Parameterization of surface fluxes

1. Parameterization of surface fluxes Bart van den Hurk (KNMI/IMAU) HTESSEL parameterization

2. General form of land surface schemes Q* H E PSN ESN Accumulation G M • Energy balance equation K(1 – a) + L – L + E + H = G • Water balance equation W/t = P – E – Rs – D S/t = Psn – Esn – M P E Rs Infiltration D HTESSEL parameterization

3. Soil hydrology • Top: F [kg/m2s] = T – Esoil – Rs + M • Bottom (free drainage) F = Rd = wK • with • T = throughfall (Pl – Eint – Wl/t) • Esoil = bare ground evaporation • Eint = evaporation from interception reservoir • Rs = surface runoff • Rd = deep runoff (drainage) • M = snow melt • Pl = liquid precipitation • Wl = interception reservoir depth • S = root extraction Pl Eint T Wl Esoil M Rs S Rd HTESSEL parameterization

4. Soil heat flux • Multi-layer scheme • Solution of diffusion equation • with • C [J/m3K] = volumetric heat capacity • T [W/mK] = thermal diffusivity • with boundary conditions • G [W/m2] at top • zero flux at bottom HTESSEL parameterization

5. Main sections • Surface tiling • Surface energy balance & vegetation • Soil heat transfer • Soil hydrology • Snow hydrology & albedo • Surface characteristics (“climate fields”) HTESSEL parameterization

6. Tile structure of HTESSEL • 6 fractions (“tiles”) • Aerodynamic coupling • Vegetatie • Verdampingsweerstand • Wortelzone • Neerslaginterceptie • Kale grond • Sneeuw HTESSEL parameterization

7. Tile structure of HTESSEL • 6 fractions (“tiles”) • Aerodynamic coupling • Wind speed • Roughness • Atmospheric stability • Vegetatie • Verdampingsweerstand • Wortelzone • Neerslaginterceptie • Kale grond • Sneeuw HTESSEL parameterization

8. Tile structure of HTESSEL • 6 fractions (“tiles”) • Aerodynamic coupling • Wind speed • Roughness • Atmospheric stability • Vegetation • Canopy resistance • Root zone • Interception • Kale grond • Sneeuw HTESSEL parameterization

9. Tile structure of HTESSEL • 6 fractions (“tiles”) • Aerodynamic coupling • Wind speed • Roughness • Atmospheric stability • Vegetation • Canopy resistance • Root zone • Interception • Bare ground • Sneeuw HTESSEL parameterization

10. Tile structure of HTESSEL • 6 fractions (“tiles”) • Aerodynamic coupling • Wind speed • Roughness • Atmospheric stability • Vegetation • Canopy resistance • Root zone • Interception • Bare ground • Snow HTESSEL parameterization

11. Tile fractions (calculated every time step) • 3 ‘static’ tiles • high vegetation • low vegetation • bare ground • 3 ‘dynamic’ tiles • interception reservoir • snow low/bare • snow forest HTESSEL parameterization

12. Parameterization of surface energy balance and evaporation HTESSEL parameterization

13. Aerodynamic exchange • Turbulent fluxes are parameterized as (for each tile): • Solution of CH requires iteration: • CH = f(L) • L = f(H) • H = f(CH) L = Monin-Obukhov length HTESSEL parameterization

14. Treatment of tiled evaporation • Potential evaporation (P): a = s = CHU = 1/raH • Transpiration (T) a = s = 1/(raH + rc) • Combined snow tile (S) T P T S T P HTESSEL parameterization

15. More on the canopy resistance • Active regulation of evaporation via stomatal aperture • Empirical (Jarvis-Stewart) approach: rc = (rc,min/LAI) f(K) f(D) f(W) HTESSEL parameterization

16. Jarvis-Stewart functions • Shortwave radiation: • Atmospheric humidity deficit (D): f3 = exp(-cD) (c  0 for forest only) HTESSEL parameterization

17. Jarvis-Stewart functions • Soil moisture ( = weighted mean liquid water over root profile): • Standard approach: linear profile 1 HTESSEL parameterization

18. Specification of vegetation types HTESSEL parameterization

19. Soil heat flux HTESSEL parameterization

20. Numerical solution • Solution of energy balance equation • With (all fluxes positive downward) • Express all components in terms of Tsk (with Tp = Tskt -1) netradiation sensible heat flux latent heat flux soil heat flux HTESSEL parameterization

21. Numerical solution • Substitute linear expressions of Tsk into energy balance equation • Sort all terms with Tsk on lhs of equation • Find Tsk = f(Tp , Tsoil , CH ,forcing, coefficients) HTESSEL parameterization

22. Soil heat transfer HTESSEL parameterization

23. Heat transport in soil • Multi-layer scheme • Solution of diffusion equation • with • C [J/m3K] = volumetric heat capacity • T [W/mK] = thermal diffusivity • with boundary conditions tiled soil heat flux direct absorption snow base heat flux HTESSEL parameterization

24. Heat capacity and thermal diffusivity • Heat capacity • sCs  2 MJ/m3K, wCw  4.2 MJ/m3K • Thermal diffusivity depends on soil moisture • dry: ~0.2 W/mK; wet: ~1.5 W/mK HTESSEL parameterization

25. Freezing of soil water • In case of melt/freezing, and extra heat capacity term is added: • The ice fraction is a diagnostic variable: fixed value, to decouple water and temperature eqs HTESSEL parameterization

26. Parameterization of soil hydrology HTESSEL parameterization

27. Soil water flow • Water flows when work is acting on it • gravity: W = mgz • acceleration: W = 0.5 mv2 • pressure gradient: W = m  dp/ = mp/ • Fluid potential (mechanical energy / unit mass) • = gz + 0.5 v2 + p/ p = gz •  g(z+z) = gh • h = /g = hydraulic head = energy / unit weight = • elevation head (z) + • velocity head (0.5 v2/g) + • pressure head ( = z = p/g) HTESSEL parameterization

28. Relation between pressure head and volumetric soil moisture content strong adhesy/ capillary forces dewatering from large to small pores retention curve HTESSEL parameterization

29. Darcy and Richards equation qz = flux HTESSEL parameterization

30. Darcy and Richards equation  = vol. soil moisture content (m3/m3) K = hydraulic conductivity (m/s) D = hydraulic diffusivity (m2/s) HTESSEL parameterization

31. Implementation in discrete form • In (discrete) flux form: • With F specified as: root extraction diffusion term gravity term HTESSEL parameterization

32. Parameterization of K and D • 2 ‘schools’ • Clapp & Hornberger ea • single parameter (b) • Van Genuchten ea • more parameters describing curvature better • Defined ‘critical’ soil moisture content • wilting point ( @  = -150m or -15 bar) • field capacity ( @  = -3m or -0.33 bar) HTESSEL parameterization

33. Boundary conditions • Top: F [kg/m2s] = T – Esoil – Rs + M • Bottom (free drainage) F = Rd = wK • with • T = throughfall (Pl – Eint – Wl/t) • Esoil = bare ground evaporation • Eint = evaporation from interception reservoir • Rs = surface runoff • Rd = deep runoff (drainage) • M = snow melt • Pl = liquid precipitation • Wl = interception reservoir depth • S = root extraction Pl Eint T Wl Esoil M Rs S Rd HTESSEL parameterization

34. Parameterization of interception • Simple budget equation • with • El = evaporation • D = dew collection • I = interception from precipitation • Points for attention: • maximum storage reservoir ~ 0.2 mm per m2 leaf/ground area • rapid process (water conservation in discrete time step needs care) • interception efficiency depends on type of precipitation (large scale precip: very efficient. convective precip: more falls off) HTESSEL parameterization

35. Parameterization of runoff • Simple approach • Infiltration excess runoff Rs = max(0, T – Imax), Imax = K() • Difficult to generate surface runoff with large grid boxes • Explicit treatment of surface runoff • ‘Arno’ scheme Infiltration curve (dep on W and orograpy) Surface runoff HTESSEL parameterization

36. Parameterization of snow HTESSEL parameterization

37. Snow parameterization • Effects of snow • energy reflector • water reservoir acting as buffer • thermal insolator • Parameterization of albedo • open vegetation/bare ground • fresh snow: albedo reset to amax (0.85) • non-melting conditions: linear decrease (0.008 day-1) • melting conditions: exponential decay • (amin = 0.5, f = 0.24) • For tall vegetation: snow is under canopy • gridbox mean albedo = fixed at 0.2 HTESSEL parameterization

38. Parameterization of snow water • Simple approach • single reservoir • with • F = snow fall • E, M = evap, melt • csn = grid box fraction with snow • Snow depth • with • sn evolving snow density (between 100 and 350 kg/m3) HTESSEL parameterization

39. Snow energy budget • with • (C)sn = heat capacity of snow • (C)i = heat capacity of ice • GsnB = basal heat flux (T/rs) • Qsn = phase change due to melting (dependent on Tsn) HTESSEL parameterization

40. Snow melt • Is energy used to warm the snow or to melt it? In some stage (Tsn 0C) it’s both! • Split time step into warming part and melting part • first bring Tsn to 0C, and compute how much energy is needed • if more energy available: melting occurs • if more energy is available than there is snow to melt: rest of energy goes into soil. HTESSEL parameterization

41. Surface characteristics(surface ‘climate fields’) HTESSEL parameterization

42. Surface climate fields • Vegetation types • Vegetation cover • Surface geopotential • Land/sea mask • oro (for runoff and for z0m(orographic part) • vegetation roughness z0m • thermal roughness z0h • monthy background (snowfree) albedo • Soil type (for hydraulic properties) HTESSEL parameterization

43. Vegetation distribution HTESSEL parameterization

44. Climatological albedo (static vegetation) Jan Jul HTESSEL parameterization

45. Prognostic quantities • 4 soil temperatures • 4 soil moisture contents • interception reservoir depth • snow depth • snow albedo • snow density • snow temperature • (skin temperature) (adjusts rapidly) HTESSEL parameterization

46. More information • Bart van den Hurk • hurkvd@knmi.nl HTESSEL parameterization