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Why do you even need to forecast rivers?

Rivers affect many aspects of many people's lives. Some of the more important reasons are listed here:

• Flooding: It's nice to know when a flood crest will occur and how high it will be, especially if it's coming toward you or your stuff.
• Utilities: Hydroelectric power is a very inexpensive source of electricity (other than the obvious huge startup cost).
• Industry: The operations of many industrial complexes and factories are heavily dependent upon the level of a nearby river.
• Commerce: On some of the larger rivers, raw materials and finished products are shipped from one place to another on river barges and other floating conveyance vehicles. Knowing how the river is flowing allows shipping personnel to make adjustments to schedules and equipment to best allow for the river conditions.
• Water supply: Reservoirs which are used to supply water for a town are usually kept as full as possible. Heavy rain upstream can force the reservoir operators release water.
• Fun: Many people enjoy recreating on, in, and near rivers and lakes. What they can do is affected by how the river is running. A good river forecast is essential to let park operators, resort personnel, and river users what to expect.

How do you forecast your rivers?

Quite well, thank you very much. Seriously, though, our river modeling system is quite complex. However, it can be broken down into seven basic steps:

1. Define your river system's hydrology
2. Estimate basin average precipitation
3. Estimate basin average runoff
4. Compute how much water is coming from upstream
5. Add together the water coming from all sources
6. Convert the total discharge into a stage
7. Make your forecast

NWS river forecasts are based, to a great extent, on data from U.S. Geological Survey stream-gaging stations. The USGS operates most of its stream-gages on a cooperative basis with other federal, state and local agencies which fund the operation of individual gaging stations. For more information, see the USGS fact sheet, "Stream Gaging and Flood Forecasting, a partnership of the USGS and NWS." See also "Streamflow Information for the Nation."

1. Define your river system's hydrology

While it is possible to forecast an entire river system as a single reach, it is highly impractical: Over a large drainage basin such as the Rio Grande, the terrain, climate, soil type, vegetation, et cetera, can vary widely from the headwaters to the mouth. And it would be almost impossible to provide forecast for specific points along the river above the mouth. But if you can, we'd like to hear from you.

There is a strategy used to divide a river into drainage basins and forecast points. The most important considerations are



• topographical - such as natural watersheds and divides,
• geographical - when a tributary meets the main stem river,
• historical - large floods in the past have caused problems there, and
• political - because people want a forecast point there.

Basins which contribute toward a forecast point can be further divided if the hydrologist thinks such a division will better describe the main watershed. How finely he or she divides the basins is up to him or her, of course, but there is a practical limit.

After the basins have been defined, the hydrologic parameters must be defined. This includes basin area, soil moisture parameters, and routing parameters. If snow accumulation and ablation calculations are included, parameters for those are needed as well, parameters such as those for mean areal temperature.

Once a river system has been divided into subbasins, this structure does not have to be changed unless forecast points are moved, added, or deleted.

2. Estimate basin average precipitation

We collect rainfall reports from synoptic stations (i.e., surface observation sites), cooperative observers, and automated precipitation gages to get an estimate of the precipitation which has fallen over a watershed. The problem with this method is we are trying to estimate a continuous variable from discrete values. Needless to say (but I will anyway), there are problems. Various methods have been developed to estimate the basin average (or mean areal) precipitation for a basin; however, all of are doomed to fail from the start. We have a saying in hydrology: "You can never gage the maximum," which refers to not being able to get a rain gage directly underneath the heaviest/most intense/largest amount of precipitation. After all, what are the chances of the heaviest rainfall of a storm being directly over a 8-inch (20 cm) rain gage? (They're not very good. Trust me on this.)

Another problem calculating mean areal precipitation (MAP) is the spatial distribution of precipitation: Did a storm occur in only one part of a basin? How did the storm move? Was it convective (stormy) or stratiform (widespread and gentle)? These are all questions the hydrologist has to keep in mind when computing MAP. Combine that with trying to figure out exactly when the rain in each part of the basin occurred, and you'll be pulling your hair out. Luckily, we can often get away with relatively easy-to-calculate estimates.

Rainfall reports come from a number of sources, but all reports can be classified as either manual or automated. Manual observations are basically what they imply: Someone physically goes to a rain gage at the same time each day, reads the amount of rainfall which fell over the last 24 hours, and reports it. These reports are collected at a weather forecast office or are called in to a computer system and are sent to the RFC on precipitation collectives throughout the day.

Automated rainfall reports are really helpful in that they report more than just a 24-hour total. In some locations, 15-minute rainfall data is reported, greatly increasing the temporal rainfall distribution for a watershed. Most of our hydrologic models use a 6-hour time step, which means that the flow and rainfall (as well as other parameters) are accumulated or averaged over a 6-hour time period. A 24-hour rainfall report is nice to know about, but without some way of breaking that value into smaller periods (such as 6, 3, or even 1 hour), it doesn't do us much good in our river models.

Automated reports come to us from



• data collection platforms (DCP): Hydrologic data is collected continuously and transmitted every 3, 4, or 6 hours via satellite to a collection center at Wallops Island, Virginia, where it is distributed to the necessary users.
• Limited Automatic Report Collectors (LARC): Reports for the last few hours, as well as the current reading, are stored at the gage, and these reports can be accessed via telephone (both voice and computer).
• Automated Local Evaluation in Real Time (ALERT) Flood Warning Systems: These are cooperative, community-operated flood detection systems using radio transmissions to communicate gage readings from the gages to a central location, or node. These systems are accessed by NWS computers, and the reports are coded into a standard form and transmitted to the river forecast centers.
• Integrated Flood Observing and Warning Systems (IFLOWS): A gage network using both radio transmissions and physical line connections for two-way communications between base stations and the gages. Data is transmitted to NWS computers and then to the river forecast centers.

The new weather radars (Weather Surveillance Radar - 1988 Doppler, or WSR-88Ds, a.k.a NEXRAD) provide hourly estimates of precipitation on a temporal and spatial resolutions never before seen in river forecasting. Although the hourly data they provide is accumulated into six-hour values, it is possible to see where and when the six-hour, basin-average rainfall actually occurred.

The part of the river model which calculates basin average precipitation doesn't care how the precipitation fell during that time. It will simulate a basin-wide 2-inch rainfall the same as if 4 inches fell in the upper half and none at the other; they both give the same basin average amount. But this knowledge is important to the hydrologist to know when the water will reach the basin outlet. But I'm getting ahead of myself here.

3. Estimate the basin average runoff

After the MAP has been calculated, the savvy hydrologist must figure out how much of that rain will end up in the river. The amount of water which eventually ends up in the channel is called runoff. On a basin-wide basis, it is usually measured in depth units (inches or millimeters), but it actually represents a volume of water (a depth of something over an area).

The amount of runoff a storm generates depends mainly on these factors:

• rainfall amount - More rainfall, more runoff. 'Nuff said.
• rainfall duration - Early in the rainfall event, most of the rain that falls is used to make up any deficit in soil moisture before it begins runs off. If the rainfall ends before the upper soil layers become saturated, then no runoff will occur. During a rainfall events for a specified time interval and a constant rainfall rate, more runoff is generated later in the storm than earlier. This will cause the greater amount of excess to run off sooner than if the same amount fell over a longer period of time.
• rainfall intensity (rainfall amount in some time period) - More intense rain leads to more intense runoff. For example, 2 inches (5 cm) in 12 hours may not be such a bad thing, but 2 inches (5 cm) in a half hour could spell trouble. Water can soak into the ground only so fast, and this infiltration rate can changes with time.
• rainfall location - A storm occuring far from the channel will generate less overland runoff which actually makes it into the channel than a storm which is directly over the channel. Traveling through the soil, the water has more of a chance to soak deeper. All water which falls directly on a stream or a reservoir is pure runoff.
• soil type - Clay and other tightly-packed soils allow less seepage than looser, sandier soils.
• soil moisture - If the soil is already saturated, a higher percentage of rainfall will run off. This can be before the rain starts (i.e., a pre-existing condition) or this state can be reached during the course of a storm.
• time of year - Typically, soils are less able to absorb water during the cold season (winter) than during the warm season (summer). Also, much more vegetation is growing during the warm season, so a much greater fraction of the water heading toward the stream is captured by plants and trees and is put directly into the atmosphere via transpiration.
• slope - Hillier terrain gives the water the tendency to move along the surface more than soak in. It also causes the water to become concentrated faster at the basin outlet, leading to higher flood crests.
• vegetation - Areas with a lot of low-lying vegetation will slow overland flow, giving it more time to soak into the ground.

In colder climes, one must consider the effect of snowmelt on the volume of runoff. Snow can melt on its own when the air temperature warms above 32 °F (0 °C), or by rain falling on the snow. Snow also melts fast when the dewpoint temperature is above 32 °F (0 °C) because water vapor from the air is condensing on the snow, melting it, and because if the dewpoint is above freezing, so is the temperature, so it's kind of a double whammy. And if it's raining? Whoooo, boy! Look out!

Any or all of these factors can combine to melt vast amounts of snow, and generate a runoff volume which is greater than the volume of rain. Therefore it is important to be able to be able to use a snow model to accurately estimate how much snow is in the snowpack. Snow courses are used from late fall to early spring to provide estimates.

Various conceptual models have been developed to estimate either the runoff potential or the actual amount of runoff. The two most common ones are the Sacramento Soil Moisture Accounting Model (SACSMA) and the Antecedent Precipitation Index (API).

Flash flooding is also subject to the conditions listed above. A flash flood occurs when a storm produces runoff which peaks above flood stage less than six hours after the initiation of the runoff.



Not only does the amount of runoff need to be calculated, but so does the timing of when the runoff will reach the channel. The runoff also needs to be converted into a discharge, which depends on the factors listed above, the area of the basin, and the location of the storms or snow or both. The unit hydrograph accomplishes both these goals.

The unit hydrograph is a relationship between the amount and timing of the runoff and the amount of discharge reaching the channel in that period of time. It is a graph with the abscissa (x-axis) being time and the ordinate (y-axis) being flow per depth (for example, cubic feet per second [cfs] per inch or cubic meters per second [cms] per centimeter). This graph describes how a basin-wide runoff of some unit depth (one inch or one centimeter) (that's where the "unit" comes from) will reach the channel: both how much runoff and when it will reach the channel. Sites or basins with a unit hydrograph which peaks very quickly and recedes quickly are known as "flashy" sites, in the sense of "flash flooding." Sites with a broad crest are less flashy, as the water reaches the channel more gradually.

The ordinates of a unit hydrograph might be scaled by the ratio of the actual runoff to one. For example, to get the magnitude and timing of overland flow to the basin outlet from two inches of runoff, double the ordinate values from the unit hydrograph. That's why the y-axis units are flow per depth (cfs/in, cms/cm), and not just flow.

4. Compute how much water is coming from upstream

Now that we know how much water this basin is contributing at the forecast point, we need to know how much is being routed from the previous forecast point or points.

No matter which routing technique is used, it should take into account the time it takes for water to move from one point to another and the attenuation of the flood wave as it moves downstream. The way a flood wave moves downstream depends on these factors:

• stages downstream - if stages downstream are falling, the floodwave will be attenuated more than if downstream stages are rising.
• channel geometry - The more the channel cross-section increases downstream, the more the flood wave will be attenuated and retarded.
• length of reach - the longer a reach, the more water will be in channel storage and the more the flood wave will be attenuated.
• crest shape - A flatter flood wave crest will be attenuated less.
• wetting the channel - The initial water is used to wet the banks.
• overbank storage - When water flows out of banks, some of the water isn't able to get back into the channel.
• seepage - Porous channel bottoms cause water to become groundwater.

River stage reports come from the same sources as those mentioned above for rainfall sites: DCPs, LARCs, ALERT and IFLOWS networks, and observers. The proper operation of these automated gages is crucial to the continued high quality of our forecasts. When a gage malfunctions, it can be annoying, but during flooding it is much more so. Sometimes observers can be called and asked for reports at a bad gage, but the frequency of those reports (three times a day if we're lucky) are nothing compared to the (as frequent as) 15-minute data available from an automated gage.

5. Add together the water coming from all sources

Now that we know how much water this basin is contributing to the flow at the forecast point (i.e., local runoff), we must add the water from all other sources within the basin. These sources are usually the local flow (runoff) and tributaries which enter the main channel below the previous forecast point. And this is added to the water which has been routed downstream from the previous forecast point using some kind of routing scheme.

It is important to only add the component discharges, not stages. We are routing through the river system a volume of water, not a height. A river stage is an artificial construct which allows one to relate the height of the river surface to the flow. This is similar to reporting barometric pressure in height units of inches of mercury (centimeters of mercury), when pressure is actually a force per area.

Reservoirs present their own set of problems. When dry weather dominates, the flow from a reservoir can be estimated pretty well - if it's not zero, it's a few hundred cubic feet per second at most. However, when flooding is occurring, trying to guess what the reservoir operator is going to do can be a hair-pulling experience to say the least. Good communication between the forecast office and the reservoir control office is needed during crisis situations and is beneficial for both parties - the reservoir operator can find out what's coming into his reservoir from upstream and what his releases are doing downstream, and the river forecaster can use the accurate releases in his simulations to better predict the flow downstream. We all work together or we work apart.

6. Convert the discharge into a stage

Since it is a relationship between two variables, a rating can be used to convert the calculated discharge into a stage. While hydrologists would like to forecast flow, the public is used to hearing about stage. If you know your house will be flooded when the river is at a certain level, you really don't care what the flow is, you just want to know how close is it going to come to your house.

Stages are converted into discharges using a rating curve. Measurements of streamflow are made by the United States Geological Survey (USGS). A set of stage-discharge points are developed, and these are plotted on a graph such as that shown above. The x-axis is discharge, and the y-axis is the stage. The shape of the rating curve reflects how at low flow, a moderate change in discharge can lead to a moderate change in stage. This relationship usually continues until the river has reached bankfull when the river starts to spread out. Now it takes a larger increase of discharge for the same stage change at low flow. A seasoned hydrologist can look at a rating curve and tell you exactly what the channel's shape is. It's almost spooky at times.

Since the geometry of the channel any forecast point is rarely exactly the same as another's geometry, each rating curve is different. For every place where a river stage is recorded, a rating has been defined for those points. So each upstream point's stage is able to be converted an "equivalent" discharge.

As much as we hate it, ratings do change with time. Floods can scour (deepen) the channel, giving a larger cross-sectional area for a given stage. If the forecaster is not aware of this, he or she will think less flow is passing the forecast point than actually is. On the other hand, slower moving rivers can deposit silt on the bottom of the river, which decreases the cross-sectional area. Less flow will be occuring than is reflected in the river stage.

7. Make your forecast

The final step for the river forecaster is to inform the public as to what he thinks the river will do in the near future. Short phrases such as CREST NEAR 21 FEET THURSDAY or REMAIN 19-20 FEET NEXT SEVERAL DAYS are very useful to the public: the forecast tells them exactly what they want to know. A time-series of stages such as shown below is equally as useful; it gives more detailed information about what the forecaster thinks river will be doing at this particular point.

We have recently gone to these time-series forecasts. A typical one looks like this:

:LATEST STAGE    22.76 FT AT 638 PM CDT ON 0507
.ER ZZZT2    0508 C DC200005072026/DH01/HGIFF/DIH6
:RIVER FORECAST      7AM        1PM        7PM        1AM
.E1 :0508:             ::         ::          /      23.0
.E2 :0508:   /      23.1/      23.1/      23.2/      23.1
.E3 :0509:   /      22.9/      22.3/      21.5/      20.5
.E4 :0510:   /      19.7/      18.8/      17.9
:  ZZZT2 (AS 23.0 FS 24.0)
: CREST ARND AS LATE SUNDAY AND INTO MONDAY.
:***********************************************************************

This is the forecast we send to the WFOs, and is not meant for public consumption. The WFO forecasters, in turn, use an application to generate a worded forecast, which includes statements of impact, future rainfall, and call-to-action.

While the 6-hour values shown are precise the nearest 0.10 foot, these values should not be taken as an absolute assured forecast. As much as we try to get a handle on our rivers and any floodwaves within them, Mother Nature always does what she wants to do. In that sense, the values should only be used as a guide; the river will likely rise or fall faster or slower than that. Should it deviate significantly (depending on the situation) from our forecast, we will update it.

As with any forecasting or predicting, the more information you can gather before you make your forecast, the better. However, when major flooding is occuring, you're always balancing "I need more data!" with "I gotta get this out now!"

Many times in critical situations, the forecaster will make a vague forecast for a few days in the future just to let the public know what's going on, then refine it as the time approaches. Unexpected rain (or flow) will probably change the forecast, so a forecast of CREST NEAR 25 FEET SATURDAY might not verify very well if today is Monday, but it can be a decent first guess, used to give the public some idea of what they can expect, and the forecast will be updated as the week passes and more about the flood wave becomes known.

The river forecast center transmits these forecasts by computer network or calls them in by telephone to interested parties:

• Weather Forecast Offices: The primary recipient of our forecasts is the National Weather Service forecast offices that we support. They translate our "skeleton" forecast into a public statement and include information such as flood impacts (roads closed or subdivision flooded), historical information (comparison to past floods) and call-to-action statements (such as "don't drive into high water" - don't laugh; you'd be surprised at how many people die this way). These enhanced forecasts are used by everyone else, from international emergency operations officers to individual home- or landowners.
• Water authorities: These groups use our forecasts to plan for reservoir inflows and releases, as well as for other flood-related operations including the issuance of their own public statements.
• Emergency managers: Elected and appointed officials, from county judges to state governors, need river forecast information for not only to effect rescues, but for planning purposes before the flood wave arrives. Issues such as staffing, rescue equipment allocation, and preventive measures (like road closures and evacuations) are all critical not only for the protection of lives and property, but also to keep the costs of a flood from becoming excessive.
8. (whad'ya mean "8"?) Move to the next segment

This forecast process (steps 2 through 7) must be repeated for every segment of a river. Hopefully, not all parts of a river will be in flood at the same time, and the forecaster can give less attention to those points with no flooding and focus his attention on those which need more attention. But if there is activity over the entire basin, it can make for a very busy day.

Some river forecasts are easy. Most are not. Experience with a river allows the forecaster to learn where that river's trouble spots are. With experience comes not only failures and successes, but learning what happened and why, and using that knowledge to make a better forecast next time. We're sorry can't hit them all. We wish we could. But we always give our best effort.