add first algo
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algo1.md
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# Comprehensive Propagation Algorithm Documentation
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## Overview
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The ntms-proptools suite consists of three interconnected applications for mm-wave (24/47 GHz) propagation analysis and prediction. All share common physics algorithms calibrated against confirmed radio contacts.
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**Calibration Contacts:**
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- 47 GHz Jun 01 2024 98.8 km (09:00 CDT)
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- 47 GHz Nov 01 2025 116.0 km (07:44 CST)
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- 24 GHz Nov 01 2025 101.0 km (07:54 CST)
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- 24 GHz Sep 07 2002 542.1 km (longest, 07:35 CDT)
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---
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## PART 1: PROP-CAST (Real-Time Station Scoring)
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### Purpose
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Live multi-station propagation scoring across ~500-mile DFW radius using current ASOS observations.
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### Data Inputs
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**Surface Observations (ASOS/NWS):**
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- Temperature (°F → °C conversion: `(tF - 32) * 5/9`)
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- Dew point (°F → °C)
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- Relative humidity (%)
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- Wind speed (knots → m/s: `knots * 1.15078`)
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- Wind direction (degrees)
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- Sea-level pressure (hPa)
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- Altimeter setting (inches Hg → hPa: `inches * 33.8639`)
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- Cloud cover (categorical: CLR, FEW, SCT, BKN, OVC, VV)
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**Frequency Configurations:**
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```javascript
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// 47 GHz Configuration
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47: {
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label: "47 GHz",
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accentHex: "#00ffa3",
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attenPerKm: (rho) => 0.006 * rho + 0.040,
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humPenalty: 1.0,
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seasonAdj: { 6:-0, 7:-0, 8:-0, 5:-0, 9:-0 },
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// Atmospheric window: between 22.235 GHz H₂O peak and 60 GHz O₂ peak
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}
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// 24 GHz Configuration
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24: {
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label: "24 GHz",
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accentHex: "#44ddff",
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attenPerKm: (rho) => 0.0067 * rho + 0.006,
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humPenalty: 1.6,
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seasonAdj: { 6:-8, 7:-10, 8:-10, 5:-4, 9:-4 },
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// Adjacent to 22.235 GHz H₂O absorption line shoulder
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}
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```
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### Physics Calculations
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#### 1. Absolute Humidity Calculation
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```javascript
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function absHumidity(rhPct, tempC) {
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// Magnus formula for saturation vapor pressure
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const es = 6.112 * Math.exp((17.67 * tempC) / (tempC + 243.5));
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// Absolute humidity in g/m³
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return (217 * (rhPct/100) * es) / (tempC + 273.15);
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}
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```
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**Formula:** ρ = 217 * (RH/100) * e_s / T
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- RH: relative humidity (%)
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- e_s: saturation vapor pressure (hPa) via Magnus formula
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- T: absolute temperature (K)
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- Result: ρ in g/m³
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#### 2. Gaseous Absorption by Frequency
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```javascript
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attenPerKm(rho) = O₂_coefficient + H₂O_coefficient * rho
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```
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**47 GHz:** 0.040 + 0.006·ρ dB/km
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- O₂ component: ~0.040 dB/km (from 60 GHz O₂ line wing)
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- H₂O component: ~0.006·ρ dB/km (22.235 GHz H₂O line wing)
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**24 GHz:** 0.006 + 0.0067·ρ dB/km
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- O₂ component: ~0.006 dB/km
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- H₂O component: ~0.0067·ρ dB/km (stronger H₂O sensitivity on 22.235 GHz shoulder)
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### Scoring Functions
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All return 0-100 scale representing propagation favorability.
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#### Score: Humidity
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```javascript
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function scoreHumidity(rho, freq) {
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const r = rho * FREQ_CONFIG[freq].humPenalty;
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if (r <= 6) return 100;
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if (r <= 9) return 95 - ((r-6)/3) * 20;
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if (r <= 13) return 75 - ((r-9)/4) * 30;
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if (r <= 18) return 45 - ((r-13)/5) * 35;
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return Math.max(0, 10 - (r-18)*2);
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}
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```
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**Penalty Factor per Frequency:**
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- 47 GHz: multiplier = 1.0
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- 24 GHz: multiplier = 1.6 (more sensitive due to H₂O line proximity)
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**Thresholds:**
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- r ≤ 6: Score 100 (dry/excellent)
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- r ≤ 9: Linear decay from 95 → 75 (excellent → good)
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- r ≤ 13: Linear decay from 75 → 45 (good → marginal)
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- r ≤ 18: Linear decay from 45 → 10 (marginal → poor)
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- r > 18: Score 0 (very humid/negligible)
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#### Score: Wind Speed
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```javascript
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function scoreWind(mph) {
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if (mph < 2) return 100;
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if (mph < 5) return 90;
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if (mph < 9) return 72;
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if (mph < 14) return 42;
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if (mph < 20) return 16;
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return 0;
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}
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```
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**Rationale:** Wind causes mechanical mixing of boundary layer, destroying temperature inversion. Still air promotes stable inversion.
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#### Score: Sky Cover
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```javascript
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function scoreSky(c) {
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return ({
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CLR: 100, SKC: 100,
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FEW: 88,
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SCT: 60,
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BKN: 25,
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OVC: 5, VV: 5
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})[c] ?? 50;
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}
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```
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**METAR Cloud Cover Legend:**
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- CLR/SKC: Clear (100)
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- FEW (1/8–2/8): 88
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- SCT (3/8–4/8): 60 (scattering)
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- BKN (5/8–7/8): 25 (broken)
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- OVC (8/8): 5 (overcast)
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- VV (vertical visibility): 5
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#### Score: Season (Month-Based)
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```javascript
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function scoreSeason(month, freq) {
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const b = ({
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1:88, 2:84, 3:72, 4:62, 5:55,
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6:42, 7:28, 8:28, 9:52, 10:68,
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11:96, 12:88
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})[month] ?? 50;
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return Math.max(0, Math.min(100, b + FREQ_CONFIG[freq].seasonAdj[month]??0));
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}
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```
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**Base Monthly Scores:**
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- Peak: November (96), December (88), January (88)
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- Summer worst: July/August (28)
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- 24 GHz additional penalties: June (-8), July (-10), August (-10), May (-4), September (-4)
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**Rationale:** Seasonal humidity variation; summer monsoon moisture increases H₂O absorption.
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#### Score: Time of Day (Inversion-Based)
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```javascript
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function scoreTimeOfDay(utcH, utcM, month) {
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const isCDT = month >= 3 && month <= 10;
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const local = (utcH + utcM/60 + (isCDT ? -5 : -6) + 24) % 24;
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const sr = [7.4,7.3,7.0,6.7,6.35,6.25,6.35,6.65,6.9,7.1,7.35,7.45][month-1];
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const d = local - sr; // hours relative to sunrise
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if (d >= -0.5 && d <= 1.5) return {s:100, lbl:"Peak — inversion maximum"};
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if (d > 1.5 && d <= 3.0) return {s:78, lbl:"Good — inversion eroding"};
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if (d > -1.5 && d < -0.5) return {s:82, lbl:"Pre-sunrise — building"};
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if (d > 3.0 && d <= 6.0) return {s:38, lbl:"Marginal — BL mixing"};
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if (local >= 21 || local <= 3) return {s:68,lbl:"Overnight — cooling"};
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if (d > 6.0) return {s:18,lbl:"Afternoon — duct unlikely"};
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return {s:48,lbl:"Early morning"};
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}
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```
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**Window Tiers:**
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1. **Peak Window** (sunrise -30min to +1.5h): Score 100 — Inversion maximum strength
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2. **Good Window** (+1.5h to +3h after sunrise): Score 78 — Inversion still present but eroding
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3. **Pre-Sunrise** (-1.5h to -30 min): Score 82 — Inversion building under clear skies
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4. **Marginal Window** (+3h to +6h after sunrise): Score 38 — Convective boundary layer growth
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5. **Overnight Cooling** (21:00 to 03:00 local): Score 68 — Weak inversion reformation
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6. **Afternoon** (+6h after sunrise): Score 18 — Full convective mixing, inversion destroyed
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**Sunrise Lookup Table (Monthly, local decimal hours):**
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```
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Jan:7.4 Feb:7.3 Mar:7.0 Apr:6.7 May:6.35 Jun:6.25
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Jul:6.35 Aug:6.65 Sep:6.9 Oct:7.1 Nov:7.35 Dec:7.45
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```
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#### Score: Temperature-Dew Point Depression
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```javascript
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function scoreTdDep(tF, tdF) {
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const d = tF - tdF;
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if (d > 22) return 96;
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if (d > 14) return 80;
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if (d > 8) return 60;
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if (d > 4) return 38;
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return 18;
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}
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```
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**Rationale:** Large Td depression indicates dry air above surface, favorable for stable stratification.
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**Thresholds (°F):**
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- >22°F: 96 (very dry aloft)
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- >14°F: 80 (good stability)
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- >8°F: 60 (moderate)
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- >4°F: 38 (marginal)
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- ≤4°F: 18 (humid aloft)
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#### Score: Pressure Tendency
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```javascript
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function scorePressure(mb, prev) {
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if (prev == null) return 58;
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const d = mb - prev;
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if (d > 2.5) return 98; // Rising pressure → anticyclone → stable
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if (d > 0.8) return 82;
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if (d > -0.5) return 60;
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if (d > -2.0) return 32;
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return 10; // Falling pressure → cyclone → unstable
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}
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```
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### Composite Propagation Score
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```javascript
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function composite(f) {
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return Math.round(
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f.humidity * 0.26 +
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f.wind * 0.18 +
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f.sky * 0.15 +
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f.timeOfDay * 0.14 +
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f.tdDep * 0.11 +
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f.season * 0.09 +
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f.pressure * 0.07
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);
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}
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```
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**Weights:**
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| Factor | Weight | Importance |
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|--------|--------|------------|
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| Humidity | 26% | Most critical (absorption) |
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| Wind | 18% | Destroys inversion |
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| Sky | 15% | Less impact than humidity |
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| Time of Day | 14% | Inversion strength varies |
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| Td Depression | 11% | Aloft stability |
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| Season | 9% | Long-term trend |
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| Pressure | 7% | Weak indicator |
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**Total: 100%**
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### Scoring Tiers
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| Score | Band | Label | Hex |
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|-------|------|-------|-----|
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| 80-100 | EXCELLENT | Green/cyan | #00ffa3 |
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| 65-79 | GOOD | Light cyan | #7dffd4 |
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| 50-64 | MARGINAL | Yellow | #ffe566 |
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| 33-49 | POOR | Orange | #ff9044 |
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| 0-32 | NEGLIGIBLE | Red | #ff4f4f |
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---
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## PART 2: PROP-ANALYZER (Historical Contact Analysis)
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### Purpose
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Analyze atmospheric conditions (ASOS + Skew-T sounding) during historical radio contacts to identify propagation mechanisms.
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### Additional Physics Calculations
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#### Refractivity Profile (Modified N-Units)
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```javascript
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// Saturation vapor pressure (Buck equation)
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function satVapPres(tC) {
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return 6.1121 * Math.exp((18.678 - tC/234.5) * (tC/(257.14 + tC)));
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}
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// N-unit profile (ITU-R P.453-14)
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const N = 77.6 * P/T + 3.73e5 * e / (T * T)
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// M-unit profile (accounts for earth curvature)
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const M = N + 0.157 * (hght - sfc_hght)
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```
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**Where:**
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- P: pressure (hPa)
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- T: absolute temperature (K)
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- e: water vapor pressure (hPa) = satVapPres(Td)
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- h: height MSL (m)
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- sfc_hght: surface height MSL (m)
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#### Duct Detection via M-Profile
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**Definition:** A duct exists where dM/dh < 0 (M decreases with height)
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```javascript
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const ducts = [];
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let inDuct = false, ductBase = null, ductBaseM = null;
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for (let i = 1; i < refractProfile.length; i++) {
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const dM = refractProfile[i].M - refractProfile[i-1].M;
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if (dM < 0 && !inDuct) {
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inDuct = true;
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ductBase = refractProfile[i-1].hAGL;
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ductBaseM = refractProfile[i-1].M;
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} else if (dM >= 0 && inDuct) {
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inDuct = false;
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const top = refractProfile[i-1].hAGL;
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const strength = ductBaseM - refractProfile[i-1].M;
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if (strength > 2) { // Filter: only significant ducts
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ducts.push({ base: ductBase, top, strength: strength.toFixed(1) });
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}
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}
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}
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```
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**M-Unit Gradient Interpretation:**
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- dM/dh < -157 /km: Super-refractive (ducting probable)
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- dM/dh < -79 /km: Enhanced refraction (extended range)
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- dM/dh > 0: Sub-refractive (reduced range)
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- dM/dh ≈ -40 /km: Standard atmosphere
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#### Inversion Detection
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```javascript
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const inversions = [];
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for (let i = 1; i < sorted.length; i++) {
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if (sorted[i].tmpc > sorted[i-1].tmpc) { // Temperature increases with height
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inversions.push({
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base: sorted[i-1].hght - sfc.hght,
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top: sorted[i].hght - sfc.hght,
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strength: sorted[i].tmpc - sorted[i-1].tmpc, // °C
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rate: strength / ((top - base) / 100) // °C per 100m
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});
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}
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}
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// Merge adjacent inversions within 200m gap
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// Keep only meaningful: strength >= 0.5°C and base < 5000m
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```
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#### Stability Indices
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**K-Index:**
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```javascript
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const kIndex = (T850 - T500) + Td850 - (T700 - Td700)
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```
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**Lifted Index (Simplified):**
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```javascript
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const li = T500 - (Tsfc - (p500_hght - sfc_hght) * 0.00976)
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```
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- LI < 0: Unstable (convection likely)
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- LI > 0: Stable (inversion maintained)
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**Precipitable Water:**
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```javascript
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PW = Σ [(MR_i + MR_{i-1})/2 * ΔP / (9.81 * 10)]
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// MR = mixing ratio = 622 * e / (P - e)
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```
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#### Boundary Layer Depth
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```javascript
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// Potential temperature
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theta = T + (9.8 * h / 1000)
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// Find height where theta > theta_sfc + 2°C
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```
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---
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## PART 3: LINK BUDGET ANALYZER (Point-to-Point Path Analysis)
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### Purpose
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Complete point-to-point RF link analysis including path clearance, Fresnel zone obstruction, and margin calculations.
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### Path Geometry
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**Maidenhead Grid Decode:** Field (20°×10°) → Square (2°×1°) → Subsquare (5'×2.5') → Extended
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**Distance:** Great-circle haversine
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### Path Clearance Physics
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#### Fresnel Zone Radius
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```javascript
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function fresnelRadius(d1m, d2m, lambdaM) {
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return Math.sqrt(lambdaM * d1m * d2m / (d1m + d2m));
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}
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// λ = 0.3 / f_GHz
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```
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#### Earth Bulge Correction
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```javascript
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function earthBulge(frac, distKm, K = 4/3) {
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const d1 = frac * distKm * 1000;
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const d2 = (1 - frac) * distKm * 1000;
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return (d1 * d2) / (2 * K * 6371000);
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}
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```
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**Effective K-factor from Surface Refractivity:**
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```javascript
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function effectiveKFactor(N_surface) {
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const N_std = 315;
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const dN_std = -40;
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const dN_est = dN_std - (N_surface - N_std) * 0.25;
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const Ke = 1 / (1 + 6371 * dN_est * 1e-6);
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return Math.max(0.5, Math.min(5.0, Ke));
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}
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function surfaceRefractivity(tC, rhPct, mslpHpa) {
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const T = tC + 273.15;
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const P = mslpHpa ?? 1013.25;
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const es = 6.112 * Math.exp(17.67 * tC / (tC + 243.5));
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const e = (rhPct / 100) * es;
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return (77.6 * P / T) + (3.73e5 * e / (T * T));
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}
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```
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#### Knife-Edge Diffraction
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```javascript
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function knifeEdgeLoss(v) {
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if (v <= -0.7787) return 0; // Clear
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if (v <= 0) return -20 * Math.log10(0.5 - 0.62 * v);
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if (v <= 1) return -20 * Math.log10(0.5 * Math.exp(-0.95 * v));
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if (v <= 2.4) {
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const inner = Math.max(0, 0.1184 - (0.38 - 0.1 * v) ** 2);
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return -20 * Math.log10(0.4 - Math.sqrt(inner));
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}
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return 20 * Math.log10(v) + 13.0; // Asymptotic
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}
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```
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**Diffraction Verdicts:**
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- v < -0.7787: CLEAR (0 dB loss)
|
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- -0.7787 < v < 0: FRESNEL_MINOR (< 3 dB)
|
||||
- 0 < v < 2.4: FRESNEL_PARTIAL (3-10 dB)
|
||||
- v > 2.4: BLOCKED (>10 dB)
|
||||
|
||||
### RF Link Budget
|
||||
|
||||
#### Free-Space Path Loss (ITU-R P.525)
|
||||
```javascript
|
||||
function fspl(distKm, fGhz) {
|
||||
return 20 * Math.log10(distKm) + 20 * Math.log10(fGhz) + 92.45;
|
||||
}
|
||||
```
|
||||
|
||||
#### Gaseous Absorption (ITU-R P.676)
|
||||
```javascript
|
||||
function gasLoss(distKm, rhoGm3, freq) {
|
||||
return (cfg.o2dBkm + cfg.h2oCoeff * rhoGm3) * distKm;
|
||||
}
|
||||
```
|
||||
|
||||
| Frequency | O₂ (dB/km) | H₂O Coeff | Notes |
|
||||
|-----------|-----------|-----------|-------|
|
||||
| 47 GHz | 0.040 | 0.006 | Clear window |
|
||||
| 24 GHz | 0.006 | 0.0067 | H₂O shoulder |
|
||||
| 10 GHz | 0.003 | 0.0005 | Clear window |
|
||||
|
||||
#### EIRP
|
||||
```javascript
|
||||
eirp = pDbm + gtxDbi - feedDb
|
||||
```
|
||||
|
||||
#### Receiver Sensitivity
|
||||
```javascript
|
||||
sensitivity = -174 + nfDb + 10 * Math.log10(bw)
|
||||
// CW: bw=500 Hz, SSB: bw=2700 Hz
|
||||
```
|
||||
|
||||
#### Duct Enhancement Estimate
|
||||
```javascript
|
||||
function ductEnhancement(propScore) {
|
||||
if (propScore >= 80) return -14; // 14 dB improvement
|
||||
if (propScore >= 65) return -10;
|
||||
if (propScore >= 50) return -6;
|
||||
if (propScore >= 33) return -2;
|
||||
return 0;
|
||||
}
|
||||
```
|
||||
|
||||
Calibrated against confirmed contacts.
|
||||
|
||||
### Success Probability
|
||||
|
||||
```javascript
|
||||
function marginToSuccess(marginDb, propScore) {
|
||||
// Margin factor (piecewise linear)
|
||||
let marginPct;
|
||||
if (marginDb <= 0) marginPct = 0;
|
||||
else if (marginDb <= 10) marginPct = (marginDb / 10) * 20;
|
||||
else if (marginDb <= 15) marginPct = 20 + ((marginDb - 10) / 5) * 20;
|
||||
else if (marginDb <= 20) marginPct = 40 + ((marginDb - 15) / 5) * 20;
|
||||
else if (marginDb <= 25) marginPct = 60 + ((marginDb - 20) / 5) * 20;
|
||||
else if (marginDb <= 30) marginPct = 80 + ((marginDb - 25) / 5) * 20;
|
||||
else marginPct = 100;
|
||||
|
||||
// Propagation factor (±30% modulation)
|
||||
const propFactor = 0.70 + (propScore / 100) * 0.60;
|
||||
|
||||
return Math.max(0, Math.min(99, Math.round(marginPct * propFactor)));
|
||||
}
|
||||
```
|
||||
|
||||
**Margin → Success Calibration:**
|
||||
- 0 dB → 0%, 10 dB → 20%, 15 dB → 40%, 20 dB → 60%, 25 dB → 80%, 30+ dB → 100%
|
||||
|
||||
**Propagation Modulation:**
|
||||
- Score 100 (excellent): ×1.30
|
||||
- Score 50 (neutral): ×1.00
|
||||
- Score 0 (poor): ×0.70
|
||||
|
||||
---
|
||||
|
||||
## Integration: Data Flow
|
||||
|
||||
```
|
||||
Weather Data (ASOS/NWS)
|
||||
↓
|
||||
[PropCast] → Composite Score 0-100
|
||||
↓
|
||||
├→ Real-time station dashboard
|
||||
└→ Input to LinkBudget (propScore parameter)
|
||||
|
||||
Sounding Data (IEM RAOB)
|
||||
↓
|
||||
[PropAnalyzer] → Refractivity profiles, ducts, inversions
|
||||
↓
|
||||
├→ Skew-T visualization
|
||||
├→ dN/dh gradient analysis
|
||||
└→ Mechanism identification
|
||||
|
||||
Path Geometry + Elevation
|
||||
↓
|
||||
[LinkBudget] → Profile analysis, Fresnel zones, clearance
|
||||
↓
|
||||
├→ Diffraction loss calculation
|
||||
├→ Link margin = RX Power - Sensitivity
|
||||
└→ Success % = marginToSuccess(margin, propScore)
|
||||
```
|
||||
|
||||
---
|
||||
|
||||
## Constants & Thresholds Reference
|
||||
|
||||
| Constant | Value | Source |
|
||||
|----------|-------|--------|
|
||||
| Humidity penalty 47 GHz | 1.0 | Minimal H₂O line sensitivity |
|
||||
| Humidity penalty 24 GHz | 1.6 | Adjacent 22.235 GHz H₂O peak |
|
||||
| Duct M-unit min depth | 2 | Noise filter |
|
||||
| Inversion min strength | 0.5°C | Below is noise |
|
||||
| Inversion height limit | 5000m AGL | Above irrelevant |
|
||||
| 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 |
|
||||
|
||||
## ITU-R References
|
||||
- P.453-14: Radio refractivity
|
||||
- P.525: Free-space path loss
|
||||
- P.676: Gaseous absorption
|
||||
- P.526: Diffraction
|
||||
Loading…
Add table
Reference in a new issue