1. 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

2. Scaling cascade and climate models

3. Formation of the general circulation on an aqua planet from a state of rest
(from Fischer et al., 1991)
Global climate

4. Continental climate
Risbey and Stone (1996)
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

5. 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.
Risbey and Stone (1996)

6. 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.

7. Dynamical processes in a global atmospheric general circulation model7

8. Climate = statistics of weather
The genesis of climate
Cs = f(Cl, Φs)
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
 “downscaling”

9. 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,

10. The case of intra-seasonal storm-related 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.

11. Canonical Correlation Analysis (CCA)
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 three-dimensional, 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 large-scale pressure anomalies in winter over the North Atlantic are associated with which intra-monthly anomalies of 50%, 80% and 90% percentiles of storm water variations at Cuxhaven

12. 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 intra-monthly storm-related water-level variations in Cuxhaven, as derived from in situ observations (solid) and estimated from the monthly mean air pressure field (dashed).

14. 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,

15. Rainfall as a 2-state first-order Markov chain
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:
The probability to have wet day following another wet day Prob(wt|wt-1) = p11 Then Prob(dt|wt-1) = 1-p11
The probability to have wet day following a dry day Prob(wt|dt-1) = p01 Then Prob(dt|dt-1) = 1-p01
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.

16. 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)

17. 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

18. Dynamical downscaling: Regional models as downscaling tool conventional set-up

19. Regional atmospheric modelling: nesting into a global state

20. 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.

21. Ensemble standard deviations of 500 hPa height [m²/s²]
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,
Ensemble standard deviations of 500 hPa height [m²/s²]

22. 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,

23. 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 big-brother 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,

24. Dynamical downscaling: Large scale constraining (spectral nudging)

25. global model variance Spatial scales Insufficiently resolved
Well resolved
Spatial scales

26. regional model variance Spatial scales Added value
Insufficiently resolved
Well resolved
Spatial scales
Added value

27. 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.

28. Known large scale state
RCM
Physiographic detail
3-d vector of state
Known large scale state
projection of full state on large-scale scale
Large-scale (spectral) nudging

29. 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

30. Useful quantities to check
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
Extremes
Regional dynamical features, such as polar lows, tropical storms, medicanes, low level jets

31. Nudging of the large scales
global
Pattern correlation coefficients for zonal wind at 500 hPa between the global reanalyses and the
RCM with standard forcing via the lateral boundaries and the
RCM with spectral nudging
Northern Europe
regional

32. 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

33. QuikSCAT/ ERA I-reanalysis Quikscat/ CCLM regional simulation
李德磊, 2015

34. QuikSCAT: Added Value – Brier skill score vs. ERA
Open Ocean:
No value added by dynamical
downscaling
Coastal region:
Added Value in complex
coastal areas
Hier sehen wir für die selben Stationen die Perzentil-Perzentil Plots für QuikSCAT.
Die Ergebnisse werden am Ende zusammengefasst, jetzt gehe ich auf den zweiten Schwerpunkt der Arbeit ein.
李德磊, 2015

35. 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 (x-axis). Scatter plots (grey dots), qq-plots and several statistical measures (李德磊 , 2015)

36. 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

37. 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

38. 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

39. Scenarios of Polar Low Formation in the North Pacific
A1B_1: -0.29
A2_1:
A1B_1: -0.29
A1B_2: -0.24
A1B_3: -0.25
陈飞 et al., 2014

40. 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)
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).

41. Extreme wind events simulated compared to local observations
simuliert
These plots are the quantile-quantile diagrams (REMO & NCEP Vs Observations) for 10-m wind speed at 2 buoys station. The first one is an Atlantic offshore buoy (ZBGSO, located at
48.7N,12.40W), already assimilated by NCEP. The second one shows results from a Mediterranean buoy (ZATOS, located at 39.96N, 24.72E, Aegean Sea), whose data have NOT been previously assimilated by NCEP.
Weisse, pers. comm.

42. Red: buoy, yellow: radar, blue: wave model run with REMO winds
significant wave height
[days]
wave direction
[days]
Red: buoy, yellow: radar, blue: wave model run with REMO winds
Gerd Gayer, pers. comm., 2001

43. What happens if we make the region
small, say: < 500 km?
very large, say global?

44. 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

45. 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

46. 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) (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

47. 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, intra-monthly percentiles, parameters of Markov processes etc. - dynamical downscaling using „state-space“ formulation of large-scale 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)