Developing Depth-Area Reduction Factor Curves

Depth-area reduction factor (DARF) curves are used to evaluate areal precipitation due to a storm event that occurs simultaneously over an entire watershed, i.e., an area where all the water in that area flows to a common drainage such as a stream or river, using available point precipitation data. According to the American Meteorological Society, for areal rainfall of a given duration and return period, the DARF is the ratio of the mean areal rainfall to the mean point rainfall for the same duration and return period in the same area. DARF curves can be developed for storm events using radar data and, as necessary, calibrating these data with point precipitation gage station data.

Historically, DARF curves were calculated using precipitation station gage data. However, due to their more complete coverage area, radar data may be the best available data source. NEXRAD N1P precipitation accumulation radar data can be used to evaluate storm events where no rain gage data are available or to supplement available rainfall data. NCEI provides an array of processed radar products available for download on NOAA’s NCDC website. One useful product is estimated ground-accumulated rainfall which converts radar data to rainfall. This accumulated rainfall estimate is based on a reflectivity-rainfall rate relationship (Z-R relationship). NOAA develops and calculates these Z-R relationships based on factors such as orographic effects and type of convection system. Often each radar station will have its own Z-R formula that determines the amount of rainfall from reflectivity data from the radar station. Since precipitation can only be measured at a point location, whereas radar data covers entire regions, it can be extremely useful to estimate precipitation from the ground-accumulated rainfall with radar data, especially in areas where rain gage stations are sparse.

DARF curves are used to predict rainfall reduction of similarly-shaped storms within the same region and can be used for flood risk assessment for the area. If one can determine how much rainfall fell over an area, one can better predict rainfall and storm runoff in locations where gages are not available.

Depth-Area Reduction Factor Curves Legend
  Figure 1: Outline of storm event used to develop a DARF curve.

Figure 1: Outline of storm event used to develop a DARF curve.

To generate a DARF curve from precipitation or radar data, the maximum storm event is mapped and outlined, as shown in Figure 1. Areas within a range of precipitation intensity are calculated to determine the areal extent of each range of precipitation values. These precipitation ranges are then calculated as a percentage of the maximum precipitation and plotted by areal extent, as shown in Figure 2 for a specific storm event. A best fit curve can then be estimated from these data, which is the final DARF curve. To generate a DARF curve for a region, this process is repeated over multiple storm events before plotting a best fit curve. With a DARF curve, one can then calculate what the maximum precipitation is over a given area within the storm event. For example, in Figure 2 the maximum point precipitation of the storm was 1.5 inches, while the maximum precipitation over a 100 mi2 within the storm event had an average precipitation of 0.5 inches (33 percent in Figure 2).

  Figure 2: Example of a DARF Curve

Figure 2: Example of a DARF Curve

DARF curves are used in surface water models such as HEC-RAS and MIKE FLOOD when estimating flood risk from storms. The DARF curve is applied within a watershed area to estimate water flowing down drainages that are located far from gaged sources, as to realistically estimate flood risks.

If you are interested in receiving a DARF curve analysis from radar and point precipitation data, get in touch with us!