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 CO 2 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 CO 2 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 CO 2 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 CO 2 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 CO 2 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 CO 2 as well. I mimicked the temperature analysis by computing, for each hour of the day, the overall average growth rate of CO 2 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 CO 2 at mid-day. In fact this implies that indeed, any time-of-day difference in CO 2 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 CO 2 –> local change, it’s CO 2 –> 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.