The fundamental relationships between atmospheric properties sensed by radars and the mean height gradients of the properties are reviewed, and various assumptions discussed. Especially, the question of the necessity for assumptions about the turbulent Prandtl number and the Richardson number is examined. A new approach based on the covariance equations is compared with the conventional approach using the variance equations. Relationships between fluctuations of conserved passive scalars are examined. Specifically, the correlation between fluctuations in potential temperature and humidity is derived and found to be essentially ±1 if molecular diffusion is ignored, but it is somewhat reduced by differing rates of molecular diffusion. The relationship of dissipation rate of their variances to dissipation rate of their covariance is given. The implications for relating refractive index variance to the mean temperature and humidity gradients are discussed, and the relationship between optical C2N and radio C2N is given in terms of those mean gradients. The theoretical relationships are compared with measurements made on a 300-m tower and with a 915-MHz, vertically pointing Doppler radar, and satisfactory agreement between theory and experiment is found except when cloud return dominates the radar backscatter.