Decompression Model

The mathematical machinery DecoJS uses to track inert gas loading across 16 theoretical tissue compartments and compute ascent limits from them. These pages are the developer-facing counterpart to pressure.html, tissue-loading.html, m-values.html, and gradient-factors.html — they assume the reader already knows what inert-gas loading is and want to see the algorithm as it is coded.

For algorithm-level orchestration (how these equations drive a simulated ascent, deco-stop search, NDL computation), see Algorithms. For the JavaScript module/function index, see Architecture.

Notation

Used consistently across all Model pages.

Symbol	Meaning	Units
$P_{amb}$	Ambient (absolute) pressure	bar
$P_{alv}$	Alveolar inert-gas partial pressure	bar
$P_t$	Tissue inert-gas pressure	bar
$P_{t,0}$	Initial tissue inert-gas pressure (segment start)	bar
$P_{alv,0}$	Initial alveolar inert-gas pressure (segment start)	bar
$T_{1/2}$	Compartment half-time	min
$k$	Rate constant, $k = \ln(2) / T_{1/2}$	min⁻¹
$R$	Rate of change of alveolar pressure ($dP_{alv}/dt$)	bar/min
$a, b$	Bühlmann M-value coefficients (per compartment, per variant)	$a$: bar; $b$: dimensionless
$M$	M-value, maximum tolerable $P_t$ at a given $P_{amb}$	bar
$GF$	Gradient factor, fraction of supersaturation budget used	0–1 internally

GF storage convention: DecoJS UI code (js/diveSetup.js) stores GF as percent (DEFAULT_GF_LOW = 100, DEFAULT_GF_HIGH = 100); algorithmic code in js/decoModel.js uses fractions (DEFAULT_GF_LOW = 1.0, DEFAULT_GF_HIGH = 1.0). Conversion happens at the boundary.

All depths are in meters, all times in minutes.

Unit constants

Defined at the top of js/decoModel.js:

// js/deco/constants.js:12-24
export const SURFACE_PRESSURE = 1.01325;       // 1 atm exactly, in bar
export const WATER_VAPOR_PRESSURE = 0.0627;    // alveolar H2O correction at 37°C, in bar
export const N2_FRACTION = 0.7902;             // N2 + Ar lumped, per ZH-L convention
export const PRESSURE_PER_METER = 0.1;         // EN 13319 convention, bar/m

N2_FRACTION = 0.7902 (not 0.79) is the standard Bühlmann convention — argon (~0.93%) is lumped into the nitrogen compartment because it has similar kinetics. PRESSURE_PER_METER = 0.1 is the default EN 13319 indicated-depth convention. getPressurePerMeter(environment) also supports freshwater (1000 kg/m³, 0.0980665 bar/m) and seawater (1025 kg/m³, 0.1005181625 bar/m). Profiles without environment.waterType remain on the EN default for backward compatibility.

SURFACE_PRESSURE remains the backward-compatible sea-level default. Altitude-aware calculations call getPressureAtAltitude(altitude) and pass the resulting absolute surface pressure through ambient-pressure conversion, initial tissue saturation, NDL, ceilings, the GF ramp, gas consumption, and the decompression scheduler. The standard atmosphere is used to convert altitude to pressure; the sandbox currently assumes the diver is fully acclimatized to the selected altitude.

Atmospheric pressure at altitude

The familiar exponential barometric equation

$$ p_{\mathrm{atm}}(h) = p_0 e^{-h/H} $$

is an isothermal approximation: it assumes a constant atmospheric temperature and a fixed scale height $H$ (approximately 8.4 km). It is useful for explaining why pressure decreases approximately exponentially with altitude, but it is not the exact equation used by DecoJS.

getPressureAtAltitude(h) uses the standard-atmosphere troposphere model, which accounts for the standard temperature lapse rate:

$$ p_{\mathrm{atm}}(h)

p_0 \left(1 - 2.25577 \times 10^{-5} h\right)^{5.25588}, \qquad p_0 = 1.01325\ \mathrm{bar}. $$

Here $h$ is altitude in metres and $p_{\mathrm{atm}}$ is the absolute atmospheric pressure at the dive site's water surface. For example, at 2,000 m the model gives approximately 0.795 bar; the exponential approximation gives approximately 0.799 bar.

The absolute ambient pressure at depth $d$ is then

$$ p_{\mathrm{amb}}(h,d)

p_{\mathrm{atm}}(h) + \frac{\rho g d}{10^5}. $$

The EN mode substitutes exactly 0.1 bar/m; the density-based modes use $\rho = 1000$ kg/m³ or 1025 kg/m³ and standard gravity. Thus, in EN mode at an altitude of 2,000 m and a depth of 7.5 m, DecoJS uses $p_{\mathrm{amb}} \approx 0.795 + 0.750 = 1.545\ \mathrm{bar}$. This local surface pressure is threaded through initial tissue saturation, inspired-gas pressure, NDL, ceilings, the GF ramp, MOD adjustment, and decompression scheduling.

Chapter TOC

1. Model-01-Compartments — the 16 ZH-L16 compartments, their half-times, the a/b coefficients, and the A/B/C variants.
2. Model-02-Haldane-Equation — constant-depth tissue loading.
3. Model-03-Schreiner-Equation — linear-rate-of-pressure-change tissue loading (the workhorse during descent and ascent).
4. Model-04-M-Values — Bühlmann M-value lines, ceiling equation, instantaneous GF.
5. Model-05-Gradient-Factors — Baker GFs, pAnchor, and the GF ramp.

Cross-cutting: Algorithms drives these equations across a full dive; References lists primary sources.