Algorithm for RAIN1 Gage Calibration

The default raingage correction algorithm provided is modeled after Brandes and Wilson (1982). The algorithm uses a basic time step of one hour, that is, GAGE totals for each hour are compared to the hourly radar totals (based on a default Z-R relationship) for the same hour. The ratio (1-hour gage accumulation/1-hour radar accumulation) is the correction factor for a gage.

The RAIN1 product is then corrected by interpolating the correction factors for all of the gages to each pixel in the RAIN1 product and multiplying the radar pixel value by the correction factor. The basic algorithm steps are as follows:

1. Gage Correction Factor Calculation for Each Gage

   The gage correction is the ratio of the (1-hour gage accumulation)/(1-hour radar accumulation).

   • The gage accumulation is taken from the GAGE product. It must be greater than the Minimum Valid Gage Accumulation for a gage correction factor to be calculated.

   • The radar accumulation for the gage is calculated by first making an uncorrected RAIN1 product for the hour and then averaging the pixels surrounding the gage (according to the Averaging Distance - see Configuring RAIN1 with Raingage Correction).

     The pixels are averaged by summing only the valid (non-thresholded) pixels and then dividing by the number of valid pixels.

     For a gage correction to be calculated, the average rainfall accumulation must be greater than the Minimum Valid Radar Accumulation, and the number of valid (non-thresholded) pixels must be greater than the Minimum Percentage Radar RAIN1 Coverage.

   • If both the gage and radar 1-hour accumulations are valid, then a gage correction is calculated for the gage. Otherwise, the gage is flagged as invalid.

   • The maximum and minimum correction factor limits are then applied.

   • This procedure is repeated for each gage.

2. Gage Correction Interpolation for Each Pixel

   The gage correction factors are then applied to the uncorrected RAIN1 product to yield the final corrected RAIN1 output product. The technique is that the rainfall accumulation value at each pixel in the uncorrected RAIN1 product is multiplied by an average correction factor.

   The average correction factor for a pixel is calculated from all gages by weighting the correction factor for each gage inversely with its distance from the pixel, that is,

   $C − + Σ C i D i Σ 1 D i$

   where $C −$ is the average gage correction for a pixel, $C i$ is the correction at a gage and $D i$ is the distance between the gage and the pixel. Note that the minimum value of $D i$ is fixed at 1 km (0.6 mi).