QG Ascent Diagnosis and Banded Heavy Rainfall

Hypsometric step Z₂ − Z₁ = (Rd·T̄v/g)·ln(p₁/p₂), so T̄v = g·ΔZ / (Rd·ln2) = 9.81·ΔZ / (287·0.693) ≈ 0.0493·ΔZ (K per m).

• Warm side: 0.0493 × 5400 ≈ 266.4 K
• Cold side: 0.0493 × 5280 ≈ 260.5 K
• ΔT̄v ≈ 5.9 K over 600 km, i.e. a gradient of about 0.98 K per 100 km.

Thermal wind |ΔV| = (Rd/f)·ln(p₁/p₂)·|∇T| = (287/1.0×10⁻⁴)(0.693)(9.8×10⁻⁶) ≈ 19.6 m s⁻¹.

So the 1000–500 hPa shear is roughly 20 m s⁻¹, directed westerly with cold air to the left (north) - the wind veers from southerly at 850 hPa to westerly at 300 hPa across the baroclinic zone.

Consistency check An 850 hPa southerly of about 18 m s⁻¹ under a 300 hPa westerly of about 36 m s⁻¹ gives a layer shear of 25–30 m s⁻¹, the same order as the 20 m s⁻¹ geostrophic value. The modest excess in the observed upper wind is not an error; it indicates ageostrophic, supergeostrophic flow in the jet exit region, which is exactly where you would expect a transverse circulation. The low-level southerly also implies warm advection at 850 hPa, i.e. the front is frontogenetic on the warm side.

The two terms The QG omega equation balances (σ∇² + f₀²∂²/∂p²)ω against the vertical derivative of vorticity advection plus the Laplacian of temperature advection.

• Vorticity term: with a positive PVA maximum near 500 hPa, ∂/∂p[−V·∇(ζ+f)] is positive below the level of maximum PVA, which forces ω < 0, i.e. ascent. This term favours rain at the point.
• Thermal term: −3.0×10⁻⁴ K s⁻¹ at 700 hPa is cold advection. A single-level value is not enough; what matters is the Laplacian of that advection in the horizontal and its vertical structure. Where cold advection is a local maximum at 700 hPa, its Laplacian is negative, which forces ω > 0, i.e. subsidence.

Which wins here The presence of cold advection at 700 hPa at the point means the point lies behind the trough axis or on the cold side of the baroclinic zone, in the drying/subsiding branch. So the two terms oppose, and the balance says the deep ascent - and therefore the heavy precipitation - is displaced downstream, into the warm-advection region ahead of the trough and along the low-level jet terminus.

Implication At the forecast point expect light precipitation or a lull between bands, not the axis of heaviest rain. Any model producing 45 mm at this point is misplacing the ascent maximum relative to the analysed thermal advection, and that is an argument for checking the front position rather than the QPF number.

Member A is better supported physically The environment has a 35 kt low-level jet, strong 850 hPa moisture flux convergence about 50 km north of the front, and a frontogenesis maximum 80 km northwest of the surface front. Frontogenesis acting on a moist, conditionally unstable air mass produces a narrow, intense band, typically on the cold side of the surface front and near the 850 hPa front - so the heavy axis should sit roughly 50–100 km north-northwest of the surface front, matching both the frontogenesis and moisture flux convergence maxima.

Member B's 12 mm spread over 300 km is what a model produces when it cannot hold a band: convective parameterization and numerical diffusion smear the frontal circulation. That is a resolution/parameterization artifact, not evidence against the banded solution.

But placement, not amount, is the real uncertainty A 30–50 km wide band at 12 hours is at or below the placement skill of any deterministic member. The correct product is not 45 mm at a point; it is a probability strip - the fraction of ensemble members exceeding, say, 25 mm - which will be a narrow corridor with 30–50% probabilities.

Verification plan At the next analysis, check the low-level jet strength, the surface front position, and the moisture flux convergence maximum. If the front verifies 50 km farther south, shift the whole band with it; do not adjust the amount.