storm runoff computation using gis
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Storm Runoff Computation Using
Spatially Distributed Terrain Parameters
by Francisco Olivera and David R. Maidment
University of Texas at AustinCenter for Research in Water Resources
1. Introduction
In rainfall-runoff computation, not only is the generation of excess precipitation
spatially distributed but also the precipitation itself, which has been a limitationfor the use of the classic unit hydrograph model for years. The theory presented in
this paper is an attempt to generalize the unit hydrograph method for runoff
response, and to do so on a spatially distributed basis in which the runoff responses from subareas of the watershed are considered separately instead of
being spatially averaged.
Although the theory of linear routing systems presented in this article is not bound
to raster representations of the study area, the model proposed here is based ongrid data structures. A grid data structure is a discrete representation of the terrain
based on identical square cells arranged in rows and columns. Grids are used to
describe spatially distributed terrain parameters (i.e. elevation, land use,impervious cover, etc.), and one grid is necessary per parameter that is to be
represented. The density of grid cells should be large enough to resemble a
continuous character of the terrain.
Starting from the digital elevation model (DEM), hydrologic features of theterrain (i.e. flow direction, flow accumulation, flow length, stream-network, and
drainage areas) can be determined using standard functions included in
commercially available geographic information system software that operates onraster terrain data. At present, DEM’s are available with a resolution of 3 arc-
seconds (approximately 90 m) for the United States, and 30 arc-seconds
(approximately 1 Km) for the entire earth, etc. Since in the case of water draining
under gravity a single downstream cell can be defined for each DEM cell, aunique connection from each cell to the watershed outlet can be determined. This
process produces a cell-network, with the shape of a spanning tree, that represents
the watershed flow system.
Flow routing consists of tracking the water throughout the cell-network. For this
purpose, a two-parameter response function is determined for each cell, in which
the parameters are related to flow time (flow velocity) and to shear effects
(dispersion) in the cell. Flow-path response functions are calculated byconvoluting the responses of the cells located within the reach. Finally, the
watershed response is obtained as the sum of the cell responses to a spatially
distributed precipitation excess.
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A deconvolution algorithm is used to estimate the precipitation excess from flow
records instead of from precipitation records. This algorithm consists of
deconvolving an observed hydrograph by an estimated watershed responsefunction (unit hydrograph) to obtain the precipitation excess. The spatial
distribution of the precipitation excess is assumed to be proportional to the runoff
coefficient.
2. Literature Review
Pilgrim (1976) carried out an experimental study consisting in tracing floodrunoff from specific points of a 0.39 Km2 watershed, near Sydney, Australia, and
measuring the travel time of the labeled particles to the outlet. A conclusion of his
study is that "at medium to high flows the travel times and average velocities become almost constant, indicating that linearity is approximated at this range of
flows". Additionally, for a watershed subdivided into non-overlapping subareas,
linearity of the routing system implies that the overall watershed response is equal
to the sum of the responses of its subareas, which is an important insight indealing with spatial variability of the watershed.
An significant attempt to linking the geomorphological characteristics with the
hydrologic response of a watershed is given by Rodriguez-Iturbe and Valdes
(1979). In their paper, Horton’s empirical laws, i.e. law of stream numbers,lengths and areas, are used to describe the geomorphology of the system. Mesa
and Mifflin (1986), Naden (1992) and Troch et al. (1994) present similar
methodologies to account for spatial variability when determining the watershedresponse. The catchment response is calculated as the convolution of a network
response and a hillslope response. The network response is calculated as the
solution of the advection-dispersion equation, weighted according to the widthfunction of the network. However, the researchers present no physically-based
methodology to determine the hillslope response.
An interesting approach to model the fast and slow responses of a catchment is
presented by Littlewood and Jakeman (1992, 1994). In their model, the watershedis idealized as two linear storage systems in parallel, representing the surface and
the subsurface water systems. The surface system is faster and affects mainly the
raising limb of the resulting hydrograph, while the subsurface system is slow anddetermines the tail of the response.
Geographic Information Systems (GIS) are tools that allow one to jump fromlumped to spatially distributed hydrologic models. The border between lumped
and distributed models is not sharp, and there are pre-GIS attempts to deal withspatially distributed terrain attributes. For example, the Hydrologic Engineering
Center (HEC) flood model HEC-1, well known as a lumped model, allows the
user to subdivide the watershed into smaller sub-basins for analysis purposes, androute their corresponding responses to the watershed outlet. In this case, the
concept of purely lumped model does not apply, although it cannot be considered
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a fully spatially distributed model either. It is therefore advisable to keep in mind
the extent to which a given model is lumped or distributed.
Grid-based GIS appears to be a very suitable tool for hydrologic modeling,mainly because "raster systems have been used for digital image processing for
decades and a mature understanding and technology has been created for thattask" (Maidment 1992 a). The ESRI Arc/Info-GRID system as well as the U.S.
Army Corps of Engineers GRASS system, work on grid data structures. Gridsystems have proven to be ideal for modeling gravity driven flow, because a
characteristic of this type of flow is that flow-directions depend entirely on
topography and not on any time dependent variable. This characteristic is whatmakes gravity driven flow easy to be modeled in a grid environment and,
consequently, grid systems include hydrologic functions as part of their
capabilities. At present, hydrologic functions, available in GRID and GRASS,allow one to determine flow direction and drainage area at any location, stream
networks, watershed delineation, and others (Maidment 1992 a).
Recently, there have been attempts to take advantage of GIS capabilities for
runoff and non-point source pollution modeling. Vieux (1991) presents a reviewof water quantity and quality modeling using GIS and, as an application example,
employs the kinematic wave method to an overland flow problem. GIS is used to
process the spatially variable terrain and the finite elements method (FEM) tosolve the mathematics. Maidment (1992 a, 1992 b, 1993) presents a grid-based
methodology for determining a spatially distributed unit hydrograph that assumes
a time-invariant flow velocity field. According to him, the velocity time-
invariance is a requirement for the existence of a unit hydrograph with a constanttime base and relative shape. This concept is also explained in this article, in the
light of the conditions for linearity of a routing system. In Maidment's articles,from a constant velocity grid, a flow time grid is obtained and subsequently theisochrone curves and the time-area diagram. The unit hydrograph is obtained as
the incremental areas of the time-area diagram, assuming a pure translation flow
process. A more elaborate flow process, accounting for both translation andstorage effects, is presented by Maidment et al. (1996 a). In their paper, the
watershed response is calculated as the sum of the responses of each individual
grid-cell, which is determined as a combined process of channel flow (translation
process) followed by a linear reservoir routing (spreading process). Olivera et al.(1995) and Olivera and Maidment (1996 a) present a grid-based, unsteady-flow,
linear approach that uses the diffusion wave method to model storm runoff and
constituent transport. In these articles, the routing from a certain location to theoutlet is calculated by convoluting the responses of the grid-cells of the drainage-
path.
Sensitivity of model results to the spatial resolution of the data has been addressed
by Vieux (1993), who discusses how the grid-cell size affects the terrain slope andflow-path length, and, in turn, the surface runoff. Vieux and Needham (1993)
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conclude that increasing the cell size shortens the streams length and increases the
sediment yield.
Attempting to account for spatial variability of the terrain in storm runoff modeling, researchers have taken either of the following paths: (1) partitioning the
hydrologic system into subsystems and applying lumped models to each of them,or (2) developing GIS interfaces to generate input files for other lumped models,
and display the results in the form of a map. In both cases, an improvement withrespect to the traditional fully lumped models has been accomplished; however,
these kind of solutions can not be considered spatially distributed. In this research,
storm runoff is modeled within GIS, redefining the use of GIS by using it as amodeling tool itself and not only as a link between the heterogeneous terrain and
an existing non-GIS model.
3. Methodology
For a spatially uniform hydrologic system, the classic unit hydrograph modelstates that
( 1 )
where t [T] is time, Q(t) [L3T-1] is the flow at the watershed outlet, AW [L2] is the
watershed area, I(t) [LT-1] is the excess precipitation, and U(t) [T-1] is the
watershed unit hydrograph. Likewise, for a spatially distributed linear systemsubdivided into uniform non-overlapping subareas, this equation takes the form of
(Maidment et al. 1996)
( 2 )
where NW is the number of subareas, Ai [L2] is the area of subarea i, I i(t) [LT-1] isthe excess precipitation in subarea i (subarea input), and U i(t) [T
-1] is the response
at the watershed outlet yield by a unit instantaneous input in subarea i. Notice that
it is because of the additivity property that characterizes linear systems, that theoverall watershed response can be calculated as the sum of the subarea responses.
From the physical point of view, this summation implies that the flow of a
subarea input to the watershed outlet is not affected by the flow of the other subarea inputs, and that all inputs can be routed simultaneously yet independently.
The use of equation (2) requires for each subarea the excess precipitation Ii(t), and
the response function Ui(t).
In this study, the subareas are taken as small square cells that resemble thecontinuous character of the landscape (see Figure 1), and, because the number of
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The methodology consists of: (1) calculating the overall watershed response as
the weighted sum of the cell responses, where the weight is given by the excess
precipitation (see equation (2)); and (2) estimating the spatially distributed excess precipitation by deconvolving the watershed flow records by the watershed
response (see equation (1)), and distributing this lumped excess precipitation
based on the terrain physical characteristics. It becomes clear that both processesare strongly related, and that one cannot be considered without the effect of the
other. Routing the excess precipitation from the terrain to the watershed outlet is
covered in Flow Routing , while estimating the volume and spatial distribution of the excess precipitation in Excess Precipitation.
3.1. Flow Routing
The response at the watershed outlet cell yield by a unit instantaneous input in a
cell is called here flow-path response function Ui(t), and consists of two parts: a flow-path redistribution function U'i(t) [L
-1] that represents the translation and
redistribution processes in the flow-path (lag-time from the cell to the outlet andspreading around the centroid of the mass slug); and a flow-path loss factor K i(t)
[-] that accounts for the losses along the flow-path. Note that, because of howlosses are accounted for, the area under the curve U'i(t) vs. t is equal to one, and
the values of K i(t) are less than one (see Figure 3).
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Figure 3: The flow-path response function results from the product of the flow-
path redistribution function and the flow-path loss factor.
Flow-path redistribution functions U'i(t) have to satisfy certain mathematical
properties so that if, for example, an input in cell A is routed to cell B and then to
the cell C, the result should be the same as if it were routed directly from A to C(see Figure 4).
Figure 4: Flow-path from cell A to cell C.
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To understand the implications of this condition, notice that the flow-path
redistribution function U'AB(t) is the probability density function of a random
variable XAB that represents the time spent by a water particle in the flow-path thatruns from cell A to cell B. Accordingly, U'BC(t) and U'AC(t) are the probability
density functions of random variables XBC and XAC, respectively. Since the time
spent in AC is the sum of the times spent in AB and BC, it follows that XAC = XAB
+ XBC. In terms of probability density functions, this is expressed as
( 3 )
where * stands for convolution integral. Equation (3) implies that the
redistribution functions should be self reproducing, i.e., the convolution of tworedistribution functions results in a function of the same type. This condition
precludes one, for example, from defining the redistribution functions as
exponential distributions; in other words, from modeling the watershed as an
array of linear reservoirs with one linear reservoir per grid cell, which is a
common but erroneous approach. In statistical terms, the type of functions thatcan be used as redistribution functions are called infinitely divisible distributions.
The normal, gamma and first-passage-times distributions are examples of infinitely divisible distributions.
From the physical point of view, if the flow-path is assumed to convey one-
dimensional unsteady flow and the inertial terms in the St. Venant momentum
equation are neglected, the flow can be modeled with the diffusion wave equation(Miller and Cunge, 1975, Lettenmaier and Wood 1993). Thus, if lateral inflow is
not considered, the flow is represented by
( 4 )
where x [L] is the distance along the flow-path, t [T] is the time, qi(t) [L3T-1] is the
flow at any time and point of the flow-path, C i [LT-1] is the kinematic wave
celerity, and Di [L2T-1] is a dispersion coefficient. For a unit-impulse input, the
solution for qi of equation (4) at the flow-path outlet is the flow-pathredistribution function U'i(t), and it results in a first-passage-times distribution
(Nauman 1981):
( 5 )
where Ti = Li / Ci is the mean value of the distribution (the lag time in the flow-
path), ∆ i = Ci Li / Di represents the spreading around the mean of the distribution
(the shear and storage effects on the flow), and L i [L] is the flow-path length.
First-passage-times distributions apply to systems bounded by a transmitting
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barrier upstream (open boundary) and an adsorbing barrier downstream (close
boundary). First-passage-times distributions are in accordance with what other
researchers have proposed to model the time spent by water in hydrologic systems(Mesa and Mifflin 1986, Naden 1992, Troch et al. 1994). Likewise, it has been
shown that other infinitely-divisible two-parameter distributions, say normal or
gamma, do not differ significantly from the first-passage-times distribution withthe same first and second moments (Olivera 1996 b). Olivera (1996 b) has also
observed that three-parameter distributions tend to overestimate the importance of
the tails with respect to the central part of the distribution.
Extending the concept of self-reproducing flow-path redistribution functions tothe cell level, allows one to model the flow based on scale-independent terrain
parameters. Since the time spent in a flow-path is equal to the sum of the time
spent on each its constituting cells, i.e., Xi = x1 + x2 + ... + x N where Xi is arandom variable that represents the time spent in the flow-path and x1, x2, ...and x N
are random variables that represent the time spent in each of the N cells that form
the flow-path, it follows
( 6 )
where U'i(t), u'1(t), u'2(t), ... u' N(t) [T-1] are the probability density functions of Xi,x1, x2, ... and x N respectively. Moreover, because U’i(t) is a first-passage-times
distribution, u'1(t), u'2(t), ... and u' N(t) are also first-passage-time distributions that
can be expressed as
( 7 )
where j refers to the cell of the flow-path, v j [LT-1] is the flow velocity, d j [L2T-1]
is the dispersion coefficient (shear and storage effects), t j [T] is the expected flow
time through the cell and l j = v j t j. Because the cell flow length l j is known, theonly two parameters needed to define u' j(t) are the flow velocity v j and the
dispersion coefficient d j. In some cases, it is preferable to define the
dimensionless Peclet number v jl j/d j - instead of the dispersion coefficient d j - to
describe the shear and storage effects in the cell. However, it should be noted that, because it involves the flow length in its definition, the Peclet number is a scale
dependent parameter.
The connection between the flow-path redistribution function and the cellredistribution functions is given by equation (6). However, the use of this
equation implies as many convolution integrations as cells are there in the
watershed. Depending on the hardware available, this process might be extremely
demanding and time consuming. A good approximation to U'i(t) - whose error falls within the limits of the uncertainty of the model parameters - can be obtained
based on the fact that (DeGroot 1986)
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(8)
where E refers to expected value (first moment) and Var to variance (secondmoment around the mean). According to this method, the approximate solution
for U'i(t) has the same first and second moments as the solution obtained with
equation (6). By equalizing the first and second moments of U'i(t) given by
equation (5) to the sum of the moments of the u' j(t) given by equation (7),
relations between Ti and ∆ i, and v j and d j are determined as
( 9 )
and
( 10 )
The main advantage of this approach is that it can be applied automatically by
using standard functions – like the weighted flow length function - included incommercially available geographic information systems software that operates on
raster terrain data.
Water losses in linear systems are represented by a first-order loss term in the
mass balance equation
( 11 )
where Λ i [T-1] is a flow-path loss coefficient. The solution of equation (11) is
given by
( 12 )
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where U'i(t) - the flow-path redistribution function - is equivalent to the flow-path
response function when losses are neglected, and exp(-Λ i t) represents the lossesin the flow-path. The flow-path loss factor K i(t) is, therefore, given by
( 13 )
Similarly, for a cell of a flow-path, it can be demonstrated that
( 14 )
where k j(t) [-] is the cell loss factor and λ j [T-1] is a cell loss coefficient.
For small losses, the cell loss factors can be approximated to the constant value k j
= exp(-λ j t j), and the flow-path loss factor to the product of the cell loss factors
( 15 )
which, considering that t j = l j / v j, is equal to
( 16 )
Finally, the flow-path response function can be expressed as
( 17 )
where Ti, ∆ i and K i are given in equations (9), (10) and (16) as functions of the
flow velocity v j, the dispersion coefficient D j and the loss coefficient λ j. Note
that if the cell inter-connectivity and the grids of v j, D j and λ j are defined, the
terrain would be fully described for flow routing purposes.
3.2. Excess Precipitation
One of the advantages of the theory of linear routing systems is that it can handle
spatially distributed inputs, letting the excess precipitation vary according to the
terrain physical characteristics, say land use, soil type or topography.
Standard engineering practice estimates excess precipitation based on soil-water balance. Willmott et al. (1985), for instance, have developed the WATBUG
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Fortran program that simulates the soil-water balance based on local temperature,
precipitation and soil water-holding capacity. Although the soil-water balance is a
physically based approach, it has been observed that it is a complicated processthat should account for a large number of parameters, that it is very sensitive to
the data available, and that it produces results that have to be interpreted with
extreme caution. Other simple excess precipitation models such as the SoilConservation Service (SCS) curve number method, or just the product of a runoff
coefficient by the precipitation, are examples of attempts of solving the problem.
However, estimating the correct excess precipitation is still far from beingachieved.
In the following, a deconvolution methodology for determining excess
precipitation from flow instead of from precipitation records is presented. Given
the flow at a specific station, and a spatially-distributed parameter that describesthe terrain tendency to generate runoff, the spatially-distributed excess
precipitation and flow parameters are calculated. The method consists of
deconvolving the observed direct runoff by the watershed unit response function.This unit response is estimated from the flow records, and considers thewatershed as a lumped system. Spatial variability of the terrain is considered later
in the process. The relation between direct runoff and excess precipitation is given
by
( 18 )
where Q(t) [L3T-1] is the direct runoff, A [L2] is the watershed area, r(t) [T-1] is the
estimated watershed unit response, and Pe(t) [LT-1] is the excess precipitation.
Determining the excess precipitation consists of solving equation (18) for Pe. The
excess precipitation is calculated at discrete time steps by trial and error, guessingvalues of Pe for each time step and then verifying if equation (18) is satisfied. An
optimization software helped in the process of determining the excess precipitation values.
Since the flow and unit response function are considered for the watershed as a
whole, the excess precipitation obtained by deconvolution is a lumped type of
result that should be distributed according to the local hydrologic characteristicsof the terrain. It is assumed that the amount of excess precipitation produced by
each cell is a function of the runoff coefficient, a well known hydrologic
parameter that can be estimated from tables available in the literature (Chow et al.
1988, Browne 1990, Pilgrim and Cordery 1993). A connection between excess precipitation in a cell and runoff coefficient is a critical assumption that allows
one to use a simple model without going through a more complicated - but not
necessarily more reliable - soil-water balance. In our model, excess precipitationin a cell Ii is assumed to be proportional to the runoff coefficient ci minus a
uniformly distributed abstractions parameter ζ (i.e., Ii = ci - ζ or 0 whichever is
greater). This abstractions parameter ζ constitutes a threshold value, andaddresses the fact that low-developed areas might yield no runoff at all. The
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abstractions parameter ζ may change from event to event depending on rainfall
intensity, soil infiltration capacity and antecedent moisture condition. Values of ci
- ζ for each cell are calculated and used as an excess precipitation scale factor.The excess precipitation generated in a cell Ii is given by
( 19 )
where
( 20 )
A j is the area of cell j, and subscript i refers to the cell where the excess
precipitation is being calculated. Note that the values of α i have an average value
of one.
To calculate the spatially-distributed flow parameters (flow velocity vi and
dispersion coefficient Di), the watershed unit response, used for the deconvolution
in equation (18), is equalized to the weighted sum of the flow-path responses
( 21 )
in which the flow-path responses Ui(t) depend on the flow parameters. In equation
(21), the left hand side represents the watershed unit response, while the righthand side is the sum of the flow-path responses corrected by a factor that accountsfor the cell area and for its tendency to generate excess precipitation. The values
of the flow parameters are tuned until equation (21) is satisfied.
The estimated excess precipitation and flow parameters can then be extrapolated
to other areas, if the same hydrologic behavior is assumed. This assumption,though, might be questionable when the areas used for calibration and application
are dissimilar. The values can also be used to estimate flow hydrographs at other
locations within the watershed, where hydrologic dissimilarity is less likely tooccur.
4. Case study: Waller Creek in Austin, Texas
Waller Creek is a 14.8 Km2 (3662 acres) watershed located within the urban coreof the City of Austin, Texas. Two flow gauging stations, set up by the US
Geological Survey (USGS), are located at 23rd and 38th Streets and have drainage
areas of 10.7 Km2 (2,643 acres) and 5.7 Km2 (1,416 acres) respectively. Themodel was calibrated with flow records of the station at 23rd Street and applied to
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Waller Creek at 38th Street for comparison with observed flows. The period of
analysis ranged from October 14, 1994, 7:45 p.m. to October 17, 1994, 6:45 p.m..
A time step of 15 minutes was used and a total of 284 time intervals wereconsidered.
The watershed was delineated using a 30 m digital elevation model (DEM), andcomprised approximately 16,500 grid-cells. A map of the drainage-area of the two
flow-gauging stations and of the spatial distribution of the runoff coefficient is presented in Figure 5. It can be noted that just upstream of 38th Street there is a
large low-developed area that generates little runoff; while just upstream of 23rd
Street the area is more developed, yielding much more excess precipitation.
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Figure 5: Waller Creek Watershed: Drainage area of the flow gauging stations
at 23rd and 38th Streets, creeks, and runoff coefficient distribution. Note that
only the gray areas generated runoff for this time period.
Additionally, from the flow records, it was noticed that the flow peaked first at
23rd Street and approximately 30 minutes later at 38th Street, which goes againstintuition because the peak time did not increase with drainage area. After the
direct-runoff/base-flow separation, it was found that, for this time period, 88% of the flow was direct runoff and 12% base flow. Note that, because of the high
impervious cover of the urban areas, direct runoff tends to be much more
important than base flow during storm events.
The methodology presented above was applied in the following steps:
STEP 1: The plot - in semi-logarithmic scale - of the flow record of the 23rd Street
station showed almost instantaneous peak times and long, straight and parallel
recession curves (see Figure 6), which suggests that the watershed responded toall storm events of the period with the same unit response function. This fact
confirms that a linear approximation is satisfactory for this hydrologic system,
because the response does not change from event to event.
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STEP 2: To calculate the flow parameters (flow velocity and dispersion
coefficients), the watershed unit response obtained in STEP 1 was reproduced asthe aggregation of the flow-path responses according to equation (21). In order to
decrease the number of parameters (one flow velocity and one dispersion
coefficient per cell), it was assumed that water flows only as overland flow or stream flow, and a single velocity value was assigned to each type of flow; as
well, a uniform dispersion coefficient was taken for the entire watershed. Finally,
an abstractions coefficient equal to ζ = 0.4 was assumed. From the physical
viewpoint, this implies that all cells with runoff coefficient less than 0.4 generateno surplus. The value of ζ = 0.4 was chosen because most cells have runoff
coefficient much greater or much less than this value, and by selecting thisnumber it was presupposed that only highly developed areas generated runoff,
while lowly developed areas generated no runoff. After these assumptions, the
number of model parameters was reduced to three: (1) overland flow velocity, (2)
stream flow velocity, and (3) dispersion coefficient. By running an optimizationroutine, it was found that the flow parameters that produced the best match
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between the observed watershed response and the one obtained as the aggregation
of the flow-path responses were: overland flow velocity = 0.27 m/s (0.898 fps), stream flow velocity = 0.27 m/s (0.898 fps) and dispersion coefficient = 1,629m2/s (17,535 ft2/s) (see Figure 7). Note that the optimization routine determined
the same value for both velocities, which indicates that in urban areas water flows
as fast over impermeable areas as it does in streams.
STEP 3: The watershed unit response, based on the parameters just calculated,
was then used to estimate the excess precipitation by deconvolution. Note that thecalculated excess precipitation and the observed flow follow the same trend,although the excess precipitation consists of somewhat concentrated pulses, while
the flow exhibits long recession curves following short rising limbs (see Figure
8).
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STEP 4: Predicted flow in Waller Creek at 38th Street was determined using the
excess precipitation calculated in STEP 3, and the model parameters obtained inSTEP 2. Figure 9 presents observed flow (labeled Observed ) and predicted flow
at 38th Street. Three predicted flow series are plotted in this figure: the first one
(labeled No abstractions) assumes an abstractions parameter ζ = 0, i.e., cellcontributions proportional to the runoff coefficient; the second one (labeled
Abstractions = 0.4) assumes an abstractions parameter ζ = 0.4, i.e., cell
contributions proportional to the runoff coefficient minus 0.4; and the third one
(labeled Proportion) is obtained as the flow at 23rd Street multiplied by the ratioof the two drainage areas. It was interesting to notice that, at least in this case, the No abstractions series and the Proportion series were almost identical, the
difference being negligible for practical purposes. With regard to the No
abstractions series, it was observed that: (1) predicted values were consistently
higher than observed values, yielding a predicted flow volume that was 41%
greater than the observed volume; and (2) predicted values followed the trend of the observed values, but shifted approximately 30 minutes (2 time-steps) to the
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left. To a great extent, these problems were solved in the Abstractions = 0.4
series. In this case: (1) the flow volume error went down to 4%, (2) the peak times
matched and no time-shift was observed, and (3) the recession curves werereproduced well.
The fact that the flow at 38th Street is only 39% of the flow at 23rd Street, instead
of 53% as the ratio of the areas, and the fact that the flow peaks first at 23rd Street
and 30 minutes later at 38th can be explained in the following way: (1) 38th Streetis fed by less developed areas than 23rd Street; (2) as an average, the developedareas that fed 38th Street are farther from the station than those that fed 23rd. This
explanation matches the geography of the area, and accounts for the peak shift
and runoff volume error. This type of hydrologic behavior evidences the need of accounting for the spatially variability of the hydrologic system.
5. Conclusions
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It is known that the spatial variability of the terrain strongly affects storm runoff
processes. While representing a watershed by a small number of lumped
parameters (i.e. drainage area, channel slope, time of concentration) has theadvantage of simplifying the hydrologic modeling, it might miss some specific
local processes that affect the overall response of the system and that can not be
considered by lumped models.
Attempting to account for spatial variability of the terrain in storm runoff modeling, researchers have taken either of the following paths: (1) partitioning the
hydrologic system into subsystems and applying lumped models to each of them,
or (2) developing GIS user-interfaces to generate input files for, and display theresults of, other lumped models. In both cases, an improvement with respect to the
traditional fully lumped models has been accomplished, but these kind of
solutions can not be considered spatially distributed. In this article, the use of GISas a modeling tool itself, and not only as a link between the heterogeneous terrain
and an existing non-GIS lumped model, has been presented.
The model developed here is a generalization of the unit hydrograph model. This
generalized version of the unit hydrograph is used to route water in the landscape, provided that the hydrologic system is assumed to be linear. The model also
allows the user to consider time- and space-varying rainfall, thus relaxing some of
the basic assumptions of the unit hydrograph. The assumption of linearity, though,has not been relaxed by using this approach.
GIS appear to be an excellent environment for modeling spatially distributed
hydrologic processes, because they have spatial functions in the vector and raster
domain (some of them specifically developed for hydrologic purposes) and a
database management system, which combined allow one to perform hydrologicmodeling and calculations connected to geographic locations. In fact, GIS is able
to store and handle more spatially distributed terrain data than can be physically
obtained from the field. Thus, when dealing with distributed models, the problemis not necessarily how to develop GIS-based hydrologic models, or how to store
and handle the data, but how to get data in an amount that is consistent with the
model and hardware/software capabilities. At present, one of the limitations of this type of models is the scarcity of spatially distributed data. With regard to GIS
software, Arc/Info-Grid provides the necessary functions and commands to
analyze the digital elevation model (DEM) and obtain hydrologic features such aswatersheds, drainage areas, and flow lengths. It also provides the weighted flow
length function, FLOWLENGTH, that has been used to calculate the first and
second moments of the cell-outlet responses automatically, thus performingsequences of convolution integrals - in an approximated way - within the
Arc/Info-Grid environment.
The importance of accounting for spatial variability of the terrain when modeling
storm runoff was evidenced by the case of Waller Creek in Austin, Texas. In thiswatershed, and according to the data set used here, peak-time did not increase
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with drainage area, and it was observed that the flow peaked first at 23rd Street
and 30 minutes later did so upstream at 38th Street. This situation reflected that
not all the terrain generates the same amount of runoff, and that the relativelocation of impervious areas in urban watersheds should be considered when
attempting to predict flows.
Predicted flow for Waller Creek at 38th Street matched reasonable well observed
records. Total runoff volume, peak times and recession curves were reproducedwell, and although some peak flow values were not matched, the overall tendency
was reproduced. This implies that not only the correct amount of water was
routed, but also at the correct velocity and with the correct spreading tendency.
Although definite conclusions could be drawn only after extensive testing of themethodology, it has become clear that the routing model is an improvement on the
currently used unit hydrograph, and that the handling of spatially distributed data
by Arc/Info proved to be adequate. However, a more elaborated excess
precipitation model might be necessary, especially if the excess precipitationcalculated at one watershed is to be exported to other watersheds.
6. References
1. Browne, F.X., Stormwater Management, in Standard Handbook of
Environmental Engineering , ed. by R.A. Corbitt, McGraw-Hill Inc., New
York, pp. 7.1-7.135, 1990.
2. Chow, V.T, D.R. Maidment and L.W. Mays, Applied Hydrology,
McGraw-Hill Inc., New York, 1988.3. Clark, C.O., Storage and the Unit Hydrograph; Trans. Am. Soc. Civ. Eng.,
ASCE , Vol 110, pp.1419-1488, 1945.4. DeGroot M.H., Probability and Statistics, Addison-Wesley PublishingCompany, Reading, Mass., 1986.
5. Lettenmaier D. P. & E. F. Wood, Hydrologic Forecast, in Handbook of Hydrology, ed. by D.R. Maidment, McGraw-Hill Inc., New York, 26.1-26.30, 1993.
6. Levenspiel O., Chemical Reaction Engineering , Wiley, New York, 1972.
7. Littlewood, I.G. and A.J. Jakeman, Characterization of Quick and SlowStreamflow Components by Unit Hydrographs for Single- and Multi-basin
Studies, in Methods of Hydrologic Basin Comparison, ed. by M.
Robinson, Institute of Hydrology, Report 120, pp. 99-111, 1992.
8. Littlewood, I.G. and A.J. Jakeman, A New Method of Rainfall-Runoff Modelling and its Applications in Catchment Hydrology, in
Environmental Modelling , ed. by P. Zannetti, Computational Mechanics
Publications, Vol II, pp. 143-171, Southampton, UK., 1994.9. Maidment, D.R., Grid-based Computation of Runoff: A Preliminary
Assessment , Hydrologic Engineering Center, US Army Corps of
Engineers, Davis, California, Contract DACW05-92-P-1983, 1992 a.
8/6/2019 Storm Runoff Computation Using Gis
http://slidepdf.com/reader/full/storm-runoff-computation-using-gis 22/23
10. Maidment, D.R., A Grid-Nework Procedure for Hydrologic Modeling ,
Hydrologic Engineering Center, US Army Corps of Engineers, Davis,
California, Contract DACW05-92-P-1983, 1992 b.11. Maidment, D.R., Developing a Spatially Distributed Unit Hydrograph by
Using GIS, in HydroGIS 93, ed. by K. Kovar and H.P. Nachtnebel, Int.
Assn. Sci. Hydrol. Publ. No. 211, pp 181-192, 1993.12. Maidment, D.R., J.F. Olivera, A. Calver, A. Eatherral and W. Fraczek, A
Unit Hydrograph Derived From a Spatially Distributed Velocity Field, Hydrologic Processes, Vol 10, No. 6, pp.831-844, John Wiley & Sons,Ltd., 1996 a.
13. Mesa, O.J. and E.R. Mifflin, On the Relative Role of Hillslope and
Network Geometry in Hydrologic Response, in Scale Problems in
Hydrology, ed. by V. K. Gupta et al., pp.1-17, D. Reidel PublishingCompany, 1986.
14. Miller, W.A. and J.A. Cunge, Simplified Equations of Unsteady Flow, inUnsteady Flow in Open Channels, ed. by K. Mahmood and V. Yevjevich,
Vol. 1, chapter 5, Water Resources Publications, Fort Collins, CO., 1975.15. Naden, P.S., Spatial Variability in Flood Estimation for Large
Catchments: The Exploitation of Channel Network Structure, Journal of
Hydrological Science, 37, 1, 2/1992, pp.53-71, 1992.
16. Nash, J.E. The Form of the Instantaneous Unit Hydrograph, IASH
publication No. 45, Vol. 3-4, pp. 114-121, 1957.
17. Nauman, E.B., Residence Time Distributions in Systems Governed by theDispersion Equation, Chemical Engineering Science Vol. 36 pp.957-966,
1981.
18. Olivera, F., D.R. Maidment and R.J. Charbeneau, Non-Point SourcePollution Analysis with GIS, Proceedings, Spring Meeting, ASCE Texas
Section, pp.275-284, April 26-28, Waco, Texas, 1995.
19. Olivera, F., and D.R. Maidment, Runoff Computation Using SpatiallyDistributed Terrain Parameters, Proceedings, ASCE - North American
Water and Environment Congress '96 (NAWEC '96), Anaheim, California,
June 22-28, 1996 a.20. Olivera, F., Doctoral Dissertation, Department of Civil Engineering,
University of Texas at Austin, 1996 b.
21. Pilgrim, D.H., Travel Times and Nonlinearity of Flood Runoff From
Tracer Measurements on a Small Watershed, Water Resources Research,Vol. 12, No. 3, pp 487-496, June 1976.
22. Pilgrim, D.H., and I. Cordery Flood Runoff, in Handbook of Hydrology,
ed. by D.R. Maidment, McGraw-Hill Inc., New York, pp. 9.1-9.42, 1993.23. Rodriguez-Iturbe, I. and J.B. Valdes, The Geomorphologic Structure of
Hydrologic Response, Water Resources Research, Vol. 15, No. 6, pp.
1409-1420, December, 1979.24. Troch, P.A., J.A. Smith, E.F.Wood and F.P. de Troch, Hydrologic
Controls of Large Floods in a Small Basin, Journal of Hydrology, 156, pp.
285-309, 1994.
8/6/2019 Storm Runoff Computation Using Gis
http://slidepdf.com/reader/full/storm-runoff-computation-using-gis 23/23
25. Vieux, B.E., Geographic Information Systems and Non-Point Source
Water Quality and Quantity Modeling, Hydrological Processes, Vol. 5,
pp. 101-113, 1991.26. Vieux, B.E., DEM Agregation and Smoothing Effects on Surface Runoff
Modeling, Journal of Computing in Civil Engineering , Vol. 7, No. 3, pp.
310-338, July, 1993.27. Vieux, B.E. and S. Needham, Nonpoint-Pollution Model Sensitivity to
Grid-Cell Size, Journal of Water Resources Planning and Management ,
Vol. 119, No. 2, pp. 141-157, March/April, 1993.28. Willmott, Cort J., Clinton M. Rowe and Yale Mintz, Climatology of the
Terrestrial Seasonal Water Cycle , Journal of Climatology, Vol. 5, pp. 589-
606, 1985.
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