Calculation of Energy Output from Pyrgeometer Sensors

One way to calculate the energy output {Wm-2} from Eppley Pyrgeometer (PIR) is to use the temperature of the dome and thermopile thermistors {mV}and the thermopile output {mV} (Albrecht and Cox, 1997).

A. Express thermopile thermistor (TT) and dome thermistor (DT) values in units of volts (Mi)

pir eq2
(1)
where
i = thermopile thermistor (T) or dome thermistor (D)
 

B. Express thermopile thermistor (TT) and dome thermistor (DT) values (Mi) in terms of resistance (Ri)

 
pir eq3
(2)

where

M = thermistor voltage {V}
44200 = resistor resistance {W}
excitation voltage = 2 {V}
88400 = resistor resistance * excitation voltage (VW)

C. Express thermopile and dome thermistor resistance values (Ri) in terms of temperature (i.e.,Tt and Td for thermopile and dome temperatures, respectively)

Use the table below. Interpolate between given values to the nearest hundredth degree.
Temperature vs Resistance for the YSI 44031 Precision Thermistor
Temperature (oC) Resistance (W) Temperature (oC) Resistance (W) Temperature (oC) Resistance (W)
-40 239800 7 21450 54 3385
-39 225000 8 20520 55 3270
-38 213200 9 19630 56 3160
-37 201100 10 18790 57 3054
-36 189600 11 17980 58 2952
-35 179200 12 17220 59 2854
-34 169300 13 16490 60 2760
-33 150000 14 15790 61 2669
-32 151200 15 15130 62 2582
-31 143000 16 14500 63 2497
-30 135200 17 13900 64 2417
-29 127900 18 13330 65 2339
-28 121100 19 12790 66 2254
-27 114600 20 12260 67 2191
-26 108500 21 11770 68 2122
-25 102900 22 11290 69 2055
-24 97490 23 10840 70 1990
-23 92430 24 10410 71 1928
-22 87660 25 10000 72 1858
-21 83150 26 9605 73 1810
-20 78910 27 9227 74 1754
-19 74910 28 8867 75 1700
-18 71100 29 8523 76 1648
-17 67570 30 8194 77 1598
-16 64200 31 7880 78 1549
-15 61020 32 7579 79 1503
-14 58010 33 7291 80 1458
-13 55170 34 7016 81 1414
-12 52480 35 6752 82 1372
-11 49940 36 6500 83 1332
-10 47540 37 6258 84 1293
-9 45270 38 6026 85 1255
-8 43110 39 5805 86 1218
-7 41070 40 5592 87 1153
-6 39140 41 5389 88 1149
-5 37310 42 5193 89 1118
-4 35570 43 5006 90 1084
-3 33930 44 4827 91 1053
-2 32370 45 4655 92 1023
-1 30890 46 4489 93 994.2
0 29490 47 4331 94 956.3
1 28150 48 4179 95 939.3
2 26890 49 4033 96 913.2
3 25690 50 3893 97 857.9
4 24550 51 3758 98 853.4
5 23460 52 3629 99 839.7
6 22430 53 3504 100 815.8

 
 

D. Calculate longwave radiant flux density according to Albrecht and Cox (1977)

pir eq 4
(3)

where

Rlw = incoming or outgoing irradiance {Wm-2}
C = Calibration Constant {Wm-2mV-1}
E = Thermopile output {mV}
s = Stephan-Boltzman constant = 5.67x10-8 Wm-2K-4
Tt = Thermopile temperature {Kelvin}
Td = Dome temperature {Kelvin}
k = 5

E. References

Albrecht, B. and S.K. Cox.  1977.  Procedures for improving pyrgeometer performance, J. of Appl. Meteorol., 16:188-197.
 

F. Example of Calculation

(data from  July 17, 1992 at 10:00 am for incoming longwave radiation at Lincoln, NE)

Given the values of

thermopile thermistor (TT) =  1657 mV ,
dome thermistor (DT) =  1666 mV,
thermopile output (E) = -0.259 mV and
calibration constant (C) = 305.81 Wm-2mV-1.
Step
 Thermopile Thermistor
Dome Thermister
A. Express in volts {V}
1.657
1.666
B. Express in Resistance {W}
9149.4267
8861.2245
C. Interpolate Resistance to Temperature {C}
27.22
28.02

D. Apply to Equation 3

pir eq 5
 

pir eq 6