Approaches are considered to estimate the background concentration level of a target species in the atmosphere from an analysis of the measured data provided by the National Physical Laboratory's differential absorption lidar (DIAL) system. The estimation of the background concentration level is necessary for an accurate quantification of the concentration level of the target species within a plume, which is the quantity of interest. The focus of the paper is on methodologies for estimating the background concentration level and, in particular, contrasting the assumptions about the functional and statistical models that underpin those methodologies. An approach is described to characterise the noise in the recorded signals, which is necessary for a reliable estimate of the background concentration level. Results for measured data provided by a field measurement are presented, and ideas for future work are discussed.

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Differential absorption lidar (DIAL), which is based on the optical analogue
of radar, provides the capability to measure remotely the concentration and
spatial distribution of compounds in the atmosphere (

The lidar technique is based on transmitting a pulse of laser radiation into
the atmosphere and measuring the light scattered by the atmosphere and
returned to the system. The DIAL system extends the basic lidar technique by
operating the laser alternately at two adjacent
wavelengths (

A critical part of the analysis of the measured data provided by the DIAL system is to estimate, and subsequently correct for, the background concentration level of the target species along the optical measurement path. This is necessary for an accurate quantification of the concentration level in the atmosphere of the target species, which may be a pollutant or greenhouse gas emission, for the purpose of source attribution and to support decisions made on the basis of that quantification. This paper is concerned with approaches to analysing the measured data provided by the DIAL system to estimate the background concentration level of the target species.

The paper is organised as follows. In Sect.

For a given elevation angle

Given measured values

evaluate an estimate

evaluate estimates

Figures

The two-step LLS approach is based on two main assumptions. Firstly, an
assumption is made about the consistency of a straight-line model with the
data

Measured signals (at off-resonant
wavelength in blue and on-resonant wavelength in red), and the positions
defined by indices

Path-integrated concentration data and straight-line model calculated using the two-step LLS approach.

Some information about the location of the plume – in terms of values of
indices

The deficiency in the statistical model for the data

An alternative analysis approach is then based on solving a GLS problem as
follows (

The above formulation of the GLS problem makes no assumption about the
functional form of the returned signals. In an alternative formulation, the
returned signal corresponding to the on-resonant wavelength is modelled as

A number of variants of the above formulations of the GLS problem are also considered:

Only the data after the window containing the plume are treated, i.e.

The parameters

The values

where

To apply the analysis approach, it is necessary to know the covariance matrix

A characterisation of the noise in the two returned signals is undertaken in
terms of estimates of the errors in the measured data for those signals. Let
index

Figure

A (multi-output) auto-regressive (AR) model is used to characterise the noise
in the signals. Let

Let

An approach to selecting the order

Residual deviations for (parts of) the
measured signals shown in Fig.

Properties of the
residual deviations shown in Fig.

Transformed residual
deviations for (parts of) the measured signals shown in
Fig.

Properties of the transformed residual deviations shown in
Fig.

Values of (left) the standard deviation

The estimated AR model determines the covariance matrix

For the signals shown in Fig.

Figure

Finally, Figs.

Values of the mean square error for (left)
different values of

In red, the results of the two-step LLS
approach applied to the data with indices

Values of the transformed residual deviations
for the signals at (left) the off-resonant wavelength, and (right) the
on-resonant wavelength, for the results of the GLS approach shown in
Fig.

As Fig.

As Fig.

As Fig.

As Fig.

Results are presented for field measurements made for six elevation angles

The analysis described in Sects.

Table

It may be expected that the results provided by the GLS approach using the
data with indices

As Fig.

As Fig.

For each elevation angle

For each elevation angle

For each elevation angle

This paper has been concerned with approaches to analysing the recorded measured data obtained using NPL's DIAL system to estimate the background concentration level of a target species in the atmosphere. The estimation of the background concentration level is necessary for an accurate quantification of the concentration level of the target species within a plume, which is the quantity of interest. The paper has focussed on methodologies for estimating the background concentration level and, in particular, contrasting the assumptions about the functional and statistical models that are part of those methodologies.

An approach to estimating the background concentration level has been
described. It uses a functional model for the path-integrated concentration
level that allows for the presence of a plume. It also uses a statistical
model in the form of an auto-regressive function to describe the noise in the
measured data for the signals corresponding to the off-resonant and
on-resonant wavelengths. The functional and statistical models are then used
to formulate a generalised least-squares problem whose solution provides
estimates of the background concentration level and other model parameters,
including the path-integrated concentration level of the target species in
the plume. Results have been presented for field measurements made for six
elevation angles using a variant of the generalised least-squares approach in
which the offset parameters

The paper describes on-going work on the analysis of the measured data
provided by NPL's DIAL system. In future publications, issues associated with the results presented in this paper will be addressed,
and further aspects of the analysis will be described, including the following:

The approach relies on the availability of knowledge about the location of the plume, which is then used as the basis for excluding data that can be expected to be inconsistent with the functional and statistical models used in the analysis. There is benefit in trying to refine and improve that knowledge to obtain a short window containing the plume and to increase the amount of data available to estimate the background concentration level. Similar developments could also be used to identify the presence of an unexpected plume.

The presented results have not included an assessment of the quality of the estimate of the background concentration level in the form of a statement of uncertainty, which is a necessary part of the quantification of the background concentration level. The assessment will need to consider not only the influence of noise in the recorded signals, which has been characterised using a particular statistical model, but also the uncertainty associated with that model, which has been estimated from an analysis of the measured data.

The presented results suggest that the statistical model obtained to characterise the noise in the recorded signals after the plume may provide only a partial description of the noise before the plume, in the sense that it captures the correlation structure of the noise but not its magnitude. A complete description of the noise is necessary if the part of the signals before the plume are to be used to obtain a reliable estimate of the background concentration level supported by an associated uncertainty.

The analysis has been applied separately and independently for each elevation angle

Additional experimental data – for example, direct measurement of the background concentration level undertaken independently, such as in situations where a plume is known not to exist – would assist in the validation of the results of the analysis.

The measured data used in this work are not publically available. The data are part of a field measurement undertaken using NPL's DIAL system to quantify the concentration level of methane in a plume produced by a methane source, and as such they are commercially sensitive. The data are used here to demonstrate and compare the described methods for the estimation of the background concentration level of methane in the proximity of the source.

Tom Gardiner, Rod Robinson, and Fabrizio Innocenti defined the models and provided the measured data from field measurements. Peter Harris, Nadia Smith, and Valerie Livina developed the analysis approaches, implemented the approaches in software, and processed the measured data to obtain numerical results. Peter Harris prepared the manuscript with contributions from all co-authors.

The National Measurement Office of the UK's Department for Business, Innovation and Skills supported this work as part of its Innovation, Research and Development programme with additional funding support through the IMPRESS (Innovative Metrology for Pollution Regulation of Emissions and area SourceS) project under the European Metrology Research Programme. Edited by: G. Pappalardo Reviewed by: two anonymous referees