condition, -rjy^ > 0, any^ will suffice to give 



error. However as the second derivative of a 

 distribution curve segment increases, the error 



also increases if j^ remains the same. If ^ is 



allowed to vary wath the second derivative, the 

 error resultant can be held constant. The error 

 can be held constant or minimized when using a 

 continuous sampler by abstracting sufficient data 

 points in the areas of greatest property change; 

 or at close spaced uniform intervals over the entire 



water column, therefore, making -^ large enough 



to handle any gradien t change. Predicting density 

 gradient changes directly from the temperature 

 and salinity data is difficult; therefore the abstract- 

 ing of closely spaced uniform interval data points 

 would be the superior method. 



An approach was made to this problem by using 

 gradient sampling in an effort to properly describe 

 the density distribution and catch the important 

 changes in gradient. However it was found that 

 the areas of greatest temperature variations are 

 not necessarily the areas of greatest variations in 

 density gradient. On the contrary, figure 8D 

 shows great variations with depth of both tem- 

 perature and salinity in the upper 200 meters but 

 almost a straight line distribution of density. On 

 the other hand, between 400 and 600 meters, the 

 temperature and salinity gradients are almost 

 vertical while the density gradient is about half 

 of the slope observed in the upper 200 meters 

 where great temperature and salinity variations 

 existed. Past practice has been to sample these 

 deeper levels more sparsely because of the less 

 acute changes exhibited by temperature and 

 salinity, however, this could lead to anomaly 

 errors. Figures lOD and llD show examples of 

 intermediate level density gradients missed by 

 the standard sampling. 



In order to compare the point sampling method 

 with that of a continuous sampler, an approach 

 similar to that used for comparing gradient sam- 

 pling with standard depth sampling was utilized. 

 Stations representing the various water types 

 found in the Ice Patrol area were plotted to pro- 

 vide vertical temperatiu-e and salinity distribution 

 curves as described above. Several of these 

 stations were then processed for the anomaly of 

 specific volume and this was plotted against depth 

 with smooth curves drawn between the points. 

 Then straight lines were drawn between the 



standard Ice Patrol sampling depths. By past 

 methods, the values at the standard depths would 

 have been numerically integrated linearizing the 

 data between each standard depth. The areas 

 bounded by the curve of the specific volume 

 anomaly and the straight lines between the stand- 

 ard sampling levels represent the errors introduced 

 in the dynamic height calculations by standard 

 level, fixed sample number method of data col- 

 lection. This error was then measiu-ed by use 

 of a planimeter to obtain the area bounded by the 

 curves which represents the integration error 

 between each depth interval (figure 12D). Table 

 HID lists the results of this analysis giving the 

 errors, plus or minus, on either side of the idealized 

 distribution curve. 



Because of the random character of the anomaly 

 distribution curve, the accumulated errors tend 

 to cancel each other and reduce the totals in most 

 cases. The trend of the curves is towards the 

 more gradual anomaly change with depth resulting 

 in an error which is positive or greater than the 

 true value. Although the accumulated error 

 represents the probable error of standard depth 

 sampling, it is obvious that from the several 

 stations so analyzed that the error ranges from 

 small to large depending on positive or negative 

 error values along the curve. Only 15 stations were 

 selected for this treatment so statistical treatment 

 is not very effective, however, the station dis- 

 tribution is an example of the variety of water 

 masses found in the survey area. 



It is attempted herein to show the conditions 

 that can exist and how great the errors can be. 

 Each water column exhibits a random distribution 

 of standard sampling depth errors and a truly 

 representative error is difficult to define. Table 

 HID indicates what can be expected by insuffi- 

 ciently describing the gradient of density and 

 basing dynamic height computations on the 

 straight line distribution between points. These 

 figures are comparable to the errors determined by 

 standard level sampling versus gradient sampling 

 shown above. 

 Continuous Sampling Devices 



A continuous sampling system which gives an 

 unlimited number of points would be the ultunate 

 solution to the problem of calculating dynamic 

 heights with a minimum of gradient errors. The 

 advantages of a continuous sampling system can 

 be offset to a greater or lesser extent by the in- 



68 



