Gravity signals of the Earth's tides are measured worldwide.
Here you see an example from the Black Forest Observatory, BFO.
Clearly, the diurnal and semi-diurnal tidal periods are visible.
The Earth is rotating within the forcing gravitational field of Moon,
Sun and planets and thus these signals are consistent with the forcing
acceleration, which can be computed from the position of the celestial
bodies.
One part of the gravity signal is the lunar tide, M2, primarily caused
by the Moon with a period of approximately 12.4 hours.
It has the highest gravity amplitude of the semi-diurnal Earth tides.
If it is compared to the forcing acceleration in detail, differences
become obvious.
This figure shows the temporal changes of the response of the Earth to
the M2 forcing for different stations in Europe.
Irregular variations are visible in the analyses.
Similar variations are apparent at some of those gravimeters.
For example at BFO and ST in Strasbourg.
Thus, the deviations from the expected response of Earth are no local
effects.
But what is their origin?
Hello and welcome.
In this video I will talk with geophysicist Eva Schroth about her
research field of tidal analysis.
Tidal analysis allows to investigate temporal variation of tidal
parameters on Earth.
You will learn what the tidal parameters are, how they can be
estimated and what kind of analysing methods are used to explain the
variations over time.
This can help to better characterise the gravitational deformation of
the Earth.
Gravimeters measure variations of the gravitational acceleration over
time.
Using those measurements, geophysicists analyse the Earth's tides.
They want to investigate how the Earth responds to the forcing
gravitational field.
This property is called the Earth's admittance.
They do this for so-called wavegroups.
A wavegroup sums the Earth's tides and defined frequency bands.
The lunatide M2 I showed you in the beginning is one such wavegroup.
This sketch illustrates the variation of the gravity signal of M2 over
time.
When this is compared to the theoretical external forcing field, a
discrepancy occurs.
This discrepancy is due to the deformation of the Earth in response to
the forcing and is described using the gravimetric factor and the
phase.
The gravimetric factor is an amplitude factor delta defined as ratio
of measure to exciting acceleration.
The phase phi accounts for the phase shift between measured signal and
forcing.
The gravimetric factor and the phase are called the tidal parameters.
The variations I showed you in the beginning were such variations of
the gravimetric factor.
How were these variations observed and how can they be explained?
Geophysicist Eva Schroth will explain this to us now.
Hi Eva!
Hi!
Before we talk about the reasons of the observed variations, could you
please explain how you determine the time dependence of the tidal
parameters and how they vary?
The tidal parameters are estimated with tidal analysis for a set of
wavegroups.
If we are interested in the temporal behaviour of the tidal
parameters, we apply tidal analysis to a shorter time window out of a
longer data set.
This is called moving window analysis.
Then the tidal parameters are plotted over time.
Here I show a simplified sketch.
The curve shows the time-dependent admittance factor of Earth's
response to the forcing of one wavegroup.
This deviation from the constant factor indicates that we miss
significant effects in the analysis.
Thus, the theoretical signal is scaled differently depending on the
position of the time window.
As a consequence, the tidal parameters vary with the beat frequency of
the wavegroup.
We saw that the tidal parameters vary over several months to years.
Can this be due to changes within the solid Earth and thus the
admittance of the Earth's body to tidal forces?
The admittance of the Earth can change if the elastic properties of
the Earth would change.
We know from geodynamics that geological processes can change the
properties of the Earth, but this would happen on geological time
scales like hundred thousands or millions of years, which is much
longer than our time series here, and it would be unlikely to be
periodic.
But what can cause the variations instead?
In the beginning I showed the similar behaviour of gravimeters in a
distance of around 100 km.
These are no local effects.
That's right.
Local effects are usually non-tidal signals like the subsurface
hydrology.
The similarity of the variations at all the European stations indicate
that they are influenced by the same source.
Originally we modelled the data including a layered 1D model of the
solid Earth and the measured air pressure in tidal analysis.
The oceans, however, are not included primarily.
But especially the oceans have a strong contribution at all tidal
frequencies because of the ocean tides.
They can influence nearby gravimeters in a similar way.
That means the gravitational loading of the ocean is changing with
time and thus has a strong influence on gravity.
Additionally, the admittance of the Earth to tidal forcing is not
constant in time.
The amplitudes of the M2 frequency, for example, show an annual
variation much stronger than it would be expected from the forcing
alone.
Therefore, the amplitudes and phases within the wavegroup always
differ from the expected values.
So the ocean tides influence the Earth tides.
How do you get information on ocean tides?
If we want to take the oceans into account, we need information about
them.
The difficulty is that there are no measurements of the oceans with a
sufficiently high spatial and temporal resolution.
Tide gauges are restricted to coasts and islands, while satellites
need several days until they pass the same point again.
Satellite data therefore suffers from temporal aliasing.
There are ocean models which include satellite data and they are able
to predict the time-independent part of the M2 amplitude quite well.
They assume the tidal amplitude to be constant and therefore are not
able to account for temporal variations of the amplitudes.
That's why I'm using sea surface heights predicted by time-stepping
non -linear non-stationary ocean models.
Usually, they do not match the real oceans as well as satellite-based
models regarding the stationary part of the M2 amplitude.
However, they potentially contain the causes of temporal variations of
tidal parameters.
I see.
And how do you include those informations in your analysis?
I calculate the loading the ocean model would cause and add it to
synthetic earth tides.
The synthetic data is then analysed exactly as the measured data and
the results are compared.
Using synthetic data instead of correcting the measurements has a
major advantage.
Namely, we can make sure that the observed variation is caused by the
ocean and not by some other effect which was not taken into account
previously.
Finally, the amplitudes of the variation of the M2 tidal parameters
are of the same order as the variations we obtain from measured data
and additionally have a similar shape.
And what can we learn from this result?
Since a while, it was assumed that the oceans cause the temporal
variations of the M2 tidal parameters.
This is now the first time that we can show that the loading of the
ocean masses is able to produce temporal variations of the correct
amplitude and frequency.
Here you see this for various gravimeters in Europe.
So we can explain to a certain extent the long-term variations of the
gravimetric factors from the beginning.
On average, they are about 1.18 and vary with time.
They express the amplitude of the recorded signal which is amplified
with respect to the forcing signal.
About 16% result from a deformation of the entire globe due to the
tidal forces.
The rest of about 2.5% primarily results from the loading of displaced
water in the oceans, giving a total factor of about 1.185 for the M2
tide.
As well, we search the cause of its temporal variation in the oceans.
And since we know this now, tidal analysis can be used to evaluate non
-stationary ocean models by their gravity effect.
We have shown that the very small temporal variations of the ocean
response can be recorded by superconducting gravimeters.
With that knowledge, gravity data could possibly be used to study
ocean response to global climate change, ocean warming and sea level
rise.
So what is the next step in your current work?
Up to now, we used global ocean models.
One would maybe expect that the masses, which are close to the
superconducting gravimeter, have a larger contribution to the total
effect.
But also the amplitudes and phases of the variation of the different
contributions are important.
We want to study which regions of the global ocean have to be taken
into account to explain the observed variation at a certain station
sufficiently well.
Okay.
Ife, thanks for these explanations of your work.
You're welcome.
In this video, you learned how tidal analysis is used to determine the
tidal parameters of gravimetric factor and the phase shift.
Eva Schroth explained how this is done using a moving window analysis.
She showed how the variations of the tidal parameters can be explained
by gravitational ocean loading and that the analysis of those tiny
signal variations may help to better understand the ocean's response
as a consequence of climate changes.
Thank you.