Title: Implementation of the quasi-normal scale elimination (QNSE) theory of turbulence in a weather prediction model HIRLAM
1Implementation 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.
6Stability functions from the QNSE model and from
the Mellor-Yamada model modified by Galperin et
al. (1988)
7Comparison 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
10Comparison with CASES-99
11Comparison with CASES-99
12 Comparison with BASE
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14Testing 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
16HIRLAM 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
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20 21 22Surface sensible heat flux New-Reference
Red positive Blue - negative
23Surface latent heat flux New-Reference
24Surface U-momentum flux New-Reference
25Surface V-momentum flux New-Reference
26Cross-section Difference in TKE
27Cross-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
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