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