COMET University Faculty Hydrometeorology Course June 2000 Dennis L. Johnson

COMET University Faculty

Hydrometeorology CourseJune 2000

Dennis L. Johnson

Dennis L. Johnson, Asst. ProfessorJuniata College

Environmental Science & Studies(814) 641-5335 (Phone)(814) 641 – 3685 (Fax)

[email protected] (Email)Http://www.Juniata.edu/~johnson/

Usual HoughtonUsual Houghton

Hydrometeorological Operations

in the “Modernized NWS”

The Runoff Picture

• Hydrology is long term and short term….

• In this course we will mainly focus on the short term:

• Floods & flood flows.

• Generating runoff/high flows.

• Predicting/forecasting flows.

• Space/time scales.

What’s a Flood?

• What is a flood?????• A rather elusive definition• Generally contains terms like:

– High water– High flows– Normal water course– Human impact(s)– Etc…

Recipe(s) for a Flood

• What causes a flood?

• What are the conditions?

• What are the types of flooding situations?

• Your area or other areas…..

My Recipes

• “BIG” heavy soaking rains…

• Low infiltration rates

• Snow melt

• Rain on snow

• Very intense precipitation

• Dam failure

• Others….??

Does a Flood Have to Happen in a Defined Water Course or

Waterway?

….and If a Flood Does Occur in an Overland Situation – Does the Nearest Stream Even Feel It?

FEMA - NFIP…(www.fema.gov/nfip)

Flood--A general and temporary condition of partial or complete inundation of normally dry land areas from:

Overflow of inland or tidal waters.

The unusual and rapid accumulation or runoff of surface waters from any source.

Mudslides (i.e., mudflows) which are proximately caused by flood, as defined above, and are akin to a river of liquid and flowing mud on the surface of normally dry land areas, as when earth is carried by a current of water and deposited along the path of the current.

The collapse or subsidence of land along the shore of a lake or other body of water as a result of erosion or undermining caused by waves or currents of water exceeding the cyclical levels which result in flood, as defined above.

What Are the Defining Characteristics of a Flood?

• Timing – rise time, recession, duration.

• Flows – peak flows, magnitude (statistical).

• Precipitation – intensity, duration, frequency….

What Controls the Timing, Flow, and Precipitation?

• The hydrology – short term and long term.

• The meteorology – short term (weather/storm type) and long term (climate).

Big Picture

Long term and short term

Long Term(Climate and the Hydrologic Cycle)

Short TermWeather (storm type) & “current hydrologic

conditions”

Some of the “Right” Combinations….

• Precipitation –vs.- infiltration– Precipitation intensity > infiltration rate– Precipitation total > infiltration capacity– “Storage” in the system is full– Human induced high water or flows– Natural alterations to the watershed

Our Focus

• More on the short term..

• The combination(s) of precipitation and hydrologic conditions that lead up to a potential flooding situation…

• “basin hydrology” – although basin hydrology looks at the long term hydrologic budget, as well.

Let’s Take a Minute to Look at Hydrology and the Properties,

Units, Concepts, & Terminology

HydrologyHydrology

… An Earth Science. It Encompasses the Occurrence, Distribution, Movement, and

Properties of the Waters of the Earth and Their Environmental Relationships." (Viessman,

Knapp, Lewis, & Harbaugh, 1977 - Introduction to Hydrology, Harper & Row

Publishers, New York)

History of Hydrology

(Hydrometeorology)

Early on….

• Early philosophers speculated on the hydrologic cycle:

• Homer believed that there existed large subterranean reservoirs that fed the rivers, seas, springs, and wells - was he wrong?

• Homer did understand the dependence of flow in the Greek aqueducts on conveyance and velocity!

History, Cont....

• In the first century B.C., Marcus Vitruvius in the treatise de Architectura Libri Decem (the engineers chief handbook), vol. 8 hypothesized that rain and snow falling in the mountains infiltrated into the earth’s surface and appeared in the lowlands as springs and streams.....

Early Success.....• 4000 b.C. The Egyptians built a dam on the Nile

to allow barren lands to again be used for agricultural purposes.

More Early Successes

• 1000’s of years later, a canal to carry fresh water from Cairo to Suez was built.

• Towns in Mesopotamia were protected by flooding from high earthen walls.

Early Disputes and Rules

• The cities of Lagash and Umma of Mesopotamia have documented water disputes.

• The Romans decree:

• Ne quis aquam oletato dolo malo ubi publice saliet si quis oletarit sestertiorum X mila multa esto.

• It is forbidden to pollute the public water supply; Any deliberate offender shall be punished by a fine of 10,000 sesterces!

Qualitative Understanding

• Near end of 15th century, Leonardo da Vinci and Bernard Palissy independently reached conclusions on the hydrologic cycle - based on a philosophical understanding.

• There was still a lack of quantitative understanding of the hydrologic cycle.

The 17th Century

• Perrault, Mariotte, and Halley began quantitative measurements and applications.

• Perrault measured rainfall and runoff over the seine river drainage basin for ~ 3 years - he illustrated that rainfall WAS adequate in quantity to account for river flows.

• Mariotte gauged the velocity of the flow in the river seine and estimated flows by also estimating river cross sectional areas.

• Halley was an astronomer! He estimated evaporation from the Mediterranean sea and correlated it to river flows into the med, concluding that river flows were sufficient enough to provide that volume of water.

The 18th Century

• Bernoulli - famous for hydraulics and fluid mechanics - the piezometer, the pitot tube, and Bernoulli’s theorem.

• The Chezy formula (channel flow).

The 19th Century

• Hagen-Poiseuille - capillary flow equation.• Darcy’s - flow in porous media.• Duptuit-Thien well formula.• Manning - open channel flow.• Systematic stream gaging.• Mostly empirical in nature.

The 20th Century

– Government agencies began to develop programs – good or bad?

– Rational analysis begins.– Sherman - unit hydrograph theory.– Horton - infiltration theory.– Snyder - unit hydrograph.– Clark - unit hydrograph.– Etc...........

Modern Day

• Very computer and data intensive

• High tech instruments

• Scale issues

• Policy issues

• Etc.................

• “Diamond edge on an old axe”……

Units & Properties of WaterUnits & Properties of Water

Property Symbol Value CommentsDensity

(mass/volume)

~1.94 slugs/ft3

~ 1.0 g/cm3Slug = lb*s2/ft

Specific Weight(weight/volume)

62.4 Lbs/ft3

9.81 kN/m3

g

Specific Volume

Specific Gravity s.g. 1.0 for water@ 32.9o F

s.g.fluid =gfluid/gwater

Vapor Pressure ~0.4 psi Vapor pressure ofthe fluid - not the

atmosphere

The WatershedThe Watershed• A watershedwatershed is an area of land that drains to a single outlet and is separated from other watersheds by a divide. • Every watershed has a drainage areadrainage area.• Related terms: drainage drainage basinbasin, sub-basinsub-basin, sub-areasub-area.

AreaArea

• 1 acre = 43,560 ft2

• 1 mi2 = 640 acres

• 1 hectare = 100m x 100m = 2.471 acres = 10,000 m2

• 1 km2 = 0.386 mi2

VolumeVolume

• 1 acre-foot = 1 ac-ft = 1 acre of water x 1 foot deep = 43,560 x 1 = 43,560 ft3.

• 1 ac-inch = 1 acre x 1 inch deep = 43,560 x 1/12 = 3,630 ft3.

• 1 ft3 = 7.48 gallons.

• 1 gallon H2O ~ 8.34 lbs.

Runoff VolumeRunoff Volume

• 1-inch of runoff over 1 square mile :

• 1/12 feet x 1 mi2 x 640 acres/mi2 x 43,560 ft2/mi2 = 2,323,200 ft3

DischargeDischarge

• 1 cfs = 1 cubic foot per second

• 1 cfs x 7.48 gal/ft3 x 3600 sec/hr x 24 hrs/day = 646,272 gpd = 0.646 MGD

• 1 cfs x 3600 sec/hr x 24 hrs/day = 86,400 cfs/day

• 86,400 cfs/day x 1 ac-ft/43,560 ft3 = 1.983 ac-ft/day (~ 2 ac-ft/day)

• 1.983 ac-ft/day x 12 inches/ft x 1 day/24 hrs = 0.992 ac-in/hr

• 1 ac-in/hr x 43,560 ft3/ac-ft x 1 hr/3600 sec x 1 ft/12 inches = 1.008 cfs

PowerPower

• Hp = HQ/550

• 1 hp = 550 ft*lb/sec = 0.7547 kilowatts

Hydrology TerminologyHydrology Terminology•StreamflowStreamflow is the movement of water through a channel.•The cross-sectional areacross-sectional area of a stream is the region bounded by the walls of the stream and the water surface. The cross-sectional area is illustrated below.•See also Manning’s “n”.Manning’s “n”.

Stream Flow

Cross-sectional Area

Hydrology TerminologyHydrology Terminology•Manning’s “n”Manning’s “n” is a measure of the roughness of a surface, and in streamflow it is the roughness of the channel bottom and it’s sides.

Diagram 2 will have a higher Manning’s “n”Manning’s “n” because it has rougher surface due to the jagged bottom and pebbles.

Diagram 1 Diagram 2

Hydrology TerminologyHydrology Terminology

HydrologicHydrologic HydraulicHydraulic

RoutingRouting

•RoutingRouting is used to account for storage and translation effects.

t

SSOOII

122121 2

1

2

1


0.0000

100.0000

200.0000

300.0000

400.0000

500.0000

600.0000

700.0000

0.0000 1.0000 2.0000 3.0000 4.0000 5.0000 6.0000 7.0000 8.0000 9.0000 10.0000

Generalized effect of routing

Hydrology TerminologyHydrology Terminology• SnowfallSnowfall is a form of precipitation that comes down in white or translucent ice crystals. •SnowmeltSnowmelt is the excess water produced by the melting of snow. This leads to flooding possibilities in the spring when temperatures begin to rise. There is generally a delay in the snowmelt response of a basin due to the melting process and travel times.•SnowpackSnowpack is the amount of annual accumulation at

higher elevations.


•RunoffRunoff is the excess precipitation and is often considered a “fast” response.•Overland flowOverland flow is the flow of water across the land surface.•Sub-surface flowSub-surface flow is the flow of water through the soil layers to the stream.•BaseflowBaseflow is the flow in a channel due to ground water or subsurface supplies. The baseflow is generally increased by precipitation events that produce enough infiltration.


• InfiltrationInfiltration is the movement of water from the surface into the soil.•The rate of infiltration is based on a number of factors, including but not limited to:

•soil types•current conditions•precipitation intensity


•The velocityvelocity of the flow is very dependent on the slope of the stream bottom. The greater the slope the greater the potential velocity of the flow.

•The “wave” speed“wave” speed is the velocity of the flood wave down the channel. The speed of this wave affects how quickly the downstream area will effected.


Energy Grade Line

Hydraulic Grade Line(water surface)

Channel Bottom

headloss

g

v

2

22

g

v

2

21

Elevation Head

Depth1

Depth2

Datum

•The energy grade lineenergy grade line represents the depth of the water surface and the velocity component of the Bernoulli equation. •The hydraulic grade linehydraulic grade line represents the depth of the water surface.

Hydrology TerminologyHydrology Terminology•Karst hydrology Karst hydrology is caused by pores and holes in limestone formations. This increases the infiltration into the limestone, reducing the runoff potential.

•The slopeslope changes the speed of runoff and therefore effects collection times.


•The frequencyfrequency of a storm event is described by its return periodreturn period. For example a two year storm event has a 1 in 2 chance of occurring in any given year.

•The probabilityprobability is also affected by the return period. Thus the probability of a 2 year storm occurring is 50%. The probability of a 100-year

event occurring is 1/100 or 1%

Basin Hydrology

PrecipitationPrecipitation• ... primary "input" for the hydrologic

cycle (or hydrologic budget). • … The patterns of the precipitation are

affected by large scale global patterns, mesoscale patterns, "regional" patterns, and micro-climates.

• … In addition to the quantity of precipitation, the spatial and temporal distributions of the precipitation have considerable effects on the hydrologic response.

SnowSnow• … response mechanisms of snow are at a much slower

time scale than for most of the other forms of precipitation.

• … The melt takes place and the runoff is "lagged" due to the physical travel processes.

• … Items to consider in the snowmelt process are the current "state" of the pack and the snow water equivalent of the snow pack., as well as the melt potential of the current climate conditions.

• … A rain-on-snow event may produce very high runoff rates and is often a difficult situation to predict due to the integral nature of the runoff and melt processes. The timing of these events is often very difficult to predict due to the inherent "lag" in the responses.

Snow HydrologySnow Hydrology

Special Thanks, Credit, and Recognition to Special Thanks, Credit, and Recognition to Don ClineDon Cline

And the And the

National Operational Hydrologic Remote Sensing Center

Why is Snow Important?Why is Snow Important?

Why is Snow Important?Why is Snow Important?

• Water Resources

• Flooding

• Economics

• Transportation


• Understanding and predicting the physical processes of:

• Snow Accumulation

• Ablation

• Melt Water Runoff


• 4 Simultaneous Estimation Problems

– the quantity of water held in snow packs– the magnitude and rate of water lost to the

atmosphere by sublimation– the timing, rate, and magnitude of snow melt– the fate of melt water

Snow Cover DistributionSnow Cover Distribution

Snow Cover DistributionSnow Cover Distribution• Three Spatial Scales

– Macroscale• Areas up to 106 km2

• Characteristic Distances of 10-1000 km• Dynamic meteorologic effects are important

– Mesoscale• Characteristic Distances of 100 m to 10 km• Redistribution of snow along relief features due to wind• Deposition and accumulation of snow may be related to terrain

variables and to vegetation cover– Microscale

• Characteristic Distances of 10 to 100 m• Differences in accumulation result from variations in air flow patterns

and transport

Snow Cover DistributionSnow Cover Distribution• Effect of Topography

– The depth of seasonal snow cover usually increases with elevation if other influencing factors do not vary with elevation

• This trend is generally due to:– increase in the number of snowfall events

– decrease in evaporation and melt

• The rate of increase with elevation may vary widely from year-to-year

– However, elevation alone is not a causative factor in snow cover distribution

• Many other factors must be considered:– slope, aspect, vegetation, wind, temperature, and characteristics of the

parent weather systems

Snow Cover DistributionSnow Cover Distribution• Effect of Vegetation

– Snow falling into a vegetation canopy is influenced by two phenomena:

• Turbulent air flow above and within the canopy

– may lead to variable snow input rates and microscale variation in snow loading on the ground

• Direct interception of snow by the canopy elements

– may either sublimate or fall to the ground

– Processes are related to vegetation type, vegetation density, and the presence of nearby open areas

Snow Cover DistributionSnow Cover Distribution• Forested Environments

– Differences in snow accumulation between different species of conifers is usually small compared to between coniferous and deciduous stands

• coniferous stands are all relatively efficient snow interceptors

• Once intercepted, cohesion between snow particles helps keep snow in the canopy for extended time periods

– snow is more susceptible to sublimation losses in the canopy than on the forest floor

» High surface area to mass ratio

Snow Cover DistributionSnow Cover Distribution• Forested Environments

– Most studies show greater snow accumulation in clearings than in the forest

– Most of the difference develops during storms, not between storms

• redistribution of intercepted snow by wind to clearings is not typically a significant factor

– Interception and subsequent sublimation are the major factors contributing to the difference

20-45%Greater SnowAccumulation


• Open Environments– Over highly exposed terrain, the effects of meso- and micro-

scale differences in vegetation and terrain features may produce wide variations in accumulation patterns.


• Open Environments– Relative accumulation on

various landscapes in an open grassland environment

• Normalized to snow accumulation on level plains under fallow

Landscape RelativeAccumulation

Level Plains Fallow 1.00 Stubble 1.15 Pasture (grazed) 0.60Gradual Hill and Valley Slopes Fallow 1.0 – 1.10 Stubble, hayland 1.0 – 1.10 Pasture (ungrazed) 1.25Steep Hill and Valley Slopes Pasture (ungrazed) 2.85 Brush 4.20Ridge and Hilltops Fallow, ungrazed pasture 0.40 – 0.50 Stubble 0.75Small Shallow Drainageways Fallow, stubble, pasture (ungrazed) 2.0 – 2.15Wide Valley Bottoms Pasture (grazed) 1.30Farm Yards Mixed Trees 2.40

Blowing SnowBlowing Snow

• Sublimation Losses– Snow particles are more exposed to atmosphere during wind transport– Sublimation losses can be very high as a result

• depends on transport rate, transport distance, temperature, humidity, wind speed, and solar radiation

Blowing SnowBlowing Snow

• Sublimation Losses

30

25

252216

225020

Mean Annual Blowing Snow Sublimation

CANADA, 1970-1976Loss in mm SWE over 1 km

Snow Pack CharacteristicsSnow Pack Characteristics


• What is a Snow Pack?– Porous Medium

• ice + air (+ liquid water)

– Generally composed of layers of different types of snow

• more or less homogeneous within one layer

– Ice is in form of crystals and grains that are usually bonded together

• forms a texture with some degree of strength


• Snow Water Equivalent (SWE)– The height of water if a snow cover is

completely melted, on a corresponding horizontal surface area.

• Snow Depth x (Snow Density/Water Density)

Density of Snow CoverDensity of Snow Cover

Snow Type Density (kg/m3)

Wild Snow

Ordinary new snow immediatelyafter falling in still air

Settling Snow

Average wind-toughened snow

Hard wind slab

New firn snow

Advanced firn snow

Thawing firn snow

10 to 30

50 to 65

70 to 90

280

350

400 to 550

550 to 650

600 to 700

Snow Depth for One Inch Water

98” to 33”

20” to 15”

14” to 11”

3.5”

2.8”

2.5” to 1.8”

1.8” to 1.5”

1.6” to 1.4”

Snow Pack CharacteristicsSnow Pack Characteristics• Liquid Water Content

– Wetness, Percentage by volume

Term Remarks

Moist

Wet

Very Wet

Slush

Dry

Approximate RangeUsually T < 0oC, but can occur at any temperature up to 0oC. Little tendency for snow grains to stick together.T = 0oC. The water is not visible even at 10x magnification. Has a distinct tendency to stick together.T = 0oC. The water can be seen at 10x magnification by its miniscus between grains, but cannot be pressed out by squeezing snow (pendular regime).

T = 0oC. The water can be pressed out by squeezing snow, but there is an appreciable amount of air (funicular regime).T = 0oC. The snow is flooded with water and contains a relatively small amount of air.

<3%

3-8%

8-15%

>15%

0%

Snow CharacteristicsSnow Characteristics• Diurnal Temperature Gradients

0 -5 -10

0

20

40

60

80

100

120

140

Temperature (oC)

EveningDay

TemperatureProfile

Snow Surface

Snow Pack

Ground Surface

Water Flow Through Snow

Water Flow through Snow• Wide Range of Flow Velocities

– 2 - 60 cm/min– Depends on several factors

• internal snow pack structure

• condition of the snow pack prior to introduction of water

• amount of water available at the snow surface

Water Flow Through Snow• Flow through Homogeneous

Snow– At melting temperature, a thin film of

water surrounds each snow grain• Much of the water can flow through this

film

– Once pores are filled, laminar flow can occur

• Very efficient mechanism for draining the snow pack

Water Flow through Snow• Four Liquid Water Regimes

• Capillary: < 1% free water– water doesn’t drain due to capillary tension

• Unsaturated: 1-14% free water– water drains by gravity, but air spaces are continuous– Pendular Regime

• Saturated: > 14% free water– water drains by gravity, but air spaces are discontinuous– Funicular Regime

• Melt/Freeze– water melts and refreezes, possible several times, before it drains from

the snow pack

Water Flow Through Snow• Flow through Heterogeneous

Snow– Preferential Flow Paths

• Dye studies reveal vertical channels or macropores in most natural snowpacks

– Ice Layers• Develop from surface melt or refreezing

• Relatively impermeable

• Forces ponding of water and lateral flow

Ice Lens

Water Flow

Ice Lenswith Ponding

Preferential Flow Paths

Water Flow Through Snow• Liquid Water Transmission

Melt and rain water arelagged and attenuated as they move through the snow cover.

Function of depth, density, ice layers, grain size, and refreezing.

122 123 124 125 126 127 128 129 1300

2

4

6

130 131 132 133 134 135 136 137 1380

2

4

6

138 139 140 141 142 143 144 145 1460

2

4

6

146 147 148 149 150 151 152 153 1540

2

4

6

Snow Melt at SurfaceOutflow from Base

Niwot Ridge, ColoradoMay 2-30, 1995

Day of Year

Rain

Snow Measurement

Snow Measurement• Snow Water Equivalent (SWE)

– Ground Observations• Snow Pillows

– SNOTEL Sites (Western U.S.)

• Snow Courses– Transects with snow depth and density

• Snow Tubes– measure volume and mass of snow cores

• Snow Pits– Measure vertical profiles of SWE, and other snow pack

variables.

Snow Measurement• Airborne Snow Survey Program (SWE)

Natural Gamma Sources

238U Series, 232Th Series, 40K SeriesSoil

Snow

Atmosphere

Radon Daughtersin Atmosphere

Cosmic Rays

Uncollided

Gamma RadiationAbsorbed by Waterin the Snow Pack

Gamma Radiationreaches

Detector in Aircraft

Scattering

0

1000

2000

3000

4000

5000

6000

400 800 1200 1600 2000 2400 2800

K40

Tl208

ENERGY (keV)

Background(No Snow)

Over-Snow

Snow Measurement• Satellite Areal Extent of Snow Cover

Snow Measurement• NOAA-16 1.6 Micron Channel

Snow Measurement• NOAA-16 1.6 Micron Channel

Visible Channel 1.6 micron Channel

SNOW

Snake River Valley, Idaho

EvaporationEvaporation• … Evaporation is a process that allows water to

change from its liquid phase to a vapor. • … Hydrologists are mostly interested in the

evaporation from the free water surface of open water or subsurface water exposed via the capillary action; however, precipitation that is intercepted by the vegetative canopy may also be evaporated and may be a significant amount in terms of the overall hydrologic budget.

• … Factors that affect evaporation are temperature, humidity and vapor pressure, radiation, and wind speed.

• … A number of equations are used to estimate evaporation. There are also a number of published tables and maps providing regional estimates of annual evaporation.

TranspirationTranspiration

• … Water may also pass to the atmosphere by being "taken up" by plants and passed on through the plant surfaces.

• … Transpiration varies greatly between plants or crops, climates, and seasons.

• … Evaporation and transpiration are often combined in a term - evapotranspiration.

• … In many areas of the country and during certain seasons evapotranspiration is a major component of the hydrologic budget and a major concern in water supply and yield estimates.

Storage - SurfaceStorage - Surface

• ... Storage - Surface is used to describe the precipitation that reaches the ground surface; however, is not available for runoff or infiltration.

• … It is instead, held in small quantities on the surface in areas, such as the leafy matter and small depressions.

• … In general, surface storage is small and only temporary in terms of the overall hydrologic budget; however, it may have an effect on a storm response as it is effectively "filled" early on a storm event.

InfiltrationInfiltration

• … Soils, depending on current conditions, have a capacity or ability to infiltrate precipitation, allowing water to move from the surface to the subsurface.

• ... "physically based” -> soil porosity, depth of soil column, saturation levels, and soil moisture.

• … The infiltration capacity of the soil column is usually expressed in terms of length per time (i.e. inches per hour).

• … As more water infiltrates, the infiltration generally decreases, thus the amount of water that can be infiltrated during the latter stages of a precipitation event is less than that at the beginning of the event.

Infiltration cont.Infiltration cont.• … Storms that have high intensity levels may

also cause excess precipitation because the intensity (inches per hour) may exceed the current infiltration capacity (inches per hour).

• … periods of low rainfall or no rainfall will allow the soil to "recover" and increase the capacity to infiltrate water.…

• Infiltrated water replenishes soil moisture and groundwater reservoirs. Infiltrated water may also resurface to become surface flow.

• … attempt to account for infiltration by estimating excess precipitation (the difference between precipitation and excess being considered infiltration), for example, the Soil Conservation Service (SCS) runoff curve number method

Subsurface FlowSubsurface Flow

• …water may move via several paths.

• …subsurface flow can be evaporated if there is a well maintained transfer mechanism to the surface. This is particularly true for areas of high ground water table (the free water surface of the groundwater) which is within the limits of the capillary action or transport abilities.

• …Vegetation may also transpire or use the water.

• …The subsurface flow may also continue to move with the groundwater table as a subsurface reservoir, which the natural system uses during periods of low precipitation.

Storage - SubsurfaceStorage - Subsurface

• … The infiltrated water may continue downward in the vertical, may move through subsurface layers in a horizontal fashion, or a combination of the two directions.

• … Movement through the subsurface system is much slower than the surface and thus there are storage delays. The water may also reach an aquifer, where it may be stored for a very long period of time.

RunoffRunoff• … runoff will be used to collectively describe the

precipitation that is not directly infiltrated into the groundwater system.

• … is generally characterized by overland, gully and rill, swale, and channel flows.

• … is that portion of a precipitation event that "quickly" reaches the stream system. The term "quickly" is used with caution as there may be great variability in response times for various flow mechanisms.

• … Runoff producing events are usually thought of as those that saturate the soil column or occur during a period when the soil is already saturated. Thus infiltration is halted or limited and excess precipitation occurs. This may also occur when the intensity rate of the precipitation is greater than the infiltration capacity.

Overland FlowOverland Flow•… Overland flow or surface flow is that precipitation that either fails to penetrate into the soil or that resurfaces at a later point due to subsurface conditions.

•… often referred to as "sheet" flow.

•… for the purposes of this discussion, overland flow (sheet and surface flow, as well) is considered to be the flow that has not had a chance to collect and begin to form gullies, rills, swales

Overland Flow (cont.)Overland Flow (cont.)•… will eventually reach defined channels and the stream system.

•… may also be infiltrated if it reaches an area that has the infiltration capacity to do so.

•… Overland flow distances are rather limited in length - National Engineering Handbook (1972) - overland flow will concentrate into gullies in less than 1000 feet.

•… Other (Seybert, Kibler, and White 1993) recommend a distance of 100 feet or less.

Gullies & RillsGullies & Rills

• ... sheet flow or overland flow will soon concentrate into gullies and rills in the process of flowing towards the stream network. The location of these gullies and rills may vary from storm to storm, depending on storm patterns, intensities, current soil and land use conditions.

SwalesSwales• … swales are of a more constant or permanent

nature.

• … do not vary in location from storm to storm.

• … Swales are a natural part of the landscape or topography that are often more apparent than gullies and rills.

• … Flow conditions and behaviors in swales are very close to that which is seen in channels.

Channel FlowChannel Flow

• … Excess precipitation ultimately reaches the stream channel system.

• … the stream system is generally more defined, it is by no means a constant or permanent entity.

• … The stream bed is constantly changing and evolving via aggredation and degradation.

• … Stream channels convey the waters of the basin to the outlet and into the next basin.

• … attenuation of the runoff hydrograph takes place.

• … Stream channel properties (flow properties) also vary with the magnitude of the flow.

Stream ChannelsStream Channels• … Channels are commonly broken into main

channel areas and overbank areas.

• … overbank areas are often referred to as floodplains.

• … Stream gaging stations are used to determine flows based on elevations in the channel and/or floodplain.

• … Bank full is often thought of as flood stage although more rigorous definitions are more applicable as they pertain to human activity and potential loss of life and property.

• … It is worth noting that the 2-year return interval flow is often thought of as "bank-full".

StreamflowStreamflow• … in the public eye -> the most important aspect

of flooding and hydrology. • … flooding from streams and rivers have the

greatest potential to impact human property and lives; although overland flow flooding, mudslides, and landslides are often just as devastating.

• … Subsurface flow also enters the stream; although in some instances and regions, stream channels lose water to the groundwater table - regardless, this must be accounted for in the modeling of the stream channel.

• … Channels also offer a storage mechanism and the resulting effect is most often an attenuation of the flood hydrograph.

Storage - ReservoirsStorage - Reservoirs• … Lakes, reservoirs, & structures, etc. are given

a separate category in the discussion of the hydrologic cycle due to the potential impact on forecasting procedures and outcomes.

• … provide a substantial storage mechanism and depending on the intended purpose of the structure will have varying impacts on the final hydrograph, as well as flooding levels.

• … This effect can vary greatly depending on the type of reservoir, the outlet configuration, and the purpose of the reservoir.

Storage - Reservoirs (cont.)Storage - Reservoirs (cont.)• … Flood control dams are used to attenuate

and store potentially destructive runoff events.

• … Other structures may have adverse effects. For example, bridges may cause additional "backwater" effects and enhance the level of flooding upstream of the bridge.

• … a catastrophic failure of a structure often has devastating effects on loss of life and property.

Simulating the Hydrologic Simulating the Hydrologic ResponseResponse

Model TypesPrecipitationLossesModeling LossesModel Components

Model TypesModel Types

• Empirical

• Analytical

• Lumped

• Distributed

Model TypesModel TypesPrecipitationLossesModeling LossesModel Components

General Goal of Most Models

Basin Process Representation

Infiltration

Excess Precip.

Interception

Storage

Time Series

Time Series

We must begin to think of the basin as a “whole”

The Basic Process

Excess Precip. Model

Excess Precip.

Excess Precip. Basin “Routing”Runoff

Hydrograph

Runoff Hydrograph

Stream “Routing”

Downstream Hydrograph

From A Basin View

Excess Precip. Model

Excess Precip.

Basin “Routing”

Runoff HydrographStream

“Routing”

Precipitation Input

• Precipitation is generally “pre-processed

• Uniform in space and time – never!

• Gages

• Radar

• satellite

PrecipitationPrecipitation• … magnitude, intensity, location, patterns, and

future estimates of the precipitation.

• … In lumped models, the precipitation is input in the form of average values over the basin. These average values are often referred to as mean aerial precipitation (MAP) values.

• … MAP's are estimated either from 1) precipitation gage data or 2) NEXRAD precipitation fields.

Precipitation (cont.)Precipitation (cont.)• … If precipitation gage data is used, then the

MAP's are usually calculated by a weighting scheme.

• … a gage (or set of gages) has influence over an area and the amount of rain having been recorded at a particular gage (or set of gages) is assigned to an area.

• … Thiessen method and the isohyetal method are two of the more popular methods.

ThiessenThiessen

•Thiessen methodThiessen method is a method for areally weighting rainfall through graphical means.

IsohyetalIsohyetal

•Isohyetal methodIsohyetal method is a method for areally weighting rainfall using contours of equal rainfall (isohyets).

NEXRADNEXRAD

•NexradNexrad is a method of areally weighting rainfall using satellite imaging of

the intensity of the rain during a storm.

Excess Precip. Models

• Physically Based

• Empirical

• Analytical

• Conceptual

• Generally Lumped

LossesLosses

• … modeled in order to account for the destiny of the precipitation that falls and the potential of the precipitation to affect the hydrograph.

• … losses include interception, evapotranspiration, depression storage, and infiltration.

• … Interception is that precipitation that is caught by the vegetative canopy and does not reach the ground for eventual infiltration or runoff.

• … Evapotranspiration is a combination of evaporation and transpiration and was previously discussed.

• … Depression storage is that precipitation that reaches the ground, yet, as the name suggests, is stored in small surface depressions and is generally satisfied during the early portion of a storm event.

Modeling LossesModeling Losses

• … simplistic methods such as a constant loss method may be used.

• … A constant loss approach assumes that the soil can constantly infiltrate the same amount of precipitation throughout the storm event. The obvious weaknesses are the neglecting of spatial variability, temporal variability, and recovery potential.

• Other methods include exponential decays (the infiltration rate decays exponentially), empirical methods, and physically based methods.

• … There are also combinations of these methods. For example, empirical coefficients may be combined with a more physically based equation. (SAC-SMA for example)

SCS Curve NumberSCS Curve Number

0.8S)+(P

)0.2S-(P = Q

2

Estimating “S”Estimating “S”

• The difficult part of applying this method to a watershed is the estimation of the watershed’s potential maximum retention, S.

• SCS developed the concept of the dimensionless curve number, CN, to aid in the estimation of S.

• CN is related to S as follows :

10 - CN

1000 = S

CN ranges from 1 to 100 (not really!)

Determine CNDetermine CN

• The Soil Conservation Service has classified over 8,500 soil series into four hydrologic groups according to their infiltration characteristics, and the proper group is determined for the soil series found.

• The hydrologic groups have been designated as A, B, C, and D.

• Group A is composed of soils considered to have a low runoff potential. These soils have a high infiltration rate even when thoroughly wetted.

• Group B soils have a moderate infiltration rate when thoroughly wetted,

• while group C soils are those which have slow infiltration rates when thoroughly wetted.

• Group D soils are those which are considered to have a high potential for runoff, since they have very slow infiltration rates when thoroughly wetted (SCS, 1972).

Determine CN, cont….Determine CN, cont….

• Once the hydrologic soil group has been determined, the curve number of the site is determined by cross-referencing land use and hydrologic condition to the soil group - SAMPLE

Land use and treatment Hydrologic soil group or Hydrologic practice condition A B C D

FallowStraight row ---- 77 86 91 94Row CropsStraight row Poor 72 81 88 91Straight row Good 67 78 85 89Contoured Poor 70 79 84 88

Initial ConditionsInitial Conditions

5-day antecedent rainfall, inches Antecedent moisture

Dormant Season Growing Season

I Less than 0.5 Less than 1.4

II 0.5 to 1.1 1.4 to 2.1

III Over 1.1 Over 2.1

Adjust CN’sAdjust CN’s

CN for AMC II Corresponding CN’s

AMC I AMC III

100 100 100

95 87 98

90 78 96

85 70 94

80 63 91

75 57 88

70 51 85

65 45 82

60 40 78

55 35 74

50 31 70

Sort of the other end of the Sort of the other end of the scale….scale….

SAC-SMASAC-SMA

• … The Sacramento Soil Moisture Accounting Model (SAC-SMA) is a conceptual model of soil moisture accounting that uses empiricism and lumped coefficients to attempt to mimic the physical constraints of water movement in a natural system.

Tension Free

Tension Free - Primary

Free - Supplemental

Upper Zone

Lower Zone

RunoffRunoff

• … Runoff is essentially the excess precipitation - the precipitation minus the losses.

• … Runoff must be transformed to streamflow at the basin outlet via a unit hydrograph.

• … In actuality, all forms of surface and subsurface flow that reach a stream channel and eventually the outlet are modeled through the use of the unit hydrograph for the general hydrologic model…

126

Unit Hydrograph TheoryUnit Hydrograph Theory

• Sherman - 1932

• Horton - 1933

• Wisler & Brater - 1949 - “the hydrograph of surface runoff resulting from a relatively short, intense rain, called a unit storm”

• The runoff hydrograph may be “made up” of runoff that is generated as flow through the soil (black, 1990)

Linearity of Unit HydrographLinearity of Unit Hydrograph• … In addition, when unit hydrograph theory is applied, it is

assumed that the watershed responds uniformly.

• … Meaning that peak flow from 2 inches of excess will be twice that of 1 inch of excess

0.0000

100.0000

200.0000

300.0000

400.0000

500.0000

600.0000

700.0000

0.0000 0.5000 1.0000 1.5000 2.0000 2.5000 3.0000 3.5000 4.0000

Unit Hydrograph “Lingo”Unit Hydrograph “Lingo”

• Duration

• Lag Time

• Time of Concentration

• Rising Limb

• Recession Limb (falling limb)

• Peak Flow

• Time to Peak (rise time)

• Recession Curve

• Separation

• Base flow

Graphical RepresentationGraphical Representation

Lag time

Time of concentration

Duration of excess precipitation.

Base flow

Methods of Developing UHG’sMethods of Developing UHG’s

• From Streamflow Data

• Synthetically– Snyder– SCS– Time-Area (Clark, 1945)

• “Fitted” Distributions

Unit HydrographUnit Hydrograph

• The hydrograph that results from 1-inch of excess precipitation (or runoff) spread uniformly in space and time over a watershed for a given duration.

• The key points :1-inch of EXCESS precipitationSpread uniformly over space - evenly over the watershedUniformly in time - the excess rate is constant over the time

intervalThere is a given duration

Derived Unit HydrographDerived Unit Hydrograph

0.0000

100.0000

200.0000

300.0000

400.0000

500.0000

600.0000

700.0000

0.00

00

0.16

00

0.32

00

0.48

00

0.64

00

0.80

00

0.96

00

1.12

00

1.28

00

1.44

00

1.60

00

1.76

00

1.92

00

2.08

00

2.24

00

2.40

00

2.56

00

2.72

00

2.88

00

3.04

00

3.20

00

3.36

00

3.52

00

3.68

00

Baseflow

Surface Response


0.0000

100.0000

200.0000

300.0000

400.0000

500.0000

600.0000

700.0000

0.0000 0.5000 1.0000 1.5000 2.0000 2.5000 3.0000 3.5000 4.0000

Total Hydrograph

Surface Response

Baseflow


Rules of Thumb :… the storm should be fairly uniform in nature and the excess precipitation should be equally as uniform throughout the basin. This may require the initial conditions throughout the basin to be spatially similar. … Second, the storm should be relatively constant in time, meaning that there should be no breaks or periods of no precipitation. … Finally, the storm should produce at least an inch of excess precipitation (the area under the hydrograph after

correcting for baseflow).

Deriving a UHG from a StormDeriving a UHG from a Stormsample watershed = 450 mi2sample watershed = 450 mi2

0

5000

10000

15000

20000

25000

0 8 16 24 32 40 48 56 64 72 80 88 96 104

112

120

128

Time (hrs.)

Flo

w (

cfs)

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

Pre

cip

itat

ion

(in

ches

)

Separation of BaseflowSeparation of Baseflow

... generally accepted that the inflection point on the recession limb of a hydrograph is the result of a change in the controlling physical processes of the excess precipitation flowing to the basin outlet.

In this example, baseflow is considered to be a straight line connecting that point at which the hydrograph begins to rise rapidly and the inflection point on the recession side of the hydrograph.

the inflection point may be found by plotting the hydrograph in semi-log fashion with flow being plotted on the log scale and noting the time at which the recession side fits a straight line.

Semi-log PlotSemi-log Plot

1

10

100

1000

10000

100000

29 34 39 44 49 54 59 64 69 74 79 84 89 94 99 104

109

114

119

124

129

134

Time (hrs.)

Flo

w (

cfs)

Recession side of hydrograph becomes linear at approximately hour

64.

Hydrograph & BaseflowHydrograph & Baseflow

0

5000

10000

15000

20000

25000

0 7 14 21 28 35 42 49 56 63 70 77 84 91 98 105

112

119

126

133

Time (hrs.)

Flo

w (

cfs)

Separate BaseflowSeparate Baseflow

0

5000

10000

15000

20000

25000

0 7 14 21 28 35 42 49 56 63 70 77 84 91 98 105

112

119

126

133

Time (hrs.)

Flo

w (

cfs)

Sample CalculationsSample Calculations• In the present example (hourly time step), the flows are summed and

then multiplied by 3600 seconds to determine the volume of runoff in cubic feet. If desired, this value may then be converted to acre-feet by dividing by 43,560 square feet per acre.

• The depth of direct runoff in feet is found by dividing the total volume of excess precipitation (now in acre-feet) by the watershed area (450 mi2 converted to 288,000 acres).

• In this example, the volume of excess precipitation or direct runoff for storm #1 was determined to be 39,692 acre-feet.

• The depth of direct runoff is found to be 0.1378 feet after dividing by the watershed area of 288,000 acres.

• Finally, the depth of direct runoff in inches is 0.1378 x 12 = 1.65 inches.

Obtain UHG OrdinatesObtain UHG Ordinates

• The ordinates of the unit hydrograph are obtained by dividing each flow in the direct runoff hydrograph by the depth of excess precipitation.

• In this example, the units of the unit hydrograph would be cfs/inch (of excess precipitation).

Final UHGFinal UHG

0

5000

10000

15000

20000

25000

0 7 14 21 28 35 42 49 56 63 70 77 84 91 98 105

112

119

126

133

Time (hrs.)

Flo

w (

cfs)

Storm #1 hydrograph

Storm#1 direct runoff hydrograph

Storm # 1 unit hydrograph

Storm #1 baseflow

Determine Duration of UHGDetermine Duration of UHG• The duration of the derived unit hydrograph is found by examining the

precipitation for the event and determining that precipitation which is in excess.

• This is generally accomplished by plotting the precipitation in hyetograph form and drawing a horizontal line such that the precipitation above this line is equal to the depth of excess precipitation as previously determined.

• This horizontal line is generally referred to as the -index and is based on the assumption of a constant or uniform infiltration rate.

• The uniform infiltration necessary to cause 1.65 inches of excess precipitation was determined to be approximately 0.2 inches per hour.

Estimating Excess Precip.Estimating Excess Precip.

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19

Time (hrs.)

Pre

cip

itat

ion

(in

ches

)

Uniform loss rate of 0.2 inches per hour.

Excess PrecipitationExcess Precipitation

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19

Time (hrs.)

Exc

ess

Pre

c. (

inch

es)

Small amounts of excess precipitation at beginning and end may

be omitted.

Derived unit hydrograph is the result of approximately 6 hours

of excess precipitation.

Average Several UHG’sAverage Several UHG’s• It is recommend that several unit hydrographs be derived and averaged.

• The unit hydrographs must be of the same duration in order to be properly averaged.

• It is often not sufficient to simply average the ordinates of the unit hydrographs in order to obtain the final unit hydrograph. A numerical average of several unit hydrographs which are different “shapes” may result in an “unrepresentative” unit hydrograph.

• It is often recommended to plot the unit hydrographs that are to be averaged. Then an average or representative unit hydrograph should be sketched or fitted to the plotted unit hydrographs.

• Finally, the average unit hydrograph must have a volume of 1 inch of runoff for the basin.

One Step Shy of a Full Derivation?

• You could part of the previous analysis for a very useful tool.

• Take a storm

• Plot streamflow

• Determine volume of runoff

• Divide by basin area

• Get depth of runoff

• Estimate total basin (mean) precipiation

• Compare!

• Do this for a variety of storm over a variety of conditions and seasons.

Synthetic UHG’sSynthetic UHG’s

• Snyder

• SCS

• Time-area

SnyderSnyder

• Since peak flow and time of peak flow are two of the most important parameters characterizing a unit hydrograph, the Snyder method employs factors defining these parameters, which are then used in the synthesis of the unit graph (Snyder, 1938).

• The parameters are Cp, the peak flow factor, and Ct, the lag factor.

• The basic assumption in this method is that basins which have similar physiographic characteristics are located in the same area will have similar values of Ct and Cp.

• Therefore, for ungaged basins, it is preferred that the basin be near or

similar to gaged basins for which these coefficients can be determined.

Basic RelationshipsBasic Relationships3.0)( catLAG LLCt

5.5LAG

durationtt

)(25.0 .. durationdurationaltLAGlagalt tttt

83 LAG

baset

t

LAG

ppeak t

ACq

640

What are the L & Lca Doing?

Final ShapeFinal ShapeThe final shape of the Snyder unit hydrograph is controlled by the

equations for width at 50% and 75% of the peak of the UHG:

SCSSCS

SCS Dimensionless UHG Features

0

0.2

0.4

0.6

0.8

1

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5

T/Tpeak

Q/Q

pe

ak

Flow ratios

Cum. Mass

Dimensionless RatiosDimensionless RatiosTime Ratios

(t/tp)Discharge Ratios

(q/qp)Mass Curve Ratios

(Qa/Q)0 .000 .000.1 .030 .001.2 .100 .006.3 .190 .012.4 .310 .035.5 .470 .065.6 .660 .107.7 .820 .163.8 .930 .228.9 .990 .300

1.0 1.000 .3751.1 .990 .4501.2 .930 .5221.3 .860 .5891.4 .780 .6501.5 .680 .7001.6 .560 .7511.7 .460 .7901.8 .390 .8221.9 .330 .8492.0 .280 .8712.2 .207 .9082.4 .147 .9342.6 .107 .9532.8 .077 .9673.0 .055 .9773.2 .040 .9843.4 .029 .9893.6 .021 .9933.8 .015 .9954.0 .011 .9974.5 .005 .9995.0 .000 1.000

Triangular RepresentationTriangular RepresentationSCS Dimensionless UHG & Triangular Representation

0

0.2

0.4

0.6

0.8

1

1.2

0.0 1.0 2.0 3.0 4.0 5.0

T/Tpeak

Q/Q

pea

k

Flow ratios

Cum. Mass

Triangular

Excess Precipitation

D

Tlag

Tc

TpTb

Point of Inflection

Triangular RepresentationTriangular Representationpb T x 2.67 T

ppbr T x 1.67 T - T T

)T + T( 2

q =

2

Tq +

2

Tq = Q rp

prppp

T + T

2Q = q

rpp

T + T

Q x A x 2 x 654.33 = q

rpp

The 645.33 is the conversion used for delivering 1-inch of runoff (the area under the unit hydrograph) from 1-square

mile in 1-hour (3600 seconds). T

Q A 484 = q

pp

SCS Dimensionless UHG & Triangular Representation

0

0.2

0.4

0.6

0.8

1

1.2

0.0 1.0 2.0 3.0 4.0 5.0

T/Tpeak

Q/Q

pea

k

Flow ratios

Cum. Mass

Triangular

Excess Precipitation

D

Tlag

Tc

TpTb

Point of Inflection

484 ?484 ?

Comes from the initial assumption that 3/8 of the volume under the UHG is under the rising limb and the remaining 5/8

is under the recession limb.

General Description Peaking Factor Limb Ratio (Recession to Rising)

Urban areas; steep slopes 575 1.25 Typical SCS 484 1.67

Mixed urban/rural 400 2.25 Rural, rolling hills 300 3.33 Rural, slight slopes 200 5.5

Rural, very flat 100 12.0

T

Q A 484 = q

pp

Time of ConcentrationTime of Concentration

• Regression Eqs.

• Segmental Approach

A Regression EquationA Regression Equation

TlagL S

Slope

08 1 0 7

1900 05

. ( ) .

(% ) .

where : Tlag = lag time in hoursL = Length of the longest drainage path in feetS = (1000/CN) - 10 (CN=curve number)%Slope = The average watershed slope in %

Segmental ApproachSegmental Approach

• More “hydraulic” in nature

• The parameter being estimated is essentially the time of concentration or longest travel time within the basin.

• In general, the longest travel time corresponds to the longest drainage path

• The flow path is broken into segments with the flow in each segment being represented by some type of flow regime.

• The most common flow representations are overland, sheet, rill and

gully, and channel flow.

A Basic ApproachA Basic Approach 2

1

kSV

McCuen (1989) and SCS (1972) provide values of k for several flow situations

(slope in %)

K Land Use / Flow Regime

0.25 Forest with heavy ground litter, hay meadow (overland flow)0.5 Trash fallow or minimum tillage cultivation; contour or strip

cropped; woodland (overland flow)0.7 Short grass pasture (overland flow)0.9 Cultivated straight row (overland flow)1.0 Nearly bare and untilled (overland flow); alluvial fans in

western mountain regions1.5 Grassed waterway2.0 Paved area (sheet flow); small upland gullies

Flow Type KSmall Tributary - Permanent or intermittent

streams which appear as solid or dashedblue lines on USGS topographic maps.

2.1

Waterway - Any overland flow route whichis a well defined swale by elevation

contours, but is not a stream section asdefined above.

1.2

Sheet Flow - Any other overland flow pathwhich does not conform to the definition of

a waterway.

0.48

Sorell & Hamilton, 1991

Time-AreaTime-Area

Time-AreaTime-Area

Time

Q % Area

Time

100%

Timeof conc.

Time-AreaTime-Area

Hypothetical ExampleHypothetical Example

• A 190 mi2 watershed is divided into 8 isochrones of travel time.

• The linear reservoir routing coefficient, R, estimated as 5.5 hours.

• A time interval of 2.0 hours will be used for the computations.

WatershedBoundary

Isochrones

2

345

66

7

8

6

6

5

7

7

1

0

Rule of ThumbRule of Thumb

R - The linear reservoir routing coefficient can be estimated as approximately 0.75

times the time of concentration.

Basin BreakdownBasin Breakdown

MapArea #

BoundingIsochrones

Area(mi2)

CumulativeArea (mi2)

CumulativeTime (hrs)

1 0-1 5 5 1.02 1-2 9 14 2.03 2-3 23 37 3.04 3-4 19 58 4.05 4-5 27 85 5.06 5-6 26 111 6.07 6-7 39 150 7.08 7-8 40 190 8.0

TOTAL 190 190 8.0

WatershedBoundary

Isochrones

2

345

66

7

8

6

6

5

7

7

1

0

Incremental AreaIncremental Area

0

5

10

15

20

25

30

35

40

Incr

emen

tal

Are

a (s

qau

re m

iles

)

1 2 3 4 5 6 7 8

Time Increment (hrs)

WatershedBoundary

Isochrones

2

345

66

7

8

6

6

5

7

7

1

0

Cumulative Time-Area CurveCumulative Time-Area Curve

0

1

2

3

4

5

6

7

8

9

0 20 40 60 80 100 120 140 160 180 200

Time (hrs)

Cu

mu

lati

ve A

rea

(sq

aure

mil

es)

WatershedBoundary

Isochrones

2

345

66

7

8

6

6

5

7

7

1

0

Trouble Getting a Time-Area Trouble Getting a Time-Area Curve?Curve?

0.5) Ti (0for 414.1 5.1 ii TTA

1.0) Ti (0.5for )1(414.11 5.1 ii TTA

Synthetic time-area curve - The U.S. Army Corps of Engineers (HEC 1990)

Instantaneous UHGInstantaneous UHG)1(

)1( iii

IUHccIIUH

tR

tc

2

2

t = the time step used n the calculation of the translation unit hydrograph

The final unit hydrograph may be found by averaging 2 instantaneous unit hydrographs that are a t time step apart.

ComputationsComputationsTime(hrs)

(1)

Inc.Area(mi2)(2)

Inc.TranslatedFlow (cfs)

(3)

Inst. UHG

(4)

IUHGLagged 2

hours(5)

2-hrUHG(cfs)(6)

0 0 0 0 02 14 4,515 1391 0 7004 44 14,190 5333 1,391 3,3606 53 17,093 8955 5,333 7,1508 79 25,478 14043 8,955 11,50010 0 0 9717 14,043 11,88012 6724 9,717 8,22014 4653 6,724 5,69016 3220 4,653 3,94018 2228 3,220 2,72020 1542 2,228 1,89022 1067 1,542 1,30024 738 1,067 90026 510 738 63028 352 510 43030 242 352 30032 168 242 20034 116 168 14036 81 116 10038 55 81 7040 39 55 5042 26 39 3044 19 26 2046 13 19 2048 13

Incremental AreasIncremental Areas

0

10

20

30

40

50

60

70

80

90

0 2 4 6 8 10

Time Increments (2 hrs)

Are

a In

crem

ents

(sq

uar

e m

iles

)

Incremental FlowsIncremental Flows

0

5000

10000

15000

20000

25000

30000

1 2 3 4 5 6

Time Increments (2 hrs)

Tra

nsl

ated

Un

it H

ydro

gra

ph

Instantaneous UHGInstantaneous UHG

0

2000

4000

6000

8000

10000

12000

14000

16000

0 10 20 30 40 50 60

Time (hrs)

Flo

w (

cfs/

inch

)

Lag & AverageLag & Average

0

2000

4000

6000

8000

10000

12000

14000

16000

0 10 20 30 40 50 60

Time (hrs)

Flo

w (

cfs/

inch

)

Let’s talk about Modeling IssuesLet’s talk about Modeling Issues

Weaknesses, strengths, etc…Weaknesses, strengths, etc…

Factors Affecting the Factors Affecting the Hydrologic ResponseHydrologic Response

• Current Conditions• Precipitation Patterns• Land Use• Channel Changes• Others…..

Channel ChangesChannel Changes

• Slopes• Storage• Rating Curve

Variable Source Area ConceptVariable Source Area Concept

Not all of the watershed is contributing during an event......

ExampleExample

And so on...And so on...

And the recession...And the recession...

Small Basin HydrologySmall Basin Hydrology

and and

Distributed ModelsDistributed Models

Why do we need Why do we need DISTRIBUTED MODELS?DISTRIBUTED MODELS?

Non-homogeneity!Non-homogeneity!

Causes of Non-homogeneityCauses of Non-homogeneity

• Small scale precipitationSmall scale precipitation

• Spatially diverse precipitation patternsSpatially diverse precipitation patterns

• Small scale basin changes – i.e. soil Small scale basin changes – i.e. soil moisture, slope, etc….moisture, slope, etc….

• Sub-basin changes – urbanizationSub-basin changes – urbanization

• Others????Others????


•Precipitation can fall in many different patterns, Precipitation can fall in many different patterns, which influences the hydrologic response.which influences the hydrologic response.

•For example, a storm may be:For example, a storm may be:•Uniform over the entire watershedUniform over the entire watershed•A storm may move up the watershedA storm may move up the watershed•A storm may move down the watershedA storm may move down the watershed•A storm may only rain on a portion of A storm may only rain on a portion of the watershed. the watershed.

ApproachesApproaches

• Many sub-basins – at least more than you Many sub-basins – at least more than you currently have…currently have…

• Hillslope processesHillslope processes

• TIN’sTIN’s

• Grids - rasterGrids - raster

Common with LumpedCommon with Lumped

• Still must compute excessStill must compute excess

• Can still use empirical, analytical, Can still use empirical, analytical, conceptual, etc….conceptual, etc….

ComputationallyComputationally

• Huge demands computationallyHuge demands computationally

• Must now keep track of flow, precip, Must now keep track of flow, precip, moisture, etc.. On hundreds to thousands moisture, etc.. On hundreds to thousands of pixels, sub-basins, etc….of pixels, sub-basins, etc….

Moving water off basinMoving water off basin

• Lumped we tended to use the UHGLumped we tended to use the UHG

• Now we tend to be more physically Now we tend to be more physically based:based:– Hydraulic equationHydraulic equation– Hydrologic routingHydrologic routing– Etc….Etc….

Documents

COMET University Faculty Hydrometeorology Course June 2000 Dennis L. Johnson