Preliminary Lohmann (VIC) Routing
Model Results
Colby Fisher
May 23, 2017

RVIC - Lohmann Routing••••Routing is performed separatelyfrom the land surface simulation,using a separate routing model(Lohmann, et al. (1996; 1998))
Each grid cell is represented by anode in the channel network
Total runoff and baseflow fromeach grid cell is first convolved
with a unit hydrographrepresenting the distribution oftravel times to the channelnetwork
The grid cell's input into thechannel network is then routed
through the channel using
linearized St. Venant's equations
http://rvic.readthedocs.io/en/latest/about/model-overview/2

Routing Model•

Routed according to the following :– In-grid flow concentration is given bybasic unit hydrograph– In-channel flow is given by theSaint Venant’s equation:

¶q
¶2q
¶q
= D 2 -C¶t¶x
¶x

D, C vary withgeography or static(Lohmann, 1996)

t– Solved using convolution

q( x, t ) = ò u (t - s)h( x, s)ds

Of Green’s (impulse response)
function, given by:

æ (Ct - x) 2 öh( x, t ) =exp ç ÷4Dt2t p tDèø

0x3

Model Setup• Simulations for the Mississippi with NLDAS Runoff– Date: 01/01/2000 to 12/31/2009, 6 months spinup before start• 0.125 degree resolution• Hourly time step and averaged to daily (also run with justdaily)• Topography: SWOT-MIP setup (Direc. derived from Dai’s DEM)
– Temporarily using a different network (Legacy code thinks there issomething wrong with the new DEM)

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Model Setup• Flow Network:Lohmann, 1998

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ResultsDaily Discharge Output

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Results – Overall TS

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Results8

Results - Stats

Mean Q (Obs) Mean Q (Model) RMSE
466.9
995.4
972.3
401.5
282.5
355.7
755.5
695.5
760.5
989.6
1180.1633.0
2188.62991.01365.33418.13639.1
1534.82083.215.9
2497.35547.18839.34985.03623.34317.32641.68129.77239.1
4111.06080.410255.5
7225.0
303.3
287.9
354.7
1294.1
39.1
1868.8
588.6
592.4
473.8

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Summary• Acceptable results from a simple model– Good stats on the monthly level (for LSMs)• Often misses timing of certain events and human influences• Can serve as a baseline for other model results• Still need to fix the flow direction issue to make sureeverything is consistent

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SWOT Assimilation Experiments• How can we use future SWOT data to better predict spatiallyand temporally consistent records of runoff and discharge?
– Statistical interpolation techniques (Paiva et al., 2015)– Data assimilation with hydrodynamic model (Pan and Wood, 2013,
Inverse Streamflow Routing)11

Inverse Streamflow Routing
Forward model (Linear Routing): y = Hx

Inverted Runoff

Where H = Green’s Impulse Response Function (Lohmann, 1996)

The integrated routing process can then be given a! r $! q $linear form:
11y t = H 0 x t + H1x t−1 ++ H k x t−k + εt

#&
# q &
yt = # 2 &
#  &
# q &
" m %

t

#&
# r &
xt = # 2 &
#  &
# r &
" n %tInversion is done through a Kalman Filter & Smoother:xˆ "t = xˆ 't + K t (y 't - H ' xˆ 't - L ' xˆ 't -k )The weight of the correction (Kalman Gain) is determined as:(K t = Pt H ' H ' Pt H ' + RtTT)-1

Smoothing window of 2x max flow length (days) was used for this study
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Inverse Streamflow RoutingExperiments with theoretical SWOT
observations to construct basin wide
discharge:••••

Utilizes a Kalman Filter & SmootherLinear routing model (Lohmann)~150 crossing ”gauges” assimilated
25 crossing “gauges” evaluated

Idealized Experiment
Initial GuesspInit

Synthetic Truth
pSyn

LSM

LSM

rInitrSyn

RoutingRoutingqInit

qSyn
InverseSmoothing

rinverted, qall13

Discharge Interpolation Experiments

Initial RunoffConditions

Discharge Data Assimilated
All Gauges

SWOT OnlyLong Term
Basin Mean

In-Situ Discharge &Min. Runoff Info

SWOT Discharge &Min. Runoff InfoDaily
Climatology

In-Situ Discharge &Some Runoff Info

SWOT Discharge &Some Runoff Info

TMPA Real Time

In-Situ Discharge &Obs. Runoff Info

SWOT Discharge &Obs. Runoff Info

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ISR – SWOT Assimilation•Application of Inverse Streamflow Routing to Ohio river basin illustrated
ability to assimilate SWOT obs.

• Performance constrained by spatial and temporal coverage:

From Fisher et al. (In Prep.)

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ISR – SWOT Assimilation•

Application of Inverse Streamflow Routing to Ohio river basin illustrated
ability to assimilate SWOT obs.

• Performance constrained by spatial and temporal coverage:• How will SWOT observe other river basins?
• How will their location and spatial
properties affect the assimilation?
From Fisher et al. (In Prep.)16

Global Basins• Inverse Streamflow was applied to 32 large global basins• Representative of a wide range of hydrologic and geographic properties

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Synthetic Experiments

Initial RunoffConditions

Discharge Data AssimilatedAll Gauges

SWOT Only

Mixed Gauges
and SWOTLong Term
Basin Mean

In-Situ Discharge &Min. Runoff Info

SWOT Discharge &Min. Runoff Info

Mixed Discharge &Min. Runoff InfoDaily
Climatology

In-Situ Discharge &Some Runoff Info

SWOT Discharge &Some Runoff Info

Mixed Discharge &Some Runoff Info

TMPA Real Time

In-Situ Discharge &Obs. Runoff Info

SWOT Discharge &Obs. Runoff Info

Mixed Discharge &Obs. Runoff Info

• Model Setup:• Initial conditions à VIC LSM forced with runoff climatology• Discharge observations à VIC LSM forced with Princeton Global Forcing• Theoretical SWOT observations à Model discharge sampled fromtheoretical 21-day, 890 km altitude, 77.6° inclination orbit• 0.25° spatial res. & daily temporal res.
• ~30% errors for observations based on current retrieval methods
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Discharge Interpolation
Assimilation using runoff climatology + SWOT
sampled discharge time series for theDanube

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Global Interpolation PerformanceNash-Sutcliffe Efficiencies (NSE) for reconstructed gauge discharge time series

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Global Interpolation PerformanceNash-Sutcliffe Efficiencies (NSE) for reconstructed gauge discharge time series

What causes the assimilation
performance to differ across basins?

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Global Applicability
SWOT orbit dictates the availabilityof data for assimilation• Depends on River:– Latitude– Size (length, width and basin area)– Orientation

Biancamaria et al., 2015

Day 1 and 2 Crossings for the:Danube & Nile

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Adding in Discharge Obs.
SWOT Only

Mixed Gauges & SWOT

TMPA

CLIM

MEAN

All Gauges

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Conclusions• For most basins we are able to use
ISR reconstruct spatially andtemporally consistent discharge

Nile River– Also reconstruct runoff fields• Utilization of SWOT observations
will be dependent on:– Timing and orientation of overpasses– Basin geometry and orientation– Availability of in-situ discharge orrunoff information to aid in theassimilation• Future work is also needed to:– Better quantify orientation of rivers
relative to orbit– Differentiate observations of rivers
and floodplain areas24Thank you,Questions?
References:• Biancamaria, S., Lettenmaier, D. P., & Pavelsky, T. M. (2015). The SWOT Mission and Its Capabilities
for Land Hydrology. Surveys in Geophysics, 1–31.
• Lohmann, D., R. Nolte-Holube, and E. Raschke, 1996: A large-scale horizontal routing model to becoupled to land surface parametrization schemes, Tellus, 48(A), 708-721.
• Lohmann, D., E. Raschke, B. Nijssen and D. P. Lettenmaier, 1998: Regional scale hydrology: I.
Formulation of the VIC-2L model coupled to a routing model, Hydrol. Sci. J., 43(1), 131-141.
• Paiva, R. C. D., Durand, M. T., & Hossain, F. (2015). Spatiotemporal interpolation of discharge across ariver network by using synthetic SWOT satellite data. Water Resources Research, 51(1), 430–449.
• Pan, M., & Wood, E. F. (2013). Inverse streamflow routing. Hydrology and Earth System Sciences,17(11), 4577–4588.
• Pavelsky, T. M., Durand, M. T., Andreadis, K. M., Beighley, R. E., Paiva, R. C. D., Allen, G. H., & Miller, Z.
F. (2014). Assessing the potential global extent of SWOT river discharge observations. Journal ofHydrology, 519(PB), 1516–1525.