# Thermometer Biases

## Introduction

Those of us who put thermometers up at our homes in order to record temperatures need to worry about whether they are actually recording the true temperature. There are two possible biases: a bias due to the location of the thermometer, and the intrinsic bias of the thermometer.

The location bias means whether an accurately calibrated thermometer is recording a different temperature than the true air temperature due to the location of the thermometer. This can be caused by a large number of different effects. Examples include:

• sunlight striking the thermometer,
• nearby hot surfaces making the location of the thermometer hotter than the true air temperature,
• nearby cool surfaces making the cooler than the true air temperature, and
• areas without adequate air ventilation that therefore do not have the same temperature as the surrounding air temperature.

The intrinsic bias simply means whether the thermometer is properly calibrated. That is, when the thermometer reads 70°, is the temperature truly 70°, or is it actually 68° or 72° due to an error in the calibration of the thermometer?

As part of trying to understand the calibration of the official Fallbrook weather station, Gaylord Moxon and I took two portable thermometers and directly measured the location biases of several places. We also measured the intrinsic relative error of several thermometers, including the new official Fallbrook thermometer.

The next two sections will discuss the location and intrinsic biases in more detail, followed by analysis of each bias from our measurements.

## Discussion of Location Biases

Nearly every location that one can think of has some possible problems. Here are some of the potential problems:

• Direct sunlight must be avoided at all costs, which will of course seriously corrupt the readings when sunlight shines on the thermometer.

• Areas like a back porch surrounded on several sides by partial walls and / or a roof will corrupt the readings by making them too low during the daytime, since that enclosure doesn't heat up to the maximum air temperature due to the thermal inertia of the enclosure. The nightly minimum temperatures will be too high since the roof and/or partial enclosure traps heat at night.

• Areas close to a roof or any other structure that will be heated up by direct sunlight will cause problems, even though it doesn't seem that this affect could be significant. Even a thermometer several feet below a roof will be corrupted by as much as 5-8° F, as I found in Altadena and Gaylord Moxon has found in Fallbrook.

• Areas exposed to radiation from concrete heated by the sun will also be biased due to that radiation. Despite having only less than ~1/16 of the field of view being heated concrete, the thermometer under my porte cochere suffers a bias of 2-4° due to such radiation.
The only location left is probably an open airy area underneath shade trees whose branches are very high, so as not to corrupt the low readings at night. If you don't have such an area, you'll either have to compromise or build a weather service type enclosure and put it in the open.

Such considerations make it clear why the weather service houses its thermometers in a standard box that has excellent ventilation. The enclosed box ensures that no direct radiation falls on the thermometer, as well as eliminating any reradiation from any heated surface. The excellent ventilation, coupled with the white-painted wood material of the box, assures that the sun on the surface of the box does not cause the inner surface of the box to be above ambient temperature.

Despite these arguments, I was skeptical about how well these little boxes in the sun would work until I measured the temperature inside one to verify how well it worked. The Weather Service knows what it is talking about here!

## Discussion of Intrinsic Biases

Probably most people who have bought a cheap thermometer from a hardware store have looked at all the different samples of the same model and noticed that every sample doesn't read the same temperature, despite being in essentially the same location. This is a direct observation of the relative intrinsic biases of those thermometers. That is, since it is not known what the true temperature is at the location of those thermometers, all one can observe is the error of an individual thermometer relative to the other thermometers.

Suppose there are five thermometers, which read 70, 71, 72, 73 and 74°, respectively. The average of all five thermometers is 72°. The bias of those thermometers relative to the average is -2, -1, 0, 1 and 2°, respectively. If I needed to buy one of those thermometers, I'd buy the one that read 72°, figuring that it was most likely to be properly calibrated.

The assumption behind that reasoning is that on average, the manufacturer tries to make their thermometers properly calibrated, but that manufacturing errors may produce a variation of ±2° (in this hypothetical example) for individual samples. However, without any other information, I have no way of knowing whether the manufacturer in fact has an error in their average calibration. Thus the true error of those thermometers might be -4, -3, -2, -1 and 0°, respectively, meaning that only the thermometer reading 74° is properly calibrated.

There is only one fundamental way to check the calibration of a thermometer. In the Fahrenheit scale, 32° is the freezing point of water and 212° is the boiling point of water (at a normal atmospheric pressure of 760 mm of mercury). A thermometer is usually a very linear device, meaning that it changes its reading by the same amount for every degree rise of temperature. Hence if the thermometer properly reads the freezing and boiling point of water, it is most likely correct over the entire range between the two.

Unfortunately, most weather thermometers read between -50° and 120°, since that is the expected range of temperatures encountered in nature. Thus it is possible only to measure the intrinsic thermometer calibration at 32°.

Another way to calibrate a thermometer is to measure it against a thermometer which has been properly calibrated. The National Institute of Standards and Technology (NIST) performs such measurements. One can have NIST calibrate a thermometer for \$259 per point or purchase a NIST-traceable thermometer, which has been compared to a NIST-calibrated thermometer, for ~\$150.

If anyone knows of a NIST-traceable thermometer in the Fallbrook area, please let me know so I can compare my thermometer to it!

## Analysis of Location Biases

A Taylor 21413 analog liquid-in-glass thermometer (a cheap ~\$10 "backpacking" thermometer) and an Oregon Scientific BAR-888 electronic thermometer (\$130) were carried to a number of locations during a two hour period to measure temperatures there. The measurements were taken between 12:41 and 2:43 p.m. PDT on 6/13/00 in Fallbrook, California at three different locales: my house (1802 Acacia Lane, elevation 690'), Mox's house (839 Via Alegre, 840'), and the official Fallbrook weather station in downtown Fallbrook (315 E. Ivy, 699'). These sites roughly form an isosceles triangle with a base of 1.1 miles between the official site and Mox's house and sides of 3.5 miles from either location to my house.

This period contained essentially the peak temperature of the day, and hence the true temperature was nearly constant during this time (see plots below). All three locations are expected to have nearly the same temperature. Even if the maximum distance difference of 3.5 miles was along the sea-breeze direction, the expected temperature change would be only a degree or two. The elevation difference would give a maximum temperature difference of 0.8°. Further, these two effects work with opposite sign in this case, partially canceling each other out, since the highest location was also the farthest from the coast.

The measurements with the Taylor thermometer were made by holding the insulated end of the thermometer. The measurements made with the Oregon Scientific thermometer were made by holding the thermometer, which may have slightly biased the readings since there was no equivalent "insulated" end to hold. In particular, the field of view of Mox's thermometer contained a larger solid angle from Mox's hand, due to the method in which it was held, which may have slightly biased the readings.

The intrinsic bias of these thermometers is irrelevant to the analysis here, since only the relative readings from these locations matter. However, our measurements may still be influenced by the fact that we were holding the thermometers, slightly altering the location seen by our thermometers and the thermometer to which we were comparing. Furthermore, since the housings of the sensors for the thermometers are different, each thermometer may sample the environment somewhat differently if there are temperature gradients across the field of view from a given location. There is evidence of this presented below.

The measurements are consistent with all three locales having the same true temperature, and with the true temperature changing by at most 1.5° during this period. As will be seen, however, the measured temperature shows significant biases due to the precise thermometer location at each locale.

The measurement locations at my house were:

• my porch thermometer, located on the north side of a post holding up one end of the porte cochere of my house. The thermometer is set off from the post by a 1" block of wood, so there is no thermal contact with the post. The thermometer thus views deep shade for 3/4 of its field of view, consisting of the shaded post, the porte cochere and the shaded part of the front of my house. About 1/8 of its field of view is a large oak tree. The remaining 1/8 is mostly of shaded concrete and the garage of the house, with less than 1/16 of the field of view being concrete heated by direct sun.

• the deep shade of the porte cochere, which is much less influenced by heated concrete; and

• my side yard thermometer, located 1' from the west wall of my house, with most of the location in the deep shade from two very large trees. However, some portion of that location has direct sunlight, coming from a gap in the trees.

The measurement locations at Gaylord Moxon's house were:

• light shade under a smallish tree in his front yard; and

• his Davis Weatherstation thermometer, located on the north side of a post holding up one end of his arbor, about 1' from the roof. The arbor is made out of wood slats. A wood cover locally shields the thermometer location from direct sun.

The measurement locations at the downtown Fallbrook fire station were:

• inside the official Weather Service white box; and
• in the shade of our bodies and a notebook in the sunny yard next to the white box.

The bias due to thermometer location is derived separately from my Taylor thermometer and from Mox's Oregon Scientific thermometer. My thermometer has a resolution of 0.5° at best, so differences of 1° are not significant.

I've classified the above locations into the following categories:

• deep shade: the deep shade of my porte cochere and inside the white box;

• light shade: my side yard, Mox's tree and next to the white box

• tjc: my porte cochere thermometer; and

• mox: Mox's Weatherstation thermometer.

Note the consistent offsets derived from both thermometers in the plots of the bias from both thermometers (remember that the absolute readings don't matter here, only the offset from the coolest readings):

• deep shade: Both locations essentially agree, and give the coolest readings. The two data points after 14:00 probably are significantly different. The cooler reading is from my porte cochere, which is a windier location than my side yard, where trees and the side of the house restrict the sea breeze. Thus this difference may be due to the sea breeze which was present at the time. Alternatively, the side yard measurement may have been biased a bit high since the side of the house next to the thermometer had been in the sun for perhaps an hour previously.

• light shade: All three locations show a consistent bias of +2° from my thermometer. The single comparison from Mox's thermometer gives +1°.

• tjc: The location of my porte cochere thermometer shows a clear bias of +3° from my thermometer and +6° from Mox's thermometer. (We were careful not to block the view of the heated concrete, so Mox's higher bias may result from his hand blocking more of the cooler portion of the field of view.) This is consistent with a bias of 2-4° derived from previous comparison to the older official Fallbrook temperatures.

• mox: The location of Mox's Weatherstation thermometer shows a clear bias of +4° from my thermometer and +4-6° from Mox's thermometer. This is consistent with the bias of 5-10° derived from previous comparison to the older official Fallbrook temperatures for June data.

The measurements showed clearly that only deep shade or the official weather station box produced an unbiased temperature reading. Even the ~20' diameter circular shade provided by a small tree still produced a bias of 1-2° due to the heated surfaces outside the shaded area.

There is a clearly increased bias at the locations of the thermometers that Mox and I use to measure our Fallbrook high temperatures, due to the influence of heated concrete for my measurements and the influence of the arbor roof on Mox's measurements. This bias is consistent with what was found previously in a comparison of our temperatures to the official Fallbrook high temperatures for a period of several years. Hence this implies that our bias is mostly due to the locations of our thermometers, and not to biases in our thermometers themselves.

## Analysis of Intrinsic Biases

Unfortunately, the data do not unambiguously allow the deduction of the intrinsic biases of the thermometers. I suspect that the reason is due to the location biases, which are different due to the observer being present in the field of view of the thermometers and due to the thermometers effectively seeing different environments due to different shielding about the sensors.

The raw data, giving the difference in the readings of one thermometer relative to another at the same location, show the problem:

ThermometerBias Relative to
TaylorOregon Scientific
tjc+2, +2-4.4
mox+2.9, +4.40.5, -0.8
Taylor--2.4, -2.8, -2.0, -5.4, -4.6, -5.2
Oregon Scientific+2.4, +2.8, +2.0, +5.4, +4.6, +5.2-
Official-2.5-5.3

The differences between the Taylor and Oregon Scientific thermometers clearly vary with time. There is a ~1.5 hour gap between the differences of {-2.4, -2.8, -2.0} and {-5.4, -4.6, -5.2}. The location bias definitely changed during that interval. Hence it is likely that this change shows that the thermometers do in fact effectively see different environments, despite being physically at the same location.

If I arbitrarily assume that the larger differences are caused by location, and thus ignore them here, I arrive at the following relative calibrations:

ThermometerBias Relative to
Taylor1996 Official
tjc+2+1.5
mox+3+2.5
Taylor--0.5
Oregon Scientific+2.5+2
Current Official-2.5-3
1996 Official+0.5-

The 1996 Official bias comes from my previous analysis of the calibration of the official Fallbrook weather station.

However, I have little confidence in the validity of this relative calibration for the tjc and mox sensors due to the probable remaining location bias. In fact, previous comparisons combined with this analysis make it likely that there is very little intrinsic bias of either sensor relative to the 1996 Official Fallbrook temperatures. That is, virtually the entire source of the previously-deduced bias is due to the location bias.

The comparison of the remaining thermometers is probably valid, since it derives from the relative bias at the location of the official Fallbrook temperature, using observations inside the weather box. These comparisons make better sense than assuming that the current official temperature is unbiased, which would make the Taylor thermometer biased high by 2.5° and the Oregon Scientific thermometer biased high by 5°, values that are probably too high to be expected from miscalibration.

I checked the calibration of my Taylor thermometer in an ice-water bath, and it correctly read 32°. However, this does not prove that the thermometer is accurate at 80° without having another calibrated data point.

Overall, I consider it likely, although not definitively proven, that the current official Fallbrook high temperatures are ~3° too low. What is known is that the current official Fallbrook high temperatures are ~3° too low as compared to the 1997 and 1998 official Fallbrook high temperatures.

## Summary

• A good thermometer location is extremely important for the accuracy of a thermometer. It looks like the official Weather Service enclosure is hard to beat, even with a fancy automated station like the current official Fallbrook thermometer.

• The previously-determined biases in the high temperatures measured by myself and by Moxon are probably due to location biases.

• It is quite likely that the current official Fallbrook high temperatures are about 3° too low.

Go to Fallbrook Weather