COADS Release 1, Supplement B

Comprehensive Ocean-Atmosphere Data Set; Release 1
Supplement B: 2° Monthly Summary Groups
Formats: MSUG.1, MSTG.1

0. Introduction

The seven group files are relatively compact alternatives to the full Monthly Summary Trimmed and Untrimmed (MST or MSU) formats, intended for studies using only a few variables or statistics. Eight important statistics for each of four related variables are grouped together in each file using a packed binary format. Thus five files are needed to represent all 19 MST variables, and two files are needed to represent all eight MSU variables. The statistics were chosen to bring together information that can be used to analyze the variability of the data and inhomogeneities of their distribution in time and space.

Cross reference is made to supp. A for standardized unpacking information, and the same notation for variables and statistics is followed or extended, also using the same type of two-dimensional table presentation.

1. Monthly Summary Trimmed Groups (MSTG)

The five trimmed groups were derived from MST (described in supp. A). Each MST was split into five MSTG records; these were written out onto the five separate group files even if every αβ (the value of the statistic α for the variable β) was missing. Thus the record structure is identical for all the groups and their parent MST file. The five trimmed groups are numbered 3-7 to distinguish them from the untrimmed groups (numbered 1-2). Groups 3-7 contain four variables each: 3 = (S, A, Q, R), 4 = (W, U, V, P), 5 = (C, R, X, Y), 6 = (D, E, F, G), and 7 = (I, J, K, L). Table B1-1a shows the bit layout in common to any MSTG, and Tables B1-1b through B1-1f show the bit layout of each of the 64-bit or 16-bit sections of groups 3 through 7, respectively, in sequential bit-order reading from top to bottom. An example showing the bit-order is given following Table B1-1f.

Table B1-1a
MSTG.1

 #   α    Statistic                             Bits
-----------------------------------------------------
          rptin                                   16
          year                                     8
          month                                    4
          2° box                                  14
          10° box                                 10
          identification checksum                 12
-----------------------------------------------------
11   3    3/6 sextile (the median)                64
 6   m    mean                                    64
 5   n    number of observations                  64
15   e    standard deviation estimate             64
 1   d    mean day-of-month of observations       16
 2   h_t    fraction of observations in daylight    16
 3   x    mean longitude of observations          16
 4   y    mean latitude of observations           16
-----------------------------------------------------
           total                                 384

Table B1-1b
Group 3
64-bit or 16-bit Sections

 #   β    Variable                  Bits  Bits
----------------------------------------------
 1   S    sea surface temperature     16     4
 2   A    air temperature             16     4
 8   Q    specific humidity           16     4
 9   R    relative humidity           16     4
----------------------------------------------
          total                       64    16

Table B1-1c
Group 4
64-bit or 16-bit Sections

 #   β    Variable                              Bits  Bits
----------------------------------------------------------
 3   W    scalar wind                             16     4
 4   U    vector wind eastward component          16     4
 5   V    vector wind northward component         16     4
 6   P    sea level pressure                      16     4
----------------------------------------------------------
          total                                   64    16

Table B1-1d
Group 5
64-bit or 16-bit Sections

 #   β    Variable                              Bits  Bits
----------------------------------------------------------
 7   C    total cloudiness                        16     4
 9   R    relative humidity                       16     4
14   X    WU                                      16     4
15   Y    WV (14-15 are wind stress parameters)   16     4
----------------------------------------------------------
          total                                   64    16

Table B1-1e
Group 6
64-bit or 16-bit Sections

 #   β    Variable                                                   Bits  Bits
--------------------------------------------------------------------------------
10   D    S - A = sea-air temperature difference                       16     4
11   E    (S - A) W = sea-air temperature difference * wind magnitude  16     4
12   F    Q_s - Q = (saturation Q at S) - Q                              16     4
13   G    FW = (Q_s - Q)W (evaporation parameter)                        16     4
--------------------------------------------------------------------------------
          total                                                        64    16

Table B1-1f
Group 7
64-bit or 16-bit Sections

 #   β    Variable                              Bits  Bits
----------------------------------------------------------
16   I    UA                                      16     4
17   J    VA                                      16     4
18   K    UQ                                      16     4
19   L    VQ (16-19 are sensible and                      
          latent heat transport parameters)       16     4
----------------------------------------------------------
          total                                   64    16

For example, group 3 contains, in order: rptin, year, month, 2° box, 10° box, and identification checksum, followed by

((αβ, β = S,A,Q,R), α = 3,m,n,e,d,h,x,y)

which defines the following matrix, with 4 rows and 8 columns:

   | α |  3    m    n    e    d    h    x    y
---|---|--------------------------------------
 β | # | 11    6    5   15    1    2    3    4
---|---|--------------------------------------
 S | 1 | 3S   mS   nS   eS   dS   hS   xS   yS
 A | 2 | 3A   mA   nA   eA   dA   hA   xA   yA
 Q | 8 | 3Q   mQ   nQ   eQ   dQ   hQ   xQ   yQ
 R | 9 | 3R   mR   nR   eR   dR   hR   xR   yR

stored in the order:

column 1, row 1,..., row 4; column 2, row 1,..., row 4; ...; column 8, row 1, ..., row 4.

2. Monthly Summary Untrimmed Groups (MSUG)

The two untrimmed groups were derived from MSU (described in supp. A). Each MSU was split into two MSUG records; these were written out onto the two separate group files even if every αβ (the value of the statistic α for the variable β) was missing. Thus the record structure is identical for all the groups and their parent MSU file. Groups 1-2 contain four variables each: 1 = (S, A, P, Q), 2 = (W, U, V, C). Table B2-1a shows the bit layout in common to any MSUG, and Tables B2-1b and B2-1c show the bit layout of each of the 64-bit or 16-bit sections of group 1 and group 2, respectively, in sequential bit-order reading from top to bottom.

Table B2-1a
MSUG.1

 #   α    Statistic                             Bits
-----------------------------------------------------
          rptin                                   16
          year                                     8
          month                                    4
          2° box                                  14
          10° box                                 10
          identification checksum                 12
-----------------------------------------------------
11   3    3/6 sextile (the median)                64
 6   m    mean                                    64
 5   n    number of observations                  64
15   e    standard deviation estimate             64
 1   d    mean day-of-month of observations       16
 2   h_u    mean hour of observations               16
 3   x    mean longitude of observations          16
 4   y    mean latitude of observations           16
-----------------------------------------------------
           total                                 384

Table B2-1b
Group 1
64-bit or 16-bit Sections

 #   β    Variable                              Bits  Bits
----------------------------------------------------------
 1   S    sea surface temperature                 16     4
 2   A    air temperature                         16     4
 6   P    sea level pressure                      16     4
 8   Q    specific humidity                       16     4
----------------------------------------------------------
          total                                   64    16

Table B2-1c
Group 2
64-bit or 16-bit Sections

 #   β    Variable                              Bits  Bits
----------------------------------------------------------
 3   W    scalar wind                             16     4
 4   U    vector wind eastward component          16     4
 5   V    vector wind northward component         16     4
 7   C    total cloudiness                        16     4
----------------------------------------------------------
          total                                   64    16

3. Reconstruction of Floating Point Data

The coded and true value ranges, the units, and the base for the fields that are unique in representation to the groups are given in Table B3-1.

Table B3-1
Unpacking Groups

 #   α   Statistic                           True value   Unit s   Base  Coded
-------------------------------------------------------------------------------
 1   d   mean day-of-month of observations        2≤30    2 days    0.0   1≤15
 2   h_t   fraction of observations in daylight   0.0≤1.0   0.1      -1     1≤11
 2   h_u   mean hour of observations                1≤23    2 hours  -0.5   1≤12
 3   x   mean longitude of observations         0.1≤1.9   0.2°     -0.5   1≤10
 4   y   mean latitude of observations          0.1≤1.9   0.2°     -0.5   1≤10
-------------------------------------------------------------------------------

Further descriptions of the fields in Table B3-1 follow. All other fields are common to the MST or MSU, with characteristics as given in sec. 2.3 of supp. A, except that some fields have different names and other differences as noted.

identification checksum
The group number, 1 for (S, A, P, Q), 2 for (W, U, V, C), 3 for (S, A, Q, R), 4 for (W, U, V, P), 5 for (C, R, X, Y), 6 for (D, E, F, G), or 7 for (I, J, K, L), must be added into the usual checksum prior to the modulo for proper identification. For example, supposing that the coded group 3 data matrix is available in an array MSTG, the checksum CK is computed and verified against the stored checksum CKS in FORTRAN as follows:
```
          INTEGER CK,J,I,MSTG(4,8),YEAR,MONTH,BOX2,BOX10,CKS
          CK = 0
          DO 500 J = 1,8
              DO 400 I = 1,4
                  CK = CK + MSTG(I,J)
     400      CONTINUE
     500  CONTINUE
          CK = CK + YEAR + MONTH + BOX2 + BOX10 + 3
          CK = MOD(CK,4095)
          IF(CK .NE. CKS) THEN
              PRINT *,'ERROR. CK = ',CK,' .NE. CKS = ',CKS
              STOP
          ENDIF
```
standard deviation estimate
Instead of the standard deviation about the mean (statistic 7, s), this robust estimate is provided from the fifth and first sextiles: e = (s₅ - s₁)/2. (This was computed using integer truncating division on the coded quantity s₅ - s₁,i.e., rounding down.) For unpacking purposes, e is treated exactly like the corresponding standard deviation of each respective variable.
mean day-of-month of observations
fraction of observations in daylight
mean hour of observations
mean longitude of observations
mean latitude of observations

The centroids of observational location in time and space are shortened in length and precision from their representation in MST and MSU. "Nice" true values are reported for d, h, x, and y using the aforementioned units and base. Because of successive rounding steps, these values actually represent intervals whose trimmed or untrimmed behavior is shown in Tables B3-2a or B3-2b. The lowest and highest intervals are always exceptions to the behavior of the central intervals, so these extreme intervals are shown explicitly with the deviation (δ) of the actual midpoint of this interval from the reported true value. Coded values greater than one and less than the maximum coded value correspond to central intervals that can be obtained by subtracting the minus value and adding the plus value to the reported true value, yielding an inclusive lower and exclusive upper bound. The actual midpoint of each central interval can be obtained in any of three ways: by taking the mean of the upper bound and the lower bound, by plugging the basex shown into the usual formula in place of base, or by adding the midpoint deviation (δ) to the reported true value. For example, the intervals and actual midpoints corresponding to true h_u values 1, 3, 5,..., 23 are [0,2.05), [2.05,4.05), [4.05,6.05),..., [22.05,23] and 1.025, 3.05, 5.05,..., 22.525.

Table B3-2a
MSTG Interval Behavior

-------|-------------------|-------------------------------|--------------------
       |      Lowest       |            Central            |       Highest      
  #  α |  Interval   δ     |    ± reported    Basex   δ    |   Interval   δ     
-------|-------------------|-------------------------------|--------------------
  1  d |   [1,3.1) +0.05   |     [-0.9,+1.1)  0.05  +0.1   |  [29.1,31] +0.05   
  2  h_t | [0,0.055) +0.0275 | [-0.045,+0.055) -0.95  +0.005 |  [0.955,1] -0.0225 
  3  x | [0,0.205) +0.0025 | [-0.095,+0.105) -0.475 +0.005 |  [1.805,2] +0.0025 
  4  y | [0,0.205) +0.0025 | [-0.095,+0.105) -0.475 +0.005 |  [1.805,2] +0.0025 
-------|-------------------|-------------------------------|--------------------

Table B3-2b
MSUG Interval Behavior

-------|-------------------|-------------------------------|--------------------
       |      Lowest       |            Central            |       Highest      
  #  α |  Interval   δ     |    ± reported    Basex   δ    |   Interval   δ     
-------|-------------------|-------------------------------|--------------------
  1  d |  [1,3.05) +0.025  |   [-0.95,+1.05)  0.025 +0.05  | [29.05,31] +0.025  
  2  h_u |  [0,2.05) +0.025  |   [-0.95,+1.05) -0.475 +0.05  | [22.05,23] -0.475  
  3  x | [0,0.205) +0.0025 | [-0.095,+0.105) -0.475 +0.005 |  [1.805,2] +0.0025 
  4  y | [0,0.205) +0.0025 | [-0.095,+0.105) -0.475 +0.005 |  [1.805,2] +0.0025 
-------|-------------------|-------------------------------|--------------------