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

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variance of S is computed; Var(S) = n(n − 1)(2n + 5) 18 and the test statistic Z, is as follows; When there are tied values, Var(S) = 1 18 [ ⎧ S − 1 , if S > 0; ⎪⎨ [Var(S)] 1/2 Z = 0, if S = 0; S + 1 ⎪⎩ , if S < 0. [Var(S)] 1/2 n(n − 1)(2n + 5) − ] g∑ t p (t p − 1)(2t p + 5) , where g is the number of tied groups and t p is the number of observations in the pth group Once Var(S i ) is computed, we pool across the K seasons and our test statistic Z is computed. p=1 If the result of the test statistic for a one sided test is greater than 1.645 we reject our null hypothesis that no trend exists at the 5% level of significance. The seasonal Kendall slope estimator procedure is as follows; First we compute individual N i slope estimates for the ith season: Q i = x il − x ik l − k , where x il the data for the i’th season of the l’th year and x ik the data for the i’th season of the k’th year (l > k). This process is computed for each of the K seasons. Then rank the N ′ 1 + N ′ 2 + . . . + N ′ K = N ′ individual slope estimates and find their median. This median is the seasonal Kendall slope estimator. 22
As most parameters consistently exhibited significant seasonality, the Seasonal Mann-Kendall test was used for trend analysis. For certain constituents the requirement that there be a minimum per season sample size of four was not met. The analysis is summarized in Table 3.4, “n/a” implies the size requirements were not met, a positive slope is indicative of an increasing trend. If the p-value of the statistic is less than our 5% significance level we reject the null hypothesis of there being no trend. 23
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 and 38: Table 3.3: Kruskal-Wallis test for
Page 39: The N ′ individual slope estimate
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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