# Evaluation and Improvement of Lidar Performance Based on Temporal and Spatial Variance Calculation
## 1 Introduction  
Lidar has proven to be an active remote sensing tool for atmospheric sciences and environmental research applications, one which can provide the atmospheric temperature, humidity, wind velocity, and aerosol optical properties by analyzing the spectra and intensity of laser echo signals [1]. The multi-wavelength polarization can be used to measure the depolarization ratio and microphysical properties by analyzing the variation of the polarization and the intensity of the lidar returns, and plays an important role in evaluating cirrus cloud and aerosol direct radiative effects [2; 3]. Vibrational Raman lidar can be used to measure aerosol extinction, water vapor, and carbon dioxide concentration by extracting the vibrational Raman spectra of nitrogen, water vapor, and carbon dioxide [4; 5]. Rotational Raman lidar can be used to measure atmospheric temperature, as the intensity of an individual pure rotational Raman line of nitrogen and oxygen depends on temperature, due toBoltzmann distribution [6]. High-spectral-resolution lidar (HSRL) is an important remote sensing tool in the application of atmospheric physics measurement, which utilizes narrow band spectral filters to separate the Mie scattering and Rayleigh scattering signals, or to measure the width (FWHM) of Rayleigh spectra, or to discriminate the frequency shift of Mie and Rayleigh spectra to realize accurate measurements of atmospheric aerosols, temperature, and wind velocity [7; 8; 9]. In atmospheric lidars, the stored lidar data not only presents the variation of atmospheric conditions, but also shows the connections with the hardware of the lidar system, especially the photo-electric converter and the data-acquisition subsystem [10; 11]. The photo-electric converter plays an important role in lidar applications; it is utilized to \"faithfully\" convert the light pulse of the laser echo signal into a new electronic pulse signal. The pulse width of the electronic pulse signal is determined by the convolution of the pulse broadening of the laser echo signal, and the time response of the photo-electric detection circuit [12]. With the advantages of a wide spectral response range, high quantum efficiency, high gain, and low noise, the photomultiplier tube (PMT) is the most widely used photo-electric conversion device in atmospheric lidar applications, and can work in both analog detection mode and photon-counting (PC) detection mode. The analog detection mode has the advantage of high linearity and is suitable for the measurement of lower atmosphere, while the PC detection mode has the advantage of high sensitivity and is suitable for atmospheric measurement in far range [13]. Understanding the characteristics of the lidar data trace is meaningful in the recognition of the performance of the lidar system, although the lidar data trace presents the variation of the atmospheric information. [PERSON] et al. found that the PC data of solar background and lidar echo signals are distributed to be Poissonian [14]. [PERSON] et al. simultaneously utilized the analog detection mode and PC detection mode in Raman lidar for aerosol and water vapor measurements, and recognized that the PC data had the characteristics of a Poisson distribution, while the analog data should not be taken as a single data point in the variance calculation [15]. [PERSON] et al. proposed a novel technique to correct the non-Poisson distributed lidar data to improve the accuracy of the lidar profile [16]. Meanwhile, the noise from PMT itself reduces the detection precision of lidar. [PERSON] et al. proposed a method to discriminate and eliminate the induced noise of PMT, and succeeded in lidar application for aerosol measurement in stratosphere [17]. [PERSON] et al. utilized the calculation of the Poisson distribution to evaluate the random error of lidar returns due to the shot noise of PMT, and corrected the airborne aerosol lidar data [14]. [PERSON] et al.