Question

A typical conditional function has the form:
Output = CON (test, out if true, out if false)

What will be the reclassified output if the following conditional reclassification function Output = CON (Layer P < 3, Layer Q, Layer R) is applied on the three input raster layers P, Q, and R?

Layer P

1	3	1
0	5	2
4	2	5

Layer Q

x	x	y
x	x	x
x	x	y

Layer R

b	b	b
a	b	b
a	b	b

• A.

  x	b	y
  x	b	x
  a	x	b

• B.

  x	b	y
  x	x	b
  a	x	b

• C.

  x	b	y
  x	x	x
  x	x	y

• D.

  x	b	x
  x	b	x
  a	x	b

Hint:

Apply the CON rule cell by cell: if Layer P is less than 3 at a cell, take the Layer Q value there, otherwise take the Layer R value there.

Answer 1

The Correct Option is A

Step 1: Understand the conditional (CON) reclassification rule.
The function \( Output = CON(\text{Layer P} < 3, \text{Layer Q}, \text{Layer R}) \) is evaluated cell by cell. For each grid cell, if the value in Layer P at that location is less than 3, the output takes the value of Layer Q at the same location, otherwise the output takes the value of Layer R at the same location.

Step 2: Write out the three input grids with row and column positions.
Layer P: row1 = (1, 3, 1), row2 = (0, 5, 2), row3 = (4, 2, 5). Layer Q: row1 = (x, x, y), row2 = (x, x, x), row3 = (x, x, y). Layer R: row1 = (b, b, b), row2 = (a, b, b), row3 = (a, b, b).

Step 3: Evaluate row 1 cell by cell.
Cell (1,1): P = 1, 1 \(<\) 3 is true, so take Q(1,1) = x. Cell (1,2): P = 3, 3 \(<\) 3 is false, so take R(1,2) = b. Cell (1,3): P = 1, 1 \(<\) 3 is true, so take Q(1,3) = y. Row 1 output: (x, b, y).

Step 4: Evaluate row 2 cell by cell.
Cell (2,1): P = 0, 0 \(<\) 3 is true, so take Q(2,1) = x. Cell (2,2): P = 5, 5 \(<\) 3 is false, so take R(2,2) = b. Cell (2,3): P = 2, 2 \(<\) 3 is true, so take Q(2,3) = x. Row 2 output: (x, b, x).

Step 5: Evaluate row 3 cell by cell.
Cell (3,1): P = 4, 4 \(<\) 3 is false, so take R(3,1) = a. Cell (3,2): P = 2, 2 \(<\) 3 is true, so take Q(3,2) = x. Cell (3,3): P = 5, 5 \(<\) 3 is false, so take R(3,3) = b. Row 3 output: (a, x, b).

Step 6: Assemble the full output grid and match to the options.
The reclassified output grid is row1 = (x, b, y), row2 = (x, b, x), row3 = (a, x, b). This exactly matches option (A). Option (B) has an incorrect row 2, (x, x, b), because cell (2,2) should be R = b, not Q = x, since P = 5 fails the less than 3 test. Option (C) uses Q everywhere in rows 2 and 3, ignoring that most of those P values are 3 or more. Option (D) has an incorrect row 1, cell (1,3), showing x instead of y.

\[ \boxed{\text{Option (A): } (x,b,y),\ (x,b,x),\ (a,x,b)} \]