Transcript No Slide Title

NEW DIRECTIONS IN LAND SURFACE MODELING
Sellers et al. (1997) list 3 generations of land surface models:
1. Simple (e.g., “bucket”) models (see previous lecture)
2. SVAT models (like Mosaic; see previous lecture)
3. Models handling carbon
In this lecture, we will:
-- Take a brief look at generation #3. (Thanks to Jim Collatz for
various carbon cycle figures.)
-- Go over an analysis of evaporation and runoff formulations that
suggests an alternative path of model evolution.
-- Describe a new land surface model that follows this alternative
path.
Why the interest in carbon? Clearly,
for questions of global climate change.
Why the interest in
modeling the land’s role in
the carbon cycle? Note, for
example, the impact of land
seasonality on the
atmospheric CO2 content.
Land sources and sinks of carbon
are net yet well quantified, as
indicated by the famous “missing
carbon sink”.
(Slightly dated) list of carbon modeling references, from a compilation by Jim Collatz:
“[Third generation models] use modern theories
relating photosynthesis and plant water relations
to provide a consistent description of energy
exchange, evapotranspiration, and carbon
exchange by plants…. The third-generation LSPs
point the way to future land models that can be
coupled with comprehensive atmospheric and
ocean models to explore different global
exchange scenarios.” -- Sellers et al.
SiB2
Many different types of carbon assimilation models exist. In the particular comparison shown
here, only SiB2 is a “SVAT-type” carbon model. All of these models, though, have the same
goal: to understand the global distribution and temporal variations of the carbon cycle at the land
surface.
Annual net primary production (g C m -2 yr-1) estimated as the average of all
model NPP estimates.
IGBP/GAIM REPORT SERIES, REPORT #5, “NET PRIMARY PRODUCTIVITY MODEL INTERCOMPARISON ACTIVITY (NPP)”, Wolfgang
Cramer and the participants* of the "Potsdam '95" NPP model intercomparison workshop
DYNAMIC VEGATION: Yet another step forward in model development
Typical GCM approach:
ignore effects of climate
variations on vegetation
Early attempts at
accounting for vegetation/
climate consistency
Fully integrated dynamic
vegetation model
Figure from Foley et al., “Coupling dynamic
models of climate and vegetation”,
Global Change Biology, 4, 561-579, 1998.
DYNAMIC VEGATION (cont.)
Mappings between climate
and vegetation exist that can
be used for the second approach
on the previous page.
Figure from Mather, The Climatic
Water Budget in Environmental
Analysis, Lexington Books.
The third approach on the previous
page requires a whole new type of
model framework.
Figure from Foley et al., “Coupling dynamic
models of climate and vegetation”,
Global Change Biology, 4, 561-579, 1998.
(Analysis introducing a possible alternative path for LSM development)
What underlies the behavior of a land surface model?
PILPS (the Project for the Intercomparison of Landsurface Parameterization
Schemes): a project in which the responses of various land surface models to
the same atmospheric forcing are quantified and compared. Overall goal: a
better understanding of land surface model (LSM) behavior.
Typical PILPS result: wide
disparity in LSM response.
How do we explain this disparity?
We can’t compare code or even
compare descriptions of the
parameterizations -- the LSMs are
too complex, and such a comparison
would soon become intractable.
Alternative approach: empirically
characterize underlying controls on
evaporation and runoff.
Reference: Koster, R. and P. C. D. Milly, The interplay
between evaporation and runoff formulations in a land
surface model, J. Climate, 10, 1578-1591, 1997.
Many of the models that performed the experiment on the previous page
performed a supplemental experiment that imposed a great many controls:
Prescribed vegetation type and fraction
Prescribed albedo
Prescribed aerodynamic resistance
No seasonal variation in vegetation parameters
No snowfall
Model disparity remained high:
In fact, model disparity is even
higher than before -- apparently,
in the control (on the previous page),
differences in the above quantities
led to compensating effects.
The experiment to the left, though,
simplifies the task of explaining differences
in LSM behavior.
Consider a simple water balance model:
w(n+1) - w(n)
Dt
= P - Ei - Rs - Ew - Q
functions of w
P
(prescribed)
Ei (prescribed)
Ew (computed)
Rs (computed)
P - Ei
w
(root zone
soil moisture)
1
25
bT
R
Q
0
Runoff ratio = R =
Rs
P - Ei
Baseflow = Q (mm/day)
0
200 400 600 800 1000
Simple case: no baseflow
Q (computed)
Transpiration efficiency = bT =
0
1
E - Ei
Ep - Ei
bT
R
0
0
200
400
bT = 0 defines lower
limit of soil moisture
600
800
1000
R = 1 defines upper
limit of soil moisture
(when no baseflow)
How might these linear relationships look?
For each model participating in the PILPS experiment, we can plot monthly
average root zone soil moisture (w) against monthly average bT, R, and Q,
for each of the 12 months. We can then fit, through simple regression,
lines that characterize (to first order) the model’s inherently complex
relationships between soil moisture and the fluxes.
bT vs w for 3 LSMs
R vs w for 3 LSMs
Fits certainly aren’t perfect, but
they do describe the first order
relationship.
Q vs w for 3 LSMs
Through these fits, we see that each LSM is characterized by
different relationships between root zone moisture and the fluxes.
dashed line:
R
heavy line:
bT
dotted line:
Q
In the simple water balance model, take Rs = R(w) (P - Ei)
Ew = bT(w) (Ep - Ei)
G = G(w)
When the fitted curves are used to define the coefficient of the Rs, Ew, and
G functions, and when the simple water balance model is used with these
values, the resulting transpiration fluxes agree very well with the
fluxes the original models simulated.
Key interpretation:
the simple linear fits
capture much of the
intrinsic behavior of
the different LSMs.
Note the the success of the simple water balance model (with coefficients
from linear fits) extends beyond the annual scale -- it also applies to the
models’ simulation of seasonal transpiration rates.
We can extend this analysis further by considering the annual mean of the water
balance equation: P - Ei = Rs + Ew = R(w) (P - Ei) + bT(w) (Ep - Ei)
The unique solution can be written:
Ew
2 D bT
=
1 + 2 D bT fR
P - Ei
where D = ( Ep - Ei ) / ( P - Ei )
(a climatic “index of dryness”)
1
bT
bT = Average of beta function
across soil moisture range
R
0
fR = Fraction of soil moisture
range over which runoff
occurs.
Assume for now
that the drainage
term can be
“folded into” the
runoff term.
wO
wr
w1
fR
bT
= shaded area / (w1-w0)
1
fR = (w1-wr)/(w1-w0)
Although the equation produces a biased evapotranspiration, it nevertheless
explains (in large part) the variability amongst the models.
as described by
bT and fR
Thus, it is the relative positions of the runoff and evaporation functions
that determine the annual transpiration rate -- not the average soil moisture.
Most important take-home lesson: soil moisture in one model need
not have the same “meaning” as that in another model. As long as the
transpiration and runoff curves have the same relative positions, two
models (e.g., Models A and B below) will behave identically, even if
they have different soil moisture ranges.
(True for simple models in simple
water balance framework and for
complex LSMs running in AGCMs.)
Model A
Model B
1
1
bT
bT
R
R
0
0
200
400
600
800
1000
0
0
200
400
600
800
1000
Sure enough, the LSMs in PILPS
have different soil moisture ranges...
…and there is no evidence that LSMs
with higher soil moistures produce
higher evaporations.
Important aside: What does “model-produced soil moisture” mean?
What are the implications of a misinterpreted soil moisture?
Common problem: GCM “A” needs to initialize its land model with realistic
soil moistures for some application (e.g., a forecast).
Misguided, dangerous, and all too common solution: Use soil moistures
generated by GCM “B” during a reanalysis or by land model “C” in an offline
forcing exercise (e.g., GSWP), after correcting for differences in layer depths
and possibly soil type.
This solution is popular because of a misconception of what “soil moisture”
means in a land model. Contrary to popular belief,
-- model “soil moisture” is not a physical quantity that can
be directly measured in the field.
-- model “soil moisture” is
best thought of as a model- specific
“index of wetness” that increases
during wet periods and decreases
during dry periods.
Should a land modeler be concerned that modeled soil moisture has a
nebulous meaning – that it doesn’t match observations?
It depends on one’s outlook. Consider that in the real world:
(1) soil moisture varies
tremendously across the
distances represented by
GCM grid cells,
wet
hundreds of km
and
(2) surface fluxes
(evaporation, runoff,
etc.) vary nonlinearly
with soil moisture.
evaporation
efficiency
soil moisture
Simple example based on the nonlinear response of the “beta function”
(evaporation efficiency) to soil moisture. (Such nonlinearity has indeed
been measured locally in the real world.)
Consider a region split into a wet half (degree of saturation = 1)
and a drier half (degree of saturation = 0.5). The average soil
moisture is 0.75.
Wet:
s=1.0
Dry:
s=0.5
Under the simplifying assumption that the potential evaporation
is the same over both sides, we have:
evaporation
efficiency
0.6
0.55
Ewet = 0.6 Ep
Edry = 0.4 Ep
Eave = 0.5 Ep
0.4
0.5
soil moisture
0.75
1.0
average soil moisture
= 0.75
E based on average
soil moisture = 0.55 Ep
The example suggests that if a land modeler is forced to represent the soil
with vertical layers, with a single variable representing the moisture in a
tremendously large area, and without any representation of subgrid process
variability, the following is the best that can be hoped for:
Unrealistic soil moisture and
Realistic areally-averaged
surface fluxes
or
Realistic soil moisture and
Unrealistic areally-averaged
surface fluxes
Arguably, for AGCM applications, a
modeler would strive for this –
given the restrictions of model
resolution, the modeler may choose
to live with a nebulous soil moisture
variable.
Clearly, inserting a soil moisture from Model A into Model B is
dangerous, even if the Model A product is a trusted reanalysis.
Extreme, idealized example:
A very wet condition for
Model A is a very dry
condition for Model B
soil moisture range
for Model B
soil moisture range
for Model A
0.
200.
“soil moisture in top meter of soil” (mm)
400.
Approaches do exist for mapping one model’s soil moisture into that of
another, for purposes of initialization. For example, we can scale using
standard normal deviates:
pdf of
soil moisture:
Model “B”
pdf of
soil moisture:
Model “A”
asB
asA
mA
mB
XA
XB
XA - mA
sA
XB - mB
=
sB
These pdfs, of course, will vary with region. A caveat: for some applications,
particularly those that employ a constantly evolving modeling system (e.g.,
data assimilation and forecasting), the decadal model output needed to
generate the pdf descriptions will probably be unavailable.
Note on the meaning of Dsoil moisture / Dt
While soil moisture has a nebulous meaning in land surface models, the time
change in soil moisture should be well-defined – e.g., the monthly change of
moisture below the land-atmosphere interface can be calculated with
Monthly change = Monthly Precipitation – Monthly Evaporation –
Monthly Runoff,
and all terms on the R.H.S. of this equation have precise, unambiguous
meanings.
In practice, intermodel differences in “monthly soil moisture change” are
much smaller than intermodel differences in absolute soil moisture (e.g.,
Entin et al., 1999). Still,
-- some differences do exist, due to differences in the size of the soil
moisture dynamic range, a function of model parameterization.
-- in any case, the transformation of a Dsoil moisture / Dt value to a
model initialization is not necessarily straightforward.
Now: Back to the discussion of evaporation, runoff, and soil moisture
In actuality (in nature and in most models), the bT function
isn’t simply linear; the value of bT plateaus out at high soil moisture.
(The linearity assumption was used mostly for convenience.) At
high enough soil moisture, the plant is no longer water stressed, and
increased soil moisture does not increase transpiration.
1
bT
R
0
0
200 400 600 800 1000
Nevertheless, the same arguments apply: it is the relative positions of the runoff
and evaporation functions that determine the annual transpiration rate.
In many recent LSMs, the value of the non-water stressed bT is given considerable attention. It
might, for example be effectively computed as a function of:
Vegetation type, LAI, greenness
Environmental stresses (e.g., temperature)
Relatively little attention has
CO2, photosynthesis
been given to the formulation of
Aerodynamic properties
runoff -- a big mistake, if accurate
Other quantities
annual evaporations are desired.
1
1
1
bT
bT
bT
R
R
R
0
0
200 400 600 800 1000
0
0
200 400 600 800 1000
0
0
200 400 600 800 1000
These two examples (from an application with the simple water balance
model) illustrate that even with the same bT function, different
evaporation rates stem from different assigned runoff functions.
Different runoff
functions lead to
different transpiration
rates
Again, relatively little attention has been given to runoff formulations, as
compared to evaporation formulations. This suggests an alternative path
of model evolution.
Essentially the
path outlined
in the Sellers et al
paper.
Current state
of LSMs
Path 1
Improved representation
of point processes (canopy
structure, soil levels,
photosynthesis physics…)
Focus on vertical,
1-D representation
Path 2
This path is useful for
improving runoff formulations.
Why? Because the main reason
for poor runoff formulations is
the inability to treat subgrid
variability accurately (see
water balance lecture).
Improved representation of
subgrid variability (e.g., of
soil moisture and its effects
on runoff and evaporation)
Focus on horizontal,
3-D representation
Recall from 3rd lecture: runoff cannot be
represented realistically with a onedimensional vertical framework.
In a typical LSM, the soil
moisture is effectively
assumed uniform in layers
a few centimeters thick
spanning hundreds of
kilometers!
Scale: hundreds of kilometers
An example of a land surface model that follows this second path: the
“NSIPP catchment LSM”.
Approach:
1. Use the hydrological catchment as the
fundamental land surface unit.
Don’t assume land surface element
has a shape defined by the overlying
atmospheric grid
2. Within each catchment, use hydrological
models for dealing with subgrid-scale soil
moisture distributions.
TOPMODEL, with a special
treatment of the unsaturated zone.
(We employ many of the ideas
introduced by Famiglietti and Wood,
1994.)
References:
Koster et al., J. Geophys. Res., 105, 24809-24822, 2000.
Ducharne et al., J. Geophys. Res., 105, 24823-24838, 2000.
Basic idea behind catchment model:
Different moisture levels
(shown here as different
water table depths)…
…lead to different areal
partitionings of the
catchment into saturated,
unstressed, and wilting
regimes.
Based on the values of these two prognostic variables (and a third [MSD], analogous
to MRZ but related to the moisture close to the surface) we can explicitly
resolve three hydrological regimes:
the saturated zone
the unsaturated but unstressed zone
the wilting zone
Wilting zone
Unsaturated zone
Saturated zone
Different physics applies in each zone. Unlike one-dimensional, “vertical column”
LSMs, we can explicitly apply these different physics.
Evaporation
Saturated area: allow unstressed transpiration, unstressed bare soil evaporation.
Unsaturated area: allow unstressed transpiration, stressed bare soil evaporation.
Wilting zone: Zero transpiration, allow stressed bare soil evaporation.
Runoff
Saturated area: All rainfall becomes surface runoff.
Unsaturated area: Infiltration allowed.
Wilting zone: Infiltration allowed.
Baseflow
Computed based on water table distribution (TOPMODEL)
A similar (though
non-spatially integrated)
calculation is performed
to determine the flux of
moisture between the
thin surface reservoir
and the root zone.
Topographic Data Requirements
1. Catchment delineations (global)
2. Statistics of topographic index within
each catchment:
-- mean
-- standard deviation
-- skew
3. Scaling approaches: what would the statistics
look like if we had higher resolution data?
These data are not used directly in the model;
rather, they are transformed into a number of
model parameters.
Figure courtesy of Colin Stark,
LDEO, Columbia University
Model parameters are derived from basic topographic statistics. In essence,
the model parameters are empirical fits to very complicated calculations.
The catchment model has been
tested in various venues, including
the PILPS 2c Red-Arkansas test.
Unstressed
fraction
Stressed fraction
Unstressed
fraction
Stressed fraction
The NSIPP Catchment LSM
is continually undergoing…
…development
…validation
New formulations for “stormflow” and for the effects
of variable depth to bedrock.
overland flow
depth to bedrock is
typically smaller at
hilltop…
stormflow
…than at
valley bottom
baseflow
The model described above represents just one possible way of treating explicitly
the subgrid variation of soil moisture in a land surface grid cell and its impact on
evaporation and (especially) runoff. Other ways certainly exist, e.g., VIC:
The point is, the importance of modeling this subgrid variability must not get lost
in our zeal to improve the one-dimensional physics in a land surface model.
Take-home lesson: more than one “evolutionary path” is needed.
Notes on output
files generated
in computer lab