Surface runoff is that portion of the rainfall, which reaches natural or man-made drainage canals, after it falls on the ground and travels to the point of consideration, and, which remains after all water losses are satisfied. The most important rainfall losses along its way of the rainfall to the water body could be defined as follows:

• Interception storage – This is the part of the rainfall, which adheres to the surface of vegetation and other aboveground objects and is returned to the atmosphere by evaporation. Its value depends on the type of vegetation, intensity and volume of the rainfall and the growth stage of the vegetation. Grass and dense shrubbery could intercept 1.2-1.8 mm of the rainfall (Novotny 2003).

• Depression storage – this is the part of the rainfall, which is detained in surface depressions, which need to be filled before the runoff could be transported further. This water evaporates or percolates to the soil. The amount of depression storage depends on the moisture content of the ground cover and topography. In many cases, the interception storage and depression storage are grouped together and evaluated as on value, termed, ‘surface storage”.

• Evapotranspiration – it represents water loss into the atmosphere by the combined effect of evaporation from soil and water surface and transpiration by plants. Transpiration denotes the water abstracted by plants from soil moisture and released to the atmosphere, as a part of their life cycle.

• Infiltration – this is the process of percolation of the surface storage into the soil . it is a function of soil permeability, moisture content, vegetation cover and other factors. After reaching the aquifer, this portion of the rainfall is known as ‘‘groundwater runoff ” and is the main source for ground water recharge. It is the source of the ‘‘base flow” in rivers and streams, maintained by springs and other forms of ground water discharges to the natural water bodies. The infiltration of ground water to sewer systems could be included in this category as well.

Considering the above-mentional losses, we could differentiate between rainfall excess and surface runoff in the following way:

• rainfall excess or ‘‘ net rain” is used to denote that part of the rainfall, which is left after the subtraction of the above mentioned losses, and is expressed as the depth of water in mm over a given surface area for a specified period of time.

• Surface runoff – it represent that part of rainfall, which has been generated by the rainfall excess, and forms part of the surface flow in natural rivers and streams. It is expressed as flow rate (volume per unit time).

Determining Rainfall Excess:

Rainfall excess could be determined by the curve number method, known as the Natural Resources Conservation Method (NRCM)), developed first in the USA. It determines the rainfall excess as a function of the rainfall volume , surface storage and infiltration (Novotny 2003). Based on extensive rainfall/runoff data variety of soil and cover condition, the method result in the development of a set curves, with a specific number, which links the 24-h rainfall with the corresponding rainfall excess. Each curve number is dependent on the type of land use, level of imperviousness, hydrologic conditions and type of soils. Different soil conditions are classified in four categories. This method was adapted for the Southern African conditions and is known as the SA-SCS method (Shulze et al. 1993).

Determining Surface Runoff:

• the rational method:

this method, also known as Lloyd-Davis method, is the oldest and most widely used method in engineering practice for determination of the design runoff quantity, during the process of drainage structures design for flood prevention. Its purpose is to determine a design surface runoff flow rate, which would be the base for the sizing of the coveying structure to transport the runoff from a given area to a point where it could be discharged safely into a natural water body or disposed on land. Thus this method focuses on a selected rainfall event, which is the most probable one to cause flooding within a given period of time. In other words, the methods determines the runoff from high intensity storms with a relatively low probability of occurrence. Therefore, the selection of an appropriate ‘design’ storm in the terms with a high frequency of pollution control and abatement is very important. The method is based on the following assumptions:

• the peak rate of runoff at any point is a direct function of the average rainfall intensity during the time of concentration to the point.

• The frequency of the peak discharge is the same as the frequency of the average rainfall intensity.

• The time of concentration is the time required for the runoff to become established from the most remote part of the drainage area to the point under consideration. it includes the overland flow time (inlet time) and the time of flow along the channel, governed by channel hydrulics.

Reported practice generally limits the use of this method to urban areas of less than 13 km2 (White 1978). For larger areas, the application of hydrograph methods is recommended. The rational method is represented in the following formula:

Q = CiA

Q= the peak runoff rate;

C= runoff coefficient, which depends on characteristics of the drainage area;

I= the average rainfall intensity (iav); and

A= the drainage area.

The drainage area information should be include the following:

• land use – the present and predicted future practice-as it affects the degree of protection to be provided and the percentage of imperviousness.

• The character of soil and cover as they may affect the runoff coefficient.

• The general magnitude of ground slopes, which, with pervious items and shape of the drainage area, well affect the time of concentration.

The application of the rational method requires information with respect to rainfall data, as well as clear understanding of the concepts and principles involved. The main parameters and procedures included in the determination of the iav value are explained below:

Time Concentration – this is the time required for the surface runoff flow to travel from the most remote part of the drainage area to the point of consideration along a conveying conduit. For urban drainage systems, the time concentration consists of the inlet time plus the time of flow in the conduit from the most remote inlet point to the point under consideration. The time of flow may be estimated closely from the hydraulic properties of the conduit. It would vary with surface slope, the nature of surface cover, and the length of the path of surface flow, as well as with variables such as the soil infiltration capacity and depression storage.

Rainfall intensity- duration relationship – they are important characteristics of any rainfall event. Usually storm events have varing intensity along its duration. The iav of the rainfall event would be equal to the cumulative depth of rainfall (in, mm) divided by the storm duration.

Unit Hydrograph Methods:

Most standard hydrology books contain a derivation of the linear theory of hydrologic systems culminating in the unit hydrograph theory. A unit hydrograph is essentially the runoff, distributed correctly in time, from a unit of excess rainfall falling in a certain predetermined time period and applied uniformly over a watershed or subbasin. Thus, the 5-min unit hydrograph is the runoff hydrograph from, say 1 in of excess rainfall falling uniformly over a 5-min interval. Determination of an actual runoff hydrograph from a storm event (term convolution) is accomplished when measured 5-min blocks of rainfall (termed a rainfall hyetograph) are multiplied by the ordinates of this unit hydrograph, shifted in time by 5-min steps and added together. use of unit hydrographs involves the determination of excess rainfall through the use of some sort initial loss and infiltration methodology.

a number of unit hydrograph types are available in the literature. Two of the most common described briefly here.

Synder’s Unit Hydrograph:

This method was developed (Snyder, 1938) for the Appalachian area watersheds ranging from 10 to 10,000 square miles. It has been applied to watersheds across th United States by the crops of Engineers and is one of the metheods found in the popular HEC-1 program.

It provides a means of generating a synthetic unit hydrograph. it relies on the calculation of lag time and peak flows through two relationships involving area, length measurments, and estimated parameters. Because it does not define the total hydrograph shape, other relationships must be used with the Snyder method for such a definition. For example, HEC-1 uses the Clark relationship for such a definition along with empirically developed estimates of the hydrograph widths at the 50 and 75% of peak levels (HEC, 1990). Details of the method can be found in Chow (1964).

SCS Synthetic Unit Hydrograph:

The Soil Conservation Service developed a family of hydrologic procedures, one of which is a synthetic unit hydrograph procedure. It has been widely used for developing rural and urban hydrographs. The unit hydrograph used by the SCS method is based upon an analysis of a large number of natural unit hydrographs from a broad cross section of geographic locations and hydrologic regions. Rainfall is a necessary input. This method is discussed in detail later in this chapter.

Continuous Simulation Models:

All of the methods described above are event models, which userainfall as the input and flood peaks and hydrographs as the output. this is because most municipal stormwater water management facilities are designe for a specified flood event, and rainfall data are readily available throughout the country. a consequence of this approach is that the complex interaction between rainfall and resulting storm runoff must be estimated, and only one or two flood events are used in the design. In contrast, continuous simulation models such as the EPAStormwater Management Model (SWMM) or the Hydrocomp Simulation Model attempt to represent the entire hydrlogic system on the computer so as simulate the natural system. In this way, the model simulates the runoff process including interception, infiltration, overland flow,channel flow..This simulates is over a long period of time and is continuous so that both flood events and low-flow events are simulated. If accurately simulated, the models will provide information on particular aspects of the runoff process, such as antecedent moisture, which is important when estimating flood peaks and hydrographs

The Unit Hydrograph:

The unit hydrograph method is an approach initially advanced by Sherman. The keystone of the method is the assumption that watershed discharge is related to the total volume of runoff, and that time factors that affect the unit-hydrograph shape are invariant.

A major step forward in hydrological analysis was the concept of the unit hydrograph introduced by the American engineer Sherman in 1932. he defined the unit hydrograph as the hydrograph of surface runoff resulting from effective rainfall falling in a unit of time such as 1 hour or 1 day and produced uniformly in space and time over the total catchment area (Sherman, 1942).

In practice, a T hour unit hydrograph is defined as resulting from a unit depth of effective rainfall falling in T hour over the catchment. The magnitude chosen for T depends on the size of the catchment and the response time to major rainfall events. The standard depth of effective rainfall was taken by Sherman to be 1 in, but with merrication, 1 mm or sometimes 1 cm is used