# Algorithm Updates — April 2026 (Full Dataset Analysis)

Analysis of 58,367 contacts matched against 41M HRRR profiles in the local database. This extends the earlier Part 2b correlation analysis with binned distance analysis across all atmospheric variables.

## Finding 1: Shallow Boundary Layer Bonus Not Supported

The algorithm previously awarded a score of 82 when HPBL < 300m (shallow BL), on the theory that shallow BL indicates a surface inversion trapping refractivity. The full dataset contradicts this:

| BL Depth | n | Avg Distance (km) | Median | Avg Refrac Gradient |
|----------|---|-------------------|--------|---------------------|
| 1000-2000m | 6,021 | **222.1** | 210.0 | -98.7 |
| 500-1000m | 10,834 | 214.2 | 188.4 | -103.2 |
| < 200m (shallow) | 7,020 | 209.6 | 178.8 | -114.0 |
| 200-500m | 10,018 | 204.1 | 178.7 | -112.3 |
| 2000m+ (deep) | 803 | 196.2 | 167.1 | -101.3 |

Medium-depth BL (1000-2000m) produces the longest average contacts, not shallow. Shallow BL does correlate with stronger refractivity gradients (-114 N/km avg), but this doesn't translate to longer contacts — likely because shallow BL often means fog/low stratus that attenuates the signal.

**Code change:** Removed the `@shallow_bl_threshold_m 300` / `@shallow_bl_score 82` refractivity fallback. Refractivity scoring now falls through to the default score when gradient is weak, regardless of BL depth.

## Finding 2: Td Depression at 24 GHz — Moist Range is Worst

At 24 GHz, the moist range (2-5C Td depression) produces the shortest contacts, while both dry and near-saturated conditions are better:

| Td Depression | n | Avg Distance (km) | Median | P90 |
|--------------|---|-------------------|--------|-----|
| 15+ (very dry) | 311 | **109.1** | 110.6 | 193.5 |
| 0-2 (saturated) | 447 | 104.9 | 108.2 | 178.2 |
| 10-15 (dry) | 278 | 99.5 | 97.8 | 179.7 |
| 5-10 (moderate) | 841 | 94.9 | 87.1 | 177.2 |
| 2-5 (moist) | 727 | **72.1** | 57.7 | 146.7 |

Near-saturation (0-2C) likely produces ducting that overcomes the absorption penalty, while the 2-5C range gives enough moisture for absorption without the refractivity benefit. Very dry conditions minimize absorption entirely.

**No code change** — the current harmful-band Td scoring already penalizes low depression. The existing curve is directionally correct; the moist-range penalty emerges naturally from the humidity and PWAT factors working together.

## Finding 3: PWAT Sweet Spot Confirmed at 20-30mm

The PWAT scoring curve already peaks at 20-30mm for beneficial bands:

| PWAT Bin | n | Avg Distance (km) | Median |
|---------|---|-------------------|--------|
| 20-30mm | 13,376 | **219.7** | 211.5 |
| < 10mm | 463 | 211.8 | 195.5 |
| 10-20mm | 8,500 | 208.3 | 183.5 |
| 40-50mm | 3,118 | 207.7 | 177.3 |
| 30-40mm | 8,947 | 203.5 | 171.8 |
| 50mm+ | 292 | 190.5 | 173.7 |

The existing code's PWAT beneficial curve (`<10→55, <20→75, <30→90, <40→70, else→50`) is well-calibrated. No change needed.

## Finding 4: Pressure Relationship Has Fine Structure

Finer pressure binning reveals a clear monotonic relationship for the bulk of the data:

| Pressure Bin | n | Avg Distance (km) | Median |
|-------------|---|-------------------|--------|
| < 970 mb | 6,010 | **242.7** | 232.9 |
| 970-980 | 5,254 | 229.8 | 225.5 |
| 980-990 | 7,234 | 207.3 | 184.2 |
| 990-1000 | 9,336 | 184.1 | 160.4 |
| 1000-1010 | 3,505 | 200.7 | 161.0 |
| 1010+ | 3,357 | 221.3 | 191.1 |

The <970 to 990-1000 range shows a clean 30% gradient. The uptick at 1010+ likely reflects high-altitude western US stations with inherently longer radio horizons, not a genuine pressure effect.

**Code change:** Refined pressure scoring bins to add a <980 tier (score 88) and increase the <1005 score from 80 to 85, better reflecting the strong low-pressure signal.

## Finding 5: Mode Distance Advantage Quantified

| Mode | n | Avg Distance (km) | Median | Max |
|------|---|-------------------|--------|-----|
| CW | 18,001 | **247.2** | 227.4 | 1,606 |
| PH (SSB) | 35,089 | 190.9 | 176.2 | 999.2 |
| FM | 180 | 141.2 | 116.5 | 664.1 |

CW achieves 29% longer average distance than SSB at 10 GHz, consistent with the ~7 dB bandwidth advantage (24% theoretical range increase). FM is 26% shorter than SSB. These ratios are useful for range estimate calibration.

## Finding 6: Refractivity Gradient is Flat Within the Bulk Distribution

| Gradient Bin | n | Avg Distance (km) | Median | Ducting % |
|-------------|---|-------------------|--------|-----------|
| < -200 (strong) | 659 | 202.2 | 189.0 | 100% |
| -200 to -150 | 2,804 | 205.0 | 179.9 | 52.8% |
| -150 to -100 | 14,113 | 211.8 | 186.6 | 0% |
| -100 to -75 | 12,138 | **215.8** | 192.3 | 0% |
| -75 to -55 | 4,390 | 207.5 | 180.0 | 0% |
| >= -55 (weak) | 592 | 176.3 | 151.9 | 0% |

The -150 to -75 range (the bulk of HRRR gradients) shows remarkably flat distance distributions. Only the weakest gradients (>= -55) show meaningfully shorter contacts. The current 8% weight is appropriate given this weak discriminatory power.

## Finding 7: Dataset is 99.5% Aug-Sep

| Month | Contacts (tropo) | Avg Distance |
|-------|-----------------|--------------|
| Aug | 29,725 | 202.4 |
| Sep | 28,468 | 198.7 |
| All other months | 174 | varies |

All atmospheric correlations in this analysis are effectively summer-only findings. Seasonal scoring curves cannot be validated from this dataset. The physics-based seasonal tables remain the best available approach for non-summer months.

## Finding 8: Commercial Link Diurnal Patterns (12,068 samples, 7 links)

Data from March 30 - April 7, 2026. All links in Princeton TX area, LOS paths.

### 68 GHz (af60, 2.82 km) — Strongest diurnal signal

| UTC Hour | Avg RX (dBm) | Std Dev | Notes |
|----------|-------------|---------|-------|
| 09-10 | **-50.7** | 0.80 | Morning best |
| 00-08 | -51.2 to -52.2 | 0.6-1.2 | Night — gradual improvement |
| 11-12 | -52.1 to -52.3 | 4-5 | Weather events (high std) |
| 13-14 | **-54.3 to -54.6** | 5-6 | Afternoon worst |
| 15-23 | -52.8 to -53.4 | 0.8-3.7 | Evening recovery |

**3.9 dB diurnal swing.** Afternoon degradation at 68 GHz is dominated by gaseous absorption increase with daytime heating and humidity rise, plus convective scintillation. The high stddev at 11-15 UTC indicates individual weather events (rain, convection) can cause 10+ dB excursions.

### 11 GHz (core-new-hope, 5.66 km) — Inverted pattern

| UTC Hour | Avg RX (dBm) | Std Dev | Notes |
|----------|-------------|---------|-------|
| 08-12 | **-49.7 to -49.8** | 2.1-2.5 | Morning best, but variable |
| 01-07 | -49.8 to -50.1 | 1.7-2.0 | Night — slightly better mean, multipath |
| 14-21 | -50.8 to -51.4 | 1.2-1.5 | Afternoon/evening — worse mean, less variable |

**1.7 dB diurnal swing.** At 11 GHz, gaseous absorption is negligible. The diurnal pattern is driven by **multipath fading** from nocturnal inversions (higher stddev at night: 2.0-2.5 vs afternoon: 1.2-1.4). Mean signal is slightly better at night despite the multipath, because the refractivity enhancement aids the direct path.

### 24 GHz (climax-to-core, 4.36 km) — Remarkably stable

**Only 0.9 dB diurnal swing** (-63.4 to -64.3). The 22.235 GHz H₂O line creates a constant absorption floor that varies minimally with diurnal moisture changes on short paths. One anomaly at 12 UTC (stddev 2.51) is likely a single rain event.

### Key insight: Diurnal sensitivity by frequency on LOS paths
- 11 GHz: 1.7 dB (multipath-dominated)
- 24 GHz: 0.9 dB (absorption floor, stable)
- 68 GHz: 3.9 dB (gaseous absorption-dominated)

This is **non-monotonic** — 24 GHz is more stable than 11 GHz. The H₂O absorption at 24 GHz is a constant penalty that doesn't fluctuate much diurnally, while 11 GHz refractivity effects create multipath that varies with inversion development.

## Finding 9: RAOB Soundings Resolve Ducting HRRR Cannot (10,935 soundings)

### RAOB vs HRRR gradient distributions

| Statistic | RAOB | HRRR (at contacts) |
|-----------|------|-------------------|
| Average | -265.4 N/km | -107.2 N/km |
| P10 | -521.7 | ~-200 |
| P50 (median) | -199.5 | ~-75 |
| P90 | -83.3 | ~-50 |
| Min | -1969.9 | — |

RAOB gradients are **2.5x stronger** than HRRR because soundings at ~10m vertical resolution capture thin surface ducts (50-100m) that HRRR's 25 hPa pressure level spacing (~250m) cannot resolve.

### Sharp ducting threshold at -200 to -300 N/km

| Gradient Bin | n | Ducting % | Avg PWAT (mm) |
|-------------|---|-----------|---------------|
| < -500 | 622 | **100%** | 26.6 |
| -500 to -300 | 967 | **99.9%** | 26.9 |
| -300 to -200 | 1,168 | **91.2%** | 29.9 |
| -200 to -150 | 879 | 31.2% | 28.5 |
| -150 to -100 | 1,061 | 1.8% | 28.7 |
| -100 to -50 | 683 | 2.2% | 27.0 |
| >= -50 | 159 | 1.9% | 20.0 |

The transition from "always ducting" to "rarely ducting" occurs between -200 and -300 N/km. This is consistent with the theoretical ducting threshold of -157 N/km (where k goes negative), with the additional gradient needed to sustain a duct layer of practical depth.

### Seasonal ducting rates from RAOB

| Month | Total | Ducting % | Avg Gradient | Avg PWAT (mm) |
|-------|-------|-----------|-------------|---------------|
| Jun | 232 | **70.3%** | -339.9 | 28.5 |
| Jul | 247 | **71.3%** | -308.0 | 28.1 |
| Oct | 99 | **65.7%** | **-350.0** | 18.9 |
| Sep | 2,073 | 56.0% | -282.3 | 26.3 |
| Aug | 2,281 | 53.7% | -258.2 | 34.0 |
| Nov | 99 | 49.5% | -248.9 | 10.8 |
| May | 128 | 41.4% | -227.4 | 20.4 |
| Apr | 86 | 32.6% | -155.1 | 13.7 |
| Feb | 84 | 20.2% | -135.4 | 6.8 |
| Jan | 61 | 14.8% | -126.3 | 8.9 |
| Mar | 54 | 14.8% | -140.9 | 10.5 |
| Dec | 100 | 12.0% | -138.7 | 8.0 |

**October is the most underrated month.** It has the strongest average gradients of any month (-350 N/km), 65.7% ducting rate (3rd highest), but was scored only 82/100 in the 10 GHz seasonal table.

**February was scored below January despite higher ducting.** Feb: 20.2% ducting, was scored 32. Jan: 14.8% ducting, scored 38.

**Code changes:**
- 10 GHz February seasonal score: 32 → 40 (now exceeds January, matching its higher ducting rate)
- 10 GHz October seasonal score: 82 → 88 (3rd highest ducting, strongest gradients)

## Updated Dataset Statistics

- **Contacts:** 58,367 total, 58,367 tropo (<3000 km)
- **HRRR profiles:** 41,071,398 (37,925 matched to contacts, 65% coverage)
- **Terrain profiles:** 58,361 (56,735 BLOCKED 97.1%, 1,284 CLEAR 2.2%, 342 FRESNEL_PARTIAL 0.6%)
- **Soundings:** 10,935 (5,539 with gradient data, 2,964 with ducting detected)
- **Commercial samples:** 12,068 (7 links, March 30 - April 7, 2026)
- **IEMRE observations:** 15,092
- **Weather stations:** 3,268
