The basic approach to determine sky temperature is simply subtracting the ambient temperature from the infrared measure temperature, as in:
Tsky = Ts – Ta
where Tsky = Corrected Sky Temperature (ºC)
Ts = Infrared Sky Measured Temperature (ºC)
Ta = Ambient temperature (ºC)
This simple approach, however, requires frequent changes to the limits - that is, the resulting cloud detection temperature is not the same as the weather changes along the year.
To improve on this, the CloudWatcher has a polynomial model to adjust the correction value depending on the ambient temperature, with different weights, given by:
Td = (K1 / 100) * (Ta - K2 / 10) + (K3 / 100) * (Exp (K4 / 1000* Ta)) ^ (K5 / 100) + T67
where Td = Correction value (ºC)
Ta = Ambient temperature ( ºC)
K1, K2, K3, K4, K5, K6 and K7 are the coefficients defined in the
Device section of the Setup TAB, or Solo configuration page
T67 (cold weather factor) calculation is shown below
Exp(n)= e (the base of natural logarithms) raised to the power of n.
A^b = a raised to the power of b
The corrected sky temperature (Tsky) is then given by:
Tsky = Ts – Td
where Tsky = Corrected Sky Temperature (ºC)
Ts = Infrared Sky Measured Temperature (ºC)
Td = Correction value (ºC)
Computing the sky temperature this way, and after proper calibration, makes it possible to have accurate detection along a wide temperature range.
Calculation of T67(cold weather) term
If Abs((K2 / 10 - Ta)) < 1 Then
T67 = Sgn(K6) * Sgn(Ta - K2 / 10) * Abs((K2 / 10 - Ta))
Else
T67 = K6 / 10 * Sgn(Ta - K2 / 10) * (Log(Abs((K2 / 10 - Ta))) / Log(10) + K7 / 100)
End If
where Sgn( x ) = function that returns the sign of x (or 0 if K6 is 0)
Log( x ) = function that returns the natural logarithm of x
Abs( x ) = function that returns the absolute value of x
In all calculations the values of the temperatures are in degrees Celsius.
Leaving K1=100, K2, K3… K7 = 0 results in the simplified Tsky = Ts – Ta
Leaving all K factors at 0, the result is the raw measured IR, that is Tsky = Ts