Satellite Gravity Field

GRACE Level-2 Processing Workflow

From GSM spherical harmonics to gridded EWH products

Technical notes and reproducible workflow records for transforming GRACE and GRACE-FO Level-2 spherical harmonic solutions into physically consistent equivalent water height products.

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Processing Pipeline

Click any processing node to inspect the scientific contract behind the step.

01 Acquire Collect monthly Level-2 GSM Stokes coefficients and product metadata. +

Principle

Input should be treated as a Level-2 gravity-field solution, usually monthly GSM spherical harmonic coefficients. The product name, processing center, release, maximum degree/order, time stamp, missing month flag, and reference frame must remain explicit.

Formula

S (θ, λ, t) = {ΔC_{l m} (t), ΔS_{l m} (t)}, 0 \leq m \leq l \leq l_{max}

Configuration example

product: HUST-Grace2024 / CSR RL06 / GFZ RL06 / JPL RL06
max_degree: 60
monthly_solution: true

Quality checks

Verify the product release and lmax.
Preserve the month identifier before any interpolation.
Keep the raw input immutable.

02 Preprocess Apply low-degree replacement, GIA correction, background-field alignment, and anomaly baseline removal. +

Principle

Preprocessing converts monthly coefficients into a consistent anomaly field. Typical operations include degree-1 geocenter replacement, C20/C30 replacement using SLR, GIA correction, optional destriping preconditions, and subtraction of a stated mean field.

Formula

{ΔC}^{'}_{l m} = ΔC_{l m} - {ΔC}_{l m, mean} - {ΔC}_{l m, GIA}

Configuration example

replace_degree1: true
replace_c20_c30: SLR
gia_model: ICE-6G_D
baseline: 2004-01..2009-12

Quality checks

State the baseline period.
Record all replacement products.
Never mix corrected and uncorrected products under one tag.

03 Filter Route de-striping, spatial smoothing, DDK, and HSAF products through explicit product tags. +

Principle

Filtering reduces correlated north-south striping and random high-degree noise while preserving physically interpretable mass signals. Gaussian, Fan, PnMm decorrelation, DDK, and HSAF should be routed as separate products rather than overwritten arrays.

Formula

\hat{x} = F {x}, F \in {Gaussian, Fan, PnMm, DDK, HSAF}

Configuration example

GAUSS_300: Gaussian smoothing, 300 km radius
FAN_300_P3M6: Fan filter with P3M6 decorrelation
DDK4: anisotropic regularization product
HSAF: Hankel spectrum analysis filtering

Quality checks

Save every filter result with a unique tag.
Record all radii and polynomial parameters.
Compare signal loss, residual stripes, and leakage behavior.

04 Synthesize Transform corrected spherical harmonics into gridded equivalent water height anomalies. +

Principle

Spherical harmonic synthesis converts corrected coefficients into equivalent water height. The Love-number correction, Earth radius, water density, grid resolution, land/ocean mask, and units must be consistent across products.

Formula

EWH (θ, λ) = \frac{a ρ_{e}}{3 ρ_{w}} Σ_{l}^{l_{max}} Σ_{m = 0}^{l} \frac{2 l + 1}{1 + k_{l}} {\bar{P}}_{l m} ({ΔC}_{l m} \cos mλ + {ΔS}_{l m} \sin mλ)

Configuration example

output_unit: cmEWH
grid: 1deg or 0.5deg
love_numbers: Wahr / Farrell
lmax: 60

Quality checks

Confirm cmEWH/mmEWH units.
Use one grid convention for comparisons.
Keep masks and coastline buffers versioned.

05 Validate Check maps, basin averages, leakage correction, trends, and independent product consistency. +

Principle

Validation should combine visual quality control with quantitative diagnostics. Basin-mean time series, annual amplitude, trend, leakage-corrected regional products, Mascon comparison, hydrology models, and altimetry are separate evidence layers.