Title: Hydrograph Modeling
1Hydrograph Modeling
- Goal Simulate the shape of a hydrograph given a
known or designed water input (rain or snowmelt)
2Hydrograph Modeling The input signal
- Hyetograph can be
- A future design event
- What happens in response to a rainstorm of a
hypothetical magnitude and duration - See http//hdsc.nws.noaa.gov/hdsc/pfds/
- A past storm
- Simulate what happened in the past
- Can serve as a calibration data set
3Hydrograph Modeling The Model
- What do we do with the input signal?
- We mathematically manipulate the signal in a way
that represents how the watershed actually
manipulates the water - Q f(P, landscape properties)
4Hydrograph Modeling
- What is a model?
- What is the purpose of a model?
- Types of Models
- Physical
- http//uwrl.usu.edu/facilities/hydraulics/projects
/projects.html - Analog
- Ohms law analogous to Darcys law
- Mathematical
- Equations to represent hydrologic process
5Types of Mathematical Models
- Process representation
- Physically Based
- Derived from equations representing actual
physics of process - i.e. energy balance snowmelt models
- Conceptual
- Short cuts full physics to capture essential
processes - Linear reservoir model
- Empirical/Regression
- i.e temperature index snowmelt model
- Stochastic
- Evaluates historical time series, based on
probability - Spatial representation
- Lumped
- Distributed
6Hydrograph Modeling
- Physically Based, distributed
Physics-based equations for each process in each
grid cell
See dhsvm.pdf Kelleners et al., 2009
Pros and cons?
7Hydrologic ModelingSystems Approach
A transfer function represents the lumped
processes operating in a watershed -Transforms
numerical inputs through simplified paramters
that lump processes to numerical
outputs -Modeled is calibrated to obtain proper
parameters -Predictions at outlet only -Read 9.5.1
P
Mathematical Transfer Function
Q
t
t
8Integrated Hydrologic Models Are Used to
Understand and Predict (Quantify) the Movement of
Water
How ? Formalization of hydrologic process
equations
Distributed Model
Semi-Distributed Model
Lumped Model
e.g Stanford Watershed Model
e.g ModHMS, PIHM, FIHM, InHM
e.g HSPF, LASCAM
Process Representation
Predicted States Resolution
Data Requirement
Computational Requirement
9Transfer Functions
- 2 Basic steps to rainfall-runoff transfer
functions - 1. Estimate losses.
- W minus losses effective precipitation (Weff)
(eqns 9-43, 9-44) - Determines the volume of streamflow response
- 2. Distribute Weff in time
- Gives shape to the hydrograph
Recall that Qef Weff
Event flow (Weff)
Base Flow
10Transfer Functions
Task Draw a line through the hyetograph
separating loss and Weff volumes (Figure 9-40)
W
Weff Qef
W
?
Losses
t
11Loss Methods
- Methods to estimate effective precipitation
- You have already done it one wayhow?
- However,
12Loss Methods
- Physically-based infiltration equations
- Chapter 6
- Green-ampt, Richards equation, Darcy
- Kinematic approximations of infiltration and
storage
Exponential Weff(t) W0e-ct c is unique to
each site
W
Uniform Werr(t) W(t) - constant
13Examples of Transfer Function Models
- Rational Method (p443)
- qpkurCrieffAd
- No loss method
- Duration of rainfall is the time of concentration
- Flood peak only
- Used for urban watersheds (see table 9-10)
- SCS Curve Number
- Estimates losses by surface properties
- Routes to stream with empirical equations
14SCS Loss Method
- SCS curve (page 445-447)
- Calculates the VOLUME of effective precipitation
based on watershed properties (soils) - Assumes that this volume is lost
15SCS Concepts
- Precipitation (W) is partitioned into 3 fates
- Vi initial abstraction storage that must be
satisfied before event flow can begin - Vr retention W that falls after initial
abstraction is satisfied but that does not
contribute to event flow - Qef Weff event flow
- Method is based on an assumption that there is a
relationship between the runoff ratio and the
amount of storage that is filled - Vr/ Vmax. Weff/(W-Vi)
- where Vmax is the maximum storage capacity of the
watershed - If Vr W-Vi-Weff,
16SCS Concept
- Assuming Vi 0.2Vmax (??)
- Vmax is determined by a Curve Number
17Curve Number
The SCS classified 8500 soils into four
hydrologic groups according to their infiltration
characteristics
18Curve Number
19Transfer Function
- 1. Estimate effective precipitation
- SCS method gives us Weff
- 2. Estimate temporal distribution
Volume of effective Precipitation or event flow
-What actually gives shape to the hydrograph?
20Transfer Function
- 2. Estimate temporal distribution of effective
precipitation - Various methods route water to stream channel
- Many are based on a time of concentration and
many other rules - SCS method
- Assumes that the runoff hydrograph is a triangle
On top of base flow
Tw duration of effective P Tc time
concentration
Q
How were these equations developed?
Tb2.67Tr
t
21Transfer Functions
- Time of concentration equations attempt to relate
residence time of water to watershed properties - The time it takes water to travel from the
hydraulically most distant part of the watershed
to the outlet - Empically derived, based on watershed properties
Once again, consider the assumptions
22Transfer Functions
- 2. Temporal distribution of effective
precipitation - Unit Hydrograph
- An X (1,2,3,) hour unit hydrograph is the
characteristic response (hydrograph) of a
watershed to a unit volume of effective water
input applied at a constant rate for x hours. - 1 inch of effective rain in 6 hours produces a 6
hour unit hydrograph
23Unit Hydrograph
- The event hydrograph that would result from 1
unit (cm, in,) of effective precipitation
(Weff1) - A watershed has a characteristic response
- This characteristic response is the model
1
Qef
1
t
24Unit Hydrograph
- How do we Develop the characteristic response
for the duration of interest the transfer
function ? - Empirical page 451
- Synthetic page 453
- How do we Apply the UH?
- For a storm of an appropriate duration, simply
multiply the y-axis of the unit hydrograph by the
depth of the actual storm (this is based
convolution integral theory)
25Unit Hydrograph
- Apply For a storm of an appropriate duration,
simply multiply the y-axis of the unit hydrograph
by the depth of the actual storm. - See spreadsheet example
- Assumes one burst of precipitation during the
duration of the storm
In this picture, what duration is 2.5 hours
Referring to? Where does 2.4 come from?
26- What if storm comes in multiple bursts?
- Application of the Convolution Integral
- Convolves an input time series with a transfer
function to produce an output time series
U(t-t) time distributed Unit Hydrograph Weff(t)
effective precipitation t time lag between
beginning time series of rainfall excess and the
UH
27- Convolution integral in discrete form
Jn-i1
28Unit Hydrograph
- Many ways to manipulate UH for storms of
different durations and intensities - S curve, instantaneous
- Thats for an engineering hydrology class
- YOU need to know assumptions of the application
29Unit Hydrograph
- How do we derive the characteristic response
(unit hydrograph)? - Empirical
30Unit Hydrograph
- How do we derive the characteristic response
(unit hydrograph)? - Empirical page 451
- Note 1. approximately equal duration
- What duration are they talking about?
- Note 8. adjust the curve until this area is
satisfactorily close to 1unit - See spreadsheet example
31Unit Hydrograph
- Assumptions
- Linear response
- Constant time base
32Unit Hydrograph
- Construction of characteristic response by
synthetic methods - Scores of approaches similar to the SCS
hydrograph method where points on the unit
hydrograph are estimated from empirical relations
to watershed properties. - Snyder
- SCS
- Clark
33Snyder Synthetic Unit Hydrograph
- 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.
The final shape of the Snyder unit hydrograph is
controlled by the equations for width at 50 and
75 of the peak of the UHG
34SCS Synthetic Unit Hydrograph
Triangular Representation
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).
35Synthetic Unit Hydrograph
- ALL are based on the assumption that runoff is
generated by overland flow - What does this mean with respect to our
discussion about old water new water? - How can Unit Hydrographs, or any model, possibly
work if the underlying concepts are incorrect?
36Other Applications
- What to do with storms of different durations?
37Other Applications
- Deriving the 1-hr UH with the S curve approach
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