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

2. Land surface in climate models 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?

3. Land surface in climate models General form of land surface schemes Energy balance equation K (1 – a) + L – L + E + H = G Water balance equation W/ t = P – E – R s – D Q* H E G PE Infiltration RsRs D

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

5. Land surface in climate models 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

6. Land surface in climate models 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

7. Land surface in climate models 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

8. Land surface in climate models 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

9. Land surface in climate models Specification of vegetation types

10. Land surface in climate models Vegetation distribution

11. Land surface in climate models Surface radiative properties: Net radiation: integrate over spectrum and angles Albedo –combination of soil and vegetation –vegetation: dependent on spectral properties of leaves (scatter coefficient l = 0.3 voor VIS, 0.8 voor NIR) nr of absorbing/reflecting layers (LAI) orientation of leaves and irradiation

12. Land surface in climate models Albedo (cntd)

13. Land surface in climate models Climatological albedo (static vegetation) Jan Jul

14. Land surface in climate models Adjustment for snow New snowfall: a = a max (= 0.85) decline with time: –non-melting conditions: linear decrease (0.008 day -1 ) –melting conditions: –(a min = 0.5, f = 0.24) For tall vegetation: snow is under canopy –gridbox mean albedo = fixed at 0.2

15. Land surface in climate models Aerodynamic exchange Turbulent fluxes are parameterized as (for each tile): Solution of C H requires iteration: –C H = f(L) –L = f(H) –H = f(C H ) L = Monin-Obukhov length s a T a +gz s a H

16. Land surface in climate models More on the canopy resistance Active regulation of evaporation via stomatal aperture Two different approaches –Empirical (Jarvis-Stewart) r c = (r c,min /LAI) f(K ) f(D) f(W) f(T) –(Semi)physiological, by modelling photosynthesis A n = f(W) CO 2 / r c A n = f(K, CO 2 ) CO 2 = f(D)

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

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

19. Land surface in climate models 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 demoEXCEL sheet

20. Land surface in climate models Numerical solution Solution of energy balance equation With (all fluxes positive downward) Express all components in terms of T sk (with T p = T sk t -1 ) net radiation sensible heat flux latent heat flux soil heat flux

21. Land surface in climate models Numerical solution Substitute linear expressions of T sk into energy balance equation Sort all terms with T sk on lhs of equation Find T sk = f(T p, T soil, C H, forcing, coefficients)

22. Land surface in climate models 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)

23. Land surface in climate models The gross vegetation carbon budget GPP = Gross Primary Production NPP = Net Primary Production AR = Autotrophic Respiration HR = Heterotrophic Respiration C = Combustion GPP 120 AR 60 HR 55 NPP 60 C4C4

24. Land surface in climate models The coupled CO 2 – H 2 O pathway in vegetation models q in = q sat (T s ) Traditional (empirical) approach: r c = r c,min f(LAI) f(light) f(temp) f(RH) f(soil m)

25. Land surface in climate models Modelling r c via photosynthesis A n = f(soil m) CO 2 / r c Thus: r c back-calculated from –Empirical soil moisture dependence –CO 2 -gradient CO 2 f(q sat – q) –Net photosynthetic rate A n A n,max Photosynthetic active Radiation (PAR) temperature [CO 2 ]

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

27. Land surface in climate models Soil heat flux Multi-layer scheme Solution of diffusion equation with – C [J/m 3 K] = volumetric heat capacity – T [W/mK] = thermal diffusivity with boundary conditions –G [W/m 2 ] at top –zero flux at bottom

28. Land surface in climate models Heat capacity and thermal diffusivity Heat capacity – s C s 2 MJ/m 3 K, w C w 4.2 MJ/m 3 K Thermal diffusivity depends on soil moisture –dry: ~0.2 W/mK; wet: ~1.5 W/mK

29. Land surface in climate models Soil water flow Water flows when work is acting on it –gravity: W = mgz –acceleration: W = 0.5 mv 2 –pressure gradient: W = m dp/ = m p/ Fluid potential (mechanical energy / unit mass) = gz + 0.5 v 2 + p/ p = g z g(z+ z) = gh h = /g = hydraulic head = energy / unit weight = –elevation head (z) + –velocity head (0.5 v 2 /g) + –pressure head ( = z = p/ g)

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

31. Land surface in climate models Darcy and Richards equation q z = flux

32. Land surface in climate models Darcy and Richards equation = vol. soil moisture content (m 3 /m 3 ) K = hydraulic conductivity (m/s) D = hydraulic diffusivity (m 2 /s)

33. Land surface in climate models Implementation in discrete form adding root extraction: In (discrete) flux form: With F specified as: root extraction diffusion term gravity term

34. Land surface in climate models 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 spreadsheetspreadsheet

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

36. Land surface in climate models Boundary conditions Top: F [kg/m 2 s] = T – E soil – R s + M Bottom (free drainage) F = R d = w K with –T = throughfall (P l – E int – W l / t) –E soil = bare ground evaporation –E int = evaporation from interception reservoir –R s = surface runoff –R d = deep runoff (drainage) –M = snow melt –P l = liquid precipitation –W l = interception reservoir depth –S = root extraction PlPl T E int WlWl M E soil RsRs RdRd S

37. Land surface in climate models Parameterization of interception Simple budget equation with –E l = evaporation –D = dew collection –I = interception from precipitation Points for attention: –maximum storage reservoir ~ 0.2 mm per m 2 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)

38. Land surface in climate models Parameterization of runoff Simple approach –Infiltration excess runoff R s = max(0, T – I max ), I max = 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

39. Land surface in climate models 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 a max (0.85) non-melting conditions: linear decrease (0.008 day -1 ) melting conditions: exponential decay –(a min = 0.5, f = 0.24) –For tall vegetation: snow is under canopy gridbox mean albedo = fixed at 0.2

40. Land surface in climate models Effect of forest albedo (BOREAS)

41. Land surface in climate models Parameterization of snow water Simple approach –single reservoir –with F = snow fall E, M = evap, melt c sn = grid box fraction with snow Snow depth –with sn evolving snow density (between 100 and 350 kg/m 3 ) More complex approaches exist (multi-layer, melting/freezing within layers, percolation of water, …)

42. Land surface in climate models Snow energy budget with –( C) sn = heat capacity of snow –( C) i = heat capacity of ice –G sn B = basal heat flux ( T/r) –Q sn = phase change due to melting (dependent on T sn )

43. Land surface in climate models Snow melt Is energy used to warm the snow or to melt it? In some stage (T sn 0 C) its both! Split time step into warming part and melting part –first bring T sn 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.

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

45. Land surface in climate models Question Model: –frozen ground does not allow vertical moisture movement –melting snow on frozen ground: runoff –water lost for the warm season Real world: –some melting water will percolate via large pores or holes –less runoff, more storage Question: how could we change our parameterization?

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