Wednesday, May 02, 2007

Maximums and Minimums

The world is heating up. One thing is for sure, is that there is scientific consensus on this issue! Analysis of maximum and minimum temperature have proven it. Both have gone up significantly world wide, and also too in Australia.

The maximum is used as a measure of how hot we are getting during the day, whilst the minimum is a measure of how cold we get during the night. But are they good variables to use as a measure of average temperature?

Maximum and minimum temperatures occur at different times of the day, often by large amounts when in different seasons. Surely a better measure would be to keep the time constant and see if the temperature has increased at that (and other) specific times?

But unfortunately, there doesn't seem to be a whole lot of good data lying around for this type of analysis. A large exception to this is Australian data. Whilst there is not as many time based data as maximum and minimum data, I feel that statistical analysis on the raw data is by far more advantageous than doing statistical analysis on a statistic (which is derived from the raw data).

So why has there been no scientific analysis on time based temperatures? For me it seems very strange that we can spend billions of dollars on global warming, yet still have not done the proper statistical analysis on temperatures?

The answer is simple. There is no reason to do further analysis on temperatures. We have already proven and clearly show that maximum and minimum temperatures are increasing - quite dramatically in fact. As we said earlier, there is scientific consensus on this. The world is heating up and this is beyond doubt.

So why do more analysis on something that is crystal clear and proven beyond recognition? So, naturally, noone has.

Hence we are stuck in a scientific world where we are spending billions of dollars on what will happen when the world heats up, and what we can do about it, yet have not done a full statistical investigation about how the world is heating up.

We know why the world is heating up (Co2 emissions, right?). We know who (humans of course). We know where (the entire world, especially where there is ice). We know what (our pagan earth). We even know when (now, and the devastating effects it will have on our children's children).

But we do not know how. We only know that maximum and minimum temperatures are increasing.

But as most scientists will argue, this is plenty of evidence to prove that we are warming up during the day and at night. In fact, evidence suggests that minimum's are increasing at an even greater rate than maximum temperatures (which lead some scientists to believe in the urban heat island effect etc.).

Whilst most will say that the maximum temperature is a reasonable statistic to relate to average temperature during the day (time based temperatures is obviously better), how good does the minimum temperature relate to the average temperature at night?

Maximum temperatures occur generally when the sun is at it's hottest. Well at least when we feel it the most. Generally this is around 3pm, but changes dramatically in the different seasons and weather conditions. 3pm is almost the middle of the day. It's a little later than the middle, and maximums occur a little later than the middle due to the atmosphere warming up (by the sun). Still, we as civilians, are always interested in the maximum predicted temperature by the weather forecasters as a reference to how hot tomorrow will be.

But when looking at minimum temperatures, the issue is different. As a general rule, as soon as the sun sets we start losing heat in the atmosphere and the temperature will slowly subside. It will keep going down and down until, you guessed it, the sun warms up the atmosphere and then rises.

So the minimum temperature will occur right at the end of night time - the period shortly before light. Is the minimum temperature therefore a good representation of night temperatures? Would you think that taking the temperature at sunset would be a good representation of how hot the day is?

The answer is quite clearly no. Whilst we can suggest that maximum temperatures is a reasonable (although not fantastic) statistic when it comes to it's relation with average daytime temperatures, the minimum temperature is a terrible representation of how cold a certain night is.

This being for a couple of reasons. One; in that it is not generally the minimum temperature around the middle of the night, and two; in that it is actually influenced by the sun.

The what? the sun? How on earth can the minimum temperature be influenced by the sun?

Well it does. A warmer sun would heat up the atmosphere at a greater rate, just at the time where we would normally achieve a minimum temperature. Warmer days (thanks to a hot sun!) would result in hotter nights. Maximum and minimum temperatures are related and both are quite dependent on the strength of the sun.

So what has any of this got to do with global warming? Well, tomorrow, we will show you exactly why minimum temperatures are a poor statistic in measuring overnight temperatures and will prove the suns influence and changing behaviour over time.

In short, we will prove to you that global warming - the increase in maximum and minimum temperatures - is primarily due to increases in solar radiation.

And you don't want to miss that!

11 comments:

Anonymous said...

nice analysis. looking forward to your next post

Steve M said...

One or two comments...

Firstly, there's been a good body of literature by the solar-terrestrial physics community looking at irradiance variations in recent times and through history - as irradiance is strongly linked with solar magnetic activity by the production of bright "faculae" during more active periods. These studies (I believe Sami Solanki and Judith Lean have both done good recent reviews) do not bear out the idea that the Sun is forcing climate sufficiently to explain observations.

Secondly, as you point out "minimum temperature will occur right at the end of night time". Exactly. This could be considered as the 'ground state' - the temperature to which the Earth will fall given the previous heating. You then say that this is an terrible indication of overnight temperatures. Yes. It is. No-one is denying that (unless there's a general public misconception I'm unaware of). The minimum temperature is exactly that, the minimum (a de facto 'ground state'). Also, in terms of calculating global means, minimum and maximum temps are robust to season and location - temporal recordings are not (they vary relative to epoch with season and latitude).

Thirdly, climate has various feedback mechanisms. If the Sun is getting brighter and warming Earth more, then given the same feedbacks, the Earth would warm. I guess this is your argument. Great, but if you modify the feedback mechanisms (with aerosols, CO2, methane, water vapour, etc.) then you also modify the response. The big question is then... how much of the observed heating is due to the Sun, and how much is due to the modified feedbacks? That question is being addressed by many solar physicists and climate scientists (and there's a substantial body of literature).

Don't get me wrong, I'm interested in your results. I'd really like to see that you're taking the physical systems into account though. Statistics is a tool that can be wielded expertly to great effect. It can also mislead. Still further, it can say nothing of note.

Questions that need to be addressed by any use of statistics are: Are my hypotheses well defined? Are they physical? Are my tests appropriate? Have all the assumptions of my test been met? (That is often ignored... many natural systems do not provide i.i.d. data, ruling out parametric tests)

I could go on, but this is your blog, not mine!

Jonathan Lowe said...

good respose steve m.
Firstly, i know there is plenty of literature out there on solar physics and the like, but this is not what this blog is about. I am after all, not a physicist, but a statistician.

Thirdly (coming back to secondly next!), i do understand the nature f statistics (it's my job, profession and area of research), hypothesis testing and appropriate test of significance (i have spent nearly 8 years studying stats at uni), so all concern relating to the reliability of the test etc. need not be upheld.

I can't do statistical tests on CO2, water vapour, aerosols, methane etc without significant data on the distribution of these and analysis of temperature data alone. I am aware of the feedback mechanisms, but i am also aware that should co2 be the major cause of global warming, then we would see an increase in temperature throughout the day and night.

Secondly (hmm), in terms of calculating global means, i agree with you on the differences of robustness in max/min and temporal recordings, however my analysis does not calculate global means, but looks at anomalies from the expected for every individual location and season. So the issue of robustness of location and season here is irrelevant. Thus making analysis of anomalies for time based data well and truly more meaningful and significant than analysis of anomalies of max/min


Thanks for the great comments steve

Phil_B said...

Steve, re your first point.

Increased solar radiation at ground level doesn't have to result from increases in solar radiation. It could equally well result from atmospheric effects, such as clouds and particulates, both of which have changed significantly in recent years.

re, your second point, changes to time based data averaged over a year (I assume Jonathan is not cheating) would not vary with season and latitude.

re, your third point. What makes Jonathan's analysis interesting is that it appears to tie observed warming, which is restricted to specific times of day, to a specific cause, increased solar radiation at ground level. Various feedbacks may well be occuring, but unless they can be shown to only operate (or operate with increased intensity) at the times the warming is observed, I fail to see their relevance.

J. Hansford said...

I was put onto this site Johnathan by a link from Andrew Bolts site.

I will put your blog in my favourites and watch with interest your project on statistical analysis of the Max and mins...

Interesting stuff. I made a few posts that didn't work though. Messed up the registration whatsit thingamajig thingy. But I got it sussed now.... apparently?

Phil_B said...

Jonathan, one specific prediction you may be able to test from your data sets.

If increases in daily minimums are caused by increased solar radiation at ground level, then the minimums should be occuring earlier in the day, because increased solar heating will exceed radiative cooling sooner(irrespective of the time of year).

Daily maximums should also occur later in the day, although I would expect the effect to be less than the change to the time of the minima.

Jonathan Lowe said...

hi phil,
i actually asked the BOM 2 days ago for time based minimum temperatures. eg, the time at which the minimum was recorded (even average time) for he Australian weather stations.

Apart from the last 10 years (which isn't good enough to measure a trend), the data does not exist. Even the last 10 years, one has to feed through minute by minute temperature records...something that would take a long time, and probably provide no extra information.

Steve M said...

Phil_b,
thanks for the comments. To reply:

Increased solar radiation at ground level doesn't have to result from increases in solar radiation. It could equally well result from atmospheric effects, such as clouds and particulates, both of which have changed significantly in recent years.
This is what I was getting at in my third point... an increase in warming could easily be due to the Earth system having been modified, thus altering transmission and feedbacks.

re, your second point, changes to time based data averaged over a year (I assume Jonathan is not cheating) would not vary with season and latitude.
I disagree. By averaging time-specific data over a year the error (due to the local time not reflecting the same part of the day/night cycle) may average to zero (or not), but that doesn't make it a good way to proceed. Tropical sites would be least affected though. Comparing 3am temperatures (for example) between a temperate (think Tasmania) and a tropical (say, near Cairns) site, would be practically meaningless. By 3am, Cairns (regardless of season) has been cooling since the early (and rapid) sunset. In summer (winter), Hobart will have been cooling for a longer (shorter) period, from a relatively higher (lower) temperature. Comparing across a latitudinal band may still have some relevance, but it would need to be interpreted very carefully.

Of course I'm not suggesting that Jonathan is not being careful or thorough, but my point is that statistics have to be done with specific regard to the system. The statistical tests may be fine, the results significant, but statistical significance is only meaningful with a good hypothesis and physically meaningful interpretation. This is what I was commenting on. I don't have a particular problem with using maxima and minima as they reflect the temperature relative to epoch.

re, your third point. What makes Jonathan's analysis interesting is that it appears to tie observed warming, which is restricted to specific times of day, to a specific cause, increased solar radiation at ground level. Various feedbacks may well be occuring, but unless they can be shown to only operate (or operate with increased intensity) at the times the warming is observed, I fail to see their relevance.
Assuming, for a moment, that observed warming is caused solely by increased solar radiation at ground level. Now, as you said in your first point, this doesn't have to come from increased solar output. The only way these can be reconciled is by the Earth system having changed. If the transmission has changed, the feedbacks will almost certainly have changed too. If the warming is at specific times of day (relative to sunrise/sunset, one would imagine, as nature doesn't have a watch) then this could be due to modified loss mechanisms. So what could modify the transmission, feedbacks, loss mechanisms, etc.? This is where we get back to understanding climate and have to look at what's changed in the system (e.g. different kinds of pollution - aerosols, particulates, CO2, methane...)

Jonathan Lowe said...

thanks stevem,
i can assure you that utmost care is taken in statistical analysis when looking at different times and areas. eg. times at 3am for example, are looked at based on a month variable (eg time at 3am in tassie in Mar 1900 is compared to time at 3am in tassie in Mar 1901 and Mar 1902...etc etc.), hence eliminating any bias that wold occur at different times of the year as well as different areas.

Phil_B said...

I should have said, re, your second point, changes to time based data averaged over a year at a specific location (I assume Jonathan is not cheating) would not vary with season and latitude.

Of course, comparing time based data between separate locations such as Cairns and Hobart would be meaningless, but Jonathan is not doing this. He is comparing data for one location over time.

Jonathan seems to have identified a phenomena that current climate models may or may not be able to handle and may require changes to the premises underlying the models. I don't know I'm not a climate modeller.

I also suspect there is more to this than has been revealed to date. My suspicion is that changes to maximum and minimum temperatures are due in large part to earlier minimums and later maximums than to overall warming. That is, we may be seeing an effect that changes daily maximum and minimum temperatures more than it contributes to warming. The effect could be climate neutral, producing no net warming at all and still produce this result if changes to radiative heating cooling balance each other out.

Also, in terms of calculating global means, minimum and maximum temps are robust to season and location

I'd question this premise.

I'd also point out that daily minimum temperatures typically occur in daytime (some time after dawn) and therefore will be effected by daytime heating particularly an increase in early morning heating.

Luke said...

Probably obvious but did you make the adjustment for the move from Post Offices to airports?