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 Bioregional Assessment Program
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 2.6.1 Surface water numerical modelling for the Hunter subregion
 2.6.1.5 Uncertainty
 2.6.1.5.1 Quantitative uncertainty analysis
The aim of the quantitative uncertainty analysis is to provide probabilistic estimates of the changes in the hydrological response variables due to coal resource development. A large number of parameter combinations are evaluated and, in line with the Approximate Bayesian Computation outlined in companion submethodology M09 (as listed in Table 1) for propagating uncertainty through models (Peeters et al., 2016), only those parameter combinations that result in acceptable model behaviour are accepted in the parameter ensemble used to make predictions.
Acceptable model behaviour is defined for each hydrological response variable based on the capability of the model to reproduce historical, observed time series of the hydrological response variable. For each hydrological response variable, a goodness of fit between model simulated and observed annual hydrological response variable is defined and an acceptance threshold defined.
The ensemble of predictions are the changes in hydrological response variable simulated with the parameter combinations for which the goodness of fit exceeds the acceptance threshold. The resulting ensembles are presented and discussed in Section 2.6.1.6.
Parameter sampling
For AWRAL, the parameters varied in the uncertainty analysis are those used in the calibration, with the addition of the parameter for scaling effective porosity, ne_scale. For AWRAR, two of eight calibrated parameters, K_rout and Lag_rout, are included in the uncertainty analysis. The remaining AWRAR parameters are set to their values from the lowstreamflow calibration and not varied in the uncertainty analysis: variability in surface water – groundwater interactions (two parameters) and catchment runoff (one parameter) is already captured in inputs from the groundwater model and AWRAL simulations; the three irrigation parameters are fixed as changes in irrigation management are not in the scope of this study.
Table 9 lists the parameters used in the uncertainty analysis and the range uniformly sampled in the design of experiment. The Australian Water Resources Assessment (AWRA) landscape model (AWRAL) and AWRA river model (AWRAR) parameters in Table 9 are explained in the AWRAL v4.5 documentation (Viney et al., 2015) and AWRAR v5.0 documentation (Dutta et al., 2015), respectively. Parameters with a large order of magnitude range in parameter bounds or which are thought to be particularly sensitive to low parameter values are transformed logarithmically to ensure that values near the minimum of the range are adequately sampled.
Three thousand parameter combinations are generated from the AWRAL and AWRAR model parameters according to the ranges and transformations shown in Table 9 using a spacefilling Latin Hypercube sampling algorithm (Santner et al., 2003) that efficiently covers the sample space. These ranges and transformations are chosen by the modelling team based on previous experience in regional and continental calibration of AWRAL (Vaze et al., 2013) and AWRAR (Dutta et al., 2015). These mostly correspond to the upper and lower limits of each parameter that are applied during calibration.
The parameter combinations generated include all the parameter combinations for the groundwater model (see companion product 2.6.2 for the Hunter subregion (Herron et al., 2018)). This linking of parameter combinations allows the results to consistently propagate from one model to another, as outlined in the model sequence section (Section 2.6.1.1).
Each of the 3000 parameter sets is used to drive AWRAL to generate a runoff time series at each 0.05 x 0.05 degree (~5 x 5 km) grid cell. The resulting runoff is accumulated to the scale of the AWRAR subcatchments and is used – in conjunction with the sampled AWRAR parameters – to drive AWRAR.
Table 9 Summary of AWRAL and AWRAR parameters for uncertainty analysis
Model 
Parameter name 
Description 
Units 
Transformation 
Minimum 
Maximum 

AWRAL 
cGsmax _hruDR 
Conversion coefficient from vegetation photosynthetic capacity index to maximum stomatal conductance 
na 
none 
0.02 
0.05 
AWRAL 
cGsmax _hruSR 
Conversion coefficient from vegetation photosynthetic capacity index to maximum stomatal conductance 
na 
none 
0.001 
0.05 
AWRAL 
ER_frac_ref _hruDR 
Ratio of average evaporation rate over average rainfall intensity during storms per unit canopy cover 
na 
none 
0.04 
0.25 
AWRAL 
FsoilEmax _hruDR 
Soil evaporation scaling factor when soil water supply is not limiting evaporation 
na 
none 
0.2 
1 
AWRAL 
FsoilEmax _hruSR 
Soil evaporation scaling factor soil water supply is not limiting evaporation 
na 
none 
0.2 
1 
AWRAL 
K_gw_scale 
Multiplier on the raster input of K_{g} 
na 
log10 
0.001 
1 
AWRAL 
K_rout_int 
Intercept coefficient for calculating K_{r} 
na 
none 
0.05 
3 
AWRAL 
K_rout_scale 
Scalar coefficient for calculating K_{r} 
na 
none 
0.05 
3 
AWRAL 
K0sat_scale 
Scalar for hydraulic conductivity (surface layer) 
na 
log10 
0.1 
10 
AWRAL 
Kdsat_scale 
Scalar for hydraulic conductivity (deep layer) 
na 
log10 
0.01 
1 
AWRAL 
Kr_coeff 
Coefficient on the ratio of K_{sat }across soil horizons for the calculation of interflow 
na 
log10 
0.01 
1 
AWRAL 
Kssat_scale 
Scalar for hydraulic conductivity (shallow layer) 
na 
log10 
0.0001 
0.1 
AWRAL 
ne_scale 
Scalar for effective porosity 
na 
none 
0.1 
1 
AWRAL 
Pref_gridscale 
Multiplier on the raster input of P_{ref} 
na 
none 
0.1 
5 
AWRAL 
S_sls_hruDR 
Specific canopy rainfall storage capacity per unit leaf area 
mm 
none 
0.03 
0.8 
AWRAL 
S_sls_hruSR 
Specific canopy rainfall storage capacity per unit leaf area 
mm 
none 
0.03 
0.8 
AWRAL 
S0max_scale 
Scalar for maximum water storage (surface layer) 
na 
none 
0.5 
5 
AWRAL 
Sdmax_scale 
Scalar for maximum water storage (deep layer) 
na 
none 
0.5 
1 
AWRAL 
slope_coeff 
Coefficient on the mapped slope for the calculation of interflow 
na 
log10 
0.01 
1 
AWRAL 
Ssmax_scale 
Scalar for maximum water storage (shallow layer) 
na 
none 
0.5 
3 
AWRAL 
Ud0_hruDR 
Maximum root water uptake rates from deep soil store 
mm/d 
log10 
0.001 
10 
AWRAR 
K_rout 
Muskingum routing parameter 
sec 
log10 
0.1 
10 
AWRAR 
Lag_rout 
Muskingum routing parameter 
sec 
log10 
0.1 
10 
AWRAL = Australian Water Resources Assessment landscape model; AWRAR = Australian Water Resources Assessment river model; na = not applicable (dimensionless)
Observations
Predictions and observations from 22 streamflow gauges whose catchments contribute flow to the surface water modelling domain in the Hunter subregion are used for uncertainty analysis. Selection of the 22 catchments is based on three criteria: (i) data length more than 10 years; (ii) not subject to major opencut and underground mine impacts; and (iii) not subject to major dam control. For these catchments, historical observations of streamflow are summarised into the nine hydrological response variables for all years. The equivalent historical simulated hydrological response variable values are computed from the 3000 design of experiment runs. The goodness of fit between these observed and simulated historical hydrological response variable values is used to constrain the 3000 parameter combinations and select the best 10% of replicates (i.e. 300 replicates) for each hydrological response variable. These 300 replicates are used for predictions in Section 2.6.1.6.
Predictions
For each of the 65 model nodes the postprocessing of design of experiment results in 3000 time series with a length of 90 years (2013–2102) of hydrological response variable values for baseline, , and coal resource development pathway (CRDP) conditions, .
These two time series are summarised through the maximum raw change (amax), the maximum percent change (pmax) and the year of maximum change (tmax). The percent change is defined as:

(1) 
As the predictions include the effect of surface water – groundwater interaction through coupling with the groundwater models, groundwater parameters will also affect the surface water predictions.
Selection of parameter combinations
The acceptance threshold for each hydrological response variable is set to the 90th percentile of the average goodness of fit between observed and simulated historical hydrological response variable values obtained from nodes at 22 streamflow gauging sites. This means that out of the 3000 model replicates, the 300 best (or 10% best) are selected for each hydrological response variable.
The selection of the 10% threshold is based on two considerations: (i) guaranteeing enough prediction samples to ensure numerical robustness; and (ii) their performance approaching that obtained from the high and lowstreamflow model calibrations. Furthermore, it is expected that the full 3000 replicates contain many with infeasible parameter combinations (caused, for example, by parameter correlations that are not considered in the independent random sampling) and that these are likely to be filtered out by sampling only the best 10% of replicates. Nevertheless, selecting the best 10% of replicates is determined arbitrarily, and the strength and weakness of this decision are further discussed in Section 2.6.1.5.2.
Product Finalisation date
 2.6.1.1 Methods
 2.6.1.2 Review of existing models
 2.6.1.3 Model development
 2.6.1.3.1 Spatial and temporal dimensions
 2.6.1.3.2 Location of model nodes
 2.6.1.3.3 Choice of seasonal scaling factors for climate trend
 2.6.1.3.4 Representing the hydrological changes from mining
 2.6.1.3.5 Modelling river management
 2.6.1.3.6 Rules to simulate industry water discharge
 References
 Datasets
 2.6.1.4 Calibration
 2.6.1.5 Uncertainty
 2.6.1.6 Prediction
 Citation
 Acknowledgements
 Currency of scientific results
 Contributors to the Technical Programme
 About this technical product