Secrets of the Earth: Gravity (2013 Outreach)

The Weather Channel’s Secrets of the Earth aired an episode called Gravity. In it, I described gravity and discussed GRACE, mantle convection, and climate change.

My more nuanced attribution statement didn’t make the cut: “Melting ice is what we expect in a warming world, and most of the warming since 1950 is very likely due to our CO2 emissions.”

Also, melting sea ice doesn’t affect gravity because it’s already floating. GRACE can only detect changes in land ice.

Here’s some of the rest of our conversation, from my memory and emails:

  1. Gravity
  2. Hudson Bay and mantle convection
  3. Climate change


What is gravity? Why is it this mysterious force?

Gravity is mysterious to physicists who are still trying to use quantum mechanics to understand how gravity works on very small scales. But the Earth is pretty big, so we can use Isaac Newton’s theory of gravity. It’s much simpler:

Every object in the universe attracts every other object to it. This gravitational force is stronger for more massive objects, and stronger the closer you are to that object.

Are there still mysteries about gravity that need to be solved?

Sure. How does gravity behave on scales smaller than an individual proton? We don’t know, because we can’t yet explain gravity in terms of quantum mechanics.

But on scales larger than an individual proton, gravity is now a useful tool for detecting mass. We use satellites like GRACE to detect mass on the surface of the Earth. Astrophysicists use similar techniques to detect dark matter around galaxies.

What is a gravity anomaly?

A gravity anomaly happens when some spot has gravity that’s very slightly different than predicted.

Why are gravity anomalies on Earth an interest to scientists?

Scientists are interested whenever predictions fail, because that’s when new discoveries happen.

I’m interested in how gravity changes with time, because these events affect lots of people.

For instance, the 2004 Sumatra earthquake produced a gravity anomaly which helps us understand how the Earth’s crust behaves before and after a megathrust earthquake.

GRACE can also detect floods, such as the 2011 floods in Australia, South America, Asia, the Mississippi River, etc. The mass of that extra water strengthened gravity. GRACE also detected the 2005 and 2010 Amazon droughts because they reduced gravity.

How does gravity affect weather on Earth? Does Earth’s weather affect gravity?

Variations in gravity don’t really affect weather, but weather definitely affects gravity. This can be used to detect some weather events.

When did scientists begin measuring gravity on Earth? What was the purpose? What instruments were used?

Scientists have been measuring gravity for over a century, both for curiosity’s sake and to find dense mineral deposits. At first, they used pendulums, then springs, then superconducting gravity meters.

Hudson Bay and mantle convection

What is mantle convection? (And can you explain “downwelling” in simple terms?)

We can see convection in a pot of water boiling on a stove. Water at the bottom is heated, which makes it less dense so it rises to the top. Then it cools, becoming more dense, so it sinks. This convective process is similar in the Earth’s mantle, except it’s a lot slower. The sinking material is known as mantle downwelling.

This graphic shows upwelling, so just reverse the red arrows to imagine the downwelling in Hudson Bay. The downward red arrow in your imagination is what’s pulling the crust down.

Halfway through this short video is a really cool animation. Again, it’s the opposite from the downwelling in Hudson Bay.

What is the temperature of mantle convection?

Mantle convection is driven by very hot (~7000°F) temperatures at the bottom where the mantle meets the outer core. Temperatures decrease as one travels upward to the crust, where they’re “only” about 1000°F.

How far below the surface does mantle convection occur? How deep is the downwelling in the Hudson Bay?

Erik Ivins tells me that mantle convection very likely extends into the deep mantle where it meets the outer core. That’s ~1800 miles below the surface.

He tells me that this conclusion comes from measurements of the boundary between the outer core and the deep mantle. That boundary is deeper than we’d expect if mantle convection didn’t extend into the deep mantle. In other words, as mantle downwelling “bounces” off the outer core, it pushes that boundary down.

How did GRACE determine that the gravity anomaly was due to the last ice age?

Scientists have known for decades that an ice sheet used to cover Canada, and that this weight pushed down the rock under the ice sheet. Thousands of years after the ice sheet melted, the ground is still rebounding. This is called post-glacial rebound (PGR).

Why was it determined that the last ice age couldn’t have been the sole reason for the gravity anomaly in the Hudson Bay?

GRACE sees two different gravity anomalies in Hudson Bay. First, gravity is low in Hudson Bay. Second, gravity in Hudson Bay is getting stronger each year.

Both mantle convection and incomplete PGR can explain why gravity is low in Hudson Bay.

But only PGR explains why gravity is getting stronger in Hudson Bay, because the ground is slowly rebounding from the pressure of the ice sheet that used to be there. On the other hand, mantle convection changes so slowly that it’s essentially permanent on these timescales, so it can’t explain changes in gravity over time.

So scientists estimated how big the ice sheet used to be, and fit that estimate only to the change in gravity over Hudson Bay to obtain the contribution from incomplete PGR.

What percentage of the gravity anomaly is due to the last ice age? Mantle convection? (Or is the jury still deliberating?)

Roughly 1/4 to 1/2 of the low gravity anomaly is due to incomplete PGR. The rest is presumably due to mantle convection.

How are ground based gravity instruments different than GRACE?

Gravity meters on the ground near Hudson Bay actually see decreasing gravity, because that ground is moving up. Since those gravity meters also move up with the ground, they’re moving farther away from the center of the Earth. Since gravity is weaker farther away from the Earth, ground-based gravity meters see decreasing gravity.

How do scientists reconcile this difference? Do they just average the results from GRACE and ground gravity meters?

No, they’re just measuring the same phenomenon in different ways. This difference is one of the counter-intuitive surprises that scientists deal with every day.

Do we know how long mantle downwelling has been occurring in the Hudson Bay?

We don’t know, but deep mantle convection can take ~200 million years just to go through one complete cycle. I don’t know how many cycles have taken place…

So the gravity loss due to mantle convection could have taken place over several 200 million year cycles?

Yes, but how many cycles I don’t know. The Laurentia craton has been relatively stable for at least several cycles, and contains the Acasta Gneiss: the oldest rocks on the planet.

So this is an extremely old part of the crust, but the current downwelling might not be that old.

So would it be safe to say the recovery would take place over “several” 200 million years?

Hypothetically, if the downwelling were to stop, It probably wouldn’t stop faster than a single convection cycle of 200 million years. Emphasis on probably: again, this isn’t my field.

Regardless, 200 million years is ~10,000 times longer than the ~20,000 years over which post glacial rebound occurs.

… and the gravity from PGR will be recovered in 5000 years?

PGR will be finished on a timescale measured in thousands of years. I don’t know enough to be more specific than that.

If downwelling involves denser material in the mantle, wouldn’t that make gravity stronger?

This is another counter-intuitive surprise that I didn’t mention.

Downwelling is where more dense material sinks. This might lead one to believe that more dense = higher gravity.

But the sinking mantle material also drags all the earth above it down with it. Thus, ironically, more dense material leads to lower gravity, but only because it dragged the ground down.

This is related to the other surprise I did mention, that gravity changes have different signs when measured by GRACE vs. ground gravity meters.

Has the gravity anomaly in the Hudson Bay affected the planet in any way?

No, but the collapse of the ice sheet that used to fill Hudson Bay probably caused the Younger Dryas. All that melted glacier water spilled into the North Atlantic, disrupting the circulation that carries heat to Europe from the tropics.

Update: Some evidence suggests that the Younger Dryas was caused by an asteroid impact.

Do we know why there’s mantle downwelling below the Hudson Bay?

What goes up must come down, so upwelling in other places must be balanced by an equal amount of downwelling somewhere. Why it occurs in Hudson Bay specifically, I don’t know.

Could the extreme downwelling in the Hudson Bay be due to the fact that the Canadian shield having deepest “continental root” on the planet?

This isn’t really my field, but I wouldn’t want to say that Hudson downwelling is due to the deep continental root. Remember that the Indian ocean gravity is even lower than Hudson Bay. Look at the third map here.

The Indian ocean gravity low has been studied, with a 1983 paper saying “An uncompensated depression is consistent with the downgoing arm of a convection cell, and also with the presence of a mechanical wake left in the upper mantle behind India as it traveled toward Asia.”

The Indian ocean gravity low has also been linked to downwelling and doesn’t have a continental root at all. Unfortunately I can’t find relevant papers more recent than 1983 in my brief search. Again, not really my field…

How much gravity was reduced by mantle downwelling in the Hudson Bay?

Tamisiea et al. 2007 (PDF) was the source of my statement that incomplete PGR can explain roughly 1/4 to 1/2 of the gravity anomaly in Hudson Bay, with mantle downwelling likely responsible for the rest. That paper also says:

“… this static field shows a single large anomaly with peak amplitude of -34 mGal (where 1 Gal = 1 cm/s/s) centered over Hudson Bay …”

Since “average” gravity is 9.81 m/s/s = 981 cm/s/s = 981000 mGal, that means the gravity anomaly over Hudson Bay is 34/981000 = 0.0035% weaker than average gravity on Earth.

Since roughly 1/2 to 3/4 of this anomaly is due to mantle downwelling, that means mantle downwelling has reduced gravity between about 0.0017% and 0.0026% relative to average gravity on Earth.

Update: Mark Tamisiea just told me about a newer article showing that “increase in water storage in an area south west of Hudson Bay, from the summer of 2003 to the summer of 2006, contributes up to half of the maximum estimated gravity rate.”

Is there any way to quantify the missing gravity due to downwelling by mass? For example, one scientist says that the gravity lost due to PGR in mass would be two Sears Towers stacked on top of each other — or 1/2 mile of water.

One could describe the gravity low in terms of removing a uniformly thick layer of rock. Just looking at the gravity map linked above, it’s clearly not uniform but this quick approximation may suffice for your purposes.

Removing a uniform layer of rock reduces gravity by 0.1119 mGal for every meter of rock removed. (As measured by GRACE, which ignores the increase in gravity that a ground gravimeter would record because it’s been lowered a meter.)

Since the Hudson gravity low peaks at -34 mGal, that means the thickness of the layer of rock removed would peak at about 300 meters. That’s about 300 yards, or a layer of rock that’s about as deep as the length of 3 football fields placed endzone-to-endzone.

That’s the total. Incomplete PGR would be a layer of rock 75 to 150 meters deep. Mantle downwelling would make up the rest: 150 to 225 meters of rock.

Note that this is at the thickest point of the removed rock layer where the gravity low is lowest. Elsewhere the removed rock layer would be thinner, but quantifying that is hard.

What does 980 Gal convert to in meters/yards/feet?

1 Gal is 1 cm per second per second, or 1 cm/s^2.

It’s a unit of acceleration, not length.

980 Gal is the average acceleration due to gravity at Earth’s surface, which is the same as 9.8 m/s^2

I converted the Hudson gravity low (lowest point: 34 mGal below average) into equivalent “missing mass” by considering the gravity due to a uniform layer of rock. This led to my conclusion that the total Hudson gravity low is equivalent to removing a layer of rock about 300 meters deep.

But this isn’t a straightforward unit conversion. It’s an approximate calculation of gravity above a perfectly uniform layer of perfectly average rock. It’s approximate mostly because the layer won’t be uniform but also because it’s not infinitely wide and perfectly flat, because rock’s density isn’t perfectly constant, because Newtonian gravity is an approximation of general relativity, etc.

Later: I’ve been thinking about your question a little more. If we use the same flat plate approximation as before, 980 Gal = 980000 mGal. If a flat plate of rock that’s 1 meter deep has gravity of 0.1119 mGal, then a flat plate ~8800 km deep (and infinitely wide) would have standard gravity of 980 Gal.

But that answer is meaningless outside of science fiction, which is why I didn’t answer your question directly…

Climate change

What else has GRACE learned about changes in gravity on Earth? e.g. glacial melting? Earthquakes?

GRACE observed a gravity anomaly due to the 2004 Sumatra earthquake, which helps us understand how the Earth’s crust behaves before and after a megathrust earthquake.

GRACE can also detect floods, such as the 2011 floods in Australia, South America, Asia, the Mississippi River, etc. The mass of that extra water strengthened gravity. GRACE also detected the 2005 and 2010 Amazon droughts because they reduced gravity.

GRACE mass trend from 2002-2010.

GRACE reveals ice mass loss in Alaska, Greenland, West Antarctica, Patagonia, etc. Furthermore, the ice sheets of Greenland and West Antarctica aren’t just losing mass, their mass loss is accelerating.

IMBIE results, Fig. 5


Ice sheets are more sensitive to warming than we previously thought.

How can understanding gravity and its anomalies help us know what’s happening on our planet and prepare for the future?

Melting ice is what we expect in a warming world, and most of the warming since 1950 is very likely due to human emissions of greenhouse gases like carbon dioxide. In my opinion, we should reduce CO2 emissions as quickly as possible and prepare for the warming that our emissions have already guaranteed.

6 Responses to “Secrets of the Earth: Gravity (2013 Outreach)”

  1. Mike Says:

    Hi, your comments on the Weather channel make me wish you would read this.

  2. Bryan Killett Says:

    I’ve read Steve Goreham’s musings, and others from the Heartland Institute. They’re always disappointing, and this article is no different: Goreham disparages the “ideology of climatism” instead of acknowledging that 45 science societies agree that most of the warming since 1950 is very likely due to human emissions of greenhouse gases. The few statements about science in Goreham’s article are all wrong:

    … carbon dioxide is not pollution but is in fact essential to life on the planet …

    We’re increasing CO2 10x faster than preceding the end-Permian extinction. The rapid rate of CO2 increase is why our emissions are dangerous pollution.

    … manmade emissions have very little effect on Earth’s climate. Water vapor, not carbon dioxide, is Earth’s dominant greenhouse gas. Emissions from human industry cause only about 1 percent of Earth’s greenhouse effect. …

    The global average concentration of atmospheric water vapor can only be increased by warming the Earth, because otherwise it just rains out of the atmosphere. CO2 doesn’t rain out, so our skyrocketing emissions stay in the atmosphere. This distinction is very important.

    Update: I’ve failed to communicate once again.

    … And contrary to predictions by all 73 of the world’s top climate models, global temperatures have failed to rise over the last 15 years.

    The last time Goreham made this claim, I pointed out that the warming has continued over the last 15 years. In fact, I’ve explained that GRACE was launched within the last 15 years, so all the ice mass loss we’ve observed happened within that time period.

  3. Mike Says:

    OK, so how do you know that the Co2 is man made?
    What about all the volcanoes going off lately?
    Tell me some data that shows it’s man made.

  4. Bryan Killett Says:

    I’ve explained that decreasing atmospheric oxygen and the increasing 12C/13C isotope ratio (etc.) show that the ~40% increase in atmospheric CO2 since the Industrial Revolution is largely due to our use of fossil fuels.

    Surprisingly, humans emit ~100x more CO2 than volcanoes.

    Here’s a 3 minute video introduction, and a longer overview.

  5. Jim Says:


    This may sound over simplistic, but wouldn’t it be cheaper to create electricity in an area such as Hudson Bay, where there is diminished gravity? I mean it has to take less energy to turn a generator impeller in lower gravity, therefore making fuel consumption lower as well, no?

    If so, why not build massive power plants in these types of locales, to lower power costs to the consumer, or something like that. For instance, pumping water out of the bay to a height tall enough to produce hydroelectric power on the way down should be less expensive.

  6. Bryan Killett Says:

    Hudson Bay’s gravity is only about 0.0035% weaker than average. We can only observe this tiny difference because our instruments (like GRACE) are so sensitive.

    Also, we can only use the difference in gravity between two points to generate electricity. That’s why the water level behind the Hoover Dam is so much higher than the water level after it. We’re basically extracting some of the energy the water would gain by falling that distance.

    A vaguely related concept is an underwater pressure battery which is like a submarine on the ocean floor. When electricity is required, they let water rush into the submarine, which turns a generator. When surplus energy is available to charge the battery, they reverse the generator and pump the water out. Since renewable energy sources like wind and solar can’t produce energy all the time, high capacity batteries will play a crucial role in our future energy grid.

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