Why nights can warm faster than days - Christy & McNider vs Davy 2016

At WUWT, Anthony Watts has written about a new paper by John Christy and Richard McNider, which was published in Journal of Applied Meteorology and Climatology of the American Meteorological Society. The researchers were looking at trends in summer-time maximum temperatures centering the analysis on three cities in Alabama, and using stations in Alabama and Tennessee. The purpose was to come up with a methodology to construct "long-term datasets by accounting for heterogeneities or changes in the observed time series without the use of station metadata".

There was a press release for the paper, which seems to have been picked up by almost no-one, except WUWT (archived here). In it the authors say:

In addition to creating some arcane mathematical tools useful for creating climate datasets, the team also found daytime high temperature data is less likely to be contaminated by surface issues — such as deforestation, construction, paving and irrigation — than nighttime low temperatures.

However I cannot find anything in the paper that supports that specific finding of contamination, or not strongly so.

In the abstract the authors say:

Summer TMax is a better proxy, when compared with daily minimum temperature and thus daily average temperature, for the deeper tropospheric temperature (where the enhanced greenhouse signal is maximized) as a result of afternoon convective mixing. Thus, TMax more closely represents a critical climate parameter: atmospheric heat content.

That's not quite the same argument as surface contamination, so I don't know if that's what John Christy and Richard McNider were referring to or if I missed something in the paper. I'm not sure if that second conclusion about atmospheric heat content is correct, either. Perhaps someone knowledgeable can contribute in the comments.

The thing is that at WUWT, Anthony Watts presented this as an argument that climate change should be measured by trends in daily maxima, which is not what the authors were arguing. Anthony supported his own unique "argument" by posting three charts of annual (not summer) maxima, minima and mean temperature trends for Las Vegas (not Alabama). I'd say he didn't read the press release, let alone the paper, or if he did he didn't understand them.

There is a difference between saying that summertime daily maxima are a better indicator of atmospheric warming (if they are), and that annual daily maxima are a better indicator of climate change. There are a lot of useful indicators of climate change. Land surface temperature trends are important to those of us who live on the surface, for example. Ocean warming is important for monitoring changes to fisheries and coral reefs (as in the current widespread destruction of and damage to coral reefs through bleaching). Monitoring melting ice is important when it comes to monitoring sea level increase.

Finding breakpoints in station data without station metadata

The paper was mainly about using summer time maximum temperature (TMax) trends for regions in Alabama to work out where there are discontinuities in the temperature data, such that they constitute break points. That is, discontinuities that could signal that a weather station has been moved, or that the time of observation has changed. From that analysis they could then generate a cohesive time series showing the actual temperature trends. The authors said:

...a major focus of this investigation is on assessing the results of a methodology used to generate relatively small-region temperature time series and trends of the average of TMax during summer [June–August (JJA)] for three population centers in the interior of the state of Alabama. 

Christy and McNider list several reasons for focusing on summer time maxima temperatures. They listed them as follows:

One unique aspect of this paper is its focus on summer daily maximum temperatures. There are a number of advantages in using JJA TMax as a climate indicator [discussed in Christy et al. (2009) and McNider et al. (2012)]:

1. TMax is less influenced by microsite changes than is TMin (Runnalls and Oke 2006) and thus TMean;
2. the JJA daytime boundary layer is almost always well mixed in this geographical region (unlike the nocturnal boundary layer), so the value of TMax represents a larger mass of the atmosphere being impacted by radiative forcing changes and therefore a more robust measurement; 
3. time-of-observation issues dependent on passages of cold fronts, for example, are virtually eliminated as the diurnal cycle is fairly consistent in JJA; 
4. the impact of major climate circulation regimes (ENSO, NAO, etc.) is minimized in the relatively quiescent tropospheric circulation of JJA; 
5. many of the early recording stations were active only in the warm half of the year; and 
6. disruptions due to severe weather are minimized. 

Other artificial shifts, such as time-of-observation changes or station moves, are still of concern. For example, observing TMax at 1700 local time (LT) risks double-counting the hottest days versus taking observations at 0700 LT, when the risk of double-counting the coldest TMin events is high. Such artificial shifts are part of the set of inhomogeneities we seek to detect and remove.

Those all seem quite reasonable in themselves for the main purpose of the paper. The authors said "the heart of this investigation is the methodology used to find and correct for inhomogeneities in climate station data." The aim was to find inhomogeneities using pairwise comparisons, without using any station metadata other than the station location. Most of the paper was devoted to this purpose, with a lot of discussion about previous studies and breakpoint detection and similar. I'm not competent to discuss the merits or otherwise of their approach to finding breakpoints. (Steven Mosher found fault with it, though he doesn't explain his reasons very clearly.) They talked about how to best recognise a breakpoint in the data of any particular station, and the width of the time window, writing:

Apparently, the character of the time series being examined here generates the most consistent reconstructions when the window-width N is 36–48 months wide, or when a potential breakpoint contains 18–24 months on either side, representing 12–16 yr of overlapping JJA observations.

Update: Victor Venema has let us know that he's written a useful comment on the techniques used in the paper to identify breakpoints - as a blog article. Dr Venema is leader of the Task Team on Homogenization of the World Meteorological Organisation.

Summer time maxima as an indicator of trends in atmospheric heat content

The argument added by Christy and McNider was that TMax was a better indicator of atmospheric heat content than TMean or TMin. This point was made in the abstract and early in the paper, but didn't resurface until toward the end, in the discussion. The authors wrote (my emphasis):

A major focus of this paper is on determining the magnitude and confidence of a single metric known as the linear trend (b1) of a 132-yr time series of JJA TMax over a region ~350km in length and ~100km in width. The philosophy of using b1 as a metric is embedded in a more fundamental physical quantity—the rate of change of the heat content of the troposphere, a metric that much more directly relates to determining the accumulation or depletion of energy in the climate system. For reasons described in the introduction, the analysis of JJA TMax is an attempt to utilize a long-measured surface variable that may be a useful proxy for the more climate-relevant variable of tropospheric heat content.

I'm wondering if something might have changed between the early version of the paper and the published version, because I couldn't find the "reasons described in the introduction", except perhaps right at the beginning where they talk about detecting the human signal and understanding the construction methodologies of time series:

Climate change investigations, especially those related to the climate’s response to the growing human influence on total forcing, depend in part on analyzing surface temperature time series of over 100 years in length. These series start at a time when the human portion of the climate forcing would have been insignificant, allowing for the possibility of detecting an emerging human signal. Various methods utilized to assemble these time series have been reported in numerous investigations (e.g., Peterson et al. 1998;Li and Lund 2012). Because the signal being sought is a small change over a long time period, it is necessary to understand the construction methodologies of these efforts, the impact of parametric variations in the methodologies, and the confidence one may have in the results (Menne and Williams 2009; Williams et al. 2012). 

The authors referred to a few studies to support their choice of summertime TMax as a proxy for tropospheric heat content, writing about a "pathway", though I'm not sure what pathway they were referring to:

A very recent example of further support for this pathway is shown in the reconstruction of temperatures in Spain in which the TMax trend was becoming increasingly cooler relative to that of TMin (Gonzalez-Hidalgo et al. 2016). As mentioned earlier, Runnalls and Oke (2006) and Christy et al. (2006, 2009) indicated such differential trends in TMax and TMin were likely due to human development around the immediate area of the weather stations and not to changes in deep atmospheric radiative forcing.

The authors then spend quite a bit of time comparing the JJA [June to August] TMax with lower troposphere trends over Alabama and over the USA. The upshot seems to be that TMax at the surface and TLT (lower troposphere) aren't in synch at smaller scales, or over Alabama, but there is a better correlation over the USA as a whole. The reasons for the differences were discussed in terms of the boundary layer and moisture.  As part of a longer conclusion, Christy and McNider wrote:

The high value of explained variance between JJA TMax and TLT over regions the size of the conterminous United States indicates JJA TMax can be useful as a proxy for tropospheric variations. This is important because the tropospheric layer represents a region where responses to forcing (i.e., enhanced greenhouse concentrations) should be most easily detected relative to the natural background. 

Whether the authors were trying to justify the UAH record of lower troposphere temperatures or not, I don't know. The next few months could shed more light on this, given the release of version 4 of RSS data. (So far, I couldn't find any published RSS v4 data that separates the troposphere above the USA, however RSS version 4 for TTT shows the lower troposphere warming faster than indicated by UAH lower troposphere data. These aren't strictly comparable. I think RSS TTT doesn't include as much of the (cooling) stratosphere as does UAH TLT, so as I understand it, it's probably a better indicator of overall tropospheric trends).

The importance of the height of the boundary layer in diurnal temperature trends

The discussion about boundary layers got me looking at other research. There was a paper published last month, in which Richard Davy and colleagues discussed the influence of the boundary layer on diurnal temperature. The diagram below was used to illustrate:

The interesting thing about Davy16, in comparison with Christy and McNider16 is that the former found that in the boreal cycle, the boundary layer depth was the strongest predictor of temperature trends in all seasons except summer, writing:

...it is the boundary-layer depth which is the strongest predictor of the strength of temperature trends in the boreal annual cycle, and in all seasons except the summer.

Despite the focus in the discussion and conclusions, Christy and McNider wasn't primarily about diurnal temperature or boundary layer impacts. It was mainly to see if they could determine breakpoints in time series data from weather stations without using station metadata. Therefore it would be unfair to compare what they wrote with a paper that is devoted solely to looking at diurnal differences in temperature trends, as Davy16 does.

Christy and McNider argue by press release that summer time temperatures should be used because, as they say in the press release (but not in the paper itself) that:

In addition to creating some arcane mathematical tools useful for creating climate datasets, the team also found daytime high temperature data is less likely to be contaminated by surface issues — such as deforestation, construction, paving and irrigation — than nighttime low temperatures.

That mention of a finding about contamination is not correct - or not that I could see. The authors did mention the difference between lower troposphere and surface trends at the local level, and they did provide data suggesting that soil moisture and precipitation may have contributed to the difference in particular years but it wasn't a major finding, nor a strong one. They also mentioned the change in land cover in rural Alabama since the 1930s, but all they say is that it "may" explain some of the temperature trends, but that "the present study cannot address this possible causality but it may be consistent with the long-term trends and reduced connectivity to TLT over Alabama."

Again, perhaps the press release was about a different version of their paper, or maybe I missed something that they wrote. Let me know if you find anything else.

Diurnal differences in warming

The paper by Richard Davy et al published last month delved much more deeply into the observed asymmetry in diurnal variations in temperature trends. In fact, that was the whole topic of the paper. As explained in the press release at ScienceDaily.com:

The layer of air just above the ground is known as the boundary-layer, and it is essentially separated from the rest of the atmosphere. At night this layer is very thin, just a few hundred meters, whereas during the day it grows up to a few kilometres. It is this cycle in the boundary-layer depth which makes the night-time temperatures more sensitive to warming than the day.

The build-up of carbon dioxide in the atmosphere from human emissions reduces the amount of radiation released into space, which increases both the night-time and day-time temperatures. However, because at night there is a much smaller volume of air that gets warmed, the extra energy added to the climate system from carbon dioxide leads to a greater warming at night than during the day.

While Christy and McNider argue that the summer time maxima is a better indicator of overall tropospheric warming, Davy16 makes the point that night time minima are very important for human endeavours. Differences in night vs daytime temperature changes affect human health as well as agriculture (cropping and animal husbandry). As stated in the press release:

Understanding the different sensitivity of night and day-time temperatures is crucial for our understanding of climate change and it's affect on human health. This daily cycle in temperature directly affects human health since night-time temperature extremes can trigger temperature-related fatalities. But it also indirectly affects human health by controlling the growth rates of vegetation, and so affecting the length and stability of crop-growing seasons.

If you are wanting to understand the differences in day vs night temperature changes, Davy16 is a good paper to read. It has references to several other papers on the subject as well, including a paper co-authored by Christy and McNider in 2012, which was focused on the boundary layer and diurnal variation in temperature trends.

Davy16 looked at the importance of the boundary layer height, together with the other known influences on diurnal temperature, namely: cloud cover, soil moisture and precipitation. All of these factors play a part. Davy16 makes the point that the impact of the planetary boundary layer (PBL) is most pronounced in higher latitude continental regions because it is colder, therefore the boundary layer is more shallow.

From the maps of the linear regression of reciprocal PBL [planetary boundary layer] depth against SAT [surface air temperature] anomaly, we expect the boundary-layer depth to be of most importance in determining the temperature response in cold, continental regions, such as Siberia, which are dominated by shallow boundary-layers. We have used station data from this region to test the prediction that the PBL will play a dominant role in determining the nature of temperature trends/variability such that: the night-time temperatures exhibit more variability and stronger trends than the day-time temperatures and that this effect will be more pronounced in winter as compared with summer. In both cases, the colder conditions can be related to shallower boundary-layers (there is a shallower boundary-layer at night than during the day, and in winter as compared with summer) and so these times are expected to have the stronger SAT response to forcing.

Decline in variability of surface temperature

One interesting point made by the authors of Davy16 was that the variability of temperatures is decreasing, particularly in night time temperatures. They wrote:

...the variability of both Tmin and Tmax have decreased with a more pronounced decrease in the variability of Tmin. There has been both a greater decrease in the number of cold extremes, and a greater increase in the number of hot extremes, in Tmin than Tmax. This illustrates the greater sensitivity of the Tmin than the Tmax to the increased forcing during this period, consistent with our expectations.

Diurnal differences arise from cloud cover, soil moisture, precipitation and boundary layer height

In Davy16, the authors make the point that the discussion of planetary boundary layer influences is something that adds to the other known influences, namely cloud cover, soil moisture and precipitation. It is particularly influential when the boundary layer is much shallower at night than during the day. That is, in higher latitudes in the cooler months. In the conclusion, the authors wrote:

While there are many factors which may asymmetrically affect the radiative forcing on the diurnal extreme temperatures, here, we demonstrate that the night-time temperatures are inherently more sensitive to perturbations to the radiation balance and will warm more rapidly on a uniform forcing (such as that from the build-up of greenhouse-gases). This effect is most pronounced in regions where there is a strong diurnal cycle in the boundary-layer depth, with shallow boundary-layers forming at night.  

Diurnal temperature range

Just after posting this article, I discovered there's another paper on diurnal temperature, by Peter Thorne and a whole host of other people, including Richard Davy. It's paywalled, but if you've an AGU subscription, you can read it here.  It is a detailed analysis of the changes in the diurnal temperature range over time. One finding is that the range has decreased globally (though not everywhere), which is consistent with the Davy16 paper I discussed above. However the estimated changes in the diurnal temperature range are an order of magnitude smaller than the increase in maximum and minimum temperatures.

Oh, I missed that this was one of a pair. The other paper is a comparison of the diurnal temperature range from different independent data sets, and can be found here.

From the WUWT comments

Sparks didn't like the UAH press release from Christy and McNider, and complained:

April 29, 2016 at 4:23 pm
“When the cool layer of air near the surface is disturbed, warmer air aloft is drawn down to the surface.”
Buzzzzz Wrong!!
Warm or “cool layer” or any “disturbed” fragment of your imagination that can invent scenarios about air is flawed.
Pressure differences in the atmosphere produce warm and cool air. you seem to suggest to me that (correct me if I’m wrong) warm and cold air come from ‘thin air’ so to speak, and that warm air floats about on a planetary scale, my god man?
“warm air blows cold air about” That’s all I heard :)

Sparks' comment drew lots of comments from other people who tried to explain the boundary layer, with examples. Leo Smith wrote:

April 30, 2016 at 1:43 am
Anyone who flies model aircraft at sunset learns about boundary layers.
AS the sun goes down the earth cools off faster than the air above, and at a given point the temperatures are roughly the same, and thermal activity ceases, and so does surface wind.
Flying in and out of that layer is ‘interesting’ 

Anthony's charts of Las Vegas temperatures fooled Tom Halla, who not only drew a flawed conclusion, but seemed to think (wrongly) that they were from the UAH authors:

April 29, 2016 at 4:25 pm
it is very interesting how one could make several mutually contradictory arguments from the graphs. By one set, Las Vegas is warming at a fairly regular rate. By another set, it was warmer in the 1940’s. Kudos to UAH.

No, the charts are complementary, not mutually contradictory. Night time minimum temperatures in Las Vegas are increasing more quickly than the daytime maximum.


Ric Werme said he thinks that surface and atmospheric temperatures are both useful:

April 29, 2016 at 4:51 pm
I bounce back and forth as to the utility of ground level low temperatures. On one hand, looking at the whole atmosphere is important, and the temperature for much of the day reflects that. Once the morning inversion burns off, then sunlight can bring the entire air column into vertical mixing and one temperature measurement covers a lot of volume.
On the other hand, ground level is where people, animals, and crops live. The crops killed in 1816 in New England were generally killed by cold morning air. Radiational cooling is important! Radiational cooling in Las Vegas is confusing, as it’s a mix of cooling slowed by greenhouses gases, but more importantly slowed by land use changes, urbanization in this case.
I’m afraid we’re stuck with both for the indefinite future. As long as we use them well, they’ll be useful.

Menicholas thinks the same:

April 29, 2016 at 5:07 pm
I did not think that the article was making the point that low temps, nighttime temps, or ground level temps are unimportant, but that one can track changes over time better and more accurately by using daytime temps, and in particular, daytime high temps.
Many of us here have the belief that nothing unusual is happening recently with the temperature, but that many of the data sets are corrupted by UHI and data tampering.
The daytime graph shows us what Tony Heller has been pointing out for a very long time…that the most recent years are not unusually hot.
Most if not all of any recent increases are because it is less cold at night.
As anyone who has spent a lot of time outside at night observing temps in various locations over a small area can attest, buildings and pavement of any sort have a profound influence on how much and how fast it cools once the sun has set. The more dramatic the nighttime cooling, the bigger the difference in temps near any structures or paving. The difference is most dramatic on clear and windless nights with low humidity, when cooling is most rapid.
These are also the times when damage to crops tends to occur.

I don't know about where Tony Heller lives, however in my part of the world, daytime temperatures have been rising rather a lot:

John Harmsworth seems to accept that the high northern latitudes are warming, but can't quite bring himself to accept that it's global, or because of CO2 emissions, or whatever:

April 29, 2016 at 8:36 pm
I don’t really argue with your assessment of these data trends. The rising trend of nighttime temps immediately makes me think UHI effect. However, there does seem to have been a strong trend of warmer temperatures in the Arctic and down to about 50 degrees latitude. I think there is every likelihood that this is related to a longer range weather trend. Not climate, which implies some sort of “paradigm change”, but an aspect of global weather patterns we don’t understand. I personally feel that AGW is based on simplistic assumptions and has become a religion that obstructs and attacks good science.

Brian Jones isn't capable of doing his own research (such as using Google).:

April 29, 2016 at 5:08 pm
What I have never seen is an analysis of when the supposed warming is occurring. Is most of it occurring at night and if so why is that the case. 

FTOP_T is a greenhouse effect denier and proud of it:

April 30, 2016 at 7:12 am
The tropopause height is variable by season due to the intensity of the sun. Higher in summer, you can calculate the surface temp by using the lapse rate from that higher point.
Thus, max temp is limited by this max height. Any moisture lowers the lapse rate so very dry in summer is the limit and tropopause height is the mechanism.
Robinson & Catling accurately calculated temps for any gaseous planet by my identifying the tropopause height and calculating down from there.
Contrary to all the AGW lunacy, the atmosphere cools the earth. There is no such thing as a “greenhouse” gas. There are radiative gases, but they do not change the lapse rate.
One day this CO2 charade is going to end.

jon gets something important to him off his chest. Not sure what that is:

April 29, 2016 at 6:29 pm
They failed to show the quantitative difference between people pulling down hot air and the heat being emitted from the asphalt etc when people are in bed, not milling around outside pulling down hot air. So how ca they claim there is a significant effect from this milling around at night?
Where’s the evidence?
Of course there’s even more milling around in the daytime (maximum temperature time) so it’s even harder to separate the two. 

Steven Mosher linked to a chart of annual maximum temperature for Alabama, and then explained his objection to something or other, probably the notion that surface summer maximums are a better indicator of atmospheric trends, or maybe something else:

April 30, 2016 at 11:12 am
The point is simple. The data for all 12 months exists.
How many seasons did they look at?
Why not look at other months.
Etc.
Also. They have developed but not independently tested an adjustment methodology.
Good science would require you to compare multiple adjustment methods. And to test it on synthetic data.
They did neither.
So you have a paper that violates the mcintyre standard.
If you introduce a new method you should test the method first. As part of a methods paper.

jim steele pontificates using flawed logic, arguing that getting hotter doesn't mean that it's getting hotter:

April 29, 2016 at 8:27 pm
If the goal is to determine how much heat is accumulating, then tracking maximum temperatures is the only valid metric. Warming minimums can skew the average upwards even when maximums are cooling. Even if minimums are rising, if maximums do not increases then there is no heat accumulation. Using the average that is biased by rising minimum temperatures typically due to landscape changes, urban waste heat and heat retaining materials, biases perception towards warming.
Maximum temperature is the only valid metric for climate chnage 

John Harmsworth thinks daytime global warming is about urban heat islands:

April 29, 2016 at 8:53 pm
I understand your assertion but I would argue strongly that daily max. Is also skewed by UHI. 

Toneb injected some science into the discussion, writing:

April 30, 2016 at 12:36 am (excerpt)
I see some on here are arguing against min temps as a measure of GW.
That metric tells us that less heat is escaping to space, and is being retained in the ground (and also the oceans).
To say that only max temps are a true measure of heat retained by the atmosphere is wrong-headed, and more importantly, does not account for that being retained by the ~93% of the energy the climate system holds – the oceans.

He has a fan in Morose, who wrote:

April 30, 2016 at 2:44 pm
I am most pleased to see a smart, obviously educated, informed and very knowledgeable climate scientist displaying their talents professionally with integrity. You are a credit to our society. Sadly, the mendacious propaganda has fooled the “poorly educated” (Trump’s classification) and perniciously politicized the topic. Most on here behave as if they’re on a reality show acting the part of a climate scientist and remain obnoxiously ignorant. Keep up the smart, well-thought out comments of science and integrity. To paraphrase Einstein it only takes one to prove him wrong, and he’d accept that graciously and embrace it. You have no competent opposition on this thread so I don’t see that happening in this forum. I know as a retired (less active) scientist you’d welcome a healthy discussion and opponent for that’s how science moves forward.

There were a few people who only see charts upside down, and claim that the world is cooling not warming. Menicholas, for example, agrees with micro6500 and writes:

April 30, 2016 at 10:56 am
“The trend is cooling, not warming.”
Agree completely.
And the more one digs down into the particulars, across a wide range of evidence types, the more obvious it becomes that this is very likely the case.
Oh, except for them deep oceans…where all that missing heat is hiding *rolls the eyes*, making our best attempts to find the truth subject to the very few individuals who control access to the measurement devices placed there.:

Data source: GISS NASA

Steve Mosher upset Anthony Watts a couple of times, which isn't difficult, with Anthony writing about nether regions and sarcasm.

References and further reading

Christy, John R., and Richard T. McNider. "Time series construction of summer surface temperatures for Alabama, 1883-2014, and comparisons with tropospheric temperature and climate model simulations." Journal of Applied Meteorology and Climatology 2016 (2016). DOI: http://dx.doi.org/10.1175/JAMC-D-15-0287.1 (open access)

Richard Davy, Igor Esau, Alexander Chernokulsky, Stephen Outten, Sergej Zilitinkevich. Diurnal asymmetry to the observed global warming. International Journal of Climatology, 2016; DOI: 10.1002/joc.4688 (open access)

• Understanding why nights are getting warmer faster than days - press release at ScienceDaily.com

Thorne, P. W., M. J. Menne, C. N. Williams, J. J. Rennie, J. H. Lawrimore, R. S. Vose, T. C. Peterson, I. Durre, R. Davy, I. Esau, et al. (2016), Reassessing changes in Diurnal Temperature Range: A new dataset and characterization of data biases, J. Geophys. Res. Atmos., 121, doi:10.1002/2015JD024583.

Thorne, P. W., M. G. Donat, R. J. H. Dunn, C. N. Williams, L. V. Alexander, J. Caesar, I. Durre, I. Harris, Z. Hausfather, P. D. Jones, et al. (2016), Reassessing changes in Diurnal Temperature Range: Intercomparison and evaluation of existing global dataset estimates., J. Geophys. Res. Atmos., 121, doi:10.1002/2015JD024584.

McNider RT, Steeneveld GJ, Holtslag AAM, Pielke Sr RA, Mackaro S, Pour-Biazar A, Walters J, Nair U, Christy J. 2012. "Response and sensitivity of the nocturnal boundary layer over land to added longwave radiative forcing." J. Geophys. Res. 117: DOI: 10.1029/2012JD017578 (open access)

Karl TR, Kukla G, Gavin J. 1984. Decreasing diurnal temperature range in the United States and Canada from 1941 through 1980. J. Clim. Appl. Meteorol. 23: 1489–1504. DOI: http://dx.doi.org/10.1175/1520-0450(1984)023<1489:DDTRIT>2.0.CO;2 (open access)

Karl, Thomas R., Richard W. Knight, Kevin P. Gallo, Thomas C. Peterson, Philip D. Jones, George Kukla, Neil Plummer, Vyacheslav Razuvayev, Janette Lindseay, and Robert J. Charlson. "A new perspective on recent global warming: asymmetric trends of daily maximum and minimum temperature." Bulletin of the American Meteorological Society 74, no. 6 (1993): 1007-1023. DOI: http://dx.doi.org/10.1175/1520-0477(1993)074<1007:ANPORG>2.0.CO;2 (open access)

Lewis SC, Karoly DJ. 2013. Evaluation of historical diurnal temperature range trends in CMIP5 models. J. Clim. 26: 9077–9089. DOI: http://dx.doi.org/10.1175/JCLI-D-13-00032.1 (open access)