Design Flood Estimation - 3 | Engineering Hydrology - Civil Engineering (CE) PDF Download

Additional information and definition of important terms

Free board 

The marginal distance that is providing above the maximum reservoir level to avoid the possibility of water spilling over the dam is known as the free board.

Hydro- meteorologically homogeneous sub-zones 

This indicates a partition of the country in terms of similar hydrological and meteorological areas. There are, in all, 26 sub-zones in the country.  This has been done together by the Central Water Commission (CWC), Research Designs and Standards Organization (RDSO), and India Meteorological Department (IMD). 

Channel routing 

The outlet of each sub-catchment is located many km upstream of the outlet of the main catchment.  The outflow of a sub-catchment will pass through the channels before finally reaching the catchment outlet.  The inflow hydrograph to a channel will get modified by the temporary storage of channel; hence it is necessary to estimate the outflow hydrograph of the channel to in order to find the flow at the outlet of the catchment outlet by a process is known as channel routing. 

Reservoir routing 

The hydrograph of a flood entering a reservoir will change in shape as it emerging out from the reservoir.  This is due to volume of water stored in reservoir temporarily.  The peak of the hydrograph will be reduced, time to peak will be delayed and base of the hydrograph will be increased.  The extent up to which an inflow hydrograph will be modified in the reservoir will be computed by the process is known as reservoir routing.

Data requirement for PMF/SPF studies

1. Watershed data 
   • Total watershed area, snowbound area, minimum and maximum elevations above the mean sea level and length of river up to the project site;
   • Lag time, travel times of reaches, and time of concentration;
   • Contributing areas, mean overland flow distances and slopes;
   • Design storm water losses, evaporation, infiltration, depression and interception losses, infiltration capacities.
   • Land use practices, soil types, surface and subsurface divides
2. Channel data
   • Channel and valley cross sections at different places under consideration to fix the gauge discharge rating curves.
   • Manning’s n or the data required to estimate channel roughness coefficient
3. Runoff data
   • Base flow estimates during design floods.
   • Available historical data on floods along with the precipitation data including that of self-recording rain gauges, if available. 
4.  Storm data 
   • Daily rainfall records of all rain gauge stations in and around the region under study
   • Rainfall data of self-recording rain gauges
   • Data of the storm dew point and maximum dew point temperatures

Steps for evaluating PMF/SPF 

1. Estimate duration of design storm Duration of design storm equivalent to base period of unit hydrograph rounded to the next nearest value which is in multiplier of 24 hours and less than and equal to 72 hours is considered to be adequate. For large catchments, the storm duration for causing the PMF is to be equivalent to 2.5 times the travel time from the farthest point (time of concentration) to the site of the structure. 
2. Selection of design storm A design storm is an estimate of the rainfall amount and distribution over a particular drainage areas accepted for use in determining the design flood.  This could either be the Probable Maximum Storm (PMF) or the Standard Project Strom (SPS).
3. Time adjustment of design storm and its critical sequencing The design hyetograph should be arranged in two bells (peak) per day.  The combination of the bell arrangement and the arrangement of the rainfall increments within each of the bell shaped spells will be representing the maximum flood producing characteristics. The critical arrangement of increment in each bell should minimize the sudden hill or sluggishness and maximizing the flood peak.  Hence, the arrangement is to be such that the time lay between peak intensities of two spells may be minimum.  The cumulative pattern of all the increments in the order of their positioning should resemble the natural mass curve pattern as observed by a Self Recording Rain gauge (SRRG) of the project region.
4. Estimate the design Unit Hydrograph Depending upon the data availability and characteristics of flood hydrograph etc, the unit hydrograph may be derived using any of the following techniques.
   • Simple method of unit hydrograph derivation from a flood event with isolated peak
   • Collin’s m ethod o Nash m ethod
   • Clarke model.
   • In case of insufficient data, synthetic unit hydrograph may be derived
5. Calculating the probable maximum flood hydrograph The critical time sequence of the design storm rainfall is superimposed on the derived design unit hydrograph to give the direct hydrograph, when added to the base flow, gives the probable maximum flood hydrograph.  Details of these calculations are given in Lecture 2.4 

Limitation of PMF/SPF calculations 

•  Requirement of long-term hydrometeorological data for estimation of design storm parameters.
• The knowledge of rainfall process as available today has severe limitations and therefore, physical modeling of rainfall to compute PMP is still not attempted.
• Maximization of historical storms for possible maximum favorable conditions is presently done on the basis of surface dew point data.  Surface dew point data may not strictly represent moisture availability in the upper atmosphere.
• Availability of self-recording rain gauge (SRRG) data for historical storms (Remember that SRRG data gives the distribution of rain fall with time).
• Many of the assumptions of the unit hydrograph theory are not satisfied in practice.
• Many a times, data of good quality and adequate quantity is not available for the derivation of unit hydrograph.

Normal Distribution 

The Normal distribution is one of the most important distributions in statistical hydrology.  This is used to fit empirical distributions with skewness coefficient close to zero.  The probability density function (PDF) of the distribution is given by 

 − ∞ < x < ∞

Where, μ is the location parameter and σ  is the scale parameter.  The cumulative distribution function (CDF) of the normal distribution is given by: 

Log – Normal Distribution

If the logarithms, lnx, of a variable x are normally distributed, then the variable x is said to be log normally distributed so that 

Where, μ_y and σ_y are the mean and standard deviation of the natural logarithm of x.  Log normal distributions can be applied to a wide variety of hydrologic events especially in the cases in which the corresponding variable has a lower bound, the frequency distribution is not symmetrical and the factors causing those are independent and multiplicative.

If the variable x has a lower boundary x₀, different from zero, and the variable z= x - x₀ follows a lognormal distribution, then x is lognormally distributed with three parameters. The probability distribution function of the lognormal distribution with parameters is 

Where, μ_y, σ_y and x₀ are called the scale, the shape and the location parameters respectively.  Parameter x₀ is generally estimated by trial and error. 

Pearson Type III Distribution

Pearson type III is a three parameter distribution, also known as Gamma distribution with three parameters.  The PDF of the distribution is given as 

The CDF of the Pearson Type III distribution is given by 

Where x₀, β, and γ are location, scale and shape parameters respectively.

Gumbel Distribution 

Gumbel distribution is a member of family of Extreme Value distributions with the value of parameter k = 0.  It is a two parameter distribution and is widely used in hydrology. The PDF is given as

And CDF is given as 

E ( X ) = μ + 0.5772α

Where, u and α are location and shape parameters respectively.

Lag Time Lag is the time between the peak flow and the centroid of rainfall.

Travel time The time taken by the water to reach the basin outlet, from the different points in the basin, is called the travel time. 

Evaporation The process of extracting moisture is known evaporation.

Infiltration Infiltration is defined as the slow passage of a liquid through a filtering medium.

Interception Interception is the act of catching the precipitation by the trees or buildings without reaching to the ground surface.

Base flow Base flow is the portion of the stream discharge that is derived from natural storage (e.g., groundwater outflow and the draining of large lakes and swamps or other source outside the net rainfall that creates surface runoff).

Base period The time between the first watering of a crop at the time of its sowing to its last watering before harvesting is called base period.  Base period is always less than crop period.

Unit hydrograph A unit hydrograph is defined as the hydrograph of runoff produced by excess rainfall of 1cm occurring uniformly over the entire drainage basin at a uniform rate over the entire specified duration.

Time of concentration The time of concentration of a drainage basin is the time required by the water to reach the outlet from the most remote point of the drainage area.