Keynote 3.2Strategies and measures for

determining the skill of dynamical downscaling

Hans von Storch;

HZG

Lund, 17. June 2014

Overview

1. The cascade: Regional climate genesis is a downscaling phenomenon.

2. On models, their purpose and their added value

3. Boundary-initial-value problem?

4. Which added value do we ask for when doing dynamical downscaling

The cascade: Regional climate genesis is a downscaling phenomenon.

The genesis of climate

Cs = f(Cl, Φs)

with

Cl = larger scale climate

Cs = smaller scale climate

Φs = physiographic detail at smaller scale

Global climate Formation of the general circulation on an aqua planet

from a state of rest

(from Fischer et al., 1991)

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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

Continental 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)

Regional climate

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.

atmosphere

?

Dynamical processes in a global atmospheric general circulation model

Parameterizations

1.are semi-empirical closures, which describe the net effect of non-resolved dynamics on the resolved scales, conditional upon the state of the resolved scales.2.depend on the chosen resolution3.are not given by first principles4.are not physics but semi-empirical Ansätze or stochastic models.5.employ a structure, which is motivated by physical arguments.

Parameterizations are used to describe the effect of micro-scale physics, but they do not represent „physics“ by themselves.

Parameterizations are not uniquely given formulations but are subjectively chosen.

Thus, the atmospheric (oceanic) dynamics are not described by a set of differential equations but by an ensemble of difference, empirical-dynamical equations, which employ different sets of semi-empirical parameterizations.

The limit x 0 does not exist.

Models are

• • • smaller than reality (finite number of processes, reduced size of phase space)

• • • simpler than reality (description of processes is idealized)

• • • closed, whereas reality is open (infinite number of external, unpredictable forcing factors is reduced to a few specified factors)

Models have a purpose.

Models are not “models of” but “models for”.

Global atmospheric and oceanic models are models for the description of atmospheric and oceanic dynamics, conditional upon large-scale forcing (solar input; land-sea distribution; topography; composition of the atmosphere)

Open question –Which resolution Δ is needed to describe large scales well (e.g., blocking)? Which part of the (spatial) is significantly affected by the cut-off of finite resolution?

For which n is the dynamics on scales nΔ well described?

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 value / 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 H. 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.

Big Brother Experiments

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.

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.

Evolution of the specific humidity at 700 hPa during the first 96 hours, sampled every 24 hours. The left column is the control bigbrother. 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, 627-646.

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)

small-- large integration area

In some cases, the kinetic energy in the interior of the nested grid can not be maintained.

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]

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. Gap in my knowledge, or Gap in mathematical knowledge

global model

Well resolved

Insufficiently resolved

Spatial scales

vari

ance

Well resolved

Insufficiently resolved

Spatial scales

vari

ance

regional model

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.

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Concept of Dynamical Downscaling

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RCM Physiographic detail3-d vector of state

Known large scale state

projection of full state on large-scale scale

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 scales smaller scales.

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

Useful quantities to check

a)Similarity of large-scale stateb)Unchanged variance of large scalesc)Dissimilarity of regional scalesd)Increased variance on regional scalese)Distributions of quantities in physiographic complex regionsf)Extremesg)Regional dynamical features, such as polar lows, tropical storms, medicanes

standard formulation large-scale nudging

Similarity of zonal wind at 850 hPa between simulations and NCEP re-analyses

large scales

medium scales

Ratio of 2m temperature st’ddev’s DJF 1992-1999 (regional scales only)

DWD/NCEP [%] DWD/REMO [%]

Marcos Garcia Sotilla, 2003

Assimilated into NCEP(Atlantic)

Not assimilated into NCEP (Ionic Sea)

Wind speed at two bouys

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Extreme value analysis of wind speed at platform K13 (southern North Sea)

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Brier skill score using QuikSCAT level 2B12 as the “truth”, global reanalysis (NCEP reanalysis) as the reference forecast, and a regional model (SN-REMO) as forecast, Winterfeldt et al. (2010).

Open Ocean: No value addedby dynamical downscaling

Coastal region:Added Valuein complexcoastal areas

Density of North Atlanticpolar low genesis

Genesis in RCM simulation constrained by NCEP reanalsysis

Bracegirdle, T. J. and S. L. Gray, 2008 Zahn, M., and H. von Storch, 2008

Summary

a)Atmospheric (and oceanic) dynamics are generated following a downscaling logic.

b)Global models can describe global features without describing any regional feature adequately.

c)Regional modelling is mathematically best described as a state space problem and not as a boundary value problem, which is mathematically ill-posed.

d)The problem of characterizing the ensemble of solutions given a set of bc’s is not solved.

e)Models are “for” not “of”.

f)Regional climate models are constructed for simulating weather statistics on regional scales, conditional upon large scale states, and regional forcings (without influence on the outside region)

g)Determining the skill of RCMs means determining the accuracy of statistics of regional scales.

h)A determination of the skill in climate change simulations is not really possible, as no reference is available for doing so.

Outlook

The possibly best regional climate model is a large-scale

constrained global model.Yoshimura, K., and M. Kanamitsu, 2008: Dynamical global downscaling of global reanalysis. Mon. Wea. Rev. 136: 2983-2998

Kim, J.E., and S.Y. Hong, 2012: A Global Atmospheric Analysis Dataset Downscaled from the NCEP–DOE Reanalysis. J. Climate 25, 2527-2534