Measurement error in reflectance data and its implications for regularizing the variogram

Measurement error is an important component of variation in most measured variables and also, therefore, in the sample variogram of field-based reflectance. The variogram of the underlying variation in reflectance is regularized and, therefore, must be continuous through the origin. The variogram of measurement error in reflectance, however, is unlikely to pass continuously through the origin. Therefore, the sample semivariance at a lag of just greater than zero, <(gamma)over cap>(nu)(0(+)), is likely to be some positive value due solely to the error in measuring reflectance. We recommend that where possible <(gamma)over cap>(nu)(0(+)) should be computed by repeated measurement of reflectance at the same location, x, and over the same support, v. If repeated measurement is not possible then in certain circumstances the nugget variance of the variogram model may be used to estimate measurement error in the sample variogram denoted gamma(nu ME). If gamma(nu ME) is not estimated and measurement error is not separated from the underlying variation then geostatistical techniques that depend on <(gamma)over cap>(nu)(h) and which are currently being applied in remote sensing may be affected. We demonstrate these ideas with a simple example involving regularizing the variogram of the Normalized Difference Vegetation Index (NDVI) of a field of pasture measured with a field radiometer.