Need help

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jeany lou

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May 16, 2012
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can someone help me with this:
*1991 land use classification
forest- 45ha.
urban- 40ha.
agriculture- 35 ha.
water bodies- 20 ha.

*1992 land use classification
forest- 40.9 ha.
urban- 46.3 ha.
agriculture- 33.5 ha.
water bodies- 19.3 ha.

Question: How can i crate a markov transition matrix? how much area is converted from forest to urban? forest to agriculture? etc.
REALLY NEED HELP. THANKS!
 
Hello, jeany lou!


\(\displaystyle \begin{array}{c}\text{1991 land use classification}\\ \hline \end{array}\)
\(\displaystyle \begin{array}{cc}\text{forest} & 45\text{ ha.} \\
\text{urban} & 40\text{ ha.} \\
\text{agriculture} & 35\text{ ha.} \\
\text{water bodies} & 20\text{ ha.} \end{array}\)

\(\displaystyle \begin{array}{c}\text{1992 land use classification} \\ \hline \end{array}\)
\(\displaystyle \begin{array}{cc}\text{forest} & 40.9\text{ ha.} \\
\text{urban} & 46.3\text{ ha.} \\
\text{agriculture} & 33.5\text{ ha.} \\
\text{water bodies} & 19.3\text{ ha.} \end{array}\)

How can i crate a markov transition matrix?
How much area is converted from forest to urban? forest to agriculture? etc.[/SIZE]
Click to expand...

I think I have an approach . . . but I could be completely wrong.


This is what we have . . .

\(\displaystyle \begin{array}{c| c|c|c|c|}
& 1991 & 1992 & \text{change} & \%\text{ change} \\ \hline
\text{forest} & 45 & 40.9 & -4.1 & \frac{\text{-}4.1}{140} = -0.0293 \\ \hline
\text{urban} & 40 & 46.3 & +6.3 & \frac{6.3}{140} = +0.0450 \\ \hline
\text{argi.} & 35 & 33.5 & -1.5 & \frac{\text{-}1.5}{140} = -0.0107 \\ \hline
\text{water} & 20 & 19.3 & -0.7 & \frac{\text{-}0.7}{140} = -0.0050 \\ \hline
\text{Total} & 140 & 140 & \;\;\;0.0 & \qquad\quad\;\; 0.0000 \\ \hline \end{array}\)


I believe the transition matrix looks like this:

. . \(\displaystyle A \;=\;\begin{pmatrix}0.9707 & 0.0293 & 0 & 0 \\ 0 & 1.045 & 0 & 0 \\ 0 & 0.0107 & 0.9893 & 0 \\ 0 & 0.0050 & 0 & 0.9950 \end{pmatrix}\)
 
what method did you use for that? by the way thank you very much! it'll surely help a lot! :)
 
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