SAR basics (Sentinel-1)

Identify the product before using pixel values

Sentinel-1 is a C-band SAR (centre frequency 5.405 GHz, wavelength ~5.55 cm) with four exclusive modes: Stripmap (SM), Interferometric Wide swath (IW), Extra Wide swath (EW) and Wave (WV). IW (250 km swath, incidence 29.1°–46.0°, VV+VH over land) is the primary mode over land [S1]. Level-1 products are [S2, S3]:

The GRD ellipsoid projection uses a terrain height that varies in azimuth but is constant in range [S3]: a GRD is not terrain corrected. IW GRD High resolution has ~20 × 22 m resolution, 10 × 10 m pixel spacing and ENL 4.4 [S2]. Product names encode mission, mode, type, resolution class, polarisation (SV, SH, DV = VV/VH, DH = HH/HV), start/stop time, absolute orbit and datatake [S2].

Raw GRD/SLC digital numbers are not backscatter. Analysis-ready collections may already be calibrated, terrain corrected and/or in dB; for example Google Earth Engine COPERNICUS/S1_GRD is thermal-noise removed, calibrated, terrain corrected and converted with 10*log10(x), while COPERNICUS/S1_GRD_FLOAT keeps power values [S4]. Read the provider's processing description before any arithmetic. Find and load products with STAC and cloud access. Shared rules: engineering, simplicity, security.

Calibrate to β⁰, σ⁰ or γ⁰ with the product LUTs

Every Level-1 product carries calibration LUTs (betaNought, sigmaNought, gamma, dn) in annotation/calibration/. For distributed targets [S5]:

σ⁰ = DN² / Aσ²      β⁰ = DN² / Aβ²      γ⁰ = DN² / Aγ²
DN = GRD amplitude, or sqrt(I² + Q²) for SLC

LUT values are bilinearly interpolated between their sub-sampled pixel/line positions [S3]. β⁰ is normalised in slant range, σ⁰ in the ground-range plane, γ⁰ in the plane perpendicular to slant range [S5]. On the annotation's ellipsoid model, σ⁰ = β⁰·sin α, γ⁰ = β⁰·tan α, so γ⁰ = σ⁰ / cos α [S5]. A noise LUT (linear power) can be scaled by the same LUT and subtracted [S3].

GDAL ≥ 3.4 applies calibration for the SIGMA0, BETA0 and GAMMA calibration subdatasets of the SAFE driver; list them with gdalinfo on the .SAFE directory [S6]. Interpolation code, the noise step and ESA's numerical check (<DN²> = 22142.71, Aσ = 319.946 → −6.65 dB) are in references/calibration-lut.md.

Keep linear power for arithmetic, dB for display and thresholds

The LUTs give natural (linear power) values; decibels are [S5]:

σ⁰_dB = 10 * log10(σ⁰_lin)        σ⁰_lin = 10 ** (σ⁰_dB / 10)
amplitude = sqrt(power)

Average in linear power, not in dB. ESA averages intensity (DN²) before calibrating an area [S5]; ASF notes power scale is appropriate for statistical analysis while dB values are not appropriate for some statistics [S7]. Averaging dB values computes a geometric mean: −5 dB and −15 dB average to −10 dB in dB but to −7.6 dB when averaged in linear power.

import numpy as np

def to_db(power):
    power = np.asarray(power, dtype="float64")
    out = np.full(power.shape, np.nan)
    np.log10(power, out=out, where=power > 0)
    return 10.0 * out                     # non-positive power stays NaN

def mean_db(db_values, axis=None):
    lin = 10.0 ** (np.asarray(db_values, dtype="float64") / 10.0)
    return to_db(np.nanmean(lin, axis=axis))

Label every raster with its quantity and scale (σ⁰ or γ⁰; linear, amplitude or dB) in metadata and filenames. Typical confusions: dB data averaged or resampled as if linear; dB thresholds applied to linear data; DN treated as σ⁰. Power values are generally close to zero (ASF suggests a 0–0.3 display stretch) [S7], so a "σ⁰" raster dominated by negative values is in dB and one with values in the hundreds or thousands is likely uncalibrated DN. The noise-equivalent σ⁰ is specified at −22 dB or better [S1]: values near that level are noise-dominated.

Speckle: filtering is a trade-off

Speckle arises from interference of returns from many scatterers in a resolution cell [S7]. Multi-looking reduces speckle at the cost of resolution: IW SLC has ENL 1, IW GRDH ENL 4.4 [S2, S3]. Spatial filters (e.g. the local-statistics Lee filter [S8]; ASF's optional Enhanced Lee, 7 × 7) smooth speckle but reduce resolution [S7]. Temporal averaging (mean or median over dates) also mitigates speckle, in which case a spatial filter may be unnecessary [S7].

• Choose and record filter type, window and order (before/after terrain correction); compare outputs with and without filtering for the task [S7].
• Filters that average pixel values should run on linear power for the same reason dates are averaged in linear power.
• Filtering blurs edges and small features; it can hide small floods or narrow rivers that a change map must report.

Terrain correction and geocoding

GRD/SLC geolocation is provided as a grid of geolocation points; GDAL's SAFE driver exposes them as GCPs with an empty coordinate system and no geotransform [S6]. Warping on GCPs (gdalwarp polynomial or thin-plate-spline transformers [S9]) is not DEM-based terrain correction. Two different corrections exist:

• Geometric terrain correction (range-Doppler geocoding with a DEM) places pixels at the correct map position despite relief [S7].
• Radiometric terrain correction (RTC) normalises backscatter by the DEM-derived illuminated area, yielding terrain-flattened γ⁰ [S10, S7].

Side-looking geometry causes foreshortening, layover and shadow; in RTC products layover/shadow areas carry no valid data and are flagged in a layover-shadow mask [S7]. Record the DEM and its vertical datum, output CRS and pixel spacing (a resampled DEM does not have finer information) [S7]. Coregistration to the DEM can improve RTC but may introduce inconsistent offsets through time; orbit-based geocoding gives more consistent alignment for time series [S7]. Use raster processing for grids and resampling.

Polarisation, water, flood and change

Sentinel-1 transmits H or V and receives both (dual pol HH+HV or VV+VH; single HH or VV) [S1]. Rough surfaces and complex structures (forest) scatter more energy back; flat surfaces reflect it away and appear dark [S1]. Cross-pol (VH) is high for volume scatterers such as vegetation [S7, S1].

• Water: calm open water has very low backscatter and can often be separated with a threshold, frequently in dB; there is no universal threshold — derive it per scene, e.g. from the valley of a bimodal histogram, then refine [S7]. Wind-roughened water is brighter (roughness raises backscatter [S1]); radar shadow and smooth surfaces such as dry sand are also dark [S7]. Validate.
• Change/flood: the log ratio log10(date2 / date1) of calibrated, co-registered images shows the direction of change (negative = decrease) [S7]. Compute ratios on positive linear power. The dB difference is 10 * log10(date2 / date1), ten times the plain log ratio; record the units used by each change threshold. Validate change maps with accuracy assessment; temporal design is in time series and change.

Incidence angle and acquisition geometry

Backscatter depends on incidence angle; ESA's processor applies range-dependent gains partly to compensate for its variation [S3], and IW spans 29.1°–46.0° [S1]. σ⁰ and γ⁰ differ by cos α, so their sensitivity to geometry differs [S5, S7].

• Build time series from the same relative orbit (and orbit direction) when comparing dates, or normalise for incidence angle and document how. Relative orbit is in the manifest, not in the product name; ESA gives relative = mod(absolute − 73, 175) + 1 for S1A (175 orbits per 12-day cycle; other units have their own offsets) [S2]. STAC fields sat:relative_orbit and sat:orbit_state carry it when present [S11].
• Revisit depends on the constellation: S1B ended in 2022; S1C (launched December 2024) and S1D (November 2025) continue the mission [S1]. Expect irregular temporal sampling across these periods.

Verify with Terraproof

Existing checks: crs.defined and raster.grid_alignment (multi-date stacks on one grid), raster.nodata_declared, raster.resampling, raster.cog_layout, and stac.provenance for source Items. The optical rs.* range checks do not apply to SAR backscatter.

python -m terraproof check s1_vv_20240101_db.tif s1_vv_20240113_db.tif --sar-expect sigma0-db
python -m terraproof check s1-item.json

--sar-expect sigma0-db (or sigma0-linear) enables sar.value_domain (sampled values plausible for the declared scale) and sar.geocoded (CRS/geotransform rather than GCP-only geometry). Plausible values and a geotransform do not prove calibration or terrain correction.

Not checked automatically: that the right LUT was used, noise removal, terrain-correction quality and DEM choice, speckle-filter suitability, orbit consistency in a time series, and water/change thresholds. Calibration-chain verification against annotation metadata is not in scope.

Sources

• S1 — ESA SentiWiki, S1 Mission: frequency, modes, IW swath/incidence 29.1°–46.0°, polarisations, primary IW VV+VH over land, NESZ −22 dB, roughness/dielectric behaviour, polarimetry, launch timeline, 12-day/175-orbit cycle.
• S2 — ESA SentiWiki, S1 Products: GRD resolution classes and Table 6 (IW GRDH 20×22 m, 10 m spacing, ENL 4.4; SLC ENL 1), naming convention, relative-orbit formulas.
• S3 — ESA SentiWiki, S1 Processing: SLC/GRD definitions, ellipsoid projection with azimuth-varying terrain height, bilinear LUT interpolation, noise LUT, incidence-angle compensating application LUT.
• S4 — Google Earth Engine, COPERNICUS/S1_GRD: preprocessing steps, 10*log10(x), S1_GRD_FLOAT.
• S5 — ESA-EOPG-CSCOP-TN-0002, Radiometric Calibration of S-1 Level-1 Products (Miranda & Meadows 2015): LUTs, DN²/A², dB, intensity averaging, sin/tan normalisation, cos α = Aγ²/Aσ².
• S6 — GDAL SAFE driver: geolocation grid as GCPs, calibration subdatasets since GDAL 3.4.
• S7 — ASF HyP3 Sentinel-1 RTC Product Guide: σ⁰/γ⁰ normalisation, power/amplitude/dB scales and statistics, speckle and Enhanced Lee filter, DEM matching, layover/shadow, log-difference change, water thresholding.
• S8 — Lee, J.-S. (1980). Digital image enhancement and noise filtering by use of local statistics. IEEE TPAMI PAMI-2(2):165–168.
• S9 — GDAL gdalwarp: GCP polynomial order and thin-plate-spline transformer.
• S10 — Small, D. (2011). Flattening Gamma: Radiometric Terrain Correction for SAR Imagery. IEEE TGRS 49(8):3081–3093.
• S11 — STAC sat extension: sat:orbit_state, sat:relative_orbit, sat:absolute_orbit.