A second calibration-study for the Delta_T UVB sensor

February 1997
Francis Massen & Nico Harpes

This report supersedes the paper " A first calibration-study for the Delta_T UV_A and UV_B sensors"

1. Preliminary comments

The two UV sensors from Delta_T (UV_A , channel #7 and UV_B, channel #8) which operate since the start in 1994 of Meteo_LCD are relative low-cost sensors, whose accuracy and even calibration was doubtful from beginning on. When we added the much more precise and sophisticated UVB and UVA Biometers from Solar Light Co., we found the following:

the readings of the Delta_T UVA sensor were correct if the voltage output was multiplied by ten. This has been implemented since mid-1996 and is documented in the data file README.html. The reading of this sensor (in W/m2) do now well agree with those of the UVA-Biometer; this latter instrument should always be used as a first choice. The Delta_T UV_A sensor will serve as a backup sensor.
the readings of the Delta_T UVB sensor (in W/m2) are absolutely non-sense, if taken literally. We tried nevertheless to correlate these readings to those of the UVB Biometer from Solar Light Co. to look for a possible consistent relation-ship, so that the Delta_T UVB sensor could be used as a backup too.

2. Calibration of the Delta_T UVB sensor

First checks showed that a consistent good relationship between the readings of the UVB Biometer which serves as the reference and the low-cost Delta_T UVB sensor can not be found over the whole range of measured effective UVB irradiances. The overall relationship seems to be a parabolic one. For best results, we tried to fit the Delta_T UVB readings to the assumed correct readings of the UVB Biometer by using two different time periods of the year:

a period in February-March, representative for having rather low irradiances and low temperature
a period in June-July, representative as being the hottest and most UVB intense of the year.

15 Feb. 1996 to 31 Mar. 1996 (1106 readings)

**Overall climatological parameters**
	mean	minimum	maximum
temperature	2.8 C	-10.8 C	17.4 C
solar irradiance	108 W/m2	0 W/m2	782 W/m2
UVB	152 mMED/h	0 mMED/h	1640 mMED/h

The computed statistical correlation between the readings of both sensors is r=0.98.

The following figure shows the Delta_T UVB readings (in W/m2) on the x-axis, and the corresponding readings (in mMED/h) of the UVB_Biometer on the y-axis.

A good fit can be given by the parabola (forced through the origin, as the very small zero offsets may be neglected):

mMED/h = 165.36*(Delta_T_UVB_reading)^2 + 190.89*(Delta_T_UVB_reading)

The goodness of the fit is R=0.99.
The standard error is:
std. error = SQRT((Sum_of(y_i -y_fit)^2)/1104) = 44 mMED/h

where y_i is the correct irradiance in mMED/h and y_fit the number obtained by applying the parabole given above to the readings (in W/m2) of the Delta_T UVB sensor.

If the effective UVB irradiance in W/m2 eff. should be found out of the Delta_T UVB readings, the parabola to apply is:

W/m2 eff. = 0.0114757*(Delta_T_UVB_reading)^2 + 0.0132474*(Delta_T_UVB_reading)

01 Jun.1996 to 24 Jul.1996 (2592 readings)

**Overall climatological parameters**
	mean	minimum	maximum
temperature	16.5 C	7.4 C	32.6 C
solar irradiance	277 W/m2	0 W/m2	1229 W/m2
UVB	491 mMED/h	0 mMED/h	2790 mMED/h

The computed statistical correlation between the readings of both sensors is r=0.98.
The following figure shows the Delta_T UVB readings (in W/m2) on the x-axis, and the corresponding readings (in mMED/h) of the UVB_Biometer on the y-axis.

A reasonable good fit can be given by the parabola:

mMED/h = 41.59*(Delta_T_UVB_reading)^2 + 350.17*(Delta_T_UVB_reading)

The figure shows that the spreading of the values around the parabola is much greater than for the precedent case. As a consequence the standard error of this fit is considerably higher:

std. error = SQRT((Sum_of(y_i -y_fit)^2)/2590) = 106 mMED/h

where y_i is the correct irradiance in mMED/h and y_fit the number obtained by applying the parabole given above to the readings (in W/m2) of the Delta_T UVB sensor.

If the effective UVB irradiance in W/m2 eff. should be found out of the Delta_T UVB readings, the parabola to apply is:

W/m2 eff. = 0.00289*(Delta_T_UVB_reading)^2 + 0.0243*(Delta_T_UVB_reading)

3. Conclusion

This analysis shows that the readings of the Delta_T UVB sensor can be used to compute a reasonable good approximation of the correct effective UVB irradiance; the accuracy of the result is poorer than that obtained by the readings of the Solar Light UVB_Biometer mod. 501. Deviations between both instruments are smaller during the colder periods with less solar irradiation. For best results, a separate parabolic fit should be used for the winter-spring-autumn and summer periods.
Whenever available, the readings of the Solar Light UVB_Biometer should be used as a measure of the correct effective UV irradiance; the fitted readings of the Delta_T UVB sensor can help in the case where data from the UVB_Biometer are not available.

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