The dome and case temperatures of the PIRs are measured by thermistors installed by Epply. The Surface Group calibrates these thermistors in our calibration laboratory using either a precision silicon oil bath or environmental (air) chamber. In the processing of these calibrations, the best fit was found to be the Steinhardt-Hart(sp?) equation:

`
1/T = a _{0} + a_{1}x + a_{2}x^{2} +
a_{3}x^{3} (1)
`

where

`
x = log(2500/mV -1) [CHECK THIS](2),
`

T is either the dome or case temperature, mV is the measured voltage
in millivolts, and `a _{0}`
through

Unfortunately, `a _{0}` in Eq. 1 always is a somewhat small
number -- about equal
to 1/300K = 0.00333. It turns out that the CR10x truncates this value to

`
R = sigma T ^{4} (3)
`

and

`
dR/R = 4 dT/T (4).
`

Thus, an error of 0.3 K at T=300 K produces an error of about 1 W/m2 at R=300 W/m2. Since the equation for longwave radiation from the PIR involves the term Tdome-Tcase, the error could be a factor of 2 larger. For some studies, such as CASES-99 and EBEX, this amount of error is unacceptable.

T_{case}:

S/N | a
_{0} | a
_{1} | a
_{2} | a
_{3} |
---|---|---|---|---|

26416 | 0.00335452 | 0.282295 | 2.92866 | 954.68 |

29260 | 0.00335383 | 0.27965 | 3.92473 | 597.175 |

31974 | 0.00335467 | 0.286452 | -2.4637 | 3868.8 |

31975 | 0.00335599 | 0.288404 | -6.90295 | 6038.71 |

31976 | 0.00335494 | 0.283467 | 1.8651 | 1587.36 |

31977 | 0.00335531 | 0.283141 | 2.81226 | 898.827 |

31978 | 0.00335437 | 0.287099 | -2.0547 | 3531.01 |

31979 | 0.00335423 | 0.287392 | -4.79718 | 4588.33 |

31980 | 0.00335494 | 0.283676 | 1.33836 | 1980.11 |

31981 | 0.00335403 | 0.283362 | 2.6255 | 1028.04 |

T_{dome}:

S/N | a
_{0} | a
_{1} | a
_{2} | a
_{3} |
---|---|---|---|---|

26416 | 0.00304556 | 0.282923 | -3.22195 | 1552.84 |

29260 | 0.00306136 | 0.253163 | 15.4003 | -2315.04 |

31974 | 0.00303966 | 0.292687 | -7.40681 | 2207.35 |

31975 | 0.00303124 | 0.30936 | -16.7272 | 3864.95 |

31976 | 0.00304992 | 0.273924 | 3.66477 | 18.4609 |

31977 | 0.00304622 | 0.280377 | -1.0274 | 1105.48 |

31978 | 0.00303889 | 0.291274 | -5.99237 | 1874.43 |

31979 | 0.00302993 | 0.307588 | -15.2242 | 3443.34 |

31980 | 0.00305007 | 0.27288 | 4.55754 | -137.92 |

31981 | 0.00304215 | 0.286235 | -4.41592 | 1743.28 |

Input | Memory display | Working |
---|---|---|

0.000004 | 0 | 0 |

0.000005 | 0 | 0 |

0.000006 | 0 | 0 |

0.00004 | 0.0000 | 0.00004 |

0.00005 | 0.0000 | 0.00005 |

0.00006 | 0.0001 | 0.00006 |

.000004 | 0.00000 | 0.000004 |

.000005 | 0.00000 | 0.000005 |

.000006 | 0.00001 | 0.000006 |

1.00004 | 1.0000 | 1.0000 |

1.00005 | 1.0000 | 1.0000 |

1.00006 | 1.0001 | 1.0001 |

Thus:

- Working value is input value truncated to 5 or 6 digits, depending on whether a leading "0" is entered.
- "Rounding" converts 0-5 to 0, 6-9 to 1.
- Displayed value is always working value rounded to 5 digits

We implement this correction by chosing a range of values for x in Eq. 1, generating a set of T values using the truncated coefficients determined above, matching the archived T values to this lookup table to determine the value of x which was measured, and computing new T values using non-truncated coefficients. This is implemented in S+ using the function fun.invert.lookup.

Note that this correction scheme also allows correction for other coeffcient problems such as a typographical error while entering coefficients or use of incorrect coefficients as were both done during CASES-99.

We have written code to apply this correction to CASES-99 and EBEX-00 data, though even these corrected values are not yet available via WWW distribution. We will change this state of affairs as soon as possible.

A more permanent solution is to make these radiometers "intelligent" (as we already do for other sensors such as our temperature/humidity sensors, barometers, and anemometers). We have several ideas of how to implement this solution, including imbedding an A/D and possibly a CPU in the PIR housing, and simply need to decide on the most cost and time-efficient method.