1. Global Downscaling Hans von Storch and Frauke Feser
von Storch, H., H. Langenberg and F. Feser, 2000: A spectral nudging technique for dynamical downscaling purposes. Mon. Wea. Rev. 128:
Yoshimura, K., and M. Kanamitsu, 2008: Dynamical global downscaling of global reanalysis. Mon. Wea. Rev., 136, 2983– 2998, doi: /2008MWR
Schubert-Frisius, M., F. Feser, H. von Storch, and S. Rast, 2017: Optimal spectral nudging for global dynamic downscaling. Mon. Wea. Rev., DOI: /MWR-D
von Storch, H., F. Feser, B. Geyer, K. Klehmet, 李德磊 (Li D.), B. Rockel, M. Schubert-Frisius, N. Tim, and E. Zorita, 2017: Regional re-analysis without local data - exploiting the downscaling paradigm. J. Geophys. Res. - Atmospheres, DOI: /2016JD026332
Hans von Storch and Frauke Feser
Institute of Coastal Research Helmholtz Zentrum Geesthacht
Germany
中国海洋大学, 12. October 1017

2. The concept of downscaling
The downscaling concept CS = f(CL, ψS) with CL = large-scale climate and CS = small-scale climate and ψS small-scale physiographic details.
The parameters describing the climate may be statistics of dynamical state variables (say stream-function, temperature, pressure) or impact variables (such as phenological data).
f may be an empirical model or a dynamical (process based) model.

3. The concept of downscaling
Both concepts, empirical an dynamical downscaling are commonly employed methods.
The regional climate is conditioned by the larger-scale climate:
Certainly applicable at mid-latitude atmosphere.
Utility for tropical atmosphere not systematically studied.
Utility for oceanic mesoscale phenomena presently studied.

4. An example of empirical downscaling: rainfall as a 2-state first-order Marchov 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.
The four parameters are p11 , p10 , k , and  = k θ (the mean). They can be estimated from the data.
Busuioc, A., and H. von Storch, 2003: Conditional stochastic model for generating daily precipitation time series, Clim. Res. 24,

5. 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)
Busuioc, A., and H. von Storch, 2003: Conditional stochastic model for generating daily precipitation time series, Clim. Res. 24,

6. Regional dynamical downscaling
A mathematically well-posed approach of regional climate modelling is achieved when the task of describing the dynamics of regional and smaller scales is formulated as a state space problem, which is conditioned by large scales.
The genesis of regional climate is better framed as a downscaling problem and not as a boundary value problem.

7. 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

8. 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 scales smaller scales.
No improvement of the dynamics and events on scales, which are already well done by the global system

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

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

11. 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

12. The case of small regions (< 500 km)
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? Mon. Wea. Rev., in press doi: /MWR-D

13. Examples of regional dynamical downscaling
李德磊 (Li D.), H. von Storch, and B. Geyer, 2016: High resolution wind hindcast over the Bohai and Yellow Sea in East Asia: evaluation and wind climatology analysis; Journal of Geophysical Research - Atmospheres 121,
陈飞 (Chen F.), and H. von Storch, 2013 : Trends and variability of North Pacific Polar Lows, Advances in Meteorology 2013, ID , 11 pages,

14. Improved presentation of in coastal regions
ERA-I-driven multidecadal simulation with RCM CCLM over East Asia (李德磊, 2016)
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

15. QuikSCAT/ ERA I-reanalysis Quikscat/ regional downscaling
李德磊, 2016

16. 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 , 2016)

17. 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

18. 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

19. 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

20. Global dynamical downscaling
Schubert-Frisius, M., F. Feser, H. von Storch, and S. Rast, 2017: Optimal spectral nudging for global dynamic downscaling. Mon. Wea. Rev., DOI: /MWR-D
von Storch, H., F. Feser, B. Geyer, K. Klehmet, 李德磊 (Li D.), B. Rockel, M. Schubert-Frisius, N. Tim, and E. Zorita, 2017: Regional re-analysis without local data - exploiting the downscaling paradigm. J. Geophys. Res. - Atmospheres, DOI: /2016JD026332
Following a suggestion by
Yoshimura, K., and M. Kanamitsu, 2008: Dynamical global downscaling of global reanalysis. Mon. Wea. Rev., 136, 2983– 2998, doi: /2008MWR
Data available at CEN, U Hamburg

21. The numerical grid of an Atmospheric General Circulation model
Forced with sea surface temperature, sea ice properties, soil properties, and solar radiation – as given by „observations“ or provided within a coupled model system
ECHAM6 T255L95,
SST and sea ice as lower boundary conditions
Spectral nudging towards NCEP I reanalysis applied for vorticity and divergence with a specific height profile
By NOAA - Public Domain,

22. High-resolution, global multidecadal climate reconstructions,
ECHAM6 T255L95
Grid resolution about 50 km
SST and sea ice as lower boundary conditions
Spectral nudging towards large-scale vorticity and divergence (≤ T30) of NCEP I reanalysis
Forced with sea surface temperature, sea ice properties, soil properties, and solar radiation – as given by „observations“ - but also by nudging towards the large scale flow state (spectral nudging)
Schubert-Frisius, et al. 2017, Monthly Weather Review
By NOAA - Public Domain,

23. 23

24. 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 the decade 1999 (Dec) (Nov). ERA-Interim re-analysis data are used as reference. Contour interval: 0.2.
The variable examined is 10-m wind, filtered by retaining T31-T135 and removing the diurnal cycle.
von Storch et al., 2017 JGR - Atmospheres

25. Tropical storm tracks in 2004: Dianmu, Songda and Tokage
Typhoon tracks according to the global downscaling simulation (ECHAM6) and according to the „Best Track Data“ (BTD).
The core pressures of the global downscaling simulation are less deep than those in BTD.

26. Simulation of extratropical storm “Christian”, October 2013
Felicia Brisc, Martina Schubert-Frisius and Frauke Feser
The storm tracks according to the global downcsaling, to a regional downscaling with a 25 km grid resolution, and to the operational German Weather Service (DWD) analysis .
The core pressures:
regional downscaling > DWD > global downscaling

28. Comparing the performance of global and regional downscaling
Global downscaling vs NCEP1
Regional downscaling vs global downscaling (similar horizontal resolution)
Regional downscaling vs global downscaling (RCM: 7 km, GCM 50 km)
Brier Skill Scores for surface wind speed of reconstructions in the Bohai and Yellow Sea, using QuikSCAT satellite data as “truth”, Dec – Nov. 2009
von Storch et al., 2017, JGR - Atmospheres

29. Added value of downscaling
Homogenously described regional detail, consistent with the prescribed large-scale state, across (up to) six decades
Improved description of regional dynamical processes because of increased spatial resolution (e.g., polar lows, tropical storms, low level jets or vortex streets).
Improved description of effects of regional physiographic patterns (in particular coasts, mountain ranges).
Regional statistics and their change in regions with insufficient observational data coverage.

30. Conclusion …
Downscaling (CS = f(CL,ψs)) works with respect to atmospheric dynamics.
A key assumption for downscaling is the reliability and homogeneity of the large scale states, which are processed in the downscaling.
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) with regional or global models
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) also in regions with little or no local observations.
For grid resolutions of 10 km and more, global reconstructions are possible, with comparable performance as regional models.