ModelId:

drainage1

SimileVersion:

4.0

A classic spatial problem is calculating the drainage pattern for a given land area. If the land is divided in to cells in a grid with the altitude of the land in each cell being known the law the drainage direction for each cell can be found by finding the neighbour with the lowest altitude.

Equations:

Equations in drainage1

Variable h : Height array

h = [height]

Where:

[height]=cell/height

Comments:

Outside the cell submodel to provide an array of heights the elements of which are addressable from inside /cell and "/cell/neighbours and self" . (Inside a submodel only values for the current instance is accessible.)

Equations in cell

Variable col

col = index(1)-(row-1)*3

Variable flow direction : Bearing from north to lower neighbour (degrees)

flow direction = if nid_min==1 then 225 elseif nid_min==2 then 180 elseif nid_min==3 then 135 elseif nid_min==4 then 270 elseif nid_min==6 then 90 elseif nid_min==7 then 315 elseif nid_min==8 then 0 elseif nid_min==9 then 45 else-1

Comments:

-1 if no lower neighbour

Variable id

id = index(1)

Variable nid_min : Neighbour ID of the lowest neighbour

nid_min = posleast([h])

Where:

[h]=neighbours and self/h

Comments:

If there is no lower neighbour the value will be the the Neighbour ID of itself, i.e. 5. The Neighbour ID is the index of the "neighbours and self" submodel instances.

Variable row

row = int((index(1)-1)/3)+1

Equations in neighbours and self

Variable col : Column of the cells neighbour's and itself

col = col+element([-1,0,1,-1,0,1,-1,0,1],index(1))

Where:

col=../col

Comments:

If the cell is at the edge of the grid some of the "neighbours" will be outside the grid.

Variable h : Height of the cell's neighbours and itself

h = if col>=1 and col<=3 and row>=1 and row<=3 then element([h],nid)else 1.0E+300

Where:

[h]=../../h

Comments:

Height is assigned the value 1.0E+300 if the "neighbours" will be outside the grid.

Variable nid : ID of the cell's neighbours and itself

nid = 3*(row-1)+col

Comments:

If the cell is at the edge of the grid some of the "neighbours" will be outside the grid

Variable row : Row of the cells neighbour's and itself

row = row+element([-1,-1,-1,0,0,0,1,1,1],index(1))

Where:

row=../row

Comments:

If the cell is at the edge of the grid some of the "neighbours" will be outside the grid.

Results:

Model tags:

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