How Evaporative
Water Losses Vary
Between Wet and
Dry Water Years as
a Function of
Elevation in the
Sierra Nevada,
California
Jessica Lundquist
University of Washington
jdlund@uw.edu
and
Steve Loheide
University of Wisconsin,
Madison
Dry Year: 18 June 2007
Granite Lakes, Yosemite National
Park, California
Wet Year:
29 June 2006
Seasonal ET is limited by Energy (snowcover,
temperature) early in the season and Dryness (moisture
availability) at the end of the season.
If they balance = Same ET in wet or dry years
Energy limited = More ET in dry years
Moisture limited = More ET in wet years
Gaylor Lakes 6/29/2006
Questions:
1) How does annual ET vary between wet and
dry years in the Sierra?
2) How does this depend on elevation?
3) What are the most crucial parameters in
modeling Sierra ET?
7/13/2005
8/13/2007
We examine two nested basins of
the Merced River in Yosemite.
Upper Basin = Merced at Happy Isles
Lower Basin = Merced at Pohono – Contribution from above Happy Isles
Discharge normalized by basin area
illustrates where most streamflow
comes from at different times of year.
Winter runoff
originates
primarily from
rain in lower
elevations.
Late summer
runoff
originates
primarily from
snowmelt at
higher
elevations.
Annual ET estimated from Water
Balance
On annual basis, storage is negligible, ET = P - R
ET = Annual Precip (from aggregated
PRISM (Daly et al. 1994)
monthly 4 km values)
Annual Runoff (sum of
annual discharge)
Precip (P) and
Runoff (Q)
vary much
more than ET,
but ET is
30-50% of
total P
ET increases with precip in Lower
Basin but not in Upper Basin
ET increases with precip in Lower
Basin but not in Upper Basin
Lower basin trend
is positive,
statistically
significant
(p<0.01), and
robust
Upper basin looks a
bit like Tague and
Christensen results
but is not robust
across all tests of
precip distributions
Simple model to address what
controls these patterns in ET
1. Start with the Penman-Monteith Equation, as
prescribed by Allen et al.(1998), for reference
potential evapotranspiration:
ET =
∆ ( Rnet − G ) + ρ air c p (e s − e) / ra
λρ water (∆ + γ (1 + rs / ra ) )
2. Use 2003-2007 met data from CA DWR
stations at Dana Meadows and Tuolumne
Meadows, Snow-17, and MODSCAG MODIS
snow-covered area to include snow processes.
3. Distribute this across 200-m elevation bins and
weight by basin area for the upper and lower
basins.
Assume actual ET is limited by 3 things:
1) No ET above tree line (>3000 m) when
fractional snow covered area (SCA)
exceeded a set threshold, where snow
cover was represented by direct MODIS
observations of fractional SCA
2) No ET when Tmin < -1˚C, indicating a
hard freeze, based on studies showing
that low soil and air temperatures inhibit
plant metabolic activity
3) Soil moisture deficit limits actual ET
A “leaky bucket” (Manabe 1969) is the
simplest way to realistically model soil
ETactual = f (θ ) ET potential
θ = soil moisture in the bucket
Above some critical value, θc,
plants transpire at the
potential rate.
Below that value, ET
decreases linearly (Brandes
and Wilcox 2000) until soil
moisture is depleted to the
wilting point, θwp.
Even a “leaky bucket” requires a lot of
poorly known parameters
flow in = snowmelt + precip
flow
out
Assign each elevation a bucket, a local
snowmelt model, and a transfer coefficient
for water to move to soils at lower elevations
ET
P + Melt + transferin − ET − transferout
∆θ =
Zr
K
tc
n
θfc
θc
tc=transfer coefficient Zr
θwp
Zr=rooting/soil depth
K=rate of soil drainage
n=porosity
soil dependent
θfc=field capacity
θc=water is limiting
veg dependent
θwp=wilting point
Model run for
2003 - 2007
because those years have
good met data and good
MODIS data
2005 and 2006 =
Wet years
2004 and 2007 =
Dry years
Criteria for a “good” model based
on water balance values for the
lower basin:
1) mean annual ET (2003-2007) for the
lower basin (54 cm);
2) mean annual difference between dry
years (2004 and 2007) and wet years
(2005 and 2006) for the lower basin
(-12 cm)
Contours = model – observed
0 = model got mean annual ET (54 cm) right
What does this mean?
1) A lot of parameter sets get mean ET right
2) There are trade-offs between soil parameters
Mean conditions for Upper Basin
are similar, but the Difference (Dry
– Wet) is more interesting.
1) Most common model – obs
difference is about 10-12 cm,
which corresponds to a model
Dry-Wet difference of about 0
= MODEL predicts the same ET in
Dry and Wet years
2) Model only matches observations
(0 line) when transfer of water
from higher to lower elevations is
high
(high transfer coefficient, tc, and high
flow rate, K)
So we pick a value that fits both the
mean ET and the ET difference:
Transfer (tc) = 75%
Flow rate (K) = 1 m/day
Field Capacity (θfc) = 0.3
Rooting Depth (Zr) = 0.75 m
With these values,
our model shows:
1) Soils are
saturated (at or
above field
capacity) the
entire time snow
is present
With these values,
our model shows:
2) Soils drain to the
wilting point at all
but the highest
elevations in
every year
With these values,
our model shows:
3) Soil moisture
stays high so long
as water from
higher elevation
snow is
transferred to
lower elevations
4) This allows for
more ET in the
wetter year
Ranking our years from dry to wet, the model
matches the lower basin observations well.
In the upper basin, ET is relatively constant.
In the model, all but the highest
elevations are moisture limited,
with more ET in wet years.
Conclusions
• Because most elevations are moisture limited,
warmer temperatures and longer growing
seasons are not likely to increase Sierra ET.
• Rather, annual ET will stay constant or vary with
water availability.
• In modeling Sierra ET, some representation of
moisture transfer from high to low elevations is
critical to represent inter-annual variations in ET.
• This is included in models like RHESSys
(Christensen et al. 2008 and Tague et al. 2009), but not in most
large-scale climate simulations.
For details, see paper: Lundquist and Loheide, 2011, Water Resources Research
Extra slides (in case of questions)
follow:
Simple model to address what
controls these patterns in ET
1. Start with the Penman-Monteith Equation, as
prescribed by Allen et al.(1998), for reference
potential evapotranspiration:
Net
Rnet − G ) + ρVapor
e s − e) / ra
∆ ( radiation
air c p (Flux
ET =
(
)
scaledλρ
by water
aerodynamic
∆ + γ (resistance
1 + rs / raand
)
other constants
2. Use 2003-2007 met data from CA DWR
stations at Dana Meadows and Tuolumne
Meadows, and MODSCAG MODIS snow-covered
area.
3. Distribute this across 200-m elevation bins and
weight by basin area for the upper and lower
basins.
Model set-up:
1) Snowmelt follows temperature-index
model with melt-factor as defined in
Snow-17 (Anderson 1973). Snowmelt
stops when MODIS detects <10% snowcovered-area in a given elevation band.
2) Precip contributes to soil moisture only
where T>0 ˚C
3) But how do we pick those soil
parameters?
2) For faster drainage rates (high K), we need a
deeper soil (rooting depth) and higher field
capacity (soil holds more) to hold onto enough
moisture to get the same ET
3) Unless we have a high transfer coefficient of
moisture from higher elevations, then a wider
range of soil depths and field capacities work
Christensen et al. 2008 and Tague et al. 2009 used
RHESSys model of Merced River above Happy
Isles, California to show that
.
• ET peaks in intermediate water years at
elevations from 1800-2600 m
Moisture limited
Energy limited
but that’s only one model, and models can vary a LOT!
Most hydrology models use
PRISM, developed by Chris
Daly at OSU, to distribute
precipitation to model grid cells.
• Parameter Regression against
Independent Slopes Model
• Breaks west and east slopes
into facets and interpolates
between stations using
elevation
• 800 m grid cells based on
1971-2000 data
Precipitation Checked
• We conducted additional analyses (not
shown)
– with Yosemite Valley precipitation scaled
using 800 m PRISM
– with 40 central-Sierra snow pillows
aggregated by elevation
– with a snow accumulation and melt model
compared to MODIS snow disappearance
dates
• Some variations in absolute values of ET
calculated, but no change in patterns and
inter-annual variability.
ET and climate = critical unknown
Climate models working to predict
Precipitation (P), but what about
Evapotranspiration (ET)?
Predictions of Colorado River decline vary from 5% to
45% depending on how models handle snow and ET.
Southwest Hydrology,
May/June 2009
90+ years of flow at Merced River at Happy
Isles, ranked by volume
1) Most common model – obs
difference is about -3 cm, which
corresponds to a model Dry-Wet
difference of about 0
= MODEL predicts the same ET in
Dry and Wet years
2) -10 cm here indicates that MODEL
predicts the more ET in Wet
years than Dry years
3) So this model is generally not
energy limited in the Upper Basin,
but our observations of precip
there area also less robust, and
snow storage can also occur at
the highest elevations in the
wettest years.