0 When was climate normal?

It's been a couple years since I took up the question of normal climate, so time for another go.  At that time, I used monthly data from Hadley, and arrived at the observation that if you're younger than 26, you've never seen a month where the global average as as cold as the 1850-2011 average, 317 consecutive months (at that point, now over 330) of warmer than 'normal' temperatures.  I'll cheat and give you some answers first, read on to see how they're established:

• Climate was 'normal' only between 1936-1977
• Every year 1987-present has been warmer than any year before that
• 1976 was warmer than any year before 1926
• 1978 (next coldest year of the recent run) was warmer than any year before 1940

Do read on to see what 'normal' winds up meaning; it's important!  One part of 'normal', as we intuitively think about it, is that you should some times above it, and sometimes below.  Having many consecutive years above 'normal' says that normal isn't really very good.  To help get quantitative about how to proceed, consider this plot of NCDC's data (warmer/colder than the 1880-2012 average -- the length of the entire record).

From this we see that every year 1977-present is above the zero line, much the same as we had in my earlier note.  But, which I paid little attention to at the time, every year in the early part of the record -- everything to 1936 -- is also below the 'normal' (0 anomaly) line.  A long run of negatives is as good a disproof of things being part of the 'normal' as a long run of positives.  Further, 1976 is much colder than all the years which follow and 1937 is much warmer than all the preceding years.  So this makes a good span, 1936-1977, to try to call 'normal'.  It does still satisfy our requirement that to call temperatures climate we want at least 20-30 years, though, at 42, we can't afford to lose many off either end of the record.

This satisfies one of the traits for 'normal' -- no long runs of always above or always below normal at the start or end of the record.  But another trait we often require is no trend.  That is a continuation of the idea that climate is stable in some meaningful sense.  The trend for 1936-1977 is indeed zero.  So for this span, it is indeed reasonable to say that there's a normal climate that weather is bouncing around.  Here's what the data themselves look like, using 1936-1977 for the reference:

This also looks a lot like what intuitions say should be the case for a 'normal' climate, not just the math coming out that way.  As it's 42 years, it's long enough to satisfy our usual requirements for a climate reference.  So now let's look at the whole record against this 'normal':

After seeing this, I have to say that our intuitive demands lead us to a highly unusual 'normal'.  The 1936-1977 span is the only long span with a trend of zero.  The first 30ish years show cooling, next 30ish are warming, the 42 year plateau 1936-1977, and then a 35 (and counting) year warming trend.

If by normal we mean what happens most often, then (for 30 year trends) what's most common is for climate to be changing, not to be some stable reference around which weather bounces. 

Detail: When was climate normal?

0 Is climate a random walk?

Let's pick up again the discussion between Tamino and me.  He has objected to my use of cumulative sums on the grounds that cumulative sums of random numbers have bad behavior statistically.  He's correct about that statistical point, naturally, which means caution is needed regarding the statistical part of my post on finding a climate normal.

But how concerned should we be as climate scientists?  Crucial to that concern is that climate be, to a fair degree, experiencing random variation.  It isn't, strictly.  As Tamino mentioned, there is certainly a trend in more recent years -- not purely random variation.  His criticism is more one against the cumulative sums method.  As Jim Bouldin mentioned in the comments recently, we do routinely transform variables in order to study topics of scientific interest.  In his case, plants.

I'll start by showing you an illustration of why Tamino is concerned.  This is a plot of the cumulative sum -- of a purely random variable, with uniformly random numbers in the range plus or minus 1 degree.  This is actually about 10 times too large for climate.  So the late period value of 40 really means 4 degrees.

Each tick mark is 1 month, but assumes that each month's random number is completely independent of each other.  That isn't the case, as Tamino has documented.  This curve manages to accumulate its 4 degrees in about 200 years.

Er, it accumulates that climate wandering in only 200 years!.  That and the smooth curves, suggest why we cannot take climate to be random wandering over long periods.  Volcanoes suggest why we cannot do so for short periods either.  Intermediate periods might be ok physically.

The upper and lower curves are growing proportional to the square root of the number of months.  Random walks are known to do this.  We can't tell whether such an accumulation will head for the warming or the cooling side, but we can be confident that over time, the cumulative sum will move away from zero.  I've loaded my spreadsheet for this in Open Office and Excel formats.  I do encourage you to pull one of these down, or write your own, and look at a few dozen examples of what can happen with cumulative sums of random numbers.  As Tamino said, you can find all kinds of interesting results -- that have nothing to do with anything meaningful.

Let's go back to that 4 degree accumulation in 200 years.  That's gargantuan compared to real climate changes.  The 200 years comes out partly because of the nature of randomness used in my spreadsheet, so don't be too wedded to it.  It could easily be more like 2000 years with a better approximation to climate's random nature.  I'll hope that Tamino or one of my more mathematical readers take this part up.  The other thing is, the accumulation is unbounded -- wait long enough and any limit you put, 4 C, 20 C, 100 C, ..., will be passed.  It will take about 25 times as long to pass 20 C warming or cooling, so maybe as fast as 5000 years!?

Regardless, however, of the exact period, the random walk is quite happy to move away from a reference climate by 4 C in a pretty short period.  Ok, long compared to how long I expect to live.  But quite short compared to the 100,000 years or so of an ice age cycle.  Global mean temperatures change by about 5 C in an ice age cycle.  So this 200 (or 2000?) year accumulation of 4 C is enormous, and fast. 

But we don't see that in the ice age records.  Temperatures cool by about 5 C going in to an ice age.  It takes a while.  The thing is, we don't see global warmings and coolings of several degrees occurring routinely each few hundred or few thousand years.  We don't see 20 C changes at all.  What we see instead is that there's a more or less smooth cooling going in to an ice age, and a more or less smooth warming coming out of one.  There are occasional large shifts in regional temperatures (the Younger Dryas, for instance, coming out of the last ice age).  But there are never such large temperature shifts as the random walk looks to expect.

The reason is, climate variation is not a purely random process.  This is no surprise, of course, and no surprise to Tamino either.  The climate system has an idea of what its reference temperature is.  That is, if temperatures are a bit higher than normal, it's more likely that the next change will be a cooling.  Not necessarily the next month, due to the autocorrelation that Tamino has mentioned.  But sooner than later.  -- Unless there's something pushing the climate to a new reference temperature.  I'll illustrate this, from data, in a post to follow.  It provides, by the way, a different way to look for a period of 'normal climate'.  The random walk has no idea whether it is currently warmer or cooler than reference, because there is no real reference.

This gives a sense that over long periods (even if we're not exactly sure of what 'long' means -- 200 years in this example) climate isn't really a random walk.

Volcanoes let us see this return to reference temperature over short periods.  When a major volcanic eruption throws a lot of dust in to the upper atmosphere, the earth cools.  This, itself, is highly non-random.  Throw junk into the upper atmosphere, cool the earth.  Never do we see a warming from it.  No surprise there.  What follows is the interesting part.  Over time, the earth warms back up to about where it was before the eruption.  That time is a few years.  If climate were just a random walk, after that eruption the earth would be as likely to cool as warm.  And a few years after the eruption, the earth could just as easily be markedly cooler as back to its normal.  Yet what we see is the earth returns to its pre-eruption temperature.  Those old enough to remember Pinatubo (1991) experienced this fact themselves.

There certainly is randomness to global climate.  If there weren't, we would be able to make perfect climate predictions.  On the other hand, the randomness is limited somehow.  The climate system does have an idea of what temperature it would be at if it weren't being disturbed by something (volcanoes, El Niño, greenhouse gas releases, etc.) and tends to return towards that.

For the discussion between Tamino and me, I'll suggest:

1. We do want to be cautious about using cumulative sums.  They have bad statistical behavior against random processes.


2. We do not have to give up on cumulative sums in studying climate.  Real climate is not a purely random process.


3. Since climate does seem to have the ability to tell where its 'normal' is, at least over very short (few year) and long (few hundred? few thousand? years) periods, we still have a chance at locating a 'normal' climate.


4. In respect to that, it is reassuring that the length of time over which the normal climate was found in the original post is 90 years -- not just 20-30.


5. "More research is needed"

#5 is the almost universal conclusion for scientific discussions.  I'll hope that Tamino or others take up the question of what more realistic noise would tell us about climate as a random walk processes.  I'll take up a different novel approach to climate myself shortly.  Instead of sums, it will be differences.  They're subject to problems, just as sums are, but they're different problems.  If we get to the same conclusions by both methods, we can be more confident of our conclusions.

Detail: Is climate a random walk?

0 How to find climate normals?

It's that time of the decade when the official 'climate normals' are computed -- according to the rules of the WMO and NOAA (in the US).  But can we find a better way of deciding 'normal'?  I'll do some thinking out loud here, and invite you to play too.  Could we even be so lucky as to find a way of defining climate normal in such a way that we don't need to worry about an early period of 'coming out of the Little Ice Age', or a later period of Anthropogenic Global Warming.

In previous posts, I illustrated that there are principles which lead to the requirement of 20-30 years to define a climate average and, separately, 20-30 years to define a climate trend.

In those approaches, we were able to make good use of the adage that climate is what you expect.  It was only after 20-30 years of data that our expectations for the mean or trend would be stable -- would not depend sensitively on how long a period we chose to be our data period.

This time, I'll pick up with a different notion or description.  A common description of climate is also that sometimes its warmer and sometimes it's cooler, but it all averages out in the end.  Let's start by looking at the Hadley-CRU temperatures, back to 1850, month by month.  I'll start with looking at temperatures relative to the average over the entire data set:

For the earlier part of the record, we see the deviations being both above and below the reference value.  On the other hand, the last 26+ years, every month since December 1984 -- 317 consecutive months, has been above the reference value.  That's not a sign of sometimes warmer, sometimes cooler.  That's the recent period being different from 'normal'.  For instance, because of a warming trend.  If you're younger than 26, you have never seen a month where the global mean was as cold as the 161 year average.  On the other hand, looking at the early part of the record, we see some years warmer than 'normal' even though most are cooler.  Further (look directly at the original data, don't take my word) there are no periods as long as even 20 years of continual below reference temperatures.  In other words, the Little Ice Age, insofar as it was global, had ended by 1850.

But, can we do something else to explore the notion of 'normal'?  Those wiggles in the curves are not all the same size.  If we were to add them up, would they sum up to zero?  They have to do so over the whole record -- that's what the average means; you have just as much above as below average, by just as much, observations.  If the numbers are mostly just wandering around, then the sums from the start of the record to a given month should also wander, sum times totalling more than zero, sometimes less.  Here's what happens for using the 161 year average as the reference:

That's clearly not a matter of climate wandering around the reference point we chose!  The first 80 years are almost uninterrupted decline in total temperature anomaly, while the last 30 are an aggressive warming -- in 30 years compensating for the 80 years of cumulative cooling at the start of the record.

A word about what this sum means.  It is an accumulation of heat or cold compared to our reference number.  It is the same concept as heating degree days, frost degree days, and cooling degree days.  Since it is summer here, I'll go with cooling degree days.  (I'll actually describe it in hours.)  Suppose you're ok with temperatures as warm as 77 F (25 C), but will want to run the air conditioner if it is warmer than that.  Of course the air conditioner has to run harder if it is hotter.  So hour by hour (day by day) what you do is add up how many degrees warmer than 77 you are.  A day with 5 cooling degree hours means you don't run the air conditioner much.  A day like today here will have something like 200 cooling degree hours.  You appreciate very much the invention of air conditioning on a day like this!

In the case of global mean temperatures, month by month, what we have above is cooling degree-months.  Let's say that glaciers all experienced global mean (which, of course they don't, but I'll use for the sake of description).  Further, let's suppose that glaciers were all in balance in 1850.  And (again not exactly true) let's assume that colder temperatures mean glacial growth.  That large accumulation of cooling degree months suggests that glaciers should have been growing from 1850 through 1930, then retreating until the present -- just now retreating to their position in 1850.  We actually observe that glaciers have retreated behind their 1850 locations, so, again this doesn't look like a good reference to choose.

The good reference temperature, and good definition of climate 'normal' will show us some temperature accumulations that cross back and forth across zero.  And about half the months should be above normal, or below normal.Given the original figure, we don't want to include the last 30 years at least.  So I took 1850-1979.  Well, again, didn't behave very well.  I backed it up a decade at a time until I finally found a period which gave a well 'behaved' in these senses 'normal'.  It is 1850-1939:

Now this looks like what we've been told climate is like -- sometimes warmer, sometimes cooler, and on average not going anywhere.  The sums hit zero 3 times in these 90 years -- about 1856, 1880, 1892, come close around 1902.  The zeroes in 1850 and 1940 are because that's how we constructed the curve, so they don't count.  Having found a period that behaves like a 'normal', now let's look at the rest of the resulting curve to the present:

Whoa!  Not only are there no more zero crossings, meaning that climate's accumulated tendency for the last 70+ years is one of warming, but it's hard to even notice any declines in the sums.  They're there, but you have to look very carefully on this scale.

The scale is another thing to look at carefully.  In the first 90 years, the largest accumulation we see is a net cooling of 30 degree-months.  It took about 20 years to get there (about 240 months), and about 20 years to warm back out of it.  Those mean a cooling or warming bias of about 1/8th (0.125) degree per month being a normal number in climate.  Numbers of that magnitude have appeared elsewhere (if you've got a memory like mine, you might recognize figures like this from earlier posts, otherwise, don't worry) which grants a certain degree of comfort.

But the more recent period, 70 years of it, shows 10 times as large an accumulation as the 'normal' period!  328 degree-months accumulating in 70 years.  This averages to a warming bias of 0.39 degrees per month, triple what happened in the normal period.

(Update) You can see the scale issue more easily in this figure, with the whole period on the same scale:

I confess I was quite surprised to see this result.  One response to that is to invite you all to find my mistake (if you can't find it, maybe I didn't make one).  My spreadsheet is available in Open Office and Excel formats.  The other thing I'll invite you to do is to use different climate data sources.  Maybe this conclusion depends on having used the HadCRU data?  Let us know what you get if you use the NCDC, NASA, JMA, and so forth data sets instead.

In the mean time, it looks like there has been a fundamental change in climate since 1940.  Something has been active since 1940 that wasn't active before 1940.  The good news being that we actually arrive at a period when we can call climate to be 'normal' -- 1850-1940.  Further, since the NOAA and GISS data start in 1880 rather than 1850, it's reassuring that our reference choice here shows 1850-1880 to be a span of zero accumulated cooling/heating.  So we could reference 1880-1940 instead.

Something else we can do is take a look at the reference value again, and how long it has been since we've been below that.  Using the anomaly values as given by HadCRU, the normal value for climate is -0.334.  The normal period they chose was quite a bit warmer than the 'normal' period of the climate system it turns out.  The last time the global mean was below the climate normal was March, 1976.  If you're 35 or younger, you have never seen a global mean below climate's real normal*.  The most recent month in the data, May 2011, is 0.667 K above the climate normal, 1.2 F warmer than normal.

*Assuming, of course, that I didn't make a mistake somewhere.

Update2: It seems that blogger is having problems with comments.  That's particularly unfortunate here as I think there are likely many good comments getting choked by the system.  If you've had this problem, please email them to me at bobg at radix dot net.  3: Problems seem to be resolved now.

Update4: Tamino has some illustration and discussion of hazards of using cumulative sums.  It's a statistical argument, naturally, so this affects portions of this post which are statistical in nature.  On the other hand, as one of the commenters there noted, there's a well-known and important paper on climate by http://www.aos.princeton.edu/WWWPUBLIC/gkv/history/Hasselmann76.pdf Hasselmann, 1976 which points out the physical importance of cumulative sums.  I'll take up these and related ideas in a full post.

Update 5 (8/8/2011): Let's also take a look at how close climate is to being random

Detail: How to find climate normals?

0 Were the 70s cold?

I was surprised to see that the 1970s weren't particularly cold.  My surprise is partly because where I lived (Chicago area) we were busy setting all-time records for cold, and that was true for much of the US and across to the UK. 

The other part of the surprise is that it's common to hear people (see them write) something on the lines of "Of course we're seeing a warming since the 70s; it was cold in the 70s!"  Surely someone along the way did their homework and checked out what the global temperatures were?

Fortunately, if we're looking at science, we don't have to assume that other people did their work, or did it correctly.  The alternate word for it is, skepticism.  Real skeptics don't make those assumptions, they do the work themselves.  The fact that it's work also explains why there are a lot of fake skeptics -- it's much easier to pick the answer you like and reject everything else.

So let's apply some real skepticism and ask what was really going on with temperatures in the 1970s.
I'm working from the NCDC global mean temperatures.  I'll take the average of each decade they give, and plot that:

That's rather disappointing.  The 1970s were the 4th warmest (of 12) decades in that record.  Actually a little worse, as you'll notice I don't have the decade starting in 2000 computed.  (I downloaded the file in 2009, it's gotten warmer since then). 4th warmest of 13 decades, behind only 1940s, 1980s, 1990s, and 2000s. But -- be a proper skeptic -- compute for yourself the average for January 2000 through December 2009.  I got +0.35 for the 1990s.

My disappointment is twofold.  First off is that the decade that I remember as being so very cold, wasn't.  In my area it was, and even for a good distance away.  But the entire US is only about 2% of the globe.  The global average could easily be quite different, and turns out that it was.  The 1970s were a relatively warm decade.

The second part of my disappointment is that those people calling themselves skeptics are clearly not skeptics.  They never computed decadal temperatures, and never looked to see whether the 1970s were particularly cold.  Not only were they not cold, but they were warmer than the two decades before them.  Real skeptics would not claim that they were cold in talking about climate change.

Detail: Were the 70s cold?

0 Climate -- cycles 1

One of the things we expect about the weather is that it will change.  Following the dictum, as I do, that climate is what you expect and weather is what you get, change is part of climate.  But what changes do we expect?  One sort of change we -- those of us living in middle or high latitudes (above, say, 30 N, or 30 S) -- expect is that winter will be colder than summer.  Namely, we expect an annual cycle to temperature.

As part of a different project, I've computed the size of the annual cycle in the 2 meter air temperature.  (When meteorologists talk about 'surface air temperature', it really means the air 2 meters above the ground). The scale is degrees Celsius for the amplitude -- the difference between the average temperature and the warmest, or between average and coldest. If you want the range between the warmest part of the annual cycle and coldest, double this number. If you want the amplitude in Fahrenheit, double it (well, multiply by 1.8).

This is a beautiful scientific picture. Why, may not be immediately obvious, and there is more to the story than the annual cycle. 

One thing is, remember that I like time series analysis, and some of the concepts from there, I'm using here.  In saying 'annual cycle', I actually mean a perfect sine wave that goes from peak to peak in exactly 1 year.  While the seasons do repeat on a 1 year basis, they don't do it precisely on a perfect sine wave.  In the sense of music, there are overtones.  Not just 1 cycle per year, but also 2 cycles and 3 cycles.  Those figures are below and I'll get to them in more detail later.

I confess that the beauty of the picture is not the color scheme or labelling, or pretty much any graphic arts aspect.  The beauty is in the science.  On seeing the picture, several ideas leap to mind:

• Annual cycle is higher over land than water
• Annual cycle is higher on eastern sides of continents than western
• Annual cycle is higher at high latitudes than low latitudes

All seem pretty reasonable at the casual eyeball level.  Putting them together, we'd expect the greatest annual cycle to be on the eastern side of a continent at high latitudes.  Siberia fits that bill well, and we do see the greatest annual cycle in eastern Siberia -- about 65 N, 130 E, 27 C!  (warmest to coldest of 54 C, 97 F!).  So that's a good start.

But here's the fun: let's try to get rigorous about it.  Is it always the case that the cycle is larger farther to the pole (still being on land, and just as far east)?  Well, no.  Antarctica is certainly farther to the pole than 65 degrees -- it goes all the way to 90, and poleward of 78 it is all land -- there's no western edge to the continent.  Yet its annual cycle is not as large as Siberia's.  More interesting, the largest annual cycles in the Antarctic are seen at the edge of the Ross Sce Shelf and the Filchner-Ronne ice shelf (Weddell Sea).  Edge of the continent rather than interior.  We also see that in southeastern Mongolia, the annual cycle is larger than in the part of Siberia to its immediate north, and for a good distance. 

Hmm.  An idea of mine is that when you have a fairly decent general rule, if something breaks the rule, you can learn something interesting by studying it.  Exceptions are more interesting in science than rule-following.

Let's now take a look at the 2 cycles per year (semi-annual cycle) figure:

A quick look at the color bar tells us that the magnitudes are substantially smaller -- maximum is only 10 C instead of 27 C.  It's also quite striking, though, that the Arctic and Antarctic are the places with the largest amplitude for this cycle.  Also northernmost Siberia and Alaska, Hudson Bay, southern Baffin Bay and ... central India (!?). 

Aside from India, the places with high amplitude semi-annual cycles a) are places that experience at least 1 day of no sun at all (namely, they're above the polar circles, 66.5 N or S) or b) have sea ice cover.  But some places that have sea ice cover (the Sea of Okhotsk, for instance) don't have a large annual cycle.  So probably we will wind up at a more complex rule.

The size of the semi-annual cycle in Antarctica is so great that it has a 'coreless winter' (van Loon's excellent term).  At the same time as the annual cycle is heading for its coldest temperatures, the semi-annual is heading for its warmest.  And with 8-10 C amplitude, that offsets a lot of the coldness you'd otherwise see.  Instead of steadily cooling off through the winter, the way, say, Siberia does (notice that Siberia doesn't have much of a semi-annual cycle), Antarctica gets cold soon, but then temperatures hold relatively steady until spring.

And we still don't know what's up with India.  (Actually, I do, but that's because I plotted some other figures.)  Some further research to be done.

At 3 cycles per year (ter-annual), the sizes are even smaller -- now reaching only up to 2.7 C.  Almost all the places with large ter-annual cycles are sea ice places, particularly the Ross Sea, Baffin Bay, north of Eastern Siberia and Western North America, and the Sea of Okhotsk. 

Excluding the sea ice places, we see northern India and the Tibetan plateau as regions with large amplitudes.  What leads to that?

Since these are expectable features of temperatures -- getting warmer and colder on a regular schedule, by observable amounts -- they're climate.  (Yes, I used at least 30 years of data!).  If we want to understand climate, these are features to understand.  If we think we have a good model for climate, they're figures to compare against.  And ideally, you'll develop a theory that can predict all these observations.

No grand final answers.  Mostly just observations.  But they're observations that strongly invite you (me, anybody interested in science) to try to answer.  The annual cycle portion of this started being studied over 90 years ago -- C. E. P. Brooks, Continentality and temperature, Quarterly Journal of the Royal Meteorological Society, 43, 159-174, 1917.  (He examined more factors than just the three I mentioned.)

I do have the numbers, and will be happy to make them available once we figure out how.  They're on an irregular grid (the spacing in longitude is regular, but the edges of the boxes in latitude are different distances apart).  I prefer working with this because it is how the data were originally developed.  But I realize that most people don't like that sort of data, and it is certainly harder to work with.  I could also construct a best approximation data set that is on a regular grid.  It would be 2 degrees spacing in latitude and longitude.  What's best, though?  Spreadsheets with latitude and longitude in a column and row respectively?  Simply listing off latitude-longitude-amplitude (for each cycle) in a plain text file?

My analysis used as its input the NCEP/NCAR reanalysis from 1962 to 2007.  The reason for that odd set of years is my other project, which starts when the International Earth Rotation Service starts providing daily observations.

An aside: One of the thing people in my fields develop is a fair knowledge of geography.  Given the number of place names I mentioned above, you see why.  It basically amounts to another sort of vocabulary.  If you want to study the earth, it helps to be able to name the place you're looking at.

Detail: Climate -- cycles 1

0 Cloud-temperature feedback

In my three feet of global warming note, I mentioned that two processes in the climate system are a) warmer temperatures -> more moisture in the atmosphere, and b) more moisture -> more severe storms.  A commenter followed up wondering how warming could actually take place, if a) more moisture -> more clouds and  b) more clouds -> cooler temperatures.

A key word there is if.  Although warmer temperatures are observed to lead to more moisture in the atmosphere, it isn't clear that more moisture actually leads to more clouds.  Section 3.4.3 of the IPCC report gives you an overview of the literature on the topic.  Depending on which scientific paper you read, it's more cloud, less cloud, or more over one surface type and less over another.  In other words, an area of significant scientific debate.

It's also a question whether more clouds mean cooler temperatures.  If you're from a cold weather climate, you've experienced that on clear days you get a nice warm daytime temperature, but also a blistering cold nighttime.  Because of those very cold nights, cloudy days can actually average warmer than a sunny day.  The daytime isn't quite as warm, but the night time is far warmer.

Let's take a deeper look in to the relationships between clouds, in particular to look at the feedback on temperature.  You'll notice that the commenter's question is about a feedback -- we start with temperature, and processes occur which ultimately lead to an effect on temperature.  What I'd originally talked about was a straightforward chain.  One thing causes another, causes another.  But no effect on the term or process that started us off.  We'll ultimately get back to the simplest climate model, as it can help shed some light on the question as well.

One aspect of the question is, just what do we mean by 'more cloud'?  If it means thicker clouds, but of the same types as already exist, that is indeed 'more'.  But it means little or no change in how much energy the clouds reflect from the sun, or how much of a blanketing effect they provide.  Most clouds are already thick enough that making them a bit thicker doesn't change their behavior as far as radiation is concerned. 

A different type of 'more' is to have more area of some cloud types.  This added area then reflects more solar energy.  But it also provides a better blanket to earthly temperature.  As result of this is, you have to look at the balance between the two effects.  This has been done, and the result is, some cloud types provide net warming of the surface, and some provide net cooling.  So your question in this becomes whether the cloudiness increase, if you do get one (the IPCC report was showing that even for total cloudiness it isn't clear whether there's more or less -- figuring out which type of cloud you have more or less of is even harder), is more of the warming type of cloud or cooling type.

But for now let's assume that warmer temperatures really do lead to more clouds, and in such a way that the net effect of those clouds is a cooling.  Can it still turn out that the climate warms anyhow?

To look at this, I'll return to the simplest climate model.  We'll have to abuse it some -- use it in ways that violate the assumptions we made in developing it.  Consequently, we can't be entirely confident about the results or trust them as closely as we'd like, but, again, it makes for a helpful heuristic to guide our thinking some before we pull out the supercomputer and start it cranking away for a few weeks.

In the simplest model, we balance incoming solar energy at the top of the atmosphere, minus what gets reflected away (among other things, by clouds), with the energy emitted by the earth.  If you the solar constant to be 1367 W/m^2 and the earth's albedo to be 0.300, you arrive at a black body temperature for the earth of 255 K (254.86), which is in fair agreement with the observations.  The earth's surface temperature, on the other hand, actually averages about 288 K.  This is our sign that to understand the surface temperature, we need more than just the black body temperature, and more processes than just the very simple energy in (at the top of the atmosphere) = energy out (at the top of the atmosphere).

Remember that the sun's rays pass through a disk of area pi * r * r, while the earth emits from an area 4 * pi * r * r.  So, if we knew how much effect changing a greenhouse gas at the surface, we could multiply this by 4 (the fact that the surface is that much bigger than what the solar rays go through) and get an equivalent change to the solar constant.  Since doubling CO2 is expected to lead to about 4 W/m^2, this means the climate effect is something like increasing the solar constant by 16 W/m^2.  If you run the simplest model with a solar constant of 1383 W/m^2, you get a black body temperature of 255.6 K, about 3/4ths of a degree warmer.  Again, this is quite different than the expected surface change (about 3 degrees K, 4 times larger), which again tells us that we need to know more than just the simplest model.

Still, it gives us our start for thinking about the effects of clouds.  Clouds do affect the earth's albedo, and that linked-to article will give you some sample numbers for what the albedo is like for different surfaces, clouds included.

Our simple method for looking at the feedback is this:
1) Start with observed solar constant and albedo, compute the earth's black body temperature
2) Increase the solar constant for the enhanced greenhouse effect, compute the new earth temperature
3) Change the albedo to represent the increased (we're assuming it's an increase) in cloud area, and compute that temperature.

If the temperature after step 3 is colder than step 1, clouds have erased the warming from greenhouse gases.  (At least they have for the black body temperature, we clearly have more work to do than this model can help us with in order to decide what happens to the surface temperature.)  If the temperature after step 3 is warmer than step one, then even though we've said that clouds increase (which is not yet observed) and it's the type of clouds that produce cooling (even more questionable), we still wind up with a net warming.

Now let's think a bit about albedo and how much it might be changing.  I'll take a very simple set of figures for illustration.  Take cloud albedo as 0.5.  Clouds can be over land -- albedo 0.2, or ocean -- albedo 0.05.  Cloud does have to be over a surface!  The importance is, increasing the area of cloud doesn't change the amount of reflected energy by the same amount everywhere.  It matters what the cloud is over.  (Over Antarctica, albedo 0.8 or so, clouds would actually lower the albedo!)  So, if we put more clouds over land (over the US one report suggests a slight increase in clouds, but then over China it's reported a decrease), the energy reflected increases by 0.3 (from 0.2 to 0.5).  On the other hand, if it's over the ocean, the energy reflected increases by 0.45 (0.05 to 0.5).  In other words, it's much more effective, in feeding back on temperature, to increase clouds over ocean than land.

We'll also remember that there's a lot more ocean (70% of the earth's surface) than land (30%).  Unfortunately for this feedback, the observations for land are the ones showing the larger changes.  The US figure (the US being about 2% of the globe) is 1.4% per decade, increase in clouds.  So, in terms of a simple estimate, we'll call it about 3 decades (which is about right), and a 5% increase in clouds.  That's over 0.02 of the globe, and is a 0.3 change in albedo.  We multiply those figures together to get an approximate net effect -- 0.05 * 0.02 * 0.3 = 0.0003.  Change of the albedo from 0.3 to 0.3003.  That cools us back down from 255.6 to 255.58, leaving us with 0.72 degrees warming instead of 0.74 -- even though we declared the feedback to exist and be of a nature to oppose the warming, it was ineffective at moderating the temperature change from greenhouse gases.

Let's make it the entire land surface of the earth (0.3) instead of just the US 2% of the globe.  15 times larger an effect, but then you also have to explain why the Chinese didn't notice it, or the Sahara desert, etc..  That is 0.0045 on albedo (0.05 * 0.3 * 0.3), raising the earth's albedo to 0.3045.  That cools us off to 255.19 K, giving a warming of 0.33.  The feedback still leaves a warming, but does noticeably reduce it.

Now let's be extreme -- distinctly more than is permitted by the observations.  Let's say that there is a 5% increase in clouds and it's over the ocean.  That makes for 0.05 * 0.7 * 0.45 increase in albedo (always I'm taking change in cloud * fraction of earth's surface that the cloud change is over * change in albedo from non-cloud to cloud conditions).  So 0.0158 change in albedo, taking us to a black body temperature of 254.15 -- making the earth 0.71 K cooler than before the greenhouse gases were added.

This points us to the central issue regarding feedbacks.  It was wrong to stop at step 3.  The temperature change due to the new albedo from step 3 has to go back to change how much greenhouse effect we get (the addition to the solar constant that we made).  Feedbacks are loops that we have to keep running around until the changes get small.  A change in warming from 0.74 to 0.72 clearly won't take long for the 0.02 effect to be resolved.  Changing from 0.74 to 0.33, probably going to take a few more cycles.  Changing from +.74 to -.71 may never converge (meaning we might just keep bouncing around, or we might just run away to some impossible answer).  We need at least a step 4 -- re-estimate the net effects on climate, and repeat your estimates in steps 2 and 3.  Repeat until successive cycles give nearly (say within 0.01 K) the same answer.

A different thing these examples point us to is how accurately we want to know albedo -- we want to observe it globally, and to better than 0.005.  In like vein, we want to know cloudiness changes more accurately than 1% per decade.  These both say things about how we need to go about observations and building new observing systems.

In any case, I think this answers anonymous's question as to how it is that we can have warming even if clouds were to have a cooling feedback.  Namely, it can happen if the clouds don't increase fast enough.  There can be a cooling from them, but not enough to offset the full effect of the greenhouse gas warming.  To be sure which way it goes, you have to get quantitative.  (And preferably with a better model than this simplest one!).  Anonymous: do you agree that your question was answered?  If not, what did I miss?


I'll flag this 'project folder' and invite folks to play with these experiments, and to contribute their own situations:

Give yourself a relationship between albedo and temperature.  Maybe it is warmer by 1 K gives higher albedo by 0.001 (this would be clouds being more widespread and of a type to cool climate).  Maybe you take -0.001 (opposite clouds, or thinking about sea ice and its albedo feedback).  Then do step 1, and cycle steps 2-4 until you do converge (give nearly the same answer from cycle to cycle).

You can also have some fun with this and consider an iceball earth.  Start with a global albedo of, say, 0.6 (something appropriate to ice), and an albedo that decreases with increasing temperature (meaning that you melt the ice and show land or ocean instead).  Kick it with some greenhouse warming due to a few hundred thousand or million years of volcanic CO2. Look at the path the temperatures take as you run through the cycles.

For the more mathematically advanced -- let your albedo function be nonlinear.  Clearly a very cold earth has a high albedo (iceball), and a very, very warm has a high albedo (i.e., so warm that we become fully cloud-covered) is also high.  But somewhere between the two, there's at least one minimum, perhaps corresponding to the present day or pre-industrial, where we have neither enormous amounts of cloud or ice.  Have a look at the stability of those conditions w.r.t. the shape of your albedo function.

Detail: Cloud-temperature feedback

0 Theory of Climate -- Examples

Now let's move from philosphy of what a Theory of Climate would look like, to some of the components.  To repeat yesterday's list:
In climate, some of our principles, or statements of theory, would include:

• Conservation of mass applies to the climate system
• Conservation of momentum applies 
• The laws of thermodynamics apply
• The general theory of relativity applies
• Quantum theory applies
• Tectonic theory
  

But notice that, as fits a  complex theory, that none of these immediately tell you that, say, the mean surface temperature of the earth should be 287 K, or how much it should change if you add a certain amount of a greenhouse gas.  Let's see, though, how these can be important to understanding climate.  This would be what our book titled 'Theory of Climate' would provide detail on.

Conservation of mass:
The water cycle is one of the climate expressions of conservation of mass.  If you evaporate water from somewhere, there is less water there.  If you condense water from vapor into cloud droplets or ice crystals (make a cloud) then there is less water vapor in that part of the atmosphere.  If those cloud droplets or ice crystals fall to earth, then there is less liquid or solid water in the cloud, but more in the patch of ground or ocean that the precipitation fell on.  This extends another step -- if some patch of ground experiences more evaporation than precipitation, it will dry out.  Or, if it is a lake or inland sea (like the Aral Sea) it will shrink.

Conservation of momentum:
This leads us to learning that winds are largely driven by pressure differences.  If something in the climate system changes the pressure differences -- say by warming the poles faster than the equator -- we expect changes to the winds.  Getting detailed about this requires paying attention to all the other effects.

Laws of thermodynamics:
This includes both conservation of energy and the entropy law.  Conservation of energy tells us that when water condenses from vapor to liquid or solid, it will release energy.  It can be quite a lot of energy -- which is what drives hurricanes and typhoons -- if you get enough water to condense.  The entropy tells us, for instance, that cloud droplets will form more readily on a nucleus of some kind -- dust or salt particle, for instance -- and something about how much.

General theory of relativity:
I don't need to worry about this in the day job, but it does apply to thinking about climate on periods longer than a few hundred thousand years.  On the few thousand to few million year time scale, the earth's orientation and orbit change (Milankovitch theory here).  Once you get past a certain point, you need to include general relativity to get an accurate orbit.

Quantum theory:
The absorption of radiation by the atmosphere depends intimately on quantum mechanics (quantum theory).  We can pretty much get away with a simple rule for emission from the surface (Stefan-Boltzmann law -- black body emission and absorption).  But the atmosphere is nowhere near a black body.  It is extremely selective about what colors of light it will absorb, and equally selective about what it will emit.  That's why we can largely ignore the major gases in the atmosphere -- nitrogen, oxygen, and argon -- and focus our attention on the rare gases water vapor, carbon dioxide, ozone, methane, and such.  Understanding the selectivity is a problem in quantum theory.

Tectonic theory:
Continents move over time, and plate tectonics is our theory for the hows, whys, and how fast.  Application of the other components of climate theory tells us that the motion of continents also changes climate.  So this is another part of a full climate theory.

Additional theories, laws, principles, ... that would be part of a full Theory of Climate are welcome.

Detail: Theory of Climate -- Examples

0 Theory of Climate -- Philosophy

Is there a theory of climate, and if so, what is it?  That turns out to be a harder question than you might think.  It's my slight rephrase of a question asked in this month's question place.  The difficulty lies in the fact that 'theory' has several different meanings.

We can dismiss the most common daily life sort of usage -- a theory is something that is false.  It's used in comments like 'That may work in theory, but it doesn't work in practice.'  If we're talking about what happens in practice, we're talking about what happens in the real world.  Scientific theories have to apply to the real world.  If your idea makes false predictions about the real world, then the idea is (at least partly) false.  And, if your idea consistently makes false statements about the world, then it is not a theory, or even a hypothesis.  If there is a scientific theory of climate, it must be making true statements.

We can also dismiss the next most common daily life usage -- a theory is a WAG (wild guess).  A common sort of theory of this type is where I, for instance, theorize that since the last time I took my car to the shop, it got good service, that the next time I go, it will as well.  There's really very little data behind that thought, and very little analysis.  But it seems like a reasonable sort of statement.  Or the 'lucky socks' theory sports fans or athletes might have.  Their team won the last time they wore a particular pair of socks, so they theorize that the team will win again (or at least have a better chance of winning) if they wear the same socks for today's game.  Again, it seems reasonable to the person making the statement, but there's little data behind it and little analysis.

Now to consider the more difficult waters, where I hope that the two philosophers I know sometimes read will comment with appropriate corrections and elaborations.

One part of math/engineering/science usage is that, in contrast to common usages, a theory is a very good thing indeed.  Actually the best you can get.  Some other terms you'll hear are conjecture, hypothesis, and law.  The 'good service' or 'lucky socks' theories, as we'd term it in common conversation, are really more in the nature of a conjecture.  We've got very little data, and very weak chains of reasoning.  But, hey, it looks ok.  After you collect more data and get stronger lines of reasoning, you have a hypothesis.  It's also better if the hypothesis covers more situations than the conjecture.  Get to the point of covering many situations, with very strong evidence and very strong lines of reasoning, and you finally have a theory.

Law is a different kettle of fish entirely.  In terms of how we do science any more, it's also an anachronistic term -- something that used to be used, but now is uncommon.  Laws, in my areas at least, are simple mathematical relations between a couple of things.  Newton's Law of Gravitation, for instance, says that the gravitational force between two bodies is proportional to the product of their masses divided by the square of their distance.  Simple relation and it's even reasonably correct.  Hard for you to test for yourself, so I'll mention another one.  Hooke's law of elasticity.  This says: take a spring (or rubber band, or piece of elastic, or bungee cord, ...) and hang it up.  Measure where the end is.  Now put a small known weight at the end and measure how much longer the spring gets.  Add a second weight, equal to the first.  You'll see (says the law)  the spring lengthen by exactly the same amount as before.  This is reasonably correct as well.  But as you keep increasing the weight, you'll eventually see the distance the spring lengthens start to change, and eventually it changes quite dramatically -- if you put enough weight on the spring, it will break.  Laws in this sense are convenient expressions of relations.  You can use them, within limits.  But there definitely are limits and, often, even the proposers knew about the limits (I think Hooke did).

One place you can see the change in how scientists think/thought about Law versus Theory is that Newton's Law of Gravitation (1600s) was replaced by Einstein's Theory of General Relativity (1910s).

Within the realm of scientific theories, though, there are two different sorts.  I'll call them the elegant and the complex.  We mostly think about the elegant theories when we think about scientific theories.  The theory of evolution, for instance, is an elegant theory.  Its elegance lies in the fact that it covers an enormous range of observations, can be used to make a large number of predictions, and, yet, can be stated in a page.

I don't believe there is an elegant theory of climate.  It is of the complex theory sort.  I have in my library, for instance, a book on Number Theory, and one on Theory of Flight.  In neither will you find a one page description of the Theory of Numbers, or the Theory of Flight.  The sense of theory involved is 'a body of principles and understandings that apply to a given subject'.  It's an elegant theory when the number of principles or understandings is small.  And, for something like flight, or numbers, and on for many areas, you have quite a few principles to work with.

In climate, some of our principles, or statements of theory, would include:

• Conservation of mass applies to the climate system
• Conservation of momentum applies 
• The laws of thermodynamics apply
• The general theory of relativity applies
• Quantum theory applies
• Tectonic theory 

I'll take up illustrating how these apply to Theory of Climate tomorrow. In the mean time, I'll invite discussion of the philosophy and additional examples of theories or laws that are part of a Theory of Climate.

Detail: Theory of Climate -- Philosophy

0 The Biggest Control Knob

I've mentioned Richard Alley before, with good reason.  You can get a flavor of the reason by looking at his Bjerkenes lecture The Biggest Control Knob: Carbon Dioxide in Earth's Climate History.

It's about 50 minutes, and you can skip the introduction to save a little time.  One thing not to miss from the introduction, so I'll mention it here, is the title of Richard's popular book The Two Mile Time Machine.  In it, he discusses how we (he) figures out what climate was like from examining ice cores.  First hand discussion.

Digressing to the personal a second, I do know him personally.  I was a guest lecturer in the 1991 edition of the class he mentions.  My thing at the time being deep ocean circulation, with some concern about how that affected atmospheric CO2 levels.



Back to his talk; he says a few things that I think are particularly useful for thinking about how science is actually done.  At one point, he notes that good scientists doing good work come to one conclusion -- one which makes for a conflict between two sorts of data.  And there are other good scientists also doing good work, but differently, who come to an answer that shows no conflict between the two types.  Now, who's right?  We need to do more work.  It isn't that one group is bad people, or doing bad science.  There's a conflict in the results, so we need to learn more, which means do more work to understand how the conflict comes about.  Probably (my opinion) it means that there's a loophole in one of the sorts of analyzing the geologic record, so that it doesn't only record what the method expects.  Finding that loophole is the challenge.

You'll see, also, something about what scientists are like inside.  Most of us aren't as demonstrative about liking our subjects.  But nobody can watch Richard for more than a few minutes and not realize that he loves his subject.  The rest of us do, too, just not so obviously.

This all actually relates well to the post I promised in my last note.  It turns on looking at ice cores and CO2, and Richard will fill you in on parts of the story that surround the two.

Detail: The Biggest Control Knob

0 One dimensional climate models

Some time back, I described the simplest meaningful climate model, and then gave a brief survey of the 16 climate models.

The next 4 I'll take up are the 4 1 dimensional climate models. These are the models that vary only in longitude, only time, only in latitude, or only in the vertical. It'll be in that order. This turns out to be the order of difficulty, and the order of interest. It isn't until the vertical that we'll get to how exactly it is that the greenhouse effect works.

On the other hand, with the model in latitude we'll see some powerful statements about the fact that energy has to move from the equator towards the pole. Not just the fact, but how much, and how it changes with latitude.

In the model with only time, we can look a little more at things we were thinking towards with the simplest model -- what happens if the solar output varies, or if the earth's albedo does. More is involved, and required, than just that. We'll have to start paying attention to how energy is taken up in the atmosphere, ocean, ice, and land. Not a very large amount of attention -- we can't tell the difference between the poles and the equator, or upper vs. lower atmosphere or ocean. But it's a start.

But for now, let's look at the simplest model in longitude only. As with any of our models, they start with the conservation of energy. The energy coming in is, as before, from the sun. How much energy arrives does not depend on what longitude we're at. Remember, even though the sun rises in the east and sets in the west -- east and west being matters of longitude -- the sun does eventually rise everywhere.

Energy coming in has to be balanced by energy going out. If it weren't, things would be changing over time and there is no time in this model. One part of the energy going out is the solar energy that gets bounced straight out. This fraction is called the albedo. Now albedo is something that can depend on longitude. For instance, land is more reflective than ocean. And along, say, 30 E, the earth is mostly land, while along, say 170 W, it is almost entirely ocean. Clouds can be anywhere. So ... we arrive at one of those unpleasant realities -- we have to get some data.

Normal business. The process arrives at telling us that we need to find averaged albedo over time (say some years) and all latitudes for each longitude. (We don't have to average over elevation because albedo is defined as the energy bounced out -- from whatever level of the atmosphere -- divided by the energy coming in.)

Once we have that, we can compute the temperatures at each longitude that will permit us to balance, with terrestrial radiation out, the incoming energy. These temperatures should be something like the blackbody temperature of the earth we found in the simplest model. But they'll vary some.

The next piece of data we'll need are the observed blackbody temperatures, by longitude. Then we'll compare the simplest model to the observations.

One thing which is possible, and we'll be looking for in our comparison, is that now we've added longitude, a new thing can happen. In the simplest model, the energy coming in had to be balanced, right there, by energy going out. Now that we have longitude, it's possible for energy to shift from one longitude to another. The Gulf Stream and North Atlantic Currents, for instance, move a lot of energy from west to east. If no energy is being transported, on the average, then the temperature for a longitude will be just what we expect. If there's a mismatch, energy has to be getting moved from one longitude to another.

I haven't collected the data yet, so I don't really know how it will turn out. I expect that clouds will cover the albedo differences between land and ocean to a fair extent, so the temperatures we'll compute will be fairly constant. I also expect that heat transport by longitude will be small -- the Gulf Stream's eastward warm current is balanced at least partly by a cool current (relative to local temperatures, that is!) at the equator.

On the other hand, I haven't looked at the data yet, so there is room for surprise. That'll be fun. Means we get to learn more than we expected.

Detail: One dimensional climate models

0 Models and Modelling

"All models are wrong. Some models are useful." George Box

Box was a modeller, and the sentiment is widely spread among modellers of all kinds. This might be a surprise to many, who imagine that modellers think they're producing gospel. The reality is, we modellers all acknowledge the first statement. We are more interested in the second -- Some models are useful.

But let's back up a bit. What is a model? In figuring out some of this, we'll see how it is that models can be imperfect, but still useful.

There are several sorts of model, is one thing to remember. On fashion runways or covers of magazines, we'll see fashion models. In hobby shops, we can get a model spacecraft or car. We could head more towards science, and find a laboratory model, or a biological model animal, statistical model, a process model, numerical model, and so on.

Common to the models is that they have some limited purpose. A fashion model is to display some fashion to advantage -- making the dress/skirt/make up/... look good. She's not to be considered an attempt to represent all women accurately. The model spacecraft is not intended to reach the moon. But you can learn something about how a spacecraft is constructed by assembling one, and the result will look like the real thing.

In talking about a laboratory model, read that as being a laboratory experiment. You hope that the set up you arrange in the lab is an accurate representation of what you're trying to study. The lab is never exactly the real thing, but if you're trying to study, say, how much a beam flexes when a weight is put in the middle, you might be able to get pretty close. If you want to know the stability of a full-size bridge with full size beams and welds and rivets assembled by real people, it'll be more a challenge -- represent the 1000 meter bridge inside your lab that's only 10 meters long. It won't be exact, but it can be good enough. Historical note for the younger set: Major bridges like the Golden Gate Bridge, Brooklyn Bridge, Tower Bridge, and such, were designed and built based on scale models like this. The Roman Aqueducts designed over 2000 years ago, still stand, and never came near a computer. They were all derived from models, not a single one of which was entirely correct.

In studying diseases, biologists use model animals. They're real animals of course. They're being used a models to study the human disease. Lab rats and such aren't humans. But, after extensive testing was done, it was discovered that the rats for some diseases, and other animals for other diseases, reacted closely enough to how humans did. Not exactly the same. But closely enough that the early experiments and tests of early ideas could be done on the rats rather than on people. The model is wrong, but useful.

Statistical models seem to be the sort that the most people are most familiar with. My note Does CO2 correlate with temperature arrives at a statistical model, for instance -- that for each 100 ppm CO2 rises, temperature rises by 1 K. It's an only marginally useful model, but useful enough to show a connection between the two variables, and an approximate order of magnitude of the size. As I mentioned then, this is not how the climate really is modelled. A good statistical model is the relationship between exercise and heart disease. A statistical model, derived from a long term study of people over decades, showed that the probability of heart disease declined as people did more aerobic exercise. Being statistical, it can't guarantee that if you walk 5 miles a week instead of 0 you'll decrease your heart disease chances by exactly X%. But it does provide strong support that you're better off if you cover 5 miles instead of 0. Digressing a second: Same study was (and is still part of) the support of the 20-25 miles per week running or walking or equivalent (30-40 km/week) suggestion for health. The good news being that while 20 is better than 10, 10 is better than 5, and 5 is way better than 0. (As always, before starting check with your doctor about your particular situation, especially if you're older, have a history of heart problems already, or are seriously overweight). This model is wrong -- it won't tell you how much better, and in some cases your own results might be a worsening. But it's useful -- most people will be better off, many by a large amount, if they exercise.

Process models started as lab experiments, but also are done in numerical models. Either way, the method is to strip out everything in the universe except for exactly and only the thing you want to study. Galileo, in studying the motion of bodies under gravity stripped the system, and slowed it down, by going to the process model of balls rolling down sloping planes. He did not fire arrows, cannon balls, use birds, or bricks, etc.. Simplified to just the ball rolling down the plane. The model was wrong -- it excluded many forces that act on birds, bricks, and all. But it was useful -- it told him something about how gravity worked. Especially, it told him that gravity didn't care about how big the ball was, it accelerated by the same rules. In climate, we might use a process model that included only how radiation travelled up and down through the atmosphere. It would specify everything else -- the winds, clouds, where the sun was, what the temperature of the surface was, and so on. Such process models are used to try to understand, for instance, what is important about clouds -- is it the number of cloud droplets, their size, some combination, ...? As a climate model, it would be wrong. But it's useful to help us design our cloud observing systems.

Numerical models, actually we need to expand this to 'general computational models' as the statistical, process, and even some disease models now, are done as computational models. These general models attempt to model relatively thoroughly (not as a process model) much of what goes on in the system of interest. An important feature being that electronic computers are not essential. The first numerical weather prediction was done by pencil, paper, and sometimes an adding machine -- more than 25 years before the first electronic computer. Bridges, cars, and planes are now also modelled in this way, in addition or instead of scale models. Again, all of them are wrong -- they all leave out things that the real system has, or treat them in ways simpler (easier to compute) than the real thing. But all can be useful -- they let us try 'what if' experiments much faster and cheaper than building scale models. Or, in the case of climate, they make it possible to try out the 'what if' at all. We just don't have any spare planets to run experiments on.

Several sorts of models, but one underlying theme -- all wrong, but they can be useful. In coming weeks, I'll be turning to some highly simplified models for the climate. The first round will be the four 1-dimensional models. Two are not very useful at all, and two will be extremely educational. These are 4 of the 16 climate models.

Detail: Models and Modelling

0 What cooling trend?

Nonsense about the 'current cooling trend' is rife across the blogosphere, and the science minded folks usually point to the fact that you need 20-30 years to define a climate trend. The lies as such don't interest me, or make for a good topic for this blog.

What's useful or interesting is that the statement itself, often linked to 'last 10 years', is not true even after allowing for substantial cherry picking. This brings us back to the interesting matter of trying to define climate. And a further reminder that if you're reading bad sources, you can't trust even the simplest of statements.

To find current temperature trends, I used the NCDC monthly temperature anomalies. The most recent month is May, 2009. To look in to current trends, then, I computed the trends from every month of the last 30 years, through to May 2009. The trend shown for January 1979 is the trend from then to May 2009. The trend for April 2009 is to May 2009. Figure 1 gives the results (actually back to 1977).



Wow, current warming trend of 120 C per century! Surely we're all going to be boiling soon? Of course not. That trend was computed from a 1 month span -- April to May of 2009. It is yet another reminder that short term variations, namely weather, can be large. It isn't climate. Climate shouldn't depend sensitively on when exactly you start your trend computation. Unfortunately that figure shows us nothing new, beyond confirming yet again (not a bad process itself, and part of the scientific approach) that weather happens, and weather variability is much larger than climate variability. So in figure 2, I zoom in a little and ignore positive trends greater than 20 C/century.



So now we can see that if someone chooses very carefully (namely, cherry picks) the starting date, they can find a cooling trend between then and May 2009 ('current'). But notice how carefully they have to choose that starting date. If it's 10 years (or any number greater than that, back to the record's start date), the trend is a warming. In fact, you can only get cooling trends occur if you choose a start date between January 2001 and January 2007 (including those months), or October, 2008. Anything farther back, or more recent, shows warming.

Both for deciding climate, and for doing science, we want our conclusions not to depend sensitively on arbitrary choices. Ending with the most recent data is not arbitrary, so we're ok there. But choosing a starting date? Science-minded folks take a figure in the range of 20-30 years, in particular 30, because over a century of experience says that 30 years is a good time period to be able to look at climate trends as opposed to weather fluctuations. i.e., not arbitrary. Choosing 2.4-8.4 years (and not 9.4, or 12, ...)? Why would we do that? Well, if we wanted to support some particular conclusion, we might do so. But that is not science.

Let's zoom our attention to the period in late 2006 through early 2007. The largest 'cooling trend' you can contrive is to start with September or October 2006, giving 3.3 C per century cooling. Of course you're flagrantly violating sensible climate practice by using 30 months instead of 30 years. But now look to April 2007, where the trend is already a warming of 3.3 C/century, and remains higher than 3.3 to the present, except for that 1 month, October 2008. If 30 months are ok for cherry pickers, why are 24 months not? They're not very different time periods; if either one is acceptable, both must be.

On the science side, as my results post illustrated, if you take 20-30 years to determine your trends, then changing the length doesn't change your answer much. We see this again in figure 2, where any trend computed with from 15-30 years of data gives nearly the same answer as to the current trend -- about 1.8 C per century (1.49 for 15 years, 1.79 for 20, 1.92 for 25, and 1.62 for 30 years). The figures do fluctuate some, which is to be expected. But changing from 30 to 24 years doesn't take us from a large cooling to an equally large warming, the way it can for months.

I'll probably take this up in a separate note, as it illustrates a different way of misleading yourself with graphs. For now, I'll just observe that if you compute the 10 year trends, rather than telling people to 'just look', then the most recent time there was a 10 year cooling trend was the 10 years ending with January, 1987 (with 0.03 C/century). The last time you had several months in a row where the 10 year trend to that month was a cooling was in the late 1970s -- 30 years and more back. At no time that the '10 year cooling trend' claim has been getting made, has it been true.

Detail: What cooling trend?

0 What is the future of weather?

The future of weather is change. Easy enough to make that statement, but since the question brings people here periodically, let's think about it some more. I earlier mentioned the topic in Weather will still happen. Entirely true, but maybe not as helpful as it could be.

Let's go back and think about what we mean in talking about weather. Partly, it means 'not climate'. Itself also not the most helpful comment. But let's continue with both weather and climate in mind. My touchstone is "Climate is what you expect, weather is what you get." Whatever it is exactly that is happening around you right now, that's weather.

We can think a little differently and decide that our expectation -- climate -- is also part of what's happening. In that case, weather is the difference between our expectations and exactly what is going on. Since I live near Washington, DC, and it's the middle of July, I expect it to be hot. More precisely, from the Weather Underground's reports for Washington National Airport, I expect today's high to be 88 F (31 C). That's the climate for that station. If the actual high were to be 88, then as far as high temperature went, we were exactly on our climatology. Conversely, we could say that there was no 'weather' -- no difference between what we expected and what we got. It looks like the forecast for today is for the high to be 5 degrees below the climatology. So it seems more likely that we'll have 'weather' of 5 degrees cooler than normal for the high.

If we look day by day for here and other middle or high latitude locations, we'll find days that are 20-30 F warmer than usual (10-15 C), and days that are 10-15 C colder than usual. That gives us a sense of how large 'weather' is -- give or take 15 C from climatology. The figure depends on locations and seasons. In the tropics the weather variations, in terms of temperatures that is, are smaller than in the middle latitudes (if I remember correctly, 5 C, 10 F, is considered a big deviation from climatology in the tropics).

The difference between scale of weather (how many degrees away from climatology you get) in tropics and the middle or high latitudes helps us see what is happening to cause weather. In the tropics, the solar input is relatively constant day by day through the year. With similar solar inputs, you reach similar temperatures day by day, and year by year. The larger differences from climatology occur when you have some big system (large cloud bands, clusters of thunderstorms, and up to hurricanes) active. The thing which drives those big systems are temperature differences. The systems then try to flatten out the temperature differences. In low latitudes, they're more effective at this, so you see smaller variations due to weather.

Come to higher latitudes, where most people live, and you see some of those tropical systems coming up your way (hurricanes, typhoons, etc.) carrying that very warm, very moist air -- replacing the more moderate air 'native' to your location. Or, here in the mid-latitudes, wait a bit and get a wave of cold air coming down from the colder higher latitudes. On top of both, you have the fact that the amount of sun you get varies by a lot through the course of a year. If the only thing happening were the change in solar input, we could calculate the temperatures, and temperature changes, we'd expect (a climate estimate) using the simplest climate model.

Now let climate change enter the picture. Will it change the fact that solar input varies little in the tropics and tremendously at the poles? No. Will it change the fact that far more solar input is in the tropics than in middle latitudes? No. Will it change the fact that weather systems respond to temperature differences across the planet by trying to smooth out those differences? No.

Since the answers to all those (and a host of others that are related) is no, weather will still happen. A little more detailed:
we'll still see days/weeks/months, even years, where the temperatures run below normal.
we'll also still see temperatures run above normal.
In the mid-latitudes, those differences on a daily basis will still be 10-15 C (20-30 F)

Now an application of climate change to our daily observations. Let's say (to keep the numbers easy) that the climate change of the last century were a 2 F (1 C) warming at my location. Before that warming occurred, the expected high would have been 86 F. Our actual high of 83 F represents 'weather' of 3 degrees F below the former normal. Given the current, warmer, climate, it means today's weather is 5 F below normal. Anything odd about 5 F off normal for a day? Hardly. The record low is 15 F below the average low, the record high is 12 F above the average high. (Tamer numbers here than I quoted above because a) it's summer and the ranges are smaller and b) I'm more knowledgeable about the weather for Chicago, which is more variable than DC.)

Weather will still happen, and have similar magnitudes to the past. What changes, as climate changes, is the average and some more subtle figures. They'll be the subject of their own note later.

Detail: What is the future of weather?

0 Another one bites the dust

Another ice shelf bites the dust, to little surprise in the polar community. In this case, it's the Wordie ice shelf, and you can see a photo and a short write up at:
http://www.reuters.com/article/environmentNews/idUSTRE5332BU20090404

The reason I'm not surprised, and anybody who has been reading the science is not surprised, is that we knew years ago that warming was going to lead to the breakup of ice shelves. See, for example:

Rapid disintegration of the Wordie Ice Shelf in response to atmospheric warming, by C. S. M. Doake & D. G. Vaughan. That was 1991. You do have to remember that glaciologists are used to things that move at glacial speeds.

The breakup was more specifically tied to atmospheric warming in a more recent (1996) paper by D. G. Vaughan & C. S. M. Doake Recent atmospheric warming and retreat of ice shelves on the Antarctic Peninsula. The authors cite the earliest suggestions of problems for Antarctic ice shelves in a warming world as Mercer's 1978 paper
West Antarctic ice sheet and CO2 greenhouse effect: a threat of disaster. Rather drastic title. But it serves to both establish that the collapse of these ice shelves due to CO2-induced climate change is an old issue, and to provide yet another example of a scientist in the 1970s who was not expecting 'another ice age' any time soon.

The scientific question left on ice shelf collapses on the Antarctic peninsula is not whether, but which one is going to go next, and how soon. For the ice shelves farther to the pole -- which are the big ones and of the greatest concern (the reason for the 'threat of disaster' in Mercer's title) for the future, we still have several scientific questions about whether, and what happens how fast if they do go.

Some folks are making comments which mix up sea ice and ice shelves. Please don't do that! See my note about ice types for the simple differences between the sorts of ice.

It's also been mentioned that the breakup of ice shelves can't change sea level. This isn't actually true. I'll take up the details in two notes to come. First, why it isn't true (you can get ahead by reading the Sea Level Change FAQ -- same process that means sea ice can change sea level applies to ice shelf ice). Second, why it is someone else published it first, even though I had the answer 10 years earlier. A bit of how science is done, and reminder that scientists are fallible.

Detail: Another one bites the dust