Graham McIntire
864a91fc5c
Inversion detection module (Propagation.Inversion): - find_inversion_top/1 walks the native profile to locate the first temperature inversion (surface-based or elevated) - bulk_richardson/3 computes the Richardson number across the inversion layer (Ri < 0.25 = turbulent, > 1 = laminar/good) - shear_magnitude/3 computes the wind shear vector magnitude - potential_temperature/2 for θ = T*(P0/P)^0.286 Theta-e module (Weather.ThetaE): - Bolton (1980) equivalent potential temperature - dewpoint_from_spfh/2 via Magnus-Tetens inversion - theta_e_jump/3 for the thermodynamic decoupling metric mix hrrr_native_derive_fields populates inversion_top_m, bulk_richardson, theta_e_jump_k, and shear_at_top_ms on existing hrrr_native_profiles rows. First real data: 2022-08-20 12Z TX profile shows inversion at 186 m, Ri = 0.16 (turbulent), θ_e jump = 0.33 K — consistent with marginal propagation conditions at that hour.
84 lines
3.2 KiB
Elixir
84 lines
3.2 KiB
Elixir
defmodule Microwaveprop.Weather.ThetaE do
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@moduledoc """
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Equivalent potential temperature (θₑ) computation using the Bolton
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(1980) approximation.
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θₑ combines temperature and moisture into a single conserved variable
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that characterizes how "juicy" an air parcel is. A sharp vertical
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θₑ gradient across the inversion top means strong thermodynamic
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decoupling between the boundary layer and the free atmosphere — which
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the meteorologist identified as a first-class propagation predictor.
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All inputs are SI: T in Kelvin, specific humidity in kg/kg, P in Pa.
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"""
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@doc """
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Compute equivalent potential temperature (K) from temperature,
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specific humidity, and pressure.
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Uses the Bolton (1980) formulation:
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θₑ = θ_dry × exp((Lv × r) / (cp × T_lcl))
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where r is mixing ratio, T_lcl is the lifting condensation level
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temperature, and θ_dry is the dry potential temperature.
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"""
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@spec compute(float, float, float) :: float
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def compute(temp_k, spfh, pressure_pa) do
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# Mixing ratio from specific humidity: r = q / (1 - q)
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r = spfh / (1.0 - spfh)
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# Water vapor pressure (Pa): e = q * P / (0.622 + 0.378 * q)
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e = spfh * pressure_pa / (0.622 + 0.378 * spfh)
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# Dry potential temperature: θ = T * (P0/P_dry)^(Rd/cp)
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# where P_dry = P - e
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p_dry = pressure_pa - e
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theta_dry = temp_k * :math.pow(100_000.0 / p_dry, 0.2854)
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# Bolton (1980) LCL temperature (Eq. 15)
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t_lcl = 2840.0 / (3.5 * :math.log(temp_k) - :math.log(e / 100.0) - 4.805) + 55.0
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# Bolton (1980) θₑ (Eq. 38, simplified)
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lv_cp = 2.5e6 / 1005.7
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theta_dry * :math.exp(lv_cp * r / t_lcl)
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end
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@doc """
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Dewpoint temperature (K) from specific humidity and pressure.
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Computes water vapor pressure from (q, P), then inverts the
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Magnus-Tetens formula to get Td.
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"""
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@spec dewpoint_from_spfh(float, float) :: float
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def dewpoint_from_spfh(spfh, pressure_pa) do
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# e = q * P / (0.622 + 0.378 * q) in Pa
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e = spfh * pressure_pa / (0.622 + 0.378 * spfh)
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e_hpa = e / 100.0
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# Invert Magnus-Tetens: Td(°C) = (243.04 * ln(e/6.1078)) / (17.625 - ln(e/6.1078))
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ln_ratio = :math.log(e_hpa / 6.1078)
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td_c = 243.04 * ln_ratio / (17.625 - ln_ratio)
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td_c + 273.15
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end
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@doc """
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θₑ jump (K) between two levels in a profile.
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Returns θₑ(top) − θₑ(base). A large positive value means the
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inversion top is much warmer+drier (thermodynamically decoupled)
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than the air below — which is what the meteorologist says we need.
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"""
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@spec theta_e_jump(map, non_neg_integer, non_neg_integer) :: float | nil
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def theta_e_jump(profile, base_idx, top_idx) do
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with t_base when is_float(t_base) <- Enum.at(profile.temp_k, base_idx),
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t_top when is_float(t_top) <- Enum.at(profile.temp_k, top_idx),
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q_base when is_float(q_base) <- Enum.at(profile.spfh, base_idx),
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q_top when is_float(q_top) <- Enum.at(profile.spfh, top_idx),
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p_base when is_float(p_base) <- Enum.at(profile.pressure_pa, base_idx),
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p_top when is_float(p_top) <- Enum.at(profile.pressure_pa, top_idx) do
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compute(t_top, q_top, p_top) - compute(t_base, q_base, p_base)
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else
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_ -> nil
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end
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end
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end
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