Alpine Summer School, 17 June 2014, Valsavarenche ... · Clear-air turbulence (CAT) • CAT occurs...
Transcript of Alpine Summer School, 17 June 2014, Valsavarenche ... · Clear-air turbulence (CAT) • CAT occurs...
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.
www.met.reading.ac.uk/~williams
Further information