recent work on pressure bias problem
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Recent work on pressure bias problem. Lucio TORRISI Italian Met. Service CNMCA – Pratica di Mare (Rome) [email protected]. Overview. Pressure bias problem: RK/LF Dynamical bottom boundary condition for vertical pressure gradient in RK core - PowerPoint PPT PresentationTRANSCRIPT
10th COSMO General Meeting, Krakow, 15-19 September 2008
Recent work on pressure bias problem
Lucio TORRISI
Italian Met. Service CNMCA – Pratica di Mare (Rome)
10th COSMO General Meeting, Krakow, 15-19 September 2008
Overview• Pressure bias problem: RK/LF• Dynamical bottom boundary condition
for vertical pressure gradient in RK core• Pressure bias problem: domain size,
model equation formulation• New reference atmosphere and
consistent p0-h averaging (Zaengl, 2008)
• Heat source term in pressure equation• Conclusion
10th COSMO General Meeting, Krakow, 15-19 September 2008
Pressure bias problem (1) • This problem was pointed out in Torrisi (2005):
“Sensitivity experiments with the Runge Kutta time integration scheme”, presentation at COSMO GM in Zurich
1) RK/LF core - Objective verification showed a difference in MSLP bias behaviour between 7km RK (red line) and LF (green line) runs.
MSLP bias difference increases with forecast time. RK runs have a larger bias, typically positive, leading to a worse RMSE.
RK
LF
10th COSMO General Meeting, Krakow, 15-19 September 2008
• In COSMO model an extrapolated boundary condition for p*, which is based on the assumption of a constant vertical gradient at the lower boundary:
Old bottom bound. cond.
=ke’ +1 ke’
10th COSMO General Meeting, Krakow, 15-19 September 2008
“Pressure Bias Problem”Blue: Old Bottom Boundary Cond.Red: Dynamic Bottom Boundary Cond.
• An improvement in RK core was obtained by the implementation of the Gassmann formulation (COSMO Newsletter No. 4) of the dynamic bottom boundary condition for metric pressure gradient term in equation for u- and v-component
Dynamical bottom bound. cond.
Old BBC
DBBC
10th COSMO General Meeting, Krakow, 15-19 September 2008
7km RK/LF comparison
LF
RK (with DBBC)
10th COSMO General Meeting, Krakow, 15-19 September 2008
RK/LF comparison
In summary:• 2.8/7km: the results of the previous experiment
(7km, winter period) show that RK and LF MSLP bias are almost the same, but small differences (depending on season, domain, location, etc) are still found (RK larger bias)
• 14 km: very big differences are found (RK has an increasing MSLP positive bias with forecast time)
Other work has been done on RK core (change in metric term discretization, change in vertical average on half levels, etc), but no positive impact was found (in some cases slight negative impact!)
10th COSMO General Meeting, Krakow, 15-19 September 2008
Pressure bias problem (2) 2) Domain size - Objective verification showed a difference in MSLP bias behaviour in 7km RK (and LF) runs having a different domain size (smaller one - red line, larger one -green line).
The larger domain, the greater MSLP bias
Larger domain
Smaller domain
10th COSMO General Meeting, Krakow, 15-19 September 2008
Pressure bias problem (3) 3) Model formulation - Objective verification showed a difference in MSLP bias behaviour between 14km COSMO LF/RK (blue line) and HRM (red line) runs.
HRM is the DWD regional hydrostatic model (LF time integration scheme) used in the CNMCA assimilation systems (3D-Var PSAS and LETKF).
MSLP bias difference increases with forecast time (COSMO larger positive bias)
COSMO(LF)
EURO-HRM
10th COSMO General Meeting, Krakow, 15-19 September 2008
Pressure bias problemThe increase of the MSLP bias with forecast time is a characteristics of COSMO model runs and it does not seem dependent only on dynamical core (point 1). This behaviour is evident using very large domain size (point 2) and particularly clear using a 14 km grid spacing (point 3). The effects on the pressure bias of two changes in the model formulation will be addressed: - Zaengl (2008) proposed a new reference atmosphere to overcome the problem of limitation in vertical extent of the model domain using the default reference atmosphere- Gassmann and Herzog (2006) reconsidered the derivation of prognostic temperature and pressure equations to remove some inconsistencies in the formulation of these equations
10th COSMO General Meeting, Krakow, 15-19 September 2008
New reference atmosphere
Introducing a reference state reduces the computational error in the calculation of pressure gradient terms in the equation of motion for not too large deviations of pressure from reference pressure. The default reference atmosphere of COSMO model is based on assuming dT/d(logp)=const. The lapse rate dT/dz becomes more and more negative with height limiting the possible vertical extent of the model domain. To overcome this problem, Zaengl (2008) implemented in COSMO model a new reference atmosphere based on a temperature profile which starts with a prescribed sea-level temperature and exponentially approaches an isothermal stratosphere. An inconsistency in the full level reference pressure calculation was also removed.
10th COSMO General Meeting, Krakow, 15-19 September 2008
New reference atmosphere
7 km 14 kmPreliminary results!
10th COSMO General Meeting, Krakow, 15-19 September 2008
• Pressure bias increase has been found in experiments using a coarser resolution (14 km) and also enlarging the size of the domain (7km). This could be an indication of some inconsistencies in the formulation of T/p budget equ.
Heat source term in p equation
bRbbCMT
MCTT
vd
TTzTTMMQc
p
td
Td )(
v
bRbbCMpvdpd ppzppMpcc
td
pd )(/ v
f
pd
sl
pd
v
pdT S
c
LS
c
L
cQ RH
1
Turbulent heat and Radiaton flux
Diabatic heating due tocloud microphysical sources
flflv PPFFF
pd
dfl
pd
v
d
v
pd
dM c
TRSS
c
TR
R
R
c
TRQ
1
Turbulent flux forwater constituents
Turbulent flux for water constituents and Precipitation (gravitational diffusion) fluxes
Cloud heat sources
10th COSMO General Meeting, Krakow, 15-19 September 2008
Heat source term in p equation• The heat and moisture terms (QT and QM) are
neglected in the COSMO model pressure equation• Gassmann and Herzog (2006) in their presentation
at LM-User Meeting “reconsidered the derivation of prognostic temperature and pressure equations in the LM”
“1. In pressure equation heat and moisture source terms neglected 2. dp/dt in T-equation eliminated after neglecting these terms 3. Formal addition of moist convection tendency, computational mixing, lateral and upper boundary relaxation terms in T/p equ.”
“This operation is equivalent to the application of a wrong continuity equation producing a mass deficiency ………………………..”
“The way to come to this result is wrong and leads to insufficient equations !” .
10th COSMO General Meeting, Krakow, 15-19 September 2008
Heat source term in p equation
1/
1 1( )
MC CM CMpd vd T M T T p
vd pd
b b b R b bpd pd
d T pc c Q Q M M M
d t c c
T T p p z T T p pc c
v
bRbb
CMpMpdvdpd
MCTTpdvdpdvdpd
ppzppMQccc
MQcccpcctd
pd
)(/
1//
v
These new terms (except for QM) were added in the p/T equations and the saturation adjustment scheme was consistently adapt to the changes in p/T equations.
The reformulated equations are:
10th COSMO General Meeting, Krakow, 15-19 September 2008
Heat source term in p equation
• In a few real cases (winter) with a 7 km grid spacing:– domain averaged total precipitation is slightly decreased– MSLP bias is reduced (except for 12-15 UTC)
LF RK7 km
OldQh_Pe
OldQh_Pe
10th COSMO General Meeting, Krakow, 15-19 September 2008
LF
RK
7 km
Heat source term in p equation
10th COSMO General Meeting, Krakow, 15-19 September 2008
Heat source term in p equation
7 km
LF
10th COSMO General Meeting, Krakow, 15-19 September 2008
Heat source term in p-equation
7 km
• In a summer period the effect of the heat source term on pressure bias seems to be different from the winter period results previously shown:– MSLP bias is reduced from 21 to 06 UTC and increased
from 9-15 UTC
Old Qh_Pe
10th COSMO General Meeting, Krakow, 15-19 September 2008
Heat source term in p-equation
14 km
Ref_atm
Ref_atm+Qh_Pe
Old
Ref_atm+Qh_Pe
Euro-HRM
10th COSMO General Meeting, Krakow, 15-19 September 2008
Pressure bias problem
• Impact of the new reference atmosphere on the pressure bias is very clear at 14km, but it quickly decreases with increasing resolution
• Impact of heat source term in pressure equation on the pressure bias is apparent in 14 km runs. The improvement is not general using a 7 km grid spacing due to a slight deterioration around 12 UTC (larger in summer period). Two runs with 2.8 km grid spacing show no significant differences except for an enhancement of precipitation maxima.
• More work is needed to understand deeply the effects of these changes!
10th COSMO General Meeting, Krakow, 15-19 September 2008
Conclusion• The pressure bias problem is typical of
COSMO model (not only of RK core!)• The pressure bias problem seems to be
mainly related to the model equation formulation. The use of prognostic p equation does not guarantee an exact mass conservation
• Problems arise in applications such as data assimilation systems, where the pressure accuracy is important
• A more conservative dynamical core for COSMO model could be an option to tackle this problem
10th COSMO General Meeting, Krakow, 15-19 September 2008
Thank you for your attention!
10th COSMO General Meeting, Krakow, 15-19 September 2008
7km RK/LF comparison
10th COSMO General Meeting, Krakow, 15-19 September 2008
7km RK/LF comparison
10th COSMO General Meeting, Krakow, 15-19 September 2008
7km RK/LF comparison