# Airborne Weather Radar > Use when you must compute airborne weather radar operating-point quantities for convective weather avoidance: convert radar reflectivity factor Z to rainfall rate and back with the Marshall-Palmer Z-R relation, estimate the antenna elevation tilt that scans a storm cell top from own altitude and slant range, derive the flat-earth ground range to the cell, check a tilt setting against ground clutter return geometry, and rate echo intensity into standard levels from the reflectivity. Produces the rainfall rate, the required tilt angle, the ground range, the clutter check verdict and the echo level that gate weather radar tilt management in the cockpit. Trigger: airborne weather radar, convective weather avoidance, storm cell top, antenna tilt, reflectivity factor, rainfall rate, marshall palmer, echo level, ground clutter. - Skill: `ashfordeou/airborne-weather-radar` (Agent Skill, multi-file: 3 files) - Install (CLI): `npx skillmds@latest add ashfordeou/airborne-weather-radar` - Raw SKILL.md: https://api.skillmd.com/api/skills/ashfordeou/airborne-weather-radar/raw - Safety review: pending - Works with: Claude Code, Claude.ai, OpenAI Codex - Category: Coding & Dev Tools - License: Apache-2.0 - Author: ashfordeOU (https://skillmd.com/u/ashfordeou) - Updated: 2026-09-17 - Page: https://skillmd.com/skills/ashfordeou/airborne-weather-radar --- # Airborne Weather Radar (avionics/surveillance/airborne-weather-radar) Use when the task is computing airborne weather radar operating-point quantities for convective weather avoidance: mapping radar reflectivity factor Z to rainfall rate through the Marshall-Palmer Z-R relation and back, pointing the antenna tilt at a storm cell top, converting slant range to displayed ground range, checking a tilt setting for ground clutter return, and rating echo intensity into standard display levels. This leaf implements the operating-point model in pure Python, stdlib only, deterministic. It pairs with the surveillance siblings for the wider air picture: air-to-air surveillance performance and collision avoidance logic live in the sibling leaves, not here. ## Domain quick reference - Marshall-Palmer Z-R relation: Z = a * R^b with Z in mm6/m3 and R in mm/h; module constants a = A_DEFAULT = 200.0 and b = B_DEFAULT = 1.6. The inverse is R = (Z / a)^(1 / b), so the pair round-trips any rate within 1e-6 relative. - dBZ scale: dBZ = 10 * log10(Z). The Z-R relation is commonly quoted in dBZ form (20 mm/h gives about 43.8 dBZ). - Cell top scan tilt: tilt = atan((cell_top_alt - own_alt) / slant_range) in degrees. The altitude difference may be negative when the cell top sits below the aircraft, and the tilt is then negative (beam points down). - Displayed ground range (flat-earth): ground = sqrt(slant_range^2 - (own_alt - target_alt)^2). The earth-curvature constant RE_ARTH = 6371000.0 m is informational only; the model is flat-earth, which is valid for the short display ranges here. - Ground clutter geometry: the lowest edge of the beam at the slant range sits at tilt - beam_width / 2. The angle to the terrain at that range is atan((terrain - own_alt) / slant_range). Clutter risk exists when the lowest beam edge lies below the terrain angle, because the beam still illuminates the ground. - Echo levels: level 1 below 30 dBZ, level 2 from 30 to 40 dBZ, level 3 from 40 to 50 dBZ, level 4 at 50 dBZ and above. Because log is monotonic, the linear Z thresholds 1000 / 10000 / 100000 mm6/m3 mark the same band edges. - RTCA DO-185 frames the airborne weather radar MOPS context. The relations above are standard engineering methodology, summary-only. ## Workflow 1. Convert rainfall to reflectivity with reflectivity_from_rainfall (Z = a * R^b) when the input is a rain rate, or invert with rainfall_from_reflectivity when the radar reports Z. 2. Confirm the conversion round-trips: the inverse of the forward value returns the starting rate within 1e-6 relative. 3. Point the beam: tilt_to_cell_top(own_altitude_m, cell_top_altitude_m, slant_range_m) returns the elevation tilt that puts the beam axis on the cell top. Negative tilt means the cell lies below the aircraft. 4. Get the displayed range: ground_range_from_slant(slant_range_m, own_altitude_m, target_altitude_m) with the default 0 m target for the surface reference. 5. Check the tilt against terrain: clutter_check(tilt_deg, own_altitude_m, slant_range_m, terrain_elevation_m, beam_width_deg) returns the beam lowest edge and the clutter verdict. 6. Rate the echo: echo_level(reflectivity) returns the standard four level category for the cockpit weather display. 7. For the full operating point in one call, run weather_radar_assessment(rainfall_mm_h, own_altitude_m, cell_top_altitude_m, slant_range_m, terrain_elevation_m, beam_width_deg) and read the six documented keys. 8. Confirm the deterministic checks with the contract test scripts/test_airborne_weather_radar.py. ## Worked example Rainfall 20 mm/h, own altitude 3048 m (10 000 ft), cell top 12 192 m (40 000 ft), slant range 111 120 m (60 NM), terrain 0 m, beam width 3 deg. - Reflectivity: Z = 200 * 20^1.6 = 24 136.71 mm6/m3 (43.83 dBZ), inside the 20 000 to 28 000 bound. At 50 mm/h the value is 104 563.96 mm6/m3, inside the 90 000 to 120 000 bound. - Rainfall round trip: rainfall_from_reflectivity(24 136.71) returns 20.00 mm/h, within 1% (1e-6 relative) of the input. - Tilt to cell top: atan(9144 / 111 120) = 4.704 deg, inside the 3.5 to 6.0 deg bound (the cell top 9144 m above the aircraft). - Ground range: sqrt(111 120^2 - 3048^2) = 111 078.19 m, within 0.5% of the slant range (displayed range is nearly the slant range at high altitude). - Clutter check: beam lowest edge 4.704 - 1.5 = 3.204 deg above the horizon. The terrain angle at 111 120 m is atan(-3048 / 111 120) = -1.57 deg, so the beam is clear of the ground and clutter_verdict is False. - Echo level: 24 136.71 mm6/m3 sits in the 40 to 50 dBZ band, so echo_level returns 3. ## Verification - Reflectivity at 20 mm/h stays in 20 000 to 28 000 mm6/m3 and at 50 mm/h in 90 000 to 120 000 mm6/m3; tilt stays in 3.5 to 6.0 deg; ground range stays within 0.5% of the slant range. - Round trip: the Z-R inverse of the forward value returns the input rate within 1e-6 relative for any rate. - Monotonicity: reflectivity rises with rainfall and tilt rises as the cell top rises. - Clutter verdict flips True when the terrain angle exceeds the beam lowest edge (terrain 1000 m at 5000 m range from own 500 m with 0 deg tilt returns True). - Every non-physical input raises ValueError: negative rainfall or reflectivity, a <= 0, b <= 0, slant range <= 0, beam width <= 0, and a slant range shorter than the altitude difference in ground_range_from_slant. - Determinism: no RNG anywhere, run-to-run identical floats. - Run the contract test offline: python3 scripts/test_airborne_weather_radar.py (32 tests, deterministic). ## Related leaves - avionics/surveillance/ads-b-surveillance: the broadcast surveillance sibling for air-to-air position and velocity performance, which owns the automatic dependent surveillance broadcast link. - avionics/surveillance/tcas-resolution-advisory: the collision avoidance sibling, which owns resolution advisory decision making and its own surveillance logic. ## Pitfalls - Replacing the module's Z-R constants: the reflectivity conversion uses Z = 200.0 * R^1.6 (A_DEFAULT, B_DEFAULT) - swapping in another Marshall-Palmer pair (say 300/1.4 for convective rain) without touching the module constants changes every reflectivity, echo level, and round trip this leaf reports. - Comparing across the dBZ and linear scales: the echo bands are 30 / 40 / 50 dBZ, which log-monotonically match the linear Z thresholds 1000 / 10000 / 100000 mm6/m3 - a rate compared as linear Z against a dBZ band edge mis-ranks the echo level. - Forgetting the tilt can go negative: tilt is atan((cell_top - own) / slant_range), so a cell top below the aircraft gives a downward pointing beam - the altitude difference is signed and a negative tilt is a valid operating point, not an input error. - Applying earth curvature to the displayed range: the model is flat-earth, ground = sqrt(slant^2 - (own - target)^2), and RE_ARTH = 6371000.0 m is informational only - at high altitude the displayed range is nearly the slant range (111 078.19 m from a 111 120 m slant), and a slant range shorter than the altitude difference raises ValueError instead of returning an imaginary square root. - Reversing the clutter comparison: clutter exists when the beam's lowest edge (tilt - beam_width / 2) lies below the terrain angle, because the beam still illuminates the ground - the worked example is clear (3.204 deg edge above a -1.57 deg terrain angle), and the verdict flips True only when the terrain angle rises above the edge, as in the 1000 m terrain case at 5000 m. - Slipping the echo band edges: level 2 spans 30 to 40 dBZ, level 3 spans 40 to 50 dBZ, and level 4 starts at 50 dBZ - the 24 136.71 mm6/m3 worked echo (43.83 dBZ) is level 3, and boundary reflectivity must be graded on the linear threshold 1000 / 10000 / 100000, not a rounded dBZ guess. ## Behavior contract (gate 3) Run the deterministic contract test (stdlib unittest, offline): python3 scripts/test_airborne_weather_radar.py The test covers the worked-example contract (reflectivity values and magnitude bounds, tilt and ground range real outputs, clutter lowest edge and verdict, echo level 3), the Z-R round trip within 1e-6 relative, both monotonicity directions, echo level band edges at 30 / 40 / 50 dBZ, clutter verdict truth and toggling geometry, exact convenience-chain keys, determinism, float output types, module constants, and ValueError rejection of every non-physical input in the spec validation list. ## Compliance - RTCA DO-185 (airborne weather radar MOPS) is referenced, reference-only and gated in standards-map.yaml: no test text or proprietary tables are reproduced. The Marshall-Palmer Z-R relation and the geometry above are standard engineering methodology, summary-only. - compliance: STANDARDS-REF, gated: false.