Index: trunk/doc/release.2015/ps1.calibration/calibration.tex
===================================================================
--- trunk/doc/release.2015/ps1.calibration/calibration.tex	(revision 41126)
+++ trunk/doc/release.2015/ps1.calibration/calibration.tex	(revision 41127)
@@ -105,14 +105,21 @@
 and to place all of the observations onto a photometric system with
 consistent zero points over the entire area surveyed, the \approx
-30,000 square degrees north of $\delta = -30$\degrees.  The
-astrometric calibration compensates for similar systematic effects so
-that positions, proper motions, and parallaxes are reliable as well.
-The Pan-STARRS Data Release 2 (DR2) astrometry is tied to the Gaia DR1
-release.
-
+30,000 square degrees north of $\delta = -30$\degrees.  \textadd{Using external
+comparisons, we demonstrate that the resulting photometic system is
+consistent across the sky to between 7 and 12.4 millimags depending on
+the filter.  For bright stars, the systematic error floor for
+individual measurementsis $(\sigma_g, \sigma_r, \sigma_i, \sigma_z,
+\sigma_y) = (14, 14, 15, 15, 18)$ millimags.}  The astrometric
+calibration compensates for similar systematic effects so that
+positions, proper motions, and parallaxes are reliable as well.  \textadd{The
+bright-star systematic error floor for individual astrometric
+measurements is 16 milliarcseconds.}  \textmod{The Pan-STARRS Data Release 2
+(DR2) astrometry is tied to the Gaia DR1 coordinate frame with a
+systematic uncertainty of $\sim 5$ milliarcseconds.}
 \end{abstract}
 
 % insert additional keywords as appropriate:
-\keywords{astrometry -- methods: statistical -- proper motions -- Surveys:\PSONE -- techniques: photometric}
+\keywords{astrometry -- methods: statistical -- proper motions --
+  Surveys:\PSONE -- techniques: photometric}
 
 \section{Introduction}\label{sec:intro}
@@ -450,5 +457,5 @@
 code restricts the exponents with the rule $i + j <= N_{\rm order}$
 where the order of the fit, $N_{\rm order}$, may be 1 to 3, under the
-restriction that sufficient stars are needed to constrain the order
+restriction that sufficient stars are needed to constrain the order.
 For each chip, a second set of polynomials describes the
 transformation from the chip coordinate systems to the focal
@@ -475,4 +482,22 @@
   M & = & C^M_{0,0} + C^M_{1,0} X + C^M_{0,1} Y + \delta M(X, Y) 
 \end{eqnarray}
+
+\textadd{These high-order transformations are required for the
+  individual chips to follow small-scale distortions due to the optics
+  (stable from exposure to exposure) as well as the atmosphere
+  (changes from over time).  The spatial scale on which the
+  astrometric deviations due to atmosphere are varying is related to
+  the isoplanetic patch size.  We note that, in the typical conditions
+  at the \PSONE\ site, if the seeing is due to low-lying atmospheric
+  layers, the isoplanetic patch scale will be a most a few arcminutes
+  \citep{1988ESOC...30..693B}, and smaller when the seeing comes from
+  higher altitudes.
+
+We also note that, in our detailed astrometric analysis within the
+database system, we perform an initial correction for several
+systematic effects including the color-dependent correction due to
+differential chromatic refraction.  The corrected chip positions are
+the inputs to the equations above (see
+Section~\ref{sec:astrometry.systematic}).}
 
 \subsection{Cross-Correlation Search}
@@ -839,5 +864,5 @@
 \cite{2012ApJ...756..158S}.  This analysis is performed by the group
 at Harvard, loading data from the raw detection files into their instance
-of the Large Scale Database \citep[LSD,][]{2011AAS...21743319J}, a
+of the Large Survey Database \citep[LSD,][]{2011AAS...21743319J}, a
 system similar to DVO used to manage the detections and determine the
 calibrations.
@@ -845,11 +870,14 @@
 Photometric nights are selected and all other exposures are ignored.
 Each night is allowed to have a single fitted zero point
-(corresponding to the sum $zp_{\rm ref} + M_{cal}$ below) and a
-single fitted value for the airmass extinction coefficient ($K_{\rm
+(corresponding to the sum $zp_{\rm ref} + M_{cal}$ below) and a single
+fitted value for the airmass extinction coefficient ($K_{\rm
   \lambda}$) per filter.  The zero points and extinction terms are
 determined as a least squares minimization process using the repeated
 measurements of the same stars from different nights to tie nights
-together.  Flat-field corrections are also determined as part of the
-minimization process.  In the original (PV1) ubercal analysis,
+together.  \textadd{This analysis relies on the chemical and
+  thermodynamic stability of the atmosphere during a photometic night
+  so that the zero point and extinction slope are stable as a result.}
+Flat-field corrections are also determined as part of the minimization
+process.  In the original (PV1) ubercal analysis,
 \cite{2012ApJ...756..158S} determined flat-field corrections for
 $2\times 2$ sub-regions of each chip in the camera and four distinct
@@ -872,9 +900,15 @@
 aided by the inclusion of multiple Medium Deep field observations
 every night, helping to tie down overall variations of the system
-throughput and acting as internal standard star fields.  The resulting
-photometric system is shown by \cite{2012ApJ...756..158S} to have reliability
-across the survey region at the level of (8.0, 7.0, 9.0, 10.7, 12.4)
-millimags in (\grizy).  As we discuss below, this conclusion is
-reinforced by our external comparison.  
+throughput and acting as internal standard star fields.  \textmod{The
+  resulting photometric system is shown by \cite{2012ApJ...756..158S}
+  to have zero-points which are consistent with those determined using
+  SDSS as an external reference, with standard deviations of (8.0,
+  7.0, 9.0, 10.7, 12.4) millimags in (\grizy).  Internal comparisons
+  show the zero-points of indidual exposures to be consistent with the
+  Ubercal solution with a standard deviation of 5 millimags.  The
+  former is an upper limit on the overall system zero-point stability,
+  since it includes errors from the SDSS zero points, while the latter
+  is likely a lower limit.  As we discuss below, this zero-point
+  consistency is confirmed by our additional external comparison.}
 
 The overall zero point for each filter is not naturally determined by
@@ -885,13 +919,17 @@
 on the reference photometric night of MJD 55744 (UT 02 July 2011).
 \cite{2014ApJ...795...45S} and \cite{2015ApJ...815..117S} have
-re-examined the photometry of Calspec standards \citep{1996AJ....111.1743B} as
-observed by PS1.  \cite{2014ApJ...795...45S} reject 2 of the 7 stars
-used by \cite{2012ApJ...750...99T} and add photometry of 5 additional
-stars.  \cite{2015ApJ...815..117S} further reject measurements of
-Calspec standards obtained close to the center of the camera field of
-view where the PSF size and shape changes very rapidly.  The result of
-this analysis modifies the over system zero points by 20 - 35
-millimags compared with the system determined by
-\cite{2012ApJ...756..158S}.
+re-examined the photometry of Calspec standards
+\citep{1996AJ....111.1743B} as observed by PS1.
+\cite{2014ApJ...795...45S} reject 2 of the 7 stars used by
+\cite{2012ApJ...750...99T} and add photometry of 5 additional stars.
+\cite{2015ApJ...815..117S} further reject measurements of Calspec
+standards obtained close to the center of the camera field of view
+where the PSF size and shape changes very rapidly.  The result of this
+analysis modifies the over system zero points by 20 - 35 millimags
+compared with the system determined by \cite{2012ApJ...756..158S}.  \textmod{We
+note that this correction to the overall system zero-point is large
+compared to the relative zero-point consistency noted by
+\cite{2012ApJ...756..158S} because the absolute zero points are not
+independently constrained by the Ubercal analysis.}
 
 % http://iopscience.iop.org/article/10.1088/0004-637X/815/2/117/pdf
@@ -1092,4 +1130,8 @@
     \sigma_i^{-2})^2}
 \end{equation}
+
+These rejections and the over-weighting of the Ubercal measurements
+are admittedly ad hoc.  Since the goal at this stage is to tie the
+non-Ubercal data to the Ubercal system, we
 
 The calculation of the relative photometry zero points is performed