Archive for the ‘climate change’ Category

Expected Rainfall… or why you shouldn’t use the mean or standard deviation

November 17, 2016

How much rain do we usually get?

There are three common answers to this: the mean (average), the median (halfway point) and the mode (most common). For a “normal distribution” these three are all the same, but in the case of Santa Barbara’s yearly rainfall they are not.

Mean 18.0 inches
Median 15.3 inches
Mode 13.4 inches

Let us look at the rainfall distribution pattern for Santa Barbara. Here I use the horizontal axis to displaying the number of inches of rain that fell in a year (rounded down to the nearest inch) against the count of the number of years that had that much rain. (These data are available from the county public works department.)

rainfall distribution

Santa Barbara’s historical rainfall data stretches back (patchily) to 1868. All in all there are 145 years of data (as of Nov 2016).

The Mode

The first problem with using the mode is calculating it. SB’s yearly rainfall is reported in hundredths of an inch. This level of precision means it is extremely unlikely that any two years will have exactly the same amount of rainfall, so there is no amount that occurs most frequently.

That, of course, is easily solved by dropping precision and just looking at the number of inches that fell in a year (as I have done in the graph above). But there’s a hidden problem with this method. I lumped years together by having a series of intervals that start at 0. But suppose I started at .5 inches instead? If this were a normal distribution that wouldn’t make much difference, but here…

rainfall distribution offset

The distribution looks quite different now. That tends to argue against the utility of the mode.

Probably if I had several thousands of years of data (and the climate didn’t change in that period) much of this variation would smooth out. But I’ve only got 145 years, and the climate is so variable that this isn’t enough.

Now let’s compare our actual distribution to a normal distribution centered on the mode and with a standard deviation set to the square root of the variation about the mode.


They do not look alike. Part of the problem is that there can never be less than no rain, but the normal distribution acts is if there could be. The variation less than the mode is much less than the variation above the mode (a range of 9 inches below, but 35 inches above).

The mechanism I choose to calculate the mode is to create a series of bins, each one inch wide and offset from one another by .1 inches. So the first bin would count all years that had between [0,1) inches, the second bin [.1,1.1), and so forth. Clearly any give year will end up in 10 bins rather than just one (but that’s fine). Then I look for the bin with the most number of years. This method suggests that the mode is at 13.4 inches — or in the bin counting years where the rainfall was between [12.9,13.9) inches.

But this does not produce stable results. Below is a graph showing the mean (blue), median (green), mode (red) of accumulated rainfall as the year progresses (rain years in Santa Barbara start in September).
Mean, Median, Mode (year to date)
(Click on the graph to see a more legible version)

The mean describes a very smooth curve. The median has small bumps, but is pretty smooth. On the other hand the mode dances all over the place with a 10 inch jump in April – from 18 inches down to 8.

Again if I had a much larger sample, presumably these fluctuations would calm a bit, but for the noisy mid-sized dataset I have available the mode does not provide a useful tool.

The Mean

The average is what we usually think of as the best metric for looking at the mid-point of a distribution. But with Santa Barbara’s rainfall it doesn’t work very well.

Because we occasionally get 45+ inches of rain this distorts the mean in a way that is not useful when trying to figure out what a normal year looks like. In fact about 61% of years have less rainfall than the average, which makes the average seem rather unusual.

The Standard Deviation

The standard deviation is defined as the square root of the variation about the mean (or as the variation about the point which minimizes the variation — which happens to be the mean).

As the mean isn’t useful to us, one might presume that the standard deviation is also not much use.

However that’s to some extent a question of semantics, we could examine the square root of the variation about the median instead.

Here we once again bump up against the asymmetry of our distribution. There is simply more variation above the median than there is below. Calculating the square root of the variation for rainfall below the median gives a value of 4.5 inches, while that above the median is 11.6, and the combined value is 8.8.

So perhaps we should look at negative and positive variation about the median instead of one combined number?
pos/neg variation about median
(the median is the dark green line, the light green solid lines show the positive and negative “standard deviation”s from the median, and the dashed lines show percentiles)

The negative 1 “standard deviation” line tracks close to the 15th percentile, and the positive 1 “standard deviation line tracks close to the 85th percentile. In a normal distribution the 1 standard deviation lines should track the 15.9th percentile and the 84.1th percentile. So my peculiar definition seems as if would describe the variations of this distribution comparably to the standard definition for a normal distribution.

But it’s so complicated to explain and use, that for most purposes using the median with percentile lines is probably better.

A better viewpoint

My friend Dave suggested looking at the logarithms of the rainfall to see if that revealed a better pattern. And it does.
It still isn’t perfect, but the mean and median have moved closer together and the standard deviation is similar on both sides of the mean. The mode is still in the wrong place for a normal distribution.

Mean 16.3 inches
Median 15.3 inches
Mode 13.5 inches

Pause or No Pause

December 15, 2015

Has there been a “pause” in Global Warming since 1998?

I contend that there has not, but it really depends on how you define “pause”. My contention is that definitions which show a pause are not statistically useful.

[My analysis is based on NASA’s Global Land-Ocean Temperature Index which may be obtained from here and is described here. Other datasets exist which may show slightly different results. Data extracted on 13 Dec 2015 (so this does not include a full year of 2015 and my analysis stops at 2014)]

So let’s start with the obvious. When was the last time the temperature was at the level of 1998? Why in 2012. And because these data are noisy let’s be a little generous and ask instead: When was the last time the temperature was within .04°C of 1998? In 2013. Since the last year of full data was 2014 you might say “Hey, basically the temperature hasn’t changed at all since 1998.” and draw a flat line on the graph from 1998 to now (or at least to 2013).

But this is a statistically poor technique. I mean if you look at the scatter plot it’s pretty clear a horizontal line doesn’t fit the points well. It’s sort of saying “Let’s assume there is no trend and see what we get.” A much better way of proving a pause is to say “Let’s assume there is a trend and prove that that trend is zero.”

The data are noisy. You can’t just draw a line from start to end and say “This is what is happening.” The simplest way to extract a trend from noisy data is to apply a linear regression found by least squares — that is to find the line which minimizes the sum of squares of the errors — the error being the difference between what the regression line predicts for the temperature of a year and the actual temperature reading.

If there be no trend, if global warming have paused, then the slope of the line will be near zero. It won’t be exactly zero because the data are noisy.

If we look at each year since 1998 and generate a line based on the data from 1998 to that year then if warming were paused we’d expect that about half the lines would have a positive slope and half a negative one.

Slopes of the regression line for each year since 1998 in °C/year
2000: -.105 2001: -.024 2002: +.013 2003: +.020
2004: +.013 2005: +.021 2006: +.020 2007: +.019
2008: +.012 2009: +.012 2010: +.014 2011: +.012
2012: +.010 2013: +.010 2014: +.011

But that’s not what we see. Instead we see almost no lines with negative slope (and those all in the years immediately following 1998). Instead the slopes roughly average .012°C/year, or about the slope found between 1960 and 1984.

In other words, the data do NOT show a pause, they show an increase comparable to increase from before the 1990s. The naughties are not paused, they are not anomalous, they are in line with the average over the last half century. It is the nineties which are odd.

But there is another statistical mistake in the claim of a “pause”. This is something called “Data Mining”. The only reason anyone might think there was a pause is because 1998 was an extraordinarily hot year for the time. If you base your data in 1998 you have to wait for a long time for the trend to catch up to the noise.

But if you look at the next year, 1999, there is no way anyone could find a pause in the data. Since 1999 temperatures have simply increased. This, by the way, is data mining in the reverse direction since 1999 was (for the time) a particularly cold year.

Slopes of the regression line for each year since 1999 in °C/year
2001: +.065 2002: +.076 2003: +.061
2004: +.038 2005: +.041 2006: +.034 2007: +.030
2008: +.020 2009: +.019 2010: +.020 2011: +.016
2012: +.014 2013: +.013 2014: +.014

Since we are only data-mining the start time if you wait long enough both trends will converge toward the same slope.

I have been told that the temperature change since 1998 is not statistically significant since it is less than two standard deviations. In a way, this is true, (ΔT(2014-1998): .11°C, σ: .067°C) but it ignores several things. First these years do not stand alone, they are a continuation a trend that started (at least) in 1960 and the change since 1960 is significant. And second 1998 is data-mining. If we pick 1999 as a base year then ΔT(2014-1999): .32°C, σ: .061°C, and the change is about 5σ which is very significant.

So I think the following graph is a much better way of looking at the data. There is no pause. Just three regions where the temperature increases, and in the two regions 1960-1984, 1999-2014 the temperature increases at about the same rate, while in one, 1986-1998, the temperature increases much faster.

Linear regression lines
1960-1984 T=.012*(year-1998)+14.355°C
1985-1998 T=.021*(year-1998)+14.488°C
1999-2014 T=.014*(year-1998)+14.492°C


My claim is that there has been no pause. Attempts to see a pause are based on two statistical mistakes, the first being data-mining, and the second being the belief that drawing line between two noisy datapoints is meaningful.

This analysis is based on statistics I learned in 10th grade. It isn’t hard.

El Niño?

December 15, 2015

Where is it?

Or rather, where is the rain it is supposed to bring us?

This rain year (Sept-Aug) has been the 22th driest in the 1 Sept-15 Dec period (out of 146 years recorded), and of those 21 only 3 had above average rainfall. But one of those 3, 1977-1978, had 42.34 inches.

So it’s not unprecedented that we’ll still have a wet year, just unlikely.

A fortnight ago the Independent ran an article claiming that in the big El Niño year of 1997-1998 rainfall in SB was delayed from its usual pattern and the big storms didn’t start until January. That was consoling. But then Weather Underground provided data from all the big El Niño years for SF and LA (but not SB) which said exactly the opposite.

So I grabbed the rainfall data provided by the county from their recording station downtown, and extracted the relevant points.

SB Rainfall Data at County Building
(in inches)
Year Sept Oct Nov 1-15 Dec 1 Sep-15 Dec
1957 0.00 1.41 0.51 2.95 4.87
1965 0.09 0.00 7.86 0.53 8.48
1972 0.00 0.04 5.69 0.73 6.46
1982 2.07 0.63 5.18 0.22 8.10
1997 0.05 0.15 4.30 5.78 10.28
2015 0.10 0.26 0.13 0.19 0.68
0.27 0.69 1.52 1.24 3.72

So the data I can find contradicts the Independent’s claim. In all prior “Big” El Niño years there was rainfall above the long term average at this point of the year at downtown SB.

The general consensus is that we will get a lot of rain this year — eventually.

But I worry.

The current definition of a big El Niño was not one that could be detected until (relatively) recently, thus we only have records for 6 big El Niño events. That’s not a big sample size…

This is supposed to be a bigger El Niño than any recorded, maybe we don’t get rain with exceptionally big El Niños. This is a warmer year than ever before, maybe that means something too… Weather is always random, maybe this year we’re just unlucky.

Paris — COP 21

December 12, 2015

So we have a new climate agreement out of Paris today.

Is it adequate? No.
Can it become adequate? Perhaps. We must hope so. It contains mechanisms within it to ratchet up the commitments as time goes on. Will people? Probably. Will it be enough?
Will people enact it? It is said to be “a legal instrument” which, I think, means the US Senate must approve it as a treaty. Which seems unlikely. So I doubt the US will agree to it. But perhaps there is some wiggle room I am not seeing.
Ah. Only some parts are legally-binding (the emissions commitments are not), and those parts which are binding are technically extensions to an existing treaty and, as such, do not require Senate approval. Tricky. [WeatherUnderground]
Will people live up to it? Let’s hope so.
However on the day after signing India reaffirmed that it intended to double its coal output (India is currently the 4th largest emitter. [Guardian]

What is adequate?

We really have no idea.

Back in the 1990s the best science suggested that a temperature rise of 2°C above pre-industrial temperatures would probably not lead to ecological catastrophe. And this has been the stated goal since then.

This year the average global surface temperature is expected to breach the 1°C mark and we are already seeming effects that 25 years ago were predicted for 2°C. In other words it is no longer possible to avoid catastrophic climate change. We are already too late. [Kevin Anderson]

For instance parts of the antarctic ice sheet have already passed a tipping point and entered a period of irreversible melting. The irreversible loss of the Amundsen ice sheet alone will raise sea-level by 1 meter in the next two centuries. [Guardian] The arctic ice cap is melting faster than expected, destroying ecosystems and the lives of humans dependent on those ecosystems. The incidence of “extreme” weather events is higher than expected.

To some extent this has been recognized at COP21 and the text now includes the aspiration to hold the level of warming to 1.5°C. However this has not resulted in anyone making a further commitment to reduce their emissions.

The commitments on the table are estimated to produce an increase somewhere between 2.7°C and 4°C, depending on whose climate models one looks at.

Some basic science

The earth has a large thermal mass. This means that it heats up slowly. Even if we were to stop producing any CO₂ (from non-ecosystem sources) the earth’s temperature would continue to increase for many decades.

We have a carbon budget. There is a limit to how much we can pump into the air before, eventually, the world will heat up by 2°C. The problem is that we can easily overshot that limit long before the temperature reaches 2°C.

Unfortunately no one knows what the carbon budget should be. We do know that about half of all carbon emitted gets quickly reabsorbed by plants, but the rest hangs around for centuries. Estimates suggest we can emit a range somewhere between another 100-400 gigatons of carbon. That’s a fairly wide uncertainty. [Yale] We are currently emitting approximately 35gigatons of CO₂ a year, and each year we emit more than we did the year before (though that increase is slowing). [Wikipedia, 2013 data] So at this rate we have anywhere from another 6 to 22 years before we would have locked in 2°C of warming. Unfortunately this dataset only includes CO₂ emissions. It does not include methane (which has a greater effect but is released in much smaller quantities), or water vapor, or other gasses. So worst case is we have about 5 years more of business as usual before for we guarantee 2°C warming eventually.

2°C is a global average

Some parts of the world are warming much more quickly than others. The oceans warm more slowly than the land. But there is a about twice as much ocean than there is land, and if the ocean takes longer to get to 2°C then the land will get there faster, and by the time the global temperature has averaged a 2°C increase the land temperature will be much higher.

The arctic heats up faster than the tropics, but the tropics have traditionally had a much narrower range of temperatures so in spite of that fact they will see exceptional conditions become normal much more rapidly. In both cases the ecosystems will not be able to adapt. In the arctic because there are large swings in temperature, polar ice caps disappear. In the tropics because the temperature is simply beyond what plants and animals can handle.

What about carbon capture?

Essentially all of the IPCC models which project that we will limit warming to 2°C require that we will have negative carbon emissions after about 2050. [Kevin Anderson] Not zero emissions, but negative. And this presupposes a technology we do not currently have.

We might develop it.

But as far as I know the funding for research into this area has been drastically cut in recent years. [Guardian]

In other words the paths the IPCC sees that might restrict warming to 2°C all depend on technology which does not exist and isn’t being developed. This is disturbing.

Positive Feedback

There are many areas of potential positive feedback which are not addressed by the IPCC, because we do not yet know enough to quantify them. And they are ignored in our climate models.

Melting permafrost will release a lot of methane into the atmosphere, a more potent heat-trapping gas than CO₂. This in term will lead to higher surface temperatures which will lead to more methane being released. We can see this happening but can’t quantify it. [Katia Moskvitch]

Warming ocean floors will release methane from methane hydrates with a similar feedback effect. [SWERUS-C3]

Warming tropics lead to droughts over the Amazon which leads to the death of rainforest trees which releases more CO₂ which leads to more warming and even fewer trees.

Ice and snow reflect more light and heat than oceans or land. As glaciers and ice caps melt the earth will absorb more heat meaning that more ice and snow will be lost.

This means that our current best guess are probably too conservative.

Sea level rise

With the ice caps and glaciers melting, and the ocean water warming and expanding, sea level is rising.

So far the global average is about half a foot higher now than it was 100 years ago. However the oceans aren’t rising at the same rate and on the east coast of the US the rise has been closer to a foot.

A paper posted on the next by [HansenDiscussion] suggests that the sea level may rise 10ft in the next 50 years and 15ft by 2100. This may be a worst case scenario, but past experience with climate predictions suggests that worst case scenarios have happened more frequently than best case ones. And we are very ignorant here.

Some context: Hurricane Sandy had a storm surge of about 13ft in New York. Hugo had a maximum surge of 20ft near Charleston. Katrina’s surge was about 27ft.

So by the end of the century New York might be constantly under more water than it was at the worst of Hurricane Sandy.

This would wipe out many coastal cities. It would destroy much farmland. Many island nations would no longer exist.

How fast can a marsh adapt? If the sea level rises by 15ft and the shoreline moves inward by many miles then marshes, which are very productive ecosystems will be wiped out.

But I thought climate changed stopped after 1998

This is a lie.

I have had the above statement questioned. So, a brief recap. I pulled down this dataset. I applied a linear regression least squares fit to the following year ranges of the global mean temperature:

1880-2014 T=.0068*(year-1998) + 14.36°C
1960-1984 T=.0118*(year-1998) + 14.35°C
1990-1998 T=.0230*(year-1998) + 14.49°C
1998-2014 T=.0108*(year-1998) + 14.52°C

The important thing to note here is the change/year which was .0068°C/year over the historical record; it was .0230°C/year in the 90s, and .0108°C/year in the period of the hiatus. So not only has the global temperature increased since 1998, but it has increased faster than the historical rate and about the same rate as during the 70s. It did slow down dramatically from the 90s, but that can be explained by the Pacific Decadal Oscillation [Nature].

However surface temperature is not a good indicator of heat transferred to the earth. And since 1998 more heat has gone into the deep ocean than happened before. With this year’s El Niño less heat is going into the ocean deeps and the surface temperature is again increasing quickly.

Remember in the last decade we have seen 8 of the hottest years on record, and the top 13 hottest years have all been since 1997. There is about 1 chance in 3.7 million of this happening if the climate were not warming. [Climate Central] And unless something amazing happens in the next 3 weeks, 2015 will be even hotter.

But isn’t extra CO₂ good for plants? Won’t warmer weather make ecosystems more productive?

There is some evidence that more CO₂ will make plants happier, but the effect is slight.

Basically ecosystems have adapted to current conditions. Changing those conditions will, in almost all cases be a change for the worse.

European grain productivity has already been reduced. [Frances Moore] The current drought exacerbated (and possibly caused) by climate change has reduced California’s agricultural productivity. Global grain productivity is expected to fall at about 1.5% per decade [David Lobell] Grains produce less protein in hot weather.

We don’t have any good metrics for measuring wild ecosystems, except long term extinction rates, but there is certainly evidence that the climate is changing faster than plants and animals can move to keep up. [Union of Concerned Scientists]

The woods I love to hike in will be very different when my niece’s children try them.

But the oceans will be the worst hit. The increase in CO₂ has led to an ongoing acidification of the water which prevents many animals from forming shells. The increase in heat has lead to bleaching coral reeves and the death of many.

More subtle changes happen too. Different species respond differently to climate change, some start breeding sooner than they would normally, others do not. Thus old ecological synchronizations are lost. A predator many start to breed in the spring before its prey does, resulting in starvation of the predator and over-population in the prey.

The oceans’ food chains are being disrupted and they are becoming less productive.

In other words, species are dying off. Humans are losing their food supplies.


The Guardian says it very well: “By comparison to what it [COP21] could have been, it’s a miracle. By comparison to what it should have been, it’s a disaster.”

The world will be less beautiful in the future.
And there will be less for humans to eat.
And there will be more humans.

Frighteningly hot

November 6, 2014

It’s hot out today. The highest I noticed was 92°F. And it is November. So I went to NOAA and downloaded temperature data for the SBA airport (which has been keeping daily records since 1941).

This year as a whole has seemed hot. I was wondering if that was just my perception, for if were true. So I was interested in the temperature anomalies for this year — that is, you pick a baseline period, usually of 30 years, and calculate average temperatures for every day of the year during that period and then you look at the current year and see whether (and by how much) the temperature is hotter or cooler.

The IPCC recommends using 1961-1990 as a baseline period. Even by 1961 there was some anthropomorphic warming, but I don’t have data from back in the 19th century.

Max Mean Min
2014 to date 3.9°F|2.1°C 3.3°F|1.8°C 2.7°F|1.5°C 263 days above average
47 below
Oct 2014 5.0°F|2.8°C 3.9°F|2.2°C 2.9°F|1.6°C 31 days above average
0 below
first 6 days
of Nov
4.1°F|2.3°C 2.5°F|1.4°C 0.8°F|0.4°C 5 days above average
1 below
6 Nov 14°F|7.8°C 10°F|5.6°C 5°F|2.8°C above average

In other words, for this year, SB is already butting up against the 2°C barrier of irreversible climate change. Of course, this is one small area, and less than a year’s data. But it frightens me.

A tale told by an idiot.

September 24, 2014

Ban Ki-moon (UN Secretary General) said that yesterday’s climate change summit was a success.
Obama said that the US (under his presidency) has done more than any other country about climate change.

My words fly up, my thoughts remain below:
Words without thoughts never to heaven go.

Hamlet III.3

Out on thee! ſeeming! I will write againſt it:

Much Ado IV.1

On Monday ~300,000 people marched in New York (and tens of thousands in other cities) protesting climate change. On Tuesday the UN held a day-long summit. This was billed as the “Last Chance” to prepare for the Paris COP 21 conference in December 2015 which is the “Last Chance” for the UN process to do any good. (I’m not sure why we are ignoring COP 20 in Lima this year).

Of course, there have been plenty of “Last Chance”s in the past, and presumably there will be plenty more in the future. No one is willing or able to commit to the needed changes.

The hope was that world leaders would come to Tuesday’s conference and make all sorts promises about reducing emissions and giving money to the poor countries who will (probably) suffer the most from climate change (like being entirely drowned as the sea level rises) but have been the least responsible.

Nothing of the sort happened. No one made any new emissions pledges. The US refused to give any money to the poor, and only a few European countries and Mexico actually did so. Nothing that was desired was achieved.

The Green Climate Fund was conceived at Copenhagen as a way of transferring money from the rich to the poor. It is supposed to have $100bn/year after 2020. Currently it has ~$2.3bn total. That’s not per year, that’s ever. It is laughable.

On the other hand they did come up with a new policy on reforestation. Um. I thought they did that at Copenhagen 5 years ago? And this new policy was established without consulting Brazil — the country with the biggest chunk of rainforest?

Maybe they need a new forest policy because REDD (the last one) didn’t work? Is there any reason to believe that this one will be any better?

One of the other few “major” commitments of the summit was to put a price on carbon. Of course the US did not agree. Nor did one of the countries soon to be underwater.

In spite of this Obama had the gall to make a speech claiming the US under his presidency had done more than any other nation on climate change, and then he volunteered to “lead the international community”. This from the man partly responsible for the disaster at Copenhagen, who has done practically nothing at home about climate change, and who made no commitments yesterday.

He led his regiment from behind
(He found it less exciting).

The Gondoliers, W.S. Gilbert

Personally I think there is a high chance that any policies Obama has promulgated will be rolled back in two years if the Republicans win the presidency. And really what has he done? All I can think of is that after 5+ years he has got the EPA to make proposals for limiting emissions from power plants. Important, yes, but only one small aspect of the problem is addressed. The US has decreased its CO2 emissions in recent years, but that has only been because natural gas has become cheap. But peak natural gas will probably happen next year. I expect the decline will slow and turn to an increase again soon…*

This is the graph which matters more than any words we heard yesterday:

The amount of CO2 in the atmosphere continues to increase, and the rate of increase is accelerating. Nothing we have tried in the last 20+ years has changed that basic fact. Nothing said yesterday will change that.

We continue to betray ourselves.

Pogo: We have met the enemy and he is us.

* Well, I did not expect my prediction to be borne out so soon, but a month after I wrote this the EIA announced that US emissions rose in 2013 at the steepest rate ever recorded. So even with cheap natural gas we aren’t doing well.


August 5, 2014

Methane is in the news at the moment for many reasons. Perhaps first is Obama’s plan to reduce CO2 output by 30% by 2030 by reducing coal consumption and increasing the use of natural gas at our power plants. When natural gas burns it produces about half the CO2 that coal does when it burns (for the same amount of heat/power output) so this seems like a big win. Unfortunately it has several problems:

  1. Natural gas is a gas. It leaks. It leaks everywhere. At wells, in pipelines, in processing facilities. No one knows how much it leaks. You might wonder why this matters, but over 100 years a given amount of natural gas will trap 20 times as much heat (cause 20 times as much global warming) as the equivalent amount of CO2. So seemingly small leaks can spell disasters. A recent article by Scientific American concludes that even if fully implemented Obama’s plan would not achieve its goal of a 30% reduction by 2030.
  2. Although we currently have a glut of natural gas that is likely to be temporary. Current projections say that shale gas production in the US will probably peak around 2015 (next year!) and decline steeply thereafter. Relying on it is stupid.
  3. Switching to natural gas will not be cheap. And that infrastructure will still be here in 20, 30, 40 years time. Unfortunately in 40 years time we cannot use it. Natural gas still produces far too much carbon. We need to get our carbon consumption down by more like 80% by 2050, and if we invest heavily in natural gas we will have a bunch of useless expensive junk in 40 years time.

A far better solution would have been to invest heavily in renewables, but that seems to be politically infeasible. Of course even reducing coal usage also seems politically infeasible so perhaps it would have been better to bite the bullet and try for something that might ultimately work…

Another interesting new story is about the recent discovery of mysterious new craters in the Siberian tundra. Three large craters have recently been found. The one which has been examined most closely was probably caused last summer (2013) when the underground methane hydrates heated up to the point where the methane came out of solution, expanded and exploded the ground above it. But there are only three craters, and that was last year.

At approximately the same time as that discovery a Swedish research vessel in the Arctic Ocean found plumes of methane gas bubbling up from 500m subsurface. This should not be happening in the Arctic, the water should be cold enough to trap the gas in hydrates. Even if it were happening the gas should be eaten by microbes before it reached the surface. But it appears that an underwater warm current is now melting the methane hydrates and releasing the gas.

One of the great imponderables (or “tipping points”) in climate sciences was if or when the methane hydrates in the tundra and oceans would release their methane. The problem is that there is an awful lot of methane trapped in these hydrates. Remember methane is a very potent greenhouse gas? The fear is that once methane starts leaking it will cause the earth to get warmer, which will cause more methane to leak, leading to a positive feedback loop where there is exponential heating as all the methane hydrates disappear.

The terrifying thing about passing a tipping point is that once passed there is absolutely nothing that can be done (on a human timescale) to return the world to its prior state. Even if we stopped burning any coal or oil or methane it would not be enough. If this is happening, we are screwed.

No one really knows how much hotter it will get. Nor how fast it will happen. The IPCC has not included this in their estimates.

But the process now seems to have begun. We will find out. Perhaps quickly (where “quickly” may mean decades or even years rather than the centuries that the IPCC has assumed we have).

Drought in Santa Barbara

January 31, 2014

It hasn’t really rained since 7 Dec. Oh we got .01 inches last Sunday (that’s the smallest amount they will measure), and a little sprinkle yesterday, but the total monthly rainfall is .01 and we average 4 inches in January. January is normally our wettest month.
The last 12 months have been the driest consecutive 12 months on record (back to 1868). The next smallest amount was 3.37 inches from Feb 1947 to Jan 1948, and then 3.74 inches from May of 1897 to April of 1898.

San Roque Creek, which is usually full of water in January as it runs beside Jesusita Trail, is currently almost dry. Oddly, it was even drier back in November — perhaps once the sycamores lost their leaves there was more water to flow?

Rainfall in Santa Barbara has always been very erratic. We rarely get the “average” amount of rain, in fact in 62% of years we get less than the average amount. We tend to think that we should get less than the average amount 50% of the time, but that’s because we assume that things are symmetrical, but the distribution of rainfall is not symmetrical — we don’t often get wet years, but when we do, they can be very wet — and that makes up for the fact that most years are dry.
RainFrequencyA graph like the one above represents a poisson distribution, rather than the more familiar normal distribution. More years get about 14 inches of rain than any other amount. So the average rainfall is 18 inches, the median rainfall is 15.5, and the most frequent amount of rainfall is 14 inches. Santa Barbara expects to be dry.

But over the last 12 months we have had 2.9 inches.

That’s extreme.

The wildflowers are dying. Annuals came popping up after the November rains. Yes, it didn’t rain much in November, or December, but our wildflowers are used to dry conditions. It rained enough for them… But there was no rain in January and as the month progressed I watched annual seedlings wither and die. Popcorn flower, stinging lupine, storksbill, phacelias, shooting stars were all recognizable from their leaves in December, but all those leaves are gone or dead now.

Some of the perennials and small shrubs have done better… The plants that were ready in November and December put out shoots or blooms, but those which normally started in January didn’t bother. Manroot (wild cucumber) is usually one of our earliest bloomers starting with the coming of the winter rains, and vines have sprung up and are blooming, but not as many as in years past, and many vines quickly wither and die. Chaparral current is another early bloomer; I saw three plants blooming in December, but none in January; generally there will be plants blooming into March. In one area the late blooming mariposa lilies put out their basal leaves in December; this area is always about a month ahead of other areas; the other areas have not put out any basal leaves.

Hillside Gooseberry normally starts to bloom in late December/early January, but this year I have seen no blooms — until yesterday. Yesterday I found a plant with one dessicated (dead) bloom.

Dry Gooseberry

Normally by now Canyon Sunflowers are showing their large yellow blooms all along Jesusita trail. This year the new leaves they put out in December have shriveled in the drought and there are no blooms. Similarly the hummingbird sage has put out leaves only to have them die. The black sage hasn’t even bothered to produce leaves this year.

Canyon Sunflower

The Bay Laurel is blooming, but only on a few plants, and even some of the ones in bloom have some dessicated buds showing they had to struggle to open. The Ceanothuses are starting to bloom a month later than normal, and I’ve only seen a few blooming (instead of hillsides covered with white or blue). The Holly Leaved Cherries have not bloomed. The Manzanitas have not bloomed.

The saddest comparison I have is of the field of lupines which often grows beside Jesusita. On the left is the field in 2014, on the right in 2010.

Field Of Lupines

Why I’m not thrilled with natural gas

October 12, 2013

The amount of carbon produced by the US has dropped slightly in recent years because we are burning more natural gas (methane) and less coal than we used to. I am interested to see just how much of a difference this makes.

Wikipedia lists the heat of combustion of various fuels, which is an approximation to the amount of energy that can be extracted from those fuels.

fuel HHV MJ/kg % carbon
hydrogen 141.8 0%
methane 55.5 12/16 = 75%
gasoline 47.3 ~85% gasoline is a mixture of varying
components and amounts so
this percentage is approximate
32.5 ~95% coal usually contains impurities,
so it isn’t quite 100% carbon

The interesting question is: For a given amount of energy output, how much carbon will be put in the atmosphere? The actual amounts are immaterial to me, I’m interested in the relative amounts, so I arbitrarily am using 1 Mega-Joule as a reference.

(Most sources quote the amount of carbon dioxide produced rather than the amount of carbon, the conversion is fairly simple, there are 12g of carbon in 44g of carbon dioxide.)

fuel g carbon/MJ g CO2/MJ
hydrogen 0g 0g
methane .75/55.5 = 13.5g 49g
gasoline .85/47.3 = 17.9g 65g
anthracite coal .95/32.5 = 29.2g 107g

So switching from coal to methane while producing the same amount of power would reduce carbon output to 13.5/29.2 = 46%. If we fueled our cars with methane (somehow, rather than gasoline) that would reduce carbon output to 13.5/17.9 = 75%.

Now the IPCC said back in 2007 that if we wanted to keep warming less than 2°C we would have to reduce our annual carbon production to ~15% of then current production by 2050. A reduction to 46% is nowhere near enough.

Doubtless many have argued that 46% is better than nothing, but the problem is that once you build a power plant it tends to continue working for decades, thus many plants built now will probably still be working in 2050. The decisions we make now will keep us from doing what needs to be done by then. If we were actively pursuing solar, wind, geothermal on a large scale then building the occasional natural gas fired power plant would not be a problem. But currently natural gas seems to be looked on as the main solution — and it isn’t.

After writing this I learned of another problem with natural gas: Leaks. You don’t have to worry about coal leaking into the atmosphere, but any badly sealed pipe anywhere in the production chain will leak methane into the atmosphere. Unfortunately methane is a considerably more potent greenhouse gas than CO2. According to Wikipedia it’s direct effect is 72 times more potent than CO2 and there are indirect effects that are harder to quantify. Basically if even 1% of natural gas leaks on its way to being burnt then you are no better off than burning coal. A recent study in Science concludes that after taking leaks into consideration natural gas is worse than diesel but better than coal. (If you don’t have access to Science here’s a summary article in the New York Times.)

Of course some of these leaks can probably be fixed, and various states are attempting to require this.

Climate Change Continues

May 20, 2013

Many newspapers have pointed out the fact that the surface temperature of the earth has not changed markedly over the last 15 years. And in turn some seem to think that because of this climate change is not happening.

Although there is more to climate change than the surface temperature of the earth let us first look at the that claim. After some time spent websearching I found NASA’s downloadable global dataset of land and (surface) ocean temperatures (actually, temperature anomalies — the difference between temperatures and a baseline average). This dataset contains monthly and yearly anomaly data back to 1880. Links to the methodology for calculating the global summary data are here.

Temperature Anomaly between 1880 and 2012 (base temperature is the average between 1950 and 1980). The black line in the upper left shows the best linear fit to the anomalies between 1998 and 2012. It increases.

Temperature Anomaly between 1880 and 2012 (base temperature is the average between 1950 and 1980). The black line in the upper left shows the best linear fit to the anomalies between 1998 and 2012. It increases.

When I first looked at the data I immediately applied a least squares linear regression on the temperatures between 1998 and 2012. Rather to my surprise the regression is not flat as I had assumed the claim was. It is not nearly as steep as the regression from 1990 to 1999, but the yearly change is about the same as the change between 1880 and 2012.

Years Temperature increase (slope of linear regression)
1880-2012 1.17°F/century
1998-2012 1.13°F/century
2000-2009 1.77°F/century
1990-1999 4.86°F/century

So what is it that hasn’t changed? Perhaps they mean the average temperature of the earth? And indeed, 1998 was (up until then) the hottest year on record, the average temperature of the following 15 years is less than the average temperature of that year alone. Well, you sort of expect that if you pick an exceptionally hot year as your baseline. On the other hand there have been 4 years hotter than it since then.

So as far as I can tell, the surface of the world continues to warm, just not as rapidly as it did in the 90s.

But why isn’t the earth warming as fast as it was? More greenhouse gasses are in the atmosphere, one would expect more heat to be trapped on the earth. The answer appears to be that in recent years more of the heat is going into warming up the deep water of the ocean and less into warming the surface. Indeed when this deep water warming is taken into account the heat transfer to the earth as a whole can be seen to be accelerating (Nuccitelli et al).

But climate change is not restricted to temperatures. The ice caps are melting, there are more droughts in our wheat-belts, more fires in areas with Mediterranean climates (who can forget that in SB there were three major fires in the 12 months from July 2008 to June 2009), more and more powerful hurricanes in the Atlantic, more flooding… Recently there have been a number of papers showing that individual storms, droughts, etc. are outside the range of historical variation.

The last time the CO₂ in the atmosphere was as high as it currently is the surface temperature of earth was about 3°C (5°F) warmer than now with the arctic as much as 8°C (15°F) warmer. Sea level was about 30 feet higher. So that’s probably the steady state condition we will obtain if the CO₂ concentration remains at its current level. We don’t know how long it will take to get there, but that’s what we’re looking at. Of course, the CO₂ concentration is still climbing year after year so as things now stand the steady-state condition will probably be even warmer — MIT estimates that by 2100 the CO₂ concentration will be about 900ppm with global temperatures rising to about 10°F higher (and Arctic temps ~20°F higher).

The climate has changed. The climate is changing. The climate will change, probably catastrophically. We just don’t know how long it will take or how far it will go…