Chapter 1:
Water Allocation Model
Second Paper focus on system dynamic and the model – October 2010
1.1
Introduction
On this chapter, a new water allocation model based on a water balance with system
dynamic abilities to allocate a combined storage is discussed. The rationale behind the
water balance is explained. How the model would operate and use is also described. The
optimum solutions of water allocation together with composite risk produces by the
model are also discussed. Finally the result of the model is presented.
1.2
Water Allocation Approach
The water allocation model is included in the model structure as shown in Error!
Reference source not found. on Section Error! Reference source not found.. The
water allocation model aims at simulating the river flow within the Campaspe River
while producing the risk profiles caused by water allocations. It takes into account the
estimated risks (environmental, groundwater and production risks) to drive the water
allocation. That is, it seeks the optimum regions of water allocation where the risks are at
minimum level. A conceptual framework of the water allocation model is shown in
Figure 1.1, which detailed the water allocation process to be satisfied from a combined
storage. Summary of the process is provided below in different parts (P1 – P7).
P1 – The combined storage for each reach is estimated. The surface water
resource for each reach is estimated from lake release, tributaries, runoff,
diversion channel and losses from the system. The sustainable limit for each reach
estimated as previously discussed in Chapter 7
P2 & P3 – The environmental flow demand and environmental risk estimation are
estimated as described in Chapter 5.
P4 & P5 – The production water demand that estimated from domestic and
irrigation water demand are estimated before the production risk is simulated as
explained in Chapter 6
P6 – The groundwater risk is estimated as discussed in Chapter 7
P7 – The water allocation model which is described on this chapter.
GW Domestic
Demand
P1
SW - % of
Entitlement
Shepparton
Formation
Domestic Water
Demand
Diversion
Channels In/Out
Combined
Storage
Campaspe
Deep Lead
Groundwater
Sustainable Limit
Surface Water
Resource
Operating Rules
Tributaries
Water Allocation
Rules
LE Release
Management Rules
P4
Reach No. r1, , , rn
Conjunctive
Water Demands
GW
Western Waranga
Channel (WWC)
SW
Environmental flow
requirements
Irrigation Water Demands
P2
Crop Type
Environmental Flow
Demand
Land Use Crop
P7
PWD
EFD
Trade-Off
Risks
Season Type
GR
P6
Estimated Natural
Flow
P5
Water Supply
ER
P3
EFD
PR
Sustainable Limit
Groundwater Level
Natural Flow
ETm
Figure 1.1: Risk Driven Water Allocation Framework.
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1.3
Risk Driven Water Allocation Model:
The model focuses on determining the allocations based on minimising the total risk at
the same time addresses the complexity behaviour of water allocation with the Campaspe
basin. That is, the model aims at finding the optimum water allocations, which occur
when risks are at minimum. The model simulates “what if” scenarios of different water
allocations in order to satisfy water demands, while at the same time produces the risk
profiles caused by when the water demands are not fully satisfied. In term of groundwater
system, the risk occurs when the sustainable yield of the system is degraded due to water
extractions from aquifers. The water releases from the reservoir is also included in the
model through policy releases using a range of releases volumes.
Within a catchment basin, the inflow equals the outflow and leftover in storage as
expressed below. Where, the combined storage (CS), TWD is the total water demands in
forms of river diversions or pumping from the groundwater system. Loss is mainly
represented by the evapotranspiration, surface runoff to adjacent basins, groundwater
through flow and deep water drainage. Inflow represents the groundwater recharge,
precipitation, tributaries contributions and channel diversions into the catchment.
CS  TWD  Loss  Inflow  Leftover
1.1
Simply the above equation represents the combined storage equals the water demands
plus the leftover storage. That is, once the water demands in terms of losses and water
demands such as irrigation and environmental flow demands are satisfied, left over
storage makes up the balance of the water balance for a specific time and space. The finer
details of a combined storage and water demands are differed from one catchment to
another, reflecting the physical nature of a particular catchment. On the Campaspe Basin,
which does not have a water treatment plant but a reservoir (Lake Eppalock),
groundwater aquifers, tributaries and channel inputs, its combined storage is represented
by the following equation.
4
n
CSt ,r    SL  Rf  L  I t
r 1
1.2
Where, CS is the combined storage on month t for reach r, SL is the groundwater
sustainable yield, Rf is the river flow estimated from tributaries and runoff minus the
losses in terms of evapotranspiration and deep drainage. L represents the releases from
the Lake Eppalock Reservoir. Inflow (I) represents any major contribution such as the
Western Waranga Channel at Reach 3. The equation represents the total available in any
given month within a particular reach.
The next equation represents the water demands within a reach, which includes the
diversions out of the river and extractions from the groundwater system. This equation
does not include the water demands for the next downstream reach.
n
AWDt ,r    EFD  PWD  DWF 
r 1
t
1.3
Where, AWD is the total allocation water for month t, EFD is the environmental flow
demand, PWD is the production water demand and DWF is the domestic water demand, it
is represented by a fixed that is subjected to change during risk assessment. The
estimation of EFD and PWD are described on previous sections. A reach water supply
within a system is represented by equation 1.4. The estimations of EFD and PWD
required the volumes allocated from the river and groundwater to satisfy the two
demands.
Although, the combined storage is estimated as per equation 1.2, the water demands for
downstream reaches must be considered at the upstream reach water allocations.
Therefore, the available water resources on an upstream reach should be estimated as per
the following equation.
5
n
WSt ,r    CSt 1,r  AWDt , r 1 
r 1
1.4
Where, WS is the water supply available to meet water demands within a reach. The
allocation of WS to satisfy different water demands from different sources (groundwater
or river) is the heart of this model. That is water allocating to meet irrigation water
demand will affect the volume of water remains in the river to satisfy EFD. This means
that a number of different water allocation scenarios are available and needed to be tested
in order to determine the optimum water allocation within a reach for a particular month.
The detail of the water balance is shown on the following equation.
r
WRtr    S  T  C  ET  IR  DD  SL  EFDm  DWD  IWD  R 
i 1
t
1.5
Where, WRt is the water resource of a reach r at month t, St is the available storage for
downstream of the Campaspe Basin, T represents tributaries into the reach, C is the
channel diversion into the reach such as the waranga western channel for Reach3. ET is
the evapotranspiration and DD is deep drainage. SL is the sustainable limit, IR is the
induced recharge on gaining parts of the river and R represents the runoff for each reach,
which accounts for precipitation. The return flow from irrigation is assumed to contribute
to the combined storage through groundwater recharge with its effect on the river being
deemed insignificant. The environmental flow demands (EFD) is to be satisfied from the
surface water only. DWD is the domestic water demands and PWD, the production water
demands, which both are satisfied from groundwater and surface water.
The runoff was estimated based on runoff coefficient estimated on CSIRO (2008) using a
lumped conceptual daily rainfall-runoff model, SIMHYD, with a Muskingum routing
method to estimate daily runoff at grids (~ 5 km x 5 km) across the entire Murray Darling
Basin. The runoff coefficient (C) for each reach is multiplied with the estimated rainfall
for the entire reach to determine the runoff as shown by equation 1.6. The observed
precipitation (P) from each rainfall station times with area (A) estimated by Thiessen
6
Polygons in GIS. The runoff coefficient is varied to calibrate the predicted flow within a
reach.
Rt   C  P  A
1.6
The model simulates the input and output from each reach while fulfilling the allocations
to meet demands result in risk profiles being produced. The risk calculations as shown in
previous sections are also included here. The calculations of the environmental risk are
comprehensive discussed in Error! Reference source not found. part of the calculations
is shown here. The probability (P) is calculated from the regulated flow. The calculation
of consequence (C) also includes the regulated flow in comparison to a range of the
environmental flow demand.
ERt  Pt 1  Ct 1
1.7
The production risk is calculated per the following equation with other details is provided
in Section Error! Reference source not found.. Production risk is equalled to yield
reduction as calculated from the production formula as shown in equation Error!
Reference source not found..
PR  Ya / Ym
1.8
The groundwater risk is calculated as per the following equation with further detail
provided in Section Error! Reference source not found.
GRt   PR / Sy t 1
1.9
Where, GR is the groundwater risk on a monthly time step t, Sy is the sustainable limit
and PR is the pumping. A pumping range for each month is assigned, where the
simulation will give a range of groundwater risk and also the effects of pumping on the
other demands and risks.
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1.3.1 Allocation Scenarios
As mentioned above, there are number of water allocation scenarios (what if) that the
model should test in order to determine the best optimum water allocations. Considering
that the model has been calibrated; there are two water allocation options that can be used
which they would reflect the dynamic nature of water allocation in the model;
1. A reach (downstream or upstream) water demands are allocated between 0 and
200% full allocation, with left over water to satisfy other reaches’ demands.
2. The allocations for downstream reaches are linked upstream to ensure that their
water demands are reserved and must be delivered to downstream reaches.
Both of the above options can achieve the same result while still account for the dynamic
nature of water allocation. Therefore, the model is fitted with option 1. The following
process outlines the way allocation scenarios are being setup in the model.
1. Set the DWD to a fixed value, for instance 800ML/month
2. Set the allocation for PWD to start with zero allocation to all reach. Then vary
Reach1 allocation by 5% increment of full allocation until it reaches 200%, while
holding the other two reaches at zero allocation.
3. Repeat step 2 but the allocation for Reach2 is being incremented by 5% while
Reach3 is still being locked at 0% allocation.
4. Repeat step 3 until all reaches are set on 200% allocation.
5. Where the water should come from (groundwater or river) is also trialled, which it
will influence the groundwater risk for each reach. For example, Reach1 will start
by satisfying water demand for PWD and DWD, 100% from the river and 0%
from groundwater. This runs for step 1 to step 4, then change to 90% from river
and 10% from groundwater. Continue this until is 0% from river and 100% from
groundwater.
8
6. Step 5 is then repeated for the other reaches.
Each time a scenario is tested, the groundwater, supply and environmental risks are
calculated. Obviously, running these scenarios one by one is a duteous job to do with
high chance of missing to run a specific scenario. Therefore, the model is required to be
implemented in a model platform that has Monte Carlo functionality to run these
scenarios. In addition, the model platform must have dynamic functionalities to reflect
the dynamic nature of the above water allocation scenarios. System dynamic functions
that are implemented on Vensim make Vensim an ideal model platform to execute the
above water allocations.
1.4
System Dynamic
A detail description of system dynamic approach is given in section Error! Reference
source not found.. On this study, is used to capture the dynamic characteristics of
contributing variables to water allocation and determine their effects due to different
water allocation scenarios. In addition, it can account for the dynamic features of water
allocation that influence risk within a basin. For example what will be the effect of water
allocation on groundwater risk if production demands (irrigation and domestic) are to be
satisfied predominantly from groundwater and little portion comes from the river. If this
is the case, then the groundwater risk may increase due to increase pumping that may
result in declined to groundwater sustainable yield. On the other hand, if a significant
amount of water is diverted from the river to satisfy production demands that
environmental flow demands may not be satisfied resulting in higher environmental risk.
If larger proportion of water is diverted upstream for production demands, how would it
affect the downstream environmental flow and production demands? The ability of
system dynamic approach to capture such dynamic features have been demonstrated in
other field of studies (as shown in section Error! Reference source not found.), thus
making it ideal for water allocation modelling.
The model is built in Vensim Professional Version 5.10e produced by Vertana Simulation
Environment. The use of Vensim allows the model to be formulated without the
complexity of mathematical formulation and language program specification. The
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Vensim modelling language is a rich and readable way of representing dynamic systems
(Elmahdi et al., 2006; Khan et al., 2009).
The schematic diagram of the model is shown in Figure 1.2. The model allocates the
water release from the lake and inflows from tributaries and runoff to domestic,
production and environmental flow demands. The domestic water demand is fixed and
subjected for sensitivity analysis. The model also looks at how much can be satisfied
from groundwater and how much can come from the river at any point of time. The
diversion upstream will influence the amount of water in the river that would be required
to satisfy demands downstream. The effects of evapotranspiration and deep drainage are
taken into account.
The model is set to run different scenarios are determined. Because the model is operated
on the professional version of Vensim, it needs to link with the environmental risk model
(ERM) which is operated in Matlab. Therefore, the output flows from the Vensim is
exported into excel, and then reads into ERM. The output risk from ERM is then
combined with the groundwater and production risks in Vensim to determine the
optimum water allocation solutions
1.4.1 Model Calibration
The model is calibrated by matching the observed flow to the observed flow before the
scenarios of water allocation are tested. The releases from Lake Eppalock, runoff
coefficient, evapotranspiration, deep drainage, and induced recharge are calibrated until
the observed and predicted river flows produce good match for all reaches. However, it is
anticipated that the model may not realistically be able to accurately match the observed
data because it hasn’t adequately account for all the losses and inflows into the system.
Because the focus of this study is to determine risks due to allocations, as long as the
model can adequately match the observed would be considered sufficient. This means
that model will not be extensively calibrated until a perfect match between the observed
and predicted river flow. However, it is crucial that the model is calibrated because it
provides a degree of calibration to risks provided from water allocations.
10
winter release
Lake
Eppalock
summer release
comparison
Comp2
month
Reach1
runoff rate2
406201
runoff rate
release
runoff data
sw dwd
DWD
pumping
proportion
tribdata
gw dwd2
tributaries
DWD2
406207
allocation
selection
dwd vol
GW
Pumping
Alloc
allocgw
allocsw
Pumping
Alloc2
GW2
dwd vol2
allocgw2
allocation
selection2
Pumping
Alloc3
Campaspe2
allocsw2
PWD
sw pwd
DD
ET
GW3
dd rate
ETa WS
total ETm
dd data
Total
Risk
PWD2
SL2 gwpwd2
sw pwd2
allocsw3
Campaspe3
<mode>
gw volume3
pumping
portion3
r3 obs PD
ET3
SL3
PWD3
sw pwd3
gw pwd3
ET2
obs data3
obs data2
ET data3
eta rate3
ET data2 ET rate2
composite ky2
Production
Risk2
ET rate3
ETa WS3
Groundwater
Risk3
Environmental
Risk2
Campaspe
Total Risk
Figure 1.2: Risk Driven Water Allocation Framework in Vensim
RIA
composite ky3
total ETm3
Production
Risk3
Total
Risk3
Total
Risk2
11
Comp3
downstream
flow3
ir data2
ETa WS2
total ETm2
Environmental
Risk
induced
recharge3
pwd vol3
r2 obs diversion
ir rate2
eta rate2
ET rate
Groundwater
Risk2
composite ky
Production
Risk
ET data
allocation
selection3
dwd vol3
allocgw3
<mode>
induced
recharge2
406265
ir rate3
runoff3
dwd volume3
gw volume2
eta rate
Groundwater
Risk
DWD3
runoff2
pumping
portion2
gw volume
gw pwd
gw dwd3
pwd vol2
<mode>
SL
ir data3
sw dwd3
dwd volume2
406225
Campaspe1
pwd vol
runoff data3
rate2
sw dwd2
dwd volume
River
downstream
406202
flow2
runoff data2
rate1
runoff rate3
Reach3
downstream
flow1
trib rate
Runoff
gw dwd
Reach2
wwc to
campaspe
Environmental
Risk3
wwc rate
WWC
rate3
Murray
River
1.4.2 Model Forecasts
The water allocation model deals with a complex system of allocating water from a combined
water resource to different water demands. How this model can be used in a river basin is an
important that must be answered on this section. There are two categories that the model can
be used for;
1. The model will look at evaluating a year ahead of allocation;
a. Specify a band of volume releases from the lake based on historical data. Let
say 0 – 20% = b1, 20% - 40% = b2, 40% - 60%, 60% - 80% and 80% - 100% =
bi. Then put together the annual hydrographs from the entire historical data for
each band. Then determine the mean flow (f) hydrograph for each band.
b. Before the irrigation season starts, run the historical data and link with the
mean flow (f)bi for the appropriate band. Do the same thing with tributaries
and losses as well.
c. Allocation – run the allocation scenarios defined in section 1.3.1.
2. The model will be used for forecasting policy scenarios under different climatic
conditions;
a. Produce a forecasted 30 years climatic data then run it under the model, with
varying allocations together with varying the climatic parameters.
b. How do I generate a 30 years of climatic data?
1.4.3 Optimum Solutions
The main objective of this water allocation model is to determine which water allocation
scenarios that can satisfy water demand when the three types of risk are at minimum and to
reveal scenarios that would be risky to achieve. However, it may be impossible to achieve
three risks being all at minimum level at one time. That is, the groundwater risk may be at
minimum value while the other risks are not. This means that it may be more than one
optimum solution.
12
As demonstrated by Figure 1.3, the optimum range would occur when risk is at low range.
The allocation volume for each demand is different from one to another and how much
should be supplied from each resource is also different. Therefore, the volumes supplied at
when risk is within the optimum allocation range would be the allocation volumes. The
optimum range should be determined during the Monte Carlo sensitivity simulation.
1.5
Composite Risk
This study deals with three different type of risk that are not directly comparable. This means
that a 0.4 of environmental risk cannot be treated as the same as the 0.4 of groundwater risk,
because they all mean different things. Therefore, a way to find the equivalent of 0.4
environmental risk equals to how much of the groundwater risk. One approach would be to
convert these three risks into a common currency such as dollar values. However, this is
faced by difficulty of estimating environmental risk with monetary value. Therefore, the
composite risk is estimated using statistical approach.
Percentile – for example 90th percentile of groundwater risk (0.3 risk value) equals the 90th
percentile of groundwater risk (0.2 risk value) and 90th percentile of environmental risk (0.4
risk value), therefore the composite risk equals 0.9, out of a total of 3.0. This means that 0.3
of groundwater is equal to 0.2 of groundwater risk.
We need to discuss this.
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Figure 1.3: Optimum range of water allocations for all demands to be supplied from the river and
groundwater aquifers.
1.6
Results
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