Supplementary Material: Spatial heterogeneity in power to detect changes in lake area in Alaskan National Wildlife Refuges
Table 1: Study area sizes and total number of lakes for six study areas in four National Wildlife Refuges, Alaska, USA. Each refuge
study area was a composite of satellite images. Study areas were different sizes based on availability of temporally overlapping remote
sensing imagery and the total refuge size.
Refuge Study Area
Number of lakes
Study Area Size (sq.km)
Yukon Flats West
699
927
Yukon Flats Central
1129
1133
Yukon Flats East
854
1845
Innoko
2066
4342
Kanuti
2434
4565
Tetlin
1481
2283
1
Table 2. Number of cells and mean number of lakes within 2.6, 12.9, or 25.9 sq km cells in each of six National Wildlife Refuge study
areas, Alaska, USA.
CELL SIZE
STUDY AREA
2.6 sq. km
12.9 sq. km
25.9 sq. km
# of Cells
Lakes/Cell
# of Cells
Lakes/Cell
# of Cells
Lakes/Cell
Yukon Flats East
131
3.3
094
07.9
053
14.4
Yukon Flats Central
207
4.2
078
14.0
035
28.7
Yukon Flats West
142
3.7
052
11.8
028
22.0
Innoko
253
3.6
145
12.3
087
20.8
Kanuti
259
4.0
164
13.4
101
23.0
Tetlin
208
5.7
072
19.2
039
35.5
2
Figure 1. The spatial distribution, across cells, of the monitoring duration (years) required to detect a significant (P<0.05) annual trend
in average lake size with a statistical power of 0.8 in the Yukon Flats Central study area for three cell sizes (2.6, 12.9, and 25.9 sq km;
left to right) and three imposed trend magnitudes (0.5%, 1.0%, and 2.0%/year; top to bottom). Statistical power was defined as the
percentage of 100 simulations where any trend significantly different from zero was detected; the time taken to detect a trend was
inversely related to both imposed trend magnitude and cell size. Blank areas reflect cells where the mixed model failed to converge or
there was incomplete data for a cell. Black dots indicate lake centroids.
3
4
Figure 2. The spatial distribution, across cells, of the monitoring duration (years) required to detect a significant (P<0.05) annual trend
in average lake size with a statistical power of 0.8 in the Yukon Flats East study area for three cell sizes (2.6, 12.9, and 25.9 sq km;
left to right) and three imposed trend magnitudes (0.5%, 1.0%, and 2.0%/year; top to bottom). Statistical power was defined as the
percentage of 100 simulations where any trend significantly different from zero was detected; the time taken to detect a trend was
inversely related to both imposed trend magnitude and cell size. Blank areas reflect cells where the mixed model failed to converge or
there was incomplete data for a cell. Black dots indicate lake centroids.
5
6
Figure 3. The spatial distribution, across cells, of the monitoring duration (years) required to detect a significant (P<0.05) annual trend
in average lake size with a statistical power of 0.8 in the Yukon Flats West study area for three cell sizes (2.6, 12.9, and 25.9 sq km;
left to right) and three imposed trend magnitudes (0.5%, 1.0%, and 2.0%/year; top to bottom). Statistical power was defined as the
percentage of 100 simulations where any trend significantly different from zero was detected; the time taken to detect a trend was
inversely related to both imposed trend magnitude and cell size. Blank areas reflect cells where the mixed model failed to converge or
there was incomplete data for a cell. Black dots indicate lake centroids.
7
8
Figure 4. The spatial distribution, across cells, of the monitoring duration (years) required to detect a significant (P<0.05) annual trend
in average lake size with a statistical power of 0.8 in the Innoko study area for three cell sizes (2.6, 12.9, and 25.9 sq km; left to right)
and three imposed trend magnitudes (0.5%, 1.0%, and 2.0%/year; top to bottom). Statistical power was defined as the percentage of
100 simulations where any trend significantly different from zero was detected; the time taken to detect a trend was inversely related
to both imposed trend magnitude and cell size. Blank areas reflect cells where the mixed model failed to converge or there was
incomplete data for a cell. Black dots indicate lake centroids.
9
10
Figure 5. The spatial distribution, across cells, of the monitoring duration (years) required to detect a significant (P<0.05) annual trend
in average lake size with a statistical power of 0.8 in the Kanuti study area for three cell sizes (2.6, 12.9, and 25.9 sq km; left to right)
and three imposed trend magnitudes (0.5%, 1.0%, and 2.0%/year; top to bottom). Statistical power was defined as the percentage of
100 simulations where any trend significantly different from zero was detected; the time taken to detect a trend was inversely related
to both imposed trend magnitude and cell size. Blank areas reflect cells where the mixed model failed to converge or there was
incomplete data for a cell. Black dots indicate lake centroids.
11
12
Figure 6. The spatial distribution, across cells, of the monitoring duration (years) required to detect a significant (P<0.05) annual trend
in average lake size with a statistical power of 0.8 in the Tetlin study area for three cell sizes (2.6, 12.9, and 25.9 sq km; left to right)
and three imposed trend magnitudes (0.5%, 1.0%, and 2.0%/year; top to bottom). Statistical power was defined as the percentage of
100 simulations where any trend significantly different from zero was detected; the time taken to detect a trend was inversely related
to both imposed trend magnitude and cell size. Blank areas reflect cells where the mixed model failed to converge or there was
incomplete data for a cell. Black dots indicate lake centroids.
13
14