CIVE 445 - ENGINEERING HYDROLOGY

CHAPTER 2D: BASIC HYDROLOGIC PRINCIPLES, RUNOFF

  • Surface runoff, or simply runoff, refers to all waters flowing on the surface of the earth, in:

    • Overland flow

    • Rill flow

    • Gully flow

    • Streamflow

    • River flow

  • Rivers carry their flow into the ocean, completing the hydrologic cycle.

  • Runoff is expressed in terms of volume or flow rate.

  • The local flow rate can be integrated over a period of time to give the accumulated runoff volume.

  • Runoff is commonly expressed in depth units, i.e., the runoff volume spread uniformly over the catchment area.

  • Runoff is also expressed as:

    • peak flow per unit drainage area,

    • peak flow per unit area per unit rainfall intensity (C),

    • peak flow per unit runoff depth, or

    • peak flow per unit drainage area per unit runoff depth.

 

Runoff components

  • Runoff has three sources:

    1. surface,

    2. interflow,

    3. groundwater.

  • Surface flow is also called direct runoff.

  • Direct runoff can produce large flow concentrations in a relatively short period of time.

  • Direct runoff is responsible for floods.

  • Interflow is mostly vertical movement of water in the unsaturated portion of the soil profile.

  • Groundwater flow takes place below the water table.

  • Groundwater is a characteristically slow process.

  • Runoff is always moving from higher to lower potential.

  • Because water table is almost horizontal, groundwater flow is almost horizontal.

  • Groundwater flow intercepts surface flow in streams and rivers.

  • Most groundwater flow is converted to surface runoff before it reaches the ocean.

  • Only about 2% of the water in the hydrologic cycle is unaccounted for as either evaporation or surface runoff.

  • This unaccounted portion is referred to as deep percolation, and is commonly neglected in water balance studies.

 

Stream types and baseflow

  • Streams can be grouped into three types:

    1. perennial,

    2. ephemeral,

    3. intermittent.

  • Perennial streams are those that always have flow.

  • During dry weather, the flow of perennial streams is baseflow, consisting mostly of groundwater flow.

  • Streams that feed from groundwater are called effluent streams.

  • Perennial and effluent streams are typical of subhumid and humid regions.


    A perennial stream: The Deschutes river, central Oregon.

  • Ephemeral streams flow only in direct response to precipitation.

  • Ephemeral streams do not intercept groundwater and have no baseflow.

  • Ephemeral streams usually contribute to groundwater by seepage through their porous channel beds.

  • Streams that feed groundwater are called influent streams.

  • Channel abstractions from influent streams are called channel transmission losses.


    Equipment to measure field hydraulic conductivity.

  • Ephemeral and influent streams are typical of semiarid and arid regions.

  • Intermittent streams are those that have intermediate properties, behaving as either perennial or ephemeral, depending on the season.


    An ephemeral stream: Tecate Creek at El Descanso, Baja California.

  • Baseflow estimates are important in yield hydrology.

  • In flood hydrology, knowledge of baseflow is necessary to separate direct and indirect runoff.

  • Baseflow is a measure of indirect runoff.

 

Antecedent moisture

  • Surface runoff depends on antecedent moisture.

  • The more antecedent moisture, the less surface runoff.

  • The most widely used method for antecedent moisture is the NRCS, which uses uses the Antecedent Moisture Condition (AMC) to characterize antecedent moisture:

    • I (dry),

    • II (average) and

    • III (wet).

  • Runoff from I is less than II, and II is less than III.

 

Rainfall-runoff relations

  • Rainfall is easier to measure than runoff.

  • From an engineering standpoint, the quantity of runoff is more important that the quantity of rainfall.

  • Runoff is assessed through rainfall-runoff relations.

  • A basic linear model of rainfall-runoff is the following:

Q = b (P - Pa)


Fig. 2-25

  • SCS runoff curve number method is a rainfall-runoff model that has a nonlinear fit to the data.

  • Method is conceptual based on empirical data.

 

Runoff concentration

  • Assume that a storm falling on a given catchment produces a uniform effective rainfall intensity over the entire catchment.

  • In such case, surface runoff will concentrate at the catchment outlet, provided the effective rainfall is sufficiently long.

  • The flow rate at the outlet increases gradually from zero to a constant maximum, or equilibrium value.

  • Surface runoff has concentrated at the catchment outlet.

  • The time to achieve the maximum discharge is referred to as the time of concentration.

  • The equilibrium flow rate is calculated as follows:

Qe = 2.78 Ie A

    where:

    • Qe = equilibrium flow rate, in L/s.

    • Ie = effective rainfall intensity, in mm/hr.

    • A = catchment area, in ha.
     

     

  • There are three types of catchment flow:

    1. superconcentrated,

    2. concentrated,

    3. subconcentrated.

  • Superconcentrated and concentrated flows are typical of small catchments (the rational method).

  • Subconcentrated flows are typical of midsize (and large) catchments (the unit hydrograph).

Fig. 2-26

 

Time of concentration

  • It is the time it takes a parcel of water to travel from the farthest point in the catchment divide to the outlet.

  • It is a function of runoff rate.

  • Most formulas for time of concentration are empirical; there are some theoretical (kinematic wave).

  • The Manning equation is also used to estimate time of concentration.

  • The speed of travel of unsteady flow is usually larger (by 33% to 67%) than the speed of travel of steady flow.

  • Time of concentration is essentially unsteady.

  • Uncertainties in flow rate have blurred the distinction between steady and unsteady velocities in open-channel flow.

  • The Kirpich formula is the most popular formula for time of concentration:

tc = 0.06628 L0.77 / S0.385

    where:

    • tc = time of concentration, in hr.

    • L = catchment length, in km.

    • S = catchment slope, in m/m.
 

  • The Hathaway formula is also popular:

tc = 0.606 (Ln)0.467 / S0.234

    where:

    • n = roughness factor (similar to Manning's).

 

Runoff diffusion and streamflow hydrographs

  • Actual catchment response is more complex than that which could be attributed solely to runoff concentration.

  • Rainfall is not uniformly distributed over space, creating nonuniformities which show as diffusion.

  • The runoff process is subject to convection and diffusion.

  • Convection is properly runoff concentration.

  • Diffusion is the mechanism acting to spread the flows in time and space.

  • Diffusion reduces the flow levels below those that could be attained by convection only.

  • Diffusion acts to smooth out catchment response.

  • The resulting hydrograph is usually continuous.

  • Typical storm hydrographs are shown below.

Fig. 2-27

 

Flow in stream channels

  • The following properties are used to describe stream channels:

    • Cross-sectional dimensions: width, depth, area

    • Cross-sectional shape

    • Longitudinal slope

    • Boundary friction

  • Channel top widths vary widely, from a few meters to several kilometers.

  • Mean flow depths vary from a fraction of a meter to as high as 60 m for very large rivers such as the Amazon.

  • Width-to-depth (aspect) ratios vary from about 10 to more than 100.

  • Water surface slope or energy slope is used as a measure of longitudinal channel slope.

  • The longer the reach, the more accurate the calculation of channel slope.

  • Boundary friction can be due to skin or form friction.

  • Since most rivers have aspect ratios greater than 10, boundary friction is synonymous with bottom friction.

 

Uniform-flow formulas

  • The Manning or Chezy formulas are used to calculate uniform flow in stream channels:

  • The Manning formula is:

V = (1/n) R2/3 S1/2

    where:

    • V= mean velocity, m/s.

    • R= hydraulic radius, m.

    • S = channel slope, in m/m.

  • Values of n vary from 0.024 to 0.079 in natural channels (measured by USGS): See manningsn.sdsu.edu

  • Values of n vary from 0.1 to 0.2 in flood plains: See manningsn2.sdsu.edu
 

  • The Chezy formula is also popular:

V = C (RS)1/2

    where:

    • C = Chezy coefficient, varying from 79 to 11 m1/2/s.

  • More typical values of Chezy C are in the range from 40 to 70 m1/2/s.

  • Unlike the Manning equation, the Chezy can be made dimensionless by dividing the coefficient by the square root of the gravitational acceleration.

  • Despite this theoretical appeal, the Manning equation has had wider acceptance in practice.

  • This is attributed to the fact that the Chezy coefficient has a tendency to vary with the hydraulic radius, such that:

C = (1/n) R1/6

  • This implies that Manning's n is a constant.

  • Experience has shown, however, that n varies with stage and discharge in natural channels.

 

River stages

  • At any point, river stage is the elevation of the water surface above a given datum.

  • River stages vary with flow rate.

  • Flow rates can be grouped into:

    • low,

    • average,

    • high.

  • Low flow is typical of the dry season, and consists mostly of baseflow.

  • High flow occurs during the wet season, and contributions are due primarily to surface runoff.

  • Average flow occurs in midseason.

  • The study of low flows is necessary to determine minimum flow rates below which a certain use would be impaired.

  • Examples:

    • irrigation water requirements,

    • hydropower generation,

    • minimum flows for compliance with water pollution regulations,

    • minimum draft for inland navigation.

  • Average flows are used to study catchment yield.

  • High flows are used to calculate floods, and for flood forecasting and flood control.

 

Rating curves

  • Given a long and prismatic channel, a single-valued relationship between stage and discharge at a cross-section defines the equilibrium rating curve.

  • For steady uniform flow, the rating curve is unique, and can be calculated with a steady flow formula such as Manning's.

  • The property of uniqueness of the rating qualifies the channel reach as a channel control.

  • Nonuniformity and unsteadiness can cause deviations from the equilibrium rating curve.

  • Flood wave theory justifies a loop in the rating.

  • In practice, the loop is usually small and can be neglected.

Fig. 2-30

  • Two other mechanisms have a bearing in the evaluation of stage-discharge relations:

    1. short-term and

    2. long-term

    sedimentation effects.

  • Short-term effect: The amount of boundary friction varies with flow rate.

  • During low flow, the bed friction consists of grain and form friction.

  • During high flows, form friction is eliminated, reducing only to grain friction.

  • The reduced friction gives rivers the capability to carry a greater discharge for a given stage (See Kennedy: Reflections on rivers.

  • This explains the shift from low-flow rating to high-flow rating.

  • Long-term sedimentation effect: Rivers continuously subject their boundaries to endless cycles of erosion and deposition, depending on the sediment load they carry.

  • Shifts in rating curve are the net result of these natural geomorphic processes.

 

Rating curve formulas

  • In spite of complexities, rating curves are a useful and practical tool in hydrologic analysis, allowing the direct conversion of stage to discharge and viceversa.

  • A widely used rating curve model is the following:

Q = a (h - ho)b

  • The proper value of reference stage ho is that which makes the stage-discharge data plot as close as possible to a straight line on log paper.

  • Subsequently, values of constants a and b are determined by regression analysis.

 

Streamflow variability

  • Streamflow varies seasonally, annually, and with geographic location.

  • On a global basis, total runoff volume is about 30% of the total precipitation volume.

  • The rest is accounted for by evaporation and evapotranspiration.

  • The runoff coefficient could be as low as 2% (Arizona) and as high as 93% (one special case in the Phillipines).

 

Seasonal variability

  • In humid climates, seasonal variability is not marked.

  • The Amazon river has a ratio of high-to-low flow of about 3-5.

  • In arid climates, seasonal variability is very marked.

  • Streams in arid climates may have a ratio of high-to-low flow of 1000 or more.

  • For ephemeral streams, this ratio is ∞ (infinity).

  • In humid climates, there is contributions of indirect runoff (groundwater flow) throughout the year.

  • In arid climates, the water table lies deep in the soil profile, and the contribution of groundwater to surface water is absent.

  • Groundwater reservoirs serve as the mechanism for the storage of large amounts of water, which are slowly transported to lower elevations.

  • The process is slow and subject to a substantial amount of diffusion.

  • The net effect is that of a permanent contribution to surface flow in the form of baseflow.

 

Annual variability

  • Annual streamflow variability is linked to the relative contributions of direct and indirect runoff.

  • During dry years, rainfall goes on to replenish the catchment's soil moisture, with little of it showing as direct runoff.

  • During wet years, the catchment's storage capacity fills up quickly, and any additional amount is entirely converted into surface runoff.

  • A line of inquiry is to focus on the mechanics of coupled surface and groundwater flow.

  • This is a very complex process, spatially distributed and temporally varying.

  • We have relied on statistics to compensate for the incomplete knowledge of the physical processes.

  • This has led to the concept of flood frequency.

  • A flood series is extracted from the stream gaging data.

  • The statistical analysis of the flood series allows the calculation of flow rates associated with selected frequencies or return periods.

  • The procedure is limited by the record length, i.e., the number of years of data.

  • With 10 years of data, do not expect to get an accurate value of the 100-yr flood.

 

Daily flow analysis

  • Variability of streamflow can be expressed in terms of the day-to-day fluctuation of flow rates at a given station.

  • Differences are due to the climate and the nature of catchment response.

  • Small and midsize catchments will usually have steep gradients and concentrate flows with negligible runoff diffusion, producing hydrographs with many high peaks and low valleys.

  • Large catchments are likely to have milder gradients and therefore, to concentrate flows with substantial runoff diffusion.

  • The diffusion mechanism acts to spread the flow in time and space, smoothing out the peaks and valleys of the hydrographs.

 

Flow-duration curve

  • Daily flow records are obtained for one or more years.

  • The length of the record indicates the total number of days in the series.

  • The daily flow series is sequenced in decreasing order, from highest to lowest, and an order number assigned.

  • For each flow value, the percent time is the ratio of its order number divided by the total number of days, and multiplied by 100.

  • The flow-duration curve is obtained by plotting flow vs percent time.

Fig. 2-31

  • The flow-duration curve allows the evaluation of the permanence of characteristic low-flow levels.

  • For instance, the flow expected to be exceeded 90% of the time can be readily determined from a flow-duration curve.

  • The permanence of low flows is increased with streamflow regulation.

  • The usual aim is to assure the permanence of a certain low-flow level 100% of the time.

  • Regulation causes a shift in the flow-duration curve by increasing the permanence of low flows while decreasing that of high flows.

  • Flow-mass curve.

 

Geographical variability of streamflow

  • Two variables help describe the geographical variability of streamflow:

    1. catchment area,

    2. mean annual precipitation.

  • The volume available for runoff is directly proportional to the catchment area.

  • This is limited by the available precipitation.

  • Catchment area is important because large catchments have milder overall gradients.

  • This causes increased runoff diffusion, increasing the chances for infiltration.

  • The net effect is a decrease of peak discharge per unit area.

  • Peak flows are directly related to catchment area (Eq. 2-52).

    Qp = c An

  • The exponent n is generally less than 1, because of runoff diffusion.

  • Therefore, peak flow per unit of catchment area is:

    qp = c / Am

  • where m = 1 - n.

  • This equation confirms that qp is inversely related to drainage area.

  • The Creager curves (Fig. 2-33) is an early example of this trend.


    Fig. 2-33

  • Values of C in the range 30-100 encompass most of the data compiled by Creager in the 1930's.

  • This range can be taken as a measure of the regional variability of flood discharges.

  • However, there is no connotation of frequency to the calculated results.

 

Go to Chapter 3.

 
060206