14 June 2017
Advanced Atmospheric and Oceanic Science Lecture Series, NUIST 南京
Downscaling: empirical and dynamical,
atmosphere and ocean
Hans von Storch
Geesthacht, Hamburg and Qingdao
Scaling cascade
and climate models
Global climate
Formation of the general
circulation on an aqua planet
from a state of rest
(from Fischer et al., 1991)
Risbey and Stone (1996)
Continental climate
Long term mean of
- zonal wind at 200 hpa,
- geopotential, height at 500 hPa, and
- band-pass filtered variance of 500 hpa
geopotential height („storm track“)
caused by planetary scale land-sea
contrast and orographic features
Regional climate
Composites of
air pressure (left)
and zonal wind
(right) for day
before intense
precip in the
Sacramento
Valley (top), on
the day of
maximum precip
(middle)
Averaged over
the ten most
intense precip
events.
Regional climates do not make up global climate.
Instead, regional climate should be understood as the result of an
interplay of global climate and regional physiographic detail.
The local processes are important for the formation of the global
climate not in terms of their details but through their overall
statistics.
Implications:
• Planetary scale climate can be modeled with dynamical models
with limited spatial resolution
• The success on planetary scales does not imply success on
regional or local scales.
• The effect of smaller scales can be described summarily
through parameterizations.
Dynamical processes in a
global atmospheric general circulation model
Climate = statistics of weather
The genesis of climate
Cs = f(Cl, Φs)
 “downscaling”
with
Cl = given by global simulations and
global re-analyses
Cs = smaller scale states or statistics
Φs = parameters representative for
regional features
f = statistical or dynamical model
Statistical downscaling:
Determining statistics of
impact variables
von Storch, H. and H. Reichardt 1997: A scenario of storm surge statistics for the
German Bight at the expected time of doubled atmospheric carbon dioxide
concentration. - J. Climate 10, 2653-2662
The case of intraseasonal stormrelated sea level
variations in
Cuxhaven (at the
mouth of the river
Elbe)
Annual percentiles of the approximately
twice-daily hig-tide water levels at
Cuxhaven after subtraction of the linear
trend in the annual mean. From top to
bottom, 99%, 90%, 80%, 50%, and
10% percentiles.
Units are centimeters.
One vector time series St is formed by the
coefficients of the first four empirical
orthogonal functions (EOFs) of winter
[December–February (DJF)] monthly mean air
pressure distributions. Prior to the EOF
analysis, the air pressure data were centered;
that is, the long-term mean distribution was
subtracted so that anomalies were obtained.
The other vector time series Qt is threedimensional, featuring the 50%, 80%,
and 90% percentiles of winter intra- monthly
storm-related water-level distributions:
Q = (q50%, q80%, q90%)
The result of a CCA is pairs of vectors (ps;k,
pq;k) and time coefficients as;k(t) and aq;k(t) so
that
St = k as,k (t) ps;k
and
Qt = k aq,k (t) pq;k
Canonical Correlation
Analysis (CCA)
The coefficients as,1 and aq,1 have maximum
correlation, the coefficients as,2 and aq,2 have
maximum correlation after subtraction of the
1st components, and so forth
The analysis describes which
anomalous monthly mean largescale pressure anomalies in winter
over the North Atlantic are
associated with which intramonthly anomalies of 50%, 80%
and 90% percentiles of storm water
variations at Cuxhaven
First two characteristics patterns ps;1 (top)
and ps;2 (bottom) of monthly mean air
pressure anomalies over the northeast
Atlantic.
The coefficients of these CCA vectors
share a maximum correlation with the
coefficients of the water-level percentile
patterns given on the right.
Units are hPa.
Time series of 90% percentiles of intramonthly storm-related water-level
variations in Cuxhaven, as derived from in
situ observations (solid) and estimated
from the monthly mean air pressure field
(dashed).
Statistical downscaling:
generating time series
through conditional
weather generators
Busuioc, A., and H. von Storch, 2003: Conditional stochastic model for
generating daily precipitation time series, Clim. Res. 24, 181-195
A „rainfall generator“ is a stochastic
process, which mimics the behavior of
rainfall as a sequence of either „wet“ or
„dry“ days. A specific rainfall generator
makes use of four parameters:
a) The probability to have wet day
following another wet day
Prob(wt|wt-1) = p11
Then Prob(dt|wt-1) = 1-p11
b) The probability to have wet day
following a dry day
Prob(wt|dt-1) = p01
Then Prob(dt|dt-1) = 1-p01
c) c) The amount of rainfall on a „wet“
day is described by a  -distribution
(k,θ) with „shape“ parameter k and
„scale“ parameter θ.
Rainfall as a 2-state
first-order Markov chain
The four parameters are p11 , p10 , k ,
and  = k θ (the mean).
They can be estimated from the data.
Patterns of the first CCA pair of
winter mean SLP and winter
parameters of precipitation
distribution derived from the
first half of the observations
(1901–1949)
Winter standardized anomalies of the precipitation distribution parameters for 1901–
1999 derived from observations (solid line) and derived indirectly from the observed
European-scale SLP anomalies using the downscaling model (dashed line) fitted
to the 1901–1949 data
Dynamical downscaling:
Regional models as
downscaling tool
conventional set-up
Regional atmospheric modelling: nesting into a global state
Regional atmospheric models serve the purpose to describe the dynamics at
regional and smaller scales well.
Ideally, regional models would return one unique solution given a set of
boundary values. However, this is not the case.
Mathematically, there is no unique solution for a given set of each boundary
values. The problem is not a boundary / initial value problem.
A numerical problem is that the wave propagation velocity depends on grid
resolution, so that waves travelling within and outside the limited area will
arrive at the outgoing boundary at different times. This problem was solved by
introducing the sponge zone, by Hughes Davis, in 1972.
The sponge-zone does not solve the problem of the non-existence of a well
defined solution of the boundary value problem.
When formulated as a boundary
value problem, and integrated on
a grid, an ensemble of solutions
emerges.
It is unknown (to me), how this
ensemble of solutions look like.
Rinke, A., and K. Dethloff, 2000: On the
sensitivity of a regional Arctic climate model
to initial and boundary conditions. Clim.
Res. 14, 101-113.
Ensemble standard deviations
of 500 hPa height [m²/s²]
Big Brother Experiments
In Big Brother experiments, a
global simulation BB with high
resolution is done.
A subarea is cut out, and
coarsened values of BB at the
boundary prescribed; then
LAM is run.
It turns out that – at least in
case of a strongly flushed flow
– the small scale dynamical
features of BB reappear in the
LAM simulation.
Denis, B., R. Laprise, D. Caya and J. Cote, 2002: Downscaling ability of one-way nested regional
climate models: The Big brother experiment. Climate Dyn. 18, 627-646.
Evolution of the specific humidity at 700 hPa
during the first 96 hours, sampled every 24
hours. The left column is the control big
brother.
The inner squares of the right column
correspond to the little-brother domain while the
area outside these squares are the filtered bigbrother humidity used to nest the little brother.
Denis, B., R. Laprise, D. Caya and J. Cote, 2002: Downscaling ability of one-way nested regional
climate models: The Big brother experiment. Climate Dyn. 18, 627-646.
Dynamical downscaling:
Large scale constraining
(spectral nudging)
variance
global model
Insufficiently
resolved
Well resolved
Spatial scales
variance
regional model
Insufficiently
resolved
Well resolved
Spatial scales
Added value
• A mathematically well-posed problem is achieved
when the task of describing the dynamics of
determining regional and smaller scales is formulated
as a state space problem, which is conditioned by
large scales.
• Physically, this means that genesis of regional
climate is better framed as a downscaling problem and
not as a boundary value problem.
3-d vector of state
RCM
Physiographic
detail
State space equation
Ψ t 1  F(Ψ t ;ηt )  εt
Observatio n equation
d t  G(Ψ t )  δt
Known large scale
statewit h
 t ,  t  model and observatio n errors
F  dynamical model
projection of full state on
G  observatio n model
large-scale scale
Ψ t*1  F(Ψ t ;ηt )
Forward integratio n :
d t*1  G (t*1 )
 Ψ t 1  Ψ t*1  K(d t*1  d t 1 )
with a suitable operator K .
Large-scale
(spectral) nudging
Expected added value
Statistics and events on scales, which are not well resolved
for the global system, but sufficiently resolved for the
regional model.
In particular, increased variance on smaller scales.
No improvement of the dynamics and events on scales,
which are already well done by the global system
Useful quantities to check
1.
2.
3.
4.
5.
Similarity of large-scale state
Unchanged variance of large scales
Dissimilarity of regional scales
Increased variance on regional scales
Distributions of quantities in physiographic complex
regions
6. Extremes
7. Regional dynamical features, such as polar lows,
tropical storms, medicanes, low level jets
Nudging of the large
scales
global
Pattern correlation coefficients for
zonal wind at 500 hPa between
the global reanalyses and the
regional
RCM with standard forcing via the
lateral boundaries and the
RCM with spectral nudging
Northern Europe
Improved presentation of
in coastal regions
• ERA-I-driven multidecadal simulation with RCM CCLM
over East Asia (李德磊, 2015)
• Grid resolution: 0.06o
• Employing spectral nudging (wind above 850 hPa, for
scales > 800 km)
• Usage of Quikscat-windfields (QS) over sea as a
reference
• Considering ratios 2QS:2ERA and 2QS:2RCM
• Determining Brier Skill score for all marine grid boxes
B = 1 – (RCM-QS)2 / (ERA-QS)2
QuikSCAT/
ERA I-reanalysis
Quikscat/
CCLM regional simulation
李德磊, 2015
QuikSCAT:
Added Value –
Brier skill score vs. ERA
Open Ocean:
No value added by dynamical
downscaling
Coastal region:
Added Value in complex
coastal areas
李德磊, 2015
Coastal stations
Offshore stations
Comparison of CCLM (left-panel, y-axis) and ERA-I (right-panel, y-axis) wind data
with observations from two coastal stations and two offshore wind observations (xaxis).
Scatter plots (grey dots), qq-plots and several statistical measures (李德磊 , 2015)
Improved representation of
sub-synoptic phenomena
• NCEP-driven multidecadal simulation with RCM CLM
over North Pacific (陈飞 et al., 2012, 2013, 2014)
• Grid resolution: about 0.4o
• Employing spectral nudging (wind above 850 hPa, for
scales > 800 km)
• Simulation of sub-synoptic phenomena
• Polar lows in the Northern North Pacific
North Pacific
Polar Lows
(陈飞 et al., 2012, 2013
and 2014)
North Pacific Polar Low
on 7 March 1977
NOAA-5 infrared satellite image at
09:58UTC 7th March 1977
Annual frequency of past polar lows
in the North Pacific
Number of detected Polar Lows in the North Pacific per Polar
Low season (PLS; October to April). The trend from 62 PLSs,
from 1948/1949 to 2009/2010, amounts to 0.17 cases/year.
陈飞 et al., 2013
Scenarios of Polar Low Formation in the North
Pacific
A1B_1: -0.29
A2_1: -0.49
A1B_1: -0.29
A1B_2: -0.24
A1B_3: -0.25
陈飞 et al., 2014
Improved representation of
forcing fields for impact models
• NCEP-driven multidecadal simulation with RCM REMO
in Europe
• Grid resolution: 0.5 o
• Employing spectral nudging (wind above 850 hPa, for
scales > 800 km)
• 1948-2010 simulation
• Wind and air pressure used to drive models of sea level
and circulation of marginal seas (not shown) for
describing currents and sea level
• Wind used to drive models of the statistics of surface
waves (ocean waves) in coastal seas (North Sea).
Extreme wind events simulated compared to local
observations
simuliert
Weisse, pers. comm.
significant wave height
[days]
wave direction
[days]
Red: buoy, yellow: radar, blue: wave model run with REMO winds
Gerd Gayer, pers. comm., 2001
What happens if we make the region
- small, say: < 500 km?
- very large, say global?
Pressure isobars
with shaded wind
speed fields
for two simulations
with (right: SN) and
without (left: NN)
spectral nudging
of a small region.
Spectral nudging is
not needed in a
small region (of
500 km or less
extension, as the
lateral steering is
sufficient for
enforcing a
(practically) unique
solution in the
interior.
Schaaf, B., H. von Storch, F. Feser: Has spectral nudging an effect for
dynamical downscaling applied in small (500 km and less) regional model
domains? – in review
Lateral constraint too weak to maintain large-scale in the interior if
flushing time too long (Example: May 1993; strongly non-zonal flow) Castro and Pielke, 2004)
In some cases, the
kinetic energy in the
interior of the nested
grid can not be
maintained.
small
-- large integration area
Global
Downscaling
with global
AGCM,
spectrally
nudged to NCEP
reanalysis.
Added value
generated in
complex coastal
and
mountaineous
regions (in red).
Global distribution of Brier Skill Score, comparing the global downscaling data with
the driving NCEP1 re-analysis, for 6 hourly 10m wind speed for the decade 1999
(Dec) - 2009 (Nov). ERA-Interim re-analysis data are used as reference. The diurnal
cycle has been taken out. Contour interval: 0.2.
Von Storch, et al., 2017, submitted
Conclusion …
• Downscaling (Cs = f(Cl,Φs)) works with respect to atmospheric
dynamics – ocean dynamics: needs more analysis.
• Several options,
- statistical downscaling, generating characteristics of
distributions and processes, such as monthly means, intramonthly percentiles, parameters of Markov processes etc.
- dynamical downscaling using „state-space“ formulation of largescale constraining (spectral nudging)
• Added value on
- medium scales (in particular coastal regions and medium scale
phenomena (in particular storms)
- in generating regional impact variables, in particular wind for
storm surges and ocean waves.
• Downscaling allows the generation of homogeneous data sets
(i.e., data sets of uniform quality across many decades of years)