergamon Press. 86 p. Pickard, G. L. 1961. Oceancgraphic features of i n l e t s i n the B r i t i s h Columbia mainland coast. J . Fish. Res. Board Can., Vol. 18 No. 6 pp 907 - 999. P i a t t , T., and D. V. Subba Rao. 1970. Primary production measurements on a natural plankton bloom. J . Fi s h . Res. Board Can. 27: pp 887 - 899. Raymont, J . E. G. 1963. Plankton and productivity i n the oceans. I n t ' l . Ser. of Monographs i n Pure and Applied Biology. Zoology Division. Vol. No. 18. 660 p. 59 Regier, H. A., P. L. Bishop, and D. J . Rapport. 1974. Planned tr a n s d i s c i p l i n a r y approaches: renewable resources and the natural environment p a r t i c u l a r l y f i s h e r i e s . J . F i s h . Res. Board Can. 31: pp 1683 - 1703. Riley, G. A. 1956. Production and u t i l i z a t i o n of organic matter, In: Oceanography of Long Island Sound, 1952 - 1954. B u l l . Bingham Oceangr. C o l l . Yale University. 15: pp 324 - 344. Sakamoto, M. 1966. The chlorophyll amount i n the euphotic zone i n seme Japanese lakes and i t s significance i n the photosynthetic production of phytoplankton ccmnunity. Bot. Mag. Tokyo No. 79 pp 77 - 78. Skellam, J . G. 1971. Some philosophical aspects of mathematical modelling i n empirical science with special reference to ecology. In: Mathematical Models i n Ecology. J e f f e r s , J . N. R. (ed.) pp 13 - 28. Steele, J . H., and I. E. Baird. 1962. Further relations between primary production, chlorophyll, and part i c u l a t e carbon. Limnol and Oceanogr. Vol. 7: pp 42 - 47. Steemann-Nielsen, E. 1952. The use of radioactive carbon C-14 f o r measuring organic production i n the sea. Journal du Conseil. Stockner, J . G., D. D. C l i f f , and K. Munro. 1975. The effects of pulp m i l l e f fluent on phytoplankton production i n coastal waters of B r i t i s h Columbia. Fish , and Mar. Serv. Canada Tech. Rep. No. 578. 99 p. Stockner, J . G., and D. D. C l i f f . 1976. Phytoplankton succession and abundance i n Howe Sound: a coastal embayment-fiord under stress. J . Fish. Res. Board Can. 33: (in press.) Strickland, J . D. H. 1960. Measuring the production of marine phyto-plankton. F i s h . Res. Board Can. B u l l . No. 122. 173 p. 60 Stxickland, J.. D. II., and T. R. Parsons. 1972. A P r a c t i c a l Handbook of Seawater Analysis. Fish. Res. Board Can. B u l l . No. 167. 311 p. Takahashi, M., K. F u j i i and T. R. Parsons. 1973. Simulation study of phytoplankton photosynthesis and growth i n the Fraser River estuary. Mar. B i o l . 19: pp 102 - 116. T a i l i n g , J. F. 1957. The phytoplankton population as a compound photosynthetic system. New Phytol. 56: pp 133 - 149. Waldichuk, M. 1972. Howe Sound as a renewable resource environment. Contribution to the Department of Environment Po s i t i o n Paper. Winter, D. F. 1973. A s i m i l a r i t y solution f o r steady-state gra v i t a -t i o n a l c i r c u l a t i o n i n f i o r d s . Est. and Coast. Mar. S c i . I: pp 387 - 400. Winter, D. F., K. Banse, and G. C. Anderson. 1975. The dynamics of phytoplankton blooms i n Puget Sound, a f i o r d i n the northwestern United States. Mar. B i o l . 29: pp 139 - 176. 61 X TABLES TABLE I OBSERVED EXTINCTION COEFFICIENT M AVERAGES AND STANDARD DEVIATIONS, HOWE SOUND, 1972 TO 1975." & DATE 9 10 Zl 5 6 Z2 Z3 JANUARY .208 .027 .204 - .207 .019 .295 - .231 — .263 .045 .185 --FEBRUARY .297 .098 .277 .079 .285 .075 .221 .053 .268 .082 .244 .067 .273 .106 MARCH .353 .095 .420 .184 .387 .126 .217 - .236 .054 .230 .040 .341 .134 APRIL .614 .298 .498 .233 .556 .247 .294 .097 .336 .090 .315 .087 .470 .308 MAY .519 .401 .719 .617 .619 .478 .327 .098 .476 .058 .386 .111 .590 .458 JUNE 1.247 .907 2.761 - 2.004 1.019 .618 .116 .779 .332 .699 .223 .846 .685 JULY 1.141 1.009 1.924 1.516 1.533 1.144 .373 .163 .663 .369 .519 .289 .647 .436 AUGUST .218 - .533 - .375 .223 .249 - .277 .013 .268 .019 .378 .098 SEPTEMBER .291 .042 1.660 1.399 .975 1.130 .201 - .639 - .420 .309 .297 -OCTOBER .423 .187 .348 .076 .385 .124 .418 .312 .493 .062 .456 .189 .556 .357 NOVEMBER .474 .181 .540 .224 .507 .171 .611 .374 .304 - .509 .318 .322 .079 DECEMBER .658 _ .322 _ .490 .238 .445 _ .294 .370 .107 .268 .051 aData collected in conjunction with studies by the Plankton Ecology Section, Pacific Environment Institute, Fisheries and Marine Service, West Vancouver, B.C. TABLE I I OBSERVED TOTAL N03 g-m ( 0 - 5 m) AVERAGES Aid STANDARD DEVIATIONS, HOWE SOUND, 1972 TO 1975. 3 DATE 9 10 Zl 5 6 Z2 Z3 JANUARY — — — — — — .300 — .270 — .285 .021 .280 — FEBRUARY .322 .047 .332 .087 .327 .057 .267 - .347 - .307 .057 - -MARCH .247 - - - .247 - .352 - .311 - .332 .029 .260 .088 APRIL' .010 - .010 - .010 0 .168 - .171 - .170 .002 .117 -MAY .029 .025 .050 .039 .040 .031 .036 .023 .033 .023 .035 .021 .070 .054 JUNE .043 - .057 - .050 .010 .037 - .090 - .064 .037 .063 -JULY .057 .042 .041 .003 .049 .026 .024 .020 .086 .107 .055 .073 .020 .014 AUGUST .107 - .060 - .084 .033 - - .010 - .010 - .010 -SEPTEMBER .097 - .083 - .090 .010 - - - - - - .010 -OCTOBER .180 .024 .170 .047 .175 .031 .019 .012 .019 .008 .019 .009 .089 .003 NOVEMBER .293 - .267 - .280 .018 .117 - - - .117 - .333 -DECEMBER .334 .038 .330 .042 .332 .033 .350 .344 .347 .004 .364 .030 ^ a t a collected i n conjunction with studies by the Plankton Ecology Section, P a c i f i c Environment I n s t i t u t e , Fisheries and Marine Service, West Vancouver, B.C. TABLE I I I OBSERVED TEMPERATURE °C AVERAGES AND STANDARD DEVIATIONS, HOWE SOUND, 1972 TO 1975. a DATE 9 10 Zl 5 6 Z2 Z3 JANUARY 5.6 0.4 5.6 1.3 5.6 0.9 5.3 1.1 5.5 1.6 5.4 1.1 6.2 0.2 FEBRUARY 5.0 5.4 0.6 5.3 0.5 5.9 0.5 6.2 0.7 6.0 0.6 6.1 0.5 MARCH 5.2 - 4.9 - 5.1 0.2 7.7 0.8 7.2 2.0 7.4 1.5 6.4 0.2 APRIL 8.1 0.8 7.7 1.1 7.9 0.9 8.8 1.7 8.4 1.5 8.6 1.4 7.6 0.6 MAY 9.1 1.6 8.6 1.2 8.9 1.3 12.2 1.3 10.5 1.0 11.0 1.3 11.4 1.8 JUNE 9.9 0.7 8.7 0.8 9.3 0.9 13.5 ' 1.6 11.8 0.6 12.7 1.4 13.3 1.7 JULY 10.9 0.8 10.1 0.6 10.5 0.8 14.6 1.6 14.4 0.5 14.5 1.3 17.2 1.9 AUGUST 13.1 0.8 12.3 0.1 12.7 0.7 15.9 1.1 14.6 1.1 15.2 1.1 17.1 1.3 SEPTEMBER 11.6 1.4 11.6 1.4 11.6 1.2 14.8 - 13.8 - 14.3 0.7 14.7 2.0 OCTOBER 10.4 1.1 10.1 1.7 10.2 1.2 10.9 2.0 11.5 0.6 11.1 1.5 11.8 2.1 NOVEMBER 7.8 1.3 7.0 1.9 7.4 1.5 8.0 0.9 8.9 - 8.3 0.8 8.4 2.1 DECEMBER 6.9 1.2 6.2 0.5 6.5 0.9 7.3 1.1 6.9 0.6 7.1 0.8 7.9 0.8 ^ a t a collected i n conjunction with studies by the Plankton Ecology Section, P a c i f i c Environment I n s t i t u t e , Fisheries and Marine Service, West Vancouver, B.C. TABLE IV OBSERVED QE/DROPHYLL '. CX^ ICENTRATION mg-m AND STANDARD DEVIATIONS, HOWE SOUND, 1972 TO 1975. a DATE 9 10 Zl 5 6 Z2 Z3 JANUARY 0.2 0.2 1.1 0.9 0.7 0.7 4.3 4.2 4.2 4.3 4.3 3.4 3.3 4.4 FEBRUARY 1.6 0.0 1.6 0.0 1.7 0.2 3.4 1.9 2.7 2.5 3.0 2.0 0 0 MARCH 48.3 74.0 6.9 1.7 31.7 57.0 5.9 - 2.8 3.2 3.8 2.9 4.2 3.1 APRIL ' 69.8 68.4 80.9 77.9 75.3 68.2 18.5 15.8 53.6 26.2 30.2 24.8 38.6 43.4 MAY 9.2 8.4 8.7 8.1 9.0 7.4 11.0 1.9 8.0 10.8 9.5 7.2 38.3 49.2 JUNE 8.6 5.2 10.0 6.7 9.3 5.0 17.2 2.6 13.4 4.7 15.3 3.8 39.6 12.6 JULY 8.8 7.5 13.3 12.4 11.0 8.8 26.5 29.6 24.8 27.6 25.6 23.4 88.8 44.5 AUGUST 5.0 3.6 3.8 2.9 4.5 3.0 32;1 4.3 15.3 1.2 23.7 10.0 27.6 11.3 SEPTEMBER 13.6 11.0 14.7 14.8 14.2 11.7 31.1 - 12.6 - 21.9 13.1 74.0 64.9 OCTOBER 11.8 2.2 14.1 9.5 12.9 5.8 28.1 9.6 25.3 i 5.8 27.0 7.6 37.4 29.4 NOVEMBER 3.6 6.3 3.2 3.5 3.4 4.5 3.8 1.6 5.0 - 4.2 1.3 5.5 6.6 DECEMBER 1.1 0.6 2.0 0.3 1.5 0.6 6.4 1.7 4.6 2.6 5.5 2.1 3.0 4.2 ^ata collected in conjunction with studies by the Plankton Ecology Section, Pacific Environment Institute, Fisheries and Marine Service, West Vancouver, B.C. TABLE V OBSERVED PRIMARY PRODUCTION mg-m AVERAGES AND STANDARD DEVIATIONS, HOWE SOUND, 1972 TO 1975. a DATE 9 V 10 Z l -~ 5 6 ' Z2 . Z3 JANUARY 78 68 78 72 78 63 69 45 240 179 154 145 107 81 FEBRUARY 100 119 136 112 118 105 92 68 202 305 147 207 94 53 MARCH 143 11 230 195 186 124 262 - 181 16 208 48 237 38 APRIL 1110 1525 1352 2223 1231 1769 639 377 982 832 786 579 993 996 MAY 300 350 331 390 316 344 380 235 '329 289 389 246 2303 2246 JUNE 102 134 87 40 94 92 1359 102 900 577 1130 455 3747 2163 JULY 218 322 536 1023 377 722 507 436 209 38 379 348 1389 1149 AUGUST 371 220 261 84 327 172 687 761 356 41 522 480 807 328 SEPTEMBER 289 280 191 161 240 211 594 - 80 - 338 363 1807 1476 OCTOBER 147 38 103 2 125 34 751 368 307 25 573 356 779 428 NOVEMBER 50 62 30 41 41 51 46 12 66 - 51 14 214 205 DECEMBER 44 2 49 9 47 6 22 16 14 8 18 11 ' 56 59 aData collected i n conjunction with studies by the Plankton Ecology. Section, P a c i f i c Environment I n s t i t u t e , Fisheries and Marine Service, West Vancouver, B.C. TABLE VI OBSERVED ZCOPLANKTON BICMASS mg-m AVERAGES AND STANDARD DEVIATIONS, HCWE SOUND, 1972 TO 1975. a DATE 9 10 Z l 5 6 Z2 Z3 JANUARY 3.8 - 6.0 - 4.9 1.6 75.8 103.5 25.7 32.6 50.7 69.1 5.0 4.5 FEBRUARY 4.5 1.9 4.7 0.5 4.6 1.2 7.3 7.0 3.3 2.9 5.3 5.2 2.8 1.7 MARCH 32.8 - 3.0 - 17.9 21.1 6.2 5.6 4.1 3.3 4.9 3.8 5.3 3.4 APRIL 14.4 3.3 16.5 8.1 15.5 5.6 15.3 13.3 11.5 7.0 13.4 9.7 13.3 7.6 MAY 74.4 38.0 144.3 177.1 113.2 132.6 34.1 23.5 29.0 22.2 31.5 20.6 60.2 43.7 JUNE 122.0 180.5 133.0 42.0 127.5 117.4 14.5 13.9 7.5 0.3 11.0 9.0 26.3 3.4 JULY 44.2 34.3 38.7 25.5 41.4 28.1 5.2 2.9 3.6 0.5 4.4 1.9 23.5 14.4 AUGUST 115.1 143.0 14.4 2.5 64.7 101.0 16.6 - 6.8 0.6 10.0 5.7 37.2 -SEPTEMBER 10.6 3.2 60.7 74.2 35.6 51.8 6.1 - 6.0 - 6.1 0.1 20.4 -OCTOBER 4.1 2.5 11.4 6.2 7.8 5.7 6.0 2.1 4.8 1.9 5.4 1.8 8.0 4.9 NOVEMBER 7.1 2.3 9.4 11.0 8.2* 6.6 11.5 - 7.4 - 9.5 2.9 15.4 16.4 DECEMBER 4.5 4.0 5.3 2.0 4.9 2.6 224.1 312.3 56.8 74.5 140.5 209.0 79.5 110.0 ^ a t a collected i n conjunction with studies by the Plankton Ecology Section, P a c i f i c Environment I n s t i t u t e , Fisheries and Marine Service, West Vancouver, B.C. 68 TABLE VII ABBREVIATIONS AND UNITS OF GRAPHICAL PARAMETERS. PARAMETER ABBREVIATION UNITS Nitrate -3 NUT g'NO^ -m Temperature TEM °C Extinction Coefficient EXT m -2 Zooplankton Biomass ZOO gdrywt-m -2 -1 Phytoplankton Productivity P.P. gC*m -day -2 Phytoplankton Stock CHL gchl a*m 69 XI FIGURES FIGURE 1. LOWER BRITISH COLUMBIA COASTLINE, HOWE SOUND. 71 FIE, I FIGURE 2. HOWE SOUND WITH BELL'S (1975) CURRENT METERING STATIONS, HS - 3 f HS - 4 AND HS - 5. 73 PIE. 2 FIGURE 3. AXIAL CROSS-SECTION THROUGH MAIN CHANNEL OF HOWE SOUND (FROM BELL, 1975). HOWE SOUND SAMPLING STATIONS WITH EASTERN CHANNEL BROKEN UP INTO MODELLING ZONES (ADAPTED FROM STOCKNER ET AL. (1975)). 77 FIE. H FIGURE 5. ANNUAL INCIDENT SOIAR RADIATION AND MATCH TO NORMAL DISTRIBUTION. 80 FIGURES 6 TO 8. OBSERVED DATA AVERAGES AND STANDARD DEVIATIONS ZONES 1, 2 AND 3. QUANTITY GRAPH MAXIMUM NUT gN0 3 -m~3 TEM °C EXT m"1 -2 ZOO gZ«m -2 -1 P.P. gC*m -day x -2 CHL gchl a-m FIGURES 9 TO 11. PURE AXENIC CULTURE PHOTOSYNTHETIC ACTION SPECTRA. ta n C U L T U R E R C T i U N S P E C T R U M E K C L C T D N C M F l C O S T R T U M IS rvi — i 1 "7E30 N R V E T L E N E T H < N M . > LO CULTURE: RCT I DN SPECTRUM R M P H I D I N I U M C H R T C R I IS + 1 1 1 1— 1 1 1 1 1 1 1 1 1 1 1 1 — I HZIZJ S 0 0 E5IZ3EI " 7 0 0 W P V E L E T N L H T H < N M . > FIGURE 12. EXTINCTION COEFFICIENT AS A FUNCTION OF WAVELENGTH AT VARIOUS DISTANCES FROM KRAFT PULP MILL AT PORT MELLON IN HOWE SOUND.(FROM STOCKNER ET AL. 1975). STATION DISTANCE FROM OUTFALL PM - 1 0.02 km PM - 2 0.20 km PM - 3 0.80 km PM - 4 1.80 km Number on l i n e = apparent color. 90 FIGURE 13. ANNUAL SQUAMISH RIVER DISCHARGE HYDROGRAPH AND MATCH TO NORMAL DISTRIBUTION. FIGURES 14 TO 19. CURRENT SPEEDS AND DIRECTIONS AT BELL'S (1975) CURRENT METERING STATIONS IN HOWE SOUND (FIGURE 2) . FIE. IH 94 FIE. IS FIE. IE 97 FIE. IB 98 FIE. 13 99 FIGURE 20. POLYNOMIAL REGRESSION OF P.P. / P MAX VS I FOR WINTER VALUES IN EASTERN QIANNEL OF HOWE SOUND. 100 FIE. 20 FIGURES 21 TO 23. ORIGINAL SIMULATIONS IN ZONES 1 TO 3, HOWE SOUND. ZDNE I SIMULRTIDN 102 FIE. 21 FDRCINE SET 1M4 5.50 ID4 3.00 RM4 E.S0 RD4 I.B0 CI» .003 ND-> .300 SI* 15.00 S2-> 12.00 534 10.00 5Z4 .010 ZDNE 2 5IMULRTIDN FIE. 22 FORCING"SET IM-» E.S0 ID-> 3.00 Z D N E 3 S I M U L R T I -ON FIE. 2 3 FORCING SET IM-> S.E0 ID-> 3.00 FIGURES 24 TO 26. ZONE SIMULATIONS - DECREASE SOLAR HEATING IN ALL ZONES 15 - DECREASE dP / dt 3.4%. Z D N E I S 1 M U L R T I D N FIE. 2H FORCINE SET ZDNE! 2 5 I tlULRT I UN 107 FIE. 25 FDRCINE SET IM4 5.50 ID4 3.00 RM4 E.50 Rt>4 I . B0 CD4 .003 N04 .300 514 15.00 524 12.00 534 10.00 524 .010 ZONE 3 'SIMULATION F I E . 2E FDRCINE-SET. IM4 lD-> 3.00 109 FIGURES 27 TO 29. ZONE SIMULATIONS. - FURTHER DECREASE SOLAR HEATING BY 15%. - INCREASE PHOTO-111I-IIBITION IN POLYNOMIAL (8) 25% FROM - 01014 I 2 TO - 0.0175 I 2 . - INCREASE dP / dt BY 17% RELATIVE TO ORIGINAL RUN. ZONE I 5 IMULRTIDN 110 FIG. 27 Z z y x UJ • n N FORCING SET IM-> E.E0 lD-> 3.00 RM-> E.50 RD-> I . B0 CO* .003 NO* .300 514 IE.00 52* 12.00 53* 10.00 5Z* .010 ZDNE 2 5IMULRTIDN FIE. 2B FDRCINE 5ET IM-> £.50 1D4 3.00 d D d I> 112 ZONE 3 5 I MULRT I DN FIG. 2a •. FORCING SET !M4 5.50 ID-> 3.00 FIGURES 30 TO 32. ZONE SXTVirjIATIONS. - CHANGE TEMPERATURE FUNCTION TO FOLLOW SOLAR RADIATION FUNCTION, MIXING REMAINS THE SAME. - SWITCH dP / dt VS I RELATIONSHIP FROM POLYNOMIAL TO HYPERBOLIC FORM. - DOUBLE NUTRIENT LOSS DUE TO PRODUCTIVITY. - OFFSET BY STARTING NUTRIENT TURNOVER FUNCTION IN JUNE AS OPPOSED TO AUGUST. 114 Z D N E I 5 I M U L H T I D N FIE. 2 0 FORCINE 5ET IM* 5.E0 ZONE 2 5IMULRTIDN' 115 FIE. 31 El FORCINE SET IM4 5.50 1D4 3.00 RM4 E.S0 RD4 I . B0 C04 .003 ND4 .300 514 15.00 524 12.00 534 10.00 5Z4 .010 116 ZDNE 3 SIMULATION FIE. 32 FDRCINE 5ET FIGURES 33 TO 35. ZONE SD1ULATIONS. - DECREASE dP / dt (LOSS TO dZ / dt BY 50%. - INCREASE NUTRIENT MIXING FROM EXTERNAL SOURCES BY A FACTOR OF 2.5 IN ZONE 3 ONLY. ZDNE 5IMULRTIDN 118 FIE. 33 FDRCINE SET 1M* 5.50 ID* 3.00 RM* E.50 RD* 1.00 CD* .003 NO* .300 51* 15.00 52* 12.00 53* 10.00 52* .010 119 ZDNE 2 5.1 MULRT I DN H E . 3H FDRCINE 5ET IM-> 5.50 ID* 3.00 ZONE 3 5 IMULRTIDN 120 FIG. 35 FORCING 5FT IM* 5.50 ID* 3.00 RM* E.50 RD* I.B0 CO* .003 ND* .300 51* 15.00 52* 12.00 53* 10.00 5Z* .010 FIGURES 36 TO 38. ZONE SIMULATIONS. - DELAY TEMPERATURE DEPENDENCE ON SOLAR RADIATION BY TWO MONTHS. 122 ZONE I 5 IMULRTIDN FIE. 3 E FDRCINE 5ET IM* S.50 IS ZDNE 2 5 I.MULHT I DN 123 FIB. 37 FORCING SET-• Z El N Z Li 1M* 5.50 ID* 3.00 RM* E.50 RD* 1.B0 CO* .003 NO* .300 51* 15.00 52* 12.00 53* 10.00 5Z* .010 124 ZONE 3 S IMULATION F I E . 3 g E3 FDRCINE 5ET FIGURES 39 TO 4 1 . ZONE SIMULATIONS. - 15% DECREASE IN SOLAR INSOLATION DEPENDENCE OF TEMPERATURE. - INCREASE EXTINCTION (^EFFICIENT DEPENDENCE ON SELF-SHADING. - LOVER INITIAL PARTICULATE CONCENTRATION. 12G ZDNE I SIMULATION FIG. 3s FORCING SET IM* S.S0 ZDNE 2 5 IMULRTI ON 127 FIE. H0 FDRCINE SET IM* 5.50 ID* 3.00 RM* E.S0 RD* I.B0 CD* .003 ND* .300 51* E.00 52* H.00 53* 3.00 5Z* .010 128 ZONE 3 5 I MULRT I ON F I E . HI FDRCINE 5ET FIGURES 42 TO 44. ZONE SIMULATIONS. - RIVER DISCHARGE FUNCTION DOUBLED. ZDNE I 5IMULHTIDN 130 FIE. H2 FDRCINE BET 1M* 5.50 ID* 3.00 RM* E.50 RD* 1.H0 CD* .003 ND* .300 51* 5.00 52* H.00 53* 3.00 5Z* .010 ZDNE 2 5 IMULRTIDN 131 FIG. H3 SI i/i n . FDRCING 5ET IM* £ . 5 0 ID* 3.00 RM* E.50 RD* 1.B0 CD* .003 ND* .300 51* E.00 52* H.00 53* 3.00 5Z* .010 ZDNE 3 5IMULHTI0N 132 FIB. HH FDRCING BET IM* 5.50 ID* 3.00 RM* E.S0 RD* I.B0 CD* .003 ND* .300 51* E.00 52* H.00 53* 3.00 5Z* .010 FIGURES 45 TO 47. ZONE SIMULATIONS. - RIVER DISCHARGE FUNCTION HALVED. 134 ZDNE I SIMULATION FIE. HE FDRCINE SET IM* E.E0 ID* 3.00 ZDNE 2 S IMULATION 135 FIE. HE FDRC1NE 5ET • Z rvi z rvi i -x hi 1M* 5.50 ID* 3.00 RM* E.50 RD* 1.B0 CD* .003 ND* .300 51* E.00 52* H.00 53* 3.00 5Z* .010 136 ZONE 3 5 I MULRT I ON F I E . FDRCINE 5ET FIGURES 48 TO 50. ZONE SIMULATIONS. - NORMAL SPRING (• •) VS DELAYED SPRING ( - I = 100 g-cal-OT~ 2-day - 1 TO END OF APRIL. 138 ZDNE I 5 IMULRT IDN FIG. HG \ FORCING 5FT IM-> 5.50 ZDNE 2 5 IMULHTI ON 139 FIE. HE FDRCINE SET IM* 5.50 ID* 3.00 RM* E.S0 RL>* I . B0 CD* .003 ND* .300 51* E.00 52* H.00 53* 3.00 52* .010 ZDNE 3 5 IMULRT I DN TIE. •, FDRCINE 5ET FIGURES 51 TO 53. HOWE SOUND (•——•) VS INDIAN ARM SIMUTATIONS. - PRODUCTIVE VOLUMES EQUAL IN ALL INDIAN ARM'ZONES. - NUTRIENT ENTPAINMENT EQUAL IN ALL INDIAN ARM ZONES. - INDIAN RIVER DISCHARGE ASSUMED TO BE 0.5 OF THAT OF SQUAMISH RIVER. - INDIAN RIVER TURBIDITY ASSUMED TO BE 0.5 OF THAT OF SQUAMISH RIVER. ZDNE I 51MULRTIDN FIE. SI FORCING 5ET IM* E.50 d D d D ZDNE 2 5 IMULRTI ON 143 FIE. 52 FDRCINE SET 1M* 5.50 ID* 3.00 RM* E.50 RD* I.00 CD* .003 ND* .300 51* E.00 52* H.00 53* 3.00 52* .010 144 . ZONE 3 51 MULRT I ON F I E . S3 FDRCINE 5ET ul D d D FIGURES 54 TO 56. HOWE SOUND (•—•) VS A THEORETICAL MORE NORTHERLY FIORD. - SOLAR INSOLATION DISTRIBUTION HAS A SMALLER SPREAD. - NUTRIENT ENTRAINMENT IN ZONE 3 IS REDUCED TO 1.5 OF THAT IN OTHER ZONES. ZDNE I 5 IMULRTIDN 146 F I E . SH IS IS L/1 EL FORCING SET IM* ID* RM* RD* CD* ND* 51* 52* 53* 52* 5.50 3.00 E.50 I .B0 .003 .300 E.00 H.00 3.00 .010 ZDNE 2 5 IMULRTIDN 147 F I E . ES FDRCING SET !M* ID* RM* RD* CD* ND* 51* 52* 53* 52* S.S0 3.00 E.50 1 .00 .003 .300 E.00 H.00 3.00 .010 ZDNE 3 5 I MULRT 1 DN F IE . SE ts d D d D 149 APPENDIX I PROGRAM LISTING 0: 5.5 = RO; 3.0 = R l ; 6.5 = R2; 1.8 = R3; 0 = Rl 1=0 1: 003 = R4; .3 = R5; .01 = R9 2: 6 = R6; 4 = R7; 3 = R8 3: R l l + 1 = R l l ; SCL 0, 39, 0, 52; PLT 4, 47 PLT 4, 37; PLT 16, 37; PEN 4: PLT 4, 35; PLT 4, 25, PLT 16, 25; PEN; PLT 4, 23; PLT 4, 13; PLT 16, 13; PEN; PLT 4, 11; PLT 4, 1 5: PLT 16, 1; PEN; PLT 24, 23; PLT 24, 13; PLT 36, 13; PEN; PLT 24, 11; PLT 24, 1; PLT 36, 1; PEN; FXD 0 6: LTR 8, 50, 331; PLT "ZONE"; PLT R l l ; PLT "SIMULATION"; FXD 2 7: LTR 27, 47, 221; PLT "FORCING SET"; LTR 28, 44, 221; PLT "IM*"; PLT RO 8: LTR 28, 42, 221; PLT "ID*"; PLT R l ; LTR 28, 40, 221; PLT "RM*"'; PLT R2 9: LTR 28, 38, 221; PLT "RD*"; PLT R3; LTR 28, 36, 221; PLT "CO*"; FXD 3; PLT R4; LTR 28, 34, 221 10: PLT "NO*"; PLT R5; LTR 28, 32, 221; PLT "SI*"; FXD 2; PLT R6; LTR 28, 30, 221; PLT "S2*"; PLT R7 11: LTR 28, 28, 221; PLT "S3*"; PLT R8; LTR 28, 26, 221; PLT VSZ*"; FXD 3 PLT R9 12: LTR 2, 39, 322; PLT "NUT"; LTR 3. 5, 46, 322; PLT "1. 0" 13: LTR 2, 27, 322; PLT "TEM"; LTR 3.5, 34, 322; PLT "20" 14: LTR 2, 15, 322; PLT "EXT"; LTR 3.5, 22, 322; PLT "2.0" 15: LTR 2, 3, 322; PLT "ZOO"; LTR 3.5; 10, 322; PLT "1.0" 16: LTR 22, 15, 322; PLT "P.P."; LTR 23.5, 22, 322; PLT "5.0" 17: LTR 22, 3, 322; PLT "CHL"; LTR 23.5, 10, 322; PLT "0.1" 18: LTR 4, 0, 221; PLT " j " ; LTR 15.5, 0, 221; PLT "D"; LTR 24, 0, 221; PLT " J " 150 19: LTR 35.5, 0, 221; PLT "D" 20: R4 = R16; .000 = R17 = R18; R5 = R19 = R20 = R21; R6 = R22; R7 = R23; R8 = R24 21: R9 = R32 = R33 = R34; 0 = X; C + ! = C; .214 = R28; .439 = R29; .293 = R30 22: 2.5 E 3 EXP (-.5 ((X - RO - 2) / Rl) +2) /f\2n Rl) = RIO 23: 2.5 E 3 EXP (-.5 ((X - RO - 2) / Rl) +2) //"(2TT Rl) = R37 24: 100.0 EXP (-.5 ((X - R2) / R3) + 2) / (2TT R3) = R31 25: 8 E - 3 * R31 = R26; 2 E - 3R31 = R27; R26 + R27 = R25 26: 5 + .025 R37 = R12; (2 R26 + R 28 R12 + R27 R13 ) / (R25 + R28) = R12 27: 5 + .025 R37 = R13; (R26 R12 + R27 R14 + R29 R13) / (R25 + R29) = R13 28: 5 + .025 R37 = R14; (R26 R13 + 8 R27 + R30 R14) / (R25 + R30) = R14 29: .6 R22 + 40 R16 + 2 = R15; .6 R23 + 40 R17 + 2 = R35 30: .6 R24 + 40 R18 +, 2 = R36; RIO / R15 = R37 31: R16 (250 R37 / (50 + R37)) EXP (.01 R12) R19 / (.3 + R19) = A; R10/R35 = R37 32: R17 (250 R37 / (50 + R37).) EXP (.01 P13) R20 / (.3 + R20) = B; RIO / R36 = R37 33: R18 (250 R37 / (50 + R37)) EXP (.01 R14) R21 / (.3 + R21) 34: IF C = 1; PLT X + 4, 37 + 10R (18 + Rll) 35: IF C - 2; PLT X + 4, 25 + .5 R (11 + Rll) 36: IF C = 3; IF Rll = 1; PLT X + 4, 13 + .5 R15 37: IF C = 3; IF Rll ? 1; PLT X + 4, 13 + .5 R (33 + R 11) 38: IF C = 4; PLT X + 4, 1 + 10R (31 + Rll) 39: IF C = 5, IF Rll = 1; PLT X + 24, 13 + 2A 40: IF C = 5; IF Rll = 2; PLT X + 24, 13 + 2B 41: IF C = 5; IF Rll = 3; PLT X + 24, 13 + 2Y 151 42: IF C = 6; PLT X + 24, 1 + 100R (15 + R l l ) / 43: R16 + .0150 A-1.R16 R32 = R16; (R27 R17 + R28 R16)/ (R25 + R28 = R16 44: R17 + .015 B - 1.R17R33 = R17 45: (R26 R16 + R27 R18 + R29 R17)/ (R25 + R29) = R17 46: R18 + .015Y-1.R18 R34 = R18 47: (R26 R17 + (1.2R27 + R30) R18) / :(R25 + R30) = R18 48: R19 - .06 A = R19; (R26* .20 + R27 R20 + R28 R19) / (R25 + R28) = R19 49: R20 - .06 B = R20; (R26 R19 + R27 R21 + R29 R20) / (R25 + R29) = R20 50: R21 - .06 Y = R21; (R26 R20 + (3R27 + R30) R21) / (R25 + R30) = R21 51: 005 = R37; IF X > 6; 02 (x - 6) = R37 52: R19 + R37 = R19; R20 + R37 = R20; R21 + 2.,5 R37 = R21 53: IF R21 <_ 0; 0 = R21 54: IF R20 < 0; 0 = R20 55: .8 (30R26 + R27 R23 + R28 R22) / (R25 + R28 = R22 56: .8 (R26 R22 + R27 R24 + R29 R23) / (R25 + R29) = R23 57: .8 (R26 R23 + (5R27 + R30) R24) / (R25 + R30) = R24 58: R32 + 35 R32 R16 = R32; .5 R32 = R32 59: (.4 R26 + R27 R33 + R28'R32) / (R25 + R28) = R32 60: R33 + 35 R33 R17 = R33; .5 R33 = R33 61: (R26 R32 + R27 R34 + R29 R33) / (R25 + R29) = R33 62: R34 + 35 R34 R18 = R34; .5 R34 = R34 63: (R26 R33 + (1.2 R27 + R30) R34) / (R25 + R30) = R34 64: IF X < 11.50; X + .50 = X; GTO 22 65: IF C < 5; PEN; GTO 20 66: 0 = C; LTR 32, 50, 221; PLT "FIG." ; STP; GTO 3 67: END R41 152 APPENDIX I I There may be seme confusion when comparing primary and secondary population levels since phytoplankton biomass i s represented by -2 . -2 g c h l a«m while zooplankton biomass i s i n g dry wt*m . In order to calculate transfer e f f i c i e n c y , these units must be related. M u l l i n et al. (1966), have shown how d i f f i c u l t i t i s to assess the carbon content of phytoplankton c e l l s because of varying carbon : chlorophyll r a t i o s . Steele and Baird (1962), noted t h i s r a t i o may vary from 25:1 i n spring to 75:1 i n summer, and P i a t t and Subba Rao (1970), have regressed the two variables and found; gC = 0.215 + 16 g c h l a f o r a bloom period. I f we assume an average r a t i o of 50:1 and an average zooplankton carbon content of 40% of dry weight, then the peak values f o r the zone 3 simulation are equivalent to P = 7.5 g C and Z = 1.4 g C. Prom these values i t i s possible to calculate an ecological transfer e f f i c i e n c y of 18%. This i s wi t h i n the range of 10 - 20% as predicted i n the l i t e r a t u r e (e.g. Parsons and Takahashi, 1973) and indicates that the simulated trophic relationship i s of appropriate magnitude.
Thesis/Dissertation
Howe Sound (B.C.)
eng
Zoology
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Graduate
Mathematical model of primary food web energetics in Howe Sound, British Columbia
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