1. COSMO General Meeting, Rome, Italy, 5-9 September 2011 Status of the implementation of the multi-layer snow scheme into the COSMO model COLOBOC meeting 5 September 2011 Ekaterina Machulskaya German Weather Service, Offenbach am Main, Germany (ekaterina.machulskaya@dwd.de)

2. 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

3. Heat conduction Melting when snow surface temperature > 0°C or when 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

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) can be of order -100 W/m² atmosphere 0 W/m² in case if there was no snow at the previous time step snow soil Q = C p · Δz · ρ · ΔT Q ≈ –100 W/m 2, Δz ≈ 10 -6 m → ΔT ≈ –10 2 … –10 3 K! can be of order 10 -6 m (depends on precipitation rate)

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, ΔT sn is the prescribed maximum of the decrease of the snow upper layer temperature per time step, C p is the heat capacity of ice, ρ sn 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: decrease of T due to decreased solar radiation more stability decrease of T due to decreased turbulent mixing 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 T g (old) from the time step of the last call of the radiation 2) at each time step in TERRA: R lw (balance of the longwave radiation at the surface) = R lw (from the radiation routine)– σT g (old) 4 + σT g (current) 4

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

9. Example: surface temperature with and without tracing withoutwith difference:

10. 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

11. COSMO General Meeting, Rome, Italy, 5-9 September 2011. Thanks to Jochen Förstner, Thomas Hanisch, and Dmitrii Mironov! Thank you for your attention!

12. Appendix

13. Derivation of the criterion