Amplification of downstream flood stage due to damming of fine-grained rivers

Abstract

River dams provide many benefits, including flood control. However, due to constantly evolving channel morphology, downstream conveyance of floodwaters following dam closure is difficult to predict. Here, we test the hypothesis that the incised, enlarged channel downstream of dams provides enhanced water conveyance, using a case study from the lower Yellow River, China. We find that, although flood stage is lowered for small floods, counterintuitively, flood stage downstream of a dam can be amplified for moderate and large floods. This arises because bed incision is accompanied by sediment coarsening, which facilitates development of large dunes that increase flow resistance and reduce velocity relative to pre-dam conditions. Our findings indicate the underlying mechanism for such flood amplification may occur in >80% of fine-grained rivers, and suggest the need to reconsider flood control strategies in such rivers worldwide.

Fig. 1. Maps of the lower Yellow River (Huanghe), China, and trends in spatio-temporal evolution of bed material grain size.

a Map of the lower Yellow River; b Detailed view of box shown in (a) illustrating locations for sampling of thalweg bed material; c Cross-sectionally averaged bed material grain size, surveyed at the seven major gauging stations, over a 50-yr period (see locations in (a). Vertical dot-dashed line demarcates the time when the Xiaolangdi Dam became operative. Horizontal dashed line demarcates the upper bound of bed material (0.15 mm) under pre-damming conditions; d Bed material grain size for the thalweg of the upper reach of the LYR. The transition between the non-impacted and impacted reaches of the LYR (blue shading) is located between Jiaoyuan Floating Bridge and the Gaocun gauge station; red markers indicate where median grain-size drops below 0.15 mm.

Fig. 2. Relation between relative bedform (roughness) height and suspension number.

A comprehensive database (gray squares), including both laboratory and field data, is compiled to determine the hump-shaped relation (solid line) between relative bedform height and suspension number, where H_d is dune height [L], H is water depth [L], u* is shear velocity [LT⁻¹], and v_s is the sediment settling velocity [LT⁻¹]. Although such hump-shaped relations are well recognized^,,, a well-tested quantitative relation remains lacking heretofore. The proposed relation, based on a parabolic equation in logarithmic space, log₁₀Y = −0.87(log₁₀X − 0.03)² − 0.53, shows a good fit and covers a wide range of laboratory and field data. The comparison among the proposed relation, the compiled database and other relations are given in Supplementary Fig. S2. Field observations of bedform heights in the dam-impacted (blue squares) and non-impacted reach (red squares) of the lower Yellow River (LYR) agree with the proposed relation very well. The squares represent the mean value of relative bedform height and error bars represent one standard deviation. In particular, the observed data from the non-impacted reach of the LYR quantify a previously-untested region of the proposed relation. As shown in Supplementary Table S3, the difference in suspension number (and thus bedform geometry) in the impacted and non-impacted reaches results mainly from bed coarsening. The hump-shaped relation indicates that if the bankfull suspension number is greater than a suspension number corresponding with the dune-size maximum (~1.1 via present model; vertical blue dashed line), bed coarsening induced by damming on the river will result in larger dunes during floods. Dashes and dashed-dotted lines represent the 50% and 90% prediction intervals (PI) of the present model, respectively.

Fig. 3. Bedform geometry for the present-day Yellow River.

a Multibeam echosounder (MBES) map of periodic, high-relief dunes (L_d/H_d ~ 20 and $H_d/\overline{H}$ ~ 40.81% ± 12.72%, where L_d and H_d are wavelength and wave height of bedforms [m], respectively and $\overline{H}$ is the average water depth [m]). These bedforms are found in abundance at Huayuankou, just downstream of Xiaolangdi Dam (see Supplementary Fig. S3 and Supplementary Table S3); b Low-relief bedforms (L_d/H_d ~ 500–2000 and $H_d/\overline{H}$ ~ 5.51% ± 3.26%) near Lijin, where bed sediment size is not impacted by the XLD dam; c Longitudinal profiles through the bedforms from the two studied reaches derived from the MBES maps. H_b and ${\overline{H}}_b$ represent the bed elevation along the transect and average bed elevation of the survey area, respectively. The fine-grained channel of the non-impacted downstream reach is characterized by low-relief bedforms, while the channel bed of the dam-impacted reach possesses high-relief dunes typical of sand-bedded rivers. The presence of low-relief bedforms is the primary reason for a lower flow resistance.

Fig. 4. Adjustment of flow resistance coefficient C_f at the impacted reach of the Yellow River, before and after construction of the XLD dam, and its subsequent impact on flood-water depth.

a The average value of C_f in the post-damming bed roughness state is three times that for the typical pre-damming state at Huayuankou, the impacted reach of the Yellow River. Elements of the box-plot include: center line, mean value; box limits, upper and lower quartiles; whiskers, max and min values; b Relation between resistance coefficient and suspension number. The resistance coefficient at Huayuankou under pre- and post-damming conditions agrees well with the proposed hump-shaped relation, e.g., log₁₀Y = −1.75(log₁₀X + 0.066)² − 1.91; c Comparison of H-q_w relations at the impacted reach of the Yellow River before and after dam construction. The figure illustrates the theoretical relation H = (C_f/gS)^1/3q_w^2/3 with C_f values inferred in (a), and independent field data collected at Huayuankou, for both pre- and post- dam conditions. The blue solid line, using averaged post-damming C_f = 0.0046, shows H is 1.4 times greater than pre-damming; blue dashed line, using the maximum post-damming C_f = 0.01, illustrates H is 2.0 times greater than pre-damming. Comparison of H-q_w relations at the non-impacted reach of the Yellow River (Lijin) before and after dam construction is shown in Supplementary Fig. S4.

Fig. 5. Evaluation and comparison of the overall flood stage for pre-dam and post-dam conditions.

a Cross-sectional profiles for pre-dam and post-dam conditions at the Huayuankou gauging station; b Pre- and post- dam flood stage and flood discharge. The red solid line is the theoretical prediction for the pre-dam flood stage based on observed cross-sections and Eq. 1 with C_f from Fig. 4b (see Text “Hydraulic prediction for the flow stage based on observed cross-sections” in Methods), and the red shaded area indicates the 95% confidence interval of the prediction uncertainty induced by the pre-dam cross-section variation. The blue solid line is the theoretical prediction for the post-dam flood stage, with the blue shaded area indicating the 95% confidence interval of the prediction uncertainty induced by the post-dam cross-section variation. The pink solid line is the theoretical prediction for the post-dam flood stage based on the post-dam cross-sections (including considerations of channel widening and bed incision) without consideration of the stage amplification effect (grain size and bedform size unchanged). c Water stage elevation changes produced by various effects. The blue solid line represents the stage elevation change induced solely by channel incision (enlargement) without consideration of the stage amplification effect. The red solid line represents the stage amplification effect. The black solid line represents the net effect of stage amplification effect and channel enlargement effect (D₅₀ = 0.30 mm). The black lines from right to left (dash, solid, dot, dot-dash) represent D₅₀ = 0.25, 0.30, 0.35, 0.40 mm, respectively. Correspondingly, the crossing-point discharges, where post-dam stages surpass the pre-dam values, are 7571, 6099, 5469, and 5164 m³ s⁻¹, respectively. Coarser beds lead to a smaller crossing-point discharge. Dot-dash vertical lines represent the flood discharges at different recurrence intervals (5, 10², 10³, 10⁴ yr).

Fig. 6. Distribution of bankfull suspension numbers for fine-grained rivers worldwide.

The vertical blue solid line represents the suspension number corresponding to the maximum resistance coefficient/dune size, obtained in the present study. This shows that 82.8% of fine-grained rivers maintain a bankfull suspension number greater than 0.9, indicating that for the majority of fine-grained rivers worldwide, bed coarsening will enhance dune size and thus flow resistance, so as to amplify flood stage. The vertical red solid line represents the suspension number (3.0) corresponding to borderline of silt-sand-bedded rivers (32.5% of fine-grained rivers worldwide), such as the Yellow River, where a bed coarsening process can act far more quickly over a short time scale, indicating a quick and strong flood amplification effect. Arrows on the x-axis indicate pre- and post- damming conditions of the lower Yellow River.