Reservoir Modeling and Storage Capacity
Introduction
The ability of the reservoir at Tillegra to supply a population of 85,000 residents was assessed using the
storage equation; St+1 = St + Qt – Dt – ΔEt –Lt; where St+1 is the storage at time t+1, St is the storage at time
t, Q is inflow, D is demand, E is evaporation losses and L is other losses (e.g. environmental flows).
Environmental flows are considered in this equation as a loss to the reservoir, however they can be also
considered as a demand. Two cases were considered when assessing the reservoir; the first case
considering a stationary climate (dealt with in this section) and the second case climate change.
Assessment of the impacts of climate change on storage will be considering in section (..)
Height – Surface Area Relationship
The proposed dam is located at latitude -32.3203 and longitude 151.6861. To calculate the surface area
at different heights, a map of the area was purchased as the map given was pixilated and had no scale.
The river height at the dam location was calculated as 87m (AHD). A 2mm grid was printed on
transparent sleeves, and using the contour lines on the map, the surface area for 3m, 13m, 23m, 33m,
43m and 53m was calculated. As the grid was relatively small, it was assumed that only small errors
would be incurred in this approximated method, it was deemed acceptable and the values for surface
area were then used to approximate volume.
Height – Volume Relationship
Volume was calculated to quantify the storage in cubic metres, as the height of the dam increased. The
volume of the reservoir was calculated using the height above 0m (87m AHD), the surface area
calculated and the trapezoidal rule. The data of can be seen in table 4.1 below.
The volume calculated in Table 4.1 is dependent of the volume
assigned to dead storage. Dead storage, under normal
conditions is not used for flow control, but rather used for
settlement of particles (Votruba, 1989). If reservoir storage
reaches dead storage, the dam has deemed to fail. Dead
storage was set at 64303 m3 at 3m AHD. As the height of the
dam is assumed to be between 30-60m, this value falls in the
5-10% range suggested (Sharda & Juyal, 2005).
From the values calculated in Table 4.1, two relationships
were calculated to give surface area and volume at any height
(h) of the dam.
Dam
Height
(m)
Surface
Area (1x106
m2)
Volume (1x106
m3)
0
0
0
3
13
23
33
43
53
0.04286875
0.62949375
1.79371875
4.09960625
7.220000
11.74660
0.064303125
3.426115625
15.542178125
45.008803125
101.606834375
196.4398421875
Figure 4.1- Height, Surface Area and Volume Data
SA (m2) = 4E-08h4 + 3E-05h3 + 0.0026h2 + 0.0076h + 0.0012, R² = 0.9999
Volume (m3) = 6E-06h4 + 0.0009h3 + 0.0021h2 + 0.0658h - 0.067, R² = 1
Both these equations have R2 approximately equal to one, which suggests both equations are good
representations of the trend in the data and can be assumed to have little error. The relationship
between the plotted data and the equations can be seen in Graphs 1 and 2 in appendix.
Model Factors
Inflow (Q)
Using Matlab and the AWBM, daily evaporation and rainfall data from November 1969 to November
2002 was analysed to give daily runoff values. These runoff values were then multiplied by the area of
the catchment (205km2) to give a daily runoff in cubic metres. As seen in the AWBM model evaluation in
section 2 of this report, the AWBM tends to dampen peak flow values for large storm events. It was then
decided that analysing the storage formula using monthly time steps would be a more accurate method
of analysis and would negate any dampening inaccuracy in the model. The daily inflow data was then
summed for each month to give total inflow (m3) for each month.
Demand (D)
Referring to section 2, demand for Tea Gardens in 2040
was estimated at 11.08GL/year. This was split into
6.75GL/year for the township, while 4.33GL/year was
estimated for the mine that has been assumed to exist in
Tea Gardens in 2040. It is assumed that the mine will
have no seasonal fluctuations on water supply and the
water demand is evenly distributed between the months
of the year. However referring to section 2, it can be seen
from graph .., that demand for the township will fluctuate
throughout the year with peak demand of 633.15ML in
January. The demand per month, distributed with
seasonal fluctuation can be seen in figure 1.
Month
Jan
Feb
Mar
Apr
May
June
July
Aug
Sept
Oct
Nov
Dec
% distribution ML/month
9.38
633.15
9.1
614.25
8.16
550.8
7.97
537.975
7.62
514.35
7.54
508.95
7.56
510.3
7.66
517.05
8.24
556.2
8.81
594.675
9.02
608.85
8.94
603.45
Figure 1: Seasonal distribution of demand
Evaporation (ΔEt)
Daily evaporation data (mm) was summed to give monthly totals. This total was then multiplied by the
surface area of the reservoir, calculated from the height (h) of the dam wall. This approximation was
assumed to be the most accurate method to calculate the loss to the reservoir storage caused by
evaporation and gave a monthly evaporation outflow in cubic metres.
Other Losses – Seepage, Losses to Aquifer and Environmental Flows (Lt)
Environmental flow in the storage analysis of Tillegra Dam can be considered as part of the demand,
however in the storage analysis is considered as a loss to the reservoir.
The Williams River is classified as a gaining stream (NSW Office of Water, 2009) which means in high
storage levels, water will move from the Dam into the aquifer, however in low storage times, water will
move from the aquifer into the reservoir to provide bank storage. Consequently, losses or gains to the
aquifer are assumed to be negligible for the purpose of this report. Seepage also can be considered as a
loss to the dam. However, it has been assumed for this report that seepage under the dam will be in
orders of magnitude lower than water demand and thus negligible.
Flow requirements of the Williams River are determined based on the conservation of ecological
processes. Social and economic requirements are also considerations. “The NSW River Flow Objectives
(RFOs) are the agreed targets for surface water flow management. They identify the key elements of the
flow regime that protect river health and water quality for ecosystems and human uses and are based
on the principle of mimicking the key characteristics of the natural flow regime. The river flow objectives
that Hunter Water can assist in achieving are:
1) Protect natural water levels in pools of creeks and wetlands during periods of no flow
2) Protect natural low flows
3) Protect or restore a proportion of moderate flows, “freshes” and high flows
4) Maintain or restore the natural inundation
patterns and distribution of floodwaters
supporting natural wetland and floodplain
ecosystems
5) Mimic the natural frequency, duration and
seasonal nature of drying periods in
naturally temporary waterways
6) Maintain or mimic natural flow variability
in all rivers
7) Maintain rates of rise and fall of river
heights within natural bounds
8) Maintain groundwaters within natural
levels, and variability, critical to surface
flows or ecosystems
9) Minimise the impact of in-stream
structures
10) Minimise downstream water quality
impacts of storage releases
11) Ensure river flow management provides
for contingencies
Table 1 Source: Aurecon 2008, Page 18)
12) Maintain or rehabilitate estuarine
processes and habitats” (Aurecon 2008)
To fulfill the RFOs, commitment from various government agencies would be required. The overall goal
would be to achieve an appropriate release strategy from the proposed dam in conjunction with the
implementation of an appropriate water sharing plan. Table 1 shows how appropriate dam releases
strategies may assist in achieving some of the RFOs.
It can be seen that strategies in Table 1 do not meet all of the listed RFOs. “Provided that the river flow
objectives are achieved for the Williams River, biodiversity and ecosystem objectives which are
interrelated to the flow components of a river will also be met.” (Aurecon 2008)
The river flow regime for the Williams River can be characterized by its flow components which depend
on the frequency of various flow levels. FIgures 1 and 2 depict how the natural river flows in the
Williams River are highly variable. Figure 1 shows the historic daily flows at the Tillegra Bridge site over
the last 77 years, highlighting the temporal variability. The flow components and aspects described in
Table 2 were derived from the analysis of the data presented in Figure 1, detailing the key functions of
each flow component. Figure 2 provides a graphical representation of flow component aspects (timing,
duration, frequency).
Figure 1 & Figure 2 (Source: Aurecon 2008)
Table 2 (Source: Aurecon 2008)
It can be seen that the minimum flow requirement for the Williams River occurs during low flow at
24ML/day (1ML/hour). It is necessary to maintain this low flow condition in the river because the low
flow connects the instream habitations and the maintenance of aquatic vegetation, whilst it also
provides refuge from high flows for biota and a passage for juvenile fish. Additionally, to maintain
habitat and sustain species population, a moderate flow between 24ML-100ML/day is required. This
range of flows gives an exceedance of 30-70%. It can be concluded that a moderate flow of 50ML/day
will approximately result in an exceedance of 50%. 50ML/day will be adopted as the average daily
environmental flow discharged from the reservoir. Overflow of the dam wall due to storm events will
account for ‘flushes’ and also help mimic natural flow variability.
To ensure that environmental flows are representative of natural flow variability, average monthly
inflow and percentage distribution (refer to appendix …for full calculation) was calculated using the
historical data. The average environmental flow (50ML/day) was distributed based on the percentage
per month, giving environmental flows higher variability throughout the year. Distributing the
environmental flows monthly also assisted fulfill criterion 2 of the RFO’s, in ensuring natural low flows
are protected throughout drier months. The percentage distribution values can be seen in figure….
below.
Season
% of
inflow
Jan
Feb
Mar
April
13.9
14.7
17.4
9.5
May
10.7
June
July
6.2
3.8
Aug
Sept
2.8
2.9
Oct
4.7
Nov
5.7
Dec
7.6
Figure 1: Monthly distribution of Environmental Flow
Other Model Considerations
Before testing can be carried out on the storage capacity of the reservoir at Tillegra, some other
variables need to be assumed, which include level of serviceability, robustness and the starting dam
water level. Combining these variables with the storage formula seen in section …, a final dam wall
height can be calculated.
Tea Gardens residents currently derive water from a borefield in the north-west of Tea Garden’s,
providing approximately 12L/s (Mid Coast Water, 2011). As the population will rise to 85,000, this
aquifer is seen as unable to supply enough water to match the increased demand. It can be neglected as
a source of supply for the purpose of this report, giving a more conservative result. This means that the
level of service of the proposed Tillegra Dam is going to be high as it is being considered as the only
source of water supply. Levels of serviceability of 95% and 100% have both been considered. When
storage levels reach the dead storage value (64303m3), the dam has deemed to fail. Considering a
serviceability of 95%, results in an average of 18 days per year of the failing to supply Tea Gardens any
water. As the aquifer has been neglected, and demand reductions such as water restrictions have been
excluded from calculations, a serviceability of 95% seems reasonable. However just to ensure supply to
Tea Gardens in extreme drought periods, a level of serviceability of 100% is more desirable and will be
accepted in calculations.
The starting dam water level refers to the level which the reservoir is filled to prior to storage
calculations commencing. Assuming the starting storage level is at full capacity, can have significant
impact if the flow records are unusually low in the early periods of the record (Sharma, 2011). From the
historical data it was noted that there was unusually low inflow between April to August 1970. These
values appear at the start of the recorded historical data, and thus to assume a starting storage of 100%
could have a large impact on the analysis. A starting capacity of 50% has been seen as the conservative
alternative to a full capacity starting height and has been assumed for the storage balance equations.
Another consideration is the robustness of the dam structure. A good measure of robustness is the
severity and frequency of water restrictions over a given time period. As can be seen in figures.. below,
Hunter Water suggests and range of restriction levels; stage 1 -60% capacity, stage 2-50%, stage 3-40%
and stage 4-30% (Hunter Water, 2011). It was deemed acceptable to accept the same water restriction
criteria for the Tillegra Dam. Although these restrictions won’t be factored into demand for calculations
(making storage behaviour conservative), the robustness of the structure needs to be analysed to
ensure that the town of Tea Gardens are not always on water restrictions.
Stages of
restriction
Water
capacity
Stage 1
60%
Stage 2
50%
Stage 3
40%
Stage 4
30%
Implemented
restrictions
Ban fixed sprinklers and
limited hours use of
hand held hoses
Same as Stage 1 with
use of hand held hoses
limited to 2 days per
week.
Ban use of mains water
for outdoor use.
Complete ban on
outdoor use.
Figure 1 and 2, Hunter Water’s Water restriction criteria (source: Hunter Water)
Storage Mass Balance and Results – Stationarity
With a level of service of 100% and a starting capacity of 50%, storage was calculated using the equation
in section…It is recommended that under stationarity, the dam wall be constructed to a height of 31m.
This gives a maximum capacity of 36.34GL (including dead storage), and a surface area of 3666071m2.
The storage behaviour under stationarity can be seen in figure .. below. The critical period from the
analysis is approximately 17 months. As can be seen from figure…, level 4 water restrictions are only
reached once for a length of 6 months over the 33 year period of analysis (1.5% of time period). It was
concluded that the robustness of the proposed Tillegra Dam is acceptable.
Storage Behavioural Diagram - Stationarity
40000000
35000000
Storage (m3)
30000000
25000000
Storage
(m^3)
20000000
15000000
Dead
Storage
10000000
5000000
5/1/2001
8/1/1999
11/1/1997
2/1/1996
5/1/1994
8/1/1992
11/1/1990
Date
2/1/1989
5/1/1987
8/1/1985
11/1/1983
2/1/1982
5/1/1980
8/1/1978
11/1/1976
2/1/1975
5/1/1973
8/1/1971
11/1/1969
0
Figure .. : Storage Behaviour under stationarity
Climate Change
Introduction
Climate change needs to be considered when designing an engineering structure for future service. To
estimate the impact of climate change on the storage calculations for Tillegra, the General Circulation
Models (GCMs) were used, and more specifically the A2 envelope as can be seen below in figure…... The
GCMs use emission scenarios and solar radiation to simulate the energy and mass balance of the earth
(Sharma, 2011). There is uncertainty in temperature and rainfall simulations evident in the error bands
in figure… This is due to the complexity of the different variables that impact future temperature and
rainfall values. Using the GCMs for estimation of the storage behaviour in 2040, could therefore incur
errors in the calculated value.
Figure .. : Temperature increase due to climate change (Sharma, 2011)
Demand
The demand of Tea Gardens in 2040 under climate change has been assumed to be the same as under a
stationary climate, although there may be some increase in water demand relating to increasing
temperature, for example in agriculture. It has been assumed however that because we have neglected
water supply from the aquifer and water restrictions (refer to section ….see above in stationarity
section), there has been enough conservative assumptions made to neglect any extra demand due to
increasing temperature caused by climate change.
Changes in Storage Behaviour due to Climate Change
Factors Precipitation Evaporation
To predict the variation in storage behaviour due to climate
change at Tillegra in 2040, the GCMA2 simulation needs to be
Summer
1.06
1.10
correlated with the local historical data at reservoir site. To do
Autumn
0.87
1.10
this the Constant Scaling Method was used. This method uses
Winter
0.93
1.04
GCM simulations to determine scaling factors as seen in figure
Spring
0.83
1.08
….(Sharma, 2011). These factors are calculated by finding
seasonal averages for both precipitation and evaporation for the
Figure…Constant scaling method seasonal
current climate (assumed as 1960-1990) and compares them to
factors for evaporation and precipitation
seasonal averages for the future climate based on GCM
simulation (2030-2049). These ‘scaling factors’ have then been multiplied by the 33 years of historical
data provided (Nov 1969 –Nov 2002) to give a large set of data for analysis of the storage behaviour.
Using the AWBM the factored daily data was used to predict daily runoff values. The daily runoff was
then summed per month to allow for monthly analysis, similar to the method used in the previous
section.
Other Model Considerations
Similarly to the case for stationarity, level of service and starting dam water level need to be defined
before the storage mass balance can be simulated. A level of service of 100% is desired and a starting
dam water level of 50% has been assumed. This is similar to the case for stationarity and an in depth
discussion on why these values were assumed can be seen in section… Similar values for these
parameters were assumed, as climate change has minimal impact on the derivation of these values.
Storage Mass Balance and Results – Stationarity
With a level of service of 100% and a starting capacity of 50%, the storage mass balance was calculated
using the equation in section… It is recommended that under climate change, the dam wall be
constructed to a height of 33m. This gives a maximum capacity of 43.85GL (including dead storage), and
a surface area of 4208946m2. The storage behaviour due to climate change can be seen in figure ..
below. Similar to the condition under stationarity, the critical period from the analysis is approximately
17 months. As can also be seen from figure…, level 4 water restrictions are only reached once for a
length of 6 months over the 33 year period of analysis (1.5% of time period). It was concluded that the
robustness of the proposed Tillegra Dam under climate change is also acceptable.
Storage Behavioural Diagram - Climate Change
50000000
45000000
40000000
Storage (m3)
35000000
30000000
25000000
20000000
Storage
(m^3)
15000000
10000000
Dead
Storage
5000000
6/1/2001
11/1/1999
4/1/1998
9/1/1996
2/1/1995
7/1/1993
12/1/1991
5/1/1990
10/1/1988
3/1/1987
8/1/1985
1/1/1984
6/1/1982
11/1/1980
4/1/1979
9/1/1977
2/1/1976
7/1/1974
12/1/1972
5/1/1971
10/1/1969
0
Date
Figure .. : Storage Behaviour under climate change
Reference
Mid Coast Water, 2011,Tea Gardens Water Supply, Accessed on 08/08/2011, [Online Source] Available
at http://www.midcoastwater.com.au/site/index.cfm?display=75246
Sharma, A, 2011, UNSW lecture notes CVEN3031
Aurecon, Tillegra Dam Planning and Environment Assesment for 2008, Accessed on 1st August 2011,
<https://majorprojects.affinitylive.com/public/ea80653d41df449feef9e479a481a546/D%20Env%20Flow
s%20&%20River%20Management.pdf>
NSW Office of Water, 2009, Hunter Unregulated and Alluvial Water Sharing Plan, accessed 08/08/2011,
[Online Source] Available at http://www.water.nsw.gov.au/Water-management/Water-sharingplans/Plans-commenced/Water-source/Hunter-Unregulated-and-Alluvial/default.aspx
-
Hunter water, 2011, Water Restrictions,Accessed 10/08/2011, [Online Source] Available at
http://www.hunterwater.com.au/Your-Account/Water-Usage/Water-Restrictions.aspx
-Votruba, L, 1989, Developments in Water Science, Accessed 4/8/11, [Online Publication]
http://books.google.com/books?id=j8dIlPJITH0C&printsec=frontcover#v=onepage&q&f=false
-Sharda and Juyal, 2005, Water Harvesting Techniques, Design of Small Dams and Hydraulic
Complements, Accessed 4/8/11, [Online Publication] Available at
http://www.docstoc.com/docs/68290300/WATER-HARVESTING-TECHNIQUES--DESIGN-OF-SMALLDAMS-AND-HYDRAULIC
Appendix
Graphical representations (Refer to Figures… below.)) of the data displayed in Section … were created in
order to observe any errors in the equations for volume and surface area.
Surface Area (m2) Vs Reservoir Height
(m)
14
y = 4E-08x4 + 3E-05x3 + 0.0026x2 + 0.0076x + 0.0012
R² = 0.9999
Area(1x106 m2)
12
10
8
Surface Area(1x106
m2)
6
Poly. ( Surface
Area(1x106 m2))
4
2
0
0
20
40
Reservoir Height (m)
Graph 1
60
Volume (m3) Vs Reservoir Height (m)
250
y = 6E-06x4 + 0.0009x3 + 0.0021x2 + 0.0658x - 0.067
R² = 1
Volume (1x106 m3)
200
150
Volume( 1x106m3)
100
Poly. (Volume(
1x106m3))
50
0
0
20
40
60
Reservoir Height (m)
Graph 2
Appendix
Storage Mass balance
The equation for storage at time t+1 is given by; St+1 = St + Qt – Dt – ΔEt –Lt. When maximum capacity of
the dam is reached (stationarity = 36.34GL, climate change = 43.85GL), the storage value needs to be
replaced by the maximum capacity storage value rather than the addition of St+1. This is because any
storage over maximum capacity becomes overflow of the dam wall. When the storage mass balance was
simulated for the historical period, starting at the beginning of simulation, any storage value over
maximum capacity was replaced by the maximum capacity, then any preceding storage value was
calculated using St+1. This ensured that there was no storage value higher than maximum capacity.
Appendix
Environmental flow monthly distribution
Season
Sum of flows
Number
of data
values
Jan
400423691.5
33
12134051.26
13.90493108
Feb
422955057
33
12816819.91
14.68734504
Mar
502447394.5
33
15225678.62
17.44775981
April
273934386.5
33
8301042.02
9.512520976
May
308235396.5
33
9340466.56
10.70364226
June
177879791.5
33
5390296.71
6.176972776
July
110168353
33
3338434.94
3.825656144
Aug
79506052
33
2409274.30
2.760891019
Sept
84696836.5
33
2566570.80
2.941143841
Oct
135567504.5
33
4108106.20
4.707655533
Nov
169604208
34
4988359.06
5.716375137
Dec
219294076
33
6645275.03
7.615106393
87264375.41
100
TOTAL
Average Inflow
% of inflow
Figure …
To mimic the natural variability in flow, the environmental flow was distributed according to the average
percentage inflow per month. These were calculated by finding the sum of each month’s inflow over the
33 years of data, and dividing by the total number of data values for that month. Then the percentage
distribution was calculated as can be seen above in figure…
Climate change-GCM Constant Scaling method
The constant scaling method used current (1960-1990) average precipitation and evaporation and
compared to future (2030-2049), to calculate seasonal factors as can be seen in table … below
Summer
Autumn
Winter
Spring
Current(1960-1990)
AVE. PREC AVE. EVAP
375.3641906
479.053518
159.5704814 209.9565796
68.25770764 126.2279141
122.2298658 404.9554683
Future (2030-3049)
AVE. PREC AVE. EVAP
399.5348268 526.2852396
139.4905586 231.0946474
63.4032972 131.3463034
101.9243592 438.9181083
Table. .. Constant Scaling factors calculated.
Factors
Summer
Autumn
Winter
Spring
Precipitation
1.06
0.87
0.93
0.83
Evaporation
1.10
1.10
1.04
1.08