Worcester Polytechnic Institute Civil and Environmental Engineering Hydrology Lecture # 3 Paul P. Mathisen Worcester Polytechnic Institute Civil and Environmental Engineering

CE 590 Hydrology Hydrologic principles Rainfall and runoff Surface water & ground water flow Watersheds and terrestrial inputs to surface water bodies Examples developed from Wachusett Reservoir Web site: http://cee.wpi.edu/hydro Instructor: Paul Mathisen (with some assistance from others)

Last time ... Brief review Some clarifications on definitions Quantitative analysis of rainfall Rainfall measurement

Today ... Review Abstractions Catchments Runoff Intro to infiltration

Water Budget E P I T R G

Rainfall / runoff rainfall depression storage overland flow streamflow

Abstractions Processes acting to reduce total ppt into effective ppt., which ultimately produces runoff Interception surface or depression storage infiltration evaporation evapotranspiration

Interception Abstraction by vegitation or other surface cover throughfall - part of ppt that reaches the ground fx of storm, vegatative cover, season amounts light storms - 25 percent moderate storms - 7 to 36 % in growing seas. heavy & longer storms - small

Interception Components Interception storage - retained by foliage evaporation loss Where .. L=interception loss (mm) S = interception storage depth (mm) K= evap.foliage surf/its horiz projection E= evap. Rate (mm/hr) t= storm duration L= S + K E t

Surface/depression storage Abstracted ppt is retained in puddles, ditches , and other depressions in surface milder the relief, greater the depression storage ex - sand - 5mm - pervious urban - 6.25 mm loam - 3.75 mm - paved areas - 1.5 mm clay - 2.5 mm

Depression storage Quantification lump in with other components such as infiltration Peak flow correction factor (SCS TR55) Vs = Sd (1 - e-kPe) where Vs is the equiv depth of depress storage (mm), Pe is precip excess, Sd is depression storage capacity (mm) [typically 10 to 50 mm], and k is a const

Infiltration Infiltration - seepage of rainfall into the ground (contribution to groundwater) R (in) t (hrs)

Antecedent moisture Infiltration has an important effect on abstracted ppt. Infiltration is dependent on initial level of soil moisture, or antecedent moisture Antecedent ppt index (API) typical depletion rate Ii = K I I-1 where Ii is index for day, Ii-1 is index for preceding day, and K= recession factor (.85-.98)

Antecedent Precipitation Index High API, greater runoff Alternative definitions Antecedent moisture condition (AMC) by SCS .. I(dry), II(avg), or III(wet) SSARR - soil moisture index (SMI) - relates runoff to SMI and ppt. intensity Runoff percent (R/P)*100

Surface runoff runoff depends on the antecedent ppt index water flowing on earth’s surface overland flow flow in rills, gullies and streams

3 components contribute to runoff surface flow interflow groundwater flow

Surface runoff in catchments Overland flow - sheet flow over land surf. rill flow - small rivulets (conc of overland) gully flow - runoff with erosive cabability streamflow - concentrated runoff river flow - confluence of streams

Catchment characteristics area Slope Shape Flow length streams (location, density, nature)

Catchment area Drainage area catchment divide Estimate: Q peak=Can leads to potential runoff volume catchment divide may differ from groundwater divide Estimate: Q peak=Can divide A

Catchment shape Form Compactness Kf=A/L2 where Kf is form ratio, and L is catchment length Compactness Kc=0.282P/A1/2 where Kc is a compactness ratio, and P is the perimeter Catchment response - conc. & timing of runoff If Kf high, or Kc~1, then rapid runoff Factors: relieve, veg. cover, drainage density, ..

Flow length - approximate equations Approximate estimate Lo=1/(2D) where D=drainage density since overland flow length is approx 1/2 of mean distance between channels More precise estimate Lo=1/[2D{1-(Sc/Ss)}1/2] where Sc is the mean channel slope and Ss is the mean surface slope

Linear measures Catchment length -length along principle watercourse length to centroid (often est. as point to 2 or more bisecting straight lines Order 0 = overland flow 1 = gets flow from 0 orders 2 = gets flow when 2 1st order streams combine etc. G L Lc

Estimating the overland flow length collector collector collector

Slope/catchment relief Relief - an elevation difference max relief = max elev diff between highest & lowest points Relief ratio=max relief/longest straight lgth

Land surface slopes Often use grid methods to get slopes hypsometric analysis = curve showning elevation of catchment above this elevation Ei-Emin Emax-Emin Ai/Ac

Stream channels Slope S1 - from max and min elev’s 0.10 - mountains 0.000006 - some tidal rivers S1 - from max and min elev’s S2 - const slope that makes shaded area above equal to shaded area below S3 - equivalent slope - break channel into subreaches & obtain slope E 2 Li up Down S3= Distance  (Li/Si 1/2)

Stream-types and baseflow perennial (always flowing) flow maintained by “base flow” during dry weather ephemeral (only in response to ppt) intermittent (only in certain times of the year)

Hydrographs Characteristics of the hydrograph Distribution of uniform rainfall

Runoff Volume or flow rate varies with time Q (cfs) Volume or flow rate varies with time may express in flow per unit drainage area, per unit runoff depth, or per both surface flow - direct runoff also get indirect runoff T (hr)

Runoff coefficients R=k P surface k urban residential: single 0.3 apts 0.5 commerial and industrial 0.9 forests 0.05-0.20 parks; farms 0.05-0.30 asphalt and pavement 0.85-1.00

First part of class ... Review Abstractions Catchments Runoff

Next ... Infiltration Definitions Physical aspects Simple models Physically based models measurement

3 components contribute to runoff surface flow interflow groundwater flow

Infiltration Infiltration - process by which ppt is abstracted by seeping into soil below ground surface define it by an instantaneous infiltration rate (mm/hr) an average infiltration rate (mm/hr) Function of rainfall intensity, soil properties and soil type, surface conditions, vegitative cover, and water quality

Physical problem unsaturated Close-up flow view on next slide

Moisture in the unsaturated zone air water water moisture content =Vwater/Vtot porosity n=Vw /Vt=Vvoid/Vtot

Capillarity & capillary fringe capillary forces result in rise of fluid 2R  hc (2 cos ) hc = rwgR In subsurface, we get a capillary fringe Vadose/unsaturated zone capillary fringe

Conditions in unsaturated zone total potential or head h = z +  where z is the elevation head and  is the pressure head (or moisture potential) is a function of  Darcy’s law applies: q=K( dh/dz  

Controls on the Range of moisture content Field capacity maximum amount of moisture the soil structure can hold agains the force of gravity upper level of moisture before rapid drainage Wilting point soil mosture at which permanent wilting of plants starts to occur

[NEXT TIME] Infiltration - quantitative approaches Estimation from water balances Horton Equation Philip’s Equation  Index Green-Ampt model Measurement