Hydrological Modelling

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Hydrological Modelling

• Dr Bill Sloan
• Lecture Notes
• Powerpoint Presentations
• Case Study Data

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Prague
Dresden
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China
Bangladesh
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Aim

• Computer modelling has become an integral part of
  the decision making process for water engineers
  and managers
• Model results are increasingly used as
  justification for infrastructure development
  (flood defences)
• Practicalities of applying a computer model very
  much easier than previously - false confidence.
• Understand some basic principles of mathematical
  modelling
• Understanding of the any simplifications that are
  made to the underlying physical processes.

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Structure

• Lectures
• mathematical models for the processes and the
  simplification required for computer modelling
  purposes
• A series of practical classes
• procedures involved in practical modelling work
  will be emphasised at the expensive of much of
  the detail on mathematical techniques

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Course Reference Books

• Bras, R.L., Hydrology an introduction to
  hydrological science, Addison-Wesley, 1990.
• Chow, V.T., D.R. Maidment, and L.W. Mays, Applied
  Hydrology, McGraw Hill Book Co. New York, 572,
  1988.
• Hornberger, G.M., J.P. Reffensperger, P.L.
  Wiberg, and K.N. Eshelman, Elements of Physical
  Hydrology, The John Hopkins University Press,
  Baltimore and London, 1998.
• James, A., An Introduction to Water Quality
  Modelling, John Wiley and Sons, Chichester, 1984.
• NERC, Flood Studies Report, pp. 5 Vols, Natural
  Environmental Research Council, Wallingford,
  1975.

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This Lecture

• Simple Water Balance Model
• Identifying Catchment Boundaries
• Visual inspection of hydrographs.
• Introduce Case Study

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• Recycling process linking water in the
  atmosphere, on the continents, and in the oceans.

• Key to modelling it is to think in terms of
  reservoirs or compartments that store water (the
  oceans, atmosphere, etc.) and the movement of
  water between them.

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Mass Balance

• Forms the basis to most hydrological and
  hydrochemical models

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Assuming constant density
V volume of water within the control
volumeL3 I volume inflow rate L3 T-1 O
volume outflow rate L3 T-1
What is a typical control volume?
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Can treat the land phase of the hydrological
cycle as comprising one compartment. For an
arbitrary area of land need to identify inputs
and outputs
p is the precipitation rate rsi is the surface
water inflow rate rso is the surface water
outflow rate rgi is the groundwater inflow
rate rgo is the groundwater outflow rate et is
the evapotranspiration
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Where is the Water Balance Model Useful?

• Extremely simple model
• Useful in characterising the hydrology of a unit
  of land over a long time,T, can assume
• ?(dV/dt)dt V(T)-V(0) 0
• ? I(t)dt ? O(t)dt
• What is a sensible value of T for this assumption
  to hold?

• Sensible first pass model to construct in any
  modelling study

• Checks that input and output data are sensible
• Gives a feel for the most important processes

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Few hydrologists get the opportunity to
characterise the hydrology of continents!
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Catchments

• Hydrologists involved in investigations of water
  resources in much smaller geographical areas
  where individual hydrological processes become
  important
• Fundamental control volume in this case is the
  catchment. Why?

rsi, and rgi can usually be neglected and
therefore number of variables in the equation is
reduced
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• A catchment is then defined as all points that
  potentially can contribute surface water to a
  particular river station.
• The topography of the land surface usually
  controls where divides are drawn.

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• Drainage system - The area upon which water falls
  and the network through which it travels to an
  outlet.
• Catchments - an area that drains water and other
  substances to a common outlet as concentrated
  flow (watersheds, drainage basin, contributing
  area)
• Subbasin - That upstream area flowing to an
  outlet as overland flow
• Pour Point - A location at which the contributing
  area can be determined.
• Drainage Divide - The boundary between two
  basins. This is an area of divergent flow.

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Traditional watershed delineation has been done
manually using contours on a topographic map.
A watershed boundary can be sketched by starting
at the outlet point and following the height of
land defining the drainage divides using the
contours on a map.
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GIS and Digital Data

• Automated algorithms for identifying drainage
  divides
• Accurate
• Fast

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• DEMs consist of an array of data representing
  elevation sampled at regularly spaced intervals

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ELEVATION VALUES
X
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The elevation values of the DEM can be grouped
into intervals. Each interval is then
represented by a different gradient color.
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• Slope
• Usually calculated on a 3x3 window with the
  center cell being the target cell.
• Slope is calculated from the center cell to each
  of the 8 neighbors
• Greatest slope is assigned to the center cell
• Flow direction is that way..

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Target Cell
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• Flow Direction
• In ArcView Spatial Analyst, the output of a Flow
  Direction is a grid whose values can range from 1
  to 255 based on the direction water would flow
  from a particular cell. The cells are assigned
  valued as shown below.

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• Flow Direction

Original Surface
Flow Direction Surface
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• Flow Direction

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• Flow Accumulation
• If we know where the flow is going then we can
  figure out what areas (cells) have more water
  flowing through them than others.
• By tracing backwards up the flow direction grid
  we can figure the number of cells flowing into
  all cells in a study area
• Accumulated flow is calculated as the accumulated
  number of all cells flowing into each downslope
  cell.

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• Flow Accumulation
• For an accumulation surface the value of each
  cell represents the total number of cells that
  flow into an individual cell
• Cells that have high accumulation are areas of
  concentrated flow and may be used to identify
  stream channels.

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Flow Accumulation Surface
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Pour Point
Contributing Area
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Visual inspection of hydrographs
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1)
2)
3)
c) East River, near Almont, Colorado
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Visual inspection of hydrographs