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Analyzing a Water Line s Risk of Freezing Attributed to Slope Aspect and Soil Texture using Frozen Water Services and the Chi-Square Goodness-of-Fit Test Matthew Reitter Department of Resource Analysis,
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Analyzing a Water Line s Risk of Freezing Attributed to Slope Aspect and Soil Texture using Frozen Water Services and the Chi-Square Goodness-of-Fit Test Matthew Reitter Department of Resource Analysis, Saint Mary s University of Minnesota, Minneapolis, MN Keywords: GIS (Geographic Information Systems), Soil, Frozen, Water Main, Frozen Water Service, Frost, Soil Texture, Slope Aspect Abstract An abnormally cold winter in led to a record number of frozen water services in the city of Minnetonka. In March of 2014, a water main 8 feet beneath the surface froze. Using soil data from the Natural Resources Conservation Service Web Soil Survey and resources available to the city, a preventative maintenance plan was implemented comparing slope aspect and soil type to similar conditions found at the frozen water main. The aim of this project is to identify whether the criteria used in the preventative maintenance plan can be disproved with soil and slope data at reported frozen water service locations throughout the city. The chi-square goodness-of-fit test was employed to determine whether slope aspect and soil texture found at frozen water services are equally distributed. Additionally, soils were subdivided based on texture in the city and above water mains. Results show slope aspect to be equally distributed among frozen water services and identify soil textures at higher risk for freezing. These will be used to identify whether the city used soil and slope data adequately in an effort to prevent additional water mains from freezing. Introduction the line to ice. If you were to ask a child living in a city where their water comes from you may get the response, from the faucet. In reality, there are hundreds of miles of pipe buried underground supplying water to homes and businesses throughout the nation. Losing water service can be an unexpected and inconvenience disruption. Water is normally shut off to repair a water valve, hydrant, main, or service line. A frozen service line is another reason for loss of service. In most cases, a water meter is not insulated and needs to be thawed from inside a residence or building. In other cases, the water service line freezes underground as frost surrounds it and turns Frozen Ground, Soil Textures, and Water Utility Construction Water freezes at or below 32 degrees Fahrenheit, depending on pressure. When water turns to ice, it expands. As the thickness of the ice increases, it acts as an insulator to the water below. Ice forms the same way in pores between soils. Soils at varying layers have varying temperatures. As frost penetrates deeper, the soil and water in the ground freeze. Layers on the top insulate those below until they freeze. In the same way, snow insulates soil as it accumulates over the winter. The more snow above the ground, the more Reitter, Matthew T Analyzing a Water Line s Risk of Freezing Attributed to Slope Aspect and Soil Texture using Frozen Water Services and the Chi-Square Goodness-of-Fit Test. Volume 16, Papers in Resource Analysis, 12 pp. Saint Mary s University of Minnesota. Minneapolis, MN. Retrieved (date) insulation it provides. Roadways are cleared of snow to provide safe travel and do not have the same insulation provided by snow allowing frost to penetrate deeper. Differing soil textures will have differing frost depths in similar conditions. Fine grained soils, like clay and silt, are more tightly packed. They are more resistant to freezing than looser soils, like sand and gravel, with more space for water to permeate (NSIDC, 2008). Figure 1 displays the soil textural triangle with soil textures and particles making up the 12 categories. The presence of finer particles in soil, like clay and silt, make it more resistant to freezing. Coarser particles in soil make it more susceptible to freezing. Therefore, soils towards the bottom left corner of the triangle are more likely to freeze than those with characteristics found towards the top and right corners of the triangle. Figure 1. Soil textural triangle used to define a soil texture in the field based on the presence of clay, sand, and silt (Image Source: Thien, 1979). Water mains and services are buried at a minimum depth, usually 7 8 feet, to prevent frost from damaging or freezing pipes. In most cases, sewer and water are constructed beneath roads within a right-of-way. This, among other reasons, makes it easier for a utility to locate valves used to shut off water lines and reduce damage to private property when making repairs (CEAM, 2013). Coincidentally, burying utilities beneath roads means frost is more likely to reach and impact pipes due to the lack of insulation at the surface. City of Minnetonka Frozen Water Services Winter of The winter of was one of the coldest on record. There were 53 days with temperatures at or below zero. It tied as the 5 th highest number of days at or below zero and was the 9 th coldest winter on record in the Twin Cities metro area (MN DNR, 2014). Under normal circumstances, snow insulates the ground and prevents frost from penetrating deep into soils. Snow removal on streets, driveways, and sidewalks enables frost to penetrate deeper into the ground than areas insulated with snow cover. As a result of the cold temperatures and routine snow removal from pavement, there was an unusually high number frozen water services reported in the city from January to March of On March 13 th, the city began a repair on a water main suspected to be frozen. They noted it was on a north facing slope with sandy soil. After cutting into the pipe they discovered the water in several feet of the pipe was frozen solid, blocking the flow of water. In an effort to prevent additional frozen water mains, the city identified hydrants on dead end water mains to be fit with garden hose adaptors providing a continuous flow of water. To identify water mains at risk, a topology was created on the existing water distribution network identifying dangles (a line with an endpoint not covered by the endpoint of another line). Dangles provided locations of dead end water 2 mains. Hydrants on dead ends were selected, buffered, and intersected with northern slope aspects (north, northwest, or northeast) and soil data matching the soil complex Malardi-Hawick, found at the frozen water main. This resulted in approximately 60 hydrants reviewed by city staff and narrowed down to 28 to be fitted with a garden hose adaptor used to continuously flow the water main. One of the first six hydrants to be fitted with a hose adaptor was found to be out of service because the water main was frozen. This led the city to believe the selection criteria was adequate for a preventative maintenance plan. Hypothesis This project explores the relationship between slope aspect and soil texture attributes in an attempt to identify common attributes found at frozen water services. These attributes will be compared to the selection criteria created by the city of Minnetonka to prevent dead end water mains from freezing. Results will be used to determine whether or not to reject the null hypothesis (H 0 ): H 0 : Water services with north facing slopes (north, northwest, or northeast) belonging to the soil complex Malardi- Hawick are more likely to have a frozen water service. If disproved, the alternate hypothesis (H A ) will be concluded to be true: H A : Water services with north facing slopes belonging to the soil complex Malardi-Hawick are not more likely to have a frozen water service. Since the Malrdi-Hawick complex is not a soil texture, it will be matched to the closest soil texture and reviewed for completeness in the sample to determine whether or not to reject H 0. Methods GIS Data Collection, Processing, and Reclassifying Required data included frozen water service locations, soil type, slope aspect, and the city s water utility distribution dataset. The Hennepin County Soil Survey data was collected from the United States Department of Agriculture Natural Resources Conservation Service Web Soil Survey website. Remaining data was collected from the city of Minnetonka s enterprise GIS database and asset management database. Soil map units where broken further by complex name. The complex name was derived by removing slope percentages at the end of the map unit name. Water service lines were digitized from the water main to the residence based on as-built drawings and service tie cards. The intersection of the water main, service line, slope aspect, and soil texture provided point attribute data with the assumption the surface was uninsulated, meaning snow had been removed from the surface. Finally, a summary of soil texture and slope aspect were created for total distances above water mains and areas within the city. These serve as the population to compare expected soil texture and slope aspect found at frozen water services. These processes were completed using ArcMap The soil map unit name did not provide a meaningful value for the analysis and needed to be reclassified into one of the 12 categories in the soil textural triangle: sand, loamy sand, sandy loam, loam, silt loam, silt, sandy clay loam, clay loam, silty clay loam, sandy clay, silty clay, and clay. Categories above are ranked in order of coarsest to finest particle size. Figure 2 illustrates an 3 Crowfork 0-10 Tomall 5 15 Hawick Malardi Component % of the unit example of a soil component from the Hennepin County Soil Survey. Soil map unit names were reclassified into soil textures through a manual process. The extent of the component was reviewed for all components found in the city. The percent of each component determined how much weight was placed on the typical profile. Values from the typical profile were reviewed and soil textures with the largest profile were selected to represent the map unit. Table 1 provides the component and typical profile for the Malard-Hawick Complex, 6 12 percent slopes. For this map unit, the two components with the greatest weight were Malardi and Hawick. generally sand based on the profile from inches of gravelly sand in the Malardi component (60-90%) and 11 to 80 inches of gravelly coarse sand in the Hawick component (10-30%). The most abundant soil texture by profile depth or cumulative depth in each of the components carried the most weight. As the extent of each component changes throughout a map unit, the results of the reclassification may contain errors. Additionally, components with multiple soil textures may not accurately represent the entire profile of the soil complex as a complexes profile and components vary from place to place. Table 1. Example of the Malardi-Hawick complex 6 12 percent slopes used to classify soil textures for each map unit name and soil complex. For this soil map unit, sand was selected as the soil texture based on the profile from inches of gravelly sand in the Malardi component (60-90%) and 11 to 80 inches of gravelly coarse sand in the Hawick component (10-30%). Component Description Malardi-Hawick complex 6 12 percent slopes Typical Profile Inches Soil Texture 0 to 10 sandy loam 10 to 15 sandy loam 15 to 29 loamy coarse sand 29 to 80 gravelly sand 0 to 7 sandy loam 7 to 11 gravelly loamy coarse sand 11 to 80 gravelly coarse sand 0 to 33 loam Figure 2. Sample of a map unit component description from the Hennepin County Soil Survey. Extent and typical profile were used to reclassify each map unit to soil texture (Image source: Steffen, 2001). 33 to 42 sandy loam 42 to 47 loamy coarse sand 47 to 80 gravelly loamy coarse sand 0 to 11 loamy sand 11 to 20 loamy fine sand 20 to 76 loamy sand Reviewing these typical profiles led to the conclusion the soil texture was 76 to 80 sand 4 Three categories in the reclassification were not in the soil textural triangle. These include: unknown, muck, and water. Muck and water were not found at any of the frozen water services and did not receive any special attention. The unknown category consisted of several soil components descriptions referencing disturbances on the landscape making the soil difficult to classify. Some of examples include pits, mining, and urban development. These units require onsite investigation to determine soil properties and for the purposes of this project were classified as unknown. Chi-Square Statistical Analysis Using the chi-square goodness-of-fit test, frequencies of soil texture and slope aspect for points where frozen water services intersected water mains were tested to determine if they are equally distributed amongst frozen water services. The chisquare was also subdivided to test a predicted ratio from the distribution of soil textures present in the city as well as soil textures found above water mains. To perform these tests the chi-square statistic was calculated using the equation: ( ) Where f i is the frequency observed in category i, f e is the frequency expected in category i if H 0 is true, and the summation is performed over all k categories of data. Degrees of freedom (v) are equal to the number of categories minus one. A confidence level of 5 percent was used on the summation of the chi-square statistic (x 2 ) to determine the critical value of the chi-square distribution. If the critical value is greater than x 2, H 0 will not be rejected. If the critical value is less than x 2, H 0 will be rejected (Zar, 2010). These tests were completed using a combination of Microsoft Excel and IBM SPSS Statistics. Results Chi-Squared Goodness-of-Fit Statistical Analysis Slope Aspect To test if slope aspect at the surface of a frozen water service was equally distributed in the sample of frozen water services, the chi-square goodness-of-fit was used to test slope aspect frequency. The hypothesis for this test was: H 0 : Slope aspect is equally distributed among frozen water services. H A : Slope aspect is not equally distributed among frozen water services. Table 2 shows expected frequency, f e, for eight categories equal to 22.25, x 2 equal to , and a critical value of Table 2. Chi-square testing equal distribution of slope aspect for all frozen water services. Chi Square Test for Slope Aspect H 0 : Slope aspect is equally distributed among frozen water services H A : Slope aspect is not equally distributed among frozen water services Slope Aspect f i f e x 2 North West Northwest Northeast Southwest South East Southeast n = v = 8-1 = 7 x ,7 = x 2 = Therefore do not reject H 0 5 Soil Textures Soil Textures Since x 2 is less than the critical value, H 0 is not rejected. Slope aspect for the frozen water services may have come from an equal distribution of slope aspects according to the goodness-of-fit test. Referencing the soil textural triangle sand, sandy loam, and loamy sand have the largest particle size which are more likely to freeze than particles on the other two corners of the triangle. Using these factors, the next test looks to identify whether soil textures have an equal distribution of slope aspect or whether frozen water services in other soil textures have an equal distribution of slope aspect. First, chi-square was tested against all frozen water services except those found in sand. The expected frequency, f e, was 13.5, x 2 was with a critical value of , suggesting slopes were equally distributed for soil textures not equal to sand. This was performed two more times with similar results (table 3) for soil textures removing sand and loamy sand and removing sand, loamy sand, and sandy loam. H 0, was not rejected for all three cases suggesting slope aspect was equally distributed for soil textures not equal to sand, loamy sand, and sandy loam. rejected at the 5 percent confidence level (table 4). When the confidence level was decreased to 10 percent, they were found to be statistically significant though only by a small margin. However the hypothesis, slope aspect is equally distributed for soil textures, was not rejected. Table 4. Chi-square testing equal distribution of slope aspect for water services with soil textures sand, loamy sand, and sandy loam. x 2 Critical Value x ,7 x ,7 H 0 Slope aspect is equally distributed x , Do Not Reject Do Not Reject Do Not Reject 1. Only Sand 2. Only Sand or Loamy Sand 3. Only Sand, Loamy Sand, or Sandy Loam Results for slope aspect were supported by the summary from the population of slope aspect for the city and slope aspect above water mains. Figure 3 shows percentages for area and linear distances of slope aspect in the city and over water mains respectively. Table 3. Chi-square testing equal distribution of slope aspect excluding soil textures sand, loamy sand, and sandy loam. x 2 Critical Value H 0 Slope aspect is equally distributed x , Do Not Reject Do Not Reject Do Not Reject 1. Not Sand 2. Not Sand or Loamy Sand 3. Not Sand, Loamy Sand, or Sandy Loam The process was reversed to look only at soil textures sand, loamy sand, and sandy loam. For sand as well as sand and loamy sand, the hypothesis was not Figure 3. Slope aspect distribution by percentage over water mains, throughout the city, and for frozen water services. There are minor differences between the three groups. 6 Frozen services had slightly more with north, northeast, west and northwest slope aspect and slightly fewer in the east and southeast slope aspect. The differences between the values did not appear to be significant and were supported by the results of the chi-square goodness-of-fit test. Based on these findings, slope aspect was not explored in greater detail. Chi-Squared Goodness-of-Fit Statistical Analysis Soil Texture Next the goodness-of-fit test was applied to soil texture with the following hypothesis: H 0 : Soil texture is equally distributed among frozen water services. H A : Soil texture is not equally distributed among frozen water services. Table 5 shows expected frequency, f e for six categories equal to , x 2 equal to , and a critical value of Because x 2 is greater than the critical value H 0 was rejected, suggesting soil texture was not equally distributed among frozen water services. Soil texture was then subdivided to match areas of soil texture in the city and the lengths of soil texture above water mains based on the soil texture making up the top percentages for each sample. Table 5. Chi-square testing equal distribution of soil texture for all frozen water services. Chi Square for Soil Texture H 0 : Soil texture is equally distributed among frozen water services H A : Soil texture is not equally distributed among frozen water services Soil Texture f i f e x 2 Sand Loam Sandy Loam Loamy Sand Unknown Clay Loam n = v = 6-1 = 5 x ,5 = x 2 = Therefore reject H Figure 4. Break down of soil texture by percentage for areas in the city and soil textures over water mains. 7 Figure 4 displays the breakdown of all soil texture in the city by percentage. Categories from the frozen water services were subdivided into categories of soil texture in the city to determine if the ratio from frozen water services fit the ratio of soil texture in the city. For this test, results from soil texture in the city were estimated to be a ratio of 4:2:1:1 for loam, sand, unknown, and sandy loam. The ratio was determined by dividing each soil texture percentage by 10 and rounding to the nearest whole number. This was tested for goodness-of-fit by subdividing frozen water services for the above ratio. Results from the test are displayed in Table 6. Table 6. Subdividing frozen water services to match ratio of soil texture found in the city. Subdividing Soil Texture based on ratio of Soil Texture in the City H 0 : Frozen water services came from a population with a ratio of 4:2:1:1 for soil textures loam, sand, unknown, and sandy loam H A : Frozen water services did not come from a population with a ratio of 4:2:1:1 for soil textures loam, sand, unknown, and sandy loam Soil Texture f i f e Ratio x 2 Loam Sand Unknown Sandy Loam n = v = 4-1 = 3 x ,3 = x 2 = Therefore reject H 0 Exp
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