cosmo general meeting, rome, italy, 5-9 september 2011 status of the implementation of the...
TRANSCRIPT
COSMO General Meeting, Rome, Italy, 5-9 September 2011
Status of the implementation of the multi-layer snow scheme
into the COSMO model
COLOBOC meeting5 September 2011
Ekaterina Machulskaya
German Weather Service, Offenbach am Main, Germany
COSMO General Meeting, Rome, Italy, 5-9 September 2011
Differences between “single-layer” and “multi-layer” models (recall)
Problems with multi-layer model, solutions
Some examples
Conclusions and outlook
Outline
•Heat conduction•Melting when snow surfacetemperature > 0°C orwhen soil surface temperature > 0°C
•Heat conduction•Liquid water transport•Gravitational compaction
+metamorphosis •Solar radiation penetration
1 layer
• arbitrary number of layers• heat conduction: implicit• latent heat and solar radiation: source terms
Numerical schemes
Implemented processes
“Single layer” “Multi-layer”
Differences between “single-layer” and “multi-layer” models
Problems: too low temperatures in the “multi-layer” model at nights
Cause 1:
explicit handling of the low boundary condition – dangerous by very thin snowpack (e.g. by the first snowfall)
can be of order -100 W/m²atmosphere
0 W/m² in case if there was no snow at the previous time step
snow
soil
Q = Cp · Δz · ρ · ΔT
Q ≈ –100 W/m2, Δz ≈ 10-6 m → ΔT ≈ –102… –103K!
can be of order 10-6 m (depends on precipitation rate)
Problems: too low temperatures in the “multi-layer” model at nights
Solution:
Maybe: invent a realistic initial snow temperature in case if there was no snow at the previous time step → formulate implicit heat diffusion through the snow-soil interface
Now: switch to single-layer model where ground heat flux is “almost implicit”(might be a solution, because anyway it probably makes no sense to resolve the vertical temperature profile in snowpack of 1 mm)
Criterion for the switching:
(Q is the heat balance on the snow surface, ΔTsn is the prescribed maximum of the decrease of the snow upper layer temperature per time step, Cp is the heat capacity of ice, ρsn is the snow density,)
snpsnsn CT
Qdth
Problems: too low temperatures in the “multi-layer” model at nights
Cause 2:
radiation routine is called not at each time step → outgoing longwave radiation “frozen” by the temperature of the last call of the radiation routine
= switch off the negative feedback:
decrease of T due to decreased
solar radiation
more stability decrease of Tdue to decreasedturbulent mixing
decrease of outgoinglongwave radiationincrease of T
Problems: too low temperatures in the “multi-layer” model at nights
Solution:
Tracing the actual outgoing longwave radiation:
1) save Tg(old) from the time step of the last call of the radiation
2) at each time step in TERRA:
Rlw (balance of the longwave radiation at the surface) =
Rlw (from the radiation routine)– σTg(old)4 + σTg(current)4
Example: surface temperaturewith and without tracing
difference:
without with
Example: surface temperaturewith and without tracing
without with
difference:
COSMO General Meeting, Rome, Italy, 5-9 September 2011.
The causes of unphysical too low temperatures of the snow surface at nights in the “multi-layer” snow model are investigated
Solutions are proposed
Experiments are set up, results are monitored
Conclusions
COSMO General Meeting, Rome, Italy, 5-9 September 2011.
Thanks to Jochen Förstner, Thomas Hanisch, and Dmitrii Mironov!
Thank you for your attention!
Appendix
Appendix
Derivation of the criterion