Some recent findings about very stable boundary layers

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Some recent findings about very stable boundary
layers

• Branko Grisogono, AMGI, Zagreb
• I.Kavcic, I.Stiperski,
• Mark Ž, Danijel B, Leif E, Larry M, Dale D,
  Thorsten M, Amela J, Sergej Z,

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• PRANDTL MODEL f , K(z)
• ASYMPTOTIC SOLUTION - WKB METHOD
• MIUU MODEL CHARACTERISTIC LENGTHSCALE
• PRANDTL-NUMERICAL MIUU SIMULATION

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CLASSIC PRANDTL MODEL

• Analytic model for a simple katabatic flow
  basic, dirty nice
• Balance between neg. buoyancy turbulent
  diffusion

z
x
a
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NEW PRANDTL f , K(z)
B. C.
Valid even for finite-amplitude
perturbations, Stiperski et al. QJRMS 2007
Kavcic Grisogono, BLM 2007
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Solutions U q K K(z)as for steady flow
Pr Km/Kh const ? K(z)Kh, e.g.
Ko(z/h)exp(-0.5z2/h2)
Grisogono Oerlemans, JAS 2001 Parmhed et al.
QJRMS 2004 etc.
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Numerical (dashed), analytic WKB (full) U i qtot,
(a) t T (b) t 10T. (a, ?, Pr, C, f) -4,
4K/km, 1.1, -8C, 1.110-4s-1. T2p/sin(a) 1-5
hours.
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Solution V(z,t)... Boring skip it
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Numerical (dashed) analytic (VWKB full), (c)
t 20T i (d) t 50T. Other parameters as
before. Vf is solution a reasonable Kconst.
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MIUU (Leifs) MODEL

• 3D, nonlinear, hydrostatic, f const
• H-O-C turb. parameterization (level 2.5 many
  fine details)
• 5 progn. Eqns U, V, Q, q, TKE (e.g. Grisogono
  Enger QJRMS 2004)
• Here
• ?x 1.9 km const, slope -2.2o, C 6.5oC
• 211 7 201 points (yconst), total (nk)402
• ?t 13 s, zTOP 5.6 km (sponge from z 4.4
  km)
• 1 m lt ?z lt 29.5 m, staggered, terrain
  influenced
• Initialized by U i V 0, Q(z) ? 5K/km

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LSTAB 2Amin (TKE)1/2/N, (TKE)1/2/S ? Too
much mixing, too elevated INV. LLJ gt LSTAB
min2A(TKE)1/2/N, A(TKE)1/2/S
Grisogono Enger, QJRMS 2004
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New lowered LSTAB (z,t) in MIUU following
simulations
Analytics used for model tuning coeff. choice
for LSTAB, as from obs. data or LES gt get model
coeff
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New L
With old L
(a)
(b)
No explicit Shear in L same res. if same weight
in L to N S
t (h)
t (h)
(t, z) for qtot q gz MIUU model old L (a)
new L (b) (f, a, g, Pr, C) (1.0310-4 s-1,
-2.2, 510-3 Km-1, 1.1, -6.5C), T 3.39 h,
(for K hmax 200 m, Kmax 2 m2s-1).
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(a)
(b)
t (h)
t (h)
(t, z) for qtot q gz from simple numerical
(a) MIUU model (b) (f, a, g, Pr, C)
(1.0310-4 s-1, -2.2, 510-3 Km-1, 1.1, -6.5C),
T 3.39 h, (for K hmax 200 m, Kmax 2 m2s-1).
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(a)
(b)
t (h)
t (h)
U(t, z) from simple numerical (a) MIUU model
(b). The rest as before. Max(Unum) 5.4 ms-1
LLJ at 16 m. The input parameters as before.
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(a)
(b)
t (h)
t (h)
V(t, z) from simple numerical (a) MIUU model
(b).The rest as before. Min(Vnum) -2.6 ms-1.
The input parameters as before.
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(a)
(b)
t (h)
t (h)
V(t, z) from simple numerical (a) MIUU model
(b).The rest as before. Min(VWKB) -2.75 ms-1.
The input parameters as before.
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(b)
(a)
q tot WKB method simple numerial (a) MIUU
model (b), after t 20 h. The input parameters
as before.
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Mauritsen et al. JAS2007, TTE TKE TPE. In
H-O-C Approach IMPORTANT TO MODEL
SABL MORE PROPERLY IN CLIMATE MODELS
-AFFECTS E.G. ICE GLACIERS MASS BALANCE VIA
MELTING, MICRO-CLIMATE
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CONCLUSION

• Agreement among analytic (WKB), numerical
• MIUU model solutions for (U, V, q)
• V(z,t) difusses up (U, ?) quasi-steady
• Limited data comparisons
• ZOOM OUT
• Very SABL, Ri -gt 8, gt tough to parameterize
  model the flows (here a partial sol. given?)
• typically NWP models are over-diffusive

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Spare slide
(b)
(a)
U(z) from WKB method simple numerical (a)
MIUU model (b), after t 20 h. The input
parameters as before.
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Spare slide
(b)
(a)
V(z) from WKB method simple numerical (a)
MIUU model (b), after t 20 h. The rest as
before.