From 88655e40a661364ef7c1be04086961b14520c51c Mon Sep 17 00:00:00 2001 From: Graham McIntire Date: Tue, 31 Mar 2026 17:00:30 -0500 Subject: [PATCH] Add meteorological foundations section to algo.md Comprehensive description of atmospheric science behind the predictions for meteorologist review: refractivity-propagation connection, four ducting mechanisms, HRRR model usage, frequency-dependent effects, diurnal/seasonal cycles, and known limitations. --- algo.md | 164 ++++++++++++++++++++++++++++++++++++++++++++++++++++++++ 1 file changed, 164 insertions(+) diff --git a/algo.md b/algo.md index 97edf2f9..b95dde1b 100644 --- a/algo.md +++ b/algo.md @@ -29,6 +29,170 @@ The regime distinction matters because refractivity effects are *inverted* betwe --- +## Meteorological Foundations + +This section describes the atmospheric science underlying the propagation predictions, written for review by meteorologists. The system predicts microwave radio propagation conditions (10-241 GHz) using NWP model output and surface observations, focusing on tropospheric ducting and gaseous absorption. + +### Why Meteorology Matters for Microwave Radio + +Microwave radio signals (wavelengths 1 mm to 3 cm) travel through the troposphere and are affected by the same atmospheric structure that meteorologists analyze daily. Unlike HF radio which depends on the ionosphere, microwave propagation is entirely a tropospheric phenomenon governed by: + +- **Temperature and moisture profiles** in the lowest 2 km AGL +- **Boundary layer structure** (mixed layer depth, capping inversions, nocturnal stable layers) +- **Synoptic-scale weather patterns** (frontal boundaries, subsidence, marine layers) +- **Gaseous composition** (water vapor and O2 density along the path) + +Under standard atmospheric conditions, microwave signals are limited to roughly line-of-sight range (~50 km for ground-level antennas). Enhanced propagation occurs when atmospheric structure bends the radio beam downward (super-refraction) or traps it in a waveguide (ducting), extending range to hundreds or thousands of kilometers. + +### The Refractivity-Propagation Connection + +Radio refractivity N is the key bridge between meteorology and propagation. N is computed from standard meteorological variables: + +``` +N = 77.6 * P/T + 3.73×10⁵ * e/T² +``` + +where P is pressure (hPa), T is temperature (K), and e is water vapor pressure (hPa). The first term is the "dry" component (pressure/temperature), the second is the "wet" component (moisture). At microwave frequencies, both terms matter — the wet term contributes roughly 20-40% of total N in the boundary layer. + +The **vertical gradient of N** (dN/dh) determines how radio beams bend: + +| dN/dh (N-units/km) | Propagation Regime | Meteorological Condition | +|---|---|---| +| > 0 | Sub-refraction (beam bends upward) | Strong lapse, well-mixed dry BL | +| 0 to −79 | Normal refraction | Standard atmosphere | +| −79 to −157 | Super-refraction (beam bends toward earth) | Moderate inversion or moisture lapse | +| < −157 | Ducting (beam trapped in waveguide) | Strong temperature inversion with moisture contrast | + +The critical threshold is **−157 N/km**: below this, the radio beam curves faster than the Earth's surface, creating a tropospheric duct. + +### Ducting Mechanisms + +Four meteorological mechanisms produce ducting conditions relevant to this system. Each creates a sharp negative refractivity gradient through a different combination of temperature increase and/or moisture decrease with height: + +**1. Radiation/Nocturnal Inversion Ducts** +- **Mechanism**: Radiative cooling of the surface after sunset creates a strong surface-based temperature inversion. Moisture is often trapped below the inversion cap. +- **Meteorological signature**: Clear skies, light winds, high pressure. Surface temperature drops rapidly after sunset while air aloft remains warm. +- **Timing**: Forms 1-3 hours after sunset, strongest just before sunrise. Dissipates within 1-2 hours of solar heating. +- **Vertical extent**: Typically 50-300m AGL (shallow boundary layer). +- **dN/dh**: −100 to −300 N/km in the inversion layer. +- **This is the primary ducting mechanism in our dataset** — the majority of amateur microwave contacts occur during dawn/sunrise windows specifically to exploit these ducts. + +**2. Advection Ducts (Marine/Coastal)** +- **Mechanism**: Warm, dry air advects over a cooler surface (ocean, lake, or cold ground). Temperature increases with height while moisture decreases sharply at the air-mass boundary. +- **Meteorological signature**: Onshore warm-air advection, sea breeze fronts, warm sector of extratropical cyclones passing over cool water. +- **Timing**: Can persist for hours to days, not limited to diurnal cycle. +- **Vertical extent**: 50-500m, can be elevated. +- **dN/dh**: −200 to −500+ N/km. Among the strongest ducts observed. +- **Relevance**: Gulf Coast, California coast, and Great Lakes regions. Our dataset shows Florida/Gulf Coast (EL) and California (CM) outperform inland regions at 10 GHz. + +**3. Subsidence Inversion Ducts** +- **Mechanism**: Large-scale sinking motion (subsidence) in high-pressure systems creates a temperature inversion aloft. Moisture below the subsidence inversion is trapped, creating a sharp dN/dh gradient at the inversion base. +- **Meteorological signature**: Ridge axis or high-pressure center, clear skies above inversion, possibly hazy/humid below. Visible on soundings as a sharp temperature increase at 800-900 hPa with dewpoint drop above. +- **Timing**: Persistent, follows synoptic-scale ridging. +- **Vertical extent**: 500-2000m AGL (elevated duct). +- **dN/dh**: −100 to −200 N/km (weaker than advection ducts but larger scale). + +**4. Frontal/Boundary Ducts** +- **Mechanism**: Temperature and moisture gradients along frontal boundaries, outflow boundaries, and drylines create localized refractivity gradients. +- **Meteorological signature**: Cold fronts (sharp moisture drop behind front), warm fronts (overrunning warm moist air), dryline passages. +- **Timing**: Transient, associated with frontal passage. +- **Our data confirms**: Low-pressure systems correlate with longer propagation distances (262 km avg vs 196 km for high pressure at 10 GHz), likely due to frontal boundary structure rather than pressure itself. + +### HRRR Model Data in the Prediction System + +The system ingests NOAA's High-Resolution Rapid Refresh (HRRR) model output as its primary atmospheric data source: + +- **Model**: HRRR v4, 3 km horizontal resolution, hourly runs, 18-hour forecasts +- **Source**: NOAA AWS S3 archive (GRIB2 format) +- **Extracted fields**: + - Surface: 2m temperature, 2m dewpoint, surface pressure, 10m wind (u/v), total cloud cover, precipitation + - Boundary layer: HPBL (planetary boundary layer height), PWAT (precipitable water) + - Upper air: temperature, dewpoint, and geopotential height at 1000, 975, 950, 925, 900, 850, 800, 700 hPa + +From these fields, the system derives: + +1. **Surface refractivity N** (ITU-R P.453-14 formula) +2. **Refractivity profile** N(h) at each pressure level +3. **Minimum refractivity gradient** dN/dh — the primary ducting indicator +4. **Modified refractivity** M(h) = N + 0.157h for duct detection (ducting where dM/dh < 0) +5. **Absolute humidity** from temperature and dewpoint +6. **Effective earth radius factor k** for terrain diffraction analysis + +**HRRR vs radiosonde comparison**: HRRR profiles have 8 standard pressure levels in the lowest 3 km, while radiosondes report at ~10m vertical resolution. This means HRRR can detect large-scale inversions but may miss thin ducting layers (<100m). Our gradient statistics reflect this: HRRR-derived gradients cluster between −40 and −130 N/km (median −70), while radiosonde-derived gradients extend to −500+ N/km. The scoring thresholds are calibrated separately for HRRR data. + +### Surface Observations (ASOS) + +ASOS stations provide ground-truth observations that complement the HRRR model: + +- **Temperature and dewpoint**: Used to compute absolute humidity and T-Td depression +- **Wind speed**: Light winds favor inversion persistence; strong winds indicate mechanical mixing +- **Sky condition**: Clear skies promote radiative cooling (nocturnal inversions); overcast prevents it +- **Pressure**: Used for absolute refractivity calculation and trend analysis +- **Precipitation**: Rain causes direct path attenuation (ITU-R P.838-3), scaling with frequency + +### Frequency-Dependent Atmospheric Effects + +A critical meteorological nuance: the same atmospheric state produces opposite effects at different frequencies. + +**At 10 GHz (3 cm wavelength)**: +- Gaseous absorption is negligible (0.012 dB/km total) +- Propagation is dominated by refractivity structure — ducts and inversions +- More moisture increases N, increasing beam bending — **humidity helps** +- Rain attenuation is mild (0.05 dB/km at 4 mm/hr) + +**At 24 GHz (1.25 cm wavelength)**: +- Near the 22.235 GHz water vapor absorption line — humidity causes significant loss +- 0.012 dB/km per g/m³ of water vapor (10x the rate at 10 GHz) +- **Humidity hurts** — dry air allows longer paths despite reduced ducting benefit +- Rain attenuation 6x higher than 10 GHz + +**At 47+ GHz (sub-cm wavelength)**: +- Increasingly dominated by gaseous absorption +- 68 GHz is near the 60 GHz O2 absorption complex (0.9 dB/km baseline) +- 241 GHz is between H2O lines at 183 and 325 GHz (0.3 dB/km per g/m³) +- Propagation windows exist at 75 GHz and 134 GHz +- **Ducting is the only mechanism** enabling contacts beyond ~20 km at these frequencies + +### Diurnal Cycle and Timing + +The boundary layer diurnal cycle is the most predictable propagation driver: + +1. **Sunset to sunrise**: Radiative cooling builds surface inversions. BL collapses from 1000-2000m (afternoon) to 100-300m. Ducting probability rises. +2. **Dawn (sunrise ± 1.5h)**: Peak inversion strength. BL is shallowest. This is the preferred operating window for amateur microwave contacts. +3. **Morning transition (sunrise + 1.5 to +3h)**: Solar heating erodes inversion from below. Ducting weakens. +4. **Afternoon (sunrise + 6h onward)**: Full convective mixing. BL deepest. Worst propagation conditions. Turbulent scattering dominates any residual refractivity gradients. + +Our data quantifies this diurnal effect by frequency: the night/dawn enhancement over afternoon baseline is +4% at 10 GHz, +28% at 24 GHz, +36% at 47 GHz, and +360% at 75 GHz. At the highest frequencies, **time of day is the dominant predictor** — more important than any single weather variable. + +### Seasonal Cycle + +Ducting probability from our radiosonde analysis (3,901 profiles, continental US): + +- **Peak**: June-July (69-77% ducting frequency). Warm, moist boundary layers with strong nocturnal inversions. +- **Secondary peak**: October-November (55-65%). Autumn radiative cooling with residual moisture. +- **Minimum**: March (10.8%). Transitional season with frequent mixing events. +- **Winter**: December-February (12-20%). Cold, dry atmosphere limits refractivity gradients. + +At 24+ GHz, the seasonal pattern inverts: **winter is best** because low absolute humidity minimizes absorption, even though ducting is less frequent. The system's band-specific seasonal scoring reflects this inversion. + +### Known Limitations and Areas for Meteorologist Review + +1. **HRRR vertical resolution**: 8 pressure levels below 700 hPa may miss thin ducting layers. Soundings show gradients 3-5x stronger than HRRR at the same locations. The system uses HRRR-calibrated thresholds, but this may underestimate ducting potential. + +2. **Mesoscale effects**: Sea breeze fronts, outflow boundaries, and terrain-induced convergence zones can create localized ducts not resolved by the 3 km HRRR grid. The system does not currently account for these sub-grid phenomena. + +3. **Precipitation model**: Rain attenuation uses ITU-R P.838-3 coefficients but has not been validated against measured data (no rain events in the commercial link dataset). Rainscatter (using rain as a scattering medium for propagation) is observed at 24 GHz but not modeled. + +4. **Fog and cloud effects**: The system uses cloud cover percentage as a sky condition proxy but does not model fog/cloud attenuation directly. At 10 GHz, fog attenuation is negligible; at 75+ GHz, dense fog can add 1-5 dB/km. + +5. **Turbulence scintillation**: Not modeled. On long LOS paths, convective turbulence causes amplitude scintillation (rapid signal fluctuations) that is distinct from multipath fading. + +6. **Time resolution**: The system updates hourly using HRRR analysis/forecast. Rapidly evolving mesoscale events (convective outflows, sea breeze onset) may be captured by the forecast hours but with reduced accuracy beyond the analysis hour. + +We welcome feedback from operational meteorologists on these assumptions and any atmospheric processes we may be underweighting or overlooking. + +--- + ## Part 1: Atmospheric Physics ### Absolute Humidity