For this one year I compared the 24hr Tmax and Tmin for midnight and 1800 hours.
21.89 C is the average Tmax recorded at 1433hrs for midnight reset versus 22.09 C using 1800 hrs reset. 10.23 C is the average Tmin for midnight reset recorded at an average time of 0793 hrs versus 10.58 C for the 1800hrs reset. These hours are in HH.HH or decimal hours instead of HHMM. So for this particular station 1800 reset produces a slight warm bias, but this station is the Watkinsvill, GA CRN station with mechanically aspirated temperature sensors. If it were a standard MMTS, the Tmax bias would change with surface wind speed because they are not mechanically aspirated and shelter condition, dirty etc. increase solar energy absorbed. A Cotton Region Shelter (CRS) has a different temperature bias, Tmax is typically warmer due to solar radiant heating, so you have a similar surface wind speed issue.
So is there some error introduced with time of observation? Yes. Is it easy to figure out what is TOBs and what is instrument error? No. Each type of station would need a different correction factor if you want to correct for the small errors. The biggest concern would be errors that bias the station trend.
Errors that tend to bias the trend, if they are step changes are easy to find and correct. You can consider each step the start of a new record, like BEST does, and no TOBs adjustment is required. NOAA decided to use TOBs adjustments for the USHCN or about 1200 surface stations which lead to the surfacestationsorg project by Anthony Watts in a effort to isolate micro-site issues that would bias a station without always producing an obvious step change.
Zeke included this graph showing TOBs adjustments which includes a long slow increase from roughly 1960 to present. Prior to NOAA defining the USHCN in the early 1980s, there has never been much need to adjust temperatures due to TOBs. The reason the USHCN was defined was so that the NWS and Department of Energy could keep trace of Global Change. Global Change/Global Warming/Climate Change tend to sensitize people to "warming" which appears to have caused a "non-random" shift in Time of Observation in order to focus on potential "record" events or maintain a more accurate record. Human observers sensitized to a issue can make changes, good or bad, that can skew simple statistical analysis. This can create an interesting problem for statisticians trying to estimated TOBs bias. If observers are constantly changing reset times to chase records or improve data quality, but actually record the proper Tmax and Tmin for the proper day, there can be no TOBs adjustment required. The observers themselves would be making corrections daily while dutifully noting what time they reset their instruments. With an 1800 hrs reset there would be only a small number of days per year that would add a bias and if the observer starts a new observation schedule then they would be adjusting to minimize the error but a statistical program would think it is adding to the error. This means that comparison to neighbor stations which also have bias related to instrumentation type and site issues might appear to be adjusted for TOBs while the station being corrected might be having error added instead. So since the human observers are intelligent, they could change TOB to improve accuracy, simple statistical analysis doesn't include one important confounding factor.
This becomes a major PITA is one is trying to quantify micro-site issues that may be masked by TOBs adjustments when the folks saying the TOBs adjustments are required based on possibly flawed statistics keep shutting down other methods of quantifying error without using the TOBs adjustments.
This is exactly what happened to Anthony Watts' most recent paper which was shot down because he didn't use TOBS adjustments. The TOBs fans make a compelling case, but without knowing why the observers made the frequent changes in observation times, you really cannot determine a valid TOBs adjustment for each station.
This graph provided by Zeke shows changes in the meta-records. Zeke mentions that in 1960 the cooperative observers were requested to change to an AM reset schedule in order to improve the accuracy of precipitation measurements (reduce evaporation). For some perspective there are about 1200 USHCN stations and about 11,000 Coop stations that were "keyed" for the climate database modernization program.
The Coop Stns ( /10) curve above indicates a peak of around 6000 coop stations and the darker line at the bottom represents USHCN TOB changes which has its largest peak at about 1918 and a smaller peak around 1950. Both of these appear as step changes on the Tmin/Tmax adjustments chart.
Around 1985 there is another peak for both TOB and MMTS for the USHCN which may have produced the tiny bump on the Tmin/Tmax adjust chart at that time on the smooth slope in adjustments starting in roughly 1960. When there should be a step change, ~1960 because of the the requested change in time of observation, there isn't one.
If the magnitude of the TOBs adjustments are estimated by using the larger cooperative network which has micro-site issues as well as instrumentation changes, then it is less likely that the TOBs adjustments correction for just for TOB.
Zeke does a much more complete analysis of the CRN stations than my one year at one station in Georgia which indicates an 8AM TOB produces a small, about -0.1 C bias. Zeke also includes chart of the TOBs changes for the USHCN stations.
Figure 1: Recorded time of observation for USHCN stations, from Menne et al 2009.
So with the majority of changes being to AM according to this Menne et al 2009 chart the TOBs adjustments should have decreased toward about +0.1 C not increase to nearly +0.3 C. That indicates there is much more going on that Zeke's interpretation of TOBs adjustments indicates. Part of that could be human observers adjusting TOB to reduce error which they might think is part of their job.
Key points: No 1960 step change apparent on the Menne et al 2009 chart. The Change in TOBs from PM to AM according to Zeke's CRN analysis should have been to less adjustment not more. Finally, different station zones and instruments would have different TOBs considerations not shown in this simple example of the need for TOBs adjustments.
Conclusion: Zeke's rehash of the NOAA explanation of TOBS adjustments leaves the same unanswered questions. Though the CRN analysis is a nice addition.