Naldmann et al. 
measurement. Figure 3 shows the full data set and the selected 
:ime periods (numbered grey shaded areas P1-P4). 
Further information on data availability and number of 
measurements of the periods are summarized in Table A2 in 
«he Supplementary Material. 
The area where the measurements were conducted is located 
in the south-eastern part of the North Sea. The prevailing ocean 
condition in this region is mainly influenced by tidal and wind- 
driven circulation systems as well as the atmospheric boundary. 
In general, a tidally well-mixed water mass can be expected, 
characterised by a typical atmospheric annual cycle. Maximum 
and minimum water temperatures range from 2-20°C over 
che year. 
For this study, temperature measurements were collected 
over a period of four months. In all individual time series, the 
characteristic seasonal variation in temperature for the region 
can be observed (see Figure 3). Since measurements were only 
caken in summer and autumn, the minimum and maximum 
‚emperatures are in the typical range of 12 -20°C. During the 
summer months, the variability of the results are typically 
slightly increased, as stronger spatial and temporal 
temperature fluctuations (heat exchange with atmosphere 
\diurnal cycle, induced by solar irradiation, variations in the 
surface layer processes) can appear. In addition, the 
measurements will be affected by the increased marine fouling 
<biofouling) during the summer and autumn months. During 
che autumn months the variability decreased but was more 
strongly influenced by other environmental factors such as 
wind and the resulting waves. 
our representative periods from the complete time series 
were chosen for the determination of the statistical parameters. 
The rationale behind this is to consider different scenarios to 
obtain a complete picture of different phases (during a long-term 
measurement) of the data collection. 
The first selected period P1 is at the beginning of the 
neasurement campaign. The sensors are freshly 
calibrated and clean (no marine fouling). In addition, 
the temperature curve shows relatively stable conditions 
with only minor seasonal fluctuations. 
The second period P2 is in the summer months (August) 
with relatively strong temperature fluctuations (diurnal 
cycle). The seasonal effect is also clearly visible (constant 
temperature increase in the summer months). In 
addition, the sensors have been in operation for a 
month, so alterations of the sensors (e.g., sensor 
drifting) and biofouling effects can have an impact on 
the data recording. 
The third period P3 had, with very low variability and 
high data availability, low external influences and stable 
temperature conditions over the entire measurement 
period. This provides the possibility to assess 
Zrontiers in Marine Science 
17 
10.3389/fmars.2022.1002153 
calibration uncertainties (in situ) as the data are 
(nearly) not dominated/influenced by external 
conditions. 
The fourth period P4 close to the end of the 
measurements in the autumn months has fairly steady 
temperature conditions, but high biofouling activity 
(autumn bloom). Moreover, individual sensors have 
already been replaced, cleaned or recalibrated. 
Statistics of the selected study periods are calculated for an 
averaging interval of 5 min, with interval size of 300 seconds 
always starting at the full minute of the interval. The chosen 
averaging interval correspond to often found measurement 
intervals in common coastal observing programs and 
campaigns, but can also be easily adapted to other intervals as 
needed. Figure 4 shows an example of the results for the 5 min 
time average (T,ean) of one of the sensors. 
As already mentioned, the choice of the averaging interval 
used is individually selectable, but should be adapted to the 
measurement environment or the measurement objectives. 
Especially for measurements at sea, there are some limitations 
in the area of energy and data storage possibilities as well as 
accessibility and maintenance options. Thus, the scientific focus 
(highest possible temporal resolution) cannot always be fully 
addressed, as the mentioned constraints must also be taken into 
account. An interval of 5 min was chosen for the calculations of 
variability and measurement uncertainty in this study. This 
selection based on the intention to resolve prevailing 
environmental conditions (e.g., tidal influences) of the 
neasuring region in the data. Furthermore, there were no 
‚estrictions on the energy supply as the cabled infrastructure 
af the Helgoland Underwater Observatory (MarGate) was used, 
so there was relative flexibility in the choice of measurement 
acquisition settings. 
To get a more definite estimate of the variability and 
uncertainty of the different temperature measurements, 
statistical parameters (standard deviation and standard error 
of the sample mean) of each single sensor are determined. The 
standard deviation (STD) is derived from the temporal 
variations of the temperature signal and indicates the 
dispersion of the individual data samples relative to the sample 
mean over that selected time period. In contrast, the standard 
arror of the mean (SEM) is a measure of the dispersion of the 
sample mean (further details in the following section). The SEM 
depends on both the STD and the sample size (N) through the 
relatively simple relationship 
STD 
SEM = — 
En (eq. 1) 
and is therefore always smaller than the STD. The SEM is 
therefore an indicator of the variability of the temperature 
samples within the period and commonly used to indicate the 
ırontiersin.ora