Theory Behind River Forecasting

Water - Where Does it Come From?

The water that flows through the rivers is merely part of a greater cycle that is occurring all around us each and every day, the Hydrologic or Water Cycle:

Click here to get a diagram of the water cycle.

Precipitation can take many forms from rain to to snow and from hail to sleet. Though different, each form of precipitation has one thing in common and that is that they each fall from clouds in the sky to the ground. When water hits the ground, it can go in two directions, vertical or horizontal. The vertical flow is when is slowly seeps into the ground and is called infiltration. The horizontal flow is called surface runoff.

Infiltrations happens when the precipitation filters into the ground and travels all the way down to the water table. The water table is the top layer of saturated ground that can be found across the planet. in places where the water table is above the surface, water fills these places until the water level is the same the water table level, thereby forming rivers and lakes. The water found in the water table is called groundwater. If there has not been any rainfall in several days, the rivers will keep falling until the river levels are the height as the water table.

Surface runoff is when precipitation moves along the surface of the ground when either the ground can no longer absorb the water, or the ground cannot absorb the water fast enough. The water flows along the surface until it finds its way into a stream, river, lake, or ocean. Surface runoff causes the stream to rise quickly after it rains because it is the fastest way water can reach a river or stream, much faster than through infiltration.

Picture yourself as a raindrop. You fall from the sky and and hit the ground. You decide that you want to reach the river as fast as possible, so you go as surface runoff and flow along with the others like yourself to a river. The river is like a ride in an amusement park, both temultulous and meandering. You finally find yourself coasting into your rest stop in either a lake or an ocean. While resting there, the sun comes out and heats things up. Things are simmering in the heat and you lose your shape slowly until you become a gas. The process of liquid water turning into a gaseous water vapor is called evaporation. You are much lighter than your previous drop form and you float up to the sky. When enough similar water drops evaporate and you climb high enough in the sky, all of you will form water drops again. This process of cooling down water vapor and forming water drops is called condensation. You find your best friend in the crowd and decided to go together. Then you find another droplet friend who wants to go along. Eventually you have so many friends together that you can't fit in the same theater. So some of your droplet friends have to leave and fall back down to the ground as rain. You go through this process over and over, thus forming the water cycle.

River Forecasting - the Basics

We have so far seen how water arrives in the rivers. Now, we can look at the way a river forecaster uses this information to make a forecast.

The Components

To be able to forecast the amount of water flowing through a certain point along a river, the forecaster breaks the flow down into three components:
  1. Baseflow: the amount of water coming from groundwater.
  2. Runoff: the amount of water coming from surface runoff.
  3. Routed Flow: the amount of water coming from an upstream point.


Baseflow, the water coming from groundwater, is never a constant value. It increases immediately after rainfall, and then it falls until the next rainfall.


Runoff comes from two sources, rainfall and snowmelt. A forecaster can estimate an amount of runoff for each type based of certain characteristics of the weather and the river basin. Snowmelt calculations are based on the air temperature and the amount of sunshine. Rainfall runoff is estimated based on the slope of the land, the amount of urbanization, the soil types, the amount of the last rainfall, the time since the last rainfall, and the amount of evaporation occurring over the basin.

When rain begins to fall, the runoff does not immediately go into the river. It takes time for the runoff to flow into the river and the amount of time depends on where in the basin the rain fell. To get a sense of how this works, envision a parking lot with a storm drain at one end. Next, think what happens if a steady, even rain fell over the entire parking lot. All of the rain wouldn't reach the drain at once, because the distance the rain needs to travel to the drain varies throughout the parking lot. Even when the rain stops, water will continue to flow into the drain until the water from the far part of the parking lot reaches the drain. If the amount of water going through that drain was recorded and put on a graph of water flow versus time, it would look something like this:

Any graph of water flow versus time is called a hydrograph. When a forecast is being made, the forecaster always uses a hydrograph of the stream at the forecast point. From this hydrograph, the forecaster can begin to make a forecast.

A special hydrograph, called the unit hydrograph, is used by forecasters when they want to know how much water will be put into the stream by runoff. The unit hydrograph is based on the basin receiving enough rain to make one inch of runoff. An inch of runoff is the equivalent to having the entire basin of a particular stream or river covered in a inch of rain that does not infiltrate into the ground. The unit hydrograph shows how much of this inch of runoff will go into the stream in a specific amount of time. Also, for the unit hydrograph to work properly, the length of time in which the runoff was generated and the time intervals on the unit hydrograph must be the same and the rain that produces the runoff much fall within the first X hours of the X hour unit hydrograph. Here at the MARFC, we use a six-hour unit hydrograph. A six-hour unit hydrograph describes how much water is flowing into the stream from runoff in six hour periods. Remember, the rain that produces the runoff must fall in the first six hour period. As you can see below, from 0 to 6 hours, 800 cubic feet per second (cfs) of runoff water has been added to the stream.

TIME     0     6    12    18    24    30    36    42    48    54    60 
FLOW     0   800  2500  4300  5700  6500  6000  5100  4200  3400  2900  
If, for instance, the runoff is something other than one inch, 0.1 inches for example, then you multiply the unit hydrograph value by the amount of runoff to find the amount of flow into the stream. In our example of 0-6 hours, 800 cfs is added for each inch of runoff. So, if only 0.1 inches of runoff is to be added, then multiply the runoff by the hydrograph value. So in our example, at the end of six hours, 0.1 * 800 = 80 cfs of water flow has been added to the stream.

Now, let's consider what would happen if we want to forecast for 24 hours. We notice that 1 inch of runoff there will give us 5700 cfs. By our example above, if the runoff amount is 0.1 inches, then we find that the amount of water flowing into the stream is 0.1 * 5700 = 570 cfs. Now what would happen if another 0.1 inches of runoff was generated by rainfall 6 hours later. Then we would look ate the 18 hour hydrograph value because you are basically looking at the amount flowing in the stream for 24 hours, but the rain did not start until after the first six hours. For 18 hours the flow amount for one inch of runoff is 4300 cfs. For 0.1 inches of runoff, the amount added to the stream flow would be 0.1 * 4300 = 430 cfs. Now the forecaster adds the amounts of the initial 0.1 inches of runoff for the 24 hour forecast and the amount for the 0.1 inches of runoff that occurred six hours later (570 cfs + 430 cfs = 1000 cfs) to get 1000 cfs to be added to the stream flow 24 hours in the future.

Upstream Flow Routing

The final component of streamflow is the routed flow, the water that is coming downstream from the previous gage point. Many different methods of routing are used, but they all rely on the same principle: all of the water that passed through the upstream point must eventually pass through the downstream point, barring human intervention. But due to various factors, such as the riverbed slope, the viscosity of water, distance between gaging points, the peak flow at the downstream location is never more than the upstream location. In most cases, the peak flow at the downstream location is lesser.

Next, Head Downstream

After the forecaster is done with a stream, or portion of a larger river basin, he or she moves to the next downstream location and begins again.

Next, the data that we use.