Naldmann et al. 
individual results. The median would be less sensitive to 
potential outliers. 
A crucial element of this study is to assess the significance of 
:he measurement result of an individual sensor and its 
uncertainty in comparison to a multi sensor approach. 
The uncertainty will be quantified from all parallel 
measuring probes and then compared with the measurement 
ancertainties derived from a single probe. To make both results 
comparable 5 min averages were calculated and then the 
standard deviation over the 4 sensors were derived. With the 
same approach described above a factor based on the student t 
distribution has to be used to take the low sample number into 
account (a=1.20, assuming 3 degrees of freedom and a 
significance of 68%). 
Im 
min n Ty—T: * 
une (1) za 57 9 
Where 7 is a specified moment in time and ug, is the value 
caken as the contribution to the uncertainty based on the 
variability of the measured parameter across all parallel 
measuring probes. As above, the combined (equation 2) and 
expanded uncertainty (equation 3) can be derived from the 
zalibration uncertainty, often confused as the overall measuring 
aıncertainty, and other influencing effects into account. 
Small scale mixing process with a scale below the distance of the 
individual sensors between each other will cause a decorrelation 
between spatial and temporal variabilities. Those major differences 
between the sensors typically occur in region of strong temporal/ 
spatial gradients as for instance the thermocline. 
As one can see from the comparison between Figures 8 and 6 
here appears to be a rather good match between both. The 
10.3389/fmars.2022.1002153 
differences can be traced down to the processes that cause strong 
Auctuations and their related spatio-temporal correlation 
Discussion 
The focus of this study has been to what extent the 
measurement result of a single sensor together with 
{he assigned uncertainty as calculated is representative for the 
observed parameter under consideration. For that purpose, 
parallel measuring probes had been used to be able to 
intercompare and judge on temperature measurement results 
of individual sensors, using the mean of the results of all 
available sensors as a reference. Only if a single sensor output 
is consistent with the mean of all sensor output and within the 
range of the calculated uncertainties can it be considered a 
reliable representative of the measured parameter. In that case 
the measurement uncertainty of the individual sensor is also 
quantifying the uncertainty range within which the consistency 
is valid. Mathematically, consistency can be expressed by 
comparing the deviation of the temperature result 7% of an 
'ndividual senor k from the mean T/ of the results of all sensors 
with the uncertainty of the deviation (see Figures 7 and 8). 
ITx Tail < ı/u? (Tx_i) + u? (Tm_i) (eq. 6) 
The index i refers to the respective values of the ij” 
measurement interval. According to eq. 6, a temperature 
measured with sensor k is considered consistent with the 
mean temperature calculated from results from all sensors, if 
the deviation from the mean is smaller than its uncertainty. It 
should be noted that, strictly speaking, a statistically consistent 
1.07 
106 
Sensor 1 
Sensor 3 
-Sensor 4 
— Multiple Sensors 
Sensor 5 
0.05 
30.04 L 
= 
5.0.03 | 
4 | 
2.02 
50 
„0 100 
Time/ri 
IGURE 8 
The standard uncertainty derived from the standard deviation between the 5 sensors within the same time interval as in Figure 6 on the right- 
ıand side (Period 2. hiah variability). In violet is the araph for the multiple sensor uncertainty 
Zrontiers in Marine Science 
ırontliersin.org