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Vflo: A REAL-TIME DISTRIBUTED HYDROLOGIC MODEL

Baxter E. Vieux, Ph.D., P.E., Principal

Jean E. Vieux, M.S., President/CEO

Vieux & Associates, Inc.

Norman, OK 73072404.292.6259

jv@vieuxinc.com

www.vieuxinc.com

Abstract: Distributed parameter watershed models that are physics-based offer distinct

advantages over conceptual rainfall-runoff models. Vflo incorporates routing of unsteady flowthrough channel and overland elements comprising a drainage network. A single catchment may

be comprised of a few hundred finite elements, and up to a million for river basins covering an

entire country. Simulation of days of response can be performed in seconds depending ondrainage network size. Parameters are derived from GIS/RS maps with inputs from multisensor

precipitation estimates in real-time or post-analysis. Distributed models better represent thespatial variability of factors that control runoff enhancing the predictability of hydrologic

processes. Spatially distributed parameters derived from soil properties, land use/cover,topography, and input from radar or multi-sensor precipitation estimates offer new possibilities

for simulating hydrologic response on a drainage network basis that is scalable from catchment

to river basin. Combining terrestrial measurements in GIS format and meteorological outputfrom radar and other sensors offers new opportunities for water management. Three case studies

are presented that demonstrate the application of Vflo for different applications and watershed

conditions/regional climate.

INTRODUCTION

Managing precious water resources, sampling protocols for water quality monitoring, protecting

lives and property from flood damage, and flood-warning systems can benefit from customizedand timely hydrologic prediction. Knowing how much runoff is occurring at any location in a

watershed requires the integration of distributed hydrologic prediction models, multisensor

estimates of precipitation from radar, satellite and gauge, and information systems for hydrologicinformation dissemination. The overall goal of the fully-distributed, physics-based hydrologic

model, Vflo, is to provide high-resolution runoff estimation for management of water from

small watersheds to river basin scale. An advantage of physics-based models is that they can besetup with minimal historical data and still generate meaningful results. Representing the factors

that control runoff in a spatially variable manner makes more accurate predictions possible. The

paper presents three case studies representative of a range of watershed conditions and climate.Additionally, a model comparison study between Vflo and CASC2D is described in this

volume by Hunter et al. (2002) for the Santa Maria Basin, Arizona.

The purpose of Vflo is to simulate the flow of water across the terrain represented by

geographical maps such as digital elevation, soils, and land use/cover. Precipitation inputsconsist of rainfall rate maps at time intervals, as small as 5 minutes, from radar or multisensor

inputs. The radar system deployed nationwide in the US, called NEXRAD (WSR-88D), provides

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unprecedented high-resolution rainfall estimates. Vieux (2001b,c) describes the use of NEXRAD

radar in hydrologic modeling within a GIS framework. When radar is supplemented withsatellite, rain gauge networks, a multisensor input results that can overcome terrain blockages

and other anomalies. The main use of the software is for simulating the hydrologic response of

basins or regions experiencing severe storms and heavy rain. The subject matter of this paper is

organized with a description of how distributed hydrologic modeling approaches; modelformulation and system design; and then preliminary results that demonstrate the application of

Vflo to watersheds under diverse conditions and regions.

Overview of hydrologic modeling approach: A model capable of using the wealth ofinformation content available in digital datasets derived from remote sensing and GIS offers the

potential for improved predictability. Understanding the limitations of hydrologic predictability

is a project of the Committee on Hydrologic Science of the National Research Council(Entekahbi et al., 2002). Woolhiser (1996) observed that hydrologic model predictions may not

be improved using GIS data if hydrologic processes are badly distorted in the model

representation. Vieux (2002) presents the need for developing synergy between distributed

hydrologic model development and the resolution and uncertainties associated with scale andobservability of spatial parameters and inputs. Model development that takes advantage of

worldwide digital data provides new opportunities in hydrologic prediction through the use of

distributed models capable of using this wealth of information content.

Classically, hydrologic models have been optimised for point measurements, and not distributed

in space and time. The most common technique in use in the US is based on the unit hydrograph

approach, first proposed by Sherman (1932), the unit hydrograph technique assumes a linearresponse to a unit input of rainfall excess. Snyder and others contributed later improvements and

modifications for ungauged watersheds as described by Bedient and Huber (2001). Practical

application of the unit hydrograph methods through the development of HEC-1 and HEC-HMS

have been advanced by the US Army Corps of Engineers, Hydrologic Engineering Center (1981,2000). These techniques often assume basin averaged or sub-basin averaged parameters and

inputs giving rise to the lumped model. Derivation of the unit hydrograph for a particular

watershed must come from stream gage records or from synthetic estimation techniques. Bothmethods assume that the rainfall is uniform over the basin and that the basin always responds to

the same degree given a unit of rainfall excess. Output is proportional to the rainfall depth and

not necessarily to the rainfall intensities during the storm. Lumped models can be less responsiveto very intense, but short-lived rainfalls, because the accumulated depth may be small and only

over a limited area of the watershed.

Distributed models avoid averaging parameters and input in order to more faithfully representwatershed characteristics. A computational scheme routes runoff from grid cell to grid cell or

other element representative of the landscape using some set of equations termed a mathematical

analogy. Analogies range from full dynamic to simplifications such as diffusive and kinematic

wave. The kinematic wave analogy is applicable in areas where the landsurface slope is thedominant gradient and where backwater effects are not important. Physics-based models use

conservation of mass, momentum, and energy equations to represent hydrologic processes,

whereas conceptual models use empirical relationships together with buckets to represent

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component processes. Moore and Grayson, (1991) describe an array of physics-based models

that capitalize on digital models of elevation, GIS and remotely sensed (GIS/RS) geospatial data.

The termphysics-based modelmeans that conservation of mass in combination with momentum

and/or energy is employed to compute hydrologic fluxes. Deterministic physics-based models

include r.water.fea (Vieux and Gauer, 1994; Vieux, 2001), CASC2D (Julien and Saghafian,1991; Ogden and Julien, 1994; Julien, et al., 1995), Systeme Hydrologique European (SHE)(Abbott et al., 1986a,b) and the Distributed Hydrology Soil Vegetation Model (DHSVM)

(Wigmosta, et al.,1994). Conceptual rainfall-runoff (CRR) models include Precipitation-Runoff

Modeling System (PRMS) by Leavesley et al. (1983), the Sacramento Soil Moisture AccountingModel (SAC-SMA) (Burnash, et al. 1973), and the HECHMS model (Hydrologic Engineering

Center, 2000) that simulate runoff generation by a variety of conceptual parameters and route the

runoff using unit hydrographs an outlet. CRR models are inherently not physics based and lump

parameters at the basin or sub-basin level.

One of the most significant errors in estimating the hydrologic response of a basin is the

precipitation input. When rain gauges sparsely arranged in or near a watershed were the solemeans of gauging the input, severe stream flow estimation errors often result. Before the advent

of radar and satellite remote sensing of the atmosphere, there was little motivation for the

development of better hydrologic models. Given high-resolution spatial and temporal resolution

of precipitation intensities, advanced hydrologic modeling techniques hold some promise inbetter hydrologic prediction. With detailed precipitation input widely available, there is more

motivation to formulate a better hydrologic model.

Vflo MODEL FORMULATION

The mathematical analogy for the governing equations is the kinematic wave analogy (KWA).

The KWA has most applicability where the principle gradient is the land surface slope. Thus inalmost all watersheds except for very flat areas, the KWA may be used. As such, this analogy

may be used wherever backwater effects are not important. The simplified momentum equation

and the continuity equation comprise the KWA. The one-dimensional continuity for overlandflow resulting from rainfall excess is expressed by:

IRx

uh

t

h=

+

)( 1

whereRis rainfall rate;Iis infiltration rate; his flow depth; and uis overland flow velocity. In

the KWA, we equate the bed slope with the friction gradient. In open channel hydraulics, this

amounts to the uniform flow assumption. Using this fact together with an appropriate relationbetween velocity, u, and flow depth, h,such as the Manning equation, we obtain

u S

nh

O=

1 2

2 3

/

/ 2

where So is the bed slope or principal land surface slope, and n is the hydraulic roughness.

Velocity and flow depth depend on the land surface slope and the friction induced by the

hydraulic roughness. For channelized flow, Eq. 1 is written with the cross-sectional area Ainstead of the flow depth h:

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qx

Q

t

A=

+

3

where Qis the discharge or flow rate in the channel, and qis the rate of lateral inflow per unit

length in the channel.

Overland flow is modeled with Eqs. 1 and 2, and channels with Eq. 3 and appropriate form of theManning uniform flow relation in Eq. 2 using the finite element method. Digital maps of soils,land use, topography and rainfall rates are used to compute and route rainfall excess through a

network formulation based on the Finite Element Method (FEM) computational scheme

described by Vieux (1988, 1990). Special treatment is required to achieve a FEM solution to the

KWA over a surface with spatially varying roughness, slope, or other parameters. Vieux et al.(1990) and Vieux (1991) presented such a solution using nodal values of parameters in a finite

element solution. This method effectively treats changes in parameter values by interpolating

nodal values across finite elements. Vieux (2001) and Vieux and Gauer (1994) describe thedevelopment of rainfall-runoff modeling based on a drainage network comprised of finite

elements. The advantage of this approach is that the kinematic wave analogy can be applied to a

spatially variable surface without numerical difficulty introduced by the shocks that wouldotherwise propagate through the system. The finite element methodology results in execution

times that are fast enough to allow real-time computation before the next radar update.

Accounting for unsteady flow in mild slopes, Vflo allows a looped rating curve for channel

elements. Essentially, the acceleration (deceleration) induced by the rising (falling) limb of thehydrograph is accounted for through the Jones Formula (Henderson, 1966). In mild slope

hydraulic conditions, looped rating curves may cause important effects on the when maximum

flow rate is observed compared with maximum stage. Vflo incorporates both distributed runoffgeneration, and routing of unsteady flow through channel and overland elements. Parameters are

derived from GIS/RS maps with inputs from multisensor precipitation estimates in real-time or

post-analysis. Inputs and parameters are described in the following sections.

Precipitation Input:The input to Vflo is from the WSR-88D radar deployed by the National

Weather Service. Depending on application and size of the hydrologic prediction area, several

different radar products may be used. Real-time data feeds from individual radars may be setup

to download and process rainfall rate for input to the model.

In the Intermountain West (IW), the WSR-88D PPS may not adequately account for mixed-

phase hydrometeors (liquid coated ice appears highly reflective to the radar). Efforts to improve

on the existing WSR-88D PPS are reported by Gourley (1998) and Howard et al. (1997). Thisproduct is known as QPE-SUMS, which is under development at the NOAA-National Severe

Storms Laboratory. Further information on QPE-SUMS development may be found on line at:http://www.nssl.noaa.gov/teams/western/qpe.

Parameters from GIS:GIS/RS data are used to derive model parameters as described below.

The choice of which GIS/RS data source to use depends on availability, resolution, andclassification detail. Methodology for deriving model parameters from GIS/RS data is described

in Vieux (2001). Example data sources are given but may vary depending on model application

and availability of data.

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Flow Direction: The flow direction map was derived from the HYDRO-1K North American

data set available online at http://edcdaac.usgs.gov/gtopo30/hydro/index.html. The HYDRO-1Kdata set is in Lambert Equal Area Azimuthal (LEA) projection with a resolution of 1000 meters

and serves as a valuable source of flow direction worldwide. The 8-directions in this map define

the connectivity of the overland and channel finite elements. The resolution of the data sets does

not matter, except that all data sets must have the same resolution and geographic projection. Toobtain the highest quality flow direction map, a stream network delineated from a Digital

Elevation Model (DEM) should be burned in. Several methods exist such as those described in

Moore et al. (1991) to bias the flow direction map towards the stream network. This technique is

advantageous in relatively flat areas, such as coastal plains or plateaus.

Slope: This map defines slope for channel and overland flow in the Manning equation. The

HYDRO-1K data set is a useful source of slope information worldwide, and is available online athttp://edcdaac.usgs.gov/gtopo30/hydro. The slope was converted from degrees to percent slope.

At this point the slope map represents overland slope (i.e. non-channel cells). The slopes of

channel cells are burned into the overland slope for the final slope map. Slope values in Vflo TM

are generated as non-percentage values (e.g. 6.56% = 0.0656), but are displayed as a percentage.

Infiltration:The infiltration map is essentially the saturated hydraulic conductivity and may be

derived from any soil map with requisite property information. For example, the STATSGO

Dominant Soil Texture is available online at http://dbwww.essc.psu.edu/. STATSGO data isavailable in LEA at a resolution of 1-km. The Dominant Soil Texture class has 16 categories

ranging from sand to silt to clay and various other combinations. The highest soil layer referred

to as Layer 1, the depth from the surface to 5-cm, was chosen. Initial infiltration values for eachsoil class should be estimated for the conditions expected in the watershed. Planned development

will account for temporal changes in soil moisture using the Green and Ampt equations.

Roughness:The hydraulic roughness map may be derived from the 30-meter Landsat data fromNational Land Cover Data (NLCD) are found at the link below. NLCD data was converted fromAlbers Conical Equal Area to LEA. The data set may be resampled to the model resolution using

a bilinear or other interpolation technique. This map controls both channel and overland flow

roughness values.

Channels:Channels are parameterized with maps defining channel width, channel side slope,and channel bed slope. This may be entered from field surveys or estimated from gauging station

information. Extending channel parameters from several measured locations to all stream reaches

may require generalization using geomorphic relationships, by stream order, or other scheme.

Shapefiles:The shapefiles in the same projection may be viewed as overlays along with finite

element connections. Point, polyline, and polygon shapefiles may be used. Shapefiles that extend

beyond the VfloTM domain do not need to be clipped to the domain. Mapped features orient the

user and allow detailed editing of the drainage network by visual comparison.

Calibration adjustment using a physically-based approach: A physics-based model

calibration scheme adjusts parameters within realistic ranges. Volume is adjusted by varying the

hydraulic conductivity, timing and peak discharge are controlled by the hydraulic roughness map

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resolution depends on available DEM resolution and the size of the basin simulated. The basin

drainage areas are 240 km2, 5000 km

2, and 31,200 km

2 for Brays Bayou, Tar River, and

Salt/Verde Rivers, respectively. At 1-km resolution, the number of grid cells equals the basin

area. Each grid cell is connected with either a channel or overland flow finite element.

Salt and Verde River:Knowing the amount of runoff expected above a reservoir permits moreefficient operation minimizing unintentional loss (spills). Sudden releases of water from

reservoirs in the Salt and Verde watersheds managed by the Salt River Project (SRP) require

downstream notification. Better information on runoff into reservoirs means better operations for

conserving water. Panel (a) in Figure 1 shows the watershed boundary of the 31,200-km2Salt

and Verde watersheds with the drainage network superimposed over landuse/cover backdrop

derived from Landsat 7. The 1-km DEM in panel (b) is used to develop the drainage network and

assign overland slope. Panel (c) is zoomed into a particular stream channel node containing a

USGS stream gauge. The hydrograph in panel (c) is generated for a test storm event.

(a) (b)

(c) (d)

Figure 1 Salt and Verde River model domain.

In operation, the model receives input from the QPE-SUMS multisensor precipitation estimates.

Further studies are planned to further parameterize the model as wintertime and summertime

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storm events are archived. Snow melt and other modifications are planned to account for runoff

processes dominant in the watersheds.

Brays Bayou, Houston, Texas: As part of a customized flood alert system for the Texas

Medical Center (TMC) and Rice University in Houston, TX, Vflo will serve as a real-time

model to predict stage in Brays Bayou. When the 240 km

2

upstream watershed receives intenseprolonged rainfall, the TMC can sustain flood damages. The upper left panel (a) in Figure 2

shows the landuse/cover derived from Landsat 7 for a portion of the Texas Gulf Coast. To the

right in panel (b) is the 1-km DEM for the same region. In panel (c) is Brays Bayou shown with

shapefiles and an image backdrop showing elevation. Panel (d) is zoomed in over a USGSstream gauging station just upstream of the TMC. The hydrograph shown in panel (e) is taken at

this location for Tropical Storm Allison. Radar was calibrated to rain gauge accumulations,

however the model was not calibrated. Radar input was derived from KHGX at the nativeresolution but aggregated to an even 15-minute interval. Physically realistic values of the

parameters were derived from soils and landuse/cover. Agreement with observed is better than

1%. The USGS stream gauge was lost during the storm, yet the field-estimated flow rate is

33,000 cfs. The predicted flow rate is 33,132 cfs.

(a) (b)

Figure 2 Vflo domain Brays Bayou simulation for Tropical Storm Allison, June 9, 2001.

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(c)

(d) (e)

Figure 2 contd.

Since Tropical Storm Allison, development is underway to operate the flood alert system known

as FAS2 using Vflo to predict stage in Brays Bayou for the TMC. Information on FAS is

online at: http://www.floodalert.org.

Tar River, North Carolina: Hurricane Floyd in 1999 produced record flooding in the Carolinas

exceeding in many locations previous flood records set during Hurricane Fran in 1996. Thisspawned a remapping of floodplains using advanced topographical measurements from LIDAR.

Tropical Storm Allison, a prodigious rain producer, caused much less damage in the Carolinas

than in Houston TX where it first made landfall. Simulation of Allison for the 5,000 km2Tar

River at Greenville, NC was conducted to test the models ability to simulate response from a

major river basin without calibration, but with physically realistic parameters. The radar data was

derived from 4x4 km digital precipitation array (DPA) NEXRAD data and was unadjusted.

Compensating errors likely exist; however, the agreement was exceedingly good, especiallywhen no calibration was performed. Panel (a) in Figure 3 shows the landuse/cover derived from

Landsat 7 along with the outline of the Tar River watershed and drainage networks. Panel (b)

shows the grid cell connectivity at 1-km resolution. Panel (c) shows two hydrographs along withdaily mean discharge from the USGS gauge. Volume agreed within 2% and peak flow within

13%. A second test was made with lumped hydraulic roughness, n=0.045.

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(c)

Figure 3 contd.

SUMMARY

A newly developed physics-based, fully-distributed hydrologic model, called Vflo, simulates

rainfall runoff in overland flow areas and routes the flow through channel networks. Advances in

worldwide digital geospatial data and radar, satellite as multisensor inputs permit unprecedentedknowledge of how much, and where runoff will occur. Combining terrestrial GIS/RS data with

meteorological radar measurements in a single model is an important advance in model

technology. Model structure is optimized to handle gridded parameters and inputs for trulydistributed simulation in real-time. Implemented in JAVA, secure access permits users in

organizations to model hydrologic response anywhere in the drainage network. Hydrologic

prediction from local to regional scales with the same model is an important advance in

technological capabilities.

ACKNOWLDEGEMENTS

The authors wish to thank Eddie Kohler, Vieux & Associates, Inc. for his assistance inpreparation of Vflo data and graphics. Support and collaboration from the NOAA-National

Severe Storms Laboratory, Salt River Project, Texas Medical Center, Federal Emergency

Management Agency, and Dr. Philip Bedient, Rice University is gratefully acknowledged.

REFERENCES

Bedient and Huber (2001). Hydrology and Floodplain Analysis, Prentice Hall, pp. 113 ff.

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