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Transcript of Guo-Yue Niu and Zong-Liang Yang Department of Geological Sciences, Jackson School of Geosciences,...
![Page 1: Guo-Yue Niu and Zong-Liang Yang Department of Geological Sciences, Jackson School of Geosciences, The University of Texas at Austin Prepared for NCEP-NCAR-NASA-OHD-UT.](https://reader037.fdocuments.net/reader037/viewer/2022110102/56649efe5503460f94c12e15/html5/thumbnails/1.jpg)
Guo-Yue Niu and Zong-Liang Yang
Department of Geological Sciences,
Jackson School of Geosciences,
The University of Texas at Austin
Prepared for NCEP-NCAR-NASA-OHD-UT telecon
March 20th, 2007
Representing Runoff and Snow in Representing Runoff and Snow in Atmospheric ModelsAtmospheric Models
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Outline
Runoff and Groundwater
A Simple TOPMODEL-Based Runoff Model (SIMTOP)
Its Performances in Various PILPS
A Simple Groundwater Model (SIMGM)
Assessment of SIMGM with GRACE ΔS
Snow Modeling
A Physically-Based Multi-Layer Snow Model
A New Snow Cover Fraction Scheme as Validated against AVHRR SCF and CMC Snow Depth and SWE
Discussion on Noah Developments
Model physics and parameters (soil and vegetation)
Testing plan
Runoff | Groundwater | Bare Snow | Snow Cover
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Runoff in Global Water Cycle
Precipitation onto landSurface 110,000km3
Precipitation on ocean surface ~ 91%
Evaporation from land~60%
River runoff~40%; ~9%
Evaporation from ocean 502,800km3
Ocean:
Eo=Po+ R
Land:
PL=EL+ R
Runoff is about 40% of the precipitation that falls on land
Runoff affects the fresh-water (salinity) budget of the ocean and thermohaline circulation.
Runoff interacts with soil moisture and groundwater.
Runoff | Groundwater | Bare Snow | Snow Cover
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Smaller scatter in T; Larger scatter (uncertainty) in runoff
2m Air Temperature (K)
winter
summer
winter
summer
Total Runoff (mm/s)
Comparison of 19 Global Climate Models (Zonal averages)
Runoff | Groundwater | Bare Snow | Snow Cover
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History of Representing Runoff in Atmospheric Models
Bucket orLeaky Bucket Models1960s-1970s(Manabe 1969)
~100km
Soil Vegetation AtmosphereTransfer Schemes (SVATs)1980s-1990s(BATS and SiB)
150mm
Runoff | Groundwater | Bare Snow | Snow Cover
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Recent Developments in Representing Runoff
1. Representing topographic effects on subgrid distribution of soil moisture and its impacts on runoff generation
(Famiglietti and Wood, 1994; Stieglitz et al. 1997; Koster et al. 2000; Chen and Kumar, 2002)
2. Representing groundwater and its impacts on runoff generation, soil moisture, and ET
Saturation in zones of convergent topography
Runoff | Groundwater | Bare Snow | Snow Cover
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Processes to Generate Surface Runoff
Infiltration excess
PP
P
qo
f
f
Saturation excess
PP
P
qrqs
qo
zwt
Severe storms
Dominantcontributor
Frozen surfaceUrban area
Runoff | Groundwater | Bare Snow | Vegetated Snow | Snow Cover
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Relationship Between Saturated Area and Water Table Depth
The saturated area showing expansion during a single rainstorm. [Dunne and Leopold, 1978]
zwt
fsat
fsat
fsat = F (zwt, λ)
λ – wetness index derived from DEM
Runoff | Groundwater | Bare Snow | Snow Cover
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DEM –Digital Elevation Model
ln(a) – contribution area
ln(S) – local slope
The higher the wetness index, the potentially wetter the pixel
1˚ x 1˚
Wetness Index: λ = ln(a/tanβ) = ln(a) – ln(S)
Runoff | Groundwater | Bare Snow | Snow Cover
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Surface Runoff Formulation and Derivation of Topographic Parameters
1˚
1˚
The Maximum Saturated Fraction of the Grid-Cell:
Fmax = CDF { λi > λm }
zm λm
Lowlandupland
zi, λi
λ
PD
F
0.1
0.2
λm
Fmax
CD
F
1.0
0.5
λλm
Runoff | Groundwater | Bare Snow | Snow Cover
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A 1 ˚x 1˚ grid-cell in the Amazon River basin
Both Gamma and exponential functions fit for the lowland part (λi > λm)
fsat = Fmaxe – C (λi – λm) fsat = Fmaxe – C f zwt
Fmax = 0.45; C = 0.6
Surface Runoff Formulation and Derivation of Topographic parameters
λi – λm = f *zwt TOPMODEL
Runoff | Groundwater | Bare Snow | Snow Cover
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Surface Runoff Formulation and Derivation of Topographic Parameters
A 1 ˚x 1˚ grid-cell in Northern Rocky Mountain
Gamma function fails, while exponential function works.
Fmax = 0.30; C = 0.5
Runoff | Groundwater | Bare Snow | Snow Cover
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Global Fmax (%)
a: Discrete Distribution
(True value)
Global mean ~ 0.37
b: Gamma Function
c: Error of Gamma (b – a)
Niu et al. (2005)
Runoff | Groundwater | Bare Snow | Snow Cover
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Derivation of Topographic Parameters
Woods and Sivapalan (2003)
C = 0.51 to 1.10
C ~ 0.6
1. Exponential function works very well in well-developed catchments. 2. The larger the catchment, the better the fitting.
Runoff | Groundwater | Bare Snow | Snow Cover
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Subsurface Runoff Formulation
Beven and Kirkby (1979)
Rsb= Rsb,max e -fD
Sivapalan et al. (1987) …
Rsb= K0/f e –λ e –f zwt
It needs very large K0, about 100 – 1000 times larger than that in LSM
Chen and Kumar (2001):
Rsb = α K0/f e –λ e –f zwt (where αK0 is the lateral K)
1) Difficulties in determining “α” globally
2) λ needs very high resolution DEM (30 m or finer) to determine slopes.
Niu et al. (2005):
Rsb = Rsb,max e –f zwt (Rsb,max= 1.0x10-4 mm/s)
Less parameters and easier to calibrate
Runoff | Groundwater | Bare Snow | Snow Cover
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A Simple TOPMODEL-Based Runoff Scheme (SIMTOP)
Surface Runoff : Rs = P Fmax e – C f zwt
p = precipitation
zwt = the depth to water table
f = the runoff decay parameter that determines recession curve
Subsurface Runoff : Rsb= Rsb,maxe –f zwt
Rsb,max = the maximum subsurface runoff when the grid-mean water table is zero. It should be related to lateral hydraulic conductivity of an aquifer and local slopes (e-λ) .
SIMTOP parameters:
Two calibration parameters Rsb,max (~10mm/day) and f (1.0~2.0)
Two topographic parameters Fmax (~0.37) and C (~0.6)
Runoff | Groundwater | Bare Snow | Snow Cover
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Diagnostic Water Table Depth from Soil Moisture Profile
Water profile under
gravity
Gravity
It fails during especially precipitation periods.Chen and Kumar (2001)
Koster et al. (2000)
Niu and Yang (2003)
Niu et al. (2005)
Equilibrium soil water profile
Ψi – zi
Ψsat – zwtGravity ( z )
Capillary ( ψ )
Runoff | Groundwater | Bare Snow | Snow Cover
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•20-year (1979-1998) meteorological forcing data at hourly time step
•218 grid-cells at 1/4 degree resolution
Torne/Kalix Rivers, Sweden and Finland (58,000 km2)
Runoff | Groundwater | Bare Snow | Snow Cover
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Modeled Streamflow in Comparison With the Observed
From Niu and Yang (2003)
Runoff | Groundwater | Bare Snow | Snow Cover
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Model Intercomparison
20 models from 11 different countries (Australia, Canada, China, France, Germany, Japan, Netherlands, Russia, Sweden, U.K., U.S.A.)
VISA – Versatile Integrator of Surface and Atmospheric processes
From Bowling et al. (2003)
OBS
Runoff | Groundwater | Bare Snow | Snow Cover
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Model Intercomparison Nijssen et al. (2003)
Runoff | Groundwater | Bare Snow | Snow Cover
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Rhone River, France (86,996 km2)
Four-year (1986-1989) meteorological data at 3-hour timestep 1,471 grid-cells at 8km x 8km.
Runoff | Groundwater | Bare Snow | Snow Cover
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15 Models from 9 countries
Runoff | Groundwater | Bare Snow | Snow Cover
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24 Runoff | Groundwater | Bare Snow | Snow Cover
From Boone et al. (2004)
River Discharge
OBS
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Snow Depth From Boone et al. (2003)
Runoff | Groundwater | Bare Snow | Vegetated Snow | Snow Cover
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Performances in GSWP2
Global Soil Moisture Databank
Courtesy of Z.-C. Guo
Runoff | Groundwater | Bare Snow | Snow Cover
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Performances in GSWP2
RMSE of Monthly-Mean Soil Moisture
RMSE of Soil Moisture Anomalies
Courtesy of Z.-C. Guo
Runoff | Groundwater | Bare Snow | Snow Cover
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Tests by UCI Famiglietti’s Group
Runoff | Groundwater | Bare Snow | Snow Cover
Blue: Observations from HCDNBlack: CLM 3.0 (SIMTOP)
Upstream area: ~74000 km2
![Page 29: Guo-Yue Niu and Zong-Liang Yang Department of Geological Sciences, Jackson School of Geosciences, The University of Texas at Austin Prepared for NCEP-NCAR-NASA-OHD-UT.](https://reader037.fdocuments.net/reader037/viewer/2022110102/56649efe5503460f94c12e15/html5/thumbnails/29.jpg)
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Summary
In SIMTOP, both surface runoff and subsurface runoff are formulated as exponential functions of the water table depth.
It is among the best runoff models in various model intercomparison projects.
But the water table depth is diagnostically derived from the equilibrium soil moisture profile.
Runoff | Groundwater | Bare Snow | Snow Cover
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Groundwater in the Climate System
1. 30% Groundwater; 1% Soil moisture
3. Groundwater controls runoff (Yeh and Eltahir, 2005)
2. Groundwater storage shows very large variations at monthly or longer timescale associated with soil water variations (Rodell and Famiglietti, 2001)
Yeh and Eltahir, 2005
Precipitation (mm/mon) GW level (m)
Str
eam
flow
(m
m/m
on)
Str
eam
flow
(m
m/m
on)
4. Groundwater affects soil moisture and ET (Gutowski et al, 2002; York et al., 2002)
Rs = P Fmax e – C f zwt
Rsb= Rsb,maxe –f zwt
(Niu et al., 2005)
Runoff | Groundwater | Bare Snow | Snow Cover
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Observational Support
Groundwater level is highly correlated with streamflow in a strong nonlinear manner and
explains 2/3 of the streamflow (Yeh and Eltahir, 2005)
Champaign
Fayette
Greene
Henry
Jo Daviess
Mcdonough
McHenry
Pike
Pope
Wayne
Runoff | Groundwater | Bare Snow | Snow Cover
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Total Soil Depth on Soil Moisture Simulation
2m
3.4m
2m
Noah Model CLM Model
wetterdrier
2m
0
Soil Moisture
Noah
CLM
Runoff | Groundwater | Bare Snow | Snow Cover
3.4m enough ?
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Prognostic Water Table depth: A Simple Groundwater Model
bot
botbota zz
zzKQ
)(
Water storage in an unconfined aquifer:
Recharge Rate:
)1(bot
bota zzK
Gravitational Drainage
sba RQ
dt
dW ya SWz /
Upward Flow under capillary forces
Runoff | Groundwater | Bare Snow | Snow Cover
Buffer Zone
3.4m
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fzsbsb eRR max,
Groundwater Discharge
Properties of the Aquifer
1. Hydraulic Conductivity:
2. Specific Yield:
SIMTOP (Niu et al., 2005)
)(,
botzzfbotsatsat eKK
2.0yS
A Simple Groundwater Model (SIMGM)
Runoff | Groundwater | Bare Snow | Snow Cover
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Validate the Model against the Valdai (0.36 km2) Data
The model reproduces SWE, ET, runoff, and water table depth.
The water table depth has two peaks and two valleys in one annual cycle
Runoff | Groundwater | Bare Snow | Snow Cover
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Validate the Model against GRDC Runoff
Good agreements between the modeled runoff and GRDC Runoff.
The modeled water table depth ranges from 2.5m in wet regions to 30m in arid regions.
Runoff | Groundwater | Bare Snow | Snow Cover
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Regional Averaged Runoff
Cold Regions
Tropical Regions
Mid-latitude Regions
Arid Regions
Runoff | Groundwater | Bare Snow | Snow Cover
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Validation Against GRACE Terrestrial Water Storage Change
GRACE
Standard NCAR CLM2
Modified CLM2
Runoff | Groundwater | Bare Snow | Snow Cover
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Validate the Model Against GRACE ΔS Anomaly
River basins unaffected by snow or frozen soil
Runoff | Groundwater | Bare Snow | Snow Cover
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Validate the model Against GRACE WTD Anomaly
GRACE ΔS / 0.2
inter-annual
inter-basin variability
Runoff | Groundwater | Bare Snow | Snow Cover
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P – E, Groundwater Recharge, and Discharge
Phase lags
Negative recharge during dry seasons
Recharge and discharge are determined by P-E.
Inter-annual and inter-basin variability
Runoff | Groundwater | Bare Snow | Snow Cover
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The Impacts of Groundwater Model on SM and ET
Bottom-layer soil moisture
Surface-layer soil moisture
ET in “hot spots”
(Koster et al., 2004)
Runoff | Groundwater | Bare Snow | Snow Cover
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43
Soil Moisture Profiles in Selected Regions
Cold Regions
Tropical Regions
Mid-latitude Regions
Arid Regions
Runoff | Groundwater | Bare Snow | Snow Cover
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44
Transpiration vs. Ground Evaporation
Groundwater has a negligible impacts on transpiration, although it greatly increases deep soil moisture;
It enhanced the ground-surface evaporation in dry seasons in correspondence to the increases in the surface-layer soil moisture.
Runoff | Groundwater | Bare Snow | Snow Cover
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45
Improved ET in Amazon Region
Runoff | Groundwater | Bare Snow | Snow Cover
ET in Amazon should be in phase of net radiation rather than precipitation because of the plenty of water
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46
Summary
1. We developed a simple groundwater model (SIMGM) for use in GCMs by representing the recharge and discharge processes in an unconfined aquifer
2. The modeled ΔS agrees very well with GRACE data in terms of inter-annual and inter-basin variability in most river basins.
3. Groundwater ΔS accounts for about 60-80% of the total ΔS anomaly;
The groundwater storage and WTD anomalies are mainly controlled by P – E, or climate.
4. It produces a much wetter soil globally; It produces about 4 – 20% more annual ET in “hot spots”.
Runoff | Groundwater | Bare Snow | Snow Cover
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47
Global Warming & Snow Cover Change
Global Temperature Anomalies
Northern Hemisphere Snow Cover Anomalies
Runoff | Groundwater | Bare Snow | Snow Cover
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48
Snow-albedo feedback
~0.6Wm-2/K
Chapin et al. (2006), Science
Snow-free days increased;
Tundra Trees
Global Warming & Snow Cover Change
Runoff | Groundwater | Bare Snow | Snow Cover
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49Snow-albedo feedback strength: ~0.6Wm-2/K; 1.1—1.3 (NCAR
CCSM)
Comparison of Snow-Albedo Feedback with other Forcing
Runoff | Groundwater | Bare Snow | Snow Cover
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50
Factors Affecting Snow Modeling
Internal processes (Snowpack Physics):
Computation method to solve snow skin temperature
Liquid water retention
Densification processes
Radiation transfer through the snowpack
External processes (Snowpack Surface Processes):
Snow surface albedo (spectral; grain size; impurity)
Snowfall (temperature criterion)
Vegetation effects (radiation transfer through the canopy; interception of snowfall by the canopy; sensible heat between the canopy and its underlying snow; subgrid vegetation distribution)
Snow cover fraction (topography; roughness; vegetation; snow depth; seasons)
Runoff | Groundwater | Bare Snow | Snow Cover
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51
Computation Method on Snow Skin Temperature
1. Diurnal cycle of skin temperature is critical for snow melting
2. Force-Restore can not solve skin temperature
0 GEHLS gggg 1. Force – Restore Method 2. Energy Balance Method
Ski
n T
. M
eltin
g E
nerg
y
Runoff | Groundwater | Bare Snow | Snow Cover
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52
Single Layer vs. Multi-layer
Energy Balance
)(2/ 1
1
TThz
kG g
sno
b
TgT1
T2
T3
0 GEHLS gggg Tg
T12/1z
snoh
G )(2/ 1
,1
TTz
kG g
sno
b
2/,1 snoz
G is smaller G is more accurate
Runoff | Groundwater | Bare Snow | Snow Cover
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53
Single Layer Vs. Multi-Layer on Skin Temperature
Thin Snow
Thick Snow
Ski
n T
. S
kin
T.
Mel
ting
Ene
rgy
Thick Snow
Runoff | Groundwater | Bare Snow | Snow Cover
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54
Liquid Water Retention & Solar Penetration Through Snowpack
Without Liquid WaterMore Solar Energy Penetrating through
snowpack
Runoff | Groundwater | Bare Snow | Snow Cover
The snow model in the NCAR CLM is such a multi-layer, physically-based snow model …
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55
(Dickinson et al., 2006)(Dickinson et al., 2006)
CCSM3 T85 - OBSCCSM3 T85 - OBS
Winter Warm Bias in NCAR SimulationsWinter Warm Bias in NCAR Simulations
CAM3 T42 - OBSCAM3 T42 - OBS
Runoff | Groundwater | Bare Snow | Snow Cover
1. Excessive LW↓ due to excessive low clouds,2. Anomalously southerly winds.Too low SCF in mid-latitude
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56
Fractional Snow Cover Intercomparison from Fractional Snow Cover Intercomparison from IPCCIPCC
Runoff | Groundwater | Bare Snow | Snow Cover
Frei and Gong, (2005)
OBS
CCSM
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57 Runoff | Groundwater | Bare Snow | Snow Cover
SCF Formulations in Different ModelsSCF Formulations in Different Models
Wide spreads indicate limited knowledge about this SCF–snow-depth relationship due to limited snow data
(Liston, 2004)
CCSM (z0= 0.05m)
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58 Runoff | Groundwater | Bare Snow | Snow Cover
Datasets:Datasets:
CMC daily SD and SWE, 18 years (1979-1996), 8000 stations, 0.25˚ (Brown et al., 2003)
AVHHR monthly SCF, 35 years (1968-2002), 1˚ (Robinson, 2000)
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59 Runoff | Groundwater | Bare Snow | Snow Cover
Observed SCF–Snow Depth RelationshipObserved SCF–Snow Depth Relationship
1. Season-dependent
2. No clear dependence on
subgrid topography variations
σh from GTOPO30
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60 Runoff | Groundwater | Bare Snow | Snow Cover
Observed SCF–Snow Depth RelationshipObserved SCF–Snow Depth Relationship
1. Related to season (snow density)2. No clear dependence on subgrid topography
variations
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61 Runoff | Groundwater | Bare Snow | Snow Cover
A New SCF–Snow Depth RelationshipA New SCF–Snow Depth Relationship
])/(5.2
tanh[0
newsnog
sno
z
hSCF
CLM
]5.2
tanh[0g
sno
z
hSCF
Yang et al. (1997)
α = 1.0
Yang et al. (1997)
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62 Runoff | Groundwater | Bare Snow | Snow Cover
Observed SCF–Snow Depth RelationshipObserved SCF–Snow Depth Relationship
α = 1.5])/(5.2
tanh[0
newsnog
sno
z
hSCF
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63 Runoff | Groundwater | Bare Snow | Snow Cover
Reconstructed Reconstructed SCFSCF
Mackenzie
St. Lawrence
Churchill
Mississippi
(α ~ 1.5)
])/(5.2
tanh[0
newsnog
sno
z
hSCF CMC
Snow DepthSWE
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64 Runoff | Groundwater | Bare Snow | Snow Cover
Modeled SCF – interannual Modeled SCF – interannual Variations Variations Driven with Qian et al. (2006) data from (1948-Driven with Qian et al. (2006) data from (1948-2004)2004)
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65 Runoff | Groundwater | Bare Snow | Snow Cover
Modeled SCF Seasonal Variations Modeled SCF Seasonal Variations (α ~ 1.0)S
CF
(%
)
18-year (1979-1996) averaged seasonal variations18-year (1979-1996) averaged seasonal variations
Eight NA large river basinsEight NA large river basins
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66 Runoff | Groundwater | Bare Snow | Snow Cover
Yearly Averaged SCF (all seasons) Yearly Averaged SCF (all seasons) (α ~ 1.0)
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67 Runoff | Groundwater | Bare Snow | Snow Cover
Trends in SCF for Individual MonthTrends in SCF for Individual Month (α ~ 1.0)
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68
Modeled Snow Depth and SWEModeled Snow Depth and SWE (α ~ 1.0)S
WE
(m
m)
Sno
w D
epth
(m
)
Runoff | Groundwater | Bare Snow | Snow Cover
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69 Runoff | Groundwater | Bare Snow | Snow Cover
Net Solar Energy and Ground-Surface Temperature
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70
Boreal Forest Regions
MODEL1 (default SCF)
MODIS
Runoff | Groundwater | Bare Snow | Snow Cover
Radiation Transfer through the Canopy
MODEL2 (Yang97
SCF)
MODISModel1Model2
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71 Runoff | Groundwater | Bare Snow | Snow Cover
Problems in Two-Stream Radiation Transfer Scheme
Cloudy leaves
Clumped crowns
“Mosaic” approach
Evenly-distributed
Two-stream
Modified two-stream
(Courtesy of RE Dickinson)
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72 Runoff | Groundwater | Bare Snow | Snow Cover
A modified Two-Stream Radiation Transfer Scheme
(Yang and Friedl, 2003)(Yang and Friedl, 2003)(Niu and Yang(Niu and Yang, 2004), 2004)
3 additional 3 additional parameters:parameters:
Crown shape (R, b)Crown shape (R, b)
Tree densityTree density
Pbc and Pwc are changing with SZA
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73 Runoff | Groundwater | Bare Snow | Snow Cover
Impacts on Surface Albedo and Transmittance
“Mosaic” approach
1. In melting season, the impacts is much greater than in winter.
2. Two-stream is not a big problem; Mosaic approach is.
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74 Runoff | Groundwater | Bare Snow | Snow Cover
Subgrid Tree distributions in the Real Subgrid Tree distributions in the Real worldworld
Modified two-stream
Real worldEssery et al.
(2007)
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75 Runoff | Groundwater | Bare Snow | Snow Cover
Interception of Snow by the CanopyInterception of Snow by the Canopy
Canopy
The interception capacity for snow is ~50 times larger than for rain
30-40% of snow never reaches ground and sublimates from the canopy
Most LSMs did not consider interception of snow by the canopy
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76 Runoff | Groundwater | Bare Snow | Snow Cover
Interception of Snow by the canopy
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77 Runoff | Groundwater | Bare Snow | Snow Cover
Impacts of Interception on Canopy SCFImpacts of Interception on Canopy SCF
Deardorff (1978)
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78 Runoff | Groundwater | Bare Snow | Snow Cover
Impacts Interception of Snow on Surface Impacts Interception of Snow on Surface AlbedoAlbedo
Default CLM intercepts rainfall, but computes surface albedo as snowfall.
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79
Factors Affecting Wintertime Land Surface Albedo
Ground snow covered fraction (SCF) Ground surface roughness length Snow depth Season Subgrid topography Snow properties Grain size Impurity Vegetation shading factors Tree cover fraction Leaf/stem area index Vegetation height (canopy fraction buried by snow) “Mosaic Approach” gaps varied with SZA
Snow on the canopy Tree cover fraction Interception capacity Meteorological conditions (wind, temperature)
Runoff | Groundwater | Bare Snow | Snow Cover
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80
Ongoing and Future Work
Noah LSM development plan:1. Topmodel approach to computing runoff,2. Simple groundwater model,3. Multi-Layer snow model,4. Snow cover fraction scheme,5. Separation of canopy and ground temperatures; dynamic vegetation6. Radiation transfer (modified two-stream) and snow interception7. Routing scheme and lateral flow of groundwater (Gochis)Retain Noah soil moisture and temperature solutions; Layer structure
and datasets (vegetation and soil)
Our Testing Plan: Point-scale: Sleepers river – snow physics and runoff (2-3 months);
BOREAS: snow interception and radiation transfer. North American rivers – snow cover, SWE, snow depth, runoff
(streamflow), GSMDB soil moisture, ARM/CART fluxes … using NLDAS data for at least 10 years (6-9 months).
Global rivers – GLDAS data against snow cover, riverflow, and GRACE TWS change (Rodell for GLDAS forcing from 2002-2007) (6 months).
Runoff | Groundwater | Bare Snow | Snow Cover
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Thank you!for your attention and
patience
Acknowledgements:
NASA and NOAA supportsRobert E DickinsonRoss BrownDavid Robinson
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82
Canopy Heat Capacity on Surface Canopy Heat Capacity on Surface TemperatureTemperature
Runoff | Groundwater | Bare Snow | Vegetated Snow | Snow Cover
“Snowball” Earth
No-snow Earth
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83
Undercanopy Turbulent Transfer-Stability Correction
Runoff | Groundwater | Bare Snow | Vegetated Snow | Snow Cover