Atmospheric turbulence

and climate change

Paul Williams

University of Reading, UK

Alpine Summer School, 17 June 2014, Valsavarenche

Turbulence in fluids

“Turbulence is the most important unsolved problem of classical physics.”

– Richard Feynman

“When I meet God, I am going to ask him two questions: Why relativity, and

why turbulence? I really believe he will have an answer for the first.”

– Werner Heisenberg

“I am an old man now, and when I die and go to heaven there are two matters

on which I hope for enlightenment. One is quantum electrodynamics, and the

other is the turbulent motion of fluids. And about the former I am rather

optimistic.”

– Horace Lamb

“Big whorls have little whorls, which feed on their velocity, And little whorls have

lesser whorls, and so on to viscosity.”

– Lewis Richardson

Turbulence in the atmosphere

Gage & Nastrom (1986)

Scales causing

aviation turbulence

(Lane et al. 2012)

Scales resolved

by models

Aviation turbulence

Aviation turbulence Annually, in the USA alone, aircraft encounter moderate turbulence (>0.5g)

65,000 times and severe turbulence (>1.0g) 5,500 times. These encounters:

Ralph et al. (1997)

– cause about 40 fatalities and 100s of serious injuries

– cause structural damage to planes

– cause flight diversions and delays

– cost airlines $150m–$500m

Aviation turbulence

“Recently turbulence plunged a United Airlines plane 300 metres

(900 feet), killing one passenger and injuring over 100 other

people on a flight from Japan to Hawaii. In other incidents,

turbulent air has ripped off aeroplane engines, snapped wings in

two, hurled food carts to the ceiling, and broken passengers’ and

flight attendants’ bones. Each year societal costs resulting from

turbulence-related incidents reach almost $100 million for human

injuries, aircraft damage, and government investigations.

Turbulence is the primary cause of nonfatal injuries to airline

passengers and crew.”

- Meteorological Applications (5)2, page 183, 1998.

Aviation turbulence

Clear-air turbulence (CAT) • CAT occurs in clear skies at cruise altitudes, above clouds and

storms

• CAT is difficult to avoid, because it cannot be seen by pilots or

detected by satellites or on-board radar

• Aircraft spend about 3% of their cruise time in light CAT (Watkins &

Browning 1973) and about 1% in moderate CAT (Sharman et al.

2006)

• CAT is forecast operationally by computing various diagnostic

measures from the large-scale flow, e.g. those due to Colson &

Panofsky (1965), Brown (1973), and Ellrod & Knapp (1992)

• World Area Forecast Centres (in London and Washington) use such

diagnostics to issue global CAT forecasts every six hours (Gill 2012)

• The diagnostics show moderate skill when evaluated against pilot

reports of turbulence, especially when used in combination

(Sharman et al. 2006)

The wind shear,

∂u/∂z, is

destabilizing

The stratification,

∂ρ/∂z, is

stabilizing

Kelvin–Helmholtz instability occurs if:

Ri = (-g/ρ ∂ρ/∂z) / (∂u/∂z)2 < ¼

height

(z)

Probable mechanism for CAT

Probable mechanism for CAT

Thorpe (1969) De sterrennacht, van Gogh (1889)

Part 1. Rigorously deriving a CAT

diagnostic from knowledge of the

fluid dynamics

In collaboration with:

John Knox, University of Georgia, Athens, USA

Don McCann, McCann Aviation Weather Research, Kansas, USA

source

term

laboratory

interface

height

Williams, Haine & Read (2005)

|.| uf

(Ford 1994)

.uf

Loss of balance → gravity waves

Hypothesised mechanism for CAT • Gravity waves generated by loss of balance destabilise the flow and

initiate Kelvin–Helmholtz instability

• Specifically, a gravity wave of non-dimensional amplitude

and phase φ locally modifies the flow (Palmer et al. 1986) according to

• Therefore, the maximum production rates of turbulent kinetic energy

(TKE) due to Kelvin–Helmholtz instability are modified by the gravity

wave according to

• We take (as seen in the laboratory), with an empirically

determined proportionality constant

• We compute both εshear and εstrat , and the final output of our algorithm is

max(εshear , εstrat)

cosˆ1andsinRiˆ1// 22 aNNazuzu

1ˆandRiˆ1)/()/( 22strat

222shear aNNazuzu

|.| ufa

||/ˆ cuNaa

• The symbols show 94

pilot reports (PIREPs) of

turbulence encountered

in the north-east USA

between 13,000 feet and

37,000 feet over a

period of 2 hours on 24

October 2007

• The contours show our

TKE diagnostic

computed from RUC2

model forecasts

Results: case study

• We produce daily CAT predictions by calculating our TKE diagnostic

using the Rapid Update Cycle (RUC2) operational numerical weather

prediction model • 20 km horizontal resolution, 25 hPa vertical resolution

• 1-hour forecasts valid at 1600 UTC each day

• We compare the predictions with pilot reports (PIREPs) of turbulence

over the entire USA from 1500-1700 UTC at or above 20,000 feet • mountain wave reports omitted objectively

• convective reports omitted by comparison with satellite imagery

• We use the period 3 November 2005 to 26 March 2006 (144 days,

5546 PIREPs)

• We compare the skill with that of the Graphical Turbulence Guidance

(GTG1) algorithm (Sharman et al. 2004), the most skillful operational

CAT forecasting method available

Results: statistical study

Federal target for

CAT forecasting

(blue star)

Knox, McCann & Williams (2008)

Receiver

Operating

Characteristic

(ROC) curves

NN

YY

Results: statistical study

Based on 98 days of CAT forecasts above 10,000 feet in 2008:

3330 PIREPs 1688 PIREPs 33 PIREPs

Results: statistical study

McCann, Knox & Williams (2012)

• Our proposed CAT forecasting algorithm is the only one to

attempt an end-to-end approach, starting with a gravity

wave forcing mechanism and ending with predicted TKE

production rates

• Unlike many CAT forecasting algorithms, ours is dynamical

in nature, not statistical

• Limitation: we assume that gravity waves produce CAT at

their point of generation, without propagating

• Our results suggest that significant improvements in CAT

forecasting could result if the method became operational,

e.g. by being added to the GTG basket of diagnostics

Part 1: Summary

Part 2. Response of CAT to

climate change

In collaboration with:

Manoj Joshi, University of East Anglia, UK

K

m/s

Motivation

Lee et al. (2008)

Zonal-mean

temperature

change

(2xCO2 – CTRL)

in four climate

models

y

T

z

u

y

z

u

equator north pole

... but cools the

stratosphere...

More CO2

warms the

troposphere...

... implying

stronger wind

shears at

cruise altitudes

Motivation

Lorenz & DeWeaver (2007)

Motivation • CAT is linked to upper-level jet streams (Koch et al. 2005), which

are projected to be strengthened by anthropogenic climate

change (Lorenz & DeWeaver 2007)

• Four CAT diagnostics have increased by 40-90% over the period

1958-2001 in the North Atlantic, USA, and European sectors in

ERA40 reanalysis data (Jaeger & Sprenger 2007)

– However, “changes in the amount and type of assimilated data used

for ERA40 were not taken into account and may have affected the

absolute values of the calculated trends”

• Moderate-or-greater upper-level turbulence has increased over

the period 1994-2005 in USA pilot reports (Wolff & Sharman 2008)

– However, “given that we only have 12 years worth of data, it is difficult

to assign much significance to this trend… a more thorough analysis

is required to verify its existence…”

Motivation Ja

eg

er

& S

pre

ng

er

(20

07

)

1958 2002 Jan Dec

Motivation F

AA

(2

00

6)

1982 2003

Number of series injuries (including fatalities) caused by

turbulence, per million flight departures (US carriers)

Caused by increase in

load factors?

Methodology • We use the GFDL-CM2.1 model (Delworth et al. 2006)

– this is a CMIP3 model with a high top level and daily data

– atmosphere resolution is 2.52.0, with 24 levels (5 above 200 hPa)

– the upper-level winds in the northern extra-tropics agree well with

reanalysis data (Reichler & Kim 2008)

– the jet stream in the North Atlantic sector strengthens under global

warming (Stouffer et al. 2006), consistent with other CMIP3 models

• We take 20 years of daily-mean data from each of two simulations:

pre-industrial control and doubled-CO2

– focus on winter, which is when Northern Hemispheric CAT is most

intense (Jaeger & Sprenger 2007)

– calculate CAT diagnostics on the 200 hPa pressure level, which close

to typical cruise altitudes

– focus on the North Atlantic flight corridor, one of the world’s busiest,

with 300 flights per day in each direction (Irvine et al. 2013)

Daily maps of TI1 in one December

22

TI1

y

u

x

v

y

v

x

u

z

u

PRE-INDUSTRIAL DOUBLED CO2

Histograms of TI1 in DJF

Williams & Joshi (2013)

50-75N,

10-60W The probability

of moderate-or-

greater (MOG)

CAT increases

by 10.8%

The median

strength of

CAT

increases by

32.8%

Diagnostic Units Pre-

Industrial

Median

Doubled-

CO2

Median

Change

( %) in

Median

Change (%)

in Frequency

of MOG

Magnitude of potential vorticity PVU 6.84 6.86 +0.3 +106.0

Colson–Panofsky index 103 kt2 -34.8 -34.3 +1.5 +167.7

Brown index 10-6 s-1 77.1 79.2 +2.7 +95.5

Magnitude of horizontal temperature gradient 10-6 K m-1 5.75 6.46 +12.2 +45.3

Magnitude of horizontal divergence 10-6 s-1 2.82 3.17 +12.3 +110.4

Magnitude of vertical shear of horizontal wind 10-3 s-1 1.88 2.14 +13.8 -1.0

Wind speed times directional shear 10-3 rad s-1 0.952 1.088 +14.2 +142.8

Flow deformation 10-6 s-1 18.6 21.5 +15.6 +96.0

Wind speed m s-1 14.9 17.3 +16.3 +94.8

Flow deformation times vertical temperature gradient 10-9 K m-1 s-1 8.17 9.97 +22.0 +147.3

Negative Richardson number - -127.2 -97.9 +23.0 +3.2

Magnitude of relative vorticity advection 10-10 s2 2.33 2.95 +26.7 +138.2

Magnitude of residual of nonlinear balance equation 10-12 s-2 161 204 +27.1 +73.8

Negative absolute vorticity advection 10-10 s-2 2.05 2.63 +28.2 +144.0

Brown energy dissipation rate 10-6 J kg-1 s-1 116 151 +30.0 +7.9

Relative vorticity squared 10-9 s-2 0.221 0.293 +32.5 +86.2

Variant 1 of Ellrod’s Turbulence Index 10-9 s-2 31.5 41.9 +32.8 +10.8

Flow deformation times wind speed 10-3 m s-2 0.251 0.341 +35.9 +92.9

Variant 2 of Ellrod’s Turbulence Index 10-9 s-2 28.8 39.4 +36.8 +11.6

Frontogenesis function 10-9 m2 s-3 K-2 56.6 86.1 +52.1 +125.6

Version 1 of North Carolina State University index 10-18 s-3 11.1 22.5 +102.9 +63.6

mostly in

range

40-170%

mostly in

range

10-40%

GTG

GTG

GTG

GTG

GTG

GTG

GTG

Agreement on change in DJF

Williams & Joshi (2013)

LHRSFO

• A basket of 21 CAT measures diagnosed from climate

simulations is significantly modified if the CO2 is doubled

• At cruise altitudes within 50-75N and 10-60W in winter,

most measures show a 10-40% increase in the median

strength of CAT and a 40-170% increase in the frequency of

occurrence of moderate-or-greater CAT

• We conclude that climate change will lead to bumpier

transatlantic flights by the middle of this century

• Implications:

– Flight paths may become more convoluted to avoid stronger, more

frequent patches of turbulence, in which case journey times will

lengthen and fuel consumption and emissions will increase

– The large-scale atmospheric circulation could be impacted, because

CAT contributes significantly to troposphere–stratosphere exchange

Part 2: Summary

Williams, PD and Joshi, MM (2013) Intensification of transatlantic aviation turbulence in

response to anthropogenic climate change. Nature Climate Change 3(7), 644-648.

Knox, JA, McCann, DW and Williams, PD (2008) Application of the Lighthill-Ford theory of

spontaneous imbalance to clear-air turbulence forecasting. Journal of the Atmospheric

Sciences 65(10), 3292-3304.

Williams, PD, Haine, TWN and Read, PL (2008) Inertia-gravity waves emitted from balanced

flow: observations, properties, and consequences. Journal of the Atmospheric Sciences

65(11), 3543-3556.

Williams, PD, Haine, TWN and Read, PL (2005) On the generation mechanisms of short-

scale unbalanced modes in rotating two-layer flows with vertical shear. Journal of Fluid

Mechanics 528, 1-22.

p.d.williams@reading.ac.uk

www.met.reading.ac.uk/~williams

Further information