Status of the implementation of the multi-layer snow scheme into the COSMO model

1. Status of the implementation of the multi-layer snow scheme into the COSMO model Ekaterina Machulskaya German Weather Service, Offenbach am Main, Germany (ekaterina.machulskaya@dwd.de) COLOBOC meeting 5 September 2011

2. Differences between “single-layer” and “multi-layer” models (recall) Problems with multi-layer model, solutions Some examples Conclusions and outlook Outline

3. Differences between “single-layer” and “multi-layer” models “Single layer” “Multi-layer” Implemented processes • Heat conduction • Liquid water transport • Gravitational compaction + • metamorphosis • Solar radiation penetration • Heat conduction • Melting when snow surface • temperature > 0°C or • when soil surface • temperature > 0°C Numerical schemes • arbitrary number of layers • heat conduction: implicit • latent heat and solar radiation: • source terms 1 layer

4. 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) atmosphere can be of order -100 W/m² can be of order 10-6 m (depends on precipitation rate) snow 0 W/m² in case if there was no snow at the previous time step soil Q = Cp· Δz · ρ· ΔT Q ≈ –100 W/m2, Δz ≈10-6 m → ΔT ≈ –102… –103K!

5. 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,)

6. 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: more stability decrease of T due to decreased turbulent mixing decrease of T due to decreased solar radiation decrease of outgoing longwave radiation increase of T

7. 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

8. Example: surface temperaturewith and without tracing with without difference:

9. Example: surface temperaturewith and without tracing without with difference:

10. 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

11. Thank you for your attention! Thanks to Jochen Förstner, Thomas Hanisch, and Dmitrii Mironov!

12. Appendix

13. Appendix Derivation of the criterion