Water balance of the flood season. Despite the large spatial variation of amount precipitation during the flood period among 4 regions (from 310 mm in region I to 605 mm in region III), their seasonal distribution in BC is relatively similar. Maximal precipitation occurs in July – August and the minimal takes place in June or September. The September minimum are more pronounced for I and II regions. The maximum evaporation occurs earlier - in June – July with rapid decline in August – September (Fig. 3).
Maximum water discharge occurs after the maximum precipitation across region I and II, probable due to their vast area. Region III is characterized by a maximum water discharge in August, however, in contrast to the Selenga basin, water discharge in June and July practically does not differ from each other. Maximum of river discharge in region IV occurs in June further followed by decline during the entire season.
The TWS seasonality is different for each region. Our estimates predict minor growth of TWS in July – August and a slight decrease of TWS in June and September within region I. Such a small TWS variability compared to P and E is associated with vast closed-drainage area with a pronounced arid climate in BC, where large quantities of precipitated water are immediately lost by evaporation. Additionally, permafrost and steep slopes (Moreido and Kalugin 2017) hamper water storage capacity.
Region II is characterized by TWS reduction by about 20 mm in June and relative stability in the remaining months. Within region III TWS decrease in June reaches 50 mm, and for the entire flood period it is up 65 mm. The region IV is characterized by a decrease of TWS by 65 mm in June – July and an increase by 20 mm in August – September.
River flow change. Variability of river flow formation conditions in BC results in high spatial variability of flood discharges Qflood – from 0.7 l/s*km2 to 39.l/s*km2 (Table 1) with coefficient of variation (the ratio of the standard deviation of the value to its mathematical expectation) from 0.25 to 1.2. Significant relationship with the Qflood is observed (at the 0.1% significance level according to Mann-Kendall test).
Qmax consistently showed larger variability (from 3.2l/s*km2 to 208 l/s*km2) with coefficient of variation from 0.32 to 2.87 accordingly. Coefficient of variation of Qmax barely depends on catchments’ area or Qmax mean value. The maximum values of the Qmax are observed in region III. The minimum values estimated here for the downstream of the Selenga and Uda rivers were close to maximum.
CVD of river flow varies from July 12 to August 6 (for 90% of the gauges from July 25), early for upper reaches of the basins and lately for lower ones. The exception is Upper Angara basin where the influence of melt runoff is significant (Sinyukovich and Chernyshov 2019b). Average standard deviation of CVD is about 12.5 days, up to 20 days in North-East part of region II and down to 9 days for gauges on Selenga river. Moreover, there is a significant relationship between coefficient of variation of Qflood and coefficient of variation of the CVD (p-val = 0.12%).
Linear rates of change per year were determined by Sen slope estimate for Qflood, Qmax, and CVD as well as their statistical significance by Mann-Kendall test. Qflood showed the most consistent pattern of change with all study regions. 42 out of 44 gauges showed negative trend. The changes were significant at 5%, 2% and 1% level for 23, 14 и 11 gauges respectively. However, trends in regions III and IV were not field significant. The location of gauges with significant/insignificant trends and their magnitudes is depicted in Fig. 4.
All four gauges on Selenga river experienced downward trends, moreover, the rate of decrease is more pronounced at the downstream section and vary from − 1.08%/year at Naushki gauge near Mongolian-Russian border to -1.51% / year at Kabansk gauge. It can be seen that higher rates of Qflood change at the lower reaches compared to the upper ones are also typical for the largest tributaries of the Selenga river in region II - the rivers Chikoy, Hilok and, to a lesser extent, Uda. These rivers as well as their tributaries and small rivers of North-East of region II showed maximum magnitude of Qflood reduction. The trends in Chikoy basin are around 0.7–1.4 %/year. Upper reaches of Hilok basin showed 1%/year Qflood trend, whereas lower reaches are dominated by rate around 2%/year. The rate of Qflood decrease for the northernmost tributaries of the Selenga river reaches 1.5–2.9% / year. Similarly, west part of region II is characterized mostly by Qflood reduction, while none of the trends were significant. The rate of reduction is about 0.5%/year – up to 1%/year in upper reaches of the basins and at lower reaches is equals 0. Near the mouth of Djida river Qflood trend reaches 0.4%/year (№ 14) – maximum value across all gauges. Region III had average Qflood reduction rate around 0.6%/year with single gauge experienced statistically significant change (№ 38). Insignificant negative trends were found for the region IV, and the trend rate decreases from the South (around − 0.65%/year) to the North (-0.17%/year).
41 out of 44 gauges showed negative trend of Qmax, statistically significant at 5%, 2% and 1% level for 17, 9 and 6 gauges correspondingly. Overall, Qmax has similar to Qflood rate of reduction and larger coefficient of variation. According to Mann-Kendall test, fewer gauges with significant Qmax trends compared to Qflood were found. At the same time, unlike Qflood, there is less pronounced change of Qmax trend downstream. Thus, the peaks of the maximum discharge have become more pronounced against the average flood peaks (Selenga, Uda, Hilok gauges). However, it is not the case for Chikoj and Turka rivers. Gauges with field significant changes of Qmax were determined only for region II. Nevertheless, there was the significant decreasing trend for Turka river in region IV.
Small number of gauges (2 out of 44) demonstrated significant CVD trend (not shown here). So, after the consideration of field significance herein, no significant trends were revealed for any region. 10 of 44 gauges had negative trend and located in North-East part of region II. Gauges with significant CVD trends (Itantsa and Bryanka rivers) also showed highest rate of Qflood reduction (<-2.5%/год).
A negative relationship between Qflood decline rate and average elevation of catchment was revealed (p-val < 5%). The connection is probably associated with an increase of average Qflood value with an increase in the average catchment height.
Precipitation and evaporation influence on river flow variation. A strong connection between P and E with Qflood revealed R2(P, E) median equals 0.66 (Fig. 5). Precipitation is a most important factor influencing Qflood in BC. A median R2(P) value is 0.63, while minimum 0.34 and maximum 0.79.
The contribution of evaporation is by order of magnitude less important: the median R2(E) estimated here is 0.022, with a minimum close to 0 and a maximum of 0.12. Furthermore, the median value of the E / P ratio is 0.9. E and P average values are similar. Low values of R2 (E) can be due to many different reasons (E may be more changeable where river flow is close to zero; moisture loss from upper soil level may does not affect much river flow formation in June–September; errors in initial E data etc.). We considered two of them:
1) E value during flood season is almost completely determined by the value of P, and
2) the variability of E is much less than the variability of P.
In general, for the BC, there is a weak positive relationship between P and E - the median value of the Pearson correlation coefficient (r) is 0.34. Moreover, more than half of the gauges (25 out of 44) had positive r value. Probably, the sign of r is determined by the main limiting factor of evaporation in the basin - the available moisture (in this case, r > 0) or potential evaporation (r < 0) (Jung et al. 2010). It seems like the small value of R2 (E) is explained mostly by the low variability of E – the median ratio standard deviation of E to standard deviation of P is 0.28. Thus, E control amount of available for runoff formation water at much less extent that P.
The three lower gauges on the Selenga river have R2(P) value around 0.71–0.76. The upper gauge (Naushki) has R2(P) value 0.59. This is consistent with vast closed drainage regions in region I, precipitation of that have been taken into account for region I precipitation amount. Overall, the minimum values of R2(P) in the region II were observed in the western part of the area, where they are 0.4–0.5. Hilok, Uda and Chikoy rivers have R2(P) values around 0.7–0.75.
Gauges of region III have R2(Р) values close to those of western part of II area (0.53–0.58), with the exception of the Utulik river, where R2(Р) is 0.34. In the region IV the Turka river showed R2(P) value typical for the eastern part of II area (0.69), while the Barguzin and Upper Angara rivers showed almost identical results – 0.50 and 0.52.
It can be seen that most of the gauges have R2(Е) values less than 0.06. Some exceptions here are two rivers of region III - Khara-Murin amd Snezhnaya with R2(Е) equal to 0.11 and 0.12 accordingly.
Precipitation change. All catchments showed decreasing trends in P with spatial distribution of linear trend rate similar to Qflood. The rate of P decline in region I was 0.65% / year (p-val = 0.1%). Western part of region II showed rate of P decline ranging between − 0.25%/year to -0.45%/year. Though, the trend was significant only for one watershed at p-val < 5%. The upper reaches of the Chikoy river are characterized by a linear trend of -0.55 – -0.65% / year. The downstream gauges over there have P decline rate up to -0.8–0.9%/year. Hilok basin is characterized P trend rate around − 0.7 – -1% / year, with large trend rate located in downstream. The highest rates of P decrease have been shown in the Uda basin – -1 – -1.5% / year, regardless of the position within the catchment, except for the upper gauge where P rate is -0.7%/year. Three of four catchments of region III have P decline rate about − 0.45% / year. However, a catchment located near Selenga delta (Table 1, №38) showed decline rate around − 1.1% / year. The region IV is characterized by a decrease in the linear trend of P magnitude from south to north - from − 1% / year in the Turka catchment and up to -0.1% in the Upper Angara catchment (Table 3). Overall, the decrease in the precipitation amount is statistically significant for I and II regions, with the median p-val across all 44 catchments being 0.03%. Like for Qflood, significant changes of P CVD for 1979–2019 was not identified - the median value of p-val of the CVD P linear trend was 66.4%, with a minimum of 9%.
Linear trends of P16 for 40 river basins were negative (Table 3), however, due to the greater variability of P16 compared to P, they were statistically significant only for the regions of the Turka and Kurba rivers (border of regions II and III). Generally, the rate of P16 decline is less than that for P. The ratio of the median of the P16 trend to the median of the P trend is 0.92. This could be the reason why the negative trend of Qmax is slightly less than for Qflood.
Table 3
Linear rates of changes P, P16, E, PET and W for BC river basins, %/year. Italic – significant at 5%, bold – at 1%.
№
|
P
|
E
|
PET
|
P16
|
W
|
1
|
-0.65
|
-0.18
|
0.43
|
-0.46
|
-0.55
|
2
|
-0.69
|
-0.15
|
0.46
|
-0.40
|
-0.51
|
3
|
-0.71
|
-0.21
|
0.48
|
-0.57
|
-0.54
|
4
|
-0.71
|
-0.21
|
0.49
|
-0.57
|
-0.54
|
5
|
-0.55
|
0.27
|
0.44
|
-0.16
|
-0.20
|
6
|
-0.61
|
0.12
|
0.58
|
-0.30
|
-0.37
|
7
|
-0.72
|
0.03
|
0.64
|
-0.54
|
-0.42
|
8
|
-0.78
|
-0.11
|
0.51
|
-0.48
|
-0.61
|
9
|
-0.64
|
-0.12
|
0.56
|
-0.31
|
-0.53
|
10
|
-0.78
|
-0.17
|
0.58
|
-0.88
|
-0.53
|
11
|
-0.80
|
-0.19
|
0.60
|
-0.90
|
-0.53
|
12
|
-0.94
|
-0.30
|
0.60
|
-0.82
|
-0.55
|
13
|
-0.29
|
0.21
|
0.37
|
-0.16
|
-0.20
|
14
|
-0.33
|
-0.02
|
0.41
|
0.00
|
-0.29
|
15
|
-0.70
|
-0.32
|
0.60
|
0.32
|
-0.62
|
16
|
-1.16
|
-0.44
|
0.60
|
-1.36
|
-0.75
|
17
|
-0.86
|
0.14
|
0.67
|
-0.82
|
-0.26
|
18
|
-0.46
|
0.23
|
0.31
|
-0.26
|
-0.17
|
19
|
-0.27
|
0.13
|
0.30
|
0.34
|
-0.25
|
20
|
-0.35
|
0.21
|
0.37
|
-0.15
|
-0.22
|
21
|
-0.22
|
0.05
|
0.35
|
0.71
|
-0.26
|
22
|
-0.51
|
0.14
|
0.52
|
-0.36
|
-0.28
|
23
|
-0.83
|
-0.83
|
0.55
|
-1.31
|
-0.71
|
24
|
-0.86
|
-0.05
|
0.61
|
-0.99
|
-0.42
|
25
|
-1.21
|
-0.82
|
0.60
|
-0.75
|
-0.84
|
26
|
-1.34
|
-0.68
|
0.64
|
-1.43
|
-0.81
|
27
|
-1.46
|
-1.03
|
0.75
|
-1.52
|
-0.75
|
28
|
-1.22
|
-0.33
|
0.69
|
-1.25
|
-0.60
|
29
|
-1.10
|
-0.53
|
0.59
|
-1.51
|
-0.75
|
30
|
-0.98
|
-0.33
|
0.55
|
-0.64
|
-0.70
|
31
|
-1.32
|
-0.14
|
0.64
|
-1.87
|
-0.71
|
32
|
-1.16
|
-0.07
|
0.69
|
-2.10
|
-0.63
|
33
|
-1.14
|
-0.05
|
0.57
|
-2.02
|
-0.55
|
34
|
-1.24
|
-0.06
|
0.70
|
-2.01
|
-0.49
|
35
|
-0.64
|
0.17
|
0.62
|
-0.54
|
-0.31
|
36
|
-0.79
|
0.07
|
0.48
|
-1.22
|
-0.37
|
37
|
-1.27
|
0.00
|
0.73
|
-1.54
|
-0.51
|
38
|
-1.09
|
0.14
|
0.68
|
-1.43
|
-0.32
|
39
|
-0.42
|
0.34
|
0.48
|
-0.26
|
-0.11
|
40
|
-0.45
|
0.35
|
0.48
|
-0.61
|
-0.06
|
41
|
-0.41
|
0.30
|
0.46
|
-0.55
|
-0.06
|
42
|
-0.09
|
0.33
|
0.43
|
-0.14
|
-0.01
|
43
|
-0.66
|
0.22
|
0.52
|
-0.94
|
-0.18
|
44
|
-0.99
|
0.30
|
0.66
|
-2.17
|
-0.23
|
Evaporation change. The spatial pattern of E trend is much more unequal compared to P or Qflood. E change rates vary from − 1.03%/year to 0.35%/year. In general, the catchment with negative P trends less than 0.8%/year indicate positive E trend. These examples include West part of region II, the upper reaches of the Hilok and Chikoy rivers, region III and northern part of region IV. A decrease in E is typical for catchments where more than 0.8%/year P decrease was observed. Overall, regions I and II showed the rate of E decrease about 0.2–0.3%/year, III region showed growth around 0.4%/year and in IV region E trend around − 0.25–0.4%/year is observed. In humid catchments, against the background of a decrease in precipitation, an increase in the amount of evaporation occurred. Within the region III, the value of E increased, even for the catchment area where the decrease in P reached 1.1% / year
Due to the small value of the E variability, even relatively small values of the E rate change (around 0.2% per year) are statistically significant. As a result, the changes in E are statistically significant for all 4 regions, however, if in the regions III and IV (increase in E) and in the I area (decrease in E) they are unidirectional, then for the II area they are multidirectional (Table 3).
It is likely that an increase in E in some catchments despite a decrease in P is associated with an increase in PET. Spatial distribution of PET trend is similar to the P, but with opposite sign. That is probably due to small PET value on days with precipitation. Region I showed the growth rate of PET at 0.43% / year. The minimum values of the PET trend across study region took place in the Jida river basin where they are equal to 0.3–0.4% / year. However, further North, in the Temnik river basin and in the south of the III region, they are 0.5% / year. The trend values are already 0.5–0.7% / year in the east part of the II area and the north of the III region. In region IV, the trend decreases from 0.66%/year in the south to 0.43%/year in the north.
On the other hand, decrease of W led to decline in evaporation moisture availability. The only catchment where decrease of W was unsignificant was the Upper Angara catchment. Other catchments showed W trend significant at 5% level. There are many more catchments that exhibit a trend than would be expected to occur by chance. Due to the low variability of W, the median value of the W trend is only 0.5%/year. The lowest rate of decrease of W was detected in Southern part of region III (0.05–0.1%), and the maximum in the Uda basin (0.6–0.8% per year). Overall, the features of the spatial pattern of the W change are similar to the change of Qflood and P.
E is closely related to PET and W in most catchments. The median value of R2(PET, W) was 0.56, with the contribution of PET being equal to 0.36. The minimum values of R2(PET, W) were obtained from Chikoy river (R2(PET, W) = 0.15). The maximum values of R2(PET, W) (0.81–0.91), as well as R2 (PET) (0.79–0.88), were obtained from catchments with the highest precipitation amount (Upper Angara, South of the region III).
Connection between precipitation elasticity of river flow and watersheds features. The number of catchment evaluated for connection between precipitation elasticity of river flow (\({\epsilon }_{p}\)) and catchments features (32) was less than that used in P and Qflood determination because of the fact that some catchments demonstrated statistically insignificant P change rate (below 5.6%), either were too vast, so value averaged over entire basin is not representative (Selenga river’s gauges).
The two catchments located in the Northwest of the Baikal basin (Khara-Murin and Snezhnaya) have \({\epsilon }_{p}\) close to 1–0.95 and 0.8 accordingly. Due to the small size of these basins (up to 3000 km2), this may be because of initial data uncertanities. However, since these catchments related to the humid climates (P/PET ratio is from 1.23 to 2.08) and continuous permafrost region, \({\epsilon }_{p}\) around 1 is physically possible. In particular, the amount of precipitation of humid areas is less connected with the amount of evaporation - r between P and E for these three catchments varies from 0.07 to 0.14. Also precipitation, not only themselves form river flow, but also contribute to the melting of permafrost, which leads to an increase in moisture available for the formation of river flow.
The median value of \({\epsilon }_{p}\) was 0.29, with a minimum of 0.03. Such a relatively low sensitivity of Qflood to P, while PET is increasing that should enhance Qflood decline due to P decline, can be explained by relatively arid climate of the considered are with median Hum equal to 1.07. So, a more definite analysis requires consideration of the water balance of the catchments in other seasons.
The correlation matrix of untransformed features of catchments and \({\epsilon }_{p}\) is given in Fig. 6.
For further study, we elaborated specific indices for the catchment parameters demonstrating a monotonic relationship with \({\epsilon }_{p}\), aiming to reach linear functions with \({\epsilon }_{p}\). In particular, the BS was transformed
$${\text{F}\text{r}}^{{\prime }}=\frac{\sqrt{\text{F}\text{r}-20}}{10}$$
and S
$${\text{S}}^{{\prime }}=\frac{1}{10}{\text{S}}^{2}+\frac{1}{10}\text{S}.$$
After linearization features \({\text{S}}^{{\prime }}\) and \({\text{B}\text{S}}^{{\prime }}\) the correlation rate band etween them and \({\epsilon }_{p}\) will be equal 0.44 and 0.82 respectively. Hence, there is strong positive correlation between \({\epsilon }_{p}\) and the following features: S′, Hum, PF, BS, and \({\text{F}\text{r}}^{{\prime }}\). These four variables had R2 around 0.67, 0.52, 0.21, 0.19 and 0.19 accordingly. After evaluation the significance of the variables by F-test and t-tset, the following features were taken for the model: \({\text{S}}^{{\prime }}\) and BS.
The following model was obtained:
$${\epsilon }_{p}\text{p}\text{r}\text{e}\text{d}\text{i}\text{c}\text{t}\text{e}\text{d}= 0.229+0.0057\bullet {\text{S}}^{{\prime }}-0.0348\bullet \text{B}\text{S} \left(3\right)$$
explaining about 74% of the \({\epsilon }_{p}\) variability (Fig. 7).