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Modelling the visual stimulus of towed fishing gear
Fisheries Research 34 Ž1998. 165–177
Modelling the visual stimulus of towed fishing gear Y.-H. Kim a , C.S. Wardle a
b,)
Institute of Marine Industry, College of Marine Science, Gyeongsang National UniÕersity, Inpyeong-Dong, Tong-Young, Kyeognam, 650-160, Republic of Korea b The Marine Laboratory, P.O. Box 101, Victoria Road, Aberdeen, AB11 9DB, UK Received 15 May 1997; accepted 28 October 1997
Abstract A number of modules are developed for a model with the aim of predicting the strength of the visual stimulus that might initiate fish reactions from any viewing point within a towed fishing gear. The first part of the model defines the properties of the undersea light field through which a trawler might tow a fishing gear including allowances for geographical position, weather, water quality and diurnal changes. A variety of light measurements are made to check day and night light levels used in the model. The underwater luminance of water, sand cloud and sea bed which form the background against which a fish sees the net components is then calculated. An example constructing the space in which a fish may react within a towed trawl gear is developed for the BT130C, North Sea trawl. This part develops an existing net frame model that creates the three-dimensional shape of the towed net from the designers net drawings. Analysis of previous observations of this trawl form the bases for simulation of sand clouds produced by the ground gear and otter board as part of the fish stimulus. Finally the simulated trawl is towed through the predicted light field and methods are developed for calculating the visibility of the net components including netting, ropes, floats, bobbins, otter boards and their sand clouds as viewed from any fish position within the net. An example of the result of these predictions, maps the stimulus strength for one fish position. q 1998 Published by Elsevier Science B.V. Keywords: Contrast; Underwater light; Model fish reaction
1. Introduction The principles of what make nets more or less visible in real underwater light conditions were investigated and developed in Kim and Wardle Ž1998.. Concentrating on the importance of vision in reactions of fish to trawls, this study applies these principles together with those already evolved for understanding the shaping of nets when towed in the sea. )
Corresponding author. Tel.: q44 1224 295339; fax: q44 1224 295511.
Combining models of the towed net geometry with the visual properties of its components in the underwater light field allows construction of an overall model of a trawl as a visual stimulus. Because trawls are towed in all conditions and different seas, the visual environment through which it is towed is first defined to form the water background against which a fish inside sees the net. Demersal trawls are complicated by being towed over the bright reflective sea bed which take the place of the darker zones seen below the fish when in midwater trawls. Turbulent sand clouds are thrown
0165-7836r98r$19.00 q 1998 Published by Elsevier Science B.V. All rights reserved. PII S 0 1 6 5 - 7 8 3 6 Ž 9 7 . 0 0 0 8 9 - 1
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Y.-H. Kim, C.S. Wardler Fisheries Research 34 (1998) 165–177
up when otter boards pass over sand or mud and form brighter screens on either side of the gear. Ground gears throw up a rippling layer of cloud screening the sea bed. There are many possible variations of this sort and simulations by computation can allow us to understand and explore variable features of the visual stimulus of nets which would otherwise be difficult and costly using sensitive and expensive equipment to repeatedly pass inside nets to make the equivalent observations. Combining our knowledge of the limits to fish behaviour, with predictions of the stimulus as it changes with the fish’s positions within the net, might also allow a further development of a dynamic model to simulate the reaction patterns of the fish. 2. Materials and methods Direct measurements of the surface light were carried out using a Photometric sensor ŽLI-COR INC, LI-210SB. with data logger ŽSolartron 3531D. or Photometer ŽLI-188B. and were made every 5 s. The photosensor was calibrated with the illuminance range from 67 to 2000 lux using a standard NPL lamp in the dark room. Day time light from sunrise to sunset was measured in the North Sea from 29 January to 9 February 1994 and on land at the Marine Laboratory between March and April 1994 and February to June 1995. The illumination at night without moonlight was measured every 10 s using a calibrated photomultiplier and data logger from dusk to dawn at a rural site near Banchory in Scotland Žlat 57.078N, long 2.578W. from 23 to 25 February 1995 and at the SOAEFD Marine Laboratory Žlat 57.138N, long 2.18W. from 13 June to 22 July 1995. Underwater light measurements were made with a photomultiplier as described in Kim and Wardle Ž1998., where many of the specialist terms are introduced. 3. Modelling, results and discussion 3.1. Modelling underwater light and background luminance The essential assumptions for the modelling of the surface light and thence underwater light are that
global surface illuminance is changed by the sun’s altitude and the maximum absolute values in a clear sky are predictable from the U.S. Navy illumination charts ŽU.S. Department of the Navy, 1952.. Light level is decreased with depth by vertical attenuation coefficients according to the optical water type classified by Jerlov Ž1976.. Illuminance and luminance are treated as photometric units. Luminance distribution within zenith and azimuth profiles in midwater is dependent on the vertical and beam attenuation coefficients. 3.1.1. DeÕelopment of the surface light model and effects of dawn, dusk and cloud The surface light prediction model by Yallop Ž1986., including effects of both sun and moon altitude has been modified using data from the illumination charts ŽU.S. Department of the Navy, 1952. and to give values when the sun’s altitude is below the horizon between y5 and y908 as a fitted fourth-order polynomial equation. The model light data are considered as in conditions of normal clear sky. Some examples of one-hour cycles of the most changeable daylight condition in cloudy weather were measured in order to give the light blockage ratio Ž C E .. C E is the ratio of the blocked value I D Žin lux. to the clear sky value IC Žin lux. by sun or moon as I D rIC . The C E values are observed from 0.12 in the darkest cloud cover Ž C L s 1. to 1 in clear sky Ž C L s 0., close to the US Navy Tables. C E can be expressed as in the following first-order linear equation ŽEq. Ž1.. when within the above range of light conditions: C E s 1 y 0.9C L
Ž 1.
3.1.2. Night light leÕel The ratio Ž NE . of the measured illuminance Ž I N . on a clear night to the calculated illuminance Ž IC . without moonlight was represented with negative sun’s altitude A S Žin degrees. below the horizon as shown in Fig. 1. The relationship between the ratio NE and A S can be expressed as follows with f 0 s 0.139 and f 1 s y0.127 ŽNo. of data s 600, r s 0.98.: NE s f 0 exp Ž f 1 A S . , Ž A S - y7 .
Ž 2.
Y.-H. Kim, C.S. Wardler Fisheries Research 34 (1998) 165–177
Fig. 1. An example of the ratio of measured light value Ž I N . to calculated light value Ž IC . plotted against the sun’s altitude below the horizon on a clear night.
The weather effects on night light are more complex than daytime because light scattering is more marked at night time ŽRoach and Gordon, 1973; Hahn et al., 1995.. Surface illuminance IS Žin lux. can be represented as follows: IS s IC C E NE
Ž 3.
3.1.3. Modelling the underwater light with depth profile The amount of daylight entering the water surface is described by the so-called Albedo which is the ratio of reflected light energy to incident light. The higher the Albedo the smaller the proportion of light entering the surface. The Albedo is increased with longer light wavelength, lower sun altitude, less cloud and shorter wave amplitudes of the sea surface ŽHojerslev, 1986.. Following Ivanoff Ž1977., the Albedo Ž A. was exponentially increased with the sun’s altitude Ž A S . from 0 to 108 and then decreased from 10 to 908 as summarised by the following equation: A s u 0 exp
Ž u1 A S .
Ž 4.
The coefficients u 0 and u1 relating to the sea surface state and sun’s altitude are shown in Table 1. The
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downwards light intensity Ž I W . just below the sea surface varies as Ž1 y A. of the surface illuminance IS . The downwelling underwater light as illuminance is decreased with depth YD Žin meters. and vertical attenuation coefficient k. The results of the light measurements from Kim and Wardle Ž1998. were interpreted in terms of the depth, water turbidity, cloud effects, wave amplitude and Albedo as shown in Table 2. The vertical attenuation coefficient k and IO in IO exp Ž k Y D . was calculated by the least-squares method for depths between 30 and 80 m. This deeper layer was considered as a homogeneous water column and illuminance was varied exponentially whereas shallower than 30 m, it changed more dramatically according to the change of the coefficient k ŽJerlov, 1976.. Practical trawling is at 30 m or deeper. Therefore, surface layer effects in the water shallower than 30 m are adjusted using the mean ratio R S of the theoretical value IO to I W at just below the water surface or could be approximated using the values from Jerlov Ž1976.. For depths greater than 30 m, the underwater illuminance I W Žin lux. can be expressed with integration of depth YD and k as follows. I W s IS Ž 1 y A . R S exp HykdŽY D . , Ž Y D ) 30 m .
Ž 5.
3.1.4. Modelling underwater background as luminance Luminance Ž L. depends on reflection factor Ž r . of an object’s surface and illuminance Ž I . as L s r Irp ŽArnold, 1976.. However the underwater background has no surface but particles in the water individually scatter the illuminance forming the
Table 1 The coefficients u 0 and u1 of Eq. Ž4. for the sea surface Albedo related to the sun’s altitude Coefficients Sun’s altitude-108
u0 u1 ra a
Sun’s altitude)108
Wave amplitude Žm.
Wave amplitude Žm.
0.5
0.5
1.0
2.0
1.0
2.0
0.0976 0.0437 0.0827 0.2626 0.1626 0.1556 0.0795 0.1307 0.0418 y0.0409 y0.0240 y0.0270 0.987 0.953 0.992 0.995 0.992 0.996
Correlation coefficient. Each no. of data is 6.
Y.-H. Kim, C.S. Wardler Fisheries Research 34 (1998) 165–177
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Table 2 An analysis of underwater light measurements for Eq. Ž5. Wave amplitude Žm.
Cloud ratio
Cloud effect
k
1 y Albedo
IS Žlux.
I W0 Žlux.
IO Žlux.
R S s IO rI W0 Ž%.
1.0 0.5 1.0 0.5 1.0
0.8 0.3 0.9 0.5 0.6
0.277 0.785 0.153 0.605 0.503
0.156 0.144 0.119 0.111 0.133
0.881 0.838 0.884 0.842 0.871
16215 14659 19089 17414 14438
3959 9637 2583 8874 6323
150 337 94 319 231
3.79 3.50 3.64 3.59 3.65
k: Vertical attenuation coefficient. IS : Calculated surface light. I W0 : Illuminance just below the sea surface. IO : Calculated from I W s IO expŽykYD .. R S : Surface light ratio. YD : Water depth Žm..
background brightness or luminance. Snell’s circle limits the direction of maximum luminance from a zenith angle of 0 to 48.68 with the sun’s altitude from 90 to 08 respectively ŽHojerslev, 1986.. The zenith angle Ž QO . for the direction of maximum light when just below the water surface will be varied by a cosine curve with the sun’s altitude Ž A S . as QO s 48.6 cosŽ A S .. The reduction ratios of the zenith angle of maximum luminance is defined as R Q and the zenith angle for maximum luminance with depth as Q Y . Then, R Q and Q Y adapted from measurements in the table of Tyler Ž1969. become:
were analysed in order to clarify the relationship among the many factors such as zenith angle, azimuth angle, water depth and cloud cover ŽHojerslev, 1986; Voss, 1988.. The ratio of radiance at azimuth 1808 to that at azimuth 08 was defined as the relative radiance L Rd . Examination of all the values of L Rd between zenith 0 and 1808 gave the minimum luminance ratio L Rm at zenith angle between 30 or 408. The L Rm for depth Y D Žin meters. can be linearly derived for cloud cover C L between C L s 0.1 and 0.7 by Eq. Ž7. with the approximate values for the coefficients Õ 0 s y0.199, Õ 1 s 1.1, Õ 2 s 0.186, and Õ 3 s y0.216:
R Q s q 0 C L q Ž q1 q q 2 C L . Y D
L Rm s Ž Õ 0 q Õ1C L . q Ž Õ 2 q Õ 3 C L . ln Ž y .
Q Y s 48.6 Ž 1 y R Q . cos Ž A S . where C L is cloud-cover ratio and depth YD and the coefficients q0 , q1 , and q2 are 1.025, 0.0106 and y0.0106, respectively. Timofeeyeva Ž1971. presents a table of radiance distribution Žradiance is the radiometric equivalent of luminance. where E s krc where k is the vertical attenuation coefficient and c is the beam attenuation coefficient. If the luminance is proportional to radiance and if zenith angle ZA s 08 is equal to maximum luminance angle Q Y , then the zenith profile as a luminance ratio L R Ž ZA . can be estimated by interpolation of E and ZA . The values for the radiance distribution underwater by Tyler Ž1969. and Tyler and Shaules Ž1964.
Ž 7.
The luminance ratio L Rd was found to change with the geometric zenith angle ZA Žin degrees. when ranged from 0 to 1808 as in the following equation: L Rd s P0 q P1 exp P2 sin Ž ZA r2 .
Ž 8.
and P0 , P1 , and P2 are shown in Table 3 and they can be approximated with L Rm . Once the luminance ratio L Rd with zenith angle is determined, general luminance ratio L R Ž A Z . varying with azimuth A Z ranged from 0 to 1808 can be estimated by Eq. Ž9.: L R Ž A Z . s W1exp W2 cos Ž A Zr2 .
Ž 9.
and the coefficients W1 and W2 are shown in Table 3 and they are closely related with L Rd .
Y.-H. Kim, C.S. Wardler Fisheries Research 34 (1998) 165–177
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Table 3 The coefficients for P0 , P1 and P2 of Eq. Ž8., and W1 and W2 of Eq. Ž9. Condition
L Rm or L Rd
Coefficients P0
No. of data
Correlation coefficient
P1 or W1
P2 or W2
0.4637 0.3861
y6.7628 y4.6525
5 5
0.983 0.985
ZA - 408 Eq. Ž8.
0.54 0.69
ZA ) 408 Eq. Ž8.
0.07 0.54 0.69
y y y
0.0187 0.3587 0.5777
4.0033 1.0410 0.5487
14 14 13
0.997 0.993 0.939
ZA ) 408 Eq. Ž9.
0.54 0.69
y y
0.4985 0.6617
0.6473 0.3816
10 10
0.978 0.984
0.5 0.6
3.1.5. Conclusions from modeling the underwater light field In conclusion, underwater relative luminance L b as converted from underwater illuminance I W has a maximum value at zenith angle Q Y and azimuth 08. The luminance distribution ratio L RŽ ZA . with zenith can be predicted by the attenuation coefficient ratio krc. The luminance ratio L RŽ A Z . with azimuth can be estimated in relation to depth and cloud ratio. Accordingly, a complete profile of azimuth and zenith
background luminance L b Ž ZA , A Z . values is determined as follows. L b Ž ZA , A Z . s L R Ž ZA . L R Ž A Z . I W rp
Ž 10 .
In addition, a symmetrical distribution of the luminance values can be assumed in the other half hemisphere as azimuth range of 180–3608. The results of the measurements of luminance distribution are shown in Table 4 where they match very well with those calculated using the prediction
Table 4 Results of illuminance measurement as light ratio with zenith angle at depth 30 m, sun’s altitude 12–208 in overcast sky C L s 0.6 Beam attenuation coefficient
Illuminance ratio with zenith Ž deg . 0
45
90
135
180
Measured Õalues 0.708 0.639 0.803 0.787 0.883 0.779 0.841 0.759 0.810
1 1 1 1 1 1 1 1 1
0.615 0.609 0.723 0.766 0.725 0.641 0.650 0.767 0.605
0.151 0.079 0.124 0.081 0.081 0.136 0.080 0.170 0.143
0.042 0.035 0.026 0.039 0.027 0.034 0.028 0.047 0.031
0.034 0.029 0.022 0.026 0.023 0.024 0.024 0.031 0.025
Mean s 0.779 S.D.s 0.068
Mean s 1 S.D.s 0
Mean s 0.686 S.D.s 0.067
Mean s 0.112 S.D.s 0.036
Mean s 0.033 S.D.s 0.007
Mean s 0.026 S.D.s 0.003
Calculated Õalues
1
0.641
0.129
0.048
0.021
a
Calculated as luminance by Eq. Ž10. with mean value of beam attenuation coefficient 0.779, vertical attenuation coefficient 0.15 and other conditions are same as measurements.
Y.-H. Kim, C.S. Wardler Fisheries Research 34 (1998) 165–177
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model as Eq. Ž10. above by a paired t-test Ž N s 5, p - 0.001.. Note the calculated values represent something like 18 of acceptance whereas the photomultiplier is centred about 808. This model showed similar results to the Hydrolight model by Mobley Ž1989.. 3.2. Complications due to sand clouds
shallow ground by Main and Sangster Ž1981. were reviewed to form an approximation of the viewing geometry. The spread SC Žin meters., the height HC Žin meters. and lateral distance LC Žin meters. from the bridle to the sand cloud respectively were diffused with increasing distance Z B Žin meters. from the otter board towards the cod-end as in Eq. Ž11.: SC , HC or LC s j0 q j1 ln Ž Z B .
The otter board sand cloud is both a visual stimulus herding fish into the net path as well as a background against which parts of the net are viewed by the fish. This study develops a model of the geometry of the sand cloud and then considers its visual contrast and contrast transmission to the fishes eye. The sand cloud as a visual stimulus looks like sky cloud with similar ephemeral and formless characteristics. The following assumptions are made in order to theoretically construct a model of a visual sand cloud. The relevant view is observed from inside the trawl gear during the towing operation. The relevant shape parameters are the maximum height and the near side spread and both have linear time dispersion. Its virtual dimensions and dispersion are affected by the dimensions and hydrodynamics of the otter board as well as by the relative speeds and directions between the towed gear and the natural water flow. 3.2.1. Modelling the geometry of the sand cloud The relative shapes of the sand cloud produced by four kinds of otter board as measured on relatively
Ž 11 .
The intercept j0 and the slope j1 are shown in Table 5. It can be assumed that the dimension of the sand cloud is changed by the dimensions of the otter board, towing conditions and sea bed characteristics with index G 1 s 1 Žvery muddy ground. and G 1 s 0 Žvery hard ground.. The intercept j0 and j1 in Eq. Ž11. could be the function of height H b and length S b of the otter board, towing speed and water flow speed and angular difference between towing and current direction. The image of the otter board sand cloud as if seen by a fish eye from positions inside the trawl net is chaotically changed with time. An example of a lateral view of the cloud slice plotted as height against the distance from the otter board can be represented as particle mapping by cloud shape ŽHockney and Eastwood, 1988. or by catalytic turbulence ŽEiswirth et al., 1995.. Another type of sand cloud near the sea bed is produced mainly by the bobbins of the ground rope and chain and appears like a waving blanket and reflects downwelling light in quite a different way compared with clear sea bed.
Table 5 The intercept j0 and the slope j1 of Eq. Ž11. for dimensions of the sand cloud formed by the otter boards as measured in the experiments of Main and Sangster Ž1981. Dimension of sand cloud
Coefficients
Kinds of otter board Flat
Vee
Polyvalent
Cambered
Spread
j0 j1
0.492 1.229
1.055 1.038
y0.660 1.305
y1.506 1.470
Height
j0 j1
0.260 0.785
0.015 0.827
0.347 0.698
y0.116 0.817
Lateral distance
j0 j1
y2.114 2.381
y2.539 2.440
0.177 1.272
y0.032 0.901
)
Each no. of data is 16 Žexcept 15 for lateral distance. and each correlation coefficient is r ) 0.97.
Y.-H. Kim, C.S. Wardler Fisheries Research 34 (1998) 165–177
3.2.2. Modelling the brightness contrast of sand cloud The results of the light measurements of the sand cloud are processed with reference to the viewing angle, attenuation coefficients and luminance ratio R C of the sand cloud or sea bed. They were also compared with measured luminance in midwater in the same conditions in Table 6. The luminance measured while looking at the large surfaces of the relatively stable sand cloud that is found near the cod-end was 1.4 to 1.8 times brighter than the midwater luminance at the same depth and viewing angle. Examples of the change of the beam attenuation coefficient sampled by entering the sand cloud with the 25 cm Transmissometer are presented in Fig. 2. The sea bed at a depth of 50–60 m showed a range of luminance ratio from 3.2 to 3.7, and was more reflective than the value of 2.6 measured in shallow water by Ivanoff et al. Ž1961.. The change of the luminance ratio of sea bed to midwater seen from a raised position can be estimated in relation to the viewing distance by the contrast reduction formula. The luminance ratio R C of sand cloud luminance to midwater luminance was measured as 0.2 when within the sand cloud and ranged from 5.5 to 1.4 between net mouth and
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Fig. 2. Examples of the variation of the beam attenuation coefficients due to entering the otter board sand clouds near the cod-end during the trawl operation.
cod-end when measured out of the sand cloud depending on the location and viewing angle ŽTable 6.. If the beam attenuation coefficient of the sand cloud Ž cS . is proportional to the density of the particles, the contrast could also be related to coefficient cS . Coefficient cS of the sand cloud might be predicted from a maximum value c m at a distance Z B from the otter
Table 6 Examples of light characteristics of sand cloud, sea bed and various components measured during trawl operation Luminancea Žlog. Objects Midwater
Luminance ratio b Ž R C .
0.740 0.752
y1.201 y0.770
y1.423 y1.282
1.668 3.255
51.6 50.1
0.752 0.757
y1.197 y0.899
y1.565 y1.470
2.334 3.721
120 120 120 90 90
53.0 50.1 49.7 49.7 50.1
0.751 0.764 0.747 0.762 0.754
y0.987 y0.749 y1.093 y0.644 y0.864
y1.622 y1.515 y1.466 y1.357 y1.283
3.709 5.217 2.363 5.159 2.624
120 70
49.1 50.6
0.749 0.754
y0.727 y0.431
y1.433 y1.172
2.708 5.512
70 90
60.8 76.0
0.713 12.5
y1.508 y3.473
y1.770 y2.763
1.827 0.195
Position
Objects
Zenith Ždeg.
Depth Žm.
Door
Door, cloud Sea bed
100 100
50.0 50.3
Bridle
Bridle, cloud Sea bed
120 120
Wing
Sea bed Wing, bridle Bobbin, net Bridle, bed Sand cloud
Mouth
Bobbin, cloud
Cod-end
To cloud In cloud
a b
Beam attenuation coefficient
Relative values as illuminance divided by p . Measured luminancermidwater luminance at the same zenith, azimuth and depth.
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Y.-H. Kim, C.S. Wardler Fisheries Research 34 (1998) 165–177
board and a towing speed Vn and a sea bed index G 1 with coefficient c j as follows: cS s c m G 1exp Ž c j Z B r V n .
Ž 12 .
If we assume that the brightness contrast of the sand cloud CSO is varied from C RS at c m to 0.8 when 0.4 c m and 0 when cS s c of water, then the apparent contrast CSZ can be represented by cS with slope i s 0.007 as follows: CSZ s CSO q i ln Ž cS . 4 C RS
Ž 13 .
The brightness contrast transmission formula of Duntly Ž1963. requires modification for sand cloud because we now have measurements of the light scattering by the sand cloud for which he assumed values. Let coefficient k b be the correction index in the power term of the equation for contrast transmission as a function of cS and zenith angle. Then, inherent contrast of the sand cloud can be estimated as expŽycSk b . by approximation from the mean value of cS s 2 if S s 3, where S is the distance Žin meters. from object to observer. An apparent contrast of the sand cloud C RC can be integrated using these arguments and coefficients as follows: C RC s CSZ exp yk b S c q k cos Ž ZA . 4
Ž 14 .
In estimating the brightness contrast of the sea bed sand cloud generated by the ground bobbins, the distance Z B becomes the distance from bobbins or chain to viewing point and the coefficients in Eqs. Ž12. – Ž14. can be adjusted accordingly. On the other hand, the contrast of the sand cloud seen against the midwater background can be simply calculated by luminance ratio as R C y 1. 3.3. Modelling the trawl as a Õisual stimulus Assumptions of the model are that the strength of the visual stimulus is determined by the brightness contrast of the net which is defined as the ratio of net luminance to background luminance. Net specifications such as twine diameter and colour as well as relative visual geometry such as zenith, azimuth, depth, viewing angle and distance will vary the luminance. The dominant wavelength of the underwater light is about 520 nm Ždark green.. The colour of the twine can be applied in the 11 colours as used
in the net contrast experiments ŽKim and Wardle, 1998.. The diameter of twine is up to 10 mm while rope is from 5 to 40 mm. The trawl geometry, as three-dimensional positions of the model nodes, is fixed for a constant towing speed. 3.3.1. Trawl geometry simulation The exact geometry of the trawl as a set of moving stimuli defines a swimming space that limits the behaviour of the fish. This geometry depends on the gear performance, its dimensions, its hydrodynamics, etc. Ferro Ž1988. developed a hydrodynamical approach to predict trawl geometry by the finite element analysis method or so-called NETSIM. This was designed to estimate the relative positions, the shape and the loading of the net. In the present study, NETSIM was used to predict the fish activity space and visual geometry of the four- panel bottom trawl BT130C towed by a 600 HP vessel ŽGalbraith, 1983.. The trawl geometry simulation can be carried out with various towing speeds, otter board spread and cod-end drag. The positions of the net nodes is represented using a three-coordinate system where qz-axis is backwards along the towing direction, qy-axis is upwards direction and qx-axis is towards starboard. This model cannot yet deal with asymmetry of the trawl gear for example when in strong lateral current or during turning of the towing direction ŽFerro and Urquhart, 1980.. 3.3.2. Modelling the contrast of nets The fish’s viewing geometry defined by viewing angles of zenith and azimuth and distance to netting can be calculated from the data of the trawl geometry. Then, as seen from this fish position the inherent contrast, apparent contrast and visibility of any part of the net can also be estimated for any of the twine colours and diameters used. These estimates also involve calculation of background luminance using the same geometry and under the chosen fishing and weather conditions. The reference water-background luminance is calculated using the model of the underwater light as above with ZA and A Z as viewing direction. Then, for example if this node is a knot in direction ZA and A Z and distance S, the inherent contrast CO can be estimated as described by Kim and Wardle Ž1998.. If the knot is seen against a background of sand cloud
Y.-H. Kim, C.S. Wardler Fisheries Research 34 (1998) 165–177
or sea bed, then the inherent contrast must be replaced by the luminance ratio R C Žmaximum value R Cm and minimum value R Cn . in Table 6 as follows:
173
Ž 16 .
of Kim and Wardle, 1998.. The light reflective index m Žas presented in table 6 of Kim and Wardle, 1998. was applied to thicker rope, being adjusted according to the scale effect shown by the range of twine diameter tested. As a check of this model, the calculated knot luminance using this method was compared with the measured value from the net contrast experiments and a background relative luminance of 1. The difference of the knot luminance between the measured L1 and calculated L1 was found to be less than 5% in 134 cases for twine colour and diameter Ž p - 0.001 by a paired t-test.. Fig. 3 shows an example of the results calculated with the completed ropernet contrast model. The symbols represent the apparent contrast for components of the theoretical ribs of the net as seen by a fish positioned at the arrow tip and in the plane of the headline of the net.
3.3.3. Modelling the contrast of ropes Because the main ropes in a trawl are almost nearly horizontal or make acute angles to the towing direction, the contrast of the rope can be estimated using the twine contrast ratio Žas presented in table 5
3.3.4. Modelling the brightness contrast of floats The contrast of the spherical floats in the headrope of the trawl can vary due to differences in their features, such as size and colour, as well as by the character of the downwelling light, viewing angle
CO1 s Ž CO q 1 . r R Cm y Ž R Cm y R Cn . Ž Z N yZ W . rSN 4 y 1
Ž 15 .
where S N is total net length and Z N is net node coordinate, Z W is wing-end coordinate. If the knot is positioned within the sand cloud, the background luminance L b and the inherent contrast of the knot should be recalculated from the underwater light model with the beam attenuation coefficient and luminance ratio R C of the sand cloud. If the knot is being viewed with sand cloud or sea bed, the contrast C R should be replaced with the integral form of contrast transmission with the adjusted index k b and distance S as described in Eq. Ž14. as follows C R s CO1exp H yc q k cos Ž ZA . 4 k b d S
Fig. 3. An example of the predicted visual stimulus of the net ŽNorth Sea trawl, at 50 m depth. produced by the model with the fish viewing position indicated at the arrow head. The filled circles indicate yve contrast and the filled triangles, qve contrast. Their size indicates the relative intensity of the visual stimulus as seen from the fish position. The alternating dark and light rings of symbols represent theoretical ribs of the net spaced at 2 m intervals in the towing direction. The fish is in the plane of the ring representing the headline.
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Y.-H. Kim, C.S. Wardler Fisheries Research 34 (1998) 165–177
and distance. A diagram of the relative positions of a float, fish and light source angle are presented as three-dimensional coordinates in Fig. 4. The variables used in the contrast estimation of the float are shown in the figure caption. The luminance of the float can be predicted by the change of reflectance with the relative viewing angle B according to the results of previous light measurements ŽKim and Wardle, 1998.. The background luminance at the upper edge of the float is zenith ZA1 and azimuth A Z1 and at the lower edge is ZA2 and A Z2 . The relative viewing angle B of the fish to the centre of the float and light source is calculated by three-dimensional geometry. Finally, the reflection factor r of the float in defined underwater light conditions and with the relative viewing geometry can be estimated using the above relative viewing angle B as zenith angle in the Eqs. Ž7. and Ž8. from Kim and Wardle Ž1998.. The background luminance ratio L R at either the upper or the lower edge can be adopted with the zenith ZA1 or ZA2 and the azimuth A Z1 or A Z2 using the underwater light model. Thus, the inherent contrast COf of the float as brighter upper
Fig. 5. The inherent contrasts Ž COf . of floats, estimated by the model, for upper brighter part Žopen symbols. and lower darker part Žsolid symbols. plotted against viewing zenith angle. The symbols indicate float colours: circles white, squares yellow and triangles orange.
part and darker lower part with viewing angle B seen against either sand cloud or sea bed with luminance ratio R c can be predicted by Eq. Ž10. and Table 6 as follows. COf s r Ž B . r Ž R C L R Ž ZA , A Z . . y 1
Fig. 4. The relevant three-dimensional viewing geometry of a spherical float, note the X, Y and Z coordinates are indicated. Abbreviations: Aqy; Zenith angle at maximum luminance of natural underwater light. D b , Diameter of the float. B; Relative viewing angle, i.e., between the viewing line from fish to centre of float and axis of light source to centre of float. Xf , Yf , Zf ; position coordinates of fish eye. X b , Y b , Z b ; centre coordinates of the float and X b s X h , Y b sY h q0.5PD b , Z b s Z h . ZA , A Z ; zenith and azimuth viewing angles from fish to float. 2Sa is the angle subtended at the fishes eye by the float.
Ž 17 .
The estimated inherent contrast of white, yellow and orange floats by this method are represented in Fig. 5. For any other colours, the change with relative viewing angle ŽB. of the reflection factor can be established as a polynomial equation by using the maximum reflection factor obtained by others for paint colours ŽWyszecki and Stiles, 1982.. The inherent self-contrast between brighter upper part Ž u. and darker lower part Ž d . of the float, can be represented as the ratio of r Ž u.rr Ž d . y 1 and apparent contrast can be estimated using Eq. Ž16.. 3.3.5. Modelling the contrast of the bobbins The relative viewing geometry of a black rubber bobbin by a fish can be calculated using the coordinates of the bobbin positions from the trawl geometry model and the fish position in the same way as calculated for floats. The reflection factor r of the
Y.-H. Kim, C.S. Wardler Fisheries Research 34 (1998) 165–177
bobbin or iron can be estimated with known illuminance conditions ŽKim and Wardle, 1998.. The zenith angle of fish to bobbins in the path of trawl gear is between horizontal 908 and downwards 1808 and the general shape of the bobbin is a round cylinder or sphere. Therefore, the contrast of the bobbin can be predicted with the relative viewing geometry and light incidence and related to the sand cloud or sea bed background as with the float. 3.3.6. Modelling the contrast of the otter board The otter board as a visual stimulus to the fish is considered as a larger plane light reflector. The otter board was usually observed as a darker object due to its vertical orientation and generally darker colour. The contrast of the inner surface of the otter board as seen from the fish position can be estimated by the relative viewing geometry and light conditions as depicted in Fig. 6. The nomenclature for the viewing geometry of the otter board is in the figure caption.
175
The viewing distance from the fish to central top of the otter board R bc , and zenith angle ZA and azimuth A Z of the fish with maximum light beam zenith ZA0 and azimuth A Z0 of otter board, which are symmetrical in the reflected plane of the otter board, can be calculated from the dimension of the otter board and the relative position of the fish and board. The luminance of the otter board at a certain point such as the upper centre can be decided by assessing the dominant incident light with zenith ZA0 and azimuth A Z0 using the underwater light model. The reflection factor r ŽB. of the otter board can be estimated from Kim and Wardle Ž1998. and Wyszecki and Stiles Ž1982. by allowing for colour and relative viewing angle B which is between the viewing line Ž ZA and A Z . and the maximum light beam Ž ZA0 and A Z0 .. The luminance of the background in midwater can be predicted by the previous luminance model with zenith ZA and azimuth A Z to the otter board. Therefore, the inherent contrast of the otter board
Fig. 6. The three-dimensional viewing geometry of the otter board note the X, Y and Z coordinates. Abbreviations: Sb; length of the otter board. Hb; height of the otter board. Sp; length of otter pendant. At; tilt angle of the otter board. Ae; angle of attack of the otter board. Ab; lead angle of the bridle. Bt; towing direction. ZA0 ; zenith of light beam to otter board. A Z0 ; azimuth of light beam to otter board. Rbc; distance from fish to the upper centre of otter board.
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can be estimated from luminance ratio L R and reflection factor r ŽB. with luminance ratio R C to sand cloud or sea bed as in Eq. Ž17.. The apparent contrast of the otter board can be estimated using Eq. Ž16. as in the net contrast. 3.4. Modelling the Õisibility of the gear components The visibility S V is defined as maximum distance at which an object can be seen by the fish eye. It can be determined by considering the image contrast and the brightness contrast threshold C T and the angle subtended at the fish’s eye by the object Že.g., 2 Sa in Fig. 4. in relation to a minimum resolvable angle A m ŽDouglas and Hawryshyn, 1990.. Due to scatter, objects that appear small when they have low contrast can appear larger when returning higher contrast values. Solid objects may appear to expand if the shaded zone becomes brighter relative to background due to change in zenith viewing direction. When relative incident luminance is reduced from 100, the visible object is changed from measured size D with reference contrast Cm until nearly invisible D V s 0 when contrast is lower than visual contrast threshold C T . The visible size of the object D V can be represented with apparent contrast C R as follows. D V s D Ž C R y C T . r Ž Cm y C T . 4
g
Ž 18 .
The measured object size D means the actual diameter of the twine, rope, float, bobbin or the virtual diameter of the knot ŽImai, 1984. or the visible length or height of the otter board, etc. and the power g could be varied with the trawl components. The maximum and apparent contrast can be estimated by the modified Eq. Ž16. for contrast transmission. S V can be calculated from A m and D V as follows: S V s D V rtan Ž A m .
Ž 19 .
S V is effected by C T and can be transformed with integration of differential d s from 0 to S V from Eq. Ž16. as follows. ln Ž C TrCO . s H yc q k cos Ž ZA . 4 k b d s
Ž 20 .
The maximum S V is determined by Eqs. Ž18. – Ž20. and can be considered as visibility of an object to the
fish eye in prevailing, viewing geometry and light conditions. In conclusion, the underwater light intensity could be predicted by the properties of the undersea light field including allowances for geographical position, weather, water quality, diurnal changes backgrounds of sand cloud and sea bed or water. The contrast of the fishing gear as a visual stimulus of the simulated trawl can be predicted for the visibility of the net components including netting, ropes, floats, bobbins, otter boards and their sand clouds as viewed from any fish position within the net under the particular light conditions.
Acknowledgements We thank Mr. Ferro for help with using NETSIM. Y.-H. Kim acknowledges the funding in part by The 1993 Professor’s Overseas Research Program of the Ministry of Education of Republic of Korea, The Korea Research Foundation, as well as support from the College of Marine Science of Gyeongsang National University and the SOAEFD Marine Laboratory, all of which helped to make this study possible.
References Arnold, G.P., 1976. The measurement of irradiance with particular reference to marine biology. In: Evance, G.C., Bainbride, R., Rackman, O. ŽEds.., Light as an ecological factor: II, The 16th symposium of the British ecological society. Blackwell Sci. Publications, pp. 1-25. Douglas, R.H., Hawryshyn, C.W., 1990. Behavioural studies of fish vision: An analysis of visual capabilities. In: Douglas, R.H., Djamgoz, M.B.A. ŽEds.., The Visual System of Fish. Chapman & Hall, pp. 373–418. Duntly, S.Q., 1963. Light in the sea. J. Opt. Soc. Am. 53, 214–233. Eiswirth, M., Bar, M., Rotermund, H.H., 1995. Spatiotemporal self-organization on isothermal catalysts. Physica D 84, 40–57. Ferro, R.S.T., 1988. Computer simulation of trawl gear shape and loading. In: Fox, S.G., Huntington, J. ŽEds.., Proceedings World Symposium on Fishing Gear and Fishing Vessel Design. Marine Institutes, Canada, pp. 259–262. Ferro, R.S.T., Urquhart, G.G., 1980. Trawl gear asymmetry during vessel maneuvers—trial methods and preliminary results. Scottish Fisheries Working Paper, 12 pp. Galbraith, R.D., 1983. The Marine Laboratory four-panel trawl. Scottish Fisheries Information Pamphlet, 8 pp.
Y.-H. Kim, C.S. Wardler Fisheries Research 34 (1998) 165–177 Hahn, C.J., Warren, S.G., London, J., 1995. The effect of moonlight on observation of cloud cover at night and application to cloud climatology. J. Climate 8, 1429–1446. Hockney, R.W., Eastwood, J.W., 1988. Computer Simulation Using Particles. Adam Hilger, Bristol, pp. 142–146. Hojerslev, N., 1986. Optical property of seawater. In: Sundermann, J., Landolt-Bornstein ŽEds.., Oceanography, Vol. 3. Springer-Verlag, Chap. 3.3, pp. 383–462. Imai, T., 1984. Experimental studies on the projective area of the Weaver’s knot-netting. Bull. Jpn. Soc. Sci. Fish. 50, 1823– 1828. Ivanoff, A., 1977. Oceanic absorption of solar energy. In: Krous, E.B. ŽEd.., Modelling and Prediction of the Upper Layers of the Ocean. Pergamon, pp. 47–71. Ivanoff, A., Jerlov, N., Waterman, T.H., 1961. A comparative study of irradiance, beam transmittance and scattering in the sea near Bermuda. Limnol. Oceanogr. 6, 129–148. Jerlov, N.G., 1976. Marine Optics. Elsevier, pp. 127–150. Kim, Y.-H., Wardle, C.S., 1998. Measuring the brightness contrast of fishing gear, the visual stimulus for fish capture. Fish. Res. 34, 153–166. Main, J., Sangster, G.I., 1981. A study of the sand clouds produced by trawl boards and their possible effect on fish capture. Scottish Fisheries Research Report 20, 20 pp.
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Mobley, C.D., 1989. A numerical model for the computation of radiance distributions in natural waters with wind-roughened surfaces. Limnol. Oceanogr. 34, 1473–1483. Roach, F.E., Gordon, J.L., 1973. The Light of the Night Sky. Reidel, 125 pp. Timofeeyeva, V.A., 1971. The diffuse reflection coefficient and its relation to the optical parameters of turbid media. Oceanic Phys. 7, 467–469. Tyler, J.E., 1969. The natural light field underwater. In: Ben-Tuvia, A., Dickson, W. ŽEds.., Proceedings of the FAO Conference on Fish Behaviour in Relation to Fishing Techniques and Tactics, Norway, Bergen, 19–27 October 1967. FAO Fisheries Report 62 Ž3., Er22, pp. 479–497. Tyler, J.E., Shaules, A., 1964. Irradiance on a flat object underwater. Appl. Opt. 3, 105–110. U.S. Department of the Navy, 1952. Natural illumination charts. Research and development project NS-714-100, 56 pp. Voss, K.J., 1988. Radiance distribution measurements in coastal water. SPIE Vol. 925, Ocean Optics IX, pp. 56–66. Wyszecki, G., Stiles, W.S., 1982. Color Science, Concepts and Method, Quantitative Data and Formulae, 2nd edn. Wiley, pp. 51–63, 514–581. Yallop, B.D., 1986. Ground illumination. NAO Technical note 57, 7 pp.
Modelling the visual stimulus of towed fishing gear Y.-H. Kim a , C.S. Wardle a
b,)
Institute of Marine Industry, College of Marine Science, Gyeongsang National UniÕersity, Inpyeong-Dong, Tong-Young, Kyeognam, 650-160, Republic of Korea b The Marine Laboratory, P.O. Box 101, Victoria Road, Aberdeen, AB11 9DB, UK Received 15 May 1997; accepted 28 October 1997
Abstract A number of modules are developed for a model with the aim of predicting the strength of the visual stimulus that might initiate fish reactions from any viewing point within a towed fishing gear. The first part of the model defines the properties of the undersea light field through which a trawler might tow a fishing gear including allowances for geographical position, weather, water quality and diurnal changes. A variety of light measurements are made to check day and night light levels used in the model. The underwater luminance of water, sand cloud and sea bed which form the background against which a fish sees the net components is then calculated. An example constructing the space in which a fish may react within a towed trawl gear is developed for the BT130C, North Sea trawl. This part develops an existing net frame model that creates the three-dimensional shape of the towed net from the designers net drawings. Analysis of previous observations of this trawl form the bases for simulation of sand clouds produced by the ground gear and otter board as part of the fish stimulus. Finally the simulated trawl is towed through the predicted light field and methods are developed for calculating the visibility of the net components including netting, ropes, floats, bobbins, otter boards and their sand clouds as viewed from any fish position within the net. An example of the result of these predictions, maps the stimulus strength for one fish position. q 1998 Published by Elsevier Science B.V. Keywords: Contrast; Underwater light; Model fish reaction
1. Introduction The principles of what make nets more or less visible in real underwater light conditions were investigated and developed in Kim and Wardle Ž1998.. Concentrating on the importance of vision in reactions of fish to trawls, this study applies these principles together with those already evolved for understanding the shaping of nets when towed in the sea. )
Corresponding author. Tel.: q44 1224 295339; fax: q44 1224 295511.
Combining models of the towed net geometry with the visual properties of its components in the underwater light field allows construction of an overall model of a trawl as a visual stimulus. Because trawls are towed in all conditions and different seas, the visual environment through which it is towed is first defined to form the water background against which a fish inside sees the net. Demersal trawls are complicated by being towed over the bright reflective sea bed which take the place of the darker zones seen below the fish when in midwater trawls. Turbulent sand clouds are thrown
0165-7836r98r$19.00 q 1998 Published by Elsevier Science B.V. All rights reserved. PII S 0 1 6 5 - 7 8 3 6 Ž 9 7 . 0 0 0 8 9 - 1
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up when otter boards pass over sand or mud and form brighter screens on either side of the gear. Ground gears throw up a rippling layer of cloud screening the sea bed. There are many possible variations of this sort and simulations by computation can allow us to understand and explore variable features of the visual stimulus of nets which would otherwise be difficult and costly using sensitive and expensive equipment to repeatedly pass inside nets to make the equivalent observations. Combining our knowledge of the limits to fish behaviour, with predictions of the stimulus as it changes with the fish’s positions within the net, might also allow a further development of a dynamic model to simulate the reaction patterns of the fish. 2. Materials and methods Direct measurements of the surface light were carried out using a Photometric sensor ŽLI-COR INC, LI-210SB. with data logger ŽSolartron 3531D. or Photometer ŽLI-188B. and were made every 5 s. The photosensor was calibrated with the illuminance range from 67 to 2000 lux using a standard NPL lamp in the dark room. Day time light from sunrise to sunset was measured in the North Sea from 29 January to 9 February 1994 and on land at the Marine Laboratory between March and April 1994 and February to June 1995. The illumination at night without moonlight was measured every 10 s using a calibrated photomultiplier and data logger from dusk to dawn at a rural site near Banchory in Scotland Žlat 57.078N, long 2.578W. from 23 to 25 February 1995 and at the SOAEFD Marine Laboratory Žlat 57.138N, long 2.18W. from 13 June to 22 July 1995. Underwater light measurements were made with a photomultiplier as described in Kim and Wardle Ž1998., where many of the specialist terms are introduced. 3. Modelling, results and discussion 3.1. Modelling underwater light and background luminance The essential assumptions for the modelling of the surface light and thence underwater light are that
global surface illuminance is changed by the sun’s altitude and the maximum absolute values in a clear sky are predictable from the U.S. Navy illumination charts ŽU.S. Department of the Navy, 1952.. Light level is decreased with depth by vertical attenuation coefficients according to the optical water type classified by Jerlov Ž1976.. Illuminance and luminance are treated as photometric units. Luminance distribution within zenith and azimuth profiles in midwater is dependent on the vertical and beam attenuation coefficients. 3.1.1. DeÕelopment of the surface light model and effects of dawn, dusk and cloud The surface light prediction model by Yallop Ž1986., including effects of both sun and moon altitude has been modified using data from the illumination charts ŽU.S. Department of the Navy, 1952. and to give values when the sun’s altitude is below the horizon between y5 and y908 as a fitted fourth-order polynomial equation. The model light data are considered as in conditions of normal clear sky. Some examples of one-hour cycles of the most changeable daylight condition in cloudy weather were measured in order to give the light blockage ratio Ž C E .. C E is the ratio of the blocked value I D Žin lux. to the clear sky value IC Žin lux. by sun or moon as I D rIC . The C E values are observed from 0.12 in the darkest cloud cover Ž C L s 1. to 1 in clear sky Ž C L s 0., close to the US Navy Tables. C E can be expressed as in the following first-order linear equation ŽEq. Ž1.. when within the above range of light conditions: C E s 1 y 0.9C L
Ž 1.
3.1.2. Night light leÕel The ratio Ž NE . of the measured illuminance Ž I N . on a clear night to the calculated illuminance Ž IC . without moonlight was represented with negative sun’s altitude A S Žin degrees. below the horizon as shown in Fig. 1. The relationship between the ratio NE and A S can be expressed as follows with f 0 s 0.139 and f 1 s y0.127 ŽNo. of data s 600, r s 0.98.: NE s f 0 exp Ž f 1 A S . , Ž A S - y7 .
Ž 2.
Y.-H. Kim, C.S. Wardler Fisheries Research 34 (1998) 165–177
Fig. 1. An example of the ratio of measured light value Ž I N . to calculated light value Ž IC . plotted against the sun’s altitude below the horizon on a clear night.
The weather effects on night light are more complex than daytime because light scattering is more marked at night time ŽRoach and Gordon, 1973; Hahn et al., 1995.. Surface illuminance IS Žin lux. can be represented as follows: IS s IC C E NE
Ž 3.
3.1.3. Modelling the underwater light with depth profile The amount of daylight entering the water surface is described by the so-called Albedo which is the ratio of reflected light energy to incident light. The higher the Albedo the smaller the proportion of light entering the surface. The Albedo is increased with longer light wavelength, lower sun altitude, less cloud and shorter wave amplitudes of the sea surface ŽHojerslev, 1986.. Following Ivanoff Ž1977., the Albedo Ž A. was exponentially increased with the sun’s altitude Ž A S . from 0 to 108 and then decreased from 10 to 908 as summarised by the following equation: A s u 0 exp
Ž u1 A S .
Ž 4.
The coefficients u 0 and u1 relating to the sea surface state and sun’s altitude are shown in Table 1. The
167
downwards light intensity Ž I W . just below the sea surface varies as Ž1 y A. of the surface illuminance IS . The downwelling underwater light as illuminance is decreased with depth YD Žin meters. and vertical attenuation coefficient k. The results of the light measurements from Kim and Wardle Ž1998. were interpreted in terms of the depth, water turbidity, cloud effects, wave amplitude and Albedo as shown in Table 2. The vertical attenuation coefficient k and IO in IO exp Ž k Y D . was calculated by the least-squares method for depths between 30 and 80 m. This deeper layer was considered as a homogeneous water column and illuminance was varied exponentially whereas shallower than 30 m, it changed more dramatically according to the change of the coefficient k ŽJerlov, 1976.. Practical trawling is at 30 m or deeper. Therefore, surface layer effects in the water shallower than 30 m are adjusted using the mean ratio R S of the theoretical value IO to I W at just below the water surface or could be approximated using the values from Jerlov Ž1976.. For depths greater than 30 m, the underwater illuminance I W Žin lux. can be expressed with integration of depth YD and k as follows. I W s IS Ž 1 y A . R S exp HykdŽY D . , Ž Y D ) 30 m .
Ž 5.
3.1.4. Modelling underwater background as luminance Luminance Ž L. depends on reflection factor Ž r . of an object’s surface and illuminance Ž I . as L s r Irp ŽArnold, 1976.. However the underwater background has no surface but particles in the water individually scatter the illuminance forming the
Table 1 The coefficients u 0 and u1 of Eq. Ž4. for the sea surface Albedo related to the sun’s altitude Coefficients Sun’s altitude-108
u0 u1 ra a
Sun’s altitude)108
Wave amplitude Žm.
Wave amplitude Žm.
0.5
0.5
1.0
2.0
1.0
2.0
0.0976 0.0437 0.0827 0.2626 0.1626 0.1556 0.0795 0.1307 0.0418 y0.0409 y0.0240 y0.0270 0.987 0.953 0.992 0.995 0.992 0.996
Correlation coefficient. Each no. of data is 6.
Y.-H. Kim, C.S. Wardler Fisheries Research 34 (1998) 165–177
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Table 2 An analysis of underwater light measurements for Eq. Ž5. Wave amplitude Žm.
Cloud ratio
Cloud effect
k
1 y Albedo
IS Žlux.
I W0 Žlux.
IO Žlux.
R S s IO rI W0 Ž%.
1.0 0.5 1.0 0.5 1.0
0.8 0.3 0.9 0.5 0.6
0.277 0.785 0.153 0.605 0.503
0.156 0.144 0.119 0.111 0.133
0.881 0.838 0.884 0.842 0.871
16215 14659 19089 17414 14438
3959 9637 2583 8874 6323
150 337 94 319 231
3.79 3.50 3.64 3.59 3.65
k: Vertical attenuation coefficient. IS : Calculated surface light. I W0 : Illuminance just below the sea surface. IO : Calculated from I W s IO expŽykYD .. R S : Surface light ratio. YD : Water depth Žm..
background brightness or luminance. Snell’s circle limits the direction of maximum luminance from a zenith angle of 0 to 48.68 with the sun’s altitude from 90 to 08 respectively ŽHojerslev, 1986.. The zenith angle Ž QO . for the direction of maximum light when just below the water surface will be varied by a cosine curve with the sun’s altitude Ž A S . as QO s 48.6 cosŽ A S .. The reduction ratios of the zenith angle of maximum luminance is defined as R Q and the zenith angle for maximum luminance with depth as Q Y . Then, R Q and Q Y adapted from measurements in the table of Tyler Ž1969. become:
were analysed in order to clarify the relationship among the many factors such as zenith angle, azimuth angle, water depth and cloud cover ŽHojerslev, 1986; Voss, 1988.. The ratio of radiance at azimuth 1808 to that at azimuth 08 was defined as the relative radiance L Rd . Examination of all the values of L Rd between zenith 0 and 1808 gave the minimum luminance ratio L Rm at zenith angle between 30 or 408. The L Rm for depth Y D Žin meters. can be linearly derived for cloud cover C L between C L s 0.1 and 0.7 by Eq. Ž7. with the approximate values for the coefficients Õ 0 s y0.199, Õ 1 s 1.1, Õ 2 s 0.186, and Õ 3 s y0.216:
R Q s q 0 C L q Ž q1 q q 2 C L . Y D
L Rm s Ž Õ 0 q Õ1C L . q Ž Õ 2 q Õ 3 C L . ln Ž y .
Q Y s 48.6 Ž 1 y R Q . cos Ž A S . where C L is cloud-cover ratio and depth YD and the coefficients q0 , q1 , and q2 are 1.025, 0.0106 and y0.0106, respectively. Timofeeyeva Ž1971. presents a table of radiance distribution Žradiance is the radiometric equivalent of luminance. where E s krc where k is the vertical attenuation coefficient and c is the beam attenuation coefficient. If the luminance is proportional to radiance and if zenith angle ZA s 08 is equal to maximum luminance angle Q Y , then the zenith profile as a luminance ratio L R Ž ZA . can be estimated by interpolation of E and ZA . The values for the radiance distribution underwater by Tyler Ž1969. and Tyler and Shaules Ž1964.
Ž 7.
The luminance ratio L Rd was found to change with the geometric zenith angle ZA Žin degrees. when ranged from 0 to 1808 as in the following equation: L Rd s P0 q P1 exp P2 sin Ž ZA r2 .
Ž 8.
and P0 , P1 , and P2 are shown in Table 3 and they can be approximated with L Rm . Once the luminance ratio L Rd with zenith angle is determined, general luminance ratio L R Ž A Z . varying with azimuth A Z ranged from 0 to 1808 can be estimated by Eq. Ž9.: L R Ž A Z . s W1exp W2 cos Ž A Zr2 .
Ž 9.
and the coefficients W1 and W2 are shown in Table 3 and they are closely related with L Rd .
Y.-H. Kim, C.S. Wardler Fisheries Research 34 (1998) 165–177
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Table 3 The coefficients for P0 , P1 and P2 of Eq. Ž8., and W1 and W2 of Eq. Ž9. Condition
L Rm or L Rd
Coefficients P0
No. of data
Correlation coefficient
P1 or W1
P2 or W2
0.4637 0.3861
y6.7628 y4.6525
5 5
0.983 0.985
ZA - 408 Eq. Ž8.
0.54 0.69
ZA ) 408 Eq. Ž8.
0.07 0.54 0.69
y y y
0.0187 0.3587 0.5777
4.0033 1.0410 0.5487
14 14 13
0.997 0.993 0.939
ZA ) 408 Eq. Ž9.
0.54 0.69
y y
0.4985 0.6617
0.6473 0.3816
10 10
0.978 0.984
0.5 0.6
3.1.5. Conclusions from modeling the underwater light field In conclusion, underwater relative luminance L b as converted from underwater illuminance I W has a maximum value at zenith angle Q Y and azimuth 08. The luminance distribution ratio L RŽ ZA . with zenith can be predicted by the attenuation coefficient ratio krc. The luminance ratio L RŽ A Z . with azimuth can be estimated in relation to depth and cloud ratio. Accordingly, a complete profile of azimuth and zenith
background luminance L b Ž ZA , A Z . values is determined as follows. L b Ž ZA , A Z . s L R Ž ZA . L R Ž A Z . I W rp
Ž 10 .
In addition, a symmetrical distribution of the luminance values can be assumed in the other half hemisphere as azimuth range of 180–3608. The results of the measurements of luminance distribution are shown in Table 4 where they match very well with those calculated using the prediction
Table 4 Results of illuminance measurement as light ratio with zenith angle at depth 30 m, sun’s altitude 12–208 in overcast sky C L s 0.6 Beam attenuation coefficient
Illuminance ratio with zenith Ž deg . 0
45
90
135
180
Measured Õalues 0.708 0.639 0.803 0.787 0.883 0.779 0.841 0.759 0.810
1 1 1 1 1 1 1 1 1
0.615 0.609 0.723 0.766 0.725 0.641 0.650 0.767 0.605
0.151 0.079 0.124 0.081 0.081 0.136 0.080 0.170 0.143
0.042 0.035 0.026 0.039 0.027 0.034 0.028 0.047 0.031
0.034 0.029 0.022 0.026 0.023 0.024 0.024 0.031 0.025
Mean s 0.779 S.D.s 0.068
Mean s 1 S.D.s 0
Mean s 0.686 S.D.s 0.067
Mean s 0.112 S.D.s 0.036
Mean s 0.033 S.D.s 0.007
Mean s 0.026 S.D.s 0.003
Calculated Õalues
1
0.641
0.129
0.048
0.021
a
Calculated as luminance by Eq. Ž10. with mean value of beam attenuation coefficient 0.779, vertical attenuation coefficient 0.15 and other conditions are same as measurements.
Y.-H. Kim, C.S. Wardler Fisheries Research 34 (1998) 165–177
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model as Eq. Ž10. above by a paired t-test Ž N s 5, p - 0.001.. Note the calculated values represent something like 18 of acceptance whereas the photomultiplier is centred about 808. This model showed similar results to the Hydrolight model by Mobley Ž1989.. 3.2. Complications due to sand clouds
shallow ground by Main and Sangster Ž1981. were reviewed to form an approximation of the viewing geometry. The spread SC Žin meters., the height HC Žin meters. and lateral distance LC Žin meters. from the bridle to the sand cloud respectively were diffused with increasing distance Z B Žin meters. from the otter board towards the cod-end as in Eq. Ž11.: SC , HC or LC s j0 q j1 ln Ž Z B .
The otter board sand cloud is both a visual stimulus herding fish into the net path as well as a background against which parts of the net are viewed by the fish. This study develops a model of the geometry of the sand cloud and then considers its visual contrast and contrast transmission to the fishes eye. The sand cloud as a visual stimulus looks like sky cloud with similar ephemeral and formless characteristics. The following assumptions are made in order to theoretically construct a model of a visual sand cloud. The relevant view is observed from inside the trawl gear during the towing operation. The relevant shape parameters are the maximum height and the near side spread and both have linear time dispersion. Its virtual dimensions and dispersion are affected by the dimensions and hydrodynamics of the otter board as well as by the relative speeds and directions between the towed gear and the natural water flow. 3.2.1. Modelling the geometry of the sand cloud The relative shapes of the sand cloud produced by four kinds of otter board as measured on relatively
Ž 11 .
The intercept j0 and the slope j1 are shown in Table 5. It can be assumed that the dimension of the sand cloud is changed by the dimensions of the otter board, towing conditions and sea bed characteristics with index G 1 s 1 Žvery muddy ground. and G 1 s 0 Žvery hard ground.. The intercept j0 and j1 in Eq. Ž11. could be the function of height H b and length S b of the otter board, towing speed and water flow speed and angular difference between towing and current direction. The image of the otter board sand cloud as if seen by a fish eye from positions inside the trawl net is chaotically changed with time. An example of a lateral view of the cloud slice plotted as height against the distance from the otter board can be represented as particle mapping by cloud shape ŽHockney and Eastwood, 1988. or by catalytic turbulence ŽEiswirth et al., 1995.. Another type of sand cloud near the sea bed is produced mainly by the bobbins of the ground rope and chain and appears like a waving blanket and reflects downwelling light in quite a different way compared with clear sea bed.
Table 5 The intercept j0 and the slope j1 of Eq. Ž11. for dimensions of the sand cloud formed by the otter boards as measured in the experiments of Main and Sangster Ž1981. Dimension of sand cloud
Coefficients
Kinds of otter board Flat
Vee
Polyvalent
Cambered
Spread
j0 j1
0.492 1.229
1.055 1.038
y0.660 1.305
y1.506 1.470
Height
j0 j1
0.260 0.785
0.015 0.827
0.347 0.698
y0.116 0.817
Lateral distance
j0 j1
y2.114 2.381
y2.539 2.440
0.177 1.272
y0.032 0.901
)
Each no. of data is 16 Žexcept 15 for lateral distance. and each correlation coefficient is r ) 0.97.
Y.-H. Kim, C.S. Wardler Fisheries Research 34 (1998) 165–177
3.2.2. Modelling the brightness contrast of sand cloud The results of the light measurements of the sand cloud are processed with reference to the viewing angle, attenuation coefficients and luminance ratio R C of the sand cloud or sea bed. They were also compared with measured luminance in midwater in the same conditions in Table 6. The luminance measured while looking at the large surfaces of the relatively stable sand cloud that is found near the cod-end was 1.4 to 1.8 times brighter than the midwater luminance at the same depth and viewing angle. Examples of the change of the beam attenuation coefficient sampled by entering the sand cloud with the 25 cm Transmissometer are presented in Fig. 2. The sea bed at a depth of 50–60 m showed a range of luminance ratio from 3.2 to 3.7, and was more reflective than the value of 2.6 measured in shallow water by Ivanoff et al. Ž1961.. The change of the luminance ratio of sea bed to midwater seen from a raised position can be estimated in relation to the viewing distance by the contrast reduction formula. The luminance ratio R C of sand cloud luminance to midwater luminance was measured as 0.2 when within the sand cloud and ranged from 5.5 to 1.4 between net mouth and
171
Fig. 2. Examples of the variation of the beam attenuation coefficients due to entering the otter board sand clouds near the cod-end during the trawl operation.
cod-end when measured out of the sand cloud depending on the location and viewing angle ŽTable 6.. If the beam attenuation coefficient of the sand cloud Ž cS . is proportional to the density of the particles, the contrast could also be related to coefficient cS . Coefficient cS of the sand cloud might be predicted from a maximum value c m at a distance Z B from the otter
Table 6 Examples of light characteristics of sand cloud, sea bed and various components measured during trawl operation Luminancea Žlog. Objects Midwater
Luminance ratio b Ž R C .
0.740 0.752
y1.201 y0.770
y1.423 y1.282
1.668 3.255
51.6 50.1
0.752 0.757
y1.197 y0.899
y1.565 y1.470
2.334 3.721
120 120 120 90 90
53.0 50.1 49.7 49.7 50.1
0.751 0.764 0.747 0.762 0.754
y0.987 y0.749 y1.093 y0.644 y0.864
y1.622 y1.515 y1.466 y1.357 y1.283
3.709 5.217 2.363 5.159 2.624
120 70
49.1 50.6
0.749 0.754
y0.727 y0.431
y1.433 y1.172
2.708 5.512
70 90
60.8 76.0
0.713 12.5
y1.508 y3.473
y1.770 y2.763
1.827 0.195
Position
Objects
Zenith Ždeg.
Depth Žm.
Door
Door, cloud Sea bed
100 100
50.0 50.3
Bridle
Bridle, cloud Sea bed
120 120
Wing
Sea bed Wing, bridle Bobbin, net Bridle, bed Sand cloud
Mouth
Bobbin, cloud
Cod-end
To cloud In cloud
a b
Beam attenuation coefficient
Relative values as illuminance divided by p . Measured luminancermidwater luminance at the same zenith, azimuth and depth.
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Y.-H. Kim, C.S. Wardler Fisheries Research 34 (1998) 165–177
board and a towing speed Vn and a sea bed index G 1 with coefficient c j as follows: cS s c m G 1exp Ž c j Z B r V n .
Ž 12 .
If we assume that the brightness contrast of the sand cloud CSO is varied from C RS at c m to 0.8 when 0.4 c m and 0 when cS s c of water, then the apparent contrast CSZ can be represented by cS with slope i s 0.007 as follows: CSZ s CSO q i ln Ž cS . 4 C RS
Ž 13 .
The brightness contrast transmission formula of Duntly Ž1963. requires modification for sand cloud because we now have measurements of the light scattering by the sand cloud for which he assumed values. Let coefficient k b be the correction index in the power term of the equation for contrast transmission as a function of cS and zenith angle. Then, inherent contrast of the sand cloud can be estimated as expŽycSk b . by approximation from the mean value of cS s 2 if S s 3, where S is the distance Žin meters. from object to observer. An apparent contrast of the sand cloud C RC can be integrated using these arguments and coefficients as follows: C RC s CSZ exp yk b S c q k cos Ž ZA . 4
Ž 14 .
In estimating the brightness contrast of the sea bed sand cloud generated by the ground bobbins, the distance Z B becomes the distance from bobbins or chain to viewing point and the coefficients in Eqs. Ž12. – Ž14. can be adjusted accordingly. On the other hand, the contrast of the sand cloud seen against the midwater background can be simply calculated by luminance ratio as R C y 1. 3.3. Modelling the trawl as a Õisual stimulus Assumptions of the model are that the strength of the visual stimulus is determined by the brightness contrast of the net which is defined as the ratio of net luminance to background luminance. Net specifications such as twine diameter and colour as well as relative visual geometry such as zenith, azimuth, depth, viewing angle and distance will vary the luminance. The dominant wavelength of the underwater light is about 520 nm Ždark green.. The colour of the twine can be applied in the 11 colours as used
in the net contrast experiments ŽKim and Wardle, 1998.. The diameter of twine is up to 10 mm while rope is from 5 to 40 mm. The trawl geometry, as three-dimensional positions of the model nodes, is fixed for a constant towing speed. 3.3.1. Trawl geometry simulation The exact geometry of the trawl as a set of moving stimuli defines a swimming space that limits the behaviour of the fish. This geometry depends on the gear performance, its dimensions, its hydrodynamics, etc. Ferro Ž1988. developed a hydrodynamical approach to predict trawl geometry by the finite element analysis method or so-called NETSIM. This was designed to estimate the relative positions, the shape and the loading of the net. In the present study, NETSIM was used to predict the fish activity space and visual geometry of the four- panel bottom trawl BT130C towed by a 600 HP vessel ŽGalbraith, 1983.. The trawl geometry simulation can be carried out with various towing speeds, otter board spread and cod-end drag. The positions of the net nodes is represented using a three-coordinate system where qz-axis is backwards along the towing direction, qy-axis is upwards direction and qx-axis is towards starboard. This model cannot yet deal with asymmetry of the trawl gear for example when in strong lateral current or during turning of the towing direction ŽFerro and Urquhart, 1980.. 3.3.2. Modelling the contrast of nets The fish’s viewing geometry defined by viewing angles of zenith and azimuth and distance to netting can be calculated from the data of the trawl geometry. Then, as seen from this fish position the inherent contrast, apparent contrast and visibility of any part of the net can also be estimated for any of the twine colours and diameters used. These estimates also involve calculation of background luminance using the same geometry and under the chosen fishing and weather conditions. The reference water-background luminance is calculated using the model of the underwater light as above with ZA and A Z as viewing direction. Then, for example if this node is a knot in direction ZA and A Z and distance S, the inherent contrast CO can be estimated as described by Kim and Wardle Ž1998.. If the knot is seen against a background of sand cloud
Y.-H. Kim, C.S. Wardler Fisheries Research 34 (1998) 165–177
or sea bed, then the inherent contrast must be replaced by the luminance ratio R C Žmaximum value R Cm and minimum value R Cn . in Table 6 as follows:
173
Ž 16 .
of Kim and Wardle, 1998.. The light reflective index m Žas presented in table 6 of Kim and Wardle, 1998. was applied to thicker rope, being adjusted according to the scale effect shown by the range of twine diameter tested. As a check of this model, the calculated knot luminance using this method was compared with the measured value from the net contrast experiments and a background relative luminance of 1. The difference of the knot luminance between the measured L1 and calculated L1 was found to be less than 5% in 134 cases for twine colour and diameter Ž p - 0.001 by a paired t-test.. Fig. 3 shows an example of the results calculated with the completed ropernet contrast model. The symbols represent the apparent contrast for components of the theoretical ribs of the net as seen by a fish positioned at the arrow tip and in the plane of the headline of the net.
3.3.3. Modelling the contrast of ropes Because the main ropes in a trawl are almost nearly horizontal or make acute angles to the towing direction, the contrast of the rope can be estimated using the twine contrast ratio Žas presented in table 5
3.3.4. Modelling the brightness contrast of floats The contrast of the spherical floats in the headrope of the trawl can vary due to differences in their features, such as size and colour, as well as by the character of the downwelling light, viewing angle
CO1 s Ž CO q 1 . r R Cm y Ž R Cm y R Cn . Ž Z N yZ W . rSN 4 y 1
Ž 15 .
where S N is total net length and Z N is net node coordinate, Z W is wing-end coordinate. If the knot is positioned within the sand cloud, the background luminance L b and the inherent contrast of the knot should be recalculated from the underwater light model with the beam attenuation coefficient and luminance ratio R C of the sand cloud. If the knot is being viewed with sand cloud or sea bed, the contrast C R should be replaced with the integral form of contrast transmission with the adjusted index k b and distance S as described in Eq. Ž14. as follows C R s CO1exp H yc q k cos Ž ZA . 4 k b d S
Fig. 3. An example of the predicted visual stimulus of the net ŽNorth Sea trawl, at 50 m depth. produced by the model with the fish viewing position indicated at the arrow head. The filled circles indicate yve contrast and the filled triangles, qve contrast. Their size indicates the relative intensity of the visual stimulus as seen from the fish position. The alternating dark and light rings of symbols represent theoretical ribs of the net spaced at 2 m intervals in the towing direction. The fish is in the plane of the ring representing the headline.
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Y.-H. Kim, C.S. Wardler Fisheries Research 34 (1998) 165–177
and distance. A diagram of the relative positions of a float, fish and light source angle are presented as three-dimensional coordinates in Fig. 4. The variables used in the contrast estimation of the float are shown in the figure caption. The luminance of the float can be predicted by the change of reflectance with the relative viewing angle B according to the results of previous light measurements ŽKim and Wardle, 1998.. The background luminance at the upper edge of the float is zenith ZA1 and azimuth A Z1 and at the lower edge is ZA2 and A Z2 . The relative viewing angle B of the fish to the centre of the float and light source is calculated by three-dimensional geometry. Finally, the reflection factor r of the float in defined underwater light conditions and with the relative viewing geometry can be estimated using the above relative viewing angle B as zenith angle in the Eqs. Ž7. and Ž8. from Kim and Wardle Ž1998.. The background luminance ratio L R at either the upper or the lower edge can be adopted with the zenith ZA1 or ZA2 and the azimuth A Z1 or A Z2 using the underwater light model. Thus, the inherent contrast COf of the float as brighter upper
Fig. 5. The inherent contrasts Ž COf . of floats, estimated by the model, for upper brighter part Žopen symbols. and lower darker part Žsolid symbols. plotted against viewing zenith angle. The symbols indicate float colours: circles white, squares yellow and triangles orange.
part and darker lower part with viewing angle B seen against either sand cloud or sea bed with luminance ratio R c can be predicted by Eq. Ž10. and Table 6 as follows. COf s r Ž B . r Ž R C L R Ž ZA , A Z . . y 1
Fig. 4. The relevant three-dimensional viewing geometry of a spherical float, note the X, Y and Z coordinates are indicated. Abbreviations: Aqy; Zenith angle at maximum luminance of natural underwater light. D b , Diameter of the float. B; Relative viewing angle, i.e., between the viewing line from fish to centre of float and axis of light source to centre of float. Xf , Yf , Zf ; position coordinates of fish eye. X b , Y b , Z b ; centre coordinates of the float and X b s X h , Y b sY h q0.5PD b , Z b s Z h . ZA , A Z ; zenith and azimuth viewing angles from fish to float. 2Sa is the angle subtended at the fishes eye by the float.
Ž 17 .
The estimated inherent contrast of white, yellow and orange floats by this method are represented in Fig. 5. For any other colours, the change with relative viewing angle ŽB. of the reflection factor can be established as a polynomial equation by using the maximum reflection factor obtained by others for paint colours ŽWyszecki and Stiles, 1982.. The inherent self-contrast between brighter upper part Ž u. and darker lower part Ž d . of the float, can be represented as the ratio of r Ž u.rr Ž d . y 1 and apparent contrast can be estimated using Eq. Ž16.. 3.3.5. Modelling the contrast of the bobbins The relative viewing geometry of a black rubber bobbin by a fish can be calculated using the coordinates of the bobbin positions from the trawl geometry model and the fish position in the same way as calculated for floats. The reflection factor r of the
Y.-H. Kim, C.S. Wardler Fisheries Research 34 (1998) 165–177
bobbin or iron can be estimated with known illuminance conditions ŽKim and Wardle, 1998.. The zenith angle of fish to bobbins in the path of trawl gear is between horizontal 908 and downwards 1808 and the general shape of the bobbin is a round cylinder or sphere. Therefore, the contrast of the bobbin can be predicted with the relative viewing geometry and light incidence and related to the sand cloud or sea bed background as with the float. 3.3.6. Modelling the contrast of the otter board The otter board as a visual stimulus to the fish is considered as a larger plane light reflector. The otter board was usually observed as a darker object due to its vertical orientation and generally darker colour. The contrast of the inner surface of the otter board as seen from the fish position can be estimated by the relative viewing geometry and light conditions as depicted in Fig. 6. The nomenclature for the viewing geometry of the otter board is in the figure caption.
175
The viewing distance from the fish to central top of the otter board R bc , and zenith angle ZA and azimuth A Z of the fish with maximum light beam zenith ZA0 and azimuth A Z0 of otter board, which are symmetrical in the reflected plane of the otter board, can be calculated from the dimension of the otter board and the relative position of the fish and board. The luminance of the otter board at a certain point such as the upper centre can be decided by assessing the dominant incident light with zenith ZA0 and azimuth A Z0 using the underwater light model. The reflection factor r ŽB. of the otter board can be estimated from Kim and Wardle Ž1998. and Wyszecki and Stiles Ž1982. by allowing for colour and relative viewing angle B which is between the viewing line Ž ZA and A Z . and the maximum light beam Ž ZA0 and A Z0 .. The luminance of the background in midwater can be predicted by the previous luminance model with zenith ZA and azimuth A Z to the otter board. Therefore, the inherent contrast of the otter board
Fig. 6. The three-dimensional viewing geometry of the otter board note the X, Y and Z coordinates. Abbreviations: Sb; length of the otter board. Hb; height of the otter board. Sp; length of otter pendant. At; tilt angle of the otter board. Ae; angle of attack of the otter board. Ab; lead angle of the bridle. Bt; towing direction. ZA0 ; zenith of light beam to otter board. A Z0 ; azimuth of light beam to otter board. Rbc; distance from fish to the upper centre of otter board.
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Y.-H. Kim, C.S. Wardler Fisheries Research 34 (1998) 165–177
can be estimated from luminance ratio L R and reflection factor r ŽB. with luminance ratio R C to sand cloud or sea bed as in Eq. Ž17.. The apparent contrast of the otter board can be estimated using Eq. Ž16. as in the net contrast. 3.4. Modelling the Õisibility of the gear components The visibility S V is defined as maximum distance at which an object can be seen by the fish eye. It can be determined by considering the image contrast and the brightness contrast threshold C T and the angle subtended at the fish’s eye by the object Že.g., 2 Sa in Fig. 4. in relation to a minimum resolvable angle A m ŽDouglas and Hawryshyn, 1990.. Due to scatter, objects that appear small when they have low contrast can appear larger when returning higher contrast values. Solid objects may appear to expand if the shaded zone becomes brighter relative to background due to change in zenith viewing direction. When relative incident luminance is reduced from 100, the visible object is changed from measured size D with reference contrast Cm until nearly invisible D V s 0 when contrast is lower than visual contrast threshold C T . The visible size of the object D V can be represented with apparent contrast C R as follows. D V s D Ž C R y C T . r Ž Cm y C T . 4
g
Ž 18 .
The measured object size D means the actual diameter of the twine, rope, float, bobbin or the virtual diameter of the knot ŽImai, 1984. or the visible length or height of the otter board, etc. and the power g could be varied with the trawl components. The maximum and apparent contrast can be estimated by the modified Eq. Ž16. for contrast transmission. S V can be calculated from A m and D V as follows: S V s D V rtan Ž A m .
Ž 19 .
S V is effected by C T and can be transformed with integration of differential d s from 0 to S V from Eq. Ž16. as follows. ln Ž C TrCO . s H yc q k cos Ž ZA . 4 k b d s
Ž 20 .
The maximum S V is determined by Eqs. Ž18. – Ž20. and can be considered as visibility of an object to the
fish eye in prevailing, viewing geometry and light conditions. In conclusion, the underwater light intensity could be predicted by the properties of the undersea light field including allowances for geographical position, weather, water quality, diurnal changes backgrounds of sand cloud and sea bed or water. The contrast of the fishing gear as a visual stimulus of the simulated trawl can be predicted for the visibility of the net components including netting, ropes, floats, bobbins, otter boards and their sand clouds as viewed from any fish position within the net under the particular light conditions.
Acknowledgements We thank Mr. Ferro for help with using NETSIM. Y.-H. Kim acknowledges the funding in part by The 1993 Professor’s Overseas Research Program of the Ministry of Education of Republic of Korea, The Korea Research Foundation, as well as support from the College of Marine Science of Gyeongsang National University and the SOAEFD Marine Laboratory, all of which helped to make this study possible.
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