Interactive Probabilistic Predictions

This web-app produces probabilistic hydrological predictions using the LS-MoM method introduced in McInerney et al (2017a). The web-app assumes the user has already calibrated their hydrological model using their preferred software and an acceptable objective function (see below). This is referred to as 'Stage 1' of the calibration. The user should upload the observed and calibrated streamflow time series, and specify the Box Cox transformation parameters (lambda and A*) used in the objective function during Stage 1. The web-app will then estimate the error model parameters (referred to as 'Stage 2') and generate probabilistic predictions in the form of streamflow time series and associated 50% and 90% prediction limits. A selection of metrics and diagnostics from Evin et al (2014) and McInerney et al (2017b) will be provided.

Objective functions

The web-app assumes a least-squares objective function, e.g. the sum-of-squared-errors (SSE) or equivalent Nash-Sutcliffe efficiency (NSE), computed from Box-Cox transformed flows (McInerney et al, 2017a). These include widely used objective functions such as the NSE (lambda=1, A*=0), the NSE on square-root transformed flows (lambda=0.5, A*=0) and the NSE on log-transformed flows (lambda=0, A*=0).

Demonstration data

By default, loading up the web-app for the first time will display probabilistic streamflow predictions for the Gingera catchment on the Cotter River (Australia), obtained from the GR4J rainfall-runoff model pre-calibrated to the log-flow NSE.

Uploading your own data

To upload your own data, create a CSV file with two columns, 'obs' and 'pred'. Obs is a time series of observed data, and pred is the corresponding time series of hydrological model predictions. Download the demo data file to see the required format: demo data file .

Further information

Further information on the importance probabilistic predictions in hydrology, and methods for generating these predictions, can be found on the Intelligent Water Decisions Blog and this talk at the 2016 DEWNR NRM Science Conference.

Contact us

Contact David McInerney for further details on how to use the web-app, the methods used for generating probabilistic predictions, and the diagnostics and performance metrics.


Evin, G., Thyer, M., Kavetski, D., McInerney, D., & Kuczera, G. (2014). Comparison of joint versus postprocessor approaches for hydrological uncertainty estimation accounting for error autocorrelation and heteroscedasticity. Water Resources Research, 50(3), 2350-2375, DOI: 10.1002/2013WR014185. McInerney, D., Thyer, M., Kavetski, D., Bennett, B., Gibbs, M. & Kuczera, G. (2017a). A simplified approach to produce probabilistic hydrological model predictions. Environmental Modelling and Software (submitted). McInerney, D., Thyer, M., Kavetski, D., Lerat, J., & Kuczera, G. (2017b). Improving probabilistic prediction of daily streamflow by identifying Pareto optimal approaches for modeling heteroscedastic residual errors. Water Resources Research, 53(3), 2199-2239, DOI: 10.1002/2016WR019168.


Model Parameters

Performance metric plot type
Residual plot type

Metric Summary