The Science of River Forecasting


Recently, NOAA’s NWS released an updated probabilistic spring flood outlook (part of the Advanced Hydrologic Prediction Service or AHPS) in order to reflect the anticipated second crest on the Red River and its tributaries. Some of the more notable numbers in this outlook were found at Fargo-Moorhead, where there is a 75 percent chance of reaching or exceeding 41 feet and a 25 percent chance of reaching or exceeding 42.8 feet. The second crest at Fargo-Moorhead and other places in the Red River Basin is expected to occur in the latter half of April.  But where do these probabilities come from?


Science of Floods. Several factors create a high potential for additional significant flooding in the Red River basin. They serve as the scientific basis for the expected second crest, and include already high flows on area rivers, saturated and/or frozen soils, widespread frozen surface water, record precipitation and recent significant snowfall, and reduced water storage on area reservoirs.  This information is all factored into the NWS River Forecast Model simulation in a numeric format. For instance, the liquid equivalent of the recent significant snowfall was between 1 and 2 inches in many locations in the southern part of the Red River Valley. This liquid equivalent information is mapped and placed into the numerical river model simulation.


Science Behind the Numbers. The factors mentioned as the science behind the numbers serve as the basis for the present conditions across the basin.  They are the “starting point” for the river model simulations.  However, it is ultimately all of the future temperatures and precipitation that dictate how fast and to what height the rivers will rise.  It’s no secret that weather forecasting is difficult, and beyond a few days the degree of error in predicting temperatures and precipitation increases, especially in the spring and fall “transition” seasons.  Unfortunately, it’s those longer-range weather factors that are the most important to flood outlooks. We look toward history to help out. 


The AHPS outlooks are based on what is called the Ensemble Streamflow Prediction or ESP. What this means is that the NWS River Forecast model takes the present conditions and then applies the weather conditions from a specific historical year (say 1995) for a 90-day period of interest (say April 9th through July 8th) to the model.  In other words, the model takes the present-day numbers representing all of the scientific factors involved in a flood and applies to them the observed temperatures and precipitation from every day in that 90-day period from the year 1995.  The result is what the river height would be if 1995’s weather occurred with the current conditions.


Wait! What does 1995 have to do with today?  Well, just a little bit. The reason the AHPS outlooks are called an ensemble is because they create simulations by applying weather for over 50 different years to the present conditions. This means that the extremes of weather in the region at this time of the year are captured…both very dry and very wet and very warm and very cold periods during the melt.  The graphic below shows an example of what the river stages at Grand Forks would look like based on each of the possible weather scenarios from 1949 to 2005.




Figure 1. ESP traces at East Grand Forks for current AHPS run on April 2, 2009.


The statistics go to work once graphs like the one above are created.  The year with the maximum simulated crest is ranked as number one, the year with the second highest as second, and so forth.   The probability of reaching the stages is calculated by dividing its rank by the number of years in the ensemble (plus one, actually…which is a well-accepted statistical formula). This ends up meaning that the lowest simulated crest has the highest probability of occurring.  So, in most cases this means that a 90% confidence is based on what would happen to the river even with very little additional precipitation. The low probabilities (like 2%) represent what could happen if a rapid melt or excessive precipitation occurred with the present basin conditions.


Luckily, all the hard work is already done for you. Click here to see the forecast points in the area, and after you select a point of interest, click on “Chance of Exceeding Levels During Entire Period” from the tabs above the hydrograph. A graphic like the one below will appear. The black triangles (labeled CS for “Conditional Simulation”) mark the probability of a certain height being reached. In the Grand Forks example, this means there is a 90% chance of the Red River rising to 49.8 feet. The blue dots (labled HS for Historical Simulation) represent what the chances of the river rising to a certain height would be using average snow cover, soil conditions, and spring river levels, not the present ones. It’s merely a judge of how unusual the pattern is (the farther apart the CS and HS markers are, the more atypical the present conditions are).  



ahps 2 

Figure 2.  Chance of Exceedence Values at East Grand Forks for current AHPS run on April 2, 2009.



What about within 7 days of the second crest? When the time for the crest nears, the forecasted weather during the next 7 days is utilize by the NWS River Forecast Model. This means that within seven days, the historical data has no impact on the forecasts. As a result, the forecasts are given with stage heights rather than probabilities.  Of course, there are literally hundreds of variables influencing the forecast heights. This means that a change in the temperature forecast of only 5 degrees five days from now could significantly change the river forecast. As a result, sometimes forecasters need to give ranges of possibilities in the river forecasts, especially when the crest is several days out. The crest height is refined slightly as it nears and confidence increases. This does sometimes result in some adjustments to the expected crest. However, in the end it is the current conditions that influence the eventual river heights. We can see from the probabilistic method that in many cases this year, no matter what the weather winds up being, major or even record flooding will occur.


For the latest river forecasts, click here and select a point of interest. The first graphic that comes up when you select a river point shows both observed stage (in blue) and the forecast stage (in green) for the next seven days.



Return to News Archive is the U.S. government's official web portal to all federal, state and local government web resources and services.