Introduction
Annual variables are useful statistics calculated for the results of
hydrograph separation. While separation is performed on a daily basis,
the summaries calculated by grwat are annual.
Examples are maximum spring flood runoff, mean annual groundwater
(“baseflow”) runoff, thaw flood runoff volume (w/o groundwater) or the
number of rain flood days. Users proficient in R can calculate such
variables simply by summarizing the results of
gr_separate() function. However, summarizing functionality
is implemented in the package for a more streamlined analysis. The
benefits are that the standardized variables can be supplemented by
additional functions that perform their statistical testing and
plotting.
First of all, we need to separate the hydrograph:
library(grwat)
data(spas) # example Spas-Zagorye data is included with grwat package
head(spas) # separate
#> # A tibble: 6 × 4
#> Date Q Temp Prec
#> <date> <dbl> <dbl> <dbl>
#> 1 1956-01-01 5.18 -6.46 0.453
#> 2 1956-01-02 5.18 -11.4 0.825
#> 3 1956-01-03 5.44 -10.7 0.26
#> 4 1956-01-04 5.44 -8.05 0.397
#> 5 1956-01-05 5.44 -11.7 0.102
#> 6 1956-01-06 5.58 -20.1 0.032
sep = gr_separate(spas, params = gr_get_params(reg = 'center'))
For more information on advanced separation, read the Advanced
separation vignette.
After that we can use gr_summarize() to summarize the
result:
# summarize
vars = gr_summarize(sep)
#> Warning in min.default(structure(numeric(0), class = "Date"), na.rm = FALSE): no
#> non-missing arguments to min; returning Inf
#> Warning in max.default(structure(numeric(0), class = "Date"), na.rm = FALSE): no
#> non-missing arguments to max; returning -Inf
#> Warning in min(means, na.rm = TRUE): no non-missing arguments to min; returning
#> Inf
head(vars)
#> # A tibble: 6 × 57
#> Year Year1 Year2 Dspstart Dspend Tsp Qy Qspmax Dspmax Qygr
#> <dbl> <dbl> <dbl> <date> <date> <int> <dbl> <dbl> <date> <dbl>
#> 1 1956 1956 1957 1956-04-08 1956-05-05 27 18.4 467 1956-04-22 8.59
#> 2 1957 1957 1958 1957-03-25 1957-05-04 40 20.2 460 1957-04-08 9.77
#> 3 1958 1958 1959 1958-04-02 1958-05-13 41 27.3 537 1958-04-21 10.2
#> 4 1959 1959 1960 1959-03-28 1959-04-28 31 27.1 406 1959-04-16 10.9
#> 5 1960 1960 1961 1960-03-27 1960-04-27 31 29.6 406 1960-04-15 12.3
#> 6 1961 1961 1962 1961-03-07 1961-05-02 56 18.8 296 1961-04-10 10.8
#> # … with 47 more variables: Qsmin <dbl>, Dsmin <date>, Qwmin <dbl>,
#> # Dwmin <date>, Q30s <dbl>, D30s1 <date>, D30s2 <date>, Q30w <dbl>,
#> # D30w1 <date>, D30w2 <date>, Q10s <dbl>, D10s1 <date>, D10s2 <date>,
#> # Q10w <dbl>, D10w1 <date>, D10w2 <date>, Q5s <dbl>, D5s1 <date>,
#> # D5s2 <date>, Q5w <dbl>, D5w1 <date>, D5w2 <date>, Wy <dbl>, Wygr <dbl>,
#> # Wsp <dbl>, Wspgr <dbl>, Wsprngr <dbl>, Wrn <dbl>, Wrngr <dbl>, Wth <dbl>,
#> # Wthgr <dbl>, Wgrs <dbl>, Ws <dbl>, Wgrw <dbl>, Ww <dbl>, Qrnmax <dbl>, …
Resulting data frame contains more than 50 variables that can be used
in the analysis of interannual changes. To get familiar with the
variables and their names, just use the gr_help_vars()
function:
gr_help_vars()
#> # A tibble: 57 × 21
#> ID Position Width Source Name_old Name Units Unitsua Unitsen Readtype
#> <dbl> <dbl> <dbl> <dbl> <chr> <chr> <chr> <chr> <chr> <chr>
#> 1 1 1 7 1 year_number Number <NA> <NA> <NA> integer
#> 2 2 8 10 1 Year1 Year1 Год Рок Year integer
#> 3 3 18 10 1 Year2 Year2 Год Рок Year integer
#> 4 4 28 15 1 datestart Dspst… Дата Дата Date Date
#> 5 5 43 15 1 datepolend Dspend Дата Дата Date Date
#> 6 57 0 0 0 PolProd Tsp Дней Дней Days integer
#> 7 6 58 10 1 Qy Qy м^3/с м^3/с m^3/s double
#> 8 7 68 10 1 Qmax Qspmax м^3/с м^3/с m^3/s double
#> 9 8 78 15 1 datemax Dspmax Дата Дата Date Date
#> 10 9 93 10 1 Qygr Qygr м^3/с м^3/с m^3/s double
#> # … with 47 more rows, and 11 more variables: Type <chr>, Test <dbl>,
#> # Desc <chr>, Descua <chr>, Descen <chr>, Group <chr>, Winter <dbl>,
#> # Chart <chr>, Color <chr>, Order <dbl>, Range <chr>
Statistical tests
Variable testing by gr_test_vars() can be used to
estimate the statistical significance of the interannual changes.
Pettitt test is performed to detect the change year — i.e. the year
which divides the time series into the statistically most differing
samples. Student (Welch) and Fisher tests are used to estimate the
significance of mean and variance differences of these samples.
Theil-Sen test calculates the trend slope value. Mann-Kendall test is
performed to reveal the significance of the trend.
gr_test_vars() returns the list of tests for each
variable:
# test all variables
tests = gr_test_vars(vars)
# view Pettitt test for Qygr
tests$ptt$Qygr
#>
#> Pettitt's test for single change-point detection
#>
#> data: vl[vl_cmp]
#> U* = 869, p-value = 8.129e-08
#> alternative hypothesis: two.sided
#> sample estimates:
#> probable change point at time K
#> 23
# view Fisher test for Q30s
tests$ft$Q30s
#>
#> F test to compare two variances
#>
#> data: d1 and d2
#> F = 0.53023, num df = 21, denom df = 41, p-value = 0.1208
#> alternative hypothesis: true ratio of variances is not equal to 1
#> 95 percent confidence interval:
#> 0.2597352 1.1887012
#> sample estimates:
#> ratio of variances
#> 0.5302307
# test only Qygr and Q30s using 1978 as fixed year and excluding 1988-1991 yrs
gr_test_vars(vars, Qygr, year = 1979, exclude = 1988:1991)
#> $ptt
#> $ptt$Qygr
#>
#> Pettitt's test for single change-point detection
#>
#> data: vl[vl_cmp]
#> U* = 777, p-value = 1.372e-07
#> alternative hypothesis: two.sided
#> sample estimates:
#> probable change point at time K
#> 23
#>
#>
#>
#> $mkt
#> $mkt$Qygr
#>
#> Mann-Kendall trend test
#>
#> data: vl[vl_cmp]
#> z = 4.6495, n = 60, p-value = 3.327e-06
#> alternative hypothesis: true S is not equal to 0
#> sample estimates:
#> S varS tau
#> 7.300000e+02 2.458333e+04 4.124294e-01
#>
#>
#>
#> $tst
#> $tst$Qygr
#>
#> Sen's slope
#>
#> data: df.theil[[2]][fltr]
#> z = 4.6495, n = 60, p-value = 3.327e-06
#> alternative hypothesis: true z is not equal to 0
#> 95 percent confidence interval:
#> 0.06251714 0.13908704
#> sample estimates:
#> Sen's slope
#> 0.09723533
#>
#>
#>
#> $ts_fit
#> $ts_fit$Qygr
#>
#> Call:
#> mblm::mblm(formula = eval(frml), dataframe = df.theil[fltr, ],
#> repeated = FALSE)
#>
#> Coefficients:
#> (Intercept) Year1
#> -161.12007 0.08728
#>
#>
#>
#> $tt
#> $tt$Qygr
#>
#> Welch Two Sample t-test
#>
#> data: d1 and d2
#> t = -8.5377, df = 47.936, p-value = 3.47e-11
#> alternative hypothesis: true difference in means is not equal to 0
#> 95 percent confidence interval:
#> -5.558042 -3.439122
#> sample estimates:
#> mean of x mean of y
#> 9.296712 13.795294
#>
#>
#>
#> $ft
#> $ft$Qygr
#>
#> F test to compare two variances
#>
#> data: d1 and d2
#> F = 0.80703, num df = 21, denom df = 37, p-value = 0.6112
#> alternative hypothesis: true ratio of variances is not equal to 1
#> 95 percent confidence interval:
#> 0.3877489 1.8252853
#> sample estimates:
#> ratio of variances
#> 0.8070288
#>
#>
#>
#> $year
#> Qygr
#> 1979
#>
#> $maxval
#> $maxval$Qygr
#> [1] 20.05682
#>
#>
#> $fixed_year
#> [1] TRUE
#>
#> $pvalues
#> N Variable Change.Year Trend M1
#> 1 1 Mean annual groundwater ("baseflow") runoff 1979 0.08728 9.29671
#> M2 MeanRatio sd1 sd2 sdRatio Mann.Kendall Pettitt Student
#> 1 13.79529 48.4 1.88588 2.09928 11.3 0 0 0
#> Fisher
#> 1 0.61116
The tests can be represented in a clear tabular form for visual
analysis:
p-values of statistical criteria
|
N
|
Variable
|
Change.Year
|
Trend
|
M1
|
M2
|
MeanRatio
|
sd1
|
sd2
|
sdRatio
|
Mann.Kendall
|
Pettitt
|
Student
|
Fisher
|
|
1
|
Annual runoff volume
|
1978
|
2e-05
|
0.06173
|
0.07133
|
15.6
|
0.01713
|
0.02187
|
27.7
|
0.89399
|
0.41581
|
0.06135
|
0.24016
|
|
2
|
Spring flood runoff volume (w/o groundwater)
|
1986
|
-0.00026
|
0.02293
|
0.01514
|
-34
|
0.01204
|
0.01083
|
-10
|
9e-05
|
0.00596
|
0.00923
|
0.55265
|
|
3
|
Annual groundwater runoff volume
|
1979
|
3e-04
|
0.02919
|
0.04468
|
53.1
|
0.00583
|
0.00916
|
57.1
|
2e-05
|
0
|
0
|
0.02898
|
|
4
|
Spring flood runoff volume (with groundwater)
|
1988
|
-0.00025
|
0.03009
|
0.0208
|
-30.9
|
0.01439
|
0.01223
|
-15
|
0.00069
|
0.01499
|
0.00744
|
0.36779
|
|
5
|
Rain flood runoff volume (w/o groundwater)
|
1975
|
0
|
0.00571
|
0.00877
|
53.6
|
0.00685
|
0.00860
|
25.5
|
0.97689
|
0.66529
|
0.14526
|
0.30919
|
|
6
|
Rain flood runoff volume (with groundwater)
|
1977
|
4e-05
|
0.01413
|
0.02377
|
68.2
|
0.01045
|
0.01585
|
51.7
|
0.52016
|
0.09611
|
0.00564
|
0.05192
|
|
7
|
Thaw flood runoff volume (w/o groundwater)
|
1983
|
-1e-05
|
0.00254
|
0.00204
|
-19.7
|
0.00305
|
0.00252
|
-17.4
|
0.388
|
0.44105
|
0.49953
|
0.28751
|
|
8
|
Thaw flood runoff volume (with groundwater)
|
2010
|
0
|
0.00749
|
0.00908
|
21.2
|
0.00494
|
0.00588
|
19
|
0.88484
|
1
|
0.41744
|
0.40141
|
|
9
|
Winter groundwater runoff volume
|
1978
|
9e-05
|
0.00742
|
0.01187
|
60
|
0.00238
|
0.00345
|
45
|
0.00017
|
1e-05
|
0
|
0.07512
|
|
10
|
Winter low flow runoff volume
|
1978
|
7e-05
|
0.00953
|
0.01349
|
41.6
|
0.00492
|
0.00502
|
2
|
0.0162
|
0.00107
|
0.00463
|
0.95422
|
|
11
|
Summer groundwater runoff volume
|
1979
|
2e-04
|
0.01474
|
0.02497
|
69.4
|
0.00451
|
0.00703
|
55.9
|
1e-05
|
0
|
0
|
0.03202
|
|
12
|
Summer low flow runoff volume
|
1977
|
0.00022
|
0.01917
|
0.03262
|
70.2
|
0.01064
|
0.01469
|
38.1
|
0.01337
|
0.00175
|
0.00013
|
0.12912
|
|
13
|
Mean annual runoff
|
1978
|
0.00067
|
19.69591
|
22.67542
|
15.1
|
5.69050
|
6.74803
|
18.6
|
0.98613
|
0.47808
|
0.07105
|
0.41506
|
|
14
|
First date of a spring flood
|
1970
|
-0.16667
|
28-Mar
|
17-Mar
|
-11
|
8.00000
|
15.00000
|
87.5
|
0.08714
|
0.10098
|
0.00272
|
0.02492
|
|
15
|
Mean annual groundwater (“baseflow”) runoff
|
1979
|
0.08862
|
9.29671
|
14.18706
|
52.6
|
1.88588
|
2.48532
|
31.8
|
1e-05
|
0
|
0
|
0.17614
|
|
16
|
Last date of a spring flood
|
1970
|
-0.26393
|
05-May
|
22-Apr
|
-13
|
6.00000
|
16.00000
|
166.7
|
0.00261
|
0.00569
|
1e-05
|
4e-04
|
|
17
|
Duration of a spring flood
|
1989
|
-0.14634
|
38.0625
|
33.9375
|
-10.8
|
7.33061
|
12.75055
|
73.9
|
0.01739
|
0.02757
|
0.11898
|
0.00284
|
|
18
|
Maximum spring flood runoff
|
1970
|
-4
|
419.78571
|
241.83
|
-42.4
|
162.94462
|
146.00771
|
-10.4
|
8e-05
|
0.01088
|
0.00152
|
0.55597
|
|
19
|
Date of a maximum spring flood runoff
|
1970
|
-0.08333
|
14-Apr
|
14-Apr
|
0
|
5.00000
|
40.00000
|
700
|
0.24607
|
0.19331
|
0.93
|
0
|
|
20
|
Spring flood runoff volume (with groundwater and rain)
|
1986
|
-0.00028
|
0.03074
|
0.02251
|
-26.8
|
0.01391
|
0.01415
|
1.7
|
0.00073
|
0.01377
|
0.02274
|
0.93649
|
|
21
|
Minimum daily winter runoff
|
1979
|
0.1206
|
4.05591
|
9.42833
|
132.5
|
1.93119
|
2.03176
|
5.2
|
0
|
0
|
0
|
0.8237
|
|
22
|
Date of minimum daily winter runoff
|
1965
|
-0.19677
|
16-Feb
|
19-Jan
|
-28
|
43.00000
|
35.00000
|
-18.6
|
0.41054
|
0.36833
|
0.10043
|
0.32859
|
|
23
|
Minimum daily summer runoff
|
1979
|
0.05578
|
4.49091
|
8.35571
|
86.1
|
2.19461
|
1.80075
|
-17.9
|
0.00205
|
0
|
0
|
0.27404
|
|
24
|
Date of minimum daily summer runoff
|
2000
|
0.33333
|
23-Jul
|
15-Aug
|
23
|
34.00000
|
31.00000
|
-8.8
|
0.1962
|
0.05942
|
0.01235
|
0.74221
|
|
25
|
Minimum 30-day averaged winter runoff
|
1979
|
0.1091
|
6.00123
|
11.19813
|
86.6
|
2.15918
|
2.88271
|
33.5
|
NA
|
0
|
0
|
0.15792
|
|
26
|
First date of minimum 30-day averaged winter runoff
|
1987
|
-0.14545
|
04-Jan
|
27-Dec
|
358
|
21.00000
|
25.00000
|
19
|
0.39944
|
0.74118
|
0.1862
|
0.44023
|
|
27
|
Minimum 30-day averaged summer runoff
|
1979
|
0.05577
|
6.23477
|
9.70019
|
55.6
|
1.69308
|
2.32512
|
37.3
|
0.00218
|
1e-05
|
0
|
0.12077
|
|
28
|
First date of minimum 30-day averaged summer runoff
|
2000
|
0.15789
|
13-Jul
|
02-Aug
|
20
|
29.00000
|
28.00000
|
-3.4
|
0.42377
|
0.09454
|
0.01189
|
0.98217
|
|
29
|
Minimum 10-day averaged winter runoff
|
1979
|
0.10384
|
5.12577
|
10.06676
|
96.4
|
1.60347
|
2.25540
|
40.7
|
0
|
0
|
0
|
0.09575
|
|
30
|
First date of minimum 10-day averaged winter runoff
|
1987
|
-0.2892
|
26-Jan
|
11-Jan
|
-15
|
32.00000
|
36.00000
|
12.5
|
0.25361
|
0.406
|
0.0805
|
0.54115
|
|
31
|
Minimum 10-day averaged summer runoff
|
1981
|
0.05427
|
5.89658
|
8.8558
|
50.2
|
1.55969
|
1.87498
|
20.2
|
0.00063
|
0
|
0
|
0.35115
|
|
32
|
First date of minimum 10-day averaged summer runoff
|
2000
|
0.33333
|
21-Jul
|
11-Aug
|
21
|
27.00000
|
31.00000
|
14.8
|
0.11213
|
0.03414
|
0.01318
|
0.45786
|
|
33
|
Minimum 5-day averaged winter runoff
|
1979
|
0.10721
|
4.77955
|
9.83214
|
105.7
|
1.63118
|
2.19704
|
34.7
|
0
|
0
|
0
|
0.14478
|
|
34
|
First date of minimum 5-day averaged winter runoff
|
1987
|
-0.14609
|
28-Jan
|
16-Jan
|
-12
|
36.00000
|
36.00000
|
0
|
0.50514
|
0.57006
|
0.16897
|
0.95117
|
|
35
|
Minimum 5-day averaged summer runoff
|
1981
|
0.05467
|
5.76225
|
8.68705
|
50.8
|
1.51068
|
1.83279
|
21.3
|
0.00038
|
0
|
0
|
0.3274
|
|
36
|
First date of minimum 5-day averaged summer runoff
|
2000
|
0.33333
|
25-Jul
|
15-Aug
|
21
|
27.00000
|
30.00000
|
11.1
|
0.10966
|
0.03414
|
0.01299
|
0.4868
|
|
37
|
Maximum thaw flood runoff
|
1984
|
-0.02084
|
26.94527
|
24.67525
|
-8.4
|
35.56889
|
35.16949
|
-1.1
|
0.67234
|
0.96366
|
0.80093
|
0.93525
|
|
38
|
Date of a maximum thaw flood runoff
|
1994
|
0.67308
|
20-Dec
|
20-Jan
|
-335
|
36.00000
|
39.00000
|
8.3
|
0.00768
|
0.00441
|
0.00269
|
0.61063
|
|
39
|
Number of thaw flood events
|
1995
|
-0.13333
|
14.83333
|
11.23077
|
-24.3
|
4.63835
|
7.27356
|
56.8
|
0.00092
|
0.00548
|
0.03221
|
0.01427
|
|
40
|
Number of thaw flood days
|
1984
|
-0.70213
|
79
|
47.05405
|
-40.4
|
20.74015
|
22.84482
|
10.1
|
5e-05
|
0
|
0
|
0.61425
|
|
41
|
Maximum rain flood runoff
|
1977
|
0.10523
|
54.75139
|
72.47261
|
32.4
|
56.94260
|
56.22200
|
-1.3
|
0.68081
|
0.52857
|
0.25418
|
0.90809
|
|
42
|
Date of a maximum rain flood runoff
|
2002
|
0.12973
|
12-Jun
|
28-Jun
|
16
|
67.00000
|
69.00000
|
3
|
0.74116
|
0.60713
|
0.4232
|
0.84757
|
|
43
|
Number of rain flood events
|
1977
|
-0.08876
|
20.05
|
14.90909
|
-25.6
|
4.29780
|
3.94036
|
-8.3
|
0.00595
|
0.00122
|
6e-05
|
0.61906
|
|
44
|
Number of rain flood days
|
1991
|
-0.13488
|
112.05882
|
99.1
|
-11.6
|
29.43091
|
38.07556
|
29.4
|
0.65125
|
0.41088
|
0.13723
|
0.15352
|
|
45
|
Relative variation of runoff during winter low flow
|
1983
|
-0.00272
|
0.44193
|
0.27215
|
-38.4
|
0.31443
|
0.23674
|
-24.7
|
0.02495
|
0.00955
|
0.02408
|
0.11426
|
|
46
|
Duration of winter low flow
|
1984
|
-0.47321
|
130.44444
|
115.2973
|
-11.6
|
18.08810
|
27.04098
|
49.5
|
0.00115
|
0.02306
|
0.00936
|
0.03571
|
|
47
|
Relative variation of runoff during summer-autumn low flow
|
1970
|
-0.00039
|
0.56005
|
0.62536
|
11.7
|
0.43161
|
0.28499
|
-34
|
0.85746
|
0.66529
|
0.60021
|
0.03682
|
|
48
|
Duration of a summer-autumn low flow
|
1999
|
0.51113
|
198.61905
|
216.63636
|
9.1
|
20.61488
|
23.16719
|
12.4
|
0.00027
|
0.00955
|
0.00394
|
0.51051
|
Interannual plots
Summarized variables can be ploted and statistically tested to reveal
interannual changes. The basic function for plotting is
gr_plot_vars(). Just pass the names of the variables that
you want to plot, and the desired plotting layout. Different background
fill colors are used to differentiate seasons:
# plot one selected variable
gr_plot_vars(vars, Qygr)
#> Warning: Removed 1 rows containing non-finite values (stat_smooth).
# plot one selected variable
gr_plot_vars(vars, Dspstart)
#> Warning: Removed 1 rows containing non-finite values (stat_smooth).
#> Warning: Removed 1 rows containing missing values (geom_point).
# plot two variables sequentially
gr_plot_vars(vars, D10w1, Wsprngr)
#> Warning: Removed 1 rows containing non-finite values (stat_smooth).
#> Removed 1 rows containing missing values (geom_point).
#> Warning: Removed 1 rows containing non-finite values (stat_smooth).
# plot four variables in matrix layout
gr_plot_vars(vars, Qspmax, Qygr, D10w1, Wsprngr,
layout = matrix(1:4, nrow = 2, byrow = TRUE))
#> Warning: Removed 1 rows containing non-finite values (stat_smooth).
#> Warning: Removed 1 rows containing non-finite values (stat_smooth).
#> Removed 1 rows containing non-finite values (stat_smooth).
#> Warning: Removed 1 rows containing missing values (geom_point).
#> Warning: Removed 1 rows containing non-finite values (stat_smooth).
Tests can be calculated on the fly during the variable plotting or
passed into tests = parameters. In this case the plots are
supplemented with trend line and change year:
# add tests calculated on the fly (only plotted variables are tested)
gr_plot_vars(vars, Qspmax, Qygr, D10w1, Wsprngr,
layout = matrix(1:4, nrow = 2, byrow = TRUE),
tests = TRUE)
#> Warning: Removed 1 rows containing non-finite values (stat_smooth).
#> Removed 1 rows containing non-finite values (stat_smooth).
#> Removed 1 rows containing non-finite values (stat_smooth).
#> Warning: Removed 1 rows containing missing values (geom_point).
#> Warning: Removed 1 rows containing non-finite values (stat_smooth).
# calculate tests beforehand
tests = gr_test_vars(vars)
gr_plot_vars(vars, D10w1, Wsprngr, Nthw, Qrnmax,
layout = matrix(1:4, nrow = 2, byrow = TRUE),
tests = tests)
#> Warning: Removed 1 rows containing non-finite values (stat_smooth).
#> Warning: Removed 1 rows containing missing values (geom_point).
#> Warning: Removed 1 rows containing non-finite values (stat_smooth).
#> Removed 1 rows containing non-finite values (stat_smooth).
#> Warning: Removed 1 rows containing missing values (geom_rect).
#> Warning: Removed 1 rows containing non-finite values (stat_smooth).
Period plots
Period plots are boxplots produced by gr_plot_periods()
for hydrograph separation variables. The data for each variable is
divided into two sample periods: before and after the change year either
set by year parameter or extracted from tests
(statistically estimated). Different background fill colors are used to
differentiate seasons:
# plot periods with fixed change year
gr_plot_periods(vars, Qygr, year = 1979)
#> Warning: Removed 1 rows containing non-finite values (stat_boxplot).
# plot periods with change year from Pettitt test
gr_plot_periods(vars, Qygr, tests = TRUE)
#> Warning: Removed 1 rows containing non-finite values (stat_boxplot).
# calculate test beforehand
gr_plot_periods(vars, Qspmax, tests = tests)
#> Warning: Removed 1 rows containing non-finite values (stat_boxplot).
# use matrix layout to plot multiple variables
gr_plot_periods(vars, Qygr, Qspmax, D10w1, Wsprngr,
layout = matrix(1:4, nrow = 2),
tests = tests)
#> Warning: Removed 1 rows containing non-finite values (stat_boxplot).
#> Removed 1 rows containing non-finite values (stat_boxplot).
#> Removed 1 rows containing non-finite values (stat_boxplot).
#> Removed 1 rows containing non-finite values (stat_boxplot).
Minimum runoff month plots
A histogram of a minimum runoff month for two periods: before and
after the change year set by year parameter. This kind of
plot is produced by gr_plot_minmonth():
# plot minimum runoff month for two periods divided by Pettitt test
gr_plot_minmonth(vars, tests = gr_test_vars(vars))
# plot minimum runoff month for two periods divided by fixed year
gr_plot_minmonth(vars, year = 1979)
Test plots
Test plots produced by gr_plot_tests() are intended to
facilitate the visual analysis of statistical tests. Currently only the
change year density is available as a plotting variable:
# plot change year from Pettitt test
gr_plot_tests(tests, type = 'year')
As can be seen from this plot, most of the variables demonstrate the
change in their statistical behavior around \(1979\) year.