## 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.

Tcase:
S/N a0 a1 a2 a3
26416 0.00335452 0.282295 2.92866 954.68
292600.003353830.279653.92473597.175
319740.003354670.286452-2.46373868.8
319750.003355990.288404-6.902956038.71
319760.003354940.2834671.86511587.36
319770.003355310.2831412.81226898.827
319780.003354370.287099-2.05473531.01
319790.003354230.287392-4.797184588.33
319800.003354940.2836761.338361980.11
319810.003354030.2833622.62551028.04

Tdome:
S/N a0 a1 a2 a3
264160.003045560.282923-3.221951552.84
292600.003061360.25316315.4003-2315.04
319740.003039660.292687-7.406812207.35
319750.003031240.30936-16.72723864.95
319760.003049920.2739243.6647718.4609
319770.003046220.280377-1.02741105.48
319780.003038890.291274-5.992371874.43
319790.003029930.307588-15.22423443.34
319800.003050070.272884.55754-137.92
319810.003042150.286235-4.415921743.28

## CR10x Truncation/Rounding

From tests of the CR10x using a simple echoing program written by Steve Semmer:
Input Memory display Working
0.00000400
0.00000500
0.00000600
0.000040.00000.00004
0.000050.00000.00005
0.000060.00010.00006
.0000040.000000.000004
.0000050.000000.000005
.0000060.000010.000006
1.000041.00001.0000
1.000051.00001.0000
1.000061.00011.0001

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.