improving the mass conservation in the semi- lagrangian scheme of the ifs/h
TRANSCRIPT
Improving the mass conservation in the semi-Lagrangian scheme of the IFS/HARMONIE model
T. Morales(1) and M. Hortal(2)
(1) Spanish Meteorological Agency (AEMet) (2) HIRLAM group
XXXIII Jornadas Científicas de la AME
Oviedo, 7 a 9 de abril de 2014
HIRLAM-B Programme
Objectives of the Programme !
Develop a LAM in order to provide a high quality operational short- and very-short-range deterministic and probabilistic analysis and forecasting system
! HARMONIE LAM developed by Aladin and HIRLAM groups ! Dynamic core of HARMONIE
! semi-Lagrangian (SL) advection
Outline:!
Motivation !
Short description of the ECMWF model Integrated Forecast System (IFS) Implementation of the semi-Lagrangian semi-implicit (SLSI) scheme in the ECMWF model
!Dry Air and Ozone mass conservation in IFS
Mass conservation of dry air Mass conservation of ozone
!Conclusions
Implementation of new numerical scheme for the SL advection with the purpose of improving the mass conservation of dry air and the remaining of the atmosphere: ozone, NOx, SO2. !
! The dynamic kernel of the global model, IFS (ECMWF), and the limited area model, HARMONIE (HIRLAM Consortium), is the same. Thus, initially carried out the modifications in the IFS, where the total mass should be conserved for later transferring the improvements made to HARMONIE LAM.
Integrated Forecast Model (IFS) Motivation
GM LAM
SLSI scheme
ECMWF HARMONIE
Outline:!
Motivation !
Short description of the ECMWF model Integrated Forecast System (IFS) Implementation of the semi-Lagrangian semi-implicit (SLSI) scheme in the ECMWF model
!Air and Ozone mass conservation in IFS
Mass conservation of dry air Mass conservation of ozone
!Conclusions
Integrated Forecast Model (IFS) Integrated Forecast System (IFS)
Hydrostatic formulation !Equations: !• Prognostic equations for couple
variables!
• Hybrid vertical coordinate!
• Continuity eq. for dry air!
• Thermodynamic eq.!
• Time integration scheme: semi-Lagrangian semi-implicit (SLSI)
(�, ⇢, ⌘)
⌘(p, ps)
Variables: !Vertical coordinate:! !!!Equations!!!!! ! !
Dx
Dt= RHS x ⌘ q,O3, NO
x
, ..
(u, v, T )
Implementation of the SLSI scheme in the ECMWF model
D~r
Dt= ~V
rt+�tA � rt��t
r
2�t= V t
M
Three time levels SL scheme
Current SL scheme: Stable Extrapolation Two Time-Level Scheme (SETTLS)
SL advection
SL trajectory
D�
Dt= 0
�t+�tA � �t
D
�t= 0
Outline:!
Motivation !
Short description of the ECMWF model Integrated Forecast System (IFS) Implementation of the semi-Lagrangian semi-implicit (SLSI) scheme in the ECMWF model
!Dry Air and Ozone mass conservation in IFS
Mass conservation of dry air Mass conservation of ozone
!Conclusions
SL trajectory (SETTLS algorithm)
Mass Conservation of dry air
Continuity equations (SLSI discretization)
rt+�tA = rtD +
�t
2([2vt � vt��t]D + vt
A)
Lnp+sup =NLEVX
k=1
�Bj(Lnp�sup +�t{@Lnpsup
@t+ vkr(Lnpsup)}�) +
��t
prefsup
�tt{NLEVX
j=1
(�prefj Dj)}
A
= without quasi-monotone filter + !!!!!!!!
bi-cubic-linear interpolation
Mass Conservation of dry air
A
RM = Reference model
RM + without QM + bi-cubic-linear in A termRM
Mass Conservation of Dry Air
Mass Conservation of dry air
40
50
60
70
80
90
100
%
0 1 2 3 4 5 6 7 8 9 10
Forecast Day
es oper 12UTC | Mean method: fairDate: 20091015 12UTC to 20091015 12UTCNHem Extratropics (lat 20.0 to 90.0, lon -180.0 to 180.0)
Anomaly correlation500hPa geopotential
CY37R1: T159L91 MR
CY38R1: T159L91 MR
T159L91
Comparative between CY37R2 and 38R2. Reference Model (RM).
Mass Conservation of dry air
55
60
65
70
75
80
85
90
95
100
%
0 1 2 3 4 5 6 7 8 9 10
Forecast Day
es oper 12UTC | Mean method: fairDate: 20091015 12UTC to 20091015 12UTCNHem Extratropics (lat 20.0 to 90.0, lon -180.0 to 180.0)
Anomaly correlation500hPa geopotential
CY37R2: RM
CY38R2: RM
CY38R2: RM without QM
40
50
60
70
80
90
100
%
0 1 2 3 4 5 6 7 8 9 10
Forecast Day
es oper 12UTC | Mean method: fairDate: 20091015 12UTC to 20091015 12UTCNHem Extratropics (lat 20.0 to 90.0, lon -180.0 to 180.0)
Anomaly correlation500hPa geopotentialT159L91
CY38R2: RM
CY38R2: RM without QM
T159L91Mass Conservation of dry air
T511L91
Consistency of semi-Lagrangian scheme for the continuity equation:
Mass Conservation of dry air
Kinetic Energy Spectrum: Comparative between CY37R2 and 38R2.
Mass Conservation of dry air
T1279L91
~ 1000 mb
~ 500 mb
~ 200 mb
Mass Conservation of dry air
Outline:!
Motivation !
Short description of the ECMWF model Integrated Forecast System (IFS) Implementation of the semi-Lagrangian semi-implicit (SLSI) scheme in the ECMWF model
!Dry Air and Ozone mass conservation in IFS
Mass conservation of dry air Mass conservation of ozone
!Conclusions
The evolution of the ozone throughout simulation period is the combination of the continuity equation and the evolution of the ozone mixing ratio.
!• continuity equation ⟶ dry air mass !
• ozone mixing ratio evolution ⟶ rO3 =gr O3
Kg Dry Air
Mass Conservation of ozone
DX
Dt= sink and source terms | X ⌘ rO3
X+A = X�
D + sink and source terms
Mass Conservation of ozone ⟶ sink and source terms = 0 ( Forecast: 10 days)
X+A = value
X+A = X�
D
gr O3 = value ⇤ kg Dry Air
Error: kind of interpolation
Error: behavior of the continuity equation
Mass Conservation of ozone
32 points !interpolations
- Departure point SL trajectory
linear reduced gaussian grid
Mass Conservation of ozone
It is not possible !to apply the !quasi-monotone filter
- Departure point SL trajectory
- Value interpolated in the levels l, l+1, l+2 and l+3
tri-cubic-linear interpolation in the vertical
value of the field = weight * cubic inter + weight * linear inter
Mass Conservation of ozone
Ozone equation without sink and source terms.
55
60
65
70
75
80
85
90
95
100
%
0 1 2 3 4 5 6 7 8 9Forecast Day
es oper 12UTC | Mean method: fairDate: 20091015 12UTC to 20091015 12UTCNHem Extratropics (lat 20.0 to 90.0, lon -180.0 to 180.0)
Anomaly correlation500hPa geopotential
Reference Model
Laitili + B-S
laitlicl + B-S
50
55
60
65
70
75
80
85
90
95
100
%
0 1 2 3 4 5 6 7 8 9Forecast Day
es oper 12UTC | Mean method: fairDate: 20091015 12UTC to 20091015 12UTCSHem Extratropics (lat -90.0 to -20.0, lon -180.0 to 180.0)
Anomaly correlation500hPa geopotential
Reference Model
Laitili + B-S
laitlicl + B-S
Mass Conservation of ozone
tri-cubic interpolation + B-S
tri-cubic-lineal in the vertical + B-S
Mass conservation of ozone (only advection )
Mass Conservation of ozone
Conclusions !• It is better to continue using interpolation methods to calculate the value of the field at the departure point of the semi-Lagrangian trajectory. !
• Reduction of the aliasing in vorticity coming from the pressure gradient terms improves the mass conservation of dry air in the continuity equation. !
• Not to apply the quasi-monotone filter in the continuity equation in the CY38R2 improves more the mass conservation of dry air. !
• Apply a cubic-linear interpolation after 32-points interpolation without the quasi-monotone filter improves the conservation of mass of ozone throughout the simulation period.