Naldmann et al. 
after about 1 month and sensor 6 was recovered for laboratory 
calibration in the middle of the experiment. 
As it was the objective of this experiment to develop a 
common procedure to calculate the uncertainty of sensor 
measurements, specifics of the design and age of the probes 
were not considered. For each sensor the maximal sample 
frequency for data collection has been configured. 
Calibration procedure 
The calibrations were performed in the calibration 
ıaboratory of the Leibniz Institute for Baltic Sea Research (the 
used instruments are described in appendix 2). This laboratory 
nas been in operation for more than 50 years and it received an 
Accreditation according to the ISO/IEC 17025 (ISO, 2022) by the 
DAKkkS (Accreditation, 2022), the national accreditation body of 
Germany. The laboratory is accredited for the measurands 
(emperature, pressure, and electrical conductivity. 
The calibration of all devices was done for the measurands 
c‚emperature and electrical conductivity. The temperature 
calibration is a comparison measurement with Standard 
Platinum Thermometers (SPRT) in a water bath. It is based on 
the International Temperature Scale (TITS-90) (Preston-Thomas, 
1990) and traceable to the International System of Units 
(SI)-system. 
The temperature probes are calibrated in a bath containing a 
volume of 80 1 of seawater. The bath consists of two 
compartments: a main volume inside, where the calibration 
device is mounted and a second volume outside, where a hose 
hat is connected to an external thermostat is installed. The 
water of the outer volume is pumped through a heating unit for 
(he stabilization of the temperature into the inner volume by 
means of a vaporizing unit for a uniform distribution. In the 
inner volume a thermistor sensor is mounted and connected to 
an external control unit. Three Standard Platinum 
Thermometers (SPRT) are mounted in the vicinity of the 
sensors of the device to be calibrated. 
The basic calibration schemes that are applied in the ocean 
science community are very similar. For temperature calibration 
Negative Temperature Coefficient (NTC) thermistor sensors are 
often used as the temperature reference. They are very stable and 
not as sensitive against mechanical stress as SPRTs. The 
advantage of the SPRTs is that the temperature between the 
fixed points is defined by the temperature resistance relation 
according to ITS-90 (Preston-Thomas, 1990). The NTC-sensors 
must be calibrated in a comparison measurement with SPRTs. 
[his is an additional source of uncertainty which contradicts the 
asserted lower uncertainties of calibrations with NTC-sensors vs. 
SPRTsSs a claim that is hard to explain. 
Zrontiers in Marine Science 
34 
10.3389/fmars.2022.1002153 
A big difference from most other calibration laboratories is 
the accreditation correspondent to the ISO/IEC 17025 (ISO, 
2022) standard. That means that the process of calibrations and 
the traceability of the results and the declared uncertainties are 
ensured. Due to stricter criteria the ascertained uncertainties are 
typically bigger than in many other unaccredited 
calibration laboratories. 
Uncertainty analysis 
Today’s ocean sensors typically provide an electrical signal 
(usually an AC or DC voltage, a frequency or a digital value) 
representing an ocean parameter measured at a specified time 
and location. Depending on the type of sensor, this signal is 
converted into the numerical value of the parameter (e.g., a 
temperature value) within the sensor with calibration coefficients 
stored within the instrument or it is necessary to calculate the 
numerical value subsequently using a calibration file. 
The values of the acquired signal are not only a result of the 
ocean parameter being measured, but it is also influenced by 
additional, external effects. It is affected by inevitable instabilities 
and inhomogeneities of the water body near the sensor during the 
acquisition of the signal. Furthermore, it is affected by the technical 
properties of the sensor, for instance, by the signal noise of the 
instrument or by sensor drift or bias. The latter are meant to be 
determined by a calibration measurement. However, the calibration 
neasurement is likewise affected by the effects mentioned above. 
Consequently, even under excellent measurement conditions, using 
calibrated sensors and excluding any instrument or other failures, it 
s impossible to know to what degree the signal value deviates from 
the value that truly represent the ocean parameter being measured. 
Hence, the true value of the sensor signal is uncertain and a method 
to quantify the uncertainty must be defined to estimate a range 
around the signal value in which the true is lying with a specified 
probability. Figure 2 illustrates the complex input of information 
affecting measured raw data points. 
In the following sections, we will propose and evaluate a 
nethod to quantify the uncertainty of a measured ocean 
parameter in a relatively simple and practical manner. To this 
end, we will use seawater temperature measurements measured 
with the sensors and measurement setup described in the section 
2. Firstly, we will show and discuss the measured data. Then, we 
will demonstrate how to quantify the uncertainties of the results 
of an individual sensor and discuss the meaning of the 
uncertainties. Afterwards, we will compare the results of 
several sensors. Based on an evaluation of the uncertainties, we 
will finally discuss to what extent the result of a single sensor is a 
good representative for the parameter of interest, compared to a 
multi-sensor measurement. 
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