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

(ekaterina.machulskaya@dwd.de)

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