Ertel potential vorticity versus B ernoulli streamfunction in earth's extratropical atmosphere

We investigate the correlation of Ertel potential vorticity, Q , with Bernoulli streamfunction, B , on potential‐temperature surfaces, θ , in Earth's atmosphere poleward of ± 30 °latitude. For input, we use the 1979–2010 CMAM30‐SD specified‐dynamics data set. We fit the model Q = Q 0 exp ⁡ [ − λ 0 ( B − B 0 ) ] separately in the midlatitude [ 30 ° , 60 ° ) and polar [ 60 ° , 90 ° ] regions, and nondimensionalize the slope parameter asλ ̂ 0 ≡ ( N H ¯ ) 2 λ 0 . In the troposphere, the peak ofλ ̂ 0is approximately 2–3 in winter and 3–4 in summer in both regions. In the stratosphere during winter, bothλ ̂ 0 | midlatandλ ̂ 0 | polarhover around unity. In spring and fall,λ ̂ 0 | polarcontinues to hover near unity, butλ ̂ 0 | midlatrises by a factor of two, with its maximum located at θ ∼ 700 to 900   K . In summer, the polar value drops to |λ ̂ 0 | polar ≪ 1 , while the midlatitude value swings negative toλ ̂ 0 | midlat ∼ − 2 to −3. In the mesosphere,λ ̂ 0exhibits incessant fluctuations with values that usually fall within the range 0 to 1. The results support the paradigm |λ ̂ 0 | ≪ 1 for dynamically active regions primarily in the vicinity of θ ∼ 3000 – 4000   K ( ∼   62 – 72   km ) in the mesosphere, whereas except in summer, we get the simple result that the monthly climate‐averaged profile, 〈λ ̂ 0 〉 , in the polar regions is nearly unity across the entire stratosphere. During extended recoveries following SSWs, the midlatitude vertical profile develops a peak near 2000 K that descends over the course of a few weeks, alongside the descent of the elevated stratopause in the polar region.