## 5 Validation of the Simulation Model
### Validation of the Humidity Sensitivity of the Model of Radiation Thermometry  
An experimental analysis of the influence of humidity on temperature, as measured by the radiation thermometer Heitronics KT19.01 II, operating in the spectral range 2 \(\upmu\)m to 2.7 \(\upmu\)m, was performed at temperatures between 1000 \({}^{\circ}\)C and 1500 \({}^{\circ}\)C. Another radiation thermometer, the Sensortherm DS09, operating in the spectral range 0.7 \(\upmu\)m to 1.1 \(\upmu\)m, was used as a stable reference for temperature measurement. Theoretical spectral simulations of the influence of humidity on radiation thermometers assess high humidity dependency of measurements using Heitronics KT19.01 II and negligible influence for the DS09; therefore, the latter is considered a stable reference in this experiment. The DS09 has been calibrated at an external institution using a primary calibration method according to ITS-90 [22]. A high temperature furnace was measured at 1000 \({}^{\circ}\)C, 1250 \({}^{\circ}\)C and 1500 \({}^{\circ}\)C. Environmental conditions were modified by using air conditioning, a humidifier and a dehumidifier. Extremely dry conditions were obtained by running air conditioning in drying mode and with an additional dehumidifier for 24 h prior to measurements. Extremely humid conditions were created by increasing the temperature inside the laboratory while running an ultrasonic humidifier with a ventilator to aid with the dispersion and mixing of air within the laboratory. The humidifier was switched off 10 min prior to measurements to avoid light scattering on airborne water droplets. The atmospheric humidity within the laboratory was measured by a calibrated data logger. Humidity was further calculated according to the Hardy ITS-90 [23] method and expressed as the partial pressure of water vapor, an independent parameter which corresponds to particle number density in the transfer path and, in turn, through optical density, to the transmissivity of the transfer path. The difference between measurements of the two pyrometers was characterized as humidity-induced error and analyzed against the partial pressure of water vapor, revealing well-correlated dependence (Figure 9). Figure 9: Plot of Heitronics KT 19.01 measurement error due to humidity, represented in units of partial pressure. A planar function was fitted to the difference in measurements of the two pyrometers over the range of partial pressure of water vapor (\(x\)) and temperature of the black body (\(y\)). A polynomial fit function was chosen (20). As linear dependence on partial pressure of water vapor (\(x\)) was observed, a first-order polynomial was chosen, whereas the second-order polynomial was chosen for the temperature of the black body (\(y\)). Fit results are listed in Table 4. The expanded uncertainty of the repeatability of measurements of the fitted function was calculated as 0.57 \({}^{\circ}\)C.  
\[fit(x,y)=p_{00}+p_{10}*x+p_{01}*y+p_{11}*x*y+p_{02}*y^{2} \tag{20}\]  
Experimental results are compared with simulated results in Figure 10. The average discrepancy between simulated and experimentally measured humidity sensitivity at 1000 \({}^{\circ}\)C to 1500 \({}^{\circ}\)C ranges from 2.8 \({}^{\circ}\)C to 3.3 \({}^{\circ}\)C, respectively, whereas the correction of the KT19 was previously measured to range from 2.8 \({}^{\circ}\)C to 4.3 \({}^{\circ}\)C. After correcting the means of measurements with average discrepancy, corresponding to Heitronics KT 19.01 correction, the standard deviation of the difference between simulated and measured humidity sensitivity ranged from 0.64 \({}^{\circ}\)C to 1.27 \({}^{\circ}\)C.  
The simulated effect of water vapor on measurement in range between 10 hPa and 24 hPa is summarized in Table 5. \begin{table}
\begin{tabular}{c c} \hline
**Coefficients** & **Values** \\ \hline \(p_{00}\) & \(-22.93\) \\ \(p_{10}\) & 0.2238 \\ \(p_{01}\) & 0.03724 \\ \(p_{11}\) & \(-0.0007649\) \\ \(p_{02}\) & \(-1.334\times 10^{-5}\) \\ \hline \end{tabular}
\end{table}