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Determining the underlying structures in modelled orographic flow

R. R. Burton1, S. B. Vosper2 and S. D. Mobbs1

1 Institute for Atmospheric Science, School of Earth and Environment, University of Leeds, Leeds, UK2 Met Office, Exeter, UK

For more information about this poster please contact Dr Ralph Burton, School of Earth and Environment, Environment, University of Leeds, Leeds, LS2 9JT Email: ralph@env.leeds.ac.uk

PCA of model runs

Motivation – severe turbulence in the Falklands Numerical Modelling

The model used to simulate the flow over the Falklands was 3DVOM [2, 3]:• Linear model for turbulent flow over hills• Terrain-following coordinates• Incorporates boundary-layer model• Mixing length scheme for turbulence• Semi-implicit finite difference scheme• Real orography dataset

A series of 725 model runs has been completed, initialised with daily radiosonde data from MPA. Of these runs, cases whereIdentifying the

surface pressure patterns associated with severe turbulence and windstorms could be a useful aid in this regard.

SURFACEPRESSURE

VERTICAL WINDSPEED

AT 400M

Turbulence and rotor cloud at MPA

Conclusions

Correlation with radiosonde profilesIn order to determine a relationship (if any) between the input profile used to drive the model and the output from the model, a similar set of PCA analyses was performed on the radiosonde profiles, using the lowest 2km of each profile. The actual profiles used are derived from the radiosonde data and are produced by the boundary-layer model.

Acknowledgments

EOF #

v(dθ/dz)

P_SURF

1 47% 47%2 24% 17%3 10% 13%4 6% 8%

Event A:positive EOF1,negative EOF 2gives a N-S wavepattern

Event B:positive EOF1,positive EOF 2gives a NE-SWwave pattern

Actual model output: surface pressure and wind vectors

Event A5/11/00

Event B8/9/01

AB

It was found that the vertical profile of v(dθ/dz) corresponds very well to the model output, in the sense that the first PC scores for the two cases show a marked degree of correlation (r = 0.72) and the first EOFs explain the same proportion of variance.

A strong inversion and large negative (northerly) meridional winds will lead to large v(dθ/dz)

First EOF for dθ/dz

A marked correlation between the first EOFs for v(dθ/dz) and surface pressure

ReferencesRalph Burton was funded by a NERC grant.

EOF 1 (P_SURF) EOF 4 (P_SURF)EOF 3 (P_SURF)

EOF 1 (W_400m)

EOF 2 (P_SURF)

EOF 2 (W_400m) EOF 4 (W_400m)EOF 3 (W_400m)EOF #no

rmal

ised

eige

nval

ue

Run #

PC

scor

e

Run #

PC

scor

e

First PC score for v(dθ/dz)

Firs

t PC

scor

e fo

r P_S

URF

Best fit: r=0.72

[1] Mobbs, S. D., Vosper, S. B., Sheridan, P. F., Cardoso, R., Burton, R. R., Arnold, S. J., Hill, M. K.,Horlacher, V. and Gadian, A. M. (2005): “Observations of downslope winds and rotors in the Falkland Islands”, Q. J. Roy. Meteor. Soc., 131, 329-351[2] Vosper, S.: (2003): “Development and testing of a high resolution mountain-wave forecastingsystem”, Meteorol. Appl. 10, 75-86[3] King, J. C., Anderson, P. S., Vaughan, D. G., Mann, G. W., Mobbs, S. D. and Vosper, S. B. (2004): “Wind-borne redistribution of snow across an Antarctic ice rise”, J. Geophys. Res., 109, D11104

The presence of inversion has alreadybeen connected with turbulence at MPA [1].This correlation suggests that an inversion, together with with a strong meridional wind at the inversion level, is linked to turbulent effects at the ground; the stronger the v(dθ/dz) signal, the stronger the response.

P_SURFW_400m

05/11/0026/02/01

20/08/01

High values of the first PC score for v(dθ/dz) corresponded to actual severe weather at MPA (see anemograph traces to the right).

P_SURF

W_400m

A marked degree of correlation is found between the

first EOFs for surface pressure and for v(dθ/dz)

This suggests that the vertical profile of v(dθ/dz) may be useful as a diagnostic in the prediction of severe weather events.

Dominant structures have been found: the first three EOFs account for 70% of the variance in the data for both surface pressure and vertical wind speed

Approximately the same amount of variance is contained in the first three EOFs for

the vertical profile of v(dθ/dz) derived from the input profile

These EOFs show distinct gravity wave patterns, as shown in both the pressure and vertical velocity structures. EOF1(P) and EOF2(P) show high drag situations, with slightly differing orientations; when either the PC scores of EOF1 and EOF 2, or both, are large and positive, we would expect a very large pressure gradient to exist around the area of MPA.

This is indeed the case (see the actual model outputs corresponding to events A and B). Output corresponding to other peaks in the time series (not shown) also display significant effects at the surface. Note that severe turbulence was observed at MPA during event A (see the photo and anemograph trace above.)

Principal Component Analysis (PCA) is an objective method for determining underlying patterns in data. The significant structures are known as empirical orthogonal functions, or EOFs.

The first EOF should account for as much of the variability as possible; the second EOF should account for as much of the remaining variability as possible; and so on.

Shown below are the significant structures present in the modelled pressure and 400m vertical velocity fields.

MPA

Mount Pleasant Airport (MPA), Falkland Islands, suffers from bouts of extreme turbulence [1].

Location of the Falkland Islandsand MPA MPA

Any insight into predicting severe weather events would be highly desirable. the measured

average wind direction in the lowest 1km of the atmosphere was from NW’ly to NE’ly were selected, leading to 94 model runs.These are thensubjected to a principal components

analysis.

NUMERICAL DOMAIN FOR THE MODEL RUNS

Proportion of variance explained explained by the EOFs for v(dθ/dz) and surface pressure

EOF value (Ks-1)

heig

ht (k

m)

.50.5

1.5

1.0

2.0

-0.4 -0.3 -0.2 -0.1 0.0-0.5

dirn.

speed5th Nov.2000