Can Hydraulic Geometry (HG) aid SWOT river discharge retrievals?
Transcript of Can Hydraulic Geometry (HG) aid SWOT river discharge retrievals?
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Can Hydraulic Geometry (HG) aid
SWOT river discharge retrievals?
Laurence C. Smith (UCLA)Matthew Mersel (UCLA)Michael Durand (Ohio State)Kostas Andreadis (Ohio State)Kostas Andreadis (Ohio State)
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SWOT will measure: At and dH/dt; dH/dx
Lakes: (At)(dH/dt) = dS/dt(storage anomaly, m3/dt)
Rivers: (At/L)(dH/dt)(vest)= dQ/dt(discharge anomaly, (m3/s)/dt)(discharge anomaly, (m3/s)/dt)
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SWOT will measure: At and dH/dt; dH/dx
Lakes: (At)(dH/dt) = dS/dt(storage anomaly, m3/dt)
Rivers: (At/L)(dH/dt)(vest)= dQ/dt(discharge anomaly, (m3/s)/dt)(discharge anomaly, (m3/s)/dt)
(estimate from assimilation of SWOT observables into hydrodynamic model; and/or Manning’s equation)
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?
… but true discharge also requires flow depth
True Bathymetry SWOT Observations
?
?
• SWOT will measure bathymetry down to the lowest water level encountered
over the mission lifetime, but will not capture the entire channel bathymetry.
• This unknown baseflow depth limits the accuracy of SWOT discharge estimates.
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?
True Bathymetry SWOT Observation
ApproximationsApproximations
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SWOT Depth Estimation
SWOT will only measure channel bathymetry down to lowest exposed banks
over mission lifetime
This unknown baseflow depth represents greatest risk to SWOT discharge
estimates
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Q = wdv
w = aQb ; d = cQf ; v = kQm
b+f+m = 1; acv = 1
HYDRAULIC GEOMETRY (HG)
(Leopold and Maddock, 1953)
d
w
discharge Q
v
d
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Q = wdv
w = aQb ; d = cQf ; v = kQm
b+f+m = 1; acv = 1
HYDRAULIC GEOMETRY (HG)
(Leopold and Maddock, 1953)
d
w
discharge Q
v
d
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Q = wdv
w = aQb ; d = cQf ; v = kQm
b+f+m = 1; acv = 1
HYDRAULIC GEOMETRY (HG)
(Leopold and Maddock, 1953)
d
w
Type 1: At-a-station (AHG)
Type 2: Downstream(DHG)
discharge Q
v
d
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Q = wdv
w = aQb ; d = cQf ; v = kQm
b+f+m = 1; acv = 1
HYDRAULIC GEOMETRY (HG)
(Leopold and Maddock, 1953)
d
w
Type 1: At-a-station (AHG)
(site-specific, multi-
temporal)
time-varying Q’s at one
location in space
v
d
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SWOT Depth Estimation
SWOT will only measure channel bathymetry down to lowest exposed banks
over mission lifetime
This unknown baseflow depth represents greatest risk to SWOT discharge
estimates
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Case study: Rio Grande River
� 4th longest river in the U.S. (>3000 km,
~472,000 km2 watershed)
� High quality cross-section data (145
surveyed; 1,235 interpolated)
� 100-year flood flow rates
Study Area
Used HEC-RAS to simulate AHG’s
(widths, depths, velocities versus range
of simulated discharges) at 145
surveyed cross-sections
-Steady state discharges
-Fixed bed
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�Contributing Watershed ≈ 2315 sq km
� ~89% in upper half of reach
Caballo Dam to American Dam
< N
100-Year Flood Discharge
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Overbank Flow
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In-Channel Flow
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AHG goodness-of-fit (n=145)
(overbank flows)
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AHG goodness-of-fit (n=145)
(within-bank flows)
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AHG b,f,m exponents, n=145
(within-bank flows)
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(Park, J. Hydrol., 1977)
w << d, v
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Q = wdv
w = aQb ; d = cQf ; v = kQm
b+f+m = 1; acv = 1
HYDRAULIC GEOMETRY (HG)
(Leopold and Maddock, 1953)
d
w
Type 1: At-a-station (AHG)
Type 2: Downstream (DHG)
(landscape scale, steady-state)Longitudinal Q’s at many
locations (e.g. bankful)
v
d
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(Booker, ESPL, 2010)
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w << d, v
(Park, J. Hydrol., 1977)v<<w > d
w << d, v
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w << d, v
(Park, J. Hydrol., 1977)
w << d, v
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(JGR, 2007)
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Proof-of-concept: First-ever mapping of AHG from space(multi-temporal MODIS, b-exponents only, 1-km posting)
(Smith and Pavelsky, WRR 2008)
High b-values imply deeper flow
depth and/or slower velocity
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At-a-station AHG (temporal, local scale):
Accumulate empirical relationships over time at each of thousands of
point locations along a river course, enabling:
(a) Power-law extrapolation of baseflow depths?
(b) Directly-measured apportionment between w, d, v at each posting for
calibration/validation of Data Assimilation methods
(c) Exponent ratios sensitive to channel form (e.g. b/f varies from 0 for
Potential value of HG for SWOT-type discharge retrievals
(c) Exponent ratios sensitive to channel form (e.g. b/f varies from 0 for
rectangular cross-section to 1 for triangular); also frictional resistance
(decreased roughness increases m/f)
Downstream DHG (systematic, landscape scale):
Goal: Accumulate empirical relationships over space, collected on same
day over large areas (steady flow, e.g. bankfull) required), enabling:
(a) Refined data-assimilation of discharge retrievals upstream and
downstream of SWOT retrievals
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Can HG aid river discharge retrievals? MAYBE (esp cal/val)
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What if it none of it works?
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What if it none of it works?
SWOT will measure: At and dH/dt; dH/dx
Lakes: (At)(dH/dt) = dS/dt(temporal storage anomaly, m3/dt)
Rivers: (At/L)(dH/dt)(vest)= dQ/dt(temporal discharge anomaly, (m3/s)/dt)(temporal discharge anomaly, (m3/s)/dt)
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What if it none of it works?
SWOT will measure: At and dH/dt; dH/dx
Lakes: (At)(dH/dt) = dS/dt(temporal storage anomaly, m3/dt)
Rivers: (At/L)(dH/dt)(vest)= dQ/dt(temporal discharge anomaly, (m3/s)/dt)(temporal discharge anomaly, (m3/s)/dt)
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What if it none of it works?
SWOT will measure: At and dH/dt; dH/dx
Lakes: (At)(dH/dt) = dS/dt(temporal storage anomaly, m3/dt)
Rivers: (At/L)(dH/dt)(vest)= dQ/dt(temporal discharge anomaly, (m3/s)/dt)(temporal discharge anomaly, (m3/s)/dt)
ALSO longitudinal discharge anomalies, dQ/dx…
… “DIFFERENTIAL DISCHARGES”
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Rio Grande: Caballo Dam to American Dam
< N
100-Year Flood Discharge
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(J. Water Res. Planning Mgmt, 2009)
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(J. Water Res. Planning Mgmt, 2009)
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What if it none of it works?
SWOT will measure: At and dH/dt; dH/dx
Lakes: (At)(dH/dt) = dS/dt(temporal storage anomaly, m3/dt)
Rivers: (At/L)(dH/dt)(vest)= dQ/dt(temporal discharge anomaly, (m3/s)/dt)(temporal discharge anomaly, (m3/s)/dt)
ALSO longitudinal discharge anomalies, dQ/dx…
… “DIFFERENTIAL DISCHARGES”
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What if it none of it works?
SWOT will measure: At and dH/dt; dH/dx
Lakes: (At)(dH/dt) = dS/dt(temporal storage anomaly, m3/dt)
Rivers: (At/L)(dH/dt)(vest)= dQ/dt(temporal discharge anomaly, (m3/s)/dt)(temporal discharge anomaly, (m3/s)/dt)
ALSO longitudinal discharge anomalies, dQ/dx…
… “DIFFERENTIAL DISCHARGES”
- will yield new science on how water gets in/out of rivers
- unprecedented for water management
- can be done in single overpass (e.g. AirSWOT)
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BACK-UP SLIDES
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SIMULATING SWOT from ground data:
(At)(dH/dt) = dS/dt
(Smith and Pavelsky, ESPL 2009)
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1.5 km2
Small lakes =
1300 km2
lakes = “steeper” area-stage rating curves
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Lake “area-effect”
(Smith and Pavelsky, ESPL 2009)
(area changes more important to dS/dt for small lakes,
height changes more important for large lakes)
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SWOT and rivers: Lena River, Siberia
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SWOT and rivers: Lena River, Siberia
(dQ vs A: power law) (TIME LAG = +8 days)
(Smith and Pavelsky, WRR 2008)
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Segmenting the Lena River with MODIS:
(Smith and Pavelsky, WRR 2008)
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Resulting “area-discharge” rating curves converge to stable stable values at ~2X valley width
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Peace-Athabasca Delta
(See Tamlin Pavelsky)
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At vs. dH/dt
(“Area-stagerelationship”
HYDRAULICGEOMETRY
relationship”
(Smith and Pavelsky,ESPL 2009)
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Hydraulic Geometry Exponents(Overbank Flow)
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(JGR, 2007)
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AHG b,f,m exponents, n=145
(overbank flows)