=Paper=
{{Paper
|id=Vol-2727/paper11
|storemode=property
|title=Analysis and Interpretation of GRACE and GRACE-FO Mission Data
|pdfUrl=https://ceur-ws.org/Vol-2727/paper11.pdf
|volume=Vol-2727
|authors=Alexander Matsulev,Konstantin Simonov,Aleksandr Zotin,Anna Metus,Tatiana Penkova,Anton Mikhalev,Nina Lugovaya,Tatiana Penkova,Anna Molyavko,Evgenia Karepova,Mikhail Sadovsky,Vladimir Shaidurov,Igor Borovikov,Roman Morozov,Margarita Favorskaya,Ivan Perevalov,Tatiana Vitova,Valery Nicheporchuk,Tatiana Penkova,Maria Senashova,Aleksey Korobko,Yulia Ponomareva,Anna Korobko,Anna Vlasenko,Natalia Zhilina,Dmitry Zhuchkov
}}
==Analysis and Interpretation of GRACE and GRACE-FO Mission Data==
https://ceur-ws.org/Vol-2727/paper11.pdf
83
Analysis and Interpretation of GRACE
and GRACE-FO Mission Data*
Alexander Matsulev1,2[0000-0001-9164-0801], Konstantin Simonov1[0000-0002-6829-3087]
аnd Aleksandr Zotin3[0000-0001-9954-9826]
1 Institute of computational modelling of the Siberian Branch
of the Russian Academy of Sciences, 50/44 Akademgorodok, 660036, Krasnoyarsk, Russia
2 Institute of Сhemistry and Сhemical Technology of the Siberian Branch
of the Russian Academy of Sciences, 50/24 Akademgorodok, 660036, Krasnoyarsk, Russia
3 Reshetnev Siberian State University of Science and Technology,
31 Krasnoyarsky Rabochy pr., 660037, Krasnoyarsk, Russia
simonovkv@icm.krasn.ru
Abstract. The study is devoted to the analysis of the features of the change in
the Equivalent Water Height (EWH) parameter over the geoid based on satellite
measurements of space systems. The GRACE and GRACE-FO satellite data
archive was used in the study. The assessment was made on the Earth as a
whole including areas of the Land and World Ocean. Interpretation of the
disturbed state of the geo environment is performed using digital maps of the
EWH parameter spatial distribution based on the histogram approach and
correlation analysis. A comparative analysis was also carried out of the studied
data of the GRACE mission and the data of the new GRACE-FO satellite
system which was launched into orbit in the summer of 2018.
Keywords: Gravitational Field, Geoid, EWH Parameter, Underwater
EarthQuakes, Space Systems GRACE and GRACE-FO, Satellite Data
Processing.
1 Introduction
The GRACE and GRACE-FO missions were originally aimed at studying the global
climate of the Earth [1-4]. Satellite measurements of the height of the water surface in
relation to the geoid contour make it possible to determine the deviation of the free
sea surface from its mean level [5]. The geoid is an equipotential surface of the
gravity field which corresponds to the average sea level at rest. Monthly data contain
the information on the deviation of the World Ocean surface from the geoid in units
of equivalent water height.
The data obtained from the site [6] contain the information on the deviation of the
World Ocean surface from the geoid in units of the Equivalent Water Level (EWH) in
* Copyright c 2020 for this paper by its authors. Use permitted under Creative Commons
License Attribution 4.0 International (CC BY 4.0).
84
cm. Basically, the EWH parameter is used to analyze the dynamic topography of the
oceans and to refine the parameters of the Earth's external gravitational field [7].
The EWH parameter reflects undifferentiated movements of the generalized mass.
Redistribution of water in the hydrosphere occurs in a thin layer around the Earth's
surface only a few kilometers wide. The masses between the geoid and water surface
have a constant density ρw equal to 1000 kg / m3.
The value of the EWH parameter is calculated based on the harmonic coefficients
of the geopotential models minus the coefficients of the averaged model EIGEN-6C
[7]. In the global model, the initial data are ground-based gravimetric measurements,
laser trajectory observations of the LAGEOS satellites (1985-2010) as well as satellite
information from the GOCE and GRACE systems.
In the high-power EIGEN-6C model, the decomposition of the geopotential occurs
to the power of the order of 1420, which corresponds to a 14-km spatial resolution.
The equivalent water is found from the ratio of the surface density ∆σ to the density
of water ρw: EWH = ∆σ/ ρw.
The analysis performed in the paper is limited to the relative changes in EWH over
the geographic space (Land and Ocean regions) through time at intervals of
approximately one month. Observations of gravity anomalies allow one to analyze
both local and global spatial and temporal aspects in search of correlations with
tectonic processes on the Earth [8-13].
Searching for spatial and temporal dependences in satellite data on the gravity
anomalies of the Earth's oceans is the purpose of the study. This requires building and
comparing a model map of random gravitational anomalies with the observed one;
building maps of the average values of the gravity anomalies and their variances;
highlighting characteristic areas and determining time dependences for the
gravitational anomalies.
2 Analysis of the GRACE System Observation Data
As part of the research it is advisable to expand the possibilities of using data from the
GRACE satellite system for analyzing global climatic and geodynamic changes on the
Earth. In this regard, it is proposed to study the new data of the GRACE-FO system in
a single time series with the data of the previous GRACE mission after their recent
revision by the development teams.
To analyze global temporal changes in the distribution function of the EWH
parameter it was decided to use histograms [14]. Using the histograms we determine
the average value of the EWH parameter as well as other statistical values (variance,
mode, median, etc.).
Based on the integral characteristics of the gravitational disturbance as a
cumulative equivalent displaced mass (areas: Ocean, Land), time dependences are
analyzed.
Let us define the cumulative equivalent mass displacement (Mass). This value
determines the total amount of the equivalent mass of water at each time interval. It is
calculated by the formula:
85
90 360
Mass EWH ( , ) R 2 sin( ) , (1)
90 0 180
where | EWH (Θ, φ) | is the modulus of the gravitational anomaly, depending on the
latitude (Θ) and longitude (φ), R is the Earth's radius, ΔΘ = Δφ = π / 180.
The value of the gravitational anomaly EWH is measured in meters and
consequently, the resulting value of Mass will be measured in tons. The value of Mass
can equivalently be determined using the histogram as an analogue of the distribution
function of the magnitude of the gravity anomalies.
Let us justify the introduction of the new distribution parameter Mass. The fact is
that the intuitively clear mean value (of the gravitational anomaly) is responsible for
the balance of approximately equal values – the decreasing and increasing equivalent
mass (EWH) which for a sufficiently long observation interval (~ a month) turns out
to be approximately equal. Consequently the average value will tend to zero.
However, if we add the decreasing and increasing masses (hereinafter Mass), then
this will be a global characteristic of the “excitation” of the climate in a given month.
This value can be determined using the histogram or using equation 1 directly from
GRACE data, taking into account the correction factor which considers the
dependence of the linear area on the latitude of the partition cell of 1 square degree.
The data on the Earth's gravitational anomalies studied in this work using the
histograms were taken from the official website of the GRACE mission (2003-2016)
[6]. The site contains materials from three processing centers: University of Texas
Center for Space Research (CSR), GeoForschungsZentrum (GFZ), and Jet Propulsion
Laboratory (JPL). In this study the data processed by the Texas Center for Space
Research were used.
The collected material of the first GRACE mission provides an interesting subject
for statistical research. Histogram analysis allows one to determine the probability
distribution function for gravitational anomalies created by the redistribution of mass
on the Earth. It is shown that the histogram, i.e. the distribution density function on
the value of the gravitational anomaly, is symmetric and close to exponential with
singularities on the distribution tails [8]. For this kind of large distribution values
(positive and negative) the anomalies should have a low probability.
The analysis of the spatial distribution of anomalies made it possible to identify 9
geographic regions in the oceans with the strongest gravitational anomalies and
maximum gravitational variability. Since gravitational anomalies are a reflection of
processes of the mass redistribution on the Earth and in this case of the oceans it is
advisable to use correlation analysis to assess the relationship.
The matrices formed based on the Pearson's correlation coefficients for the time
series of the considered areas allowed one to identify strong positive and negative
correlations, as well as the lack of communication. For the comparative analysis of
the GRACE and GRACE-FO observation data (new mission) a joint processing of the
corresponding data of the L3 level was performed.
The GRACE-FO observation data was obtained from the website: “https://podaac-
tools.jpl.nasa.gov/drive/files/allData/gracefo/L3/ocean_mass/RL06/v03/CSR”. It
should be noted that the available GRACE measurements were at the L5 level. In this
86
regard, it was necessary to evaluate the obtained distributions as well as the
possibility of using the developed methodology for new data from the GRACE-FO
mission.
The experimental data from GRACE (2002-2017) GRACE-FO (2018-2030) were
taken from a pair of satellites located at a distance of ~ 200 km from each other in the
polar orbit at an altitude of ~ 400 km. The data include the spatial position of each
satellite relative to the Earth, their mutual distances and absolute (proper)
accelerations. To correctly compare the old and new data it is necessary to analyze the
data of the level L3. For the desired estimate the corresponding histograms of the
gravitational anomalies were generated in logarithmic coordinates (Fig. 1) where the
value of the gravitational anomalies (in meters) is indicated along the X axis.
Fig. 1. Average histogram for GRACE-FO data (blue) and histogram for GRACE data (red).
3 Results of the Time Dependence Analysis in GRACE
Observational Data
This section presents the results of the analysis of the vibrational components of the
studied quantities. These are the movements of mass in the atmosphere, in the ocean
on the surface and below the Earth. All these components add up and cease to be
distinguishable in the EWH parameter. It is necessary to distinguish the terms in the
general motion of mass on the Earth.
This is possible using additional knowledge about a specific type of the mass
motion. The most important and significant contribution to changes in the gravity
field is made by the movement of water. A joint analysis of the data on the Land and
Ocean identifying common and individual patterns will improve the understanding of
global climate change on the Earth.
In the analysis of the spatial component, we will limit ourselves only to the
division of the geo-environment into the Land and Ocean. The time dependence is set
by the time intervals for which the average value of the EWH parameter is
determined, depending on the geographic coordinates on the Earth's surface. Each
time interval corresponds to a histogram of frequencies of various EWH values.
Histograms are quite a complex object (vector) for analysis since they are subject
to changes. Therefore, each histogram was characterized with a more simple value – a
scalar. A more suitable parameter of the histogram is the sum of the decreasing and
87
increasing masses in the current time interval. This value characterizes the intensity of
the mass transfer, i.e. the intensity of climatic processes that are actually associated
with the transfer of water – these are clouds, precipitation, etc.
From the methodological point of view the spectral analysis of the time
dependence of the mass transfer intensity is not a standard Fourier analysis. This is
due to the fact that we are dealing with time intervals of different duration and
average (which are not instantaneous) values of the investigated quantity. There will
be a significant uncertainty in the resulting spectrogram or periodogram. As for the
monthly period which is set by the motion of the moon and which determines tidal
phenomena both on the Land and Ocean, the irregularity in the time intervals greatly
aggravates the situation.
If the time intervals coincide with the synodic (for example, the period of the
Moon's revolution), then the error in determining the influence of tides on the EWH
parameter will be more or less systematic. In the study we will restrict ourselves to
identifying only the annual and semiannual oscillatory components and polynomial
trend – a polynomial of the 3rd degree.
To assess the existing data we use the least squares method. First we define the
polynomial trend and eliminate it from the data, and then, we isolate the indicated
annual and semi-annual oscillatory modes. The stepped graph below highlights this
feature of the data. Let us start with the simplest model – we assume that the average
values are reached in the middle of each interval.
Consider the time dependence of the Mass value for the Ocean and Land according
to GRACE & GRACE-FO data. The polynomial trends for the Land and Ocean are
presented in Fig. 2, the blue graph corresponds to the Ocean and the red one to the
Land, and the dots represent the corresponding trends (3rd degree polynomials).
Along the axes, time is given in years and the mass is presented in tons. Note that in
2007 there was a minimum, and now the trend is increasing.
As it can be seen, the trends for the Land and Ocean are approximately similar to
each other, and this is indeed the case since the polynomial coefficients for the Land
are about 3 times larger than those for the Ocean.
Fig. 2. Polynomial trends of Mass for the Ocean and Land according to GRACE and
GRACE-FO.
88
The estimation of the correlation of the Mass value between the Ocean and Land
according to GRACE and GRACE-FO data is shown in Fig. 3. It can be seen that the
graphs of the mass dependence on the Land and Ocean are rather strongly correlated.
Here, the corresponding cloud of correlations and the Pearson correlation coefficient
= 0.728 are given.
Fig. 3. Correlation field between the time series of the Land and Ocean Mass values according
to GRACE and GRACE-FO data.
4 Results of the Vibrational Component Analysis of the Ocean
and Land Mass Quantities
When using the standard Fourier analysis methods in processing time series of data
from the GRACE & GRACE-FO missions, one encounters difficulties due to the fact
that (possibly contrary to the original intentions), the time intervals in these data are
not regular and there are gaps in the data.
The method which appears to be convenient in this situation is the Least Squares
Method. At the same time, first a polynomial trend is identified - this is a polynomial
of the 3rd degree, and after its removal, the oscillatory semi-annual and annual
components of the time series are determined by the same method. The results of the
analysis of the vibrational components of the Ocean and Land Mass values are shown
in Figures 4-7.
Fig. 4. Time dependance of vibrational components of Ocean and Land mass.
89
The spaced plots for the Ocean (blue + 106 tons) and Land (red) of the equivalent
mass of water involved in the movement, presented together with the annual and
semi-annual fluctuations revealed by the least squares method, are shown in Fig. 4. In
Fig 4 the dotted line demonstrates the annual and semi-annual vibrational modes.
The annual and semiannual vibrational modes of the Ocean and Land mass
quantities are shown in Fig. 5. The figure represents only the vibrational trends of the
Land (red) and Ocean (blue) free from “noise”. It should be noted that the range of
fluctuations increases markedly, especially for the Ocean as we approach the current
maximum.
Fig. 5. Annual and semiannual vibrational modes of the Ocean and Land mass quantities.
The global annual and semiannual vibrational modes of the total value of Mass of the
Ocean and Land are shown in Fig. 6. Fig. 6 shows the total value (i.e. Land and
Ocean) free from the trend and noise fluctuations in EWH moving throughout the
Earth. The image demonstrates only the points corresponding to the experimental
time intervals of the data files.
Fig. 6. Global annual and semi-annual oscillatory modes of the total mass of the Ocean and
Land.
In order to better demonstrate the changes in the intensity of the mass transfer on the
Earth during the year –we will give the annual and semi-annual harmonics on a
separate graph for each season (Fig. 7). Here, we can see that for the Land the minima
90
are reached at the beginning and in the middle of the year. This corresponds to winter
in the Northern and Southern hemispheres of the Earth, and the maxima are shifted by
3 months. As for the Ocean the minima occur in April and November and the maxima
are observed in early February and mid-July.
Fig. 7. Annual and semi-annual harmonics of the changes in the intensity of the mass transfer
on the Earth during the year (seasonally).
5 Conclusion
In our previous study, using GRACE-OCEAN data we came to the conclusion that in
general the Ocean behaves in an intuitive way with a certain variability which may be
natural (thermodynamic). Also earlier within the framework of this variability, several
zones of the Ocean were identified for which the variability was the strongest and of
oscillatory origin with the annual and semi-annual components. It has now been
established that the fluctuations identified earlier occur on the Earth as a whole and
the fluctuations in the Ocean are gaining momentum.
In addition, the identified trends (polynomial of the 3rd degree) both for the Ocean
and Land have now an increasing character. However, if to look at the trends as at a
long-period fluctuation, one can see that at the beginning of the analyzed time interval
(2002-2020) the trends had a descending character and passed (simultaneously) a
minimum (~ 2007) and then, started to grow. Therefore, we are probably dealing with
an oscillatory process with the periodicity of 13-14 years.
Based on the statistical analysis of the changes in the EWH parameter for the Land
and World Ocean it is shown that the temporal patterns obtained according to the
observations of the GRACE mission persist in the data of the new GRACE-FO
mission for the main detected anomalies.
Consequently, GRACE and GRACE-FO data are in good agreement with each
other. In the data for the Earth as a whole as well as for the Land and over the Ocean,
long-term and short-term trends are revealed, i.e. oscillatory components. The
identified trends are likely to be associated with global climate changes on the Earth.
91
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