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

A traceable path from monthly gravity-field coefficients to validated products.

GSM 01Acquire Collect monthly Level-2 GSM Stokes coefficients and product metadata. C₂₀ 02Preprocess Apply low-degree replacement, GIA correction, background-field alignment, and anomaly baseline removal. F 03Filter Route de-striping, spatial smoothing, DDK, and HSAF products through explicit product tags. Σ 04Synthesize Transform corrected spherical harmonics into gridded equivalent water height anomalies. QC 05Validate Check maps, basin averages, leakage correction, trends, and independent product consistency.

Processing Pipeline

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

GSM 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.

C₂₀ 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.

F 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.

Σ 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.

QC 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.