Proposed standardized definitions for vertical resolution and uncertainty in the NDACC lidar ozone and temperature algorithms – Part 1: Vertical resolution
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 desc...
| Main Authors: | , , , , , , , |
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| Format: | Article |
| Language: | English |
| Published: |
Copernicus Publications
2016-08-01
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| Series: | Atmospheric Measurement Techniques |
| Online Access: | http://www.atmos-meas-tech.net/9/4029/2016/amt-9-4029-2016.pdf |
| Summary: | 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.
<br><br>
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 Δ<i>z</i> = <i>δ</i><i>z</i> × <i>H</i><sub>FWHM</sub>, where <i>δ</i><i>z</i> is the lidar's sampling resolution and
<i>H</i><sub>FWHM</sub> is the full width at half maximum (FWHM) of the response, measured
in sampling intervals.
<br><br>
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 <i>f</i><sub>C</sub>,
defined as the frequency at which the gain equals 0.5, is computed. Vertical
resolution is then defined by Δ<i>z</i> = <i>δ</i><i>z</i>∕(2<i>f</i><sub>C</sub>). Unlike
common practice in the field of spectral analysis, a factor 2<i>f</i><sub>C</sub> instead
of <i>f</i><sub>C</sub> 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 Δ<i>z</i> = <i>δ</i><i>z</i> (one sampling bin).
<br><br>
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.
<br><br>
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. |
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| ISSN: | 1867-1381 1867-8548 |