Implementation of the quasi-normal scale elimination (QNSE) theory of turbulence in a weather prediction model HIRLAM - PowerPoint PPT Presentation

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Implementation of the quasi-normal scale elimination (QNSE) theory of turbulence in a weather prediction model HIRLAM

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Title: Implementation of the quasi-normal scale elimination (QNSE) theory of turbulence in a weather prediction model HIRLAM


1
Implementation of the quasi-normal scale
elimination (QNSE) theory of turbulence in a
weather prediction model HIRLAM
  • Veniamin Perov¹, Boris Galperin² and
  • Semion Sukoriansky³
  • 1.Swedish Meteorological and Hydrological
    Institute (SMHI), Norrköping, Sweden
  • 2. College of Marine Science, University of South
  • Florida, St. Petersburg, Florida, USA
  • 3. Ben-Gurion University of the Negev,
    Beer-Sheva, Israel

2
  • Numerical weather prediction (NWP) models
    involve eddy viscosity and eddy diffusivity, Km
    and Kh, that account for unresolved turbulent
    mixing and diffusion.
  • The most sophisticated turbulent closure models
    used today for NWP belong to the family of
    Reynolds stress models.
  • These models are formulated for the physical
    space variables they consider a hierarchy of
    turbulent correlations and employ a rational way
    of its truncation.
  • In the process, unknown correlation are related
    to the known ones via closure assumptions that
    are based upon preservation of tensorial
    properties and the principle of invariant
    modelling

3
  • according to which the constants in the closure
    relationships are universal
  • Although a great deal of progress has been
    achieved with Reynolds stress closure models over
    the years, these are still situations in which
    these models fail. The most difficult flows for
    the Reynolds stress modelling are those with
    anisotropy and waves because these processes are
    scale-dependent and cannot be included in the
    closure assumptions that pertain to
    ensemble-averages quantities.
  • Here we employ an alternative approach of
    deriving expressions for Km and Kh using the
    spectral space presentation. The spectral model
    produces expressions for Km and Kh based upon a
    self-consistent procedure of small-scale modes
    elimination.

4
  • This procedure is based upon the quasi-Gaussian
    mapping of the velocity and temperature using the
    Langevun equations.
  • Turbulence and waves are treated as one entity
    and the effect of the internal waves is easily
    identifiable.
  • When averaging is extended to all scales, the
    method yields a Reynolds-averaged, Navier-Stokes
    based model.
  • The details can be found in the paper A
    quasinormal scale elimination model of turbulent
    flows with stable stratification, Phys. Fluids,
    17,085107-1-28, 2005, by Sukoriansky S, Galperin
    B. and Staroselsky I.

5
Results from the theory
The turbulent coefficients are recast in terms of
gradient Richardson number Ri N2/ S2 or Froude
number Fr e / NK
  • Normalized turbulent exchange coefficients as
    functions of Ri and Fr.
  • For Rigt0.1, both vertical viscosity and
    diffusivity decrease, with the diffusivity
    decreasing faster than the viscosity (residual
    mixing due to effect of IGW?)
  • Horizontal mixing increases with Ri. The model
    accounts for flow anisotropy.
  • The crossover from neutral to stratified flow
    regime is replicated. No critical Ri.

6
Stability functions from the QNSE model and from
the Mellor-Yamada model modified by Galperin et
al. (1988)
7
Comparison with experimental data
Vertical turbulent Prandtl number as a function
of Ri. Data points are laboratory measurements by
Huq and Stewart (2004) solid line represents our
models results.
Inverse Prandtl number kz /nz as a function of
Ri. Experimental data points are from Monti et
al. (2002).
8
New K- e model

In our model
Detering Etlin, 1985 introduced correction to
C1 due to the Earth rotation We generalized it to
include stratification
where
The constants are

The model is implemented in the 1D version of the
weather forecast model HIRLAM
9
Neutral ABL
  • Comparison with Leipzig wind profile

10
Comparison with CASES-99
11
Comparison with CASES-99
12
Comparison with BASE
13
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14
Testing in the numerical weather prediction
system HIRLAM
  • NWP system HIRLAM High Resolution Limited Area
    Model
  • Covers the North-East Atlantic, Europe, and
    Greenland
  • Hydrostatic model 438x336 points 22km x 22km
    resolution
  • 40 vertical levels
  • Lateral boundary conditions are from ECMWF
    operations
  • Massive data assimilation over 1000 stations
    all over Europe
  • Data assimilation cycle is 6 hours
  • From each 00, 06, 12, 18 UTC, a 48 hours
    forecast is run
  • Total 120, 48 h forecasts in one month
    (January 2005)
  • We replace Km and Kh for stable stratification
    only run parallel experiment analyze the
    difference (new-reference)
  • Region of interest Scandinavia

15

HIRLAM turbulence K-l scheme

16
HIRLAM turbulence K-l scheme
  • Results (versions before 6.2)
  • Positive bias in the wind direction, accompanied
    by too strong near surface winds
  • Too fast deepening and too slow filling of
    cyclones, making HIRLAM too active towards the
    end of the forecast period

17

HIRLAM turbulence K-l scheme

Increasing of the vertical mixing of momentum
under stable stratif. Verification score becames
better, but Intercomparison in GABLS shows very
deep BL and a wind profile has its maximum at the
wrong place (too high)
18

Modification of HIRLAM K-l scheme

19
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20

21

22
Surface sensible heat flux New-Reference
Red positive Blue - negative
23
Surface latent heat flux New-Reference
24
Surface U-momentum flux New-Reference
25
Surface V-momentum flux New-Reference
26
Cross-section Difference in TKE
27
Cross-section Difference in temperature
28
Conclusions
  • Anisotropic turbulent viscosities and
    diffusivities are in good agreement with
    experimental data
  • The model recognizes the horizontal-vertical
    anisotropy introduces by stable stratification
    and provides expressions for the horizontal and
    vertical turbulent viscosities and diffusivities.
    This is a real possibility to include 3-D
    turbulence in NWP and mesoscale models
  • Theory has been implemented in 1-D K-e and K-l
    models of stratified ABL
  • Good agreement with BASE, SHEBA and CASES99 data
    sets has been found in 1-D model for cases of
    moderate and strong stratification
  • Theory has been implemented in K-l scheme of 3-D
    NWP model HIRLAM
  • The new K-l scheme improves predictive skills of
    mean sea level pressure and 2M temperature for
    48h weather forecasts over Scandinavia (stable
    BL) for January 2005

29
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