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Aquacultural Engineering 23 (2000) 121–179
AquaFarm: simulation and decision support for
aquaculture facility design and management
planning
Douglas H. Ernst
a,
*, John P. Bolte
a
, Shree S. Nath
b
a
Biosystems Analysis Group,Department of Bioresource Engineering,Oregon State Uni6ersity,
Gilmore Hall
102
B,Cor6allis,OR
97331
,USA
b
Skillings–Connolly,Inc.,
5016
Lacy Boule6ard S.E., Lacy,WA
98503
,USA
Received 20 September 1998; accepted 3 September 1999
Abstract
Development and application of a software product for aquaculture facility design and
management planning are described (AquaFarm, Oregon State University©). AquaFarm
provides: (1) simulation of physical, chemical, and biological unit processes; (2) simulation of
facility and fish culture management; (3) compilation of facility resource and enterprise
budgets; and (4) a graphical user interface and data management capabilities. These
analytical tools are combined into an interactive, decision support system for the simulation,
analysis, and evaluation of alternative design and management strategies. The quantitative
methods and models used in AquaFarm are primarily adapted from the aquaculture science
and engineering literature and mechanistic in nature. In addition, new methods have been
developed and empirically based simplifications implemented as required to construct a
comprehensive, practically oriented, system level, aquaculture simulator. In the use of
AquaFarm, aquaculture production facilities can be of any design and management inten-
sity, for purposes of broodfish maturation, egg incubation, and/or growout of finfish or
crustaceans in cage, single pass, serial reuse, water recirculation, or solar-algae pond systems.
The user has total control over all facility and management specifications, including site
climate and water supplies, components and configurations of fish culture systems, fish and
facility management strategies, unit costs of budget items, and production species and
objectives (target fish weights/states and numbers at given future dates). In addition,
parameters of unit process models are accessible to the user, including species-specific
parameters of fish performance models. Based on these given specifications, aquaculture
www.elsevier.nl/locate/aqua-online
* Corresponding author. Tel.: +1-541-7523917; fax: +1-541-7372082.
E-mail address
:
ernstd@engr.orst.edu (D.H. Ernst)
0144-8609/00/$ - see front matter © 2000 Elsevier Science B.V. All rights reserved.
PII: S0144-8609(00)00045-5
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Aquacultural Engineering
23 (2000) 121–179
facilities are simulated, resource requirements and enterprise budgets compiled, and opera-
tion and management schedules determined so that fish production objectives are achieved.
When facility requirements or production objectives are found to be operationally or
economically unacceptable, desired results are obtained through iterative design refinement.
Facility performance is reported to the user as management schedules, summary reports,
enterprise budgets, and tabular and graphical compilations of time-series data for unit
process, fish, and water quality variables. Application of AquaFarm to various types of
aquaculture systems is demonstrated. AquaFarm is applicable to a range of aquaculture
interests, including education, development, and production. © 2000 Elsevier Science B.V.
All rights reserved.
Keywords
:
Aquaculture; Decision support system; Computer; Design; Modeling; Simulation; Software
1. Introduction
Aquaculture facility design and management planning require expertise in a
variety of disciplines and an ability to perform computationally intensive analyses.
First, following specification of the physical, chemical, biological, and management
processes used to represent a given facility, quantitative procedures are required to
model these processes, project future facility performance, and determine facility
operational constraints and capacities. Second, management of large datasets is
often necessary, including facility and management specifications, projected facility
performance and management schedules, and resource and economic budgets.
Finally, design procedures require many calculations, especially when: (1) multiple
fish lots and fish rearing units are considered; (2) simulation procedures are used to
generate facility performance and management schedules; (3) alternative design and
management strategies are compared; (4) designs are adjusted and optimized
through a series of iterative facility performance tests; and (5) production econom-
ics are compared over a range of production scales. Such analyses can be used to
optimize production output with respect to required management intensity and
resource consumption (or costs) and to explore tradeoffs between fish biomass
densities maintained and fish production throughput achieved (residence time of
fish in a facility).
To address these challenges, computer software tools for facility design and
management planning can embody expertise in aquaculture science and engineering
and serve as mechanisms of technology transfer to education, development, and
production. In addition, computer tools can assume the burden of data manage-
ment and calculation processing and thereby reduce the workload of design and
planning analyses. A current listing and description of software for aquaculture
siting, planning, design, and management is available on the Internet (Ernst, 1998).
Much of this software falls under the general heading of decision support systems
(Sprague and Watson, 1986; Hopgood, 1991), in which quantitative methods and
models, rule-based planning and diagnostic procedures (expert systems), and data-
bases are packaged into interactive software applications. The application of
decision support systems to aquaculture is relatively recent and has been preceded
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23 (2000) 121–179
by the development of simulation models for research purposes. Foretelling these
trends, decision support systems have been developed for agriculture for purposes
of market analysis, selection of crop cultivars, crop production, disease diagnosis,
and pesticide application.
The purpose of this paper is to provide an overview of the development and
application of AquaFarm (Ver. 1.0, Microsoft Windows
®
, Oregon State Univer-
sity©). AquaFarm is a simulation and decision support software product for the
design and management planning of finfish and crustacean aquaculture facilities
(Ernst, 2000b). Major topics in this discussion are: (1) the division of aquaculture
production systems into functional components and associated models, including
unit processes, management procedures, and resource accounting; and (2) the
flexible reintegration of these components into system-level simulation models and
design procedures that are adaptable to various aquaculture system types and
production objectives. To provide this overview at a reasonable length, methods
and models of physical, chemical, and biological unit processes used in AquaFarm
are presented as abbreviated summaries in an appendix to this paper. The appendix
is organized according to domain experts and unit processes. Example applications
of AquaFarm to typical design and planning problems are provided but rigorous
case studies are beyond the scope of this paper. Completed and ongoing calibration
and validation procedures for AquaFarm are discussed.
2. AquaFarm development
The aquaculture science and engineering literature was applicable to the develop-
ment of AquaFarm through three major avenues. First, studies concerned with
aquaculture unit processes and system performance provided models and modeling
overviews for a wide range of physical, chemical, and biological unit processes and
system types (Chen and Orlob, 1975; Muir, 1982; Bernard, 1983; Allen et al., 1984;
James, 1984; Svirezhev et al., 1984; Cuenco et al., 1985a,b,c; Fritz, 1985;
Tchobanoglous and Schroeder, 1985; Cuenco, 1989; Piedrahita, 1990; Brune and
Tomasso, 1991; Colt and Orwicz, 1991b; McLean et al., 1991; Piedrahita, 1991;
Weatherly et al., 1993; Timmons and Losordo, 1994; Wood et al., 1996; Piedrahita
et al., 1997). Additional methods and models were newly developed for AquaFarm,
including empirically based simplifications, as required to achieve comprehensive
coverage of aquaculture system modeling while avoiding excessive levels of com-
plexity and input data requirements. AquaFarm is primarily based on mechanistic
principles, with empirical components added as necessary to support practically
oriented design and management analyses for a wide range of users.
A second area of useful literature were studies that provided methods and results
of aquaculture production trials that could be used for the calibration and
validation of unit process and fish performance models. These studies consisted
mainly of technical papers, plus a few published databases, and are cited as they are
used in this paper. Finally, papers reporting software development for end users
have introduced computerized analysis tools and decision support systems to
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Aquacultural Engineering
23 (2000) 121–179
aquaculture educators, developers, and producers (Bourke et al., 1993; Lannan,
1993; Nath, 1996; Leung and El-Gayar, 1997; Piedrahita et al., 1997; Schulstad,
1997; Wilton et al., 1997; Stagnitti and Austin, 1998). These reported software
applications range widely in their internal mechanisms and intended purpose. The
software POND (Nath et al., 2000) is most similar to AquaFarm and some
program modules have been jointly developed.
In the development of AquaFarm, it was desired to maintain a practical balance
between the responsibilities required from users and the analytical capacity pro-
vided by AquaFarm. These objectives are somewhat opposed, and a considerable
level of user responsibility was found necessary to achieve desired levels of analysis.
User responsibilities required in the use of AquaFarm consist of facility specifica-
tions, model parameters, and decisions regarding alternative facility designs and
management strategies. Facility specifications include items such as facility location
(for generated climates) or climatic regimes (for file-based climates), source water
variables, components and configurations of water transport, water treatment, and
fish culture systems, management strategies, and production objectives. While
approximate environmental conditions, typical facility configurations, and typical
management strategies can be provided by AquaFarm, it is not possible to avoid
user responsibility for these site-specific variables. In contrast, model parameters for
passive unit processes (e.g. passive heat and gas transfer and biological processes)
are ideally independent of site-specific conditions, given the use of sufficiently
developed models. Validated, default values are provided for all parameters.
However, due to the necessity of simplifying assumptions and aggregated processes
in aquacultural modeling, model parameters may be dependent on site-specific
conditions to some degree (Svirezhev et al., 1984). Thus, model parameters for
passive unit processes have been made user accessible for any necessary adjustment.
Finally, while the purpose of AquaFarm is to support design and management
decisions, these decisions must still be made by the user. As a result, some level of
user responsibility cannot be avoided regarding the underlying processes impacting
system performance and implications of alternative decisions on facility perfor-
mance and economics. Possible methods to alleviate user responsibilities are
discussed in the conclusion to this paper.
AquaFarm was developed to support a wide range of extensive and intensive,
fishery-supplementation and food-fish aquaculture facilities, and a wide range of
user perspectives (e.g. educators, developers, and producers), within a single soft-
ware application. Differing analytical needs of these various systems and users have
been addressed through an adaptable user interface. An alternative strategy would
have been the development of separate software applications for each major type of
aquaculture, type of user, and user knowledge level. The development approach
used was chosen to avoid requirements for redundant programming, given the large
overlap in analytical methods, simulation processing, graphical interface, and data
management requirements over the range of aquaculture system types and analyti-
cal perspectives. In addition, some aquaculture system types are not easily catego-
rized, for example intensive tank-based recirculation systems characterized by
significant levels of phytoplankton and semi-intensive pond-based systems using
recirculation systems for phytoplankton management.
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AquaFarm is a stand-alone computer application, programmed in Borland
C++
®
and requiring a PC-based Microsoft Windows
®
operating environment.
The C++ computer language was chosen for its popularity, portability, availabil-
ity of software developer tools, compatibility with the chosen graphical user
interface (Microsoft Windows
®
), and support of object oriented programming
(OOP; Budd 1991; Nath et al., 2000). According to OOP methods, all components
of AquaFarm are represented as program ‘objects’. These objects are used to
represent abstract entities (e.g. dialog box templates) and real world entities (e.g.
fish rearing units) and are organized into hierarchical structures. Each object
contains data, local and inherited methods, and mechanisms to communicate with
other objects as needed. The modular, structured program architecture supported
by OOP is particularly suited to the development of complex system models such as
AquaFarm.
3. AquaFarm design procedure
AquaFarm supports interactive design procedures, utilizing progressive levels of
analysis complexity, simulation based analyses, and iterative design refinement
(James, 1984e). These procedures are used to develop design and management
specifications, until production objectives are achieved or are determined to be
biologically or practically infeasible. This decision making process is user directed
and can be used to design new systems or determine production capacities for
existing systems. The analysis resolution level (Table 1) is set so that the complexity
of design analyses is matched to levels appropriate for the type of aquaculture
system and stage of the design procedure. This is accomplished by user control over
the particular variables and processes considered in a given simulation. For
example, dissolved oxygen can be ignored or modeled as a function of one or more
sources and sinks, including water flow, passive and active gas transfer, fish
consumption, and bacterial and phytoplankton processes. Major steps of a typical
design procedure are listed below and flow charted in Fig. 1. A summary of input
and output data considered by AquaFarm is provided in Table 2.
1. Resolution. An analysis resolution level is selected that is compatible with the
type of facility and stage of the design procedure.
2. Specification. Facility environment, design, and management specifications are
established, based on known and tentative information.
3. Simulation. The facility is simulated to generate facility performance summaries
and operation schedules over the course of one or more production seasons.
4. Evaluation. Predicted facility performance and operation are reviewed and
evaluated, using summary reports, tabular and graphical data presentation,
management logs, and enterprise budgets.
5. Iteration. As necessary, facility design, management methods, and/or produc-
tion objectives are adjusted so that production objectives and other desired
results are achieved (go to step 1 or 2).
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Table 1
Variables and processes considered by AquaFarm for analysis resolution levels (ARL) I–V
a
ARL Facility unit and fish lot processesWater quality and loading variables
Day length (h)
b
Weather, water mechanics andI
Temperature (°C)
b
stratification, water and salinity mass
Salinity (ppt)
b
balances, and passive/active heat
Water flow rate (m
3
day
−1
) transfer.
Hydraulic loading (m
3
m
−2
day
−1
)
d
Fish survival, development andHydraulic retention (d
−1
)
b
growth, feeding on prepared feeds,Water velocity (cm s
−1
and fish body lengths s
−1
)
b
and natural fish productivity basedFish biomass density (kg m
−3
)
b
on fish density.Fish biomass loading (kg m
−3
day
−1
)
b,e
Feed loading (kg day
−1
per m
3
day
−1
=kg m
−3
)
b,e
II Dissolved oxygen (DO, mg O
2
l
−1
and% saturation)
b
Oxygen mass balances based on
water flow, passive and activeCumulative oxygen consumption (COC, mg O
2
l
−1
)
b
transfer, and fish metabolism.
Mass balances for listed compounds,III pH (NBS)
b,c
including acid-base chemistry, gasTotal alkalinity (mg CaCO
3
l
−1
)
c
Hardness (mg CaCO
3
L
−1
)
c
transfer, solids settling, soil
Dissolved nitrogen (DN, mg N
2
l
−1
) processes, filtration of solids and
Total gas pressure (% saturation and mm Hg)
b
compounds, compound addition,
bacterial processes, and fishCarbon dioxide (DC, mg CO
2
l
−1
and% sat.)
b,c
Dissolved inorganic carbon (DIC, mg C L
−1
)
c
metabolite excretion
Total ammonia nitrogen (TAN, mg N l
−1
)
c
Unionized ammonia (mg NH
3
-N l
−1
)
b,c
Nitrite (mg NO
2
-N l
−1
)
b,c
Nitrate (mg NO
3
-N L
−1
)
b
Dissolved inorganic nitrogen (DIN, mg N l
−1
)
Dissolved inorganic phosphorous (DIP, mg P l
−1
)
c
Generic fish treatment chemical (mg l
−1
)
b
Generic water treatment chemical (mg l
−1
)
b
Particulate inorganic and organic solids (mg l
−1
, dw)
b
Settled inorganic and organic solids (g m
−2
, dw)
IV Phytoplankton processes included inPhytoplankton density (g C m
−3
and mg chl-a m
–3
)
mass balances and natural fishSecchi disk visibility depth (cm)
productivity
Total borate (mg B L
−1
)
c
V Mass balances for listed compounds
Total silicate (mg Si L
–1
)
c
Total sulfate (mg S L
–1
)
c
Total sulfide (mg S L
–1
)
b,c
a
Variables and processes considered at each level include those in lower levels. Processes at each level
can be individually selected.
b
Water quality and loading variables to which fish performance can respond.
c
Compounds participating in acid-base and precipitation-dissolution chemistry.
d
Hydraulic loading is based on water surface area and flow rate.
e
Fish and feed loading are based on water flow rate.
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Fig. 1. Flowchart of the decision support procedure used by AquaFarm for aquaculture facility design
and management planning, including progressive analysis levels and iterative procedures of facility and
management specification, simulation, and evaluation.
In conjunction with progressive analysis resolution, a design procedure can be
staged by the level of scope and detail used in specifying physical components and
management strategies of a given facility. For example, design analyses can start
with fish performance, using simplified facilities and a minimum of water quality
variables and unit processes. When satisfactory results are achieved at simpler
levels, increased levels of complexity for modeling facility performance and man-
agement strategies are used. By this approach, the feasibility of rearing a given
species and biomass of fish under expected environmental conditions is determined
before the specific culture system, resource, and economic requirements necessary to
provide this culture environment are developed. Major stages of a typical design
procedure are listed below, but this progression is completely user controlled.
1. Production trajectory. Fish development, growth, and feeding schedules for
broodfish maturation, egg incubation, and/or fish growout are determined based
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Aquacultural Engineering
23 (2000) 121–179
on initial and target fish states. Environmental quality concerns are limited to
water temperature and day length, and unit processes are limited to water flow
and heat transfer.
2. Production scale. Required water area and volume requirements for fish rearing
units are determined, based on initial and target fish numbers, management
methods, and biomass density criteria. Natural fish productivity, if considered,
is a function of fish density only.
3. Biomass support. Based on fish feed and metabolic loading, facility water
transport and treatment systems are constructed to provide fish rearing units
with required water flow rates and water quality. The particular variables and
unit processes considered depend on the type of facility. Natural fish productiv-
ity, if considered, is a function of fish density and primary productivity.
4. Management schedules. Fish and facility management methods and schedules
are finalized, including operation of culture systems, fish lot handling, and fish
number, weight, and feeding schedules.
5. Resource budgets. Resource and enterprise budgets are generated and reviewed.
Table 2
Summary of input specification and output performance data considered by AquaFarm
Input specification data
Possible adjustment of parameters for passive physical, chemical, and biological unit processes and
fish performance models
Facility location (or climate data files), optional facility housing and controlled climate, and water
quality and capacity of source water(s)
Configuration of facility units for facility water transport, water treatment, and fish culture systems
Specifications of individual facility units, including dimensions, elevations and hydraulics, soil and
materials, housing, and water transport and treatment processes
Fish species, fish and facility management strategies, and production objectives (target fish
weights/states and numbers at given future dates)
Unit costs for budget items and additional budget items not generated by AquaFarm
Output performance data
Fish number and development schedules for broodfish maturation and egg incubation
Fish number, weight, and feed application schedules for fish growout, including optional
consideration of fish weight distributions within a fish lot
Fish rearing unit usage and fish lot handling schedules
Tabular and graphical compilations of time-series data for fish performance variables, reported on
a fish population and individual fish lot basis, including fish numbers and state, bioenergetic and
feeding variables, and biomass loading and water quality variables
Tabular and graphical compilations of time-series data for facility performance variables, reported
on a facility and individual facility unit basis, including climate, water quality, fish and feed
loading, water flow rates and budgets, compound budgets, process rates, resource use, waste
production, and water discharge
Fish production reports, resource use summaries, and enterprise budgets
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Fig. 2. Overview of the software architecture and program components that comprise AquaFarm (see
Table 3 for facility unit descriptions). Connecting lines denote communication pathways for method and
data access.
4. AquaFarm architecture and components
AquaFarm consists of six major components: (1) graphical user interface; (2)
data manager; (3) simulation manager; (4) domain experts; (5) facility components;
and (6) facility managers (Fig. 2). The first three of these are specific to AquaFarm
while the last three represent real-world entities. Domain experts provide expertise
in various knowledge domains and include an aquatic chemist, aquacultural
engineer, aquatic biologist, fish biologist, and enterprise accountant. Facility com-
ponents represent the physical facility and include facility units, resource units, fish
stocks, fish populations, and fish lots. Facility managers are responsible for facility
management tasks and production scheduling and include a physical plant manager
and fish culture manager.
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4
.
1
.User interface and data management
The user interface is typical of window based software, providing a hierarchical
menu system and selectable viewing windows that support general-to-specific
interface navigation. Types of windows include tool bars, facility maps, specifica-
tion sheets, output tables and graphs, management schedules, budget spreadsheets,
and user help screens. An example of the interface is shown in Fig. 3 (see
recirculation systems under AquaFarm application for additional explanation).
According to the type of facility under design and analysis resolution level in use,
user access to windows, controls, and data fields is limited to relevant items. Data
files are used to store and retrieve user projects, with specification and review
mechanisms for data files provided within AquaFarm. Output data can be exported
in delimited format for use in computer spreadsheets.
Fig. 3. Example window of AquaFarm’s user interface, showing the main menu and a facility map. The
example shown is a water recirculation facility, consisting of fish rearing units supplied by a single
recirculation loop with a water makeup supply and water/solids discharge (see Table 3 for key to facility
unit names).
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23 (2000) 121–179
4
.
2
.Domain experts
Domain experts provide expertise in aquaculture science and engineering in the
form of quantitative methods and models. These methods consist of property,
equilibrium, and rate calculations of physical, chemical, and biological unit pro-
cesses and their rules of application. These methods are used to calculate terms in
facility-unit and fish-lot state equations and to support management analyses. The
documentation required to fully describe these methods is not possible within the
size constraints of this paper. Methods of the aquatic chemist, aquacultural
engineer, aquatic biologist, and fish biologist are summarized in the appendix, and
the enterprise accountant is described below.
4
.
2
.
1
.Enterprise accountant
The enterprise accountant is responsible for compiling enterprise budgets, which
are used to quantify net profit or loss over specified production periods (Meade,
1989; Engle et al., 1997). Enterprise budgets are particularly appropriate for
comparing alternative facility designs, in which partial budgets are utilized that
focus on cost and revenue items significantly influenced by proposed changes.
Additional financial statements (e.g. cash flow and net worth), economic feasibility
analyses (e.g. net present value and internal rate of return), and market analyses are
required for comprehensive economic analyses (Shang, 1981; Allen et al., 1984;
Meade, 1989) but are not supported by AquaFarm.
Cost items (e.g. fish feed) and revenue items (e.g. produced fish) can be specified
and budgets can be summarized according to various production bases, time
periods, and cost types. Item and budget bases include per unit production area, per
unit fish production, and per total facility. Item and budget periods include daily,
annual, and user specified periods. Cost types include fixed and variable costs, as
determined by their independence or dependence on production output, respec-
tively. Fixed costs include items such as management, maintenance, insurance,
taxes, interest on owned capital (opportunity costs), interest on borrowed capital,
and depreciation for durable assets with finite lifetimes. Variable costs include items
such as seasonal labor, energy and materials, equipment repair, and interest on
operational capital.
Enterprise budgets are built by combining simulation-generated and user-spe-
cified cost and revenue items. Simulation generated items are those directly associ-
ated with aquaculture production and therefore predictable by AquaFarm, e.g.
facility units, energy and material consumption, and produced fish and wastes.
AquaFarm determines total quantities for these items (numbers of units), but the
user is responsible for unit costs and other specifications (e.g. interest rates, useful
lives, and salvage values). User specified items include additional cost and revenue
items outside the scope of AquaFarm, e.g. supplies, equipment, facility infrastruc-
ture, and labor. For user specified items that are scalable, the use of unitized cost
bases (i.e. per unit production area or production output) alleviates the need to
re-specify item quantities when working through multiple design scenarios. The
budget is shown in spreadsheet format for the selected budget basis and period,
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Aquacultural Engineering
23 (2000) 121–179
with cost and revenue items totaled and net profit or loss calculated. Net profit
values can also be used as net return values to cost items that are not included in
the budget, e.g. net return to land, labor, and/or management.
4
.
3
.Facility site,facility units,and resource units
An aquaculture facility is represented by a facility site, facility units, and resource
units. A facility site consists of a given location (latitude, longitude, and altitude),
ambient or controlled climate, and configuration of facility units. Facility units
consist of water transport units, water treatment units, and fish rearing units (Table
3). Resource units supply energy and material resources to facility units, maintain
combined peak and mean usage rates for sizing of resource supplies, and compile
total resource quantities for use in enterprise budgets (Table 4). A facility configu-
ration is completely user specified and can consist of any combination of facility
unit types linked into serial and parallel arrays. A facility is built by selecting (from
menu), positioning, and connecting facility units on the facility map. Each type of
facility unit is provided with characteristic processes at construction, to which
additional processes are added as needed. Facility units are shown to scale, in plan
view, color coded by type, and labeled by name. To visualize the progress of
simulations, date and time are shown, colors used for water flow routes denote
presence of water flow, and fish icons over rearing units denote presence of fish as
they are stocked, removed, and moved within the facility.
4
.
3
.
1
.Facility-unit specifications
Facility unit specifications include housing, dimensions and materials, and ac-
tively managed processes of water transport, water treatment, and fish production.
The purpose of these specifications is to support facility unit modeling. Individual
unit processes and associated specifications can be ignored or included, depending
on user design objectives and analysis resolution level. Default facility unit specifi-
cations are provided during facility construction, but these variables are highly
specific to a particular design project and therefore accessible. Managed (active)
processes of water transport, water treatment, and fish production are operated
according to the specifications of individual facility units, in addition to manage-
ment criteria and protocols assigned to facility managers. Water quality is specified
for water sources, including temperature regimes, gas saturation levels, optional
carbon dioxide and calcium carbonate equilibria conditions, and constant values
for the remaining variables. For soil lined facility units, soils are indirectly specified
through given water seepage and compound uptake and release rates.
Facility units can be housed in greenhouses or buildings, with controlled air
temperature, relative humidity, day length, and light intensity (solar shading and/or
artificial lighting). Facility units can be any shape and dimensions, constructed from
soil or materials, and any elevation relative to local soil grade. Top, side, and/or
bottom walls can be constructed from a variety of structural, insulating, water
impermeable, and cage mesh materials. Hydraulic specifications include facility unit
elevations and slope, water flow type (basin, gravity, cascade, or pressurized), water
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23 (2000) 121–179
Table 3
Facility unit types and primary processes
a
Primary processesFacility unit type
Water transport units
Facility influent flow capacity and water qualitySource (SRC)
Discharge (DCH) Facility effluent cumulative water and compound discharge
Water pump performance and power/air consumption forPump (PMP)
centrifugal and airlift pumps
Pressurized and gravity water flow mechanicsPipe (PIP)
Gravity water flow mechanicsChannel (CHN)
Blender/splitter (ABS) Flow stream blending for temperature and salinity adjustment
and flow stream division for specialized management (e.g.
recirculation) (active)
Flow stream blending, division, and redirection (passive)Flow node (PBS)
Water treatment units
Water basin/tank (BSN/TNK) Water retention for head and sump tanks and a variety of
water treatment processes
Gas exchanger (GAS) Water aeration, degassing, and oxygenation in air-contact
units and pure oxygen absorbers, including packed/spray
columns, water surface aerators, submerged venturis and
diffusers, and oxygenators
Heat exchanger (HCX) Water heating and chilling using inline and in-tank, elements
and exchangers
Mechanical filter (FLT) Filtration of particulate solids, including granular media
filters, porous media filters, micro screens, particle separators
(hydroclones, swirl separators), and foam fractionators
Chemical filter (CFL) Filtration of ammonium by ion-exchange (clinoptilolite) and
chlorine by adsorption (granular activated carbon)
Biological filter (BIO) Bacterial conversion of nitrogen compounds by fixed-film
nitrification or denitrification biofilters (trickling, RBC,
expandable granular media, and fluidized bed). Wetland and
hydroponic units for nutrient uptake (DIN and DIP) and
retention of particulate solids.
Compound supplier (CHM) Addition of water treatment compounds for water
conditioning, nutrient supply, disinfection, and fish treatment
Fish rearing units
Broodfish maturation: biomass, feed, and metabolic loadingBroodfish holding (BRU)
Egg incubator (ERU) Egg incubation: biomass and metabolic loading
Growout rearing (FRY-, FNG-, Fish growout: biomass, feed, and metabolic loading (default
types: fry, fingerling, and juvenile/adult)J/A-GRU)
a
Names in parentheses are abbreviations for facility mapping. Processes in addition to primary
processes can be considered depending on facility unit type (e.g. inclusion of gas exchangers and
compound suppliers in fish rearing units or hydraulic solids removal in a water splitter)
flow direction (longitudinal, lateral, or circular), and configuration of influent and
effluent ports. The hydraulic integrity and practicality of gravity and pressurized
flow configurations specified by the user are verified prior to simulation, with help
messages provided as required.
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4
.
3
.
2
.Facility-unit state 6ariables
In addition to facility unit specifications, which are fixed variables for a given
simulation, facility units are defined by dynamic state variables that vary over the
course of a simulation (Table 1). Most of these variables correspond to those
typically used. Fish and feed loading variables and cumulative oxygen consumption
(Colt and Orwicz, 1991b) are included to support analyses that use these variables
as management criteria and for reporting purposes. Alkalinity and pH relationships
include consideration of dissolved inorganic carbon (carbon dioxide and carbon-
Table 4
Resources produced and consumed by an aquaculture facility that can be calculated by AquaFarm
a
Resource type Resource description (given units reported per day, per year, or per production
season)
Total numbers of each type of facility unit and quantities of materials used (m
2
Facility units
or m
3
): metal, wood, concrete, fiberglass, PVC, PE, ABS, acrylic, glass, shade
tarp, and insulation
Supply water Source water consumption (m
3
)
Discharge water Cumulative discharge water (m
3
) and quantities of solids, DIN, DIP, BOD, and
COD (kg)
Waste sludge (kg, dw), spent filter media (m
3
), and dead fish (kg)Waste materials
Energy consumed by facility lighting, water pumps, gas and heat exchangers,Energy
UV sterilizers, etc., expressed as electrical power (kWhr) or energy equivalent of
liquid fuels (L; gasoline, methanol, and diesel) or gas fuels (m
3
; natural gas,
propane, and methane)
Compressed air for air-lift pumps, column aerators (optional), air diffusers, andCompressed air
foam fractionators (m
3
; equivalent energy as kWhr for air compression and
delivery)
Water treatment Compounds added to water for water treatment (kg): (1) Inorganic and organic
compounds fertilizers (user specified composition), (2) pH and alkalinity adjustment
compounds (carbon dioxide, nitric, sulfuric, and phosphoric acid, sodium
hydroxide, sodium bicarbonate and carbonate, agricultural limestone, and
hydrated and burnt lime), and (3) pure oxygen, sea salt, and various
user-defined fish/egg treatment, water conditioning, and water disinfection
compounds
Filter media for mechanical, chemical, and biological filters (m
3
): sand, expandedFilter media
plastic, plastic beads, gravel/rock, fabric, clinoptilolite, granular activated
carbon, and hydroponic and wetland materials. Quantities include original and
replacement media, the latter based on the allowed number of regeneration
cycles
Prepared fish feeds (kg): larval, flake, mash, pellet sizes 0.5 to 10.0 mm, andFish feed
broodfish feeds
Stocked and Broodfish, eggs, and growout fish (number, kg) input and output by the facility
produced fish
To assist specification of required labor, the enterprise budget provides: (1) perLabor
unit production area and per unit fish production cost bases; (2) total time of
fish culture (days); and (3) numbers of management tasks completed for process
rate adjustments and fish feeding and handling events
a
Additional facility infrastructure, equipment, supplies, and labor resources are the responsibility of
the user and are specified at the facility enterprise budget.
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ates) and additional constituents of alkalinity (conjugate bases of dissociated acids).
Constituents of dissolved inorganic nitrogen include ammonia, nitrite, and nitrate,
and dissolved nitrogen gas can be considered. Dissolved inorganic phosphorous is
considered equivalent to soluble reactive phosphorous (orthophosphate) and con-
sists of ionization products of orthophosphoric acid (Boyd, 1990). For simplicity,
other dissolved forms of phosphorous are not considered and inorganic phospho-
rous applied as fertilizer is assumed to hydrolyze to the ortho form based on given
fertilizer solubilities. Nitrogen and phosphorous are variable constituents of organic
particulate solids, released in dissolved form when these solids are oxidized. Fish
and water treatment chemicals are user-defined compounds that may be used for a
variety of purposes, such as control of fish pathogens, water disinfectants and
compounds present in source waters (e.g. ozone and chlorine), and water condition-
ing (e.g. dechlorination). Borate, silicate, and sulfate compounds can have minor
impacts on acid-base chemistry, especially for seawater systems, but can normally
be ignored.
Particulate solids are comprised of suspended and settleable, inorganic and
organic solids (expressed in terms of dry weight, dw; live phytoplankton not
included). Suspended inorganic solids (clay turbidity) are considered in order to
account for their impact on water clarity (expressed as Secchi disk visibility), which
is a function of total particulate solid and phytoplankton concentrations. Settleable
inorganic and organic solids originate from various sources, e.g. in/organic fertiliz-
ers, dead phytoplankton, uneaten feed, and fish fecal material. Settling rates and
carbon, nitrogen, and phosphorous contents of these solids depend on their sources.
Settled solids originate from combined inorganic and organic settleable solids, and
their composition varies in response to their sources.
4
.
3
.
3
.Facility-unit processes
Physical, chemical, and biological mass-transfer processes and associated com-
pound sources and sinks that can occur in facility units are listed in Table 5. In
addition, water flow mechanics and heat transfer are represented by energy transfer
processes. Methods used to model these mass and energy transfer processes (unit
processes) are summarized in Appendix A. Unit processes can be individually
selected for consideration, depending on user design objectives and analysis resolu-
tion level. Unit processes can be passive, active, or both passive and active, and are
simulated accordingly. Examples of passive processes are water surface heat and gas
transfer, bacterial processes, and primary productivity. Passive processes may be
uncontrolled or indirectly controlled, e.g. primary productivity can be indirectly
managed through the control of nutrient levels. Actively managed processes are
directly controlled to maintain water quantity and quality variables at desired
levels. Examples of active processes are water flow rate, heating, aeration, solids
filtration, and compound addition. Air-water gas transfer of a fish pond is an
example of a combined passive-active process, in which aeration is used in response
to low oxygen levels but passive air-water gas transfer is also significant. Generally,
in the context of this discussion, passive processes are defined by model parameters
and active processes are defined by facility specifications.
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Table 5
Presence of sources (added: +) and sinks (removed: −) of the listed compounds for the physical, chemical, and biological mass transfer processes
occurring in facility units
a
Facility unit processes
b
Compound
FLT CHM SOL SST OXD NIT DNT NPP FSM FSCDIFFLO CMP
00−0−− 0+− 0+/−DO +/− +
0 000+0/−00DN 000+/−+/−
00Salinity 0+/− 000 000+00
+/− 00− + +/−+/− ++ 00Alkalinity +/− −
+/−+/− 0 000 00 0 00+0Hardness
+/−+/− +/− 0+− +− + 0+/− + 0DIC
+/− 0+− 0−0+TAN 0−+–+/−
Nitrite +/−+/− 00+/− 00 0 000−0
+/− 0++ −−0++/− 0Nitrate −+0
0+/− +/− 0+00−+ 00 +−DIP
0+/− 0−− 0−+ + −0+−Particulate solids
0+− 0−000Settled solids −0000
0 000Phytoplankton 0+/− + 0−00−0
0 000 00−0+0−Treatment chem. +/− −
0+/− + 000 00 0 0−00Sulfide
00 0 000 00 0 00B, Si, S (sulfate) 0+/−
a
See Table 1 for definitions of compound names. Use of ‘0’ denotes absence of mass transfer or lack of consideration by AquaFarm.
b
FLO, influent (+) and effluent flow (−) (also water seepage and precipitation, see text); DIF, passive and active, air-water gas diffusion (DIC as DC
and TAN as unionized ammonia); CMP, compound addition to water; FLT, mechanical, chemical, and hydroponic/wetland biological filters (other
biological filters under NIT and DNT); CHM, calcium carbonate dissolution (+) and precipitation (−) and decay of treatment chemicals; SOL, soil release
(+) and uptake (−); SST, solids settling (in/organic particulate solids; no settling of live phytoplankton); OXD, heterotrophic bacterial processes; NIT,
nitrification bacterial processes (passive and biological filters); DNT, denitrification bacterial processes (passive and biological filters); NPP, phytoplankton
processes for NPP\0 (if NPPB0, reverse signs). Alkalinity is removed for TAN uptake and added for nitrate and DNuptake. DN use depends on presence
of blue-green algae and DIN levels. Dead phytoplankton become particulate organic solids; FSM, fish metabolic processes, compound excretion (+) and
consumption (−); FSC, fish consumption of endogenous food resources.
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In addition to compounds, the water volume contained by a facility unit is
subject to mass transfer, including influent and effluent flow, seepage infiltration
and loss, precipitation and runoff, and evaporation. Compound transfer via water
transfer are based on the assumptions that seepage water constituents are compara-
ble to the bulk water volume, precipitation water is pure other than dissolved gases,
and evaporation water has no constituents. Settled solids accumulate as a function
of contributing particulate solids and settling rates, their lack of disturbance
(scouring), and incomplete bacterial oxidation. The accumulation of settled solids
can remove significant quantities of nutrients and oxygen demand and provide local
anaerobic conditions that support denitrification. Settled solids can be removed by
periodic manual procedures (e.g. rearing unit vacuuming and filter cleaning) or
continuous hydraulic procedures (e.g. dual-drain effluent configurations).
Facility unit differential equations are based on completely mixed hydraulics
(James, 1984a; Tchobanoglous and Schroeder, 1985). While plug-flow hydraulics
characterize certain types of facility units, e.g. raceway fish rearing units, the
necessity to consider plug-flow hydraulics with respect to overall simulation accu-
racy is currently being assessed. When water stratification is considered, a facility
unit is modeled as two horizontal water layers of equal depth, and process rates and
state variables associated with each layer are maintained separately. Each of these
layers is completely mixed internally, and layers inter-mix at a rate dependent on
environmental conditions. Possible stratified processes include physical processes
(e.g. surface heat and gas transfer), chemical processes (e.g. pond soils), and
biological processes (e.g. primary productivity and settled solid oxidation). Possible
stratified water quality variables include temperature, dissolved gases, pH and
alkalinity, nitrogen and phosphorous compounds, and organic particulate solids.
For simplification, phytoplankton are assumed to maintain a homogenous distribu-
tion over the water column.
4
.
3
.
4
.Water transport units
Water transport units are used to contain, blend, divide, and control water flow
streams (Table 3). Water transport units are installed as necessary to adequately
represent water transport systems and determine flow rate capacity limits and pump
power requirements. To simplify facility construction, pipe fittings (e.g. elbows,
tees, and valves) and short lengths of pipes and channels can be ignored. For clarity
in facility mapping, however, water flow nodes can be used to represent all points
of blending, division, and redirection of water flow streams by pipe fittings and
channel junctions. Any facility unit can have multiple influent and effluent flow
streams. Minor head losses of pipefittings are calculated as a proportion of the
major head losses of associated pipe lengths. Flow control devices for pipes and
channels are assumed to exist, but they are not explicitly defined. Specialized water
blenders and splitters are used for designated purposes, such as water flow blending
for temperature and salinity adjustment and water flow division to achieve desired
water recirculation rates.
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4
.
3
.
5
.Water treatment units
Water treatment units are used to add, remove, and convert water borne
compounds and adjust water temperature (Table 3). Water treatment units typically
specialize in a particular unit process, but processes can be combined with a single
facility unit as desired. Water treatment processes are primarily defined by their
given efficiencies or control levels. Specifications include set-point levels, set-point
tolerances, efficiencies of energy and material transfer, minimum and maximum
allowed process rates, and process control methods.
Process efficiency is the primary control variable for filtration processes that
remove compounds from the water. For mechanical and chemical filters, process
efficiency is specified as percent removal of the given compound per pass of water
through the filter. For biological filters, process efficiency is specified as kinetic
parameters of bacterial processes. For all filters, periodic requirements for media
cleaning (removal of accumulated solids) or regeneration (e.g. clinoptilolite and
granular activated carbon) over the course of a simulation can be accomplished
manually by the facility manager or automatically by the facility unit.
Set-point level is the primary control variable for processes that add compounds
to the water and for temperature adjustment, for which the units used to express
set-point levels are those of the controlled variable. Pond fertilization is managed
with respect to set points for DIC, DIN, and/or DIP. For each process, constant
rate, simple on/off, and proportional (throttled) process control methods can be
used, the latter providing process rates that vary continuously or in discrete steps
over their given operational ranges. Integral-derivative process control can be
combined with proportional control so that the rate of change and projected future
level of the controlled variable are considered in rate adjustments. Proportional and
integral-derivative controls are used to minimize oscillation of the controlled
variable around its set-point level (Heisler, 1984). Process control can be accom-
plished manually by the facility manager or automatically by the facility unit. For
some conditions, for example when both heaters and chillers are present, the
controlled variable can be both decreased and increased to achieve a given set
point. More typically, controlled variables can only be decreased or increased, for
example the addition of a compound to achieve a desired concentration. Set-point
tolerances and minimum and maximum allowed process rates are normally required
for realistic simulations, for example diurnal control of fish pond aerators in
response to dissolved oxygen.
4
.
3
.
6
.Fish rearing units
Fish rearing units can be designated for particular fish stocks (species), fish life
stages (broodfish, eggs, and growout fish), and fish size stages (e.g. fry, fingerling,
and juvenile/adult) (Table 3). This supports movement of fish lots within the facility
based on fish size and management of multiple life stage, multi-species, and
polyculture facilities. Fish rearing units can include most water treatment processes,
e.g. fertilization, liming, and aeration for pond based aquaculture, and can utilize
process control methods as described for water treatment units.
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4
.
4
.Fish stocks,populations,and lots
Production fish are represented at three levels of organization: fish stocks, fish
populations, and fish lots. A fish stock consists of one or more fish populations,
and a fish population is divided into one or more fish lots. A fish stock is a fish
species or genetically distinct stock of fish, identified by common and scientific
names and defined by a set of biological performance parameters. Parameter values
are provided for major aquaculture species and can be added for additional
aquaculture species. Fish populations provide a level of organization for the
management and reporting tasks of related, cohort fish lots. Fish populations are
uniquely identified by their origin fish stock, life stage (broodfish, egg, or growout),
and production year. Broodfish, egg, and growout fish populations from the same
fish stock are linked by life stage transfers, i.e. from broodfish spawning to egg
stocking and from egg hatching to larvae/fry stocking.
Fish lots are fish management units within a fish population. Fish lots are defined
by their current location (rearing unit), population size, and development state. The
latter consists of accumulated temperature units (ATU) and photoperiod units
(APU) for broodfish lots, accumulated temperature units for egg lots, and fish body
weights for growout fish lots. At a point in time, fish lot states are maintained as
mean values and fish weights within a growout fish lot can be represented as weight
distributions (histograms). Variability in fish weights within a growout fish lot can
be due to variability present at facility input, fish lot division and combining, and
variability in fish growth rates due to competition for limited food resources. Target
values for fish lot numbers and states are specified as production objectives or, in
the case of broodfish and egg target states, represent biological requirements. Initial
values for these variables can be user specified, result from life stage transfers, or
result from fish stocking conditions that are required to achieve fish production
objectives. Intermediate fish lot numbers and states are predicted by simulation.
Methods used to model fish survival, development and growth, feeding, and
metabolism are summarized in Appendix A, under the fish biologist domain expert.
4
.
5
.Facility managers
The facility managers are the physical plant manager and the fish culture
manager. Facility managers are assigned: (1) responsibilities and variables to be
monitored; (2) criteria for evaluation of monitored variables; and (3) allowed
responses to correct problems. Facility managers utilize domain experts for adjust-
ing process rates and solving management problems. A management task can be
fully, partially, or not successful, depending on the availability of required facility
resources. The number of possible management responsibilities and responses
increases with analysis resolution and facility complexity. Facility managers per-
form their tasks at a given management time step, so that the desired management
intensity is emulated. Facility managers report problems and responses to manage-
ment logs.
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4
.
5
.
1
.Physical plant manager
Actively managed mass and energy transfer processes of facility units are
controlled by the physical plant manager to maintain water quantity and quality
variables at desired levels, including water flow, heat and gas transfer, and
compound conversion, addition, and removal. Based on facility specifications,
active process rates can be adjusted: (1) manually, to emulate manual tasks of the
physical plant manager (e.g. manual on-demand aeration); or (2) automatically, to
emulate automated process control (e.g. automated on-demand aeration). Manual
management tasks are simulated at the management time step, and automated
management tasks are simulated at the simulation time step. For aquaculture
facilities, water flow rates are based on demands at fish rearing units, as determined
by the fish culture manager. For non-aquaculture facilities, water flow rates are
controlled at water sources, to give constant or varying water flow rates. Water flow
rates can be constrained by source water capacities and by water flow mechanics
and hydraulic loading constraints of facility units. Water management schemes
include: (1) static water management with loss makeup to maintain minimum
volumes; (2) water flow-through with optional serial reuse; and (3) water recircula-
tion at specified water recirculation and makeup rates.
4
.
5
.
2
.Fish culture manager —production objecti6es
The fish culture manager is responsible for maintaining fish environmental
criteria and satisfying fish production objectives. This is accomplished through the
control of water flow and treatment processes, fish feeding rates, and fish biomass
management. These tasks are performed according to assigned management respon-
sibilities, fish handling and biomass loading management strategies, and available
facility resources. Fish production objectives are not achieved if they exceed fish
performance capacity or required facility resources are not available.
Fish production objectives are specified as: (1) calendar dates; (2) fish population
numbers; and (3) fish development states (broodfish and eggs) or weights (growout
fish) at initial fish stocking and target transfer events. Fish transfer events include
fish input to the facility, fish life stage transfers within the facility, and fish
release/harvest from the facility. Alternatively, fish stocking specifications can be
determined by AquaFarm such that target objectives are achieved. Production
objectives are specified as combined quantities for fish populations and are divided
into component values for fish lots. Fish lots within a fish population can be
managed in a uniform manner or individually specified for temporal staging of fish
production. Fish management size stages can be specified for growout lots to allow
assignment of designated rearing units (e.g. fry, fingerling, and on-growing) and
types of fish feed (pellet size and composition) based on fish size.
4
.
5
.
3
.Fish culture manager–en6ironmental criteria
Environmental conditions are monitored at each management time step and
evaluated in relation to management criteria. Variables that can be responded to
include water exchange rate and velocity, fish biomass density and loading rate,
feed loading rate, cumulative oxygen consumption, dissolved oxygen saturation,
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Fig. 4. Management of fish lot stocking, division, combining, and transfer, as based on fish input and
output of the facility, life stage transfers within the facility, and fish management strategies. Fish state
(see text for definitions) of individual fish lots can be maintained as histograms, normal distributions, or
mean values.
carbon dioxide saturation, and concentrations of un-ionized ammonia and particu-
late solids (Table 1). In addition, water temperature, day length, and/or feed
availability can be controlled to achieve desired fish development and growth rates.
Management criteria are based on reported biological criteria for the given fish
species and allowed deviations beyond designated, optimal biological ranges. Bio-
logical criteria are provided and user accessible for major aquaculture species and
may be added for additional aquaculture species. For lower analysis resolution
levels and systems with known capacities, water exchange rate, fish biomass density
and loading rate, and/or feed loading rate can serve as measures of metabolic
loading. Biomass density management can consider critical density thresholds
regarding natural fish productivity and production intensity constraints, in addition
to metabolic support considerations. For fish stocking, biomass density constraints
are used to allocate fish lots among rearing units.
4
.
5
.
4
.Fish culture manager–fish lot handling and biomass management
Fish lot handling events include fish lot stocking, combining, division, and
transfer. Fish lot handling events can occur in response to: (1) fish input to the
facility; (2) high variability in fish state within a fish lot; (3) low or high fish biomass
density; (4) unacceptable biomass loading or water quality conditions; and (5)
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achievement of threshold fish size stages, life stage transfers, and release or harvest
target fish states (Fig. 4). Fish handling and biomass management responsibilities
are defined by the following options.
1. The use of rearing units is prioritized such that minimum overall fish densities
are maintained and either (a) fish lots are never combined or (b) lots are
combined only as required to stock all lots. Alternatively, the use of rearing
units is prioritized such that maximum overall fish densities are maintained
and either (c) lots are combined as required to stock all lots or (d) lots are
combined whenever possible to minimize use of rearing units and maximize
fish densities.
2. If a facility holds multiple fish stocks, then either (a) different stocks are
maintained in separate rearing units (multi-species facilities) or (b) designated
stocks are combined within rearing units (polyculture facilities).
3. Fish lots are divided at stocking events to multiple rearing units as required by
fish density constraints (yes/no). During culture, fish lots are transferred to
smaller rearing units if fish densities are too low (yes/no), and/or fish lots are
transferred whole or divided to larger rearing units if fish density is too high
(yes/no).
4. Based on specified fish biomass loading and water quality criteria, (a) rearing
unit water flow rates are adjusted and/or (b) fish lots are transferred whole or
divided to additional rearing units (adjustment of active process rates of fish
rearing units is based directly on given set-point levels).
5. Growout fish lots are graded and divided during culture to reduce excessive
variability in fish weight (yes/no) and/or remove culls (yes/no). Growout fish
lots are high graded and divided at transfer events to leave low grades for
further culture (yes/no) and/or remove culls (yes/no).
4
.
5
.
5
.Fish culture manager–management intensity and risk
Management intensity and risk levels are established through multiple specifica-
tions, including the type of facility, fish production objectives, fish lot handling
strategies, fish biomass loading relative to maximum capacities, and degree of
production staging and maximization of cumulative production. Based on these
specifications, management intensity can range from simple batch stocking and
harvest practices to staged, continuous culture, high grade harvesting and restock-
ing practices (Watten, 1992; Summerfelt et al., 1993). Management intensity is also
defined by the size of the management time step, allowed variability in growout fish
weights, minimum adjustment increments of process rates, and allowed tolerances
for environmental variables to exceed optimal biological ranges. Management risk
is quantified as a failure response time (FRT, hours) for fish rearing units. FRT is
the predicted time between failure of biomass support processes (e.g. water flow or
in-pond aeration) and occurrence of fish mortality. Management risk is controlled
by establishing a minimum allowed FRT for the facility. If rearing unit FRT values
fall below this minimum, then fish biomass density is reduced, using the given fish
lot handling rules.
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4
.
5
.
6
.Fish culture manager–broodfish maturation and egg incubation
Broodfish maturation is defined by accumulated temperature and/or photo-
period units. Spawning occurs when required levels of these units are achieved, as
defined by species-specific parameters maintained by the fish biologist. Water
temperature and day length can be controlled to achieve desired maturation rates
and spawning dates. Fish population number and spawning calculations account
for female-male sex ratios, egg production per female, and fish spawning charac-
teristics (i.e. once per year, repeat spawn, or death after spawning).
Egg development is defined by accumulated temperature units. Achievement of
development stages (eyed egg, hatched larvae, and first-feeding fry) is based on
temperature unit requirements of each stage, as defined by species-specific
parameters maintained by the fish biologist. Egg handling can be restricted dur-
ing sensitive development stages. Water temperature can be controlled to achieve
desired development rates and first-feeding dates.
4
.
5
.
7
.Fish culture manager —fish growout
Feeding strategies for fish growout can be based on: (1) endogenous (natural)
food resources only; (2) natural foods plus supplemental prepared feeds; or (3)
prepared feeds only. Natural food resources can be managed indirectly by con-
trol of fish densities and maintenance of nutrient levels for primary productivity.
Prepared feeds are defined by their proximate composition and pellet size, and
specific feed types can be assigned to specific fish size stages. Prepared feeds are
applied as necessary to achieve target growth rates, based on initial and target
fish weights and dates and considering any contributions from natural foods. For
daily simulations, prepared feed is applied once per day. For diurnal simulations,
feed is applied according to the specified number of feedings per day and length
of the daily feeding period, which can be specific to fish size stage. In addition,
the impact of feed allocation strategies and application rates on food conversion
efficiency and fish growth variability due to competition for limited food re-
sources can be considered.
5. Facility and management simulation
5
.
1
.Simulation processing
Following the establishment of facility and management specifications, facility
units and fish lots are integrated and facility managers, fish populations, and
resource units are updated over a series of time steps that total the simulation
period. Facility components and managers are classified as simulation objects
at their highest level of hierarchical abstraction in the object oriented pro-
gramming architecture. The simulation of these objects is administered by the
simulation manager. The simulation manager (1) maintains a simulation time
clock; (2) sends update commands to simulation objects based on their time
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steps; and (3) for purposes of numerical integration, maintains arrays of state
variables and finite difference terms for the differential equations of facility units
and fish lots. The simulation manager processes simulation objects in a generic
manner and has no need to be concerned with specific details of individual
objects, e.g. differential equations used to calculate difference terms or the man-
agement protocols used by facility managers.
Manual procedures of the physical plant and fish culture managers are discon-
tinuous, discrete events. Managers respond to update commands over a series of
management time steps by reviewing their assigned responsibilities, responding as
facility resources allow, and logging management problems and completed tasks
to management logs. In contrast, facility units and fish lots consist of continuous
processes, represented by sets of simultaneous differential equations. Facility
units and fish lots are simulated by solving state equations, updating state
variables, and logging state variable and process rate data over a series of
simulation time steps. The state variables and equations used for facility units
and fish lots depend on the analysis resolution level, fish performance methods,
and passive and active unit processes under consideration. At each simulation
step, domain experts are used to calculate property, equilibrium, and process
rate terms used in differential equations and management tasks.
5
.
2
.Deterministic simulation
Simulations performed by AquaFarm are deterministic, in which identical
results are predicted given the same set of input parameters and variable values,
and all parameters and variables are expressed as mean values. Deterministic
simulations can be based on worst, best, and mean case scenarios, however,
as controlled by the use of worst, best, and mean expected values for input
parameters and variables. Stochastic simulations are not currently supported by
AquaFarm and their potential utility to AquaFarm users is under review.
Stochastic simulations require multiple simulation runs (e.g. 30– 100) to generate
probability distributions of predicted state variables, in which selected parameters
and input variables vary stochastically within and between simulations (e.g.
Griffin et al., 1981; Straskraba and Gnauck, 1985; Cuenco, 1989; Lu and
Piedrahita, 1998). For aquaculture systems characterized by stochastic pro-
cesses, the use of deterministic simulations represents a major analytical simplifi-
cation. For example, solar-algae ponds are subject to stochastic climate variables
(solar radiation, cloud cover, and wind speed) and similarly managed ponds
often show high variability between ponds in primary productivity and re-
lated variables. However, the additional complexity of accomplishing and in-
terpreting stochastic simulations is considerable and prolonged computer pro-
cessing times are required. As in most aquacultural modeling studies, it is
assumed that deterministic simulations are useful for facility design and short
and long term management decisions, even when significant stochastic behavior
exists.
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5
.
3
.Numerical integration
Facility unit and fish lot differential equations can be solved by numerical or
analytical methods. Under numerical integration, differential equations are used as
finite difference equations to calculate finite difference terms (unit mass or energy
per time). Related simulation objects are processed as a group, as determined by the
existence of shared variables and simultaneous processes. State variables and finite
difference terms of related simulation objects are collected into arrays at each
simulation step and solved by the simulation manager using simultaneous, fourth-
order Runge– Kutta integration (RK4; Elliot, 1984). RK4 integration is a powerful
numerical integration method, capable of solving complex sets of simultaneous
differential equations. However, RK4 integration may require small time steps, on
the order of minutes to hours, when high rates of energy or mass transfer
characterized by first-order kinetics exist in facility units (e.g. high rates of water
flow, active gas transfer, or fixed-film bacterial processes). In addition, RK4
integration requires four iterations per time step for the calculation of difference
terms and update of state variables. Together, these requirements may result in
excessively long simulation execution times (e.g. 3 min, real time), depending on the
number of simulation objects, length of the simulation period, and computer
processing capacity.
5
.
4
.Analytical integration
Analytical integration methods can accommodate high rate, first-order processes
at large time steps (e.g. 1 day) and can be used to minimize required calculations
and simulation execution times. However, aquaculture facilities are typically char-
acterized by simultaneous processes within and among facility units, and achieve-
ment of analytical solutions normally requires the use of simplifying assumptions.
To explore tradeoffs between mathematical rigor and simulation processing times,
combined numerical-analytical and simplified analytical integration methods were
developed. For combined numerical-analytical integration, difference terms for each
of the four cycles of RK4 integration are calculated using analytical integration.
For simplified analytical integration, differential equations are simplified to a level
where analytical solutions can be attained (Elliot, 1984). By this simplification,
some simultaneous processes are unlinked, and thus simulation objects and the
variables they contain are updated in order of their increasing dependence on other
objects and variables. The simulation order used is facility climate, up to down
stream facility units, and finally fish lots. In addition, variables within a facility unit
are updated in order of increasing dependence on other variables, beginning with
water temperature.
5
.
5
.Management and simulation time steps
The size of the management time step is based on the desired management
intensity, i.e. the time interval between successive, periodic tasks of the facility and
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fish culture managers. The size of the simulation time step is based on the nature
of the aquaculture system and temporal resolution required to adequately capture
system dynamics. Daily simulations (e.g. 1-day time step), for which diurnal
variables and processes are expressed and used as daily means, always represent
some level of simplification at a degree depending on the type of facility and
analysis resolution level. For example, all fish culture systems are at least character-
ized by diurnal fish process, resulting from day-versus-night activity levels and
feeding rates of fish. However, diurnal simulations (e.g. 1-h time step) are required
only when the variability of process rates and state variables within a day period,
and associated management responses, must be considered to adequately represent
the system. For example, diurnal simulations may be used for solar-algae ponds for
high-resolution modeling of heat transfer and primary productivity, and they may
be used for intensive systems for high-resolution modeling of fish feeding and
metabolism. Any consideration of process management within a 24-h period
requires diurnal simulations, e.g. pre-dawn aeration for pond-based systems or
diurnal control of oxygen injection rates for intensive systems. For RK4 integra-
tion, daily simulations may require time steps of less than one day, but variables
and processes are still used as daily means.
6. AquaFarm testing, calibration, and validation
The program code modules comprising AquaFarm were tested, debugged, and
verified to perform according to the previously reported or newly developed
methods from which they were developed. Testing alone was sufficient to validate
data input and output, management, and display tasks, integration procedures for
differential equations, and simulation of facility management. Similarly, the validity
of actively managed processes was largely dependent on given process specifications
(e.g. water treatment efficiencies) and confirmed by direct testing. Finally, Aqua-
Farm was verified to provide full ranges of expected results (dependent variables)
for all types of extensive and intensive aquaculture systems, solely by adjustment of
input parameters and independent variables over their reasonable ranges. In sum,
this testing verified the internal and external consistency of AquaFarm (Cuenco,
1989) and indicated sufficient development of the collected parameters, variables,
and unit processes considered and their combined expression as differential equa-
tions and integrated functions.
Requirements for calibration and validation of the component models (Cuenco,
1989) used in AquaFarm was variable, depending on the nature of these models
and their level of development in the supporting literature. Calibration is the
process of determining values for model parameters (equation coefficients and
exponents) through regression procedures using empirical datasets. Due to the wide
use of mechanistic models in AquaFarm, most parameters have inherent meaning
with respect to the processes they represent and can be directly estimated using
reported values. Validation is the process of testing how much confidence can be
placed on simulation results. Calibration and validation accomplishments to date
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23 (2000) 121–179
are given in Appendix A. For some component models, these accomplishments are
preliminary and/or rely on parameter values from the supporting literature. Com-
pletion of calibration and validation procedures for selected, unit process models is
ongoing, as described in the conclusion to this paper.
7. AquaFarm application
Application of AquaFarm to various aquaculture systems and analyses is demon-
strated in the following examples. For each exercise, site-specific facility variables,
management strategies, and model parameters were entered into AquaFarm. Addi-
tional parameters of unit process models were based on default values provided by
AquaFarm. Simulations were then performed to generate fish culture schedules,
chronologies of facility state variables and processes, and required resources to
achieve fish production objectives. Finally, predicted performance data were com-
pared to empirical data from representative studies in the literature.
Reporting of the specifications and results of these simulation exercises is limited
to overviews, with a focus on core issues of fish performance and dominant facility
processes. The specifications and results presented are not necessarily meant to
represent critical variables, but rather to illustrate the range of detail and analytical
capacities available in AquaFarm. The design procedure presented earlier is not
demonstrated, rather the results of a single simulation are presented for each system
type. Enterprise budgets are not presented, for which unit costs are highly specific
to location and budget formats have already been described. While not shown,
however, any of these examples could use a series of simulations to consider
resource use, management intensity, and budgetary requirements over a range of
fish production levels and alternative design and management strategies.
For all of these exercises, it is emphasized that the accuracy of simulation results
relative to empirically determined results was highly dependent on the accuracy of
site-specific variables and parameters. When simulation results are said to be
‘comparable’ to the referenced studies, it is meant that simulation results were
within the range of reported results and showed similar cause-and-effect behavior
for independent and dependent variables. Conclusions for these exercises include
the caveat that fully comprehensive reporting of methods and results were not
available in the studies used, as is typical in technical papers, requiring the
estimation of some design and management variables.
In these simulation exercises, results showed close agreement between simplified
analytical integration and rigorous numerical (RK4) integration for a variety of
system types, using time steps of 1 day for daily simulations and 1 h for diurnal
simulations. For daily simulations especially, in which state variables (as daily
means) normally change relatively slowly over time, simplifications used to uncou-
ple simultaneous processes so that analytical solutions could be achieved were
clearly supported. Combined analytical-numerical integration was successful in
achieving considerably larger time steps than allowed by purely numerical
integration.
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7
.
1
.Tilapia production in ponds
AquaFarm was applied to the production of Nile tilapia (Oreochromis niloticus)
in tropical (10° latitude) solar-algae ponds. Specifications and results of this exercise
are provided in Table 6 and Figs, 5, 6, and 7. Diurnal simulations were used and
water stratification was considered. Agriculture limestone (calcium carbonate) and
fertilizer were applied to maintain DIC (in terms of alkalinity), DIN, and DIP
nutrient levels for primary productivity. Fertilized ponds received lime and fertilizer
only. Fertilized-fed ponds received lime and fertilizer by the same management
criteria as fertilized ponds, with additional application of pelletized feed as required
to achieve target fish growth rates. Fertilizer consisted of combined chicken manure
and ammonium nitrate, with the latter added to achieve a nitrogen-phosphorous ratio
of 5.0, based on the manure nitrogen and phosphorous contents (Lin et al., 1997).
Predicted water quality regimes and fertilizer and feed requirements were com-
parable to reported values for tilapia production under similar site and management
conditions. As expected, total lime application rates were in the low range of reported
rates (Boyd, 1990; Boyd and Bowman, 1997), for which pond source water had low
alkalinity but soils were assumed to already be neutralized with respect to exchange
acidity (base unsaturation). The nitrogen and phosphorous application rates used
were within reported ranges for tilapia production in fertilized ponds, which range
2.0– 4.0 kg N ha
−1
day
−1
at N:P ratios that range 1:1– 8:1 (Lin et al., 1997). For
fertilized and fertilized-fed ponds, simulated fish growth rates and total production
per hectare, fish density level at the onset of feeding, and required feed application
rates were comparable to reported results (Diana et al., 1996; Diana, 1997; Lin
et al., 1997). Fish production and application of fertilizer and feed were adequately
estimated using a daily time step with no consideration of water stratification.
However, as generally found for solar-algae ponds, diurnal simulations and con-
sideration of stratification were required to estimate extremes in water quality
regimes. Typical diurnal profiles of temperature and dissolved oxygen, as shown in
Fig. 7 for mid summer, were comparable to reported profiles for stratified tropical
ponds (Losordo and Piedrahita, 1991; Piedrahita et al., 1993; Culberson and
Piedrahita, 1994). The maximum divergence in water quality between the top and
bottom layers was controlled by the specified regime of daily-minimum layer mixing
rates.
7
.
2
.Catfish production in ponds
AquaFarm was applied to production of channel catfish (Ictaluras punctatus)in
temperate (30° latitude) solar-algae ponds. Specifications and results of this exercise
are provided in Table 7 and Figs. 8, 9, and 10. Diurnal simulations were used and
water stratification was considered. Single fish stocking and harvest events were used
to simplify this example, rather than the periodic high-grade harvesting and partial
re-stocking methods typically employed for catfish production. Target fish numbers
and weights were specified such that feed application rate increased to a maximum
of 110 kg ha
−1
day
−1
, in order to emulate conditions used in Cole and Boyd
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Table 6
Example application: tilapia production in fertilized and fed ponds
Specifications
Facility Location: 10 N latitude; 10 m elevation
Weather: annual regimes for air temperature, cloud cover, precipitation, and
water mixing index (stratification)
Source water quality: 20 mg l
−1
alkalinity and equilibrium gas
concentrations
Levee type, clay lined ponds, 1.0 ha in area, and 1.0 m average depthCulture systems
Water makeup to replace losses and maintain depth
Pond unit processes used: water budget, passive heat transfer, seasonal water
stratification, passive gas transfer, solids settling, primary productivity,
bacterial processes (organic oxidation, nitrification, and denitrification), soil
processes, and fish processes
Fertilizer composition: chicken manure with ammonium nitrate added to
achieve an N:P ratio of 5.0, with a combined composition of 22.4% N,
4.48% P, and 70% dry wt. organic solids
Feed composition: 35% protein, 1.5% phosphorous
Fertilized ponds (see Table 1 for units): agricultural limestone and mixed
inorganic/organic fertilizer applied to maintain DIC (alkalinity \640), DIN
(\61.0), and DIP (\60.1), beginning 6 weeks prior to fish stocking
Fertilized-fed ponds: additional application of prepared feed as required to
achieve target fish growth rates
Culture period: March 1 to Oct. 1 (215 days)Fish production
objectives
Fish number: 10 000–9000 fish ha
−1
at 10% mortality
Fish weight: 1.0 g at stocking to weight available on Oct. 1 for fertilized
ponds, and 1.0–512 g target weight for fertilized-fed ponds
Results
Fertilized pond applications: total lime applied 1870 kg ha
−1
, fertilizerFish production
applied at a mean rate of 12.3 kg ha
−1
d
−1
(2.8 kg N ha
−1
day
−1
and 0.55
kgPha
−1
day
−1
) over the pond pre-conditioning and fish rearing period
Fertilized-fed pond applications: total lime applied 1900 kg ha
−1
, fertilizer
requirements reduced about 10%, supplemental feed applied at an increasing
rate to a maximum of 65 kg ha
−1
day
−1
over a 70-day end period
Fertilized pond production: 332 g fish at 3000 kg fish ha
−1
on Oct. 1
Fertilized-fed pond production: 512 g fish at 4600 kg fish ha
−1
on Oct. 1,
80% fish feeding index (% maximum ration) to achieve target weight, and
170% food conversion efficiency (based on applied feed only, mortality
included)
Fertilized pond water quality (for fish culture period, including diurnal and
stratification extremes; see Table 1 for units): temperature 22–34; DO
2.8–14.5; pH 7.0–9.5; DC 0.01–7.8; NO
3
0.60–0.74; TAN 0.25–0.53, NH
3
0.01–0.25; phytoplankton 8.5–10.8; NPP −0.5–6.0 (whole column)
Fert.-fed pond water quality (for fish culture period, including diurnal and
stratification extremes; see Table 1 for units): similar to fertilized pond,
except DO 1.6–14.5; pH 6.9–9.5, DC 0.01–10.3
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Fig. 5. Simulated data (1-h time step) for tilapia production in fertilized ponds over a 7-month culture
period. The temperature band represents the diurnal temperature regime. Critical standing crop (CSC,
1600 kg ha
−1
) with respect to natural food resources occurs at the peak FBP and inflection point of fish
growth rate.
Fig. 6. Simulated data (1-h time step) for tilapia production in fertilized and fed ponds over a 7-month
culture period. The temperature band represents the diurnal temperature regime. Critical standing crop
(CSC, 1600 kg ha
−1
) with respect to natural food resources is achieved, followed by a short decline in
FBP until the onset of supplemental feeding.
(1986) and Tucker and van der Ploeg (1993). Aeration was used as required to
maintain bottom-layer dissolved oxygen above a minimum level (30% saturation),
for which aerator specifications were matched to Cole and Boyd (1986). The
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production period, from June 1 year 1 to October 31 year 2 (519 days), included a
fish over-wintering period.
Feed application rates increased over the rearing period in association with
increasing fish biomass density as well as varying with water temperature. Fish
feeding and growth rates were within typical ranges (Tucker, 1985). Predicted water
quality regimes and aeration requirements were comparable to reported values for
catfish production, including aeration timing, maximum power requirement, and
cumulative power use (Cole and Boyd, 1986; Brune and Drapcho, 1991; Tucker and
van der Ploeg, 1993; Schwartz and Boyd, 1994). To match reported aeration
requirements (Cole and Boyd, 1986), accurate specifications were required for
aerator size, standard aerator efficiency, and minimum allowed dissolved oxygen
levels.
7
.
3
.Shrimp production in ponds
AquaFarm was applied to semi-intensive production of marine (penaeid) shrimp
in tropical (10° latitude), fertilized, fed, and aerated solar-algae ponds. Results of
this exercise (not shown) compared well to marine shrimp production studies (Fast
and Lester, 1992; Wyban, 1992; Briggs and Funge-Smith, 1994), including shrimp
growth, aeration requirements, and water quality regimes. For estimating natural
food resources and timing the initiation of prepared feed application, empirically
based critical standing crop (e.g. 100– 300 kg ha
−1
) and carrying capacity shrimp
densities were used without consideration of NPP, given the benthic location and
variety of food resources utilized by shrimp. Pond water exchange rates of 0.0– 30%
Fig. 7. Simulated data (1-h time step) for tilapia production in fertilized ponds, for a few mid-summer
days within the 7-month culture period. Diurnal, stratified profiles of temperature and dissolved oxygen
are shown, for the top layer, bottom layer, and water column mean. Daily water-column turnover occurs
from :00:00 to 09:00 h.
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Table 7
Example application: channel catfish production in ponds
Specifications
Location: 32 N latitude, 100 m elevationFacility
Weather: annual regimes for air temperature, cloud cover, precipitation, and water
mixing index (stratification)
Source water quality: 100 mg l
−1
alkalinity and equilibrium gas concentrations
Culture Levee type, clay lined ponds, 5.0 ha in area, and 1.0 m average depth
Water makeup to replace losses and maintain depthsystems
Pond unit processes used: water budget, passive heat transfer, seasonal water
stratification, passive and active gas transfer, solids settling, primary productivity,
bacterial processes (organic oxidation, nitrification, and denitrification), soil
processes, and fish processes
Aeration: on at B30% and off at \640% DO saturation based on water quality of
bottom water layer, maximum aeration rate 6.25 kW ha
−1
, and aerator SAE 1.2
kg O
2
kWhr
−1
Fish Culture period: June 1, year 1 to Oct. 31, year 2 (518 days)
production Fish number: 12 000 to 10 500 fish ha
−1
at 12.5% mortality
Fish weight: 1.0 g at stocking to 880 g target weightobjectives
Results
80% fish feeding index (% maximum ration)Fish
production 50% food conversion efficiency
9250 kg ha
−1
maximum fish biomass density
110 kg ha
−1
day
−1
maximum feed application rate
Aeration power use: total of 4260 kWhr ha
−1
, for 672 total hours of operation,
ranging from 2 to 7 h per day, over a period of 4 months
Water quality (see Fig. 8 and Fig. 9): DIN averaged 72% TAN and 28% nitrate,
alkalinity 80–100 mg l
−1
, and diurnal NPP −0.4–5.0 g C m
−3
day
−1
(whole
column)
per day were simulated and compared, including impacts on pond water quality,
tradeoffs in relation to aeration requirements, and compound and BOD loading
rates on receiving waters.
Regarding shrimp biomass density constraints with respect to dissolved oxygen,
it has been suggested that while air-water gas exchange limits production of finfish
such as tilapia and catfish, advective transport of oxygen through the water column
to the benthic region limits production of bottom dwelling shrimp (Garcia and
Brune, 1989; Brune and Drapcho, 1991). Simulation results indicated that consider-
ation of this proposed ‘diffusive boundary layer’ in which the shrimp reside, located
in the bottom few centimeters of the water column, was required to achieve
reported aeration rates for shrimp ponds. This boundary layer is not considered in
the two-layer thermal stratification model used in AquaFarm, it acts in addition to
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thermal stratification, and it is present in aerated/mixed ponds where thermal
stratification is broken down. Therefore, it was accounted for by the minimum
dissolved oxygen criterion used for aeration management. By increasing this
Fig. 8. Simulated data (1-h time step) for catfish production in fed ponds, showing the last 7 months of
the 17 month culture period. Bands for water quality variables represent diurnal, stratified regimes, and
top and bottom layers of the water column are shown for temperature and dissolved oxygen. Bottom
bands overlay top bands to a large degree and daily water-column turnover is occurring.
Fig. 9. Simulated data (1-h time step) for catfish production in fed ponds, showing the last 7 months of
the 17 month culture period. Bands for water quality variables represent diurnal, stratified regimes, for
which means of the top and bottom layers of the water column are shown and daily water-column
turnover is occurring (see Table 1 for definitions of variables).
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Fig. 10. Simulated oxygen budget data (1-h time step) for catfish production in fed ponds, for a few days
in late August in the last 7 months of the culture period and in the vicinity of peak feeding and NPP
rates. Diurnal, water column stratification and turnover are occurring, for which top and bottom layers
for NPP and BR are shown. Budget items include passive and active gas transfer (PGT and AGT), net
primary productivity (NPP), bacterial respiration (BR), and fish oxygen consumption.
criterion, the concentration gradient necessary to transfer oxygen into the benthic
boundary layer was provided and aeration power requirements were increased.
7
.
4
.Salmon production in tanks and cages
AquaFarm was applied to Atlantic salmon (Salmo salar) production, including
egg incubation, production of 45.0 g smolts in single-pass, flow-through tanks, and
production of 4.0 kg marketable fish in seawater cages. Specifications and results of
this exercise are provided in Table 8 and Figs. 11 and 12. Egg, smolt, and growout
production stages were linked by their temporal sequence and population numbers,
for which dates and population numbers were given for the input of fertilized eggs
and output of harvested fish. Based on the intermediate target date for first-feeding
fry, egg incubation was controlled by adjusting water temperatures to an increasing
8– 10°C regime using water blending. Smolt and harvest target fish weights were
achieved through control of feed application rates.
This example demonstrates some of the detail that can be used in fish lot
management, but results of multiple fish lots are not shown. Results were compara-
ble to production data given in Laird and Needham (1988). Accurate estimations
for expected source water quality and temperature regimes and assumed water
exchange rates of cages were critical inputs for this exercise, in which unit processes
of smolt tanks and salmon cages were dominated by fish metabolism and water
advection. This example demonstrates the use of biomass densities and water
exchange rates as management criteria. Alternatively, required water flow rates and
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Table 8
Example application: Atlantic salmon production in tanks and cages
Specifications
Facility Location: 57 N latitude, 0 m elevation
Weather: annual regimes for air temperature and cloud cover
Source water quality: annual water temperature regimes, 50 mg l
−1
alkalinity for
freshwater, 100 mg l
−1
alkalinity and 35 ppt salinity for seawater, and equilibrium
gas concentrations
Culture Egg incubators: parallel configuration, water flow rates at 2.0 l min
−1
per 10 000
eggs and 5.0 l min
−1
per 10 000 alevin (hatched fry)systems
Smolt tanks: 10 m
3
cylindrical tanks, parallel configuration, maximum fish density
30 kg m
−3
, and water retention time 30 minutes
Growout cages: 1500 m
3
, cylindrical, seawater cages, maximum fish density 22 kg
m
−3
, and assumed water retention time 1.0 h
Number WeightsStage DatesFish
production
objectives
15 000–12 000 Egg to 0.2 gJan. 21, year 1 to MayEgg to first-feeding fry
1, year 1 (100 days)
Fry to smolt 12 000–6600 0.2–45.0 gMay 1, year 1 to May
1, year 2 (365 days)
45.0–4000 gMay 1, year 2 to Oct. 10 000–8500Smolt to harvest
1, year 3 (520 days)
Egg: 20% mortality
Smolt: 5% cull removal at 0.75 g fish; 5% cull removal at 2.0 g fish; 75%
high-grade for potential yearling smolts at 10.0 g fish; 10% mortality, and 48%
protein feed
Growout: no handling other than harvest; 15% mortality, and 45% protein feed
Results
Each smolt tank was stocked from the output of one egg incubatorSmolt
production Total fish loss due to mortality and low-grade removal required an initial 12 000
fish per tank to achieve a final target smolt density of 30 kg m
−3
70% fish feeding index (% maximum ration) and 67% food conversion efficiency
(includes cull and mortality losses)
Maximum fish respiration rate: 170 mg O
2
kg fish
−1
h
−1
Water quality (see Table 1 for units): DO ]77% sat.; DC 5355% sat.; TAN
50.30; NH3 50.003; pH 7.7–8.2; and particulate solids 52.9
Each cage was stocked with the output of 1.5 smolt tanksCage growout
Total fish loss due to mortality required an initial 10 000 smolts per cage to
achieve a final target fish density of 22 kg m
−3
90% fish feeding index (% maximum ration) and 52% food conversion efficiency
(includes mortality losses)
Water quality (see Table 1 for units): DO \665% sat.; DC B178% sat.; TAN
B0.37; NH3 B0.005; pH 8.0–8.2; and particulate solids B3.5
Total compound loading on supporting water body per 1000 kg fish produced:
680 kg dry wt. solids; 750 kg BOD; 80 kg DIN; and 20 kg DIP
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Fig. 11. Simulated data (1-day time step) for Atlantic salmon smolt production in flow-through tanks
over a 12-month culture period. Values represent daily means (see Table 1 for definitions of variables).
Fig. 12. Simulated data (1-day time step) for Atlantic salmon growout in marine cages over a 17-month
culture period. Values represent daily means (see Table 1 for definitions of variables).
allowed biomass loading rates could have been based on water quality variables
such as dissolved oxygen, COC, carbon dioxide, and un-ionized ammonia.
7
.
5
.Salmon production using serial water reuse
AquaFarm was applied to hatchery production of spring chinook salmon
(Oncorhynchus tshawytscha) utilizing serial raceways, pure oxygen absorbers be-
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tween raceways, and water reuse. Specifications and results of this exercise are
provided in Table 9 and Figs. 13 and 14. The purpose of this example is to
demonstrate the simulation of diurnal fish metabolic rates resulting from feed
application during daylight hours and diurnal temperature oscillations. Such
considerations can be applied to any type of aquaculture system, when it is desired
to account for impacts of diurnal fish metabolism on water quality. Parameters
used for modeling fish feeding and metabolic rates were calibrated using empirical
data for a given week, with the calibrated model then applied to the following week
at the same hatchery.
Results were comparable to production data given in Ewing et al. (1994) and
additional, unpublished, continuous monitoring data from spring chinook
hatcheries in the same region. Fish rearing-unit processes were dominated by fish
metabolism and water advection, a relatively simple modeling exercise. This
example demonstrates the use of diurnal simulations to assess daily peak loading
rates of fish biomass support and cumulative impacts of fish metabolism on water
quality under serial water reuse. This type of exercise can be used to assess impacts
of management variables on water quality, including fish biomass loading, oxygen
injection rates by constant or demand-based process control, and temporal
distribution of feeding events over daylight hours. Based on management tolerance
for short term, sub-optimal water quality, daily peak-mean ratios of fish biomass
support requirements (Colt and Orwicz, 1991b) can then be derived for use in
simulations using daily time steps. Daily peak-mean ratios are applied to
management variables such as water flow rates of fish rearing units.
Table 9
Example application: spring chinook production in raceways
Specifications
Location: 45 N latitude, 370 m elevationFacility
Weather: annual parameters for air temperature and cloud cover
Source water quality: annual temperature regimes, 20 mg l
−1
alkalinity, and
equilibrium gas concentrations
Culture Serial rearing-unit configuration with water reuse
systems Pure oxygen absorbers placed between raceways, with automated oxygen addition
rates based on a 100% saturation set-point
Three 105 m
3
raceways per series, operated at a raceway water retention time of 1
hand6kgm
−3
fish density at the given fish size
Fish Fry to pre-smolt growout: culture period for purposes of this exercise limited to
production June 1–10, with 222 000, 2.5 g fish per raceway on June 1 and using 50% protein
objectives feed
Results
Mean values for 10 day analysis period: 2.9 g fish weight, 6.1 kg m
−3
fish density,Fish
3.7% bw per day feeding rate, 85% food conversion efficiencyproduction
Fish respiration rate: 200–480 mg O
2
kg fish
−1
h
−1
, showing diurnal, sinusoidal
profiles in rates and resulting impacts on water quality
158 D.H.Ernst et al.
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Aquacultural Engineering
23 (2000) 121–179
Fig. 13. Simulated data (smooth lines; 1-h time step) and empirical data (jagged lines; continuous
monitoring) for Pacific salmon hatchery production in raceways, showing a single day (June 1) within
the culture period. Data points shown for feeding represent time of feeding and feeding rates, and an
association between feeding times and peaks in OC are evident (see Table 1 for definitions of variables).
Fig. 14. Simulated data (1-h time step) for Pacific salmon hatchery production in three, serial raceways
(numbered 1, 2, and 3, up to down stream), showing a few days at the beginning of June within the
culture period. Oxygen is added between raceways so that influent DO levels of raceways are equal but
fish metabolites are shown to be accumulating (see Table 1 for definitions of variables).
7
.
6
.Fish production using water recirculation
AquaFarm was applied to the intensive production of rainbow trout (Heinen et
al., 1996), hybrid striped bass (Tuncer et al., 1990; Singh et al., 1997), and tilapia
159D.H.Ernst et al.
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Aquacultural Engineering
23 (2000) 121–179
(Rosati et al., 1997; Twarowska et al., 1997) in semiclosed (e.g. 2.0 system
exchanges per day) and minimal-exchange (e.g. 0.075 system exchanges per day)
water recirculation systems. As described in the listed references, major systems
components included: (1) fish rearing units, including rectangular cross flow and
single and dual drain circular and polygonal tanks; (2) sump tanks and pumps; (3)
water heaters; (4) aerators and oxygenators; (4) carbon dioxide strippers; (6)
particle separators, parallel-tube settling basins, expandable granular media filters
(bead filters), and microscreen filters for solids removal; (7) trickling, fluidized bed,
and expandable granular media biofilters for nitrification; (8) alkalinity control by
addition of various carbonate compounds; (9) water disinfection units; and (10)
settling basins for discharged water/solids. An example facility map is shown in
Fig. 3, for which redundant, parallel water treatment units are used singularly or
together depending on water flow rate. Additional passive processes required to
model these systems included heat transfer under controlled climates, gas transfer,
solid settling, bacterial oxidation of organic solids, and nitrification and
denitrification. AquaFarm was also applied to tilapia and catfish production in
green water (phytoplankton present) recirculation systems (Drapcho and Brune,
1989; Cole et al., 1997; Lutz, 1997; Avnimelech, 1998). These systems varied widely
in design but essentially consisted of intensively fed fish rearing units, coupled with
one or more facility units for growth and/or harvesting of algae, oxidation of
particulate solids, settling and physical removal of particulate solids, gas exchange,
and water transport.
For each of these systems, a facility was constructed according to the supporting
study, using estimated specifications when facility design and management were
not sufficiently reported. Results of these exercises (not shown) were generally
comparable to reported results, including fish production, solid waste production
and composition, consumption of resources (e.g. energy, water, feed, oxygen, and
alkalinity compounds), and water quality regimes. However, comparisons between
simulated and reported results were limited by a lack of sufficient reporting detail
in the studies used. In contrast to extensive systems, simulation results were largely
a function of facility unit specifications (e.g. oxygenators, biofilters, and solid
filters) and were less dependent on parameters of passive unit processes. These
actively managed unit processes are modeled in terms of their given efficiencies.
For example, oxygen absorption efficiencies for oxygenators, nitrification
efficiencies for biofilters, and solid removal efficiencies for solid filters are specified,
rather than calculating these efficiencies from a host of additional facility unit
specifications.
8. Conclusion
8
.
1
.De6elopment status of AquaFarm
The purpose of this paper has been to provide an overview of the components,
methods, and capacities of AquaFarm, a simulation and decision support system
160 D.H.Ernst et al.
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Aquacultural Engineering
23 (2000) 121–179
for aquaculture design and management planning. A comprehensive description
of the methods and application of AquaFarm is available in Ernst (2000b).
Decision support is accomplished through the provision of expertise in a variety
of disciplines and the processing of computationally intensive analyses, as
typically encountered in system-level aquacultural engineering. Due to the
considerable level of work required in the development of AquaFarm, a staged
development approach is being used. The first stage of this development, as
described in this paper, consists of the partitioning of aquaculture systems into
functional components and the flexible recombination of these components into
system-level simulation models and design procedures. Additional development
stages currently in progress consist of ongoing validation concerns, user testing,
and incorporation of user feedback.
The methods and results presented indicate that AquaFarm provides useful
and sufficiently accurate decision support functionality. This conclusion is based
on: (1) the use of published, generally accepted modeling and simulation
procedures; (2) full user access to input parameters and variables and an assumed
level of user responsibility for input data; and (3) the successful completion of
extensive testing and a wide range of simulation exercises. Because AquaFarm
was primarily developed from the existing literature, it is assumed reasonable
that some burden of proof can be placed on this literature. At the least,
AquaFarm supports many of the engineering analyses that would otherwise be
used, with the benefit of computerization of these tasks. However, AquaFarm
will not be widely released until completion of additional validation and user
testing.
8
.
2
.Continued de6elopment of AquaFarm
A number of development tasks are in progress to quantify the degree of
confidence that can be placed on predicted facility performance variables and to
alleviate or assist user responsibilities where possible. Prioritized objectives of these
tasks are to:
1. Complete sensitivity studies and validation procedures for selected component
models and combined models (facility models).
2. Provide pre-designed, exemplary facilities, for a range of aquaculture system
types, that can be used as a starting point for new projects or tutorials for
new users.
3. Establish a base of selected users from aquaculture education, development,
and production. Based on their feedback, assess and improve the capacity of
AquaFarm to address user needs, present reasonable levels of user responsibil-
ity, and provide a navigable interface.
4. Provide interface navigation aids to help guide users through project specifica-
tion, simulation, and evaluation procedures.
5. Provide capabilities within AquaFarm to derive parameters for fish perfor-
mance models from user supplied datasets.
161D.H.Ernst et al.
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Aquacultural Engineering
23 (2000) 121–179
As discussed earlier, the simplifying assumptions and aggregated processes used
in aquaculture modelling make it difficult to derive a single set of parameter values
that provides sufficient simulation accuracy for all culture conditions of a given
aquaculture species. This problem can be addressed by providing capabilities to
utilize user-supplied datasets (e.g. historical fish production and water quality) for
the derivation of site-specific model parameters. Initially, this effort will concentrate
on fish performance, due to its central role in facility design, management, and
resource and enterprise budgets. In addition, AquaFarm is being used to perform
sensitivity studies in order to rank input parameters and variables with respect to
their level of impact on simulation results. This will show where calibration and
validation procedures should be concentrated and where user responsibilities for
accurate input data are most pronounced.
Given the scope and resolution of AquaFarm, required levels of work and
supporting data for calibration and validation procedures are considerable and
present an ultimate constraint to this endeavor. Ideally, these datasets should include
complete descriptions of environmental conditions, system components, manage-
ment protocols, and resulting fish and facility performance variables. Practically,
however, such datasets are not readily available. For intensive, water reuse and
recirculating aquaculture systems, most available research has been conducted on
individual unit processes or system components and calibration and validation
efforts must often proceed at this level. System level studies are available in the
literature, mainly as technical papers, but generally lack sufficient reporting of
methods and results for detailed calibration and validation procedures. In contrast,
for extensive and semi-intensive, pond based aquaculture, publicly available data-
bases are available and their usefulness in the development of pond simulation
models and decision support systems has been demonstrated (e.g. Froese and Pauly,
1996; Piedrahita et al., 1997; Ernst et al., 1997; Ernst and Bolte, 1999; Nath et al.,
2000). In addition, many technical papers available for pond based aquaculture
contain fairly comprehensive reporting of methods and results, given that their scope
can normally be limited to ponds with no need to consider water transport and
treatment systems. However, results from pond studies can also be more difficult to
interpret, given the stochastic nature of these systems, the difficulty of isolating
individual unit processes (e.g. components of oxygen mass balances), and the
difficulty of monitoring site-specific conditions and processes such as pond micro-cli-
mates, soil processes, sediment accumulation, and water seepage.The authors
gratefully acknowledge the support provided by Sea Grant (National Oceanic and
Atomspheric Administration, US Dept of Commerce; project no. R/Aq-42) and the
Bonneville Pwer Adminstration (US Dept. of Energy; project no. DE-FC79-
89BP03024) and indirect support provided
by the Pond Dynamics/Aquaculture Collaborative Research Support Program (US
Agency for International Development).
Appendix A. Domain expert methods
A.
1
.Aquatic chemist
:
methods,application,and 6alidation
162 D.H.Ernst et al.
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Aquacultural Engineering
23 (2000) 121–179
A.
1
.
1
.Physical Properties of Water
A.
1
.
1
.
1
.Methods. Water density and specific weight (Millero and Poisson, 1981),
heat capacity (Millero et al., 1973), vapor pressure (Green and Carritt, 1967),
dynamic and kinematic viscosity (Millero, 1974), and latent heat of vaporization
(Brooker, 1967) are calculated as function of water temperature and salinity.
A.
1
.
1
.
2
.Application. Properties are used in physical process models.
A.
1
.
1
.
3
.Validation. Calculated property values were equivalent to values in the
listed references for temperatures of 0– 40°C and salinities of 0 – 40 ppt.
A.
1
.
2
.Dissol6ed gas equilibria
A.
1
.
2
.
1
.Methods. Equilibria concentrations of nitrogen, oxygen, and carbon diox-
ide gases are a function of water temperature and salinity and gas-phase composi-
tion and total pressure (Colt, 1984). Gas saturation levels are based on equilibria
and existing gas concentrations.
A.
1
.
2
.
2
.Application. Equilibria concentrations are used in gas mass balances. Gas
saturation levels are used for interpreting and reporting water quality.
A.
1
.
2
.
3
.Validation. Calculated equilibria values were equivalent to values in Colt
(1984) for temperatures of 0– 40°C, salinities of 0 – 40 ppt, air and pure-oxygen gas
phases, and full ranges in elevation, barometric pressure, water depth, and hydro-
static pressure.
A.
1
.
3
.Acid-base and precipitation-dissolution chemistry
A.
1
.
3
.
1
.Methods. Equilibrium pH and compound specie concentrations are a
function of total compound concentrations, water temperature, and water salinity
(Snoeyink and Jenkins, 1980; Stumm and Morgan, 1981; Butler, 1982; Fritz, 1985).
Solutions for equilibrium conditions are based on equilibrium, mass balance, and
charge balance equations and presence of a carbon dioxide gas phase and/or
calcium carbonate solid phase, solved by numerical methods. Derivations of these
functions are used to calculate required quantities of acid-base compounds for
alkalinity and pH adjustment. Compounds participating in acid-base and precipita-
tion-dissolution chemistry are listed in Table 1.
A.
1
.
3
.
2
.Application. Equilibria values are used for water quality interpretation and
reporting, ionization fraction terms in mass balance equations, and determination
of pH levels after addition and removal of acid-base compounds and carbon
dioxide. Alkalinity and pH adjustment to specified levels can be used for static or
flowing water.
163D.H.Ernst et al.
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Aquacultural Engineering
23 (2000) 121–179
A.
1
.
3
.
3
.Validation. Calculated equilibria values were equivalent to values in the
listed references for temperatures of 0– 40°C, salinities of 0 – 40 ppt, full ranges of
compound concentrations, and presence of carbon dioxide and calcium carbonate
phases. Alkalinity and pH adjustments using a variety of compounds were ver-
ified. Example problems in the listed references were successfully completed.
A.
2
.Aquacultural engineer
:
methods,application,and 6alidation
A.
2
.
1
.Facility climate
A.
2
.
1
.
1
.Methods. Climate variables include daily mean solar radiation, air tem-
perature, precipitation, wind speed, relative humidity, cloud cover, time of sun-
rise and sunset, day length, and diurnal regimes of solar radiation and air
temperature. Predicted annual and diurnal regimes of climate variables are: (1)
interpolated from user-supplied historical datasets; (2) defined by controlled cli-
mates; or (3) calculated as a function of facility latitude and altitude, seasonal
parameters, and time of year and day (Card et al., 1976; Fritz et al., 1980;
Kreider and Kreith, 1981; Straskraba and Gnauck, 1985; Hsieh, 1986; Nath,
1996).
A.
2
.
1
.
2
.Application. Climate variables are used for heat and gas transfer, water
stratification, water budgets, primary productivity, and fish culture day length.
A.
2
.
1
.
3
.Validation. Generation of historically based and controlled climates was
validated by testing. For calculated climates: (1) times of sunrise, sunset, and day
lengths were equivalent to values in the listed references; (2) solar radiation values
approximated values in the listed references given that sufficiently accurate cloud
cover values were used; and (3) remaining variables corresponded to specified
seasonal parameters.
A.
2
.
2
.Passi6e and acti6e heat transfer
A.
2
.
2
.
1
.Methods. Heat energy transfer modes include solar and long wave radia-
tion, water evaporation and flow, and heat convection-conduction at air-water,
air-wall-water, and heater/chiller-water interfaces. Heat transfer with soil is not
considered. Heat transfer rates are a function of climate variables and facility unit
(1) water volume and flow rate; (2) air-water and air-wall-water surface areas; (3)
wall dimensions and materials; and (4) heat transfer rates of heaters and chillers
(Henderson and Perry, 1976; Welty et al., 1976; Fritz et al., 1980; Heisler, 1984;
Midwest Plan Service, 1987; Creswell, 1993; Nath, 1996).
A.
2
.
2
.
2
.Application. Heat transfer rates are used in heat balances for prediction
of water temperatures and calculation of energy requirements for heaters and chillers.
164 D.H.Ernst et al.
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Aquacultural Engineering
23 (2000) 121–179
Heat transfer rates of each mode are individually quantified and available to the
user as heat transfer budgets.
A.
2
.
2
.
3
.Validation. Example problems for tanks and pipes given in the supporting
references were successfully completed (e.g. Henderson and Perry, 1976; Welty et
al., 1976). Applications to outdoor fish ponds in tropical regions showed good fit
to empirical water temperature data given the use of empirical climate data for
the same period (Nath, 1996). Trial applications to outdoor fish ponds using
calculated climate variables and water stratification showed reasonable agreement
with reported annual temperature regimes.
A.
2
.
3
.Water thermal stratification
A.
2
.
3
.
1
.Methods. Water stratification is modeled using two (top and bottom)
horizontal water layers of equal depth, in which mass and energy transfer pro-
cesses are separately maintained for each layer and occur between layers (e.g. heat
and gas transfer). Daily minimum layer mixing rates (% day
−1
; water mixing
index, WMI) are interpolated from given annual regimes of monthly mean values.
Minimum mixing rates are increased as a function of layer water temperatures
which result from passive heat transfer, and thus daily and seasonal water column
turnover is considered.
A.
2
.
3
.
2
.Application. If water stratification is present, then facility units are mod-
eled as two, inter-mixing water bodies with distinct state variables and unit
processes.
A.
2
.
3
.
3
.Validation. Trial applications to outdoor fish ponds using calcu-
lated climate variables and WMI values of 1.0 (highly stratified) to 24.0 (un-
stratified) showed results comparable to reported temperature and dissolved oxy-
gen depth-time profiles, including profile amplitude, shape, and seasonal changes
(Losordo and Piedrahita, 1991; Piedrahita et al., 1993; Culberson and Piedrahita,
1994).
A.
2
.
4
.Water flow mechanics
A.
2
.
4
.
1
.Methods. Gravity and pressurized flow capacities for facility units and
pump power requirements for pressurized systems are based on facility unit
elevations (slope), dimensions, materials, pump and motor efficiencies, and serial/
parallel configurations (Mott, 1979; Jensen, 1983). Water and air flow rates for
airlift pumps are based on pump depth, lift, and diameter (Castro and Zielinski,
1980; Loyless and Malone, 1998). Facility units can have specific head loss
considerations (e.g. media filters) and/or hydraulic loading constraints (e.g. bi-
ofilters and sedimentation basins).
165D.H.Ernst et al.
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Aquacultural Engineering
23 (2000) 121–179
A.
2
.
4
.
2
.Application. Water flow rate capacities and total dynamic head, net positive
suction head, and energy (or compressed air) requirements of water pumping are
used for water flow modeling, flow rate management, and water pump resource
requirements.
A.
2
.
4
.
3
.Validation. Example problems given in the supporting references were
successfully completed.
A.
2
.
5
.Water budgets
A.
2
.
5
.
1
.Methods. Facility unit water budgets (water mass balances) include influent
and effluent flow rates, seepage infiltration and loss, precipitation and watershed
runoff, and evaporation. Influent flow rate is a management variable, seepage is
user specified, precipitation and evaporation are based on climate variables, and
effluent flow rate is calculated from other water budget terms.
A.
2
.
5
.
2
.Application. Water budgets are used to manage influent flow rates, as
required to maintain water depth (makeup) or overflow rate (exchange), and to
quantify water resource requirements. The various water transfer routes listed
above are considered in heat and compound transfer.
A.
2
.
5
.
3
.Validation. Applications to outdoor fish ponds in tropical regions showed
good fit to empirical water budget data given the use of empirical climate data for
the same period and sufficiently accurate seepage estimates (Nath and Bolte, 1998).
For indoor systems, water budget terms in addition to influent and effluent flow can
normally be ignored.
A.
2
.
6
.Passi6e and acti6e gas transfer
A.
2
.
6
.
1
.Methods. Oxygen transfer coefficients for passive diffusion (gas-liquid
phase diffusion) are a function of water depth, water velocity, and wind speed
(Banks and Herrera, 1977; Rathbun, 1977; Tchobanoglous and Burton, 1991; Boyd
and Teichert-Coddington, 1992). Oxygen transfer coefficients for active diffusion of
air-contact units are a function of energy application rate, standard aeration
efficiency (kg O
2
kWh
−1
), and application conditions (Boyd and Watten, 1989;
Colt and Orwicz, 1991a; Watten, 1994). Transfer coefficients for other gases (listed
in Table 5) are calculated from oxygen coefficients by gas diffusivity transforma-
tions, consideration of air-film versus liquid-film diffusion constraints, and consid-
eration of de/hydration rates for carbon dioxide (Thibodeaux, 1979; Stumm and
Morgan, 1981; Grace and Piedrahita, 1994). For pure oxygen absorbers, gas
transfer rates are based on oxygen absorption efficiency (%), oxygen transfer
efficiency (kg O
2
kWh
−1
), and gas stripping efficiencies for nitrogen and carbon
dioxide (Watten et al., 1991; Watten, 1994).
166 D.H.Ernst et al.
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Aquacultural Engineering
23 (2000) 121–179
A.
2
.
6
.
2
.Application. Gas transfer coefficients and rates are used in gas mass
balances and to calculate power, compressed air, and oxygen requirements of gas
exchangers.
A.
2
.
6
.
3
.Validation. For passive gas transfer, trial applications to exposed water
bodies gave results comparable to reported dissolved oxygen and carbon dioxide
regimes. For active transfer, method validity is largely dependent on given specifi-
cations of air-contact units and oxygen absorbers.
A.
2
.
7
.Solids settling
(
sedimentation
)
A.
2
.
7
.
1
.Methods. Settling of particulate solids is based on water overflow rates (m
day
−1
) and velocities (cm s
−1
) and particle settling velocities (m day
−1
) and
scouring velocities (cm s
−1
) (James, 1984b; Tchobanoglous and Schroeder, 1985;
Chen et al., 1994). A weighted-mean particle settling velocity is used according to
contributing solid sources. Use of open media (e.g. biofilters and parallel tube/
plate clarifiers), flow baffles, and dual-drain effluent configurations (Timmons et
al., 1998) for solids management is accounted for in the specifications of individ-
ual facility units.
A.
2
.
7
.
2
.Application. Solid settling rates are used in solid mass balances and to
quantify accumulation of settled solids in facility units, required solids removal
from facility units, and facility solid waste production.
A.
2
.
7
.
3
.Validation. Method validity depends mainly on the accuracy of particle
settling rates, for which the use of reported values gave reasonable results.
A.
2
.
8
.Solids filtration and fractionation
A.
2
.
8
.
1
.Methods. Filtration and fractionation of particulate solids by various
types of mechanical filters are based on specified solid removal efficiencies (%)
(Tchobanoglous and Schroeder, 1985; Chen et al., 1994; Timmons, 1994). Solids
accumulating in filters are periodically removed, according to solid holding capac-
ities and allowable pressure loss. Airflow rate requirements of fractionators are
based on specified gas-liquid flow rate ratios.
A.
2
.
8
.
2
.Application. Solids filtration and fractionation rates are used in solid mass
balances and to quantify accumulation of filtered solids, required solids removal
from filters, and facility solid waste production.
A.
2
.
8
.
3
.Validation. Method validity depends on the accuracy of given solid
removal efficiencies, which are highly specific to filter design and operation.
167D.H.Ernst et al.
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Aquacultural Engineering
23 (2000) 121–179
A.
2
.
9
.Chemical filtration
A.
2
.
9
.
1
.Methods. Removal of ammonium by ion-exchange and chlorine by
adsorption is based on specified compound removal efficiencies (%) (Liao and
Lin, 1981; Tchobanoglous and Schroeder, 1985). Filter media is periodically
regenerated according to media compound capacity and any accumulation of
solids.
A.
2
.
9
.
2
.Application. Compound filtration rates are used in compound mass balances
and to quantify accumulation of filtered compounds and media regeneration
requirements.
A.
2
.
9
.
3
.Validation. Method validity depends on the accuracy of given compound
removal efficiencies, which are highly specific to filter design and operation.
A.
2
.
10
.Compound addition
A.
2
.
10
.
1
.Methods. Compound addition rates are based on set-point concentrations,
compound purity (%) and solubility (%), and water flow rate (may be static water).
A.
2
.
10
.
2
.Application. Compound addition rates are used in compound mass
balances and to calculate required compound quantities.
A.
2
.
10
.
3
.Validation. Method validity was confirmed by achievement of specified
set-point concentrations for a variety of compounds, water quality conditions, and
static and flowing water.
A.
3
.Aquatic biologist
:
methods,application,and 6alidation
A.
3
.
1
.Soil processes
A.
3
.
1
.
1
.Methods. Soil processes consist of the combined physical, chemical, and
biological uptake and release of compounds (listed in Table 5) across the soil-water
interface (Boyd and Musig, 1981; Boyd, 1982, 1990; Eppes et al., 1989; Berthelson,
1993; Boyd and Bowman, 1997; Szabo and Olah, 1998; Steeby, 1998). Daily mean
compound uptake (% day
−1
) and release (g m
−2
day
−1
) rates are interpolated from
given annual regimes of monthly mean values. Compound transfer due to water
seepage is considered separately.
A.
3
.
1
.
2
.Application. Soil process rates are used in compound mass balances.
A.
3
.
1
.
3
.Validation. Method validity depends on the accuracy of given compound
uptake and release rates, for which empirically based values are available in the
listed references.
168 D.H.Ernst et al.
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Aquacultural Engineering
23 (2000) 121–179
A.
3
.
2
.Bacterial processes
A.
3
.
2
.
1
.Methods. Bacterial processes include heterotrophic oxidation of organic
solids, nitrification of ammonia and nitrite, and denitrification of nitrate (Fritz et
al., 1979; Brune and Gunther, 1981; James, 1984a,d; Fritz, 1985; Tchobanoglous
and Burton, 1991; Malone et al., 1993; Chen et al., 1993; Lu and Piedrahita, 1993;
Wheaton et al., 1994a,b). Bacterial processes can occur in the water column, in
settled solids, and on water-containment and filter-media surfaces. Consumption
rates of primary substrates are a function of temperature, pH, and standard specific
rates (day
−1
generally, and g TAN m
−2
day
−1
or g TAN m
−2
day
−1
ppm TAN
–1
for biofilters), using multiple substrate Michaelis– Menten kinetics. Consumption
and excretion rates of additional compounds are based on metabolic stoichiometry.
Heterotrophic bacteria are assumed to always be at non-limiting biomass densities.
For de/nitrifying bacteria, bacterial response times to changes in substrate loading
rates are considered. Nitrogen fixing blue-green algae (Cyanobacteria) are consid-
ered under phytoplankton processes.
A.
3
.
2
.
2
.Application. Bacterial process rates are used in mass balances for particu-
late and settled organic solids and related metabolic compounds.
A.
3
.
2
.
3
.Validation. Trial applications under various water quality conditions gave
results comparable to reported water quality regimes and reported decay rates of
particulate and settled solids.
A.
3
.
3
.Phytoplankton processes
A.
3
.
3
.
1
.Methods. Phytoplankton is modeled as a single functional group of
combined species (e.g. diatoms, green algae, and blue-green algae). Gross primary
productivity (GPP; g C m
−3
day
−1
) is a function of: (1) phytoplankton density (g
Cm
−3
); (2) maximum specific growth rate (d
−1
); (3) light intensity penetrating the
water surface and column; (4) water temperature and pH; and (5) DIC, DIN, and
DIP using multiple substrate Michaelis– Menten kinetics. Net primary productivity
(NPP;gCm
−3
day
−1
) is a function of GPP and phytoplankton respiration.
Consumption and excretion rates of additional compounds are based on metabolic
stoichiometry, for which DN fixation by blue-green algae (Cyanobacteria) can be
considered. Grazing by zooplankton is not considered and can be accounted for in
the phytoplankton death rate term. (References used include: Steele, 1962; Eppley
et al., 1969; Toetz et al., 1973; Almazan and Boyd, 1978a; Fritz et al., 1979; El
Samra and Olah, 1979; McCarthy, 1981; Stumm and Morgan, 1981; Field and
Effler, 1982; Svirezhev et al., 1984; James, 1984c; Fritz, 1985; Straskraba and
Gnauck, 1985; Lin et al., 1989; Piedrahita, 1990; Piedrahita et al., 1993; Giovannini
and Piedrahita, 1994; Nath, 1996).
A.
3
.
3
.
2
.Application. Phytoplankton process rates are used in mass balances for
phytoplankton, related metabolic compounds, and organic solids (dead phyto-
plankton contribute directly to particulate organic solids).
169D.H.Ernst et al.
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Aquacultural Engineering
23 (2000) 121–179
A.
3
.
3
.
3
.Validation. Trial applications under various climate and water quality
conditions gave results comparable to phytoplankton density and NPP regimes
reported in the literature.
A.
4
.Fish biologist
:
methods,application,and 6alidation
A.
4
.
1
.Fish water quality criteria and performance scalars
A.
4
.
1
.
1
.Methods. Fish water quality criteria consist of specie specific, minimum and
maximum values for tolerance and optimum ranges of water quality variables (Fry,
1947, 1971; Warren and Davis, 1967; Warren, 1971; Brett, 1979; Brett and Groves,
1979; Svirezhev et al., 1984; Cuenco et al., 1985b; Ernst, 2000b). Fish performance
scalars vary from 0 to 100% as water quality variables vary from tolerance extremes
to the optimum region. Scalars are calculated for each variable, using linear,
exponential, and/or polynomial functions, and combined based on their product
(interactive variables) and/or minimum (non-interactive variables). Fish perfor-
mance scalars are applied to broodfish maturation rate, egg development rate, and
fish feeding and growth rates. Benthic culture species (e.g. shrimp) in stratified
rearing units are subject to benthic water quality, otherwise water column mean
values are used.
A.
4
.
1
.
2
.Application. Fish performance scaling is used to account for the impact of
water quality on fish development and growth rates.
A.
4
.
1
.
3
.Validation. Method validity depends on the accuracy of given water quality
criteria and is limited by the simplifying assumptions used.
A.
4
.
2
.Fish mortality
A.
4
.
2
.
1
.Methods. Fish lot mortality is a function of time and a given daily
mortality rate (% day
−1
), assuming exponential decay, for which the mortality rate
is calculated from the expected total mortality for the culture period. For growout
fish, mortality rates can be specific to fish size-stages. Total fish lot mortality occurs
when one or more water quality variables exceed their tolerance range for a period
of 1 day or more.
A.
4
.
2
.
2
.Application. Mortality rates are used to estimate fish population numbers
over the culture period based on initial fish numbers. Fish population numbers are
required to determine fish biomass levels from mean fish weights.
A.
4
.
2
.
3
.Validation. Method validity depends on the accuracy of given mortality
rates.
170 D.H.Ernst et al.
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Aquacultural Engineering
23 (2000) 121–179
A.
4
.
3
.Fish maturation and spawning
A.
4
.
3
.
1
.Methods. Fish sexual maturation is based on accumulated temperature
units (ATU, degree-days) and/or photoperiod units (APU, hour-days) required to
achieve spawning condition, for fish above a minimum size and within required
temperature and day length ranges (Blaxter, 1969; Hoar, 1969; Piper et al., 1986).
A specified female-male sex ratio is used for spawning and egg production per
female is a function of fish size (length or weight). Depending on fish species, fish
can spawn once per year, repeat spawn, or die after spawning.
A.
4
.
3
.
2
.Application. Fish maturation rates are used to schedule broodfish matura-
tion periods and spawning events. Broodfish egg production is used to generate egg
population numbers from broodfish population numbers.
A.
4
.
3
.
3
.Validation. Method validity depends on the accuracy of given maturation
and fecundity parameters.
A.
4
.
4
.Egg incubation
A.
4
.
4
.
1
.Methods. Egg and larvae development is based on accumulated tempera-
ture units (ATU, degree-days) required to achieve major development stages: eyed
egg, hatched larvae, and first-feeding fry (Blaxter, 1969; Piper et al., 1986).
A.
4
.
4
.
2
.Application. Egg development rates are used to schedule egg incubation
periods and handling events.
A.
4
.
4
.
3
.Validation. Method validity depends on the accuracy of given temperature
unit requirements.
A.
4
.
5
.Fish growth
A.
4
.
5
.
1
.Methods. Maximum fish growth rates at maximum feeding rates (at or near
satiation) are a function of fish size, water temperature, water quality (optional),
and feed quality (optional) (Ernst, 2000a). Maximum growth rates are adjusted to
target growth rates by control of feeding rates. Alternative growth models include
the: (1) length growth rate function (Haskell, 1959; Ricker, 1975, 1979; Piper et al.,
1986; Soderberg, 1990, 1992); (2) double-logarithmic specific growth rate function
(Parker and Larkin, 1959; Iwama and Tautz, 1981; Jobling, 1983; Allen et al., 1984;
Jensen, 1985; Weatherley and Gill, 1987; Hepher, 1988); (3) von Bertalanffy growth
function (Ricker, 1975; Hopkins et al., 1988; Hopkins, 1992; Prein et al., 1993;
Froese and Pauly, 1996); and (4) anabolic-catabolic bioenergetic growth function
(Ursin, 1967, 1979; Brett and Groves, 1979; Liu and Chang, 1992; Nath 1996).
A.
4
.
5
.
2
.Application. Fish growth rates are used to generate fish weight schedules.
Weight schedules are combined with population schedules to generate fish biomass
schedules.
171D.H.Ernst et al.
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Aquacultural Engineering
23 (2000) 121–179
A.
4
.
5
.
3
.Validation. The listed methods have been calibrated and validated for
various fish species and calibration procedures have been described (see references).
Reported and newly derived parameters used in trial applications with various fish
species gave results comparable to reported fish weight schedules.
A.
4
.
6
.Natural fish producti6ity
A.
4
.
6
.
1
.Methods. Natural (endogenous) fish productivity (NFP; kg fish ha
−1
day
−1
) is determined by empirically based estimates of NFP as a function of
primary productivity and/or fish biomass density (kg fish ha
−1
), the latter utilizing
‘critical standing crop’ and ‘carrying capacity’ density parameters (McConnell et
al., 1977; Almazan and Boyd, 1978b; Colman and Edwards, 1987; Hepher, 1988;
Schroeder et al., 1990; Knud-Hansen et al., 1991; Diana, 1997; Ernst, 2000a). The
procedure accounts for trends in NFP over a fish culture period, in which
endogenous food resources may be initially high or unlimiting and subsequently
exhausted, as a function of increasing fish density and food consumption in
association with fish growth.
A.
4
.
6
.
2
.Application. NFP is applied to fish feeding and growth rates and can be
used alone or in conjunction with supplemental, prepared feeds. Fish consumption
rates of phytoplankton and organic solids are included in their respective mass
balances.
A.
4
.
6
.
3
.Validation. Method validity is largely dependent on the given, empirically
based parameters used to relate primary productivity, fish density, and NFP. Trial
applications to pond based tilapia production gave characteristic profiles of fish
productivity over time that were comparable to productivity regimes reported in the
literature.
A.
4
.
7
.Fish feeding
(
prepared feeds
)
A.
4
.
7
.
1
.Methods. Maximum fish feeding rates (at or near satiation) are a function
of fish size, water temperature, water quality (optional), and feed quality (optional).
Maximum feeding rates are adjusted to actual feed application rates based on target
fish growth rates. The response of food conversion efficiency to feeding rate (Brett,
1979; Corey and English, 1985), fish competition for limited food resources, and
contributions from endogenous food resources can be considered. Alternative feed
models include: (1) feed rate tables (feed manufacturers and aquaculture literature);
(2) food conversion efficiency functions or tables used in conjunction with fish
growth rates; (3) double-log specific feeding rate function (Balarin and Haller, 1982;
Ernst et al., 1989); and (4) bioenergetic feeding function (Nath 1996).
A.
4
.
7
.
2
.Application. Fish feeding rates are used to generate feed application
schedules and to compile total feed quantities. Fish feeding rates are used in fish
metabolic modeling.
172 D.H.Ernst et al.
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Aquacultural Engineering
23 (2000) 121–179
A.
4
.
7
.
3
.Validation. The listed methods have been calibrated and validated for
various fish species and calibration procedures have been described (see listed
references). Reported and newly derived parameters used in trial applications with
various fish species gave results comparable to reported feed application rate
schedules.
A.
4
.
8
.Fish metabolism
A.
4
.
8
.
1
.Methods. Fish oxygen consumption, metabolite excretion, and fecal eges-
tion rates (g-compound kg-fish
−1
day
−1
) are a function of fish feeding rate,
digestion and conversion efficiencies, feed composition and stoichiometry of feed
catabolism, fish composition (optional), water quality (optional), and baseline
standard metabolism (optional) (Speece, 1973; Brett and Zala, 1975; Huisman,
1976; Brett, 1979; Brett and Groves, 1979; Hepher, 1988; Meyer-Burgdorff et al.,
1989; Colt and Orwicz, 1991b; Jobling, 1994; Ernst, 2000a). For eggs, metabolic
rates are a function of water temperature. Daily simulations use daily mean
metabolic rates. Diurnal simulations can be used to consider daily profiles of fish
metabolism based on diurnal water temperatures and fish feeding times and
amounts.
A.
4
.
8
.
2
.Application. Fish oxygen consumption and metabolite/fecal excretion rates
are used in their respective mass balances.
A.
4
.
8
.
3
.Validation. Method validity depends on the accuracy of given metabolic
parameters (see listed references) and calculated efficiencies of food digestion and
conversion. Reported and newly derived parameters and methods used in trial
applications with various fish species gave results comparable to reported metabolic
rates.
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