Tag Archives: Global Warming

How Fast is the Sea Rising?

I’m not asking how fast it was rising. I looked at that in the last post, using three different reconstructions of sea level since 1900 based on tide gauge data. And my goal wasn’t really to estimate the rate of sea level rise, as much as it was to show that the rate has not been steady, it has changed over time; in fact it has gotten faster (acceleration).
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The Truth about Sea Level Rise

It’s easy to see that sea level rise has not been steady. It has accelerated.

In fact it has accelerated a lot, especially recently. For most of the 20th century, it rose sometimes faster, sometimes slower, but for the last few decades its rise has picked up speed. The clearest demonstration is the change in global mean sea level. There are several different estimates of that based on historical data from tide gauges around the world, which differ on how much and how fast sea level has risen, but they all show — without a doubt — that the rise has not been steady.

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An Honest Appraisal of the Global Temperature Trend — Part 2

Readers were kind enough to point to the newest revision of global temperature data from the Hadley Centre/Climate Research Unit in the U.K., the HadCRUT5 data (a revision of the HadCRUT4) data.

The HadCRUT4 data were in disagreement with the other surface temperature data sets, namely those from NASA, Berkeley Earth, and NOAA. But the new HadCRUT5 data set agrees with them excellently:

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An Honest Appraisal of the Global Temperature Trend

The “Heartland Institute” is hosting their 14th annual “ICCC” convention this weekend in Las Vegas, Nevada, to carry on their mission as one of the world’s leading organizations of climate deniers. One of the sessions listed on their schedule for this very morning is about the latest global temperature trends, hosted by none other than Anthony Watts, Roy Spencer, and Ross McKitrick. I’m familiar with their work.

I thought it would be a good idea to present an honest appraisal of the subject at hand.

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One Look at a Graph

Paul Homewood objects to the U.K. Met Office telling people that “Arctic sea ice decline continues.” Of course his opinion is echoed at WUWT.

It’s Paul Homewood whose claims are false.

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Hurricane Ida: Climate Change makes a Monster Storm

Warm sea water is what powers hurricanes. Usually, sea surface temperature (SST) in the Gulf of Mexico needs to exceed 29°C to intensify a hurricane, and every fraction of a degree above 29°C increases the chance — dramatically — of not just intensifying, but super-charging it, creating a “monster storm.”

Which makes one wonder … if a storm passes by, what are the odds the sea surface temperature (SST) will exceed 29°C? Or more? Have the odds changed over time? Of course SST isn’t the only factor at play, only fools say so, but only bigger fools deny its impact on tropical storms.

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3 Graphs

Earth is heating up.

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European Heat

The memory is still fresh, in the minds of Americans, of the fearful heat wave which struck the Pacific Northwest in late June, reaching temperatures never before imagined in the region. It drives home the point that the effects of climate change are here, now, to stay — and that includes more and hotter heat waves.

Convincing Americans of that is made easier by the fact that we ourselves have seen it happen in our own back yard. I suspect it’s downright easy to convince Europeans — because they’ve seen it before. More than once.

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Northwest Heat Wave

When extreme heat gripped the Pacific northwest recently, people noticed. They noticed in Seattle, Washington, where they set an all-time record high of 104°F on June 27th, only to break it the next day at 108°F. They noticed in Portland, Oregon, where they set the all-time record high of 112°F on June 27th, only to break it the next day at 116°F. They noticed in Lytton, Canada, where they set the all-time record high for all of Canada at 121°F, only to burn to the ground the following day.

Naturally this has led to speculation about the relationship of this particular heat wave to man-made climate change (global warming). One of the reasons we expect global warming to increase extreme heat, is illustrated in this graph:

It compares two probability distributions, one (in yellow) with a lower average, another (in red) with a higher average. As the average (i.e. the mean) temperature increases, the amount of extreme heat increases dramatically — provided, of course, that the shape of the distribution remains the same.


Does the shape of the distribution remain the same? Of course not — at least, not perfectly so. But it turns out that for summer in the Pacific Northwest, the change in shape is quite small, in fact so small it’s hard to confirm it exists at all, while change in the average sticks out like a sore thumb.

Let’s use data for daily high temperature averaged over the “Pacific Northwest” as defined by the study region of a recent attribution study of the connection between this event and climate change, shown by the box in this map:

It covers the region from latitude 45°N to 52°N, longitude 119°E to 123°E. The data are from the ERA5 re-analysis data set, which was also used in that attribution study. It’s provided in Kelvins, but I converted that to degrees Fahrenheit for a more familiar temperature scale (at least, for my American readers). And here it is, daily temperature for the study region from 1950 through the end of June 2021:

Here’s data for just temperatures over 85°F, to show where the extreme heat has happened:

Note that before this year, the average temperature throughout the region never exceeded 95°F, but this year it easily broke 100°F.

I’ll define summer as the months June, July, and August. Here’s the data for just the summer months:

It’s straightforward to average the temperature during each year, except we should leave out the year 2021 because it’s not over yet. Averages for each year (except 2021) look like this:

The red line is the linear trend (from linear regression), is strongly statistically significant (p-value < .0001), and indicates that the average summertime temperature increased 3.9°F from 1950 through 2020.

There’s no doubt that the average has changed over time — nobody in his right mind disputes that. But what about the distribution itself? Has its shape changed, and in particular, what has happened to the “extreme heat” end of the distribution?

Let’s look at the hottest temperature for each year, but just for fun let’s omit this year’s record-breaking value:

The trend line (in red) is estimated by linear regression, is strongly statistically significant (p-value 0.001), and suggests an increase in yearly maximum temperature of 4°F from 1950 through 2020. So, for summer at least, it’s not just the average that has gotten hotter, so too has the yearly maximum value.

Still, I’d like to get at the distribution itself for summertime. To that end, I’ll transform temperature into temperature anomaly by subtracting, for each value, the average for that time of year. Doing so, I remove the annual cycle from the data (which is still present because early and late summer are cooler than mid-summer). Here are the anomalies:

They aren’t too different from the temperature data itself.

Now let’s separate the anomaly data into two big intervals of time: “early” from 1950 to 1985, and “late” from 1985 to now. We can estimate the probability distribution for each by making a histogram, as well as a smooth estimate, and I’ll compare them with pre-2000 data in blue and post-2000 data in red (solid lines are smoothed estimates):

It’s rather striking how almost all of the negative anomalies are less likely lately than earlier, and almost all of the positive anomalies are more likely now than before. It certainly seems plausible that the “late” distribution has the same shape as the “early” distribution, but shifted to the right, toward higher temperatures.

Let’s focus on the extreme-heat end by looking at the survival function (which is 1 minus the cdf, or cumulative distribution function) for high temperature anomalies:

There’s no doubt, the Pacific northwest is getting more extreme heat. But is that just because the distribution shifted to the right, or is shape change part of the story?

Let’s compute probability distributions, not for the anomalies as we just did, but for the anomalies offset by a constant to make their average values the same (in particular, zero). I’ll call these “De-Trended” anomalies (a crude term). Here are the histograms and smooth estimates of the probability density function:

There may be some shape change, but perhaps not — perhaps the differences are just random fluctuations within the uncertainty range. We’ll get a better idea of what’s happening on the high end with the survival function:

Again, it’s plausible that they are the same because they are almost entirely within each other’s uncertainty range. It is possible that the distribution has changed at the high end with the appearance of de-trended anomalies not before see, but the statistics don’t confirm that yet.

Perhaps the “go-to” statistical test for whether two distributions are the same, is the Kolmogorov-Smirnov test. When I use it to compare the anomalies (not de-trended), it proves they are different (p-value 0.00000000000000022), which of course they are because they have a different mean value. But when I compare the de-trended anomalies, there is no significant evidence of a difference between the distributions. The p-value is 0.4974 — not even close to significant.

My bottom line: The evidence demonstrates that extreme heat has gotten more frequent and more severe, and we can expect it to continue, because the probability distribution has shifted to hotter values with no confirmable change in its shape. But it is possible (not yet confirmed) that the recent heat wave is so much hotter than we’ve seen before that there’s more going on — which means we can expect even worse.

Yet people continue to dispute even the simple idea, which is easily shown for the Pacific northwest, that the increase in the average has brought with it an increase in extreme heat. One such is Judith Curry (from whom I got the first graph shown), who gives references to the peer-reviewed literature which I went and read, only to make me wonder whether or not she read them. At least she delivers on the promise of her blog title: hot air.

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Supermoon Flooding

You may recall when I posted about flooding from high tide alone, even without storm surge or rainfall. It’s because of sea level rise. No doubt. It’s getting worse. No doubt.

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