There are six different rainfall-runoff models made available to River Forecast Centers. The MARFC uses the "API Event Based" model. API stands for Antecedent Precipitation Index, meaning that the model uses an index number based on previous rainfall amounts and the length of time since the rainfall. This index value is then used on a graph that relates rainfall to runoff. This process used to be performed entirely on a series of charts and tables. This tried and true model has now been entirely computerized.
There are also a variety of routing methods available to be used in our forecast models. At the MARFC, we primarily use the Lag and K method. The lag value represents how long the water takes to get from one forecast point to the next. K indicates the amount of attenuation occurring, or how a wave of water is lowered and spread out as it flows downstream. No matter how much the peak of the water flow is lessened, the same amount of water must pass through the downstream point, barring human intervention. A graphical example of attenuation can be found in this JPEG file.
Then, after examining the model output, the forecaster then prepares the written forecast. The forecasts that we write are not released to the public, only within the NWS. The office whose area of responsibility includes one of our forecast points is responsible for issuing public statements regarding that particular section of river.
Here's an example of one of our internal forecast products.
For an example of a public forecast product, please see the Forecasts section.