Hjellvik et al : Measurement error in marine survey catches 



721 



Table 1 



Summary statistics for the parallel trawling experiments; time, vessel, position (latitude, longitude), the number of hauls in) and 

 the average per cod weight w (in kg) within each group. The vessels involved were Johan Hjort (.JM),Anny Krsemer (LIZY), G. O. 

 Sars (GS), Jan Mayen (JM), and Michael Sars (MS). 



of Marine Research, Bergen (IMR), (Jakobsen et al.M, 

 parallel trawling experiments were used to compare the 

 efficiency of the participating vessels with gear types as 

 given in Table 1 and Figure 1. During a parallel haul the 

 vessels operated about 500 meters apart and used radio 

 contact to assure proper coordination during hauls. We 

 analyzed ten parallel trawl experiments performed by the 

 IMR during the last decade (Table 1). The data from 1991 

 are described in Michalsen et al. (1996). Two hauls with 

 unstable bottom contact were excluded from the 1991 data 

 (Michalsen et al., 1996). Similarly, two hauls from 1995 

 were excluded — one where trawl geometry measurements 

 indicated problems with the doors and another with highly 

 different recorded towed distances (0.7 and 2.2 nautical 

 miles [nmi]). Let d, denote the towed distance for haul ; 

 andvesselj;j=l, ... ,n;y=l,2 wheren is the total number of 

 hauls. The average recorded distance is d ={2n ) ' X -'X '=■ 

 d, , = 1.33 nautical mile (average duration in time is 27 

 minutes), with 0.8 < d,.^ < 1.8 in 98% of the cases. The abso- 

 lute values |d, j-c/, 9I ofthe differences in towed distance 

 for the two vessels in the same haul, are 0, 0.1, 0.2, 0.3, 0.4, 

 and 0.6 in 43, 45, 31, 6, 4, and 1 cases, respectively. 



The data were subdivided into 10 groups so that the 

 same two vessels performed all hauls within a group, 

 within a period of one to three days, and usually in a small 

 geographical area. Group 10 is an exception where the 

 trawl stations are evenly spread over about 60 nmi both in 

 the east-west and in the north-south directions. 



The statistical model 



Any study of uncertainty depends on the stochastic model 

 adopted. Two different statistical models may yield quite 



' Jakobsen, T., K. Korsbrekke, 8. Mehl, and O. Nakken. 1997. 

 Norwegian combined acoustic and bottom trawl surveys for 

 demersal fish in the Barents Sea during winter ICES CM 

 1997A':17:l-26. Institute of Marine Research, P.O.Box 1870 

 Nordnes, 5817 Bergen, Norway. 



different uncertainty estimates. A general model for a 

 series of survey measurements [y^,i=l, ... ,11} is given by 



>',=/'^i' 



.^,p' + f,. 



i = 1, ... ,n. 



where 



/■ = a deterministic function, which in general 

 is unknown; and 

 X = the zth measurements of p explanatory 

 variables, such as geographical location, 

 depth, or time. 



If all of the relevant explanatory variables were included, 

 f, would represent the residual uncertainty. In practice, all 

 conceivable explanatory factors will not be observed, and 

 often /'is assumed to be linear. 



A difficulty in assessing the uncertainty of fish 

 abundance estimates is that we cannot carry out 

 a controlled experiment, where the setting of each 

 experiment is identical. In such an idealized series of 

 experiments the explanatory variables x,i, ... ,x,p would be 

 fixed, and e would be the only source of random variation 

 so that for a series of A'^ experiments. 



y^=f(x.„...,x) + e^. 



1, ... ,N. 



The standard error of f^, could then be estimated directly 

 from the observations {y^l as 



1 



N- 



\l 



<.>'*->') 



and the correctness of the model could be tested by a new 

 series of experiments for a new set of fixed values for the 

 explanatory variables. 



The closest we can come to such an idealized experiment 

 is that of parallel trawling described above. The values of 

 the explanatory variables, such as geographical location 

 and depth, will vary somewhat from one vessel to another, 



