Naldmann et al. 
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10.3389/fmars.2022.1002153 
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"IGURE 5 
‚ime series of 5 min temperature means for P3 (dots, left panel A), while temperature variability was small and (a part of) P2 (right panel B with 
nigh variability). The insets magnify 20 min time windows and show the spreads of the raw data. 
figure on the left-hand side, collected on 23/24 September 2020 
between 22:40 and 01:40 (corresponding to time period P3), 
have been measured during rather stable environmental 
conditions. The overall change in temperature within that time 
interval amounts to about 60 mK. The figure shows the 
arithmetic means of 5 min intervals, indicated by the dots. 
Che inset magnifies a representative 20 min period. There, the 
original raw data are shown without any separate averaging to 
illustrate the scattering of the original sensor signals. Two of the 
sensors had a sampling rate of 60/min or more (green and yellow 
lines), while the other two had a sampling rate of 6/min (blue 
and orange). 
The results shown in the figure on the right, measured in the 
time between 11 August 2020 at 19:18 to 22:18 (corresponds to 
measurements in period P2), have been measured under highly 
variable environmental conditions. The variations in 
:emperature amounts to almost one degree Celsius within 
period P2. Again, the inset shows the fluctuations of the 
unaveraged raw signals. The spread of the temperature signal 
is in the range of up to 100 mK, compared to a few mK during 
che calm period. Numerical values for the sensors are shown in 
che Supplementary Materials, Appendix 1, Table A4. 
Based on the “Guide to the expression of uncertainty in 
measurement” (GUM, 2008) the combined uncertainty u„(T) of a 
‚emperature measurement result 7'can be calculated by combining 
the standard uncertainties of individual contributions, here: 
2 
u.(T) Ua + Ufne (eq. 2) 
Ucal 18 the standard uncertainty assigned to the calibration 
and ug„.is the standard uncertainty attributed to the variability 
during the measurement. The standard uncertainty indicates a 
range + around the best estimate of the measured parameter 
value, in which the true value is assumed with a probability 
Zrontiers in Marine Science 
JC 
around 68%. The expanded uncertainty indicates a respective 
95% range, which is usually calculated by multiplying the 
standard uncertainty with a factor of 2 (see section 6 of 
{GUM, 2008) Hence, 
Measured value = best estimate + uncertainty (68 %) 
Measured value = best estimate £ 2 -uncertainty (95 %) 
The numerical value of 4.41 is provided in the calibration 
certificate of a sensor. As mentioned, up„c is the standard 
uncertainty assigned to the variability of the parameter, which 
corresponds to the fluctuation of the measured values. The 
numerical value of ug. depends on the chosen representation 
of the parameter, meaning on how the best estimate is 
determined. Here, we will consider two kinds of representation: 
(i) Temperature, at a specific time, is estimated by a single 
measurement (“raw data”) 
(ii) Temperature, at a specific time, is estimated by the 
arithmetic mean of values measured in a 5 min interval 
around this point in time (“5 min means”) 
[t must be noted that equation 2 is a rather simple, but 
practical approach, than can be expected to cover the major 
uncertainty contributions. However, depending on the scientific 
task, other contributions might become relevant. More details 
are given in (Bushnell, 2019). 
(i) Temperature estimated by a single measurement 
(“raw data”) 
If, for whatever reason, the scientific evaluation of a 
neasurement series requires use of the raw data rather than 
averaged values, the fluctuation uncertainty of a single raw data 
value must be estimated. Usually, it is determined by quantifying 
the spread of fluctuating data measured under stable 
measurement conditions. However, only data measured under 
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