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The Non-Local Scheme in CAM3Michael A. Brunke
introduction
surface layer
outer layer
free atmosphereh
0.1h
0
z
PBL
cc zC
KCw
Cwzt
C
introduction
surface layer
outer layer
free atmosphereh
0.1h
0
z
PBL
cc zC
KCw
freePBL ,maxPBLin KKKc
Cwzt
C
introduction
surface layer
outer layer
free atmosphereh
0.1h
0
z
PBL
cc zC
KCw
Cwzt
C
input and outputinput parameterspotential temperature
temperaturespecific humidity
height above surfacepressure
wind speedsurface wind stress
surface SH fluxsurface constituent flux
output parameterskinematic sfc. const. flux
eddy diffusivitiescountergradient terms
convective temp. excessconvective hum. excesssurface friction velocity
Obukhov lengthPBL height
free atmosphere Kc
RiFz
K ccc V2
2/1181 RiRiFc 280101
1RiRi
RiFc
Ri < 0 Ri > 0
2z
zgRi v
v
V
(Holtslag and Boville 1993)
free atmosphere Kc
RiFz
K ccc V2
2/1181 RiRiFc 280101
1RiRi
RiFc
Ri < 0 Ri > 0
2z
zgRi v
v
V
25C F
determination of h
h = z where Ri = Ricr = 0.3(Vogelezang and Holtslag 1996)
2*
2
1
2
1
1
uvzvuzu
zzzg
Ris
s
vvv
m
svvv w
wb
s
1
sensitivity of h formulation
L26 L52 L104 20 mMedian (m) -73 14 38 79
Clear IQR (m) 290 161 128 137r 0.48 0.80 0.81 0.79
Median (m) -153 -18 12 47Cloudy IQR (m) 792 396 326 370
r 0.06 0.78 0.79 0.76Zeng et al., 2004: Marine atmospheric boundary layer height over the Eastern Pacific: data analysis and model evaluation. J. Climate, 17, 4159-4170.
determination of h
h = z where Ri = Ricr = 0.3
2*
2
1
2
1
1
uvzvuzu
zzzg
Ris
s
vvv
m
svvv w
wb
s
1
28
C3
F0
determination of Kc
2
,
2
1
1
hz
zkwK
hz
zkwK
tHq
mm
determination of Kc
2
,
2
1
1
hz
zkwK
hz
zkwK
tHq
mm
turbulent velocity scales
m
m
uw
*
h
t
uw
*
3/1
151
Lz
m
2/1
151
Lz
hLz
h 51 Lz
h 5
z / L < 0 0 z / L 1
z / L > 1
Lz
m 51 Lz
m 5
turbulent velocity scales
m
m
uw
*
h
t
uw
*
3/1
151
Lz
m
2/1
151
Lz
hLz
h 51 Lz
h 5
z / L < 0 0 z / L 1
z / L > 1
Prm
t
ww
mm
h
ww
hh
akLhLh *1.0
1.01.0
Pr
Lz
m 51 Lz
m 5
turbulent velocity scales
m
m
uw
*
h
t
uw
*
3/1
151
Lz
m
2/1
151
Lz
hLz
h 51 Lz
h 5
z / L < 0 0 z / L 1
z / L > 1
Prm
t
ww
mm
h
ww
hh
akLhLh *1.0
1.01.0
Pr
Lz
m 51 Lz
m 5
216
C8
F0
turbulent velocity scales
m
m
uw
*
h
t
uw
*
3/1
151
Lz
m
2/1
151
Lz
hLz
h 51 Lz
h 5
z / L < 0 0 z / L 1
z / L > 1
Prm
t
ww
mm
h
ww
hh
akLhLh *1.0
1.01.0
Pr
Lz
m 51 Lz
m 5
816
C8
F6
countergradient term
hwCww
am
sc 2
*
3/1
*
hwg
w sv
vs
countergradient term
hwCww
am
sc 2
*
3/1
*
hwg
w sv
vs
817
C1
F0
scheme sensitivity
Tested sensitivity to choices for: Ricr b a
2*
2
1
2
1
1
uvzvuzu
zzzg
Ris
s
vvv
m
svvv w
wb
s
1
hwCww
am
sc 2
*
Scheme sensitivity to critical Ri
-6.0%
-4.0%
-2.0%
0.0%
2.0%
4.0%
6.0%
8.0%
1 2 3 4% d
iffe
ren
ce Series1
Series2
Series3
Series4
+25%
+10%
-10%
-25%
h Km Kh h
Scheme sensitivity to beta
-1.0%
-0.5%
0.0%
0.5%
1.0%
1.5%
2.0%
2.5%
1 2 3 4
% d
iffe
ren
ce Series1
Series2
Series3
Series4
+25%
+10%
-10%
-25%
h Km Kh h
Scheme sensitivity to convective temperature excess
-60.0%
-50.0%
-40.0%
-30.0%
-20.0%
-10.0%
0.0%
10.0%
20.0%
30.0%
1 2 3 4
% d
iffe
ren
ce
Series1
h Km Kh h
Scheme sensitivity to b
-15.0%
-10.0%
-5.0%
0.0%
5.0%
10.0%
15.0%
1 2 3 4
% d
iffe
ren
ce Series1
Series2
Series3
Series4
+25%
+10%
-10%
-25%
h Km Kh h
Scheme sensitivity to a
-30.0%
-20.0%
-10.0%
0.0%
10.0%
20.0%
30.0%
1 2 3 4
% d
iffe
ren
ce Series1
Series2
Series3
Series4
+25%
+10%
-10%
-25%
h Km Kh h
look-up table?Not much value added by a LUT.
Simple formulation Module runs very quickly.
Pull h’s from a LUT? Model run to get LUT values could be run
at L31.
summary CAM3 uses standard non-local turbulence scheme in
PBL. 17 tunable constants and 8 arbitrary functions. Scheme not sensitive to Ricr and ; are sensitive to b
and a Convective temperature excess is needed. LUT probably not necessary except maybe to get h.
