Use of Epply PIR with Campbell CR10x Data Logger

Introduction

Starting with CASES-97 (possibly SCMS), ATD/SSSF (now ATD/RTF) Surface Group started interfacing radiation and soil sensors to our ADAM and EVE data systems through Campbell CR10x data loggers. This was done primarily to take advantage of special soil sensor interfacing available through the CR10x's and also significantly reduced the length of cable required for the relatively low-level analog signals of the radiometers.

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 = a₀ + a₁x + a₂x² + a₃x³ (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 a₀ through a₃ are the calibration coefficients.

Unfortunately, a₀ 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 10^-5 or 10^-6 K^-1, which corresponds to 0.03 or 0.3 K. From the Stefan-Boltzman law

R = sigma T⁴ (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.

Epply Tdome/Tcase Coefficients

The actual values of a₀-a₃ for the various sensors [determined in August 1999 (pre CASES99)] are given below.

T_case:

S/N a₀ a₁ a₂ a₃
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

S/N	`a₀`	`a₁`	`a₂`	`a₃`
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 a₀ a₁ a₂ a₃
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

S/N	`a₀`	`a₁`	`a₂`	`a₃`
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

CR10x Truncation/Rounding

From tests of the CR10x using a simple echoing program written by Steve Semmer:

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

These "rules" are simulated in S+ by the functions f.x and f.x0, depending on whether a leading 0 was input.

Correction Method

Despite the use of a 4th-order polynomial, there is a one-to-one mapping of input voltage to temperature using Eq. 1 and the above coefficients. Thus, it is possible to "unapply" the truncated coefficients and reapply non-truncated coefficients in post-processing. Since the calibration is non-linear, it is not strictly possible to correct the standard 5-minute averages saved by the Surface Group, however we expect that temperature changes over 5 minutes are small in most cases, allowing even these average data to be corrected.

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.

Solution

Our current (beginning with IHOP02) solution to this problem is to use a simple polynomial for the IHOP02 program, which has calibration coefficients which are more in the range of numerical values of the CR10x. We thus accept that the residuals to laboratory calibration fits are somewhat worse.

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.