Hydrodynamic method for estimating production carrying capacity of coastal finfish cage aquaculture in Southeast Asia

Journal Pre-proof Hydrodynamic method for estimating production carrying capacity of coastal finfish cage aquaculture in Southeast Asia ´ ın Niederndorfer, Jose´ Manuel Roberto Mayerle, Katharina Rois´ ´ Fernandez Jaramillo, Karl-Heinz Runte

PII:

S0144-8609(19)30096-2

DOI:

https://doi.org/10.1016/j.aquaeng.2019.102038

Reference:

AQUE 102038

To appear in:

Aquacultural Engineering

Received Date:

22 July 2019

Revised Date:

27 November 2019

Accepted Date:

12 December 2019

´ Please cite this article as: Mayerle R, Niederndorfer KR, Fernandez Jaramillo JM, Runte K-Heinz, Hydrodynamic method for estimating production carrying capacity of coastal finfish cage aquaculture in Southeast Asia, Aquacultural Engineering (2019), doi: https://doi.org/10.1016/j.aquaeng.2019.102038

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Hydrodynamic method for estimating production carrying capacity of coastal finfish cage aquaculture in Southeast Asia

Roberto Mayerle* [email protected], Katharina Róisín Niederndorfer [email protected], José Manuel Fernández Jaramillo [email protected]

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kiel.de, and Karl-Heinz Runte [email protected]

Research and Technology Centre Westcoast of the University of Kiel, Hafentoern 1, 25761 Buesum,

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Germany

Highlights

Alternative method for modeling marine finfish floating cages

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Modeling approach to estimate PCC

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Dimensional analysis used in conjunction with 3D model simulations

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Dimensionless relationship derived for estimation of PCC

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Relevance of flow Reynolds number at fish farms and falling velocity of waste

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PCC determined using current velocities from dynamic models

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One method for modeling marine cage culture in regions with scarce data

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Method suitable for the assessment of currently operating aquaculture sites

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Successful validation using measurements of sediment quality underneath farms

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Abstract

This paper presents the development of a simple and generally applicable hydrodynamic method for the estimation of production carrying capacity (PCC) of coastal finfish cage 1

aquaculture. Dimensional analysis was used to find significant and general interdependencies between the hydrodynamics at fish farm locations and particulate wastes deposited on the seafloor by fish farms. Modeled ratios of deposition to emission of particulate wastes underneath fish farms were found to be primarily a function of the flow Reynolds numbers at the farming locations and the non-dimensional settling velocity of emitted wastes. In the non-dimensional model, farming conditions include daily feed rate, proportion of unconsumed feed, and carbon content in feed and fish feces. The relationship can be used to estimate the PCC of floating net cages imposing a threshold value for deposition. Results of in-situ assessments of the benthic impacts of several fish farms in an

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aquaculture site in the northwest of Bali, Indonesia were used to validate and demonstrate the effectiveness of the method. Predicted results were able to clearly identify fish farms

operating beyond ecologically sustainable carrying capacity. The proposed method has broad

applicability and could help make decisions regarding the estimation of production potential

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of individual farms in pristine areas, for providing first estimates in sites that have scarce data, and for assessment, expansion, and optimization of the currently operating

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aquaculture sites in Southeast Asia, China and potentially other data-poor island nations. As

entire aquaculture region.

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the method relies on dynamic models, it enables straightforward assessments over the

Keywords: Finfish cage aquaculture; production carrying capacity; assessment of benthic impacts,

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Introduction

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field validation, Pegametan Bay Indonesia

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In the past decades, global average fish consumption has increased significantly. As a result, aquaculture has now surpassed global capture fisheries in seafood production (FAO, 2016).

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Currently, Asia accounts for nearly 90 percent of global aquaculture production (FAO, 2018). China will continue to remain the world’s leading producer for the next decades, whereas several Southeast Asian countries and India are expected to intensify their production (World Bank, 2013; FAO, 2018).

Rapid expansion of coastal mariculture in Asia requires a significant increase in the cultivation area. However, this can exert considerable strain on aquatic and terrestrial resources as well as on the environment. As the current systems for spatial planning and siting of aquaculture facilities in many Asian countries are insufficient or non-existent and data are usually scarce, there is a need for 2

systematic procedures that allow for the growth and development of the aquaculture industry, while working towards minimal impacts to the surrounding ecosystem. To this end, the Food and Agricultural Organisation of the United Nations (FAO) has proposed the ecosystem approach to aquaculture (EAA) as a strategy for sustainable development of aquaculture sites (FAO, 2010). The essential steps of an EAA include scoping, zoning, site selection, and carrying capacity (Aguilar-Manjarrez et al., 2017). The adoption of environmentally sustainable practices and managerial schemes following the guidelines of the EAA is essential for enhancing sustainable development and expansion of the industry; moreover, it is a pre-requisite to assure compliance with the existing regulatory framework (Soto et al., 2008).

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Carrying capacity is the primary concept of EAA. Although production plays a significant role in the method, a more comprehensive approach that also considers physical, ecological, and social carrying capacity was proposed by Ross et al. (2013). Physical carrying capacity or site selection comprises the identification of sites or potential aquaculture zones from which specific site selection can be

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made for actual farm development. Production carrying capacity (PCC), which is the subject of this paper, estimates the maximum aquaculture production of individual fish farms, and is typically considered at the farm level. Ecological carrying capacity (ECC) is defined as the magnitude of

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aquaculture production that can be supported by the entire site without leading to significant changes to ecological processes, services, species, populations, or communities in the environment.

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Social carrying capacity has been defined as the amount of aquaculture that can be developed without adverse social impacts. The latter is of significant relevance for developing countries in Southeast Asia that are facing a shift from traditional fisheries to modern aquaculture practices.

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Physical carrying capacity is relatively straightforward to determine but requires substantial field data with good spatial coverage to assess site function and find suitable locations for fish farms.

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High-resolution simulations of tides and waves that cover the aquaculture site can deliver a significant amount of the required information (Mayerle et al., 2009; Windupranata and Mayerle, 2009; Mayerle et al., 2017). Estimation of PCC and ECC still presents many challenges, particularly

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regarding the implementation of the required sediment and water quality standards. This difficulty is mainly due to an absence of data and the difficulty of conducting in-situ investigations for determining threshold values for factors, such as seafloor waste deposition and determination of concentrations of fish farm nutrients that do not exceed the assimilative capacity of the affected ecosystem. This paper summarizes the development of a simple method to estimate PCC of the coastal finfish cage aquaculture fish farms typical to Southeast Asia, in places where data are scarce. Several

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methods, that have implemented models with different levels of sophistication, have been developed to predict environmental changes with different nutrient loading from dissolved and particulate waste matter generated by fish cage aquaculture. DEPOMOD is an excellent model to evaluate the impact of fish farms on the benthic community and is currently the approved standard for assessing the impact of loading of organic carbon in sediments. However, it addresses the transport of particulate waste exclusively from the cages to the sediment in the near-field (Cromey et al., 2002a). Other models, such as the AquaModel, provide a complete dynamic model for farm operation and environmental impact to estimate both near-field and far-field effects of fish farms (Kiefer et al., 2011). These models are essential to determine mariculture siting and to estimate the carrying capacity and potential environmental impacts at farm locations. However, they require a

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sizeable number of input data, which can be difficult to obtain, particularly in remote areas. There is a need for simple methods that help provide an initial estimate of the potential production of

individual finfish farms at the feasibility stage. This initial estimate is extremely relevant when a coastal area is being investigated for its mariculture potential, especially when very little

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environmental data are available.

The purpose of the method developed here is to estimate the PCC of individual coastal finfish farms,

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with specific reference to the dynamics of emitted particulate organic wastes. In this paper, a detailed derivation of the hydrodynamic method for estimation of PCC is presented. Dimensional

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analysis was applied to determine meaningful and general relations between the most relevant parameters that affect particulate waste transport and deposition beneath fish farms. Threedimensional numerical modeling of the transport and deposition of particulate waste under fish

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farms was used to confirm the derived non-dimensional relationship empirically. In-situ assessment of the sediment quality underneath fish farms was performed to validate the proposed method. Furthermore, results of the model application to the aquaculture site in the northwest of Bali have

Mariculture site in the northwest of Bali

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also been presented.

This study focuses on a coastal aquaculture site in the northwest of Bali. This site is one of the leading production centers of high-value coastal finfish aquaculture commodities in Indonesia. The northwest part of the island remains relatively unpopulated compared to the more touristic regions in the south. The operation of finfish farms is expanding at a significant rate in this region. Currently, there are two main operating sites, namely Pegametan Bay and Patas, both located about 50 km west of Singaraja. Pegametan Bay to the west is more confined and well-protected by coral reefs.

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Water depths along tidal channels are up to about 20-25 m. Patas is more exposed, with water depths up to 40-50 m. In this study, Pegametan Bay (8.13 °S, 114.6 °E) was selected for investigations. Apart from being one of the main centers of high-value marine finfish aquaculture production in Indonesia, this site is located in the vicinity of the Gondol Research Institute for Mariculture (GRIM) under the Indonesian Ministry of Marine Affairs and Fisheries, thus facilitating site investigations and continuous monitoring. The model area covers about 35 km² along a coastal stretch of around 10 km. Figure 1 shows an overview of the study area using a satellite image. The prominent characteristics of the site are a

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coral reef system embedding two large tidal channels that embrace a central coral reef platform. The depth of water is less than 1 m in the coral reef area and is greater than 50 m at the reef slope facing the Bali Sea. The reefs divide the inner bay into two main channels, wherein water depths reach about 20-25 m.

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Several depositional environments can be distinguished in Pegametan Bay. In the deeper channel beds, medium to light grey mud prevails. Lower mud layers observed in sampled sediment cores

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often show plastic consistencies as a result of consolidation. Muddy to sandy carbonate sediments with coarser coral debris embedded are spread along the flanks of the channels whereas in the

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shallow channel systems and adjacent reef flats, fine to coarse carbonate sands are common. Water flow in the bay is tide-dominated, having a mean tidal range of about 1.8 m. Current velocities in the tidal channels are generally below 0.05 m/s but can reach 0.4 m/s during spring tides.

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Velocities in the eastern channel are mostly higher than in the western tidal channel, as the eastern channel is open to both ends of the bay. The channel to the west is slightly shallower and current velocities reduce as the channel ends on the coastline. Model simulation results were used to

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improve the understanding of flow patterns in the bay and assist in site selection. Furthermore, the model was used to generate data required for the development of an empirical equation for the

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estimation of PCC.

Even though Indonesia does not lie in the main path of severe storms and hurricanes that the region experiences, winds at the study site in Bali can reach speeds of about 6 m/s and 12 m/s during southeast and northwest monsoons, respectively (Kalnay et al., 1996). Seawater temperatures in the bay are in the range of 28 °C to 30 °C and salinity varies between 28 and 30 PSU. Freshwater enters the bay mainly through diffuse runoff and small streams, which only exist during the rainy season.

PLEASE INSERT FIG01PegametanBay.jpg 5

Finfish mariculture using floating net cages has been practiced in Pegametan Bay since 2001, with a total of 30 farms operating in 2015. Finfish species cultured in the bay include Asian seabass (Lates calcarifer), humpback grouper (Cromileptes altivelis), and some species of ornamental fish. A bulk of the standing stock consists of tiger grouper (Epinephelus fuscoguttatus). Total fish production of high-value commodities reached about 1,200 tonnes in 2015 (Pusat Data Statistik dan Informasi, 2015). Operative fish farms in Pegametan Bay in 2015 are of varying sizes. The floating net cages of most farms are the ones typically used in Indonesia, that is the fish farms consist of wooden rafts kept afloat by plastic drums (see Figure 2a). Each cage typically measures 3 m × 3 m × 3 m. They are connected to form a floating raft to reduce the effect of waves and currents. In 2015, the size of the traditional farms at this site varied from 6 to 380 cages. The stocking density of these farms for

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cultivation of grouper is about 10-20 kg/m3. Following the trends recently observed elsewhere in

Indonesia, there are two bigger fish farms in the eastern channel with 7-8 circular floating units of

high-density polyethylene (HDPE) for nursery and on-growing. The cages are 20 m in diameter, have a depth of about 6-7 m, and are located relatively close to each other (see Figure 2b). Asian seabass

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is cultured in these farms. The stocking densities of these larger fish farms reach values of about 25-

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PLEASE INSERT FIG02TypesFishFarms

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30 kg/m3 for the cultivation of seabass.

The location of the 30 operating fish farms and the suitable areas for coastal finfish farming in

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Pegametan Bay are shown in Figure 3. Green colors indicate those areas suitable for installation and operation of floating net cages. The potential aquaculture areas were identified based on environmental suitability criteria and threshold values. Data from tide-flow and wave model

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simulations covering the entire bay combined with in-situ measurements helped regions suitable for finfish cage aquaculture to be designated. Detailed descriptions of the steps adopted in the

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identification of suitable locations in Pegametan Bay are summarized in Niederndorfer (2017) and Mayerle et al. (2017). The results of the site selection procedure showed that most of the existing farms are located within suitable areas, reflecting the experience of fish farmers in the region. Out of the 30 farms, six farms are located on the far west of the bay, namely farms 5, 6, 7, 10, 11, and 12 (Figure 3). These are not placed in locations that are ideal for coastal finfish aquaculture. Notice that these farms are located within the inner parts of the bay in places with reduced flushing. The remaining farms are placed within areas identified as suitable for floating net fish farms. However, there is ample suitable space 6

for expansion of farming activity on the far east of the bay and in the outer regions of the western channel (see Figure 3). Provided that the existing fish farms operate within acceptable limits of carrying capacity, fish production in the bay could be increased considerably.

PLEASE INSERT FIG03PhysCarryingCapacity 3

Sustainability criteria that control PCC of coastal finfish cage farms

Among all the fish farm wastes, particulate organic wastes in the form of uneaten feed and feces is found to cause the most significant ecological damage to the benthic community beneath fish farms

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(Beveridge, 2004; Holmer et al., 2008; ; Vezzulli et al., 2008; Riera et al., 2011). Seafloor sediments underneath farms can be affected by excessive deposition of particulate organic wastes from feed

and excrements (Wu, 1995; Pearson and Black, 2001; Kalantzi and Karakassis, 2006; Sanz-Lázaro and Marín, 2008). Fish farm wastes usually contain high concentrations of carbon, nitrogen, and

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phosphorous as compared to seafloor sediments (Beveridge, 2004). If the assimilative capacity of the benthic community is exceeded, the degradation of excessive organic matter may cause oxygen

Tsutsumi, 1995; Mazzola et al., 2000).

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depletion, eventually leading to a reduction in benthic macrofauna diversity (Brown et al., 1987;

Organic matter deposited on the seafloor increase oxygen demand and stress, or kill organisms

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located therein. When the rate of deposition surpasses the critical threshold values, bacterial oxygen demand for degrading this waste surpasses the oxygen supply of sediments. As a result, the oxygen supply gets exhausted, and bacterial decomposition turns anoxic and slows down. This change

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triggers processes such as denitrification, desulphurization, and methanogenesis associated with the production of toxic gases, which severely affects sediment quality and benthic habitats.

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The carbon content of sediments has been shown to be a good indicator of the benthic environment disturbances (Hyland et al., 2005; Kalantzi and Karakassis, 2006). Investigations carried out at several

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marine finfish aquaculture sites, which represent different environmental settings, have revealed that the benthic community experiences adverse changes for threshold rates of particle carbon deposition values ranging from about 1 to 5 gC/m2d (Hargrave, 1994; Angel et al., 1995; Findlay and Watling, 1997; Chamberlain and Stucchi, 2007; Kutti et al., 2008; Backman et al., 2009). In particular, currents can influence flushing of the system and affect oxygen supply. Farming sites characterized by deeper water and strong currents are more resilient environments than shallow water systems with low current velocities (Pearson and Black, 2001; Keeley et al., 2013). It is recommended to avoid places with less flushing and smaller water depth. This is because further waste deposition 7

associated with detrimental impacts to the benthic community is expected. In this study, the rate of particle carbon deposition was used to assess the impact of fish farm waste on the seafloor. 4

Dimensional analysis of transport and deposition of particulate waste generated by floating cages

The transport and deposition of particulate wastes from fish farms is a complex process involving many variables. In this study, dimensionless analysis was adopted to reduce the complexity of the processes involved. The number of variables specifying the process was decreased by finding meaningful and general relations between them.

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The ratio of deposition to emission rates of particulate organic carbon, Dw/Ew, can be expressed in a functional form as: 𝐷𝑤 𝐸𝑤

= Φ(𝑉, ℎ, 𝜐, 𝑔, 𝜌, 𝜌𝑠 , 𝐷, 𝑛)

(1)

Where, Φ denotes the functional dependence, V is the characteristic velocity of the flow, h is the

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water depth, ν is the kinematic viscosity of water, g is the acceleration due to gravity, ρ is the density of water, ρs is the density of particles, D is the characteristic particle size, and n is the Manning’s

= Φ(𝑉, ℎ, 𝜐, 𝑔, 𝜌, 𝜌𝑠 , 𝐷)

(2)

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𝐷𝑤 𝐸𝑤

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roughness coefficient. For a given Manning's roughness, the functional relationship reads:

Dimensional analysis for a given bed roughness value is, as follows:

Where, 𝑠 − 1 =

𝑉3

= Φ (𝑠 − 1, 𝑔𝜐 ,

𝑉 𝑔𝐷 , ) √𝑔ℎ 𝑉 2

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𝐷𝑤 𝐸𝑤 (𝜌𝑠 −𝜌) 𝜌

is the relative density. The Froude number

(3) 𝑉 √𝑔ℎ

is very small for tidal flows

typical to coastal aquaculture sites. As the settling of waste material in a turbulent flow towards the

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bed is not affected by the free surface effects, the effect of the Froude number is only of secondorder importance. Combining group two and three in equation 3 results in the Reynolds number (Re) 𝑉ℎ . 𝜐

Furthermore, groups two and four in equation 3 can be combined to form the non-

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of the flow,

dimensional term

𝑔𝐷 3 , 𝜐2

which is used to consider the settling velocity, as shown below. As a result,

Dw/Ew can be described by the following function: 𝐷𝑤 𝐸𝑤

= Φ (𝑠 − 1,

𝑉ℎ 𝑔𝐷 3 , 𝜐2 ) 𝜐

(4)

The settling velocity of a particle ws is related to its diameter, as follows:

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4(𝑠−1)𝑔𝐷 3𝐶𝐷

𝑤𝑠 = √

(5)

Where, CD is the drag coefficient of the particles. Assuming nearly constant CD, the following is obtained: 𝑤2

𝑠 𝐷 ≈ 𝑔(𝑠−1)

(6)

Substituting for D in the third non-dimensional parameter in equation 4 and absorbing the relative density 𝑠 − 1 in the above expression for D, the functional relationship for a given value of bed roughness coefficient becomes: 𝑉ℎ

𝑤3

𝑠 = Φ ( 𝜐 , (𝑠−1)𝑔𝜐 )

(7)

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𝐷𝑤 𝐸𝑤

Note that the relative density 𝑠 − 1 and the third group in equation 4 are absorbed into the term 𝑤𝑠3 (𝑠−1)𝑔𝜐

which is the non-dimensional settling velocity ws*, as proposed by Dietrich (1982). Thus, for a

𝐷𝑤 𝐸𝑤

(8)

Numerical modeling of transport and deposition of waste from floating cages

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= Φ(R e , ws∗ )

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given bed roughness, the functional relationship for Dw/Ew can be expressed as:

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5.1 Model setup

To empirically confirm equation 8, large amounts of data on Dw/Ew, Re, and ws* from fish farms were needed. Collecting this field data is difficult, time-consuming, and costly. Therefore, in this study,

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results from numerical model simulations were used instead. A three-dimensional process-based model for simulation of tide-induced currents was set up for Pegametan Bay with the Delft3D modeling suite (Deltares, 2014a,b). The tide-flow model was

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coupled to a water quality model to provide information on hydrodynamics and deposition rates of particulate waste underneath fish farms. The computation was performed on three curvilinear grids

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with increasing grid resolution towards the coast. Figure 4 shows the horizontal setup of the model grid. Sub-domain decomposition was adopted to permit grid refinements from the coarse model covering parts of the Bali Sea to the more refined model covering Pegametan Bay. Horizontal grid resolution ranged from 800 m in the larger-scale model to about 25 m near the coast. To resolve the flow and transport of matter in three dimensions, the coastal model grid was vertically divided into five sigma-layers, each covering 20% of the water depth. Model development in the offshore region relied on data from global databases and global operational models. Bathymetry was compiled using data from the General Bathymetric Chart of the 9

Oceans (IOC, IHO, BODC, 2003) Near-shore bathymetric data was complemented by field measurements collected in 2008 using a single-beam echo sounder (Bakosurtanal, 2008).

PLEASE INSERT FIG04ModelSequence Figure 5 shows the model bathymetry in Pegametan Bay. The bathymetry is characterized by a coral reef and two tidal channels with water depths up to about 25 m (see also Figure 1). The channel to the west is wider than the eastern, but as it ends on the coastline, current velocities are smaller. The eastern tidal channel is narrower and open to the sea on both ends, leading to higher current velocities. A detailed description of the tide-flow and water quality models can be found in sections

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5.2 and 5.3, respectively.

PLEASE INSERT FIG05ModelDomain

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5.2 Tide-flow model

The tide-flow model is composed of three grids. Both outer models covering parts of the Bali Sea are resolved using two-dimensional depth-integrated approximations. The coastal model covering the

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Pegametan Bay uses a three-dimensional model approximation. The outermost model is driven by astronomic forcing at the open sea boundaries with the Bali Sea and Bali Strait. Tidal constituents

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were extracted from the Global Tidal Model (Egbert and Erofeeva, 2002). To account for meteorological forcing, wind and pressure fields that vary in space and time were extracted from the Global Forecast System from the National Centers for Environmental Prediction in the United States

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and were imposed at the free surface of the models for the entire simulated periods. Figure 6 shows typical instantaneous depth-averaged current velocities of a spring tidal cycle for the

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coastal model. Colors indicate the ranges of water depths in the modeled area. Modeled water levels and current velocities at three fish farming locations are shown in Figure 7. Modeled free surface current velocities are shown for farm 15 on the western channel and farms 20 and 28 on the

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eastern channel. The location of the farms is indicated in Figure 3. Modeled velocities cover 14 days. It can be seen that velocities at all three locations are generally lower than 0.02-0.03 m/s. This low velocity is especially observed in the case of farm 15 on the western channel. On the eastern channel, velocity values reach about 0.15-0.20 m/s during spring tides.

PLEASE INSERT FIG06SimulatedCurrentVel

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PLEASE INSERT FIG07WLCurr The performance of the tide-flow model was assessed by comparing computed with measured water level time series registered at a tidal gauge located within the model area. The location of the tidal gauge is indicated in Figure 5. Water levels were recorded using a data logger. A simulation period of 31 days was considered for validation. Figure 8 gives a comparison of the measured and computed water level time series. Water levels are predicted well with the model. The mean and standard deviations of computed water levels from measured water levels were found to be 0.05 m and 0.07 m, respectively.

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PLEASE INSERT FIG08FlowValid-rev

Current velocity can be affected by bed roughness. Generally, the effect of changes in bottom

roughness on the flow is more pronounced at locations with shallower water depths and/or higher flow velocities, where greater bed roughness causes a decrease in flow velocities. Changes in bed

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roughness have little effect on current directions and no significant effect on water levels. In this study, the effect of bed roughness on flow was investigated. Computation was carried out for

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Manning’s coefficients equal to 0.02, 0.03, and 0.035 sm-1/3. A comparison of the results for several simulations using different bed roughness showed that for the given conditions, the effect of bed

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roughness on the current velocities was minor at farming locations with water depths higher than 67 m.

Sensitivity studies to assess the effect of wind shear at the free surface on hydrodynamics were also

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carried out. The tide-flow model was run with and without the presence of winds. The effect of wind on water depth and flow velocity was investigated. The simulations included winds blowing from north-northeast direction with speeds up to 12 m/s. The results showed that water depth and

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current velocity were slightly affected by wind. Wind affected the current magnitude and direction only in the shallower regions of the study area, particularly the coral reefs, between two tidal

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channels (see Figure 1).

5.3 Water quality model Transport of particulates by advection and diffusion was computed by the coupling of the tide-flow model with the water quality model. The water quality model solves the advection-diffusion equation in three dimensions for different scalar quantities transported by the flow (Deltares, 2014b). The rate of deposition of particles is determined by the settling velocity of the particulate fish farm wastes (ws), the concentration of suspended sediments near the bed (Cb), and the ratio of the bed shear stress (τb) to the critical shear stress for sedimentation (τd). In this study, the settling of 11

particles on the seabed was set to occur when τb was less than a critical shear stress for sedimentation, as proposed by Krone (1962). Variations in the critical shear stress for deposition affect the amount of deposited material, with higher values of critical shear stress leading to greater deposition. Cromey et al. (2002a) used a critical shear stress for deposition of 0.004 N/m2 in simulations using the DEPOMOD model to predict the accumulation of solids on the seabed arising from fish farms, and associated changes in benthic community. In the present study, the critical shear stress for deposition was also set at 0.004 N/m2. Similar to the deposition process, particulate matter can be resuspended in the model if the actual

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bottom shear stress exceeds the critical shear stress for resuspension. Critical shear stresses for resuspension have been found to vary from about 0.018 N/m² to 0.059 N/m² (Cromey et al., 2002b). In this study, simulations with and without resuspension were compared, by assuming a critical shear stress for erosion of 0.018 N/m2. Including resuspension led to reduced deposition rates

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directly below the fish farms at locations where the actual shear stresses exceeded the critical shear stress for erosion. To exercise caution, this study exclusively considers sedimentation processes. Generation of data to confirm the relationship for estimation of the rate of deposition of

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waste from floating cages

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6.1 Scenario runs

The tide-flow model was used to compute water depths, current velocities, and the transport and deposition rates of emitted particulate waste from hypothetical fish farms in the Pegametan Bay.

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Model simulations were carried out for typical tidal conditions, farm emission rates, and settling velocities of particulate fish waste of the cultivated species. A neap spring tidal cycle spanning 15 days was simulated. Tidal constituents extracted from the Global Tidal Model (Egbert and Erofeeva,

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2002) were imposed at the open sea boundaries of the outer model (see Figure 4). In the water quality model, 30 locations along the eastern and western tidal channels of the

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Pegametan Bay Model were defined as hypothetical fish farms with particulate farm waste emissions. The locations were selected to cover a large variation in water depths, current velocities, and flow Re. Figure 5 shows the bathymetry of the model and the 30 selected hypothetical locations. Mean water depths at the selected monitoring points varied between 6.2 m and 18.7 m. Current velocity values averaged over a full neap spring tidal cycle range between 0.01 m/s and 0.06 m/s. The spatial variation of tide average flow Reynolds numbers is shown in Figure 9. Colors indicate the ranges of flow Re. In this study, the flow Re was defined employing the depth-averaged current

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velocity and water depth-averaged over the simulation period. Flow Re values at the 30 fish monitoring locations ranged from about 50,000 to 780,000. As the eastern tidal channel is open to the Bali Sea on both ends, current velocities and flow Re are higher than on the western channel, provided that water depths are similar in each channel. The data required to confirm equation 8 were generated by conducting simulations for a range of emission rates from fish farms resembling stocking density values typical to coastal floating finfish farms in Indonesia. Simulations were performed for constant stocking densities of fish farms corresponding to the biomass at the end of the grow-out period varying from 5 to 40 kg/m3. In the simulations, the particulate carbon emission Ew at a fish farm point was released at the upper layer

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of the three-dimensional model, covering the upper 20% of the water column. Similarly, to account for the whole range of settling velocities of feed waste and feces, ten different classes of settling

velocity values ranging from 0.01 to 0.1 m/s were considered in the simulations. To assess the effect of bed roughness on waste accumulation, simulations were performed for three different Manning´s

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coefficients; namely 0.02, 0.03, and 0.035 sm-1/3.

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PLEASE INSERT FIG09ReynoldsNumber

The rate of carbon deposition on the seafloor (Dw) at a given location over the simulated period is

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shown for two different falling velocities (Figure 10). Flow Re at the point location is ~245,000. Simulations were performed considering a constant rate of emission from the fish farm and a threshold of carbon load on the seafloor equal to 5 gC/m2d. The variation in tidal elevation (Figure

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10a) and depth-averaged current velocity (Figure 10b) are also shown. The resulting rate of sedimentation beneath the emission point for falling velocities of waste, which is equal to 0.01 and 0.07 m/s, are shown in Figure 10c. The tide averaged Dw values corresponding to each falling velocity

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of waste are also indicated.

The effect of falling velocity on the sedimentation of waste beneath the fish farming point becomes

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evident from the fact that smaller the falling velocity, slower is the rate of deposition. This is because most of the waste is transported away and only a small portion is deposited below the point of release. During periods of sudden increase in current velocity, the rate of deposition decreases as the particulates are transported in suspension farther away from the source point. While generating data to confirm equation 8, Dw is taken as the time-averaged rate of deposition over the entire simulated period. PLEASE INSERT FIG10SimulatedDeposition

13

6.2 Simplifications and assumptions To simplify the derivation of the methodology, several simplifications and assumptions in the generation of data were made to confirm equation 8. The most relevant ones are discussed below. The accumulation of materials underneath fish farms was related to the undisturbed current velocity that is the effect of the fish farms on current velocities was disregarded. To assess the relevance of this simplification, 3D model simulations covering a neap spring tidal cycle were done for a range of square fish farming sizes with horizontal dimension equal to 10, 25, 50, 70 and 100 m. The effect of the cages was accounted for through porosities. The results showed that the effect of fish farms on current velocities increased with their size and current magnitude. For fish farms with horizontal

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dimension of up to about 25 m and current velocities up to about 0.02-0.03 m/s, this effect turned out to be minor. Care should be taken in the application of the methodology, particularly for large fish farms and high current velocities.

The waste material was released from a single model cell equivalent to a square fish farm with

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horizontal dimension of about 25 m. The effect of the size of the area of release was disregarded. Simulations covering a neap spring tidal cycle were done for a wide range of releasing areas to assess the effect of the size of the released area on the accumulation beneath the releasing cell.

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Square areas of release with horizontal dimension equal to 10, 25, 50, 70 and 100 m were considered. It was found that irrespective of the area of release and flow Re, maximum

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accumulation occurred in the middle of the releasing area. The results also showed that there was an increase in the rate of accumulation with the area of release for farm sizes with horizontal dimension up to about 50 m. For larger areas of release, accumulation remains approximately

the method.

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constant. As a result, attention should be given to the size of the area of release in the application of

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Furthermore, the model was run with waste discharges from one location at a time to avoid interaction between wastes released from different locations. In many instances, however, a large percentage of the material is transported away from fish farms. The effect of the material that

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leaves the fish farm boundaries is assessed in a follow-up step of the methodology that focuses on the determination of ecological carrying capacity (ECC), which is not handled in this paper. For that, sediment transport simulations of particulate matter and nutrient concentrations released from all the fish farms are carried out. As a result, potential accumulation zones and hot spots of nutrients due to the cumulative effect of all fish farms in the site can be identified. By adjusting the size of fish farms and rearranging farming locations, the best siting leading to the maximum fish production without harming the environment is defined.

14

Additionally, the emission from a fish farm, with a given stocking density, was considered as particulate carbon concentration at a constant rate. Flocculation and hindered settling were not taken into account in the model. Similarly, processes in the deposited sediment layer, such as consolidation, burial, or bioturbation, were not considered. Within a computational cell, particulates may be broken down by biogeochemical processes, thus changing mass balance. In this study, the mineralization of carbon in the water column was disregarded. It was assumed that the settling times in the shallow coastal area were short compared to the time needed for mineralization. The deposition rate was taken from the bottom-most grid layer covering the lowest 20% of the water column. A constant critical shear stress for deposition equal to 0.004 N/m2 was considered and

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resuspension was disregarded in the simulations. Based on this analysis, the proposed hydrodynamic method for determining PCC of finfish farms can be a useful tool for approximating the impacts of cages in a given site, especially in data-poor regions with small farm scenarios. However, care should be taken in the application of the methodology,

particularly concerning the magnitude of current velocity at fish farming locations and the size of the

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fish farm. To account for these effects, a scaling factor defined from ground samples taken beneath fish farms was introduced (see section 10). By tuning the scaling factor with ground samples,

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simplifications and assumptions are taken into consideration. 6.3 Results

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It was found that the maximum deposition of fish farm waste takes place immediately below the fish farm point, independent of flow Re, ws, and critical shear stress for deposition. Particles with larger settling velocity led to enhanced deposition under the fish farms irrespective of the flow Re. In

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contrast, particles of smaller ws experienced greater transport and diffusion in the flow, depositing over larger areas of seabed, leading to lower average deposition rates beneath the farm point. Furthermore, the waste was spread over larger areas in the locations where Re was larger. Higher

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stocking densities and higher carbon loads led to higher average deposition of carbon below the cages without significantly affecting the total area of deposition. The ratio of settled to emitted

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material at each monitoring point was not affected by the emission rates. For the conditions in question, the effect of bed roughness turned out to be insignificant on the accumulation of particulates underneath fish farms. 7

Dimensionless relationship for estimation of PCC of coastal finfish floating cages

The results of the model simulations were used to calculate the ratios Dw/Ew at the 30 hypothetical locations, shown in Figure 5. Ew is defined as the rate of particulate organic carbon emission from the fish farm in gC/m2d corresponding to the simulated spatial averaged farm stocking densities. Ew 15

is assumed constant throughout the simulated period. Dw is the rate of particulate organic carbon in gC/m2d of the bottom layer underneath monitoring points. Dw is considered as the modeled timeaveraged daily deposition rate occurring in the model cells below the farm point affected by the emission over the simulated period (see Figure 10c). The flow Re is determined based on the depthaveraged current velocities and water depths averaged over the simulated period. Figure 11 shows the variation of Dw/Ew with flow Re for the ten different classes of settling velocity values. Combining the results of dimensional analysis and numerical modeling leads to a functional description of the relation between the ratio of emitted to deposited particulate organic matter, the hydrodynamic character of the fish farm location, and the characteristic settling velocity of the

captures the relationships between the model parameters. PLEASE INSERT FIG11DiagramReNumber

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particulates. It is clear from Figure 11 that the non-dimensional presentation of the data successfully

The interdependence of the various parameters can be expressed as an empirical equation, as

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shown in Figure 11. The following single relationship resulted from the multiple regression analysis performed for the whole data set:

= 𝛼[0.16 ∙ 𝑙𝑜𝑔(𝑤𝑠 ) − 0.42 ∙ 𝑙𝑜𝑔(𝑅𝑒) + 2.83]

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𝐷𝑤 𝐸𝑤

(9)

The correlation coefficient of equation 9 is equal to 0.94. The effect of bed roughness on the

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accumulation of particles underneath fish farms was minor for the considered range of roughness. The relation clearly shows the decrease in the ratio Dw/Ew with the flow Re number for the full range of ws. For low values of flow Re in the order of 100,000 and large settling velocities of waste, the

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ratio Dw/Ew rises to about 0.9-0.95, indicating that most of the waste settled under the releasing point. On the other hand, for large Re values of about 700,000 and small settling velocities of emitted waste, only a small proportion of the emitted particles (less than 20%) settled on the seafloor. The

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scatter increased with a decrease in falling velocity as the dispersion of particles occurred over larger areas. To account for the simplifications and assumptions made in the derivation of equation 9 as

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well as the uncertainties in the selection of the ranges of input data, a correction coefficient 𝛼 was introduced to the relationship.  is defined based on in-situ monitoring of sediment quality underneath fish farms. A detailed description of its determination is provided in section 10. 8

Hydrodynamic method for estimation of PCC of coastal finfish floating cages

The steps for application of the proposed method to produce estimations of environmentally sustainable stocking densities and PCC of fish farms are summarized in this section. First, environmentally sustainable Dw/Ew ratios corresponding to the flow Re at the fish farming location 16

and the ranges of falling velocities of waste are determined using equation 9. Then, for a given threshold carbon load on the seafloor, permissible farm emissions are estimated for the fish farm location. Subsequently, ranges of stocking densities that match the fish farm emissions are obtained. This is done by taking into account the daily feeding rate, the proportion of ingested and excreted feed, and losses to the environment with the respective carbon percentages for the species under cultivation. The daily feeding rate or food conversion ratio is the dominant source of emission of particulate organic carbon. However, during feeding, some of the feed is not consumed by the fish but lost directly to the environment as uneaten trash fish or dry pellets. The proportion of wasted feed depends on the feed type, feeding practice, and the skill of the fish farmer. The total amount of particulate carbon being wasted depends on its content in the feed and the assumed share of

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wasted feed. A proportion of the feed being ingested by the fish will not be digested. This proportion depends on the type of feed and fish metabolism. The amount of particulate carbon being emitted

via feces is based on the C content of the feed ingested and the assumed proportion of consumed C, which is excreted as feces. Having determined the stocking densities, the correction coefficient 𝛼 in

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equation 9 is determined for the site under investigation. In-situ assessment of the sediment quality underneath selected fish farms, which is used in conjunction with information on farm size and

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operating stocking density, is used for this purpose. A more detailed description of the estimation of the correction coefficient is presented in section 10. Finally, the ecologically sustainable stocking density is estimated for the farm in question. Provided that the operating stocking density of the fish

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farm being assessed is equal to or lower than the predicted density, the fish farm is environmentally sustainable. Otherwise, production parameters, such as the cage depth and feed type need to be

9

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adjusted to prevent adverse effects due to excessive particulate carbon emissions. Benthic impacts due to fish farming at the site in Bali

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Appraisals of the benthic impacts due to the operation of fish farms were carried out in the aquaculture site in Pegametan Bay. Assessments of the sediment quality underneath several fish farms were performed on November 2015 and January 2016. The twelve largest farms currently in

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operation, that are responsible for about 80% of the fish production in Pegametan Bay, were selected for assessments, which includes farms numbered 2, 11, 13, 15, 16 and 18 in the western channel and farms 20, 21, 23, 27, 28 and 30 in the eastern channel (see Figure 3). In total, 54 samples were collected. 5-6 samples were taken beneath the two largest farms (numbered 21 and 30), and three samples were taken under the others. The number of samples randomly collected by divers underneath the fish farms selected for the assessment are listed in Figure 12. Sediment samples were also gathered at fourteen reference locations along the two tidal channels to obtain

17

representative information of undisturbed conditions. Ground samples were taken at sufficient distances from fish farms to reflect conditions without farming impact (see Figure 3). Samples were analyzed for the main biogeochemical benthic parameters, namely particulate organic nitrogen (PON), particulate organic carbon, organic matter (OM), total dissolved sulfide (TDS), and redox potential (Eh). PON in sediments was determined by combustion/gas chromatography using CN-Analyser Euro EA, manufactured by HekaTech. OM was obtained through loss on ignition at 550 °C (Dean, 1974) using muffle furnace HeraeusTM M110T. TDS, temperature, and Eh in the sediments pore water were recorded with metrologically prepared probes (ATM H2S-sensor 15091001 and WTW SenTix® PtR). The most evident indicators of benthic impact turned out to be PON and TDS in

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sediments pore water. PON usually degrades rapidly in tropical oligotrophic environments. Dissolved sulfides in the pore water of sediments stem from sulfate reduction during the breakdown of organic substances under anoxic conditions.

Figure 12 shows the variation of average values of OM with PON in the sediment samples taken

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underneath each fish farm. The effect of organic waste on the seafloor due to fish farming is evident underneath farms where the deposition rates of organic waste exceed the bacterial decomposition of waste. This effect is particularly true for fish farms 21 and 30. It can be seen that the geochemical

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response to particulate waste fluxes significantly differs from the conditions observed beneath the remaining farms and at reference locations. The high stocking densities of these farms (25-30

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kg/m3), in combination with high cage depths of 6–7 m, lead to major enhancements of farm emissions compared to the traditional fish farms. As a result, the upper 12 cm of the sediment cores collected under these two farms consisted mainly of pure organic mud with significant enrichments

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of OM and PON. The sediment under these farms is characterized by a black colored matrix caused by iron sulfides, a strong H2S-smell, light mats of sulfur bacteria covering the sediment surface, and

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very low redox potential.

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PLEASE INSERT FIG12OMversusPON PON concentrations underneath the remaining farms with cage depths of about 3 m and stocking densities ranging between about 10-20 kg/m3 (see Table 2) were widely comparable to those measured at reference locations (see white dots in Figure 12). Particulate waste emission from most of these farms was fully compensated through degradation processes, such that waste accumulation was not observed. Slight increase in PON concentrations compared to those detected at reference locations could indicate that re-mineralization of recently settled organic waste is in progress during sampling. Hence, PON was not yet completely degraded. 18

Atypical observations were made underneath farm 11 in the western channel (see Figure 3). With 380 cages and a stocking density on the order of about 18 kg/m3, this farm is currently the thirdlargest farm in the bay. Based on the site selection process, farm 11 is located in areas of Pegametan Bay identified that are unsuitable for fish farming (Niederndorfer, 2017; Mayerle et al., 2017), most probably due to simulated average current velocities calculated to be much lower than the recommended threshold value of about 0.01 m/s. PON concentrations proved to be significantly higher than the values measured at pristine reference locations (see Figure 12). In particular, one of the three sediment samples taken under farm 11 shows extremely high PON concentrations compared to those recorded underneath the two largest farms 21 and 30. It appears that rates of waste deposition and bacterial re-mineralization were already out of balance underneath farm 11,

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which could indicate that the threshold of PCC had been reached or exceeded. The farm appears to be operating just at or beyond the production limit at which the geochemical conditions at the seafloor underneath the farm may deteriorate.

PON in the sediment samples taken underneath several fish farms and at reference locations proved

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to be a useful indicator of the degree of sediment deterioration due to fish farming. The results

showed that in Pegametan Bay samples of the superficial sediment layer with PON concentrations of

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up to about 1.5 mg/g are characterized by the absence of waste accumulation due to fish farming. As the analysis is relatively simple, it will be adopted for continuous assessment of sediment quality

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of the aquaculture site and for validation as well as fine tuning of the proposed method. 10 Correction coefficient to account for the simplifications and assumptions

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A correction factor α was introduced to account for the simplifications and assumptions made in the derivation of equation 9. Results of benthic monitoring underneath selected fish farms were used to determine the correction factor for the site in Pegametan Bay. Two fish farms were selected

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for determining this value. In addition to farm 11, which appears to be operating just at or beyond the production limit, farm 2, with the lowest flow Re and a relatively high stocking density (see Table

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2), was chosen for determining the correction coefficient. Table 1 lists the ranges of input parameters adopted in the predictions for Pegametan Bay with their respective sources. The threshold of carbon load on the seafloor was set equal to 5 gC/m2d. Table 1: Parameters used in the predictions for Pegametan Bay Parameter Daily feeding rate pellets (%) Proportion of wasted feed pellets (%) Percentage of C in pellets (%) Proportion of C excreted as feces (%) Feces Falling velocity (m/s)

Fish species Grouper 0.8-1.0 24 48 21 0.001-0.005

Seabass 0.8-1.0 38 48 10 0.001- 0.005

Source of data Sim et al. (2005) Chu (2002), Brigolin et al. (2014) Alongi et al. (2009) Lupatsch (2009), Brigolin et al. (2014) Brigolin et al. (2014)

19

Pellets

0.04-0.05

0.07-0.10

Chu (2002), Piedecausa et al. (2009)

The determination of the correction factor was performed by matching the predictions of stocking densities to the operating values at fish farms 2 and 11. Predictions were calculated, ensuring that the minimum values just exceed the current operating values (see Table 2). For the conditions in question, the correction factor was calculated to be equal to about 0.13. According to the field assessments, farm 2 operates with stocking densities in the order of 14.5 kg/m3, whereas predicted sustainable densities using equation 9 in conjunction with a correction coefficient of 0.13 range between 14.9 and 29.9 kg/m3. Similarly, farm 11 operates with stocking densities of 18 kg/m3,

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whereas the predicted sustainable values range between 19.2 and 45.5 kg/m3. 11 Validation of the hydrodynamic method for the aquaculture site in Bali

The method was validated using the results of the assessments of the benthic conditions underneath the monitored fish farms. Predictions were conducted considering the input parameters listed in

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Table 1 in conjunction with a correction coefficient in equation 9 equal to 0.13. As farms 2 and 11 were used to determine the correction coefficient, they were excluded from the validation.

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The results obtained are shown in Table 2. The predictions were found to agree with field observations. The predicted sustainable stocking densities of all traditional fish farms with cage depths of 3 m (farms numbered 13, 15, 16, 18, 20, 23, 27, and 28) were higher than the currently

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operating stocking densities (see Figure 13a and Table 2). The results are in accordance with the sustainable environmental conditions encountered underneath these farms. On the other hand, predicted sustainable stocking densities of the two largest farms in the bay, namely farm 21 (9.5 to

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14.8 kg/m3) and farm 30 (10.1 to 15.5 kg/m3) that cultivated seabass were far lower than the actual operating conditions, with current stocking densities in the order of 25-30 kg/m3 (see Figure 13b).

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The high stocking density of these two fish farms having cage depths of 6-7 m leads to excessive waste emissions that cannot be assimilated by the benthic community underneath the farms. As

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both farms comprise 7 to 8 cages, a large area of the seafloor is expected to be impacted. Table 2: Predicted sustainable stocking densities versus actual operating stocking densities Fish farm number 02 * 18 13 11* 15 23 16

Fish farm dimensions Number of cages 250 168 166 380 320 212 100

Flow Re

Cage depth (m)

3

61,370 99,440 123,130 132,410 139,670 145,070 171,450

Stocking density (kg/m3) Operating ** 14.5 12.4 22.0 18.0 20.0 13.5 14.6

Predicted 14.9- 29.9 17.3- 38.6 18.7- 44.3 19.2- 45.5 19.6- 46.4 19.8- 46.7 21.2- 48.9

20

27 20 28 21 30 Note:

182 319 321 7 cir. 8 cir.

6

243,180 332,970 586,840 280,640 328,602

15.0 12.4 9.8 25-30 25-30

24.9- 53.8 29.4- 59.0 43.7- 71.6 9.5- 14.8 10.1- 15.5

* Fish farms used for determination of the correction factor ** Stocking density values based on assessments carried out in December 2015

12 Predictions for coastal aquaculture site in Pegametan Bay Results of the model application to the aquaculture site in Pegametan Bay are presented in this

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section. The parameters listed in Table 1 were used for predictions using a correction coefficient of 0.13. Figure 13a and 13b show predicted stocking densities over the entire suitable area, considering cage depths equal to 3 m and 6 m, respectively. It can be seen that farms with cage depths of 3 m can hold stocking densities of about 30 kg/m3 or more, throughout the entire suitable area of the bay (Figure 13a). On the other hand, predictions showed that farms with cage depths of 6 m are

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non-sustainable to operate with stocking densities greater than 15 kg/m3 (see Figure 13b). In most of the suitable areas, the sustainable stocking densities are much lower, in the order of 5 to 9 kg/m3.

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These results indicate that for cultivating seabass and grouper in the Pegametan Bay site fish farms

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should be limited to cage depths not exceeding about 3 to 4 m.

13 Conclusions

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A simple and generally applicable hydrodynamic method to predict environmentally sustainable stocking densities and PCC of individual coastal finfish aquaculture farms was proposed for coastal sites in Southeast Asia, China, and other island nations that have scarce data. Dimensionless analysis

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was adopted to find meaningful and general relations between the particulate waste released and deposited underneath fish farms.

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Investigations were performed on a target coastal finfish aquaculture site of high-value commodities in the northwest of Bali, Indonesia. A three-dimensional tide-flow model coupled to a transport model was used to compute the deposition rates of particulate waste from fish cages at several locations throughout the site. Data for the derivation of empirical equation was generated using a large number of model simulations for typical hydrodynamic conditions and farm emission rates. A simple relationship was derived to estimate the rate of deposition of carbon underneath fish farms. Non-dimensional presentation of the numerical results leads to general applicability influenced primarily by the flow Re, the settling velocity of particulate waste, and the criterion for onset of 21

benthic deterioration underneath fish farms. The maximum ecologically sustainable stocking density and cage depth at fish farming locations are obtained by imposing a criterion for the rate of deposition at which benthic deterioration in the farms is expected to start. Predictions take note of farming conditions into consideration, such as daily feeding rate, proportion of wasted feed, and excrete feces, as well as the percentage of carbon in feed and feces. A correction coefficient was introduced to account for the simplifications and assumptions made in the derivation of the empirical relationship and the estimation of the waste emissions from the fish farms. In-situ assessments of the benthic conditions underneath farms, in conjunction with specific farming conditions, are used to determine this coefficient. The proposed method was successfully applied to the aquaculture site in the northwest of Bali. In-

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situ assessments of the benthic conditions underneath the largest farms were used to validate the method. PON in the sediment samples collected underneath several fish farms and at reference

locations to reflect environmental conditions without farming impact were adopted to assess the

degree of sediment deterioration due to fish farming. Predicted results were able to clearly identify

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fish farms operating beyond ecologically sustainable carrying capacity. For the site in question, fish farms cultivating grouper and seabass should be limited to cage depths of about 3-4 m. As

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substantial parts of the suitable areas are currently not being used, fish production could be increased considerably in the site. However, predicted results should be analyzed with caution and conditions underneath fish farms should be monitored continuously considering the simplifications

the assumed in-situ conditions.

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and assumptions made in the derivation of the relationship and the dependency of the prediction on

The proposed method is general enough to be applicable to other sites in Southeast Asia and China.

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By combining results of dynamic circulation models with the derived empirical equation for estimation of the rate of deposition of waste, PCC can be determined at any location by imposing a

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threshold value. The method can be applied to any coastal aquaculture site provided that simulated current velocities or in-situ measurements covering representative hydrodynamic conditions at the fish farming location are available. The method has broad applicability and should help make

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decisions regarding the estimation of production potential both in pristine regions in the early stages of aquaculture development, and for the assessment, expansion, and optimization of currently operating sites. Given the non-dimensional nature of the derived relationship for the estimation of PCC, the functional relationship can be continuously extended and confirmed using results from other sites. The proposed method could assist greatly with the planning and development of coastal sites selected for finfish mariculture and with the assessment of the environmental impact associated with the proposed fish farm sites.

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Conflict of Interest

According to or knowledge there are no conflict of interests with other publications and authors.

Acknowledgments The authors wish to thank the German Ministry of Education and Research (BMBF) and the Indonesia Ministry of Marine Affairs and Fisheries for funding the SPICE project (Funding numbers

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03F0393A and 03F0469A) from 2003 to 2011. The support and cooperation of the Gondol Research Institute for Mariculture (GRIM) in Bali, Indonesia, and of the Research and Technology Centre

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Westcoast in Buesum, Germany throughout the project is highly appreciated.

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FAO, 2018. The State of World Fisheries and Aquaculture 2018 - Meeting the sustainable development goals. Rome. Licence: CC BY-NC-SA 3.0 http://www.fao.org/fishery/affris/species-profiles/barramundi/feeding-formulation/en/.

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Holmer, M., Argyrou, M., Dalsgaard, T., Danovaro, R., Diaz-Almela, E., Duarte, C.M., Frederiksen, M., Grau, A., Karakassis, I., Marbà, N., Mirto, S., Pérez, M., Pusceddu, A. and Tsapakis, M., 2008. Effects of fish farm waste on Posidonia oceanica meadows: synthesis and provision of monitoring and management tools. Mar. Pollut. Bull. 56, 1618–29.

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Keeley N.B., Forrest B.M. and Macleod C.K., 2013. Novel observations of benthic enrichment in contrasting low regimes with implications for marine farm monitoring and management. Mar Pollut Bull 2013; 66:105–16. Kiefer, D.A., J.E. Rensel, F.J. O’Brien, D.W. Fredriksson and Irish, J.,. 2011. An Ecosystem design for marine aquaculture site selection and operation. NOAA Marine Aquaculture Initiative Program, Final Report. Award Number: NA08OAR4170859. System Science Applications, Irvine CA. in association with United States Naval Academy and Woods Hole Oceanographic Institution. 181 p. Krone, R., 1962. Flume studies of transport of sediment in estuarial shoaling processes (Finalreport). Berkeley, USA.

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José Manuel Fernández Jaramillo

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Civil engineering (2001) and Master of use of water resources (2006) from the National University of Colombia, Medellín. PhD studies at the Research and Technology Centre West Coast of the University of Kiel, Germany, (2014) in integration of artificial neural networks (ANN) for improving the water level forecast in an operational model in the North Sea. Involved in the investigation of optimization of numerical models, data assimilation and application of ANNs for reconstruction, prediction and data classification of hydrodynamic and environmental information. Involved in research projects of the institution in the coastal areas of Germany, Saudi Arabia, Indonesia and Israel.

Roberto Mayerle

Expert in the development of numerical models and information systems for the management of coastal areas. Graduated as a civil engineer in 1979 in Brazil. Obtained his PhD at the 28

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University of Newcastle-upon-Tyne in the UK in 1988. From 1989 till 1992, in-charge of the development of multi-dimensional flow and sediment transport models in close cooperation with the US Army Engineers at the National Centre for Computational Hydroscience and Engineering in Oxfort/USA. From 1992 till 1996, Postdoctoral Researcher at the Institute of Fluid Mechanics, University of Hannover, Germany. Since 1996 Director of the Research and Technology Centre of Kiel University.

Katharina Róisín Niederndorfer

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Graduation in 2003 in physical geography with emphasis on life cycle assessment at the Goethe University in Frankfurt/M. Until 2004 engaged with sustainable material development and material flow balances at EPEA GmbH in Hamburg. In 2006 graduation at the University of Kiel in coastal geosciences and engineering focusing on monitoring of particulate matter emissions from mariculture operations. Doctoral degree in 2017 with a proposal of a practical method to estimate the ecological carrying capacity for finfish mariculture. Since 2006 and ongoing: surveying and numerical modelling of hydromorphological dynamics and mariculture environmental effects in national and international projects.

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Karl-Heinz Runte

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Studies at the Universities of Bochum and Kiel, Germany, graduation in the field of Coastal Geology and Sedimentology in 1985. Till 1990, independent expert on water resources, PhD studies and graduation at the Research and Technology Centre West Coast of Kiel University with focus on tidal flat dynamics. Till 2018 involvement in marine research projects of the University of Kiel emphasizing surveying and modeling of sediment dynamics, water and sediment pollution and sustainable aquaculture development in the North and Baltic Seas, Germany, Red Sea, Saudi Arabia, Bohai Sea, China, and the Indonesian Seas.

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Figure 1: Study area Pegametan Bay. Satellite image September 17, 2014. ©Google

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a) Rectangular cages with 3 m depths

b) Circular cages with 6-7 m depths

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Figure 2: Types of fish farms in operation at the study site in the northwest of Bali, Indonesia.

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Figure 3: Physical carrying capacity and fish farming locations in the site in northwest of Bali (Mayerle et al., 2017).

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Figure 4: Downscaling model sequence for the coastal aquaculture site in Pegametan Bay.

Figure 5: Model domain, bathymetry, and location of hypothetical fish farms (white circles) in Pegametan Bay. The arrow indicates the position of the tidal gauge.

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Figure 6: Simulated current velocities at 21:00 on 10.12.2008 in Pegametan Bay. Colors denote depths of water.

Figure 7: Simulated water levels and current velocities at three fish farms in Pegametan Bay.

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Figure 8: Comparison of measured and modeled water levels in Pegametan Bay.

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Figure 9: Tide average flow Reynolds numbers in Pegametan Bay.

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particles of 0.01 m/s and 0.07 m/s.

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Figure 10: Simulated deposition of particulate waste DW below a fish farm for falling velocities of

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Figure 11: Dw/Ew versus flow Re number of 30 hypothetical locations for different falling velocities.

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Figure 12: OM versus PON at reference locations and underneath the largest fish farms in

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Pegametan Bay.

a) Cage depth equal to 3 m

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B Cage depth equal to 6 m

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Figure 13: Predicted stocking densities in suitable sites of Pegametan Bay.

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