Is Arctic Amplification an Averaging Error?

Guest Essay by Kip Hansen — 15 April 2025 — 1200 words

Looking over one of my earlier essays, I found a note pointing to a very interesting journal paper whose findings raised an important question.  The paper is not new, it is almost a  decade old:  “Spatiotemporal Divergence of the Warming Hiatus over Land Based on Different Definitions of Mean Temperature”; Zhou & Wang (2016) [ pdf here ].

The paper was looking into this issue, as stated in the introduction:

“Despite the ongoing increase in atmospheric greenhouse gases, the global mean surface temperature (GMST) has remained rather steady and has even decreased in the central and eastern Pacific since 1983. This cooling trend is referred to as the global ‘warming hiatus’.”

We can see what they were concerned about with in this graph:

That is not the issue I am discussing in this essay, but I am basing this on the same study by Zhou and Wang.

In their discussion,  Zhou and Wang say this:

“Most of the existing studies were based on global analyses of T_a [elsewhere referred to as T_avg – kh], including those performed by several groups, such as the National Oceanic and Atmospheric Administration’s (NOAA) National Climatic Data Center (NCDC) with the Global Historical Climatology Network (GHCN, the Goddard Institute for Space Studies (GISS), and a joint effort between the Met Office Hadley Center and the University of East Anglia Climate Research Unit with Temperature, version 4 (CRUTEM4).  All of the global temperature analyses for climate detection and attribution over land performed by the aforementioned groups relied heavily on T₂.”

T₂ is defined as “the average of daily minimum and maximum temperatures”.    To be clear, virtually all the global temperature analyses rely on that metric  T₂  [ sometimes called T_avg].

An alternate to T₂ is T₂₄  — “T₂₄ was calculated from the integral [meaning, arithmetic average – kh] of the continuous temperature measurements, i.e., 24 hourly temperature measurements from midnight to midnight local time.”

The author’s find that:

“However, the warming rates of T₂ and T₂₄ are significantly different at regional and seasonal scales because T2 only samples air temperature twice daily and cannot accurately reflect land-atmosphere and incoming radiation variations in the temperature diurnal cycle.”

Warming rates were found to be significantly different, regionally  and seasonally, based on the method of determining the Daily Average Temperature for each weather station, further blended in by whatever processes to achieve a metric called Global Mean Surface Temperature (many different versions:  Land, Land and Sea, various gridding, etc)   or any of its regional siblings. 

Now, regular readers will recall that I have mentioned before that T_avg  (called T₂  in this paper because  it is the average daily temperature  found by averaging only 2 temperatures, the daily high, T_max, and the daily low, T_min) is not really the daily average temperature at all.  Strictly it can be considered the Daily Median Temperature (considering the available data set as having only the two values, Max (high)  and Min (low))  or the “Mean of the High and Low for the day” – neither of those are a proper average of the temperatures for a location (say, a weather station) for a 24 hour period.

Zhou and Wang correctly state that T₂ or T_avg “cannot accurately reflect land-atmosphere and incoming radiation variations in the temperature diurnal cycle.”

So what is the difference that Zhou and Wang found? 

“The trend has a standard deviation of 0.43 °C/decade for T2 and 0.41 °C/decade for T24, and 0.38 °C/decade for their trend difference in 5° × 5° grids. The use of T2 amplifies the regional contrasts of the warming rate, i.e., the trend underestimation in the US and overestimation at high latitudes by T2.”

The method for determining Daily Average Temperatures in all the major GMST data sets has always generally been T₂, mostly to maintain consistency with older records, which are available only as T_min and T_max.

From the paper:

“For a global average (with incomplete coverage), T2 has an important error of annual trend (0.027 °C/decade) with respect to T24 (0.002 °C/decade) during the period 1998–2013 (Table 1).”

That comes out to be a 0.025°C/decade difference. 

That may not be a lot – but in 50 years, that’s 0.125°C.

But Zhou and Wang definitely find that the averaging method used for Daily Average Temperature,  and thus all GSMT_(land), may be responsible for some of the seemingly higher rates of warming seen in our GSMT_(land) graphs from the various groups. 

They find specifically that warming rate suffers an “overestimation at high latitudes by T₂.”

This is what we often see from NASA:

Let’s see what Zhou and Wang found:

The above shows temperature trends per decade, warming and cooling by colored dots. I have put yellow boxes around the higher latitudes in the north.  Using T₂  is on the left, and T₂₄ on the right.  Far fewer red dots show when using T₂₄.   What is missing is the great Polar or Arctic Amplification.  There are warming spots in the north using T₂₄ but not nearly as many, as clearly shown in the following which shows Annual Trends under T₂ and T₂₄.

The green boxes are the areas more closely investigated by Zhou and Wang.

So, What?

I don’t know – what you see above and what you read in Zhou and Wang (2016) is what you get here (in very truncated form).

The the area denoted by green box A1 (Eastern Europe), the use of T₂ instead of T₂₄ increases the decadal trend by 0.14°C. But in A3, the higher latitudes of the South America, the increase in decadal trend is a whopping 0.53°C . 

But what is blazeingly obvious is that using (T_min + T_max)/2 [the mean between the daily high and the daily low] as the Daily Average Temperatures [T_avg or T₂] for individual stations led to a magnification of the decadal temperature trend between 1998 and 2013;  increasing the global land decadal trend by 0.0125°C/decade.   Not that much – but for five decades, that comes up to an increase in GMST_(land) of 0.0625, six one-hundredths of a degree C.

And that is merely  interesting. 

But even more interesting is that “the T2 trend shows a markedly higher overestimation in warm seasons (by ~57%) than in cold seasons (by ~3%) both regionally and globally”.  And the sharp faster warming in the highest northern latitudes is greatly reduced when Daily Average Temperature is calculated using T₂₄:  “the continuous temperature measurements, i.e., 24 hourly temperature measurements from midnight to midnight local time.”

Bottom Line:

1.  Methods and definitions matter and can change our understanding of claimed rates of change of Global Mean Temperature. As covered in my series “The Laws of Averages”, not all averages give the same result or the same meaning.  Some averages obscure the physical facts.

2.  “…the use of T2 may bias the temperature trend over globe and regions” and “the sharp faster warming in the highest northern latitudes is greatly reduced” by using T₂₄  to calculate warming trends.

3.  Zhou and Wang recommend using the Integrated Surface Database-Hourly (ISD-H, [T24]) available from NOAA.

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Author’s Comment:

I am not entirely sure about the impact of Zhou and Wang (2016) except the fact that I have not seen, in any of the NOAA and NASA global warming/climate change material,  any hint that this important paper made any difference in their approaches to calculating warming trends.

Zhou and Wang validates those of us who have railed against the T₂ approach to daily temperatures and puts to rest the insistence of some that “it doesn’t make any difference” because “we are looking at trends” or “anomalies” or “trends of anomalies”.   

Does it mean that the massive polar amplification seen in all the warming maps – that dark red swath across the top of the northern hemisphere – is an averaging method artifact?  

Just maybe….some of it at least.

Thanks for reading.

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