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: There were 2 warnings in `dplyr::summarise()`.
#> The first warning was:
#> ℹ In argument: `Dspstart = min(.data$Date[which(.data$Qspri > 0)])`.
#> ℹ In group 19: `Year1 = 1974`.
#> Caused by warning in `min.default()`:
#> ! no non-missing arguments to min; returning Inf
#> ℹ Run `dplyr::last_dplyr_warnings()` to see the 1 remaining warning.
#> Warning: There was 1 warning in `dplyr::summarise()`.
#> ℹ In argument: `Q30w = condrollmean(.data$Q, .data$Season == 2, 30)`.
#> ℹ In group 64: `Year = 2020`.
#> Caused by warning in `min()`:
#> ! 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 
#> # ℹ 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>, Qthmax <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  
#> # ℹ 47 more rows
#> # ℹ 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 
#>  0.09732298 
#> 
#> 
#> 
#> $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 = -8.537, df = 47.955, p-value = 3.466e-11
#> alternative hypothesis: true difference in means is not equal to 0
#> 95 percent confidence interval:
#>  -5.558891 -3.439535
#> sample estimates:
#> mean of x mean of y 
#>  9.296712 13.795925 
#> 
#> 
#> 
#> $ft
#> $ft$Qygr
#> 
#>  F test to compare two variances
#> 
#> data:  d1 and d2
#> F = 0.80619, num df = 21, denom df = 37, p-value = 0.6093
#> alternative hypothesis: true ratio of variances is not equal to 1
#> 95 percent confidence interval:
#>  0.3873477 1.8233967
#> sample estimates:
#> ratio of variances 
#>          0.8061938 
#> 
#> 
#> 
#> $year
#> Qygr 
#> 1979 
#> 
#> $maxval
#> $maxval$Qygr
#> [1] 20.07168
#> 
#> 
#> $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 13.79593      48.4 1.88588 2.10036    11.4            0       0       0
#>    Fisher
#> 1 0.60934

The tests can be represented in a clear tabular form for visual analysis:

gr_kable_tests(tests)

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	0.02186	27.6	0.89399	0.41581	0.0613	0.2411
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	0.02912
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	0.49915	0.28712
8	Thaw flood runoff volume (with groundwater)	2010	0	0.00749	0.00906	21	0.00494	0.00586	18.6	0.89399	1	0.42048	0.40685
9	Winter groundwater runoff volume	1978	9e-05	0.00742	0.01187	60	0.00238	0.00345	45	0.00017	1e-05	0	0.07593
10	Winter low flow runoff volume	1978	7e-05	0.00953	0.01348	41.4	0.00492	0.00502	2	0.0162	0.00107	0.00465	0.95809
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	22.67725	15.1	5.69050	6.75317	18.7	0.98613	0.47808	0.07096	0.41292
14	First date of a spring flood	1970	-0.16667	28-Mar	17-Mar	-11	8.00000	15.00000	87.5	0.08608	0.09934	0.00269	0.02471
15	Mean annual groundwater (“baseflow”) runoff	1979	0.08862	9.29671	14.18763	52.6	1.88588	2.48605	31.8	1e-05	0	0	0.17569
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	-0.14286	38.0625	33.96875	-10.8	7.33061	12.73168	73.7	0.01852	0.02812	0.12133	0.00291
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	9.84738	106	1.63118	2.26105	38.6	0	0	0	0.11047
34	First date of minimum 5-day averaged winter runoff	1987	-0.16667	28-Jan	15-Jan	-13	36.00000	36.00000	0	0.45822	0.54022	0.15385	0.9972
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	-0.70242	79	47.02703	-40.5	20.74015	22.84426	10.1	5e-05	0	0	0.61434
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	0.27211	-38.4	0.31443	0.23671	-24.7	0.02495	0.00955	0.02404	0.11406
46	Duration of winter low flow	1984	-0.47597	130.44444	115.27027	-11.6	18.08810	27.07361	49.7	0.00115	0.02306	0.0093	0.03518
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 row containing non-finite outside the scale range
#> (`stat_smooth()`).


# plot one selected variable
gr_plot_vars(vars, Dspstart) 
#> Warning: Removed 1 row containing non-finite outside the scale range
#> (`stat_smooth()`).
#> Warning: Removed 1 row containing missing values or values outside the scale range
#> (`geom_point()`).


# plot two variables sequentially
gr_plot_vars(vars, D10w1, Wsprngr)
#> Warning: Removed 1 row containing non-finite outside the scale range (`stat_smooth()`).
#> Removed 1 row containing missing values or values outside the scale range
#> (`geom_point()`).

#> Warning: Removed 1 row containing non-finite outside the scale range
#> (`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 row containing non-finite outside the scale range
#> (`stat_smooth()`).
#> Warning: Removed 1 row containing non-finite outside the scale range (`stat_smooth()`).
#> Removed 1 row containing non-finite outside the scale range (`stat_smooth()`).
#> Warning: Removed 1 row containing missing values or values outside the scale range
#> (`geom_point()`).
#> Warning: Removed 1 row containing non-finite outside the scale range
#> (`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 row containing non-finite outside the scale range (`stat_smooth()`).
#> Removed 1 row containing non-finite outside the scale range (`stat_smooth()`).
#> Removed 1 row containing non-finite outside the scale range (`stat_smooth()`).
#> Warning: Removed 1 row containing missing values or values outside the scale range
#> (`geom_point()`).
#> Warning: Removed 1 row containing non-finite outside the scale range
#> (`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 row containing non-finite outside the scale range
#> (`stat_smooth()`).
#> Warning: Removed 1 row containing missing values or values outside the scale range
#> (`geom_point()`).
#> Warning: Removed 1 row containing non-finite outside the scale range (`stat_smooth()`).
#> Removed 1 row containing non-finite outside the scale range (`stat_smooth()`).
#> Warning: Removed 1 row containing missing values or values outside the scale range
#> (`geom_rect()`).
#> Warning: Removed 1 row containing non-finite outside the scale range
#> (`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 row containing non-finite outside the scale range
#> (`stat_boxplot()`).


# plot periods with change year from Pettitt test
gr_plot_periods(vars, Qygr, tests = TRUE)
#> Warning: Removed 1 row containing non-finite outside the scale range
#> (`stat_boxplot()`).


# calculate test beforehand
gr_plot_periods(vars, Qspmax, tests = tests)
#> Warning: Removed 1 row containing non-finite outside the scale range
#> (`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 row containing non-finite outside the scale range (`stat_boxplot()`).
#> Removed 1 row containing non-finite outside the scale range (`stat_boxplot()`).
#> Removed 1 row containing non-finite outside the scale range (`stat_boxplot()`).
#> Removed 1 row containing non-finite outside the scale range (`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.