MAPPING AND SIMULATING SYSTEMATICS DUE TO SPATIALLY VARYING OBSERVING CONDITIONS IN DES SCIENCE VERIFICATION DATA

Mapping potential sources of systematics, such as observing conditions, is a routine operation in modern galaxy surveys. For the SDSS, this mapping was relatively straightforward since SDSS was a single-epoch survey. Therefore, direct mapping between sky position and images could be established⁴⁶ (e.g., Ross et al. 2011, 2012; Leistedt & Peiris 2014). In other words, any of the properties of SDSS images (e.g., seeing) directly project onto the sky. This is no longer the case for DES, which is a multi-epoch survey where several single-epoch CCD images are processed and stacked into "coadd" images from which galaxies and stars are then extracted. The nominal depth in the main DES survey requires up to 10 tilings in each band, while deeper regions require an order of magnitude more (i.e., in the SN fields, which are dedicated to the DES supernova program). The coadding process is performed in non-overlapping regions called "tiles," which are 0.75 × 0.75 deg² squares constructed to cover and uniquely decompose the entire DES footprint. As a consequence of the multi-epoch nature of DES, there is not a unique value of, e.g., seeing at each sky position, but rather a distribution of values corresponding to the coadded single-epoch images. This is illustrated in Figure 1, which shows the footprints and properties of a set of single-epoch images used in an arbitrary coadd, that is, part of the DES–SV data (described in the next section). The seeing, airmass, and background noise (as well as many other properties not shown here) exhibit strong fluctuations and correlations. Combined with the nontrivial geometrical overlap between these images, this demonstrates the need for a flexible projection framework. In the standard processing pipeline, these images are processed and coadded in tiles (black line of Figure 1) with the DESDM software, using the software packages described in Sevilla et al. (2011), Desai et al. (2012), and Mohr et al. (2012)⁴⁷ The operations performed in these codes unavoidably mix the image properties across the coadds and affect the properties of the detected sources. The geometry of the DECam focal plane—a hexagonal shape with 62 science CCDs (Honscheid et al. 2008; Flaugher et al. 2015)—may also be imprinted in the reduced data. Therefore, one would like to access the full distribution of the single-epoch properties and connect it to the coadds, catalogs, and sky coordinates.

Zoom In Zoom Out Reset image size

To construct sky maps of the single-epoch properties, we proceed as follows. We first connect the single-epochs and coadds, and keep track of which images were processed and coadded by the DESDM software. We then resolve the geometry of all images so that a given position on the sky is connected to a single coadd image and to a set of single-exposure CCDs. This is realized by accessing the images individually and using the WCS⁴⁸ transformations to convert local image coordinates into equatorial coordinates. We also make sure these transformations match the procedures used in the DES software.⁴⁹ Finally, we employ the HEALPix pixelization (Górski et al. 2005) and connect the tree of geometrically resolved images to HEALPix pixels on the sky. All HEALPix maps shown in this paper use ${N}_{\mathrm{side}}=4096$, providing a pixel area of 0.74 arcmin².

The previous construction gives access to the full joint distribution of single-epoch and coadd image properties on the sky. This is a complicated object since each HEALPix pixel contains a vector of image properties. As mentioned before, a crucial product is the projection of this joint distribution into scalar sky maps. This requires the computation of one value (such as a summary statistic) per pixel, e.g., compressing the vector of seeing values in each pixel into mean, median, standard deviation, or even minimum and maximum values. This process can be done for any quantity of interest with arbitrary weights. This is how any potential source of spatial systematics arising from single-epoch images can be mapped onto the sky. Figure 2 shows the result of projecting some of the properties of the images of Figure 1. We see that the geometry of the CCDs as well as the relative orientations of the focal planes for the various exposures strongly affect the coverage and mean properties of the survey.

Zoom In Zoom Out Reset image size

SV data refers to the testing data acquired between 2012 November and 2013 February, processed by the "SVA1" version of the DESDM pipeline (B. Yanny et al. 2015, in prepration) and consisting of 858 coadd tiles, 665 of which have data in all five grizY bands. The SV data cover more than 300 deg² in total, split into contiguous regions of interest: the large SPT-E and SPT-W regions (≈200 and 50 deg², respectively), the RXC J2248, Bullet, and El Gordo known rich clusters (≈10 deg² each), COSMOS (≈6 deg²), and the Supernovae fields SN-E, SN-X, SN-S, and SN-C (≈10 deg² each). The footprint of DES–SV is shown in Figure 3 with the various fields labeled.

Zoom In Zoom Out Reset image size

To create maps for the full SV data set, we create a symbolic tree of CCD and coadd images, resolve their geometries, and project them into HEALPix maps. However, unlike the illustration shown in Figures 1 and 2, we now crop the projection to each tile (the black contour of Figure 1) since the DESDM software separately processes tiles using the stacks of CCD images. We perform this projection in the full SV area and stitch the projected coadds to assemble the full SV footprint. In terms of outputs, we project the following quantities in the five grizY bands: airmass, seeing, sky brightness, sky sigma (defined later in this paragraph), and exposure time. These can all affect the quality of the photometric measurements (see, e.g., Li et al. 2016). We compress the multi-epoch information into average and total maps (e.g., mean seeing and total exposure time). For the former, a natural choice would be to take the uniformly weighted average in each HEALPix pixel. However, this choice is probably too simplistic because, in practice, images are coadded using weights derived from the flux variance. More precisely, the DESDM pipeline provides a "weight" or "variance" map for each single-epoch image, which is the inverse variance of the flux in each pixel, a quantity coined "sky sigma" and denoted by σ_i in the remainder of this paper. For an image i and a given pixel, the value of sky sigma depends on a number of parameters, including the flux itself, the gain of the amplifier, the readout noise, the bias correction, and the flat-fielding. These quantities are measured by DESDM and yield an estimate of a variance map for each image. Single-epoch images are coadded using these maps such that the coadded flux is the weighted average over all exposures,

$$\begin{eqnarray}&&{F}_{{\rm{tot}}}=\displaystyle \frac{{\sum }_{i}{w}_{i}{p}_{i}{F}_{i}}{{\sum }_{i}{w}_{i}},\end{eqnarray} \tag{ 1 }$$

in each coadd pixel, where ${w}_{i}={({p}_{i}^{2}{\sigma }_{i}^{2})}^{-1}$. The extra p_is are rescaling factors to enforce a common photometric calibration to the single-epoch fluxes. They read

$$\begin{eqnarray}&&{p}_{i}={100}^{({m}_{{\rm{Z}}}-{m}_{{\rm{Zi}}})/5},\end{eqnarray} \tag{ 2 }$$

where m_Zi is the zero-point magnitude of the single-epochs and m_Z is that of the coadd image. The variance of the total flux in each pixel of the coadd image is given by

$$\begin{eqnarray}&&{\sigma }_{{\rm{tot}}}^{2}={\left[\displaystyle \sum _{i}{w}_{i}\right]}^{-1}.\end{eqnarray} \tag{ 3 }$$

A detailed discussion of these quantities is beyond the scope of this paper, but we note that ${\sigma }_{{\rm{tot}}}^{2}$ is proportional to the magnitude limit of the survey. In the above formulae, we omitted the pixel indexing in σ_i, but the coadding and the evaluation of ${\sigma }_{{\rm{tot}}}^{2}$ must be performed pixel by pixel across the coadd image. The technicalities of this process (including the projection and coadding) are handled by the SWARP software (Bertin et al. 2002). However, the projection formalism presented above can be used to quickly estimate ${\sigma }_{{\rm{tot}}}^{2}$ (and for example construct approximate magnitude limit maps). For this purpose, we compute an average sky sigma per single-epoch CCD image, defined as the pixel average of σ_i across the CCD. Rather than computing σ_i and ${\sigma }_{{\rm{tot}}}^{2}$ per pixel, we only need to calculate σ_i per CCD and ${\sigma }_{{\rm{tot}}}^{2}$ in the distinct regions of image overlap, as shown in Figure 1. Averaging sky sigma across CCDs yields a significant reduction of the complexity of the full projection, which needs to be performed for the five bands for a number of quantities of interest, using several hundred thousand single-epoch images. Finally, any quantity of interest can be averaged using the same weights w_i (which we call "sky sigma weights"), which is more useful than the unweighted average. The effective seeing of the coadd images is better approximated by the sky-sigma-weighted mean since the coadds are based on these weights.

Using CCD-averaged quantities significantly speeds up the projection and leads to a more flexible and faster algorithm for producing maps of quantities of interest with various weighting schemes (e.g., mean, sky sigma, or exposure weighted mean, median, etc.). The relative difference between maps constructed with and without the CCD-averaging approximation is of the order of 1%–3%, which is well below the precision needed for using such maps in large-scale null tests. Sub-CCD fluctuations might prove useful for small-scale null tests and can be projected using MANGLE (Hamilton & Tegmark 2004; Swanson et al. 2008). However, the present work shows that large-scale fluctuations are correctly captured by using CCD-averaged properties. Our tests indicate that the quality of this approximation improves with the survey area and number of exposures.

A number of maps were constructed for the DES–SV data in order to capture the spatial fluctuations of the observing conditions and other observational quantities. These maps are used in numerous SV analyses to perform spatial null tests with the data (e.g., Becker et al. 2015; Jarvis et al. 2015; Vikram et al. 2015; Crocce et al. 2016; Giannantonio et al. 2016). Figure 4 shows some of the main maps for the i band: the total exposure time, the mean sky sigma, and total sky sigma, as well as the minimum, maximum, and mean seeing. All of the quantities were calculated according to the previous scheme, i.e., the weighted average method and the sky sigma weights, with the exception of the mean sky sigma maps. This is because the weighted sky sigma is equivalent to the total sky sigma described above. Showing both maps sheds light on the difference between adding the noise properties linearly or in quadrature. In the following, we analyze these maps and detail the implications for the analyses of SV data. We focus on the SPT-E and W regions since they are the largest contiguous regions of data.

Zoom In Zoom Out Reset image size

The maps shown in Figure 4 exhibit significant structure and features on all scales, mostly because DES data have three intrinsic scales on which their properties can vary: the size of the DECam focal plane (2.2 deg diameter field of view), the coadd tile (0.75 × 0.75 deg²), and the single CCD (0.3 × 0.15 deg²). In spite of the random offsets and overlap of the focal plane when obtaining images and coadding them, these three scales become imprinted in the projected observing conditions. For example, the focal plane geometry is clearly visible in the total sky sigma maps in a number of regions. This is due to a significantly lesser or greater number of observations, or to their respective noise levels (sky sigma). Also, the mean seeing map is affected by outliers, i.e., by extreme (low or high) values of seeing in the set of single-epochs, as shown in the min/max maps in the bottom of Figure 4. The rectangular CCD geometry is also visible in the maps, especially near the edges. In addition, the observing properties of the 62 CCDs in a given single-epoch are very correlated since they experience quasi-identical observing conditions. By contrast, correlations between exposures are due to proximity in time, for example, if the observations were taken the same night. Finally, the tile edges are particularly visible in truncated regions or due to applying different zero-point magnitudes (e.g., the center of SPT-W, or the sharp transition in the upper part of SPT-E).

To identify which scales may be affected by the features described above, we compute the full-sky angular power spectra of the maps in Figure 4 (the full SV, not only the SPT-E and W regions). The results are shown in Figure 5; all of the spectra are made dimensionless and normalized such that ${\sum }_{{\ell }}{C}_{{\ell }}=1$ to clarify the comparison. As seen before, all of the maps exhibit significant power on all scales. The labels show which multipole ranges correspond to the typical scales of the SV fields, DECam focal plane, tiles, and CCDs. It is important to note that many of the features of Figure 5 are due to the sky coverage (i.e., the footprint) of the SV, not the correlations in the observed regions. This is emphasized by an extra line showing the power spectrum of the DES–SV footprint mask. Here, we do not deconvolve the effect of the mask on the power spectra because it typically redistributes the power between the ℓ modes. In the pseudo-spectrum estimation method, this deconvolution assumes flat priors on the power spectra, while quadratic maximum likelihood estimators can incorporate more flexible priors on the power spectra (see, e.g., Leistedt et al. 2013). This deconvolution would significantly affect the observed power spectra due to the small sky coverage of SV data. By contrast, not deconvolving the mask enables one to separate the scales affected by the survey coverage and by the observing conditions. The significant power in the ${\ell }\in [0,200]$ range is mostly due to the size and shape of the SV fields (all fields except SPT-E and W have approximately the size of the focal plane). In the other power spectra, any power in excess of the black line is due to structure within the fields, i.e., to the features described previously. As expected, airmass and seeing maps mostly have additional power on small scales. However, the sky sigma maps have much more power on all scales, particularly around the focal plane and coadd scales.

Zoom In Zoom Out Reset image size

As seen in Figure 4, the maps of the observing conditions are correlated. Figure 6 shows the Pearson correlation coefficients of the DES–SV maps in the gri bands (calculated for the full SV area). These spatial correlations have two origins: time correlations between observations made closely spaced in time, and physical correlations between some of the properties. For example, the noise level and seeing are correlated.

Zoom In Zoom Out Reset image size

In conclusion, the observing conditions fluctuate significantly over a wide range of scales and may affect the properties of the galaxies detected in DES coadd images. Any resulting spurious spatial correlations that propagate into the galaxy catalogs will need to be detected and eliminated. Typical techniques to mitigate these effects in clustering analyses include modeling the survey window function (e.g., Maddox et al. 1996; Blake et al. 2010), or using cross-correlations (Scranton et al. 2002; Ross et al. 2011, 2012; Ho et al. 2012; Crocce et al. 2016) or mode-projection (Leistedt et al. 2013; Leistedt & Peiris 2014) to correct or mask the spatial modes affected by the observing conditions. It is important to note that these approaches require the availability of accurate templates of the sources of systematics, which were precisely constructed in this section. We now turn to a concrete example of the use of these templates.

Photometric redshifts (photo-z)—redshifts estimated from broadband fluxes and colors—are one of the main sources of uncertainties in imaging surveys, and it is essential to reproduce this aspect of the data with BCC-UFig galaxies. We employ three photo-z codes: BPZ (Benítez 2000; Coe et al. 2006), TPZ (Carrasco Kind & Brunner 2013, 2014), and ANNz2 (Sadeh et al. 2015). These rely on very distinct algorithms that were tested on early SV data in Sánchez et al. (2014). They have also been used in the main SV clustering and cosmic shear analyses (Becker et al. 2015; Jarvis et al. 2015; Crocce et al. 2016; Giannantonio et al. 2016). For details on the three codes and an updated comparison using SV data, we refer the reader to Bonnett et al. (2015). Here, we only provide a brief summary of the three algorithms and focus on comparing the redshift distributions inferred from the SV data and the BCC-UFig simulation.

BPZ is a Bayesian template fitting photo-z code that relies on a set of calibrated template spectra which are redshifted and converted into template colors using the DES filters. This code computes a posterior probability for the redshift of each object, given its observed colors and errors, by fitting for all templates and marginalizing over the choice of template. By contrast, TPZ and ANNz2 are machine learning codes that must be trained on a representative sample of the data to infer a set of heuristic rules (i.e., a flexible data-driven model) to compute the redshift from the observed photometric colors. TPZ is a publicly available code⁵⁰ based on prediction trees and random forests, while ANNz2 uses a combination of machine learning algorithms, including neural networks and k-nearest neighbors. The three photo-z codes deliver a redshift probability distribution function (PDF) and a photo-z point estimate, usually measured as the mean or the mode of the PDF.

We employ the BPZ, TPZ, and ANNz2 algorithms that were trained and calibrated on the SV data, more specifically, on the sample of galaxies presented in Bonnett et al. (2015) for which spectroscopic redshifts are also available (about 46,000 galaxies). This sample is shown in red in Figure 3 and was used to calibrate the BPZ template prior and train the TPZ and ANNz2 methods. Note that we only use mag_auto magnitudes and colors with BPZ and ANNz2, and we only include the magnitude errors in the training of TPZ (where they are used to perturb the magnitudes when re-training the prediction trees, in order to obtain reliable redshift posterior PDFs).

Following most analyses of SV (e.g., Crocce et al. 2016; Giannantonio et al. 2016), we create five BCC-UFig redshift samples by selecting objects with photometric redshift falling in a top hat window of size Δz = 0.2 in the range 0.2 < z < 1.2. We use the ANNz2 photo-z point estimates to bin our data in the redshift ranges, i.e., to select the objects that fall in each redshift bin. We then reconstruct the N(z) by stacking the redshift PDFs of the selected objects for the three codes. Figure 8  shows the redshift distributions of the SV data samples compared with their BCC-UFig counterparts. We recall that the BCC-UFig and SV data were subject to the same color and quality cuts, and were restricted to the same portion of the sky: the SPT-E region analysis mask shown in Figure 7. Hence, the inferred redshift distributions should match relatively well since the colors of the BCC-UFig galaxies were shown to correctly match those of the data in Chang et al. (2014). This is confirmed by Figure 8: when comparing the left and right panels, the features and relative amplitudes between the N(z) inferred from the three codes are very similar.

Zoom In Zoom Out Reset image size

An important difference between the left and right panels is that the true redshift distributions can be calculated for the BCC-UFig and be compared with the distributions inferred using photometric redshifts. Analyzing the detailed performance of the photo-z codes is beyond the scope of this paper; a full investigation in the context of the weak-lensing SV data samples is presented in Bonnett et al. (2015). However, the results of Figure 8 show that most of the features of data redshift distributions are recovered in the simulation. For instance, BPZ yields wider N(z)s than machine learning methods, but is less accurate near z ∼ 0.4 due to the layout of the DES grizY filters and the limitations of the set of template spectra. Also, the redshift distributions inferred by TPZ are narrower than the true underlying distribution. These features persist when selecting galaxies with BPZ or TPZ photo-z point estimates. Selecting with ANNz2 minimizes the width of the inferred N(z) from the three methods and reduces the amount of low-redshift outliers in the third bin.

The comparison of true and inferred redshift distributions is not trivial with the SV data given the small sample sizes of spectroscopically confirmed galaxies, especially at high redshift. For this reason, a realistic survey simulation like BCC-UFig is a powerful tool for testing critical analysis stages, such as photometric redshift estimation, in regimes that are difficult to explore with the data. More specifically, Figure 8 demonstrates that the features seen in the redshift distributions calculated for the SV data are compatible with and well-reproduced by the BCC-UFig simulation.

We now challenge an assumption made above (and in current SV analyses): the fact that the redshift distributions can be spatially averaged over a large area without accounting for systematics (here the entire SPT-E region). While the analysis of SV data is restricted to the most uniform regions, as shown by the analysis mask in Figure 7, these include unavoidable residual depth and quality fluctuations. The mean N(z) is the main quantity of interest for cosmological analyses. However, its variance due to statistical and systematic uncertainties must be evaluated in order to assess the robustness of theoretical clustering and gravitational lensing predictions using the N(z). As we will see below, the statistical fluctuations are small, as expected from the area and number density of objects. However, it is essential to test for residual spatial systematics in the inferred redshift distributions.

Here, we focus on testing the variability of the N(z) distributions due to residual depth fluctuations and observational systematics in the SPT-E region. For each of the quantities presented in the previous section (e.g., seeing), we compute the median value and use it to split each redshift sample into two subsamples. These cover different regions of the sky observed under different conditions. We compute the difference between the redshift distributions corresponding to the two patches, i.e., taking the redshift distribution of the galaxies in the region where the systematic is above the median value, and subtracting that of the galaxies in the other region. Figures 9 and 10 show these differences for the i-band seeing and exposure time, respectively; these are two significant sources of spatially varying depth in the SV data (e.g., Crocce et al. 2016). Importantly, the variance obtained by randomly splitting the redshift samples (instead of splitting based on observing conditions) is of the order of 0.01 in all redshift bins.

Zoom In Zoom Out Reset image size

Zoom In Zoom Out Reset image size

These figures indicate that the N(z) differences are significant compared to the sample variance. This is as expected since good regions (e.g., low seeing or high exposure time) have lower noise and better photometry. As a consequence, the photo-z codes will have better overall quality and yield narrower redshift PDFs. Therefore, the derived redshift distributions when selecting objects in top hat redshift windows will be more accurate. In our difference convention, this translates into a positive bump surrounded by wells in Figure 9 (since we take the difference between low seeing minus high-seeing regions), and the opposite in Figure 10 (where we compute low exposure time minus high exposure time). This is indeed observed in most bins, even though this depends on the details of the photometric redshift estimation.

While the observed N(z) fluctuations are significant compared to the sample variance, they are small compared to the overall amplitudes shown in Figure 8 (less than 5% in all the cases we tested). This can be seen not only in the histograms of the true redshifts from BCC-UFig, but also in the N(z) inferred from the photo-z codes. In fact, in the right panels corresponding to BCC-UFig, these distributions follow the fluctuations of the true redshifts. This is not the case in all of the panels because low- and high-redshift objects suffer from other issues that make the comparison difficult. In particular, we did not re-weight the redshift distributions to adjust the color distributions of the training, validation, and data samples, as in Bonnett et al. (2015) and Sánchez et al. (2014). Such corrections do not affect the comparison between the data and the simulation.

This analysis provides an estimate of the order of magnitude of the N(z) fluctuations due to observational sources of systematics and spatially varying depth in the SV data. Provided that the mean N(z) is properly characterized, these fluctuations will not bias the cosmological analyses. However, because they are due to residual spatial systematics, they may cause other types of contamination in the galaxy catalogs. This is shown in Crocce et al. (2016) and in the next section, where seeing is found to spuriously correlate with the SV data and contaminate the clustering measurements.

We now turn to the spatial properties of the BCC-UFig redshift samples. Figure 11 shows the average galaxy density measured in the previous redshift samples as a function of a few sources of systematics (median exposure time, seeing, and sky sigma). We create these data points by jointly analyzing HEALPix maps (at ${N}_{\mathrm{side}}=4096$) of the galaxy redshift bins (SV data and BCC-UFig) and the maps of observing conditions presented in the previous sections. Prior to estimation, all maps are divided by their mean values, so that the observables are dimensionless and concentrated near the central values (1, 1) in the panels of Figure 11. The dynamical range explored by the galaxy densities in each panel depends on the observational quantity under consideration. For example, normalized seeing values are mostly concentrated between 0.9 and 1.1, while exposure times span a wider range, as can be verified in Figure 4. The error bars are obtained by jack-knife re-sampling in 50 sky regions, which is possible thanks to the large number of objects (greater than 10⁴ in each region).

Zoom In Zoom Out Reset image size

Analogous galaxy density measurements are shown in Suchyta et al. (2016) and Crocce et al. (2016) using the SV data. Figure 11 shows very similar trends and amplitudes despite using different maps (the median maps instead of the weighted mean maps). The most significant fluctuations are due to the r- and i-band seeing, particularly in the first and last redshift bins, in agreement with what is found in Suchyta et al. (2016) and Crocce et al. (2016). Other observational properties create similar but smaller fluctuations. Remarkably, the BCC-UFig redshift samples exhibit similar galaxy density fluctuations in most bins. In particular, Figure 11 shows that the characteristic features of the seeing and sky sigma fluctuations as a function of galaxy density are reproduced by BCC-UFig. This demonstrates that the simulation succeeds in capturing some of the galaxy density fluctuations caused by the systematics considered here. The remaining qualitative and quantitative discrepancies are likely due to the approximations adopted in the simulation. The most significant effect is likely the incorporation of observing conditions at the tile level instead of the single-epoch images: the current implementation limits the spatial resolution of systematics to relatively large scales.

More generally, it is interesting to quantify the extent to which the maps capture depth fluctuations in the data. This is because the effects described above—spurious spatial variations in the redshift distributions and galaxy densities—are usually corrected for or marginalized over in cosmological analyses. This is either done at the level of the survey window function or in the measured power spectra or correlation functions. We do not attempt to develop and validate such a model since this must be done in the context of a specific analysis at hand (e.g., clustering), which is beyond the scope of this paper. However, we demonstrate that the maps trace the main sources of systematics by showing that they strongly correlate with depth fluctuations and stellar contamination. Figure 12 shows the Pearson correlation coefficient of some relevant observing condition maps with the following: (1) a map of the stars misclassified as galaxies (by the "modest" classifier) in the BCC-UFig galaxy sample described above; (2) maps of the average i-band magnitude errors in the BCC-UFig and SV data ("Gold" catalog, see Crocce et al. 2016) in mag_auto_i magnitude bins. Figure 12 shows that the exposure time and total sky sigma maps strongly correlate with the magnitude errors in all bands and magnitude bins, in both the data and the simulation, demonstrating that the maps capture most of the depth fluctuations. In fact, a depth map of the SVA1 "Gold" catalog was constructed using the method described in detail in E. Rykoff et al. (2015, in preparation). Briefly, a coarse depth map is first constructed by fitting the magnitude–magnitude error relation of galaxies, exploiting the fact that the magnitude errors satisfy ${\sigma }_{m}\propto {\sigma }_{F}/F$, where F and σ_F are the galaxy flux and its standard deviation. This relation depends on the local limiting magnitude of the survey, which can be estimated in coarse HEALPix pixels where there are enough galaxies to obtain precise limiting magnitude estimates (but at low spatial resolution). This map is then refined by constructing a data-driven model of the depth based on the maps of the observing conditions presented here, which are available at very high resolution (using machine learning algorithms, see E. Rykoff et al. 2015, in preparation). The maps were also used in Crocce et al. (2016) to build a linear model of the spurious correlations observed in the angular correlation functions and correct for them.

Zoom In Zoom Out Reset image size

Note that the correlations between the noise and the magnitude errors are less significant in the simulation than in the data. This is due to the approximation highlighted previously: BCC-UFig is based on simulated coadd images, not on simulated single-epochs. Hence, systematics at scales smaller than the coadds are not resolved. The previous section showed that this approximation correctly reproduced systematics in the galaxy densities and redshift distributions, which are due to large-scale fluctuations of the observing conditions (e.g., seeing). However, fluctuations in the noise and depth can be significant on sub-coadd scales. This explains why the correlation coefficient between the map of total sky sigma and the magnitude errors in BCC-UFig is less significant than what was found in the data.

Finally, as shown in Figure 12, the observing condition maps correlate with the stellar contamination in the BCC-UFig samples. This test cannot be performed with the SV data since object types are only available for a small sample of spectroscopically confirmed sources, restricted to a small region of the sky, as shown in the previous sections. A large, realistic simulation such as BCC-UFig allows us to confirm that the observing conditions trace the main sources of spatial systematics in the galaxy samples, and can be used to model and remove them in cosmological studies.