Example 3. Tensor (Wind Stress)

Next, consider a data object consisting of a horizontal wind stress tensor measured over an $x$-$y$ coordinate grid at the surface of the earth. The wind stress tensor has four components, two along each of the dimensions of the grid. We take the $x$ and $y$ to be the coordinates of a $100 \times 75$ grid on which the tensors are defined. Suppose further that we attach no time to these data. (They may be time-independent estimates to be used in some sort of simple model.)

Thus, there are two Level 0 dimensions, each having 2 grid points: $S_{xx}$, $S_{xy}$, $S_{yx}$, $S_{yy}$, where $S_{ij}$ is the wind stress in the $i$ direction on the surface normal to the $j$ direction. The data have two Level 1 dimensions: $x$ and $y$. The data object has data records, so it must have a Level 2 dimension; we will use a generic index counter as the Level 2 dimension.

To complicate matters just a little more, we will assume that the data are written out as the array: S(wind stress in $x$ direction, $x$, wind stress in $y$ direction, $y$). The data object fields will be as follows (indices start at 1):

OBJDESC.

NDIM0 = 2

NDIM1 = 2

NDIM2 = 1

NDIM3 = 0

DIMSPEC0.

INDEX = (1, 3)

GPTNUM = (2, 2)

DIMSPEC1.

INDEX = (2, 4)

DESNUM = (1, 1)

DIMSPEC2.

INDEX = -1

DESCRIP0.

DATFMT = (single precision floating-point, single precision floating-point, single precision floating-point, single precision floating-point)

VARTYPE = ($S_{xx}$, $S_{xy}$, $S_{yx}$, $S_{yy}$)

UNITS = (Pa, Pa, Pa, Pa)

DESCRIP1.

DEXSORT = 1

NDEX = 1

RECSORT = 0

START = 1

END = -1

GPTNUM = 100

DUPNUM = 0

DESSUP = 0

DESFMT = long integer

DESTYPE = $x$

UNITS = no units

STORG = 1

DESCVAL.

DLEVEL = 1

LEVEL = 1

DINDEX = 0

DEXSORT = 1

NDEX = 1

RECSORT = 0

AVALS = (1, 1)

DESCRIP1.

DEXSORT = 2

NDEX = 2

RECSORT = 0

START = 1

END = -1

GPTNUM = 75

DUPNUM = 0

DESSUP = 0

DESFMT = long integer

DESTYPE = $y$

UNITS = no units

STORG = 1

DESCVAL.

DLEVEL = 1

LEVEL = 1

DINDEX = 0

DEXSORT = 2

NDEX = 2

RECSORT = 0

AVALS = (1, 1)

DESCRIP2.

NDEX = 0

DUPNUM = 0

DESSUP = 0

DESFMT = long integer

DESTYPE = index

UNITS = no units

STORG = 1

DESCVAL.

DLEVEL = 2

LEVEL = 2

DINDEX = 0

DEXSORT = 1

NDEX = 1

RECSORT = 0

AVALS = (1, 1)