Articles | Volume 9, issue 8
Research article
25 Aug 2016
Research article |  | 25 Aug 2016

Proposed standardized definitions for vertical resolution and uncertainty in the NDACC lidar ozone and temperature algorithms – Part 1: Vertical resolution

Thierry Leblanc, Robert J. Sica, Joanna A. E. van Gijsel, Sophie Godin-Beekmann, Alexander Haefele, Thomas Trickl, Guillaume Payen, and Frank Gabarrot

Abstract. A standardized approach for the definition and reporting of vertical resolution of the ozone and temperature lidar profiles contributing to the Network for the Detection for Atmospheric Composition Change (NDACC) database is proposed. Two standardized definitions homogeneously and unequivocally describing the impact of vertical filtering are recommended.

The first proposed definition is based on the width of the response to a finite-impulse-type perturbation. The response is computed by convolving the filter coefficients with an impulse function, namely, a Kronecker delta function for smoothing filters, and a Heaviside step function for derivative filters. Once the response has been computed, the proposed standardized definition of vertical resolution is given by Δz = δz  ×  HFWHM, where δz is the lidar's sampling resolution and HFWHM is the full width at half maximum (FWHM) of the response, measured in sampling intervals.

The second proposed definition relates to digital filtering theory. After applying a Laplace transform to a set of filter coefficients, the filter's gain characterizing the effect of the filter on the signal in the frequency domain is computed, from which the cut-off frequency fC, defined as the frequency at which the gain equals 0.5, is computed. Vertical resolution is then defined by Δz = δz∕(2fC). Unlike common practice in the field of spectral analysis, a factor 2fC instead of fC is used here to yield vertical resolution values nearly equal to the values obtained with the impulse response definition using the same filter coefficients. When using either of the proposed definitions, unsmoothed signals yield the best possible vertical resolution Δz = δz (one sampling bin).

Numerical tools were developed to support the implementation of these definitions across all NDACC lidar groups. The tools consist of ready-to-use “plug-in” routines written in several programming languages that can be inserted into any lidar data processing software and called each time a filtering operation occurs in the data processing chain.

When data processing implies multiple smoothing operations, the filtering information is analytically propagated through the multiple calls to the routines in order for the standardized values of vertical resolution to remain theoretically and numerically exact at the very end of data processing.

Short summary
This article prescribes two standardized formulations for the reporting of vertical resolution of lidar ozone and temperature profiles across an entire atmospheric observation network. Thanks to these standardized definitions, profiles from various instruments and techniques can be compared without ambiguity when interpreting their ability to resolve vertically fine geophysical structures.