Storages are used to hold water for varying periods. They include dams and other reservoirs; weir pools; urban detention, retention or retarding basins; and natural lakes. In regulated river systems, storages control the supply of water to consumptive and non-consumptive users, and may also provide flood mitigation and environmental services. Typically, inflows to storages include stream flow from upstream catchments, rainfall over the storage surface area, recharge from groundwater, and runoff from the local catchment surrounding the storage. Outflows from storages include controlled releases and spills. Losses from storages include evaporation from the storage surface area and seepage to groundwater.

Controlled releases from a storage include discharge via regulated outlet structures such as gated spillways, valves, pumps and gates. The amount of water released is dependent upon downstream demands, storage operating rules and maximum and minimum release constraints. In river systems with ownership, releases are also influenced by owners’ shares within the storage and the ownership of the outlet capacity.

Spills via gated spillways are modelled by specifying a minimum release for the gated spillway as a function of reservoir level. Pre-releases for flood control may be modelled using either the minimum release functionality of the gated spillway or a minimum flow node, for more complex pre-release rules such as seasonal targets.

Uncontrolled spills occur when a storage fills above the minimum level of an un-gated spillway, or the capacity of the gates on a gated spillway to control outflows is exceeded. Uncontrolled outflow may also occur through an uncontrolled outlet such as an ungated pipe culvert and via leakage through the dam wall.

The modelling of the physical operation of storages in Source is described below. Other functionalities related to storages are described in other SRG sections; these functionalities include:

The ability to model the physical behaviour of storages is essential for fulfilling one of the primary purposes of Source, which is to model regulated river systems.


This node, in common with all others, is treated as a point location even though the storage represented may have large dimensions. It can therefore be considered to be site scale. It is used at every model time-step.

Principal developer

eWater CRC



Scientific provenance

The principles of modelling the physical behaviour of storages have been presented in many text books over many years. Recent examples include books by Loucks and van Beek (2005), and McMahon and Adeloye (2005).

The approach adopted in Source uses numerical integration to solve the water balance equation for each model time-step, rather than the more usual finite difference approach. The advantage of numerical integration is that the technique is time-step independent whereas the finite difference technique will give different answers depending on the time-step used.


Source version 2.16


A storage is represented as a node. It is connected to a single upstream link and can have multiple downstream links.

Structure and processes



The following definitions supplement those in the eWater Glossary:


An entity that owns a share of water in a river system; not the same as a water user.


The person using the River Manager software.

Maximum Storage Level

The highest level at which water is contained within a storage. This level is the highest level defined in the storage dimensions.

Full Supply Level (FSL)

Spillway crest level for an uncontrolled spillway; for a controlled (gated) spillway, the maximum level for water supply storage based on operating and management decisions such as to maintain airspace for flood mitigation.

Dead Storage

The level/volume below which water cannot be released from the storage, that is equal to the lowest outlet invert level. This may differ from the inactive storage (or minimum operating) level, which may be defined at a higher level for water quality or power generation purposes


Any flow into or out of a storage, including inflow, controlled releases, spills, rainfall, evaporation, leakage and groundwater loss or gain.

Net Flux

The total flux combining all individual fluxes (inflow, rainfall, evaporation, groundwater flux and discharge).


Levelin metres relative to the Australian Height Datum.

Minimum Release

The minimum rate of discharge from a storage when all outlets are closed and flow is only over spillway or through an uncontrolled outlet (including leakage).

Maximum Release

The rate of discharge from a storage when all outlets are fully open


The level of the base of the inside of a conduit (as distinct from the base of the outside, which includes the thickness of the casing)


Piecewise linear


water released in excess of the downstream requirements.


In summary, the adopted approach involves calculating the minimum and maximum discharge based on current inflows anduser defineddischarge, gain and loss relationships. Where there are multiple outlet paths, the minimum and maximum discharge is calculated for each path, assuming all paths are operational. If orders are less than the maximum discharge relationship, the order can be released. Otherwise, the order is constrained at the maximum discharge.

Source assumes that any flows (fluxes) into or out of the storage are averaged across the time-step. Flows and changes in storage volume are calculated by integrating across the time-step, assuming the reservoir has a level pool. The calculation process involves defining a series ofuser definedpiecewise linear relationships which describe storage dimensions, discharge relationships, and any losses and gains (such as evaporation and groundwater fluxes).

Calculation of storage mass balance

The calculation of storage mass balance during a model time-step is based on solving for the change in storage that occurs taking into account inflows, releases and all other loss and gain fluxes (eg net evaporation, seepage and spills).

Inflow, loss and gain fluxes, and outflows are assumed to be averaged over a model time-step. The combination of these fluxes describes the change in storage volume over a time-step. Fluxes and changes in storage volume are calculated by integrating across the time-step. This involves fulfilling the requirements outlined below.

Evaluation of net evaporation loss from storage

Inflow is generally estimated to the dam wall, and there is potential to double count water from the drowned section of the dam. This can be significant, especially where the reservoir area is a significant proportion of the catchment area. Hence, an adjustment is necessary to minimise the effect of double counting, and this is achieved by calculating the net evaporation loss. The net evaporation loss is the difference between the actual evaporation from the open water surface of the reservoir (Eo) and the actual evapotranspiration (Et) from the reservoir area assuming no dam (McMahon and Mein,1986: p136-137 & p185).

Linsley et al (1982) summarise the requirement for adjusting evaporation losses for the effect of the reservoir area as follows: "In reservoir design, the engineer is really concerned with the increased loss over the reservoir site resulting from the construction of the dam, ie. reservoir evaporation less evapotranspiration under natural conditions". This holds equally for modelling the behaviour of existing reservoirs. The mass balance calculations described below take this adjustment into account.

Model set up

Model set up:

Figure 1. Examples of piecewise linear relationships between outflows and storage volume
(a) Controlled outflows with gated spillway
(b) Outflows with uncontrolled spillway

Flow phase

During the flow phase, the potential minimum and maximum discharges from a storage are calculated for a given model time-step based on current inflows, flux data and theuser definedpiecewise linear relationships. If orders on a given outlet are less than the maximum discharge, the order can be released. Otherwise, the order is constrained at the maximum allowable discharge. The steps involved in these calculations for a given model time-step are discussed in the next sections, but in summary they are as follows:

As PWL relationships are used, each segment of a given PWL relationship may be expressed in terms of Equation 1:

Equation 1


Q average flow per unit time

v volume

dt time

m, c slope and intercept of the segment, respectively

The mass balance equation is (Equation 2):

Equation 2


I inflow

R runoff from storage area that would occur if this area were dry

P rainfall over the storage area in the current model time-step

Eo open water evaporation in the current model time-step

S groundwater flux (note a negative value of S means a gain to the storage; a positive value is equivalent to seepage)

U uncontrolled outflows

O controlled outflows

The runoff, rainfall and open water evaporation depth values read in as data are converted to volumes by multiplying them by the appropriate storage surface area. Also the term (Eo - P + R) is the net evaporation loss referred to in the section on evaluation of net evaporation loss from storage above.

Calculations for a given time-step where there is one outlet and one owner

Step 1: Evaluate PWL relationships for the following fluxes:

Interpolation is needed to bring all of these to a common set of storage volume, area and depth coordinates.

Step 2: Calculate the slope (m) and intercept (c) of each segment of the PWL relationships between storage volume and each individual flux derived in the previous step (see Figure 2) using Equations 3 and 4:

Figure 30. Example of a piecewise linear relationship between a flux and storage volume

Equation 3
Equation 4


F1, F2 dependent variable (eg fluxes) at each end of a segment in the PWL relationship

v1, v2 equivalent storage volumes

Recall that the minimum controlled outflows are usually zero in all segments of the PWL relationship, except that when there is a gated spillway there may be mandatory minimum release requirements once the volume in the storage exceeds certain thresholds, as illustrated in Figure 1(a). Also, as inflows are constant, m = 0 and c = inflow value for inflows.

Step 3: By combining c and m values for individual fluxes by substituting into Equation 2, PWL relationships expressed in terms of c and m values are derived for:

Step 4: To find the storage volume at the end of a time-step and outflows during the time-step, it is necessary to integrate Equation 1 with respect to time. The general form of the resultant equation is Equation 5:

Equation 5


t time, as a fraction of the model time-step (ie. 0 ≤ t ≤ 1)

k a constant

Other terms as previously defined.

Equation 5 applies only when m ≠ 0, ie. when the net flux through the storage is variable across a segment of piecewise linear relationship. When m = 0, Equation 6:

Equation 6

The constant k can be calculated from Equation 5 by setting time t = 0 (start of time-step) and v = storage volume at start of time-step (v0). Hence Equation 7:

Equation 7

Step 5: The segment of the PWL relationships the volume at the start of the time-step lies in is established by searching for the case where:

Step 6: For both minimum and maximum outflow cases, evaluation of the storage volume at the end of the time-step (vt) and outflows during the time-step involves an iterative process in which the segment of the PWL relationships vt lies in is established. Firstly, it is assumed the storage volume at the end of the time-step lies in the same segment of the PWL relationships as the storage volume at the start of the time-step, and vis estimated using Equation 5 with t = 1.

Step 7: The validity of the above assumption is then checked:



Step 8: If not, then the required result lies in another segment of the PWL relationship (higher or lower), and it is necessary to establish the fraction of the time-step when the storage volume goes out of the current segment. This is calculated using Equation 8:

Equation 8


t time that storage volume exits current segment, as a fraction of the model time-step

te cumulative time since start of time-step that storage volume exits current segment, as a fraction of the model time-step (noting that initially te= 0)

Other terms as previously defined.

The remaining fraction of the time-step is tr = 1 - te.

Step 9: Individual flux volumes (Net Loss, S, each component of D) for the current segment are determined using the value of t from step 7 or step 8 as appropriate, using Equation 9:

Equation 9


t time

vF volume leaving or entering a storage due to a particular flux (initially vF = 0)

mF slope of the linear relationship for the individual flux

mT slope of the linear relationship for the Net Flux

cF intercept of the linear relationship for the individual flux

cT intercept of the linear relationship for the Net Flux

k constant defined using Equation 7 for the Net Flux

Note that when mF = 0 or mT = 0, Equation 10:

Equation 10

Step 10: If t ≠ 1 then the cycle starting from step 4 through to step 9 is repeated for the new segment, using Equation 5 with t = tr. A new value of k has to be calculated using Equation 7, still with t = 0. Values of c and m appropriate for the new segment, previously calculated with Equation 3 and Equation 4, are used.

Step 11: When t = 1 orders are compared with minimum and maximum release rates:

Equation 11
Equation 12

Step 12: If there are orders in this time-step and minimum release < orders < maximum release, steps 4 to 11 are repeated using constant outflows from step 11 (ie. m = 0 and c = outflow value) instead of the relationships that are a function of storage volume used previously.

Step 13: The final storage volume is recalculated by substituting the individual flux volumes into Equation 13:

Equation 13


I, Eo, P, R, S, U and O are calculated individual flux volumes

The result is checked to ensure it is equal to the final result for vt obtained in step 6 (ie the result from Equation 5 with t = 1).

Calculations for a given time-step where there is more than one outlet but only one owner.

This functionality is still under development as at September 2011 (Source version 2.16).

Calculations for a given time-step where thereismore than one outlet and more than one owner

This functionality is still under development as at September 2011 (Source version 2.16).

Multiple outlet paths

When a storage has more than one outlet path, the adaptive storage release method is automatically used by Source. Releases from storages with one outlet path are assumed to be constant through the time-step (limited by volume to the min/max release curves).  The Adaptive Storage Release method generates a release curve based on the orders combined with the outlet curve. With this method, the storage releases at the maximum release rate where the storage cannot release at ordered rate. The storage releases at minimum release rate when it is greater than the order. The adaptive storage release method generates small artifacts when switching between the order and maximum/minimum release rates. However, provides better handling of releases when there are multiple outlets with big operating ranges.

Manual overriding of certain calculated storage parameters

For modelling forreal timeriver operations using River Operator, in Source, there is a ‘warm-up’ period where the model is run to ensure modelled fluxes equal observed values. Forecast releases are then used to predict the river response to a range of scenarios before the operator makes a decision on how much water to release or which path (multiple supply paths) to send water down. Source provides functionality which allows the user to manually override the simulated releases and storage volume/levels during the observed period. It also provides the ability to input forecast releases that override the model values.

Points to note include:

Input data

Data requirements are discussed in the Theory section above. Full details on input data are provided in the Source User Guide.

Parameters and settings

Whileuser definedinput relationships are generally expressed in terms of storage levels, these are converted to volume relationships within the model. Alluser definedrelationships are entered as, or converted to, piecewise linear (PWL) relationships. All sets of values in the relationships should be monotonically increasing unless noted otherwise. The intervals within the PWL relationships should be sufficiently small that the assumption of linearity, and linear interpolation, are approximately correct.

Where the storage volume rises above the highest value specified in the PWL relationship, values are linearly extrapolated using the slope of the line for the last twouser definedco-ordinates. It is preferable for the user to define all PWL relationships to include extremes, as linear extrapolation may not appropriately represent the desired behaviour.

The PWL relationships must start at a zero volume or zero discharge, and are not extrapolated below the lowest values.

Calibration parameters

Storage parameters the user may want to use in calibration mode include:

This uses the functionality for overriding calculated values discussed in the section on Manual overriding of certain calculated storage parameters above.

Output data

Outputs from the storage node include the following results:

Reference list

Linsley, R.K., Kohler, M.A. and Paulhus, J.L.H. (1982) Hydrology for Engineers. 3rd Ed., McGraw Hill, Auckland.

Loucks, D.P. and van Beek, E. (2005) Water resources systems planning and management: an introduction to methods, models and applications. UNESCO, Paris and WL | Delft Hydraulics, The Netherlands. 680 pp. ISBN 92-3-103998-9. []

McMahon, T.A. and Adeloye, A.J. (2005) Water Resources Yield. Water Resources Publications LLC, Highlands Ranch, Colorado, USA. ISBN 1-887201-38-6.

McMahon, T.A. and Mein, R.G. (1986) River and Reservoir Yield. Water Resources Publications, Littleton, Colorado, USA. ISBN 0-918334-61-6.


Maidment, D. R. (Editor in Chief) (1993). Handbook of Hydrology. McGraw-Hill.

McJannet, D.L., Webster, I.T., Stenson, M.P., Sherman, B.S. (2008). Estimating open water evaporation for the Murray Darling Basin. A report to the Australian Government from the CSIRO Murray-Darling Basin Sustainable Yields Project. CSIRO, Australia. 50pp.

Simonovic, S P (2009) Managing Water Resources: methods and tools for a systems approach. UNESCO, Paris, and Earthscan, London. ISBN 978-92-3-104078-8.