Odd Introduction to a New Paper

The Rabett has an interesting post about a paper that appeared recently in Climate of the Past on temperature trends in data measured at the Mauna Loa Observatory (MLO). Most of us are very familiar with the data on CO2 concentration from Mauna Loa, but I didn’t know there’s also temperature data from the same location since 1977. Interestingly, the data are not just monthly, not just daily, they’re hourly, and because MLO is an atmospheric observatory, the data were recorded not just to the nearest whole degree, but to the nearest 0.1 deg.C.


Malamud, Turcotte, and Grimmond estimated trends in the data from 1977 through the end of 2006 (there’s a bit of 2007 data but not nearly the whole year). They did so for each hour of the day, in order to determine trends in the daytime pattern as well as the overall daily mean. Even before it was published, their research came under scathing criticism from Tim Curtin at Jennifer Marohasy’s blog as part of a general denigration of estimated warming in Hawaii. Curtin is up to his usual level of competence — deplorable. Those who wish to delve into that interesting drama can get the story from the Rabett (at the first link).

There are a few things which, analysis-wise, I did differently, but it makes little difference to the final results. They began by removing 7 leap days, then they infilled missing values. If data for a missing hour were present for that same hour within 7 days both before and after, the preceding and succeeding values were averaged. If not, values were substituted from the subsequent year for the same hour and day of the year. They needed to interpolate missing values because they didn’t remove the annual cycle from the data, so missing values could introduce a substantial bias. I omitted the interpolation step, instead removing the annual cycle to define anomaly. I think this is a better way, since there were a couple of sizeable gaps of about a month’s time which I’d prefer not to interpolate. Removing the annual cycle also reduces the data variance, allowing for smaller error ranges — but the improvement is not very much. I repeat that their procedure is valid and the results I got are not significantly different from theirs.

They then computed annual averages for each hour. This eliminates any measurable autocorrelation from the data. The autocorrelation of daily values is substantial, and doesn’t follow a simple pattern like AR(1) or ARMA(1,1), so I think this is a good approach.

Finally they estimated trends by least-squares regression, separately for each hour of the day. This not only enabled them to estimate the overall rate of warming during the period of record, they also obtained an estimated warming rate for each hour of the day.

I estimated the annual cycle by a 6th-order Fourier series fit, then subtracted that from the data to define anomaly. Then I carried out the same procedure as Malamud et al., computing annual averages and estimating the trend by linear regression. The numbers I got are very similar to theirs, in fact they’re “statistically” the same since the differences are far less than the uncertainties.

Malamud et al. found that most hours of the day showed a warming trend, which was strongest during nighttime hours. For the midnight hour they estimate warming at a rate of 0.039 deg.C/yr (the stated error range is 1-sigma, i.e., the standard error):

I got a slightly lower figure, 0.037 deg.C/yr (numbers in parentheses are standard errors, i.e., 1-sigma, and note this graph gives the rate per century rather than the rate per year):

The standard errors according to both analyses are much larger than the differences between the results.

For noontime, Malamud et al. estimate cooling at a rate of -0.014 deg.C/yr:

I got cooling at -0.016 deg.C/yr:

Again, the differences are much less than the standard errors.

Here’s their estimate of the warming rates for each hour of the day:

And here’s mine:

Again, our results are the same, but my graph looks different because I plotted 2-sigma error bars to give approximate 95% confidence intervals whereas they plotted 1-sigma error bars. There’s nothing wrong with that, in fact it’s extremely common, but I just couldn’t bring myself to plot 1-sigma error bars.

It’s clear that analysis-wise, Malamud et al. got the right answers.

In addition, they studied the patterns for individual seasons, showing that warming overall was greatest in spring and smallest in fall/winter:

They also estimated the diurnal temperature range (DTR), showing that has declined substantially:

It’s abundantly clear that for this very high-quality data set, temperature has warmed overall but the diurnal temperature range has declined so that there has been noontime cooling but considerably greater nighttime warming.

While I endorse their data analysis, there are parts of the discussion about which I’m highly skeptical.

They interpret their results by tying the local pattern of temperature changes directly to changing CO2 concentration. I’m not a climate scientist — but my impression is that the chain of causality is different. While the overall trend is indeed due to global warming, it’s truly global temperature that is directly influenced by greenhouse gas concentrations. Local and regional patterns follow suit, but the differences between different locations are more governed by other factors. In fact, I would expect the local nature of Mauna Loa temperature to be a combination of overall global warming with such influences as changes in evaporation and humidity, and regional factors like the el Nino southern oscillation. On the whole, I find their attribution of local patterns directly to CO2 changes, and their argument that Mauna Loa temperature patterns can be interpreted in a global context, entirely unconvincing.

And there’s one aspect of their discussion which I find, frankly, simply not credible:


A possible explanation for the middle of the day cooling is that the enhanced surface heating is actually resulting in greater mixing and therefore a decrease in the near-surface green house gas concentration which would reduce incoming longwave radiation.

Again, I’m not a climate scientist or atmospheric physicist, but I was under the distinct impression that CO2 is reasonably well-mixed, not only geographically, but in terms of altitude, except at locations which are major sources such as large metropolitan and industrial areas. The Mauna Loa observatory is on the “big island,” which is pretty rural, and it’s at high altitude as well, so I expect it to be isolated from such influences. Therefore even if there is greater atmospheric mixing at mid-day, I wouldn’t expect that to reduce near-surface greenhouse gas concentrations. If in fact there is a diurnal pattern in CO2 concentration and/or its rate of growth, I would expect that to be due to the diurnal cycle of plant respiration, not due to greater or lesser atmospheric mixing.

This is something we can investigate with actual data, because we can access hourly data for CO2 as well. I mimicked the temperature analysis by computing, for each hour of the day, the overall average growth rate of CO2 at MLO, to look for a mid-day decrease relative to other hours. Here’s the result:

There’s no sign of lesser growth in CO2 at mid-day. In fact this implies that indeed, any time-of-day difference in CO2 growth rates is due to the daily cycle of plant respiration.

On the whole, I suspect they read way too much into the possible relationship between local Mauna Loa temperature trends and the global state. To my mind, the causal relationship is not CO2 –> local change, it’s CO2 –> global change –> local change. Nonetheless, their trend analysis of MLO temperature records is sound, establishing local warming overall, with pronounced nighttime warming and slight (in fact not really statistically significant) mid-day cooling combing to significantly reduce the diurnal temperature range.

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29 responses to “Odd Introduction to a New Paper

  1. Last paragraph,
    “mid-day cooling combing to significantly reduce the diurnal temperature range.”
    “combing” or “combining?”

    A question too, I don’t fully understand the suggestion that the hourly CO2 change graph implies a changing diurnal pattern due to plant respiration. The diurnal CO2 range may exist due to plant respiration but the shifting range would either imply a shifting behavior in plant respiration (slowly becoming less during the day? and why?) or that some other factor is at play to enhance the CO2 range. I don’t think the last graph you gave can point toward either answer any better than the other.

    [Response: I think it does, because the diurnal cycle of the change in CO2 growth rate matches what we expect of the diurnal cycle of plant respiration. But I agree that it's hardly settled. In any case, there's no sign of lesser mid-day growth rate in CO2 concentration, and all hours of the day have seen substantial growth of CO2 concentration.]

    • So this is clear too, I am not trying to promote the alternative proposed in the paper, I agree with your discussion on it.

  2. David B. Benson

    At what altitude is the temperature being measured? Is the enough data to estimate (the diurnal variations in) the lapse rate for that location?

  3. I think that the temperature record at Mauna Loa is interesting for at least a few reasons. If you look at global warming projections for the tropics (roughly 25S to 25N), you see amplified warming with height and weak horizontal gradients in the temperature trend, particularly in the free troposphere (above roughly 850 hPa or ~5,000 feet). There are good physical reasons for this behavior. In the tropical free troposphere, horizontal temperature gradients are constrained to be weak because waves and the Hadley circulation efficiently redistribute heat throughout the entire tropical belt. In the middle and high latitudes (where the Rossby radius of deformation is smaller), this constraint does not hold and temperature gradients can be larger. The amplification of the temperature trend with height in the tropics results because the free tropospheric temperature lapse rate tends to follow the moist adiabatic lapse rate of the deep convective regions, and the moist adiabatic lapse rate decreases (temperatures decrease less with height) as surface temperatures warm. (“Skeptics” like to argue that the absence of this upper tropospheric “hot spot” in the tropics is evidence the climate models are wrong, but evidence increasingly suggests that the missing hot spot is due to problems with the radiosonde observations.)

    The end result is that I would expect the Mauna Loa temperature trend to be larger than the surface trend (rough estimate based on Mauna Loa elevation and my feeling of moist adiabatic lapse rate adjustment suggests around a factor of 2 larger) and more representative of large spatial scales than in non-tropical, non-elevated regions. However, Mauna Loa is a volcano on an island with fairly complex topography, so I would expect some local influence that I don’t have a good feel for. Also, I don’t have a good idea for the diurnal variability, but I agree that the authors’ explanation is not plausible.

  4. I’ll send Bruce over here, but my impression of the idea was that MLO is so high and barren that it does sample the free troposphere. CO2 variations from plant respiration in the jungle below would take some time to get up there, and be smeared out by the ascent. Anyhow that was my guess

  5. CO2 variation from the jungle below is actually a problem at MLO:

    There is often a diurnal wind flow pattern on Mauna Loa driven by warming of the surface during the day and cooling during the night. During the day warm air flows up the slope, typically reaching the observatory at 9 am local time (19 UTC) or later. The upslope air may have CO2 that has been lowered by plants removing CO2 through photosynthesis at lower elevations on the island, although the CO2 decrease arrives later than the change in wind direction, because the observatory is surrounded by miles of bare lava. In Figure 2 the downslope wind changed to upslope during hour 18. Upslope winds can persist through ~7 pm local time (5 UTC, next day, or hour 29 in Figure 2). Hours that are likely affected by local photosynthesis are indicated by a ā€œUā€ flag in the hourly data file, and by the blue color in Figure 2. The selection to minimize this potential non-background bias takes place as part of step 4. At night the flow is often downslope, bringing background air. However, that air is sometimes contaminated by CO2 emissions from the crater of Mauna Loa. As the air meanders down the slope that situation is characterized by high variability of the CO2 mole fraction. In Figure 2, downslope winds resumed in hour 28. Hour 33 in Figure 2 is the first of an episode of high variability lasting 7 hours.

  6. Just eyeballing the CO2 chart, this looks like the first derivative of diurnal temperature. (Which should be easily confirmable with the data you have on hand.) Perhaps what we’re seeing is the change in absorption and release rates of CO2 from oceanic top layers (and/or soils) due to temperature changes.

    Regarding midday cooling, anyone who has spent much time on tropical islands knows that cumulus clouds form over the islands during the daytime due to convection and evapotranspiration. We should expect increasing warmth to increase both of these processes, leading (paradoxically) to increased midday low cloud cover. Note that this is very much a microclimate response, not a global one.

  7. Following up on the previous comment, remember too that Mauna Loa is at 13000 feet, so another factor might be the increase in mean density altitude at which the daytime cumulus forms. As that goes up, the top of the mountain would become increasingly likely to be clouded over rather than clear.

  8. Thanks for this post. While the data for on location may not be important in the big picture, it is fascinating to have such accurate hour-by-hour data to play with.

  9. It is known that the GHE is more noticeable at night.

    Could it be that the local temp variation would be negative over this period without the GHE (for whatever reason), and thus it appears so when the GHE is less pronounced?

  10. On a tangentially related issue…

    Does anyone know anything about cooling of the tropopause over the tropics? And elsewhere for that matter.

    I’ve been using NCEP/NCAR composites to look at the recent cold winters and their cause, mainly the suggested solar role. The cooling pattern is common to all the recent years I’ve looked at, e.g. 2005

    I suspect that this is part of the pattern of cooling of the stratosphere but haven’t found anything concrete on it.

    Can anyone help?

  11. Would US Air Force bases be a good source for such detailed temperature data?
    They have to monitor weather conditions at all times for flight safety and as long they don’t regularly toss out records after they reach a certain age, they could be a real gold mine of information.
    I was thinking in particular about the base on Guam

  12. 0.37 deg C per decade at midnight? MLO is at 19N; as GISSTemp latitdue bands show (http://data.giss.nasa.gov/gistemp/graphs/Fig.B.lrg.gif), 0.16 C per decade is the rate usually quoted for low N latitudes from globally averaged data. That’s a bit less than the mean of 0.2C per decade on the ‘all hours’ graphic. Makes me a believer in ‘nights warming faster than days’.

  13. David B. Benson

    The next to last paragraph of the paper offers an explanation for the slight downward trend in daytime temperatures at the Mauna Loa observatory.

  14. David B. Benson

    “Each day the cloud cover rolls up Mauna Loa from the Hilo area. It fills the saddle first, then reaches the observatory by late afternoon. This is a daily cycle.” from
    http://www.photolib.noaa.gov/htmls/corp2685.htm

  15. Greetings,

    I apologize for being off-topic, but perhaps Tamino could write a post about a rather curious new choice of fit in Roy Spencer’s “Latest Global Temps” graph?

    [Response: Precisely which graph are you referring to? Do you have a link?]

  16. I have not seen any of this before, but after reading the paper and this/Eli’s blog, I am surprised that the reactions to the article are not much more critical than they have been. I have no problems with the statistics, but getting data and calculating trends for CO2 or temperature as a function of time of day is rather trivial and would make a good undergraduate thesis for an end of semester project. But the climatological implications forwarded by this paper do not at all follow and their discussions of attribution (or what it means in the context of IPCC’s climate sensitivity estimates, etc) are borderline nonsensical. Even if some of the calculations are algebraically or statistically correct, this paper adds no insight into atmospheric physics or “climate of the past” and shouldn’t have published.

    They spend a page talking about how their T trend estimates are in line with the very large range you’d get from multiplying climate sensitivity by 5.35 ln(C/Co). So what? Given the uncertainties in CS, that would probably be true for an incredibly large number of individual stations. In any case, given that we are far out of equilibrium, it would have been better to use a transient climate sensitivity. They did not even compute dF correctly in the follow up to equation 1 , since you get about 0.86 W/m2 with their values (not 0.72), though I suspect that is a typo in what they used for their 2006 CO2 concentrations, which looks more like 2011 values. But a transient sensitivity closer to about 1.5 C for a doubling of CO2 is appropriate (see e.g., Table 4.1, Assessment of Climate Models: Strengths and Limitations, USCCP), in which case they’d get dT=(1.5/3.7)*(0.72) divided by the time interval ~0.009 C/yr. That is just on the edge (if not outside) of the low end of their value “dT/dt =0.021Ā±0.011C/yr.” inally, how does a coincidental agreement with IPCC dT/dt estimates imply that the site is necessarily a global representative?

    Also, the radiative forcing for CO2 is not a globally uniform field, even though CO2 concentrations are well mixed. It tends to be higher at TOA in the tropics and lower in the tropics for downward radiation to the surface, per 2xCO2. To do the radiative transfer right you need to account for different temperature structures/tropopause heights and overlap with water vapor/clouds, which gives the forcing heterogenity.

    Their next section on DTR is meaningless and says nothing physical other than agreement or disagreement of Mauna Loa compared with other studies that do a spatial average. Again, so what?

    Their following discussion section is just qualitative hand-waving, there is no attribution. Mauna Loa is such a regional area, it should be affected by much more than just CO2 (they warn in section 3 that the PDO matters here, as if this means something). They ignore many other studies on global or regional DTR trends that show trends are largely the result of global dimming/brightening, clouds/humidity changes, or other regional influences and not necessarily CO2. Their high school level thought experiment about day vs. night mixing and back radiation is hopelessly unconvincing, and also ignores the top of the atmosphere perspective of the greenhouse effect people like raypierre have cautioned for in other studies of this sort, like
    http://www.realclimate.org/index.php/archives/2005/11/busy-week-for-water-vapor/

  17. Interesting past discussion on Measuring CO2 levels at Mauna Loa, and the diurnal cycle, ending earlier this year:

    http://www.skepticalscience.com/Measuring-CO2-levels-from-the-volcano-at-Mauna-Loa.html

    Note the last part: [The Mauna Loa volcano rises high above the Pacific on the Island of Hawaii. "Here, the background concentration of carbon dioxide should not be influenced by forests or soils, or an inversion or the weather,ā€ Tans says. All that is stripped away.] which is from http://www.climatecentral.org/news/in-the-curve-monitoring-rising-carbon-emissions.