Practice note: Estimation and Assessment of Inflows

This practice note is one of a set developed to provide consistency and transparency of river system models being used within the Murray–Darling Basin. The notes cover modelling practices, such as naming conventions for folder structures, to model methods, such as for flow routing and residual inflow estimation, and have been developed through a collaboration between the MDBA and Basin States.

Produced in collaboration with:

This practice note, 'Estimation and Assessment of Inflows', describes the general principles and a high-level method that should be adopted when estimating inflows during the calibration of a reach water balance. It aims to:

Detail when inflows should be included in a reach water balance.
Identify methods that may be used to estimate inflows.
Describe how to assess whether the inflow estimates are within reasonable bounds at a mean annual timescale

Background

Catchment hydrological processes are complex and influenced by factors including climate, soil, land use, and topography. A model of a reach water balance requires calibration of different flux components. These components include inflows from gauged tributary catchments and inflows from indirectly gauged areas. Inflows from indirectly gauged areas are usually estimated from a combination of upstream and downstream gauges. In the calibration of the reach model, inflows from gauged tributaries often require infilling and extension to cover the calibration period. Due to interaction between the different reach fluxes, flows from indirectly gauged areas are more difficult to estimate than inflows from gauged tributaries due to the lack of observed data for calibration.

The conceptualisation of a river reach should include gauged inflows, indirectly gauged inflows and a lumped loss. This lumped loss represents any losses that are not captured by modelling of explicit losses. Explicit losses include, reach net evaporation, seepage, groundwater interactions, etc. The interactions between the inflows from the indirectly gauged areas and the lumped loss node result in the estimation of one component impacting the estimation of the other component. For example, if the modeller overestimates the residual inflow, then the loss will also be overestimated to match the flows at the downstream gauge.

While the method for estimating the inflow from gauges and indirectly gauged areas can vary, having checks to ensure that estimates for inflow from both directly and indirectly gauged areas are within reasonable bounds increases our confidence in the reach model and the estimation of other fluxes such as lumped losses. At the mean annual timescale, the Budyko framework has been widely used to estimate mean annual runoff. The works of Zhang et al. (2001) and Zhang et al. (2004) provide methods to estimate mean annual evapotranspiration (ET) based on different land cover types (forest and grass) for a worldwide data set and an Australian data set respectively. This work can be used to define bounds on estimates of residual inflows at the mean annual time step. Neumann et al. (2017) further built on this work to provide some upper and lower bounds for runoff coefficients in the Murray–Darling Basin. These bounds can be used to test that inflow estimates are within the expected range at the mean annual timescale.

This Practice Note aims to detail the general principles that should be adopted when estimating gauged and indirectly gauged inflows and details a simple check based on work outlined in Neumann et al. (2017) to ensure that the mean annual inflow estimate for a reach is within reasonable bounds.

General principles

Modelling Inflows

Before deciding on the method to generate inflow time series, future model scenarios, such as climate change runs should be considered, and the modelling approach should be appropriate for these scenarios.
The reach conceptualisation should include the location of inflows from gauged areas and indirectly gauged areas (Figure 1). Inflow nodes should be used to represent all flow expected to materially contribute to the water balance. This would include:
1. Inflows from gauged catchments that represent the bounds of the water management model.
2. Inflows from gauged tributaries.
3. Inflows from ungauged and indirectly gauged areas, where flows from these areas are likely to impact on the management of surface water resources.
For Storage Inflows
1. A back-calculation process should be used to estimate storage inflows. A separate practice note will cover the back-calculation process (yet to be written).
2. The outputs from the back-calculation process should be used during calibration and infilled and extended using the same method as gauged inflows.
For Gauged Inflows
1. Observed flow data should be used during calibration and infilled and extended to cover the period required.
For Indirectly Gauged Inflows (Residual Inflows)
1. Inflows from indirectly gauged areas should be estimated using a method that ensures the magnitude is realistic and based on an assessment of the catchment's area and rainfall.
2. The methods used to derive the inflows from indirectly gauged areas (residual inflow) will be dependent on the level of information and data available for the reach.
3. The modeller should decide on the metrics used to assess model performance in reaches with indirectly gauged inflows before calibration. When deciding on the metrics, the modeller should consider:
  1. The location of the reach.
  2. The management processes that may be impacted by residual inflow estimates (e.g. supplementary flow access, environmental water triggers, floodplain harvesting triggers).
4. The location of the inflow in relation to routing links in reach should be considered, in some cases travel time of residual inflows will be important to the overall reach water balance and it may make sense to split the residual inflow into areas upstream and downstream of routing links.
Infilling and extension of inflows
1. Before calibration, gauged inflow data may need to be infilled or extended to cover the calibration period. (See Practice note: Infilling and Extension of Streamflow Data) Where there are minimal gaps in the data, and rainfall-runoff modelling will be used to infill and the extend the data, no infilling of observed data is required prior to calibration.
2. Before scenario modelling, all inflows should be extended to cover the period of long-term model run.
3. Rainfall-runoff models should be used to infill and extend all inflow data sets.
4. The Guidelines for water management modelling: Guidelines for rainfall-runoff modelling should be consulted to guide the calibration of your chosen rainfall-runoff model.

Assessing Inflow Estimates

All inflow estimates should be checked to ensure that the value is plausible on a mean annual basis when compared to nearby catchments and independent runoff yield data sets and calculation techniques. Figure 2 provides a useful starting point for determining whether your mean annual inflow is within the plausible range.
The reach calibration report should document how all inflows compare to independent runoff estimates.
If the inflows fall outside the expected bounds for mean annual estimates, the inflows should be:
1. revised, or
2. a justification made as to why the inflows fall outside these bounds in the model calibration report.

Figure 1: Gauged and indirectly gauged catchment areas.

Figure 2: Estimated mean annual runoff across the basin, based on Teng et al. (2012).

Suggested Method for Modelling Inflows

Before the calibration of inflows, the modeller should agree on the criteria used for assessing if the inflow estimate improves the model calibration. The inflow site should be classified based on the data available, the flow regime, the location in the catchment, and, the potential impact of the inflow estimate on management decisions. The modeller should classify inflows into one of the three inflow types described below. The modeller should consider the inflow type when deciding on what is important during the calibration of models that estimate inflows. The reach type to consider are:

Headwater inflows (upstream of storage/regulation) – In these catchments, the volume and seasonality of the catchment inflow are important when there is regulation downstream. The exact timing of events also becomes important when there is unregulated use below the inflow. In catchments primarily associated with regulated use, the calibration should focus on achieving the best match for flow volume on a seasonal basis at the downstream gauge or the estimated storage inflows. Where unregulated use is an issue event reproduction should also be a focus.
Intermediate reaches – catchments which are downstream of one or more gauge or storage. Inflows in these regulated reaches may be used to meet regulated demands or trigger releases for environmental purposes. In these reaches the timing of flow events is important. The prediction of gauged tributary inflows and residual inflows should focus on improving the timing and volume of key events at the downstream gauge during the calibration period. These events may impact on management triggers such as supplementary flow access and floodplain harvesting.
Lower (Fresher) reaches - catchments that are primarily event-driven (caused by local rainfall) and the timing and magnitude of events are important as these may trigger a management action (e.g. supplementary flow access, environmental watering decisions, floodplain harvesting). In these reaches, the objective of the calibration should be capturing changes to threshold driven management decisions and modelling of floodplain harvesting.

The location of the inflow will help determine the method for calibration of inflows. The method will vary depending on if the inflows are directly gauged or indirectly gauged and if the inflow is in the regulated or unregulated section of the river system.

Estimation of Storage Inflows

Based on the period of observed storage data, inflows to the storage can be determined via a back-calculation based on the recorded storage data and releases
Back-calculated inflows can then be treated as gauged flows at that location and are extended to cover the period of calibration using the same method as gauged catchment inflows.

For Gauged Catchment Inflows (Headwater Inflows and Gauged Tributary Inflows)

The observed data sets should be infilled and extended to cover the period required for calibration.
Appropriate methods for infilling and extending observed data during calibration periods include:
- Factoring of flow from an appropriate donor catchment based on area.
- The use of regression relationships based on a range of measured variables such as flow in an adjacent gauged catchment with similar physical properties.
- Calibration of rainfall-runoff models to the observed flow data and infilling and extending the observed record with the outputs of the rainfall-runoff model.
- During calibration, infilled observed gauged data or storage inflows should be used wherever possible.

Inflows from Indirectly Gauged Catchments (Residual Inflows – Intermediate and Lower Reaches)

Reach conceptualisation should decide where the residual inflow and lumped loss node will be placed in relation to other reach nodes and routing links. The inclusion of the residual inflow upstream of the demands will make additional water available to water users in this reach, while inclusion downstream may restrict water usage if inflows are significant in the reach. Where there are significant travels times in a reach, it may be appropriate to consider how best to represent the residual and multiple inflows (upstream and downstream of routing links) may be required.
During reach conceptualisation, data on residual reach area, rainfall, and, ET (see Practice note: Selecting climate data) should be obtained as well as the location of any ungauged tributaries that may provide significant inflows, particularly during flood events relative to the location of significant irrigation activities. Understanding the location of ungauged tributaries is particularly important for reaches where there is floodplain harvesting activity or unregulated secondary entitlements that can extract water from particular ungauged tributaries.
The modeller should decide on the criteria for assessing whether the reach calibration is improved by including a residual inflow before the calibration of the residual inflow (See the general principles for Indirectly Gauged Inflows above). In addition to matching the relative long-term average yield at the downstream gauge, the modeller should consider whether timing and magnitude of particular flow events are important, particularly events that may trigger management actions such as supplementary flow access, environmental watering decisions and floodplain harvesting.
The initial estimation of the residual inflow should occur after the initial estimate of the lumped loss. Ideally, estimation of the loss would be based on a period when inflows are known to be low; it may be appropriate to have an iterative process for estimating the lumped loss and the residual inflow.
Methods that may be used for estimation of the residual inflow include:
1. Estimation of residual inflows based on differences between the modelled flows at the downstream gauge (before inclusion of the residual inflow) and observed flows at the downstream gauge. Using the difference between the upstream flows passed through a reach model and the downstream flows allow the modeller to match the flows at the downstream gauges while also considering other fluxes in the reach. The methods used to estimate the residual based on the difference between observed and modelled flow include:
  1. Manually determining the difference in the flows at the reach outlet.
  2. Using an optimisation tool to calibrate rainfall-runoff within the reach model, to match the flows at the downstream gauges considering the other reach fluxes. The output from the rainfall-runoff model provides an estimate of the residual inflows.
2. Development of a regression relationship which may use a range of measured variables, such as flow in an adjacent gauged catchment with similar physical properties, to estimate the residual inflow from the indirectly gauged area. This concept can be extended to the regionalisation of sets of rainfall-runoff model parameters calibrated to suitable donor catchment and applied to the residual inflow catchment.
3. Factoring of flows from an appropriate donor catchment based on the catchment area or other appropriate catchment properties.
  
  The model purpose needs to be considered when deciding on the method used to estimate residual inflows. For example in climate change scenarios suitable methods will be dependent on how climate change adjustments will be applied
Initial effort for estimating the residual inflow should be minimal but should be sufficient to determine whether the inclusion of a residual inflow improves the reach calibration. Assessment of improvement should depend on the location of the reach and not just be based on significant improvement in the mass balance at the downstream node. For example, in lower (fresher) reaches of the river system, significant improvement might be seen in the prediction of surplus flow events with the inclusion of a residual, but with no improvement seen in the long-term mass balance at the gauge.
Where an initial calibration of the residual inflow indicates no improvement in model performance, then it may be appropriate to set the residual inflow to zero if this will not reduce model applicability for making management decisions.
Residual inflow estimates should be compared to yield from other gauged catchments, on a depth of average runoff per hectare basis, as a check that the estimate is consistent with measured yields and a general understanding of the topography, soils and rainfall for each area.
Regardless of the approach used to estimate the residual inflow, the calibration report for the reach should document how the residual inflow was estimated. Ideally, there should also be some process identified whereby residual inflows can be re-derived or adjusted to develop inflow sets that can be used in predictive analyses such as climate change assessments.

Infilling and Extension of Inflows

Rainfall-runoff models should be used to infill and extend all inflow data sets.
The rainfall-runoff model can either be calibrated to gauged data, or parameters could be transferred from a suitable donor catchment.
The Guidelines for water management modelling: Guidelines for rainfall-runoff modelling should be used to guide the calibration of your chosen rainfall-runoff model.

Assessing the magnitude of inflow estimates at the mean annual time step

The implementation of the method outlined below relates to the Murray Darling Basin. If the method is to be used outside the Murray Darling Basin, the appropriate w factors for the upper and lower bounds should be considered prior to implementation.

The period over which the mean annual flow will be assessed should be agreed. In most cases, this period of assessment will be longer than the calibration period.
Mean annual inflow is determined based on the daily time series used as input to the model for inflows for the reach. This inflow estimate would normally be calculated in ML per year. The start month of the year should allow for the best assessment given seasonal influences, e.g. where winter rains are a driver a January start date is appropriate but if summer rainfall is more important a July start will better capture complete summer seasons.
This inflow estimate is converted into mm by dividing the mean annual value in ML per year by the catchment area in km2.
The runoff coefficient is determined by dividing the mean annual inflow (Q) by the mean annual rainfall for the area (P). Both of these values should have the same units (mm).
The aridity index for the area is determined by dividing the mean annual potential evapotranspiration (E₀) for the area by the mean annual rainfall (P). The mean annual potential evaporation is based on SILO patched point Morton Wet evapotranspiration as detailed in the climate data practice note (Practice note: Selecting climate data).
Based on the aridity index of the area generating the inflow the expected range for the runoff coefficient can be determined using Equation 1. Based on data used in Neumann et al. 2017, an upper bound with a w value of 2.42, and, a lower bound with w value of 4.39 are recommended. These bounds have been selected to incorporate 90% of the catchment used in the data set shown in Figures 3 and 4.

Equation 1

where Q/P is the runoff coefficient, E0/P is the aridity index and w is the model parameter related to catchment characteristics.
The runoff coefficient for the residual inflow can then be compared with the upper and lower runoff coefficient estimates from Equation 1. Figure 5 provides a visual comparison for all reaches within a catchment and shows the upper and lower bounds based on Equation 1 for each reach and the modelled runoff coefficient.
If the estimate of the residual inflow falls outside these bounds, the reasons should be investigated, and either the residual inflows should be revised or a justification for why residuals would fall outside the bounds should be provided.
In addition to comparing the residual inflow to the independent estimates from Equation 1, the residual inflows should also be compared to neighbouring reaches to see if there are unexpected changes in runoff coefficients as you move from wetter to more arid parts of the catchment. Figure 5 also provides this comparison of all reaches in an example catchment.

Figure 3: Taken from Neumann et al. (2017). The figure shows the catchments within the Murray–Darling Basin used to determine the upper and lower bound on for the runoff coefficient based on the aridity index of the catchment.

Figure 4: The observed aridity index and runoff coefficients from Neumann et al. (2017). Showing that suggested upper and lower bounds, which incorporate 90% of the observed data points.

Figure 5: Example of how the results of the comparison between rainfall-runoff coefficients and bounds from Equation 1 could be presented.

Companion Practice Notes

Links to the relevant section of the eWater Documentation

Inflow node

References

Neumann, L.E., Brown, A., Zhang, L., Zheng, H.X., Davidson, A.J., Egan, C. and Korn, A. (2017). Assessing residual inflow and loss estimates methods in river reach calibration using the Budyko Framework. In Syme, G., Hatton MacDonald, D., Fulton, B. and Piantadosi, J. (eds) MODSIM2017, 22nd International Congress on Modelling and Simulation. Modelling and Simulation Society of Australia and New Zealand, December 2017. https://www.mssanz.org.au/modsim2017/L6/neumann.pdf

Teng, J., Chiew, F.H.S., and Vaze, J. (2012). Estimation of Climate Change Impact on Mean Annual Runoff across Continental Australia Using Budyko and Fu Equations and Hydrological Models. Journal of Hydrometeorology, 13, 1094–1106.

Zhang, L. Hickel, K., Dawes, W.R., Chiew, F. and Western, A. (2004). A rational function approach for estimating mean annual evapotranspiration. Water Resources Research, 40, W02502, doi:10.1029/2003WR002710.

Zhang, L., Dawes, W.R. and Walker, G.R. (2001). The response of mean annual evapotranspiration to vegetation changes at the catchment scale. Water Resources Research, 37: 701–708.