PRINT VERSION MODULE
- To get familiarized with a few Statistical
- To grasp difference between empirical
vs. theoretical frequency distribution
- To understand & perform various
tests to ensure fitness of data for flood frequency analysis
- To learn how to plot confidence band
and its significance
- To grasp the meaning and significance
of confidence band; confidence limit; outliers; expected probability
The goal of flood forecast is to issue
advance warning about water level or discharge large enough that
threatens safety of structures and flood plain activities. As observed
in previous module, an advance warning of this nature help authorities
adopt a series of measures to contain adverse impacts of flood.
Unlike several other disasters, approaching
flood can be forecast ahead of its occurrence with advance collection
of hydro-meteorological data, and its transformation into flood
water level or flood hydrograph. Succeeding paragraphs of this module
unfolds a range of commonly employed models in India.
According to the various concepts used
in developing models, the models can be classified into five categories.
on correlation/coaxial diagrams between two variables or even
equations developed using regression/multiple linear regression
techniques which combines independent variable with one or more
than one variable;
||Rainfall run-off model
||i) Lumped, & Distributed
||i) Dynamic Wave routing
||Data driven hydrological
||i) Artificial Neural
||ii) Fuzzy expert system
design for FF
(Adaptive Neuro-Fuzzy Inference System) models
Forecasters in India have developed a
large set of correlation, and coaxial diagrams which display the
pattern of correlation exhibited by two or more variables. Such
charts are relatively less complex, and are quite popular among
its users. Nevertheless, they need periodical updating to account
for constant alteration in catchment characteristics and river regime.
One out of several such diagrams used in India is shown here. When
a number of tributaries affect the water level at the forecasting
station, the variation in water level at base station (base station
is a location upstream of forecast station) on the main river as
well as base stations on the tributariesare considered to prepare
co-axial diagrams. One such diagram developed for formulation of
forecast at Patna (Gandhighat) on river Ganga is shown in Fig.1.
In this diagram, water level fluctuation at Patna takes into account
the variation in water level at Buxar on river Ganga; Darauli on
river Ghaghra; Chopan on river Sone; and Rewaghat on river Gandak.
This concept can also be
extended to account for rainfall in upland area. Fig.2 is for formulating
the forecasts at Khowang on river Brahmaputra considering rise and
fall in water level at Naharkatia site. Additionally, rainfall observation
at Naharkatia is also accounted for to incorporate its likely influence
to the water level at Khowang.
However, these charts carry
limitations in that they provide only peak flow or water level information,
and drop no hint about the shape of likely flood hydrograph at forecast
site. This aside, there is absence of statistical test to measure
the strength of correlation between dependent and independent variables.
Nevertheless, such diagrams are proved quite useful in absence of
fully developed network of hydro-meteorological stations; skilled
personnel to operate sophisticated models; and seamless flow of
data from remote locations to forecast centre.
Unlike previous method, this method defines
relationship mathematically among variables by 'regression/multiple
regression techniques'. The strength of such pattern is easily determined
by correlation coefficient, 'r', and thus subjective judgment of
a person in drawing a best-fit line is eliminated. Mathematical
equations offer much ease in calculation of dependent variable,
and in turn speed up forecast process. Chart at Fig. 3 displays
an equation that estimates water level at downstream location, Mahemdabad,
Gujarat with change in water level at upstream site. A respectable
degree of r2 as 0.9854 is achieved by introducing a time
lag/shift of 4 hrs between two sets of data. The arrival of this
time lag is based on output obtained through cross-correlogram technique.
With no time lag, two sets of data are poorly correlated.
Another approach is to develop
a mathematical model relating forecast station water level with
water level of a tributary joining in-between base and forecasting
station, and of base station. This method is elaborated by an example
comprising three stations. Location of stations may be visualized
as shown in Fig.4. Table 1 lists water levels observed at these
A linear multiple regression
equation with X1 as dependent variable and X2, X3 independent variables
can be expressed as below.
The coefficients a, b and
c are estimated by the method of least square. Three equations noted
down below help solve three unknowns.
This can also be arranged
in matrix form. Below is an arrangement of three matrices; where
[X1], [R] and [A] are 3*1, 3*3, 3*1 matrix
Substituting all summation
terms, we get
Matrix [A] containing all
three unknown coefficients is solved by multiplying [R]-1 matrix
with [X1] matrix.
= [R]-1 [X1]
Solving the matrix in MS
Excel results regression equation as below:
= - 223.017 + 2.71 X2-0.0003 X3
Computed/estimated X1 with
the help of this equation appears in the last column of first table.
Correlation coefficient, r for the defined equation is 0.99
suggesting higher degree of correlation among variables and can
be adopted as forecast model.
Standard Deviation (SD)
and Sest are needed to estimate r2. To determine SD,
reader may consult flood frequency module. Sestis determined
by _/ S(Xi,
obs- Xi,comp)2/(n-2). Finally,
r2 is determined by following equation.
Equation of the type
X1 = a . X2 b1. X3
b2 .. can also be evaluated by converting them into a
linear form by logarithmic transformation. Secondly, in the current
example, two independent variables are water level. Reader can substitute
it by other variables or add more variables to this equation. Solution
of coefficients follows similar steps.
Another relationship derived by multiple
regression technique determines the change in water level at forecast
site bases on the variations recorded at two upstream sites, commonly
known as base stations. While preceding equation relates water levels
of two sites, this equation correlates variation in water levels
at different sites.
A Mathematical Model
using Muskingum Outflow Equation (after Hydrology by H M Raghunath)
According to Muskingum method, outflow
and inflow at two time steps, (t+1)& trelated to by equation
For a few initial time steps
of observed inflow hydrograph, such as I1, I2 ---,
I4, and O1, O2 ---, O4
of outflow hydrograph, a set of equations, with the help of eq.
(I) can be written as below
Now, assuming that discharge
and water level curves at either location a straight line; and denoting
water level at upstream and downstream sites as H & G respectively
(Fig. 5), we can say that
Replacing discharge component
of equations (II) & (III) with this, we get
Or, we can simply write
these equations as
Equation (VI) combines change
in water level at downstream site with changes in water level at
upstream site. At this stage, reader may please note thatsubscripts
4, 3, 2 in above equation denotes difference water level at time
(t+1), t & (t-1) at respective stations.
A set of equations,like this, may be obtained by suitably picking
up data from observed hydrographs to estimate coefficients x1,
x2, & x3by matrix method as elaborated
earlier. While doing so, it is highly recommended to check'r2' value
to ensure that model is worth for the purpose it is defined. This
sort of equation can be developed for rising and falling stages
separately. Further refinement is possible by dividing stages into
two or three ranges with each range represented by unique equation
(please see Fig.5). Additionally, equation (VI) considers only one
station/site in the upstream. In case, water level at downstream
site happens to be affected by more than one site, a modified Muskingum
equation can be written as
Where, H, H', H''represent
water level at three upstream sites. Number of equations formed
in this manner need to be solved for coefficients by matrix method.
The steps involved in the process with same set of data used in
previous example are illustrated below:
With two independent variables (water
level at two upstream sites) and one dependent variable (water level
at forecast station), equation (VI) takes following form.
With known water levels at respective
sites (Fig. 4 & Table 1), a set of values each representing
change in water level at various time interval is tabulated next
in matrix form
Values of coefficients are
determined by solving the matrix by an equation given below. Here,
equations are more than number of unknown. Therefore, H is a rectangular
matrix.In MS excel, standard deviation, matrix multiplication, inverse
and transpose commands are defined by STDEV, MMULT, MINVERSE, and
TRANSPOSE respectively. Cell (s), where user intends to get result
needs to be selected before executing the function.
With coefficients indicted
in above table, a mathematical equation takes following form for
use in flood forecast.
While seeking to define
an equation by this approach, caution is needed toward the inherent
assumption associated with the method, i.e. a plot between water
level and discharge should closely follow a linear trend in that
range for which user/forecaster intends to relate parameters. A
comparison between observed vs. computed water level at X1 and relevant
statistical parameters which measure the strength of model are presented
in Table 2.
Example below is an excerpt from Manual
on Flood Forecasting (p 239-244), published by CWC in 1989, wherein
3-hr duration unit hydrograph (owing to 1mm effective rainfall over
the basin/catchment)for a basin area of 8570 sqkm is given along
with mean rainfall events over the basin. The base flow at the beginning
of storm is 300 cumec. As per the report received at 1900 hrs on
13th September, the average rainfall observed at different hours
was as follows:
Additional information available is a
diagram, Fig. 6(based on historical data) correlating total rainfall
and runoff in varying base flow conditions (shown right). Referring
to this diagram, runoff against a base flow of 300 cumec and 54.3
mm rainfall is 14.5mm implying a loss of 39.8mm during rainfall
period. Form this, it is gathered that there is a loss rate of 4.43
mm per hour.
This point beyond, a model
is developed in HEC-HMS by keying in information gathered as above(Fig.7).
Basin in the model is represented by an element 'subbasin1'. This
element hosts basin information; loss mechanism;transformation process
and base flow contribution besides observed hydrograph at terminus
point, if available (Fig.8).Convolution of UH can be attempted in
MS excel also. HEC-HMS software can be downloaded by visiting site
, and is available for free.
Once, model is ready with
a network of elements and all inputs; a 'run' is performed to generate
resulting flood hydrograph which closely resembles the ordinates
listed in the Manual. A hypothetical elevation vs. discharge rating
is also fed in the model to produce water level corresponding to
variation in discharge at terminal location (Fig. 9).
Table 3 lists a set of output
information that is quite handy for issuance of forecast ahead of
its actual occurrence. Even though the ordinate's interval is every
three hours in the current listing, user can elect appropriate interval
to extract information of his desire.
Quasi Distributed Model
Following illustration demonstrates,
with the help of Fig. 10, application of UH in conjunction with
MUSKNIGUM routing method to estimate magnitude of flood and time
of its occurrence. The set of data inputted here remains the same
as for previous case. According to procedures illustrated in earlier
example, UH considered for analysis represents an area of 8570 sqkm,
and its convolution is based on average areal rainfall over the
region. This concept of convolution of UH runs a risk of overestimating
the flood because of departure from one of its fundamental assumption
that rainfall is uniformly distributed over the region for a specified
time. This may not be true for an area as large as 8570 sqkm. Additionally,
this approach ignores likely impact of channel storage on flood
attenuation. In order to adhere to this basic assumption, UH concept
is usually applicable for an area less than or upto 5000 sqkm. Example
quoted in the manual (p 244-253) overcomes this violation by sub-dividing
the entire basin into three sub-basins A, B & C of area 2040
sqkm, 3470 sqkm and 3060 sqkm respectively, and assuming contribution
of rain gauges a, b & c to respective sub-basins only. Accordingly,
ordinates of UH has also been altered by a ratio between area of
the respective part to the total area. Routing of flow along the
reach is done by MUSKINGHUM method. Parameters K, X have been taken
from the example and its stability is ensured by adhering to constraint,
such as 2KX should be less than T. Additionally, equal contribution
of 100 cumec as base flow from three parts is assumed. A basin delineated
into three parts with two routing reaches is presented below. As
discussed earlier, rainfall recorded at rain gauge 'c' contributes
to sub-basin 'C', and therefore, its flood appears at basin outlet
having propagated through reach -1 and reach -2. Similarly, sub-basin
'B' receives rainfall observed at rain gauge 'b', and resulting
runoff travels through reach- 2 only. Sub-basin 'A' responds to
rainfall at 'a', and its effect is visible at outlet (no routing
is involved in this case).
In agreement with discussion
in preceding paragraph, UH for each basin& Muskingum parameters
for two reaches are given in Tables 4 & 5.
Rainfall excess at each
station is at Table 6.
A model (Fig. 11) duplicating
three sub-basins and its reaches is created in HEC-HMS followed
by data entry. HEC-HMS generated runoff at Outlet (Junction-2) appears
at Fig. 12. Also shown there is change in water level according
to fluctuation in discharge at this point of basin. Option is also
available to mark warning level to distinguish critical period when
there will be heightened risk because of swelling river.
Table7 lists ordinates of
flood hydrograph against time and compares with the result as presented
in Manual. Options are also available in the HEC-HMS to observe
resulting hydrographs for each and every element shown in model.
- Regardless of duration of rainfall
and its distribution over time, UH of known duration, say t-hr
is to be fed in the HEC-HMS keeping its ordinates spaced at t-hr
apart. For example, if UH of 1mm rainfall derived is of 3hr duration,
ordinates of UH must be entered at 3hr interval. Software automatically
converts this UH to duration according to rainfall distribution
over catchment. This process rid us of steps needed for conversion
of a UH from one duration to another.
- A relationship between stage/water
level and corresponding discharge at forecast station is best
represented by a rating curve or a power equation of the type
Q = c*(G-G0)^b.
Caution is required here to feed latest rating curve of the site
in the software; which is best estimate of the prevailing river
regime. Secondly, fitting a rating curve does need some technical
skill. HYMOS software performs this task with ease.
Forecast estimated by applying hydrological
models such as one presented in preceding paragraphs tends to vary
widely from real values, where assumptions in unit hydrograph or
routing models are violated by prevailing hydro-meteorological conditions
over catchment. For example, rainfall is non-uniform over the basin;
it is not stationary and moving across the basin; rainfall is concentrated
in one pocket and leaving holes elsewhere. Apart from this, soil
type and land-use pattern also vary over the catchment/basin that
govern the rising and falling limb of resulting hydrograph. In lumped
model, these characteristics are represented by a single SCS CN
(curve number) applicable for entire area under study. Scenario,where
spatial and temporal variations are dominating factors, demands
application of distributed model to accurately capture the basin
Presented here is a distributed model
developed and analyzed using Water Modeling System (WMS) and HEC-HMS.
WMS software developers, on request, provide one time license key
for 14 days for software evaluation purpose only. For its continued
use, one needs to buy it. In this model, WMS software first delineates
a watershed for an outlet point selected by the user, and thereafter
creates grid (Fig. 13 & 14).
For each grid, it determines
CN values according to its soil type and land-use cover. Once land
component is over, software prepares a gridded precipitation database
based on rainfall input provided by the user. A set of these gridded
information are subsequently exported to HEC-HMS for simulation
run. HEC-HMS calculates the rainfall excess and route it to outlet
by MODCLARK method (Fig. 15). A couple of screenshots display model
set-up and results obtained at the end. WMS software can be downloaded
by visiting site http://www.aquaveo.com/downloads.
Lumped, & Distributed Routing
(a) Storage equation
The Muskingum method of stream flow routing
is most frequently used because of its simplicity, as it works with
known inflow hydrograph and some fitted parameters without seeking
additional information. However, in order to get high degree of
accuracy, this method should be for gradually varied flow and not
in cases where reach is often affected by backwater or unsteady
flow condition. The two fundamental equations for stream flow routing
by Muskingum method are:
S = Prism storage + Wedge storage
= K.Q0 + K.X.(Q1-Q0)
||A constant in time unit
denotes the time of travel of flood wave through the reach.
So, if flood wave velocity or celerity is C, C equals L/K, where
L is reach length.
||A dimensionless factor
which defines the relative weights given to inflow and outflow
in determining storage. (Mostly varies between 0.1 & 0.3
and ranges between 0 & 0.5)
|Q1 or I =
|Q0 orO =
(b) Continuity Equation
The coefficients are connected by the
+ C1 + C2 = 1
Equation (I) with known coefficients,
Co, C1& C2 computes outflow
with inflow and outflow at time t & t+1. However, accurate estimation/selection
of K, X, Dt and subdivision of river
reach is central to successfulMuskingum routing. That is why these
parameters are also termed as 'tuning knobs' of the model
and merit due attention at the time of their estimation.
Determination of K
Even if the feasible range for the parameter
X is (0, 0.5), there are other constraints apply to selection of
X. With Muskingum routing, the distance step, Dx,
is defined indirectly by the number of steps into which a reach
is divided for routing.
We will dig into example data set presented
below (Table 8) to estimate these values. Later with HEC-HMS, optimized
value for these parameters will be extracted. As with other models,
Dx/Dt is selected
in a manner to approximate c, where c = average wave speed (also
celerity) over a distance increment Dx.
If total reach length is L, and travel
time is K, Wave speed, C is
= L/K = L/n.Dt
If there are n sub-reaches, and each
sub-reach requires Dt time for discharge
to flow past, K = n.Dt
So, the number of steps,
For current example, distance between
two stations is around 112 km;an estimated value of K is assessed
about 34 hour with table 1(time interval between inflow peak and
outflow peak- a rough estimation for K to begin with). Inflow flood
hydrograph ordinates are at 2 hours interval, the routing reach
should be divided in 17 steps, i.e. 34/2 to get the outflow hydrograph
112 km below. This leads to less attenuation as compared to routing
carried out in a single step for the entire reach.
Secondly, the parameters K, X and computational
time step ?t must also be selected in a manner so as to ensure that
the Muskingum model/its coefficients must be rational. This implies
that the parenthetical terms of the coefficients C1, C2 and C3 must
be non- negative. To maintain this, values of K and X must be so
chosen so that the combination falls within the shaded region shown
below. In other words, K, X &Dt must
satisfy a condition given by
Parameters chosen in violation of this
condition produce an un-stable solution and HEC-HMS will prompt
the user in its message box accordingly.Against this backdrop and
selected K and Dt, estimated X is 0.03
Having defined Muskingum parameters,
application of HEC-HMS in routing a reach by Muskingum method is
demonstrated. A screenshot (Fig.16) displays the river network and
its feeding boundary developed using Geo-HMS extension installed
on ArcView software, and a model set up in the HEC-HMS.
Routing parameters for reach
entered in HEC-HMS is exactly the same as deliberated above (Fig.17).
After first 'Run', screenshot
(Fig. 18) plots the simulated result against observed discharge
at downstream end along with variation in water level (water level
vs. outflow relation used here is made-up one, and is used for demonstration
purpose only). The water level profile can be picked up for forecast
purpose. Also seen is inflow hydrograph at upstream end. Reader
may notice the lower right box (also message box) of Fig. 16 reporting
no instability with elected Muskingum parameters. Fig. 19 is summary
result for this 'Run'.
At this stage, HEC-HMS offers
another useful tool to optimize Muskingum parameters having finished
first 'Run'. Screenshot at Fig.20 displays initial and optimized
values of Muskingum parameters along with simulated and observed
outflow, which is a slight improvement upon first 'Run'. Reader
may adopt this new set of parameters to finalize their model for
forecasting trial. In doing so, it must be noticed that river regime
is not a fixed entity over time and tends to exhibitcontinual changes
in its course, geometry. That is why it had better develop a model
based on flood events occurred recently, and discard earlier model
to eliminate possibility of largevariation in forecast value.
Muskingum method operates
with steady or gradually varied flow, and does not reveal any information
in between the base and forecast station. That is why it is also
termed as 'Lumped model'. If the forecaster intends to gather water
profile and its propagation along river reach, distributed models,
such as Muskingum-Cunge, Kinematic Wave could be alternatives. This
module skips discussion about these methods for the present. Next
version of this module will also discuss these methods at length.
Nevertheless, keen readers may refer to 'Technical Reference Manual'
of HEC-HMS for more information about it.
Dynamic Wave Routing Technique
To demonstrate the strength
of this approach through an example, the succeeding part of this
module illustrates the application of HEC-RAS software in routing
an unsteady flow hydraulically. HEC-RAS software is a one-dimensional
flow hydraulic model designed to aid hydraulic engineers in channel
flow analysis and flood-plain determination. The results of the
model can be applied in floodplain management studies including
flood forecasting. Like HEC-HMS, this software is also available
for free, and can be downloaded from web-page http://www.hec.usace.army.mil/software/hec-ras/hecras-download.html
By the end of this part
of module, you will be able to:
Import and edit cross-sectional
Perform a unsteadyflow
simulation for flood forecasting
View and analyze HEC-RAS
output and use GIS RAS mapper for flood delineation.
In this part, a real case
study of unsteady flood modelling through HEC-RAS has been dealt
with for a reach (Karad - Kurundwad, chainage 140 km to 260 km)
in Krishna river. Lateral inflows to the main river on the corresponding
dates have been considered at Sangam, where tributary Panchganga
contributes to the Krishna flow. The technique provides a reliableinitialization
of stage/discharge profile for the flood forecast. The examinations
includingthe initialization of stage profile, conservation of mass,
iteration convergence, Manning's N,effectiveness evaluation, and
convergence with optimum theta (implicit weighing factor) values
are conductedto verify the forecast capability.The forecasting results
show that the stage recalculated by updatingthe Manning N,
in current time has a good agreementwith the observed stage.
Hydraulic routing employs
the full dynamic wave (St. Venant) equations. These are the continuity
equation and the momentum equation, which take the place of the
storage-discharge relationship used in hydrologic routing. The equations
describe flood wave propagation with respect to distance and time.
Henderson (1966) rewrites the momentum equation as follows:
Sf = friction slope (frictional forces),
So = channel bed slope (gravity forces),
2ndterm = pressure differential;
3rdterm = convective acceleration, in m/sec2;
Last term = local acceleration, in m/sec2
The full dynamic wave equations
are considered to be the most accurate solution to unsteady,
one dimensional flow, but are based on the following assumptions
used to derive the equations (Henderson, 1966):
Velocity is constant
and the water surface is horizontal across any channel section.
Flows are gradually
varied with hydrostatic pressure prevailing such that vertical
acceleration can be neglected.
No lateral circulation
are considered fixed and therefore not susceptible to erosion
Water density is uniform
and flow resistance can be described by empirical formulae (Manning,
Chezy) Solution to the dynamic wave equations can be divided
into two categories: approximations of the full dynamic wave
equations, and the complete solution.
Dynamic Wave Routing solution
Complete hydraulic models
solve the full Saint Venant equations simultaneously for unsteady
flow along the length of a channel. They provide the most accurate
solutions available for calculating an outflow hydrograph while
considering the effects of channel storage and wave shape (Bedient
and Huber, 1988). The models are categorized by their numerical
solution schemes which include characteristic, finite difference,
and finite element methods.
The finite difference method describes each point on a finite grid
by the two partial differential equations and solves them using
either an explicit or implicit numerical solution technique. Explicit
methods solve the equations point by point in space and time along
one time line until all the unknowns are evaluated then advance
to the next time line (Fread, 1985). Implicit methods simultaneously
solve the set of equations for all points along a time line and
then proceed to the next time line (Liggett and Cunge, 1975). The
implicit method has fewer stability problems and can use larger
time steps than the explicit method. Finite element methods can
be used to solve the Saint Venant equations (Cooley and Mom, 1976).
The method is commonly applied to two-dimensional models.
The assumptions given above
for all hydraulic models (one-dimensional flow, fixed channel, constant
density, and resistance described by empirical coefficients) apply
to dynamic routing. It is also assumed that the cross sections used
in the model fully describe the river's geometry, storage, and flow
The major drawback to fully
dynamic routing models is that they are time-consuming and data
intensive, and the numerical solutions often fail to converge when
rapid changes (in time or space) are being modeled. This can be
addressed by adjusting the time and distance steps used in the model;
sometimes, however, memory or computational time limits the number
of time and distance steps that may be used. Additionally, fully
dynamic one-dimensional routing models do not describe situations
(such as lakes and major confluences) where lateral velocities and
forces are important.
Start the HEC-RAS 4.1.0
program. The following window should subsequently show up (Fig.
Henceforth, this window
will be referred to as the main project window. A Project
in RAS refers to all of the data sets associated with a particular
river system. To define a new project, select File/New Project
to bring up the main project window (Fig. 22).
You first need to select
your working directory, and then a title (say Karad_FF), and file
name (Karad_FF.prj). All project filenames for HEC-RAS are assigned
the extension ".prj". Click on the OK button and
a window will open confirming the information you just entered.
Again click the OK button. The project line in your main
project window should now be filled in. The Project Description
line at the bottom of the main project window allows you to type
a detailed name for the actual short Project name. If desired,
you may click on the ellipsis to the right of the Description
bar, and additional space for you to type a lengthy Description
will appear. Any time you see an ellipsis in a window in HEC-RAS,
it means you may access additional space for writing descriptive
For each HEC-RAS project,
there are three required components-
The Geometry data, for instance, consists of a description
of the size, shape, and connectivity of stream cross-sections.
Flow data contains discharge rates.
Plan data contains information pertinent to the run specifications
of the model, including a description of the flow regime.
Each of these components
is explored below individually. The schematic picture in Fig. 23
depicts the Krishna -Koyna river confluence at Karad and we will
be analyzing a reach Karad - Kurundwad.
and Editing Geometric Data
The first of the components,
we will consider now, is the channel geometry. To analyze stream
flow, HEC-RAS represents a stream channel and floodplain as a series
of cross-sections along the channel. To create our geometric model,
we can do it by three ways.
i) From HMS DSS files
ii) From Geo-RAS (derived from DEM/TIN)
iii) By manual entry of Geometric data
This HEC-RAS geometry file
contains physical parameters describing cross-sections. To view
the data, select Edit/Geometric Data from the project window. The
cross sections of Krishna are obtained from Upper Krishna Division
topographic survey record.
The resulting view (Fig.
24)shows a schematic of Krishna& its tributary Koynariver with
the area of study. This is the main geometric data editing window.
The red tick marks denote individual cross-sections. Choices under
the View menu provide for zoom and pan tools. The six buttons
on the left side of the screen are used to input and edit geometric
data. The and
used to create the reach schematic. A reach is simply a subsection
of a river, and a junction occurs at the confluence of two rivers.
Since our reach schematic is already defined, we have no need to
use these buttons. The
, , and
buttons are used to input and edit geometric descriptions for cross-sections,
and hydraulic structures such as bridges, culverts, and weirs. The
allows you to associate an image file (photograph) with a particular
cross-section. Click on the button
to open the cross-section data window:
The data used to describe
the cross-sections include the river station/XS number, lateral
and elevation coordinates for each terrain point (station &
elevation columns), Manning's roughness coefficients (Table
9), reach lengths between adjacent cross-sections, left and right
bank station, and channel contraction and expansion coefficients
(here 0.1 & 0.3 have been taken for smooth transitions) (refer
to page 87 of Technical Reference Manual of HEC-RAS). These data
are obtained by field surveys (Fig. 25).
buttons can be used to toggle between different cross-sections.
To edit data, simply double-click on the field of interest. You
may notice that this action caused all of the data fields to turn
red and it enabled the "Apply Data" button. Whenever you
see input data colored red in
HEC-RAS, it means that you are in edit mode. There are two ways
to leave the edit mode:
Click the "Apply
Data" button. The data fields will turn black,
indicating you're out of edit mode, and the data changes are
Editing. You'll leave the edit mode without changing
any of the data.
To actually see what
the Kurundwad X-section (Fig. 26)looks like; select
the Plot/Plot Cross-Section menu item on this window.
The cross-section points
appear black and bank stations are denoted with red. Manning roughness
coefficients appear across the top of the plot. Again, the
buttons can be used to maneuver between different cross-sections.
Any solid black areas occurring in a cross-section represent blocked
obstructions. These are areas in the cross-section through which
no flow can occur. Some cross-sections contain green arrows
and gray areas. This symbolism is indicative of the presence
of a bridge or culvert. Input data and plots specifically associated
with bridges and culverts can be accessed from the main geometric
data editor window by clicking on the
button. Take a little time to familiarize
yourself with the geometric data by flipping through some different
cross-sections and bridges/culverts. When you are finished, return
to the geometric editor window and select File/Save Geometric
Data. Return to the main project window using File/Exit Geometry
and Editing Flow Data
Enter the flow editor using
Edit/Unsteady Flow Data from the main project window. Instead of
importing an existing HEC-RAS flow file, you can use stream flow
output from an HEC-HMS model run.
The coordinates of the cursor
(time, flow rate) are displayed at the bottom right corner of the
plot. Gridlines can be shown by invoking the Options/Grid menu item.
The direct step method uses
a known water surface elevation (and several hydraulic parameters)
to calculate the water surface elevation at an adjacent cross-section.
For a sub-critical flow regime, computations begin at the d/s end.
The present data set corresponds to1st& 2nd July, 2006 flood.
The Flood Hydrograph at Karad (July 1 & 2, 2006) and Rating
Curve at Kurundwad are entered as per the actual available dataset.
Click on the Initial conditions and enter the value of initial flow
at Karad. The initial flow of 888.04 m3/s at Karad on the day 1
at 0100 hrs is entered. Click on OK. The flood hydrograph and rating
curve plots along with data view can be seen in Fig 28&29.
All of the required flow
parameters have now been entered into the model. From the file menu,
select Save unsteady Flow Data and save the flow data under the
name "Karad flows."
Click on the button from
the unsteady flow data window. HEC-RAS allows the user to set the
boundary conditions and Initial conditions at the
points (u/s, d/s or internal locations) or as shown in Fig. 27.
The boundary conditions and initial flow conditions are filled in
as per the actual data.
Similarly, enter the values
for Kurundwad after clicking on the rating curve button and see
the curve by pressing the Plot data option.
If you want the rating curve
at known site, then you can enter it by clicking on Options>Observed
(measured) data> rating curves (gages) (Fig. 30).
To leave the flow data editor
and return to the HEC-RAS project window, choose File/Exit Flow
With the geometry and flow
files established, select Run/ Unsteady Flow Analysis from
the project window. But before running the model, one final step
is required: definition of a plan. The plan specifies the geometry
and flow files to be used in the simulation. To define a plan, select
File/New Plan andYou'll be subsequently asked to provide
a plan title and a 12 character identifier as depicted in the Fig.
To execute the model, ensure
that the flow model parameters set properly, and click compute
However, the output view
(Fig. 33) also shows the elevation of the total energy head line
(shown in the legend as "EG 02Jul2010 0700"), the water
surface ("WS 02Jul2010 0700"). As with the cross-section
geometry editor, you can use the
button to scroll to other cross-sections. For a profile of the entire
reach, select View/Water Surface Profiles from the project
Using the Options/Zoom
In menu option, you can focus on a particular stretch of reach
to see how the water surface relates to structures in the channel
such as bridges. Other available options for graphical display of
output data include plots of velocity distribution (View/Cross-Sections/Options/Velocity
Distribution) and pseudo 3D plots (View/X-Y-Z Perspective
Plots). Spend a little time playing around with some of the
For hydraulic design, it
is often useful to know the calculated values of various hydraulic
parameters. HEC-RAS offers numerous options for tabular output data
display. From project window, choose View/ Detailed Output Table.
It is to note that the simulated value is 1674.38
m3/s against the actual observed value of 1674.34
m3/s at Kurundwad (Fig. 34) (X-section_1)(0800 hrs on
2nd July, 2006, i.e, end of simulation period). The simulated water
level is 529.37m against observed value of 529.145
Additional tabular output
data can be accessed from the invoking View/Profile Output Table
(Fig.35) from the main project window. Numerous formats and data
types can be viewed by selecting different tables from the Std.
The resulting table includes
a number of hydraulic parameters, including water surface elevation,
head losses, and cross-sectional area. At the bottom of the window,
error and notes (if any) resulting from the steady flow computations
are shown. As you scroll through the cross-sections, take a look
at some of the error messages. For this model, some X-sections have
been added as the warning it showed to interpolate cross section.
of the model
The vital factors which
affect the model stability and numerical accuracy are:
Cross Section Spacing
Computation time step
Theta weighting factor
Cross sections should be
placed at representative locations to describe the changes in geometry.
Additional cross sections should be added at locations where changes
occur in discharge, slope, velocity, and roughness. Cross sections
must also be added at levees, bridges, culverts, and other structures.
Bed slope plays an important role in cross section spacing. Steeper
slopes require more cross sections. Streams flowing at high velocities
may require cross sections on the order of 30m or less. Larger uniform
rivers with flat slopes may only require cross sections on the order
of 300m or more.
Theta is a weighting applied
to the finite difference approximations when solving the unsteady
flow equations. Theoretically Theta can vary from 0.5 to 1.0. However
a practical limit is from 0.6 to 1.0. Theta of 1.0 provides the
most stability. Theta of 0.6 provides the most accuracy. The default
in RAS is 1.0. Once the model is developed, reduce theta towards
0.6, as long as the model stays stable. The stability problems are
Too large time step.
Not enough X-sections
Model goes to critical
depth - RAS is limited to subcritical flow for unsteady flow
simulations. Bad d/s boundary condition (i.e. rating curve or
slope for normal depth). Bad X- section properties, commonly
caused by: levee options, ineffective flow areas, Manning's
n values, etc.
If this happens, note the
simulation time when the program either blew up or first started
to oscillate. Turn on the "Detailed Output for Debugging"
option and re-run the program. View the text file that contains
the detailed log output of the computations. Locate the simulation
output at the simulation time when the solution first started to
go bad. Find the river station locations that did not meet the solution
tolerances. Then check the data in this general area.
of the Model
The model can be calibrated
by changing the hydraulic parameters. Open Unsteady flowanalysis>Options>Computation
options and tolerances. The theta (implicit
weighing factor) value as shown in figure can be changed from 0.6
to 1 and repeated simulations can be run with changed iterations
and Changed Manning's N to validate the actual results
(Fig. 36). Some Manning's N values have been cited
from the literature (Fig. 37), but the actual values are to be calibrated
to have the model match with the real conditions. (Page 81 of Reference
Manual). You can also set the initial conditions during simulation
and write detailed log output for debugging by clicking options>
Output Options as shown in Figure 19. You can check
data before execution by clicking Option>Check data before
The present simulation yielded
very fitting results as regards discharge, but the water level difference
remained at 22cms (529.37m simulated against 529.15m obs). The simulated
matching results may be because of the single reach simulation,
recent observed X-sections and no other streams joining the reach
except at Sangam. Further, this might have accrued due to the exact
observed data input at the X-section points.
Data driven hydrologic models
Sometimes,it is argued that deterministic,
reductionist models are inappropriate for real-time forecasting
because of the inherent uncertainty that characterizes river catchment
dynamics and the problems of model overparameterization. The advantages
of alternative, efficiently parameterized data-based mechanistic
models, identified and estimated using statistical methods, are
Neuromorphic modelling techniques are
now well established methods for describing physical processes occurring
in the aquatic environment. The development in information technology
over the last decade has presented opportunities of extended computational
ability together with improved data manipulation, storage and retrieval.
As a result, the Neuromorphic models are now being used more extensively
in the management, design and operation of water based assets. The
reason behind this is that in many areas of applications pertaining
to the complex flow systems, the demands on computing time are of
such a magnitude, which is far from acceptable. An elementary brief
part of ANN has been added here in the distance learning course
for easy insight, though there are advanced architectures like recurrent
neural network (RNN), radial basis function (RBF),self-organizing
map (SOM) and othersused in flood forecasting
Artificial Neural Networks
An artificial neural network is nothing
but a collection of interconnected processing elements (PEs). The
connection strengths, also called the network weights, can be adapted
such that the network's output matches a desired response.
Fig. 38depicts a typical
multilayer perceptron, which has been used in this research, which
resembles a black box model, where a set of a data like x1, x2,
xn are fed directly to the network through the input layer,
and subsequently produces expected result y in the output layer.
The output is determined by the architecture of the network.
In multi-layered perceptron, hidden layer
means a third layer of processing elements or units in between the
input and output layers that increases computational power. In principle,
the hidden layer can be more than one layer. In practice the number
of neurons in this layer is evaluated by trial and error. Hornik
et al. (1989) proved that a single hidden layer containing a sufficient
number of neurons can be used to approximate any measurable functional
relationship between the input data and the output variable to any
desired accuracy. In addition, De Villars and Barnard (1993) showed
that an ANN comprising of two hidden layers tends to be less accurate
than its single hidden layer counterpart. In this, a single hidden
layer ANN has been used.
Each input xi (i =1,
,n) is attenuated
by a factor wij, more commonly called a weight of the network, which
is associated with the connection linking input xi to hidden neuron
j (j = 1,
.,k), where, k is the number of neurons in the single
hidden layer. The weighted sum of the incoming signals entering
a neuron is fed via an activation function, which is non-linear,
producing a value that in turn, act as an input signal sent to the
output layer. This is repeated for the output weights. The following
expression gives the output value of the network.
Where, the sigmoidal activation function
Y is given by
This function given at eq.
2 is a continuous function that varies gradually between asymptotic
values 0 and 1 or -1 and +1. Where, a is
the slope parameter, which adjusts the abruptness of the function
as it changes between the two asymptotic values. Sigmoid functions
are differentiable, which is an important feature of neural network
To obtain the best approximations, it
is needed to determine the optimum set of weights wij
and aj that will yield the least mean square value of
the desired response. Thus the following performance criterion needs
to be satisfied.
The configuration chosen
for the ANN models are shown in Fig. 39, where the bias inputs have
the effect of lowering or increasing the net result of the activation
function. The activation used is the sigmoidal function, which has
the purpose of limiting the permissible amplitude range of the output
values to some finite value.
of the data
It is mentioned that the sigmoidal function
can take the values ranging in the (0, 1) domain, a normalisation
of the values of the input variables are done. The standard procedure
in neural network theory gives the normalisation equation used for
Where: X - actual value
of a numeric column, Xmin - minimum actual value of the
column, Xmax - maximum actual value of the column, SRmin
- lower scaling range limit , SRmax - upper scaling range
limit and SF - scaling factor, Xp-pre-processed value.
Numerous goodness of fit statistical
criteria are proposed in the literature for evaluating hydrological
modelling results. Here, only two of these are considered in this
study, namely RMSE, and Nash - Sutcliffe coefficient (1970). RMSE
can take any positive value but the closer it is to zero, the better
the model performs. When the Nash value is between 0 and 1, the
forecast model does better than simply forecasting using yo.
The closer the Nash index is to one, the better. These performance
criteria are used as basis of comparison to select the best model.
is defined by
Where, Yo = Observed
daily gauge of the catchment on day i;
Yp = Predicted daily gauge of the catchment on day i;
As could be seen from Fig 40, the modelproved
their capability in predicting the data, especially the stage data,
which shows a high correlation of the observed and predicted data.
ii) Fuzzy expert system design for flood forecasting
Linguistic terms are chosen to describe
the input variable stage and the results. Further refinement of
the models could not be achieved by adding extra membership functions.
Gaussian membership functions (the function is generally suited
for Indian rivers) can be used. Applying a similar method of data
classification, membership functions are determined for the output
Some years of average hourlystage data
and expert knowledge are used to create a rule base for the fuzzy
logic model. Rules are defined for both the high and low extreme
conditions, with regard to actual occurrences, because of the physical
nature of the relationships. Depending on number of membership functions
for each input variable; the minimum rule base is created. For each
data point, all rules are evaluated.
The platform selected for the fuzzy logic
expert system is MATLAB and MATLAB'S Fuzzy Logic Toolbox. The variables
are combined into rules using the concept of 'AND'. The fuzzy operator
'minimum' is applied as the 'AND' function to combine the variables.
No weightings are applied, which means no rule is emphasized as
more important in respect to estimating the discharge. Implication
is performed with the minimum function, and aggregation is performed
with the maximum function. The centre of gravity method is applied
as a means of defuzzification of the output membership functions
to determine a crisp set. Based on this structure a baseline model
fuzzy logic expert system for stage-discharge relationship is constructed
for the G&D stations. Alternate functions for the expert system
are investigated through sensitivity analysis.
A sensitivity analysis is performed for
the fuzzy logic operator AND, and for methods of implication, aggregation
and defuzzification. The results of changing a single operator or
method while the rest of the model is held constant are compared
with the results from the baseline model. The results are evaluated
on the basis of correct linguistic matches. Based on this sensitivity
analysis, the AND operator 'minimum' and the implication method
'minimum' are found to perform better than the product method. The
fuzzy logic and ANN models are evaluated based on their ability
to predict the discharge.
ANFIS (Adaptive Neuro-Fuzzy Inference System) models
The hybrid system of learning has been
attempted at combining ANN and fuzzy logic for developing the stage-discharge
relationship to achieve a faster rate of convergence by controlling
the learning rate parameter with fuzzy rules. The objective is to
get a minimizer, which has a low computing cost and a large convergence
domain. This learning ability is achieved by presenting a training
set of different examples to the network and using learning algorithm,
which changes the weights in such a way that the network reproduces
a correct output with the correct input values. The main dissimilarity
between fuzzy logic system (FLS) and neural network is that FLS
uses heuristic knowledge to form rules and tunes these rules using
sample data, whereas NN forms "rules" based entirely on
data. Sugeno type ANFIS can be used. Gaussian membership functions
can be used with rule bases, because of their low computational
requirements and as it has the important properties of smooth mapping,
universal approximation, normal distributions can be approximated
well by this type of functions.Learning rate control by fuzzy logic
has been depicted at fig 41. ( FLC - fuzzy logic controller, MLP
- multilayer perceptron
and comparison of results
The ANN, fuzzy and neuro-fuzzy
models thus developed is validated and compared with the observed
data points and the statistical measures of goodness-of-fit of the
neuromorphic models. Numerous goodness of fit statistical criteria
are proposed in the literature for evaluating hydrological modelling
results. Goodness of fit can be tested from standard statistics
literature as has been shown in the aforesaid ANN paragraph.Fig
42 shows the validation and comparison of models with observed data.
As could be seen in preceding paragraphs,
advance warning about the incoming flood peak and its probable time
of occurrence can be achieved by several models. However, selection
of a particular method or model, and its accuracy for a given site
is largely governed by threefactors - data availability; forecaster's
knowledge of, and his experience with the basin; and forecaster's
familiarity with software to be used in the forecast process.
The illustrated texts mentioned in this
module are just the trail of a beginning and more of the subject
and in-depth precision knowledge base, the readers are suggested
to refer to advanced literature layouts.
- Flood forecasting
Manual, (1989), Central Water Commission, New Delhi
- Raghunath, H M., (2006),
Book on Hydrology principles analysis and design, New Age International
- Technical references
Manual, (2004), HEC-HMS, USACE
- Technical references
Manual, (2004), HEC-RAS, USACE
- Wheater, H. S., Jakeman,
A. J. &Beven. K. J. (1993) Progress and directions in rainfall-run-of
modelling. In Modelling change in environmental systems (ed. A.
J. Jakeman, M. B. Beck &M. J. McAleer), pp. 101-132, Wiley.
LITERATURES OM NEURAL NETWORK AND FUZZY LOGIC CAN BE FOUND AT THE FOLLOWOING
- Dastorani, M.T. and Wright., N.G., 2002,
Artificial neural network based real-time river flow prediction, Hydroinformatics,
Proc. of 5th Int. Conf., Cardiff, UK.
- Haykin, Simon, (1999) Neural Networks:
A Comprehensive Foundation, Prentice Hall.
- Karunanithi, N., Genny, W.J., and Whitley,
D 1994. Neural networks for river flow prediction., journal of Computational
Civil eng, 8(2),201-220.
- McCulloch, W.S., Pitts, W. 1943. A logical
calculus of the ideas imminent in nervous activity.Bull.Math.Biosphys.5,
- Nash, J.E., and Sutcliffe, J.V., 1970.
River flow forecasting through conceptual models, part-1- A discussion
of principles. Journal of Hydrology, 10(3), 282-290.
- Rajsekharan, S. and G. A Vijayalakshmi
Pai, 1996. Neural networks, fuzzy logic and genetic algorithm, Prentice
Hall of India, pp-34-86.
- Rumelhart, D.E, Hinton, G.E, and Williams,
R.J, 1986. "Learning internal representation by back propagation
errors.", Nature 323, 533-536.
- Sankhua, R. N, 2006, Application of artificial
neural network for daily river stage forecast in the Brahmaputra River,
Water and Energy International Journal, CBIP, New Delhi, Vol. 63, No
3, pp.55-62, Jul.-Sep.
- Sankhua, R. N, 2006, Monitoring of Morphological
Changes of Indian Rivers through ANN Based Spatio-Temporal Model- An
approach, National Seminar on silting of rivers in India, February,
12-13, New Delhi.
- Sankhua, R. N, 2006, Spatio-Temporal
Modeling of Hydrological Variability for the river Brahmaputra using
Artificial Neural Network, proc. International Symposium on Role of
Water Sciences in Transboundary River Basin Management, Ubon Ratchathani,
Thailand, March 10-12,pp-25-31
- Zhu, M.L, and Fujita, M (1994), "Comparisons
between fuzzy reasoning and neural networks methods to forecast runoff
discharge." J. of Hydroscience, Hydraulic eng., 12(2), 131-141.
R N Sankhua, Director, National Water Academy, CWC, Pune
A K Srivastava, Director, National Water Academy, CWC, Pune
of this module hereby acknowledge the invaluable support received
from Shri D S Chaskar, Director, National Water Academy, CWC, Pune
in presentation of this module in current shape.