FireSpreadDirection
Calculate fire behavior in direction of maximum spread
Description
Calculate fire behavior in direction of maximum spread
Reference
source_ref: WildlandFire.jl/fire_spread_direction.jl Calculate fire behavior in direction of maximum spread
Parameters
| Name | Units | Default | Description |
|---|---|---|---|
B_coeff | Wind coefficient B (dimensionless) | ||
ω | Wind direction relative to upslope | ||
C_coeff | Wind coefficient C (dimensionless) | ||
one | 1 | Dimensionless one for unit balancing | |
U_ref | 0.00508 | Reference wind speed (1 ft/min in m/s) | |
φs | Slope factor (dimensionless) | ||
R0 | No-wind no-slope rate of spread | ||
E_coeff | Wind coefficient E (dimensionless) | ||
c_Z | 0.559235 | Length-to-width ratio coefficient (SI) | |
β_ratio | Relative packing ratio β/β_op (dimensionless) | ||
φw | Wind factor (dimensionless) |
Observed
| Name | Units | Default | Description |
|---|---|---|---|
Z | Fire length-to-width ratio (dimensionless) | ||
φ_combined | Combined wind+slope factor magnitude (dimensionless) | ||
α | Direction of maximum spread relative to upslope | ||
U_E | Effective wind speed in direction of maximum spread | ||
φ_E | Effective wind factor in direction of maximum spread (dimensionless) | ||
R_H | Rate of spread in direction of maximum spread (head fire) |
Observed expressions
$$ Z = one + U_{E} \cdot c_{Z} $$Fire length-to-width ratio (dimensionless)
$$ φ_{combined} = \sqrt{\left(\cos\left(ω\right) \cdot φw + φs\right)^{2} + \sin\left(ω\right)^{2} \cdot φw^{2}} $$Combined wind+slope factor magnitude (dimensionless)
$$ α = \mathrm{atan2}\left(\sin\left(ω\right) \cdot φw, \cos\left(ω\right) \cdot φw + φs\right) $$Direction of maximum spread relative to upslope
$$ U_{E} = U_{ref} \cdot \frac{β_{ratio}^{E_{coeff}} \cdot φ_{E}}{C_{coeff}}^{\frac{one}{B_{coeff}}} $$Effective wind speed in direction of maximum spread
$$ φ_{E} = φ_{combined} $$Effective wind factor in direction of maximum spread (dimensionless)
$$ R_{H} = R0 \cdot \left(one + φ_{combined}\right) $$Rate of spread in direction of maximum spread (head fire)
Raw .esm
Raw .esm JSON (this component)
{
"variables": {
"Z": {
"type": "unknown",
"description": "Fire length-to-width ratio (dimensionless)"
},
"B_coeff": {
"type": "parameter",
"description": "Wind coefficient B (dimensionless)"
},
"ω": {
"type": "parameter",
"description": "Wind direction relative to upslope"
},
"C_coeff": {
"type": "parameter",
"description": "Wind coefficient C (dimensionless)"
},
"φ_combined": {
"type": "unknown",
"description": "Combined wind+slope factor magnitude (dimensionless)"
},
"one": {
"default": 1,
"type": "parameter",
"description": "Dimensionless one for unit balancing"
},
"U_ref": {
"default": 0.00508,
"type": "parameter",
"description": "Reference wind speed (1 ft/min in m/s)"
},
"α": {
"type": "unknown",
"description": "Direction of maximum spread relative to upslope"
},
"φs": {
"type": "parameter",
"description": "Slope factor (dimensionless)"
},
"R0": {
"type": "parameter",
"description": "No-wind no-slope rate of spread"
},
"E_coeff": {
"type": "parameter",
"description": "Wind coefficient E (dimensionless)"
},
"U_E": {
"type": "unknown",
"description": "Effective wind speed in direction of maximum spread"
},
"c_Z": {
"default": 0.559235,
"type": "parameter",
"description": "Length-to-width ratio coefficient (SI)"
},
"φ_E": {
"type": "unknown",
"description": "Effective wind factor in direction of maximum spread (dimensionless)"
},
"R_H": {
"type": "unknown",
"description": "Rate of spread in direction of maximum spread (head fire)"
},
"β_ratio": {
"type": "parameter",
"description": "Relative packing ratio β/β_op (dimensionless)"
},
"φw": {
"type": "parameter",
"description": "Wind factor (dimensionless)"
}
},
"reference": {
"notes": "source_ref: WildlandFire.jl/fire_spread_direction.jl\nCalculate fire behavior in direction of maximum spread"
},
"equations": [
{
"rhs": {
"args": [
{
"args": [
{
"args": [
{
"args": [
{
"args": [
{
"args": [
"ω"
],
"op": "cos"
},
"φw"
],
"op": "*"
},
"φs"
],
"op": "+"
},
2
],
"op": "^"
},
{
"args": [
{
"args": [
{
"args": [
"ω"
],
"op": "sin"
},
2
],
"op": "^"
},
{
"args": [
"φw",
2
],
"op": "^"
}
],
"op": "*"
}
],
"op": "+"
}
],
"op": "sqrt"
},
"lhs": "φ_combined"
},
{
"rhs": {
"args": [
"R0",
{
"args": [
"one",
"φ_combined"
],
"op": "+"
}
],
"op": "*"
},
"lhs": "R_H"
},
{
"rhs": {
"args": [
{
"args": [
{
"args": [
"ω"
],
"op": "sin"
},
"φw"
],
"op": "*"
},
{
"args": [
{
"args": [
{
"args": [
"ω"
],
"op": "cos"
},
"φw"
],
"op": "*"
},
"φs"
],
"op": "+"
}
],
"op": "atan2"
},
"lhs": "α"
},
{
"rhs": "φ_combined",
"lhs": "φ_E"
},
{
"rhs": {
"args": [
"U_ref",
{
"args": [
{
"args": [
{
"args": [
{
"args": [
"β_ratio",
"E_coeff"
],
"op": "^"
},
"φ_E"
],
"op": "*"
},
"C_coeff"
],
"op": "/"
},
{
"args": [
"one",
"B_coeff"
],
"op": "/"
}
],
"op": "^"
}
],
"op": "*"
},
"lhs": "U_E"
},
{
"rhs": {
"args": [
"one",
{
"args": [
"U_E",
"c_Z"
],
"op": "*"
}
],
"op": "+"
},
"lhs": "Z"
}
],
"tests": [],
"analyses": []
}