2021-Appendix-VIII---7Q10---Flow-Trends

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NC Division of Water Resources
Planning Section
Modeling and Assessment Branch
Memorandum

October 28, 2020

To: Fred Tarver and Forest Shepherd, Basin Planning Branch
From: Adugna Kebede, Modeling and Assessment Branch
Subject: Streamflow Trends for selected Chowan River Basin Stations

The Modeling and Assessment Branch (MAB) carried out streamflow trend analysis for selected
Chowan River Basin stations.

Trends in 7Q10 flows for selected Chowan River Basin flow gages were explored using the
Mann-Kendall trend test. The 7Q10 is the lowest 7-day average flow that occurs (on average)
once every 10 years. It is the low-flow estimate which is mostly used to define critical
conditions to set permit limits for NPDES dischargers. The trend analysis was performed using
the USGS Computer Program for the Kendall Family of Trend Tests (Helsel, et al., 2006). In
addition, temporal changes in daily streamflow statistics across an annual time period for the
period of record were explored using the EGRET software (Hirsch and De Cicco, 2015). These
included, water year daily minimum flow, 7-day minimum flow, daily median flow, daily mean
flow, and daily maximum flow. The USGS defines the water year as beginning on October 1 and
ending on September 30 the following year. A recently developed exploratory tool, the
Quantile-Kendall plot (Hirsch, 2018, Choquette, et al., 2019) was also used to evaluate flow
trends across the range of streamflow values at a given site for an annual time-frame.

The Mann-Kendall Test
The Mann-Kendall test is used to perform trend analysis on 7Q10 flow data for selected
Chowan USGS stations (Table 1). The Mann-Kendall test is a statistical test widely used for the
analysis of trend in hydrologic time series. It is a non-parametric test where the null hypothesis
H0 is that there is no trend and the alternative hypothesis H1, is that there is a trend. The trend
test was performed using the USGS Computer Program for the Kendall Family of Trend Tests.
The 7Q10 data used for the analysis were estimated using the Water Resources Information,
Storage, Analysis, and Retrieval System (WRISARS), hosted by NC Division of Water Resources.
The 7Q10 values were computed for a 10-year and 30-year window. These values represent the
first year of the forward looking window where N= 10 and N =30. More than a 10-year or 30-
year window was required to capture the respective number of years with complete records for
some stations.

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Table 1: Selected USGS gaging stations in the Chowan Basin
Station USGS Gage Period of Record
Ahoskie Creek at Ahoskie, NC 02053500 1950-2019
Potecasi Creek near Union, NC 02053200 1958-2019
Nottoway River near Sebrell, VA 02047000 1941-2019
Meherrin River at Emporia, VA 02052000 1951-2019
Blackwater River near Franklin, VA 02049500 1944-2019

The results of the trend test on the data from the selected USGS gages are given in Table 2 and
Table 3 and Figure 1. The results show that significantly increasing trend in the 30-yr window
7Q10 flows are observed for Ahoskie Creek at Ahoskie, NC and Nottoway River near Sebrell, VA
and significantly decreasing trend for Potecasi Creek near Union, NC and Blackwater River near
Franklin, VA. The trend for Meherrin River at Emporia, VA was not significant. For the 10-yr
window 7Q10 flows, increasing trend was observed for Ahoskie Creek at Ahoskie, NC and
decreasing trends were observed for Potecasi Creek near Union, NC and Blackwater River near
Franklin, VA. The 10-yr window 7Q10 flows trend for Nottoway River near Sebrell, VA and for
Meherrin River at Emporia, VA were not significant.

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Table 2: Trends1 in annual 7Q10 streamflow for selected waterbodies in the Chowan Basin (30-Year 7Q10)
Station USGS
Gage
Period of
Record
Kendall's
Tau
Mann-Kendall
Statistic (S)
Slope
(cfs/year) Trend*
Ahoskie Creek at Ahoskie, NC 02053500 1950-2019 0.406 228 0.02 Increasing
Potecasi Creek near Union, NC 02053200 1958-2019 -0.699 -193 -0.0714 Decreasing
Nottoway River near Sebrell, VA 02047000 1941-2019 0.264 238 0.04864 Increasing
Meherrin River at Emporia, VA 02052000 1951-2019 -0.239 -104 -0.1775 No significant Trend
Blackwater River near Franklin, VA 02049500 1944-2019 -0.934 -692 -0.04091 Decreasing

Table 3: Trends1 in annual 7Q10 streamflow for selected waterbodies in the Chowan Basin (10-Year 7Q10)
Station USGS
Gage
Period of
Record
Kendall's
Tau
Mann-Kendall
Statistic (S)
Slope
(cfs/year) Trend*
Ahoskie Creek at Ahoskie, NC 02053500 1950-2019 0.212 303 0.01423 Increasing
Potecasi Creek near Union, NC 02053200 1958-2019 -0.603 -570 -0.0333 Decreasing
Nottoway River near Sebrell, VA 02047000 1941-2019 -0.055 -108 -0.0308 No significant Trend
Meherrin River at Emporia, VA 02052000 1951-2019 -0.106 -130 -0.11 No Significant trend
Blackwater River near Franklin, VA 02049500 1944-2019 -0.592 -1013 -0.03115 Decreasing
1Mann-Kendall trend test (USGS Computer Program for the Kendall Family of Trend Tests)
*A threshold significance level of 0.05 (α=0.05) was used; a p-value of less than 0.05 means that the trend is considered significant

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0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
1.6
1.8
1950 1952 1954 1956 1958 1960 1962 1964 1966 1968 1970 1972 1974 1976 1978 1980 1982
7Q
1
0

(
c
f
s
)
Year (First year of forward Looking time interval)
Ahoskie Creek at Ahoskie NC (USGS0205300) -7Q10 Flow (N=30 Years)
7q10
LOWESS Fit (f=0.3)
7Q10 (N=54 yrs)
Q =-37.895 +(0.02*Year)
The tau correlation coefficient is 0.406
S = 228.
z = 3.392
p = 0.0007
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
1950 1954 1958 1962 1966 1970 1974 1978 1982 1986 1990 1994 1998 2002
7Q
1
0

(
c
f
s
)
Year (First year of forward Looking time interval)
Ahoskie Creek at Ahoskie NC (USGS0205300) -7Q10 Flow (N=10 Years)
7Q10
LOWESS Fit(f=0.3)
7Q10 (N=54 yrs)
Q =-26.712 + 0.01423*Year
The tau correlation coefficient is 0.212
S = 303.
z = 2.254
p = 0.0242
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
1.6
1.8
1958 1960 1962 1964 1966 1968 1970 1972 1974 1976 1978 1980
7Q
1
0

(
c
f
s
)
Year (First year of forward Looking time interval)
Potecasi Creek near Union, NC (USGS02053200) -7Q10 Flow (N=30 Years)
7Q10
LOWESS(f=0.3)
7Q10 (N=53 yrs)
Q= 74.363 -0.0714 * Year
The tau correlation coefficient is -0.699
S = -193.
z = -4.767
p = 0.0000
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
1958 1961 1964 1967 1970 1973 1976 1979 1982 1985 1988 1991 1994 1997 2000
7Q
1
0

(
c
f
s
)
Year (First year of forward Looking time interval)
Potecasi Creek near Union, NC (USGS02053200) -7Q10 Flow (N=10 Years)
7Q10
LOWESS(f=0.3)
7Q10 (N=53 yrs)
Q= 67.113 -0.03333 * Year
The tau correlation coefficient is -0.603
S = -570.
z = -5.762
p = 0.0000

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0.0
5.0
10.0
15.0
20.0
25.0
30.0
1941 1945 1949 1953 1957 1961 1965 1969 1973 1977 1981
7Q
1
0

(
c
f
s
)
Year (First year of forward Looking time interval)
Nottoway River near Sebrell, VA (USGS02047000) -7Q10 Flow (N=30 Years)
7Q10
7Q10 (N=72 yrs)
LOWESS Fit (f=0.3)
Q= 73.145 +0.04864 * Year
The tau correlation coefficient is 0.264
S = 238.
z = 2.480
p = 0.0131
0.0
10.0
20.0
30.0
40.0
50.0
60.0
1941 1946 1951 1956 1961 1966 1971 1976 1981 1986 1991 1996 2001
7Q
1
0

(
c
f
s
)
Year (First year of forward Looking time interval)
Nottoway River near Sebrell, VA (USGS02047000) -7Q10 Flow (N=10 Years)
7Q10 (N=72 yrs)
7Q10
LOWESS(f=0.3)
Q= 82.288 -0.03080 * Year
The tau correlation coefficient is -0.055
S = -108.
z = -0.635
p = 0.5257
0.0
5.0
10.0
15.0
20.0
25.0
30.0
35.0
1951 1953 1955 1957 1959 1961 1963 1965 1967 1969 1971 1973 1975 1977 1979
7Q
1
0

(
c
f
s
)
Year (First year of forward Looking time interval)
Meherrin River at Emporia, VA (USGS0205000 ) -7Q10 Flow (N=30 Years)
7q10
LOWESS Fit(f=0.3)
7Q10 (N=56 yrs)
Q= 370.65 -0.1775 * Year
The tau correlation coefficient is -0.239
S = -104.
z = -1.838
p = 0.0661
0.0
5.0
10.0
15.0
20.0
25.0
30.0
35.0
1951 1955 1959 1963 1967 1971 1975 1979 1983 1987 1991 1995 1999
7Q
1
0

(
c
f
s
)
Year (First year of forward Looking time interval)
Meherrin River at Emporia, VA (USGS0205000 ) -7Q10 Flow (N=10 Years)
7Q10
LOWESS(f=0.3)
7Q10 (N=56 yrs)
Q= 239.98 -0.1100 * Year
The tau correlation coefficient is -0.106
S = -130.
z = -1.079
p = 0.2805

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Figure 1. Trend in 7Q10 flow at selected Chowan River Basin Stations
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
1.6
1.8
2.0
1944 1948 1952 1956 1960 1964 1968 1972 1976 1980
7Q
1
0

(
c
f
s
)
Year (First year of forward Looking time interval)
Blackwater River near Franklin, VA (USGS02049500 ) -7Q10 Flow (N=30 Years)
7Q10
LOWESS Fit(f=0.3)
7Q10 (N=68 yrs)
Q = 80.925 -(0.04091*Year)
The tau correlation coefficient is -0.934
S = -692.
z = -8.365
p = 0.0000
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
4.0
4.5
1944 1948 1952 1956 1960 1964 1968 1972 1976 1980 1984 1988 1992 1996 2000
7Q
1
0

(
c
f
s
)
Year (First year of forward Looking time interval)
Blackwater River near Franklin, VA (USGS02049500 ) -7Q10 Flow (N=10 Years)
7Q10
LOWESS(f=0.3)
7Q10 (N=68 yrs)
Q =62.357-(0.03115 *Year)
The tau correlation coefficient is
-0.592
S = -1013.
z = -6.621
p = 0.0000

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Trends in Daily flow for annual time-frame
In addition to the trend test for the 7Q10 flows, trends in the water year daily minimum flow, 7-
day minimum flow, daily median flow, daily mean flow, and daily maximum flow were
performed for the period of record at the selected stations to explore the nature and extent of
the streamflow changes in the Chowan Basin using the EGRET software (Hirsch and De Cicco,
2015). The plots for Ahoskie Creek station are provided (Figure 2) to show examples of these
plots. The plots for the other stations are included in Appendix A.

Using the site Ahoskie Creek at Ahoskie, NC for the period from February 1, 1950, through
September 30, 2019, as an example, trends in daily flow statistics for an annual time-frame are
shown in Fig. 2. Positive trends are observed in all five annual statistics except the water year
mean daily flow, which has shown a negative trend. The slopes, indicating trend magnitude, are
quite different for the different statistics. The largest slope is associated with the annual
minimum day flows (2.9% per year). The smallest positive slope is for the median daily flow
(0.11% per year). A trend of 2.9% per year in the slope of the annual minimum day indicates a
total increase in the annual minimum day's flow over this 70-year period of 640%. The trend in
the median daily flow of 0.11% per year translates to a total increase of 8% over this period.
Negative trends are observed in the mean daily flow with a reduction of -0.076% per year. This
indicates that the annual mean daily flow decreased by a total of 5% over the 70-year period.
For Ahoskie Creek, the trend in flow across the full range of the flow distribution is positive and
of substantial magnitude, particularly for the lower extremes of the flow distribution for all five
annual statistics except the water year mean daily flow.

Summary of the trend results in selected flow statistics for the selected Chowan River Basin
stations is given in Table 4. The results show that there were significant upward trends in
minimum day and 7-day minimum flow for Ahoskie Creek and significant downward trend for
Nottoway River and Blackwater River. The trends for median and mean flows were not
significant for the selected sites. While the maximum day flow increased significantly for the
Blackwater River the trends in maximum day flow for the other stations were not significant.

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Figure 2. Trend in selected flow statistics for Ahoskie Creek, Ahoskie. NC

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Table 4. Trends in selected flow statistics for selected waterbodies in the Chowan Basin
Station USGS
Gage Minimum 7-day Minimum Median Mean Maximum
Ahoskie Creek at Ahoskie, NC 02053500
Increasing
(2.9% per year)*
Increasing
(2.5% per year)
No trend
(0.11 per year)
No trend
(-0.076 per year)
No trend
(0.58% per year)
Potecasi Creek near Union, NC 02053200
No trend
(-0.25% per year)
No trend
(0.021% per year)
No trend
(-0.32% per year)
No trend
(-0.021% per year)
No trend
(0.68% per year)
Nottoway River near Sebrell, VA 02047000
Decreasing
(-0.8% per year)
Decreasing
(-0.87% per year)
No Trend
(-0.2% per year)
No Trend
(-0.012% per year)
No Trend
(0.071% per year)
Meherrin River at Emporia, VA 02052000
No trend
(0.39% per year)
No trend
(-0.32% per year)
No trend
(-0.38% per year)
No trend
(-0.21% per year)
No trend
(0.26% per year)
Blackwater River near Franklin, VA 02049500
Decreasing
(-2% per year)
Decreasing
(-2.2% per year)
No Trend
(0.09% per year)
No Trend
(0.18% per year)
Increasing
(0.81% per year)
* Slope in % per year is shown in parenthesis

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Quantile-Kendall plot
A recently developed type of plot, the Quantile-Kendall plot (Hirsch, 2018), was used to explore
flow trends at the selected sites in the Chowan River Basin. The Quantile-Kendall plot (Hirsch,
2018) is an exploratory plot constructed using a trend slope computed for a given order
statistic. The Quantile-Kendall plots, derived using daily flow records, are used to evaluate flow
trends across the range of flow values at a given site for a specified time-frame (Annual time
frame for the Chowan analysis). Flows from every year are ranked from 1 to 365 (one being the
lowest flow of the year). A trend slope is then calculated for the first ordered flow for each year
over the specified period of years and this slope is plotted as the left most point on the graphs.
The trend test and the associated Thiel-Sen slope estimates are computed and plotted in a
similar manner for each consecutive rank. The 365th rank is the slope representing the highest
flows for each year. The Quantile-Kendall plots for an annual timeframe show results of 365
Mann-Kendall trend tests, and the associated Thiel-Sen slope estimates, for each of the 365
ranks (order statistics) over a specified period of years.

In these plots, the trend slopes are computed using the Thiel-Sen slope estimator (Sen, 1968;
Thiel, 1950) of the logarithms of the values shown and then transformed to percentage changes
per year (Hirsch and De Cicco, 2015). The strength of the statistical evidence for these
trends is evaluated using the Mann-Kendall trend test, adjusted for serial correlation using the
adjustment method proposed by Yue et al. (2002). The strength of the evidence is characterized
by the likelihood that the direction of the estimated trend is correct, computed from the
Mann-Kendall test p-values as [1 − (p / 2)]. The color in these plots represents the p value for
the Mann-Kendall test for trend as described above. Red indicates a trend that is significant at
alpha = 0.05. Black indicates an attained significance between 0.05 and 0.1. The grey dots are
trends that are not significant at the alpha level of 0.1. The likelihood designations follow the
pattern used by Hirsch et al. (2015) and are shown in this table.

Likelihood designation Range of likelihood values
Highly likely 0.95 to 1.00
Very likely 0.90 to <0.95
Likely 0.67 to <0.90
Uncertain 0.50 to <0.67

Using the stream gage at Ahoskie Creek at Ahoskie, NC as an example, trends in flow across the
entire frequency distribution of flows are shown in the Quantile-Kendall plot in Fig. 3. There are
substantial positive trends at the lower extreme of the flow distribution (less than 0.01 non-
exceedance probability) and highly likely negative trends in the upper middle part of the flow
duration curve (0.6 to 0.9 non-exceedance probability). These trends can be considered very
likely or highly likely upwards for almost all order statistics in the lower extreme of the
distribution. The percentage increases in low flows were much more substantial than those at
high flows and were the least substantial near the median and higher flow part of the

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distribution. The trends in middle range flow (0.025 - 0.6 non-exceedance probability) and in
the higher flow range (>0.9 non-exceedance probability) are classified as unlikely.
Quantile-Kendall plots comparing flow trend results among the five selected sites for the period
of record are shown in Fig. 4 to Fig 7. The flow trends indicated that positive or negative trends
were unlikely across the entire frequency distribution of flows for Potecasi Creek near Union,
NC and Meherrin River at Emporia, VA stations. For Nottoway River near Sebrell, VA, only the
flows in the range of 0.10 to 0.20 non-exceedance probability were observed to exhibit very
likely downward trend. For the Blackwater River near Franklin, VA site there are substantial
negative trends at the lower extreme of the flow distribution (less than 0.05 non-exceedance
probability) and considerable positive trends at the higher extreme of the flow duration curve
(> 0.95 non-exceedance probability), and these trends can be considered very likely or highly
likely downwards for almost all order statistics in the lower extreme of the distribution, and
very likely upwards for all flows in the higher extreme part of the distribution.
Overall the Ahoskie and the Black River period of record show the greatest evidence for flow
trends among these sites.
.

Figure 3. Quantile-Kendall plots for Ahoskie Creek
Figure 3

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Figures 4 to 7. Quantile-Kendall plots for selected Chowan River Basin Stations
Figure 7
Figure 4 Figure 5
Figure 6

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Summary
Trends in streamflow for selected Chowan River Basin flow gages were explored using the
Mann-Kendall trend test. In addition, temporal changes in daily streamflow statistics across an
annual time period for the period of record were explored using the EGRET. The Quantile-
Kendall plot was also used to evaluate flow trends across the range of streamflow values at a
given site for an annual time-frame. While the 30-Year 7Q10 flow increased significantly for
Ahoskie Creek and Nottoway River it decreased for Blackwater River and Potecasi Creek.
Significantly upward trends were observed in minimum day and 7-day minimum flow for
Ahoskie Creek and significant downward trend were observed for Nottoway River and
Blackwater River. The maximum day flow increased significantly for the Blackwater River. The
Quantile-Kendall plot show that trends for Ahoskie Creek can be considered very likely or highly
likely upwards for almost all order statistics in the lower extreme of the distribution, and very
likely or highly likely downwards for all flows in the upper middle part of the distribution. For
Blackwater River, these trends can be considered very likely or highly likely downwards for
almost all order statistics in the lower extreme of the distribution, and very likely upwards for
all flows in the higher extreme part of the distribution. The Ahoskie and the Blackwater River
period of record show the overall greatest evidence for flow trends among these sites.

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References

Choquette, A.F., Hirsch, R.M., Murphy, J.C., Johnson, L.T. and R.B. Confesor Jr. 2019. Tracking
changes in nutrient delivery to western Lake Erie: Approaches to compensate for variability and
trends in streamflow. J. Great Lakes Research, Volume 45, Issue 1, 21-39

Helsel, D.R., Mueller, D.K., and Slack, J.R., 2006, Computer program for the Kendall family of
trend tests: U.S. Geological Survey Scientific Investigations Report 2005–5275, 4 p.

Hirsch, R.M., 2018. Daily Streamflow Trend Analysis. U.S. Geological Survey Office of
Water Information Blog at: https://owi.usgs.gov/blog/Quantile-Kendall/ (38 pp.).

Hirsch, R.M., De Cicco, L.A., 2015. User Guide to Exploration and Graphics for RivEr Trends
(EGRET) and dataRetrieval: R Packages for Hydrologic Data, Version 2.0, U.S. Geological
Survey Techniques Methods, 4-A10. U.S. Geological Survey, Reston, VA (93 pp.
(at: doi:10.3133/tm4A10); with updates (2018) EGRET Version

Sen, P.K., 1968. Estimates of the regression coefficient based on Kendall's tau. J. Am. Stat.
Assoc. 63 (324), 1379–1389.

Yue, S., Pilon, P., Phinney, B., Cavadias, G., 2002. The influence of autocorrelation on the
ability to detect trend in hydrological series. Hydrol. Process. 16, 1807–1829.

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Appendix A
Plots of Selected Flow Statistics

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