Cold Fronts and their relationship to density currents: A case study and idealised modelling experiments

Victoria SinclairUniversity of HelsinkI

David SchultzUniversity of Helsinki, FMI,

University of Manchester, UK

Overview• Previous work and some theory concerning cold

fronts and density currents

• A Case Study– Observations– AROME simulation

• Idealised Modeling Experiments– 2D density current and 3D cold front– Quantify governing dynamics

Can cold fronts be considered density currents?

Plenty of papers state that a cold front resembles a density current in appearance

Visual similarity does not equal dynamical similarity

Tower observations of a cold front, Colorado

Shapiro et al. 1985

Density Current theory

0.5ghc k

• Coriolis force can be neglected

• Equations exists which predict the speed of movement as a function of density difference and the depth

• Density currents have a low-level feeder flow behind the leading edge: the wind speeds behind the front (u) are greater than the speed that the gravity current moves at (c)

1

1

Du pfvDt xDv pfuDt y

XX

0u c

Fronts Theory

• Fronts are often assumed to be balanced, at least in the cross front direction

• Acceleration term is assumed to be small.

1

1

Du pfvDt xDv pfuDt y

XX

• No formula to predict the speed that fronts move at

• Uncertainty remains as to what factors control the speed that cold fronts move at

Questions• What controls the speed that cold fronts move

at?– Why do some cold fronts propagate – i.e. move faster

than the normal component of the wind?– Why do some cold fronts move slower than the

normal wind, and hence share a feature with gravity currents?

• When do cold fronts collapse to resemble density currents?

• Are collapsed cold fronts dynamically similar to density currents?

Motivation

• Cold fronts that evolve into gravity current type features can produce hazardous weather

• The scale of a collapsed front means that even high resolution NWP models will not capture the structure and evolution well

Case Study: synoptic evolution

• Developed as a frontal wave on pre-existing front• Mature front and is far from the parent low• Simulated event with AROME 33h1, 2.5km

12 UTC 29 Oct 00 UTC 30 Oct 00 UTC 31 Oct

Shallow frontal zone 00:11 UTC

• Radial wind speeds from Kumpula Radar

• Cold air is confined to a shallow layer

• Resembles a density current

6 m/s

7 m/s

Image provided by Matti Leskinen

Temperature at Kivenlahti

Observations AROME

black: 5 m red: 26 mblue: 48 mmagenta: 93 m

grey: 141 mgreen: 218 mbrown: 266 m orange: 296 m

black: 2 m blue: 38 mmagenta: 112 m

green: 200 m orange: 300 m

Temperature at Kuopio

Observations AROME

black: 5 m red: 26 mblue: 48 mmagenta: 93 m

grey: 141 mgreen: 218 mbrown: 266 m orange: 296 m

black: 2 m blue: 38 mmagenta: 112 m

green: 200 m orange: 300 m

Heat Fluxes

SMEAR III SMEAR II

BLACK: observed. GREY: AROME

Data provided by Annika Nordbo and Ivan Mammarella

AROME Potential Temperature 900hPa

Location of Cold Front from AROME

Averaged speed of front between 22:00 UTC and 02:00 UTC

Section B = 5.03 ms-1

Section C = 5.47 ms-1

Section A = 6.92 ms-1

Front is located objectively

Hewson (1998)

Jenker et al (2010)

Black: 18:00 UTC

Red: 20:00 UTC

Green: 22:00 UTC

Blue: 00:00 UTC

Purple: 02:00 UTC

Cyan: 04:00 UTC

BB

A

C

Wind Speeds from AROME

• Wind speeds decrease behind the front• Unconvincing evidence of a “feeder flow”

920 hPa 990 hPa

u – c > 0 especially in south u – c ≈ 0

Ascent, potential temperature Simulated Radar reflectivity

22 UTC, B 00 UTC, B

22 UTC, A 00 UTC, A

Case Study Conclusions• Shallow and narrow front

– stable mid-troposphere– Stable BL may have prevented frontolysis by turbulent

mixing

• Dynamics differ to density current dynamics– No clear feeder flow

• Prefrontal boundary layer appears to affect structure

Idealised Modelling with WRF

Idealized Experiment

• WRF-ARW– Weather Research and Forecasting –

Advance Research WRF. V3.1– Non-Hydrostatic, range of physics options– Supported by NCAR

• First simulated a 2D density current at high resolution (100m grid spacing)

• Calculate force balance.

Density Current

5 – 10 minutes : 20.5 ms-1

10 – 15 minutes: 15.3 ms-1

Force Balancelowest model level (995 hPa)

Blue: Potential temperature

Red: Pressure Gradient Force

Purple: Coriolis

Black: Acceleration

Simulate a Cold Front

• Model a full 3D baroclinic life cycle• Include two nested domains over the cold

front– horizontal grid spacing is 100km : 20km : 4km– All nests have 64 levels, model top at 100hPa

• Initial experiment has no moisture and no physical parameterizations

Potential temperature and surface pressure. Day 4.5. Parent domain

Potential Temperature and wind vectors. 20 km domain

Potential temperature and vertical motion

Force balance

Purple: Coriolis

Black: Acceleration

Blue: Potential temperature

Red: Pressure Gradient Force

LEVEL 1 ~ 975 h Pa LEVEL 7 ~ 805 h Pa

Force Balance 5 hrs later

Blue: Potential temperature

Red: Pressure Gradient Force

LEVEL 1 ~ 975 h Pa LEVEL 7 ~ 805 h Pa

Purple: Coriolis

Black: Acceleration

Blue: Potential temperature

Red: Pressure Gradient Force

Conclusions• Idealised cold front does not visually resemble a

density current, but does have many interesting features

• The force balance shows a three way balance near the cold front

• HYPOTHESIS– friction and turbulence will change force balance– Trailing part of cold front will be visually more similar

to density currents

Future work

• Higher resolution (1km) simulation of cold front, include boundary layer scheme

• Different baroclinic life cycles

• Simulate 3D density current at comparable resolution to cold front case

Thank you

You can look at more animations on my webpages

www.atm.helsinki.fi/~vsinclai

Force Balance: 5 hrs later

Force Balance across cold front