Geoscience Reference
In-Depth Information
J
∑
J
∑
J
∑
1
J
)
MIN(R
..j
,
MIN(R
..j
, S
j
)
MIN(R
..j
, R
j
)
..
..
j
=
1
j
=
1
j
=
1
J
∑
J
∑
J
∑
D
∑
D
∑
D
∑
W
d
⋅
MIN(R
d
⋅
j
, E
d
⋅
j
)
W
d
⋅
MIN(R
d
⋅
j
, S
d
⋅
j
)
W
d
⋅
MIN(R
d
⋅
j
, F
d
⋅
j
)
=
1
=
1
=
1
d
=
1
j
d
=
1
j
d
=
1
j
D
∑
D
∑
D
∑
W
d
⋅
W
d
⋅
W
d
⋅
d
=
1
d
=
1
d
=
1
D
∑
Nd
J
∑
D
∑
Nd
J
∑
D
∑
Nd
J
∑
∑
∑
∑
W
dn
MIN(R
dnj
, A
dnj
)
W
dn
W
dn
MIN(R
dnj
, B
dnj
)
MIN(R
dnj
, S
dnj
)
=
1
=
1
d
=
1
n
=
1
j
d
=
1
n
=
1
j
=
1
d
=
1
n
=
1
j
D
∑
Nd
D
∑
Nd
D
∑
Nd
∑
∑
∑
W
dn
W
dn
W
dn
d
=
1
n
=
1
d
=
1
n
=
1
d
=
1
n
=
1
J
∑
J
∑
J
∑
D
∑
Nd
D
∑
Nd
D
∑
Nd
∑
∑
∑
W
dn
MIN(R
dnj
, E
d
⋅
j
)
W
dn
MIN(R
dnj
, S
d
⋅
j
)
W
dn
MIN(R
dnj
, F
d
⋅
j
)
d
1
1
d
1
n
1
=
n
=
=
1
j
=
=
=
1
j
d
=
1
n
=
1
=
1
j
D
∑
Nd
D
∑
D
∑
Nd
Nd
∑
∑
∑
W
dn
W
dn
W
dn
d
=
1
n
=
1
d
=
1
n
=
1
d
=
1
n
=
1
J
∑
J
∑
J
∑
D
∑
Nd
D
∑
Nd
D
∑
Nd
1
J
∑
∑
∑
W
dn
MIN(R
dnj
, )
W
dn
MIN(R
dnj
, S
j
)
W
dn
MIN(R
dnj
, R
j
)
⋅⋅
⋅⋅
d
=
1
n
=
1
=
1
j
d
=
1
n
=
1
=
1
j
d
=
1
n
=
1
=
1
j
Nd
Nd
D
∑
Nd
D
∑
D
∑
∑
∑
∑
W
dn
W
dn
W
dn
d
=
1
n
=
1
d
=
1
n
=
1
d
=
1
n
=
1
n
m
Information of Quantity
p
Figure 17.3
Expressions for 15 points defined by a combination of the information of quantity and location. The
vertical axis shows information of location and the horizontal axis shows information of quantity.
The text defines the variables.
the other maps are derived from an adjustment to the comparison map, such that the proportion of
membership for each of the
in the other maps (Foody, 1992). This adjustment
is necessary to answer the question, What would be the agreement between the reference map and
the comparison map, if the scientist who created the comparison map would have had no information
of quantity during its production? The adjustment holds the level of information of location constant
while adjusting each grid cell such that the quantity of each of the
J
categories is 1/
J
.
Equations 17.12 and 17.13 give the necessary adjustment to each grid cell in order to scale the
comparison map to express no information of quantity:
J
categories in the landscape is 1/
J
AS
J
Ê
1
/
ˆ
=
,
if
1
/
J
£
(17.12)
S
Á
˜
dnj
dnj
◊◊
j
S
Ë
◊◊
j
¯
S
Ê
Á
ˆ
˜
◊◊
j
=- -
11
S
,
else
Ê
Ë
ˆ
¯
dnj
1
/
J
ES
J
Ê
1
/
ˆ
=
,
if
1
/
J
£
(17.13)
S
Á
˜
dj
◊
dj
◊
◊◊
j
S
Ë
◊◊
j
¯
