KMA Grade 9 Meteorologist cheat sheet

Hydrostatic balance: dp/dz = -ρg; the hypsometric equation z2 - z1 = (R·T̄/g)·ln(p1/p2) gives thickness from mean virtual temperature.

Geostrophic wind: Vg = (1/(ρf))·k × ∇p; in pressure coordinates ug = -(1/(ρf))·∂p/∂y and vg = (1/(ρf))·∂p/∂x.

Coriolis parameter f = 2Ω·sin φ; zero at the equator, about 1.46×10⁻⁴ s⁻¹ at 30° and 2.29×10⁻⁴ s⁻¹ at 45° latitude.

Natural Rossby radius of deformation LR = NH/f (or √(gH)/f for shallow water); it sets the scale separating balanced flow from gravity-wave response.

Potential vorticity (Ertel): PV = (1/ρ)·ζa·∇θ; conserved for adiabatic, frictionless flow, so PV anomalies track troughs and ridges on isentropic surfaces.

Quasi-geostrophic omega equation: ascent is forced by positive differential vorticity advection and warm-air advection; descent by the reverse.

Thermal wind: ∂Vg/∂ln p = -(R/f)·k × ∇T; wind veers with height when temperature falls toward the cold side (warm advection).

Continuity in pressure coordinates: ∇·V + ∂ω/∂p = 0; near-surface convergence implies upward motion ω < 0 above.

Gradient wind adds centrifugal term: Vgr²/R + f·Vgr = (1/ρ)·∂p/∂n; subgeostrophic around a low, supergeostrophic around a high.

First law: dq = cp·dT - α·dp; dry adiabatic lapse rate Γd = g/cp ≈ 9.8 K/km; saturated rate Γs is smaller and approaches Γd aloft.

Potential temperature θ = T·(p0/p)^(Rd/cp) with p0 = 1000 hPa and Rd/cp ≈ 0.286; θ is conserved in dry adiabatic processes.

Equivalent potential temperature θe = θ·exp(Lv·rs/(cp·T)); conserved in moist adiabatic ascent and used to trace air masses.

Clausius-Clapeyron: es increases about 6-7% per K; saturation vapor pressure over water exceeds that over ice below 0 °C.

Relative humidity RH = e/es × 100%; dew point Td is the temperature at which e equals es, so T - Td approximates the LCL spread (~125 m per °C).

Lifting condensation level: zLCL ≈ 125·(T - Td) m; the wet-bulb temperature lies between T and Td.

CAPE = ∫(Tv_parcel - Tv_env)·g·dln p from LFC to EL; CIN is the negative area below the LFC that must be overcome.

Skew-T log-p reading: dry adiabats, moist adiabats, mixing ratio lines, and isotherms; parcel path curvature locates LCL, LFC, and EL.

Mid-latitude cyclone life cycle: wave development on the polar front, frontal fracture, bent-back occlusion, warm-core seclusion, and cold-core decay.

Norwegian frontal model: warm front slope ~1:150, cold front ~1:50; the cold front typically advances faster and overtakes the warm front.

Squall-line and QLCS hazards: bowing segments, rear-inflow jets, bookend vortices, and mesovortices producing brief tornadoes at line ends.

Supercell structure: rotating mesocyclone, bounded weak-echo region, hook echo, and vault; right-mover deviates from mean wind due to propagation.

Mesoscale convective system stratiform region trails the convective line; the transition zone hosts the stratiform rain and rear-inflow notch.

Sea-breeze front forms when differential heating creates a solenoidal circulation; onshore penetration is 10-50 km, deeper with strong synoptic offshore flow absent.

Tropical cyclone structure: warm core, eyewall updrafts, spiral rainbands, and outflow cirrus; intensification favored by warm SSTs (>26.5 °C) and low vertical shear.

Frontogenesis function includes confluence, horizontal shear, and diabatic terms; frontogenesis sharpens temperature gradients and strengthens the secondary circulation.

Surface analysis conventions: isobars every 4 hPa, H/L centers, frontal symbols, and station-model plots with temperature, dew point, pressure tendency, and wind barbs.

500-hPa analysis: troughs and ridges, vorticity maxima, and jet streaks; the polar jet marks the strongest baroclinic zone aloft.

Jet streak quadrants: the left-exit and right-entrance regions favor upper divergence, ascent, and surface cyclogenesis.

Model guidance hierarchy: deterministic (global and regional), ensembles for probability, and post-processing; spread among members indicates forecast uncertainty.

Forecast verification metrics: bias (mean error), MAE, RMSE, and Brier score for probabilistic forecasts; lower is better for all except bias sign.

Persistence and climatology are baseline forecasts; a model must beat these baselines to add skill, especially at short and long leads.

Severe weather parameters: bulk shear > 15 m/s supports organized storms; SBCAPE > 1000 J/kg with shear favors supercells.

Nowcasting relies on radar extrapolation, satellite trends, and surface observations; skill decays rapidly beyond 2-6 hours for convection.

Solar constant ≈ 1361 W/m²; planetary albedo ≈ 0.30; effective emission temperature from Stefan-Boltzmann gives about 255 K.

Greenhouse effect raises surface temperature to ~288 K by trapping outgoing longwave; key absorbers are H2O, CO2, CH4, N2O, and O3.

Radiative forcing of doubled CO2 ≈ 3.7 W/m²; equilibrium climate sensitivity is about 2.5-4 °C, with transient response lower.

Energy balance: absorbed shortwave equals emitted longwave plus sensible and latent fluxes; net imbalance drives warming or cooling.

General circulation: Hadley, Ferrel, and polar cells; ITCZ near the thermal equator, subtropical highs near 30°, and mid-latitude westerlies.

El Niño-Southern Oscillation: warm SST anomalies in the eastern equatorial Pacific weaken the Walker circulation; La Niña is the reverse.

Köppen climate classification uses monthly temperature and precipitation thresholds; tropical (A), dry (B), temperate (C), continental (D), polar (E).

Radiative transfer: Beer-Lambert law I = I0·exp(-k·u); optical depth depends on absorber amount and absorption cross-section.

Radiosonde measures pressure, temperature, humidity, and wind with height; mandatory and significant levels define the sounding; GPS provides height.

Doppler radar measures reflectivity (dBZ), radial velocity, and dual-pol variables (ZDR, KDP, ρhv); velocity folding occurs when radial speed exceeds Nyquist.

Geostationary satellites give frequent full-disk imagery; polar orbiters give higher resolution and microwave sounding for temperature and humidity profiles.

Satellite channels: visible (cloud albedo), infrared (cloud-top temperature), water vapor (mid-tropospheric moisture), and microwave (precipitation, SST).

NWP data assimilation combines observations with a background (first guess) using analysis increments; 4D-Var and ensemble Kalman filter are common methods.

Model parameterizations represent subgrid processes: radiation, convection, boundary-layer turbulence, microphysics, and land surface.

Ensemble prediction generates spread from initial-condition perturbations and model physics diversity; probability of exceedance is derived from member counts.

Verification and bias correction: model output statistics (MOS) and anomaly correction reduce systematic NWP errors at station level.

Hydrostatic balance: dp/dz = -ρg; the hypsometric equation z2 - z1 = (R·T̄/g)·ln(p1/p2) gives thickness from mean virtual temperature.

Geostrophic wind: Vg = (1/(ρf))·k × ∇p; in pressure coordinates ug = -(1/(ρf))·∂p/∂y and vg = (1/(ρf))·∂p/∂x.

Coriolis parameter f = 2Ω·sin φ; zero at the equator, about 1.46×10⁻⁴ s⁻¹ at 30° and 2.29×10⁻⁴ s⁻¹ at 45° latitude.

Natural Rossby radius of deformation LR = NH/f (or √(gH)/f for shallow water); it sets the scale separating balanced flow from gravity-wave response.

Potential vorticity (Ertel): PV = (1/ρ)·ζa·∇θ; conserved for adiabatic, frictionless flow, so PV anomalies track troughs and ridges on isentropic surfaces.

Quasi-geostrophic omega equation: ascent is forced by positive differential vorticity advection and warm-air advection; descent by the reverse.

Thermal wind: ∂Vg/∂ln p = -(R/f)·k × ∇T; wind veers with height when temperature falls toward the cold side (warm advection).

Continuity in pressure coordinates: ∇·V + ∂ω/∂p = 0; near-surface convergence implies upward motion ω < 0 above.

Gradient wind adds centrifugal term: Vgr²/R + f·Vgr = (1/ρ)·∂p/∂n; subgeostrophic around a low, supergeostrophic around a high.

First law: dq = cp·dT - α·dp; dry adiabatic lapse rate Γd = g/cp ≈ 9.8 K/km; saturated rate Γs is smaller and approaches Γd aloft.

Potential temperature θ = T·(p0/p)^(Rd/cp) with p0 = 1000 hPa and Rd/cp ≈ 0.286; θ is conserved in dry adiabatic processes.

Equivalent potential temperature θe = θ·exp(Lv·rs/(cp·T)); conserved in moist adiabatic ascent and used to trace air masses.

Clausius-Clapeyron: es increases about 6-7% per K; saturation vapor pressure over water exceeds that over ice below 0 °C.

Relative humidity RH = e/es × 100%; dew point Td is the temperature at which e equals es, so T - Td approximates the LCL spread (~125 m per °C).

Lifting condensation level: zLCL ≈ 125·(T - Td) m; the wet-bulb temperature lies between T and Td.

CAPE = ∫(Tv_parcel - Tv_env)·g·dln p from LFC to EL; CIN is the negative area below the LFC that must be overcome.

Skew-T log-p reading: dry adiabats, moist adiabats, mixing ratio lines, and isotherms; parcel path curvature locates LCL, LFC, and EL.

Mid-latitude cyclone life cycle: wave development on the polar front, frontal fracture, bent-back occlusion, warm-core seclusion, and cold-core decay.

Norwegian frontal model: warm front slope ~1:150, cold front ~1:50; the cold front typically advances faster and overtakes the warm front.

Squall-line and QLCS hazards: bowing segments, rear-inflow jets, bookend vortices, and mesovortices producing brief tornadoes at line ends.

Supercell structure: rotating mesocyclone, bounded weak-echo region, hook echo, and vault; right-mover deviates from mean wind due to propagation.

Mesoscale convective system stratiform region trails the convective line; the transition zone hosts the stratiform rain and rear-inflow notch.

Sea-breeze front forms when differential heating creates a solenoidal circulation; onshore penetration is 10-50 km, deeper with strong synoptic offshore flow absent.

Tropical cyclone structure: warm core, eyewall updrafts, spiral rainbands, and outflow cirrus; intensification favored by warm SSTs (>26.5 °C) and low vertical shear.

Frontogenesis function includes confluence, horizontal shear, and diabatic terms; frontogenesis sharpens temperature gradients and strengthens the secondary circulation.

Surface analysis conventions: isobars every 4 hPa, H/L centers, frontal symbols, and station-model plots with temperature, dew point, pressure tendency, and wind barbs.

500-hPa analysis: troughs and ridges, vorticity maxima, and jet streaks; the polar jet marks the strongest baroclinic zone aloft.

Jet streak quadrants: the left-exit and right-entrance regions favor upper divergence, ascent, and surface cyclogenesis.

Model guidance hierarchy: deterministic (global and regional), ensembles for probability, and post-processing; spread among members indicates forecast uncertainty.

Forecast verification metrics: bias (mean error), MAE, RMSE, and Brier score for probabilistic forecasts; lower is better for all except bias sign.

Persistence and climatology are baseline forecasts; a model must beat these baselines to add skill, especially at short and long leads.

Severe weather parameters: bulk shear > 15 m/s supports organized storms; SBCAPE > 1000 J/kg with shear favors supercells.

Nowcasting relies on radar extrapolation, satellite trends, and surface observations; skill decays rapidly beyond 2-6 hours for convection.

Solar constant ≈ 1361 W/m²; planetary albedo ≈ 0.30; effective emission temperature from Stefan-Boltzmann gives about 255 K.

Greenhouse effect raises surface temperature to ~288 K by trapping outgoing longwave; key absorbers are H2O, CO2, CH4, N2O, and O3.

Radiative forcing of doubled CO2 ≈ 3.7 W/m²; equilibrium climate sensitivity is about 2.5-4 °C, with transient response lower.

Energy balance: absorbed shortwave equals emitted longwave plus sensible and latent fluxes; net imbalance drives warming or cooling.

General circulation: Hadley, Ferrel, and polar cells; ITCZ near the thermal equator, subtropical highs near 30°, and mid-latitude westerlies.

El Niño-Southern Oscillation: warm SST anomalies in the eastern equatorial Pacific weaken the Walker circulation; La Niña is the reverse.

Köppen climate classification uses monthly temperature and precipitation thresholds; tropical (A), dry (B), temperate (C), continental (D), polar (E).

Radiative transfer: Beer-Lambert law I = I0·exp(-k·u); optical depth depends on absorber amount and absorption cross-section.

Radiosonde measures pressure, temperature, humidity, and wind with height; mandatory and significant levels define the sounding; GPS provides height.

Doppler radar measures reflectivity (dBZ), radial velocity, and dual-pol variables (ZDR, KDP, ρhv); velocity folding occurs when radial speed exceeds Nyquist.

Geostationary satellites give frequent full-disk imagery; polar orbiters give higher resolution and microwave sounding for temperature and humidity profiles.

Satellite channels: visible (cloud albedo), infrared (cloud-top temperature), water vapor (mid-tropospheric moisture), and microwave (precipitation, SST).

NWP data assimilation combines observations with a background (first guess) using analysis increments; 4D-Var and ensemble Kalman filter are common methods.

Model parameterizations represent subgrid processes: radiation, convection, boundary-layer turbulence, microphysics, and land surface.

Ensemble prediction generates spread from initial-condition perturbations and model physics diversity; probability of exceedance is derived from member counts.

Verification and bias correction: model output statistics (MOS) and anomaly correction reduce systematic NWP errors at station level.