# Statistical Analysis of Sediment Phosphorus from Silver Lake and Lake Casey in 2002

**Statistical Analysis of Sediment Phosphorus from Silver Lake and Lake Casey in 2002**

## Iowa Lakes Project

Amy Oelmann

Undergraduate Student

Department of Mathematics

University of Northern Iowa

Mark D. Ecker

Associate Professor

Department of Mathematics

University of Northern Iowa

## October 7, 2002

I. Introduction

During the summer of 2002, a group of students and faculty members at the University of Northern Iowa continued their study of water quality of two lakes in Iowa. Water quality variables in Silver Lake had been sampled at 20 different sites during the summer of 2001, and those same sites were used for a sediment phosphorus analysis in the summer of 2002. Water quality variables in Lake Casey had been sampled at 23 different sites in 2001, and those sites were also used in the current sediment phosphorus analysis.

**II. Sediment Depth Profile: Silver Lake**

Each of the 20 sites in Silver Lake were sampled, with 7 sediment phosphorus concentrations obtained from each site, each at a different depth. The circles in each map represent the sites where the data were obtained, and the numbers are the concentration of phosphorus at that particular site. Figure 1 is the Silver Lake sediment phosphorus depth profile map from 0 to 2 inches, produced in July of 2002. Table 1 contains the summary statistics for the 0 to 2 inch sediment depth.

Figure 1

The majority of the sites with the largest concentration of sediment phosphorus in Silver Lake are in the middle of the lake. The samples taken near the perimeter of the lake have a fairly low phosphorus concentration. The highest phosphorus level near the perimeter of the lake is in the southeast corner, where there is a hog lot that is adjacent to the lake.

Table 1

*** Summary Statistics for data in: sdp02 ***

*** Silver Lake Depth Profile from 0 to 2 inches ***

Concentration

Mean: 500.4680

Std Dev.: 452.9522

Min: 11.9500

1st Qu.: 41.1225

Median: 514.1700

3rd Qu.: 788.9400

Max: 1315.3800

The mean sediment phosphorus concentration for the 0 to 2 inch depth is 500.468 ug/g. Some of the samples taken in the lake are much higher than 500. There is a range of concentrations in the 0 to 2 inch depth level equal to 1303.43, (11.95 to 1315.38).

Figure 2 is the Silver Lake sediment phosphorus levels for a depth of 2 to 4 inches. Table 2 contains the summary statistics for the 2 to 4 inch sediment depth.

Figure 2

There were not as many samples taken at the depth 2 to 4 inches. The largest concentrations of phosphorus are located towards the middle of the lake. The smaller concentrations seem to be near the perimeter. Again, the largest concentration around the perimeter of the lake is in the area where the hog lot is located.

Table 2

*** Summary Statistics for data in: sdp24 ***

*** Silver Lake Depth Profile from 2 to 4 inches ***

Concentration

Mean: 656.6200

Std Dev.: 443.4256

Min: 11.0000

1st Qu.: 412.1600

Median: 762.1700

3rd Qu.: 938.8450

Max: 1193.9600

The mean phosphorus concentration for this depth is slightly larger than the mean from the surface (0 to 2 inch depth), but there is also less data. The spread again is very large, with a range of 1182.96, (from 1193.96 down to just 11).

Figure 3 is the Silver Lake sediment phosphorus levels for a depth of 4 to 6 inches. Table 3 contains the summary statistics for the 4 to 6 inch sediment depth.

Figure 3

More samples were taken at this depth than the last, but many of the 20 sites have not been sampled. The concentrations are generally higher than in the previous two depth profiles. Most of the concentrations are in the hundreds, and only one is less than that. The lowest concentration is located on the west side of the lake, near where the lake bends.

Table 3

*** Summary Statistics for data in: sdp46 ***

*** Silver Lake Depth Profile from 4 to 6 inches ***

Concentration

Mean: 580.5158

Std Dev.: 333.2194

Min: 16.7300

1st Qu.: 220.7850

Median: 730.6050

3rd Qu.: 793.3425

Max: 972.0700

The mean and the median in the previous two depths were very close to each other, but as is shows in Table 3, they are very different at the depth of 4 to 6 inches. There is a difference of 150.0892. The range of concentrations at the depth of 4 to 6 inches is 995.34.

Figure 4 is the Silver Lake sediment phosphorus levels for a depth of 6 to 8 inches. Table 4 contains the summary statistics for the 6 to 8 inch sediment depth.

Figure 4

The concentrations at this level are even larger than before, with the largest still being near the middle of the lake. The smallest concentration is at the northeast corner.

Table 4

*** Summary Statistics for data in: sdp68 ***

*** Silver Lake Depth Profile from 6 to 8 inches ***

Concentration

Mean: 542.4463

Std Dev.: 252.2672

Min: 140.0900

1st Qu.: 410.0025

Median: 522.4100

3rd Qu.: 727.4850

Max: 926.5300

Table 4 shows the summary statistics for the sediment phosphorus at a depth of 6 to 8 inches. The range is 786.44, which spreads from 140.09 to 926.53. The mean and median at this depth have a difference of only 20. But the site with the smallest concentration is much larger than it has been previously. It is now over 100 (140.09 ug/g) while it has been under 17 the three depths before.

Figure 5 is the Silver Lake sediment phosphorus levels for a depth of 8 to 10 inches. Table 5 contains the summary statistics for the 8 to 10 inch sediment depth.

Figure 5

The results for the 8 to 10 inch depth, concentrations are not much different than seen previously. The largest concentration is towards the middle of the lake, and the smaller ones are near the perimeter.

Table 5

*** Summary Statistics for data in: sdp810 ***

*** Silver Lake Depth Profile from 8 to 10 inches ***

Concentration

Mean: 416.3350

Std Dev.: 267.7539

Min: 107.5800

1st Qu.: 309.3600

Median: 374.8650

3rd Qu.: 454.4750

Max: 1056.8400

Table 5 shows that the largest concentration at this depth is 1056.84 ug/g. Figure 5 shows that this site is located near the middle of the lake, but towards the area where the hog lot runs into the lake. The range at the 8 to 10 inch depth is 949.26..

Figure 6 is the Silver Lake sediment phosphorus levels for a depth of 10 to 12 inches. Table 6 contains the summary statistics for the 10 to 12 inch sediment depth.

Figure 6

Looking at Figure 6, it is obvious that there are not many sites that were sampled at this depth profile. The sites that have been sampled, however, seem to be having lower sediment concentrations than previously. The site with the largest concentration is still in the middle of the lake, but near the location of the hog lot.

Table 6

*** Summary Statistics for data in: sdp1012 ***

*** Silver Lake Depth Profile from 10 to 12 inches ***

Concentration

Mean: 318.6814

Std Dev.: 141.5339

Min: 190.0400

1st Qu.: 224.2500

Median: 259.6300

3rd Qu.: 368.6550

Max: 595.2900

The largest concentration at the depth of 10 to 12 inches is only 595.29 ug/g. This is much smaller than many of the previous maximum concentrations. The spread at this depth is from 190.04 to 595.29, which gives a range of 405.25. The range at this depth is also much smaller than seen previously.

Figure 7 is the Silver Lake sediment phosphorus levels for a depth greater than 12 inches. Table 7 contains the summary statistics for the greater than 12 inch sediment depth.

Figure 7

There were only 8 sites sampled at the depths greater than 12 inches, and there were no concentrations obtained at the far west side of the lake. The phosphorus concentrations seem to be getting smaller with depth, but the site with the largest concentration is still located in the middle of the lake, near the hog lot.

Table 7

*** Summary Statistics for data in: sdp12more ***

*** Silver Lake Depth Profile greater than 12 inches ***

Concentration

Mean: 319.4287

Std Dev.: 183.1106

Min: 192.6900

1st Qu.: 230.2275

Median: 241.9000

3rd Qu.: 301.7050

Max: 729.8100

Table 7 shows that the largest concentration was 729.81 ug/g, and this was at the same site as it was previously. The range at the depths greater than 12 inches is 537.12.

**III. Overall Conclusions for Silver Lake**

Overall, the average sediment concentration at each depth profile in Silver Lake was well over 300 ug/g, with a maximum mean value of 656.62. The site in the middle of the lake, near the Eastern shore, just West of the hog lot area, consistently has some of the highest concentrations.

**IV. Sediment Depth Profile: Lake Casey**

Figure 8 is the Lake Casey sediment phosphorus levels for a depth of 0 to 2 inches. Table 8 contains the summary statistics for the 0 to 2 inch sediment depth.

Figure 8

Three sites in Figure 8 do not have a phosphorus concentration level. These sites are where the water flows into the lake. No sediment samples were obtained at these inflow areas (for any depth). The sites with the largest concentration of sediment data are towards the middle of the lake. At the surface depth however, the site with the largest concentration is very close to the site with the lowest concentration.

Table 8

*** Summary Statistics for data in: cdp02 ***

*** Casey Lake Depth Profile from 0 to 2 inches ***

Concentration

Mean: 340.2670

Std Dev.: 116.2254

Min: 164.9600

1st Qu.: 255.0925

Median: 337.5700

3rd Qu.: 409.5325

Max: 600.0700

Table 8 shows that the range of concentrations at this depth is 435.11, (164.96 to 600.07). The largest concentration is 600.07 ug/g.

Figure 9 is the Lake Casey sediment phosphorus levels for a depth of 2 to 4 inches. Table 9 contains the summary statistics for the 2 to 4 inch sediment depth.

Figure 9

Again, there is no data for the three inflow sites, and the largest concentrations are towards the center of the lake. As you can see in Figure 9, the site with the largest concentration is the same from the surface sediment phosphorus analysis, but the site with the smallest concentration has changed.

Table 9

*** Summary Statistics for data in: cdp24 ***

*** Casey Lake Depth Profile from 2 to 4 inches ***

Concentration

Mean: 361.5740

Std Dev.: 177.5681

Min: 134.3600

1st Qu.: 238.8325

Median: 311.2750

3rd Qu.: 437.7475

Max: 807.5900

The largest concentration at the depth from 2 to 4 inches was 807.59 ug/g, which is much larger than the largest concentration at the surface depth. The range is 673.23.

Figure 10 is the Lake Casey sediment phosphorus levels for a depth of 4 to 6 inches. Table 10 contains the summary statistics for the 4 to 6 inch sediment depth.

Figure 10

Figure 10 shows that again the largest concentrations are in the middle of the lake, and there are no observations for the three inflow sites. However, the other twenty sites have still been sampled at this depth. The site with the smallest concentration has again changed, but the site with the largest concentration remains the same.

Table 10

*** Summary Statistics for data in: cdp46 ***

*** Casey Lake Depth Profile from 4 to 6 inches ***

Concentration

Mean: 313.5215

Std Dev.: 138.1307

Min: 81.7600

1st Qu.: 240.2650

Median: 273.0200

3rd Qu.: 369.8500

Max: 708.1300

The largest concentration for this depth is 708.13 ug/g, and the range is 626.37. The smallest concentration at this depth is the smallest seen so far in Lake Casey, with a concentration of only 81.76 ug/g.

Figure 11 is the Lake Casey sediment phosphorus levels for a depth of 6 to 8 inches. Table 11 contains the summary statistics for the 6 to 8 inch sediment depth.

Figure 11

The site with the largest concentration is again at the same site as it has been previously, but the smallest concentration has changed. Some of the largest concentrations are in the western part of the lake. There is no data for the three inflow sites, and there is one other site that has not been sampled at this depth.

Table 11

*** Summary Statistics for data in: cdp68 ***

*** Casey Lake Depth Profile from 6 to 8 inches ***

Concentration

Mean: 344.9953

Std Dev.: 168.3929

Min: 165.9200

1st Qu.: 249.5900

Median: 305.5300

3rd Qu.: 381.0850

Max: 925.2100

Table 11 shows that the largest concentration at the depth of 6 to 8 inches is 925.21 ug/g, and the smallest is 165.92. Therefore that the range is 759.29.

Figure 12 is the Lake Casey sediment phosphorus levels for a depth of 8 to 10 inches. Table 12 contains the summary statistics for the 8 to 10 inch sediment depth.

Figure 12

Figure 12 shows that there are more sites that have not been sampled, along with the three inflow sites. The site with the largest concentration of sediment data has changed for the first time in Lake Casey. It is now in the western part of the lake. The depth from 8 to 10 inches is very different than the previous depths. The site with the smallest concentration has also changed.

Table 12

*** Summary Statistics for data in: cdp810 ***

*** Casey Lake Depth Profile from 8 to 10 inches ***

Concentration

Mean: 355.6043

Std Dev.: 150.7004

Min: 171.6500

1st Qu.: 256.2850

Median: 340.9200

3rd Qu.: 373.1950

Max: 803.7700

The range for the 8 to 10 inch depth profile is 632.12, with the largest phosphorus concentration being 803.77 ug/g.

Figure 13 is the Lake Casey sediment phosphorus levels for a depth of 10 to 12 inches. Table 13 contains the summary statistics for the 10 to 12 inch sediment depth.

Figure 13

There are very few sites that have been sampled in Figure 13. The site that has had the largest concentration for the majority of the depths was not even sampled at the 10 to 12 inch depth profile.

Table 13

*** Summary Statistics for data in: cdp1012 ***

*** Casey Lake Depth Profile from 10 to 12 inches ***

Concentration

Mean: 343.6529

Std Dev.: 133.6405

Min: 223.2900

1st Qu.: 243.3800

Median: 276.8500

3rd Qu.: 418.3800

Max: 581.9100

The largest concentration at the depth of 10 to 12 inches is 581.91 ug/g, which is much smaller than the previous depth. The range for this depth is 358.62.

Figure 14 is the Lake Casey sediment phosphorus levels for a depth greater than 12 inches. Table 14 contains the summary statistics for the greater than 12 inch sediment depth.

Figure 14

The site with the largest concentration in Figure 14 is the same site as in Figure 13. There are even less sites sampled at the depths greater than 12 inches, and still no samples taken at the three inflow sites.

Table 14

*** Summary Statistics for data in: cdp12more ***

*** Casey Lake Depth Profile greater than 12 inches ***

Concentration

Mean: 389.1780

Std Dev.: 157.0977

Min: 250.0700

1st Qu.: 260.5900

Median: 345.7000

3rd Qu.: 465.6200

Max: 623.9100

Table 14 shows that the smallest concentration was 250.07 ug/g, and the largest was 623.91 ug/g. The range for the concentrations at the depths greater than 12 inches is 373.84.

**V. Overall Conclusions for Lake Casey**

Overall, the average sediment concentration at each depth profile in Lake Casey are consistently around the 300-level ug/g, with a minimum mean value of 313.52 and a maximum value of 389.18. The site that contained the largest phosphorus concentration for most depth profiles is toward the middle of the lake, just south of the inflow area near the east edge.

**VI. Variogram Analysis**

Figure 15 is the Variogram Cloud for Silver Lake from the depth 0 to 2 inches. The variogram reflects the spatial correlation as a function of distance for all possible pairs of sites. See Carlson and Ecker (2002) for a review of variogram analysis.

Figure 15

Figure 16 is the Empirical Variogram for Silver Lake from the depth 0 to 2 inches.

Figure 16

There is very little evidence of spatial correlation shown in Figure 16. The circles tend towards a line, but there are a few outliers that make the significance not very strong. A horizontal line would indicate no spatial correlation. None of the other depth analysis of phosphorus data (for either Silver Lake or Lake Casey) indicated any evidence of spatial correlation.

VII. Wetlands

Another part of the project this summer was mapping the wetland area just North of Cedar Falls. This area included Beaver Creek, and several lakes and ponds that drain into the Cedar River. Brad Woodle walked along the creek, and around the lakes and ponds recording points using a GPS system. Then, the points were downloaded onto a computer, which produced several maps of the area. Figure 17 is the map that was made showing all of the lakes and ponds in that area. Figure 18 is the same map, including Beaver Creek.

Figure 17

Figure 18

It appears that the lakes and ponds in the wetland area drain into Beaver Creek, which will eventually flow into the Cedar River.

VIII. Reference

Carlson, E. and Ecker, M.D. "A Statistical Examination of Water Quality in Two Iowa Lakes" (2002). *American Journal of Undergraduate Research*. 1(2), pp. 31-45.

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