Have there really been more earthquakes than average?

Update: January 3rd, 2011 – A final update on 2010 numbers posted right here.

Damage in Santiago, Chile. Photo by Reuters/Marco Fredes

After the massive earthquake this past weekend in Chile, MSNBC published a sensationalistic piece entitled, “Is nature out of control?” The Wall Street Journal asked if three massive earthquakes around the world in two months are related and a cause for alarm. The mainstream media, always searching for sensationalistic or fear mongering news, has latched onto the question; are we seeing more earthquakes than normal?

Well, not really.

To better understand why, let’s take a look at how many earthquakes occur each year on average. The USGS has a fascinating page of earthquake facts and statistics, with the following table:

Magnitude Average Annually
8 and higher 1 ¹
7 – 7.9 17 ²
6 – 6.9 134 ²
5 – 5.9 1319 ²
4 – 4.9 13,000
(estimated)
3 – 3.9 130,000
(estimated)
2 – 2.9 1,300,000
(estimated)

¹ Based on observations since 1900.
² Based on observations since 1990.

For our analysis, let’s take earthquakes based in the magnitude 6.0 – 6.9 range. Why am I picking earthquakes in the M6 range? It’s arbitrary. You can repeat this process for earthquakes of any range. Based on data recorded since 1990, we’d expect to see an earthquake within this magnitude range occur every 2.7 days or so.

So here we are, on March 1st, 2010, the 60th day of the year. How many earthquakes in the M6.0 – M6.9 range have we had this year? According to this handy search tool from the USGS, there have been 25 earthquakes of M6.0 – M6.9 in 2010.

That works out to roughly one earthquake in the magnitude 6 range every 2.4 days. That doesn’t seem totally unreasonable or a reason for alarm, but we should do some further work to put it in context.

We can plot up the number of earthquakes per year and come up with a standard deviation, assuming a normal distribution of earthquakes in any given magnitude range.

``` Total results: 21 Mean (average): 2.67143 Standard deviation: 0.41732 ```

So, the number of magnitude 6 earthquakes that we’ve had in 2010 falls within one standard deviation of the mean. If we were to plot up a graph, it’d look like this. The error bars represent one standard deviation.

Awesome! Well, what about those ranges of values that fall outside of one standard deviation from the mean? For those that don’t understand how statistics works, check out the following bell curve from Wikipedia.

This shows roughly the percentage of values that you’d expect to fall within a specific standard deviation away from the mean value.

Dark blue is less than one standard deviation from the mean. For the normal distribution, this accounts for about 68% of the set (dark blue), while two standard deviations from the mean (medium and dark blue) account for about 95%, and three standard deviations (light, medium, and dark blue) account for about 99.7%.

So, if we modify our graph to show an error bar of 2 standard deviations, you’ll notice that every result since 1990 fits inside this model! Statistically speaking, you would expect to find 95% of all results falling within two standard deviations of your average. Simply put, there is absolutely nothing strange happening.

In fact, thanks to this normal curve you can basically predict, with a 99.7% chance of success (three standard deviations), that an earthquake of equal to or greater than M6.0 will occur somewhere around the world within the next 3.5 days. Update: Proven correct! A M6.4 earthquake occurred in Taiwan on March 3rd.

Alright, so what’s with all the coverage on earthquakes? It sure seems like a lot is happening, right? We can attribute this to observer bias. The massive devastation in Haiti warranted a large amount of news coverage. Because this is so fresh in everyone’s mind, people are more likely to notice any news or information related to earthquakes anywhere in the world. An earthquake of M6.0 or greater, usually garners international attention.

It’s the same principle that happens whenever you acquire some new toy, gadget, or piece of clothing. Suddenly, you notice that particular item around all the time. It’s like everyone has it.

So, bottom line, the Earth isn’t becoming more active, more dangerous, or even “out of control.” Despite the fear mongering and what esteemed mainstream media networks would have you believe, the simple reality is that the numbers prove things are happening at an expected rate. Keep that in mind the next time a large earthquake happens and everyone is wondering why the Earth seems so active!

Update (April 21, 2010): Chris Rowan at Highly Allochthonous has a great post on yearly earthquake averages and variability with larger magnitudes.

In the last 28 years, there have been on average around 13 such ‘significant’ earthquakes a year, with a magnitude 8 occuring about every year and a half. This average rate is marked by the grey line on the plot: if we extraplolate the six major earthquakes recorded in the first four months, 2010 is on course to experience 18 major earthquakes, a little above average but well within the variability shown by the whole dataset (and it’s actually closer to the centennial average of 16 major quakes a year reported by the USGS above).

Water vapor and climate change

Just saw this absolutely ridiculous article posted on Digg, by way of the Guardian: “Water vapour caused one-third of global warming in 1990s, study reveals.”

That’s gotta be one of the more sensationalist titles ever written in the climate change debate, which will help fuel and legitimize claims made by climate change deniers. Anyway, the article does have some interesting nuggets and things that should be discussed.

Scientists have underestimated the role that water vapour plays in determining global temperature changes, according to a new study that could fuel further attacks on the science of climate change.

The research, led by one of the world’s top climate scientists, suggests that almost one-third of the global warming recorded during the 1990s was due to an increase in water vapour in the high atmosphere, not human emissions of greenhouse gases. A subsequent decline in water vapour after 2000 could explain a recent slowdown in global temperature rise, the scientists add.

Basically, scientists need to do a better job modeling how water vapor plays a role in climate change. That said, there are few interesting things to consider, that this article fails to mention:

• Examples of common greenhouse gases are CH4 (methane), CO2 (carbon dioxide), N2O (nitrous oxide), and H2O (water!).
• The atmospheric concentration of CO2 and CH4 *is* increasing, mainly due to anthropogenic causes (burning coal, oil, and natural gas).
• In general, the concentration of H2O in the atmosphere varies (but is dependent on atmospheric temperature), however there is a complex relationship between increased H2O -> increased cloud cover -> increased albedo.

The second thing to consider is the relative impact each of these gases have on trapping heat. In general, all greenhouse gases are compared to CO2 (which has a value of 1.0). This is called the global warming potential.

Methane is 25x stronger at trapping heat than carbon dioxide! Again, the atmospheric concentration of both of these gases is increasing. What is water vapor’s effect on trapping heat?

A GWP is not usually calculated for water vapour. Water vapour has a significant influence with regard to absorbing infrared radiation (which is the green house effect); however its concentration in the atmosphere mainly depends on air temperature. As there is no possibility to directly influence atmospheric water vapour concentration, the GWP-level for water vapour is not calculated.

Anyway, how do we know that concentrations of carbon dioxide and other greenhouse gases are increasing? I wrote an article about that on the Geology News Blog awhile ago. Check it out.

The Known Universe

This video of The Known Universe is from the American Museum of Natural History’s Hayden Planetarium in New York City, and zooms out from the mountains of Tibet, showing every single satellite (artificial and not), star, and known galaxy in the universe. Absolutely incredible!

Can you imagine if this was displayed in the Cal Academy of Sciences’ Morrison Planetarium? (Which, if you haven’t been, is probably the most amazing planetarium in the world).

My immediate reaction on seeing this video was thinking back to the Powers of 10 video that I saw in a junior high math class, probably around 1995 or so.

[Via Kottke]

A Glorious Dawn – Carl Sagan and Stephen Hawking

Using auto-tune and clips from Carl Sagan and Stephen Hawking to explain the Universe. Beautiful

And here is another song done by the same artist, this time featuring Carl Sagan, Richard Feynman, Neil deGrasse Tyson, and Bill Nye.

[Via Mental Floss]

Visiting the International Space Station

I keep joking that I need to keep a dream journal, since I have ridiculously vivid dreams every single night.

Last night, I apparently won a trip to the International Space Station. Unfortunately, in my haste to “pack” for the trip, I didn’t bring very much. Nor did I know that I would be in space for 6 months.

When I finally reached the space station, I realized that I had forgotten my DSLR. I also forgot the charging cable for my iPhone (hey – that means no games of chess or sudoku!).

Oh, and the station apparently had gravity as well. That meant there was no fun to be had floating through doorways and such!

Over on the Geology News blog, I posted two videos I recorded yesterday playing with the new version of Google Earth.

The first video examines Monterey Canyon, an underwater canyon near Monterey, California. The second video is the area that Spirit, a Mars Exploration Rover, landed at in January 2004.

Amount of Water Discharge in the Zanja near Mill Creek, Mentone, California

I. Introduction

The Zanja roughly translates to “ditch” in Spanish and was built in the early 1800’s by Native Americans, under the guidance of Spanish missionaries, to bring water to an outpost of Mission San Gabriel. [1]

My parents own a house along the Zanja in Mentone. Water flows at roughly bank full depth year round. The Zanja has been the subject of a number of lawsuits between various municipalities and the home owners who live along its banks. These lawsuits have focused on the issue of water rights since the county and various cities want to divert the flow of the Zanja and use it for drinking water, effectively cutting off the flow of the Zanja to the homeowners. A settlement was eventually reached in which both sides agreed not to use the water for drinking or irrigation, and the Zanja would continue to be allowed to flow through the private properties of homeowners who lived along its banks.

Many of these lawsuits happened when I was fairly young, so I don’t remember many details about them, or the studies both sides presented for their cases. Regardless of this, I was curious to see how much water flows through the Zanja. Was the amount of water that the cities wanted to get their hands on that significant? Thanks to reading the book Cadillac Desert and recently finishing a geomorphology class, my curiosity got the best of me. So I set out to find just how much water is flowing through the Zanja.

II. Methods

In order to determine the amount of water flowing through a given spot in the Zanja at any one second, I needed to find 3 variables: Depth (D), Width (W) and Water Velocity. The depth was easily determined by simply measuring across a specific spot, which we’ll call cross section ‘A’. Depth was determined by taking a series of 3 measurements across cross section ‘A’ and then averaging them. Velocity was probably the most difficult aspect. I measured the distance between two points along the bank and then threw a tennis ball in the water, recording the amount of time (T) it took for the ball to move between those two points (H). I repeated this process six times and then came up with the average time it took for the tennis ball to cover that distance.

Once I had the physical data, I did some calculations to come up with a cross sectional area of the water at that point (W x Davg) as well as the Water Velocity (H/T). The calculations for cross section was in inches and I wanted feet. Since W x Davg gives units in terms of square inches, I divided by 1 square foot (144 inches) to convert to square feet. Water Velocity was already measured in terms of feet per second, so no conversions were necessary.

III. Results

Legend:
Davg = Average depth
W = Width of stream
H = Distance between two points along river
Vavg = Velocity of tennis ball averaged over 6 trials
A = Area of Cross Section ‘A’
Qw = Amount of water discharge

Davg = 6.3 inches
W = 89 inches
H = 7 feet
Vavg = .97 ft/sec
A = ( Davg x W) = 561 sq. inches / 144 sq. inches = 3.9 sq. feet
Qw = A x Vavg = 3.9 sq. feet x .97 feet per second = 3.8 cubic feet per second

IV. Discussion

My final result, after rounding to the correct amount of significant figures was 3.8 cubic feet per second. Comparing this to the discharge of many famous rivers, this amount is extraordinarily miniscule. The Mississippi River has an average discharge of 470,000 cubic feet per second. [2] The Santa Ana River, which flows to the west of the Zanja, and where much of its water ultimately ends up, has a mean annual discharge of 33.8 cubic feet per second. [3] For being one of the largest rivers in Southern California, this is a very small amount. Needless to say, we do live in a very arid environment.

Does enough water flow through the Zanja to justify local municipalities trying to take it? To simplify things when dealing with quantities of water, many organizations speak in terms of acre-feet. An acre-foot is the amount of water a family of four will need for one year. [4] According to Google, 1 acre-foot is equivalent to 43,560 cubic feet. Dividing this by 3.8 cubic feet per second, we find that it takes 11,463 seconds (or just over 3 hours) to fill the amount of space required by one acre-foot of water.

According to the 2000 census, the nearby city of Redlands has a population of 63,591 people. To simplify calculations, I divided by 4 to come up with the number of “families” who will be needing water, or the number of acre-feet that Redlands would need. Almost 16,000 acre-feet! Multiplying that by 3 hours per acre-foot, it would take nearly 5 and a half years to store enough water from the Zanja to supply the residential needs of Redlands for one year. As you can see, that in itself isn’t too practical. Not accounting for evaporation or infiltration, by itself the Zanja would be able to meet about 20% of the residential needs for the city of Redlands. This isn’t that much in the scheme of things and almost doesn’t justify the cost and effort that would be needed to bring the water into Redlands or any other city. However, in Southern California, water is nearly more valuable than gold.

V. Conclusions

My data should be taken with a grain of salt as most of the data is based on rough estimates and many assumptions. There are quite a few sources of error, such as average velocity. In most cases, you would measure velocity just below the surface, where water is flowing the fastest, as well as taking a variety of discharge measurements for multiple locations and averaging those to get an overall discharge for the river. My data represents the amount of discharge at a single spot on the Zanja and I would assume it is roughly average, based on my observations of the water level over the years. However, I have no data to quantify that.

Regardless of these issues, the amount of water flowing through the Zanja at any given moment is quite small. Given the scarcity of water in Southern California, the cost and consequences of removing the water from its “natural” channel to use for drinking water outweigh the cost of leaving the water in the channel for many to enjoy, as it runs through Redlands and many of its parks.

VI. References

[1] How big where their footprints? “Mission Era 1,” [online]:  [Accessed 30th May, 2004].

[2] LA Coast. “Mississippi River Delta Basin,” [online]: [Accessed 30th May, 2004].

[3] 1999 California Hydrologic Data Report. “11051500 SANTA ANA RIVER NEAR MENTONE, CA,” [online] [Accessed 30th May, 2004].

[4] National Resources Defense Council. “Drawdown – Groundwater Mining on Black Mesa,” [online] [Accessed 30th May, 2004].