prop/algo.md

# Microwave Propagation Algorithm — Unified

## Overview

Propagation scoring and prediction for microwave amateur radio bands (10-241 GHz), calibrated against 57,488 tropospheric QSOs with distance data, validated against commercial terrestrial links at 11/24/68 GHz, and grounded in ITU-R atmospheric models.

The algorithm has two operating regimes:
1. **Beyond-LOS** — Ham radio paths (50-1000+ km) where atmospheric ducting and refraction are essential. This is the primary use case. Terrain analysis confirms **97.2% of all QSO paths are terrain-blocked** (average diffraction loss 36.2 dB), making atmospheric propagation mechanisms the sole enabler.
2. **LOS** — Known fixed links or short paths with clear Fresnel clearance where gaseous absorption is the dominant variable.

The regime distinction matters because refractivity effects are *inverted* between the two: enhanced refraction extends beyond-LOS range but causes multipath fading on short LOS paths.

### Calibration Dataset

**QSO data:** 58,282 total QSOs across 13+ bands (ARRL Microwave Contest, 1992-2024). 57,488 with tropospheric distance data after excluding 4 EME contacts (QRA64D/JT4F modes >3,000 km). Enriched with weather from 1,299 ASOS stations (58,398 surface observations), 112 RAOB stations (3,901 soundings), 4,522 HRRR model profiles, 3,675 IEMRE gridded hourly observations, and 58,276 terrain path profiles.

**Link data:** 7 commercial links near DFW (Princeton TX area) at 11/24/68 GHz, polled via SNMP at 5-minute intervals. All links use KTKI ASOS for weather correlation. Live polling is active; historical dataset from March 14-29 2026 (18,540 samples) was used for initial algorithm validation.

**Terrain analysis:** 58,276 QSO paths profiled — 56,658 BLOCKED (97.2%, avg 36.2 dB diffraction), 1,277 CLEAR (2.2%), 341 FRESNEL_PARTIAL (0.6%). Blocked paths average *longer* distances than clear paths (215 km vs 84 km at 10 GHz) because ducting enables beyond-LOS paths by definition.

**Confirmed long-range contacts:**
- 47 GHz: 116.0 km (Nov 2025), 98.8 km (Jun 2024)
- 24 GHz: 710.0 km (rainscatter, CW), 542.1 km (Sep 2002, longest tropo)
- 10 GHz: 2,393 km (longest tropospheric in dataset)

**Additional data sources (not yet integrated into scoring):**
- Solar indices: 9,586 daily values (1998-2026) — SFI, SSN, Ap/Kp. Not relevant for tropospheric microwave propagation but available for future VHF/sporadic-E extension.
- IEMRE gridded hourly data: weather at QSO endpoint grid points (0.125° resolution) with percentage sky cover, soil temperature, wind components. More granular than nearest-ASOS matching.

---

## Part 1: Atmospheric Physics

### Absolute Humidity

The single most important weather variable. Temperature and relative humidity are proxies; absolute humidity (g/m^3) directly determines gaseous absorption.

```
rho = 217 * (RH/100) * e_s / T_kelvin

e_s = 6.112 * exp(17.67 * T_c / (T_c + 243.5))    # Magnus formula (hPa)
```

### Surface Refractivity (ITU-R P.453-14)

```
N = 77.6 * P / T + 3.73e5 * e / T^2

P: pressure (hPa)
T: absolute temperature (K)
e: water vapor pressure (hPa) = 6.112 * exp(17.67 * Td_c / (Td_c + 243.5))
```

N is a compound variable: both dry air (pressure/temperature) and moisture contribute. At 10 GHz, higher N increases beam bending (beneficial for beyond-LOS). At 24+ GHz, higher N usually means more moisture = more absorption (harmful), though the refractivity benefit partially offsets this.

### Modified Refractivity (M-units)

```
M = N + 0.157 * (h_agl)

h_agl: height above ground level (m)
```

Ducting occurs where dM/dh < 0 (M decreases with height). Duct strength = delta-M across the inversion layer.

### Gaseous Absorption (ITU-R P.676-13)

Total absorption per km = O2 component (fixed) + H2O component (humidity-dependent):

| Band | f (GHz) | O2 (dB/km) | H2O Coeff (dB/km per g/m^3) | Total @ 7.5 g/m^3 | Dominant Constraint |
|------|---------|------------|---------------------------|-------------------|---------------------|
| 10G | 10.368 | 0.008 | 0.0005 | 0.012 | Negligible absorption |
| 24G | 24.192 | 0.015 | 0.012 | 0.105 | 22.235 GHz H2O line |
| 47G | 47.088 | 0.045 | 0.003 | 0.068 | O2 wing + mild H2O |
| 68G | 68.040 | 0.90 | 0.007 | 0.95 | 60 GHz O2 band wing |
| 75G | 76.032 | 0.012 | 0.006 | 0.057 | Window band |
| 122G | 122.250 | 0.80 | 0.010 | 0.875 | 118.75 GHz O2 wing |
| 134G | 134.928 | 0.08 | 0.015 | 0.193 | Between O2 118 & H2O 183 |
| 142G | 142.000 | 0.05 | 0.025 | 0.238 | Approaching H2O 183 |
| 241G | 241.000 | 0.08 | 0.30 | 2.33 | Between H2O 183 & H2O 325 |

The 11 GHz and 24 GHz coefficients are validated by commercial link measurements. The 68 GHz coefficient is directly measured (0.1 dB/km per g/m^3 increase on a 2.8 km path, consistent with ITU-R model when O2 wing contribution is included).

### Rain Attenuation (ITU-R P.838-3)

gamma_R = k * R^alpha (dB/km), R = rain rate (mm/hr):

| Band | k_H | alpha_H | Light 4mm/hr | Moderate 10mm/hr | Heavy 25mm/hr |
|------|------|------|-------------|-----------------|--------------|
| 10G | 0.010 | 1.28 | 0.05 | 0.19 | 0.56 |
| 24G | 0.070 | 1.07 | 0.31 | 0.81 | 2.04 |
| 47G | 0.187 | 0.93 | 0.68 | 1.58 | 3.69 |
| 68G | 0.310 | 0.86 | 0.98 | 2.18 | 4.73 |
| 75G | 0.345 | 0.84 | 1.07 | 2.40 | 5.18 |
| 122G | 0.498 | 0.77 | 1.32 | 2.93 | 5.91 |
| 241G | 0.550 | 0.70 | 1.30 | 2.76 | 5.20 |

Rain model is NOT validated by measured data (no rain events in link dataset). Coefficients are from ITU-R P.838-3 and interpolation.

### Free-Space Path Loss (ITU-R P.525)

```
FSPL = 20 * log10(d_km) + 20 * log10(f_GHz) + 92.45    (dB)
```

### Fresnel Zone Radius

```
r_fresnel = sqrt(lambda * d1 * d2 / (d1 + d2))

lambda = 0.3 / f_GHz    (meters)
```

### Earth Bulge

```
bulge = (d1 * d2) / (2 * K * 6371000)

K: effective earth radius factor (standard = 4/3)
```

### Effective K-Factor from Surface N

```
dN_est = -40 - (N_surface - 315) * 0.25
K = 1 / (1 + 6371 * dN_est * 1e-6)
K clamped to [0.5, 5.0]
```

---

## Part 2: Key Empirical Findings

These findings drive the scoring model's design. Each contradicts or refines assumptions from simpler models.

### Finding 1: Humidity Effect Reverses by Frequency

The most important discovery. At 10 GHz, more moisture = longer paths (refractivity dominates, absorption negligible). At 24+ GHz, more moisture = shorter paths (absorption dominates).

**10 GHz — humidity helps (N=53,013 QSOs):**

| Abs. Humidity | Avg Dist | P90 Dist |
|---------------|----------|----------|
| 5-8 g/m^3 | 193 km | 342 km |
| 11-14 g/m^3 | 215 km | 383 km |
| 17+ g/m^3 | 230 km | 519 km |

**24 GHz — humidity hurts (N=3,639 QSOs):**

| Abs. Humidity | Avg Dist | P90 Dist |
|---------------|----------|----------|
| 5-8 g/m^3 | 115 km | 154 km |
| 11-14 g/m^3 | 105 km | 174 km |
| 17+ g/m^3 | 53 km | 103 km |

**47 GHz — humidity hurts, less severely (N=689 QSOs):**

| Abs. Humidity | Avg Dist | P90 Dist |
|---------------|----------|----------|
| 0-5 g/m^3 | 191 km | 234 km |
| 11-14 g/m^3 | 71 km | 114 km |

### Finding 2: Wind Penalty Is Overrated

Data shows no meaningful penalty for wind on achieved distance:

| Wind | 10G Avg | 24G Avg | 47G Avg |
|------|---------|---------|---------|
| Calm (0-3 kts) | 216 | 84 | -- |
| Light (3-7 kts) | 214 | 100 | 77 |
| Moderate (7-12 kts) | 220 | 113 | 77 |

Wind may reduce inversion quality but also creates boundary-layer dynamics that can enhance propagation. Weight reduced from 18% to 8%.

### Finding 3: Low Pressure Correlates with Longer Distances

Contradicts the original model's high-pressure = good assumption:

| Pressure | 10G Avg | 10G P90 | 24G Avg | 47G Avg |
|----------|---------|---------|---------|---------|
| <1010 | 262 | 506 | 119 | 111 |
| 1015-1020 | 217 | 383 | 97 | 74 |
| 1025+ | 196 | 354 | 122 | -- |

Low pressure systems bring frontal boundaries with strong temperature/moisture gradients that create inversions and ducts. The key is gradient structure, not absolute pressure.

### Finding 4: Boundary Layer Depth — Time-Dependent Sweet Spot

Sounding data (3,901 profiles) reveals that BL depth interpretation depends on sounding time:

| Sounding Time | Avg BL Depth | Ducting % | Mechanism |
|---------------|-------------|-----------|-----------|
| 00Z (evening) | 1,370m | 54.0% | Elevated ducts within deep residual BL |
| 12Z (morning) | 335m | 53.7% | Surface/radiation ducts from shallow nocturnal BL |

Ducting rate is identical at both times (~54%), but via different mechanisms. At 12Z, shallow BL (<500m) is the signature. At 00Z, the duct is typically elevated within a deeper residual boundary layer. A single BL depth threshold won't work across both regimes — use BL depth relative to expected diurnal range.

HRRR profile data (4,522 profiles) confirms the relationship is monotonic:

| BL Depth Bin | Count | Avg N | Avg Min Gradient |
|-------------|-------|-------|------------------|
| 0-200m | 1,096 | 342.6 | -93.7 |
| 200-500m | 1,091 | 346.6 | -81.5 |
| 500-1000m | 1,242 | 337.0 | -70.1 |
| 1000-1500m | 735 | 328.8 | -58.3 |
| 1500-2000m | 299 | 325.2 | -51.0 |
| 2000m+ | 60 | 309.4 | -45.4 |

### Finding 5: Binary Duct Detection Is Weak — Use Continuous Gradient

Ducting is the **majority case** in soundings: 2,099 ducting (53.8%) vs 1,800 non-ducting (46.2%). Binary detection has near-zero discriminating power.

| Ducting | Count | Avg N | Avg Min Gradient | Avg BL Depth | Avg K-Index | Avg LI |
|---------|-------|-------|------------------|-------------|-------------|--------|
| No | 1,800 | 327.4 | -123.4 | 986m | 16.7 | 22.8 |
| Yes | 2,099 | 340.2 | -388.7 | 738m | 12.7 | 25.3 |

The continuous gradient (-389 vs -123) is the real signal — a 3x magnitude difference. HRRR data shows 79% of profiles in "Enhanced" regime (gradient -40 to -100), so the scoring must discriminate *within* the enhanced category, not just between standard and enhanced.

**Stability indices and ducting:**
- K-index is **lower** for ducting (12.7 vs 16.7) — stable atmosphere favors ducting, not convection
- Lifted Index is **higher** for ducting (25.3 vs 22.8) — confirms stability correlation
- **Precipitable water is identical** (28.0 mm) for both ducting and non-ducting — PWAT is NOT a useful ducting discriminator. It plateaus as a gradient predictor above ~15mm.

### Finding 6: Diurnal Signal Variation Sets a Noise Floor

Commercial link data shows 1-5 dB daily variation even on perfectly clear, stable days. The algorithm should convey that even an "EXCELLENT" score has +/-2-3 dB inherent uncertainty.

### Finding 7: LOS vs Beyond-LOS Regimes Are Inverted

On short LOS paths (3-7 km), sub-refractive conditions (dN/dh > -40/km) produce the best signal — minimal multipath, clean beam coupling. On long beyond-LOS paths (50-500+ km), enhanced refraction/ducting is essential. The algorithm must handle both regimes.

### Finding 8: Time-of-Day Effect Scales with Frequency

Night/dawn (22Z-10Z) enhancement vs afternoon baseline, from QSO distance data:

| Band | Afternoon Avg | Night/Dawn Avg | Enhancement | P90 Boost |
|------|--------------|----------------|-------------|-----------|
| 10 GHz | 209.7 km | 218.6 km | +4% | +8% |
| 24 GHz | 93.8 km | 119.7 km | +28% | +16% |
| 47 GHz | 63.5 km | 86.6 km | +36% | +42% |
| 75 GHz | 38.1 km | 175.4 km | +360% | +237% |

At 10 GHz the effect is modest. At 47+ GHz it is the **dominant variable**, more important than most weather parameters. The 75 GHz result is from only 20 night/dawn QSOs but the 4.6x multiplier is consistent with strong ducting being the *only* path at that frequency.

### Finding 9: Ducting Peaks June-July, Not August

Monthly ducting probability from 3,901 soundings:

| Month | Soundings | Ducting % | Avg N | Avg Min Gradient | Avg PWAT (mm) |
|-------|-----------|-----------|-------|------------------|---------------|
| Jan | 32 | 21.9% | 306.2 | -133.4 | 9.5 |
| Feb | 58 | 17.2% | 304.4 | -132.7 | 6.6 |
| Mar | 37 | **10.8%** | 293.3 | -112.5 | 6.6 |
| Apr | 64 | 37.5% | 306.0 | -152.0 | 14.0 |
| May | 68 | 48.5% | 323.3 | -233.1 | 20.5 |
| Jun | 134 | **68.7%** | 335.0 | -322.7 | 28.6 |
| Jul | 85 | **76.5%** | 339.3 | -301.4 | 27.6 |
| Aug | 1,700 | 53.9% | 341.9 | -260.7 | 33.3 |
| Sep | 1,564 | 56.4% | 332.4 | -286.5 | 26.2 |
| Oct | 48 | 60.4% | 321.5 | -314.3 | 17.9 |
| Nov | 53 | 56.6% | 308.4 | -264.3 | 10.6 |
| Dec | 58 | 12.1% | 305.0 | -139.8 | 10.5 |

**March is the worst month** (10.8%), not winter. December-February averages ~17%. The sharp ramp April→July is nonlinear. Contest data (Aug-Sep) slightly undersamples the true ducting peak (Jun-Jul at 69-77%). Note: Aug/Sep have disproportionate sounding counts because data is enriched from QSO time windows during contest months.

### Finding 10: Mode Matters — CW Has 24% Range Advantage

| Mode | QSOs | Avg Distance |
|------|------|-------------|
| CW | 19,863 | 232.2 km |
| PH (SSB) | 37,077 | 186.5 km |
| FM | 178 | 144.1 km |
| DG (digital) | 122 | 192.4 km |

The CW advantage (~7 dB bandwidth: 10*log10(2700/500)) translates to 24% longer average distances. Scoring tier range estimates should be qualified by mode. One confirmed 710 km rainscatter contact at 24 GHz (CW mode).

---

## Part 3: Band Configuration

```elixir
@band_configs %{
  10_000 => %{
    label: "10 GHz",
    o2_db_km: 0.008,
    h2o_coeff: 0.0005,
    humidity_effect: :beneficial,  # More moisture = more refractivity = longer paths
    humidity_penalty: 0.0,
    rain_k: 0.010, rain_alpha: 1.28,
    # Seasonal pattern INVERTED from 24+ GHz: ducting + humidity both help 10G
    # Ducting peaks Jun-Jul (69-77%), March worst (10.8%), Dec-Feb ~12-22%
    # Score tracks ducting probability scaled to 0-100
    seasonal_base: %{1 => 38, 2 => 32, 3 => 22, 4 => 55, 5 => 68,
                     6 => 90, 7 => 95, 8 => 75, 9 => 78, 10 => 82,
                     11 => 78, 12 => 25},
    seasonal_adj: %{},
    typical_range_km: 200,
    extended_range_km: 500,
    exceptional_range_km: 1000
  },
  24_000 => %{
    label: "24 GHz",
    o2_db_km: 0.015,
    h2o_coeff: 0.012,           # Validated by commercial link data
    humidity_effect: :harmful,   # 22.235 GHz H2O line shoulder
    humidity_penalty: 1.6,
    rain_k: 0.070, rain_alpha: 1.07,
    # 24G: humidity hurts, so best in dry months. But March is worst for ducting.
    # Balance: winter dry + some ducting > spring dry + no ducting
    seasonal_base: %{1 => 88, 2 => 84, 3 => 68, 4 => 62, 5 => 51,
                     6 => 34, 7 => 18, 8 => 18, 9 => 48, 10 => 68,
                     11 => 96, 12 => 88},
    seasonal_adj: %{5 => -4, 6 => -8, 7 => -10, 8 => -10, 9 => -4},
    typical_range_km: 100,
    extended_range_km: 250,
    exceptional_range_km: 500
  },
  47_000 => %{
    label: "47 GHz",
    o2_db_km: 0.045,
    h2o_coeff: 0.003,
    humidity_effect: :harmful,
    humidity_penalty: 1.0,       # Window band, moderate H2O sensitivity
    rain_k: 0.187, rain_alpha: 0.93,
    seasonal_base: %{1 => 90, 2 => 88, 3 => 78, 4 => 68, 5 => 55,
                     6 => 38, 7 => 22, 8 => 22, 9 => 48, 10 => 74,
                     11 => 96, 12 => 90},
    seasonal_adj: %{},
    typical_range_km: 70,
    extended_range_km: 150,
    exceptional_range_km: 300
  },
  68_000 => %{
    label: "68 GHz",
    o2_db_km: 0.90,             # 60 GHz O2 band wing — validated by link data
    h2o_coeff: 0.007,           # Measured: ~0.1 dB/km per g/m^3 on 2.8 km path
    humidity_effect: :harmful,
    humidity_penalty: 1.4,
    rain_k: 0.310, rain_alpha: 0.86,
    seasonal_base: %{1 => 90, 2 => 88, 3 => 78, 4 => 65, 5 => 50,
                     6 => 32, 7 => 18, 8 => 18, 9 => 44, 10 => 70,
                     11 => 92, 12 => 90},
    seasonal_adj: %{},
    typical_range_km: 40,
    extended_range_km: 80,
    exceptional_range_km: 150
  },
  75_000 => %{
    label: "75 GHz",
    o2_db_km: 0.012,
    h2o_coeff: 0.006,
    humidity_effect: :harmful,
    humidity_penalty: 1.2,
    rain_k: 0.345, rain_alpha: 0.84,
    seasonal_base: %{1 => 90, 2 => 90, 3 => 80, 4 => 68, 5 => 55,
                     6 => 38, 7 => 22, 8 => 22, 9 => 48, 10 => 74,
                     11 => 96, 12 => 90},
    seasonal_adj: %{},
    typical_range_km: 50,
    extended_range_km: 120,
    exceptional_range_km: 250
  },
  122_000 => %{
    label: "122 GHz",
    o2_db_km: 0.80,             # 118.75 GHz O2 wing — weather independent
    h2o_coeff: 0.010,
    humidity_effect: :harmful,
    humidity_penalty: 1.0,
    rain_k: 0.498, rain_alpha: 0.77,
    seasonal_base: %{1 => 92, 2 => 90, 3 => 78, 4 => 62, 5 => 45,
                     6 => 28, 7 => 15, 8 => 15, 9 => 38, 10 => 68,
                     11 => 92, 12 => 92},
    seasonal_adj: %{},
    typical_range_km: 30,
    extended_range_km: 80,
    exceptional_range_km: 140
  },
  134_000 => %{
    label: "134 GHz",
    o2_db_km: 0.08,
    h2o_coeff: 0.015,
    humidity_effect: :harmful,
    humidity_penalty: 1.3,
    rain_k: 0.520, rain_alpha: 0.75,
    seasonal_base: %{1 => 92, 2 => 90, 3 => 78, 4 => 65, 5 => 48,
                     6 => 30, 7 => 18, 8 => 18, 9 => 42, 10 => 70,
                     11 => 92, 12 => 92},
    seasonal_adj: %{},
    typical_range_km: 40,
    extended_range_km: 100,
    exceptional_range_km: 160
  },
  241_000 => %{
    label: "241 GHz",
    o2_db_km: 0.08,
    h2o_coeff: 0.30,            # Extreme H2O sensitivity (183/325 GHz lines)
    humidity_effect: :harmful,
    humidity_penalty: 3.0,
    rain_k: 0.550, rain_alpha: 0.70,
    seasonal_base: %{1 => 95, 2 => 92, 3 => 75, 4 => 55, 5 => 35,
                     6 => 15, 7 => 8, 8 => 8, 9 => 30, 10 => 65,
                     11 => 95, 12 => 95},
    seasonal_adj: %{},
    typical_range_km: 10,
    extended_range_km: 50,
    exceptional_range_km: 115
  }
}
```

---

## Part 4: Scoring Functions (Beyond-LOS Regime)

All scores return 0-100. The beyond-LOS regime is the primary use case for ham radio propagation prediction.

### 1. Humidity Score — Frequency-Dependent

The critical insight: moisture helps at 10 GHz (refractivity) and hurts at 24+ GHz (absorption).

```elixir
def score_humidity(abs_humidity_gm3, band_config) do
  case band_config.humidity_effect do
    :beneficial ->
      # 10 GHz: more moisture = higher surface N = more beam bending
      # Extreme humidity risks scintillation
      cond do
        abs_humidity_gm3 < 4  -> 55   # Very dry — poor refractivity
        abs_humidity_gm3 < 7  -> 70   # Dry
        abs_humidity_gm3 < 10 -> 82   # Moderate
        abs_humidity_gm3 < 14 -> 90   # Good refractivity
        abs_humidity_gm3 < 18 -> 95   # Excellent refractivity
        abs_humidity_gm3 < 22 -> 88   # High — scintillation onset
        true                  -> 75   # Tropical — scintillation risk
      end

    :harmful ->
      # 24+ GHz: H2O absorption dominates
      # Penalty factor scales by band (1.0 for 47G window, 1.6 for 24G near line, 3.0 for 241G)
      r = abs_humidity_gm3 * band_config.humidity_penalty
      cond do
        r <= 6  -> 100
        r <= 9  -> round(95 - (r - 6) / 3 * 20)
        r <= 13 -> round(75 - (r - 9) / 4 * 30)
        r <= 18 -> round(45 - (r - 13) / 5 * 35)
        true    -> max(0, round(10 - (r - 18) * 2))
      end
  end
end
```

### 2. Time of Day Score — Inversion Lifecycle

The strongest diurnal predictor in the data. Dawn shows the highest P90 distances; late evening shows elevated averages.

```elixir
@sunrise_table [7.4, 7.3, 7.0, 6.7, 6.35, 6.25,
                6.35, 6.65, 6.9, 7.1, 7.35, 7.45]

def score_time_of_day(utc_hour, utc_minute, month) do
  offset = if month >= 3 and month <= 10, do: -5, else: -6  # CDT/CST
  local = rem(utc_hour + utc_minute / 60 + offset + 24, 24)
  sunrise = Enum.at(@sunrise_table, month - 1)
  d = local - sunrise  # hours relative to sunrise

  cond do
    d >= -1.5 and d <= 1.5 ->
      {100, "Peak — inversion maximum"}

    d > 1.5 and d <= 3.0 ->
      {78, "Good — inversion eroding"}

    d > -3.0 and d < -1.5 ->
      {82, "Pre-dawn — inversion building"}

    d > 3.0 and d <= 6.0 ->
      {38, "Marginal — boundary layer mixing"}

    local >= 20.0 or local <= 1.0 ->
      {72, "Evening — cooling, inversion reforming"}

    d > 6.0 ->
      {18, "Afternoon — full convective mixing"}

    true ->
      {55, "Night — gradual cooling"}
  end
end
```

### 3. Temperature-Dewpoint Depression — Frequency-Split

Large depression = dry aloft = favorable for 24+ GHz. Small depression = moist = favorable for 10 GHz refractivity (but near-saturation risks fog).

```elixir
def score_td_depression(temp_f, dewpoint_f, band_config) do
  dep = temp_f - dewpoint_f

  case band_config.humidity_effect do
    :beneficial ->
      cond do
        dep < 3  -> 40   # Near saturation — fog/scattering risk
        dep < 8  -> 75   # Moist — good refractivity
        dep < 14 -> 85   # Moderate — balanced
        dep < 22 -> 70   # Dry — reduced refractivity
        true     -> 55   # Very dry — poor refractivity
      end

    :harmful ->
      cond do
        dep > 22 -> 96   # Very dry aloft
        dep > 14 -> 80   # Good stability
        dep > 8  -> 60   # Moderate
        dep > 4  -> 38   # Marginal
        true     -> 18   # Humid aloft
      end
  end
end
```

### 4. Sky Cover Score

Data shows modest impact at 24/47 GHz, near-zero at 10 GHz. VV (vertical visibility / fog) is a moderate penalty due to near-surface moisture content. Supports both METAR categories (from ASOS) and percentage sky cover (from IEMRE gridded data).

```elixir
def score_sky(condition) when is_binary(condition) do
  # METAR category from ASOS
  case condition do
    c when c in ["CLR", "SKC"] -> 100
    "FEW" -> 88
    "SCT" -> 60
    "BKN" -> 25
    "OVC" -> 5
    "VV"  -> 5
    _     -> 50
  end
end

def score_sky(pct) when is_number(pct) do
  # Percentage sky cover from IEMRE (0-100%)
  cond do
    pct <= 6   -> 100  # CLR equivalent
    pct <= 25  -> 88   # FEW
    pct <= 50  -> 60   # SCT
    pct <= 87  -> 25   # BKN
    true       -> 5    # OVC
  end
end
```

### 5. Season Score

Per-band lookup with optional adjustments. 24 GHz gets additional summer penalties due to Gulf moisture.

```elixir
def score_season(month, band_config) do
  base = Map.get(band_config.seasonal_base, month, 50)
  adj = Map.get(band_config.seasonal_adj, month, 0)
  max(0, min(100, base + adj))
end
```

### 6. Wind Score — Reduced Weight

Data shows minimal impact on achieved distance. Retain mild penalty only for very high winds (turbulent scintillation).

```elixir
def score_wind(speed_kts) do
  cond do
    speed_kts < 5  -> 100
    speed_kts < 10 -> 90
    speed_kts < 15 -> 75
    speed_kts < 20 -> 55
    speed_kts < 25 -> 35
    true           -> 15
  end
end
```

### 7. Rain Score

Not validated by measured data. Based on ITU-R P.838-3 attenuation per km. At 10 GHz, moderate rain is tolerable. Above 75 GHz, even light rain effectively kills the path.

```elixir
def score_rain(rain_rate_mmhr, band_config) do
  if rain_rate_mmhr == nil or rain_rate_mmhr == 0 do
    100
  else
    gamma = band_config.rain_k * :math.pow(rain_rate_mmhr, band_config.rain_alpha)
    cond do
      gamma < 0.1 -> 95
      gamma < 0.5 -> 75
      gamma < 1.0 -> 50
      gamma < 2.0 -> 25
      gamma < 5.0 -> 10
      true        -> 0
    end
  end
end
```

### 8. Pressure Score — Gradient-Focused

Data contradicts the original high-pressure-is-good model. Frontal boundaries (changing pressure) create the strongest refractive gradients. Rising post-frontal pressure and slowly falling pre-frontal pressure both score well.

```elixir
def score_pressure(current_mb, previous_mb) do
  case previous_mb do
    nil ->
      # No trend — mild scoring on absolute value
      cond do
        current_mb > 1025 -> 55   # Strong ridge
        current_mb > 1018 -> 65   # Mild high
        current_mb > 1010 -> 60   # Normal
        current_mb > 1005 -> 55   # Low
        true              -> 40   # Very low — active weather
      end

    prev ->
      delta = current_mb - prev
      cond do
        delta > 2.5  -> 80   # Rising rapidly — post-frontal clearing
        delta > 0.8  -> 70   # Rising — stabilizing
        delta > -0.5 -> 60   # Steady — neutral
        delta > -2.0 -> 65   # Falling slowly — approaching front, duct possible
        true         -> 45   # Falling rapidly — active weather
      end
  end
end
```

### 9. Refractivity Score — When Sounding/HRRR Data Available

Best predictor when available. Binary duct detection is useless (54% baseline rate). Use continuous gradient magnitude and BL depth instead. Surface-based ducts (base=0) matter more than elevated ducts.

From sounding data: avg gradient -389 N/km for ducting events vs -123 for non-ducting. From HRRR: BL depth < 200m correlates with avg gradient of -93.7 (approaching super-refraction).

```elixir
def score_refractivity(sounding_or_hrrr, band_config) do
  cond do
    sounding_or_hrrr == nil -> 50  # No data — neutral

    sounding_or_hrrr.min_dn_dh < -500 ->
      # Strong ducting — gradient 3x non-ducting average
      case band_config.humidity_effect do
        :beneficial -> 98   # 10 GHz benefits most from ducting
        :harmful    -> 85   # Higher bands benefit but absorption limits range
      end

    sounding_or_hrrr.min_dn_dh < -300 ->
      # Moderate ducting — near ducting average of -389
      case band_config.humidity_effect do
        :beneficial -> 92
        :harmful    -> 78
      end

    sounding_or_hrrr.min_dn_dh < -200 ->
      80  # Enhanced refraction — above non-ducting average of -123

    # BL depth signal: shallow BL at 12Z = strong surface duct potential
    sounding_or_hrrr.bl_depth_m != nil and
    sounding_or_hrrr.bl_depth_m < 300 ->
      82  # Very shallow BL — strong inversion cap (12Z signature)

    sounding_or_hrrr.min_dn_dh < -100 ->
      65  # Mild enhancement

    sounding_or_hrrr.min_dn_dh < -60 ->
      55  # Slightly enhanced — within the broad "Enhanced" HRRR regime

    true ->
      42  # Standard/sub-refractive — HRRR shows only 5% of profiles here
  end
end
```

---

## Part 5: Composite Score

### Weights

Revised from expanded dataset. Key changes: refractivity weight doubled (HRRR now provides hourly data, not just 12-hourly soundings), time-of-day weight increased (data shows it's the dominant variable above 24 GHz), pressure reduced (weak standalone predictor, 5% was still generous).

| Factor | Weight | Rationale |
|--------|--------|-----------|
| Humidity | 20% | Dominant variable, but split role by frequency |
| Time of Day | 20% | First-order effect at 24+ GHz (28-360% enhancement at night) |
| Td Depression | 12% | Proxy for humidity aloft — strong signal |
| Refractivity | 10% | Best predictor; HRRR provides hourly coverage, sounding gradient is 3x discriminator |
| Sky Cover | 10% | Modest effect, mainly at higher frequencies |
| Season | 10% | Long-term baseline — now ducting-calibrated per band |
| Wind | 6% | Data shows minimal impact; penalty only for extremes |
| Rain | 8% | Critical for 24+ GHz paths |
| Pressure | 4% | Weak standalone predictor |

```elixir
def composite_score(factors) do
  round(
    factors.humidity      * 0.20 +
    factors.time_of_day   * 0.20 +
    factors.td_depression * 0.12 +
    factors.refractivity  * 0.10 +
    factors.sky           * 0.10 +
    factors.season        * 0.10 +
    factors.wind          * 0.06 +
    factors.rain          * 0.08 +
    factors.pressure      * 0.04
  )
end
```

### Score Tiers with Per-Band Range Estimates

Range estimates are for CW mode. For SSB/phone, reduce by ~20%. For FM, reduce by ~40%.

Database stats for reference: 10G avg=213 km, P90=383 km, max=2,393 km. 24G avg=98 km, P90=179 km, max=710 km. 47G avg=66 km, P90=122 km, max=343 km. 75G avg=64 km, P90=177 km, max=289 km.

| Score | Label | 10G | 24G | 47G | 75G |
|-------|-------|-----|-----|-----|-----|
| 80-100 | EXCELLENT | 400-2000+ km | 200-500 km | 120-300 km | 80-200+ km |
| 65-79 | GOOD | 250-400 km | 120-200 km | 80-120 km | 50-80 km |
| 50-64 | MARGINAL | 150-250 km | 70-120 km | 50-80 km | 30-50 km |
| 33-49 | POOR | 80-150 km | 40-70 km | 25-50 km | 15-30 km |
| 0-32 | NEGLIGIBLE | <80 km | <40 km | <25 km | <15 km |

| Color | Hex |
|-------|-----|
| EXCELLENT | #00ffa3 |
| GOOD | #7dffd4 |
| MARGINAL | #ffe566 |
| POOR | #ff9044 |
| NEGLIGIBLE | #ff4f4f |

---

## Part 6: LOS Regime Scoring

For known fixed links or short paths with confirmed Fresnel clearance. Key difference: sub-refraction is neutral/beneficial (minimal multipath), and gaseous absorption is the primary variable.

### LOS Refractivity Score

```elixir
def score_refractivity_los(dn_dh) do
  cond do
    dn_dh > 0     -> 60   # Strong sub-refraction — unusual but not harmful
    dn_dh > -30   -> 85   # Moderate sub-refraction — stable, clean signal
    dn_dh > -40   -> 75   # Near standard
    dn_dh > -80   -> 60   # Enhanced — multipath onset
    dn_dh > -157  -> 45   # Strong enhancement — multipath likely
    true          -> 30   # Super-refraction — significant multipath fading
  end
end
```

### LOS Surface N Score

Higher N often means more moisture = more absorption at 24+ GHz. Validated by link data: N < 310 gave best 68 GHz signal, N > 340 gave worst.

```elixir
def score_surface_n(n_value, band_config) do
  case band_config.humidity_effect do
    :beneficial ->
      cond do
        n_value > 350 -> 90
        n_value > 330 -> 80
        n_value > 315 -> 65
        n_value > 300 -> 50
        true          -> 35
      end

    :harmful ->
      cond do
        n_value < 300 -> 90
        n_value < 315 -> 80
        n_value < 330 -> 65
        n_value < 345 -> 50
        true          -> 35
      end
  end
end
```

### LOS vs Beyond-LOS Selection

```elixir
def compute_score(conditions, band_config, path_type \\ :beyond_los) do
  base_factors = %{
    humidity: score_humidity(conditions.abs_humidity, band_config),
    wind: score_wind(conditions.wind_speed_kts),
    sky: score_sky(conditions.sky_condition),
    time_of_day: score_time_of_day(conditions.utc_hour, conditions.utc_minute, conditions.month) |> elem(0),
    td_depression: score_td_depression(conditions.temp_f, conditions.dewpoint_f, band_config),
    season: score_season(conditions.month, band_config),
    pressure: score_pressure(conditions.slp, conditions.prev_slp),
    rain: score_rain(conditions.rain_rate, band_config)
  }

  factors = case path_type do
    :beyond_los ->
      Map.put(base_factors, :refractivity,
        score_refractivity(conditions.sounding, band_config))

    :los ->
      Map.put(base_factors, :refractivity,
        score_refractivity_los(conditions.dn_dh))
  end

  %{score: composite_score(factors), factors: factors}
end
```

---

## Part 7: Link Budget

For point-to-point path analysis with known station parameters.

### EIRP

```
eirp_dbm = tx_power_dbm + tx_antenna_dbi - feed_loss_db
```

### Receiver Sensitivity

```
sensitivity_dbm = -174 + noise_figure_db + 10 * log10(bandwidth_hz)

CW: bandwidth = 500 Hz
SSB: bandwidth = 2700 Hz
```

### Total Path Loss

```
total_loss = FSPL + gaseous_absorption + rain_attenuation + diffraction_loss - duct_enhancement

gaseous_absorption = (o2_db_km + h2o_coeff * rho) * distance_km
rain_attenuation = gamma_R * distance_km * rain_effective_fraction
```

### Duct Enhancement (Beyond-LOS Only)

Calibrated against confirmed contacts:

```elixir
def duct_enhancement_db(prop_score) do
  cond do
    prop_score >= 80 -> -14   # 14 dB improvement
    prop_score >= 65 -> -10
    prop_score >= 50 -> -6
    prop_score >= 33 -> -2
    true             -> 0
  end
end
```

### Knife-Edge Diffraction (ITU-R P.526)

```elixir
def knife_edge_loss(v) do
  cond do
    v <= -0.7787 -> 0                                              # Clear
    v <= 0       -> -20 * :math.log10(0.5 - 0.62 * v)
    v <= 1       -> -20 * :math.log10(0.5 * :math.exp(-0.95 * v))
    v <= 2.4     ->
      inner = max(0, 0.1184 - (0.38 - 0.1 * v) ** 2)
      -20 * :math.log10(0.4 - :math.sqrt(inner))
    true         -> 20 * :math.log10(v) + 13.0                    # Asymptotic
  end
end
```

### Success Probability

```elixir
def margin_to_success(margin_db, prop_score) do
  margin_pct = cond do
    margin_db <= 0  -> 0
    margin_db <= 10 -> margin_db / 10 * 20
    margin_db <= 15 -> 20 + (margin_db - 10) / 5 * 20
    margin_db <= 20 -> 40 + (margin_db - 15) / 5 * 20
    margin_db <= 25 -> 60 + (margin_db - 20) / 5 * 20
    margin_db <= 30 -> 80 + (margin_db - 25) / 5 * 20
    true            -> 100
  end

  # Propagation modulation: score 100 -> x1.30, score 50 -> x1.00, score 0 -> x0.70
  prop_factor = 0.70 + (prop_score / 100) * 0.60
  max(0, min(99, round(margin_pct * prop_factor)))
end
```

### Note: Antenna Height & Duct Coupling Geometry

Antenna height and dish elevation angle affect how efficiently a station couples into an atmospheric duct. This is a real physical effect but is **second-order** to duct characteristics at the ranges this model targets (50-1000+ km).

**Why it's not in the scoring model:**
- At >300 km, the duct's own refractive gradient (k-factor) dominates over all antenna geometry. The required aim angle to graze a duct converges toward 0° regardless of antenna height.
- Antenna height differences in the 15-21m range (typical amateur stations) shift beam geometry by ~0.001° at long range — well within the ±2-3 dB noise floor from diurnal variation.
- The primary benefit of antenna height (50+ ft) is clearing local obstructions and ground clutter in the near field (0-20 km), not geometric coupling to the duct layer.
- VE4MA (50 ft, flat prairie) and W5LUA (70 ft, suburban) achieve similar range classes, confirming duct geometry is the dominant term.

**Where it matters — beamwidth vs frequency:**
At 10 GHz a typical 60cm dish has ~3° beamwidth, making elevation angle errors forgiving. At 24 GHz beamwidth shrinks to ~1.5°, at 47 GHz to <1°. A 0.3° aim error that is irrelevant at 10 GHz becomes a contact killer at 47 GHz. If station profiles (antenna height, dish size, elevation setting) are added in the future, a frequency-dependent **beamwidth coupling penalty** in `margin_to_success` would be the right integration point — penalizing paths where the required aim angle to the detected duct layer exceeds the antenna's half-power beamwidth.

---

## Part 8: Short-Term Prediction Model

### Approach

Extrapolate current conditions forward 1-6 hours using observed trends, diurnal models, and forecast data when available.

### Prediction Confidence

Based on commercial link signal prediction accuracy:

| Horizon | Observed Accuracy | Confidence |
|---------|-------------------|------------|
| Current | +/- 1 dB | 95% |
| +30 min | +/- 1.5 dB | 90% |
| +1 hr | +/- 2 dB | 85% |
| +2 hr | +/- 3 dB | 75% |
| +3 hr | +/- 4 dB | 60% |
| +6 hr | +/- 5 dB | 40% |

### Diurnal Temperature Model

```elixir
def project_temperature(current_temp_f, trend_per_hour, hours_ahead,
                        future_local_hour, month) do
  sunrise = Enum.at(@sunrise_table, month - 1)

  diurnal_rate = cond do
    future_local_hour < sunrise - 1 -> -0.5    # Pre-dawn: slow cooling
    future_local_hour < sunrise + 2 -> 0.0     # Sunrise transition
    future_local_hour < 15          -> 2.0     # Morning: warming
    future_local_hour < 18          -> 0.5     # Late afternoon
    future_local_hour < 21          -> -1.5    # Evening: cooling
    true                            -> -1.0    # Night: slow cooling
  end

  # Blend: current trend dominates short-term, diurnal model dominates long-term
  weight = min(1.0, hours_ahead / 4.0)
  blended_rate = trend_per_hour * (1.0 - weight) + diurnal_rate * weight
  current_temp_f + blended_rate * hours_ahead
end
```

### Prediction Flow

```elixir
def predict_scores(current_obs, obs_3hr_ago, forecast, band_config) do
  temp_trend = (current_obs.temp_f - obs_3hr_ago.temp_f) / 3
  dp_trend = (current_obs.dewpoint_f - obs_3hr_ago.dewpoint_f) / 3
  pressure_trend = (current_obs.slp - obs_3hr_ago.slp) / 3

  for hours_ahead <- 1..6 do
    future_time = DateTime.add(current_obs.observed_at, hours_ahead * 3600)
    month = future_time.month

    projected_temp = project_temperature(current_obs.temp_f, temp_trend,
                       hours_ahead, future_time.hour, month)
    projected_dp = current_obs.dewpoint_f + dp_trend * hours_ahead
    projected_slp = current_obs.slp + pressure_trend * hours_ahead
    projected_sky = forecast_value(forecast, :sky, hours_ahead) || current_obs.sky_condition
    projected_rain = forecast_value(forecast, :rain_rate, hours_ahead) || 0
    projected_wind = forecast_value(forecast, :wind_kts, hours_ahead) || current_obs.wind_speed_kts

    # Compute absolute humidity from projected values
    tc = (projected_temp - 32) * 5 / 9
    td_c = (projected_dp - 32) * 5 / 9
    es = 6.112 * :math.exp(17.67 * tc / (tc + 243.5))
    ed = 6.112 * :math.exp(17.67 * td_c / (td_c + 243.5))
    rh = min(100, ed / es * 100)
    abs_hum = 217 * (rh / 100) * es / (tc + 273.15)

    factors = %{
      humidity: score_humidity(abs_hum, band_config),
      wind: score_wind(projected_wind),
      sky: score_sky(projected_sky),
      time_of_day: score_time_of_day(future_time.hour, future_time.minute, month) |> elem(0),
      td_depression: score_td_depression(projected_temp, projected_dp, band_config),
      season: score_season(month, band_config),
      pressure: score_pressure(projected_slp, current_obs.slp),
      rain: score_rain(projected_rain, band_config),
      refractivity: 50  # Cannot predict from surface obs alone
    }

    %{
      hours_ahead: hours_ahead,
      time: future_time,
      score: composite_score(factors),
      factors: factors,
      confidence: prediction_confidence(hours_ahead)
    }
  end
end

def prediction_confidence(hours_ahead) do
  case hours_ahead do
    1 -> 0.85
    2 -> 0.75
    3 -> 0.60
    4 -> 0.50
    5 -> 0.40
    6 -> 0.30
    _ -> 0.20
  end
end
```

---

## Part 9: Sounding & Refractivity Analysis

### Refractivity Profile from Sounding

```elixir
def compute_refractivity_profile(levels, sfc_height_m) do
  Enum.map(levels, fn level ->
    t_k = level.temp_c + 273.15
    e = 6.1121 * :math.exp((18.678 - level.temp_c / 234.5) * (level.temp_c / (257.14 + level.temp_c)))
    e_actual = if level.dewpoint_c, do: 6.1121 * :math.exp((18.678 - level.dewpoint_c / 234.5) * (level.dewpoint_c / (257.14 + level.dewpoint_c))), else: 0

    n = 77.6 * level.pressure_hpa / t_k + 3.73e5 * e_actual / (t_k * t_k)
    h_agl = level.height_m - sfc_height_m
    m = n + 0.157 * h_agl

    %{height_agl: h_agl, n: n, m: m, temp_c: level.temp_c, dewpoint_c: level.dewpoint_c}
  end)
end
```

### Duct Detection

Duct exists where dM/dh < 0. Filter for strength > 2 M-units.

```elixir
def detect_ducts(profile) do
  profile
  |> Enum.chunk_every(2, 1, :discard)
  |> Enum.reduce({[], nil}, fn [below, above], {ducts, duct_start} ->
    dm = above.m - below.m

    cond do
      dm < 0 and duct_start == nil ->
        {ducts, %{base: below.height_agl, base_m: below.m}}

      dm >= 0 and duct_start != nil ->
        strength = duct_start.base_m - below.m
        if strength > 2 do
          duct = %{base: duct_start.base, top: below.height_agl, strength: strength}
          {[duct | ducts], nil}
        else
          {ducts, nil}
        end

      true ->
        {ducts, duct_start}
    end
  end)
  |> elem(0)
  |> Enum.reverse()
end
```

### Inversion Detection

Temperature increasing with height. Merge adjacent inversions within 200m gap. Filter: strength >= 0.5C, base < 5000m AGL.

### Stability Indices

```
K-Index = (T850 - T500) + Td850 - (T700 - Td700)

Lifted Index = T500 - (Tsfc - (h500 - h_sfc) * 0.00976)
  LI < 0: Unstable (convection likely, inversion destroyed)
  LI > 0: Stable (inversion maintained)

Precipitable Water = sum[(MR_i + MR_{i-1}) / 2 * dP / (9.81 * 10)]
  MR = 622 * e / (P - e)
```

### Boundary Layer Depth

Find height where potential temperature (theta = T + 9.8 * h/1000) exceeds surface theta by 2C. The 500-1000m sweet spot indicates an elevated inversion — high enough to trap signals, not so deep that full mixing has occurred.

---

## Part 10: Band-Specific Propagation Mechanisms

### Coupling Sensitivity by Frequency

Duct coupling geometry becomes increasingly critical at higher frequencies due to narrower antenna beamwidths. A dish aimed 0.3° away from the optimal duct grazing angle:
- **10 GHz** (~3° beamwidth): Still within half-power beam — negligible loss
- **24 GHz** (~1.5° beamwidth): Approaching beam edge — moderate coupling loss
- **47 GHz** (<1° beamwidth): Outside half-power beam — potential contact killer
- **75+ GHz** (<0.5° beamwidth): Precision aim required — elevation error dominates

For surface ducts, the beam must arrive at <0.5° grazing incidence to be trapped. For elevated ducts (500-1500m AGL), the optimal elevation angle is path-distance dependent: slightly positive at close range, near-zero at the "sweet spot" distance, and slightly negative at extreme range due to Earth curvature.

### 10 GHz (3cm) — Tropospheric Ducting Band

**Primary mechanisms:** Ducting, enhanced refraction
**Key variable:** Refractivity profile, NOT humidity absorption (0.012 dB/km total is negligible)
**Best conditions:** Moderate-high humidity (12-20 g/m^3), temperature inversions, stable atmosphere, late evening through early morning
**Best months:** June-July (ducting probability 69-77%). August contest data undersamples peak season.
**Worst month:** March (10.8% ducting — worse than deep winter)
**Dataset:** 53,013 QSOs, avg 213 km, P90 383 km, max 2,393 km. CW avg 232 km vs PH avg 187 km.
**Unique:** Largely insensitive to rain. Can propagate through cloud decks. Marine ducting produces 1000+ km coastal paths. Frontal boundaries create strong refractive gradients. 97.2% of paths are terrain-blocked — ducting IS the propagation mechanism.

### 24 GHz (1.2cm) — Water Vapor Line Band

**Primary mechanisms:** Ducting (reduced by absorption), enhanced refraction
**Key variable:** Absolute humidity (22.235 GHz H2O line makes this THE most humidity-sensitive band)
**Best conditions:** Very dry air (<8 g/m^3), cold season (Nov-Mar), clear skies, pre-dawn through early morning
**Night enhancement:** +28% avg distance, +16% P90 vs afternoon (119.7 km vs 93.8 km)
**Dataset:** 3,639 QSOs, avg 98 km, P90 179 km, max 710 km (rainscatter CW).
**Unique:** 10x more sensitive to water vapor than 10 GHz. Summer Gulf moisture devastates range. Rain scatter is a viable alternative mechanism (710 km QSO documented). March is the worst ducting month (10.8%) but also has low humidity, creating a tension between ducting availability and absorption loss.

### 47 GHz (6mm) — Atmospheric Window

**Primary mechanisms:** Ducting (in atmospheric window), enhanced LOS
**Key variable:** Balance of humidity and refractivity; very dry air dramatically helps
**Best conditions:** Dry air (<8 g/m^3), clear skies, strong inversions, early morning
**Night enhancement:** +36% avg distance, +42% P90 vs afternoon (86.6 km vs 63.5 km). Time-of-day is the dominant variable at this frequency.
**Dataset:** 689 QSOs, avg 66 km, P90 122 km, max 343 km.
**Unique:** Window between 22 GHz H2O and 60 GHz O2. O2 absorption ~0.045 dB/km is fixed. Ducting is the ONLY way beyond ~150 km.

### 68 GHz — V-Band Edge

**Primary mechanisms:** LOS only (O2 absorption limits range)
**Key variable:** O2 wing absorption (~0.9 dB/km, weather-independent) + humidity
**Best conditions:** Cold/dry air, no precipitation, short paths
**Unique:** Validated by link data showing 3-5 dB diurnal fades on 2.8 km path. O2 absorption caps practical range regardless of conditions. Viable for short links (<5 km), very challenging for beyond-LOS.

### 75 GHz (4mm) — Window Band

**Primary mechanisms:** Rare ducting, enhanced LOS
**Key variable:** Dry air + no precipitation
**Best conditions:** Very dry (<5 g/m^3), no rain, strong inversions, winter, night/dawn
**Night enhancement:** +360% avg distance vs afternoon (175.4 km vs 38.1 km). At this frequency, nighttime propagation is essentially a different regime. Daytime contacts are limited to ~40 km; nighttime contacts regularly exceed 150 km.
**Dataset:** 104 QSOs, avg 64 km, P90 177 km, max 289 km.
**Unique:** 289 km record (California marine duct). Rain attenuation severe (~1 dB/km at 4 mm/hr).

### 122 GHz (2.5mm) — O2 Line Wing

**Primary mechanisms:** Enhanced LOS, rare ducting
**Key variable:** O2 absorption from 118.75 GHz line (~0.8 dB/km, cannot be improved by weather)
**Best conditions:** Cold temperatures (reduce O2 line broadening), very dry, no rain
**Unique:** 139 km record (California, February). Practically limited to ~50 km reliable paths.

### 134 GHz — Mini Window

**Primary mechanisms:** Enhanced LOS
**Key variable:** Between O2 118 and H2O 183 lines
**Best conditions:** Cold, dry, no precipitation
**Unique:** 157 km record (Germany, March). Better than 122 GHz due to distance from O2 line.

### 241 GHz (1.2mm) — Submillimeter

**Primary mechanisms:** LOS only
**Key variable:** H2O absorption dominates (~0.3 dB/km per g/m^3)
**Best conditions:** Extremely dry (<3 g/m^3), winter-only in most US locations, high altitude stations
**Unique:** 114 km record (Virginia, January). Total path loss at 100 km is ~410 dB without ducting. Realistic to display "viable / not viable" rather than a score.

---

## Part 11: Data Flow & Implementation

```
Surface Observations (ASOS, every 5-20 min)
  -> temp, dewpoint, wind, pressure, sky, visibility, wx_codes
  -> compute: abs_humidity, Td depression
  -> per-band scoring functions
  -> composite score per band
  -> 6-hour prediction timeline

HRRR Model (hourly, per grid point)
  -> refractivity profile, dN/dh gradient, ducts, BL depth, PWAT, surface N
  -> refractivity score component (10% weight — best discriminator)
  -> 4,522 profiles in DB: 79% Enhanced, 15% Super, 5% Standard, 0.7% Ducting
  -> Key thresholds: gradient < -300 = moderate ducting, < -500 = strong ducting
  -> HPBL < 200m = strongest signal for enhanced propagation

Sounding Data (RAOB 00Z/12Z)
  -> 3,901 soundings from 112 stations
  -> Same derived params as HRRR but only twice daily
  -> 54% show ducting — binary flag useless, gradient magnitude is the signal
  -> K-index INVERSELY correlates with ducting (12.7 ducting vs 16.7 non-ducting)
  -> PWAT is NOT a ducting discriminator (identical 28.0 mm both cases)

IEMRE Gridded Data (hourly, 0.125° resolution)
  -> temp, dewpoint, sky_cover_pct, wind (u/v), precip at QSO endpoint locations
  -> More granular than nearest-ASOS matching
  -> 3,675 gridded observations in DB, enriched per-QSO

Terrain Data (SRTM)
  -> path profile, Fresnel clearance, earth bulge
  -> 97.2% of QSO paths are BLOCKED (avg 36.2 dB diffraction loss)
  -> 2.2% CLEAR, 0.6% FRESNEL_PARTIAL
  -> Blocked paths average LONGER distances (215 km) than clear paths (84 km)
  -> Determines LOS vs beyond-LOS regime
  -> diffraction loss calculation

Commercial Link Data (SNMP polling, 5-min intervals)
  -> 7 links at 11/24/68 GHz near DFW
  -> rx_power_0, rx_power_1 (dual-chain MIMO on af11x), tx_power
  -> Signal variation scales with frequency: 68G > 24G > 11G
  -> Correlated with KTKI ASOS surface obs

Link Budget (point-to-point)
  -> FSPL + gaseous + rain + diffraction - duct enhancement
  -> margin = RX power - sensitivity
  -> success % = margin_to_success(margin, prop_score)
  -> Note: 36 dB avg diffraction > 14 dB max duct enhancement
     (gap closed by station EIRP + receiver sensitivity + troposcatter)
```

### Display: Band Conditions Panel

For each band:
- Current score (0-100, colored badge)
- Estimated range (km, from score tier table, qualified by mode)
- Key limiting factor ("High humidity: 16 g/m^3", "Strong inversion detected")
- Trend arrow (improving/stable/degrading from last hour)
- 6-hour prediction timeline with confidence shading

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## Constants Reference

| Constant | Value | Source |
|----------|-------|--------|
| Earth radius | 6371 km | WGS-84 mean |
| Standard K-factor | 4/3 | Standard atmosphere |
| Standard surface N | 315 | ITU-R P.453 |
| Standard dN/dh | -40 /km | ITU-R P.453 |
| Humidity penalty 24 GHz | 1.6 | Near 22.235 GHz H2O peak |
| Humidity penalty 47 GHz | 1.0 | Atmospheric window |
| Humidity penalty 68 GHz | 1.4 | 60 GHz O2 wing + H2O |
| Humidity penalty 241 GHz | 3.0 | Between H2O 183 & 325 |
| Duct M-unit threshold | 2 | Noise filter |
| Inversion min strength | 0.5C | Below is noise |
| Inversion height limit | 5000m AGL | Above irrelevant |
| BL depth shallow threshold | <300m | HRRR: avg gradient -93.7 at BL<200m |
| Ducting gradient threshold | -300 N/km | Sounding avg for ducting events: -389 |
| Non-ducting gradient avg | -123 N/km | Sounding avg for non-ducting events |
| Ducting surface N threshold | 330 | Above this, ducting probability >50% |
| Signal prediction floor | +/- 2-3 dB | Measured from link data |
| CW bandwidth advantage | ~7 dB | 10*log10(2700/500); 24% range increase |

## ITU-R References

- P.453-14: Radio refractivity
- P.525: Free-space path loss
- P.676-13: Gaseous absorption (O2 + H2O)
- P.838-3: Specific rain attenuation
- P.526: Diffraction
- P.452: Interference between stations

## Data References

- ARRL Microwave Contest QSO database: 58,282 total, 57,488 tropospheric with distance (1992-2024)
- IEM ASOS observations: 1,299 stations, 58,398 surface observations
- IEM RAOB soundings: 112 stations, 3,901 soundings
- IEMRE gridded hourly: 3,675 observations at 0.125° resolution
- HRRR model profiles: 4,522 profiles with refractivity, BL depth, PWAT
- Terrain profiles: 58,276 QSO paths (97.2% blocked, avg 36.2 dB diffraction)
- Commercial link data: 7 links at 11/24/68 GHz near DFW, SNMP-polled
- Solar indices: 9,586 daily values (1998-2026) — reserved for future use

## Known Data Quality Issues

- **EME contamination**: 4 QSOs >3,000 km remain in dataset (QRA64D/JT4F modes). Filter on `distance_km < 3000` for tropospheric analysis.
- **Unmodeled bands**: 142, 145, 288, 322, 403, 411 GHz have 1-4 QSOs each but no band_config entries. Too sparse for statistical analysis.
- **Sounding data recency**: Latest soundings are from Sep 2024. Ingestion pipeline may need restart for live enrichment.
- **Surface obs density**: Historical obs are sparse (~1 per 4.7 days per station) because they were fetched per-QSO-window. Live polling is now active for continuous coverage.
- **Weather codes (wx_codes)**: Stored in surface_observations but unused by scoring. Direct fog/thunderstorm/freezing-rain detection could supplement indirect inference from Td depression and sky condition.