\documentclass[11pt,epsfig]{article}
\usepackage{epsfig}
\usepackage{multicol} 

\topmargin -0.5in
\oddsidemargin -0.125in
\textwidth 6.5in
\textheight 9in

\def\A{${A}$}
\def\AV{${A_v}$}
\def\AH{${A_h}$}
\def\B{${B}$}
\def\BV{${B_v}$}
\def\BH{${B_h}$}
\def\sigmao{$\sigma^o$\ }
\def\sig{$\sigma^o$~}
\def\signo{$\sigma^o$}
\def\sigo {$\sigma^o$}
\def\sigest {$\widehat{\sigma}^o$}
\def\sigstd {$\kappa$}
\def\polrat {$\gamma$}
\def\deg{^\circ}

\def\doublesp{\large \renewcommand{\baselinestretch}{1.5} \normalsize}
\def\singlesp{\large \renewcommand{\baselinestretch}{1.0} \normalsize}

\begin{document}
\title{A QuikScat/SeaWinds Sigma-0 Browse Product}
\author{David G. Long \\
Microwave Earth Remote Sensing Laboratory\\
	BYU Center for Remote Sensing\\
        Brigham Young University \\
        459 Clyde Building, Provo, UT  84602\\
        long@ee.byu.edu \\  
	}

\date{Version 2.0\\ \today}

\maketitle

\begin{abstract}

Following up on the successful NSCAT mission, the QuikScat/SeaWinds scatterometer
(Qscat) provides normalized radar cross section ($\sigma^o$) measurements of the 
Earth's surface at unprecedented coverage and resolution.  While originally designed 
for wind observation, scatterometers have proven useful in a variety of land and ice studies.
To aid in the selection of regions and time periods for study, a global \sigmao browse product
is produced by Brigham Young University.  This product consists of spatial and temporal
averages of Qscat L1B \sigmao values over a one-day period. This report briefly 
describes this \sigmao browse product.

\end{abstract}

\section{Introduction}

Though the mission was cut short by the loss of the host spacecraft, NSCAT was
an unqualified success.  In addition to advances from its primary wind
observation mission.  NSCAT data has also had an impact on a variety of polar ice
\cite{cryo} and tropical vegetation \cite{long:views} studies.  In particular,
NSCAT data is very effective in mapping the extent of sea ice \cite{quinn,quinn_qscat}. 
It is clear that scatterometers can continue to play an increasingly important role in
monitoring tropical vegetation and polar ice in the future. 

As a follow-up/replacement for the NSCAT mission, the QuikScat/SeaWinds
scatterometer (Qscat) provides measurements of the near-surface ocean wind field with
unprecedented coverage and resolution.  Qscat makes dual polarization measurements of
the normalized radar cross section ($\sigma^o$) at both vertical and horizontal
polarization.  The \sigmao measurements are finding application in land, ice, and ocean
studies. As an aid to the selection of data to support such studies, Brigham Young
University is producing a simple global \sigmao browse product.  This report describes 
this product.


\section{Qscat \sigmao Browse Product}

Unlike NSCAT which made \sigmao measurements over a broad range of incidence
angles, Qscat makes \sigmao measurements at each of two nominal incidence
angles, $46^\circ$ and $54.1^\circ$, corresponding to the inner and outer beams. 
The inner beam measurement is horizontal-polarization while the outer beam is
vertical-polarization. Since it is undesirable to combine measurements from different
polarizations, measurements from each beam are kept separate.  We note that the
variation in incidence angle over an orbit is small, typically less than a few
tenths of a degree.  For this reason, the incidence angle variation is not
considered in this browse product.

Qscat \sigmao measurements are reported in two forms: termed `eggs' and
`slices' in the Qscat L1B files.  These differ in their spatial sizes and shapes.
The nominal instantaneous Qscat antenna footprint is an ellipse.  However, the
on-board range-doppler processing incorporated in the instruments improves the 
resolution.  Using the on-board processor, twelve individual \sigmao measurements
are obtained for each footprint, though only 8 are reported in the L1B data product.  
These individual measurements are termed `slices'.  The slices are typically 6 km long
(depending on the instrument mode and antenna beam) by 25 km wide.  The summed
measurements of the 8 center slices are known as `egg' measurements and are
reported in the standard L1B product.  The effective resolution of the egg
measurement nearly matches the elliptical 3 dB antenna footprint (approximately
15 km by 25 km depending on the antenna beam and instrument mode).  Although lower
resolution, the egg measurements have smaller measurement variance ($K_p^2)$ than
slice measurements and are also less sensitive to calibration errors.  For this reason
the \sigmao browse product defined here is based on the egg measurements.

The \sigmao browse product consists of a suite of images produced for three areas: 
(see Table \ref{tab:standardregions})
1) a global rectangular lat/lon grid, 2) a southern hemisphere polar stereographic 
projection, and 3) a northern hemisphere polar stereographic projection.  The grid
resolution for the global projection is 5 pixels/deg, or about 22.5 km/pixel at the equator. 
The polar stereographic projections use a $70^\circ$ reference latitude with a
nominal grid size of about 22.5 km.  The global projection product is best suited
for equatorial and mid-latitude views, while the polar stereographic projections
are best suited for high-latitude views.  While the global browse product includes
the entire globe, the projection distortion results in sampling problems
in the polar regions; hence the production of separate polar products. 
The polar stereographic views include only measurements above a high latitude cutoff
of $52^\circ$.

\begin{table}[hhhtb]
\centering
\begin{tabular}{l|c|r|r|r|r|c}
Region & Region &\multicolumn{2}{|c|}{Lower-Left Corner} &
\multicolumn{2}{|c|}{Upper-Right Corner} & Region Code \\
Name & Abreviation & Latitude & Longitude & Latitude & Longitude & Number \\ \hline
Southern Hemisphere & S & -90.0   &     -180.0  &    -52.0   &    180.0 & 100 \\
Northern Hemisphere & N &  52.0   &     -180.0  &     90.0   &    180.0 & 111 \\
Global              & G & -90.0   &     -180.0  &     90.0   &    180.0 & 500 \\
\end{tabular}
\caption{Browse product regions. The Northern and Southern hemisphere images (code
100 and 111) are produced in polar stereographic form while a rectangular projection
in lat/long is used for the global image (code 500).
\label{tab:standardregions} }
\end{table}

In producing the browse \sigmao images, the center of each L1B egg \sigmao measurement
is located.  The measurement is averaged into the image grid element (pixel) in which 
the center of the measurement falls, i.e., the measurements are gridded 
into earth-located pixels based on their location.  The effective resolution of the 
image products is less than the pixel resolution, or approximately 55-60 km at the 
equator.  The resulting images are temporal averages over a one day period of all 
the \sigmao measurements whose centers fall within each image pixel area.  We note 
that using slice \sigmao measurements rather than egg \sigmao would improve the 
effective resolution somewhat, though not significantly.  The resulting browse image 
product is stored in the BYU Microwave Earth Remote Sensing (MERS) {\bf SIR} file 
format described in Section 4.  The file format includes a header which
contains location transformation information. 

Viewer and reader programs for the BYU MERS {\bf SIR} file format are available on line 
from the BYU MERS web and anonymous ftp sites at URLs {\tt http://www.mers.byu.edu/}
and \\
{\tt ftp://ftp.cers.byu.edu/}, respectively.  A standard file naming
convention for Qscat products (described below) is used.

The \sigmao browse products are produced from L1B data.  Only measurements flagged as
`usable' in the L1B file are included in the browse product.  One set of image products
is produced per mission Julian day.  For each of the three projections, three
separate image products are produced:  the mean \sigmao value in each pixel,
the normalized standard deviation of the measurement in each pixel, and the count of
the number of measurements used in each pixel.  Each image browse product is stored in
a separate file.  Overlapping swaths are averaged.



\section{Product file name format}

The standardized data file naming scheme is:
$$
QS\_Xb{\bf p}{\bf T}{\bf R}3C{\bf YEARDAY}.date
$$
where {\bf p} is the one character polarization (`h' or `v') designator, {\bf T} is
the one character image type code (`a', `C', or `V'), {\bf R} is the one character
region (`G'=Global, `N'=Northern Hemisphere, and `S'=Southern Hemisphere), {\bf
YEAR} is a four digit year code, {\bf DAY} is a three digit Julian day code, and
$date$ file extension  is an 11 character string containing the file production date.

In the file name the product type is denoted by a one character type designator (see
Table \ref{tab:type}).
\begin{enumerate}
\item[{\bf a:}] Mean \sigmao value expressed in dB of the absolute value.  Negative
\sigmao values are denoted by setting the corresponding pixel of the count image
to a negative. The \sigmao values are clipped to $\pm32.5$ dB with $-33$
used to denote no available data.  For QuikScat/SeaWinds, the reference incidence
angles are approximately H-pol (inner beam) $46^\circ$ and V-pol (outer beam)
$54.1^\circ$. 
\item[{\bf C:}] counts. The absolute value indicates the number of \sigmao
measurements which hit the pixel during the imaging interval.  Negative values
indicate that the corresponding mean \sigmao value is negative.  Zero denotes no
data.
\item[{\bf V:}] The normalized standard deviation ($K_p$) image defined as the standard
deviation of the \sigmao measurements hitting each grid element divided by the mean
\sigmao value.  No estimate is made if the mean \sigmao is negative and zero is
returned. A negative V value indicates no data.
\item[{\bf x:}] Longitude image ($0^\circ$ to $360^\circ$).  This product contains an
`image' whose data is the longitude of the center of the image pixel and is provided
for convenience of the user.  Since only a single image is needed for the full
image, the naming convention for this product is somewhat different than data
products.  
\item[{\bf y:}] Latitude image ($-90^\circ$ to $90^\circ$).  This product contains
an `image' whose data is the longitude of the center of the image pixel and is
provided for convenience of the user.  Since only a single image is needed for the
full image, the naming convention for this product is somewhat different than data
products.  
\end{enumerate}

\begin{table}[hhhtb]
\centering
\begin{tabular}{c|c|l}
$T$ (type) & Code Number & Description \\ \hline
 	a & 1 & \sigmao (in dB) \\
	 C & 8 & counts or hits (measurements) per pixel \\
 	V &23 & standard deviation image (unitless)\\
 	x & 3 & longitude image (deg) \\
 	y &31 & latitude image (deg) \\
\end{tabular}
\caption{Standard internal type codes for products \label{tab:type} }
\end{table}

A sample product listing is available in Appendix A. Table \ref{tab:sizes} gives
the approximate file sizes for the BYU {\tt SIR format} \sigmao browse product 
files for each region. 

\begin{table}[hhhtb]
\centering
\begin{tabular}{l|c|c|c}
Region  & File size & Pixel Size & Region Code \\
Name & (MB) & (X$\times$Y) & Number \\ \hline
Southern Hemisphere  &  0.3 &  $388\times388$ & 100 \\
Northern Hemisphere  &  0.3 &  $388\times388$ & 111 \\
Global               &  3.2 & $1800\times900$ & 500 \\
\end{tabular}
\caption{Approximate \sigmao browse product file sizes for each region. 
\label{tab:sizes} }
\end{table}

Two auxiliary image files are available for each region.  These files contain
the longitude and latitude for the center of each pixel, respectively. 
The files are in the same format as the product but have a latitude value 
or longitude value instead of a \sigmao value stored in the image.   The naming
scheme for the auxilary files is:
$$
QS\_Xbl{\bf T}{\bf R}3C.date
$$
where {\bf T} is the one character image type code (`x', or `y'), {\bf R} is the
one character region (`G'=Global, `N'=Northern Hemisphere, and `S'=Southern
Hemisphere), and $date$ file extension is an 11 character string containing the date
of the file's creation.  This file is not expected to change over the life of the mission
so only one file of each type per region is created.



\section{User Notes}

The \sigmao browse products described herein are intended to help users to identify
features of interest directly in the Qscat \sigmao measurements by providing a
spatial and temporal (over one day) average view of the Qscat \sigmao measurements.
Note that in producing the mean \sigmao product, all \sigmao measurements
(from a single beam) falling within a single pixel are averaged.  Thus, the
forward-looking and aft-looking measurements are averaged and the resulting average is
over the various azimuth angles of the measurements.  The azimuth angles of the
measurements hitting a given location vary with the pixel location and with time
and may be further affected by missing or low-quality data.  Discontinuities and
artifacts can occur at swath edges and in areas where the surface shows significant
azimuth dependence (e.g., over the ocean).  The normalized standard deviation ($K_p$)
images can be useful in evaluating temporal and azimuth variation in the \sigmao
measurements.

Computation of the average \sigmao value is done in normal space (not in dB) with
negative values included.  If the resulting average is negative, the sign of the
corresponding count image pixel is set to negative.  Thus, count images can have
both postive and negative values.  In practice, negative averages occur primarily 
over the ocean in low wind speed regions.   The count images are also
useful for creating multi-day averages and as a quality control. Note that due to
the rotation of the antenna, the cross-track density of \sigmao measurements varies
with more measurements at the outer edges of the swath than at the swath center.  As
a result, swath edges are clearly visible in the count images.  Some areas of the 
Earth's surface are not covered in a single day, resulting in diamond shaped regions of no
coverage in mid-latitude and equatorial averages.  These no coverage regions are 
larger in the h-pol images than in the v-pol images due to the narrower swath of
the h-pol measurements.



%\clearpage 

\section{The BYU {\tt SIR} File Format}

The BYU-MERS {\tt SIR} image format was developed by the Brigham Young University 
(BYU) Microwave Earth Remote Sensing (MERS) laboratory to store a variety of image
types along with the information required to Earth-locate the image pixels.

A {\tt SIR} format file consists of one or more 512 byte headers followed by the
image data and additional zero padding to insure that the file is a multiple of
512 bytes long\footnote{This ensures that images can be transferred to and from
all platforms without loss using binary ftp.}.  The file header record contains
all of the information required to read the remainder of the file and the map
projection information required to map pixels to lat/long on the Earth surface. 
The image pixel values generally represent floating point values and may be stored 
in one of three ways.  The primary way is as 2 byte integers (with the high order 
byte first), though the pixels may be stored as single bytes or IEEE floating point
values.   Scale factors are stored in the header to convert the integer or byte 
pixel values to native floating point units.  The image is stored in row-scanned
(left to right) order from the lower left corner (the origin of the image) up 
through the upper right corner.  
By default, the location of a pixel is identified with its lower-left
corner.  The origin pixel (1,1) is the lower left corner of the image.  The array
index $n$ of the $(i,j)^{th}$ pixel where $i$ is horizontal and $j$ is vertical is
given by $n=(j-1)*N_x+i$ where $N_x$ is the horizontal dimension of the image.
The last pixel stored in the file is at ($N_x,N_y$).

The sir file header contains various numerical values and strings which describe the
image contents. For example, a no-data flag value is set in the header as well
as a nominal display range and the minimum and maximum representable value. 
Optional secondary header records (512 bytes) can be used to
store additional, non-standard information.

The standard {\tt SIR} file format supports a variety of image projections
including:
\begin{enumerate}
  \item Rectangular array (no projection)
  \item Rectangular lat/lon array
  \item Two different types of Lambert equal-area projections which can be 
     used in either non-polar or polar projections
  \item Polar stereographic projections
  \item EASE grid polar projection with various resolutions
  \item EASE global projection with various resolutions
\end{enumerate}
For the Qscat global \sigmao browse products, only the rectangular array and polar
stereographic projections are used.  Also, the browse product naming scheme is not
SIR-standard.

Readers for the {\tt SIR} file format are available in C, FORTRAN, Matlab, and
IDL/PVWAVE.  A customized version of the unix {\bf xv} program which can read, display, and print
{\tt SIR} format files is also available.  Viewer and reader programs are available on line 
from the BYU MERS web and anonymous ftp sites at URLs {\tt http://www.mers.byu.edu/}
and {\tt ftp://ftp.cers.byu.edu/pub/sir}, respectively\footnote{The reader code may be 
copied and modified and freely distributed so long as (1) original or modified code is 
not redistributed for profit and (2) acknowledgment is made that the original code was 
obtained from the  Microwave Earth Remote Sensing Laboratory at Brigham 
Young University,  Provo, UT.}.  Documentation for these readers are located there.
Sample files and various utility and display routines are also available.
(Be sure to use binary ftp to transfer {\tt .sir} files!) 
Adobe Photoshop can display the image data {\tt .sir} file stored as two-byte integers. 
Read the file as `raw', specify a 512 header and 16 bit data, and enter the pixel
size. 


\newpage


\begin{thebibliography}{1}

\bibitem{cryo}
D.G.~Long and M.R.~Drinkwater, ``Cryosphere Applications of NSCAT Data,'' 
{\em IEEE Trans. Geosci. Remote Sens.}, Vol. 37, No. 3, pp. 1671-1684, 1999.

\bibitem{long:views}
D.G.~Long, ``NSCAT Views Land and Ice,'' {\em Proc. Int.
Geosci. Rem. Sens. Sym.}, pp. 1973-1975, Seattle, Washington, 6-10
July, 1998.

\bibitem{quinn}
Q.P.~Remund and D.G.~Long, ``Polar Sea Ice Extent Mapping Using Ku-Band
Scatterometer Data,'' {\em J. Geophys. Res.}, Vol. 104, No. C5, pp. 11515-11527,
1999.

\bibitem{quinn_qscat}
Q.P.~Remund and D.G.~Long, ``Sea Ice Mapping Algorithm for QuikSCAT and
SeaWinds,'' {\em  Proc. Int. Geosci. Rem. Sens. Sym.}, pp. 1686-1688, Seattle,
Washington, 6-10 July, 1998.


\end{thebibliography}

%\clearpage
%\newpage

\appendix
\centerline{\bf\Large Appendix}
\section{Sample Product Listing}

The following is a sample listing of the browse product files for data corresponding
to JD001, 1999.  See Section 3 for information on how to read the BYU {\tt SIR} file format.

\subsubsection*{Browse Products}
\begin{multicols}{2}
\noindent
{\tt 
QS\_XbhaG3C1999001.19990020101    \\
QS\_XbhVG3C1999001.19990020101    \\
QS\_XbhKG3C1999001.19990020101    \\
QS\_XbvaG3C1999001.19990020101    \\
QS\_XbvVG3C1999001.19990020101    \\
QS\_XbvKG3C1999001.19990020101    \\
QS\_XbhaG3C1999001.19990020101    \\
QS\_XbhVN3C1999001.19990020101    \\
QS\_XbhKN3C1999001.19990020101    \\
QS\_XbvaN3C1999001.19990020101    \\
QS\_XbvVN3C1999001.19990020101    \\
QS\_XbvKN3C1999001.19990020101    \\
QS\_XbhaS3C1999001.19990020101    \\
QS\_XbhVS3C1999001.19990020101    \\
QS\_XbhKS3C1999001.19990020101    \\
QS\_XbvaS3C1999001.19990020101    \\
QS\_XbvVS3C1999001.19990020101    \\
QS\_XbvKS3C1999001.19990020101    \\
}
\end{multicols}

\subsubsection*{Auxiliary Products}
\begin{multicols}{2}
\noindent
{\tt 
QS\_XbxG3C.19990020101    \\
QS\_XbyG3C.19990020101    \\
QS\_XbxN3C.19990020101    \\
QS\_XbyN3C.19990020101    \\
QS\_XbxS3C.19990020101    \\
QS\_XbyS3C.19990020101    \\
}
\end{multicols}

\section{Sample Images}

Samples of selected Qscat \sigmao browse images from JD 250, 2000 are presented 
in the following.  Note that the images have been reduced in size for printing.

\begin{figure}[hhhhtb]
\epsfig{file=QS_XbhaG3C1999245.19992491643.ps,width=6.5in,bbllx=0.472in,bblly=3.661in,bburx=8.028in,bbury=7.389in}
\caption{QS\_XbhaG3C1999245.19992491643 (H-pol Global \sigmao browse image).
 Grey scale extends from -32 dB to 0 dB.}
\end{figure}

\begin{figure}[hhhhtb]
\epsfig{file=QS_XbvaG3C1999245.19992491643.ps,width=6.5in,bbllx=0.472in,bblly=3.661in,bburx=8.028in,bbury=7.389in}
\caption{QS\_XbvaG3C1999245.19992491643 (V-pol Global \sigmao browse image).
 Grey scale extends from -32 dB to 0 dB.}
\end{figure}

\begin{figure}[hhhhtb]
\epsfig{file=QS_XbvCG3C1999245.19992491643.ps,width=6.5in,bbllx=0.472in,bblly=3.661in,bburx=8.028in,bbury=7.389in}
\caption{QS\_XbvCG3C1999245.19992491643 (V-pol Global count image).
 Grey scale extends from 0 to 50.}
\end{figure}

\begin{figure}[hhhhtb]
\epsfig{file=QS_XbvVG3C1999245.19992491643.ps,width=6.5in,bbllx=0.472in,bblly=3.661in,bburx=8.028in,bbury=7.389in}
\caption{QS\_XbvVG3C1999245.19992491643 (V-pol Global standard 
deviation ($K_p$) image).  Grey scale extends from 0.0 to 1.0.}
\end{figure}

\begin{figure}[hhhhtb]
\epsfig{file=QS_XbhaN3C1999245.19992491643.ps,bbllx=1.555in,bblly=2.806in,bburx=6.944in,bbury=8.195in}
\caption{QS\_XbhaN3C1999245.19992491643 (H-pol Northern Hemisphere \sigmao browse image).
 Grey scale extends from -32 to 0 dB.}
\end{figure}

\begin{figure}[hhhhtb]
\epsfig{file=QS_XbvaN3C1999245.19992491643.ps,bbllx=1.555in,bblly=2.806in,bburx=6.944in,bbury=8.195in}
\caption{QS\_XbvaN3C1999245.19992491643 (V-pol Northern Hemisphere \sigmao browse image).
 Grey scale extends from -32 to 0 dB.}
\end{figure}

\begin{figure}[hhhhtb]
\epsfig{file=QS_XbhaS3C1999245.19992491643.ps,bbllx=1.555in,bblly=2.806in,bburx=6.944in,bbury=8.195in}
\caption{QS\_XbhaS3C1999245.19992491643 (H-pol Southern Hemisphere \sigmao browse image).
 Grey scale extends from -32 to 0 dB.}
\end{figure}

\begin{figure}[hhhhtb]
\epsfig{file=QS_XbvaS3C1999245.19992491643.ps,bbllx=1.555in,bblly=2.806in,bburx=6.944in,bbury=8.195in}
\caption{QS\_XbvaS3C1999245.19992491643 (V-pol Southern Hemisphere \sigmao browse image).
 Grey scale extends from -32 to 0 dB.}
\end{figure}


\begin{figure}[hhhhtb]
\epsfig{file=QS_XbvCN3C1999245.19992491643.ps,bbllx=1.555in,bblly=2.806in,bburx=6.944in,bbury=8.195in}
\caption{QS\_XbvCN3C1999245.19992491643 (V-pol Northern Hemisphere count image).
 Grey scale extends from 0 to 50.}
\end{figure}

\begin{figure}[hhhhtb]
\epsfig{file=QS_XbvVN3C1999245.19992491643.ps,bbllx=1.555in,bblly=2.806in,bburx=6.944in,bbury=8.195in}
\caption{QS\_XbvVN3C1999245.19992491643 (V-pol Northern Hemisphere standard 
deviation ($K_p$) image).  Grey scale extends from 0.0 to 1.0.}
\end{figure}

\begin{figure}[hhhhtb]
\epsfig{file=QS_XbxN3C.2000047.ps,bbllx=1.555in,bblly=2.806in,bburx=6.944in,bbury=8.195in}
\caption{QS\_XbxN3C.2000047.eps (Northern Hemisphere longitude image).
Grey scale extends from 0 to 360 deg.}
\end{figure}

\begin{figure}[hhhhtb]
\epsfig{file=QS_XbyN3C.2000047.ps,bbllx=1.555in,bblly=2.806in,bburx=6.944in,bbury=8.195in}
\caption{QS\_XbyN3C.2000047.eps (Northern Hemisphere latitude image).
Grey scale extends from -90 to 90 deg.}
\end{figure}


\end{document}\end

