Alpine Summer School, 17 June 2014, Valsavarenche

Atmospheric turbulence and climate change

Paul Williams University of Reading, UK

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

Scales causing aviation turbulence (Lane et al. 2012)

Scales resolved by models

Gage & Nastrom (1986)

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: – cause about 40 fatalities and 100s of serious injuries – cause structural damage to planes – cause flight diversions and delays – cost airlines $150m–$500m

Ralph et al. (1997)

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)

Probable mechanism for CAT

height (z)

The stratification, ∂ρ/∂z, is stabilizing

The wind shear, ∂u/∂z, is destabilizing Kelvin–Helmholtz instability occurs if: Ri = (-g/ρ ∂ρ/∂z) / (∂u/∂z)2 < ¼

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

Loss of balance → gravity waves  f u.

source term

 | f u. |

(Ford 1994)

laboratory interface height

Williams, Haine & Read (2005)

Hypothesised mechanism for CAT • Gravity waves generated by loss of balance destabilise the flow and initiate Kelvin–Helmholtz instability ˆ  a N /| u c | • Specifically, a gravity wave of non-dimensional amplitude a and phase φ locally modifies the flow (Palmer et al. 1986) according to



u / z  u / z 1 aˆ Ri sin



and N 2  N 2 1 aˆ cos 

• Therefore, the maximum production rates of turbulent kinetic energy (TKE) due to Kelvin–Helmholtz instability are modified by the gravity wave according to



shear   (u / z)  (u / z) 1 aˆ Ri 2

2



2

and strat   N 2  N 2 aˆ 1

• We take a  | f u. | (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)

Results: case study • 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: statistical 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 Receiver Operating Characteristic (ROC) curves

YY

Federal target for CAT forecasting (blue star)

NN Knox, McCann & Williams (2008)

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

3330 PIREPs

1688 PIREPs

33 PIREPs

McCann, Knox & Williams (2012)

Part 1: Summary • 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 2. Response of CAT to climate change In collaboration with:

Manoj Joshi, University of East Anglia, UK

K

m/s

Motivation

Zonal-mean temperature change (2xCO2 – CTRL) in four climate models

Lee et al. (2008)

Motivation ... but cools the stratosphere...

More CO2 warms the troposphere...

z

u u T  z y

y equator

... implying stronger wind shears at cruise altitudes north pole

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…”

Jaeger & Sprenger (2007)

Motivation

1958

2002 Jan

Dec

Motivation Number of series injuries (including fatalities) caused by turbulence, per million flight departures (US carriers)

FAA (2006)

Caused by increase in load factors?

1982

2003

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 2.52.0, 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 PRE-INDUSTRIAL

TI1 

u z

DOUBLED CO2

2

 u v   v u          x y   x y 

2

Histograms of TI1 in DJF

The median strength of CAT increases by 32.8%

50-75N, 10-60W

The probability of moderate-orgreater (MOG) CAT increases by 10.8%

Williams & Joshi (2013)

Diagnostic

Units

PreIndustrial Median

DoubledCO2 Median

Change ( %) in Median

Change (%) in Frequency of MOG

Magnitude of potential vorticity

PVU

6.84

6.86

+0.3

+106.0

103 kt2

-34.8

-34.3

+1.5

+167.7

10-6 s-1

77.1

79.2

+2.7

+95.5

10-6 K m-1

5.75

6.46

+12.2

+45.3

2.82 mostly in 1.88 range 0.952 10-40% 18.6

3.17

+12.3

+110.4

2.14

+13.8

-1.0

1.088

+14.2

+142.8

21.5

+15.6

+96.0

GTG Colson–Panofsky index

Brown index GTG Magnitude of horizontal temperature gradient

Magnitude of horizontal divergence

10-6 s-1

Magnitude of vertical shear of horizontal wind

10-3 s-1

Wind speed times directional shear Flow deformation Wind speed Flow deformation times vertical temperature gradient GTG Negative Richardson number

Magnitude of relative vorticity advection GTG Magnitude of residual of nonlinear balance equation

Negative absolute vorticity advection Brown energy dissipation rate Relative vorticity squared GTG Variant 1 of Ellrod’s Turbulence Index

Flow deformation times wind speed Variant 2 of Ellrod’s Turbulence Index GTG Frontogenesis function GTG Version 1 of North Carolina State University index

10-3 rad s-1 10-6 s-1 m s-1

14.9

17.3

+16.3

+94.8

10-9 K m-1 s-1

8.17

9.97

+22.0

+147.3

-127.2 mostly in 2.33 range 161 40-170% 2.05

-97.9

+23.0

+3.2

2.95

+26.7

+138.2

204

+27.1

+73.8

2.63

+28.2

+144.0

10-6 J kg-1 s-1

116

151

+30.0

+7.9

10-9 s-2

0.221

0.293

+32.5

+86.2

10-9 s-2

31.5

41.9

+32.8

+10.8

10-3 m s-2

0.251

0.341

+35.9

+92.9

10-9 s-2

28.8

39.4

+36.8

+11.6

10-9 m2 s-3 K-2

56.6

86.1

+52.1

+125.6

10-18 s-3

11.1

22.5

+102.9

+63.6

10-10 s2 10-12 s-2

10-10 s-2

Agreement on change in DJF

LHRSFO

Williams & Joshi (2013)

Part 2: Summary • A basket of 21 CAT measures diagnosed from climate simulations is significantly modified if the CO2 is doubled • At cruise altitudes within 50-75N and 10-60W 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

Further information 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 shortscale unbalanced modes in rotating two-layer flows with vertical shear. Journal of Fluid Mechanics 528, 1-22.

[email protected] www.met.reading.ac.uk/~williams