The document discusses hydrological modeling, explaining different types of models used to analyze water systems, including conceptual, analog, statistical, and stochastic models. It describes methods like the rational method and SCS curve number method for estimating runoff, highlighting the significance of parameters like time of concentration and flow measurement techniques. Additionally, it covers sources of streamflow, mechanisms that affect streamflow, and the use of hydrographs to visualize flow rates over time.

1. Hydrological modelling
• A hydrologic model is a simplification of a
real-world system (e.g., surface water, soil
water, wetland, groundwater, estuary) that
aids in understanding, predicting, and
managing water resources. Both the flow and
quality of water are commonly studied using
hydrologic models.

2. Conceptual models
• Conceptual models are commonly used to
represent the important components
(e.g., features, events, and processes) that relate
hydrologic inputs to outputs. These components
describe the important functions of the system of
interest, and are often constructed using entities
(stores of water) and relationships between these
entitites (flows or fluxes between stores). The
conceptual model is coupled with scenarios to
describe specific events (either input or outcome
scenarios)

3. • For example, a watershed model could be represented
using tributaries as boxes with arrows pointing toward
a box that represents the main river.
• The conceptual model would then specify the
important watershed features (e.g., land use, land
cover, soils, subsoils, geology, wetlands, lakes),
atmospheric exchanges (e.g., precipitation,
evapotranspiration), human uses (e.g., agricultural,
municipal, industrial, navigation, thermo- and hydro-
electric power generation), flow processes (e.g.,
overland, interflow, baseflow, channel flow), transport
processes (e.g., sediments, nutrients, pathogens), and
events (e.g., low-, flood-, and mean-flow conditions).

4. • Model scope and complexity is dependent on
modeling objectives, with greater detail
required if human or environmental systems
are subject to greater risk. Systems
modeling can be used for building conceptual
models that are then populated using
mathematical relationships.

5. Analog models
• Prior to the advent of computer models, hydrologic
modeling used analog models to simulate flow and
transport systems. Unlike mathematical models that
use equations to describe, predict, and manage
hydrologic systems, analog models use non-
mathematical approaches to simulate hydrology.
• Two general categories of analog models are
common; scale analogs that use miniaturized versions
of the physical system and process analogs that use
comparable physics (e.g., electricity, heat, diffusion) to
mimic the system of interest.

6. Statistical models
• Statistical models are a type of mathematical
model that are commonly used in hydrology
to describe data, as well as relationships
between data. Using statistical methods,
hydrologists develop empirical
relationships between observed variables, find
trends in historical data, or forecast probable
storm or drought events

7. Stochastic models
• These models based on data are black box systems,
using mathematical and statistical concepts to link a
certain input (for instance rainfall) to the model output
(for instance runoff). Commonly used techniques
are regression, transfer functions, neural
networks and system identification. These models are
known as stochastic hydrology models. Data based
models have been used within hydrology to simulate
the rainfall-runoff relationship, represent the impacts
of antecedent moisture and perform real-time control
on systems.

8. Rational Method
• The rational method is appropriate for
estimating peak discharges for small drainage
areas of up to about 200 acres (80 hectares)
with no significant flood storage. The method
provides the designer with a peak discharge
value, but does not provide a time series of
flow nor flow volume.

9. Assumptions and Limitations
• Use of the rational method includes the
following assumptions and limitations:
• The method is applicable if tc for the drainage
area is less than the duration of peak rainfall
intensity.
• The calculated runoff is directly proportional
to the rainfall intensity.
• Rainfall intensity is uniform throughout the
duration of the storm.

10. • The frequency of occurrence for the peak discharge is
the same as the frequency of the rainfall producing
that event.
• Rainfall is distributed uniformly over the drainage area.
• The minimum duration to be used for computation of
rainfall intensity is 10 minutes. If the time of
concentration computed for the drainage area is less
than 10 minutes, then 10 minutes should be adopted
for rainfall intensity computations.
• The rational method does not account for storage in
the drainage area. Available storage is assumed to be
filled.

11. Rational Method

12. • Procedure for using the Rational Method
• The rational formula estimates the peak rate
of runoff at a specific location in a watershed
as a function of the drainage area, runoff
coefficient, and mean rainfall intensity for a
duration equal to the time of concentration.
The rational formula is:

14. • Where:
• Q = maximum rate of runoff (cfs or m3/sec.)
• C = runoff coefficient
• I = average rainfall intensity (in./hr. or mm/hr.)
• A = drainage area (ac or ha)
• Z = conversion factor, 1 for English, 360 for
metric

15. Rainfall Intensity
• The rainfall intensity (I) is the average rainfall
rate in in./hr. for a specific rainfall duration
and a selected frequency. The duration is
assumed to be equal to the time of
concentration. For drainage areas in Texas,
you may compute the rainfall intensity using
Equation 4-21, which is known as a rainfall
intensity-duration-frequency (IDF) relationship
(power-law model).

16. Runoff Coefficients
• Urban Watersheds
• Table 4-10 suggests ranges of C values for
urban watersheds for various combinations of
land use and soil/surface type. This table is
typical of design guides found in civil
engineering texts dealing with hydrology.

17. Table 4-10: Runoff Coefficients for Urban Watersheds
Type of drainage area Runoff coefficient
Business:
Downtown areas 0.70-0.95
Neighborhood areas 0.30-0.70
Residential:
Single-family areas 0.30-0.50
Multi-units, detached 0.40-0.60
Multi-units, attached 0.60-0.75
Suburban 0.35-0.40
Apartment dwelling areas 0.30-0.70
Industrial:
Light areas 0.30-0.80
Heavy areas 0.60-0.90
Parks, cemeteries 0.10-0.25
Playgrounds 0.30-0.40
Railroad yards 0.30-0.40
Unimproved areas:
Sand or sandy loam soil, 0-3% 0.15-0.20
Sand or sandy loam soil, 3-5% 0.20-0.25
Black or loessial soil, 0-3% 0.18-0.25
Black or loessial soil, 3-5% 0.25-0.30
Black or loessial soil, > 5% 0.70-0.80
Deep sand area 0.05-0.15
Steep grassed slopes 0.70
Lawns:
Sandy soil, flat 2% 0.05-0.10
Sandy soil, average 2-7% 0.10-0.15
Sandy soil, steep 7% 0.15-0.20
Heavy soil, flat 2% 0.13-0.17
Heavy soil, average 2-7% 0.18-0.22
Heavy soil, steep 7% 0.25-0.35
Streets:
Asphaltic 0.85-0.95
Concrete 0.90-0.95
Brick 0.70-0.85
Drives and walks 0.75-0.95
Roofs 0.75-0.9

18. Time of concentration
• Time of concentration is a concept used in
hydrology to measure the response of a
watershed to a rain event. It is defined as
the time needed for water to flow from the
most remote point in a watershed to the
watershed outlet. It is a function of the
topography, geology, and land use within the
watershed.

19. • Time of concentration is useful in predicting flow
rates that would result from hypothetical storms,
which are based on statistically derived return
periods through IDF curves. For many (often
economic) reasons, it is important for engineers
and hydrologists to be able to accurately predict
the response of a watershed to a given rain
event. This can be important for infrastructure
development (design of bridges, culverts, etc.)
and management, as well as to assess flood
risk such as the ARkStorm-scenario.

21. • This image shows the basic principle which leads
to determination of the time of concentration.
Much like a topographic map showing lines of
equal elevation, a map with isolines can be
constructed to show locations with the same
travel time to the watershed outlet. In this
simplified example, the watershed outlet is
located at the bottom of the picture with a
stream flowing through it. Moving up the map,
we can say that rainfall which lands on all of the
places along the first yellow line will reach the
watershed outlet at exactly the same time.

22. • This is true for every yellow line, with each
line further away from the outlet
corresponding to a greater travel time for
runoff traveling to the outlet.
• Furthermore, as this image shows, the spatial
representation of travel time can be
transformed into a cumulative distribution
plot detailing how travel times are distributed
throughout the area of the watershed.

23. SCS Curve Number Method
• The SCS curve number method is a simiple,
widely used and efficient method for
determining the approxient amount of runoff
from a rainfall even in a particular area.
Although the method is designed for a single
storm event, it can be scaled to find average
annual runoff values.

24. • The stat requirments for this method are very
low, rainfall amount and curve number. The
curve number is based on the area's
hydrologic soil group, land use , treatment and
hydrologic condition. The 2 former being of
greatest importance.

26. • The initial equation (1) is based on trends
observed in data from collected sites,
therefore it is an emperical equation instead
of a physically based equation. After further
empirical evaulation of the trends in the data
base, the initial abstractions, Ia, could be
defined as a percentage of S (2).

27. • With this assumption, the equation (3) could
be written in a more simplified form with only
3 variables. The parameter CN is a
transformation of S, and it is used to make
interpolating, averaging, and weighting
operations more linear (4).

28. • With the following chart, the amount of runoff
can be found if the rainfall amount (in inches) and
curve number is known.
• There are two advantages of using L-THIA over a
manual method. One, the availablity of the data.
L-THIA provides the rainfall data for any area in
the United States. Two, L-THIA completes this
caluculation for every rainfall event for thirty
years and then reports the average annual runoff
value.

29. Time area Method
• Time-area unit hydrograph theory establishes
a relationship between the travel time and a
portion of a basin that may contribute runoff
during that travel time. The area closest to the
basin outlet will contribute to the final runoff
hydrograph much sooner than the areas on
the basin boundary.

30. • In applying this method, the watershed is
traditionally broken into areas of
approximately travel time. These lines of
equal travel time are known as isochrones.
Figure 1 illustrates the breaking of a
watershed into areas by isochrones. The mean
travel time of each sub-area is calculated and
the resulting time-area curve is produced.

32. • Most of the "time-area" methods utilize a
common, basic approach in determining the
final unit hydrograph. The cumulative time-
area curve is formed by summing the
incremental areas (6 in Figure 1) and the
corresponding travel times.

33. • Thus, the total time can be thought of as the
time of concentration of the watershed with
100% of the basin area being accounted for at
the time of concentration. Each of the partial
areas (between isochrones) responds in the
time associated with that area.

34. • Therefore; the cumulative time-area curve is a
summation of the individual areas. The
contributions of the individual areas can be
illustrated with a histogram. One can visualize
a uniform depth of water (1" for a unit
hydrograph) on each of the zones within the
isochrones.

35. • The volume of water of each area reaches the
outlet at the travel time associated with that
area. This is effectively a volume over a time
period, which is a flow. Figure 2 illustrates
a time-discharge histogram associated with
the hypothetical basin of Figure 1.

37. • The time-area histogram is really
a translation hydrograph because the volume
of water on each area within the basin is
simply "translated" to the outlet using the
associated travel time for the translation time.
A this point a unit hydrograph (in discrete
form) exists.

38. • This "instantaneous" unit hydrograph is the
result of 1-inch of instantaneous excess
precipitation being placed on the individual
areas and then translated to the outlet of the
basin, arriving at the time associated with the
travel time of area.

39. STREAM FLOW HYDROGRAPH
• Streamflow, or channel runoff, is the flow
of water in streams, rivers, and other channels,
and is a major element of the water cycle. It is
one component of the runoff of water from the
land to waterbodies, the other component
being surface runoff. Water flowing in channels
comes from surface runoff from adjacent
hillslopes, from groundwater flow out of the
ground, and from water discharged from pipes

40. • The discharge of water flowing in a channel is
measured using stream gauges or can be
estimated by the Manning equation. The
record of flow over time is called
a hydrograph. Flooding occurs when the
volume of water exceeds the capacity of the
channel.

41. Sources of streamflow
• Surface and subsurface sources: Stream discharge
is derived from four sources: channel
precipitation, overland flow, interflow, and
groundwater.
• Channel precipitation is the moisture falling
directly on the water surface, and in most
streams, it adds very little to discharge.
Groundwater, on the other hand, is a major
source of discharge, and in large streams, it
accounts for the bulk of the average daily flow.

42. • Groundwater enters the streambed where the
channel intersects the water table, providing a
steady supply of water, termed baseflow,
during both dry and rainy periods.

43. • Because of the large supply of groundwater
available to the streams and the slowness of
the response of groundwater to precipitation
events, baseflow changes only gradually over
time, and it is rarely the main cause of
flooding.

44. • However, it does contribute to flooding by
providing a stage onto which runoff from
other sources is superimposed.

45. • Interflow is water that infiltrates the soil and
then moves laterally to the stream channel in
the zone above the water table. Much of this
water is transmitted within the soil itself,
some of it moving within the horizons. Next to
baseflow, it is the most important source of
discharge for streams in forested lands.
Overland flow in heavily forested areas makes
negligible contributions to streamflow.

46. Mechanisms that cause changes in
streamflow
• Natural mechanisms
• Runoff from rainfall and snowmelt
• Evaporation from soil and surface-water bodies
• Transpiration by vegetation
• Ground-water discharge from aquifers
• Ground-water recharge from surface-water
bodies
• Sedimentation of lakes and wetlands
• Formation or dissipation of glaciers, snowfields,
and permafrost

47. Human-induced mechanisms
• Surface-water withdrawals and transbasin diversions
• River-flow regulation for hydropower and navigation
• Construction,removal, and sedimentation of reservoirs
and stormwater detention ponds
• Stream channelization and levee construction
• Drainage or restoration of wetlands
• Land-use changes such as urbanization that alter rates
of erosion, infiltration, overland flow, or
evapotranspiration
• Wastewater outfalls
• Irrigation wastewater return flow

48. Measurement
• Streamflow is measured as an amount of water
passing through a specific point over time.
• The units used in the United States are cubic feet
per second, while in majority of other
countries cubic meters per second are utilized.
One cubic foot is equal to 0.028 cubic meters.
• There are a variety of ways to measure the
discharge of a stream or canal.
• A stream gauge provides continuous flow over
time at one location for water resource and
environmental management or other purposes

49. • Streamflow values are better indicators than
gage height of conditions along the whole
river. Measurements of streamflow are made
about every six weeks by United States
Geological Survey (USGS) personnel. They
wade into the stream to make the
measurement or do so from a boat, bridge, or
cableway over the stream.

50. • For each streamgaging station, a relation
between gage height and streamflow is
determined by simultaneous measurements
of gage height and streamflow over the
natural range of flows (from very low flows to
floods).

51. • This relation provides the current condition
streamflow data from that station.For
purposes that do not require a continuous
measurement of stream flow over time,
current meters or acoustic Doppler velocity
profilers can be used. For small streams — a
few meters wide or smaller — weirs may be
installed.

52. Hydrograph
• A hydrograph is a graph showing the rate of
flow (discharge) versus time past a specific
point in a river, or other channel or conduit
carrying flow. The rate of flow is typically
expressed in cubic meters or cubic feet per
second (cms or cfs).

53. • It can also refer to a graph showing the
volume of water reaching a particular outfall,
or location in a sewerage network. Graphs are
commonly used in the design of sewerage,
more specifically, the design of surface
water sewerage systems and combined
sewers.

54. • The discharge is measured at a specific point in a river and is typically time variant.
• Rising limb: The rising limb of hydro graph, also known as concentration curve,
reflects a prolonged increase in discharge from a catchment area, typically in
response to a rainfall event
• Recession (or falling) limb: The recession limb extends from the peak flow rate
onward. The end of stormflow (a.k.a. quickflow or direct runoff) and the return to
groundwater-derived flow (base flow) is often taken as the point of inflection of
the recession limb. The recession limb represents the withdrawal of water from
the storage built up in the basin during the earlier phases of the hydrograph.
• Peak discharge: the highest point on the hydro graph when the rate of discharge is
greatest
• Lag time: the time interval from the center of mass of rainfall excess to the peak of
the resulting hydrograph
• Time to peak: time interval from the start of the resulting hydro graph
• Discharge: the rate of flow (volume per unit time) passing a specific location in a
river or other channel

56. Unit hydrograph
• A unit hydrograph (UH) is the hypothetical
unit response of a watershed (in terms of
runoff volume and timing) to a unit input of
rainfall. It can be defined as the direct runoff
hydrograph (DRH) resulting from one unit
(e.g., one cm or one inch) of effective
rainfall occurring uniformly over that
watershed at a uniform rate over a unit period
of time.

57. • As a UH is applicable only to the direct runoff
component of a hydrograph (i.e., surface runoff), a
separate determination of the baseflow component is
required
• A UH is specific to a particular watershed, and specific
to a particular length of time corresponding to the
duration of the effective rainfall. That is, the UH is
specified as being the 1-hour, 6-hour, or 24-hour UH, or
any other length of time up to the time of
concentration of direct runoff at the watershed outlet.
Thus, for a given watershed, there can be many unit
hydrographs, each one corresponding to a different
duration of effective rainfall.

58. • To be Continued in Next class