Notes on Temperature-Dependent Lidar Equations

Notes on Lidar interpolation

Representation of the earth’s surface as a point cloud (xi, yi, zi, where x and y are the horizonal coordinate axes, z is the vertical, and i is the index of the point) is often done using Light Distance And Ranging (LiDAR) technology from the air or ground (a general reference for much of what follows is El-Sheimy, et al., 2005). This technology uses a scanning laser from a known position to m...

New examination of the Raman lidar technique for water vapor and aerosols I: evaluating the temperature dependent lidar equations

The intent of this paper and its companion is to compile together the essential information required for the analysis of Raman lidar water vapor and aerosol data acquired using a single laser wavelength. In this first paper several details concerning the evaluation of the lidar equation when measuring Raman scattering are considered. These details include the influence of the temperature depend...

Notes on Difference Equations

We shall develop here a galois theory for difference equations. In the PicardVessiot galois theory for differential equations, the basic objects of study are the Picard-Vessiot extension of a field and its associated galois group. Recall that a Picard-Vessiot extension of a differential field k is an extension K generated by a fundamental set of solutions of a linear differential equation and h...

Notes on Wave Equations

2.1.1 Full Maxwell’s Equations The full set of Maxwell’s equations come in two forms. The first form is called either the integral or volume form and is shown in Table 2.1. These set of four equations show the interrelationships of the basic physical quantities studied in electromagnetics, which are summarized in Table 2.2. This form of Maxwell’s equations elegantly relates volumeand area-integ...

On the Navier-stokes Equations with Temperature-dependent Transport Coefficients