Estimation of the capture efficiency of trawl gear. I: Development of a theoretical model

Fisheries Research, 16 ( 1 9 9 3 ) 2 3 9 - 2 5 3

239

Elsevier Science Publishers B.V., A m s t e r d a m

Estimation of the capture efficiency of trawl gear. I: Development of a theoretical model William Dickson Bath Lodge, Stonehaven, AB3 2DE, UK (Accepted 16 October 1992 )

ABSTRACT Dickson, W., 1992. Estimation of the capture efficiency of trawl gear. I: Development of a theoretical model. Fish. Res., 16: 239-253. Bottom trawl surveys are conducted almost worldwide usually with simplistic assumptions aboul the area swept clean of fish. There is also a common assumption, for lack of anything better, that the trawl is giving an unbiased sample both as to species and size of the local demersal fish abundance. The general feeling that the assumptions are wrong has not led to much quantitative improvement on them. This paper starts with a brief review of previous attempts to set up a general model of trawl herding and capture. From the stock assessment viewpoint it is the fish depletion rate caused by the whole system, trawler warps and trawl gear that is of concern. This is not as yet entirely measurable. The conventional meaning of efficiency for the gear research worker is output/input meaning, here, catch/encounters. The relationship between these two concepts is discussed. The paper goes on to show how work already published can be extended to estimate the absolute efficiency of the trawl net with bobbin groundrope. This can be done by species length group. The next step shows how to incorporate sweep efficiency and then otterboard effect so that efficiency of the whole gear back to the otterboards is derived. This also means that the effective spread in terms of encounters at the otterboards can be estimated. Part II of this paper applies the theory to previously published comparative fishing data.

INTRODUCTION

Bottom trawl surveys are conducted almost worldwide, usually with simplistic assumptions about the area swept clean. Commonly, the horizontal spread of the net mouth, or a little more than that to make some allowance for the sweeps, is used in swept area calculations. Sweep lengths were sometimes changed for practical reasons with no alteration made to the swept area assumption. All this is in spite of it being well known that there are many kinds of fishing gear, each suited for particular fisheries species and sizes. Survey trawls should, theoretically, sample all sizes and all species that are Correspondence to: W. Dickson, Bath Lodge, Stonehaven, AB3 2DE, UK.

© 1993 Elsevier Science Publishers B.V. All rights reserved 0 1 6 5 - 7 8 3 6 / 9 3 / $ 0 6 . 0 0

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w. DICKSON

present, so of particular concern in the north-east Arctic surveys has been the under sampling of small cod (Gadus morhua L. ) and haddock (Melanogrammus aeglefinus L. ) by bottom trawl (Hylen et al., 1986). It was also becoming apparent that the use of different sweep lengths was probably biassing the size composition of the samples. Experiments were conducted by Eng~s and God~ (1989a) with different sweep lengths, 2 and 0.5× the length of the 40 m sweeps normally used on the standard sampling rig. However, catch ratios established by comparative fishing are by definition relative, and remain so until the absolute efficiency of one of the gears is established. It was progress toward establishing the absolute efficiency of the trawl net itself by size groups, which encouraged a fresh attempt at establishing the efficiency and size selectivity of the whole gear. This first paper describes and defines the catch efficiency of any bottom trawl as a function of various parameters. The second paper deals with the practical application of the theory (Dickson, 1993 ). The Introduction continues with a brief historical review of other attempts.

Previous attempts to set up a general model of trawl herding and capture An early attempt was made by Foster (1969), where the fish being herded was supposed to move a step away from the sweep and at right angles to it. Each time the sweep overtook the fish, it either escaped or made another step, thus the total chances of escape were related to the number of steps. The idea was not really applicable to roundfish, whose reactions to trawl herding were not known in any detail at that time. About the same time Bridger (1969) gave results arising from a new high opening trawl compared with the standard Granton trawl. He did consider the problem by length group. He also postulated that the sweeps were more effective by day and the net more effective by night. The first of these has since found supporting evidence. Strange (1984) wrote a historical review of the same data as Bridger, plus subsequent trials between Granton trawls rigged with different sweep lengths and otterboard sizes. All showed that sweep length, otterboard spread and sweep angle are important parameters. Harden-Jones et al. (1977) obtained some real (absolute rather than relative) measurements of trawl and sweep efficiency by using acoustic tags attached to flatfish and following events on a sector scanner as the fish were approached by the trawl. His efficiency was success rate after the fish were between the otterboards, an important point. As the experiment has not been repeated, this probably reflects the prodigious use of ships time required if results are to be treated by size group, plus the severe problems associated with extending the method to roundfish in deep water. Using a submersible, counting and estimating cod size by visual, optical means, Korotokov (1984) was able to estimate cod abundance by size group prior to trawling over the same ground. He found what he called a catchability coefficient of 0.05 for

ESTIMATION OF THE CAPTURE EFFICIENCY OF TRAWL GEAR. 1

241

30 cm cod, with a curve rising slowly at first to a m a x i m u m of 0.4 at 60 cm, falling thereafter to 0.1 at 80 cm. Observations of roundfish concentrating between the otterboards and heading toward the net in good visibility by Main and Sangster ( 1981 ), gave some indication of an otterboard effect. This was discussed in more detail by Wardle (1986) and reasons were given as to why the optical response should be so. It is now clear that reaction to the otterboards, and not to only sweeps and sand clouds, must be included in any general attempt at modelling the capture process. Independent information on undisturbed cod and haddock abundance before the arrival of trawler and trawl remains unavailable. Observations at the trawl only give information, largely qualitative, on abundance after it is disturbed by the approach of trawler and trawl. Comparative fishing yields only relative results. Thus, the problem of modelling the capture process quantitatively seemed to have reached impasse until EngAs and God~ ( 1989b ), with their bag experiments, showed how many small cod and haddock were escaping between the groundrope bobbins. Codend catch was also measured as were gear operating dimensions, and since with a small mesh net escapes could be discounted, it seemed reasonable to extrapolate the escapes to what would occur over the whole net spread. The performance of the net can now be considered in terms of c a t c h / ( c a t c h + escapes ) by species length group. This provides an anchor point at the net end from which to proceed to fit relative comparative fishing data, working backwards toward the otterboards as is done in the second paper. MATERIALS AND METHODS

The survey trawl was as shown in Fig. 1, and the rigging between otterboards and net as shown in Fig. 2. The trawl was normally rigged with bobbin groundgear, weighing 180 kg in water. A fuller description of the ground gear can be found in EngAs and Godo (1989b). A shrimp trawl is used to avoid escape through the mesh of the forward part of the trawl.

Theoretical method This section works from the undisturbed fish abundance and its vertical distribution toward the catching end. There are established formulae in this process which are used in Part II to handle inputs from the data sets. A list of symbols used is given in the Appendix.

True fish abundance and uncertainties arising in trawl catch rate estimates There is a true undisturbed fish abundance for each species and size group

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ESTIMATION OF THE CAPTURE EFFICIENCY OF TRAWL GEAR. I

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I i oserreh here

- ~. U ' ~ . . - I " ~

Q~I)

, o . . (=o ~,*..L~o)

Fig. 2. Sweep rigging. !

2

3

[

I /A-V1

Kv=

KX, ]

Fig. 3. Hypothetical undisturbed vertical profile of fish abundance is as in Zone 1. Before the arrival of the ship there is the possibility that the vertical profile is disturbed in Zone 2. Between the ship and the gear in Zone 3 there is a further possibility that the fish are driven down by vessel noise, by vessel lights, by the warps, so that the vertical profile becomes as shown in the figure. It is the vertical availability coefficient kv3 at the otterboards that determines the number of encounters with the gear. In Zone 4 there is herding and avoidance. The same four zones may be used to consider possible lateral disturbances. in the p a t h o f t h e t r a w l e r a n d trawl gear. Such a b u n d a n c e , Na, is usually cons i d e r e d in n u m b e r p e r s q u a r e n a u t i c a l mile for s u r v e y p u r p o s e s , o r n u m b e r p e r s q u a r e cable (0.1 n a u t i c a l m i l e ) 2 for m o r e fine g r a i n e d w o r k r e l a t e d to fishing gear p e r f o r m a n c e . E a c h species a n d length g r o u p (slg) is d i s t r i b u t e d in a h y p o t h e t i c a l v e r t i c a l profile, as s h o w n in Fig. 3. T h e p r o p o r t i o n o f the profile for t h a t species a n d length g r o u p in the u n d i s t u r b e d state w i t h i n the vertical gape o f the trawl is/~1. C o n s i d e r first the possible effect o n the verti-

244

w. DICKSON

cal distribution made by the approach of trawler and trawl gear. The approach of the vessel may cause a new vertical profile with a corresponding value of kv2. A third vertical profile can have arisen by the time the trawl boards reach the fish with a corresponding value of k~3. To estimate the true abundance by species length group by trawl, the value ofkv3 has to be known. Those within the whole profile which arrive within the path of the trawl boards, may be considered as arrivals. Only the proportion within the trawl gape may be considered as encounters. Change in vertical profile alone does not change the number of arrivals. Any change in the horizontal distribution of the species length group on the approach of vessel and prior to approach of the trawl boards, in principle changes both the number of possible arrivals and encounters. To estimate the true abundance by trawl, the factor of lateral thinning or compression compared with the undisturbed lateral distribution, has to be known. This factor, kh, is such that in the undisturbed state, kh~ = l, under the vessel it is kh2, and on the approach of the trawl boards it is kha. At present, it is not known whether kh2 and kh3, for cod and haddock of any size group, are greater than, less than, or equal to unity. On the approach of a vessel, cod (if they react at all) tend to dive so that the tendency is for ~1 < kvz
ESTIMATIONOF THE CAPTUREEFFICIENCYOF TRAWLGEAR. I

245

such that the abundance becomes N~kh3. Thus the number of arrivals throughout the water column is given by arrivals =yb VtNakh3

( 1)

where Yb is otterboard spread, V is towing speed, t is time. Many of these arrivals pass the otterboards above trawl headline height, so that the number of encounters with the trawl gear becomes encounters =Yb VtNakh3kv3

(2 )

where kv3 is the proportion of the vertical profile at the trawl doors, reached by headline height. Overall gear efficiency k = catch/encounters. The units of efficiency are dimensionless as is conventional. Thus catch = Yb VtNa kh3kv3k

(3)

Catch can also be derived from other equations, commonly for stock assessment catch c = qfN where q is catchability coefficient, f i s fishing effort (e.g. days trawling), N is the total stock (a number) and c/N is the fishing mortality coefficient F, so that q=F/f. Usually F is considered over 1 year. The idea of relating swept area to the catch equation originated with Baranov (1918) and was developed by Beverton and Holt (1956). For a species like cod q can be quite variable (O. Nakken, personal communication, 1987). This arises because q is inclusive not only of the catchability of the gear, but also such things as changes in vertical availability from year to year, changes in fish concentrations and the degree of success fishermen have in locating them. Also, over periods of several years q is susceptible to improvement in fishing tactics, gear improvements, echosounder and navaid improvements etc. What is required to isolate the gear catchability (or effectiveness) is a short term version of the catch equation, relating the catch to the towing time and the localised place where the fishing is done. This may be written as

C=qatNa

(4)

Thus equating eqn. (3) with eqn. (4) gives effectiveness qa =

Yb

Vkh3kv3k (units

m 2s- i )

(5)

Thus gear effectiveness includes parameters determining encounter rate as well as the overall gear efficiency term which converts encounters between otterboards into catch. Note that when comparing two gears, 1 and 2, even towing close together to reduce the effect of variability in N~, and for the same length of time and at the same towing speed, it is the effectiveness and not in general the efficiency ratios that are being compared.

C1 yblkhatkv3jkl C2 - - Yb2 kh32 kv32 k2

(6)

246

w. DICKSON

To strictly compare efficiencies kl and k2, the spreads Yb~ and Yb2 have to be the same to ensure that kh31=kh3z and the headline heights are the same, so that kv3~= kv32. Also, since different trawlers may have different effects on kh and kv, the gears should be switched between ships in an even handed way. Even comparing two sweep lengths with the same net and with operating dimensions of both gears measured, there remains to consider, when interpreting results, how close C1/ C2 = Ybl kh31 kv31 k~/ (Yb2kh32 kv32 k2 ) is to C~/ C2 = Ybl

kl/ (Yb2 k2). Trawl efficiency and sweep efficiency To proceed further it is necessary to go to the net and work forwards toward the otterboards. Trawl net efficiency, kn = catch/encounters between the wing tips, which is the same thing as catch/(catch+escapes) between the wing tips. An extrapolated estimate of the escapes between the wing tips is made from the bag catches of Eng~s and Godo (1989b), values of STC and BC being taken from their Table 2, p. 274. Thus for present purposes k, = STC/ ( 19.5 BC/11.5 + S T C ) . The wing span is 19.5 m and the bobbin groundrope span is 11.5 m. The bags tend to capture mostly smaller fish, and bigger ones have some alternative means of escape. Even if the bags were extended to the wing ends, they would not include the following observed means of escape viz: ( 1 ) A few larger fish may pass between the port and starboard wing ends, re-cross the line, and swim out. This escape route concerns mainly faster swimming species. (2) Some larger haddock swim up and over the headline. (3) Some of the larger fish (mostly cod) can remain swimming in front of the groundrope when the gear is hauled. Escape of those fish remaining in front of the groundrope can be predicted by considering the swimming speed endurance, for example as interpolated from Fig. 4. The values used here are those whereby in Arctic water temperatures, cod can achieve 400 m at 1.9 body lengths s -~ and 100 m at 2.8 bodylengths s -~. The distance that can be swum at a towing speed of 1.5 m s -I is then interpolated by length group, and taken as a proportion of the 30 min towing distance. The net efficiency is then reduced by this amount. With these estimates of net efficiency, it is possible to consider the sweep efficiencies in herding the fish into the path of the net. Sweep efficiency, ks = number herded/encounters over the sweep path width. The encounters at the net include both those fish directly in the path of the net, and those herded into the path of the net from the sweep path so

y ,k=kn [y.

-y.) l

(7)

where Yb is board spread, and Yn is net spread. It is convenient to put effective path-width, Ye=Yb k, with the proviso that

247

ESTIMATION OF THE CAPTURE EFFICIENCY OF TRAWL GEAR, 1

o

tO

to

o 0 tt~

o

o

o

0

0.5

1 1.5 Speed (m/s)

2

25

Fig. 4. Distance swum before exhaustion at a range of speeds in cod, interpolated and redrawn from Blaxter (1969).

while this is the effective path-width in terms of the encounters presented between the otterboards and up to headline height, it may not quite be the effective path-width in terms of stock depletion because of possible changes in vertical and horizontal distribution on the approach of ship and warps.

Allowingfor otterboard effect Otterboards are big enough to have an important effect on fish herding or avoidance. For this reason it seemed necessary to attempt to bring their influ-

248

w. DICKSON

ence into the equations. The principle follows Wardle (1986) in that the fish in front of the otterboards are split into two groups. One group remaining to the outside and lost, the other group keeping one eye on the board, thus moving toward the centre line, and gradually turning to face toward the net. This is what has come to be known as the fountain effect. Reaction distance can be expected to be different night and day, by depth, and water clarity. These are not distinguished in the data set used, consequently, the approach here has to be rather general. The procedure is to set up parameters in the equations which allow for varied reaction distance and allow for both positive (herding) and negative (avoidance) effects. In this way, excursion of these parameters in the various comparative fishing equations, show up as improbable, credible, or even helpful in the analysis of the results. The distance of hydrodynamic influence on the high pressure side of the board is quite small (approximately 1 m ) , even for a big board. The water flow from the otterboard flows over the top and round the back of it. Fish immediately on the inside of the board can be sucked out. Others could follow them. The sand cloud at this point is low down, and the area immediately behind the otterboard and over the low sand cloud may present itself as an escape route, particularly for fish which are above otterboard height, but still below headline height. The warp can be expected to have some negative effect immediately in front of the otterboard. Like a sweep in the wrong direction, the warp up to the height of the headline will have roughly 2.5 m path-width. Occasionally fish are seen escaping over the otterboard, more commonly few or no fish are seen near the otterboard. Negative effect is severe because fish are removed from the system. Proceeding to introduce this concept into the equations, let the positive effect be acting over a path-width Rbi (both boards, Rbi=board paths inward) and herding inwards from the splitting line. Let the negative effect be acting over a path-width Rbo (both boards, Rbo = board paths outwards) and removing fish from the system. Because of the negative effect, the amount of fish available to the gear is reduced so that without positive effect the equation becomes

Y¢=kn[y.-I'k~(yb--y~--Rbo) ]

(8)

The fountain effect is difficult to model because although the otterboards appear to give the initial impetus to inward movement, that must soon be taken over by the effect of sweeps and sand clouds. Once the impetus is under way there is also the reaction of fish to each other. One simple suggestion made to the author has been to consider a like number of fish to those from path-width Rbi displacing those within the remaining sweep path-width (Yb--Y,--Rbo--Rbi) to finish up with a like number added to those within path-width y,. Thus, the equation becomes

ESTIMATIONOFTHECAPTUREEFFICIENCYOFTRAWLGEAR.I

249

Ye = k n [Yn +Rbi + ks (Yb --Yn --Rbo --Rbi) ]

(9)

It is also possible to consider that only some of the fish displaced from pathwidth Rbi displace a like number into path-width Yn and the rest remain to increase the fish density in the remaining sweep path, for instance Y~= / ~ [y, +Rbi/2 + ks(yb --Yn --Rbo --Rbi + Rbi/2 ) ] Ye = kn [Yn +Rbi/2+ks(yb --Yn --Rbo --Rbi/2) ]

(10)

Another possibility is to consider that the fish within (Yb-Rbo) are squeezed into the path-width (Yb-Rbo--Rbi) thus increasing the density there in proportion (Yb- Rbo) / (Yb-- Rbo-- Rbi ), and the remaining path over which the sweeps and sand clouds herd fish, is (Yb-Y~- Rbo--Rbi ). The equation thus becomes Ye = kn [yn + ks(Yb --Yn --Rbo --Rbi) ] (Yb --Rbo)/(Yb --gbo --Rbi)

( 11)

Equations (9)-(11 ) deal with different intensities of the fountain effect. All are discussed in Part II. CONSTRAINTS

There are certain constraints on the values of kn, Ye, and ks. At the lower end of the fish size range, values will tend to zero. Net efficiency and effective spread should have a decreasing slope with increase of length, and may eventually have a negative slope if the fish grow that big. The slope of the sweep efficiency should likewise decrease gradually, but there is no apparent reason for it to have a negative slope at the top end. The maximum value of Ye can hardly be > Yb, and if it is < yn for commercial fish, one can suspect gear defects. None of the efficiencies should be > 1. Discontinuities in the changes of slope are hardly likely. None of the slopes should go through the origin, but rather approach zero at a small fish length, and the slope in this region might also be expected to go through an inflexion. Another constraint is that values for kn, ye and ks, established for the standard gear (bobbin groundrope and 40 m sweeps) must be kept the same whatever other rig with which the standard gear is compared. CALCULATION METHOD

The procedure can be carried out with a hand calculator. More easily eqns. (9), (10) or ( 11 ) can be programmed on a personal computer to present results in spreadsheet form. Columns represent fish size groups and for two gears being compared the rows are Rbi, kn~, kn2, Ye~/Ye2, ks1, ks2, Yej, Y~2,kl and

250

w. DICKSON

k2. Measured parameters Ybl, Yb2, Yrll and Y,2 and a fixed Rbo a r e entered as inputs. The first four rows are also input, Rbi a s seems reasonable, kn~, kn2 resulting from the bag experimental data and Ye~/Ye2 from the experimental catch ratio data. Examples can be seen in Tables 4-8 in Part II (Dickson, 1993). Enter any range of values in row ye~ and all the remaining values emerge on the spreadsheet. These are then scanned for compliance with the constraints and new values of the variable inputs entered until a coherent table emerges. The same process is repeated with comparisons, Gear 1 vs. 3 and Gear I vs. 4. The whole process is iterative and the narrowing of the permissible range of variable inputs soon becomes apparent. CONCLUSION

It was necessary to look at the trawl gear selectivity problem working backwards from the trawl net itself toward the otterboards to provide an interim solution. In terms ofdemersal fish encountered by the trawl gear within otterboard spread and up to headline height, formulae have been derived which allow better estimates of effective path-width by fish size group. The principles as described should be generally applicable for any demersal fish. How they are applied in practice to cod and haddock in the north eastern Arctic is the subject of Part II (Dickson, 1993). The possibility of trawl catch, size selection and swept area abundance estimates being affected by the passage of the trawler and warps over the fish has been outlined. While there is no consensus on how serious these effects are, increasing depth simplifies the problems. Those who use swept area methods in trawl surveys cannot wait until all problems have been resolved.

REFERENCES Baranov, T.I., 1918. On the question of the biological basis of fisheries. (Rep. Div. Fish Management and Scientific Study of the Fishing Industry, I. Nauch. issledov, iktiol. Inst. Izv, 1, Moscow, pp. 81-128. Beverton, R.J.H. and Holt, S.J., 1956. A review of methods of estimating fish populations, with special reference to sources of bias in catch sampling. Rapp. P.-V. Rrun. Cons. Int. Explor. Met, 140:( 1 ) 67-83. Blaxter, J.H.S., 1969. Swimming speeds of fish. In: A. Ben-Tuvia and W. Dickson (Editors), Proc. FAO Conf. Fish Behaviour in Relation to Fishing Techniques and Tactics, Bergen, 1927 October 1967. FAO Fisheries Rep. 2 (62), 69-100. Bridget, J.P., 1969. The behaviour of demersal fish in the path of a trawl. In: A. Ben-Tuvia and W. Dickson (Editors), Proc. FAO Conf. Fish Behaviour in Relation to Fishing Techniques and Tactics, Bergen, 19-27 October 1967. FAO Fisheries Rep. 3 (62), 695-715. Dickson, W., 1993. Estimation of the capture efficiency of trawl gear. I1: Testing a theoretical model. Fish. Res., 16: 255-272. Enghs, A. and O,R. Godo, 1989a. The effect of different sweep lengths on the length composition of bottom-sampling trawl catches. J. Cons., 45: 263-268.

ESTIMATION OF THE CAPTURE EFFICIENCY OF TRAWL GEAR. I

25 l

Eng~s, A. and O.R. Godo, 1989b. Escape offish under the fishing line of a Norwegian sampling trawl and its influence on survey results. J. Cons., 45: 269-276. Foster, J.J., 1969. The influence of fish behaviour on trawl design with special reference to mathematical interpretations of observations on the swimming speeds of fish and results of C.F. experiments. A. Ben-Tuvia and W. Dickson (Editors), Proc. FAO Conf. Fish Behaviour in Relation to Fishing Techniques and Tactics, Bergen, 19-27 October 1967. FAO Fisheries Rep. 3 (62), 731-773. Harden-Jones, F.R., Margetts, A.R., Greer Walker, M. and Arnold, G.P., 1977. The efficiency of the Granton otter trawl determined by sector-scanning sonar and acoustic transponding tags. Rapp. P.-V. R6un. Cons. Int. Explor. Met, 170, 45-51. Hylen, A., Nakken, O. and Sunnana, K., 1986. The use of acoustic and bottom trawl surveys in the assessment of the north east Arctic cod and haddock stock. In: M. Alton (Editor), A Workshop on Comparative Biology, Assessment and Management of Gadoids from the North Pacific and Atlantic Oceans, Seattle, WA, pp. 473-498. Korotkov, V.K., 1984. Fish behaviour in a catching zone and influence of bottom trawl rig elements on selectivity. Int. Counc. Explor. Sea, CM 1984/B:15, 14 pp. Main, J. and Sangster, G.I., 1981. A study of the fish capture process in a bottom trawl by direct observations from an underwater vehicle. Scott. Fish. Res. Rep., No. 23, 23 pp. Mitson, R.B., 1982. Acoustic detection and estimation of fish near the seabed and surfacc. Syrup. Fisheries Acoustics, Bergen, 21-24 June 1984, FAO Fisheries Rep. (300), FAO, Romc, pp. 27-34. Strange, E.S., 1984. Review of the fishing trials with Granton and Saro deep sea trawl gear 1963 1967. Scott. Fish. Working Pap., 8/84, 60 pp. Wardle~ C.S., 1986. Fish behaviour and fishing gear. In: T.J. Pitcher (Editor), The Behaviour of Teleost Fishes. Croom Helm, London, pp. 463-495.

Horizontal movement coefficient ( 1 to 2) Vertical profile 2

Vertical reach coefficient 2

Abundance at approach of otterboards Horizontal movement coefficient ( 1 to 3) Vertical profile 3

Vertical reach coefficient 3

kh2

k~2

Na3

kv3

R~

V

Yb

Path-width

Encounters

Otterboard spread (trawl path-width ) Towing speed (w.r.t. earth ) Arrivals

Abundance under vessel

N~2

kh3

Vertical reach coefficient 1

kv~

Vertical profile

Number by (slg) in whole water column in trawl path, arrivals = Naa V t Yb/1852 Number by (slg) below height in trawl path, encounters = arrivals kv3 Inside Yb, which is cleared of encounters (escapes at otterboard). Not exactly known, but can be given a range of values including 0

Proportion of Na3 up to headline height above bottom

By (slg) operates on ?Casuch that Na3=kh3 Na kh3 may be > 1, < 1 (largely unknown) Percentage of N~,z by depth interval above bottom

Proportion of Na2 up to headline height above bottom By (slg) throughout the whole water column

By (slg) operates on Na such that Na2 = kh2 Na, kh2 may be > 1, = 1, < 1 (largely unknown) Percentage of Na2 by depth interval above bottom

Proportion of N~ up to headline height above bottom By (slg) throughout the whole water column

m

Number

Number

Knot

m

Number/(nautical mile) 2 Dimensionless

Number/(nautical mile) 2 Dimensionless

Number/(nautical mile) 2 Dimensionless

Number/(nautical mile) 2 Dimensionless

Number/(nautical mile) 2 Dimensionless

Number (nautical mile)2

By species length group (slg) throughout the whole water column Percentage of N~ by depth interval above bottom

Na

Undisturbed abundance

Units

List of symbols

APPENDIX

©

Number

Trawl efficiency

Effective spread

Catch Effort (fishing time) Catchability coefficient Stock size Effectiveness

STC

k

Y~

f q N qa

C

Number

path-

BC

Yn

Net efficiency

Rbi --

Net spread Remaining sweep width Sweep efficiency

Extra path-width

k.

ks

Yb-- Rbo -

Yn

Rbi

By (slg) operates on those encounters within the remaining sweep path plus those from Rbi, herding them towards the net mouth By (slg) operates on all those encounters which are herded to the net path plus those that are already in the net path. kn is extrapolated from bag catches relative to codend catch By (slg) in bag catches extrapolated to 11.5 m (bobbin groundrope spread) By (slg) in trawl codend during bag catch experiments By (slg) operates on encounters such that c a t c h = k encounters Ye = k Yt,. Note that effective spread is based on encounters By (slg)

Inside (yb - - R ~ ), which is cleared of those encounters now moving inward and toward the net mouth Not exactly known, but can be given a range of values including 0 Measured between top wing ends (net path-width )

m 2 s- i, nm 2 h-

Number s, h, etc. s - l , year -~, etc. Number

m

Dimensionless

Number

Number

Dimensionless

Dimensionless

m

F(/

m

1 etc.

t"

© "11

rn 7

m

,..]

¢3

IX

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