CLIM 714

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Water Balance at the Land Surface
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Water Balance for a Single Land Surface Slab,
Without Snow(e.g., standard bucket model)
Terms on LHS come from the climate
model. Strongly dependent on cloudiness,
water vapor, etc.
Terms on RHS come are determined by the land
surface model.
P E
R
w

• P E R CwDw/Dt miscellaneous

where P Precipitation E
Evaporation R Runoff (effectively
consisting of surface runoff and baseflow) Cw
Water holding capacity of surface slab Dw
Change in the degree of saturation of the surface
slab Dt time step length miscellaneous
conversion to plant sugars, human consumption,
etc.
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Usually, a combination of water balances is
considered. For example
Water balance associated with canopy interception
reservoir
Eint interception loss Dc drainage through
canopy (throughfall) DWc change in
canopy interception storage
P
Eint
Wc
Dc
Water balance in a snowpack
DWsnow Dt
P Esnow M
Esnow sublimation rate M snowmelt DWsnow
change in snow amount
(infinite capacity possible)
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Water balance in a surface layer
M Dc Ebs Etr1 Rs Q12 CW1DW1/Dt
MDc
Ebs Etr1
Rs
w1
Water storage
Q12
Ebs evaporation from bare soil Etr1
evapotranspiration from layer 1 Q12 water
transport from layer 1 to layer 2 CW1 water
holding capacity of layer 1 DW1 change in
degree of saturation of layer 1
w2
w3
Water balance in a subsurface layer (e.g., 2nd
layer down)
Q12 Q23 Etr2 CW2DW2/Dt
Note some models may include an additional,
lateral subsurface runoff term
Etr2 evapotranspiration from layer 2 Q23
water transport from layer 2 to layer 3 CW2
water holding capacity of layer 2 DW2 change in
degree of saturation of layer 2
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Water balance in the lowest layer
Qn,n-1 QD Etr-n CWnDWn/Dt
Etr-n evapotranspiration from layer n, if
allowed QD Drainage out of the soil column
(baseflow)
A model may compute all of these water balances,
taking care to ensure consistency between
connecting fluxes (in analogy with the energy
balance calculation).
P
Eint
Esnow
P
Ebs
Dc
Etr1
Etr2
Etr3
Rs
M
W1
Q12
W2
W3
Q23
QD
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Precipitation, P
Getting the land surface hydrology right in a
climate model is difficult largely because of the
precipitation term. At least three aspects of
precipitation must be handled accurately
a. Spatially-averaged
precipitation amounts (along
with annual means and seasonal totals)
b. Subgrid distribution.
c. Temporal variability and
temporal correlations. Otherwise, even with a
perfect land surface model,
Perfect land surface model
Garbage in
Garbage out
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Accurate precipitation measurements are limited
by availability of rain gauges.
Each box is 250 km on a side
and by inherent inaccuracies in satellite-derive
d precipitation data
How Good is the Estimated SSM/I Rain Rate
Climatology Data?
Over oceans, no truth data available for
validations Nonsystematic error includes
sampling and random Sampling error dominates F-13
and F-14 SSM/I, with similar sampling have
similar error TMI has a slightly less,
nonsystematic error Combining F-13 F-14 almost
satisfy the TRMM 1 mm/day and 10 for heavy
rain GPM with 8 satellites will have 50 less
error than combining F-13 F-14
Technical notes for figure
Figure compliments of Al Chang, NASA/GSFC
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Precipitation subgrid variability (1)
The bottom storm is more evenly distributed over
the catchment than the top storm. Intuitively,
the top storm will produce more runoff,
even though the average storm depth over the
catchment (E(Yo)) is smaller. Key points --
Specifying subgrid variability of
precipitation is critical to an accurate modeling
of surface hydrology. -- A GCM is typically
unable to specify the spatial structure of a
given storm. The LSM typically has to guess
it.
From Fennessey, Eagleson, Qinliang, and
Rodriguez-Iturbe, 1986.
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Precipitation subgrid variability (2)
Here, the two storms have similar spatial
structure and total precipitation amounts. The
locations of the storms, however, are different.
If the top storm fell on more mountainous terrain
than the bottom storm, the top storm
might produce more runoff Key point A GCM is
typically unable to specify the subgrid location
of a given storm. The LSM typically has to
guess it.
From Fennessey, Eagleson, Qinliang, and
Rodriguez-Iturbe, 1986.
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GPM Mission Design
Core
Constellation

• Core Satellite
• TRMM-like spacecraft (NASA)
• H2-A rocket launch (NASDA)
• Non-sun-synchronous orbit
• 65 inclination
• 400 km altitude
• Dual frequency radar (NASDA)
• K-Ka Bands (13.6-35 GHz)
• 4 km horizontal resolution
• 250 m vertical resolution
• Multifrequency radiometer (NASA)
• 10.7, 19, 22, 37, 85, (150/183 ?) GHz VH

• Constellation Satellites
• Pre-existing operational-experimental dedicated
  satellites with PMW radiometers
• Revisit time
• 3-hour goal at 90 of time
• Sun-synch non-sun- synch orbits
• 600-900 km altitudes

• Precipitation Validation Sites for Error
  Characterization
• Select/globally distributed ground validation
  Supersites (research quality radar, up looking
  radiometer-radar-profiler system,
  raingage-disdrometer network, T-q soundings)
• Dense frequently reporting regional raingage
  networks

• Precipitation Processing Center
• Produces global precipitation products
• Products defined by GPM partners

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Precipitation temporal correlations
Temporal correlations are very important -- but
are largely ignored -- in GCM formulations that
assume subgrid precipitation distributions. This
is especially true when the time step for the
land calculation is of the order of minutes. Why
are temporal correlations important? Consider
three consecutive time steps at a GCM land
surface grid cell
Case 2 should produce, for example, stronger
runoff.
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Throughfall
Simplest approach represent the interception
reservoir as a bucket that gets filled
during precipitation events and emptied during
subsequent evaporation. Throughfall occurs when
the precipitation water spills over the top of
the bucket.
Capacity of bucket is typically a function of
leaf area index, a measure of how many leaves are
present.
This works, but because it ignores subgrid
precipitation variability (e.g., fractional
wetting), it is overly simple.
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Spatial precipitation variability and
interception loss
SiBs approach (Sellers et al, 1986)
Precipitation assumed to fall according to some
prescribed distribution
Area above line is considered throughfall
Capacity of reservoir
Note SiB allows some of the precipitation to
fall to the ground without touching the canopy.
Original water in reservoir
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Temporal precipitation variability and
interception loss
Mosaic LSMs approach
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Evaporation
See notes from energy balance lecture. Note,
though, locations of moisture sinks for bare
soil evaporation and transpiration Bare soil
evaporation water is usually taken from the top
soil layer. Transpiration water is usually taken
from the soil layers that comprise the root zone.
Different amounts may be taken from different
layers depending on -- layer
thickness -- assumed root density
profile
e.g., transpiration water taken from these
layers but not this layer
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Runoff a. Overland flow (i) flow
generated over permanently saturated zones near a
river channel system Dunne
runoff (ii) flow generated because
precipitation rate exceeds the infiltration
capacity of the soil (a function of
soil permeability, soil water
content, etc.) Hortonian runoff b. Interflow
(rapid lateral subsurface flow through macropores
and seepage zones in the soil c. Baseflow
(return flow to stream system from groundwater)
Runoff (streamflow) is affected by such things
as -- Spatial and temporal distributions of
precipitation -- Evaporation sinks --
Infiltration characteristics of the soil --
Watershed topography -- Presence of lakes and
reservoirs
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Modeling runoff basin scale When variations in
precipitation, topography, soil characteristics,
etc., can be explicitly accounted for (as in
so-called spatially distributed
hydrological basin models), runoff can be
predicted fairly accurately. The
TOPMODEL approach uses the statistics of
topography to characterize the spatial distributio
n of water table depth in a basin, with
consequent impacts on runoff generation.
simulated
observed
From Beven, K., Spatially distributed modeling
conceptual approach to runoff prediction, in
Recent Advances in the Modeling of Hydrologic
Systems, ed. By Bowles and OConnell, p.
373-387, Kluwer Academeic Pub., 1991.
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Modeling runoff GCM scale Surface runoff
formulations in GCMs are generally very crude,
for at least two reasons (i) Developers of
GCM precipitation schemes have focused on
producing accurate precipitation means,
not on producing accurate subgrid spatial
and temporal variability. (ii) GCM land
surface models generally represent the
hydrological state of the grid cell
with grid-cell average soil moistures -- the time
evolution of subgrid soil moisture
distributions is not monitored.
At best, we can expect first-order success
with these runoff
formulations
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Controls in nature
Framework of typical LSM
SCALE HUNDREDS OF KILOMETERS
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Note that because of the inherent inconsistency
between nature and the typical LSMs soil layer
framework, no best approach for modeling runoff
exists. Current LSM approaches are all over the
place. Typically, though, runoff is a function
of the amount of moisture in the top soil layer.
Bucket model total runoff P M - E if this
is positive and the bucket is full.
total runoff 0 otherwise.
GISS Model II total runoff max( 0.5 P
Dt, excess over capacity ).
SiB surface runoff excess over
infiltration capacity,
assuming subgrid distribution of
throughfall.
Other approaches will be discussed later in the
course.
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Where does GCM runoff go once its produced? It
may disappear (i.e., since it eventually ends
up in the ocean anyway, it may be no longer
considered by the land model -- it may be
effectively removed and forgotten), or it may be
routed, using routing networks like this. The
routed runoff can be compared to streamgauge
measurements.
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(Implied) Global Annual River Discharge (kg/yr)
Historical estimates of river discharge are all
over the place -- more evidence of uncertainty in
our estimates of the global water cycle.
B0
P1
P2
P3
Legacy of estimates Schlosser and Houser, 2004
(submitted)
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Satellite measurements may provide valuable
runoff data. (The methodology is still in its
infancy.)
Observations River and Lake Stage
Jehil Reservoir, Afghanistan
TOPEX/POSEIDON-Radar Backscatter
Jehil Reservoir1990
Jehil Reservoir1999
Jehil Reservoir2001 (dry)
Jehil Reservoir1998
Application of satellite radar altimetry and
imagery to drought investigation. C.
Birkett/ESSIC
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Soil Moisture Transport, Baseflow
First, some useful definitions
Porosity (n) The ratio of the volume of pore
space in the soil to the total volume of the
soil. When a soil with a porosity of 0.5 is
completely dry, it is 50 rock by volume and 50
air by volume. Volumetric moisture content (q)
The ratio of the volume of water in the soil to
the total volume of soil. When the soil is fully
saturated, q n. Degree of saturation (w) The
ratio of the volume of water in the soil to the
volume of water at saturation. By definition, w
q /n. Pressure head (y) A measure of the degree
to which the soil holds on to its water through
tension forces. More specifically, y p/rg,
where r is the density of water, g is
gravitational acceleration, and p is the fluid
pressure. Elevation head (z) The height of soil
element above an arbitrary baseline. Hydraulic
head (h) The sum of the pressure head and the
elevation head. Wilting point The soil
moisture content (measured either in degree of
saturation or pressure head) at which plants can
no longer draw the moisture from the soil. When
modeling the root zone, this is often considered
to be the lowest moisture content
possible. Field capacity The water content
obtained when a saturated soil drains to the
point where the surface tension on the soil
particles balances the gravitational forces
causing drainage.
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Estimating water transport in the saturated zone
(i.e., below water table)
Darcys Law states that Q/A flow per
unit normal area - K where K
hydraulic conductivity h
hydraulic head L separation
distance
h2 - h1
L
More generally, q - K h
q specific discharge Q/A
Generalized Darcys Law relates flow to
gravitational and pressure forces. (Recall h
y z)
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Hydraulic conductivity, K, is related to the
soils specific permability
Where r is the fluids density and m is its
dynamic viscosity. K is thus a function of soil
and fluid properties.
K varies tremendously with soil type. Small
variations in soil type, say across a field
site, could lead to orders of magnitude
difference in the ability to transport moisture.
From Freeze and Cherry
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Moisture transport in the unsaturated zone (e.g.,
in the soil near the surface) can also be
computed with Darcys law, if appropriate correcti
ons are made to pressure head and hydraulic
conductivity.
qr residual moisture specific retention
Z
If atmospheric pressure defined to be 0.
qr
Recall q ratio of water volume
to soil volume, n porosity
Soil moisture profile
capillary fringe
p lt 0
p 0
q
qn
Water table
p gt 0
Recall w degree of saturation,
q/n
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Soil parameter values used in GSWP, from Cosby
m/s
m
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Three things that complicate moisture transport
in the unsaturated zone
1. Extreme nonlinearity. b may have values
between 4 and 10. If b10, then K(q)
Ksaturated w 23
2. Hysteresis Values of parameters not
really a unique function of moisture state
they depend in part whether the soil has
previously been wet or previously been
dry -- whether the soil is wetting up or
drying down.
From Freeze and Cherry
3. Anisotropy. Hydraulic conductivity may
vary with the direction of flow.
For a given head gradient, flow in this
direction may be easier than flow in this
direction
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GCM approaches to modeling subsurface
flow Typically, -- Assume homogeneity
of soil constant Ksat, ysat
-- Ignore hysteresis -- Concentrate on
vertical transports only --
Concentrate only on unsaturated zone and
determination of moisture drainage to
water table
Discretization of Darcys law (e.g., SiB) Darcys
law for vertical flow can be written
q - K h qz - K
- K (z y)
- K (
1)
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One possible discretization of Darcys law
(continued)
Characterize the soil as stacked layers (d
thickness)
Compute for each layer i yi ysat wi
-b Ki Ksat wi 2b3
Compute flow from layer i to layer i1
yi - y i1
qz i,i1 K
1
d
K average K across distance (diKi
di1Ki1)/(didi1) d effective depth for
computing gradient 0.5 (didi1)
For drainage out the bottom of the soil column
(QD), one might equate it to the hydraulic
conductivity in the lowest layer. SiB, for
example, goes beyond this by also applying a
mean slope angle term, sin x QD K3 sin x
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Its important to keep in mind that the different
LSMs use very different discretizations of the
soil column -- there is no one right way to do
it.
Discretizations and moisture transport paths for
a wide variety of LSMs, as outlined by Wetzel
and Chang (1996)
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Energy balance versus water balance
Water balance Implicit solution usually not
necessary Results in updated water storage
prognostics
Energy balance Implicit solution usually
necessary Results in updated temperature
prognostics
How are the energy and water budgets connected?
1. Evaporation appears in both. 2. Albedo varies
with soil moisture content. 3. Thermal
conductivity varies with soil moisture
content. 4. Thermal emissivity varies with soil
moisture content.
Question Can we address how the energy and water
budgets together control evaporation rates?
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Budykos analysis of energy and water controls
over evaporation
These assymptotes act as barriers to evaporation.
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The equation in fact characterizes the combined
energy and water balance behavior of GCMs in
general...
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and can thus be used to explain, in part,
differences in GCM behavior.
Each letter corresponds to a different GCM
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What determines the shape of Budykos curve?
If only annual means mattered, the observed curve
should look like this
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Seasonality, however, is important.
41
Note that if these seasonal effects alone were
considered, the observed curve would actually
look like this
42
This effect can bring the curve in line with the
observed curve. Note, though, that other effects
also contribute to a regions evaporation rate,
including land surface properties and the
temporal variation of precipitation.
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Budykos analysis discussion
1. Annual precipitation and net radiation
control, to first order, annual evaporation
rates. 2. The spread of points around the Budyko
curve is large, though, due to various additional
factors -- phasing of seasonal P
and Rnet cycles -- interseasonal
storage of moisture -- Other land
surface or meteorological effects (vegetation
type and resistance,
topography, rainfall statistics, ) 3. Note
also -- Land surface processes
affect the precipitation and net radiation
forcing -- theres not truly a
clean separation between land
and atmospheric effects. -- The
lands effects on hourly, daily and monthly
evaporation are relatively
much more important than they are on annual
evaporation.
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Budykos equation for mean annual evaporation
Modification for interannual variability
See Koster and Suarez, 1999
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E
sE
P
sP
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Equation works well when tested with GCM data
curve derived from Budyko equation