Parameterization of surface fluxes

1. Parameterization of surface fluxes Bart van den Hurk (KNMI/IMAU) Land surface in climate models

2. Orders of magnitude • Estimate the energy balance of a given surface type • What surface? • What time averaging? Peak during day? Seasonal/annual mean? • How much net radiation? • What is the Bowen ratio (H/LE)? • How much soil heat storage? • Is this the complete energy balance? • The same for the water balance • How much precipitation? • How much evaporation? • How much runoff? • How deep is the annual cycle of soil storage? • And the snow reservoir? Land surface in climate models

3. General form of land surface schemes P E Q* H E Rs Infiltration D G • Energy balance equation K(1 – a) + L – L + E + H = G • Water balance equation W/t = P – E – Rs – D Land surface in climate models

4. Structure of a land-surface scheme (LSS or SVAT) • 6 fractions (“tiles”) • Aerodynamic coupling • Vegetatie • Verdampingsweerstand • Wortelzone • Neerslaginterceptie • Kale grond • Sneeuw Land surface in climate models

5. Structure of a land-surface scheme (LSS or SVAT) • 6 fractions (“tiles”) • Aerodynamic coupling • Wind speed • Roughness • Atmospheric stability • Vegetatie • Verdampingsweerstand • Wortelzone • Neerslaginterceptie • Kale grond • Sneeuw Land surface in climate models

6. Structure of a land-surface scheme (LSS or SVAT) • 6 fractions (“tiles”) • Aerodynamic coupling • Wind speed • Roughness • Atmospheric stability • Vegetation • Canopy resistance • Root zone • Interception • Kale grond • Sneeuw Land surface in climate models

7. Structure of a land-surface scheme (LSS or SVAT) • 6 fractions (“tiles”) • Aerodynamic coupling • Wind speed • Roughness • Atmospheric stability • Vegetation • Canopy resistance • Root zone • Interception • Bare ground • Sneeuw Land surface in climate models

8. Structure of a land-surface scheme (LSS or SVAT) • 6 fractions (“tiles”) • Aerodynamic coupling • Wind speed • Roughness • Atmospheric stability • Vegetation • Canopy resistance • Root zone • Interception • Bare ground • Snow Land surface in climate models

9. Specification of vegetation types Land surface in climate models

10. Vegetation distribution Land surface in climate models

11. Aerodynamic exchange • Turbulent fluxes are parameterized as (for each tile): • Solution of CH requires iteration: • CH = f(L) • L = f(H) • H = f(CH) a  Ta+gz a H s s L = Monin-Obukhov length Land surface in climate models

12. More on the canopy resistance • Active regulation of evaporation via stomatal aperture • Two different approaches • Empirical (Jarvis-Stewart) rc = (rc,min/LAI) f(K) f(D) f(W) f(T) • (Semi)physiological, by modelling photosynthesis An =  f(W) CO2 / rc An = f(K, CO2) CO2 = f(D) Land surface in climate models

13. Jarvis-Stewart functions • Shortwave radiation: • Atmospheric humidity deficit (D): f3 = exp(-cD) (c depends on veg.type) Land surface in climate models

14. Jarvis-Stewart functions • Soil moisture (W = weighted mean over root profile): • Standard approach: linear profile f2 = 0 (W < Wpwp) = (W-Wpwp)/(Wcap-Wpwp) (Wpwp<W<Wcap) = 1 (W > Wcap) • Alternative functions (e.g. RACMO2) Lenderink et al, 2003 Land surface in climate models

15. Effective rooting depth • Amount of soil water that can actively be reached by vegetation • Depends on • root depth (bucket depth) • stress function • typical time series of precip & evaporation • See EXCEL sheet for demo Land surface in climate models

16. 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 Land surface in climate models

17. 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) Land surface in climate models

18. Carbon exchange • Carbon & water exchange is coupled • Carbon pathway: • assimilation via photosynthesis • storage in biomass • above ground leaves • below ground roots • structural biomass (stems) • decay (leave fall, harvest, food) • respiration for maintenance, energy etc • autotrophic (by plants) • heterotrophic (decay by other organisms) Land surface in climate models

19. The gross vegetation carbon budget GPP = Gross Primary Production NPP = Net Primary Production AR = Autotrophic Respiration HR = Heterotrophic Respiration C = Combustion GPP 120 C 4 AR 60 HR 55 NPP 60 Land surface in climate models

20. The coupled CO2 – H2O pathway in vegetation models • qin = qsat(Ts) • Traditional (“empirical”) approach: rc = rc,min f(LAI)  f(light)  f(temp)  f(RH)  f(soil m) Land surface in climate models

21. Modelling rc via photosynthesis • An =  f(soil m) CO2 / rc • Thus: rc back-calculated from • Empirical soil moisture dependence • CO2-gradient CO2 • f(qsat – q) • Net photosynthetic rate An • An,max • Photosynthetic active Radiation (PAR) • temperature • [CO2] Land surface in climate models

22. Parameterization of soil and snow hydrology Bart van den Hurk (KNMI/IMAU) Land surface in climate models

23. 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 Land surface in climate models

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 Land surface in climate models

25. 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) Land surface in climate models

26. Relation between pressure head and volumetric soil moisture content strong adhesy/ capillary forces dewatering from large to small pores retention curve Land surface in climate models

27. 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 ( @  = -1m or -0.1 bar) • Effect on water balance: see spreadsheet Land surface in climate models

28. pF curves and plant stress • Canopy resistance depends on relative soil moisture content, scaled between wilting point and field capacity Land surface in climate models

29. 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 Land surface in climate models

30. 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 Land surface in climate models

31. 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 Land surface in climate models

32. 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) • More complex approaches exist (multi-layer, melting/freezing within layers, percolation of water, …) Land surface in climate models

33. Snow energy budget • with • (C)sn = heat capacity of snow • (C)i = heat capacity of ice • GsnB = basal heat flux (T/r) • Qsn = phase change due to melting (dependent on Tsn) Land surface in climate models

34. 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. Land surface in climate models

35. Exercise • Given: • Derive the Penman-Monteith equation: Land surface in climate models

36. More information • Bart van den Hurk • hurkvd@knmi.nl Land surface in climate models