Statistical Analysis of Trends in the Red River Over a 45 Year Period

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v.1.56. CAS# n/a WQStat Plus BOX & WHISKERS PLOT TM Emerson,Sthfldwy,Selkirk 50 37 25 12 0 2/1-3/31 140 obs. 4/1-5/31 179 obs. 6/1-8/31 242 obs. 9/1-1/31 352 obs. Constituent: Dissolved Potassium (mg/l) Facility: WQTrendAnalysis Data File: ZZ Figure Date: 3.3: 6/4/09 Boxplots of Dissolved Potassium Time: (mg/l) 7:54 depicting AM the seasonal View: pattern zz of the constituent amongst all three monitoring stations Create PDF files without this message by purchasing novaPDF printer (http://www.novapdf.com) with each other and inversely with discharge. The second typical seasonal pattern observed had maximum concentrations occurring in conjunction with high summer/fall discharge levels. The parameter demonstrating this pattern is dissolved sulphate. Significant seasonality was detected for dissolved potassium, it is low in Feb/Mar but slightly higher in other seasons (Figure 3.3). The seasonality patterns of the remaining constituents can be seen in appendix Figures A.9 to A.16. In order to test for trend the seasonal Mann-Kendall test and Sen’s slope was used for the stations that exhibited seasonality. The null hypothesis for this test is that no temporal trend exists versus the alternate hypothesis that a significant upward (or downward) temporal trend exists. The direction of the alternative hypothesis (upward/downward) is specified and hence this is a one-sided test. Sen’s slope estimator procedure is a simple nonparametric procedure developed by Sen (1968) and presented in Gilbert (1987) to estimate true slope. 20
The N ′ individual slope estimates, Q, are computed for each time period: where Q = x′ i − x i i ′ − i , x ′ i and x i are the data values at time i ′ and i (in days), respectively, i ′ > 1 and; N ′ is the number of observations in the pth group Sen’s slope estimator is then calculated by choosing the middle-ranked slope as follows; ⎧ ⎪⎨ Q [N ′ =n(n−1)/2] if N ′ is odd ( ) 1 ⎪⎩ Q ′ 2 N + Q ′ N =n(n+2) if N ′ is even; 2 2 where n is the number of time periods;this value is multiplied by 365 to give the yearly slope value. The seasonal Mann-Kendall test is an extension of the Mann-Kendall test for trend that removes seasonal cycles. To compute the seasonal Mann-Kendall statistic, S i , for each season there must be a minimum sample size of four data points in each season. S i = n∑ i −1 ∑n i k=1 l=k+1 sgn(x il − x ik ) where S i is the statistic for the ith season and ⎧ −1, if x < 0; ⎪⎨ sgn(x) = 0, if x = 0; ⎪⎩ 1, if x > 0. With use of the normal approximation (i.e.: greater than 41 observations) the Mann-Kendall test statistic, S is calculated. When there are no tied values, the 21
Page 1 and 2: Statistical Analysis of Trends in t
Page 3 and 4: 5 Comparison of Non-Parametric and
Page 5 and 6: List of Figures 1.1 The Red River B
Page 7 and 8: A.8 Boxplot of Specific Conductance
Page 9 and 10: A.41 Dissolved Calcium Flow Adjustm
Page 11 and 12: A.67 Dissolved Sulphate Flow Adjust
Page 13 and 14: A.93 Specific Conductance Flow Adju
Page 15 and 16: Mann-Kendall or Seasonal Mann-Kenda
Page 17 and 18: Using ancillary data, data obtained
Page 19 and 20: Chapter 1 Introduction The Red Rive
Page 21 and 22: oped by Aldo Vecchia (United States
Page 23 and 24: Chapter 2 Streamflow Data and Conce
Page 25 and 26: Table 2.1: Selected characteristics
Page 27 and 28: of testing for seasonality. If it y
Page 29 and 30: Table 2.3: Sample size of stations
Page 31 and 32: Figure 3.1: Mean monthly streamflow
Page 33 and 34: v.1.56. CAS# n/a WQStat Plus TM BOX
Page 35 and 36: concentrations of major anions and
Page 37: Table 3.3: Kruskal-Wallis test for
Page 41 and 42: As most parameters consistently exh
Page 43 and 44: Table 3.4: Seasonal Mann-Kendall Te
Page 45 and 46: Chapter 4 Parametric Methods used f
Page 47 and 48: log denotes the base-10 logarithm;
Page 49 and 50: Figure 4.1: Daily Streamflow at Eme
Page 51 and 52: Figures 4.3-4.8 depict the recorded
Page 53 and 54: 1 1 CONCENTR CONCENTR 1955 1960 196
Page 55 and 56: Table 4.1: Fitted Single Linear Tre
Page 57 and 58: Chapter 5 Comparison of Non-Paramet
Page 59 and 60: 5.2 Future Recommendations First an
Page 61 and 62: • Uses full power of the maximum
Page 63 and 64: Hamed, Khaled.,; 2008, Trend Detect
Page 65 and 66: Appendix A Figures A.1 Boxplots of
Page 67 and 68: v.1.56. CAS# n/a WQStat Plus TM BOX
Page 69 and 70: Figure A.7: Boxplot of Total Dissol
Page 71 and 72: v.1.56. CAS# n/a WQStat Plus BOX &
Page 73 and 74: Figure A.13: Seasonality pattern of
Page 75 and 76: A.3 Non-Parametric Trend Results Th
Page 77 and 78: Figure A.19: Long term temporal tre
Page 85 and 86: A.4 Parametric Trend Results The fo
Page 87 and 88: Figure A.31: Dissolved Sodium at Em
Page 89 and 90:
Figure A.33: Dissolved Magnesium at
Page 91 and 92:
Figure A.35: Dissolved Chloride at
Page 93 and 94:
Figure A.37: Specific Conductance a
Page 95 and 96:
05102500 RED RIVER OF THE NORTH AT
Page 97 and 98:
1 1 CONCENTR CONCENTR 500 RED RIVER
Page 99 and 100:
CONCENTR 500 RED RIVER OF THE NORTH
Page 101 and 102:
Page 103 and 104:
CONCENTR ● CONCENTR 0 0 1955 1960
Page 105 and 106:
CONCENTR CONCENTR 00 RED RIVER OF T
Page 107 and 108:
Page 109 and 110:
CONCENTR 1 1.5 ! ! ! ! !! ! ! ! ! !
Page 111 and 112:
CONCENTR 0.5 1 ! ! ! ! !! ! !! ! !
Page 113 and 114:
Page 115 and 116:
CONCENTR ! ! ! ! ! ! ! ! ! ! ! ! !
Page 117 and 118:
CONCENTR ! CONCENTR 2 2 1955 1960 1
Page 119 and 120:
A.5.2 South Floodway at St. Norbert
Page 121 and 122:
CONCENT ! CONCENT 2 2 floodway dspc
Page 123 and 124:
A.5.3 Selkirk Monitoring Station 10
Page 125 and 126:
CONCENT ! CONCENT 2 2 selkirk dspc
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Statistical Analysis of Trends in the Red River Over a 45 Year Period

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