S. Lovejoy, D. Varon
Physics dept., McGill U.
Abstract
What is the climate?
Prevailing definitions of climate are not much different from “the
climate is what you expect, the weather is what you get”. Following
discoveries in the 1980’s, analyses using new nonlinear geophysics
techniques show that this dictum is fundamentally wrong. In addition to the
weather and climate, there is a qualitatively distinct intermediate
“macroweather” regime spanning a factor of ≈ 1000 in scale from about 10
days to 30 years. Mean temperature fluctuations increase up to about 5 K at
10 days (the lifetime of planetary structures), then decrease to about 0.2 K
at 30 years, and then increase again to about 5 K at glacial-interglacial
scales. Averaging macroweather over periods increasing to ≈ 30 yrs yields
apparently converging values: macroweather is “what you expect”.
Macroweather averages over ≈30 years have the lowest variability, yield well
defined “climate states” and justify the otherwise ad hoc “climate normal”
period. However, moving to longer periods, these states increasingly
fluctuate: just as with the weather, the
climate changes in an apparently unstable manner; the climate is not what
you expect. The trichotomy weather – macroweather – climate opens up
new vistas. Some of these:
a) Forecasts: exploitation of the long-term memory allow stochastic
forecasts.
b) Attribution: statistical testing to distinguish natural and anthropogenic
changes.
c) Data analysis: systematic scale by scale statistical evaluation and
comparisons of data, paleodata and multiproxies,
d) Regionalization: space-time relations in the macroweather and climate
regimes show how the notion of “regional” depends on the time scale.
e) Model uncertainty: assessing the extent by which existing models are
missing important slow processes.
“Climate is what you expect, weather is what you get.”
Lazarus Long, character in R. Heinlein 1973 (also attributed to Mark Twain)
“...let me express my conviction that ... a definition [of climate],
when found must agree in spirit with the statement, ‘climate is
what you expect’.”
Difference, Tendency, Haar fluctua2ons E. Lorenz, 1995
“Climate is conventionally defined as the long-term statistics of the weather…
[we propose]…to expand the definition of climate to encompass the oceanic
and terrestrial spheres as well as chemical components of the atmosphere”.
“Climate in a narrow sense is usually defined as the "average weather" ... The
classical period is 30 years, as defined by the World Meteorological Organization
(WMO)… Climate in a wider sense is the state, including a statistical description, of
the climate system.”
Differences: The difference in temperature between t
and t+Δt
Tendency: The average of the temperature (with overall mean
removed)
between t and t+Δt
-Intergovernmental Panel on Climate Change, 2007
Trichotomy not Dichotomy
ΔI = ϕ Δt
Climate
(10-30 yrs to
50,000 yrs)
=constant
Weather:
Δt < τw (≈ 10 days): H>0,
Fluctuations grow with scale
(10 days to
10-30 yrs)
H ≈ -0.4: Fluctuations Decreasing
(up to 10 days)
forcing
5K
20CR
grid
Scale
75oN
lw
0.5
-0.4
10-2
10-1
Why
“Macroweather” ?
75N
Global
10-4
10-3
10-2
10-1
1
2
10
20th C reanalysis
≈10 days
≈10 -100 yrs
Glacial/
interglacial
amplitude
10yrs
100yrs
25S
Vostok
1000
Data
-
GRIP
Two data sources only GRIP, 20CR
20CR
weather
0.4
Multiproxies
Surface
Models
<2003
0.1 K
Low frequency weather
PDO
Weather
τo
60
R
10 yrs
- 50o
τc for Temperature, Rainrate
latitude
- 0.4
- 0.6
macroweather
Data: 20CR, 1871-2008
2
3
1 year
macroweather
Log10 <
Log10 t (yrs)
1.5
2.0
-0.2
100 yrs
-0.5
Temepratures
and forcings
(using 4.5K/
W/m2
sensitivity)
5K Gao
0.4
RF CO2
Vostok
±3K
Krivova
2007
Spectrum of hourly temperature data from 4
stations in US note the scaling weather regime
(high requencies) and the near flat low frequency
macroweather regime
climate
RMS Temperature fluctuations as functions over land, SST, Pacific Decadal
Oscillation (PDO), globally averaged surface temperatures and a theoretical
quasi Gaussian (Orenstein-Uhlenbeck) process.
Global
Surface
0.1 K
0.1 K
0.5K
Shapiro
2011
102
multiproxies
1500-1980
multiproxie
s
20 K
Veizer
(3.8K/δ18O)
Hourly
Station
scale
45oN
τw= 10 days
(3.8K/δ18O)
104
105
106
yrs
0.1 K
τc=25yrs
107 108 109
Log10Δt (yrs)
(1K/
δ18O)
10-4
10-3
Epica
±3K
±2K
(D converted to T)
0.5
20CR 75oN
grid
10-2
10
10-1
102
0.4
Zachos
(3.8K/δ18O)
Huybers
climate
0.5K
τlc= 50kyrs
103
104 105 106
- 0.5
NH
multiproxies
Huybers
(3.8K/δ18O)
0.2 K
Steinhilber
2009
τlc= 50kyrs
-0.1
weather
Macroweather
107 108 109
Log10Δt (yrs)
Surface
20CR
global
Selected RMS Temperature fluctuations compared to those from selected
radiative forcings assuming 4.5K/W/m2.
Veizer
(3.8K/δ18O)
(D converted to T)
GRIP
55cm
0.4
(3.8K/δ18O)
105
climat
e
Vostok
Zachos
103
Low
frequency
climate
Log10<ΔT2>1/2 (K)
10 K
5K
- 0.5
104
NH
-0.1
All: 1 hour-5.53x108yrs
±2K
(Antarctic)
>2003
-0.5
climate
0.5
10
105yrs
τlc= 50kyrs
±2K
102
104
multiproxies
±3K
0.5
Log10 t (yrs)
1 K 1yr
-2
10
TIMS
satellite
(solar)
paleo
5K
Vostok
2009
Log10<ΔT2>1/2 (K) Benthic
20 K
10 K
Orbital
Variations of
90o N midJune
insolation/20
(K)
Macroweather
τc=25yrs
Climate Sensitivities
T2>1/2
(D converted
to T)
Macroweathe
r
climate
Vostok
- 0.5
NH
4
0.2 K
T
50o
1.0
- 0.2
Global
average
Longitud
e to
longitud
e spread
(T)
40
20
Monthly temperature series from 1911-2010 on a 5ox5o grid; the NOAA NCDC data
-0.4
1yr 0.5
- 0.5
OU process
τc (yrs)
1
weather
Log10 < T2>1/2 (K)
0.2
0.5
Ocean
“weathe
r”
1 day
0.4
102
1 K 1yr
(days)
Precipitation fluctuations as functions
of latitude (CPC, gages 1949-1976, US
and 20CR reanalysis, 1871-2008)
1K
SST
Low frequency
Ocean
“weather”
-1
Log10 t
τc=25yrs
0.5
Log10Δt (yrs)
-0.1
±2K
(D converted
to T)
(1K/δ18O)
0.4
±3K
Epica
55cm
- 0.5
0.1 K
weather
(control)
2K
Longitud
e to
longitud
e spread
(R)
-0.5
5K GRIP
10
1 K 1yr
Global
Surface
series
- 2.5
Log10 < ΔT2>1/2 (K)
102
τw= 10 days
Log10Δt (yrs)
0.01 mm/hr
EFS
0.4
80
- 2.0
Northern Hemisphere
(control) FIF
(cascade)
10-2
-0.4
Paleo ice cores
10K
τc=25yrs
0.5
20CR global
0.001 mm/hr
climate
20CR grid
all globe
10-4 10-3
20K
< ΔT2>1/2
5K
0.4
(1) = H= -0.42
-0.1
- 0.5
RMS Temperature fluctuations as functions of
latitude (and 20CR reanalysis, 1871-2008)
Multiproxies
Low frequency weather, low frequency “ocean
Low
weather”
τw
2
macroweather
Land
Ocean Drifter data:
εo ≈10-8 m2/s3
τo≈ εo1/3L-2/3 ≈ 1 yr
1
t
0.25K
0.6
frequency
weather
Log 10
weather
IPSL
Lovejoy and Schertzer 2011
-1
2
0.5K
Scale
Macroweather
- 1.5
2K
-0.3
5N,S
Log10Δt (yrs)
0.5 K
20CR
- 0.5
global
FIF
0.5
25N
Log10
10K(K)
Hourly
Station
scale
45oN
(1) = H = 0.15
- 1.0
5K
75S
1K
Orbital
forcing
-0.4
20K
multiproxies
20CR 75oN
grid
0.2 mm/hr
Log10 S ( t )
Log10< R>
mm/hr
Composite paleo-instrumental
temperature spectrum
Log10 < ΔT2>1/2 (K)
H ≈ 0.4: Fluctuations Growing
Data versus
models: Global
Scale, no climate
Instrumental data+
Atmospheric dynamics to 100 kyrs:
Three scaling regimes – not two
Weather
Climate:
(10- 100 yrs ≈) τc <≈ Δt <≈ 100 kyrs: H>0,
Fluctuations grow with scale; atmospheric states are
“unstable”, subject to “climate change”.
10-5
Wide scale range composites of
atmospheric variability
Macroweather
Macroweather:
(10 days ≈) τw<Δt<τc (≈ 10- 100 yrs): H<0,
Fluctuations diminish with scale;
atmospheric states are “stable”.
GRIP δ18O
Tendency fluctua2ons When 1 > H > 0: Haar ≈
difference
When 0 > H > -1: Haar ≈
tendency
Rela2ons: H ≈ 0.4: Fluctuations Growing
Difference fluctua2ons The difference between the average of
the temperature from t and t+Δt/2 and
from t+Δt/2 and t+Δt
Haar: Temperature
H
a) Forecasts/predictions: exploitation of the long-term
memory allow stochastic forecasts.
b) Attribution: statistical testing to distinguish natural and
anthropogenic changes.
c) Data analysis: systematic scale by scale statistical
evaluation and comparisons of data, paleodata and
multiproxies,
d) Regionalization: space-time relations in the
macroweather and climate regimes show how the notion
of “regional” depends on the time scale.
e) Model uncertainty: assessing the extent by which
existing models are missing important slow processes.
Schema2c of fluctua2ons -Committee on Radiative Forcing Effects on Climate, 2005 US National Academy of
Science Characteristics of the three regimes
Possible collaborative topics
climate