DSS for Integrated
Water Resources
Management (IWRM)
IWRM model representation,
scenarios, optimization
DDr. Kurt Fedra
kurt@ess.co.at
ESS GmbH, Austria
http://www.ess.co.at
Environmental Software & Services A-2352 Gumpoldskirchen
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Main topics:
model representation of river basin and
water resources:
• conservation laws,
• hydrological cycle, precipitation, EVT,
• Basin topology: cascading reservoirs,
routing, GW
• water quality;
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IWRM: what to decide ?
• Water allocation (sectoral: agriculture,
domestic, industrial, recreational, environmental
(dilution ?), hydropower, shipping, or geographic:
upstream/downstream)
• Waste allocation: permitting, emission
standards, treatment
• Development projects (investment)
• Strategic planning: regional/national
development, security, sustainability
(climate change)
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Decision support paradigms
• Information systems (menu of options)
• Scenario analysis (and comparison)
WHAT IF
• Rational maximization
HOW TO (reach objectives),
 optimization
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DSS structure:
Analytical core:
•
•
Design of alternatives
Assessment and evaluation, alternatives
WHY Model based analysis:
• Impossible to experiment in the
real world (costs)
• Impossible to try enough
alternatives (time)
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Model representation
Conservation laws:
Mass conservation, mass budget
inputs - output - storage change = 0
Water is neither generated nor lost within
the system, but can change state
(evaporation, ice) or be incorporated
into products (crops, beverages).
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Model representation
Hydrological Cycle:
Water evaporates from land
and sea, precipitates,
evaporates, forms runoff,
gets stored, diverted and/or
used (consumptive use),
percolates into groundwater.
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Dynamic water budget
Rainfall-runoff model
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Model representation
Precipitation:
• THE key variable == input
• High variability in time and space
(synoptic observation: weather radar)
• High measurement error
 large uncertainties
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Model representation
Evapotranspiration
• Evaporation: phase change from
liquid to gaseous, function of
temperature and vapour pressure
• Transpiration: physiological vapour
production by plants (evaporation from
stomata, and animals in respiration )
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Model representation
Evaporation: Penman-Monteith
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Penman-Monteith
where:
Rn is the net radiation,
G is the soil heat flux,
(es - ea) represents the
vapour pressure deficit of the air,
ra is the mean air density at constant pressure,
cp is the specific heat of the air,
Δ represents the slope of the saturation vapour pressure
temperature relationship,
γ is the psychrometric constant,
rs and ra are the (bulk) surface and aerodynamic resistances.
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Evapotranspiration
Simple practical method:
• Degree day method:
EVTP = a * avg.air Temperature
a is in the order of 0.1 mm/oK
varies with land cover/vegetation and humidity, wind
exposure
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Model representation
Cascading non-linear
reservoirs:
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Model representation
“reservoir” water budget:
precipitation
EVTP
Surface runoff
dS
 IN  EVPT  OUT
dt
b
OUT  a * S
Outflow is a non-linear
function of storage
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Interflow
Infiltration
percolation
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Water demand
Consumptive use
Intake
(quality constr.,
conveyance loss
return flow
(pollution)
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Demand node
(production
process)
recycling
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Model representation
Runoff of excess storage that exceeds the
“reservoir” capacity:
• from canopy (interception storage)
• soil surface (exceeding infiltration capacity
 Hortonian sheet flow, flash floods)
• Unsaturated zone:
– horizontal interflow
– vertical percolation (> field capacity)
• Saturated zone: Darcy flow of groundwater,
f of head difference and conductivity
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Model representation
Navier-Stokes equations:
Fi

V
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Navier-Stokes Equations
, , : viscosities
Divergence:
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Kronecker
Delta
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Model representation
Open channel flow:
The empirical Manning formula states:
where:
–
–
–
–
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1 2 / 3 1/ 2
V  Rh * S
n
V is the cross-sectional average velocity (m/s)
n is the Manning coefficient of roughness (0.01 – 0.075)
Rh is the hydraulic radius (m)
S is the slope of the water surface or the linear hydraulic head
loss (m/m) (S = hf / L)
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Model representation
Hydraulic radius: Rh
part of the channels resistance that controls
speed of flow:
A: cross section
P: wetted perimeter
A
Rh 
P
P=b+c+d
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Reaches
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Channel Flow Routing
Muskingum routing:
S = K [ xI + ( 1 - x ) O ]
where
S
I
O
K
= reach storage
= inflow rate
= outflow rate
= storage parameter (~ travel time)
X
= storage parameter
(0 - 0.5, describes attenuation)
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Model representation
Groundwater
Laminar flow (Darcy) depends on
• elevation difference (gravity)
• conductivity (resistance)
• cross-sectional area
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Model representation
Water quality:
• BOD/DO (Streeter-Phelps)
• Nutrients (fertilizer, NO3 in GW)
• Agrochemicals (toxic, persistent,
bioaccumulating)
• Heavy metals (industrial waste)
• Turbidity, sediments, erosion, siltation
• Water borne diseases
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Streeter-Phelps (DO, BOD)
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Streeter-Phelps (DO, BOD)
dD
 k d BOD 0 exp( k d t )  K r D
dt
where
D  oxygen deficit
L  total BOD
0
k  BOD oxydation rate K  aeration coefficien t
d
r
k L
d
0
D (t ) 
(exp(  k t )  exp(  K t ))  D exp t (  K t )
d
r
0
r
K k
r
d
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Streeter-Phelps (DO, BOD)
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Streeter-Phelps (DO, BOD)
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Model representation
Data requirements
• Physiography
• Hydro-meteorology
• Drainage network, structures
• Demand areas (nodes)
• Pollution sources
• Techno-economics
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Multi criteria optimization
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Reaches
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Model purpose
Structure the problem:
• WHAT FOR (purpose)
Questions to be answered ?
Identify gaps in understanding
Define data requirements
Define validation strategy
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Model purpose
WHAT FOR, WHY (not how)
• Model is a TOOL for purpose
• No BEST model (or hammer …)
• Choice of model and data
requirements depend on the
QUESTION to be answered
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Modeling and DSS
MOST IMPORTANT: ask good
questions (that can be answered to
support decisions)
Model application is an experiment,
hypothesis testing: does it make
sense, does it add up ?
Multiple models (agreement ?)
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