60 



both instrumentation and data handling. We need, therefore, to devise our ex- 

 periments and instruments so that we obtain as many observations as practical 

 in the most logical manner. It would seem that th'e criteria of how many obser- 

 vations are needed will depend upon our ability to interpolate between our ob- 

 served points. 



Investigators are apt to become over-confident of their work on the basis 

 of observed points which fit a given assumption. This can be quite dangerous, 

 particularly if the assumption was made after the data was taken. I would like 

 to add a word of caution and recommend that the precision of a set of tempera- 

 ture-depth points be determined by "the reliability and precision of interpolated 

 temperatures" rather than on the temperatures at the measured depths. 



Because it is not mathematically feasible to determine the precision of 

 interpolation along an unknown curve, we interpolate from point to point on the 

 basis of an assumed temperature-depth distribution. For example our mind 

 will usually only permit so many inflection points. In other words, our preci- 

 sion of interpolation is intimately connected with how many inflection points we 

 think exist in the actual curve. • 



In order to arrive at thumb rules for interpolating data of this kind, I 

 would suggest that in areas where the temperature structure is well known and 

 appears linear, we can interpolate to within say 2% of the temperature difference 

 between thermometers. Where the temperature structure is not well known, or 

 is not nearly linear, it is doubtful if we can estimate temperatures to within 5% 

 of the difference between temperatures. In essence, it is emphasized that im- 

 portant small scale fluctuations can exist in the temperature structure of the 

 ocean and escape our present methods of measuring and analysis. I would, 

 therefore, suggest that we tend to think of a temperature-depth trace as a fuzzy 

 band rather than as a mathematical line. Furthermore, we should remember 

 that this band is opaque, and much of the future progress in oceanography will 

 come through learning more about the small scale changes. 



Figure 4 shows a set of temperature-depth points with several types of 

 interpretation made on the data to illustrate the points in question. 



First, we have a smooth line drawn connecting the points as one would 

 normally do. Second, we have a series of rectangles with opposite corners con- 

 necting adjacent points. While a total error as large as the area of these blocks 

 is perhaps ridiculous, we must remember that any one point could make an ex- 

 cursion as great as this without even introducing a reversal of temperature. 



Third, we have placed a pair of temperature points midway in depth be- 

 tween observed points assuming that we can interpolate to within about 5% of the 

 temperature difference between points. Then we have drawn a wide line to indi- 

 cate the extent of the fine structure which may still be beyond the powers of our 

 data to disclose. 



I want to emphasize that most of our deep water theories of the ocean 

 have been built up on a mass of data which is incapable of showing fine structure, 

 particularly as usually analyzed. 



• ERRORS IN TEMPERATURE DATA 



In taking and interpreting any oceanographic temperature measurement 

 we must remember that many factors come in. Components of error are nu- 

 merous, and oftentimes very subtle. A listing of some of the sources may help 



