Rainfall Runoff

Introduction

• Not all rainfall contributes to runoff at a catchment outlet
• Excess rainfall propels runoff at the catchment outlet
• Understanding factors preventing runoff is key to using observed hydrographs
• Rain during initial storm phases stores on vegetation as interception or in depressions (puddles) as depression storage
• The soil surface saturates and leads to water runoff toward the channel during continued rainfall
• Surface retention denotes part of storm rainfall that does not appear as infiltration or surface runoff
• Interception by vegetation remains relatively unimportant in moderate-to-severe floods
• Small depressions fill rapidly, initiating overland flow after rainfall starts
• Some flows move to significant depressions, while major overland flows feed streams
• Infiltration enables water penetration from ground surface to subsurface layers
• Infiltration represents the primary factor responsible for water losses, causing rainfall to not appear as runoff in streams
• Rainwater infiltrates upon exceeding soil's infiltration capacity, so only excess rainfall leads to runoff

Hyetographs

• Graph plotting rainfall over a basin along a time scale
• The infiltration indices method is simple and popular for separating losses from a hyetograph
• Hydrological flood calculations benefit from a constant infiltration rate value, incorporating all rainfall losses over the storm duration
• Infiltration index refers to the average infiltration rate
• $-index and W-index commonly used for infiltration, accounting for infiltration and other losses through trial/error, lacking loss-type differentiation (e.g., interception, depression, infiltration)

Phi-Index

• The rate of rainfall above which the rainfall volume equals the runoff volume is the $-index/constant loss rate
• Expressed mathematically, the $-index becomes the average rainfall above which the rainfall volume matches the direct runoff volume
• If the rainfall intensity falls below 4, then the infiltration rate matches the rainfall intensity
• Rainfall intensity exceeding $ means the disparity between rainfall and infiltration during a time interval represents the direct runoff volume
• Rainfall amount exceeding the index amounts to excess rainfall
• Runoff magnitudes can therefore be estimated for any rainfall hyetograph
• Considers abstraction of total losses
• Expressed mathematically as:
  • Φ = (P - R) / te, where:
    • P = total storm precipitation (mm or cm),
    • R = total direct surface runoff (mm or cm),
    • te = duration of the excess rainfall (hours),
    • Φ = uniform infiltration rate (mm/hr or cm/hr).
• Antecedent precipitation conditions causing significant interception, depression, and evaporation may need subtraction from rainfall before $-index application
• accounts predominantly for water losses from storms
• Well-known that constant infiltration capacity occurs
• $-index method to be interpreted as method.
• Well-known that infiltration capacity decreases over time, rendering the method somewhat unrealistic
• Infiltration underestimated for early rainfall, overestimated later due to changing infiltration capacity with time
• Determining one storm's $-value and extrapolating to another remains difficult
• The simple derivation of this often used method can be seen in the examples

W-Index

• Refines the $-index by subtracting the initial losses from the total abstractions
• Calculates an average infiltration rate
• Expressed as:
  • W = (P - R - Ia) / te, where:
    • P = total storm precipitation (cm),
    • R = total storm runoff (cm),
    • Ia = initial losses (cm),
    • te = duration of excess rainfall (hours), and
    • W = average infiltration rate (cm/hr).

Hydrographs

• Necessary for design of structures like dams, spillways, and bridge culverts
• Quantitative data is needed on peak flows and time distribution of runoff
• Describes the temporal flow variation at a catchment/basin outlet
• The flow rate or water depth change per unit time expresses flow
• Yields runoff distribution from excess rainfall in a catchment
• Measured at gauging sites at catchment outlets
• Gauging records systematically kept by the Central Water Commission and state agencies in India, for major/medium basins
• Sherman's (1932) theory involves linearity, and time/space invariance
• Unit hydrographs are derived from available rainfall-runoff records for gauged catchments
• Derivation procedures rely on storm type: single or multi-period
• Thunderstorms generally are regarded as single-period storms due to intensity and short duration
• Frontal storms with longer durations, to be regarded as multi-period storms
• A unit hydrograph converts rainfall ( excess rainfall) into direct surface runoff
• Duration is typically the duration of the excess rainfall block
• S-curve and utilization methods can derive unit hydrograph
• Former approach changes available unit hydrograph duration to any duration length
• Topics to be included
  • unit hydrograph theory, assumptions, limitations
  • derivation of unit hydrograph and factors influencing its derivation
  • instantaneous unit hydrograph (IUH)
  • S-curve
  • change of unit hydrograph duration
  • derivation of average unit hydrograph

Unit Hydrograph Definition

• A hydrograph of surface runoff directly derived from unit excess rainfall that occurs uniformly across the catchment area during a discrete time
• Excess rainfall excludes abstraction from hydrological factors
• Includes water loss from infiltration
• A unit excess rainfall volume measures 1 mm to be considered as the standard value since rainfall usually reads in mm
• UH can be derived from 1 cm ER in certain cases
• Unit time selection stems from the duration of a storm and catchment location size
• Small catchments have assumed periods of either 1 or 2 hours whereas larger catchments commonly adopt even 12 hours

Unit Hydrograph Theory and Assumptions

• Acts as a multiplier to convert excess rainfall into direct surface runoff
• The discharge streamflow hydrograph is considered to be a direct product
• Multiplying effect varies with time, as the flows of each time period within the graph show a trend
• Unit hydrographs apply to each excess rainfall block and resulting water block, added for direct computing, with further base flow additions to obtain final flood hydrographs

Constant Base Length Assumption

• Base of direct surface runoff corresponds to rainfall amount within a period
• Independent of runoff volume in the catchment

Proportional Ordinate Assumption

• Ordinate of DSRO at a time, i.e., Q(t), is proportional to the total rainfall in an excess
  • Therefore Q₁(t) = k PE₁ and Q₂(t) = k PE₂.
    • Q(t) is the ordinate of DSRO at any time t
    • for the ith storm with a rainfall of volume PEi, k is a constant

Concurrent Flow Assumption

• Surface runoff hydrograph from a rain section
• unaffected by simultaneous runoff from other part
• the accumulated surface runoff represents the total
  • Figure 3.3 exemplifies this, as a hydrograph resulting from rainfall PE₁, another from PE₂.
    • DSRO stemming from rainfall PE₁does not get affected by the DSRO of rainfall PE₂
    • The added sum presents a cumulated addition

Uniform Excess Rainfall in Time Assumption

• Excess is due to consistent rainfall, for the excess rainfall
• Equals rainfall divided by the period
• The data gathered for storm
  • short and dense
  • The created the time domain
    • the peak is singular

Factors Affecting Unit Hydrograph Shape

• Rainfall distribution and physiographic influence factors consist of
  • shapes
  • slope
  • vegetation
  • soil type

Rainfall Distribution

• Affects intensity and the hyetograph pattern shape
• Resulting hydrograph from rainfall in the lower basin is rapid due to the rain in a short span while
  • A slow hydrograph of longer rain indicates otherwise

Catchment Physiography

• With time, there exists a physical change
• Vegetative degrades

Base-flow Separation

• Establish surface flow correspondence relative to rain input
  • rainfall discharge, with its information
• Surface obtains quick flow response while the slow removes the response
• There are three ways which have previously been introduced
  • Method 1- Drawing a line from the rising edge to the point of dropping for direct runoff
  • In Fig. 3.4, endpoint A has direct runoff marked
  • B is runoff marked
• Following points,
  • N = 0.83 A0.2 (3.3)
  • Where A= 2 , in the above equation
  • Is the runoff

Methods

• Method 2 the base follows the peak at point C
  • Connect to B, as and CB flow is on the surface or the bottom
  • This occurs in common engineering aspects to derive a UH
• Method 3 water flow in the flow the inflection coordinate
• EF connects is realistic in situations where the stream reaches that time. All flows are local and chosen based on how accurate that flow's estimation is