Types of Spatial Data Analysis Flashcards
Explain the analytical measures: Adjacency, interaction and neighbourhood.
Adjacency is a nominal or binary equivalent of distance. Two spatial entities are either adjacent or not adjacent. They are adjacent if they share a common boundary. They can also be adjacent if they are within a specified distance.
Interaction is a combination of distance and adjacency. Interaction is based on the idea that nearer things are “more related” than distant things.
Neighbourhoods can be a spatial entity that is adjacent to many other entities. It can also be a region of space around an entity, or proximity polygons where each one shares a common boundary with the entity.
What is Moran’s Index?
Moran’s Index is a measure of spatial autocorrelation. Spatial autocorrelation is characterised by a correlation in a signal among nearby locations in space.
What is a variogram?
Variogram is a function that describes the degree of spatial dependency of a field or process.
It is used for exploring spatial variability between all pairs of points within a specified distance. Variability can be isotropic or direction dependent.
Explain the working principles of interpolation methods: Thiessen polygons, inverse distance weighting, density maps, trend surface, regression method and Kriging.
Local interpolation methods:
Thiessen polygons: Each new point is assigned the value of its nearest sample point. It is easy to use with qualitative data. It assumes homogeneity within borders. However, it is difficult to evaluate accuracy.
Inverse distant weighting: The unknown value at a point x is estimated by taking a weighted average over the known values. Each known value is weighted by its distance from the point x. The weight decreases exponentially (rth power of the distance)
Global interpolation methods:
Density maps show a surface estimated from samples. The density at each point is computed by summing values from all values within a circle of radius d, then dividing the sum by the area of the circle. The resolution is d.
Trend surfaces fit a polynomial surface to the data using a regression analysis. The two independent variables represent two perpendicular spatial dimensions. The dependent variable represents a regionalised variable (e.g. elevation). It results in a continuously smooth surface from irregular data, or isolates regional trends from local variations.
Regression analysis is used to model spatial relationships and determine the magnitude of those relationships. They are used to make predictions. It finds a line that describes how one parameter depends on a large number of parameters. Least square methods are used to position the line so the distance from the line to each point is minimised.
Kriging is a regression technique used to approximate or interpolate data at unmeasured locations. It is based on the analysis of variograms. The basic equation used in ordinary kriging is:
What is map algebra? Which operations can be applied?
Map algebra involves combining raster layers cell by cell using Boolean operators.
Where is both A and B
Where is A or B
Where is B but not A
Where is neither A nor B
Algebraic operations (+, -, *, /, log, etc.)
What are slope and aspect?
Slope (degrees) is a cell’s elevation compared to those of its eight neighbours. Aspect is the horizontal direction in which a slope faces.
What is flow analysis in hydrology? Explain the working principles of a typical algorithm for flow analysis.
Flow analysis uses slope/aspect data to model flow distribution from each cell in a terrain model. It is based on the following assumptions:
From any point in the terrain, the water flows according to the topographic form of the cell and its eight neighbour cells
Water is evenly distributed over the grid cells (i.e. homogeneous precipitation)
Infiltration capacity over the surface is set to 0 (not porous)
The surface is bare (e.g. no vegetation)
Evapotranspiration is set to 0
The basic process is:
- Identify cells with the highest height value
- Compute the output flow from the cell:
Fout = Fin + Flocal
Fin: Flow received by the cell
Flocal: Flow produced in the cell (e.g. precipitation) - Compute to which neighbouring cells the output flow will go. If the form is concave, flow is divided between the two cells that is in the direction of the steepest gradient of the second-order polynomial surface.
- Repeat 1-3 until all cells have been visited
What is line-of-sight? Where can it be applied?
Line-of-sight determines the parts of the landscape that can be seen from a given origin point. This can be used to measure the spreading of traffic noise from roads, as well as the locations for mobile phone towers.
- Draw a straight line between the given point (original cell) and each of the other cells in the digital elevation model (DEM).
- Determine if the line crosses any cell that is higher than the line.
- If there is a higher cell on the line, the destination cell cannot be seen from the original cell. In this case, the destination cell is assigned a value of 0.
How does the Dijkstra’s algorithm work?
Dijkstra’s algorithm solves the shortest path problem for a graph.
- Assign a tentative distance value (e.g. cumulative costs, travel time, etc.) to every node (zero for the initial node and infinity for others)
- Calculate the distances between the current node (initial node) and its unvisited neighbors
- When all neighbours are considered, mark the current node as visited. A visited node will never be checked again.
- Stop if the destination node has been marked as visited. The algorithm has finished.
- Select the unvisited node that is marked with the smallest tentative distance and set it as the new current node. Then repeat from step 2.
What is a minimum spanning tree?
In a connected, undirected graph, a minimum spanning tree is the sub-graph that connects all the vertices together with the lowest weight or distance.
All nodes should be isolated and the total sum of edges should be minimised.
All edges that are longer than a threshold distance can be removed.
Clusters are created by the connecting points.
What is a cost surface?
Cost surface and least cost path is a raster grid of cells with cost values. Each cell contains a value representing the cost that a particular activity or object would be in that cell. It is used to determine the cost of crossing each raster cell, as well as the minimum cost to reach other raster cells from a starting point.
What is a cellular model?
Cellular model is used to model a system, where each cell is in a state. The state of each cell changes with time. The change is defined by a series of rules and depends on the current state of the cell as well as the states of its neighbours.
Pedestrian modelling
Modelling of urban growth of a city around a street network
