3.1. Siltation Rate
The slow silting rate of Wapienica reservoir (
Table 3) is due to the small sediment yield load flowing into the reservoir. Of this reservoir’s catchment, 97% is covered by forests. Due to the small size of the catchment and low intensity of erosion processes, the degree of silting is only 4.3% after over 70 years of operation. The reservoirs Głuchów and Brzóza Królewska, as well as Cierpisz, also close small-area catchments (
Table 2) located in areas with reduced slopes. Such a location for the reservoirs means that the intensity of the sediment load transport to the reservoirs is small and the silting ratio after several years of operation is about 20%. The reservoirs Krempna and Zesławice are the most intensively silted. The reservoir Krempna is located in a mountainous area with intensive surface erosion, and the catchment of the reservoir Zesławice, whereby 78% of the area is used for agricultural purposes, is covered with loess. It can be observed that a small reservoir becomes silted up faster if the siltation rate reaches 20% over a dozen years of operation (
Table 3), in contrast to large reservoirs that achieve that level over centuries [
46,
47,
48,
49]. Krempna-1, Krempna-2, Zesławice, Głuchów reservoirs are characterized with such fast silting up, as well as Cierpisz reservoir in the period after its desilting and rebuilding
i.e., from 1990 to present (
Table 3). The siltation rate of reservoirs is compared best with mean annual silting ratio—S
R, M (
Table 3). According to Hartung [
50], mean annual loss of capacity in large reservoirs is 0.25%; in medium-sized reservoirs it is above 0.5%; and in small water bodies, it is 3.0%. The S
R, M of Wapienica equal to 0.1% indicates that capacity reduction is typical for large reservoirs. Conversely, the siltation rate of Ożanna reservoirs is similar to medium-sized reservoirs (S
R, M = 0.5%).
The examined small reservoirs of the Upper Vistula basin are characterized by an intense silting rate. The silting degree after fifteen to twenty years of operation usually reaches 40%–50%. Among them, two reservoirs (Cierpisz and Wapiennica) are the exception. Small reservoirs in different climate areas around the world also silt up quickly. Dendy [
51], based on research conducted in the United States on 17 small reservoirs with capacities from 22 thousand m
3 to 1.17 million m
3, demonstrated that after six to ten years of operation, the degree of silting ranged from less than 4% to 17%. However, after 14 years of operation, the silting degree reached 37%–65%. Much more diverse silting intensity is characteristic of small reservoirs in Tunisia. The data presented in the paper by Jebari
et al. [
47] indicate that some of the reservoirs after ten years of operation are silted up 30%–40%, but among them there are some reservoirs whose silting degree is only a few percent. Among 23 reservoirs analyzed in the studies of Jebari
et al. [
47], two of them were silted in
ca. 70%, respectively, after 6 and 8 years of operation.
The examined reservoirs in the Upper Vistula basin are located in catchments, where mean annual runoff is very low (
Table 3), and the determined capacity-inflow ratios are less than 1%. One exception is the reservoir Wapienica. The sediment trap efficiency of those reservoirs, determined from the Brune nomogram, is on average 12.0%–37%, while for the Głuchów reservoir it is only 2.3%, and for the reservoir Wapienica—67.7%. This would mean that the reservoirs retain only a small portion of the incoming sediment. The STE value—the sediment trap efficiency defined as the percentage of total inflowing sediment retained in a reservoir and determined from the Brune nomogram [
43]—is underestimated because, as shown by the research results [
40], the STE value of those reservoirs is
ca. 90%.The STE of small reservoirs was determined by Michalec [
40] as quotient of sediment mass deposited in the first year of operation and total sediment mass flowing into the reservoir in the first year of operation. The mass of deposited sediment was calculated from the transformed Goncharov [
52] equation based on silting measurements.
Table 3.
Volume of deposited sediment and silting ratio of the studied reservoirs in several years of operation [
40].
Table 3.
Volume of deposited sediment and silting ratio of the studied reservoirs in several years of operation [40].
Reservoir | Year | Years of Operation | Volume of Sediment V (m3) | Silting Ratio in Several Years of Operation SR (%) | Mean Annual Silting Ratio SR, M (%) |
---|
Krempna-1 | 1986 | 15 | 35,660 | 29.9 | 2.0 |
Krempna-2 | 1996 | 9 | 27,040 | 24.1 | 2.7 |
1997 | 10 | 30,460 | 27.2 | 2.7 |
1998 | 11 | 34,640 | 30.9 | 2.8 |
1999 | 12 | 38,000 | 33.9 | 2.8 |
2000 | 13 | 40,140 | 35.8 | 2.8 |
2002 | 15 | 44,200 | 39.5 | 2.6 |
2003 | 16 | 44,900 | 40.1 | 2.5 |
2005 | 18 | 45,810 | 40.9 | 2.3 |
Zesławice | 1968 | 2 | 26,970 | 11.8 | 5.9 |
1969 | 3 | 70,430 | 30.9 | 10.3 |
1970 | 4 | 75,780 | 33.2 | 8.3 |
1971 | 5 | 76,250 | 33.4 | 6.7 |
1974 | 8 | 86,190 | 37.8 | 4.7 |
1983 | 17 | 116,090 | 50.9 | 3.0 |
Głuchów | 2002 | 7 | 4,130 | 18.3 | 2.6 |
2009 | 14 | 5,890 | 26.1 | 1.9 |
Brzóza Królewska | 2002 | 7 | 4,180 | 8.5 | 1.2 |
2009 | 14 | 6,400 | 13.1 | 0.9 |
Ożanna | 1998 | 20 | 26,000 | 10.3 | 0.5 |
2003 | 25 | 30,200 | 12.0 | 0.5 |
Cierpisz | 1990 | 34 | 15,000 | 43.5 | 1.3 |
2001 | 11 | 6,100 | 17.7 | 1.6 |
2003 | 13 | 6,750 | 19.6 | 1.5 |
Wapienica | 1967 | 36 | 24,250 | 2.2 | 0.1 |
2003 | 71 | 46,800 | 4.3 | 0.1 |
3.2. Sediment Distribution
When trying to apply Annandale’s method [
31] to determine the sediment load distribution in small reservoirs, segments were separated in each of the reservoirs. These segments constituted partial volumes contained between adjacent cross-sections. The volume of accumulated sediment load, determined based on field measurements, was identified in these segments. Subsequently, regression relationships were identified for specific wetted perimeters (P) and distances from the dam’s wall (x) of each cross-section of the reservoir. The exemplary relationship identified for the reservoir Krempna-2 is shown in
Figure 3.
Figure 3.
Relationship between the wetted perimeter (P) and the distance from the dam (x) established for the water reservoir Krempna-2.
Figure 3.
Relationship between the wetted perimeter (P) and the distance from the dam (x) established for the water reservoir Krempna-2.
At this point, attention should be paid to the method of determining the longitudinal gradient dP/dx, which in the above example is 0.264, determined for the distance x given in meters. Annandale calculated the values of longitudinal gradients (
Figure 1) for distances x in kilometers. The examined small reservoirs are from 440 to 1000 m long. The length of the reservoirs studied by Annadale [
31] ranged from several to a few dozen kilometers. When adopting the distance x for the exemplary reservoir Krempna-2 in kilometers, the obtained longitudinal gradient dP/dx would be 264.0,
i.e., a value beyond the scope given in
Figure 1, in which the sediment distribution curve values dP/dx range from 0.02 to 1.20. The values dP/dx determined according to the methodology of Annandale [
31] are a thousand times larger than the ones given in
Table 4. It appears that the use of the sediment distribution curves (
Figure 1) is impossible. The values dP/dx calculated with the distance in meters, but not in kilometers, will enable the comparison of sediment distribution according to the function given in
Figure 1 and determined based on field measurements.
Table 4.
Longitudinal gradient (dP/dx) and capacity-inflow ratio (C-I) in the studied reservoirs.
Table 4.
Longitudinal gradient (dP/dx) and capacity-inflow ratio (C-I) in the studied reservoirs.
Reservoir | Longitudinal Gradient dP/dx (-) | Mean Annual Runoff Q (m3·s−1) | Capacity-Inflow Ratio C-I (%) |
---|
Brzóza Królewska | 0.49 | 0.224 | 0.69 |
Ożanna | 0.28 | 1.006 | 0.79 |
Krempna-1 | 0.23 | 2.030 | 0.37 |
Krempna-2 | 0.26 | 2.030 | 0.35 |
Cierpisz | 0.19 | 0.393 | 0.28 |
Zesławice | 0.18 | 0.709 | 0.66 |
Głuchów | 0.14 | 0.567 | 0.13 |
Wapienica | 0.05 | 0.120 | 2.91 |
By applying Annandale’s method [
31], the longitudinal gradient dP/dx was determined for distances x given in meters. The values dP/dx calculated for Krempna-1 and Krempna-2 reservoirs are 0.23 and 0.26, respectively. Due to geometry unaltered by dredging and reconstruction, the value dP/dx for the reservoirs Zesławice-1 and Zesławice-2 equals 0.18. The dP/dx values for the remaining reservoirs are given in
Table 4, where the calculated mean annual runoff (Q) and capacity-inflow ratio (C-I) are also presented.
Capacity-inflow ratio of the examined reservoirs is less than 1%, except for Wapienica reservoir for which C-I is equal to 2.91 (
Table 4). However, mean annual silting ratio (S
R, M) of these reservoirs (
Table 3) is from 0.5% to 10.3%. Such silting ratios according to Hartung [
50] correspond to siltation rate of small reservoirs. Therefore, a small reservoir in the Upper Vistula basing can be defined as such that has the capacity-inflow ratio below 1%.
The forecast of sediment load distribution was prepared for eight examined reservoirs. In the case of the reservoirs Krempna-1 and Krempna-2, the course of sediment load distribution curve, defined by the calculations, is similar to the curve determined based on the measurements (
Table 5,
Figure 4). The sediment load accumulates in the near-dam zone of the Krempna reservoir, thus in accordance with the assumptions of Annandale’s method. Silting of the reservoir Brzóza Królewska proceeds in a similar way. Segments of the near-dam and central zones of these reservoirs are characterized by the highest relative silting, expressed by the silting ratio of each segment.
Table 5.
Comparison of the results of sediment distribution forecast in the reservoir Krempna-2 according to Annandale’s method [
31] (A. method) and results of silting measurements (measure.) in 1996.
Table 5.
Comparison of the results of sediment distribution forecast in the reservoir Krempna-2 according to Annandale’s method [31] (A. method) and results of silting measurements (measure.) in 1996.
Segment | L/LFSL | Σ(V/VFSL) | V/VFSL | Volume of Deposited Sediment (m3) |
---|
A. Method | Measure. |
---|
1 | 0.03 | 0.05 | 0.05 | 1,351 | 877 |
2 | 0.11 | 0.21 | 0.16 | 4,327 | 4,150 |
3 | 0.25 | 0.43 | 0.22 | 5,949 | 5,900 |
4 | 0.39 | 0.62 | 0.19 | 5,138 | 4,959 |
5 | 0.49 | 0.72 | 0.10 | 2,704 | 2,763 |
6 | 0.59 | 0.81 | 0.09 | 2,434 | 1,657 |
7 | 0.75 | 0.90 | 0.09 | 2,433 | 3,401 |
8 | 0.85 | 0.95 | 0.05 | 1,352 | 1,931 |
9 | 1.00 | 1.00 | 0.05 | 1,352 | 1,402 |
Sum | 1.00 | 27,040 | 27,040 |
Figure 4.
Sediment distribution in the reservoir Krempna-2 in 2000 determined according to measurements and Annandale’s method.
Figure 4.
Sediment distribution in the reservoir Krempna-2 in 2000 determined according to measurements and Annandale’s method.
The calculated amount of the deposited sediment load according to Annandale’s method is greater than the one measured in the segments closest to the dam. The further from the dam, the smaller the difference between the results becomes, amounting only to a few percent. The exemplary graph of sediment load distribution in 2000, calculated using Annandale’s method [
31] and determined according to the measurements, are presented in
Figure 4.
The sediment is deposited at the inlet rather than near the dam wall. Only in the case of two reservoirs, Krempna-2 and Brzóza Królewska, is the sediment deposited near the dam, just as predicted by the Annandale’s calculations. All other reservoirs used in this research have higher amounts of deposits located closer to their inlets. For this reason, the results of sediment distribution forecast in small reservoirs according to Annandale’s method [
31] do not correspond to the actual state. The examples are given below calculations of sediment load deposits in the reservoir Zesławice-1 in 1974 (
Table 6) and 1983 (
Figure 5). Segments at the inlet to the reservoir are characterized by the greatest relative silting, while according to calculations using Annandale’s method [
31], their relative silting will be significantly smaller.
Table 6.
Comparison of the results of sediment distribution forecast in the reservoir Zesławice according to Annandale’s method [
31] (A. method) and results of silting measurements (measure.) in 1974.
Table 6.
Comparison of the results of sediment distribution forecast in the reservoir Zesławice according to Annandale’s method [31] (A. method) and results of silting measurements (measure.) in 1974.
Segment | L/LFSL | Σ(V/VFSL) | V/VFSL | Volume of Deposited Sediment (m3) |
---|
A. Method | Measure. |
---|
1 | 0.02 | 0.03 | 0.03 | 2585 | 84 |
2 | 0.08 | 0.18 | 0.15 | 12,929 | 2,119 |
3 | 0.15 | 0.30 | 0.12 | 10,343 | 5,137 |
4 | 0.22 | 0.42 | 0.12 | 10,343 | 5,275 |
5 | 0.29 | 0.53 | 0.11 | 9,481 | 5,467 |
6 | 0.36 | 0.62 | 0.09 | 7,757 | 5,865 |
7 | 0.43 | 0.70 | 0.08 | 6,895 | 5,920 |
8 | 0.50 | 0.76 | 0.06 | 5,172 | 6,060 |
9 | 0.57 | 0.82 | 0.06 | 5,172 | 6,852 |
10 | 0.64 | 0.87 | 0.05 | 4,310 | 7,512 |
11 | 0.72 | 0.90 | 0.03 | 2,585 | 7,889 |
Sum | 1.00 | 86,190 | 86,190 |
Figure 5.
Sediment distribution in the reservoir Zesławice-1 in 1983 determined according to measurements and Annandale’s method [
31].
Figure 5.
Sediment distribution in the reservoir Zesławice-1 in 1983 determined according to measurements and Annandale’s method [
31].
Annandale [
31] developed the relationship presented in
Figure 1 for 11 reservoirs, whose silting degree ranged between 7.85% and 44.94%. This relationship was developed for the results of silting measurements of reservoirs with various silting ratios (S
R). Annandale did not consider the variability of sediment distribution in the reservoir depending on its silting ratio.
Figure 6a,b present the relative sediment load distribution in the reservoirs Krempna-2 and Zesławice, respectively. The sediment distribution curves change slightly with the increase in the silting ratio, which was observed in all examined reservoirs. In the reservoir, where the sediments are retained mainly in the middle and the inlet zone, these zones of the reservoir are characterized by increased relative volume of sediment load deposits. One example is the reservoir in Zesławice (
Figure 5a)—in the part of the reservoir from 0.35 to 0.8 of the relative distance from the dam there was a significant increase in sediment load deposits in 1983 (S
R = 50.9%), as compared to 1969 (S
R = 30.9%). In the reservoir Krempna-12, where the sediment load is accumulated according to the course of distribution curves presented by Annandale (
Figure 1),
i.e., its greatest volume is deposited in the near-dam zone of the reservoir, the relative volume of sediments accumulated in the near-dam and central zone decreased together with the increase of silting ratio. Within nine years there was a small reduction in relative volume of sediments in the section from 0.11 to 0.5 of the relative distance from the dam of the reservoir Krempna-2 (
Figure 6b) with the increase of silting degree from 24.2% to 40.9%. After analyzing these examples, it may be stated that the change in silting degree, even by about 20%, has a negligible impact on the sediment distribution curves in the reservoirs.
Figure 6.
Sediment distribution within water reservoirs: (a) Zesławice and (b) Krempna-2 in several years of operation.
Figure 6.
Sediment distribution within water reservoirs: (a) Zesławice and (b) Krempna-2 in several years of operation.
Dendy [
51] in his paper did not present the results of measurements of deposit volumes in different parts of the reservoirs. He only stated that “most of the sediment was deposited in the upstream end of the reservoirs near the elevation of the conservation pool. Proportion of the total sediment deposited in the sediment pool ranged from 30 to 100 percent.” Dendy [
45] presented the distribution of sediments on the graph of horizontal distribution of sediment deposits indicating that the sediment in these reservoirs is deposited mainly at the inlet to the reservoir, or at most proportionally to the ratio of the conservation pool volume upstream from a given location (V) to the total volume (V
t) of the conservation pool, designated as V/V
t. For two reservoirs, the horizontal distribution of sediment deposits developed by Dendy shows a proportional increase in the volume of sediment deposits to the increase in the value of V/V
t. This means that in some reservoirs, a significant portion of the sediment is deposited closer to the dam. Unfortunately, Dendy [
45] in his paper did not present the geometric characteristics of the reservoirs, which would allow verification of the proposed modification of the Annandale’s method.
3.3. Modification of the Annandale Method
A graph presenting the dependence between the sum of dimensionless sediment load volume Σ(V/V
FSL) as a function of relative distance from the dam L/L
FSL (
Figure 7) was developed based on the results of silting measurements of the examined small reservoirs.
Figure 7.
Sediment distribution within small reservoirs. The points were established according to a field survey for separated segments of examined reservoirs.
Figure 7.
Sediment distribution within small reservoirs. The points were established according to a field survey for separated segments of examined reservoirs.
According to Annandale [
31], the relationship between the dimensionless cumulative mass curves explaining sediment distribution as a function of dP/dx (
Figure 1) was verified through the identified limits. If dP/dx → 0, it corresponds with the situation where only a small disturbance exists in the channel. As Annandale reported [
31], under such circumstances the sediment will be deposited in the proximity of the disturbance with very little build-up in the upstream direction. The dimensionless cumulative curve will then have a shape as shown by curve A in
Figure 8a. As demonstrated by the analysis of the curves dP/dx on the graph developed by Annandale (
Figure 1), in such conditions the sediment is deposited by the dam. For dP/dx of 0.02 over 60% of sediment is deposited in the relative distance of 0.2 from the dam. On the other hand, when dP/dx → ∞, a condition similar to a river flowing into an ocean exists, and the major volume of sediment will be deposited in the vicinity of the river mouth (curve B in
Figure 8a). This is illustrated by the curve dP/dx with the value of 1.20 (
Figure 1)—the sediment will be relatively proportionally distributed over the entire length of the reservoir.
It means that in 11 reservoirs studied by Annadale, sediment is transported through the whole reservoir and deposited in segments near the dam wall. The higher the longitudinal gradient of the reservoir, the more even sediment distribution is over the reservoir segments. The study of the Upper Vistula reservoirs indicates that sediment is deposited evenly over the whole length of the reservoirs when longitudinal gradient reaches the value of
ca. 0.19 (see Cierpisz reservoir—
Figure 7). In small reservoirs of Upper Vistula, this situation is inverted compared to Annadale’s: the higher the longitudinal gradient, the more the sediment is deposited near the dam wall. The results obtained from the studies of small reservoirs located in the Upper Vistula basin indicate a different arrangement of curves dP/dx (
Figure 7) compared to the relationship given by Annandale (
Figure 1). In the case of the examined reservoirs, when dP/dx → 0, it corresponds to the situation when less sediment is deposited in the near-dam zone, while the predominant portion is deposited at the inlet to the reservoir (curve A in
Figure 8b). However, in conditions corresponding to the ratio dP/dx tending to infinity, the sediment is deposited near the dam wall (curve B in
Figure 8b).
Figure 8.
Extremes of dimensionless curves: (
a) according to Annandale [
31]; (
b) according to the results of experiments on small reservoirs located in the Upper Vistula basin.
Figure 8.
Extremes of dimensionless curves: (
a) according to Annandale [
31]; (
b) according to the results of experiments on small reservoirs located in the Upper Vistula basin.