Probabilistic Streamflow Forecasts: How to Interpret HydroForecast’s Confidence Intervals

HydroForecast is a probabilistic model, which means that we provide a range of streamflow values to expect and the likelihood of each potential flow to occur. Below is an example image of the HydroForecast dashboard, which has the mean predicted flow value represented by the dark blue line and the shaded dark blue and light blue, 50% and 90%, confidence intervals surrounding the mean.

This means that there is a 50% chance flows will fall within the dark blue shaded region and a 90% likelihood flows will occur within the light blue shaded region.

When thinking about a probability distribution, the 90% confidence interval represents the range of values within the lower 0.05 quantile and the upper 0.95 quantile, as shown in the schematic below.

Another way to think of the boundaries of the 90% confidence interval is that 95% of the streamflow predictions fall above the lower bound and 5% will exceed the upper bound.

Accessing the Full Range of Possibilities

Even though we only display the 50% and 90% confidence intervals in the dashboard, you can also access more confidence intervals from our API. We provide the following in our API (in parentheses is the parameter you would query):

• Quantile 0.99 (discharge_q0.99)
• Quantile 0.975 (discharge_q0.975)
• Quantile 0.95 (discharge_q0.95)
• Quantile 0.9 (discharge_q0.9)
• Quantile 0.75 (discharge_q0.75)
• Mean flow predictions (discharge_mean)
• Median flow predictions (discharge_q0.5)
• Quantile 0.25 (discharge_q0.25)
• Quantile 0.1 (discharge_q0.1)
• Quantile 0.05 (discharge_q0.05)
• Quantile 0.025 (discharge_q0.025)
• Quantile 0.01 (discharge_q0.01)

To learn more about how to access these values from the API see our support doc page.

How to Use Confidence Intervals

In general, we advise customers to use our mean flow predictions. However, the confidence intervals are especially valuable when making operational decisions  in cases where the weather forecasts may not agree. Generally speaking, when you’re deciding what to wear in the morning and one  weather forecast says it will rain, another app says clear skies and another says mist, you might carry an umbrella just in case.  If every weather app says clear skies and sunny, it’s probably safe to leave the umbrella at home.  

Looking at the cumulative rainfall schematic in the HydroForecast Dashboard is a great way to assess whether or not the weather inputs are agreeing. In the schematic below, we show an example where four different weather models all predict precipitation, but varying levels of intensity. On this occasion, we anticipate wider confidence intervals because the predicted precipitation inputs that directly feed into HydroForecast would result in a greater uncertainty.

Temperature forecasts is another key weather input into HydroForecast that offers insight into the range of streamflow predictions to expect. In the case below, we show how on March 23rd two weather forecasts predicted temperatures above freezing, where one stays below freezing later than the others. This is another example of when varying weather inputs and uncertainties can feed into wider confidence intervals.