hydrology september 13, 1999 dr. arthur c. miller penn state university

HYDROLOGYSeptember 13, 1999

Dr. Arthur C. Miller

Penn State University

OutlineOutline Introductions Goals of this Course Overview of the Hydrologic Cycle Defining a Watershed Watershed Reponses Modeling the Watershed Response

- Unit Hydrographs

- Precipitation

- Excess Precipitation

- Convolution

- Routing

Regression Equations Wrap-up

Purpose of the Hydrology CoursePurpose of the Hydrology Course

• Increase participants understanding of the Hydrologic Cycle

• Introduce participants to basic terminology and concepts of hydrology and hydrologic forecasting as applied watershed response.

• Establish the course objectives as per the expectations of the participants.

In the end, it is intended that participants will have a better understanding of the

hydrologic response of a watershed, the assumptions in the process, and the

responsibilities associated with interpreting and issuing a hydrologic

analysis.

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)

Units ??

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

AreaArea Volume Runoff Volume Discharge

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.

• 1 m3

Area VolumeVolume Runoff Volume Discharge

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

Area Volume Runoff VolumeRunoff Volume Discharge

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

Area Volume Runoff Volume DischargeDischarge

Hydrologic CycleHydrologic CycleTopicsPrecipitationEvaporationTranspirationStorage-surfaceInfiltrationStorage - SubsurfaceRunoffWater MovementStreamflowStorage-Reservoirs

PrecipitationPrecipitation• ... primary "input"

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

• … Knowing and understanding the general, regional, and local precipitation patterns greatly aids forecasters in determining QPF values.

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

PrecipitationPrecipitation -SnowEvaporationTranspirationStorage-surfaceInfiltrationStorage - SubsurfaceRunoffWater MovementStreamflowStorage-Reservoirs

SnowSnow• ... nature of the modeling efforts that are required.

• … 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.

PrecipitationPrecipitation -Snow-SnowEvaporationTranspirationStorage-surfaceInfiltrationStorage - SubsurfaceRunoffWater MovementStreamflowStorage-Reservoirs

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.

PrecipitationEvaporationEvaporationTranspirationStorage-surfaceInfiltrationStorage - SubsurfaceRunoffWater MovementStreamflowStorage-Reservoirs

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.

PrecipitationEvaporationTranspirationTranspirationStorage-surfaceInfiltrationStorage - SubsurfaceRunoffWater MovementStreamflowStorage-Reservoirs

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.

PrecipitationEvaporationTranspirationStorage-surfaceStorage-surfaceInfiltrationStorage - SubsurfaceRunoffWater MovementStreamflowStorage-Reservoirs

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.

PrecipitationEvaporationTranspirationStorage-surfaceInfiltrationInfiltration -SubsurfaceStorage - SubsurfaceRunoffWater MovementStreamflowStorage-Reservoirs

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

PrecipitationEvaporationTranspirationStorage-surfaceInfiltrationInfiltration -SubsurfaceStorage - SubsurfaceRunoffWater MovementStreamflowStorage-Reservoirs

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.

PrecipitationEvaporationTranspirationStorage-surfaceInfiltrationInfiltration -Subsurface-SubsurfaceStorage - SubsurfaceRunoffWater MovementStreamflowStorage-Reservoirs

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.

• … In the NWS River Forecast System (RFS), the subsurface storage is represented by imaginary zones or "tanks". These tanks release the stored water at a given or calibrated rate. The released water from the subsurface zones is added to the surface runoff for convolution with the unit hydrograph.

PrecipitationEvaporationTranspirationStorage-surfaceInfiltrationStorage - SubsurfaceRunoffWater MovementStreamflowStorage-Reservoirs

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.

PrecipitationEvaporationTranspirationStorage-surfaceInfiltrationStorage - SubsurfaceRunoffWater MovementStreamflowStorage-Reservoirs

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

PrecipitationEvaporationTranspirationStorage-surfaceInfiltrationStorage - SubsurfaceRunoffWater MovementWater Movement -Overland flow-Overland flow -Gullies and Rills -Swales -Channel Flow -Stream ChannelsStreamflowStorage-Reservoirs

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 100 feet.

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

PrecipitationEvaporationTranspirationStorage-surfaceInfiltrationStorage - SubsurfaceRunoffWater MovementWater Movement -Overland flow-Overland flow -Gullies and Rills -Swales -Channel Flow -Stream ChannelsStreamflowStorage-Reservoirs

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.

PrecipitationEvaporationTranspirationStorage-surfaceInfiltrationStorage - SubsurfaceRunoffWater MovementWater Movement -Overland flow -Gullies and Rills-Gullies and Rills -Swales -Channel Flow -Stream ChannelsStreamflowStorage-Reservoirs

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.

PrecipitationEvaporationTranspirationStorage-surfaceInfiltrationStorage - SubsurfaceRunoffWater MovementWater Movement -Overland flow -Gullies and Rills -Swales-Swales -Channel Flow -Stream ChannelsStreamflowStorage-Reservoirs

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.

PrecipitationEvaporationTranspirationStorage-surfaceInfiltrationStorage - SubsurfaceRunoffWater MovementWater Movement -Overland flow -Gullies and Rills -Swales -Channel Flow-Channel Flow -Stream ChannelsStreamflowStorage-Reservoirs

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".

PrecipitationEvaporationTranspirationStorage-surfaceInfiltrationStorage - SubsurfaceRunoffWater MovementWater Movement -Overland flow -Gullies and Rills -Swales -Channel Flow -Stream Channels-Stream ChannelsStreamflowStorage-Reservoirs

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.

PrecipitationEvaporationTranspirationStorage-surfaceInfiltrationStorage - SubsurfaceRunoffWater MovementStreamflowStreamflowStorage-Reservoirs

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.

PrecipitationEvaporationTranspirationStorage-surfaceInfiltrationStorage - SubsurfaceRunoffWater MovementStreamflowStorage-ReservoirsStorage-Reservoirs

Storage - Reservoirs (cont.)Storage - Reservoirs (cont.)

• … Flood control dams are used to attenuate and store potentially destructive runoff events.

• … Other structures may 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.

PrecipitationEvaporationTranspirationStorage-surfaceInfiltrationStorage - SubsurfaceRunoffWater MovementStreamflowStorage-ReservoirsStorage-Reservoirs

The WatershedThe WatershedWatershedWatershed

•Defining•ContoursContours•Topo mapsTopo maps•Digital DataDigital Data

• A watershedwatershed is an area of land that drains to a single outlet and is separated from other watersheds by a divide.

• Hydrologic analysis and synthesis focus on the watershed.

The WatershedThe WatershedWatershedWatershed -drainage area -drainage basin -sub-basin -sub-area•DefiningDefining•ContoursContours•Topo mapsTopo maps•Digital DataDigital Data•CharacteristicsCharacteristics

•Every watershed has a drainage areadrainage area.• Related terms: drainage basindrainage basin, sub-sub-basinbasin, sub-areasub-area.

Defining a WatershedDefining a WatershedWatershedWatershed•Defining

•delineation•ContoursContours•Topo mapsTopo maps•Digital DataDigital Data•CharacteristicsCharacteristics

• Defining a watershed is generally referred to as delineating the watershed.

• The process involves determining that area within which water would drain to a common point.

• It is often easier to visualize the concept by pretending the ground surface is impermeable like cement.

Defining a WatershedDefining a WatershedWatershedWatershed•Defining•ContoursContours•Topo mapsTopo maps•Digital DataDigital Data•CharacteristicsCharacteristics

Contours are lines of constant elevation.

Contours “point” or “curve” uphill at stream crossings.

Contours (generally) have constant spacing.


• At right, the watershed has been delineated, using the contours, for the indicated watershed outlet.

• The streams/channel sections have also been highlighted within the watershed.


• The most common form of mapping used for delineation are the USGS topographical maps.

• The most common map scale is the 7.5 minute 1:24,000 scale.

Defining a WatershedDefining a WatershedWatershedWatershed•Defining•ContoursContours•Topo mapsTopo maps•Digital DataDigital Data

•GISGIS•DEM’sDEM’s

•CharacteristicsCharacteristics

• The use of electronic or digital data and mapping has become rather common place in the field of hydrology.

• GIS or Geographical Information Systems are used to manage, manipulate, and analyze digital data.

• One of the most common GIS data sets is a Digital Elevation Models or DEM’s.


• There are a VERY large number of watershed characteristics and properties that are used in various aspects of hydrologic analysis and synthesis.

• Many of these characteristics and properties may be somewhat ambiguous in nature and difficult to measure and/or estimate.

• Some of the more common characteristics are :

Watershed CharacteristicsWatershed Characteristics

• AreaArea

• SlopeSlope

• Land UseLand Use

• SoilsSoils

• GeologyGeology

• ClimateClimate

• GeomorphologyGeomorphology

Watershed CharacteristicsWatershed CharacteristicsAreaAreaSlopeSlopeLand UseLand UseSoilsSoilsGeologyGeologyUrbanizationUrbanizationWater bodiesWater bodiesGeomorphologyGeomorphology

Area is measured in units of L2.

Typical units are : acres, square miles, hectares, and square kilometers.

A GIS automatically calculates the area of the watershed as it is delineated.

When a GIS is not used - other methods are used to determine the area.

A plainimeter is a common tool.

The area of the basin is generally thought of as that area that would or could contribute runoff to the outlet of the watershed during a rain event.


The slope is a watershed parameter that may take on several meanings. Recall that slope is rise over run or a measure of the change in elevation with distance.

The slope may be the average slope of the main channel that drains the outlet.

The slope may be the slope of the watershed as defined by the change in elevation from the outlet to the highest point divided by the distance to that point.

A Note on SlopesA Note on Slopes DEM Contours (5m) Slopes (>10%)


Land Use is a critical element in the hydrologic response of a watershed.

The land use may determine the amount of runoff, the timing of the runoff, and the quality of the runoff. Land use may also drive such factors as evaporation, transpiration, and heat fluxes between the earth’s surface and the surrounding atmosphere.

Typical land use classifications may include : forested, agricultural, urban, etc.. There may also be sub-classes of these groups : new growth forest, densely populated urban, row crops, etc…

There are a number of electronic land use data sets or coverages available.

A site visit to the watershed is ALWAYS a good idea.


Soils are also very important in the overall hydrologic cycle, as well as the hydrologic response.

Soils have a variety of properties that are relevant to the hydrologist : infiltration, infiltration capacity, conductivity (horizontal and vertical), % organic,hydrologic soil group, etc..

County, state, and national soil surveys are available for most areas of the country.


The underlying geology has great influences on the infiltration and the ultimate fate of infiltrated water.

Bedrock and depth to bedrock, clay layers, etc.. should be documented.

AS an example, limestone areas are known to have large cracks or openings. These large openings and cavities allow for high infiltration rates and storage, which may result in lower runoff volumes.


Urbanization is given its own category, even though it is essentially a land use or land cover.

Urbanization greatly increases the runoff as the land’s natural ability to infiltrate and retain water has been severely reduced or eliminated all together.

Urbanization not only increases the volume of runoff, but it also “speeds up” the response. This is due to the rapid channelization of the runoff.


The presence of water bodies such as lakes, ponds, dams, and other wetlands may have significant impact on the response of a watershed.

Water bodies have the effect of delaying and storing runoff and this the overall responseis delayed and reduced in timing and peak flow, respectively.

Some water bodies are man-made and may be “controlled” or “regulated”.


Geomorphology is used to describe the stream netwrok that drains the watershed.

Metrics such as width, depth, and slope may be used.

Additionally, measurements of sinuosity (a measure of how “windy” the streams are), as well how many streams there are and how far apart they are may greatly affect the response of a watershed.

Stream density (miles of stream/square mile or drainage area) is another common metric.


A very common descriptor of the geomorphology of a drainage basin is the stream order. One of the most common methods of defining stream order is the Horton stream ordering system.

In this system, a first order stream is an unbranched tributary.

Second order streams occur when two first order streams come together.

A third order stream results from two second order streams, and so on.

When a first and second order stream come togoether, the result is still a second order stream.


Geomorphology is used to describe the stream network that drains the watershed.

Metrics such as width, depth, and slope may be used.

Additionally, measurements of sinuosity (a measure of how “windy” the streams are), as well how many streams there are and how far apart they are may greatly affect the response of a watershed.

Stream density (miles of stream/square mile or drainage area) is another common metric.

The Watershed ResponseThe Watershed Response

Long Term –vs.- Short Long Term –vs.- Short InfiltrationInfiltrationEvapotranspirationEvapotranspirationStorageStorageSubsurface FlowSubsurface FlowSurface RunoffSurface RunoffBaseflow Baseflow The Runoff HydrographThe Runoff Hydrograph


Long Term –vs.- ShortLong Term –vs.- Short InfiltrationInfiltrationEvapotranspirationEvapotranspirationStorageStorageSubsurface FlowSubsurface FlowSurface RunoffSurface RunoffBaseflow Baseflow The Runoff HydrographThe Runoff Hydrograph

Establish your GOALS & NEEDS

Short term => “Event Model”

Long Term => “Continuous”


Long Term –vs.- ShortLong Term –vs.- Short InfiltrationInfiltrationEvapotranspirationEvapotranspirationStorageStorageSubsurface FlowSubsurface FlowSurface RunoffSurface RunoffBaseflow Baseflow The Runoff HydrographThe Runoff Hydrograph

Event Model•A few hours to a few days•Initial conditions - CRITICAL

Continuous•Long Term•Initial Conditions - maintained?

FOCUSFOCUS

Long Term –vs.- Short Long Term –vs.- Short InfiltrationInfiltrationEvapotranspirationEvapotranspirationStorageStorageSubsurface FlowSubsurface FlowSurface RunoffSurface RunoffBaseflowBaseflow The Runoff HydrographThe Runoff Hydrograph

Surface Runoff - Surface Runoff - recallrecall

• Overland

• Gullies & Rills

• Swales

• Stream Channels


BaseflowBaseflow

Long Term –vs.- Short Long Term –vs.- Short InfiltrationInfiltrationEvapotranspirationEvapotranspirationStorageStorageSubsurface FlowSubsurface FlowSurface RunoffSurface RunoffBaseflowBaseflow The Runoff HydrographThe Runoff Hydrograph

• A “slower” response

• For subsurface supplies or storage

• Contribution mostly in long term or “tail” or event.

• May be an inflow or outflow!

The Runoff HydrographThe Runoff Hydrograph


0.0000

100.0000

200.0000

300.0000

400.0000

500.0000

600.0000

700.0000

0.0000

0.1600

0.3200

0.4800

0.6400

0.8000

0.9600

1.1200

1.2800

1.4400

1.6000

1.7600

1.9200

2.0800

2.2400

2.4000

2.5600

2.7200

2.8800

3.0400

3.2000

3.3600

3.5200

3.6800

Baseflow

Surface Response

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.


StreamflowStreamflowRating CurvesRating Curves

Rating CurvesRating Curves


StreamflowStreamflowRating CurvesRating Curves

Rating Curve for a sample watershed

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218

0 2000 4000 6000 8000 10000 12000 14000 16000

Q total (cfs)

Wat

er

Su

rfac

e E

lev

. (ft

)

• Rating curves establish a relationship between depth and the amount of flow in a channel.

Factors Affecting the Factors Affecting the Hydrologic ResponseHydrologic Response

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

hydrology september 13, 1999 dr. arthur c. miller penn state university

Documents

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