The dependent variability of the ocean is a function of the depth movement and 

 the slope of the temperature depth trace at that point. Thus the influence of internal 

 waves would produce a change in temperature at a given depth or a temperature 

 variability which is actually a function of the water mass movement. (It should be 

 noted that internal waves do not consist of random motion, and therefore (a^) 

 DEP. will not represent a true average condition. Instead, an average based on 

 harmonic wave motion should be employed.) Equation 5 also indicates a dependent 

 error in the temperature sensing element due to the error in the depth sensing 

 element. This error can be related to the depth error as follows: 



(^ \ = '■'^D'^ INDEP 



^'^T/'dep 2 (6) 



Combining (5) and (6) : 

 Where S is the slope of the temperature-depth trace in ft/degree. 



o 



Similarly the standard deviation in depth is related to the temperature error 

 and the independent error as follows : 



(''d)inst =\/2(aD)iNDEP ^ S'2(aT)j^pgp (8) 



The significance of the dependent error of temperature due to errors in depth 

 can be best described as follows : Let us suppose we have an instrument capable of 

 measuring to within .01 °F and we wish to determine the temperature at a depth of 

 100 feet. Let us further suppose that at a depth of 100 feet the temperature varies 

 from 70° at 95 feet to 60° at 105 feet, or 1° per foot. Let us further suppose that we 

 are not able to locate the exact depth of the temperature sensing element to better 

 than ± 5 feet. 



While the temperature recorder may be accurate to within .01 °F, the location 

 will not be known except to within the nearest five feet ; hence the element may have 

 been anywhere from 95 to 105 feet. The temperature variation through this area is 

 ten degrees; hence, the absolute value of the temperature at 100 feet cannot be de- 

 termined' with any greater accuracy than ±5°. This relatively poor accuracy is a 

 result of the dependent error in temperature due to the error in depth. 



4.4. Measurements of Instrument Error by Special Tests 



Since it is mathematically impossible to segregate the variability of the ocean 

 and the instrument errors by observing a set of measurements, it is desirous when- 

 ever possible to determine instrument error independent of such measurements. This 

 can often be done in special test such as will be discussed later. Whenever such 

 errors can be independently determined they may be assumed to be contributing in 

 accordance with Equation 1, and the independent value obtained may be subtracted 

 from the equation to determine by difference the desired ocean variability com- 

 ponents. 



