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Atmospheric Earth operators

20 operators in the atmospheric_earth category of the live registry. Each is a named formula you can compose inside a state contract or call directly through POST /api/zeq/compute. KO42 is always on; add up to three more per call (total ≤ 4), per the 7-step protocol.

OperatorDescriptionEquation
AEO10Ekman pumping vertical velocity induced by wind stress curl at the top of the planetary boundary layer driving large-scale circulations.w_e = \frac{1}{\rho f}\nabla \times \vec{\tau} = \frac{1}{\rho f}\left(\frac{\partial \tau_y}{\partial x} - \frac{\partial \tau_x}{\partial y}\right)
AEO11Radiative transfer equation describing the change in radiation intensity along a path through absorption, emission, and scattering processes.\mu\frac{dI}{d\tau} = I - B(T), \quad \tau = \int \kappa \rho dz
AEO12Cloud microphysics parameterization governing droplet nucleation, growth by condensation and collision-coalescence, and precipitation formation.\frac{dr}{dt} = \frac{G}{r}(S - 1) - \frac{1}{r^2}\frac{dr_c}{dt} + \Gamma_{collision} - \Gamma_{evaporation}
AEO13Climate energy balance model equating incoming solar radiation against reflected shortwave and emitted longwave to determine equilibrium temperature.C\frac{dT}{dt} = (1-\alpha)Q_{solar} - \epsilon \sigma T^4 + \Delta F_{greenhouse} + \Delta F_{aerosol}
AEO14Hurricane potential intensity theory estimating maximum sustained wind speed from sea surface temperature and outflow temperature thermodynamic limits.\frac{\partial v_{max}}{\partial t} = \frac{C_k}{C_d} \frac{T_s - T_o}{T_o} \frac{v_{max}^2}{r_{max}} - C_d \frac{v_{max}^3}{r_{max}} + \beta \frac{\partial T}{\partial z}
AEO16Atmospheric boundary layer height parameterization from surface heat flux, friction velocity, and static stability of the overlying atmosphere.\frac{\partial \vec{v}}{\partial t} = -f\hat{k} \times (\vec{v} - \vec{v}g) + \frac{\partial}{\partial z}\left(K\frac{\partial \vec{v}}{\partial z}\right) + \vec{F}{surface}
AEO17Gravity wave propagation in a stratified atmosphere relating wave frequency, horizontal wavenumber, and buoyancy frequency to vertical structure.\omega^2 = \frac{N^2 k^2 + f^2 m^2}{k^2 + m^2}, \quad c_p = \frac{\omega}{k}
AEO18Monsoon dynamics modeling the seasonal reversal of large-scale circulation driven by differential land-ocean heating and moisture transport.\frac{\partial T}{\partial t} = -\vec{v} \cdot \nabla T + Q_{rad} + Q_{latent} - \alpha(T - T_{eq}) + \beta \nabla \cdot \vec{v}
AEO19Urban heat island intensity estimating the temperature excess of a city over its rural surroundings from surface energy balance modifications.\Delta T_{UHI} = \frac{Q_{anthropogenic}}{\rho c_p u H} + \frac{\Delta R_{net}}{\rho c_p u} - \frac{\Delta E}{\rho c_p u L_v}
AEO2Thermodynamic energy equation for the atmosphere balancing diabatic heating, adiabatic compression, and advective temperature changes.\frac{dT}{dt} = \frac{1}{\rho c_p}\frac{dp}{dt} + \frac{Q_{rad} + Q_{latent} + Q_{sensible}}{c_p} + \frac{\nu}{c_p}\Phi + \frac{K}{c_p}\nabla^2 T
AEO20Gaussian plume dispersion model predicting downwind pollutant concentration from source strength, wind speed, and atmospheric stability class.\frac{\partial C}{\partial t} + \vec{v} \cdot \nabla C = \nabla \cdot (K\nabla C) + S - L - \lambda C
AEO21Lightning discharge model describing the electrical breakdown of air when the electric field exceeds the dielectric strength between charge regions.\frac{dE}{dt} = \frac{J}{\epsilon_0} - \sigma E - \nabla \cdot (\mu n E) + S_{ionization}
AEO22Carbon cycle box model tracking carbon fluxes between atmosphere, ocean, biosphere, and lithosphere reservoirs over various timescales.\frac{dC}{dt} = F_{fossil} + F_{landuse} - F_{ocean} - F_{terrestrial} + \nabla \cdot (D\nabla C)
AEO23Stratospheric ozone chemistry describing catalytic destruction cycles by nitrogen oxides and chlorofluorocarbons depleting the ozone layer.\frac{d[O_3]}{dt} = J_1[O_2] - k_1[O_3][O] + k_2[O][O_2][M] - \sum_i k_{3i}[X_i][O_3]
AEO24Aerosol-cloud interaction parameterization linking aerosol number concentration to cloud droplet size, albedo, and precipitation efficiency.\frac{dN_d}{dN_a} = \frac{k}{2} \left(\frac{N_a}{S}\right)^{-k/2} \left[1 - \tanh^2\left(\frac{\ln(N_a/N_0)}{\sqrt{2}\ln\sigma}\right)\right]
AEO4Geostrophic wind relation balancing the large-scale pressure gradient force against the Coriolis force to determine wind velocity.\vec{v}_g = \frac{1}{f\rho}\hat{k} \times \nabla p, \quad f = 2\Omega \sin\phi
AEO5Thermal wind equation linking the vertical shear of the geostrophic wind to the horizontal temperature gradient through hydrostatic balance.\frac{\partial \vec{v}_g}{\partial z} = -\frac{g}{fT}\hat{k} \times \nabla T + \frac{R}{f}\hat{k} \times \nabla \ln p
AEO6Potential temperature converting in-situ temperature to the value at a reference pressure via Poisson's adiabatic relation.\theta = T\left(\frac{p_0}{p}\right)^{R/c_p}, \quad \frac{d\theta}{dt} = \frac{\theta}{T c_p}(Q_{diabatic})
AEO8Quasi-geostrophic potential vorticity combining relative vorticity, planetary vorticity, and static stability into a conserved diagnostic quantity.q = \nabla^2 \psi + f + \frac{\partial}{\partial z}\left(\frac{f_0^2}{N^2}\frac{\partial \psi}{\partial z}\right), \quad \frac{Dq}{Dt} = 0
AEO9Brunt-Vaisala buoyancy frequency measuring atmospheric static stability from the vertical gradient of potential temperature.N^2 = \frac{g}{\theta}\frac{\partial \theta}{\partial z} = \frac{g}{T}\left(\frac{\partial T}{\partial z} + \Gamma_d\right)

Compute with one of these​

curl -sS -X POST https://zeqsdk.com/api/zeq/compute \
  -H "Authorization: Bearer $ZEQ_KEY" \
  -H "Content-Type: application/json" \
  -d '{"operators":["AEO10"],"inputs":{}}'

The response carries the bare physics value, its unit and uncertainty, the generated master equation, and a signed envelope you can verify on any node.

See also​