Satellite Gravity: GRACE & GOCE

Srinivas Bettadpur, Associate Professor, Dept of Aerospace Engineering & Engineering Mechanics

and Center for Space Research University of Texas at Austin

Airborne Gravimetry for Geodesy – Summer School Silver Springs, MD, USA (May 23-27, 2016)

Presentation Viewpoint

• Global gravity field models derived from satellite data serve as a long-wavelength reference, to support the interpretation of in situ data. – While this may not be literally exact, it serves as basis for the flow of this

presentation

• Therefore, I choose to classify the audience engagement with

satellite gravity data into three levels: – Level-3: Start with “satellite-only” fields – resolution ≈ 300-100 km – Level-2: Start with Inter-technique data fusion

• GOCE, GRACE, GRACE-FO, GNSS-tracking of low Earth orbiters, etc – Level-1: Process mission datasets at “lower” levels (metrology)

Level-3 Use of Global Satellite Models

Level-3: Many global models available…

Level-3: Broad User Guidelines… • Many global models are available.

• All models provide spherical harmonic coefficients

– Nmax ranges from 180 to 280 – Data span ranges from 3 years to 12 years – Infinite variety of analyst noise

• Spatio-Temporal Error Characteristics

– Low Degrees – Generally very well determined – Mid Degrees – Strongly influenced by analyst choices in data fusion – High Degrees – Recognizable/unique error characteristics

• A typical Level-3 User will, therefore, put in most effort in the

recognition of (and accounting for) these unique error patterns.

The GGM05 Model Suite

• GGM05S – A “GRACE-only” model

• Outcome of CSR_RL05 monthly time-variable gravity models

• Unconstrained estimates to d/o 180

• GGM05G – A “GRACE+GOCE” model

• Coefficients of a “smooth” (EGM08-like) field adjusted using band-pass filtered (10-50 mHz) GOCE data (XX+XZ+YY+ZZ).

• Polar gap filled with synthetic gradients derived from 150x150 GGM05S at 200-km altitude

• Added GGM05S after extensive experimentation with relative weights of GRACE and GOCE – trading long-wavelength benefits relative to short wavelength artifacts

• GGM05C – A GRACE + GOCE + DTU13

Ten-year combination of GRACE monthly estimates (March 2003 to April 2013)

Gravity anomalies from GGM05S to degree/order 180 (100 km smoothing)

GGM05S

Combine GGM05S with GOCE + polar gap fill from GGM05S

Gravity anomalies from GGM05G to degree/order 240 (50 km smoothing)

GGM05G

Variations Relative to EGM08

Image on left shows, in addition to the land gravity corrections: 1. Corrections to potential MDT

built into EGM08 (evident in Southern Oceans)

2. GRACE-related artifacts (≈2-4 cm) evident over mid-Pacific

3. Near coastal artifacts (≈10 cm) arise likely from the transition between three datasets across the coasts in EGM2008

(Pavlis et al. 2012)

Smoothed

Surface Gravity Test Statistics

No solution is best everywhere, though all show improvement in areas where no gravity data was available for EGM2008

GRAV-D data comparisons show little discrimination between models

Level-3 User would carry out further analysis at spatial scales of typical interest to this audience

GOCO05S

GGM05G

MDT residuals before spectral filtering (no smoothing). Color scale runs ± 35 cm

GOCO05S

GGM05G

MDT residuals after spectral filtering (no smoothing). Color scale runs ± 35 cm

No need any longer to use GRACE-only models for this purpose

Level-3: A Way Forward

• Choose one (or many) candidate global field(s) – Use fields derived using both GRACE and GOCE datasets. – No reason any more to use any (current-day) GRACE-only fields

• (High-resolution time-variable signals due to ice-loss are “few-mm”)

• For the local region of interest, empirically build error

covariance – By inspection – Upon comparison with in situ data

• Use, thereafter, the global models with your own error

estimates

Level-2: Build your own ‘satellite-only’ field

Ingredients Needed: Estimates and covariance matrices for individual datasets from each satellite gravity mission

And then on to the concerns of Level-3 user…

Level-2: GRACE Variations

• Variable Data Quality: – 2003-2010: Flight platform was most stable; relatively constant altitude.

• Exclude certain durations with very poor ground-track coverage – Post-2010: Strike a balance between poor environmental control and lower

altitude (higher noise at wavelengths shorter than ≈ 500 km, compared to earlier in mission).

• Formal covariance certainly does NOT reflect true errors in

the mean field harmonics – For tuning GGM05G errors, a very “engineering” approach was adopted – We think we have a way to do this is a formally correct way in next Release-06

(due Spring/Summer 2017)

• Stray issues

– Choice of the degree-2 harmonics should be solveable

Level-2: GOCE Variations

• Variable Data Sensitivity – GOCE mission identifies spans with variable extent of instrument calibration

and with lowering altitude

• Consider treating each component of the gravity gradient

independently, for its regional information contribution

• Handle polar gap “carefully” – This may scare the space-geodesists more than it does the physical geodesists

Level-2 Work: Covariance Tuning & Relative Weighting

Level-1: To the basics…

Level-1: Checklist • Global or Local Solutions? Go for global solutions

• Do I need a supercomputer? Wouldn’t hurt, as it allows for rapid

parameteric experiments – Each processing by itself is not too onerous computationally

• Differential Corrections with Variational Equations and a spherical

harmonic model will work. – All roads lead to the same place with unconstrained solutions – “striations” with

GRACE, and “orange-peel” with GRACE+GOCE – Regularization or stabilization are the only meaningful game-changers in this

domain, for purposes of needs of this audience.

• Specialized software is needed, and is considerable effort to

assemble. – Some knowledge of aerospace systems will be needed, as well. – Data screening requires a LOT of effort

Editing Orbits kbr residuals

Post-fir kbr residuals

Oct 2004 Year:2004 DOY:304

From:65000 sec To:69000 sec

Before Extra Editing

Starting Early in the Space Age

• The Pear-Shape of the Earth (1959) was estimated from studies of the orbits of Vanguard-1 satellites.

From: O’Keefe, Eckels & Squires, Science, New Series, Vol. 129, No. 3348 (Feb 27, 1959) pp 565-566 Over the next four decades, a wide

variety of techniques of observing orbital motion of near-Earth satellites were used to determine and analyze the variations in Earth’s gravity field: Optical Measurements Radar and Radio Ranging Satellite Laser Ranging Global Positioning System Radar Altimetry

Status Just Before GRACE • 30+ years of analysis of terrestrial tracking data:

– Hemispheric scale estimates, used as validation/constraints on climate models – Formulation: Short-arc, Precision Orbit Determination, with numerical

adjustment of model parameters

GIA + Atmosphere + Hydrology + Glaciers + …

Figure 1, Cheng & Tapley (JGR v 109, Sep 2004)

20 years later

500 km 89° 5+2+2 years

Rockot (via DLR)

3 x 1.3 x 0.9 m No panel 440 kg

0.2 µ/s (& better) < 1 cm SLR/GPS

Otherwise “perfect” record

GRM Gradio

Aristoteles TIDES

GAMES ….

GRACE

Measurement Concept

(GOCE)

Gravity Observations & Orbits

(Seasat to OSTM)

Acceleration g = ∇ U

Potential U

Gradients G = ∇ g

Velocity

∫ g

Position

∫∫ g

Altimetry

Gravimetry

Gradiometry

Doppler SLR/GPS

Earth’s gravity field variation spectrum ranges from sub-diurnal to millenial time-scales, and is visible at all spatial (local to global) wavelengths. Variations are caused by external (luni-solar tides) and internal (oceans, atmosphere, ice, elastic Earth) influences, and can be regular (tides), irregular (climate), or episodic (earthquakes). Measurement of higher derivatives of gravity provides better determination of small spatial-scale features.

(Lageos 1/2, and other geodetic sats) (TDRSS, Doris)

Observations of satellite motion and analysis of perturbations

Ground-based GPS Receiver

GPS Satellites

Nominal separation

Mass anomaly (fixed or moving)

GRACE: Mission Concept

Ground-based GPS Receiver

Leading satellite - approaching the anomaly - feels a greater gravitational attraction:

Separation Increases

GPS Satellites

Mass anomaly

GRACE: Mission Concept

Ground-based GPS Receiver

Trailing satellite - also approaching the mass anomaly - accelerates and catches up:

Decreasing Separation

GPS Satellites

Mass anomaly

GRACE: Mission Concept

Ground-based GPS Receiver

Leading satellite is far from the anomaly, and is not affected by it; while the trailing satellite - having just

passed the anomaly - is being tugged backwards: Increasing Separation.

GPS Satellites

Mass anomaly

GRACE: Mission Concept

Ground-based GPS Receiver

Trailing satellite catches back up with leading satellite but the ‘signature’ of

mass ‘lump’ has been observed in K-band range data

GPS Satellites

Mass anomaly

GRACE: Mission Concept

KBR Signal Content

Full KBR Range - Bias

Cubic Spline Residual (30 second knots)

Topography Along Groundtrack

(glk/jpl)

Mission Systems Instruments • HAIRS (JPL/SSL/APL) • SuperSTAR (ONERA) • Star Cameras (DTU) • GPS Receiver (JPL) Satellite (JPL/Astrium) Launcher (DLR/Eurockot) Operations (DLR/GSOC) Science (CSR/JPL/GFZ) Orbit Launched: March 17, 2002 Initial Altitude: 500 km Inclination: 89 deg Eccentricity: ~0.001 Separation Distance: ~220 km Lifetime: 5 years Non-Repeat Ground Track, Earth Pointed, 3-Axis Stable

Science Goals High resolution, mean & time variable gravity field mapping for Earth System Science applications.

GRACE Mission

The Satellites

Orders of Magnitude

Virtually all of this signal is due to the phase difference between the two satellites traveling in eccentric orbits.

Effect Gravitational Acceleration

Sat-to-Sat Range

Sat-to-Sat Range-Rate

Sat-to-Sat Acceleration

Moon 1.04E-6 3.2 mm 7.8 micron/s 15 nm/s^2

Sun 9.95E-7 1.6 mm 5.9 micron/s 7.3 nm/s^2

Solid Earth Tides 1.96E-7 0.13 mm 0.27 micron/s 0.7 nm/s^2

Ocean Tides 7.41E-8 122 microns 0.6 micron/s 5 nm/s^2

Atmosphere + non-tidal Oceans

3.33E-8 10 microns 0.12 micron/s 1 nm/s^2

GRACE Signal 7.50E-8 127 microns 0.7 micron/s 5.4 nm/s^2

Various Perturbations

Acceleration Units: 1 milli-Gal = 10-5 m/s2 ≈ 1 micro-g; 100 mGal = 1 mm/s2

9.8 m/s2

9.78 – 9.832 m/s2 equator-to-pole

Permanent deviations

from gravity of an oblate spheroid

reflect crustal/tectonic structure, and

are ≈ ± 100 micro-g at Earth surface

(4th & 5th decimal places in “g”)

Time-Averaged Gravity From Space

Color scale from WGM2012/BGI

The Known Variations • Largest time variations are due to

planetary perturbations and solid tides, and generally well-known.

• Ocean tides (top-right) are known (to a large extent) from radar altimetry and in situ measurements.

• Non-tidal atmospheric and ocean variations (bottom-right) are less-well known (measurements and models)

• NOTES: – Images drawn to Nmax = 100 (and hence the

“smeared” appearance), and show RMS about the mean within one month (April 2010).

– Atmospheric/Oceanic variations are quite variable from month-to-month; and are shown without the thermal (S2) variations.

What is left? Hydrological and Ice-Sheet variations (along with errors in tides, atmosphere, oceans, etc) This mass re-distribution measurement gives insights into their causative climate processes. These processes could not be observed uniformly globally, at this scale, before GRACE. Compare the ±6 nano-g scale of this animation with the ±100 micro-g for the static field;

New Observations from GRACE

Acceleration Units: 1 micro-Gal = 10-8 m/s2; or 1 nano-g

These are inter-satellite acceleration residuals with respect to the background gravity field accelerations. Continental hydrology and ice-sheet changes are the most conspicuous omissions from the background models, and hence most visible in data residuals.

Late mission (Nov 2013, right) residuals show the growing ice-mass loss compared to the early mission residuals (Nov 2002, top).

Relative Accelerations on GRACE s/c

While relative accelerations are shown for geographic specificity, we adjust gravity models to relative range-rate – fitting to ≈20 nm/s at low frequencies, and 200 nm/s at high frequencies

Observation Geometry

Distribution of Data in a Bin

Location of all data for calendar year 2008 is shown

All GRACE Data in a Bin

Each vertical “pass” represents one visit (70-80 seconds) to this bin Within each pass, data is well approximated by a line or a quadratic Trend within each pass is part of an overall, long-period signal during that orbit

Representing Time Variability in the Bin

Considerable variation within one month (largely part of the annual signal) Outliers are also evident.

A “quiet” bin

Sub-Seasonal Variations: A Simulation

Note arrows, showing location of large, rapid soil-moisture variations that are missed by GRACE due to orbital coverage – This is Motivation for a future GRACE constellation.

Schematic For Data Analysis

Processing Schematic

Flight Data Intersatellite Range Accelerometry Attitude GPS Ranging

Level-1 Processing ρall

Fnon-grav

δρgrav -

Time-series products created in ground processing

Level-2 Processing

Consolidate regionally or

globally

δGrav δMass or δPressure

Map products created in ground processing

<Grav>

Gravity change (Feb 2004 - mean)

Mean gravity

Location of GRACE measurements Feb 2004

Fgrav

All “known” gravitational influences are removed using geophysical models derived from other data

It should be emphasized that GRACE provides mass “anomalies” relative to a long-term average

The Dynamical System

• Parametrized Modeling of Orbit Dynamics

• Physics: Newtonian Mechanics * • Gravitational & non-gravitational accelerations • State of the System defined by

– Position & Velocity; and – Suite of models for grav & non-grav accelerations

• System Parameters are: – Initial position & velocity at some epoch – Parameters within models for grav & non-grav accelerations – Other “nuisance” parameters

• Propagation using numerical integration techniques – Non-linear system includes sophisticated models for orbit dynamics – Propagate non-linear state AS WELL AS variational equations

* With relativistic corrections

The Observations

• Observations: Measurements of instantaneous position or velocity relative to an observatory: e.g. – Distances from terrestrial observatories

• using radio or laser techniques – GPS ranging – GRACE inter-satellite ranging

• Differential Corrections, with iterations

– Estimate corrections to nominal values of System Parameters – Linearized least-squares, using variational equations – Multi-sensor data fusion – Optimal Weighting

Piecewise Constant Representation

• The continuous spatial and temporal spectrum of natural mass flux processes is represented by piece-wise constant models.

• For each time “piece”, the gravity field of the Earth is represented by the coefficients of a spherical harmonic expansion.

• The GRACE project deliverable is a time-sequence of such harmonic coefficients – Presently, we deliver monthly products – Representations other than the spherical harmonic coefficients are

popular.

Background Gravity Model

Predicted Obs GRACE Obs

Estimate

Science from the mission is a conjunction of Estimates and the errors of Omission and Commission in the Background Gravity Model

Resolution & Accuracy

Elements in Data Reduction All strategies to extract mass anomalies from GRACE data

have these elements in common, though they may be mixed in various ways:

1. Relationship between range (or its derivatives) and the

in situ gravitational potential 2. Downward continuation method, suitably stabilized 3. Inversion from gravitational potential to mass anomalies 4. Error reduction methodologies

For GRACE data products, the latter two are the responsibility of the users. For GRACE-FO, a nominal mass anomaly dataset will be produced by the mission. User interpretation must depend on a knowledge of background models.

GRACE & the User

Satellite data

Level-1 data

Gravity Models

Mass Flux Est

Level-1 Skills - Aerospace Engg - Filtering/Data Proc

Level-2 Skills - Geodesy - Geodynamics

Level-3 Skills - Geophysics - Geodesy

Payoff

Complete flexibility High resolution data (10 Hz versus 0.2 Hz) Need to “learn” the instruments

Optimally adapted, regionally tailored science Adaptive spatio/temporal resolution Alternative methods/Error reduction

Adaptability in science applications Post-proc Error reduction

Dual One-Way Ranging System

Dual One-Way Range Measurement

Image from GRACE at GFZ

Layout in Satellite

Z acc

X acc

Y acc

K-Band Ranging System Leading Satellite

Ka Down Converter Ka Down Converter

USO Ka X’mtr

Ka X’mtr

GPS Rcvr

15 cm Horn

L1 L2

Ka Down Converter Ka Down Converter

USO Ka X’mtr Ka

X’mtr

GPS Rcvr

15 cm Horn

L1 L2

24 GHz

32 GHz Trailing Satellite

10 Hz K/Ka Band Phase; 1 Hz GPS L1/L2

GPS Receiver is the nerve center for the instrument: • Extracts K/Ka band phase data; • Extracts GPS phase data; • Processes star camera images • Provides time reference for satellites

Dual One-Way Range Concept Sat-1 Sat-2

• Each one-way phase measurement is similar to GPS phase measurement • Dual-frequency (24 & 32 GHz) measurements • The range-change (& hence gravity) information is implicit in the time-of-flight • Derivatives of range are numerically obtained in data pre-processing

Raw K-Band Phase Data

Level-1 Processing Required (not necessarily in this order): Unwrap phase & identify all breaks Register data from both s/c to common GPS epoch Make dual-one-way range combination Outlier identification & normal-pointing

At the end of Level-1 Processing

10 Hz Level-1A data has been reduced to 5-sec Level-1B data

After the “Known” effects are removed…

Effects of the a priori static and time-variable gravity; as well as non-gravitational influences have been removed. These “residuals” form the basis of piece-wise gravity adjustment visualized earlier as “new” signals.

Sheard et al. 2012 (J. of Geodesy December 2012, Volume 86, Issue 12, pp 1083-1095)

SuperSTAR Accelerometer

Sensor Axes

Operating Principle

• Electrostatic Suspension of proof mass – Proof mass: 72 g, 5x5x1 cm, Titanium Alloy – Held motionless relative to an electrode cage – Proof-mass to cage displacement detection by high

resolution capacitive sensors – Electrostatic levitation keep the proof mass centered

within the cage – Restoring voltage needed on the cage is a measure of

the proof-mass acceleration in 6 d.o.f

• Measures both linear & angular accelerations

What the Accelerometer Measures

desired signal

CG offset is Actively Controlled the “twangs”

Verification by analysis

Pending Verification

Work in Progress in Validation Phase

(affects s/c configuration)

General Remarks, in closing…

Image: http://www.orbitessera.com

Orbital Geometry

Key angles relative to “Earth-fixed” processes are: Argument of Latitude Node relative to Greenwich

Orbit Perturbation Spectrum

1/perigee Secular Resonances n-cpr M-dailies

≈ 1 cpr ≈ n cpr Local (RTN) Frame

(GRACE)

Orbital Elements (early techniques)

In-plane (a, e, ω, M) perturbations observed by GRACE

In-plane & Out-of-plane (e, ω, and I, Ω) (later, GPS-based, methods observed low n-cpr)

amplitudes decrease as perturbation frequencies increase -->

amplitudes decrease as perturbation frequencies increase -->

Observational limitations led to “lumped-harmonic” or inseparability effects

Early Ground Based Tracking Space-Based Tracking & Later

GRACE mission measurement b/w

Pathway for error

susceptibility

Observation Spectrum

Secular Resonant m-Dailies Sub-Rev

Global Variability

Regional Variability

Large-Amplitude Perturbations

Small-Amplitude Perturbations

Long-period stability of measurements is difficult to assure

Very high precision measurements are required

Overview

• User may engage with “satellite-only” mean Earth gravity field models at several levels, with differing effort.

• Regional use of global satellite-only fields today clearly benefits from dedicated error analysis efforts.

• Available satellite-only fields are useful for guiding strategies for combination of heterogeneous datasets across overlapping spatial domains (e.g. coastal blending in case of EGM08) – This should be even more useful as the spatial resolution improves with next-

generation satellite-only mean fields.

Looking Ahead

• Next generation (RL06) products, due out in Spring/Summer 2017, should present improved mean field – Formal error calibration – Including contributions from data collected at lowest altitudes – Reduction of systematic errors

• LRI data from GRACE-FO mission should contribute

meaningfully to the mean field estimates.

Thank you for your attention…

OPTIONAL: Validation of Gravity Fields

Basics • Gravity field has been parametrized, modeled, and estimated

from the GRACE data. – Following discussion is carried out in terms of a gravity field estimated as a

piecewise constant, spherical harmonic coefficient set. – Can be easily extended to other parametrization strategies

• Some common methods

– INTERNAL: • Data residuals after fit • Statistical consistency • Visualization & sanity checks

– EXTERNAL: • Low degree harmonic comparisons with SLR & EOP • Ocean circulation comparisons at long wavelengths • Inter-comparisons with output from geophysical models • (If you are lucky) Regional comparisons with in situ data

INTERNAL: Data Residuals: Check if residuals are clustered in regions of large signal

INTERNAL: Visualizing the formal errors

This is useful for assessments of effects of evolution of mission geometry and data collection strategies.

INTERNAL: Statistics of the Gravity Field

Overview • In GRACE data processing, say we estimate one set of geopotential

harmonic coefficients for each month of data.

• We define the “Variability” as deviations from ensemble average, that is:

• We visualize the variability in several ways: – Scatter: Degree root sum-squared of the spherical harmonic variability

– Sequences, montages or movies of maps of the variability

Each point above is a root sum-squares averaged over M individual fields. The Y-axis should be in units of the geopotential harmonics, but multiplication by ae converts it to units of geoid height. The Y-axis then represents contribution to global RMS from terms of each degree (there is sound statistical basis for this).

Signal

Degree “Error” Statistics

Degree/Order Distribution of Error

Launch until May-2003 Early months limited by the star camera noise

2003-07 until 2010-12 Best quality products

2011-Jan until present Limited by absence of thermal control

Calibrated Errors (& Covariances)

A power-law relationship between residual scatter and formal errors is derived, separately for each span. The formal error covariance matrix is inflated using this power law. The standard deviations are delivered to archives.

Functionals of the Potential

Quantity Units Remarks

Geoid Height mm of geoid meters for static field

Gravity Anomaly nanoGal microGal for static field

Equivalent Water Layer cm of water --

Gravity Gradients microEU milliEU for static field

Mass Density Layer kg/m2 Use GT for basin averages

Radial Loading Displacement mm --

Geoid height requires simple multiplication of the variability by ae, invoking Bruns’ formula. All others need degree-dependent operations.

The estimated geopotential harmonics are hardly ever mapped geographically in the units of potential. Common functionals of geopotential, used for mapping, are shown in the table below.

Spectral Operators

Radial Displacement follows from

Mass Density Layer

Radial Gradient

Equivalent Water Layer

Gravity Anomaly

Geoid Height

Each quantity, therefore, emphasizes a different part of the error spectrum

The next set of images show variability for the month (RL04) of May, 2010, for n=60, smoothed to 400 km,

and Variability is defined relative to 2010 mean

Different quantities and different smoothings can highlight problems in different parts of the spectrum

INTERNAL: Visualizations of the data and the fields

EXTERNAL: Low degree harmonics

C20 from GRACE and SLR GRACE estimates dominated by long-period aliases

EXTERNAL: Ocean circulation

Each month’s gravity field should be able to stand on its own, as a good model of the Earth’s gravity field. This is a quick sanity check of the quality. Other such tests could be envisaged…

EGM08 – Zonal (no smoothing)

Correlation of geostrophic currents computed from various geoid models with the circulation from ARGO data (Roemmich & Gilson 2009, via Kosempa and

Chambers 2012; relative to 2000 m; courtesy of D. Chambers)

Test Statistics (Ocean Circulation)

Gravity solution Zonal Meridional GGM05S (GRACE only) 0.83 0.37 EGM2008 0.86 0.44 GOCE only (XX+YY+ZZ+XZ) 0.88 0.49 GGM05G (GRACE+GOCE) 0.88 0.51 GOCO05S (GRACE+GOCE+Reg) 0.88 0.55 EIGEN6C4 (GRACE+GOCE+Terr) 0.88 0.55 • Tests to 180x180 with 300 km smoothing, and is at its limit of usefulness

• Up-weighting GRACE improves the meridional correlations at the long wavelengths, but increase the striations at short wavelengths

While the example here was illustrated for a mean Earth gravity field model, it works well for discovering

problems in monthly fields, as well…

EXTERNAL: Comparisons with geophysical model output

This works very well visually when working at a global scale. On regional scales, this is far less certain. But by this time, you are no longer only validating – you are engaged in geophysical analysis.

GRACE satellite monitoring of large depletion in water storage in response to the 2011 drought in Texas

Geophysical Research Letters Volume 40, Issue 13, pages 3395-3401, 3 JUL 2013 DOI: 10.1002/grl.50655 http://onlinelibrary.wiley.com/doi/10.1002/grl.50655/full#grl50655-fig-0003

There is wide divergence among the model predictions of soil moisture. Combination of improvements in modeling & in situ data are needed to correctly disaggregate the total.

Long et al. 2013