Measurement errors and corrections applied during data processing

I n a l l CTD measurements, random e r r o r s a r i s e from the e l e c t r o n i c n o i s e and the d i g i t i z i n g i n t e r v a l . Systematic e r r o r s have been caused by the response time of the sensors due t o r a p i d l y changing f i e l d s and by the i n a c c u r a c i e s i n v o l v e d i n the c a l i b r a t i o n of the s e n s o r s .

An ME-Multisonde was used (MS 38) which was equipped w i t h one p r e s s u r e gauge and p a i r s of thermometers (Rosemount PT 200) and l a r g e c o n d u c t i v i t y c e l l s . The a c c u r a c i e s guaranteed by the manufacturer a r e l i s t e d i n t a b l e 1.

Due to t e c h n i c a l reasons we reduce the o r g i n a l 1 6 - b i t r e s o l u t i o n t o 15 b i t , which l e d t o a d i g i t i z i n g i n t e r v a l of 2 mK, 0.002 mS/cm and 0.02 dbar f o r the thermometers, c o n d u c t i v i t y c e l l s and the p r e s s u r e gauge.

The s y s t e m a t i c e r r o r s o c c u r i n g turned out t o be much more important then t h e s e random i n a c c u r a c i e s , which we can t h e r e f o r e n e g l e c t i n our e r r o r a n a l y s i s .

A major problem f o r the accuracy of the measurements was the i n e f f i c i e n t c a l i b r a t i o n . The sensor c a l i b r a t i o n s were c a r r i e d out by the manufacturer and i t turns o u t , that they o v e r - e s t i m a t e d the a c c u r a c y . For p r e s s u r e and s a l i n i t y a way was found to improve the c a l i b r a t i o n , f o r temperature no c o r r e c t i o n could be found f o r the i n a c c u r a c i e s d e t e c t e d by comparing both sensors w i t h each o t h e r .

The o t h e r important source of i n a c c u r a c y was the heat f l o w , e s p e c i a l l y i n the thermometers and the p r e s s u r e gauge.

Temperature and c o n d u c t i v i t y were measured w i t h two sensors each. As both sensor p a i r s can be t r e a t e d as independent measurements of the same w a t e r , the a n a l y s i s of the d i f f e r e n c e between them gave us a d d i t i o n a l i n f o r m a t i o n about the a c c u r a c i e s and the impact of a p p l i e d c o r r e c t i o n and e d i t i n g methods upon t h e measurements.

I n the f o l l o w i n g s e c t i o n s the problems and the attempt t o s o l v e them a r e d e s c r i b e d f o r each parameter r e s p e c t i v e l y .

P r e s s u r e

A s y s t e m a t i c e r r o r of the pressure measurement i s caused by the r a p i d change of temperature of the surrounding water. The p r e s s u r e s t r a i n gauge of the CTD-probe i s mounted i n s i d e the f i s h ' s h u l l . I t s good thermal contact t o the p r e s s u r e v e s s e l which has a much l a r g e r thermal c a p a c i t y than the sensor i t s e l f damp the temperature change of the sensor.

S m a l l holes on the s i d e of the f i s h ' s body p r o v i d e the contact of water i n s i d e w i t h the o u t s i d e . Although we have no q u a n t i t a t i v e measurement of the temperature i n the I n t e r i o r of the f i s h , we assume the temperature range o u t s i d e the f i s h of 5 to 8 K between the t u r n i n g p o i n t s of a p r o f i l e t o be suppressed by a f a c t o r of t h r e e , which i s supported by the r e s u l t s of an e a r l i e r t e s t c r u i s e . The e r r o r i n the p r e s s u r e s i g n a l c o u l d be e s t i m a t e d t o approximately 0.1 x 10 Pa/K.

We decided to t r e a t the ascending and descending p a r t s of the f i s h t r a c k s e p a r a t e l y to get c o n s i s t a n t data s e t s which are not a f f e c t e d r e l a t i v e l y by t h i s s y s t e m a t i c e r r o r .

The e f f e c t of dynamic p r e s s u r e , caused by the passage of the f i s h through the water i s a l s o a s y s t e m a t i c e r r o r estimated f o r a towing speed

_•, 2 t*

of 5 m s ^l, according to p = V2 P" i s of order 1 x 10 Pa.

The c a l i b r a t i o n of the p r e s s u r e sensor done by the manufacturer turned out to be i n c o r r e c t . I t showed a n e g a t i v e o f f s e t . The f a c t t h a t the towed f i s h o f t e n reached the sea s u r f a c e allowed t h i s e r r o r t o be c o r r e c t e d . A s c a t t e r diagram of the p r e s s u r e at the upper t u r n i n g p o i n t s versus the temperature along the s e c t i o n s was p l o t t e d ( f i g u r e 4.6.2). I t was assumed, t h a t the minimum pressure at d i f f e r e n t temperature v a l u e s i s the sea s u r f a c e p r e s s u r e , a statement which i s supported by frequent s i g h t i n g s of the f i s h at the s u r f a c e . The s o l i d l i n e i n t h i s graph was used t o c o r r e c t the data by s h i f t i n g the whole p r o f i l e a c c o r d i n g to i t s sea s u r f a c e tem-p e r a t u r e v a l u e . To overcome the d i f f i c u l t y t h a t not a l l tem-p r o f i l e s reached the s u r f a c e s the p r o f i l e s of each four-hour s e c t i o n were s h i f t e d e q u a l l y a c c o r d i n g t o the four-hour mean s u r f a c e temperature. We a l s o took account of the f a c t , t h a t the p r e s s u r e sensor i s 0.7 m below the top of the f i s h .

Taking these d e t a i l s i n t o account y i e l d s an a b s o l u t e e r r o r of

± 0.2 x 10 Pa around the upper t u r n i n g p o i n t where the sea s u r f a c e i s a r e l a t i v e l y w e l l d e f i n e d r e f e r e n c e l e v e l . In the deeper l a y e r s the u n c e r -t a i n -t i e s i n c r e a s e -towards -the lower -t u r n i n g p o i n -t where -the combina-tion of

thermal e f f e c t s , s e n s o r - l a g , c a l i b r a t i o n u n c e r t a i n t i e s , and dynamical

+ h

p r e s s u r e add up to an e r r o r of - 1.6 x 10 Pa.

Temperature

Before the c a l i b r a t i o n of the temperature s i g n a l i n the 2nd p r o c e s s i n g s t a g e , a simple time constant c o r r e c t i o n f o r the thermometers was c a r r i e d o u t . The a l g o r i t h m a p p l i e d t o the data i s shown i n the f o l l o w i n g e q u a t i o n ;

AT T = T + x ~

At

where T^m i s the measured temperature and x the time constant of the thermo-meter. This time constant was estimated e m p i r i c a l l y by t r y i n g to reduce the s p i k e s i n the computed s a l i n i t y s i g n a l . A time constant of about 85 ms (1.36 raw data c y c l e s ) was found to be most a p p r o p r i a t e . This value i s supported by the values g i v e n by the Rosemount company of about 120 ms.

N e v e r t h e l e s s i t was not p o s s i b l e t o get r i d of a l l s a l i n i t y s p i k e s and so i t was decided to e d i t s a l i n i t y s e p a r a t e l y .

By h o r i z o n t a l l y averaging mean and standard d e v i a t i o n p r o f i l e s of the d i f f e r e n c e T j - T² were c a l c u l a t e d . They are presented i n f i g . 5.1.1a u s i n g raw data and i n f i g . 5.1.Id c a l c u l a t e d from data t h a t had passed a l l d a t a p r o c e s s i n g s t a g e s . A s y s t e m a t i c mean d i f f e r e n c e of - 10 mK l i m i t s t h e q u a l i t y of the c a l i b r a t i o n . Why the d i f f e r e n c e becomes p o s i t i v e i n the h i g h g r a d i e n t zone around 20 m i s not understood. Randomly d i s t r i b u t e d d i f f e r e n c e s were found along t h e whole p r o f i l e , i n c r e a s i n g p r o p o r t i o n a l l y w i t h t h e l o c a l v e r t i c a l temperature g r a d i e n t .

These d i f f e r e n c e s can be produced alone by r o l l i n g movements of the f i s h , because t h e i r magnitude i s c o n s i s t e n t w i t h the observed r o l l angles and the v e r t i c a l temperature g r a d i e n t .

The comparison of f i g . 5.1.1a and f i g . 5.1.Id show t h a t the data p r o c e s s i n g d i d not change the s t a t i s t i c s of the temperature measurement.

The mean p r o f i l e s a r e i d e n t i c a l c o n s i d e r i n g the depth s h i f t due t o c o r r e c t i o n of the p r e s s u r e o f f s e t . The standard d e v i a t i o n i s s l i g h t l y d i m i n i s h e d a f t e r b l o c k a v e r a g i n g .

I t i s not c l e a r how the temperature changes along the sensor c a b l e s , which were p a r t l y i n s i d e t h e f i s h , w i l l e f f e c t t h e measurements, but i t was

assumed to be n e g l i g i b l e . From the manufacturer of the CTD sonde we r e c e i v e d the f o l l o w i n g a c c u r a c i e s :

A b s o l u t e accuracy - 10 mK r e l a t i v e accuracy - 3 mK

C o n d u c t i v i t y

The main source of e r r o r i n the c o n d u c t i v i t y s i g n a l i s due to c a l i b r a t i o n i n a c c u r a c i e s . I t was assumed, that the temperature e f f e c t was n e g l i g i b l e and f o u l i n g by d r i f t i n g m a t e r i a l does not occur. We d i d not t r y to c o r r e c t the c o n d u c t i v i t y i t s e l f , but the s a l i n i t y as d e s c r i b e d i n the f o l l o w i n g s e c t i o n .

S a l i n i t y

I t was mentioned above that the c a l i b r a t i o n of the c o n d u c t i v i t y sensors turned out to be i n a c c u r a t e . To improve the accuracy we compared s a l i n i t i e s of water samples, taken every hour at h u l l depth w i t h C T D - s a l i n i t i e s matching i n time and space. Data p a i r s from regions w i t h h i g h v e r t i c a l or h o r i z o n t a l g r a d i e n t s were r e j e c t e d . Data from low v a r i a b i l i t y regions were used f o r a l i n e a r r e g r e s s i o n ( f i g . 4.6.1) c a l c u l a t i n g the c o e f f i c i e n t s f o r a l i n e a r t r a n s f o r m a t i o n to c o r r e c t the measured s a l i n i t y v a l u e s . The r e s i d u a l of the r e g r e s s i o n a n a l y s i s was 0.023 x 1 0 "³.

The mismatch i n the response of the thermometers and c o n d u c t i v i t y c e l l s was the most severe problem i n the data s e t . The time l a g of the thermometer caused by a time-constant of about 120 ms (a v a l u e g i v e n by the m a n u f a c t u r e r ) i s an i n t r i n s i c property of the sensor, whereas the water-exchange time i n the c o n d u c t i v i t y c e l l i s a f u n c t i o n of e l e c t r o d e spacing and the speed at which the f i s h p e n e t r a t e s the water. We decided to use an e m p i r i c a l method t o minimize these e f f e c t s by a p p l y i n g a temperature time constant c o r r e c t i o n of T - 0.085 s. This value was determined by m i n i m i z i n g the d i f f e r e n c e i n temperature and s a l i n i t y at those p a r t s of the a s c e n d i n g and descending p a r t s of the p r o f i l e s , which were c l o s e to the t u r n i n g p o i n t s of the f i s h .

I n these r e g i o n s , h o r i z o n t a l d i f f e r e n c e s i n the parameters should be s m a l l . The second c r i t e r i o n f o r the c h o i c e of t h i s v a l u e was the s y m m e t r i c a l d i s t r i b u t i o n of the remaining s a l i n i t y s p i k e s a l o n g t h e mean p r o f i l e s .

T h i s c o r r e c t i o n a l s o reduced the s i z e of s a l i n i t y s p i k e s but c o u l d not e l i m i n a t e them a l l . We decided t o use a median f i l t e r (Sy, 1985), a t e c h n i q u e

which e l i m i n a t e s s p i k e s but does not a f f e c t sharp g r a d i e n t s . The w i d t h of t h i s f i l t e r was chosen to have a minimum e f f e c t on the s t a t i s t i c s of the p r o f i l e s . Furthermore we block-averaged the data over the range of the f i l t e r w i d t h .

Another use of the median f i l t e r upon d e n s i t y and a r e - i t e r a t i o n of s a l i n i t y from temperature and f i l t e r e d d e n s i t y d i d not have much e f f e c t i n the improvement of the d a t a .

I n s p i t e of t h i s e d i t i n g scheme t h e r e are s t i l l remaining s i n g l e s p i k e s m a i n l y i n the zone of h i g h v e r t i c a l g r a d i e n t s j u s t below the mixed l a y e r which was a l s o the r e g i o n of maximum d i v i n g speed. Most of the remaining s p i k e s have magnitudes l e s s than 0.02 x 1 0 "³ and only v e r y few s p i k e s exceed 0.07 x 1 0 "³.

The e f f e c t of a l l the c o r r e c t i o n procedures on the s a l i n i t y data can be seen by comparing raw data and ready processed average p r o f i l e s of the d i f f e r e n c e S i ~ S² ( f i g . 5.1.1b and f i g . S . l . l . e ) . The r e c a l i b r a t i o n s h i f t e d the mean p r o f i l e towards the z e r o l i n e . I t s v e r t i c a l s t r u c t u r e was not changed s i g n i f i c a n t l y . The d e v i a t i o n from z e r o remains l e s s than 0.01 x 1 0 "³ a t the upper boundary of the t h e r m o e l i n e and values between 0.02 and 0.015 a t the deeper p a r t s to v a l u e s around 0.01 x 10~~ ³, which i s i n the o r d e r of magnitude which c o u l d be expected f o r d i f f e r e n c e s due to r o l l i n g of the i n s t r u m e n t .

The comparison of water sample s a l i n i t i e s w i t h the e d i t e d C T D - s a l i n i t i e s a l o n g s e c t i o n B102 ( f i g u r e 5.1.2) shows to which extent the a b s o l u t e a c c u r a c y of s a l i n i t y c o u l d be improved. The d i f f e r e n c e between sensor p a i r 1

+ -

3

and sensor p a i r 2 remains mainly w i t h i n the l i m i t s of -0.01 x 10 . The water

+ _ 3

sample-CTD-differences do not exceed -0.01 x 10 , except i n r e g i o n s of h i g h h o r i z o n t a l g r a d i e n t s , where the non-perfect s y n c h r o n i z a t i o n of sampling and CTD-measurements may have l e d t o a mismatch i n the r e s u l t i n g s a l i n i t i e s . Density

The e r r o r s i n the d e n s i t y ( O j . ) a r e an a c c u m u l a t i o n of the e r r o r s of temperature and s a l i n i t y s i n c e d e n s i t y i s a f u n c t i o n of s a l i n i t y and temperature

3o 3cr^t

£ , ^e + c ^>

O" „ S ™ 1

t 3s oT

w i t h e * 0.02 x 1 0 ~³ and ©r = 0.01 K the e r r o r s i n s a l i n i t y and temperature.

T e s t s f o r d i f f e r e n t regions and d i f f e r e n t v e r t i c a l g r a d i e n t s r e v e a l v a l u e s of to be l e s s than 0.005 kg m~³.

As f o r temperature and s a l i n i t y mean p r o f i l e s of the d i f f e r e n c e s

°tl ~ °t2 ^{a r e} presented i n f i g . 5.1.1c and 5 . 1 . I f . As w i t h s a l i n i t y the e d i t i n g reduces the v a r i a b i l i t y of the sensor d i f f e r e n c e s to the r o l l i n g range.

5.2 n u m e r i c a l e s t i m a t i o n of u n c e r t a i n t i e s i n d e r i v e d q u a n t i t i e s .

D e r i v e d q u a n t i t i e s such as s a l i n i t y and d e n s i t y were i n f l u e n c e d by the d i f f e r e n t time response of thermometers and c o n d u c t i v i t y s e n s o r s . F o l l o w i n g v a r i o u s n o n - a n a l y t i c a l stages i n the data p r o c e s s i n g scheme, the u n c e r t a i n t i e s i n the d e r i v e d v a r i a b l e s can only be estimated by a n u m e r i c a l experiment.

Therefore a s y n t h e t i c set of p r o f i l e s of temperature and s a l i n i t y were generated and f rom these the corresponding c o n d u c t i v i t y p r o f i l e was d e r i v e d . The shape of the p r o f i l e s were as c l o s e t o the observed p r o f i l e s as p o s s i b l e , a l t h o u g h they are s i m p l i f i e d due to t h e i r a n a l y t i c a l c o n s t r u c t i o n . The s a l i n i t y p r o f i l e was constant w i t h depth and the i n i t i a l temperature p r o f i l e has a mixed l a y e r and decays e x p o n e n t i a l l y below 20 m w i t h r e a l i s t i c v e r t i c a l g r a d i e n t s . The i n i t i a l set of p r o f i l e s i s shown i n f i g u r e 5.2.1.

The time constant of the thermometer was g i v e n by the Rosemount Company t o 120 m i l l i s e c o n d s and i n a simple l a b o r a t o r y t e s t t h i s v a l u e was proved t o be a c c u r a t e .

The f l u s h i n g time of the c o n d u c t i v i t y c e l l v a r i e s w i t h the p e n e t r a t i o n speed of the f i s h . T y p i c a l parameters were a towing speed of 5 m s "¹ and a d i v i n g r a t e of 2 m s "¹ r e s u l t i n g I n a f l u s h i n g time of about 10 m i l l i s e c o n d s .

W i t h these values i n mind, we f i l t e r e d the i n i t i a l temperature p r o f i l e a c c o r d i n g t o :

ar

T = Tm ⁺ \ ~~~ (5.2.1)

3t

where T i s the i n i t i a l temperature, Tr; = 110 m i l l i s e c o n d s the d i f f e r e n c e I n the response c h a r a c t e r i s t i c between temperature and c o n d u c t i v i t y and T^m the r e s u l t i n g (measured) temperature.

I n f i n i t e d i f f e r e n c e s t h i s e q u a t i o n i s w r i t t e n as

T n \ =( i ) m ( i ) ^T f \ +— ( vm ( i ) m ( i - l )^T f*\ ~ ^T n ) (5.2.2) 1 x '

w i t h At = 62.5 m i l l i s e c o n d s g i v e n by the sampling r a t e o f the CTD. From t h i s e q u a t i o n an e x p r e s s i o n f o r T^m( ^ j was d e r i v e d :

T t-\ " ⁺ " ^T r* o (5.2.3)

m(x) ( l ) m ( i - l ) 1+a 1+a w i t h a = — = c o n s t a n t . x

At

The i n i t i a l c o n d i t i o n f o r T ... w i t h i = l i s g i v e n by T ... = T,,,, which i s

m ( i ) ° ^J m ( l ) ( 1 ) '

t r u e f o r the mixed l a y e r . The c o n d u c t i v i t y p r o f i l e remains unchanged. The d a t a were processed f o l l o w i n g the scheme of the data p r o c e s s i n g f l o w diagram ( f i g u r e 4.1) and at each stage the r e s u l t i n g s a l i n i t y and d e n s i t y p r o f i l e was compared w i t h the I n i t i a l p r o f i l e s . Two n u m e r i c a l experiments were c a r r i e d out, the f i r s t w i t h a constant d i v i n g r a t e of 2 m s ~¹ and the second w i t h a non-uniform d i v i n g r a t e , which v a r i e s between 1 m s " "¹ and 4 m s^_1 w i t h the maximum speed i n t h e r e g i o n of the s t r o n g e s t v e r t i c a l g r a d i e n t ( a t 20 m). The d i v i n g r a t e i n the second experiment was tuned t o be s i m i l a r t o the d i v i n g c h a r a c t e r i s t i c s of the f i s h during the NOA'81 e x p e d i t i o n . The f i r s t step i n the d a t a p r o c e s s i n g was the a p p l i c a t i o n of the e m p i r i c a l l y estimated time constant x = 85 m i l l i s e c o n d s t o t h e temperature d a t a . F i g u r e 5.2.2 shows the s a l i n i t y d i f f e r e n c e between t h e i n i t i a l p r o f i l e and the d e r i v e d s a l i n i t y f o r both experiments. In t h i s s t a g e ( l a f o r constant d i v i n g speed) t h e v a r i a b l e d i v i n g r a t e ( I l a ) l e d t o an i n c r e a s e of the maximum s a l i n i t y e r r o r by a f a c t o r of two. The range, i n which the s a l i n i t y e r r o r exceeds 0.01 x 1 0 "³ i s c o n c e n t r a t e d i n t h e top 8 m

of the thermocline f o r case ( l a ) and about 15 m f o r case ( H a ) . The median f i l t e r ( l b , l i b ) had no e f f e c t on these p r o f i l e s , but the f o l l o w i n g b l o c k average ( f i g u r e I c , l i e ) can s h i f t the ' e r r o r r e g i o n ' i n t o the mixed l a y e r which might l e a d to an e r r o r i n the d e t e r m i n a t i o n of mixed l a y e r depth.

Remaining i n v e r s i o n s i n the d e n s i t y p r o f i l e caused by the weak slope of the f i s h - t r a c k at the lower t u r n i n g p o i n t s were e l i m i n a t e d by a p p l y i n g the median f i l t e r a l s o to the d e n s i t y p r o f i l e , and s a l i n i t y was r e - i t e r a t e d from the r e s u l t i n g d e n s i t y and the temperature p r o f i l e ( f i g u r e s I d , l i d ) . The r e s u l t s of t h i s experiment are shown i n f i g u r e 5.2.3 where Eg, the e r r o r i n s a l i n i t y i s p l o t t e d as a f u n c t i o n of 3T/3z. For case ( I ) w i t h a constant d i v i n g r a t e of 2 m s~ ¹ the e r r o r i n s a l i n i t y i s a l i n e a r f u n c t i o n of the r a t e of change of temperature, and z^s i s o n l y g r e a t e r than 0.02 i n r e g i o n s , where 3T/9z exceeds 0.45°K m~^l. For case ( I I ) t h e s a l i n i t y e r r o r exceeds 0.02 a t 3T/ 8z g r e a t e r than 0.25°K m^{_ 1}.

Temperature g r a d i e n t s of t h i s magnitude (0.25°K m~ *) were observed not o n l y at the top of the p y c n o c l i n e , but the anomalously high d i v i n g r a t e s were only at present In the top 30 m of the f i s h t r a c k , whereas i n the remaining p a r t s of the p r o f i l e the d i v i n g speed was about 2 m s^-1. T h e r e f o r e e r r o r s i n s a l i n i t y caused by the nonperfect time-constant c o r r e c t i o n were e s t i m a t e d to be l e s s than 0.02 x 10" ³ f o r the major f r a c t i o n of the p r o f i l e s , and o n l y very c l o s e to the top of the seasonal t h e r m o c l i n e the e r r o r may reach 0.05 x 1 0 ~³.

Where temperature i n v e r s i o n s occur, the e r r o r i n s a l i n i t y i s expected to be l e s s than 0.02 x 1 0 "3, assuming t h a t the d i v i n g r a t e was about 2 m s_ 1

over the depth range of the i n v e r s i o n .

The d e n s i t y p r o f i l e i s a l s o I n f l u e n c e d by the mismatch I n the time response of the thermometer and c o n d u c t i v i t y c e l l . T h e r e f o r e the same p r o -cedure was c a r r i e d out f o r d e n s i t y and the r e s u l t i s shown i n f i g u r e 5.2.4.

The e r r o r s i n d e n s i t y were remarkably reduced d u r i n g the p r o c e s s i n g s t a g e s ; n e v e r t h e l e s s the maximum e r r o r i n d e n s i t y i s 0.025 kg m~³ at constant d i v i n g speed ( f i g u r e 5.2.3 case I d ) and about 0.05 k g m^{- 3} a t v a r i a b l e d i v i n g speed. This e r r o r i s l i m i t e d to the top of the p y c n o c l i n e and case l i d can be t r e a t e d as a worst case example f o r the top 10 metres of the p y c n o c l i n e . Everywhere e l s e the e r r o r i n d e n s i t y would be l e s s than 0.01 kg m~³.

The e r r o r s i n the d e n s i t y p r o f i l e would a l s o i n f l u e n c e the spacing between p a i r s of i s o p y c n a l s , which were d e r i v e d i n the 7 t h p r o c e s s i n g stage

( f i g u r e 4.1). F i r s t l y the i n t e r p o l a t i o n onto standard d e n s i t y s u r f a c e s b e i n g 0.025 kg m~3 apart was c a r r i e d out f o r the i n i t i a l d e n s i t y p r o f i l e and the f i n a l e d i t i n g s t a g e . Afterwards the p r e s s u r e d i f f e r e n c e between d e n s i t y surfaces being 0.1 kg m^{- 3} apart was determined, and the r e s u l t i n g d i f f e r e n c e between the t r u e i s o p y c n i c spacing and the f i n a l product ( a f t e r e d i t i n g ) i s presented i n f i g u r e 5.2.5 and 5.2.6. Except f o r the top of the s e a s o n a l p y c n o c l i n e , the e r r o r i n i s o p y c n i c spacing i n t h i s model i s c l o s e t o the v e r t i c a l r e s o l u t i o n (12.5 cm). N e v e r t h e l e s s , i n the r e g i o n of s t r o n g e s t v e r t i c a l g r a d i e n t s t h i s e r r o r may exceed 20 % of the t r u e s p a c i n g f o r the case of non-uniform d i v i n g speed. Below t h i s r e g i o n the e r r o r i n i s o p y c n i c spacing i s l e s s than 5 %. The accuracy of i s o p y c n i c spacing r e s u l t i n g from the mismatch i n the time response of our sensors i s

eAp = m"

T h i s n u m e r i c a l study has a l s o shown t h a t a r e d u c t i o n of the e r r o r s i n s a l i n i t y r e q u i r e s a r e d u c t i o n of the d i v i n g r a t e , which should be c o n s t a n t over the t o t a l depth range. On the o t h e r hand, a r e d u c t i o n of the d i v i n g speed w i l l r e s u l t i n a weaker slope of the f i s h t r a c k and the occurrence of d e n s i t y i n v e r s i o n s due to i n t e r n a l waves i s more l i k e l y .

The apparent t h i c k n e s s , caused by the slope of the i n t e r n a l waves compared t o i n c l i n a t i o n of the f i s h t r a c k , w i l l be i n c r e a s e d , i f the d i v i n g r a t e i s reduced. Therefore one has t o choose a compromise a c c o r d i n g to the s c i e n t i f i c o b j e c t i v e s of the data s e t .

Im Dokument 3D1 I iTH-'EeR- m (Seite 36-44)