# Precipitation:Interpolation Between Gages

The rainfall interpolation technique for spatially varied rainfall is specified with either the **RAIN_INV_DIST** or **RAIN_THIESSEN** project cards. No interpolation method can create information without creating uncertainty. All interpolation methods “estimate” the spatially varied field from point measurements, introducing uncertainty. The Thiessen polygon method is simply a nearest-neighbor approach, while the inverse distance squared method produces smooth fields based on the assumption that the influence of a measured value decreases with the distance from the point of measurement squared. The spatial variability of instantaneous rainfall is correlated at a scale of only several km at most. Use caution. It is not appropriate to use rain gage data at distances greater than the correlation length of the rainfall rate field. For example, the use of 15-minute rain gage data from a gage that is 30 km from the catchment is completely unrealistic, making calibration impossible. If you have no rain gages in the catchment separated by less distance than the correlation length of the rainfall field, you do not have enough data to calibrate GSSHA.

For example, Ogden and Julien (1993) calculated the correlation length of radar-estimated rainfall rates from multi-parameter observations of convective rainfall. Putting aside the discussion of the appropriateness of the correlation length as indicator of spatial structure due to the anisotropy and non-stationary of rainfall, the calculated correlation length was on the order of 2.5 km. This means that a rain gage network with inter-gage distances greater than this distance will not capture the true spatial variability of rainfall. There is also a chance that significant rainfall will be completely missed by such a network.

The U.S. National Weather Service network of WSR-88D next generation (NEXRAD) weather radars offer the potential of providing rainfall estimates in locations where there are no rain gages. There are numerous error sources that affect the conversion of radar observations into rainfall rate estimates. Discussions of radar errors are beyond the scope of this manual. NEXRAD precipitation estimates can be used in GSSHA, by formatting the data into a GSSHA precipitation file using the RADAR precipitation type card. When using NEXRAD rainfall estimates, GSSHA assigns a rain gauge at the center of each radar data pixel. When combined with Thiessen polygon rainfall interpolation, this reproduces the original radar pixels. The use of inverse-distance squared interpolation should not be used with radar data.

## GSSHA User's Manual

- 6 Precipitation
- 6.1 Spatially and Temporally Uniform Precipitation
- 6.2 Spatially and Temporally Varied Precipitation
- 6.3
**Interpolation Between Gages** - 6.4 Interception