“Extreme Weather and Climate Change”

by Daniel Huber, Jay Gulledge

This report got a mention the other day to help explain, or rather, conceptualize what climate change is and isn’t.

Note that it’s from 2011. How optimistic and innocent we were.

Change vs cause

The authors open by noting that climate change doesn’t “cause” events. We need to disabuse ourselves of that rhetoric and framing and find another way to explain climate change.

Using re-insurance data for natural disasters

Often, we hear of new calamitous events and of records being broken, but that still doesn’t help us gain an understanding of the overall trend and risk of climate change.

For this, the authors obtained a dataset on global natural disasters for 1980–2010 from the world’s largest re-insurance company, Munich Re.1:

The report does not include the dataset, but has this illustrative chart:

Chart showing an increasing change in natural disasters with 2010 near an all-time high.

This is not very readable, so here is the version without the legend:

Chart showing an increasing change in natural disasters with 2010 near an all-time high.

Munich Re also track the cost of natural disasters in fatalities and financial losses.

However, Munich Re’s dataset is from their NatCatSERVICE database. Unfortunately, there are two additional problems:

  1. You can only export the data as PDF reports.
  2. You get this lovely disclaimer at the bottom of it:

    The content of this presentation (including, without limitation, text, pictures, graphics, as well as the arrangement thereof) is protected under copyright law and other protective legislation. These materials or any portions thereof may be used solely for personal and non-commercial purposes. Any other use requires Munich Re’s prior written approval.

    Munich Re has used its discretion, best judgement and every reasonable effort in compiling the information and components contained in this presentation. It may not be held liable, however, for the completeness, correctness, topicality and technical accuracy of any information contained herein. Munich Re assumes no liability with regard to updating the information or other content provided in this presentation or to adapting this to conform with future events or developments.

So this is probably why the discussion in the report isn’t more specific. I do recommend you go to their analysis tool and do the following to get an updated report from 1980–2016:

  1. Click “Start Analysis”
  2. Drag the bottom period marker back to 1980
  3. Click “Events” in the left sidebar
  4. Click “Number of events” in the right sidebar
  5. Click “Show” to see it in the browser
  6. Click “Download” to get the full report

Or you can click this chart link to see the chart of 16,532 events from 1980–2016 yourself.

With the in-browser chart, you can scrape the values and use them for your own research. Just note that these folks seem quite litigious.

While the 1980–2010 shows a concerning upwards trend in natural disasters, the 2011–16 data is even more unambiguous about the trend.

Huber and Gulledge (H&G) note about the data that:

More than 90 percent of all disasters and 65 of associated economic damages were weather and climate related[.]

What is climate change?

H&G go back to the basics of what is basically a distinction between weather and climate. Climate is by definition a macro trend as opposed to weather events.

In their words:

Climate is the average of many weather events over [a] span of years. By definition, therefore, an isolated event lacks useful information about climate trends.

This is expanded into a definition of climate change:

Climate change is defined by changes in mean climate conditions.

The problem with means and trends, however, is where it leaves us when discussing single events.

Climate change as risk and probability

So not only can we not talk about climate change as something that causes extreme events, our conceptualization of climate is also that of a more abstract trend than something individual and tangible.

Dismissing an individual event as happenstance because scientists did not link it individually to climate change fosters a dangerously passive attitude toward rising climate risk.

In other words, we need to integrate “risk” into our climate vocabulary.

More on this in a bit.

Manifestations of extreme weather

This report is also useful in listing many of the ways extreme weather manifests itself:

  • Temperature highs
    • Contrasted by a lack of temperature lows
  • Energy demand highs
  • Areas affected differently than before
  • Precipitation: highs and lows (drought)
  • Humidity highs
  • Snowfall highs

Beyond the quantitative measures of averages and frequency over time, there’s also the qualitative matter of intensity:

  • High temperatures in a short period results in heat waves and wildfires
  • Heavy precipitation in a short period results in flooding and mud slides

“Flash” heat and downpour aren’t necessarily growing at the same rate as overall temperature and precipitation increases; they may even outpace them.


Still other regions may not experience a change in total rainfall amounts but might see rain come in rarer, more intense bursts, potentially leading to flash floods punctuating periods of chronic drought.

Minimum-temperature extremes

What I really love about this report is its use of charts that tend to pop up on Twitter every now and then.

We’ve already illustrated climate change through an increase in natural disasters.

This chart showing US temperature extremes may possibly the most famous (and intelligible) visualization of climate change next to the Hockey Stick graph that I’ve come across:

Chart showing an growing trend for both minimum high and low temperatures.

As great as the chart is, it’s one that doesn’t explain itself as much as the people who share it would have us think. Here is the description of the chart in by H&G, broken up into paragraphs by me:

Changes in land area (as percent of total) in the contiguous 48 U.S. states experiencing extreme nightly low temperatures during summer.

Extreme is defined as temperatures falling in the upper (red bars) or lower (blue bars) 10th percentile of the local period of record.

Green lines represent decade-long averages.

The area of land experiencing unusually cold temperatures has decreased over the past century, while the area of land experiencing unusually hot temperatures (red bars) reached record levels during the past decade. During the Dust Bowl period of the 1930s, far less land area experienced unusually hot temperatures.

To recapitulate:

  • An “extreme temperature” here means the upper or lower 10 percentile of the local period of record.
    • Make sure you remember what a percentile is—it’s not a per cent.
  • The two green trend lines are the temperature averages by decade using a 9-point binomial filter function2.
  • There are also two (unmentioned) flat temperature means.

It is very clear that there is a trend here: the extreme temperature lows are diminishing, while the highs are increasing unambiguously.

When I try to understand something, reproducing the finding with the original source data goes a long way. So let’s try to recreate this chart to make sure we have the right idea.

First, go to the graph section of NOAA’s US Climate Extremes Index (CEI).

We full out the form according to what the report said:

  • Region: Contiguous US
  • Period: Summer (June–August)
  • Indicator: Extremes in minimum temperatures (Step 2)

This gives us our table, and after a long-ass time, a chart if we’re lucky. The Excel icon by “Download” is our CSV file.

As an important aside, it is abundantly clear that NOAA NCDC’s data is beyond invaluable in charting and understand climate change. Protect the data at all costs, and poke around the site to see more great—and horrifying—charts about climate change.

I’m going to process this in R with ggplot2. That may sound like Urdu to you, but I’m basically just going to make a bar chart (or histogram) with the “Warm” column above the x-axis and the “Cold” column below.

Here is the R code for it:

# getRversion() => 3.4.1
# packageVersion("ggplot2") => 2.2.1

# NOAA adds title row; skip
temps <- read.csv(url("https://www.ncdc.noaa.gov/extremes/cei/us/2/06-08/data.csv"), skip=1)
# temps <- read.csv("data/us2-06-08-data.csv", skip=1)

# Make "Below" values negative; *-1
temps$Much.Below.Normal <- temps$Much.Below.Normal*-1

red <- "#D7191C" # ColorBrewer
blue <- "#2C7BB6" # ColorBrewer
black <- "#444444"

ggplot(temps, mapping = aes(x=Date)) +
  geom_bar(stat="identity", mapping = aes(y=Much.Above.Normal), fill=red, color=black) +
    geom_smooth(mapping = aes(y=Much.Above.Normal), color=red) +
    geom_hline(yintercept=mean(temps$Much.Above.Normal), linetype="dashed") +
  geom_bar(stat="identity", mapping = aes(y=Much.Below.Normal), fill=blue, color=black) +
    geom_smooth(mapping = aes(y=Much.Below.Normal), color=blue) +
    geom_hline(yintercept=mean(temps$Much.Below.Normal), linetype="dashed") +
  scale_x_continuous(breaks = seq(1910,2010, by=10)) +
  scale_y_continuous(breaks = seq(-60,60, by=10),
                     limits = c(-60,60),
                     sec.axis = sec_axis(~.+0)) +
  labs(x="Year", y="Temperature relative to normal (%)", caption="ndarville.com/reading/") +
  ggtitle("US extremes for minimum temperatures in Summer (Jun-Aug)")

Which renders this chart:

Our own, better-looking, version of the temperature chart.

Click the link for a much larger 800×600 version.

Here is the original chart for comparison’s sake:

Chart showing an growing trend for both minimum high and low temperatures.

Looks like we found the original data and recreated the chart. This means:

  1. We have the source data for future references.
  2. We can update the chart as more data comes in.
    • I mean, hopefully, what with this administration and all.
  3. We actually know what we’re talking about when we talk about this data.

You’ll notice that the decade averages look a little different; I honestly couldn’t be arsed to figure out a “9-point binomial per-decade” regression, so I just went with a default LOESS regression. It comes with a standard error margin, too.

You don’t see this part unless you read the code, but I decided to hide the legend to allow more space for the chart itself for narrower spaces

Explaining risk

H&G pointed out that we need to add risk to our climate-change vocabulary.

We’ve grumbled over how we can’t extricate single weather events from larger climate trends to discuss them on an individual basis. But we also saw how the re-insurance industry hasn’t shied away from documenting the threat and consequences of climate change.

With our statistical approach and data for a quantitative and qualitative assessment of climate change that looks at frequency and intensity, H&B conclude:

[A] probability-based risk management framework is the correct way to consider the link between climate change and extreme weather.

H&B bring up a story of a study of a Texas drought in 2011 where someone estimated three sources that “contributed” to the drought’s intensity:

  • La Niña: 79%
  • Atlantic Multidecadal Oscillation: 4%
  • Global warming: 17%

More important, though, they end the discussion of this with, emphasis mine:

Although information about uncertainty is lacking in this analysis, it clearly identifies global warming as one of the risk factors.

“Risk factor” is another useful way to think of climate change or global warming.

They use examples like lack of exercise and smoking for heart disease and lunge cancer respectively, not as causes of, but risk factors that increase their probability.

Consider this David Leonhardt as an example of how to balance using the right language and conceptualization with explaining climate change and convincing people of its urgency:

The language in this Vox video is also worth watching:

Climate as probability distribution

Risk can be thought of as a continuous range of possibilities, each with a different likelihood of occurring; extreme outcomes reside on the low-probability tails of the range or distribution. For example, climate change is widening the probability distribution for temperature extremes and shifting the mean and the low-probability tails toward more frequent and intense heat events (Fig. 4).

And from a bit farther back in the report:

Risk cannot be thought of in a discontinuous way, with singular events having predictive power about specific future events. Risk is the accumulation of all future possibilities weighted by their probabilities of occurrence. Therefore, an increase in either disaster frequency or severity increases the risk. Events can be ordered on a future timeline and ranked by expectations about their frequency, but this only describes what we expect to happen on average over a long period of time; it does not predict individual events. Consequently, impacts are uncertain in the short term, but the risk of impacts will rise in a predictable fashion. Risk therefore tells us what future climate conditions we should plan for in order to minimize the expected costs of weather-related disasters over the lifetime of long-lived investments, such as houses, levees, pipelines, and emergency management infrastructure.

This is as clearly as we can conceptualize and explain climate change as probability distributions.

H&G illustrate climate change as a risk factor and climate as a probability distribution by bringing in chapter 2.7 of IPCC’s 2001 report, “The Scientific Basis”. It has the title “Has Climate Variability, or have Climate Extremes, Changed?” and features these three charts:

Three IPCC charts showing the change in probability occurrence with an increase in just mean, just variance and mean and variance.

This is the simplified version with just one chart H&G include:

The report's version of the chart above. Just one chart.

Like the previous US temperature chart, I love this one, even though it’s got a lot going on.

Let’s try to recreate it in R:

# getRversion() => 3.4.1
# packageVersion("ggplot2") => 2.2.1


dat <- seq(-3,3, by=.1)

red <- "#D7191C" # ColorBrewer
blue <- "#2C7BB6" # ColorBrewer

p <- ggplot(data = data.frame(x = dat), aes(x)) +
  scale_x_continuous(breaks = c(-3,0,3),
                     labels=c("Cold", "Average", "Hot"),
                     limits=c(-5,5)) +
  scale_y_continuous(breaks = NULL, expand=c(0,0)) +
  labs(x="Temperature", y="", caption="ndarville.com/reading/") +
  ggtitle("Conceptual temperature distribution w/ and w/o climate change") +
  stat_function(fun=dnorm, n=101, color=blue,
                args = list(mean=0, sd=1), linetype="dashed")

increasedmean <- p +
  stat_function(fun=dnorm, n=101, color=red,
                args = list(mean=1, sd=1))
increasedvariance <- p +
  stat_function(fun=dnorm, n=101, color=red,
                args = list(mean=0, sd=1.2))
increasedboth <- p +
  stat_function(fun=dnorm, n=101, color=red,
                args = list(mean=1, sd=1.2))


Which gives us:

Rendering of temperature distributions with and without climate change

I’m just going to do the chart of an increased variance and mean in one, but I rendered others, too: mean version and variance version.

Because this is my first time using R, I couldn’t figure out how to colour the lower and upper deciles with quantile subsetting, but I don’t know how much they end up adding anyway.

You may wonder why the newer distribution has a shorter right tail. Rest assured it doesn’t; I just limited the x-axis range which cut it off.

What we can infer from this chart is that more extreme high temperatures become likelier with extreme lows less likely. The flattening of the distribution shows edge cases getting more likely. Some use the terminology 10, 25, 100- and 500-year events etc, but they are fundamentally confusing and misleading—perhaps even to the people who use them. Besides, either you understand a probability distribution or you don’t.

This, to me, is one of the best ways for us to conceptualize climate change, and due to its simple statistics and mathematics, it’s as dressed down a scientific example you can get. Because our only two parameters to tweak are the mean and variance (sd in the code above), this makes playing around dynamic code straightforward for teachers and learners alike.

Let’s get real

This is just a conceptual chart; what would a real probability distribution look like?

For this, H&G hit up a 2004 chart by Schar et al. with climate data from 1961–1990 redrawn by Barton et al. in 2010. By our 2017, a long time ago, especially if you recall our temperature chart.

Still, its visualization vividly underscores how deeply f— … erm, the gravity of our predicament.

Temperature distributions for 1961--1990 and 2071-2100 (projected). It looks bad, man.

This is fine.

Doom and gloom aside, this is way better than the “x-year event” terminology. Suddenly, the implausible becomes very plausible, all while reminding us just what kind of outlier 2003 was.

So this is where I get a little annoyed with this report, because its endnotes a pretty horrendous; not to toot my own investigatory horn, but it shouldn’t take this much effort to find the original data. The first chart had a shorturl that lead to a 404, but I eventually figured out where the data was from.

With this chart, it took a lot more effort.

  • 38: National Climatic Data Center, (2011). U.S. Climate Extremes Index, National Oceanic and Atmospheric Administration. Retrieved November 22, 2011, from: http://1.usa.gov/vAH4Qx.
  • 42: Barton, N.H., Briggs, D.E.G., Eisen, J.A., Goldstein, D.B. & Patel, N.H. (2010). Evolution. Cold Spring Harbor Laboratory Press, Cold Spring Harbor, NY.

The first source just links to NOAA’s CEI page. The latter is a book that isn’t available for free and doesn’t list its specific references online.

So we’re back to scouring the page to figure out where the hell this came from, just like with the first chart.


Googling for this turned up literally one hit:

site:https://www.ncdc.noaa.gov/ “2071-2100”

And it didn’t even have the data.

After some more research and reading through the Google hits for "1961-1990" "2071-2100" heat wave, it turns out that they used the wrong friggin’ endnote. They refer to endnote 38 (NOAA CEI) while listing “Schar et al.” who’s in endnote 40. Leave aside the fact that his name is Schär.

You might think whining about this stuff is a weird, rambling tangent, but we are literally nowhere if we throw around figures without sourcing and don’t share our datasets. Open data is simply mandatory for verification, education, and reproducibility.

We need to make climate change research accessible!

Finally, we can [google the paper and download it as PDF][] (doi:10.1038/nature02300) (Schär et al., 2004). It’s actually a pretty neat article, no wonder it gets quoted.

This part of the abstract is relevant:

We propose that a regime with an increased variability of temperatures (in addition to increases in mean temperature) may be able to account for summer 2003.

It cites these two sources for its data:

  • 8: Aschwanden, A. et al. Bereinigte Zeitreihen: Die Ergebnisse des Projekts KLIMA90 (MeteoSwiss, Zürich, 1996).
  • 9: Bergert, M. et al. Homogenisierung von Klimamessreihen und Berechnung der Normwerte 1961-–1990 Veröffentlichungen der MeteoSchweiz, 67, MeteoSwiss, Zürich, (2003).

These two articles lead us to the Swiss Federal Office of Meteorology and Climatology, MeteoSwiss.

Let’s see what data Schär et al. picked and what they did with it, emphases mine:

To minimize contamination by local meteorological and instrumental conditions, we amalgamate four independent and particularly reliable stations (Basel-Binningen, Geneva, Bern-Liebefeld, and Zürich) into one single series with monthly temporal resolution. This series is representative for the northwestern foothills of the Alps. Figure 1b–e displays the statistical distribution of monthly and seasonal temperatures.

Poking around the site a bit lead me to “Homogenous monthly data”.

We pick the three datasets from the above quote; each yield a .txt file of this form:

Federal Office of Meteorology and Climatology MeteoSwiss
MeteoSchweiz / MeteoSuisse / MeteoSvizzera / MeteoSwiss

Monthly homogenized values

Station:                  Basel / Binningen
Altitude [m asl]:         316 m
Coordinates:              47° 32.5' N / 7° 35.0' E

Reference date of homogenization:
         Temperature:     01.12.2008
         Precipitation:   01.12.2007

Last inhomogeneity provisionally corrected:
         Temperature:     no
         Precipitation:   no

         Temperature:     °C
         Precipitation:   mm

Missing values:           NA

Data source:              MeteoSwiss
Creation date:            7.09.2017

Year  Month        Temperature      Precipitation
1864      1               -5.5               20.6
1864      2               -0.2               16.0
1864      3                6.0               48.4
1864      4                8.2               49.0
1864      5               13.1               53.2
1864      6               15.3              139.9
1864      7               17.4               50.0
1864      8               16.1               59.4
1864      9               13.2               81.2
1864     10                7.1               10.2
1864     11                3.9               74.1
1864     12               -2.2                4.4
1865      1                1.3               49.7
1865      2               -1.0               69.1
1865      3                0.7               30.1
1865      4               12.9               11.7
1865      5               15.9               85.3
1865      6               16.2               67.1
1865      7               19.4               36.9
1865      8               16.4              122.1
1865      9               15.3                0.0
1865     10                9.8               99.3
1865     11                5.4               70.1
1865     12               -1.1               10.3
1866      1                3.0               36.9

… etc.

As you can see, the data is continuously updated, and I wager this is why I had to pick equivalent datasets with slightly different names:

  1. “Basel / Binningen” (BAS)
  2. “Genève-Cointrin” (GVE)
  3. “Bern / Zollikofen” (BER)
  4. “Zürich / Fluntern”3 (SMA)

Schär et al. then take the Summer (JJA) data and “amalgamate” it in their own parlance.

In other words, the act of data selection is as follows:

  1. Use MeteoSwiss’s temperature data
  2. Limit that to four measuring stations
  3. Limit that to June-July-August
  4. Combine it into one chart

Let’s get to it:

# getRversion() => 3.4.1
# packageVersion("ggplot2") => 2.2.1

bas <- read.table(url("http://www.meteoswiss.admin.ch/product/output/climate-data/homogenous-monthly-data-processing/data/homog_mo_BAS.txt"), skip=27, header=TRUE)
gve <- read.table(url("http://www.meteoswiss.admin.ch/product/output/climate-data/homogenous-monthly-data-processing/data/homog_mo_GVE.txt"), skip=27, header=TRUE)
ber <- read.table(url("http://www.meteoswiss.admin.ch/product/output/climate-data/homogenous-monthly-data-processing/data/homog_mo_BER.txt"), skip=27, header=TRUE)
sma <- read.table(url("http://www.meteoswiss.admin.ch/product/output/climate-data/homogenous-monthly-data-processing/data/homog_mo_SMA.txt"), skip=27, header=TRUE)
# bas <- read.table("data/homog_mo_BAS.txt"), skip=27, header=TRUE)
# gve <- read.table("data/homog_mo_GVE.txt"), skip=27, header=TRUE)
# ber <- read.table("data/homog_mo_BER.txt"), skip=27, header=TRUE)
# sma <- read.table("data/homog_mo_SMA.txt"), skip=27, header=TRUE)

# Combine into one
temps <- rbind(bas, gve, ber, sma)
# Subset for JJA months
jja.temps <- subset(temps, temps$Month == 6 | bas$Month == 7 | temps$Month == 8)
# Average rows with same year value, cf stackoverflow.com/a/18765852/3710111
yearly.temps <- aggregate(.~Year, FUN=mean, data=jja.temps[, -2])
# Create subset for years 1961-1990 like example
yearly.temps.subset <- subset(yearly.temps, yearly.temps$Year >= 1961 & yearly.temps$Year <= 1990)

# Create constant for year 2003
year.2003.temps <- subset(yearly.temps, yearly.temps$Year == 2003)$Temperature

ggplot(yearly.temps.subset, aes(x=Temperature)) +
  scale_x_continuous(breaks = seq(12,28, by=2),
                     limits = c(12,28)) +
  scale_y_continuous(breaks = FALSE,
                     limits = c(0,1)) + # TODO: Remove confusing space beneath minimum
  labs(x="Temperature", y="Frequency", caption="ndarville.com/reading/") +
  ggtitle("1961-1990") +
  stat_function(fun = dnorm,
                args = list(mean = mean(yearly.temps.subset$Temperature, na.rm = TRUE),
                            sd = sd(yearly.temps.subset$Temperature, na.rm = TRUE)),
                color="#444444") +
  geom_vline(xintercept=year.2003.temps, linetype="dashed", color="#D7191C") +
    angle=90) +
  geom_vline(xintercept=yearly.temps.subset$Temperature, color="#2C7BB6")

Here is the result—I suggest you click it for the larger version, as always.

Distribution of Swiss temps

Thank god, the 2003 value lines up with the original, so it looks like we may have found the right datasets—or ones close enough anyway.

I’m not going to try to reproduce the “fitted Gaussian distribution”; consider that your exercise. But.

Since we’re into September, August just passed, which means we have the data up to and including 2017. The first chart spans 1961–1990, 29 years. Rather than try guesstimating the future of the climate, how about we take another 29-year-old look at 1988–2017 instead?

Incidentally, I was born in 1987, so these are the temperatures for my life, charted:

# ...
yearly.temps.subset <- subset(yearly.temps, yearly.temps$Year >= 1988 & yearly.temps$Year <= 2017)
# ...

Distribution of Swiss temps 1961--1990 Distribution of Swiss temps 1988--2017; clear moves to the right

I tried to line the two ups as much as possible, but I think the trend is still quite visible.

When comparing this to Schär et al.’s original chart and projection, consider this:

  • My two charts for 1961–1990 and 1988–2017 are 29 years apart.
  • The projection is for 2071–2100; 110 years ahead of our 1961–1990 chart and 83 of 1988–2017.
  • The pace of climate change is faster than we’d like to think.

Furthermore, look at how the mean temperature is already changing—and what it’s projected to.

Closing thoughts

If I ever have to give people a link to bring them quickly up to speed on what climate change is and how to explain it, I can do no better than this article.

Unfortunately, the slog of finding the original data to wrap my head around the research and science due to the limited sourcing has been frustrating, but worse, deters readers from understanding and believing the full scope of the arguments and climate science within. One point docked.

Using the tools and language of this report to explain and teach climate change is like telling someone to stare directly at the Sun; it’s hardly good for your health to do for extended periods of time, because let’s face it; the prospects are fucking depressing unless you’re a member of a doomsday cult.

This isn’t the first time we were faced with bleak prospects and poor odds, and we owe it to others and ourselves to confront people with the realities; if they want to fuck up the world and future generations, let them do it while staring at the facts with open eyes.

Maybe we can also help make climate science and facts cool again. The world does not need that many computer scientists.


These are the three datasets I used for the three (types of) charts, lest you forget.

Project files on GitHub

This has been a large exercise in finding the original sources and data and ensuring their reproducibility. Obviously I’d be remiss not to make all this available to everyone as accessibly as possible.

Go to my new open-climate repo on GitHub and check out the files for this reading of H&G’s report. GitHub unfortunately does not support R Notebooks as of this writing, so no interactive playground for now.


All this work and what if someone ends up snatching all my images and redistribute them elsewhere?

Well, that thinking is actually addressed in this very piece. Because what is a data visualization without any confidence in its underlying data? You’ll be sharing my plot of the data, but if you don’t know what the data is, you’re only appealing to the confirmation bias in people—not their scientific rigour.

When I add “ndarville.com/reading/” in the bottom right of the chart, it’s less of a credit-taking watermark; it’s to represent the data and code that goes together with the data visualization. To only share either is to do no service to the people you purport to help understand our cataclysmic and urgent predicament.

Climate-change reporting and open data are sine qua non.

Now get to work.

  1. “Topics Geo natural catastrophes 2010: analyses, assessments, positions” (2011). Referenced by Scientific American in “Insurance Company Ranks 2010 among Worst Years Ever for Climate Disasters”↩︎

  2. I am not that hardcore with statistics, so I don’t know why they use this particular regression, but I’m sure they know what they’re doing. ↩︎

  3. Note that the search field doesn’t treat “u” and “ü” as the same character, so just type “z” for Zürich instead of “zu”. ↩︎