METODOLOGÍA EN CASCADA

Merging or gluing together analogue and photon counting data is a common practice in order to get more orders of magnitude of lidar signal. There are lots of different ideas about how to find the coefficients, and how to apply them. The CRL group agrees with some of these, but has not implemented these procedures as of yet. Other methods are not appropriate to use. Some methods to glue profiles together are explored here, but as this is a whole field of study in and of itself, a more detailed survey of gluing and merging options for analogue (ANA) and photon counting (PC) profiles is beyond the scope of this thesis. CRL used the first method which worked well enough to continue calibration of the depolarization measurements, although improvements may be made in future.

Making a cutoffbased on altitude to switch from PC to ANA in the glued profile

Arguments are made here instead for keeping the cutoff criteria for switching between PC and ANA based on raw photon counting rates rather than altitude. The altitude-cutoff method works well for lidars which have no clouds in their data. One example of such a lidar is the Purple Crow Lidar in London, Ontario, which glues its profiles primarily for use in making stratospheric temperature profiles. There are no clouds included in any of the

useable data. Their profiles always have approximately the same count rates at the same altitudes from day to day. That means that if they have a large enough range for which both ANA and PC profiles are linear, then the little bit of variation in the ideal cutoffvalue for altitude from one to the other can vary and still be in that linear range, even on days where there is more moon background, sun background, or lower laser power.

This does not work at all for CRL, which is primarily a tropospheric instrument de- signed for studying clouds. More often than not, a cloud appears in the data brighter than 20 MHz (requiring analogue signals), surrounded by regions above and below with count rates smaller than 20 MHz (where PC would be better). Clearly for CRL, making the switch between analogue signals at low altitudes, and photon counting signals at high altitudes, cannot be done with a single constant cutoffin altitude.

Doing a linear regression on each profile of data to find gluing coefficients for each

minute

CRL uses carefully curated measurements from a clear sky date, combining the entire night’s data together, when determining gluing coefficients.

Checking gluing coefficients for every lidar profile can be computationally intensive, and is not necessarily instructive unless all profiles contain a variety of count rates within the linearly-responding region of the PC channel, coming mostly from regions of clear air. In the case of clouds, this makes no sense. Petty and Turner 2006 [104] derive gluing coefficients profile-by-profile (in the same manner as CRL, but only with a single profile’s data at a time), but recognize that fits cannot be attempted when there are clouds, or when the sky background is greater than the 50 MHz maximum of the linear region of their PC channel. They suggest instead calculating ana priorislope and offset, and adjusting these every couple of hours, whenever a suitable situation presents itself.

One advantage to calculating glue coefficients minute-by-minute is that there are statis- tical fluctuations in the glue coefficients, according to [104], which cannot be removed by

statistical screening. It is possible that CRL gets around this issue by removing the constant background signal with every shot before gluing. So long as the statistical fluctuations dis- cussed in [104] are constant in altitude (i.e. the shape of the dark counts profile remains the same, and just migrates to larger or smaller values, as we seem to find with CRL), then the CRL’s background removal procedure removes these statistical fluctuations for each scan. This bears further investigation for CRL. In any event, CRL measurements are more often cloudy than not. The times for suitable gluing coefficient measurements may be few and far between as a result.

It has been found by Newsom et al. 2009 [105] that the glue coefficients change with time of day, due to the solar background. This effect may be smaller for CRL than it is for other lidars. The field of view of the CRL is smaller than the field of view for many other lidars. Also, the CRL’s depolarization measurements are made in the green, and not in the UV, where most sunlight photons lie. A recent study by Zhang et al. 2014 [106] has followed the work of Newsom et al. and has attempted to use their method, but with more stringent restrictions on the quality of data going into each profile’s fit to find the glue coefficients. They have found that when lots of daytime low-correlation data was included, more variation in slope from daytime to nighttime was produced. When this low-correlation data was not used, there were fewer data points in the daytime fits, but the overall trend of the slope was constant over 24 hours. This is encouraging for CRL which calculates its slopes but once in a while.

There is at least one paper on this subject whose language implies a gluing procedure which does not make sense at all. In this paper, gluing coefficients are derived profile by profile, and it is stated that the calibration valuesaandbchange depending on the weather, but this is not strictly-speaking true; the values calculated in a cloudy day are not different gluing coefficients at all – in fact, the data are ineligible to be used for calculating the gluing coefficients in the first place. Yes, values calculated using the same regression method will be different from clear sky days to days with a thick cloud (and therefore saturated PC count

profiles), but that’s because the cloudy PC values are in effect “wrong” for this purpose. Analogue count rates are compared there with oversaturated photon counting rates.

CRL uses a single set of gluing coefficients for as long as possible, just checking peri- odically to ensure that they are still valid.

One possible benefit to calculating the gluing coefficients for a clear portion of each night, or a portion of each night with good linear ranges in both channels is that this makes a good check that the gluing values are not changing too much day to day, and thus checking that the system itself (hardware especially) is not changing too much, either. This is the sort of calibration measurements done not so that an effect may be corrected, but to have a record of changes in the system over time. The gluing values should be consistent with time, within a reasonable range. If the hardware does not change, neither should the gluing coefficients. If one is worried about long-term drift in the analogue floating voltage shape, perhaps it would be better to track these changes directly with dark count measurements.

Standard operating procedure for CRL is to use one single set of carefully curated gluing coefficients for as long as they are viable. Checks are made regularly when clear sky measurements are available. If the lidar is not changing, then neither should the gluing coefficients.

Newsom et al. [105] merge their measurements in a similar manner to that used for CRL, but do not remove the sky backgrounds, first. They find that the gluing coefficients drift with time of day as the sunlit background increases. They report that D. Whiteman has communicated to them (2008) that this diurnal variation is less when backgrounds are removed, as in [107].

CRL removes the backgrounds, in general, before gluing. This is likely to continue as standard procedure, as it may also get around the problem of fluctuating analogue electronic noise profiles (see above).

Using a lamp mapping technique

Walker et al. [102] use light from a halogen lamp, rather than from the sky, to calculate gluing coefficients. The lamp may be positioned at various locations above the telescope by means of a precisely-controlled kinematic stage, thus controlling the amount of signal entering the detector. As CRL does not have such a scanning lamp available, it cannot make use of this method.

Using a maximum-likelihood reconstruction of photon count using the data from both channels to influence the resulting profile

Veberiˇc et al. 2012 [108] model the behaviour of the PC and the ANA channel, with backgrounds still in, and minimize the errors when using a variety of input count profiles.

This is a great idea which may be instituted at CRL in the future. It uses all the informa- tion contained within the two profiles. This paper also points out many of the drawbacks to the usual gluing methods in use, and addresses some of these. The reference itself is quite clear, and so the information within it will not be repeated here.