Hydrologic Theory

• One of the principal objectives in hydrology is to transform rainfall that has fallen over a watershed area into flows to be expected in the receiving stream.

• Losses must be considered such as infiltration or evaporation (long-term)

• Watershed characteristics are important

The Watershed Response

• As rain falls over a watershed area, a certain portion will infiltrate the soil. Some water will evaporate back.

• Rainfall that does not infiltrate or evaporate is available as overland flow and runs off to the nearest stream.

• Smaller tributaries or streams then begin to flow and contribute their load to the main channel at confluences.

• As accumulation continues, the streamflow rises to a maximum (peak flow) and a flood wave moves downstream through the main channel.

• The flow eventually recedes or subsides as all areas drain out.• The portion of the rainfall that does not contribute to direct surface runoff is

termed Rainfall Abstractions (intercepted by vegetation, infiltrated into the ground surface, retained in depression as puddles or returned to the atmosphere through transpiration and evaporation.

• The portion that contributes to surface runoff is called Effective Precipitation.

1. Orographic: wind-induced mechanical process of lifting over mountain ranges

2. Convective: thermodynamic process of heating at or near surface – summer, large cities and tropic

3. Cyclonic: Frontal systems and buoyancy effects - winter

Causes of PrecipitationCauses of Precipitation

Precipitation lifting mechanisms

Average Annual PrecipitationAverage Annual Precipitation

Determination of Runoff VolumeCase I: (for Dp > Dli and Dr > Ds)

Dr = Dp – Dli – Di – Ds – De

Case II: (for Dp ≤ Dli and Dr ≤ Ds)

Dr = 0

Where:Dr = total depth of runoff (effective precipitation)Dp = total depth of precipitation (rainfall)Dli = total initial loss (interception)Di = total depth infiltrated after initial lossesDs = total depression storage depthDe = transpiration and evaporation losses (often ignored for short-duration stormwater events) Volume of runoff (Vr) or effective precipitation

Vr = Dr x A

Unit Hydrograph Theory• The unit hydrograph represents the basin response to 1 inch (1

cm) of uniform net rainfall for a specified duration.

• A graphical representation of discharge over time and provides peak flow rate

• Linear method (principles of linearity and superposition apply)

• Works best for relatively small subareas - in the range of 1 to 10 sq miles.

• Several computational methods exist and most widely used for surface runoff.

• Could be measured (for gaged watershed) or computed (synthesized)

Inst. Hydrograph Response

• Rainfall falls over the basin

• Intensity I reaches the outlet -   

  response based on travel time

• Produces a total storm response

  hydrograph as shown

• Little delay and no storage

• The above only occurs in small

  urban basins or parking lots

Ii

QQi i = I= Iii A A

Small BasinSmall Basin

Unit Hydrograph (UH) Method

T

Q

• Linear transform method

• Converts complex rainfall to

  streamflow at outlet

• Produces a total

storm  hydrograph from given

UH

• Used in complex watersheds

• Each subarea is uniform

• Storage effects considered

Pi

Uj

Hydrograph - Watershed Flow Response to Rainfall

• Peak Flow and time to peak relate to area/shape of watershed

• Area under curve is the volume of direct RO

• Time Base is time that flow exceeds baseflow

• Time to peak or Lag is measured from center of mass of rainfall pattern

Hydrograph

Volume of Runoff

Direct RO

Ou

tflo

w

Time

Time Base

Peak Flow

Lag or time to peak

RFRF

Net Rainfall (effective

precipitation)

Rising Limb

Crest

Falling Limb

Recession

Base Flow

Direct Runoff DRO

Hydrograph RelationsHydrograph Relations

Hydrologic Budget•Quantifying components of the hydrologic cycle.•Precipitation and surface runoff phases are of greatest interest in hydraulic design (also, easiest to estimate)•Sources of hydrologic data:

–National Oceanic and Atmospheric Administration (NOAA): Environmental Data (Climatological)–National Weather Service (NWS) (Rainfall depths, rainfall intensities)–The US Geological Survey (USGS) (Stream gages – flowrate cfs)–The U.S. Army Corps of Engineers (lake evaporation, inches)

Rainfall Averaging MethodsRainfall Averaging Methods

• Arithmetic

• Thiessen PolygonDivide area into polygons; Method: •draw lines between each gage •construct perpendicular bisector for each line •extend bisectors to form polygons

• Isohyetal Contours•lines of equal precipitation. •Multiply average precipitation by area of subarea •Sum for all subareas •Divide by total area

Uses of precipitation Data

Engineering – design of flood control structures: design to contain

extreme flows (Maximum amount of predicted rainfall)– design of bridges, culverts, storm drains, other

structures: design for large, but not extremely large flows

– Design of large scale water storage and water supply systems (Minimum amount of predicted rainfall)

• Water resource management – examine consistency of precipitation

Typical Streamflow GageTypical Streamflow Gage

High FlowHigh Flow

• Measure V (anemometer) at 0.2 and 0.8 of depth

• Average V and multiply by (width * depth)

• Sum up across stream to get total Q = (Vi Di Wi)

Stream Cross-Section for QStream Cross-Section for Q