Land-Surface Modeling
19 November 2012
Thematic Outline of Basic Concepts
• What are the physical processes that are relevant to
land-surface modeling?
• How are these processes represented by a landsurface model?
• How do land-surface models and data assimilation
systems operate with atmospheric models?
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.
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.
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.
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…
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
Land-Surface Modeling
surface
substrate
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.
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.
First Principles of LSMs
Radiative Forcing:
R  Q  q1     I   I 
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
First Principles of LSMs
Surface Water Budget:

 P  ET  RO  D
t
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.
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.
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
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
Vertical Heat Transport
thermal
conductivity
heat acapacity
Moister soils
require
more thermal energy
Moister soils have
greater ability to
to warm by 1°C / 1 K than drier soils
conduct heat because of soil moisture
because of soil moisture dependence. dependence.
thermal diffusivity
thermal
admittance
Higher soil moisture
content promotes a Soil moisture
dependence
relies on ratio
greater ability to transfer heat across a between increases in ks and Cs.
surface (rather than being trapped).
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.,
H s  k s
Ts
z
Hs = heat flux (positive upward)
ks = soil thermal conductivity
z = vertical coordinate (positive upward)
Ts = substrate temperature
Vertical Heat Transport
• Change of substrate temperature with time…
– Change due to the vertical convergence of the heat flux:
Ts
T 
1 H s
1 


  ks s 
t
Cs z
Cs z 
z 
– If we make the approximation that thermal conductivity is
constant with height within the substrate, we can write:
Ts k s  2Ts
 2Ts

 Ks 2
2
t Cs z
z
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.
Vertical Heat Transport
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.
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.
Application: Daily Temperature Oscillation
• Manifestation of vertical extent of thermal transport:
Ts z
   1/ 2 
 
 T sfc exp z
  K s P  
amplitude at sfc.
P = wave period
(diurnal = 24 h,
annual = 365 d)
amplitude at z
• The amplitude of the temperature oscillation
decreases exponentially with increasing depth.
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.
Application: Temperature Oscillation
• The amplitude of this oscillation is greater when…
– Large conductivity (ks)
– Small heat capacity (Cs)
large thermal diffusivity
• 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.
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.
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.
Vertical Water Transport
height of
water table
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.
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)
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.
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
Soil Moisture Budget
Soil Moisture Budget:

q
   Et
t
z
Θ = volumetric soil water content (dimensionless)
Et = loss to plant canopy by evapotranspiration
Liquid Water Mixing Ratio Tendency:
q  
  K   
 
  K   D


D

 

t z 
z  z z 
z 
KΘ = hydraulic conductivity (associated with infiltration)
DΘ = soil water diffusivity (associated with surface-tension)
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:


K   K s 
 s 
2b 3
 bKs s   
D  



  s 
b 3
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).
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
Surface Energy Budget
Surface sensible and latent heat fluxes:
H  Ca K Ha
T
T
  c p K Ha
z ls
z ls
LE  Ca KWa
q
q
  c p KWa
z ls
z ls
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.
Surface Energy Budget
Assumption: fluxes approximately constant with height
H  c p DH Tg  Ta 

LE  LDW qs,sat Tg   qa

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 temperature
Ta = atmospheric temperature near the surface
qs,sat = saturation specific humidity at Tg
qa = atmospheric mixing ratio near the surface
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).
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.
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.
Land-Surface Modeling
• Perspective: an LDAS provides information about the
initial state to an LSM coupled to an NWP model.
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.
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)
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.