Land-Surface Modeling

1. Land-Surface Modeling 19 November 2012

2. Thematic Outline of Basic Concepts • What are the physical processes that are relevant to land-surface modeling? • How are these processes represented by a land-surface model? • How do land-surface models and data assimilation systems operate with atmospheric models?

3. Land-Surface Modeling • A land-surface model must be able to accurately depict the interactions of… • …the surface with the atmosphere • …the substrate with the surface • Here, we take the surface to refer to land and the substrate to refer to the sub-soil (sub-surface) layer. • Ocean modeling and air-sea interaction are important, but a separate, extensive set of lectures in their own right.

4. Land-Surface Modeling • Land-surface modeling requires the accurate representation of heat and moisture transfer within the surface and between it and the atmosphere. • Accurate atmospheric input to the surface is required for this to be achieved, however. • Land-surface modeling is thus best viewed as a coupled system between the atmosphere and surface.

5. Constructs for Land-Surface Modeling • Land-Surface Model (LSM) • Run simultaneously with an atmospheric model to predict primarily surface-atmosphere heat and moisture transfer. • Land Data Assimilation System (LDAS) • A standalone version of the LSM that synthesizes atmospheric inputs and surface information to predict the initial states of relevant land-surface fields. • Necessary for accurate atmospheric model initialization as such data are not routinely observed over wide areas.

6. Why Use an LDAS? • Necessary to spin-up realistic soil state fields. • True whether direct observations exist or not. • Akin to doing data assimilation for an atmospheric model. • Help to correct the initial estimates for soil state fields • Like atmospheric models, LSMs are imperfect! • Need to constrain soil state estimate to reality! • Note: when running a model, use the same LSM as was used to create the initial soil state fields! • Output from LSM may not work well with another LSM…

7. Land-Surface Modeling • LSM Input… • Land state variables (vegetation, soil moisture, soil temperature, topography, etc.) • Atmospheric information (winds, temperature, precipitation, radiative forcing) • LSM Output… • Surface latent and sensible heat fluxes • Reflected shortwave and emitted longwave radiation • Updated soil state (temperature and moisture) fields

8. Land-Surface Modeling surface substrate

9. Land-Surface Modeling • An LSM must be able to accurately simulate physical processes influencing heat and moisture transport… • …within the substrate • …along the surface-substrate interface • …along the atmosphere-surface interface • A full listing of relevant processes may be found on pgs. 172-174 of the text.

10. First Principles of LSMs Surface Energy Balance: R = LE + H + G R = net radiative forcing LE = latent heating H = sensible heating (surface<->atmosphere) G = sensible heating (substrate<->surface) Land-surface modeling deals with how to compute the land-surface terms of the surface energy budget.

11. First Principles of LSMs Radiative Forcing: Q = direct solar radiation incident at surface q = diffuse solar radiation incident at surface α = albedo (1-α = transmittance) I↑ = outgoing longwave radiation emitted by surface I↓ = absorbed longwave radiation emitted by atmosphere Note: typically computed by radiation parameterization

12. First Principles of LSMs Surface Water Budget: Θ = volumetric soil water content (dimensionless) P = precipitation, snowmelt, deposition, irrigation input ET = loss due to evapotranspiration RO = loss due to lateral runoff D = loss due to gravitational drainage to lower layers Land-surface modeling deals with how to compute the forcing terms of the surface water budget.

13. Second Principles of LSMs • Basic concepts: heat and moisture budget • Concepts influencing these budgets… • Vertical heat transport within the substrate • Vertical moisture transport within the substrate • Moisture transport within and by vegetation • We next describe the basic physics behind each of these concepts.

14. Vertical Heat Transport • Thermal Conductivity (ks): ability of the substance to transfer heat • Dependent upon soil composition (moisture content, density of soil vs. that of air, type of soil, etc.) • Heat Capacity (Cs): amount of heat required to raise the temperature of a unit volume by 1°C/1 K • Also dependent upon soil composition • Related: specific heat (cs), amount of heat required to raise the temperature of a unit mass by 1°C/1 K

15. Vertical Heat Transport • Thermal Diffusivity (Ks): ratio of thermal conductivity to the heat capacity (ks/Cs) • Controlling influence upon the rate of speed at which a temperature change propagates through a medium • Analogous to an exchange coefficient • Thermal Admittance (μs): the rate at which a surface can accept or release heat energy [μs = (ksCs)½] • Admittance of both the soil and atmosphere are important • Higher admittance = reduced temperature change because heat is transferred efficiently rather than stored locally

16. Vertical Heat Transport Moister soils require more thermal energy to warm by 1°C / 1 K than drier soils because of soil moisture dependence. thermal conductivity Moister soils have a greater ability to conduct heat because of soil moisture dependence. heat capacity thermal diffusivity thermal admittance Higher soil moisture content promotes a greater ability to transfer heat across a surface (rather than being trapped). Soil moisture dependence relies on ratio between increases in ks and Cs.

17. Vertical Heat Transport • Vertical heat transport in the substrate… • Primarily by conduction (molecular diffusion) • Down-gradient (from high to low) • Magnitude is proportional to that of the vertical temperature gradient and thermal conductivity, i.e., Hs = heat flux (positive upward) ks = soil thermal conductivity z = vertical coordinate (positive upward) Ts = substrate temperature

18. Vertical Heat Transport • Change of substrate temperature with time… • Change due to the vertical convergence of the heat flux: • If we make the approximation that thermal conductivity is constant with height within the substrate, we can write: Thus, Ts changes as a function of its second derivative with respect to depth and the thermal diffusivity (conductivity divided by capacity) of the soil.

19. Vertical Heat Transport

20. Vertical Heat Transport • Daytime: warmer surface than substrate… • First derivative of Ts with height is positive. • Second derivative is also positive. • Because the first derivative is more positive at the top of the substrate than at the bottom. • With Ks positive-definite, Ts increases with time. • This results in a warming of the substrate with time.

21. Vertical Heat Transport • Nighttime: warmer substrate than surface… • First derivative of Ts with height is negative. • Second derivative is also negative. • Because the first derivative changes is more negative at the top of the substrate than at the bottom. • With Ks positive-definite, Ts decreases with time. • This results in a cooling of the substrate with time.

22. Application: Daily Temperature Oscillation • Manifestation of vertical extent of thermal transport: • The amplitude of the temperature oscillation decreases exponentially with increasing depth. amplitude at sfc. P = wave period (diurnal = 24 h, annual = 365 d) amplitude at z

23. Application: Temperature Oscillation daily annual Note deamplification of wave with increasing depth, increased depth over a longer duration, and time lag of maximum and minimum temperature with increasing depth.

24. Application: Temperature Oscillation • The amplitude of this oscillation is greater when… • Large conductivity (ks) • Small heat capacity (Cs) • If the exchange of heat from the atmosphere to the surface and substrate is large, the temperature oscillation is larger and penetrates deeper. • Further discussion: pg. 180 of the text. large thermal diffusivity

25. Vertical Water Transport • Five mechanisms, two applicable to water vapor and three to liquid water. • Those applicable to water vapor… • Convection: occurs if/when lapse rate of soil temperature exceeds the dry adiabatic lapse rate. Permits upward water vapor transport through dry soils via buoyant plumes. • Vapor Diffusion: down-gradient, molecular-level diffusion of water vapor. Proportional to soil water vapor content.

26. Vertical Water Transport • Changes in the height of the water table below the substrate • A water surface must be in dynamic equilibrium with its surrounding fluid. • Thus, local water excesses or deficits are reconciled by lateral water movement. • This can locally raise the water table where initially lower, or vice versa.

27. Vertical Water Transport height of water table

28. Vertical Water Transport • Surface-tension (molecular bonding/capillary) effects • Dependent upon soil moisture content and how well the soil can be permeated by water (porosity) • With stronger surface tension, water molecules are more strongly bound to soil particles. • Typically with wetter, less porous soils. • Permits water to gradually move upward via molecular attraction. • Generally manifest in the lower substrate, between the water table and the relatively dry layer above it. • Movement is typically from wetter to drier soils.

29. Vertical Water Transport • Downward infiltration from the surface • Driven by gravity, controlled by surface-tension, and influenced by the soils’ ability to retain water. • Water intake comes from rainfall, snowmelt, irrigation, etc. • Relevant definitions… • Hydraulic conductivity: ability of soil to transport water vertically; greatest when soil is wet and porous • Soil moisture potential: amount of energy needed to extract a given amount of water from a given type of soil (inverse of conductivity)

30. Water Transport by Vegetation • Influences the energy budget at the surface as well as the soil moisture content. • Relevant processes… • Extraction of substrate water by plants • Evaporation of surface water collected on the plant canopy • Transpiration of water vapor out of plant leaves’ pores • Largely dependent upon vegetation type and density, atmospheric moisture content, time of day/year, and heat and water stresses. • Physics behind transpiration are not well-understood, however.

31. Soil Moisture Budget • As we did for soil temperature, we now wish to express the soil moisture budget mathematically. • This expression will apply to subsurface layers and thus does not include direct effects of precipitation, evaporation, and runoff. • The surface soil moisture budget must include information about these import and export processes. • Mathematical manifestation: vertical moisture flux

32. Soil Moisture Budget Soil Moisture Budget: Θ = volumetric soil water content (dimensionless) Et = loss to plant canopy by evapotranspiration Liquid Water Mixing Ratio Tendency: KΘ = hydraulic conductivity (associated with infiltration) DΘ = soil water diffusivity (associated with surface-tension)

33. Soil Moisture Budget • Both KΘ and DΘ are highly non-linearly dependent upon soil moisture content and soil type. • Different models use different formulations; the example from the text is given by: Subscripts of s denote saturation values. b = empirically-derived coefficient Ψ = soil moisture potential Note dependence upon both soil moisture (via Θ) and soil type (parameters above).

34. Surface Energy Budget • General idea: transport from the surface to the atmosphere occurs via conduction (laminar sublayer). • Above the laminar sublayer, transport occurs via turbulent eddies. • We will effectively encapsulate both within our formulations for the surface heat and moisture fluxes. • Manifest via eddy (rather than molecular) diffusivities

35. Surface Energy Budget Surface sensible and latent heat fluxes: Ca = heat capacity of atmosphere cp = specific heat of atmosphere at constant pressure q = specific humidity KHa = diffusivity of heat in air KWa = diffusivity of moisture in air Subscripts of “ls” denote computation in laminar sublayer.

36. Surface Energy Budget Assumption: fluxes approximately constant with height DH = exchange coefficient for heat DW = exchange coefficient for moisture Both are integral functions of KH and KW with large dependence upon stability, wind speed, and surface roughness. Tg = ground temperatureTa = atmospheric temperature near the surface qs,sat = saturation specific humidity at Tg qa = atmospheric mixing ratio near the surface

37. Surface Energy Budget • Interpretation… • Flux direction: dependent upon the magnitude of Tg and/or qs,sat versus Ta and/or qa. • Flux magnitude: dependent upon the magnitude of the differences between the above variables. • Examples… • Sensible heat flux is large and upward when Tg >> Ta and DH is large (near-surface winds strong). • Latent heat flux is large and upward when Tg is warm (large qs,sat), qs >> qa, and DW is large (near-surface winds strong).

38. Two Short Digressions • Importance of accurate topography specification… • Finer grid spacing and effective resolution = better representation of sharp gradients in terrain height. • Permits more accurate forecasts of orographically-driven phenomena.

39. Two Short Digressions • Urban canopy-related issues… • Differences from standard land-surface modeling… • Different surface characteristics (albedo, conductivity, permeability) • Different roughness lengths (buildings rougher than vegetation) • Shadowing and heat trapping by buildings (moreso than vegetation) • Three methods to handle… • Explicitly resolve buildings (computationally expensive, data limits) • Use an LSM that includes explicit large-scale urban representation • Use an urban canopy parameterization to approximate effects • For more information: see the references in the course text.

40. Land-Surface Modeling • Perspective: an LDAS provides information about the initial state to an LSM coupled to an NWP model.

41. Land-Surface Modeling • Landscape mapping provides information about soil type, vegetation type and cover, and related fields. • Look-up tables provide values of transfer-related coefficients based upon the landscape mapping. • The “initial” land-surface state estimate is provided by a cycled LSM; it is modified by atmospheric input.

42. Land-Surface Modeling • An LSM solves the relevant heat and moisture transport equations in finite difference form… • Surface energy balance • Radiation balance • Surface water budget • Soil temperature tendency • Soil moisture tendency • Sensible heat flux • Latent heat flux (substrate sensible heat flux solved using heat flux equation, radiation from parameterizations) (precipitation from NWP model, evapotranspiration parameterized, drainage solved from moisture flux equation) (substrate evolution)

43. Land-Surface Modeling • An LSM typically employs a surface layer as well as one to four substrate layers (e.g., 0-10 cm, 10-40 cm, 40-100 cm, 100-200 cm). • A fairly conclusive list of how LSMs differ from one another can be found on pg. 189 of the course text.