The quantitative interpretation of weather radar measurements

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Abstract
The effects of beam smoothing and post‐detection integration on radar measurements of reflectivity and meteorological quantities are re‐examined for a simple but general model of space variability of reflectivity. The radar equation is derived for the variable field of reflectivity factor and a set of equations is developed giving the true model values of reflectivity, as well as its first and second derivatives, in terms of the measured quantities. Radar measurements are interpreted as averages over the measurement cell and as point values at the centre of the cell. The biases associated with both interpretations for linear, square‐law and logarithmic detectors are studied. It is shown that these biases depend on the parameter inferred from the radar received power (reflectivity factor, rain rate, etc.), the receiver response and the interpretation given to the measurements (point or averages).

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