# Evaluation and Improvement of Lidar Performance Based on Temporal and Spatial Variance Calculation
## 5 Discussion  
In this paper, most of the works were implemented using spatial variance, considering that the lidar system constant remains unchanged in a single probing trace. Within a limited range interval, the distributions of the spatial variance were more stable than the distributions of the temporal variance, in which multiple lidar probing traces were used to construct the sample distributions. The results of the temporal variances not only show the variation of atmospheric condition with time, but also present the variations of the lidar system constant in different probing profiles, especially the influences of the laser jitter. The concept of temporal variance was proposed for studies of the time scale of the atmosphere. Although the technique of data merging is performed using the spatial variance calculation, the calculation of temporal variance can be applied using data merging as well, which produces a similar result as the spatial variance.  
The traditional method for data merging between analog data and PC data is to investigate the transfer coefficients \(a\) and \(b\) by minimizing the differences between the transformed PC data and the raw PC data within a linear region with the count rate range of 1-20 MHz [15; 28]. The lower count rate and upper count rate of the linear region are affected by atmospheric conditions and by the performance of the data acquisition hardware, as the A/D card for analog detection mode and the PC system for PC detection mode are two independent devices [15]. Recorded data can be affected by ground noise in the analog detection chain and by discriminator level in the PC detection chain, which makes the linear region system-dependent and results in relatively large transformation errors due to different linear intervals [29]. The distributions of the transfer coefficients \(a\) and \(b\) for a number of data traces obtained from the scan measurements were investigated using both the variance-based gluing method and the traditional method, which are shown in Figure 13. For both merging methods, an identical linear relationship between \(a\) and \(b\) was found, with about 5% difference in the slope. The longitudinal distribution of trace characteristics (points with coordinates defined by \(a\) and \(b\) values) along the fitted line was found to be Gaussian in the case of variance-based gluing. In the case of the traditional method, no smooth functional dependence cloud be found, which implies that this method was more affected by the variation of the atmospheric condition in the lidar field of view. This paper provides a new idea for data merging between analog data and PC data, which makes the glued profiles have the uniform properties of variance-mean distributions.  
In both investigations of the dead time of the PC system and the transfer coefficients \(a\) and \(b\) in variance-based data gluing (Equations (6) and (7)), the results were weighted by the larger values due  
Figure 13: Distribution of the transfer coefficients of \(a\) and \(b\) for a number of data traces obtained at different scan measurements. An identical linear relationship was found for both the variance-based gluing method and the traditional method (green line).  
to the large dynamic range. In the estimation of the dead time of the PC system, the research purpose was to correct the pile-up effect of PC data, which influenced the accuracy heavily when using the head part of the PC data with larger values. However, in the data gluing, only the analog data with a range interval starting at the head of the trace to where the signal to noise ratio was continuously greater than 10 were contributed to the retrieval procedure. The transfer coefficients \(a\) and \(b\) were used to transform the analog data to PC-like data using a linear transformation, especially the head of the analog data, which is the head part of the normalized lidar data trace used to uniformly express atmospheric conditions.