Naldmann et al. 
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10.3389/fmars.2022.1002153 
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aA u ln 
Jul 23, 00:00 Jul 23, 12:00 
A nn 
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——_— af A a a 
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2020 
IGURE 4 
:xample of measured temperature data from a single sensor (Sensor 1) for period P1. The upper panel shows the temperature data (grey 
markers indicate the raw data and the blue line indicates the averaged 5 min data sets. The lower panels show the STD (black line) and the SEM 
‘orange line) for the corresponding 5 min averaging intervals). Numbers in the colours of the respective lines indicate the values of the averaged 
statistical parameters for the complete 5 min intervals. 
uncertainty (Lee et al., 2015) (Altmann, 2005). 
Results for Tmean STD and SEM of all sensors and periods 
are summarised in Table A4 in the appendix. For all individual 
sensors and periods, the results are comparable and in the same 
range, there are no clear or obvious deviations. The variations 
are also rather small and in the normal measuring range. As 
expected, the highest variabilities are observed in the second 
period and the lowest during the last period. The mean STD for 
the 5 min mean values of the second period is about five times 
larger than in the last period, which confirmed the increased 
variation in the measurement of this second period. In contrast, 
the variability in the first period is only half that in the second 
period. Accordingly, the calculated uncertainties (SEM) are also 
nighest in the second period, while in the other periods the 
uncertainties are lower with lowest values in the third period. In 
summary, the SEM values are all within a tolerable range and are 
comparable across all sensors and periods. The values in the 
:ables (see the Supplementary Materials, Appendix 1, Tables A3 
and A4) are only the average values for the selected (in this case 
{ve minutes) time interval. As shown in Figure 4, the values in 
che selected interval can vary greatly in variability and 
ancertainty. This should always be taken into account when 
particularly temporal fine-scale measurements are necessary 
or required. 
The results also show the influence of the applied size of the 
sampling interval. Three (of the six) sensors have a longer 
sampling interval, which results in a larger uncertainty because 
of the factor 1/YN for the calculation of SEM. The difference is 
Zrontiers in Marine Science 
i&8 
low but can be clearly seen. As mentioned before, the selected 
sampling interval depends also on various boundary conditions 
(sometimes it is not possible to run a shorter sampling interval 
due to limitations of the measurement set-up or insufficient 
energy supply) and measurement targets. The influence on the 
results of the average values (T,.an) is rather insignificant. The 
results show a good correlation in this case. Again, the choice is 
up to the user and the specific measurement task. 
To look more closely at quantifying measurement 
uncertainty, in the next subsection we will focus on 
contribution to the calibration uncertainty, and the 
uncertainty related to the fluctuations of the individual sensor 
outputs. Other systematic contributions are the instrument 
resolution/quantization error that amounts to 0.14 mK for 
sensors 1-3 while for sensors 4-6 that amounts to 0.03 mK 
which is negligibly small. The long-term stability that is below 
5% of the systematic uncertainty budget is not considered 
significant for this study. 
4.2 Quantification of the uncertainty 
of single sensor measurements for 
two 3 h intervals 
Four out of the six sensors have been evaluated, since only 
these have measured temperatures in both selected periods. 
Figure 5 shows the results of temperature measurements of the 
four sensors in two three-hour periods. The results shown in the 
ırontiersin.ora