Surface temperature uncertainty, quantified

sky also wrote that, “The year-to-year VARIABILITY of the aggregate mean for relatively small samples of stations repeatedly shows agreement well within ~.25K at the 2-sigma level. That provides a more appropriate bound for the sampling and measurement uncertainty associated with climate indices.
This is the usual approach in surface climate science, to examine the numbers themselves and look at their aggregate variance as a guide to their validity without paying any attention to the instruments. This reveals nothing about any systematic error that may be in the data.
Systematic error does not cancel in an average. It just averages as the data. There hasn’t been any survey for how instrumental systematic error may correlate across small regions. So, to suppose that correlated trends imply low-error data is to assume what should be demonstrated.
Whether trends approximately reproduce locally doesn’t reveal anything about instrumental accuracy in the subordinate data. The only way to assess the magnitude of systematic error is to test an instrumental measurement against a known standard.

By the way, here’s the title and abstract of the second paper, to also be published in E&E and then ignored. This work was the other part of the original longer paper rejected by JAMC.
Title: “Imposed And Neglected Uncertainty In The Global Average Surface Air Temperature Index”
Abstract: “The statistical error model commonly applied to monthly surface station temperatures assumes a physically incomplete climatology that forces deterministic temperature trends to be interpreted as measurement errors. Large artefactual uncertainties are thereby imposed onto the global average surface air temperature record. To illustrate this problem, representative monthly and annual uncertainties were calculated using air temperature data sets from globally distributed surface climate stations, yielding (+/-)2.7 C and (+/-)6.3 C, respectively. Further, the magnitude uncertainty in the 1961-1990 global air temperature annual anomaly normal, entirely neglected until now, is found to be (+/-)0.17 C. After combining magnitude uncertainty with the previously reported (+/-)0.46 C lower limit of measurement error, the 1856-2004 global surface air temperature anomaly with its 95% confidence interval is 0.8(+/-)0.98 C. Thus, the global average surface air temperature trend is statistically indistinguishable from 0 C. Regulatory policies aimed at influencing global surface air temperature are not empirically justifiable.”
The (+/-)0.17 C “magnitude uncertainty” in the normal mean is the standard deviation of the 1961-1990 yearly anomalies around the CRU mean anomaly normal of the same period. This gives a measure of the climate ‘jitter’ during the normal period, and amounts to an uncertainty in the magnitude of the normal mean. As such, it must be propagated into the annual anomalies that are calculated by subtraction from the normal mean. This statistical practice, after all, is merely the standard for calculating empirical uncertainties in physical science.
Anyway, it was also interesting to discover that the ‘jitter’ standard deviation of annual anomalies over the total of years from 1856 – 2004, relative to the normal mean, was (+/-)0.28 C. The paper points out that if the governing climate regime was unchanging for the duration, then (+/-)0.28 C is a 1-sigma measure of the “natural variability” of climate during this entire period.
The 95% confidence interval of recent natural variability for 1856-2004 is then (+/-)0.56 C, which all by itself discounts causality in 70% of the total warming since 1856. That is, provisionally crediting the mean temperature trend, it’s hardly different from a random process that exhibits the pseudo-trends expected from a stochastic process plus persistence.

This will be a point-by-point rebuttal of EFS_Junior’s criticism.
First, as we go through this, keep in mind that my paper discusses unaddressed uncertainty in the standard calculation of global average surface temperature, not in recent trends in regional temperatures that form the base of EFS_Junior’s critique.
However, to EFS_Junior’s answer about why my analysis is wrong:
Point 1: “Long answer? Separation of the total temperature error term … into two mutually exclusive, independent, and unrelated terms is bogus, unnecessary, and without merit.”
Reply 1: Let’s look at what’s done in Brohan, 2006: Under Section 2.3.1 “Station Errors,” they write T_actual = T_ob + e_ob + C_H + e_H + e_RC, where T_ob, e_ob are observed temperature and its error, C_H, e_H are homogenization and its error, and e_RC is miscalculation or misreporting error.
So, Brohan, et al. separated their temperature errors into three (not two) mutually exclusive, independent, and unrelated terms, and presumably that is bogus, unnecessary, and without merit.
EFS_Junior mentioned in his preamble that he has a copy of my article reference 17, which is Bevington and Robinson, “Data Reduction and Error Analysis for the Physical Sciences.” Pages 1&2 in B&R say this: “Our interest is in uncertainties introduced by random fluctuations in our measurements, and systematic errors that limit the precision and accuracy of our results…(italics in original). They go on to distinguish between precision and accuracy, and on page 3 between systematic errors and random errors.
On page 3, systematic errors are described as due to observer mistakes, equipment failures, and experimental conditions. Random errors are described as fluctuational. Bevington and Robinson thus distinguish these error types as mutually exclusive, independent, and unrelated as to both source and behavior.
But, according to EFS_Junior, separation of error terms into mutually exclusive, independent, and unrelated terms is bogus, unnecessary, and without merit.
In the JCGM 100:2008 “Evaluation of measurement data — Guide to the expression of uncertainty in measurement,” put out by Working Group 1 of the Joint Committee for Guides in Metrology (JCGM/WG 1), random error is orthogonally distinguished from systematic error.
Random error is “stochastic temporal and spatial variations of influence quantities [and its] expectation value is zero.” In contrast, systematic error is defined as the “effect of an influence quantity on a measurement result,” that produces a mean value different from the true value and further that, “systematic error and its causes cannot be completely known.”
Once again, error types are separated into mutually exclusive, independent, and unrelated terms, which we now know is bogus, unnecessary, and without merit..
In both Bevington & Robinson (p. 11) and in the JCGM manual (Section C.2.20), the variance about a mean goes as s^2 = [(1/(N-1)]*[sum-over-N(x-x_bar)^2]. As, by definition, systematic error yields an error mean different from zero, the dispersion of systematic error about its mean goes as s^2 and does not diminish as 1/(sqrtN). This is the approach taken in my paper, and it is the documented correct approach.
EFS_Junior’s critique against separating total error into its component types is wrong.
Further, evaluating separate sources of error is standard practice in experimental science. Doing so is really the only way to determine the contribution each sort of error makes to a measurement. EFS_Junior, in his critique, is dismissing perhaps the most critical method of assessing the meaning and significance of an experimental result.
In Brohan 2006, e_ob is represented as the guesstimated (+/-)0.2 C average of Folland, et al, 2001, which is discussed in detail in my paper.
The contribution of systematic error to e_ob, due to uncontrolled environmental variables, is not discussed at all in Brohan, 2006. This analytical lacuna is what sparked my inquiry.
Point 2: EFS_Junior also wrote that, “[he] only considers the +/- term, the “paper” never discusses bias offset errors, and assumes all errors are symmetric about a zero mean.”
Reply 2: The first part of my paper describes basic sorts of random error, and with that as context goes to show that the average (+/-)0.2 C error taken by Brohan, 2006, and Folland, 2001 isn’t random at all.
After that, Section 3.2.2 discusses systematic error and its sources in surface air temperature measurements. Bias mean offsets and standard deviations for three sensor systems are calculated and presented in Table 1. The top of page 978 has this sentence: “All these systematic errors, including the microclimatic effects, vary erratically in time and space [40-45], and can impose nonstationary and unpredictable biases and errors in sensor temperature measurements and data sets.”
Figures 1 and 2 show fits to three data sets of systematic error in temperature measurements. For clarity of graphical presentation, the bias means were subtracted to produce an artificial mean of zero. Maybe that misled EFS_Junior, although it’s explicitly mentioned in both figure legends.
That is, I directly and obviously discussed bias error offsets and nonstationary error, which by definition does not have a mean of zero. So, I did not assume all errors are symmetrical about a zero mean, and it’s obvious that I did not.
Somehow, EFS_Junior apparently missed all of this, even after two readings.
Let’s also add that if I had believed all errors are symmetrical about zero, I’d have had to also believe that all these errors would diminish as 1/sqrtN, and would go to zero at large N. The lower limit of error would then be uniformly zero, and my paper would have no point. So, EFS_Junior is claiming that my paper reflects an assumption about error that completely contradicts the actual and explicit analysis of error present in the paper. That, after two readings.
More about bias errors: under “Systematic Errors” page 3 of Bevington and Robinson gives an example where subtracting a bias offset error actually increased the inaccuracy of a result, because the bias correction itself was an estimate. Climate scientist colleagues of EFS_Junior regularly “correct” their data sets by subtracting estimated bias offsets, and then go on to assume improved accuracy.
Bevington and Robinson, in contrast, go on to advise that one must explicitly take account of new uncertainties that may be introduced by bias corrections. How is that done in bias-corrected temperature data sets, when the uncontrolled systematic effects on the initial measurements are unknown?
Point 3: EFS_Junior wrote, “The total error does NOT propagate through the temperature array system as sigma, it also does not propagate through the system as sigma/SQRT(N), as usual, the truth lies somewhere in between these two limits.”
Reply 3: I didn’t calculate “total error.” I calculated a lower limit of sensor measurement error, principally due to systematic effects right at the instrument.
Total error also includes discontinuities due to instrumental changes, extrapolations due to sparse data, missing data, dropped stations, moved stations, station spatial inhomogeneity, observer read bias, time-of-observation bias, albedo changes, the hotly-debated UHI, and what else? So what if these things propagate differently than 1/sqrtN, or differently from sigma itself?
My paper isn’t concerned with them. That’s why “lower limit” is included in the title and in the text.
Systematic instrumental error does propagate as 1/[sqrt(N/(N-1)], and at large N the adjudged guesstimated (+/-)0.2 C station error of Brohan, 2006/Folland, 2001 also does propagate as sigma.
All the rest of the errors must be calculated in their own particular way, and summed with the basic instrumental error to get the “total error.” All the other sources of error would merely add to instrumental error error. EFS_Junior’s point 3 is irrelevant.
Finally, the point about the HAWS data.
Point 4: EFS_Junior wrote, “for the 23 HAWS (all station correlations of anomalies between any two stations has been done, the resulting plots all look Gaussian (need to do some binning to be sure) with zero mean).” and “Bottom line? If the total error was as claimed, I would never be able to extract a very real low frequency temperature trend line signature with a resulting R^2= 0.99.”
Reply 4: This claim deserves some comment. EFS_Junior wrote that, “the data sets are all of (IMHO) very high quality with all temperatures reported at 0.1C resolution (for all years I downloaded to date, 1982-2010 inclusive).”
The newest sensors used in Canada were reported in E. Milewska and W. D. Hogg (2002) Atmos-Ocean 40, 333–359, to be “Yellow Springs International (YSI) Model 44212 thermistors in a Stevenson screen.” The Campbell Science manual (pdf download) reports the manufacturer specification average accuracy for these probes to be (+/-)0.1 C. Well and good.
K. G. Hubbard and X. Lin (2002) GRL 29, 1425 (doi:10.1029/2001GL013191) reported on the field resolution of the PRT HMP45C probe (pdf download), also inside a Stevenson screen. The HMP45C probe has a closely comparable manufacturer’s specification of (+/-)0.2 C accuracy at 20 C.
Systematic error reduced the field resolution of the HMP45C in a Stevenson screen to an average bias offset of 0.34(+/-)0.53 C (article Table 1). Subtracting 0.34 C from all the recorded temperatures would not remove the dispersion uncertainty of (+/-)0.53 C. The (+/-)0.53 C propagates as 1/(sqrt[N/(N-1)] into any average of that data.
Maybe in Canada the resolution of thermistor probes is not degraded by systematic effects in the field while housed inside Stevenson screens, but unless that has been demonstrated, EFS_Junior’s claim of (+/-)0.1 C accuracy is no more than special pleading.
It’s worth quoting Milewska and Hogg a little more extensively: “Climatological records of high temporal resolution have been generating interest recently, because of their direct applicability to climate change impact studies. Finding adjustment factors for these daily and sub-diurnal observations – synoptic, hourly – is a challenging task. A single bias adjustment value will not work well on any day or time of the day, it might even introduce additional uncertainty by over or under correcting on a given day. The magnitude of the adjustment factor depends on meteorological conditions and thus should vary from one day to another. For example, wind speed and cloudiness are the two main controlling weather elements that determine the value of the adjustment in the case of temperature. Larger factors may be required for calm clear nights, when siting biases are magnified due to the increased response of the ground surface to radiative cooling… (bolding added)”
Milewska and Hogg seem to know about B&R’s caution concerning bias offset subtraction. One is led to wonder whether EFS_Junior worried about whether any bias removal might degrade his data further when he compiled his temperature series. Did he know even the average magnitude of any systematic biases in his data? Well, but of course the reported accuracy was (+/-)0.1 C.
Milewska and Hogg don’t report any attempt to quantify the field resolutions of their YSI sensors in Stevenson screens by comparison with a high-precision sensor like the R. M. Young aspirated probe, but do mention the manufacturer’s estimated field resolution. Thus, Milewska and Hogg: “The sensors are generally reliable with manufacturer specified accuracy, which is the closeness of the agreement between the result of a measurement and the “true” value, of (+/-)0.3°C.”
So, Canadian AWOS and RTD sensors in Stevenson screens are admitted to have a field accuracy of (+/-)0.3 C. If we believe Hubbard and Lin’s actual field test, they’re likely to have an accuracy of no better than (+/-)0.5 C. But, they were reported to (+/-)0.1 C, and we’re told that was apparently good enough to trust uncritically.
EFS_Junior reports that arctic “areas are warming at ~0.25C/year…“, which is 0.05 C inside the estimated inaccuracy envelope reported by Milewska and Hogg, and half the 1-sigma uncertainty reported by Hubbard and Lin. So, EFS_Junior’s “(+/- 0.15 C/year)” is clearly over-optimistic.
Note that the (+/-)0.3 C is an accuracy measure, not a precision measure. There is no reason to think that in the field the true inaccuracy is symmetric about a mean of zero. An assumption that the field inaccuracy diminishes as 1/(sqrtN) is empirically unjustified.
Finally, point 5: EFS_Junior wrote, “Bottom line? If the total error was as claimed, I would never be able to extract a very real low frequency temperature trend line signature with a resulting R^2= 0.99.”
Reply 5: EFS_Junior emailed me about this earlier. In reply, I pointed out that if sensor measurement error = e_tot = e_sys + e_ran, then averaging daily temperatures would make e_ran diminish as 1/(sqrtN). However, e_sys remains undiminished, and would just factor into the mean. The systematic error would be completely invisible, and hide its contribution within the data. That is, without prior methodological testing, data + systematic error looks just like data + no error. Apparently EFS_Junior found this very standard caution unconvincing.
In the case of data distorted by resident e_sys, any trend that emerges would be contaminated by the uncompensated systematic error. This error may even reflect the degradation of the sensor over time. Any “true” trend may be greater or smaller than the observed trend, but whatever the true trend is, it’s unknown when systematic error is uncompensated.
Even comparingf trends from adjoining stations, to show “homogeneity” of data, gives no reason to dismiss the impact of systematic error. Uncontrolled environmental variables can be regional as much as local. Regionally extensive environmental variables can impact regional sensors in analogous systematic ways, to impose analogous systematic errors. In data averaged over longer times, one might expect the systematic effects of regional environmental variables to emerge most strongly. It’s conceivable that the systematic effects that follow meteorological trends (e.g., of trends in insolation or wind) could impose analogous but spurious low-frequency trends on independent data sets from stations scattered across a contiguous region.
This possibility has never been tested — at least to my knowledge after searching the literature. So, EFS_Junior’s claim of “never be able to extract…” is without empirical merit.
On the other hand, I do know of one sensor test of a different sort that does indicate the possibility of regionally extensive environmental systematic effects on temperature sensors. At some point I intend to write this up, along with some related analysis.
The rest of EFS_Junior’s critique was polemical, with an appeal to authority and considerable gratuitous disrespect directed toward E&E. There’s no need to reply to that.

I’m reposting this from tAV. Anthony expressed a similar sentiment at the head of this post:
I’d like to add that though I’ve offered to send reprints on request, I’d ask that those of you who have access to academic accounts, or who have fine personal incomes, to please purchase the article from Energy and Environment, here.
Energy and Environment has proved to be one of the few remaining journals in climate science where one can anticipate a uniformly dispassionate and even constructive critical review. In the principled stand of its editor, Dr. Sonja Boehmer-Christiansen and its Multi-Science publisher, Dr. William Hughes, E&E has been thoroughly in support of open and transparent science when so many have abridged it.
The journal merits support, and deserves to recover their fair profit for publishing my article.
Thanks very much,
Pat

Reply, Part 1.
This Part 1 of what will be a point-by-point reply to EFS_Junior’s follow-up critique of my article. I’ll begin with what he did discuss, and finish with what he did not. EFS_Junior’s comments will be enquoted.
EFS Point 1. “You need to simplify your reply above. As it stands now I don’t even know what you mean.”
Reply 1. I wish you’d been more specific. But assuming it’s the bit about e_tot: the total instrumental error in any single measurement, e_tot, will be the sum of the random error e_ran and the systematic error e_sys. Each kind of error contributes a spurious magnitude to the observation.
In measuring a temperature, for example, the magnitude of the observed temperature “t_i” is a sum of the “true” magnitude, “tau_i” plus the magnitudes of all the errors affecting that particular measurement.
So for any measured temperature, t_i = tau_i + e_ran_i + e_sys_i, where “i” is the measurement index (i = 1,2, …, n).
As usual, e_ran is stationary by definition. When multiple measurements of temperature are averaged, the total of e_ran will diminish as 1/sqrtN in the mean temperature, T_bar. The details of this are discussed in Cases 1-3 in my paper.
However, e_sys is not stationary. It typically arises from uncontrolled variables that are of unknown magnitude and unknown variability. Therefore, e_sys can vary between sequential measurements, doesn’t have a mean of zero, and permanently impacts the magnitude of the measurement.
The e_sys of each observation enters into any mean of multiple observations. In the mean, the total of e_sys goes as (1/(N-1)*sqrt[sum-over-N(e_sys_i)^2], and never diminishes to zero. At large N, the total of e_sys approaches (e_sys)avg, and the mean temperature is T_bar(+/-)(e_sys)avg.
The only way to know the magnitude of e_sys(avg) in a set of measurements is to have done prior tests of the methodology, using the same instrument to measure precisely known standards under conditions a close as possible to those to be used for the experimental measurements.
This is the message in the statistical sources mentioned in my previous post.
EFS Point 2. “The bottom line is that 23 HAWS stations all show (roughly) the same low frequency trend lines. And that’s just a plain cold harf fact. 23 HAWS stations all showing the same systematic errors? I think NOT!”
Reply 2. First, I refer you to the classic paper of Hansen and Lebedeff [1]. I’m sure you have a copy. Please look at their Figure 3, where, Hansen and Lebedeff show pair-wise correlation coefficients of temperature measurements among many hundreds of surface stations.
Here it is, in their own words: “At middle and high latitudes the correlations approach unity as the station separation becomes small; the correlations fall below 0.5 at a station separation of about 1200 km, on the average. At low latitudes the mean correlation is only 0.5 at small station separation. The distance over which strong correlations are maintained at high latitudes probably reflects the dominance of mixing by large-scale eddies. At low latitudes the most active atmospheric dynamical scales are smaller, but apparently there are also substantial coherent temperature variations on very large scales (for example, due to the quasi-biennial oscillation, Southern Oscillation, and E1 Nino phenomena), which account for the slight tendency toward positive correlations at large station separations. We examined the dependence of the correlations on the direction of the line connecting the two stations. For the regions for which this check was performed, the United States and Europe, no substantial dependence on direction was found. For example, in these regions the average correlation coefficient for 1000-km separation was found to be within the range 0.5-0.6 for each of the directions defined by 45 [degree] intervals.”
In short, Hansen and Lebedeff show large correlations of recorded temperature compared between pair-wise surface stations The correlations extend for considerable distances. Temperature correlation becomes more than 0.8 at distances less than 250 km for latitudes greater than 23 degrees. At distances less than 250 km between the equator and 23 degrees, regional correlations are ~0.5.
Next, we turn to the work of Hubbard and Lin [2]. They tested the temperature measurements “of dual temperature systems for ASOS, MMTS, and Gill shield (with HMP45C sensor), as well as one aspirated (ASP-ES) and one non-aspirated (NON-ES) shield from Eastern Scientific Inc. (with HMP45C), and one CRS (with HMP45C)” against the simultaneous measurements from a high-precision R. M. Young probe in an aspirated shield. “CRS” is Cotton Regional Shelter (the Stevenson Screen).
The three-panel Figure 2 in their paper shows the distribution of bias temperatures during day, night, and average for all six of the tested sensors.
Figure 2 legend is: “Statistical distributions of (a) daytime air temperature biases, (b) nighttime air temperature biases, and (c) overall air temperature biases for all air temperature systems in the measurements.” The data include thousands of temperatures (April through August, 2000), recorded at 0.1 Hz for 5 minutes each, representing 30 measurements per recorded temperature. So, random error was diminished by 1/5.5 in each reported temperature.
The average bias envelope for the HMP45C probe in the CRS shield was asymmetric. Ir showed a large excess of too-warm temperatures. The bias mean(+/-)sigma was 0.34(+/-)0.53, however, this isn’t the whole story.
A distribution of temperatures skewed toward warm, inserts a variable warm bias into the temperature record, during the thousands of measurements. This systematic temperature bias was primarily the impact on the sensor of solar loading and wind speeds.
This warm bias is a systematic error in the instrument that will not be revealed by any test looking for errors due to random artifacts, or any changes external to the instrument.
If the HMP45C/CRS warm bias was not distributed randomly in time, it will induce a spurious trend into the temperature data. A spurious warming trend will show up if the systematic bias is more pronounced late in the data set. Or, counter intuitively, if a warm systematic bias is asymmetrically distributed into the early part of the data set, it can produce a spurious cooling trend.
Figure 2 of Hubbard and Lin shows that every single one of the six sensor systems they examined showed an excess bias asymmetry toward too warm temperatures (also shown in their Table 1).
Now we combine the results of Hansen and Lebedeff with those of Hubbard and Lin:
1. High correlations of temperatures exist among regionally adjacent surface stations, extending over at least 250 km.
2. Regional correlations of temperature require regional correlations of climate. The results of Hansen and Lebedeff mean climate is correlated over distance.
3. Local temperatures are governed by local climate (sun and wind, and even snow albedo [3]).
4. Systematic biases are induced into air temperature measurements by the same climatic effects that produce the air temperature itself.
5. Regionally correlated air temperatures therefore require regionally correlated systematic effects.
6. Temperature sensors of regionally adjacent surface stations systematically biased by correlated climates produce correlated systematic biases.
7. Correlated systematic errors will be present in the air temperature records of regionally adjacent surface stations.
8. The tested sensors were of different configurations and all of them displayed systematic error similarly skewed to excess warm temperatures.
9. Surface stations with different types of sensors will produce correlated systematic errors.
Conclusion 1: Systematic errors are inevitably present in air temperature measurements.
Conclusion 2: These systematic errors will certainly propagate into the recorded air temperature time series of surface stations.
Conclusion 3: Systematic errors in surface air temperature records will be correlated among regional surface stations.
Therefore: Spurious temperature trends within the data of one surface station will correlate with similar spurious trends in the temperature data of regionally adjacent surface stations.
Observation: This strong likelihood of regionally correlated temperature biases, which is predicted by published work, has completely escaped the notice of the climate science community.
Finally: Spurious trends due to systematic error that appear in data, and that correlate among the records of adjacent surface stations, will look exactly like real trends.
Examining correlations within temperature-time series trends from adjacent surface stations will not reveal the contamination of the temperature series by systematic error.
Correlations of temperature-time series among adjacent surface stations do not, and in-and-of-themselves will never, disprove the existence of systematic error in the data.
It’s particularly relevant to your HAWS data that Hansen and Lebedeff noted the strongest regional temperature correlations in the highest latitudes. That means the systematic error will also be most strongly correlated at the same high latitudes where HAWS data were collected.
Hansen and Lebedeff compared station temperatures, not anomalies. Their temperatures were large in magnitude compared to the (+/-)0.46 C lower limit of error. Therefore their correlations are real. However, anomalies are of the same magnitude as the (+/-)0.46 C lower limit. This is evidenced by the 0.25(+/-)0.15 C HAWS trend you mentioned.
As the HAWS trend is smaller than the 1-sigma lower limit systematic error, there is no reason to believe it is real.
This leads to:
EFS Point 3. “Further you claim that systematic error eould be “would be completely invisible” well than, that works for me! This is the same as stating that systematic error averages out to zero for each station or to the ensamble average of any N stations.”
Reply 3. “Invisible” means invisible, not ‘averages out to zero.’ Invisible means systematic error will not show up in any statistical test posterior to collecting the data.
Data contaminated with systematic error will look like real data, except that it will be false data. In the case of temperature, the magnitudes will be wrong, and the trends may be spurious. How the spurious data will appear depends on the magnitudes, distributions, and changeability of the uncontrolled variables that affected the sensor while the temperatures were being measured.
Overcoming these problems is why Hubbard and Lin have spent so much effort developing real time filtering methods for surface station temperatures.
EFS Point 4: “Your second paragraph makes no sense whatsoeven, and is quite obviously circuitous. If this argument were actually true, than no analyses could ever be conducted on any raw data set whatsoever. It’s akin to saying collect the raw data, than do nothing with the raw collected data. Sad, really sad.”
Reply 4. We can agree on the “sad.” By now, you should have realized that surface air temperatures contaminated by systematic error are useless for detailed comparisons. You should also have realized by now that field air temperatures are undoubtedly contaminated by systematic error.
It means that the conclusion of my E&E paper obtains, namely that, “no analyses could ever be conducted on any raw [surface air temperature] data set whatsoever” that are more accurate than about (+/-)0.46 C.
Part 2 will be forthcoming.
References:
1. Hansen, J. and Lebedeff, S., Global Trends of Measured Surface Air Temperature, J. Geophys. Res. (1987) 92 (D11), 13345-13372.
2. Hubbard, K.G. and Lin, X., Realtime data filtering models for air temperature measurements, Geophys. Res. Lett. (2002) 29(10), 1425 1-4; doi: 10.1029/2001GL013191.
3. Lin, X., Hubbard, K.G. and Baker, C.B., Surface Air Temperature Records Biased by Snow-Covered Surface, Int. J. Climatol. (2005) 25, 1223-1236; doi: 10.1002/joc.1184.

This is Part II of my reply to the critique of my paper by EFS_Junior. Part I of my reply is here.
EFS Point 5. “Your third paragraph plays with the concept of region, so is the Northern Hmisphere (NH) a region? Because I’m quite sure that I can show some autocorrelation/cross correlation with any two NH regional stations simply due to similar seasonal and diurnal behaviors (note that these would have to be cross correlated first to determine the diurnal lag coefficient).”
Reply 5. “Region” can be empirically defined in terms of the 1987 results of Hansen and Lebedeff [1], who showed air temperature correlations across 1200 km. For convenience, we can define as a region, locales where correlation is, say, 0.68 (1-sigma) or better. For latitudes north or south of 23 degrees, that might be 500 km. For zero to 23 degrees, that might be 100 km. Of course, one can define them as one likes, but an evidence-based qualifier is required.
As pointed out in Reply Part I, instrumental systematic error is produced by the same uncontrolled environmental variables that determine surface air temperature. So, systematic errors in the temperature record will be about as regionally correlated as the temperature measurements themselves.
EFS Point 6: “This also plays somewhat into the LLN, as it would be virtually impossible (p ~ 0) to take multiple stations from any region (no matter how small or how large) with the expectation (p ~ 1) that all these stations used the exact same sensors over time, have identical systematic errors over time, etceteras.”
Reply 6. Again as pointed out in Reply Part I, the field calibrations from Hubbard and Lin [2] show that sensors in six very different shields exhibit the same direction of systematic skew in measured temperatures (see also [3-5]). Therefore, it is an empirically justifiable surmise that regional systematic errors will remain correlated no matter the sort of temperature sensor employed. Your analysis is therefore not appropriate to the question.
EFS Point 7: “Autocorrelations exceeding 0.8, 0.9, 0.99, 0.999 with slopes of 0.98, 0.99, 1.00, 1.01, 1.02 for any two stations, is empirical proof that there is an underlying relationship between them, that whatever errors exist in these measurements, that these errors are not systematic in nature, to the degree, or in the manner, that the author claims.”
Reply 7. Climate stations measure surface air temperatures (among other observables). We know that surface air temperatures are regionally correlated. Clearly, then, any long-term trends in air temperatures will also be regionally correlated. The total average lower limit systematic-plus-station-error of (+/-)0.32 C is much smaller than the magnitude of the recorded air temperatures. Therefore, although the 20th century temperature measurements are contaminated with at least (+/-)0.32 C of error, our knowledge of these air temperatures is not seriously impacted by that lower limit of error.
However, the (+/-)0.46 C lower limit of error in an annual anomaly is not smaller than the air temperature anomalies themselves, which are calculated by subtraction of station air temperatures from a climate normal. That means any anomaly trend in temperatures smaller than (+/-)0.46 C, over the time-range of interest, is not physically distinguishable from zero.
As noted above, the regional correlation of systematic error in surface air temperature, guaranteed by the systematic correlation of surface air temperature itself plus the analogous response errors of various air temperature sensors, will also guarantee that spurious anomaly trends smaller than (+/-)0.46 C will be regionally correlated. This spurious regional correlation will mislead any scientist who neglects the effects of systematic error, or any one who fails to understand that systematic errors follow uncontrolled systematic climate variables.
As the systematic errors entering the measurements of 20th century air temperatures are unknown, it is impossible to correct 20th century air temperatures for these errors. It is only possible to measure contemporary systematic errors by monitoring sensor systems similar to 20th century systems, in order to estimate an average representative uncertainty due to the systematic error present in the 20th century measurements. This experiment would require deploying high precision temperature sensors at multiple (>,=100) locations world-wide to monitor “true” air temperatures – making a precision data-base against which concurrently recorded standard sensor temperature measurements could be compared. See reference [2] for what such an experiment might look like.
EFS Point 8. “It’s akin to saying “you can’t do that because x, y, z, …” but than doing so anyway…”
Reply 8. This point is answered in Reply 7.
EFS Point 9. “In your 4th paragraph/sentence you again make a baseless statement, as empirical evidence abounds as to the sameness of the global temperaure trends (land based and satellite eras, a random selection of a small group of land based records, say, for example, 10 < N < 100), that these trends are very similar for the 23 HAWS as well as to larger networks (but with lower trend lines for the global mean temperature trends), that these 23 HAWS trend lines are, in the aggrigate, quite similar in shape to the global trend lines.”
Reply 9. As noted in Reply 7, regional trends in temperature do not necessarily indicate the credibility of regional anomaly trends. Climate stations globally all use similar temperature sensors. Over the bulk of the 20th century, these were LIG thermometers in CRS shelters, or worse. There is every reason to think that the systematic error contaminating their temperature measurements would vary as the air temperature. When regional and global annual anomalies are calculated, the trends should usually (but perhaps not always) be preserved, except that any trend smaller than (+/-)0.46 C would be indistinguishable from spurious (zero).
Your empirical correlations would be credible indicators of real annual anomaly trends only if all measurement errors were random.
EFS Point 10. “In closing, any temperature record has a total error associated with it, whatever that error is, it does not stop one from extracting very real low frequency information with an associated very high degree of statistical confidence.”
Reply 10. Only when the low frequency trend is greater than (+/-)0.46 C. And that emergence would only grant 68% confidence. You’d need a 0.92 C trend to attain the usual 95% (p<0.05) statistical confidence.
EFS Point 11. “If this were not true, if this were not the case, than all low frequency temperature trand lines would indeed exhibit truly random behaviors, with R^2 approaching zero in all cases.”
Reply 11. Not when the error is systematic and regionally correlated.
EFS Point 12. “That because we can demonstrate well defined low frequency trend lines with associated high degrees of statistical confidence, that we can choose large N, and still obtain well defined low frequency trend lines with associated high degrees of statistical confidence, suggests umabigiously, based on the LLN, that these emperical results are real with probability approaching one (p ~ 1).”
Reply 12. 1/sqrtN reduction of error works only with random error.
Your entire analysis rests upon the assumption that random error exhausts all the instrumental error present in the surface air temperature record. It doesn’t. Unfortunately, the climate scientists who compile surface air temperature-time series have thoroughly neglected the systematic error suffered by temperature sensors. This neglect has led them to false confidence and to publish empirically unjustifiable conclusions.
The unappreciated error in the surface air temperature has further misled climate modelers to place false confidence in the temperature calibration accuracy of GCMs, and even further has led to false precision when so-called proxy paleo-temperature reconstructions are normalized to the instrumental record.
Final Part III is forthcoming.
References:
1. Hansen, J. and Lebedeff, S., Global Trends of Measured Surface Air Temperature, J. Geophys. Res., 1987, 92 (D11), 13345-13372.
2. Hubbard, K.G. and Lin, X., Realtime data filtering models for air temperature measurements, Geophys. Res. Lett., 2002, 29 (10), 1425 1-4; doi: 10.1029/2001GL013191.
3. Hubbard, K.G., Lin, X., Baker, C.B. and Sun, B., Air Temperature Comparison between the MMTS and the USCRN Temperature Systems, J. Atmos. Ocean. Technol., 2004, 21 1590-1597.
4. Lin, X. and Hubbard, K.G., Sensor and Electronic Biases/Errors in Air Temperature Measurements in Common Weather Station Networks, J. Atmos. Ocean. Technol., 2004, 21 1025-1032.
5. Lin, X., Hubbard, K.G. and Meyer, G.E., Airflow Characteristics of Commonly Used Temperature Radiation Shields, J. Atmos. Oceanic Technol., 2001, 18 (3), 329-339.