This is a version of my TOBS nailed post, with graphics. The numbers come from my first post in the series, which took three years of hourly data from Boulder, Colorado, and looked at the effect of TOBS (time of observation) measures. That post is the place to look for detail on how it works. A post with much more data is here.
For now, I want to follow the recent post in relating TOBS to fundamentals. What is our measure of average temperature over a period? Sometimes people strenuously urge that the usual TAVG, the average of daily recorded min and max, should be replaced by a proper integral over the day. And they would be right, if we had the historic data. But we don't.
What we do have are records of min and max as recorded daily (at various times of day) by min/max thermometers. These give not the actual daily min/max, but the min/max in the preceding 24 hours (with regular resetting). So they are, averaged over time, a reasonable measure of average temperature, but a measure that depends on the time of observation.
Let me show that with a plot of the three years of Boulder data. I have taken the mean of the hourly data, and compared with the measure that a notional observer would report from reading a min/max every day at at 2AM, or at 5AM and so until 11 pm. I show the 365 day centered running mean that you would get by each of these schemes. The running mean removes the seasonal cycle. The legend shows the colors, with a link to the respective curves. Left axis °F, right in °C. x-axis days after 31 Dec 2008.
So the various TAVG curves are reasonable measures, in that they track the black mean curve with a roughly constant offset. But the offsets are very dependent on time of obs.
If you stick with one such measure, the offset does not matter much. Its effect would go away on taking anomalies. But if you switch between measures (change TOBS), the effect can be large.
TOBS adjustment is effectively calibrating this measure, relative to a reference. If you change measures, you have to recalibrate.
When we refer to "raw" or "unadjusted" monthly data, it should be remembered that it is not just the original readings. It incorporates an averaging procedure. The outcome of that depends on the time of observation. If that changes, then it's a different measure, as much as if you changed to a differently calibrated thermometer.
Below the fold, I'll show some plots of monthly averages, and a difference plot that may make the stability of the TOBS dependence clearer.
Here now is a version of the above plot shown as differences from the hourly mean. You can see that the curves generally remain in order as TOBS varies, but the spacing is not constant. TOBS adjustment will not be precise year-to-year. But fortunately for most applications, a number of years will be averaged. And there is a lot more hourly data available near most places, so an accurate mean adjustment can be derived.
The "coolest" measure is at 5am, when it often happens that a cold minimum is split and attributed to two separate days. 8am is similar but 11am is already on the warm side of neutral, and 2pm is the time most likely to split and double count warm afternoons, making a warm bias. 5pm is a bit less so, and 11 pm has a slight cool bias relative to hourly.
You may wonder about monthly means. I showed annual first, because the seasonal cycle is so large. In fact, although the various measures fluctuate a lot more, changing the axis to accommodate seasonality makes them look a lot smoother. Here is the plot:
The extra noise is apparent when plotting differences from the mean. Here is how it looks:
It's natural to look at that and say that we should have no truck with such noise. But it's part of the actual measure that we are using. That's how the min/max varies relative to the hourly mean, which we'd certainly use if we had a long record of it. One day we will.