{"@context":{"@language":"en","Affiliation":"http:\/\/vivoweb.org\/ontology\/core#departmentOrSchool","AggregatedSourceRepository":"http:\/\/www.europeana.eu\/schemas\/edm\/dataProvider","Campus":"https:\/\/open.library.ubc.ca\/terms#degreeCampus","Creator":"http:\/\/purl.org\/dc\/terms\/creator","DateAvailable":"http:\/\/purl.org\/dc\/terms\/issued","DateIssued":"http:\/\/purl.org\/dc\/terms\/issued","Degree":"http:\/\/vivoweb.org\/ontology\/core#relatedDegree","DegreeGrantor":"https:\/\/open.library.ubc.ca\/terms#degreeGrantor","Description":"http:\/\/purl.org\/dc\/terms\/description","DigitalResourceOriginalRecord":"http:\/\/www.europeana.eu\/schemas\/edm\/aggregatedCHO","FullText":"http:\/\/www.w3.org\/2009\/08\/skos-reference\/skos.html#note","Genre":"http:\/\/www.europeana.eu\/schemas\/edm\/hasType","IsShownAt":"http:\/\/www.europeana.eu\/schemas\/edm\/isShownAt","Language":"http:\/\/purl.org\/dc\/terms\/language","Program":"https:\/\/open.library.ubc.ca\/terms#degreeDiscipline","Provider":"http:\/\/www.europeana.eu\/schemas\/edm\/provider","Publisher":"http:\/\/purl.org\/dc\/terms\/publisher","Rights":"http:\/\/purl.org\/dc\/terms\/rights","ScholarlyLevel":"https:\/\/open.library.ubc.ca\/terms#scholarLevel","Title":"http:\/\/purl.org\/dc\/terms\/title","Type":"http:\/\/purl.org\/dc\/terms\/type","URI":"https:\/\/open.library.ubc.ca\/terms#identifierURI","SortDate":"http:\/\/purl.org\/dc\/terms\/date"},"Affiliation":[{"@value":"Applied Science, Faculty of","@language":"en"},{"@value":"Civil Engineering, Department of","@language":"en"}],"AggregatedSourceRepository":[{"@value":"DSpace","@language":"en"}],"Campus":[{"@value":"UBCV","@language":"en"}],"Creator":[{"@value":"McLean, William Eric","@language":"en"}],"DateAvailable":[{"@value":"2010-03-23T17:14:10Z","@language":"en"}],"DateIssued":[{"@value":"1979","@language":"en"}],"Degree":[{"@value":"Master of Science - MSc","@language":"en"}],"DegreeGrantor":[{"@value":"University of British Columbia","@language":"en"}],"Description":[{"@value":"The rearing of salmon fry for release to the ocean stands out as the most complex, expensive, and critical feature of hatchery production. This complex process not only involves decisions concerning space, food, and water flow requirements, but also involves choosing optimum release times and sizes and management strategies.\r\nFor a rearing program to be consistently successful, decision making must be based on some sort of rational understanding of how these requirements\r\nare influenced by the rearing environment. At present, this understanding\r\nis often based on intuition and site specific experience. A formalized model developed from fundamental knowledge and pooled experience can augment the present knowledge base.\r\nThis thesis presents a framework within which the rearing process can be understood more clearly. Where reliable data or basic physiological understanding exists, simple deterministic models have been developed. These models quantify the relationships between the most important rearing requirements and the web of environmental factors which affect them.\r\nThe key environmental factors have been identified as water temperature, ration level, time, and the degree of hatchery disturbance. Under normal hatchery conditions these factors have been used to predict fish growth or weight at a particular time by means of a generalized growth model. This information has been combined with environmental factors to determine oxygen consumption and metabolite production rates. The metabolites\r\nconsidered are ammonia-N, un-ionized ammonia-N, carbon dioxide, and suspended solids. Translating these consumption and production rates into predictions about pond environmental conditions is an important element of the model because it is this information which can be used directly by decision makers (design and operations personnel).\r\nThis has been achieved by developing a simplified picture of flow through a rearing pond; ponds have been assumed to approximate either ideal \"plug flow\" or ideal \"mixed flow\" type reactors. Using this approximation plus background water quality information, a model of the distribution and concentration of metabolites and oxygen within the rearing\r\npond has been developed.\r\nThe combined equations can be used to predict fish weight, pond density and oxygen and metabolite concentrations over the rearing period. Conversely, if constraints are placed on these factors, space, flow, and ration requirements can be similarly predicted.\r\nRealistic, constraints for salmon culture have been discussed briefly. These reflect some of the most recent information on the effects of time and size at release and pond environmental conditions on smolt viability. It is emphasized that the primary function of the \"Rearing Model\" is to provide a framework of predictive relationships; it is not designed to set guidelines for rearing.","@language":"en"}],"DigitalResourceOriginalRecord":[{"@value":"https:\/\/circle.library.ubc.ca\/rest\/handle\/2429\/22332?expand=metadata","@language":"en"}],"FullText":[{"@value":"A REARING MODEL FOR SALMONIDS by WILLIAM ERIC McLEAN B. Sc., University of British Columbia, 1967 A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF SCIENCE in THE FACULTY OF GRADUATE STUDIES (Interdisciplinary Program) The Departments of Bio-Resource Engineering and Civil Engineering. We accept this thesis as* conforming to the required standard ( P a c i f i c B i o l o g i c a l Station, Nanaimo) ( C i v i l Engineering) (Bio-Resource Engineering) THE UNIVERSITY OF BRITISH COLUMBIA August, 1979 (c) William Eric McLean, 1979 I n p r e s e n t i n g t h i s t h e s i s i n p a r t i a l f u l f i l m e n t o f t h e r e q u i r e m e n t s f o r an a d v a n c e d d e g r e e a t t h e U n i v e r s i t y o f B r i t i s h C o l u m b i a , I a g r e e t h a t t h e L i b r a r y s h a l l make i t f r e e l y a v a i l a b l e f o r r e f e r e n c e a n d s t u d y . I f u r t h e r a g r e e t h a t p e r m i s s i o n f o r e x t e n s i v e c o p y i n g o f t h i s t h e s i s f o r s c h o l a r l y p u r p o s e s may be g r a n t e d by t h e Head o f my D e p a r t m e n t o r by h i s r e p r e s e n t a t i v e s . I t i s u n d e r s t o o d t h a t c o p y i n g o r p u b l i c a t i o n o f t h i s t h e s i s f o r f i n a n c i a l g a i n s h a l l n o t be a l l o w e d w i t h o u t my w r i t t e n p e r m i s s i o n . D e p a r t m e n t o f The U n i v e r s i t y o f B r i t i s h C o l u m b i a 2075 W e s b r o o k P l a c e V a n c o u v e r , C a n a d a V6T 1W5 D a t e DE-6 BP 75-51 1 E i i ABSTRACT The rearing of salmon fry for release to the ocean stands out as the most complex, expensive, and critical feature of hatchery production. This complex process not only involves decisions concerning space, food, and water flow requirements, but also involves choosing optimum release times and sizes and management strategies. For a rearing program to be consistently successful, decision making must be based on some sort of rational understanding of how these require-ments are influenced by the rearing environment. At present, this under-standing is often based on intuition and site specific experience. A formalized model developed from fundamental knowledge and pooled experience can augment the present knowledge base. This thesis presents a framework within which the rearing process can be understood more clearly. Where reliable data or basic physiological understanding exists, simple deterministic models have been developed. These models quantify the relationships between the most important rearing requirements and the web of environmental factors which affect them. The key environmental factors have been identified as water temperature, ration level, time, and the degree of hatchery disturbance. Under normal hatchery conditions these factors have been used to predict fish growth or weight at a particular time by means of a generalized growth model. i i i This information has been combined with environmental factors to determine oxygen consumption and metabolite production rates. The meta-bolites considered are ammonia-N, un-ionized ammonia-N, carbon dioxide, and suspended solids. Translating these consumption and production rates into predictions about pond environmental conditions is an important element of the model,.,because i t is this information which can be used directly by decision makers (design and operations personnel). This has been achieved by developing a simplified picture of flow through a rearing pond; ponds have been assumed to approximate either ideal \"plug flow\" or ideal \"mixed flow\" type reactors. Using this approximation plus background water quality information, a model of the distribution and concentration of metabolites and oxygen within the rear-ing pond has been developed. The combined equations can be used to predict fish weight, pond density and oxygen and metabolite concentrations over the rearing period. Conversely, i f constraints are placed on these factors, space, flow, and ration requirements can be similarly predicted. Realistic, constraints for salmon culture have been discussed briefly. These reflect some of the most recent information on the effects of time and size at release and pond environmental conditions on smolt viability. It is emphasized that the primary function of the \"Rearing Model\" is to provide a framework of predictive relationships; i t is not designed to set guidelines for rearing. iv TABLE OF CONTENTS Page ABSTRACT 11 TABLE OF CONTENTS iv LIST OF TABLES v i LIST OF FIGURES v i i ACKNCWLEDGEMENTS x i CHAPTER I INTRODUCTION .. 1 II THE REARING PROCESS 5 III A REARING MODEL 8 A. Introduction 8 B. Some Guidelines for Rearing 8 C. Model Formulation 16 D. Individual Components 24 1. Background and Initial Conditions . . . . 24 a. Water quality 25 b. Fish culture and rearing pond information . 27 c. Assumptions 27 2. Pond Flow Characteristics 28 3. Fish Growth 35 a. Development of a growth model . . . . 35 b. Solutions of the growth equations . . 40 c. Comparisons with measured values. . . 43 d. Application of the growth model . . . 46 4. Oxygen Concentration 47 a. Development of an oxygen model. . . . 47 b. Comparisons with other models . . . . 53 c. Comparisons with measured average daily oxygen consumption rates. . . . 57 d. Development of a safety factor. . . . 59 e. Application 62 5. Carbon Dioxide and pH 65 a. Carbon dioxide 65 b. pH changes 65 V Page 6. Ammonia-N 66 a. Introduction 66 b. Ammonia-N model components 68 c. Comparisons with other models . . . . 71 d. Comparisons with measured values. . . 73 7. Un-ionized Ammonia-N. . 78 8. Suspended Solids 79 a. Review 79 b. Theoretical solids model 80 c. Solids discharge rates and comparisons with other models . . . . 82 9. Density 86 IV SYNTHESIS OF MODEL COMPONENTS 92 a. Illustrative example 92 b. Application 96 V DISCUSSION AND CONCLUSIONS 108 BIBLIOGRAPHY 116 APPENDIX I 120 APPENDIX II 121 APPENDIX III 122 APPENDIX IV . 124 APPENDIX V 127 APPENDIX VI 129 APPENDIX VII 133 v i LIST OF TABLES TABLE Page 1 General release weights and dates and rearing periods for each of the four species of salmonids cultured in Federal and Provincial hatcheries in British Columbia 1 2 Model relating factors identified in the \"conceptual framework\" 21 3 A comparison of predicted and actual weights for hatchery coho on a reduced ration 45 4 Mean percentage differences between predicted oxygen consumption rates and measured average daily values. . . 58 5 Abrupt dissolved oxygen drops resulting from typical hatchery disturbances to crowded rearing ponds . . . . . 6l 6 Ammonia-N excretion rates for starved fish; model projections vs. actual measurements. The proposed ammonia-N model is represented by equation 54 77 7 Model predictions of suspended solids output rates at a feed rate of one percent per day and various temperatures and fish weights. Equations 67 and 72 are sensitive to fish weight and temperature whereas equations 63 and 66 depend only on the feeding level . . 84 8 Typical fish densities at a number of British Columbia hatcheries. These values have been plotted on the density vs. weight curves shown in Figure 26 91 9 Basic parameters (independent variables) and Factors (dependent variables) required to characterize the rearing process at a given time 98 10 A comparison of results as a function of the method used to solve the growth equation; % error=P-E x100%, c = correction factor E 126 v i i LIST OF FIGURES FIGURE Page 1 A schematic representation of the rearing process. Blocks represent model components; l i n e s represent information flow. 6 2 Dissolved oxygen c r i t e r i a f o r freshwater rearing developed by Davis (1975). Minimum oxygen con-centrations to meet protection levels A, B, and C have been plotted against water temperature. 10 3 Effect of migrant weight on s u r v i v a l rates f o r four species of salmon reared at Big Qualicum Sainon Development Project (F. J. Fraser, pers. comm.) 13 4 Y i e l d of adult biomass from different sized smolts (gm) released i n A p r i l , May.j and June (B i l t o n and Jenkinson, 1978) 14 5 Percent survival vs. smolt weight at release f o r hatchery reared steelhead i n C a l i f o r n i a , Oregon, and Washington (Royal, 1972) 15 6 The c y c l i c chain of events required to develop a model - t h i s i s referred to as a \"Policy Validation Cycle\" by Van Gigch (1974) I 8 7 Contrasting temperature regimes of two hatchery water supplies: A, Chilliwack River; B, Cold Creek. . . 26 8 The oxygen consumption rate as a function of the environmental oxygen l e v e l . Above the \"in c i p i e n t l i m i t i n g tension\" the oxygen con-sumption rate i s independent of the environ-mental oxygen l e v e l (Davis, 1975) 31 9 Metabolite concentrations within i d e a l plug flow and i d e a l mixed flow type ponds. The idealized concentration \" c 0 \" has been plotted against the pond length (measured from inflow to outflow); a background metabolite concentration of \"c^\" has been assumed 33 v i i i FIGURE Page 10 The concentration profile at the pond outflow after injection of a \"slug\" of tracer. \"A\" represents an ideal plug flow reactor and \"B\" represents an ideal mixed flow reactor 34 11 Concentration profile for non-ideal tanks. \"A\" rep-resents extreme short circuiting and \"B\" represents parallel paths 34 12 Fraction of the maximum specific growth rate as a function of the ration level: values shown have been calculated for 10 gm fish at a water temperature of 10\u00b0C. The maintenance ration \"Fma\" gives zero growth while the maximum ration \"Fmax\" yields max-imum growth (l.O). The relationship has been described by a sine curve 37 13 Specific growth rate x 100 for 1 gm fish at the maximum ration as a function of water temperature. The relationship is described by a polynomial 39 14 Percent error between the weights predicted by the incremental method (P) and the exact method (E) as a function of the exact weight (% error =(P-E)\/E X 100%). Predictions were made using one or five day time in-crements; weight projections were made assuming an in i t i a l weight of one gram, a maximum ration and. a constant temperature of 10\u00b0C 42 15 Comparison of predicted and measured growth at reduced ration levels. Ninety-five % confidence intervals of selected measured values are shown 44 16 Weight projections over a 170 day rearing period. Predictions have been made at three different ration levels and a hypothetical temperature regime 48 17 Oxygen consumption rate as a function of the feeding level. In this case, the feeding level is expressed as the fraction of the maximum ration. The linear relationship is shown for two different fish weights . . . 52 ix FIGURE Page 18 Average daily oxygen consumption projections at 10\u00b0C vs. fish weight. A number of different models have been used. The present model (equation 33) has been calculated at f u l l ration (f = l) and at half of the maximum ration (f - 0.5) 56 19 Oxygen consumption rate pattern for a typical undisturbed hatchery rearing pond over a 24-hour period. This curve was measured for coho smolts in April; the average daily temperature was 9.5\u00b0C . . . 60 20 Water flow requirements per 1,000,000 ten gram fish as a function of temperature. Maximum ration and 60% ration projections have been made; an average daily oxygen level of 8 mg\/l has been maintained in the pond effluent. 64 21 Effect of load rate on pond outflow pH levels. Projections were made at a temperature of 11.7 \u00b0C, a fish weight of 9.1 gm, and feeding levels of 60% of the maximum ration. A background carbon dioxide concentration of 1.0 mg\/l and an alkalinity of 40 mg\/l as CaCO^ were assumed. , . 67 22 A simplified schematic representation of the flow of nitrogen in the rearing process , 69 23 Ammonia-N excretion rates vs. feeding levels for 15 gm fish at a water temperature of 15\u00b0C The proposed model (equation 54) is shown as a dashed line. Other models are labelled by their equation (eq.) number 74 24 Average daily ammonia-N excretion rates vs. pre-dicted values over a period of major pond dis-turbances (April 14, 15) and over a period of stability (April 20 - May 5) 7 5 25 Suspended solids output rates as a function of the feeding level. Predictions have been made for 10 gm fish at a water temperature of 10\u00b0C 83 26 Density as a function of fish weight as predicted by various theoretical models. Actual densities from Table 6 have been displayed and labelled by number. . . 90 X FIGURE Page 27 Growth projection assuming an i n i t i a l weight of 0.3 gm. The temperature regime and ration level are also indicated: the notation \"f = 0.9\" indicates that 90% of the maximum daily allowance is being fed. A marking program at day 230 is assumed to c suppress growth for a short time period 99 28 Maximum load rate and minimum water requirements -per 1,000,000 fish to meet \"Level A\" oxygen criteria developed by Davis (1975) 100 29 Maximum load rate and minimum water requirement per 1,000,000 fish to meet \"Level B\" oxygen criteria developed by Davis (1975) . . 101 30 Un-ionized ammonia-N concentrations in the pond outflows; ponds are loaded to meet either Level A or B oxygen criteria 102 31 Total ammonia-N concentration in the pond outflows; ponds are loaded to meet either Level A or B oxygen criteria 103 32 Carbon dioxide concentrations in the pond outflows; ponds are loaded to meet either Level A or B oxygen criteria 104 33 Suspended solids concentrations in the pond outflows; ponds are loaded to meet either Level A or B oxygen criteria 105 34 pH of pond inflow and outflows; ponds are loaded to meet either Level A or B oxygen criteria 106 35 Volume requirements per 1,000,000 fish over the rearing period: conservative density criteria based on experience have been assumed 107 36 Oxygen concentration in the pond outflow as a function of the load rate. As the pond dissolved oxygen level falls below \"Cr\", the oxygen uptake rate is suppressed by the reduced environmental oxygen level. The \"solid\" line incorporates this effect while the \"dashed\" line assumes that the uptake rate is independent of the oxygen concentration . 112 x i ACKNOWLEDGEMENTS The author i s grateful to Dr. J. R. Brett of the Fisheries and Marine Service, Professor S. 0. Russell of the Department of C i v i l Engineering, and Professor J. W. Zahradnik of the Department of Bio-Resource Engineering for their guidance and encouragement. Comments and criticisms from their diverse areas of expertise have been invaluable in making this interdisciplinary study possible. Many of the physiological relationships which this work has been based on have been investigated by Dr. J. R. Brett and his colleagues at the Pacific Biological Station. Special thanks are due to this group for their generosity in providing information and support. The f i e l d measurements and observations cited i n this thesis were made at a number of production f a c i l i t i e s ; however, intensive monitoring programs were carried out at the Quinsam and Big Qualicum hatchefies. The author would like to extend his gratitude to managers Jim Van Tine and Dick Harvey for their cooperation, during the pre-liminary stages of this work. Operations biologists Don Sinclair, Dave Wilson, and Ted Perry of Fisheries and Marine Service have also been very helpful. Their input has been extremely valuable i n defining the problems related to the design and operation of production rearing f a c i l i t i e s . Special acknowledgement i s made to Miss Crystal Spicer for her care in preparing the f i n a l draft of the thesis. 1 I INTRODUCTION The production of salmonids for ocean release frcm British Col-umbia hatcheries has reached 17*000,000 fish per year (Fisheries and Marine Service, 1978), With the implementation of the Salmonid En-hancement Program this figure should increase to 68,000,000 fish per year by 1985. The most expensive and critical feature of hatchery production is the \"Rearing Process\". Simply stated, this process in-volves feeding fry to the release or smolt stage. Table 1 summarizes major aspects of the rearing process for various species. TABLE 1. General release weights and dates and rearing periods for each of the four species of salmonids cultured in Federal and Provincial hatcheries in British Columbia. Species Initial Weight (gm) Final Weight at Release (m) Release Date Approximate Rearing Period (days) Coho 0.30 15 - 30 May-June 400 Steelhead 0.25 40 - 60 May-June 400 Chinook 0.50 4-10 June 100 Chum 0.25 0.8 - 1.5 April-May 60 Hatchery rearing is carried out in order to increase the ocean survival of the released smolts. It is now generally felt that ocean survival is to a large extent, dependent on the rearing strategy; op-timum survivals occur i f healthy smolts of the \"right size\" are released at the \"correct time\". 2 A r t i f i c i a l rearing activities take place under a tremendous variety of background conditions. Temperatures vary from 0.5\u00b0C to 25\u00b0C. Some systems are characterized by nearly year round constant temperature re-gimes while others have extreme temperature fluctuations. Water quality is also variable between systems. The alkalinity, pH, solids, ammonia-N, carbon dioxide, hardness, metal concentration and disease incidence are often site specific. Many rearing pond types are possible. Some of the pond parameters which can be varied are dimensions, shape, flow, outflow and internal baffle structures and construction material. Concrete ponds usually rely on a standard hatchery diet as the major food input while some gravel bottom ponds may have significant inputs of natural food. At the onset of a new rearing program, hatchery designers, opera-tions biologists, and fish Culturists usually have only background in-formation such as temperature, water quality and disease monitoring data available. With this information, optimum pond designs and rearing strategies must be developed. Decisions faced by designers involve specification of: a) water flow requirements; given water quality, disease back-ground and production targets. b) space (volume) requirements. c) construction material, inflow and outflow structures, pond shape, flow measurement and alarm systems. d) inflow water pretreatment requirements - temperature or pH may have to be manipulated for example, before production targets can be met. 3 e) flexibility in pond operation - for example, recycling pond effluent may be feasible. f) effluent treatment requirements. The operation of a rearing facility and achievement of production goals involves daily decisions concerning: a) choice of ration level to achieve a smolt of a given weight by a given release date. b) allocation of limited space and water flow resources among different groups of fish - for example, a multi-species hatchery may have to deal simultaneously with coho fry (0.4 gm), coho smolts (20 gm), Chinook fry (0.6 gm), steelhead fry (0.3 gm), and steelhead smolts (40 gm). c) effects of fish culture practices and the hatchery environment on disease susceptibility and the condition of the fish. d) effects of background conditions on general health and growth rates. Designers and fish culturists inevitably face these concerns during the implementation and operation of a large scale fish culture program. Often, intuition and experience must be the sole basis of decision making. This is especially true where fundamental understanding or critical data are lacking. A rearing model attempts to identify and integrate what is fundament-ally known about the growth and survival of fish in the fish culture envir-onment; i t must then express these relationships quantitatively. This ex-ercise attempts to augment rather than replace the intuition and experience of the hatchery manager or design biologist. A model is based on prin-ciples common to a l l rearing processes. It should interpret the perfor-mance of large scale production units in terms of fundamental knowledge. 4 Because many data voids inevitably exist in complex real l i f e situations, intuition and experience are critical in final decision making. However, with the research and development of the past twenty years enough biological knowledge .exists to develop a simplified rearing model. This model wil l provide, at least, a framework around which designers and fish culturists can make quantitative projections. It should also help identify data voids to research personnel. 5 II THE REARING PROCESS The primary objective of any hatchery rearing program involves the release of an optimum number of healthy fish at a certain size and time. The factors affecting this process are numerous and have been thoroughly reviewed by Klontz (1978) \u2022 A few of the main factors are water temp-erature regime, water quality, pond flow, pond volume, pond dimensions, ration level, and ration quality. Fish culturists have through exper-ience, learned how these factors interrelate qualitatively. The process of modelling wil l attempt to analyze Rearing as a system of components; relationships between components w i l l then be expressed quantitatively. A simplified view of the rearing process is presented in Figure 1. On a given day against specified environmental conditions, a ration in-put results in metabolic activity. A weight increase may result, fish density (biomass\/vol.) may increase, oxygen w i l l be consumed and waste products wil l be produced. These changes vary with time as background conditions and fish weight vary. In Figure 1, each box represents a set of relationships whereas lines represent the information flow re-quired to interrelate each component. The pond condition at a particular time represents the overall state of the rearing system. Fish culturists must interpret these conditions in light of the primary objectives of the rearing operation. For example, i f a weight release target of 20 grams at 400 days has been set and the actual weight at 200 days is 7 grams, a judgement must be made in light of anticipated background conditions. Ration levels or water temperatures may have to be adjusted. Background and Initial Conditions temp, regime species number in i t i a l weight water quality disease back-ground Growth Ration pensitf tkyged A U ^ I Uh-ioniped Suspended KN Bolids arbon bioxid Pond Condition Ammonial-N f > t \\t \\ f Pond Flow Characteristics > f FIGURE 1. A schematic representation of the rearing process. Blocks represent model components; lines represent information flow,. 7 If tin-ionized ammonia levels are judged too high, a fish culturist may consider one of the following actions: reducing ration level, changing ration composition, increasing flow, decreasing numbers of fish, decreas-ing the water temperatures, decreasing pH. Here again, judgements must be made in light of the primary rearing objectives. Primary objectives can be restated as follows. The goal is to release fish: 1. at a particular weight 2. at a particular time 3. in such numbers (n) that the returns are maximized. The number returning can be expressed as the product of n times the survival rate. Therefore, the objective is to maximize returns \"R\": R = n x s(n, wr, tr) (l) where: n = number of smolts released wr = weight at release tr = time of release s(n,wr,tr) = the fraction surviving; which, from a facility with limited water and space, is itself a function of the number of smolts released. It should be noted that a model must be able to predict pond conditions given certain background information and ration levels. However, i f constraints on the pond environment are made, then the model should be able to specify limits on background conditions. Because of this, background and i n i t i a l conditions should not be thought of as fixed. Often, water temperatures can be manipulated to some degree. Also, the number of fish, water flow, and water quality can sometimes be altered in attempting to maintain a satisfactory pond environment. 8 ' III A REARING MODEL A. Introduction The rearing process will be considered as a system of interacting components. The choice of components is somewhat arbitrary; however, they are meant to reflect key factors which are known to dramatically affect the success of rearing programs. Model components and their interactions are schematically presented in Figure 1. The main focus of the thesis is to determine quantitatively how the various compon-ents interact in large-scale rearing operations. For instance, the model should be able to predict whether an increase in temperature would cause a decrease in pond oxygen levels, and i f so, by how much. Of course, the model cannot judge whether this is undesirable; i t is only designed to be a predictive tool. The judgement as to whether specific environmental conditions are desirable or not depends on the perception and experience of the fish culturist or operations biologist. In order to put specific oxygen levels, ammonia concentrations, growth rates, etc., in perspective, a brief review of some useful rearing criteria will be made. B. Some Guidelines for Rearing In order to meet rearing program objectives (page 7), a salmon culture operation must pay attention to environmental conditions, growth rates and the timing of smolt releases. The oxygen concentration has long been recognized as a key envir-onmental factor in determining satisfactory pond conditions. It is sug-gested that oxygen criteria developed by Davis (1975) be adopted for hatchery use. '9 Davis ( 1 9 7 5 ) has thoroughly reviewed the literature and derived realistic minimum oxygen requirements based on sublethal responses. Briefly, these criteria are based on establishing both a sufficient oxygen tension (partial pressure in units of mm of Hg) and a sufficient oxygen content (mg\/l). The oxygen tension establishes a pressure gradient for driving oxygen across the g i l l s , whereas the oxygen con-tent f u l f i l l s the needs of fish metabolism. Cxygen criteria for fresh water salmon rearing are shown in Figure 2 as a function of temperature. The three protection levels reflect the fraction of the population exhibiting effects of reduced dissolved oxygen. If levels A, B, or C are met, then 1%, 50%, and 8 5 % respectively, of the individuals in a population would be affected. It should be noted that a level of safety is exceeded i f the oxygen concentration drops below the established c r i -teria for more than a few hours a day. Ammonia-N is the major end product of protein catabolism in fish and so is always present during rearing activity. The un-ionized form is recognized as a powerful cellular poison even at low concentrations (Fromm and Gillette, 1968). Burrows (1964),using Chinook fingerlings, demonstrated sublethal effects after prolonged exposure to un-ionized ammonia-N concentrations of 3 ug\/l. The Environmental Protection Agency (1972) recommends an upper limit of 20 ug\/l while Westers (1976) suggests an upper limit of 12 ug\/l for salmon rearing. Recent work has indicated that 2 ug\/l un-ionized ammonia caused reductions in the growth rates of pink salmon alevins (D. F. Alderdice, pers. comm.) Establishing a safe level is difficult; however, a limit of 2 ug\/l is tentatively suggested (Sigma Resource Consultants Ltd, 1979). 12 3-2 i i \u2022 I i > i i i i i i 1 1 1 1 \u2014 \u2014 i 1 1 1 0 1 2 3 k 5 6 7 8 9 10 11 12 13 Ik 15 16 17 18 19 20 Tempterature (\u00b0C) FIGURE 2. Dissolved oxygen criteria for fresh water rearing developed by Davis (1975). Minimum oxygen ^ concentrations to meet protection levels A, B, and C have been plotted against water temperature. o 11 The fraction of the total ammonia-N in the un-ionized form depends on the pH and temperature. Pond pH levels, however, are directly affected by the carbon dioxide production of the fish. It is this interaction between ammonia-N and pH that gives the carbon dioxide component of the model its importance. Levels of carbon dioxide or pH shifts caused by the carbon dioxide are generally not of sufficient magnitude to affect rearing operations. However, carbon dioxide levels should be kept below 25 mg\/l and pH levels should be maintained between 6.5 and 8.5 (Sigma Resource Consultants Ltd., 1979). There is seme evidence that carbon dioxide and pH may have subtle effects \u00a9n the toxicity of the un-ionized ammonia itsel f . Lloyd and Herbet (i960) found that un-ionized ammonia toxicity increased when the carbon dioxide concentration increased from 3.2 mg\/l to 48.0 mg\/l (pH dropped from 8.2 to 7.0). This suggests that when comparing rearing environments, un-ionized ammonia, carbon dioxide, and pH information are required. Waste food and feces cause increases in the suspended solids con-centration of the rearing environment. Meaningful criteria are difficult to establish because the effects depend on the physical and chemical nature of the solids. The Environmental Protection Agency (1972) recom-mends a limit of 25 mg\/l. However, personal observation and communication with fish culturists suggests that \"fine\" waste food particles cause sig-nificant g i l l irritation at concentrations far below 25 mg\/l. 12 These factors along with the density (number or weight of fish per unit volume) and water velocity determine the condition of the rearing environment. Fish culture experience has taught that high environmental quality increases the probability of a successful rearing operation while a poor environment can be lethal. It should be pointed out, however, that during normal operation, environmental quality rarely degenerates to the point of causing outright mortalities. For example, only in the case of an accident (pump failure) would oxygen ever drop to a lethal level*. More often, the rearing environment is looked on as exerting some degree of sublethal \"stress\". These stresses, depending on their sev-erity, can precipitate disease outbreaks (Wedemeyer, 1974). As would be expected, this indirect mechanism is impossible to quantify at this time; as experience with ocean released fish is accumulated, a probabil-ist i c relationship between the quality of the rearing environment and the smolt viability will eventually be established. Insight into optimum growth rates and release times is slowly being gained. It i s now generally felt that ocean survival i s , to a large extent, dependent on the rearing strategy; optimum survivals occur i f smolts of the \"right size\" are released at the \"correct time\". Obser-vations made at the Big Qualicum River Salmon Development Project (F. J. Fraser, pers. comm.) over a number of years illustrates in a general way, the relationship between survival and release size (Figure 3). Bilton (1978) has performed extensive, controlled exper-iments with coho salmon and has demonstrated a clear relationship between survival and release sizes and times (Figure 4). FIGURE 3. Effect of migrant weight on survival rates for four species of salmon reared at Big Qualicum Salmon Development Project (F. J. Fraser, pers. comm.). 14: FIGURE 4. Yield of adult biomass from different sized smolts (gm) released in April, May, and June (Bilton and Jenkinson, 1978) Steelhead Smolt Weight (gm) at Release Percent survival vs. smolt weight at release for hatchery reared steelhead in California, Oregon, and Washington (Royal, 1972). 16 Royal (1972) has correlated adult returns for Washington State steelhead with smolt weight at release (Figure 5 )\u00bb General release sizes and times cannot be stated; however, at the present time, British Columbia hatcheries are attempting to release salmon smolts near weights and times shown in Table 1. In the next decade, rearing strategy wil l undoubtedly be refined as new information becomes available. This introductory discussion was intended to present the main factors involved in the rearing model and emphasize their significance in the production of young salmon. C. Model Formulation The procedures used to develop the model have been formalized by Van Gigch (1974). These techniques provide a systematic way of trans-forming qualitative statements or observations into reliable quantita-tive projections. In essence, this scheme is an extension of the \"scientific method\". This traditional sequence of events (problem or event defined; observa-tions made; hypothesis postulated; experiment designed; measurements made; hypothesis accepted or rejected) is viewed by Van Gigch (1974) as a \"hierarchy of models\"! The The Policy The > The The Numerical Decision Process Theory Experiment v Function ^nd Action Within this new terminology, \"the process\" involves developing a conceptual framework to describe observations concerning the event or problem being studied. This step must not only define relevant factors but also set boundaries to the problem being considered. 17 The next step in the process involves posing a cogent explanation or theory of the preliminary observations. Building a theory w i l l necessarily involve a number of simplifications and assumptions, but in essence w i l l attempt to describe in a qualitative way at least, how the various factors interact. The derivation of a \"numerical function\" or mathematical model requires testing of the theory against measurement data or ideally, against the results of controlled experiments. The \"experiment model\" requires postulating a hypothesis concerning the form of the relation-ship between model factors and a r i g i d statement of the conditions under which the hypothesis i s to be tested. If the hypothesis i s accepted, a mathematical function or model of the data can be developed. This allows the modeller to make inferences and predictions about new situations. Because the consequences of alternative combinations of factors can be projected, Van Gigch (1974) terms this stage of the model \"the policy decision and action component\". A detailed view of this concept of model development has been presented schematically in Figure 6. Before considering the mathematical model in de t a i l , i t w i l l be useful to take an overview of the rearing model i n light of the cycle presented i n Figure 6. The development of the conceptual framework i s a major task because the problem or phenomenon being studied must be stated i n a way that allows analysis and quantification. This process draws extensively on the fi s h culture literature and on the experience of operations and research personnel. Conceptual Framework Phenomenon or Process Observation Concept Definition Concept > Def initio] Concept Definitioi Theory or Model[ -S\u00b1 owing Among Factors And Variables Relationship -^Hypothesis ^ Measurement \u2014 * \u2014 ^ \u2014 Yes {Accept Theory as Explanation of] Causal Relationship No Results Testing the Hypothesis Mapping of Property into Numbers No reneralization \u2014 r -Prediction I 1 c i * f3) 6) pH pHo f 7(Co, WQ, T) 7) ammonia-N No f 8(Ni, F, T, w, H, f 3) 8) un-ionized ammonia-N (No)u f9(No, pHo, T, f 3 ) 9) suspended solids So = fl0(^\u00bb F\u00bb T> w> f3) 10) density D = f l \u00bb f^, f3\u00bb.. = functions T - temperature t = time WQ background water quality co = pond outflow metabolite concentration w = fish weight w o i n i t i a l fish weight where: t = mean residence time (min) V = volume of reactor (l) Q = flow (l\/min). A slug of tracer in the inflow of a pond approximating plug flow con-ditions would also appear at the outflow as a slug (Figure 10). 29 - Mixed flow reactor: Circulating type ponds often approximate this type of reactor. Water is introduced and is uniformly mixed within a short period of time. For a mixed flow reactor, the mean residence time is also given by V\/Q. A slug of tracer introduced into the inflow would be quickly mixed throughout the entire volume to give a peak concentration \"co\". The con-centration of the tracer in the outflow would then begin to decrease expo-nentially (Figure 10). If we consider a rearing pond approximating one of these ideal reactors, then the concentration of a metabolite at the outflow can be predicted from: dc = RD or c 0 = c i + RDt (5) dt Zo HO where: c Q = concentration at outflow (mg\/l) C j [ = inflow concentration (mg\/l) R = rate of metabolite production or oxygen consumption \/ mg \\ kg of fish*hr D = uniform density of fish over pond volume or total biomass ~ volume (B\/v) (kg\/l) t = mean residence time (min). If we assume steady flow and no stagnant areas, then t = V\/Q, so: c = C ; + RDV 0 1 Q60 substituting D = B gives: V c Q = c \u00b1 + RL (6) 6-0 where: L = B\/Q, load rate or biomass per flow (kg per l\/min). Equation 6 is the fundamental relationship between the effluent metabolite concentration (c Q) and the fish load rate (L). 30 Equation 5 involves a serious limitation; metabolite production or oxygen consumption rates have been assumed to be independent of the meta-bolite concentrations. In the case of oxygen consumption, i t is well known that below a certain concentration (referred to as the incipient limiting tension) the rate of oxygen uptake is dependent on the environmental oxygen level. This relationship has been described graphically in Figure 8. It should be noted that equation 5 is not valid below the incipient limiting tension. In normal chemical terminology, the crit i c a l oxygen level (denoted as \"Cr\" in Figure 8) represents the transition from zero order kinetics to first order kinetics as the oxygen concentration drops below \"Cr\". The simple zero order reaction represented by equation 5 becomes: dc = -D(Kc+b) (7) dt oO where: K = slope of the line describing the relationship between \"R\" and \"c\" at c Mean measured values and confidence i n t e r v a l s P r e d i c t e d values June 17 1977 160 180 200 Time (days) 240 300 320 340 360 May 3 1978 FIGURE 15. Comparison of predicted and measured growth at reduced r a t i o n l e v e l s . N i n e t y - f i v e percent ; confidence i n t e r v a l s of selected measured values are shown. 45 It can be seen frcm Figure 15 that growth is accurately predicted up until early October. At this time some effect other than fish size, temp-erature, or ration level suppressed growth and the model began to predict higher than actual values. However, by restarting the model at a mean weight of 13.2 gm on day 154, accurate projections were made to the end of the rearing period. Actual and predicted weights on days 94 and 321 are compared in Table 3. Both days are near the end of computing periods when differences should be greatest. In both cases differences between predicted and actual values were not significant at the.0.05 level. Actual mean weights were estimated frcm a random sample of 150 fish. The 95% confidence intervals were calculated in the usual manner (mean + 1.96S\/^i50'). Because of uncertainties in the pond inventory and hence in the feeding levels, confidence limits were also calculated for predicted values. TABLE 3. A comparison of predicted and actual weights for hatchery coho on a reduced ration. Day Predicted 95% Confidence Measured 95% Confidence Weight (gm) Interval Mean Weight Interval (gen) 94 10.87 10.73 to 11.01 11.28 10.62 to 11.93 321 25.06 24.05 to 26.06 24.83 23.68 to 25.98 46 The period between the middle of October and the end of November i s important because i t i d e n t i f i e s a l i m i t a t i o n of the model. I t i s i n t e r -esting t o note that t h i s i s a period of diminishing l i g h t i n t e n s i t y and shortening photoperiod. I t should also be noted that an intensive marking program and pond transfer were begun on October 2 3 r d . During the next f i v e days, the ration was d r a s t i c a l l y reduced and intensive f i s h handling occurred. To thoroughly define the li m i t a t i o n s of the growth model, many com-parisons should be made over a wide range of temperatures and rati o n l e v e l s . This process has begun but i s d i f f i c u l t due to the uncertainty associated with hatchery data. At present, i t w i l l be hypothesized that the growth equations provide a r e a l i s t i c means f o r specifying the pot e n t i a l for growth under a given temperature regime and ra t i o n l e v e l . d. Application of the growth model Stauffer's equations can be used to predict the expected growth at new hatchery s i t e s . I f the monthly mean temperatures, the ponding date, and the i n i t i a l f i s h size are known, then the potential growth can be eas i l y predicted f o r various ration l e v e l s . Maximum growth i s usually desirable f o r Chinook and steelhead so rations are often near the th e o r e t i c a l maximum rat i o n . This i s often required i f the target weight i s not to be exceeded at release time. I f the temperature regime of a system i s described by a continuous function, then the growth equations become simple and convenient to use. In t h i s presentation, growth projections f o r new systems have been made using a Fourier series approximation of the yearly temperature regime. (Appendix I) 47 These techniques have been used to predict the weight vs time curves shown in Figure 16; projections have been made at various ration levels on a hypothetical temperature regime. If the ration provided is expressed as a fraction of the maximum ration and the temperature regime is described as a continuous function, growth projections can be simply obtained in the field using a minimum of computing equipment (hand-held programmable calculator). However, the model must be used with an appreciation for its limitations. Because of the simplicity of obtaining model projections, many simulation trials at various ration levels can be run. If the target weights and release times are known, the model will indicate the required ration level. This can immediately be translated into a daily feeding chart. 4. Oxygen Concentration a. Development of an oxygen model The oxygen concentration component of the rearing model is based on a relationship between the oxygen consumption rate \"R0\" and the ration level \"F\", fish weight \"w\", and the water temperature \"T\". If \"Ro\" is known, then the oxygen concentration at the rearing pond outflow can be predicted: xft = x. - RoL (21) \u00b0 1 \"So where: x^ = inflow dissolved oxygen (mg\/l) L = load rate (kg per l\/min) Ro = oxygen consumption ( mg ) . kghr If the fraction saturation of the inflow water is \"S\", then the oxygen concentration can be related to temperature by: x-L = S 475 (Weber 1970) (22) T + 32.035 49 So i f reaeration is insignificant, the oxygen at the pond outflow \"x0\" is given by: x n = S 475 - RoL (23) T + 32.035 60 where: x Q = oxygen concentration (mg\/l) S = fraction of saturation T = temperature \u00b0C Ro = oxygen consumption(_mg_) kghr L = load rate (kg per l\/min) . However, i f aeration within the pond is significant, then the Streeter Phelps equation must be used (Nemerow 1974)* In this case, oxygen at the outflow is given by: x Q = x g - RoM(l-e- k V\/ Q) - (x - X i ) e - k V \/ Q (24) V60k s 1 where: k = aeration constant (min\"\"^ \") Q = flow (l\/min) V = volume (1) x a \u00ab saturated oxygen concentration (mg\/l) (Appendix V). In this presentation, equation 23 w i l l be used to predict oxygen concentration. In other words, reaeration will not be considered. Enough basic experimental work has been performed to relate oxygen con-sumption to ration level, fish weight and water temperature. Brett (1974) has measured \"feeding metabolic rates\" of young sockeye at various tempera-tures. Oxygen consumption \"Ro\" increased linearly with ration level: (Ro) 2 Q = B + AF (25) where: F = ration level % dry food\/day A, B = constants (Ro)2Q = average daily oxygen consumption ( mg )for 20 gm fish. kghr If equation 25 is expressed in terms of the fraction of the maximum ration fed \"f\" (rather than F), then: (Ro) 2 0 = B + [A(Fmax)20]f (26) where: f = F\/(Fmax)2o (Fmax)2Q - maximum ration for 20 gm fish (equation 15). Brett's (1974) measurements were carried out at temperatures of 5, 10, 15, 20, and 23\u00b0C over ration levels ranging from 0 to excess. The average fish weight was 20 grams t 10 grams. The constants A and B have been modelled after Brett's (1974) data, (a fish moisture content of 75% has been assumed). Slopes and intercepts are closely approximated by: B = exp(0.6491nT+2.760) = 15.7998T0*649 and, (27) A = exp(0.328lnT+4.097) - 60.1595T0*328 (28) where: T = temperature (\u00b0C), 5\u00b0C 10 6.689 x 10\"2 -0.194 2.12 Ro (equation 37) has been plotted as a function of fish weight \"w\" at 10\u00b0C in Figure 18. It should be noted that the feed rate has not been considered in this model. Elliott (1969) also considered oxygen consumption independent of feed-ing level. Oxygen consumption levels \"Ro\" have been related empirically to water temperature at various fish weights by the following set of equations: weight (gm) equations 1.85$w^ 5.90 Ro = (21.807T+1.28) - (1.1191T-2.8526) (w-1.85) (38) 5.90-resented by equation 54* Source Temp. Weight Measured (\u00b0C) (gm) NH4-N excretion rate (_mgj. kghr Projected NH,-N excretion rate (_mg_) kghr Brett and Zala 15 \u2022 29 7.27 * 0.20 eq. 54 5.2 (1975) eq. 55 9.7 (sockeye) eq. 56 9.6 eq. 57 0 eq. 58 0 eq. 59 0 Fromm (1963) 13 129 3.4 eq. 54 4.1 (\u2022rainbow trout) (12-14) - eq. 55 -42 eq. 56 - 7 eq. 57 0 eq. 58 0 eq. 59 0 78 7. Un-ionized Ammonia-N Aqueous ammonia exists in the following equilibrium (Thurston et. a l . , 1974). NH3(g) + nH20(l) ^=t NH3 \u2022 nH20(aq) ^ NH^ + OH\" + (n-l) H20 (6l) An ammonia solution therefore contains both ionized (NH4+) and un-ionized (NH^(g)) ammonia. This distinction is important because the toxicity of ammonia solutions has been associated with the un-ionized form (Fromm and Gillette, 1968). Thurston et. a l . (1974) has derived equations relating the un-ionized ammonia-N concentration (Nu) to the total ammonia concen-tration (N T), pH, and temperature (T): Nu * Hp (1 + lO^'^yho3 (62) where: Nu = un-ionized ammonia-N concentration in ug\/l (ppb). N^, = total ammonia-N concentration in mg\/l (ppm). pka = the negative log of the ionization constant: pka = 0.0901821 + 2729.92 . T+273.16 In summary, the rate of ammonia-N excretion can be related to the fish culture environment (temperature, fish weight, etc.) by equation 54. Knowledge of the load rate (L) and background ammonia-N levels (N^) allows calculation of the total ammonia-N at the pond outflow (equation 60). Equations 47 and 62 can then be used to predict the un-ionized ammonia-N levels (Nu). 79 8. Suspended Solids Suspended solids generated from rearing facilities consists mainly of feces and waste food. Because fine particles can irritate gi l l s ; suspended solids plays an important part in determining the overall environmental condition of the pond. a. Review Liao and Mayo (1974) have related the rate of suspended solids generation \"Rs\" to the feeding level: Rs - 216.67F (63) where: Rs = mg kghr F = feed rate % body weight per day. Willoughby et. a l . (1972) has also developed an empirical relationship between the increase in the suspended solids concentration through a rear-ing unit and the feed rate: Concentration increase in mg\/l (C) = food fed (lb) per USGPM x 25 (6k) Converting this expression to metric units yields: C = 2.086FB (65) Q where: C = concentration increase (mg\/l) F = feed rate (% body wt. per day) B = biomass (kg) Q = flow (l\/min) . This expression can be rearranged to give: Rs = CQ60 = 125.16F (66) B 80 Klontz et a l . (1978) has related suspended solids production rates to both feeding level and dietary efficiency: Rs = 4l6.67[0.95(lbs. fed - (lbs. fed x efficiency))] (67) where: Rs = mg kghr efficiency = lbs, growth . lbs. fed The factor \"o.95\" apparently indicates that 95% of the metabolic wastes will be solids. Equations 63, 66, and 67 represent empirical models frequently used to predict the solids output of rearing facilities. b. Theoretical solids model The previous attempts to relate growth, oxygen consumption, ammonia production and carbon dioxide generation to environmental conditions, naturally leads to questions about the solids balance in the rearing process. Construction of a simple theoretical balance using previously developed model components provides some insight into the generation of solids during rearing. Because of the complex behavior of solids in production ponds, this effort can not be expected to yield an accurate predictive model. Unlike dissolved substances, solids tend to settle (depending on the water velocity and pond depth) and are therefore flushed out of the ponds dis-continuous ly (during cleanings, etc.). Also, settled material may dissolve over time. Calculated outputs may only be useful as indicators of potential long term average discharge rates. 81 The solids generated during rearing depends on the difference between the ration input and the food either assimilated as growth or metabolized: Rs = Food - Growth - M (68) where: Rs = solids production Food = feed rate Growth = beiomass increase M = material metabolized. If these quantities are expressed in grams of dry material per grams of fish per day, the difference \"Rs\" should represent the theoretical solids production. The three terms in the equation have been quantified previously: Food = _F_ 100 (69) where: Food = gm dry food per gm fish per day F = gm dry food per 100 gm fish per day. The \"Growth\" term in equation 68 represents the gain of dry material per day per gram of fish (a fish moisture content of 75% has been assumed): Growth = 0.25(wn+1-wn) = 0.25(wneg~wn) = 0.25(eg-l) (70) wn wn where:- Growth = gm dry growth per gm per day g = specific growth rate (equation 10) wn = fish weight on the nth day wn-^ = fish weight one day later. The weight of material metabolized \"M\" can be directly related to the oxygen consumption and ammonia-N and carbon dioxide production (see Appendix VII). \"M\" is given by: M = 1.957% + 0.691 Ro (71) where: M = material metabolized (gm dry material per gm of fish per day) Ro = oxygen consumption in units of gm of oxygen per gm fish per day 82 RN = nitrogen per gm of fish per day. Substituting expressions for \"Food\" (equation 69), \"Growth\" (equation 70) and \"M\" (equation 71) into equation 68 gives the suspended solids output in units of grams per grams of fish per day. Converting the terms in equation 71 to more common units of mg\/kghr and expressing the nitrogen excretion rate in terms of ammonia nitrogen production gives: Rs = 416.667F - 10,4l6.668(eg-l) - 3.403RNH3 - 0.691Ro (72) where: Rs = suspended solids output rate (\u2022 mg ) kghr F = feed rate (gm per 100 gm fish per day) Fmax g = specific growth rate RNH^ = ammonia-N production rate ( mg ) kghr Ro = oxygen consumption rate ( mg ). kghr Food in excess of the maximum ration is assumed to contribute directly to the suspended solids output. c. Solids discharge rates and comparisons with other models Solids production rates are plotted against feed rates for 10 gram fish at 10\u00b0C in Figure 25. The circled points are predicted from the theoretical model (equation 72). Above the maximum ration of 2% per day the solids output increases rapidly. Equation 67 (Klontz et a l . 1978) predicts a minimum output at intermediate feeding levels; this reflects increasing growth efficiency as the \"optimum\" ration is approached (Figure 25). 1 Feed Rate (gm food per 100 gm fish per day) FIGURE 25. Suspended solids output rates as a function of the feeding level. Predictions have been made for 10 gm fish at a water temperature of 10\u00b0C using the equations discussed in the text. 00 84 It should be noted that equation 63 (Liao and May, 1974) and equation 65 (Willoughby et a l . , 1972) depend only on the feeding level. Because equations 67 and 72 involve the effects of growth and metabolism on food utilization, they are also sensitive to fish weight and temperature. Solids production rates at a feed rate of about 1% per day at various fish weights and temperatures are shown in Table 7. It should be emphasized that model predictions may only represent the potential long term average output. The day to day solids discharge rate would depend on the water velocity, depth, dimensions, and on the construc-tion material of the rearing pond; the rate would also depend on pond cleaning practices. TABLE 7. Model predictions of suspended solids output rates at a feed rate of 1% per day and various temperatures and fish weights. Equations 67 and 72 are sensitive to fish weight and tempera-ture, whereas equations 63 and 66 depend only on the feeding level. Weight Temp. Feed Rate Suspended Solids Output Rate (kgnr) (gm) (\u00b0c) (%\/day) eq. 63 eq. 66 eq. 67 eq. 72 5 10 1 215 124 82 175 2 10 1 215 124 132 186 30 5 1 215 124 267 271 1 15 1 215 124 427 217 85 In summary, the suspended solids predictions \"Rs\" given by equation 72 are based simply on the solids balance dictated by the previously developed \"Growth\" and \"Metabolite models. For example, 10 gm fish at 10\u00b0C and a ration level of 0.991 assimilated 0.212 gm of dry material as growth and metabolized 0.386 gm of food per 100 gm of fish per day. The difference of 0.393 gm represents the potential solids discharge rate. These values are summarized below: W = 10 gm T = 10\u00b0C - Food:, 0,991 gm dry matter per 100 gm fish per day. - Metabolized: 0,386 gm dry matter per 100 gm fish per day. - Growth (dry): 0.212 gm dry matter per 100 gm fish per day. - Solid Waste: 0.393 gm dry matter per 100 gm fish per day = (0.991 - 0.386 - 0.212). If the fish size and\/or water temperatures are altered, the solids balance is shifted. If the temperature were increased to 15\u00b0C and the fish weight reduced to 1 gm in the previous example, maintenance requirements would increase and a loss in weight would occur; the resulting distribution is shown below: W = 1 gm T = 15\u00b0C - Food: 0.991 gm dry matter per 100 gm fish per day. - Metabolized: 0.492 gm dry matter per 100 gm fish per day. - Growth (dry): -0.022 gm dry matter per 100 gm fish per day. - Solids Waste: 0.521 gm dry matter per 100 gm fish per day. 86 Solids projections based on equation 72 represent theoretical discharge rates consistent with the other model components. Although these rates are untested by comparison with actual data, predictions are comparable to those made using established empirical models. As with previous rate expressions, pond outflow concentration (mg\/l) can be calculated by substituting \"Rs\" into equation 6. 9. Density Density is usually expressed in terms of the number of fish per cubic foot of rearing space or in terms of the pounds of fish per cubic foot. In metric units this becomes the number of fish per liter or the grams of fish per l i t e r (or kg per m ). In symbols: Dn \u00ab n (73) V where: Dn = number density (fish\/liter) n = number of fish V = volume (l) Dw = nw (74) V where: Dw = weight density (gm\/l) w = fish weight (gm) Most density or space requirement criteria are based solely on experience. Density guidelines are often rationalized by reference to such crowding effects as stress (which acts as a disease trigger), disease transmission, and reduced growth rates. 87 Three frequently used methods f o r calculating maximum allowable densities w i l l be reviewed. These projections w i l l be contrasted with some load densities currently used i n B r i t i s h Columbia hatcheries. Be-cause the physiological basis of density effects i s not w e l l understood, a general density model w i l l not be developed. Westers and Pratt (1976) have based density c r i t e r i a on \"R\", the pond exchange rate. \"R\" i s defined as the number of pond volume changes per hour: R = 60Q = 60 (75) V t where: R = exchanges per hour Q = flow (l\/min) V = pond volume ( l ) t = mean residence time (min). I f both sides of equation 75 are mul t i p l i e d by the biomass B(kg) and the expression i s rearranged, we get: Dw = 16.67LR (76) where: Dw = density (gm\/l) = B1000 V L = load rate (kg per l\/min) = B . Q The load rate \"L\" i s determined so that the effluent oxygen levels are maintained above 5 mg\/l and the un-ionized ammonia concentrations are kept below 12.5 u g \/ l . The space required (V, l i t e r s ) f o r \"n\" f i s h i s given by equation 77* V = nw (77) 16.67LR 88 Westers suggests that for salmon culture, an exchange rate of \"4\" be maintained. Burrows (1968) has expressed maximum allowable densities as a function of fish weight \"w\" . Dw = 11.54 + 0.914w ; w<5 gm. (78) Dw = 14.43 + 0.353w ; w>5 gm. (79) These criteria were developed for salmon. Klontz (1978) has derived density criteria as a function of fish length and species. The density index \"a\" or maximum density per unit of fish length for various species is shown below: Species Density Index \"a\" ( gm ) lite r cm Coho 2.52 Chinook 1.89 Rainbow 3*16 Cutthroat 1.89 The density in \"gm\/liter\"' is given by: Dw = a X 3 If a typical relationship between length and weight of w = (0.01l)j\u00a3 is assumed, then density can be expressed in terms of weight \"w\" by: Dw = 11.33W1\/3 (coho) (80) o l\/3 Dw = 8.50w ' (chinook) (8l) Dw = 14.21W1\/3 (rainbow) (82) l\/3 Dw = 8.50w ' (cutthroat) (83) 89 These different methods of calculating the maximum allowable density (or minimum space requirement) are contrasted i n Figure 26 where density pro-jections have been made as a function of f i s h weight. The load rate \"L\" for use i n equation 76 has been calculated assuming a temperature of 10\u00b0C, a maximum ration and a minimum dissolved oxygen of 8 mg\/l. Densities found i n some t y p i c a l B r i t i s h Columbia rearing operations are summarized i n Table 8 (D. \"Wilson, pers. comm.). A l l of these f a c i l i t i e s have experienced some success; these densities have been displayed i n Figure 26 to emphasize the tremendous range of densities i n common use. General density c r i t e r i a are impossible to establish at t h i s time. Maximum densities can only be established by experience; c r i t e r i a w i l l be affected by the pond design, species, disease backgound of the stock, background water q u a l i t y , load rate and rearing program objectives. FIGURE 26 Density aa a function of fish weight as predicted by various theoretical models. Actual densities from Table 6 have been displayed and labelled by number. TABLE 8 . Typical fish densities at a number of British Columbia hatcheries. These values have been plotted on the density V3 weight curves shewn in Figure 2 6 . Location Pond Type Volume (1) Species II J N Load Rate (kg per l\/min) \"R\" Exchange Rate (hr - 1) Fish Weight (gm) Dw Density (gm\/l) Dn Density (no.\/l) 1) Abbotsford Provincial Hatchery Circular 0.99 m deep 6.13 m dia. 30,000 Steelhead 1.20 2.0 55 40 0.727 2) Robertson Creek Hatchery 3) Robertson Creek Hatchery Circular 1.52 m deep 3.05 m dia. Earthen Channel 11,129 293,000 Chinook Coho 0.29 0.20 1.2 5.2 4.5 2 5 . 2 4.0 17.1 0.90 0.68 4) Robertson Creek Hatchery Concrete Raceway 424,700 Chinook 0.26 3.6 5.3 15.7 2.94 5) Big Qualicum Hatchery Earthen Channel 1 , 5 6 1 , 0 0 0 Coho 0.28 2.1 18.2 9.8 0.537 6) Big Qualicum Hatchery Concrete Raceway 339,800 Chinook 0.20 6.0 5.9 19.7 3.86 7) Quinsam Hatchery Burrows Circulating 102,000 Coho 0.92 1 . 6 1 2 5 24.5 0..98 8) Quinsam Hatchery Burrows Circulating 102,000 Coho 0.46 1 . 6 1 2 5 1 2 . 2 5 0.49 9) Quinsam Hatchery Burrows Circulating 102,000 Chinook 0.769 1 . 6 1 7 20.6 2.94 10) Quinsam Hatchery Trough 1,584-8 Chinook 0.396 8.6 1.2 5 6 . 8 46.2 11) Quinsam Hatchery Trough 1,584.8 Chinook 0.499 8.6 1.7 71.1 4 2 . 1 92 IV SYNTHESIS OF MODEL COMPONENTS Individual components can easily be combined to give additional insight into the rearing process. This can be illustrated by means of a hypothetical example. a. Illustrative example Consider the typical situation where a hatchery designer has infor-mation about the background water quality and temperature regime of a new water supply and is faced with the problems of determining: - water flow requirements - space requirements - feeding and rearing schedules to meet target release weights. The first step in solving these problems is to compile required background fish culture and water quality information. Although this is a hypothetical example, numerical values are typical of hatchery water supplies, (i) background fish culture information: In this hypothetical case, coho are ready for ponding around March 15; this date therefore, is the beginning of the rearing period (day 0). The average weight of newly ponded fry is 0.3 gm. The incidence of bacterial diseases in the system is high enough that a substantial disease risk to hatchery stocks exists. As part of a routine assessment procedure, 15% of the coho fingerlings w i l l be marked (handled) sometime during the rearing period. 93 ( i i ) background water qu a l i t y information: I t w i l l be assumed that the inflow water i s of high q u a l i t y . Some background levels are shown below: Parameter Background Concentrations Dissolved Oxygen 100 % saturated (s = l ) Ammonia-N 10 ug\/l Carbon Dioxide 1.5 mg\/l Bicarbonate A l k a l i n i t y 50 mg\/l as CaCO^ Suspended Solids 2 mg\/l These parameters are assumed to be constant except for a b r i e f period during the spring. Suppose the carbon dioxide concentration drops to 0.75 nig\/l and the ammonia-N value increases to 30 ug\/l f o r a brie f period around the 100th day of rearing. The temperature regime i s shown i n Figure 27 and i s described by the Fourier series: T = 7.7056 + 3.9067cos2Kt + 0.2278cos4trt + 2.0sin2ltt + 0.991sin4TTt (84) 365 363 363 365 ( i i i ) rearing strategy: Previous experience of the designer suggests that optimum su r v i v a l w i l l r e s u l t from a release of 25 gm smolts i n mid May the following year (after 420 days of rearing). I t i s also f e l t that because of the disease r i s k , oxygen levels should not drop below protection l e v e l A (see c r i t e r i a developed by Davis (1975), Figure 2 ) . With background information and constraints established, a rearing and feeding schedule can be developed using the growth model (equation 11). 94 Figure 27 shows one possible feeding regime to achieve a 25 gm smolt at 420 days. Ninety percent of the maximum daily ration is fed for the fi r s t 100 days; 60% is fed over the next 100 days, while 45% of the maximum daily allowance is fed over the remainder of the rearing period. Marking is performed during a low temperature period (day 230); l i t t l e growth takes place during this disturbance. This is only one possibility for achieving release objectives; often temperatures can be manipulated to achieve similar results. The maximum possible load rates (and therefore minimum water requirements) to meet level A protection criteria for oxygen were then calculated using equations 40, 41, and 43\u00ab Results have been plotted in Figure 28. Both the load rates (kg of fish per l\/min) and water requirements per 1,000,000 fish (l\/min per 1,000,000) have been shown. It can be seen that water requirement maximums occur at days 150 and 420. To achieve \"level A protection\" for a population of 1,000,000 fish, peak flows of 19,000 l\/min and 31,000 l\/min are required on the 150th and 420th day. Considerably less water is required i f a level B protection criterion is judged acceptable. Water requirements to meet level B are shown in Figure 29. It can be seen that flows of 10,000 l\/min on the 150th day and 18,000 l\/min on the 420th day are required. A water requirement curve based on level A (Figure 28) will be an acceptable statement of water flow needs as long as the un-ionized ammonia-N, carbon dioxide, suspended solids, ammonia-N, and pH values are within limits. Although setting limits on these parameters is complex and somewhat subject-ive, the following standards are tentatively proposed: (see page 8) 95 - suspended solids - un-ionized ammonia-N - carbon dioxide * 2 ug\/1 - 25 mg\/l - 25 mg\/l - pH 6.5 - pH < 8.5 It should be emphasized that the function of the model is to predict the values of these parameters over the rearing period; i t is not designed to set water quality standards. As noted previously, the setting of standards will be influenced by the disease history of the fish, water temperatures, pond design, and the experience and perceptions of the operator. Un-ionized ammonia-N, total ammonia-N, carbon dioxide, suspended solids, and pH levels have been predicted from equations 6 2 , 6 0 , 45, 72, 6 , and 47j these parameters are plotted against time in Figures 30, 31, 32, and 33. Because concentrations were within acceptable limits over the entire rearing period, no further modifications to the water use curves shown in Figure 28 and Figure 29 are required. In this example, oxygen concentration is the first limiting factor; water flow requirements have been predicted from the oxygen consumption rate which in turn has been influenced by the water temperature, ration level, degree of hatchery disturbance, and the average weight of the fish. As was noted previously, rearing space requirements (at the present time) are based more on experience than on basic principles. If a conser-vative density \"Dw\" vs weight \"w\" relationship of \"Dw = 11 + 0.25w\" was assumed (see broken line in Figure 2 6 ) , then space requirements could be 3 predicted from equation 73. Volume requirements (m ) per 1,000,000 fish are plotted against time in Figure 35. 96 This example illustrates a rational approach to determining the require-ments of a hypothetical rearing program; projections are based on the \"Rearing Model\", the best available water quality criteria, and the exper-ience of the designer. b. Application The general rearing model can be used to solve a variety of problems. Two basic approaches can be taken. Firstly, the model can be used to predict pond conditions (e.g. oxygen concentration, etc.) i f basic fish culture objectives and water quality background information are available. Secondly, , i f constraints are imposed on environmental conditions (e.g. un-ionized ammonia-N - 2ug\/l, etc.), then the model gives predictions as to the min-imum water flow and space requirements (see Illustrative Example). In either case, a certain minimum amount of information is required. Examination of equations 2 through 73 shows that twelve parameters must be specified in order to characterize the rearing process at a particular time. This is illustrated in Table 9. Because the relationships between \"basic parameters\" and \"factors\" shown in Table 9 are expressed quantitatively, a great deal of flexibility exists in making model projections. In the previous \"Illustrative Example\", c* 3 T, wo, wf, Ci, A, (Ni)-p, arid Si were specified; constraints were placed on x<>*Nu, Rs, Dw, Co, t, and pHo and allowable R, Q, V, and n values were predicted (ration, flow, and space requirements per 1,000,000 fish). We could have just as easily specified crt., F, wo, wf, Ci, A, (Ni)^. and Si; placed constraints on t, xo, Nu, Rs, Dw, Co, and pHo and predicted T, Q, V, and n (temperature regime plus space and flow requirements). The manipulation of parameters simply depends on the requirements of the model user. 97 Model equations are simple enough that useful predictions can be made with a minimum of computing equipment. A l l projections in this report were made with a small programmable calculator\/printer. Programs were stored on magnetic cards. Obviously, more sophisticated equipment would allow greater speed, convenience, and flexibility. 98 TABLE 9. Basic parameters (independent variables) and Factors (dependent variables) required to characterize the rearing process at a given time. BASIC PARAMETERS t % oxygen saturation of inflow Q * flow V, volume T \u00bb temperature t time wo > i n i t i a l weight wf i f i n a l weight C i > inflow CO2 A > background a l k a l i n i t y ( N i ) T * background t o t a l NH^ -N S i background solids n t numbers of f i s h FACTORS . , inflow oxygen concentration x Q , outflow oxygen concentration Ro , oxygen consumption rate L , load rate F , ration l e v e l Rc , CO2 production rate Co , C0 2 outflow concentration pHi, pH inflow pHo, pH outflow , t o t a l ammonia production rate (No) T, t o t a l outflow ammonia concentration Nu , outflow un-ionized ammonia cone. Rs , solids production rate So , outflow solids concentration Dw , weight density Dn , number density RNH3 25 r FIGURE 27. Growth projection assuming an i n i t i a l weight of 0.3 gm. The temperature regime ? and ration level are also indicated: the notation \"f = 0.9\" indicates that 90% of the maximum daily allowance is being fed. A marking program at day 230 is assumed to suppress growth. ^ S Q Water Requirements (l\/min per 1,000,000 fish) ^ ^ water requirement^per 1 ^ * 0 0 0 0 50 100 150 200 D a y s \u00ab . U k 250 300 350 FIGURE 29. Maximum load rate and minimum water requirements per 1,000,000 f i s h to meet Level B oxygen c r i t e r i a developed by Davis (1975). Loaded to meet Level B oxygen criteria Loaded to meet Level A oxygen criteria 150 250 300 350 200 Days FIGURE 30. Un-ionized ammonia-N concentrations in the pond outflows; ponds are loaded to meet exther Level A or B oxygen criteria. 400 800 r D a y s FIGURE 3 1 . Total ammonia-N concentration i n the pond outflows; ponds are loaded to meet either Level A or B oxygen c r i t e r i a . o VjJ FIGURE 32. Carbon dioxide concentrations in the pond outflows; ponds are loaded to meet either Level A or B oxygen criteria. 20r Pond loaded to meet Level B Pond loaded to meet Level A 0 50 100 150 200 250 300 350 400 420 Days FIGURE 33. Suspended solids concentrations in the pond outflows; ponds are loaded to meet either Level A or B oxygen criteria. o 0 50 100 150 200 250 300 350 400 420 Days FIGURE 3U\u00bb pH of pond infow and outflow; ponds are loaded to meet either Level A or B oxygen criteria. 2000 108 V DISCUSSION AND CONCLUSIONS The approach adopted to modelling the rearing process concentrates on establishing simple deterministic relationships between the most significant factors known to affect rearing success. This has produced a set of rela-tionships that can be useful in facility design and operation but which are s t i l l very dependent on the judgement and experience of the user. For example, oxygen constraints, although reflecting sound criteria established by Davis (1975), s t i l l require a decision whether to accept level \"A\", \"B\", or \"C\" criteria. If level \"CV rather than \"A\" oxygen criteria are used, the number of smolts released may be doubled or tripled. Although this trade-off seems profitable the implications to adult production are not clear. As noted previously, reduced environmental quality may have subtle effects on the ability of the smolts to survive. At present, specification of environmental constraints, release sizes, etc., often reflect the hatchery operators intuitive feelings about how to optimize adult production. The problem of objectively setting rearing goals and constraints stands as an important limitation of the present \"Rearing Model\". This limitation should not be interpreted as a criticism; i t is a natural consequence of the simple deterministic approach taken to predict such factors as fish weight and oxygen concentration. It is unlikely that any factor as complex as ocean survival wi l l ever be related deterministically to the rearing environment. As more survival information becomes available both through assessment of production facilities and controlled experiments, the possibility of developing probabilistic relationships between survival and rearing conditions wi l l develop. 109 This is a necessary step in the establishment of optimum rearing criteria. Until such a probabilistic model is developed, rearing objectives must s t i l l be determined through intuition and experience on a site specific basis. The relationships presented in this thesis represent the first stage in the development of a general rearing model. Basically, a conceptual framework has been proposed and quantitative relationships have been pre-sented. Although these relationships have been built frcm a detailed analysis of fundamental information, they have only been tested against a limited amount of data. In effect, one loop of Van Gigch1s (1974) \"model validation cycle\" has been made (see Figure 6). To accomplish this, a minimum of computing equipment has been used. Individual equations are simple enough that they can be conveniently ex-plored with a hand-held programmable calculator. The next step in the evolution of the model should involve integrating the equations into a single flexible program. This would allow rapid comparison of model predictions with new data; deviations would eventually lead to the modification and refinement of the present equations. Development of an integrated, flexible program would also allow the model to be used in solving hatchery operations and design problems. At present, using equations one at a time on a programmable calculator is awkward; requir-ing an intimate knowledge of the model. Within the bounds of the present deterministic model, same serious weaknesses exist. Pond environmental conditions are based on the average effluent concentrations. If pond hydraulic characteristics deviate sub-stantially from those of ideal containers, metabolite concentrations could 110 be much higher in specific areas of the pond than predicted by equations 6 and 9. Additional \"tracer\" information is necessary to identify significant deviations from ideal flow conditions. Water velocity considerations have also been omitted from the structure of the model. Although rearing pond velocities were not considered an important factor to fish growth (Stauffer, 1973)* i t is felt that velocity may have important effects on fish \"condition\". Velocity may also affect the solids concentrations in ponds (Westers, 1977). Westers maintains that low water velocities (0.25 ft\/sec) allow solids to be removed (by settling on bottom), thus leading to improved environmental conditions. Burrows (1970) on the other hand, recommends relatively high water velocities in circulat-ing ponds in order to achieve a self cleaning action. Although there is no agreement on the lower water velocity limits, upper limits impose obvious constraints. Flow requirements must not only satisfy water quality criteria, they must also establish velocity patterns which allow the fish to hold and maneuver. It is these upper velocity limits that often prevent fish culturists from forcing a high flow through a limited rearing volume. The present model could be refined to predict oxygen concentrations below the critical oxygen level \"Cr\" (see Figure 8) . As noted previously, oxygen predictions neglect the effects of oxygen concentration on the rate of oxygen consumption. This leads to inflated uptake values at oxygen concentrations below the incipient limiting-tension. I l l This problem can be i l l u s t r a t e d by an example. I f pond outflow oxygen lev e l s are above \"Cr\", then the outflow concentration \"x 0\" i s a simple l i n e a r function of the load rate \"L\" (see equation 6, page 23);, x 0 = X j _ - ROL\/60. At outflow concentrations below \"Cr\" however, \"x 0\" values are predicted using the \" f i r s t order\" equation 7 (see page 30). Separating variables and solving t h i s equation over the appropriate l i m i t s of integration gives: (85) since L = Dt, ln(Kx n+b) - ln(KCr+b) = - K [L-L P J . (86) 60 L r where: Cr = c r i t i c a l oxygen concentration L C r = \"I\"oad r a t e r e c l u i r e c * t o S i v e t n e c r i t i c a l oxygen concentration at the pond outflow x Q = outflow oxygen concentration at load rate \"L\". I f t y p i c a l R , x^, Cr, K, and b values of 280 mg , 11.33 mg\/l, 6.5 mg\/l, kghr 43 l i t e r s \/ k g h r , and 0 mg\/kghr are assumed respectively, then outflow oxygen concentrations as a function of load rate \"L\" can be predicted: x 0 * 11.33 - 4.67L , i f x Q > C r (or L ^ L ^ ) x Q = 0.0233 exp(6.375 - 0.717L) , i f x Q < C r (or L > L C r ) . These equations are plotted i n Figure 36. The dashed l i n e represents the \"low\" estimates of pond outflow oxygen concentrations based on the assumption that uptake rates are independent of the oxygen concentration. This omission does not severely affect the accuracy of model predictions unless rearing i s being carried out at oxygen levels below 5 mg\/l (Figure 36), x D = 11.33 - A.67L \u2022Cr\" 0 0.5 1.0 1.5 Load Rate (kg per l\/min) 2.0 2.5 FIGURE 36. Oxygen concentration in the pond outflow as a function of the load rate. As the pond dissolved oxygen level falls below \"Cr\", the oxygen uptake rate is suppressed by the reduced environmental oxygen level. The \"solid\" line incorporates this effect, while the \"dashed\" line assumes that the uptake rate is independent of the oxygen concentration. 113 Incorporating this refinement would require detailed uptake vs concentration relationships at oxygen levels below Crj such relationships, being complex, would probably be affected by water temperature and fish weight. With pond oxygen levels most often being the first limiting factor, maximum load rate projections will usually be based on equation 21; x Q = x i - RoL\/60 , or: L = (x. - x )60 ( 87) Ro where: x^ = inflow oxygen concentration (mg\/l) x 0 = outflow oxygen concentration (mg\/l) Ro = average daily oxygen consumption rate ( mg ) kghr L = load rate (kg per l\/min). By setting the outflow oxygen concentration \"x0\" at the desired level, the allowable load rate can be calculated. It should be noted however, that the consumption rates \"Ro\" and therefore the pond outflow concentrations, are average daily values. This implies that for half of the day, oxygen levels may be below the levels specified in equation 87. This problem was approached by applying a safety factor to the average daily consumption rate \"Ro\". The safety factor was developed from oxygen data taken at the Quinsam Hatchery and guarantees that oxygen concentrations wil l exceed the specified levels for no more than 2.4 hours per day (10%). This factor reflects daily oxygen consumption peaks which in turn reflect both fish cultural activities around the ponds and the daily temperature pulse. Because daily temperature regimes vary widely between water supplies, this safety factor should be considered site specific. 114 There are several obvious limitations associated with the proposed model. The pH equation involves a simplification in that only the bicar-bonate\/ carbonate buffer system has been considered. Although this approx-imation is adequate for many natural water supplies, i t may be suspect in the case of ground water. Also, in modelling pond suspended solids and ammonia-N output, bacterial action on the pond bottom and walls has not been considered. This is probably an insignificant factor in concrete ponds but in the case of large semi-natural channels bacterial or algal action would probably have important effects on output rates. Further-more, none of the equations have been refined to the point where they are sensitive to species differences. The ammonia-N excretion model is based on the difference between the nitrogen in the ration and the nitrogen assimilated as growth. It was found that measured ammonia values only accounted for about 40% of this theoretical nitrogen waste. Therefore, a scaling factor was derived to relate ammonia-N excretion to the theoretical waste nitrogen. This implies that 62% of the nitrogen input could not be accounted for as growth or as ammonia-N. This discrepency was assumed to represent other nitrogenous waste products (e.g. urea), fecal losses and direct food wastage. The scaling factor unfortunately, has only been tested over a limited range of conditions; additional data is required for small fish at high ration levels. The simple deterministic approach used to develop this model necessarily concentrates on parameters that are easily quantified. Consequently, chemical and physical needs have been stressed. Such factors as the degree of bank cover, diet composition, construction material, access to a range of water velocities and fish densities and access to natural food have not been discussed. 1 1 5 These factors may exert significant indirect effects. To date, their role is not clear as successful rearing programs have been carried out in both highly a r t i f i c i a l concrete ponds and in semi-natural channels. The present \"Rearing Model\" has attempted to relate the prime fish culture parameters (fish weight, water temperature, ration level, and hatchery disturbance) to factors which are vital to rearing success. It stresses the effects of ration level because this factor has often been omitted in previous modelling efforts and because i t is easily manipulated by fish culturists. The model also emphasizes the dynamic nature of the rearing process; variations in oxygen level, fish weight, etc., can easily be projected over the entire rearing period. Hopefully, this undertaking has at least established a framework around which this complex process can be understood more clearly. This framework should remain intact although the details w i l l undoubtedly change as new information becomes available. BIBLIOGRAPHY ALDERDICE, D. F. Resources Service Branch, Fisheries and Marine Service, Dept. of Fisheries and Oceans Canada, Pacific Bio-logical Station, Nanaimo, B. C, personal communication. BILTON, H. T. 1978. Returns of adult coho salmon in relation to mean size and time at release of juveniles. Fish Res. Board Can. Tech. Rep. 8 3 2 : 73 p. BRETT, J. R., J. E. SHELBOURN AND C. T. SHOOP. 1 9 6 9 . Growth rate and body composition of fingerling sockeye salmon, Oncorhyn-chus nerka, in relation to temperature and ration size. J. Fish. Res. Board Can. 26: 2363-2394. BRETT, J. R. 1 9 6 5 . The relation of size to rate of oxygen consump-tion and sustained swimming speed of sockeye salmon (Oncorhyn-chus nerka). J. Fish. Res. Board Can., 2 2 : 1 4 9 1 - 1 5 0 1 . BRETT, J. R. 1 9 7 6 . Feeding metabolic rates of sockeye salmon, Oncorhynchus nerka, in relation to ration level and temperature, Envir. Can. Fish. Mar. Serv. Tech. Rep. No. 675* 18 p. BRETT, J. R. AND T. D. D. GROVES. 1 9 7 9 . Physiological energetics, p. 2 7 9 - 3 5 2 . In W. S. Hoar and D. J. Randall [ed.] Fish physiol-ogy. Vol. VIII. Academic Press Inc., New York, N. Y. BRETT, J. R. AND C. A. ZALA. 1975. Daily pattern of nitrogen excre-tion and oxygen consumption of sockeye salmon (Oncorhynchus nerka) under controlled conditions. J . Fish. Res. Board Can. 3 2 : 2 4 7 9 - 2 4 8 6 . BRITISH COLUMBIA RESEARCH COUNCIL. 1 9 7 6 . Enhancement of the Water Reclamation System for Abbotsford Trout Hatchery. Report pre-pared by: Division of Applied Biology, B. C. Research, Vancouver, B. C. for British Columbia Dept. of Public Works. BROWN, W. C. AND G. BRENGEIMANN. 1 9 6 5 . Energy metabolism, p. 1 0 3 0 - 1 0 4 9 . In T. C. Ruch and H. D. Patton [ed.] Physiology and Biophysics. W. B. Saunders Co., Philadelphia and London. BURROWS, R. E. 1 9 7 0 . The rectangular circulating rearing pond. Prog. Fish-Cult., 3 2 : 6 7 - 8 O . BURROWS, R. E. 1964. Effects of accumulated excretory products on hatchery reared salmonids. U. S. Fish and Wildlife Service, Re-search Report No. 6 6 . 1 2 p. BURROWS. R. E. AND B. D. COMBS. 1968. Controlled environment for sal-mon propagation. Prog. Fish-Cult., July: 1 2 3 - 1 3 6 . 117 CLARK, d. W., W. VIE3SMAN (Jr.) AND M. J. HAMMER. 1971. Water Supply and Pollution Control. International Textbook Company, Scranton, Pennsylvania, 66l p. DAVIS, J. C. 1975. Minimal dissolved oxygen requirements of aquatic l i f e with emphasis on Canadian species: a review. J. Fish. Res. Board Can. 32: 2295-2332. ECKENFELDER, W. W. (Jr.). 1970. Water Quality Engineering for Prac-ticing Engineers. Barnes and Noble, Inc., New York, N. V\/. 328 p. ELLIOTT, J. W. 1969. The oxygen requirements of chinook salmon. Prog. Fish-Cult., 31: 67-73. ENVIRONMENTAL PROTECTION AGENCY. 1972. Water Quality Criteria, 1972. U. S. Environmental Protection Agency, Washington, D. C. 594 p. FISHERIES AND MARINE SERVICE. 1978. A Report on the Proceedings of the Salmonid Culture Managers Conference. Dept. of Fisheries and Environment, Vancouver, B. C. FRASER, F. J. Resource Service Branch, Fisheries and Marine Service, Vancouver, personal communication. FRQMM, P. 0. 1963. Studies on renal and extra-renal excretion in a freshwater teleost, Salmo Gairdneri. Comp. Biochem. Physiol. 10: 121-128. FROMM, P. 0. AND J. R. GILLETTE. 1968. Effect of ambient ammonia on blood ammonia and nitrogen excretion of rainbow trout (Salmo Gairdneri). Comp. Biochem. Physiol. 26: 887-896. GROVES, T. D. D. 1970. Body composition changes during growth in young sockeye (Oncorhynchus nerka) in fresh water. J. Fish. Res. Board Can. 27: 929-942. HARTMAN, J. 1976. Ammonia production and oxygen consumption of Brown Trout (Salmo trutta fario) in three pass water reuse system. Michigan Department of Natural Resources, Lansing, Michigan 48909. KLONTZ, G. W., I. R. BROCK AND J. A. McNAIR. 1978. Aquaculture Tech-niques: Water Use and Discharge Quality. Research technical com-pletion report, project A-054-IDA, Idaho Water Resource Research Institute, University of Idaho, Moscow, Idaho. 114 p. LEVENSPIEL, 0. 1972. Chemical Reaction Engineering, 2nd ed. John Wiley and Sons, Inc., New York, N. Y. 578 p. LIAO, P. D. 1971. Water requirements of salmonids. Prog. Fish-Cult., 33: 210-220. 118 LIAO, P. B. AND R. D. MAYO. 1974. Intensified fish culture combining water reconditioning with pollution abatement. Aquaculture, 3: 61-85. LLOYD, R. AND D. W. M. HERBERT. I960. The influence of carbon dioxide on the toxicity of urn-ionized ammonia to Rainbow Trout (Salmo Gairdnerii Richardson). Ann. appl. Biol. 48, (2): 399-404i McLEAN, W. E. AND F. J. FRASER. 1974. Ammonia and urea production of coho salmon under hatchery conditions. Dept. of Environment, Fisheries and Marine Service, Vancouver, B. C. Report No. EPS 5-PR-74-5. MOBERLY, S. A. AND L. ROBERT. 1977. Japan Salmon Hatchery Review. Alaska Department of Fish and Game, Division of Fisheries Rehab-ilitation, Enhancement and Development. 124 p. NEMEROW, N. L. 1974. Scientific Stream Pollution Analysis. McGraw-Hill Inc. New York, N. Y. ROYAL, L. A. 1972. An examination of the anadromous trout program of the Washington State Game Department. Department of Game, Olympia Washington. 176 p. SIGMA RESOURCE CONSULTANTS LTD. 1979. 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Van Nostrand Company Inc. New York, N. Y. 353 P\u00ab 119 WEBER, W. J. (JR.). 1970. Physicoehemical Processes for Water Quality Control. Wiley-Interscience, New York, N. Y. 640 p. WEDEMEYER, G. A. 1974. Stress as a predisposing factor in fish diseases. U. S. Fish and Wildlife Service, Division of Cooperative Research, Washington, D. C. 8 p. WEST, C. Enhancement Services Branch, Fisheries and Marine Service, Dept. of Fisheries and Oceans Canada, Vancouver, B. C, personal communication. WESTERS, H. AND K. H. PRATT. 1976. The rational design of fish hatch-eries based on characteristics,of fish metabolism. Michigan Depart-ment of Natural Resources, Fisheries Division. 10 p. WILLOUGHBY, H., N. LARSEN AND J. T. BROWN. 1972. The pollutional effects of fish hatcheries. American Fishes and U. S. Trout News, 17: 6-20. WILSON, D. Enhancement Services Branch, Fisheries and Marine Service, Dept. of Fisheries and Oceans Canada, Vancouver, B. C, personal c cmmunication. WINDELL, J. T., J. W. FOLTZ AND J. A. SAROKON. 1978. Effect o f f i s h size, temperature and amount fed on nutrient digestibility of a pelleted diet by rainbow trout, Salmo gairdneri. Trans. Amer. Fish. Soc. 107: 6l3-6l6. 120 Appendix I Fourier analysis can be used to obtain a mathematical -approximation of a periodic empirical curve (Wayland, 1957). If the temperature curve is described by mean weekly or monthly temperatures and the curve is assumed to be periodic with period \"P\", then the continuous representation of the temperature curve \"f( t ) \" is given by: An adequate approximation of the curve can often be obtained i f only five coefficients are evaluated by numerical integration. This operation can be easily performed on most programmable calculators using Simpson's or the Trapazoidal rule. The continuous approximation to the temperature regime becomes: where the fourier coefficients a, o* an* n* can be calculated from: This series can be expanded i f a closer approximation is desired. 121 Appendix II Proximate analysis of some typical hatchery diets as stated by the manufacturer; Oregon Moist Swedish Ewos Pellet (Astra Chemicals) Abernathy Protein (%) > 35.0 52.0 > 45 Moisture (%) 4 35.0 7.0 4 10 Carbohydrate (%) 17.5 Fat (%) \u00a3.5.0 10.0 > 8 Ash (%) Cellulose (%) ^ 4.0 3.5 122 Appendix III The growth equation could be solved explicitly (weight vs time) i f the ration level was expressed in terms of the fraction of the difference between the maximum and maintenance levels, rather than as a fraction of the maximum ration itself. At present, a feeding level of \"0.6\" means \"0.6\" of the maximum ration (0.6Fmax). In this notation, an unknown fraction (which depends on temperature and fish weight) is involved in maintenance while the remainder represents the potential for growth. Another approach might involve \"Fmax - Fma\". In this case, a feed-ing level of \"0.6\" would mean \"0.6\" of the difference between maximum and maintenance rations (0.6(Fmax - Fma)); the actual daily feed rate \"F\" would be: F = Fma + 0.6(Fmax - Fma). If this approach to feeding was adopted, explicit solutions to the growth equations could be simply obtained. At feeding level the daily feed rate \"F\" would be: F = Fma + ot(Fmax - Fma) (l) Substituting this expression into equation 12_(see page 36) gives: g = GsinTf_oc (2) 2 If temperatures are within the range of linearity of the growth polynomial (equation 13), then the average daily temperature \"Ta\" over a time period may be considered. Therefore: G = Aw~B (3) where:: A * 0.0304(aj+a2(l.8Ta+32) + ....(see equation 13) w = fish weight (gm) B = 0.3333 Ta = average daily temperature (\u00b0C) t = time (days) 123 Substituting aquation 3 into equation 2 gives: g = Aw\"\"BsinK tx = 1 dw (4) 2 wdt Solving for \"w\" yields a simple expression for weight against time: w = (w_B + ABsinT\u00a3* t ) X \/ B (5) 2 If the average daily temperature over a time period is 10\u00b0C, then the expression for \"w\" vs \"t\" becomes: w = ( w \u00b0 , 3 3 3 3 + 0.0101741sinTXoct)3*0003 (6) 2 At a feeding level of c<= 0, only the maintenance ration would be fed (F = Fma) and growth would be G. At \u00a9<. = 0.5* the daily feed rate would be \"F = Fma + 0.5(Fmax - Fma)\" and the prediction of weight vs time would become: w - ( w 0 0 s 3 3 3 3 + 0.0071942t) 3 # 0 0 0 3 (7) Appendix IV The small error that results when the \"incremental method\" is used to solve the growth equation can be eliminated by means of a correction factor. The problem arises because the specific growth rate decreases continuously as the fish weight increases. Consider growth over a 5-day time increment. The final weight \"w^\" is predicted from equation 11:: wx = w Qe 5 g (1) where: wQ = i n i t i a l weight g = specific growth rate However, \"g\" is not only based on the ration level and average daily temperature over the 5-day interval, but also on the i n i t i a l weight \"w0\" (see equations 12 and 13). If the average daily ration level and temperatures are known, then \"g\" is given by: g - Aw'0*3333 (2) where: A = constant derived frcm equations 12 and 13. It can be seen that the growth rate decreases from g Q = Aw0\"\"\u00b0*3333 at the beginning of the time interval to g^ = Aw^ \"\"\u00b0*3333 f i v e days later. Use of \"g 0\" over the entire interval introduces a small positive error; this error is compounded over each increment. The error can be eliminated by using the average growth rate \"g\" rather than \"g0\" in equation 1. \"I\" is given by: g = cg D (3) where: c = correction factor g 0 = i n i t i a l growth rate g = average growth rate over the 5-day increment, g is also given by: A \\ w-\u00b0' 3 3 3 3dw , A L \u00b0 \u00bb 6 6 6 7 . w 0.66671 ( 4 ) (w, - wj \\ -0.6667K-\u2122 ) L 0 J 1 o' Jw 0 1 O' 125 If \"w \" is approximated by \"UQe^g\u00b0\" and \"g 0 = Aw0~0*333\", then: c - g - e 3' 3 3 3 5 go - 1 i (5) go O.6667(e5go-i) The corrected weight at the end of a time increment is given by: W l = w o e 5 C S \u00b0 <6) where: c= correction factor calculated from equation 5. If the exact expression for w^ , -(w^ = w e 0 ^ 0 ) , is substituted into equation 4, the expression involving the correction factor \"c\" becomes: c = e3.3335g0c . , ^ ( ? ) O.6667(e5cgo-1) \"c\" can be solved to any degree of accuracy by expanding the exponentials in a MacLaurin series. For example, i f the exponentials are expanded to the third term: e3.3335gQc s x + 3 #333 5 g o C + (3^3335^2 ( g ) 2 e^goc * ! + 5 g o c + (5g o C)2 (9) 2 and substituted into equation 7, \"c\" can be solved for: c = 5.556lgQ - 3.3335 + (11.1122 + 74.0797go + 30.8702g\/)2 . (10) l6.6675g0 Different methods of making growth projections are compared in Table 10. In order to make exact predictions using equation 19, an in i t i a l weight of 1 gram, a maximum ration and a constant temperature of 10\u00b0C have been assumed. Use of correction factors given by equations 5 or 8 gives results that are within 0.1 % of the exact values. It should be noted that the corrected incremental method allows accurate, and general solutions of the growth equations to be made. TABLE 10. A ccmparison of results as a function of the method used to solve the growth equation; % error = P - E x 100%, c = correction factor. E Exact (gm) Time \u2022 \"E\" Incremental Method ( T=5 days) (days) (Equation 19) c \u2022= 1 % error c=equation 5 % error c=equation 8 % error 100 8.2125 8.4381 2.75 8.2055 -0.085 8.2226 0.123 200 27.9604 28.7635 2.87 27.9397 -0.074 27.9906 0.108 400 130.3596 133.6157 2.50 130.2908 -0.053 130.4572 0.075 127 Appendix V The oxygen deficit incurred as water moves through a rearing pond ideally depends on the oxygen consumption of the fish and the reaeration effects of the pond. The rate at which the deficit is generated can be expressed by the Streeter Phelps equation: dD = A - kD (1) dt where A = rate of oxygen concentration decrease ( mg ) Imin k = aeration constant (min\" ) D * oxygen deficit (mg\/l) or the difference between saturated value and actual concentration. The rate of decrease in the oxygen concentration \"A\" can be related to fish culture parameters by: A \u00bb RoQL (2) V60 where: Q = flow (l\/min) V = volume (l) L = load rate (kgitin or kg per l\/min) 1 Ro = oxygen consumption ( mg ) kghr Substituting equation 2 into equation 1 and solving for the oxygen deficit at the pond outflow \"Do\" yields: Do = Ro^(l-e- k V\/ Q) +Die\" k V\/Q (3) VoOk where: Do = deficit at outflow = x a - x Q Di = deficit at inflow = x s - x^ x g = saturation values Substituting expressions for \"Do\" and \"Di\" into equation 3 and solving for \"xo\" gives: x 0 = x s - RoLQ (1 - e-^\/Q) - (x s - x J e ^ \/ Q (4) VoOk If the inflow water is 100 % saturated (XJ_ = x s ) , equation 4 reduces to: x o - x - RoLQ(l - e\" k V\/ Q) (5) \u00b0 3 V60k Reaeration effects can be estimated i f \"k\" is approximated by: k = CUn (Weber, 1970) (6) where: k = aeration constant (day\"1) U = average stream velocity (ft\/sec) H = average stream depth (ft) n, m, and C are constants. In this example, \"n\", \"m\", and \"C\" are assumed to be 0.5, 1.5, and 12.9 respectively (Eckenfelder, 1970; Clark et al, 1971). Consider a typical pond with a mean residence time of 30 minutes, a mean water velocity of 1 ft\/sec and an average depth\"of 3 feet. Assume the pond is loaded at 1.2 kg per l\/min and the fish are consuming oxygen at a rate of 300 mg\/kghr. The combined effects of oxygen consumption and reaeration are predicted by substituting appropriate values into equations5 and 6: x Q = x. - 5.85 If the inflow oxygen concentration is 11 mg\/l, the outflow level, in this case, would be 11 - 5.85 or 5.15 mg\/l. If reaeration is not considered, the outflow concentration would be simply given by equation 21: x Q = Xj_ - RoL = 11 - 6 = 5.0 mg\/l. o0~ In this example, reaeration effects (0.15 mg\/l) are small compared to the 6.0 mg\/l deficit caused by the metabolism of the fish. Neglecting reaeration effects in simple flow-through rearing ponds would not introduce serious errors in predicting outflow oxygen concentrations. 129 Appendix VI Carbon dioxide production tends to lower the pH of natural waters. The effects can be quantified i f the carbonate-bicarbonate system i s assumed to be predominant. This i s usually a valid assumption for natural waters i f a conservative pH range (6.5 to 8.5) i s considered. In aqueous carbonate systems, carbon can be i n the ILjCO^, CC^', or HCOj form depending on pH and temperature. The notation B^CO^ denotes the t o t a l analytical concentration of dissolved carbon dioxide. H2C03\" = [CG 2(aq) + H 2C0 3] (l) It should be noted that less than 0.3 % of the carbon dioxide i s hydrated (H 2C0 3) at 25\u00b0C (Stumm and Morgan, 1970). If an amount of carbon dioxide \"C\" i s added to a solution, the pH drops such that:: C = ( C T ) p H l - ( CT)pH 2 ( 2) where: (CT)pH^ = t o t a l concentration at pH-j_ (C-r.)pjj2 = t o t a l concentration at pH2. Note: C T = [H2C03*] + [HC03\"] + [C0 3 =] (3) Let od = [HC03\"] (4) Cip <*2 \" Cg0 3=] (5) but, \\ = [H +I][HC0 3~]\/[H 2C0 3 ] ,1st'ionization constant (6) and, K 2 = [H +][C0 3 =] \/[HCC>3~ ] , 2nd ionization constant (7) so, [HC03~] = K ^ C C y ] (8) [H +] and, [C0 3 =] = K2[HC03\"]. (9) [H +] 130 Substituting equations 8 and 9 into 4 and 5 gives: \u00ab 1 = ( c ! ? + 1 \\ k f ( 1 0 ) c t 2 = ( m 2 \u2022 [ H i j + i y - 1 ( I D V Ki K 2 K 2 y Neglecting the small amount of ammonia present, the alkalinity can be expressed as: [Alk] = [HCO3] + 2[G03=] = [OH\"] - [H+] (12) or [Alk] = C T(\u00ab1 + 2<*2) + [ 0 H r ] - [H+] (13) solving for Cp gives: C T = [Alk] - [OH\"] + [H+] ( 1 4 ) + 2