🌳 C14-Radiokarbon-Kalibration

📐 Mathematische Formulierung

Zwei-Phasen Recovery-Funktion F₀(t'):

Phase 1 (0 ≤ t' < t_switch):
  F₀(t') = F₀_start + (F₀_mid - F₀_start) × (1 - e^(-t'/τ₁))

Phase 2 (t' ≥ t_switch):
  F₀(t') = F₀_mid + (F₀_post - F₀_mid) × (1 - e^(-(t'-t_switch)/τ₂))

Wobei:
  t' = Jahre seit Flut (t' = Jahr - FLUT_YEAR)
  τ₁ = Zeitkonstante Phase 1 (schnell, ~220 a)
  τ₂ = Zeitkonstante Phase 2 (langsam, ~1500 a)
  t_switch = Umschaltpunkt (~150 Jahre nach Flut)
  F₀_start = pMC bei Flut (~1.55%)
  F₀_mid = pMC bei t_switch (~55%)
  F₀_post = Equilibrium (~100%)

Physikalische Interpretation:
  Phase 1: Atmosphäre füllt sich schnell (kleine Box)
  Phase 2: Ozean/Biosphäre equilibriert langsam (große Box)
      

🔬 The Two-Phase Recovery Model (v6.0)

Why two phases?

The model describes the ¹⁴C recovery following a global collapse of the carbon cycle. Recovery proceeds in two characteristic phases:

AF = years after the Flood.

Physical interpretation:

• Phase 1: the atmosphere and fast reservoirs (surface ocean, foliage) refill first
• Phase 2: slow reservoirs (deep ocean, forests, soils) reach equilibrium
• Fossil carbon: the release of "dead" carbon during/after the Flood slows equilibration

📊 For context: Standard box models for small perturbations around a stable equilibrium (bomb pulse, Miyake events) yield shorter τ values (τ₁≈35 yr, τ₂≈350 yr). The longer effective time constants in the post-Flood scenario are physically consistent, because here collapsed reservoirs are rebuilt, not merely mixed.

🎲 Bayesian Multi-Sample Analysis

What does the Bayesian analysis do?

• Combines multiple samples in a statistically sound way
• Accounts for stratigraphic constraints (A is older than B)
• Computes precise confidence intervals (HPD: Highest Posterior Density)
• Uses MCMC (Markov Chain Monte Carlo), like OxCal

Parameters:

📈 Timeline Visualization

Shows:

• 🔴 Red points: biblical events (Flood, Exodus, David, Jerusalem…)
• 🔵 Blue points: IntCal20 dendrochronology (actual tree-ring measurements)
• 🟢 Green points: astronomical fixpoints (solar eclipses, Ptolemaic Canon)
• 🟣 Purple points: bomb pulse (1950–2025, nuclear tests)

⚓ Chronological Anchors

What are anchors? Fixpoints with a known calendar year AND a pMC value, used for calibration.

Sources:

• Biblical chronology: 1 Kings 6:1 framework (Flood 2518 BC; genealogical / Ussher-type, cf. Answers in Genesis)
• Dendrochronology: IntCal20 (Reimer et al. 2020)
• Astronomy: Assur solar eclipse (763 BC), Ptolemaic Canon
• Bomb pulse: atmospheric ¹⁴C measurements (1950–2025)

JSON format: anchors are loaded from anchors.json in the same directory.

🎯 Phase Classification

🔧 Calibration Methodology

Algorithm:

1. Find bracketing anchors: locate two anchors with t₁ ≤ t_target ≤ t₂
2. Linear interpolation: t = t₁ + (pmc − pmc₁) × (t₂ − t₁) / (pmc₂ − pmc₁)
3. Two-phase correction: apply the recovery model for physically consistent values
4. Confidence rating:
   • Exact: Δpmc < 0.05% (effectively on an anchor)
   • Near: Δpmc < 0.3% (very close to an anchor)
   • Interpolation: normal (between anchors)
   • Extrapolation: outside the anchor range (warning!)

❓ FAQ

Q: Why do my results differ from conventional dates?

A: This tool uses the Young-Earth chronology (Flood at 2518 BC; a ~6,500-year framework derived from 1 Kings 6:1 and the Genesis genealogies). Conventional tools assume timescales of millions of years.

Q: What is the difference between pMC and BP?

A: pMC (percent Modern Carbon) = the ¹⁴C fraction relative to 1950 CE. BP (Before Present) = conventional age in years before 1950. Formula: BP = −8033 × ln(pMC/100)

Q: What do τ₁ and τ₂ mean?

A: They are the time constants of the two-phase recovery model:

• τ₁ (200 yr): the initial fast recovery, as the atmosphere and near-surface reservoirs (surface ocean, fast biosphere) refill.
• τ₂ (1200 yr): the slow deep-ocean mixing and biosphere regeneration (forests, soils).

Note: these effective time constants are longer than the values for small perturbations around a stable equilibrium (bomb pulse: τ₁≈35 yr, τ₂≈350 yr). This is physically consistent: the post-Flood recovery describes the rebuilding of collapsed reservoirs, not merely their mixing. The release of fossil carbon further slows ¹⁴C equilibration.

Q: How do I load my own anchors?

A: Create an anchors.json file in the same directory as the tool. See the Anchors tab for the format.