Intro to:

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Week 1 639.047
Intro to Mathematical Modeling Basic
Hydrologic/ Hydraulic Concepts HEC software
systems
Loading HMS and DSSVue Touring HMS Running and
viewing a simulation
Hands-on
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Week 2 639.047
HMS Linear reservoirs Unit Hydrographs
Precip Model options Basin Model Options
Basin Model Examples Build our first model from
scratch
Hands-on
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What is a model? A useful simplification of a
complex reality
Abstraction Fidelity
Behavior Mechanism
Whats the goal?
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Abstraction Fidelity
Behavior Mechanism
Art Insight Beauty
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Mathematical Modeling
Abstraction Fidelity
Behavior Mechanism
Table 2-2. What is a mathematical
model? simplified systems that are used to
represent real-life systems and may be
substitutes of the real systems for certain
purposes. The models express mathematically
formalized concepts of the real systems (Diskin,
1970) a symbolic mathematical representation
of an idealized situation that has the important
structural properties of the real system.
(Woolhiser and Brakensiek, 1982) idealized
representationsThey consist of mathematical
relationships that state a theory or hypothesis
(Meta Systems, 1971)
-HMS Technical Reference Model
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Common distinctions made among mathematical
models
Empirical (system theoretic) or Conceptual
(mechanistic/theoretical) This distinction
focuses on the knowledge base upon which
the mathematical models are built. A conceptual
model is built upon a base of knowledge of the
pertinent physical, chemical, and biological
processes that act on the input to produce the
output. An empirical model, on the other hand, is
built upon observation of input and output,
without seeking to represent explicitly
the process of conversion. HEC-HMS includes
both empirical and conceptual models. For
example, Snyders unit hydrograph (UH) model is
empirical the model is fitted with
observed precipitation and runoff. The
kinematic-wave runoff model is conceptual it is
based upon fundamental principles of
shallow free-surface flow.
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Common distinctions made among mathematical
models
Lumped or Distributed A distributed model is
one in which the spatial (geographic) variations
of characteristics and processes are
considered explicitly, while in a lumped model,
these spatial variations are averaged or ignored.
HEC-HMS includes primarily lumped models. The
ModClark model is an exception.
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Common distinctions made among mathematical
models
Event or Continuous This distinction applies
primarily to models of watershed-runoff processes.
An event model simulates a single storm.
The duration of the storm may range from a few
hours to a few days. A continuous model simulates
a longer period, predicting watershed response
both during and between precipitation events.
Most of the models included in HEC-HMS are event
models. But the system is very flexible and can
support continuous simulation via SMA approaches
or external linkages.
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Types of River Models Hydrologic
Hydraulic Load
Biological (Channel Floodplain)
Conservation of Momentum and Mass for solvent and
solutes predicts Conc. transport Over time
Various predicts habitat quality or
Population size Or composition
Conservation of Mass Conservation of Momentum
(energy) predicts Depth, Velocity distributions
over time
Conservation of Mass continuity predicts
Water discharge rate over time
Theory base
WSP HEC-2 HEC-RAS HEC-4 SWMM
HEC-6 SWMM AGNIPSSWAT HEC-RAS BASINS
Rational method HEC-1 HEC-HMS TR-20 TR-55
HSI IFIM RIVPAKS SEM MLR
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Basic Theoretical Concepts
Conservation of Mass Water Balance (Continuity
Equation) Input rate Output rate
dStorage/dt Conservation of Momentum
(Energy)Newtons 2nd Law of Motion
S external forces Mass acceleration

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P precipitation E evaporation T
transpiration R runoff F infiltration G
groundwater flow Q streamflow
Mass balance applied to a hydrologic system
Constructing a water balance equation for a
simple landscape...
Q
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I-O dS (P Gin) - ( T E R Gout Q)
dSlake dSG dSR if Gin, Gout, and Rout
0 P-T-E-Q dST P-ET-Q dST
P precipitation E evaporation T
transpiration R runoff F infiltration G
groundwater flow Q streamflow
ST
Q
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at equilibrium P-ET-Q dS 0 P-ET-Q 0 P
ET Q and Q P - ET
P precipitation E evaporation T
transpiration R runoff F infiltration G
groundwater flow Q streamflow
But what if dS ltgt0? Dynamic simulation
Q
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Basic concepts in storage
For any mass balance including a water balance
d/dt Storage input - output output Q
input - d/dt Storage Storagetotal ò (input -
output) dt
Qin
cfs
Qout
Storage volume
time
i.e. hydrologic storage is caused by time delay
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All hydrographs can be thought of as being shaped
by stormflow passing through a sequential series
of simple storage compartments e.g. catchments,
channels, reservoirs,floodplains...
Approaches to accouting for storage effects
generally fall into 2 groups hydrologic and
hydraulic routing methods
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HEC Software Systems
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HEC has 3 main Integrated nextGEN Modeling
Products and several more recent
Hydrologic Modeling System
HMS Hydrologic Database Manager
DSSVue Floodplain and Channel Hydraulics RAS
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HMS Project Components Basin Model Precipitation
Model Control specification Data Inputs
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Basin Model is built from 7 types of hydrologic
element Subbasin Reach Junctions Reservoi
rs Diversions Sink Source
Each element has one or more alternate Methods
(modeling methods) Basin model gt Elements gt
Methods gt Parameters
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DssVue Main Database Window
Reads and writes .dss files
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Simulations are run from the MainWindow
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Control Specification Window
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Basin Model Window
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639.047 Week 2
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Basic concepts in storage and routing
Mass balance requires
d/dt Storage input - output output Q
input - d/dt Storage Storagetotal ò (input -
output) dt
Qin
cfs
Qout
Storage volume
time
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Basic concepts in storage and routing Mass
balance constraints suggest a simple linear
reservoir model
All hydrographs can be thought of as being shaped
by excess precipitation passing through a
sequential series of simple storage compartments
where storage can be represented by e.g.
catchments gtgtchannelsgtgtreservoirsgtgtfloodplains...
Storagetotal ò (input - output) dt
The number of compartments is arbitrary, and if
a compartment's output is proportional to the the
water is has in storage, then the resulting model
is referred to as a Linear Reservoir Model
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Mass balance constraints suggest water flow
through the Landscape can be represented as a
simple linear reservoir model
for a chain of n compartments d/dt Storagen
inputn outputn d/dt Storagen outputn-1
outputn mass balance assumption outputn kn
Storagen linear rate
assumption
Implies where
n 1.2.3.4.
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Unit Hydrograph Theory UH
D
Obs. Hydrograph
Assumptions DRO hydrographs are linear (i.e.
proportional) and time invariant
DRO Hydrograph
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DRO Hydrograph
Adjust Q to give 1 unit DRO by dividing Q
values by 1/DRO total as depth
Unit Hydrograph
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Because of their assumed linearity... Unit
hydrographs (UH) of short duration can be used to
generate longer duration UH
S-curve Method
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S-curve Method
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Hydrograph Convolution
UHs can also be used to estimate DRO hydrographs
from complex precip events...
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Hydrograph Convolution
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Synthetic unit hydrographs
Methods Snyder SCS Epsey
Empirical relationships for key parameters
Qp Peak Q tp time to peak Q Tr rise
time D precip duration Tr B time base
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Snyders Synthetic Unit Hydrograph method
Qpeak(cfs) 640 Cp AREA(mi2)
tp
Tbase(days) 3 tp/8
tp(hrs) Ct(L Lc )0.3
Cp storage coeff. from .4 to .8 Ct coeff.
ususally 1.8-2.2 0.4-8.0
Lclength along channel to watershed centroid L
length of main stem to divide (ft)
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y average watershed slope L length to divide
(ft)
SCS Synthetic Unit Hydrograph Method
D
tp
Qpeak(cfs) 484 AREA Trise
lag time
Trise(hrs) D tp 2
Qpeak
tp(hrs) L .8 ( S1) .7
1900 y .5
time
Rise time
Fall time
Trise
B
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100 sq mile catchment -2 hrs at 1 in/hr,
uniformly distributed -same but SCS standard storm
No-where River
a
b
c
Can you get it to work? Try first without
channels. How does lumping parameters change
output? How does adding river routing change
output? Use DSSView to compare results
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639.047 Week 3
Adding Reality Event versus Continuous
simulations Lumped versus distributed structure
Linear Reservoir Model
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Continuous versus EventWhats the difference?

• Events short and wet ignore ET and antecedant
  moisure (local water storage) variations
• i.e. a place always has a characteristic unit
  hydrograph
• Continuous really hydrologic response depends on
  existing level of storage in the landscape, and
  that varies between storms with ET rate.

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In SMA Methods Instead of a single I/O reservoir
for each Sub-basin we add reality by
including a series of linear reservoir with
explicit water-balances for each
In HMS requires addition of SMA units (and
parameterizations) To the LOSS and BaseFlow
Models
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Lumped vs.
Distributed
Resolution issues Averaging Error Translation
error
Solution Increase spatial resolution by
disaggregating to more homogeneous units
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• Muskegon River Model
• 41 sub-basins for 2400 sq miles
• (82 external SMA units)
• 41 Groundwater inputs
• Junctions
• 20 explicit river reaches
• 1 sink

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MDEQ Cedar Creek Model 13 sub-basins for 100 sq.
miles 7 explicit river segments 8 junctions 4
reservoirs (pools)
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• Muskegon River Model
• 41 sub-basins for 2400 sq miles
• (82 external SMA units)
• 41 Groundwater inputs
• Junctions
• 20 explicit river reaches
• 1 sink

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Fully distributed Modeling requires a gridded
Approach
HMS handles Gridded Precipitation exte
rnal Hec Programs Gridded Losses SCS SMA Gridd
ed Transforms ModClark SUH
All Use a Grid File to define gridded structure
by sub-basin Can be built manually or from Arview
using GeoHMS extension.
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Climate Data Basin info
Ext Fortran Code for SMA
DSS file
Excess Precip Gage rec
Ext MODFLOW
Groundwater Gage rec
HEC-HMS
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639.047 Week 4
Adding Reality Channel routing issues
Adding Hydraulic constraints
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Basic concepts in storage
For any mass balance including a water balance
d/dt Storage input - output output Q
input - d/dt Storage Storagetotal ò (input -
output) dt
Qin
cfs
Qout
Storage volume
time
i.e. hydrologic storage is caused by time delay
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Basic concepts in storage and routing
Hydrologic routing based on mass balance
constraint output Q f(input - d/dt
Storage) Simple hydrologic routing as in our
linear reservoirs model Q k
Storage output Q f( storage depth)
rating curve, hydraulic geometry
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Basic concepts in storage and routing
Hydrologic routing through channels is more
complex based on mass balance constraint Complex
hydrologic routing channels d/dt Storage
input - output output Q f(input - d/dt
Storage) output Q f(input,output )
wedge storage
DRO Base
Prism storage
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Basic concepts in storage and routing
Complex Hydrologic routing based on mass balance
constraint Complex hydrologic routing
Muskingum Routing McCarthy (1938) proposed a
method which uses the continuity constraint and a
simple empirically fit storage function that
depends on both input and output rate S K x I
(1-x)O where xweighting factor, ranges from
0 to 0.5averages about 0.2 Ktravel time of
flood wave through segment (days), S/xI(1-x)O
x Input(1-x)Output
storage
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Hydraulic routing based on mass balance
constraint, and momentum eq
St. Venant eqs
Mass balance d/dt Storage input - output Sum
of external forces D momentum d(Ff Fgrav
Fvp)/dt d(massvelocity)/dt
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Theprectical basic for RAS modelling
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Kinematic Wave Diffusion Muskingum-Cunge Dy
namic wave approximation RAS Full Dynamic
Wave DWOPER, FLDWAV
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Upper Pere Marquette example
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Upper Pere Marquette example
A
B
C
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Upper Pere Marquette example
Landuse
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Upper Pere Marquette example
SCS curve
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Upper Pere Marquette example
Basin data
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Upper Pere Marquette example
Channel data
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Introduction to river modeling Hydrologic
Flood plain Load
Habitat Channel Hydraulics
Conservation of Mass, Energy Etotal Z D
V2/2g Q Area SR/n QW D V Routing
Energy predicts Depth, Vel
Conservation of Momentum and Mass predicts
Conc. transport
Empirical predicts utilization
Conservation of Mass QP-ET /- D Storage QW D
V Runoff Routing predicts DRO Q
Precip-runoff Rational method HEC-1 HEC-HMS TR-20
TR-55
Flow conditions WSP HEC-2 HEC-RAS HEC-4
Erosion,WQ HEC-6 SWMM AGNIPSSWAT
Biology HSI IFIM RIVPAKS SEM MLR
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HEC-HMS Set up and Application To analyze a
hydrologic system with HEC-HMS, the program user
must complete the following steps 1. Start a
new project 2. Create gage data 3. Enter basin
model data 4. Enter precipitation model data 5.
Enter control specifications 6. Configure a run
(and name it) 7. Compute!