**Abstract**

Mapping functions and gradients in GNSS and VLBI applications were introduced in the sixties and seventies to model the microwave propagation delays in the troposphere, and they were proven to be the perfect tools for these applications. In this work, we revisit the physical and mathematical basis of these tools in the context of meteorology and climate applications and propose an alternative approach for the wet delay part. This alternative approach is based on perturbation theory, where the base case is an exponential decay of the wet refractivity with altitude. The perturbation is modeled as a set of orthogonal functions in space and time, with the ability to separate eddy-scale variations of the wet refractivity.

**Keywords:** GNSS meteorology, positioning, VLBI, deep space tracking, neutral delays, mapping functions, gradients
