Uncertainty in the Spatial Interpolation of PM10 Monitoring Data in Southern California

Introduction

The Contourer allows the user to select whether the output be a full X by Y grid of contoured values or a table of contoured values for specific locations. In this analysis the output was both the grid and table formats. The pseudocode below describes the details of the contouring algorithm.

Contour
	Functionality:	transform data from table format into grid format
	Input:	Table - a set of data points
		WeightFunc - distance weight function
		Radius - distance constraint
		MinPoints - minimum required number of data points within Radius
		MaxPoints - maximum number of data points used in calculation of a grid cell
	Output:	Grid - uniformly distributed set of data points
function Contour(out Grid, in Table, in WeightFunc, in Radius, in MinPoints, in MaxPoints)
{
	for each Cell in Grid
		CalcCell
}

CalcCell
	Functionality:	calculate value of a grid cell given a table of data points around it
function CalcCell(in out Cell, in Table, in WeightFunc, in Radius, in MinPoints, in MaxPoints)
{
	PointList = an empty list of table points
	for each point in Table that is not null
		if the distance between the point and the cell is less than Radius then
			add point to the PointList, sorted by distance
	Cell value = Interpolate PointList
}

Interpolate
	Functionality:	interpolate over a sorted list of data points
function Interpolate(in PointList, in WeightFunc, in MinPoints, in MaxPoints)
{
	if number of points in PointList < MinPoints return null value

	TotalWeight = 0
	Sum = 0
	WeightExp = 0 if WeightFunc = 1
		    1 if WeightFunc = 1/r
		    2 if WeightFunc = 1/r2, etc
	
	for first MaxPoints in PointList
		Dist = point distance from cell
		Weight = 1 / (Dist^WeightExp)
		TotalWeight = TotalWeight + Weight
		Sum = Sum + Weight * point value
		
	if TotalWeight = 0 return null value
	Sum = Sum / TotalWeight
	return Sum
}