Hydrology

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Hydrology

• Simple model
• for
• Nete
• Acad. year 2003-2004
• FLTBW

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Grote Nete (Varendonck downstream of Laak
tributary)

• Documentation
• A 386 km²
• NB 51.5.33
• OL 4.56.52
• X 190476
• Y 198097
• MASL 13 m

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Map Nete catchment area
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(Very) simple model
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Equations ( in excel, matlab, etc..)

• Soil reservoir storage S (overflow ? )
• provisional SPtSt-1 Raint ETt
• If (SPt lt 0) then (St 0) and (ETactt
  ETtSPt) else (StSPt)and (ETacttETt )
• if (St gt Smax) then (Perct St Smax) and
  (St Smax) else Perct0
• Linear (drainage) reservoir
• RtRt-1 exp( -1/K)Perct (1-exp( -1/K))

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Physical meaning ???

• Overflow soil reservoir
• FC (field capacity) maximum storage before fast
  percolation
• PWP (permanent wilting point ) ET stops
• Linear reservoir (similarity !!!! )
• could subsurface drainage reservoir
• could storage reservoir of the river system

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Subsurface model appropiate for Nete cathment

• Sandy and flat soils infiltration is large
  little surface runoff
• Shallow watertables subsurface drainage to
  ditches and rivers

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Schematic Hooghoudt-drainage model
h
D
De
L
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Reaction factor ?
With Ksat conductivity (soil type)
De equivalent depth (topography and soil
layers) m the storage
coefficient (soil wetness!!!! ) L
the drainspacing (distance rivers/ditches)
Derivation drainage and soil physics Storage
coeff wet soils have less storage !!
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Rivers/dicthes network drain the subsurface
phreatic water tables
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Subsurface Drainage (sandy soils in the Nete
catchment )
subsurface water divide
topographic surface divide
topography
phreatic wt
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Catchment land characteristics

• Nete catchment rather sandy soils and flat
  topography
• Urban runoff impervious surface ( high CN) of
  roads, roofs, parkinglots etc..
• Fast component shallow watertable (small Smax
  and fast reaction)
• Slow component deeper watertable ( larger Smax
  and slower reaction

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Simple Model

• divide the total area in fractions urban runoff,
  fast component, slow component furban, ffast 2
  parameters because sum of fractions 1
• urban runoff by CN ( 1 parameter)
• fast component by overflow reservoir (Smaxfast)
  into linear reservoir (Kfast) (2)
• fast component by overflow reservoir (Smaxfast)
  into linear reservoir (Kfast) (2)
• Total model parameters 2122 7 parameters

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Optimisation of parameters

• In spreadsheet Excel /tools/solver
• by changing cells ( parameters )
• Search until a criterium is optimal
• commonly least squares sum of squared errors
  (SSE) mimimum
• is equivalent to maximum R2 1- SSE/SSTO
  sometimes called efficiency in hydrology
• Remark
• In software like Matlab, R many alternative
  algorithms
• local search Nelder and Mead, BFGS, Marquardt
• global search (sometimes called genetic
  algorthims) SANN (simulated annealing), SCE
  (scuffled complex evolution)
• other criteria possible even multicriteria (
  Pareto e.g.)

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/Tools/Solver in Excel
Constraints keep physical meaning of the
parameters and avoid degeneration of the search
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Calibration lt gt Validation

• Calibration is fitting model results on the
  observed by changing the model parameters
  towards an optimum for the fit criteria (danger
  for overfitting by too many parameters)
• Diagnostics in statistics are based on
  assumptions for the error Nid(0,s2) not valid
  in hydrology !!!
• Best solution use (a) period(s) not used in
  calibration to validate the model

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Nete calibration-validation
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