Runoff: Components, Characteristics & Estimation PDF

RUNOFF **COMPONENTS OF STREAM FLOW** When a storm occurs, a portion of rainfall infiltrates into the ground and some portionmay evaporate. The rest flows as a thin sheet of water over the land surface which is termed asoverland flow.If there is a relatively impermeable stratum in the subsoil, the...

RUNOFF **COMPONENTS OF STREAM FLOW** When a storm occurs, a portion of rainfall infiltrates into the ground and some portionmay evaporate. The rest flows as a thin sheet of water over the land surface which is termed asoverland flow.If there is a relatively impermeable stratum in the subsoil, the infiltratingwater moves laterally in the surface soil and joins the stream flow, which is termed as underflow(subsurface flow) or interflow, Fig. below. If there is no impeding layer in the subsoil the infiltrating water percolates into the ground as deep seepage and builds up the ground water table(GWT or phreatic surface). The ground water may also contribute to the stream flow, if theGWT is higher than the water surface level of the stream, creating a hydraulic gradient towards the stream. Low soil permeability favours overland flow. While all the three types offlow contribute to the stream flow, it is the overland flow, which reaches first the streamchannel, the interflow being slower reaches after a few hours and the ground water flow beingthe slowest reaches the stream channel after some days. The term direct runoff is used toinclude the overland flow and the interflow. If the snow melt contributes to the stream flow itcan be included with the direct runoff (from rainfall).  Direct surface flow can be analysed for relatively large drainage areas by the unithydrograph method and for smaller areas by overland flow analysis. The direct runoff resultsfrom the occurrence of an immediately preceding storm while the ground water contribution,which takes days or months to reach the stream, in all probability has no direct relation withthe immediately preceding storm. The ground water flow into the stream would have continued even if there had been no storm immediately preceding. It is for this reason it is termed as*base flow*in hydrograph analysis. When the overland flow starts (due to a storm) some flowing water is held in puddles, pits and small ponds; this water stored is called *depression storage*.The volume of water intransit in the overland flow which has not yet reached the stream channel is called *surface detention*or *detention storage*.The portion of runoff in a rising flood in a stream, which isabsorbed by the permeable boundaries of the stream above the normal phreatic surface iscalled bank storage.  **CATCHMENT CHARACTERISTICS** The entire area of a river basin whose surface runoff (due to a storm) drains into the river in the basin is considered as a hydrologic unit and is called *drainage basin*, watershed or catchmentarea of the river flowing (Fig. below). The boundary line, along a topographic ridge, separatingtwo adjacent drainage basins is called *drainage divide*. The single point or location at which allsurface drainage from a basin comes together or concentrates as outflow from the basin in the stream channel is called *concentration point or measuring point*, since the stream outflow is usually measured at this point. The time required for the rain falling at the most distant point in a drainage area (i.e.,on the *fringe* of the catchment) to reach the concentration point iscalled the *concentration time*. This is a very significant variable since only such *[storms of duration greater than the time of concentration]* will be able to produce runoff from the entire catchment area and cause high intensity floods.  The characteristics of the drainage net may be physically described by: i. *The number of streams* ii. *The length of streams* iii. *Stream density* iv. *Drainage density* The stream density of a drainage basin is expressed as the number of streams per square kilometre. Drainage density is expressed as the total length of all stream channels (perennial and intermittent) per unit area of the basin and serves as an index of the areal channel development of the basin  Drainage density varies inversely as the length of overland flow and indicates the drainage efficiency of the basin. A high value indicates a well-developed network and torrential runoff causing intense floods while a low value indicates moderate runoff and high permeability of the terrain. Horton has suggested a method of determining the slope of large drainage areas, i.e.,the area is subdivided into a number of square grids of equal size. The number of contourscrossed by each subdividing line is counted and the lengths of the grid lines are scaled. Thenthe slope of the basin is given by  The boundary line along a topographic ridge, separating two adjacent drainage basinsis called the *drainage divide*. The line of the ground water table from which the water tableslopes downward away from the line on both sides, is called the ground water divide. The shape of a drainage basin can generally be expressed by:  The compactness coefficient is independent of the size of the catchment and is dependent only on the slope.A fan-shaped catchment produces greater flood intensity since all the tributaries arenearly of the same length and hence the time of concentration is nearly the same and is less,whereas in the fern-shaped catchments, the time of concentration is more and the discharge isdistributed over a long period (figure below).  Schumm S.A. (1956) used an 'elongation ratio *(E~r~)*', defined as the ratio of the diameterof a circle of the same area as the basin to the maximum basin length; the values range from0.4 to 1.0. Miller V.C. (1953) used a dimensionless 'circularity ratio *(Cr)'*, defined as the ratio of the basin area to the area of a circle having the same perimeter as the basin; the values range from0.2 to 0.8. The drainage basin characteristics influence the time lag of the unit hydrograph andpeak flow (Taylor and Scwartz, 1952). **Example** The contour map of basin is subdivided into a number of square size grids of equal size by drawing horizontal and vertical lines as shown in the figure below. The contour interval is 25 cm.  The number of contour intersections by vertical lines is 75 and by horizontal lines 126.The total length of the vertical grid segments (after multiplying by the scale) is 53260 m and ofthe horizontal grid segments 55250 m. Determine the mean slope of the basin. **Solution** Slope in the vertical direction \ [\$\$S\_{v} = \\frac{N\_{c} - C.I.}{\\sum\_{}\^{}Y} = \\frac{75\\ x\\ 25}{55260} = 0.0352\\ m/m\$\$]{.math.display}\ Slope in the horizontal direction \ [\$\$S\_{x} = \\frac{N\_{\\text{c\\ }}\\text{x\\ C.I.}}{\\sum\_{}\^{}X} = \\frac{126\\ x\\ 25}{55250} = 0.0570\\ m/m\$\$]{.math.display}\ Mean slope of the basin \ [\$\$S = \\frac{S\_{v} + S\_{x}}{2} = \\frac{0.0352 + 0.0570}{2} = 0.0461\\frac{m}{m}\\text{or\\ }\\mathbf{4.61\\%}\$\$]{.math.display}\ From Horton's equation; \ [\$\$S = \\frac{1.5(C.I.)N\_{c}}{\\sum\_{}\^{}L} = \\frac{1.5\\ x\\ 25\\ (75 + 126)}{(53260 + 55250)} = 0.0695\\ or\\ \\mathbf{6.95\\%}\$\$]{.math.display}\ **Example** A basin has an area of 26560 km^2^, perimeter 965 km and length of the basin is 230 km. Determine: (i) form factor, (ii) compactness coefficient, (iii) elongation ratio, and (iv)circularity ratio. **Solution:** i. Form factor, [\$F\_{f} = \\frac{W\_{b}}{L\_{b}} = \\frac{A}{{L\_{b}}\^{2}} = \\frac{26560}{230\^{2}} = \\mathbf{0.502}\$]{.math.inline} ii. Compactness Coefficient, C~c~ \ [\$\$C\_{c} = \\frac{P\_{b}}{2\\pi R}\$\$]{.math.display}\ Radius (R) of an equivalent circular area \ [                                             *A*= *πR*^2^]{.math.display}\ \ [                                          26560 = (*π*)(*R*^2^)]{.math.display}\ \ [                                                    *R* = 91.9 *km*]{.math.display}\ \ [\$\$C\_{c} = \\frac{965}{2\\pi(91.9)} = \\mathbf{1.67}\$\$]{.math.display}\ iii. Elongation ratio, E~r~ \ [\$\$E\_{r} = \\frac{2R}{L\_{b}} = \\frac{2(91.9)}{230} = \\mathbf{0.8}\$\$]{.math.display}\ iv. Circularity ratio, C~r~ \ [\$\$C\_{r} = \\frac{A}{\\text{πR}\^{\'2}}\$\$]{.math.display}\ Therefore, \ [\$\$C\_{r} = \\frac{A}{\\pi R\^{\'2}} = \\frac{26560}{\\pi{(153.5)}\^{2}} = \\mathbf{0.358}\$\$]{.math.display}\ **CLASSIFICATION OF STREAMS** Streams may be classified as: 1. Influent and effluent streams 2. Intermittent and perennial streams 1. *Influent and Effluent Streams*  When the GWT is above water surface elevation in the stream, the ground water feed sthe stream, (Fig. below). Such streams are called *effluent streams*. The base flow of surface streamsis the effluent seepage from the drainage basin. Most of the perennial streams are mainlyeffluent streams.  2. *Intermittent and Perennial streams* **FACTORS AFFECTING RUNOFF** The various factors, which affect the runoff from a drainage basin depend upon thefollowing characteristics: Low intensity storms over longer spells contribute to ground water storage and producerelatively less runoff. A high intensity storm or smaller area covered by it increases the runoffsince the losses like infiltration and evaporation are less. If there is a succession of storms, therunoff will increase due to initial wetness of the soil due to antecedent rainfall. Rain duringsummer season will produce less runoff, while that during winter will produce more. Greater humidity decreases evaporation. The pressure distribution in the atmospherehelps the movement of storms. Snow storage and specially the frozen ground greatly increasethe runoff. Peak runoff (if expressed as cumec/km^2^) decreases as the catchment area increases dueto higher time of concentration. A fan-shaped catchment produces greater flood intensity thana fern-shaped catchment. Steep rocky catchments with less vegetation will produce more runoff compared to flat tracts with more vegetation. If the vegetation is thick greater is the absorption of water, soless runoff. If the direction of the storm producing rain is down the stream receiving the surface flow, it will produce greater flood discharge than when it is up the stream. If the catchment is located on the orographic side (windward side) of the mountains, it receives greaterprecipitation and hence gives a greater runoff. If it is on the leeward side, it gets less precipitation and so less runoff. Similarly, catchments located at higher altitude will receive moreprecipitation and yield greater runoff. The land use pattern---arable land, grass land, forest orcultivated area, greatly affect runoff. The storage in channels and depressions (valley storage) will reduce the flood magnitude. Upstream reservoirs, lakes and tanks will moderate the flood magnitudes due to theirstorage effects. For drainage basins having previous deposits, large ground water storage maybe created, which may also contribute to the stream flow in the form of delayed runoff. **ESTIMATION OF RUNOFF** Runoff is that balance of rain water, which flows or runs over the natural ground surface afterlosses by evaporation, interception and infiltration. The yield of a catchment (usually means annual yield) is the net quantity of wateravailable for storage, after all losses, for the purposes of water resources utilisation and planning, like irrigation, water supply, etc. *Maximum flood discharge*. It is the discharge in times of flooding of the catchment area,i.e.,when the intensity of rainfall is greatest and the condition of the catchment regardinghumidity is also favourable for an appreciable runoff. **Runoff Estimation** The runoff from rainfall may be estimated by the following methods: 1. Empirical formulae, curves and tables 2. Infiltration method 3. Rational method 4. Overland flow hydrograph 5. Unit hydrograph method 6. Coaxial graphical correlation 1. *Empirical formulae, curves and tables* [*R* = *aP* + *b* ]{.math.inline} - gives a straight line plot [*R* = *aP*^*n*^]{.math.inline} - gives exponential curve  2. *Infiltration Method* By deducting the infiltration loss, i.e., the area under the infiltration curves, from the total precipitation or by the use of infiltration indices. These methods are largely empirical and the derived values are applicableonly when the rainfall characteristics and the initial soil moisture conditions are identical tothose for which these are derived. 3. *Rational Method* A rational approach is to obtain the yield of a catchment by assuming a suitable runoff coefficient. \ [*Yield* = *CAP* ]{.math.display}\ \ [*Where* *A* = *area* *of* *cathchment* ]{.math.display}\ [*P* = *precipitation*      *C* = *runoff* *coefficient* ]{.math.inline} **Example** A 4-hour rain of average intensity 1 cm/hr falls over the fern leaf type catchmentas shown in the Fig. below. The time of concentration from the lines AA, BB, CC and DD are 1, 2, 3and 4 hours, respectively, to the site 0 where the discharge measurements are made. The valuesof the runoff coefficient C are 0.5, 0.6, and 0.7 for the 1st, 2nd and 3rd hours of rainfall, respectively and attains a constant value of 0.8 after 3 hours. Determine the discharge at site 0.  Solution:  4. *Overland Flow Hydrograph* Overland flow occurs as a thin sheet of water over theground surface (soon after a storm starts), joins a stream channel, and then flows in the channel to the concentration point. Overland flow is relatively slow and is the dominant type offlow in the case of very small areas such as air ports, municipal block areas and flow frombroad surfaces into storm drains and gutters. But in the case of large drainage areas, thelength of overland flow is so short in comparison with the channel flow distance (before reachingthe concentration point) that the total concentration time is mainly a function of channel velocity. Overland flow is essentially a uniform flow over the surface (Fig. 4.11) as developed by C.F. Izzard (1948). The Reynolds number  Experiments indicate that the overland flow can be assumed to be laminar if Re≤1000and turbulent if Re\> 1000 with a transition region of uncertainty in the vicinity of Re= 1000.Izzard suggested that for rectangular drainage areas, laminar flow can be assumed if theproduct,where i~net~is the net rainfall in cm/hr and lis the length of overland flowin metres. Finite difference methods, based upon the method of characteristics have also beenused to develop overland flow hydrographs. 5. *Unit Hydrograph Method*  The theory of unit hydrograph is based on the following assumptions: i. The net rainfall is of uniform intensity within its duration (unit period) ii. The net rainfall uniformly occurs over the entire area of the drainage basin. iii. For a given basin, the base period of the hydrographs of direct runoff corresponding to net rains of different intensities but the same unit duration, is constant iv. The ordinates of direct runoff hydrographs due to net rains of different intensities (but same unit duration) are proportional. v. A unit hydrograph reflects all the physical characteristics of the basin **Example** A small watershed consists of 1.5 km^2^ of cultivated area (c = 0.2), 2.5 km^2^ under forest (c = 0.1) and 1 km^2^ under grass cover (c = 0.35). There is a fall of 20 m in a watercourse of length 2 km. [\$I = \\frac{80T\^{0.2}}{{(t + 12)}\^{0.5})},\\ \$]{.math.inline}I in cm/hr, T-yr, t-min. Estimate the peak rate of runoff for 25-year frequency. Solution: Time of concentration (Kirpich's formula --modified) \ [*t*~*c*~ = 0.02*L*^0.8^*S*^ − 0.4^,     *t*~*c*~ *in* *min*, *L* *in* *meters* ]{.math.display}\ \ [\$\$= \\ {0.02\\left( 2000 \\right)}\^{0.8}\\left( \\frac{20}{2000} \\right)\^{- 0.4} = 55\\ min\$\$]{.math.display}\ \ [\$\$I = \\frac{80\\ x\\ 25\^{0.2}}{\\left( 55 + 12 \\right)\^{0.5}} = 18.6\\frac{\\text{cm}}{\\text{hr}}\$\$]{.math.display}\ \ [\$\$Q = CIA = 2.78I\\ \\left( \\sum\_{}\^{}{C\_{i}A\_{i}} \\right) = 2.78\\ x\\ 18.6\\ \\left( 1.5\\ x\\ 0.2 + 2.5\\ x\\ 0.1 + 1\\ x\\ 0.35 \\right) = 46.5\\ \$\$]{.math.display}\ **STREAM GAUGING** **Methods of Measuring Stream Flow** The most satisfactory determination of the runoff from a catchment is by measuring thedischarge of the stream draining it, which is termed as stream gauging. A gauging stationisthe place or section on a stream where discharge measurements are made. Some of the usualmethods of stream gauging are given below: a. *Venturiflumes or standing wave flumes* (critical depth meter) for small channels b. *Weirs or anicuts* \ [*Q* = *CLH*^3/2^]{.math.display}\ \ [*where* : *Q* = *stream* *discharge*, ]{.math.display}\ \ [*C* = *coefficient* *of* *weir*,]{.math.display}\ \ [ *L* = *length* *of* *weir* (or anicut),]{.math.display}\ \ [ *H* = *head* (depth of flow)over the weircrest]{.math.display}\ c. *Slope-area method:* \ [*Q* = *AV* ]{.math.display}\ \ [\$\$V = C\\sqrt{\\text{RS}}\\ \\ \\ \\ - Chezy\\ \$\$]{.math.display}\ \ [\$\$V = \\frac{1}{n}R\^{2/3}S\^{1/2} - Manning\$\$]{.math.display}\ Chezy's[\$C\\ = \\ \\frac{1}{n}R\^{1/6}\\ ,\\ \\ \\ \\ \\ \\ R = \\frac{A}{P}\$]{.math.inline} Where: C = Chezy's constant N = Manning's coefficient of roughness R = hydraulic mean radius A = cross-sectional area of flow P = wetted perimeter S = water surface slope (bed slope) The cross-sectional area A is obtained by taking soundings below the water level at intervals of, say, 6 m and plotting the profile of the cross-section and drawing the high flood level or water surface level. The water surface slope is determined by means of gauges placed at the ends of thereach, say 1 km upstream of the gauging station and 1 km downstream of the gauging station(in a straight reach; if ∆his the difference in water levels in a length Lof the reach, thenS=∆h/L. The slope may also be determined by means of flood marks on either side and theirsubsequent levelling. Careful notes on the nature of bed and banks, vegetation etc. should be made and ifpossible a photograph may be taken. From this, the constants C(Chezy's) and n(Manning's)can be found from the Tables. The slope-area method is often used to estimate peak floods where no gauging stationexists. d. *Contracted area methods:* The drop in water surface in contracted sections as in bridge openings (see figure below) canal falls etc. is measured and the discharge is approximately given by \ [\$\$Q = C\_{d}A\_{1}\\sqrt{2g\\ (\\mathrm{\\Delta}h + \\ h\_{a})}\$\$]{.math.display}\ Where: C~d~ = coefficient of discharge A~1~ = area of the most contracted section [*Δh*]{.math.inline} = difference in water surface between the upstream and downs stream ends (of the pier) h~a~ = head due to the velocity of approach  e. *Sluiceways, spillways and power conduits.* The flow through any of the outlets in a dam or the sum of the flows through these gives the discharge at any time. f. *Salt-concentration method.* The discharge is determined by introducing a chemical,generally common salt, at a known constant rate into flowing water and determining the quantity of chemical in the stream at a section downstream sufficiently distant to ensure thoroughmixing of the chemical with water. The discharge \ [\$\$Q = \\ \\frac{c - c\_{2}}{c\_{2} - c\_{1}}q\$\$]{.math.display}\ Where: q = quantity of solution injected (cc/sec) c = amount of salt in dosing solution (g/cc) c~1~= concentration of salt originally (before dosing) in the stream (g/cc) c~2~= concentration of salt in the sample downstream (g/cc) This method is best suited for turbulent waters as the turbulence helps in through mixing of the chemical; this is a costly process. g. *Area-velocity methods* *Q = AV* The area of cross-section of flow may be determined by sounding and plotting the profile.The mean velocity of flow (V) may be determined by making velocity measurements. The velocitydistributions in a cross-section and in a vertical in a stream are shown in Fig. below (a) and (b) andas such the methods of velocity measurements are as follows: