ZTF Ubercalibration (Zubercal)

ZTF Calibration Home

Topics
Motivation for using Zubercal.
Initial Zubercal tests.
Improving the Zuber calibration.
Correlations of physical observables.
Inclusion of PSF-based parameters.
Atmospheric Transparency.
The Importance of Transparancy Changes.
A Broader Investigation of Transparancy Variations.
Nightly Photometric Variations.
Correcting photometry for Transparancy Variations.


Motivation for Ubercalibration of ZTF photometry

The current photometric calibration of ZTF is based on the comparison of each individual quadrant image with a set of calibration stars selected from PS1 DR1 for each quadrant. These PS1 stars have been ubercalibrated with photometry noted to be good to approx 1% and are selected within a colour, magnitude and density (crowding) range as noted in the ZSDS. However, due to the differing stellar density and reddening properties of ZTF fields, the result of these selections is that a different population of calibrators used in different fields. This in turn results in substantial variations in the accuracy of the zero points and colour calibrations. Principally, the lack of available calibration stars limits the resulting accuracy of the calibration.


Zero point accuracy. A comparison between the number of PSF stars within a ZTF quadrant with the zero points RMS in that quadrant.

The number of calibrator stars is clearly related to the number of PSF catalog sources. In the plot above we show how the RMS varies with stellar density. Clearly when there are fewer than 1000 catalog sources we always have a ZP rms greater than 0.02. This is likewise the case in densely crowded fields with > 150000 PSF stars. Clearly if the zero points are not accurate at this level, the photometry cannot be. In fact, the photometry only reaches 1.5% RMS in fields with between 20,000 and 70,000 stars. Thus, in order to reach 1% or better, we have no choice but to improve the accuracy of the zero points using additional information.

Additional sources that limit the calibration accuracy include the degeneracy of PS1 colours for sources with g - r > 1.1 colours in the ZTF r-band calibration. As well as the very strong dependency of colour coefficients on reddening.

In g-band, the calibration is limited by large systematic variations between readout channels, as well as a software-based bias in the derived colour coefficients with skylevel and the number of calibrator stars (as noted above).

Strong colour and spatial dependency in PSF shape is seen within CCDs and across the full camera. In part these dependencies have been traced back to the colour dependency of the CCD themselves, which appear related to radial variations in thickness of the CCDs. These effects, along with scattering from the filter holders, and dust spot transmission colour dependency, result in signicant spatial systematic offsets. These systematics certainly vary with time as the structure within flatfields has been found to vary with time.


Zubercal tests

Due to the limitations of performing calibrations on a single image basis it was decided to test the possiblity of calibrating full nights of data on a quadrant or area. This approach is expected mitigate problems such as having too few calibration stars in some fields/images. We also:
replace the g-r colour term with the more appropriate r-i (for r-band),
explicitly take into account source differential reddening wrt PS1 (which in r-band is primarily responsible for the variation in the colour term between fields),
explicitly take airmass into account (which is currently implicitly included in the zero point determination),
explicitly include the colour term for the airmass-based extinction (which is incompletely included in the current colour term determination).

As an intial test, a recent set of r-band data was selected under the assumption that such data has better characteristics than older data due to improvments in readout methods, linearity corrections, etc. The first set of data was taken from 2020-04-29.

Tests were made to determine the approximate dependency of the zeropoints on source airmass, magnitude, E(B-V), (r-i)_PS1. Results of the initials fits provided photometry that was more poorly calibrated than current photometry.


A comparison of photometry sigmas. The red points show the sigma without colour term. The green points are the regular calibrated photometry and black points are the new calibration. The left shows the data when a magnitude^2 term is included

Since the raw ZTF photometry is well known to included a magnitude bias when compared to PS1, an additional magnitude squared term was added to account for this. This source is believed to be due to a combination of non-linearity and the brighter-fatter effect. This additional slight non-linear dependence is evident within the photometry when we make a HESS diagram of the magnitude distribution.


A Hess diagram of the calbrator star magnitudes. Black dashed-line: constant magnitude dependence. Blue line: linear magnitude dependence. Red line: quadratic dependence.

However, even with the second order term the results of fitting r-band data for a single quadrant (RC0) from an entire night is less accurate as the current single image calibration.

Nevertheless, when we spatially bin the residual differences between ZTF and PS1 magnitudes we see the same structure as we had found before. This suggests that the spatial structure can now be determined on a nightly basis. Although, this structure is clearly similar to the prior determination.


A comparison between the spatial structure found with calibrator stars on 2020-04-29 (left) and our prior analysis for r-band CCD01 (right).

To determine why the newly calibrated photometry was inferior to the current analysis we compared the distribution of photometry in terms of magnitude, airmass, E(B-V), colour and time.


The zero point and magnitude distribution for the calibrated photometry. Left: data calibtrated with zero point, Middle: data calibrated with ZP and colour coefficients. Right: newly Zuber calibrated photometry.

In the above plot we see that the ZTF photometry calibrated with on zero point offsets is not symetric above the average zero point suggesting a bias with source brightness. The photometry including the calibrated colour coefficients is nearly symetric. However, in the middle plot we some significant outliers below the average zero point that are not seen in our new calibration since the new calibration includes reddening.

Calibrated photometric zero points versus the observed airmass. Plots ordered as above.

In the plot above we see the colour dependence of ZP calibrated data with increasing airmass. That is, the zero points decrease due to extinction as expected. This effect is corrected in the current ZTF calibration include colour coefficients. The new Zuber calibration removes the trend, but exhibits more structure than the current calibration. In particular, some significant outlying data is seen.

The r-i colour dependence of ZTF calibrated photometry. Plots ordered as above.

In the plot above we see how the data without colour calibration exhibits a very strong trend with colour since ZTF filters do not match PS1 filters. In the middle plot we see that even the current colour calibrated data still exhibits a strong colour trend for the small number of calibrator sources with r-i > 0.8. In the new calibration we see improvement. However, the calibration is clearly still not ideal.

Calibrated photometric zero points versus the Schlegel et al. (1998?) E(B-V) value for each object. Plots are ordered as above.

In the plots above we see significant structure in the calibration versus reddening for both the current calibration without colour correction and the new Zubercal. The main feature is a dog leg in the values at around E(B-V)=0.15. This feature was seen g-r colours in our prior work.

The time dependence of the calibrated zero points. The triangles and crosses give the average ZP for each image. Plots ordered as above.

In the above plots we see how the zero points change with time. The data without colour calibration shows a significant overall trend, due to airmass, along with additional structure. The photometry calibrated with the current systems shows very little variation in average zero points with time. The new Zubercal calibration shows the same kind of rapidly varying structure as the left plot. In the right plot we see two images have low zero points that clearly stick out.


Image corresponding to the two points with low zero points (near time offsets of 0.28 and 0.32 days).

In the above images we see the reason that the two image stick out in terms of their zero points. Notably these two bad qaulity images are not obvious in the distribution of values with current calibration due to the calibration not requiring any consistency between successive images.

The most important point of the ZP vs time plots is that the zero points vary significantly on short timescales. In the following table (from Stubbs et al.?) we show the variations in zero points that have been determined for a range of different timescales. For the table we see that a 0.02 mag variation is not unexpected in r-band observations on timescales of less than 1 hour. Thus, the observed variations are expected, but not accounted for in our initial Zubercal calibration.


Scatter in zero points due to variations in transmission on different timescales.

Further evidence for very significant changes in ZP caused by clouds is seen in our earlier work. The spikes suggest that in ZTF data far greater variations in image depth of over a magnitude are not uncommon. However, the presence of cloud are not typically evident in the images since skylevel only show when the moonlight, or other external sources, are present as shown below:


Image sky background level versus change in zero point from the field average.

In order to test the importance of the transparency variation induced zero point changes we determined the nightly average zero point and subtracted the difference between the Zubercal frame average.


The photometric scatter as a function of magnitude for various calibrations. Red points: current calibation without colour term. Black points: new calibration with varying zero points. Green points: Current ZTF calibrations including zero points. Magenta points: new calibration corrected to nightly average zero point.

As we can see from the above plot, correcting the zero points to the frame average produces an accuracy the same as the current calibration. However, more importantly, even with all the noted changes it does not improve on it.


Improving Zubercal

From the results above it is clear that more work is required to improve the calibration beyond the current level. The data taken on 2020-04-29 contains many fields with differing extinction levels taken at differing airmasses. These variations make it difficult to determine the source of the time-resolved zero point varitions. To address this we selected additional ZTF r-band photometry taken on 2020-11-13. This set contains a couple of individual fields that were observed approximately 200 times in sequence during the night. Thus, we remove an possible uncertainties due to differing reddening, crowding, pointing, etc. The sole varations are due to airmass and transpancy variations. With this data we initially concentrated on the r-band data taken for fields 614 and 661.

Correlations between ZP and instrument data

In order to determine how much the physical factors affecting the observations might also be affecting the photometry we investigated corrlatations between the zero point variations and other observables measured at the telescope. We determined the pearson and spearman correlation coefficients between ZPs and temperature, humidity, seeing, tip, tilt, wind speed, wind direction, and focus. We discovered that, although the seeing was strongly correlated with the values of tip and tilt (as expected), the zero point variations were not correlated with the seeing or most of the other parameters.


Variations in the photometric zero point for field 661 on 2019-11-13 (black points) along with scaled variations in the focus value (green points).

We found that the zero point variations were slightly correlated with the focus. This is shown in the figure above where we plot the variation in the photometric zero point over time along with a scaled variation in focus over time. Thus variations in focus may be of slight use in determining the variations in the zero point.


The relationship between focus and airmass values for observations of ZTF field 661 on 2019-11-13 and the relationship between frame averaged Chi values and focus.

In the above plot we see that there is a strong relationship between the focus and airmass and a moderate relationship between focus and the averaged photometric Chi values for a frame. The first plot most likely just tells us that the focus is varying with time as the airmass does, while the second plot tells us that the PSF model we used was not ideal for the observations that were taken at lower airmass (noting values given in the left plot).


Including Chi and Sharpness parameters

As our prior work had suggested that the PSF fit quality parameters chi and sharpness were related to photometric residuals, the next step was test how including this information in the calibration would improve the photometry.


Variation in the Chi values for bright sources with time and airmass. The connected lines show the field averaged values.

In the plots above we see the strong variation in the distribution of Chi values for repeated observations of bright calibrators (and the average) in field 614, over time, and also versus airmass. The Chi variation with airmass simply reflect the decrease in airmass for these particular observations with time.


The affects of Sharpness. Left: variation in sharpness values for bright sources with zero point for r-band data in field 661 taken on 2019-11-13. Right: Variation in sharpness with source brightness.

In the figures above we show the importance of the PSF sharpness parameter. We see that these bright sources exhibit a strong trend in sharpness that affects the measured magnitudes. In the right plot we see that the distribution of sharpness changes slightly with magnitude. These results follow the results of our prior analysis. However, here we did not find significant variation in chi and sharpness with colour. This is likely due to the limited nature of this data set.


The distribution of photometric errors for fields 614 and 661 after various calibration steps. Red points: pure ZP calibration, blue: current ZTF calibtrations, black: Zubercal with average zero point offsets, orange: Zubercal including zero point offsets along with chi and sharpness terms. The right plot is a zoomed version of the left one.

When we add chi and sharpness measurements to our fits we see improvement in our calibrations. In the above plots we see that we are finally reach a 1% calibration level for bright stars observed in an uninterupted sequence. In fact, even the Zubercal without fitting chi and sharpness terms show less scatter than the current ZTF calibration. Notably, at the faint magnitude end, the calibrations do not improve the scatter. Indeed they all appear slightly worse. Even the current calibrations. Given that this photometry is dominated by statistics it is unclear how much improvement in scatter can be made with any calibration. It is also worth noting that there are numbers of calibrator stars above the main locus. These may be variable stars or edge stars.

The calibration improvements with the addition of chi and sharpness parameters are not so clear in the fields that were not measured in sequence since those fields were significant affected by transparency changes as noted below.


Atmospheric Transparency


Wavelength dependency of the components of atmospheric extinction. Left: extinction by component. Right top: combined transmission spectrum. Right bottom: extinction model with the additional water and O2 components.

In the plot above we show the various atmospheric components responsible for transparency variations. Considering this we can see that there are numerous possibilties for atmospheric changes to significantly impact photometric calibration. In addition to these components, clouds create a grey (wavelength independent) extinction that can be complete in optical bands.

Mie (Aerosol) scattering vs Rayleigh scattering


Optical thickness for Rayleigh vs (Mie) Aerosol atmospheric components as a function of altitude/pressure.

Considering the locations of the various atmospheric components we note that most aerosols are trapped in the boundary layer, approximately 2 km thick while Rayleigh scattering occurs over full atmospheric scale height. These two components also have very different scattering phase functions as shown above. That is, light interacting with aerosols is forward scattered while Rayleigh scattering is much more isotropic.

The amount of scattering is dependent on speciation. For example, there is approximately a factor of three varation in Rayleigh cross sections from H20, O2, N2, to CO2. This suggests that factionally varying atmospheric water content may vary the amount of Rayleigh scattering at a given pressure (or airmass). However, this variation has been found to be 0.2% at 500nm.

We further note that atmospheric component changes, such in Rayleigh scattering due to pressure changes and O2 variations, have been found to stable over moderate timescales, while seasonal varations in O3 has an even smaller effect.


The Importance of Transparency Variations

To consider how transparency variations might have affected our Zubercal calibration we look variations in ZPs and colour coefficents in the current individual frame calibrations.


Zuber calibrated vs original photometric zero points vs time for two nights different nights. Left: original zero points. Right zero points corrected from airmass and reddening. Red points: data from 2019-11-13. Green points: data from 2020-04-29.

In the figures above we compare how the zero points vary overtime. The left figure shows significant variation since airmass and reddening are included in the zero point. Removing these terms from the ero points in the right plots we less variation in some parts of the plot. However, we see that there is still significant variation.


Corrected photometric zero points vs time for two nights. Red points: data from 2019-11-13. Green points: data from 2020-04-29.

When we zoom in or the zero points we see that there is still significant variation. This variation is significant even when observing the same field repeated as seen in the red points between 0.85 and 1 day. When observations were taken different fields at different locations 0.75 < t < 0.85 the variation are larger. However, the variations in the green points in the left plot are also different fields. These variations, such as the rise near t = 0.65 days, are actually caused by transpancy changes due to variation in clouds, water and aerosols.


Photometric calibration colour coefficients for 2020-04-29 (green) and 2019-11-13 (red). Left: uncorrected. Right: corrected for the airmass colour term and reddening.

In the plot above we show the colour coefficents determined during the regular calibration as well as those corrected for the airmass colour term and reddening. Here we see that the colour term is changing over time. This suggests that the cause of the transpancy variation is not clouds (which produce grey extinction). This also tell us that the extinction on this night cannot be fit with a single colour term. Furthermore, the photometric variations do not obey a simple linear model where atmospheric extinction is linearly varying with time (as assumed by in Ubercal calibrations of SDSS and PS1). Thus, to account for this a much more complex time dependent model is required in the presence of vary transperancy (i.e. non-photometric data).


A Broader Investigation of Transparency Variations

To better understand whether it is possible to model ZTF transperancy variations during a single night we extracted photometric zero points and colour terms for 91 fields that had been observed in continuous sequences with > 50 images taken on a single night. In some cases these fields were often observed in sequences on multiple nights. So, in total this data consisted 184 image sequences from single nights.

For each image sequence we determined the average and RMS scatter in the airmass-corrected ZPs, colour coefficients, sky levels, FWHM, ellipicity and position angle. Initial checks of this data showed that there was a very broad range on behaviour during these image sequences.


Variation in ZPs and colour coeffificents due to atmospheric extinction for field 679 observations taken on a single photometric night.

In the plots above we see an example of set of continous observations for a single field (and quadrant). Over this time we see that atmospheric variations give rise to a complex structure of image ZPs that clearly cannot be approximated as a linear or even quadratic variaton over time. Note, the change in the image ZPs is seen to coinside with a slight change in colour coefficents. Thus, the ZP change cannot be accounted by either airmass variation or a single colour-dependent airmass variation.

Comparing this result with the prior plots above, this strongly suggests that the transparency variation in this case could not be due to clouds alone. Rather, another colour dependent atmospheric component, such as an aerosol (Mie scattering), or water vapor (molecular absorption) must be present. A change in air pressure could perhaps cause such a change since the ZP difference is small only 0.05 mags.


Variation in ZPs and colour coefficents in field 310 on 2018-12-22 in a continous sequence of images taken on one night. Blue line, the ZP values. Red line, the corresponding colour coeffients offset by 26.2.

In the plot above we show the airmass corrected zero points for observations of ZTF field 310 taken on 2018-12-22. Here we see relatively well behaved data with a significantly disturbed region between 0.815 and 0.86 days.


A sequence of three consecuting images corresponding the minimum ZP values for field 310 on 2018-12-22.

In the plots above we show a sequence of three images for field 310 taken over the span of a couple of minutes. Here we a discrete cloud enter and leave the field-of-view. The colour coefficients in the previous plot suggest the extinction due to this cloud is not purely gray as expected. However, the interpretion is not completely clear since it is clear that not all of the calibration stars will be extincted to the same extent. Thus, both the ZP and colour coefficent are likely to be generally inaccurate.


Variation in ZPs and colour coefficents in a continous sequences of images taken on single nights. Left: observations of field 333 taken on 2018-07-16. Right: field 333 taken on 2019-02-12. Blue line, the ZP values. Red line, the corresponding colour coeffients offset by 26.2.

In the plots above we show the zero points for a sequence of images of ZTF fields 333 and 666. In the case of field 333 there were no obvious discrete clouds seen in the images. Here the colour coefficients only vary slightly compared to the prior example. However, extinction changes do correlate with changes in colour to some degree. For field 666 there is no clear variation in colour coefficents while the zero points varies significantly (suggesting grey extinction).


Variation in ZPs and colour coefficents in a continous sequences of images taken on single nights. Observations are of field 260 taken on 2019-01-10. Blue points: ZPs. Red points: colour coefficients offset by 26.2. The plot on the right is a zoom of the left.

In the above plot we see large variations in transparency that give rise to a slight but clear variation the calibration colour coefficients. Once the clouds pass the ZPs and colour coefficients become stable. However, it is not clear when all of the cloud has passed since sources on the edge of an image could still be effected without changing the fit ZP and colour term.


Observations of field 260 r-band, CCD1, quadrant 1, taken approximately 30 mins apart on the night of 2019-01-10.

In the plot above we show images corresponding to the calibrations given above. Here we see the appearance of cloud causing a strong transparency grandient across the image. The variation in ZP over the ~30 min span between the two images is ~0.8 magnitudes. The most important point to note here is that a single zero point or colour term cannot correct for such transparency variations across an image.

To consider more generally how complex the problem of transparency is with cloud, below we plot the measured optical depth of thick (av. depth 14) cumulus clouds vs thin cumulus clouds (av. depth 7). These figures are from Wen et al. (2008). From this plot we see that variations in optical depth of up to a factor of ~40 can occur across 0.5km. Assuming the average Palomar wind speed of 11km/hr, we can expect to such changes over ~3 mins. So in such extreme cases, ZTF photometry would vary by 4 magnitudes in Zp over ~5 ZTF exposures. Most cases are not this extreme.


Optical depth of thick (av. depth 14) cumulus clouds vs thin cumulus clouds (av. depth 7). From Wen et al. (2008).

Conclusion

Considering all of the results above we can clearly say that varying atmospheric conditions have effects on ZTF photometry that, in the absence of any concurrent measurements with a photometric monitoring telescope (as per SDSS, LSST, etc.), will be very difficult to correct to a high level of accuracy. In fact, even separating bad data from good data is a serious problem because ZPs that might be considered OK data on one night, might signify data affected by variations in transparency on another, since the baseline transparency level changes from night to night. For example, r-band ZPs of > 26.1 suggest the data is good. However, as seen from the plot above, rapidly vary transparency is still seen in such data.

The assumption made in prior Ubercalibation efforts by other surveys, that transparency can generally be modelled as simple linear variation during a night, appears to be fantasy. At Palomar such truly photometric circumstances are likely valid for much less than half of the data.


Other Sources of Rapid Photometric Variations



Variation in ZPs and colour coefficents in field 331 in a continous sequence of images taken on non-photometric night.

In the plots above we see a much more dramatic variation in zero point over time for one night of observations of field 331. At the first the image depth improves and then dramatically drops at around deltaT=0.15. In the right image we see that any colour dependency of this change is uncertain (suggestive of cloud). However, instead the bottom two plots show that the depth is correlated with seeing and ellipicity. The most surpising point is the depth increases with poorer seeing and greater ellipticity. This is occurance is completely counterintuitive. However, here it is likely that the photometry is actually bogus due the bad seeing in this very crowded field. Thus changes in photometric zero points during a night cannot be account for by transparency changes alone.


The Distribution of Nightly Photometric Variations

In order to get a better general idea of atmospheric transparency variations we decided to look at how the individual measurements vary wrt the median. We start by computing the changes in r-band ZPs and colour coefficents for each observation of CCD0, quadrant 1, relative to the median values for a field.

Variation in ZP and colour coefficients relative to the median values. Note, ZPs are corrected for variation with airmass.

In this plot we see that, although there can be large variations in ZPs, due to cloud, the variations in colour coefficents are typically relatively small (<~ 0.02), This suggests that clouds that cause the major variations are gray. Nevertheless, we can see that there is a trend at low levels of absorption.

To get a better idea of atmospheric variations during a night, we take the values from the 184 sequences of images taken on individual nights and subtract the nightly average ZP and colour coefficient values from each.


Variation in ZP and colour coefficients relative to the nightly average values for sequences. ZP is corrected for airmass variations. The dashed lined has a slope of -1.

In the plot above see that there is indeed a clear variation in colour with ZP. Here is this correlation is likely the combination of real variation in colour with ZP along with correlated errors (since ZP and colour coeff are jointly fit). This figure also shows that the variation in ZP and colour coefficient during the span of a few hours tends to be relatively small (delZP < 0.04, delcoeff < 0.02), although some far larger values are seen (as shown above).


Correcting Photometry for Transparency Variations


R-band observations on the night of 2018-12-14. In the left plot we show ZPs and colour coefficents for field 769, r-band, CCD1, quadrant 1. The blue points show the ZPs and red the colour coefficients. In the right plot, we show the ZP vs skylevel for all r-band observations on 2018-12-14. The black points are from field 769.

In the plot above we see that the decrease in zero point due to the clouds in a field is well tracked by the change in background in that field. However, as we noted above, the skylevel is dependent on lunar phase and separation. As the righthand figure shows, the slope of the extinction line varies between fields when multiple fields are observed within a night, as well as between nights. Thus, on the bulk of nights, when there is little lunar illumination, the skylevel cannot be used to track extinction accurately. However, based on i-band observations Zou et al. (2010, AJ, 140, 602) suggest that the relationship between transparency and skylevel can be determined based on the lunar phase function, lunar elevation, and skylevel. They also note that only 50% of Gemini North observations are photometric (extinction < 0.3 mags, <2% variation). Nevertheless, the skylevel/transparency fits do not appear accurate beyond a 10% level.

Historical Transparency Variations in Other Observatories



Tranparency variations with wavelength measured at two observatories based on three atmospheric components (Aerosol optical depth, AOD 550nm), Precipitible Water Vapor (PWV), O3 (Ozone)). Plots are based on MERRA-2 data and come from Guyonnet et al.~(2019).

In the above plots we show the results of Guyonnet et al.~(2019) based on MERRA-2 atmospheric data (0.5 x 0.6 deg resolution). From the above plot we see that there is significant variation in transmission over time with wavelength (particularly at CTIO). The PWV nightly variations can range from 1 to 10% at the red end where they would effect ZTF i-band observations. In r-band (lambda < 750nm) the variations are up to ~2% within a night. The PWV does not include liquid droplets in clouds. The transmission model plotted above includes molecular O2 absorption which is important in r and i-band.

A large fraction of the transparency variation is attributed to aerosols. These aerosol tracers include sea salt, dust, black carbon, organic carbon and sulfate. This component is found to vary by >100mmag annually, and 10-20mmag overnight. However, the uncertainties in the AOD (Aerosol optical depth) component are very large (~22 mmag) and thus the MERRA-2 data is not ideal for determining transparency at Palomar. A source of colour variation within g and r-band filters could be due to O3 in the 500 to 700nm region (Chappuis band). However, this component has a very small effect (<0.1% overnight) as shown above.

One possiblity for correcting transparency is to model a grid of variations. Sky transparency can be modelled with MODTRAN, but this costs thousands of dollars. A possible alternative is lowtran. However, this seems to be out of date and incomplete (see note on aerosols). Another possibilty is LibTranRad. This if free and has been compared to MODTRAN for LSST simulations and found to give very close results, except of i-band since O2 cannot be varied. However, these simulations did not include aerosols (or clouds), which are very important as noted above.

Tests of how well variations in airmass are modelled by standard photometric fitting have been carried out by (Stubbs et al. 2018) and show that linear and quadratic airmasses terms used in fitting extinction are not ideal.