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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.
                 The paradigm
• 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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