SECTION 4.0 



APPLICATION OF ERROR TERMINOLOGY 

 TO THE BATHYTHERMOGRAPH 



The previous sections have described the mathematical definitions of errors and form the 

 basis upon which the errors of the Bathythermograph can be analyzed and classified. 



Consider first the true temperature value of any one point in the ocean at any one instant 

 of time. Since temperature is an arbitrary reference level of thermal energy, it is subject to 

 the errors of the reference instruments. However, a temperature can be defined within any ac- 

 curacy desired, say for instance, ± 0.01 °F. 



Thus at time 9 and depth D the temperature T can be assumed to have a definite value 

 within the accuracy desired. At time 9 plus a9 and at the same depth D a second temperature 

 T-j can also be observed to the accuracy desired. 



The question arises as to the exact relationship between T, and To. In a liquid medium such 

 as the ocean the relationship between T] and Ta can reflect the following four basic changes: 

 (1) inaccuracies in the temperature sensing element (since temperature is a relative condi- 

 tion, the accuracy of the sensing element cannot be eliminated, even theoretically) ; (2) the 

 change in the heat content of the mass of water, under measurement; (3) translation of the 

 mass of water during the interval a9, this change in mass reflecting a new temperature condi- 

 tion, or (4) where D is subject to accuracy of measurement, this change can reflect a change in 

 the location of the instrument making the measurement during time a9. 



It is particularly important to note that any variations observed when a series of tem- 

 perature measurements are made can be caused by any one of the four factors mentioned 

 above. Thus when it is desired to study and make determinations concerning the change of the 

 temperature in the ocean or the mass displacement occurring in the ocean, one must consider 

 and recognize the variations which can arise from variations in the accuracy of the depth and 

 temperature sensing elements. Conversely when concerned with establishing accuracy of the 

 temperature and depth sensing elements one must be cognizant of the relative mass and tem- 

 perature changes which are occurring in the ocean at the same time. 



The actual changes in the temperature of the ocean and mass displacement during time 

 theta (according to the above terminology) is ocean variability. The changes occurring as a 

 result of the depth measuring element and the temperature sensing element, according to our 

 mathematical definitions, are instrument errors, or more generally indeterminate errors. 



Unfortunately, when dealing with a series of temperature measurements in the ocean, it 

 is impossible to distinguish between the two types of changes; hence, ocean variability is 

 always subject to the limitation of definition by the order of magnitude of the instrument 

 errors. Conversely a study of instrument errors is limited by any ocean variabilities which may 

 exist at the time the measurements are taken. 



Probable values of the temperature of the ocean under various conditions can be 

 established through series of measurements which take into account ocean variability and in- 

 strument erorrs. The accuracy of such a probable value is limited by the instrument accuracy 

 and by the ocean variability which is occurring at that time. 



4.1. Determinate Errors of the Bathythermograph 



The location of the pen arm of the Bathythermograph with respect to the glass 

 slide is an arbitrary one, since there are no marks on the glass slide which indicate 

 actual values of the temperatures or depth. It is necessary to translate the tempera- 



