Dirmeyer

1
Land Surface ParameterizationsPart I Basic
Concepts

• Paul Dirmeyer
• Center for Ocean-Land-Atmosphere Studies

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Parameterizations

• parameterization
• noun Etymology New Latin, from para- Greek
  metron measure
• 1 a function or representation using empirical
  relationships or arbitrary constants whose value
  characterizes a member of a system (as a family
  of curves) also a quantity (as a mean or
  variance) that describes a statistical population
  
• 2 an approximation of any of a set of physical
  properties whose values determine the
  characteristics or behavior of something

Land surface models are parameterizations of the
large-scale behavior of the land surface.
Whereas the laws of thermodynamics and fluid
mechanics are well known and easily scalable (the
basis of ocean and atmosphere models), the
physics of the land surface is, by and large,
complex, imperfectly understood, and not easily
scalable.
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The Bucket Model

• The first attempt to model an interactive land
  surface in a GCM was only about 35 years ago
• Manabe, S., 1969 Climate and the circulation, I.
  The atmospheric circulation and the hydrology of
  the earth's surface. Mon. Wea. Rev., 97, 739-774.
• Evaporation was calculated by a simple linear
  relationship
• where w is the soil wetness and b is a moisture
  availability factor that varies with soil
  moisture content. Typically b has a form like

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The Bucket Model

• The soil water capacity of a bucket is typically
  15 cm of water.
• Why 15? The assumption is that the active soil
  column is 1 m deep. Soil porosity is around
  0.45, so that column can hold 45 cm of water at
  saturation. The first third is below the wilting
  point, and unavailable for evaporation. The
  middle third is available, across the range from
  completely stressed to completely unstressed.
  The last (wettest) third is above field
  capacity, where any additional precipitation runs
  off. So the bucket represents the middle third
  of 45 cm 15 cm. Of course, this is all quite
  arbitrary.
• There is also the leaky bucket where runoff can
  occur below b  1.

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Other Methods
Whereas the bucket uses the beta method, there
is an alternative empirical method called the
alpha method
a is a function of soil wetness, e is the vapor
pressure, es is the saturated vapor pressure at
atmospheric temperature TC, e is the
psychrometric constant, ps is surface atmopsheric
pressure, r is the density of air, and ra is the
aerodynamic resistance. There is also a
threshold method

• Where Ec is the evaporative flux from the soil.
  The alpha and beta methods reduce to the
  threshold method with the appropriate choices of
  a and b
• a exp(-y) with ? being the matric potential
• b  1 for Ep 

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Uncertainty Leads to Variety
As an example of the many forms for expressing
potential evaporation, the following appendix is
from a paper by Fedderer et al (1996)
Notice the various independent variables
listed temperature, humidity, wind speed, solar
radiation, canopy radiative properties,
roughness, cloud cover, atmospheric stability,
even length of day.
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The Green Bucket

• The simplest improvement one can make on the
  Bucket Model is to add a proxy of vegetation
  effects

This is how evaporation was calculated in the
NCEP reanalysis model!
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Vertical Structure in the Soil

• The next level of complexity is to include
  vertical structure (i.e., more than one layer) in
  the soil. The simplest approach is known as the
  Force Restore method. It is still used today
  in some LSSs for heat or moisture transfer, but
  it is considered primitive.
• Heat (or moisture) flows down gradient

Where is the heat flux vector (only vertical
in our case), k is the thermal conductivity of
the medium (soil), and C is the heat capacity of
the soil. Substituting for
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Vertical Structure in the Soil
In the force-restore formulation, it is assumed
that conductivity does not vary with depth, so
that the prediction equation for surface
temperature simplifies to
The general solution for a parabolic PDE of this
type is straightforward
?j is the e-folding depth at the frequency w,
where the vertical coordinate z is positive
downwards from the surface.
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Vertical Structure in the Soil
For a single forcing frequency w (omitting the
subscript j )
So that
This is typically applied to two main forcing
frequencies the diurnal cycle and the annual
cycle. This gives us, two layers a shallow
layer that can be penetrated by the diurnal
cycle, and a deeper layer that is affected by the
annual cycle
The depths where these equations apply are a
function of the heat capacity, conductivity and
frequency of forcing. Often the heat capacity is
made a function of soil wetness, so that the
depths may vary in time as soil wetness changes.
That makes this scheme very difficult to validate
with measurements in the field!! And what if
there are forcings at other frequencies??
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Discrete Vertical Layers - Heat

• Most LSSs have discrete vertical layers,
  increasing in thickness with depth. This last
  point is borne from the derivation of the
  Force-Restore method, which shows that small
  spatial variations (with strong vertical
  gradients) are necessarily damped out as they
  penetrate the soil, leaving larger, broader
  structures to penetrate further. Thus, vertical
  resolution must be highest near the surface, and
  can be much coarser at depth.
• Going back to our diffusion equations (now
  strictly in the vertical)

We no longer constrain k to be constant it may
vary with depth. Conductivity depends on soil
texture, soil wetness and soil structure, and
there are many different ways to estimate it (all
based on some kind of curve-fit to laboratory
measurements). C is a function of soil texture
and wetness q
qs is the porosity of the soil.
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Discrete Vertical Layers - Water
Turning to soil wetness, from Darcys law
Note the resemblance to the heat diffusion
equation on the previous page. Now F is the
vertical moisture flux. There are two forces at
work in the vertical. One is the force of
gravity pulling water down. The other is the
down-gradient diffusion of water which may be
either up or down, depending on the profile of
soil moisture. The flux can be expressed as
Where k(q) is the hydraulic conductivity, and
l(q) is the hydraulic diffusivity both functions
soil wetness.
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Conductivity and Diffusivity
Substituting into the predictive equation, we get
There are many functional relationships, all
empirical, to express k and l in terms of soil
wetness. They allow reduction of the above
predictive equation to a single unknown. Most
common in land surface schemes is the Clapp and
Hornberger relationship
This approach lends itself to discretization into
layers of finite thickness
Where i is the layer number (typically 3-10
layers), and i1/2 refers to the interface
between layers i and i1.
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Relating l and k to Soil Moisture
There are many alternatives to the Clapp
Hornberger approach. Some are tailored to fit
special situations very accurately. Some try to
fit a broad range of soils reasonably well.
Clapp Hornberger is a broad approach. Many
hydrologists prefer the method of van Genuchten
There are many variations on these two main
approaches, as well as others both empirical, and
based on knowledge of soil particle and pore size
distributions.
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Beyond the Unsaturated Zone
Typically the layers of a discrete soil model are
restricted to the first few meters below the
surface. At the bottom of the lowest layer,
drainage is assumed to go into base flow, never
to return. However, some models account for the
water table, its contribution to runoff, and its
ability to return soil water to the surface.
These are a function of the depth of the water
table
The logarithmic term is called the topographic
index, which is a function of the local slope b
and the upstream area a. Models that use a
topographic index to determine the depth of the
water table use the TOPmodel concept.
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Simulating the Water Table
One variant is the VIC (Variable Infiltration
Capacity) model.
The figure at right shows how the fraction of
precipitation P that contributes to runoff (Qd)
increases as soil moisture Wo increases. Here i
is the infiltration capacity, As is the fraction
of a grid cell for which the infiltration
capacity is less than i, and B determines the
shape of the infiltration curve
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The Family Tree
Two main original SVATS (Soil-Vegetation-Atmospher
e Transfer Schemes) BATS (Biosphere Atmosphere
Transfer Scheme Dickinson et al 1986) and SiB
(Simple Biosphere Sellers et al. 1986). These
were among the first to include the effects of
vegetation, although still in a highly empirical
way. BATS uses simple curve fits, based on
observational data, to keep the model efficient
while including a broad range of important
processes. SiB is quasi-physical, and attempts to
simulate vegetation processes more directly. The
original SiB and its SiBlings are based on the
idea that plant moisture stress regulates ET.
The latest evolutions of both models have shifted
to a more realistic approach, where ET controls
are based on photosynthesis demands. Most LSSs in
the world today derive in some way from these two
models, either by inspiration, formulation, or
direct use of portions of their code.
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Transpiration Formulations
These are as varied as the potential evaporation
formulations
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Vegetation Type vs. Plant Functional Type
These terms are often used interchangeably.
Plant Functional Type (PFT) is a term used more
by ecologists, and is more accurate in describing
how vegetation is classified in LSSs. Most
schemes use a small number of plant functional
types, usually fewer than ten. They are primarily
based on characteristics of growth form (tree,
shrub, grass), leaf form (broad leaf, needle
leaf), leaf phenology (evergreen, deciduous), and
leaf physiology (C3, C4). C3/C4 refers to the
specific chemical process used to create sugar
from water, CO2, and light (called the
"photosynthetic pathway"). All plants do C3
photosynthesis. The C3 pathway, also called
Photosynthetic Carbon Reduction, involves
catalysis by an enzyme called "RUBISCO" (the most
abundant protein on the planet). It evolved when
CO2 was more abundant in the atmosphere, and O2
was rarer. RUBISCO. The problem with C3 is that
RUBISCO can also catalyze reactions with O2
(called photorespiration) which does nothing to
feed the plant. About 6 CO2 are fixed by RUBISCO
for every 1 O2. "C3" comes from the fact that
the first product of CO2 fixation is
3-phospho-glycerate, a 3-carbon compound.
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C3 C4
Some plants (mostly grasses in warm regions) have
evolved another pathway called C4.
Plants with C4 achieve a lower rate of
photorespiration than their pure C3 counterparts.
They produce a 4-carbon compound - oxaloacetic
acid. In the C4 pathway, no O2 is fixed, so the
process is more efficient. But it is also more
temperature sensitive.
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Handling Vegetation Heterogeneity
Some examples BATS, SiBBig leaf models with
one vegetation type per grid LSM Includes a few
extra hybrid vegetation types to account for
some common, simple vegetation combinations Mosaic
A number of defined homogeneous vegetation
types tile each grid with fractions of
each Sechiba Like Mosaic, except fluxes are not
blended at the surface, but at the top of the
boundary layer

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Soil Heterogeneity
Runoff
Infiltration Many LSSs represent the transient
and highly spatially variable nature of
convective precipitation by assuming a sub-grid
distribution of rain where most of the rain falls
over a very small area. This
enhances runoff. Also, soil texture may vary
greatly over a distance of meters. Diffusivity
and conductivity can vary by orders of magnitude
over a grid box. Evaporation Stressed (no
evapotranspiration), unstressed (ET below the
potential rate), and saturated (wetlands, rivers,
etc.) (e.g., new model from Koster Ducharne)
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CHASM (CHAmeleon Surface Model)
Desborough (1999) developed an LSS which can can
be operated in a variety of surface energy/water
balance modes ranging from Manabe's simple
bucket, up to a complex SVAT scheme.
Comparison of modes of complexity of CHASM in
four PILPS experiments GCM-derived a) tropical
forest and b) grassland sites from PILPS(1) c)
Cabauw PILPS 2(b) d) HAPEX MOBILHY PILPS 2(a).
Dots represent all of the participating PILPS
models. CHASM modes from simplest to most
complex M69 (Manabe bucket), SIMP (has snow and
baseflow) SIMP-A (has stability correction in
flux terms) RS (includes a surface resistance at
the value shown (s m-1)) SLAM (full SVAT scheme
with canopy resistance and tiles a la Mosaic.
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Carbon

• Leaf photosynthesis is limited by one of three
  things
• availability of light
• maximum rate of the Rubisco enzyme process
• Carbon compound export (C3) or PEP-Carboxylase
  limitation (C4)
• The rate of carbon flux into the plant can be
  modeled in the same way as transpiration out of
  the plant as a diffusive flux through the
  stomata, regulated by stomatal conductance.
• When carbon is in the model, the CO2 gradients
  can also affect rc. The rate at which
  photosynthesis "fixes" carbon in the plant
  (converts from gaseous CO2 to sugars) affects the
  CO2 concentration in the leaf, and thus the flux
  rate

Thus, a carbon budget can be kept along with the
water and energy budgets. These models can be
used in ecology and global change
studies. Fancier elements can be added, like
nutrient (nitrogen) dependence, storage of carbon
in the soil, etc.
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Choosing Parameters
With a complex LSS, how does one choose all the
parameters? Some are measured in the field,
although it is necessary to extrapolate
measurements for a few or one species to all
members of a vegetation type. This leaves a
great deal of uncertainty (and potentially
inaccuracy) for simulations where a complete set
of parameters are not available. And some
parameters are not measurable. Another
alternative is to calibrate the model at
locations with observed fluxes (but not
necessarily observed model parameters). This can
be done by changing each parameter one-at-a-time.
A better approach is to use a multi-criteria
method where all parameters are tuned
simultaneously to minimize errors across multiple
measured variables.
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Optimal Approaches to Parameters
One can remove almost all of the error from one
variable this way, at the expense of errors in
other variables. One cannot remove all the
errors in all fluxes this way, because the LSS is
not perfect, and does not include every process
in the real world. It has been found that when
models are tuned to minimize error in this way,
complex schemes generally perform better than
simple schemes, but the rate of improvement
decays as complexity increases.
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What About Snow?

• Snow is a complicating factor, as is
  freezing/thawing of soil. It is a lot easier to
  simulate land surface processes during the warm
  season than during the cold season. Snow affects
  absorption of solar radiation (high albedo),
  surface temperature (insulation), evaporation
  (availability of moisture).
• Simple (e.g., original SiB) any snow is spread
  uniformly across the grid box.
• Problem albedo goes way up with the first
  snowflake.
• Fractional coverage snow coverage ramps up from
  0 to some critical snow depth, to allow albedo to
  increase gradually.
• Problem a deep snowpack will have vertical
  gradients in temperature, density, and radiation
  penetration.
• Multi-level snow model Like a multi-level soil
  model.
• What about vegetation and snow?
• As snow accumulates, it covers low vegetation
  (e.g. grass). But snow remains under a canopy,
  and can be shaded or obscured (even under the
  branches of a deciduous canopy). This was not
  taken into account in most models until recently.
  This omission lead to a cold bias over snow in
  both the NCEP and ECMWF forecast models, and was
  diagnosed with the aid of data from remote
  sensing and the BOREAS field experiment.

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Other Heterogeneities
Precipitation Convective rainfall may be assumed
to fall non-uniformly over a grid box. Most of
the rain falls with high intensity over a
fraction of the area. This means less
precipitation infiltrates the soil, and more
precipitation runs off than would happen with a
steady, uniform rain. The parameterization of
sub-grid precipitation allows for a more
realistic surface water balance. Temperature Asid
e from the mosaic tiling of surface cover types,
the variation of temperature with elevation
within a grid box may also be included. This can
be very important in mountainous terrain.
Orography can also be tied to sub-grid
distributions of snow. Lakes/Wetlands Open water
from large rivers or lakes can be an important
source of moisture fluxes and temperature
moderation in certain conditions (e.g., arid
regions, early winter (high latent and sensible
heat flux), and spring (frozen water, reduced
fluxes). Seasonal wetlands can also affect
fluxes well into the dry season where monsoon
seasonality is dominant. Some LSSs even include
an explicit lake model (usually either a slab
model, or a one-dimensional column model)
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Going 2-D
It is important to recognize the difference
between what happens at a point (e.g. a weather
station, or a flux tower) and what happens over
an area (as represented in a GCM). Most
observational data are at individual points.
Once a LSS is developed and calibrated in this
way, it is often used in a GCM or regional model
with little or no adjustment. This is especially
true for hydrology
Imagine what happens as a small storm moves
across the area of a grid box. At the point (j)
there is no rain, then a brief period of heavy
rain rates, then no rain. But averaged over the
box, there is a nearly constant, light rain rate.
A LSS calibrated to produce the proper
partitioning of runoff and infiltration at a
point, where rain rates are observed to fluctuate
strongly, will produce little or no runoff when
applied over large grids. Either the sub-grid
distribution of rainfall must be parameterized,
or the runoff parameterization must be
reformulated to be appropriate at the larger
spatial scale.
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Other Elements
River routing Most LSS do not concern themselves
with water once it runs off. A river routing
model is a means to couple the land to the ocean.
More sophisticated routing models can simulate
the interaction between the atmosphere and water
bodies, seasonally inundated wetlands, and even
floods. Human activity The effects of human
land use/abuse on the distribution of vegetation,
or on its seasonal cycle (e.g. planting and
harvesting, or grazing by livestock) can be
simulated. Fire Both natural and man-made fires
affect both the land surface, and the atmosphere
(aerosol production, radiative effects of smoke).
These effects can be locally and regionally
important.
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Other Elements
Falls Storms can cause treefalls or cropfalls
over areas of importance at the mesoscale. The
importance of this kind of land cover change on
local climate is only beginning to be
investigated. Species competition, global
change On longer time scales, the evolution of
the biosphere as a whole can be modeled. This
can be done statistically, by mapping vegetation
types to particular climate zones and soil types,
or dynamically by extending the carbon modeling
to whole plant modeling (including growth, death,
and competition between species or plant
functional types). The first studies focused on
the changes induced by ice-age fluctuations,
where paleological evidence exists for the
migration of vegetation. Emphasis is now
shifting to prediction of responses to climate
change and global warming.
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