# Generic Modelling Techniques

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Generic Modelling Techniques
• Why and what are their original?
• Outline the types
• Developing a conceptual model
History
Theory (physics)             Catchment Models            Applications

Bernoulli, Chezy
1800       Dalton,1802; evaporation
Darcy,1856; Saturated Flow
Manning, 1891; Open Channel flow        Sherman,1932;         Hydrological design
1900   Green and Ampt,1911; infiltration       Unit hydrograph
Richards,1931; unsaturated flow        Gumbel, 1941          Hydrological design
Hortonian runoff,1933              Extreme flow analysis
Acrobat Document
1950                                          Lumped Conceptual          Research
1960                                          modelling
1970
Phyically based            Research +
1980                                          distributed modelling      Occasionally
impacts
1990                                          Lumped Conceptual          Impacts of
modelling                  change
FORWARD
• Mathematical models for small scale
hydrological processes are tried and tested.
Darcy’s Law

Combined with
mass balance
gives you the
groundwater flow
equations

Back
• Soilwater processes

Back
Black Box Models
– Widely used in hydrology, as early as 1932
(Sherman, 1932) hydrologist were employing
such models in engineering design to convert
rainfall into discharge at the outlet of a
catchment. They are still used extensively by
practising engineers and in models such as
flood forecasting systems where short term
(hours-days) predictions are required.
• For a control volume (e.g. a catchment)
select some arbitrary mathematical function
that will convert
• Input series(e.g. rainfall time series)
• To an output (e.g. discharge)
Rainfall              Black Box               River
Function                Discharge
Parameters/constants in the
Temperature     function are unknown and
have to be estimated on the
basis of some observed data

Back
Intuition
Eden

90
80
70
Flow (Cumecs)

60
50
Flow
40
30
20
10
0
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19
Year (starting 1968)
1 .0 0
R e la tiv e c u m u la tiv e F r e q u e n c y
0 .9 0

0 .8 0

0 .7 0

0 .6 0

0 .5 0

0 .4 0
O b s e r ve d
0 .3 0                                     F lo o d s

0 .2 0                                     N o rm a l
D i s tr i b u ti o n
0 .1 0
" "
0 .0 0
0   100              200    300

An n u a l m a x im a

Back
Schematic for a lumped model
Simulating Runoff

SNOW
CANOPY               PACK

SURFACE
WATER

SOIL WATER

MAIN
CHANNEL
GROUNDWATER         NETWORK

Back
Distributed Modelling     Canopy?
Penman
Montieth
Surface?
Saturated
2-D St-Venant                           Subsurface?

Unsaturated
3-D Groundwater
Subsurface?
Equation
Richards’s
Equation
Distributed Data ?
Problems
•   Spatial scale
•   Time scale
•   Lack of physical data
•   Lack of Hydrological data
•   Hydrologists have had great success in
modelling small scale processes but much
less at integrating them over a catchment
because of the problems of finding
representative parameters
Back
Generic Types
• Physically based distributed models
– Most comprehensive models
Groundwater models; Research Scientists;
A Few Decision Support Systems
• Black box deterministic models
• Lumped conceptual deterministic models
Pragamtism

• Stochastic Models
– Most widely used.
Engineering design. Rainfall modelling.
Lumped conceptual models
or

Deterministic conceptual models
• Pragmatic solution
Conceptual implies that the modeller has a conceptual
picture of the physical processes that are occurring in
the catchment
Deterministic means that a given set of parameters and
inputs exactly determine the output. No
stochastic/randomness
Lumped infers some sort of averaging process; spatially
averaged hydrological variables are simulated rather
than attempting to determine the value of the spatially
distributed values of the variables
• Retain some of the physical laws (e.g.
conservation of mass) in their mathematical
formulation, without trying to exactly model
reality.
• They are commonly based on analogies of
catchments or river networks as a set of
storage reservoirs with different properties.
The process of constructing a
conceptual model
• The key to constructing a conceptual model of any system is to
decompose the it into its main processes.
• Draw a schematic diagram of how these processes interact.
• Write a mathematical description of each of the processes.
• Translate that description into computer code.
• Glue together all the components adhering to the structure in your
schematic diagram
• Assign parameter values (i.e. the constants in your mathematical
descriptions)
• Run the model
Visual inspection of hydrographs
Visual inspection of hydrographs
12.00

10.00

8.00
cumecs

6.00

4.00

2.00

0.00
5-Jan-98   25-Jan-98 14-Feb-98   6-Mar-98 26-Mar-98 15-Apr-98
-2.00
time
What do we need to model @ Forsinard
Schematic for a lumped model
Simulating Runoff

SNOW
CANOPY               PACK

SURFACE
WATER

SOIL WATER

MAIN
CHANNEL
GROUNDWATER         NETWORK

Back
Are they anything more than
complicated black-box models
The component hydrological processes that are used in
conceptual models are those that have been shown to hold
at small scales (plots of ground a few m2).
At these scales the parameters can easily be identified,
through field experimentation. Same equations hold?
Been shown that the parameters required to produce
realistic results are not just an average of the small scale
parameters.
 Parameters cannot be identified through field
experimentation and do not directly represent physical
properties of the catchment.
Therefore, you need to calibrate the model using historic
hydrological data.
Potentially, they suffer from exactly the same problems as
black-box models. In that, if something changes in the
catchment or the input data (e.g. rainfall) exceeds the range
of that used in the calibration procedure the model may
produce unrealistic results.
However(alternative argument)
• Even thought the parameters can not be directly measured
in the field and have been calibrated, they are associated
with a physically reasonable mathematical description.
Therefore, in simulating change it is possible to perturb the
calibrated parameters realistically.
Evapotranspiration
Evapotranspiration

Evaporation               Transpiration

Open                        Vegetation
Soil                                 Plants
water                        surfaces

27
Measuring Evapotranspiration
•Lysimeters
•A large block of undisturbed soil covered by representative vegetation is
surrounded by a watertight container driven into the ground. A sealing
base with a drainpipe is secured to the bottom of the block and a weighing
device established underneath.

Et  Rainfall - Percolation  Weight change

•The accuracy of the lysimetry for action evapotranspiration measurement
is dependent on the sensitivity of the weighing mechanism. To detect large
changes in soil moisture content, large samples are required.

•Alternatively, soil moisture can be determined by a neutron probe
Factors Controlling Evaporation
•   Water molecules are continually being exchanged between liquid and vapour
– if the number passing to vapour exceeds that passing to liquid evaporation
is taking place
– water passing from liquid to vapour absorbs 590 cal of heat per gram
– evaporation can occur until saturation humidity is reached in the
atmosphere

Rn

Dry Air
Strong wind

e is the
difference
between actual and
saturated humidity
Things that can limit the rate of evaporation

• There are three main factors influencing evaporation from a free
surface:
 the supply of energy required to provide the latent heat of vaporisation
 the ability to transport the vapour away from the evaporative surface
 the supply of moisture at the evaporative surface

Consider two extremes
1. Vapour transport does not limit evaporation rate
Energy supply dictates evaporation rate
Calculate using energy balance model (sensible heat loss = 0)
2. Available energy does not limit evaporation rate
Have to account for the ability to transport vapour (ignoring energy)
Calculate using aerodynamic model (sensible heat loss = 0)
Energy Balance (sensible heat flux zero)
Continuity of Mass
net                                            dh
V  rW A       rW AE
sensible heat   radiation,        vapour flow                  dt
to air, HS      Rn                rate, V     where E is the evaporation rate (-dh/dt)

Energy Balance
rA                     dH
 Rn  H s  G  lV V
dt
Therefore, combining the two mass and
energy balance equations:
h                      rW
1
E          ( Rn  H S  G )
area, A                            lV rW
heat conducted to             If all incoming net radiation is absorbed by
ground, G
evaporation (HS & G = 0):
Rn
Er 
lv rW
31
Potential rate of evaporation

(i) Energy Balance Method

Er  0.0353Rn        (mm/day)

where Rn is the net radiation in Watts/m2
(i) Aerodynamic Method
Ea  B(eas  ea ) (mm/day)
where eas and ea are the saturated water vapour pressure and actual
water vapour pressure respectively and B is the Bowen ratio:
 17.27T 
eas  611exp             (Pa)
 237.3  T 
 17.27Td       
ea  611 exp 
 237 .3  T    
   (Pa)
           d   
T is air temperature and Td is the dew point temperature in oC
0.102u2
B                2
  z2  
ln 
z 
  0 
Potential
Evaporation
Er  Ea
E
 
Potential
Evapotranspiration

Er  Ea
E
   (1  rs / ra )
Relationship between Actual and
Potential Evapotranspiration in
soils
Data courtesy of John
Albertson, California

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 views: 4 posted: 4/15/2011 language: English pages: 35