The Diagnosis of Synoptic-Scale Vertical Motion in an Operational Environment

The Diagnosis of Synoptic-Scale Vertical Motion in an Operational EnvironmentBy Dale R. Durran and Leonard W. SnellmanAbstractThe physical reason for quasi-geostrophic vertical motion is reviewed. Various techniques for estimating synoptic-scale vertical motion are examined, and their utility (or lack thereof) is illustrated by a case study. The Q-vector approach appears to provide the best means of calculating vertical motions numerically. The vertical motion can be estimated by eye with reasonable accuracy by examining the advection of vorticity by the thermal wind or by examining the relative wind and the isobar field on an isentropic chart. The traditional form of the omega equation is not well suited for practical calculation.Quasi- Geostrophic Vertical MotionKeeps geostrophic advection from changes in the hydrostatic and geostrophic balancesVertical velocity is present to control thermal wind balanceSimple for forecastingEasy to calculate and understandIn synoptic scales- Decent approximation of total vertical velocityQuasi- Geostrophic Vertical VelocityThe Q-G vertical velocity is calculated from the Q-G Omega equation

Left hand side ~ -

Case StudyFeb. 12, 1986At 1200 UTC

Case Study

Using the Omega EquationThe second term on the RHS can be proportional to -1 times the temperature advection.

Using the Omega Equation- Second Term

700 mb heights (solid) and 850-500 mb thickness (dashed)-1 times 700 mb warm advection8Using the Omega Equation- Second Term

Laplacian of the 700 mb warm advectionUsing the Omega Equation- First Term

500 mb heights (solid) and absolute vorticity (dashed)500 mb vorticity advectionUsing the Omega Equation- First Term

Increase in vorticity advection with height at 500 mbSecond Test- Trenberths ApproximationEstimate the Q-G vertical velocity without numerical computationQ-G omega equation can be written as:1st term (increase in vorticity advection with height) = advection of absolute vorticity by the thermal wind + advection of thermal vorticity by the wind2nd term (laplacian of warm advection) = advection of relative vorticity by the thermal wind advection of thermal vorticity by the wind + terms involving the deformation of the wind fieldAscent should be located where there is advection of vorticity by the thermal wind

Second Test- Trenberths Approximation

Advection of 500 mb vorticity by the 700-300 mb thermal windThird Test- Hoskins Approximation Neither the Laplacian of the warm advection nor the rate of change of vorticity advection with height should be regarded as a cause of synoptic scale vertical motion. quasi-geostrophic vertical motion is caused by the tendency for advection by the geostrophic wind to destroy thermal wind balance.

Therefore instead of calculating the total forcing from the QG omega equation, Hoskins used Q vectors.

Third Test- Hoskins Approximation Q vectors allow us to view the ageostrophic horizontal wind

. in the lower branch of the circulation that forms to sustain thermal wind balance as a synoptic disturbance formsIt points to rising motion15Third Test- Hoskins Approximation

Hoskins et al showed that the RHS of equation 1 (the Q-G omega equation) goes as -2(the divergence of Q)

Divergence of the Q vectorRising motions producing the precip in NW oregon as part of an ageo circulation with strong low level flow into the region from the NW. Forcing for QG vertical motion can be seen using the divergence of the q vector16Third Test- Hoskins Approximation

Divergence of the Q-vectors at 500 mbTotal forcing for omega at 500 mb from test 1Divergence of the Q vectors at 500 mbThis result is different than the total forcing for omega at 500 mb. This is because finite differences because the RHS of equation 1 is not equal to the finite differences for the divergence of the Q vectors. I am not too familiar with this but I will try to explain why this is in the next test

17Third TestDefined a 3D height field Numerical calculations with high horizontal and vertical resolutionHorizontal resolution0.5 degree latitude by 0.5 degree longitudeChanges in vertical resolutionFirst 2 images: 200 mbData from the 700, 500 and 300 mb levels usedSecond 2: 50 mbData from the 550, 500 and 450 mb levels usedThird Test

Total forcing for with p = 200 mb. (a) is calculated with traditional omega equation and (b) is calculated with divergence of Q vectorsMajor differences! D:19Third Test

Total forcing of with p = 50 mb.Results

500 mb divergence of Q vectorsHere is the 500 mb divergence of Q vectors and the right side shows the rain areas. This corresponds to areas of precip (upward motion aloft). This however does not account for the rainfall along the N. Cali coast. Which could be due to 1. some mesoscale process creating the rainfall/orographic phenomenon. 2. lack of data over the Pacific ocean. 21Results

Total forcing for omega at 500 mb using Eq. 1Does not do near as good a job as the Q vectors in showing precip.22Results

Divergence of the Q vectors at 500 mbAdvection of 500 mb vorticity by the 700-300 mb thermal wind from Eq. 3 Very similar results of upward motion at 500 mb from the Trenberths approximation and the Hoskins experiment with Q vectors corresponding to precip at the surface. 23ConclusionsQ-G vertical motion is the result of keeping the balance between the hydrostatic and geostrophic balance Q-G vertical motion at 500 mb calculated from the forcing terms in the omega equation matched up with the observed precipitation at the surface in the case studyApproximation of RHS of equation 1 is ~ to holds true in the middle troposphere (Trenberth(1978))Cannot estimate the total forcing using equation 1 (increase in vorticity advection with height + Laplacian of warm advection) without numerical calculations.ConclusionsUse Trenberths approximation (advection of vorticity by the thermal wind) if no access to numerical calculationsIf calculating the Q-G omega equation numerically use Hoskins method of using Q-vectorsErrors are smaller in Trenberth and Hoskins methods due to the cancellation of the advection of thermal vorticity by the wind (a large term)Referenceshttp://journals.ametsoc.org/doi/abs/10.1175/1520-0434(1987)002%3C0017:TDOSSV%3E2.0.CO;2