_e Menn et al. 
is the true temperature of seawater, I*R is the power of the self- 
heating due to the current I passing through the sensor resistance 
R, es is the emissivity or absorptivity of the sensor’s surface, E 
is the irradiance, o' is the Stefan-Boltzmann constant, and T, is 
the temperature of the walls (surrounding the sensor) assumed 
to be emitting as a blackbody. The heat transfer coefficient h 
is the key quantity to understand the intensity of the thermal 
transfer between the surface of the sensor and the fluid. It takes 
into account the conjugate effects of conduction, convection, and 
radiation in the surrounding medium. 
We can consider the self-heating as negligible, because the 
thermistor is fed by a micro-current leading to the maximum 
error of a few hundred of micro-degrees. If we consider that the 
radiative environment is almost at the same temperature as the 
surface of the sensor, T% Ts, then the second part of the right- 
hand-side of Equation (1) can be neglected. The temperature 
measurement error can then be described by: 
esE 
(Ts — Ts) = = 
ıh 
(2) 
For a fluid flowing perpendicularly past a cylinder, h can be 
approximated by the equation: 
H — 
KkNu 
D 
(3) 
where k is the thermal conductivity of the fluid and Nu the 
Nusselt number for a cylinder in a transverse flow. In the case 
of water, the following empirical expression is often used to 
calculate Nu in conditions of laminar flow (Schlichting, 1979): 
Nu = 0.66 Pr 1/9 Re? (4) 
Pr is the Prandlt number. It describes a fluid with a dynamic 
viscosity and a specific heat capacity Cp: 
Dr - WC: 
5) 
Re is the Reynolds number. It describes the flow of a fluid which 
would have a speed V and a density p: 
VD 
Re = PYT 
4 
(6) 
The Equation (6) is valid when RePr > 0.2. In the case of a surface 
seawater with a practical salinity of 35, a temperature of 15°C, 
even with a very low speed V = 0.001m s71, RePr = 8.33 (with 
D = 1.2 mm). Combining Equations (2-6) gives: 
1/2 
esE D 
(Is — Ta) = m (3) 7) 
The relation (7) shows that the error due to the irradiance is 
proportional to the square root of the diameter of the cylindrical 
sensor (all other parameters assumed equal). Applied to the 
HRSST sensor with D = 0.12 cm and to the SST analog sensor 
rontiers in Marine Science | www.frontiersin.or 
SVP-BRST Fiducial Reference Network 
TABLE 1 | Comparison of ratios D/V and response times for the HRSST sensor 
and the SST analog sensor in a seawater at 15°C and S = 35. 
HRSST sensor SST Analog sensor 
Sensor diameter (cm) 
Water velocity (m/s) 
Thermal conductivity (W/m/°C) 
3eynolds 
DPrandt! 
Vusselt 
DANO-5 
deat transfer coefficient (W/cm”/°C) 
Aass of the sensor (g} 
Jesponse time (ms} 
With a water velocity of 1 m/s, the HRSST is in laminar fux conditions whereas the SST 
analog sensor is in less favorable, turhulent condiHans. 
with an average diameter D = 1.4cm, the radiative error is 
divided by 3.4, to the advantage of the HRSST sensor, when the 
same environmental conditions are considered. 
The size difference between the SST analog sensor and the 
ARSST sensor also has an effect on the response time rt. If we 
neglect the exchange by radiation, most of the heat exchanged 
between the sensor and the medium is the result of convection, 
described by the coefficient h. The quantity of heat propagating 
in the sensor of mass m and specific heat capacity Cps, results 
in a temperature variation dT during the time dt. The balance 
equation can be written: 
dT 
hA (Ts - Tsw) Fr MCps 
Q 
Its resolution leads to the equation: 
T To = Ta —-To.(1-eF) (9) 
where To is the initial temperature of the sensor and rt is the ratio: 
(10) 
[n Equation (9), the time for which £t = rt represents the 
constant 1 - e7! = 0.632 which defines the response time rt. 
The Table 1 shows that for a very low seawater velocity and the 
same environmental conditions, the response time Tt is about 7 
times larger for the SST analog sensor than for the HRSST sensor. 
Table 1 also shows the results of (D/V)°> ratios for two flow 
speeds. Figure 3 shows the response times of hoth sensors, as a 
function of velocitv. 
x MCps 
hA 
CALIBRATION AND LABORATORY TESTS 
OF THE HRSST SENSORS 
One of difficulties in constituting a 100-buoy reference network is 
to calibrate all the buoys with an uncertainty close to a few milli- 
degrees. The solution found was to first calibrate the MoSens 
Qantembear 2019 I Valııme A 1 Article R7£