Module 5 - Optimization and Hypothesis Testing

Learning Objectives for Module 5

This module explores strategies to identify the best possible path or the best possible locations of features to maximize opportunity while minimizing cost. These optimization and orienteering strategies involve heuristic approaches and network analyses. Slope, reclassify, cost distance, and cost path were some of the tools introduced in this module. Also involved are inferential statistics, wherein one can perform null hypothesis testing. To do so, the ways in which the samples are taken must be considered, such as a completely random distribution, randomized complete block, split block, etc. Confidence levels around which the hypothesis are tested define the stringency of the test and at which level the null hypothesis is rejected.

Problem:

This exercise was designed to examine the development of the least cost path for a power line between two sites in southern California. The main objectives were to keep costs down while being cognizant of public safety.

Analysis Procedure:

As some terrain is more optimal for the construction process, using a digital elevation module can facilitate the process of identifying appropriate areas as influenced by its physical nature. It is important also to consider land use types. For public safety reasons, for example, it may not be feasible to construct the power line in residential areas. After the data types have been identified, the layers need to be scaled to the same units. Cost-weighted analysis can then be performed on this reclassified data resulting in cost distance and cost direction layers. These layers are inputs for the least cost path analysis, with an output being the path that minimizes cost while optimizing opportunity.

Results:

The output of this analysis was a potential location for the construction of the power transmission line (Figure 1). This construction area avoided waterways, residential areas, and sub-optimal terrain as much as possible thus minimizing the cost of construction.

Figure 1. Map of area feasible for power line construction in southern California.

Application and Reflection:

The ability to identify the best possible paths or best possible locations to place features can be a powerful means of maximizing quality. For example, in agricultural applications, researchers on a research farm may wish to know which location is the best area to put a field for a trial. It is well known that different soil types have different water holding capacities, pH levels, cation exchange capacities, textures, and organic matter content, among other things. If the field is placed in an area with several different soil types and variable topography, the results of the experimental trial may be heavily influenced by the characteristics of the ground upon which the crops are planted. Depending on the research questions of the experiment, an analysis can be performed that is weighted according to the primary soil traits that influence those questions and guide the best placement of the field.

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