Sand as a stable and sustainable resource for nourishing the Mississippi River delta

Transcription

1 SUPPLEMENTARY INFORMATION DOI: /NGEO14 Sand as a stable and sustainable resource for nourishing the Mississippi River delta Jeffrey A. Nittrouer and Enrica Viparelli Modeling methods This model is based on a customized version of RTe-bookAgDegBWChezy, an Excel workbook with embedded VBA code 1, to study riverbed degradation in response to a reduction in sand supply at the upstream end of the study reach. The model governing equations are: 1) a backwater formulation for flow hydraulics; ) the Engelund-Hansen equation for total sand load (suspended load plus bedload) ; and 3) a standard form of the Exner equation 3 of sediment continuity. Bed resistance is characterized by a specified dimensionless Chezy resistance coefficient 1. Response time to cutoff of sediment supply is studied in terms of a hypothetical, but nevertheless specifically relevant case. The reach is first assumed to be in equilibrium 4 : that is, a condition characterized by neither net channel bed erosion nor net channel bed deposition, using the present-day sand transport rate just upstream of the Old River Control Structure. The sediment supply at Cairo is then reduced to one-quarter of this ambient value at t = 0 yr, sediment transport is calculated for the ensuing years, and the bed is allowed to evolve over time. NATURE GEOSCIENCE 1

2 A 75% decrease in sand load at the upstream end of the modeled reach is chosen because studies of sediment load in the lower Mississippi River show that as a result of human influences and engineering works (i.e., dam construction, revetment structures, etc.) primarily in the Missouri River basin, which supplies one-half of the total Mississippi River sediment load the sediment load in the Lower Mississippi River basin (Cairo, IL, to Old River Control Structure, LA) has decreased by about 75% since pre-human modifications 5. Here we concern ourselves with only the response time associated with the change in sand supply, however since estimates of sand loads in the Lower Mississippi River prior to human modifications are not available, we assume that the 75% reduction in total sediment supply reflects the reduction in sand load as well. To simplify our calculations, additional assumptions are made as follows: 1) because the sand load at the downstream end of the model domain has not declined for at least the past 40 years (Fig. c manuscript), we use measured yearly values collected here to determine an initial equilibrium condition; ) the reduction in sediment supply is modeled with a step function so that the response of the system in short time scales (i.e., engineering time scales) should be faster than in the real case (hence, we model a conservative case); 3) we assume that the river is morphologically active during flood events, so that we may neglect periods of low flow in the calculations 1,6,7 ; 4) the flow duration curve is thus replaced by a bankfull flood flow 6 and in intermittency factor, I f, that represent the fraction of the year in which the river is in flood. Thus, the river is morphologically inactive for the time fraction (1-I f ) 1,8. In the numerical simulations discussed below I f = ,9.

3 To investigate the effects of a sudden drop in sand load at the upstream end of the studied reach of the lower Mississippi River, we assume that: 1) the bankfull discharge (Q) is reasonably approximated as a constant value equal to 35,000 m 3 s -1 in the studied reach 6,10 ; ) this value is not effected by engineering works; and 3) it also reasonably characterizes the lower Mississippi River flood regime over timescales of decades to centuries. These assumptions are substantiated by flow duration curves constructed from water-discharge data collected at Memphis, TN, and Tarbert Landing, MS (Supplementary Fig. 1), which cover a long series of daily flows (1933 to 1994 at Memphis, and 1930 to 013 at Tarbert Landing). Justification for the assumption of constant bankfull discharge for the entire model domain is based on the comparison between the flow duration curves from 1933 to 1994 (Supplementary Fig. 1a). When the entire record of data is considered, the flood flow with a probability of exceedance value of 0.01 is for all practical purposes equal to 35,000 m 3 s -1 at both of the stations. Furthermore, a comparison between pre and post 1960 s (i.e., pre and post dams on the Missouri River) is presented in Supplementary Figs. 1b and 1c (Memphis and Tarbert Landing, respectively), and these plots clearly show that there is no significant difference between the pre- and post-dam flow-duration curves. Finally, the comparison between post-dam flow-duration curves and the decadal flow-duration curves is presented in Supplementary Figs. 1d and 1e (Memphis and Tarbert Landing respectively), to confirm that there is not a significant change in flow regime within the model domain over the past 50 years. We assume a constant sand load of 39.6 Mt/yr between Cairo, IL, and Knox Landing, MS. This value is estimated by using the measured annual suspended sand flux value at Tarbert Landing ( Mt/yr), adding 5% to account for bedform sediment transport 9,11 (i.e., 7.5 Mt/yr 3

4 total), and adding 30% to this value to account for the sand diverted into the Atchafalaya River basin at the Old River Control Structure (as per standard USACE policy for distributing water and sediment at the Old River Control Structure 5 ). This calculated value is independently confirmed by measurements for sand-transport values of 41.1 Mt/yr at Vicksburg, MS, collected by the USGS and USACE 1. For our model, the equilibrium state 1 is characterized by a reach-average constant transport capacity of the river matched by the sand load, given a constant flow depth (H), bed slope (S), a bankfull width (B), water discharge per unit width (q w, where q w =Q B -1 ), and bed material load per unit width (q t ) in the streamwise direction x. We use present-day values measured for the lower Mississippi River including 13 : a cross-section-averaged bankfull depth of 0 m, a channel bed slope of 7x10-5, and a bankfull width of 1100 m (Table 1). Flow hydrodynamics at equilibrium are thus steady (constant in time) and uniform (constant in space), and are described by the normal flow equations of conservation of mass and streamwise momentum, Eqs. (1a) and (1b), respectively: q w = UH τ = ρghs (1a, b) b where U denotes the mean flow velocity, ρ is the density of the water, g represents the acceleration of gravity, and τ b is the bed shear stress, defined as: τ = () U b ρc f where C f denotes the non-dimensional friction coefficient 1, assumed constant in the present model and calibrated as discussed below. equation : Bed material load per unit channel width (q t ) is computed with the Engelund-Hansen q t τ b = β RgDD (3) C f ρrgd 4

5 where R represents the submerged specific gravity of the sediment, D denotes the characteristic diameter size of the bed material, and β is an adjustment factor of the load relation (discussed below). Given the bankfull discharge, Q, the equilibrium channel slope S, and the bankfull channel width and depth, B and H, substituting Eqs. (1a) and (1b) in Eq. () the friction coefficient, C f, is estimated as follows: 3 gsh C f =. (4) q w For this case, C f is equal to , which corresponds to a non-dimensional Chezy friction coefficient, C z, of 14.55, (where: C z = 1/(C f ) 0.5 ). This value, calculated based on measured values from the Mississippi River 13, is consistent with other large, low-slope sand-bed rivers 14. In the Engelund-Hansen equation (Eq. 3) the sand load is a function of the characteristic sand size diameter, D, which varies from ~0.6 mm at Cairo to ~0.3 mm at Knox Landing 15. At mobile bed equilibrium, however, the sand load per unit channel width must equal the mean annual sand load, i.e Mt/yr, divided by the bankfull channel width. The adjustment factor β is introduced to adapt the general form of the Engelund-Hansen equation to the modeled Mississippi River reach. A grain size of 0.45 mm results in an adjustment factor of 0.64; the corresponding adjustment factors for 0.3 mm and 0.6 mm sand are 0.43 and 0.85, respectively. The numerical simulations are performed with an upstream sediment boundary condition corresponding to a sudden reduction of sediment supply at Cairo to one-fourth of the ambient value, i.e. 10 Mt/yr. At the downstream end of the modeled reach, the initial bed elevation is set equal to 0, because this location approximately corresponds to where the channel bed elevation drops below mean sea level. Water surface elevation at Knox Landing is held equal to the sum of the initial bed elevation and the ambient bankfull depth throughout the run. Backwater effects 5

6 from farther downstream are not considered because the objective is to study the downstream affects due to a reduction of sediment supply at Cairo. A standard one-dimensional Exner equation 3 conserves mass to calculate the change in channel bed elevation ( η) based on the spatial divergence in calculated sediment flux ( q t ), where the spatial step ( x) is 6800 m (the approximate downstream length of a Lower Mississippi River reach segment): ( λ ) η qt 1 p = (5) t x and where λ p denotes the bed porosity (assumed to be 0.40), and t is the temporal interval (0.1 yr). In order to evaluate output sensitivity, we test the model using a reasonable (natural) range for the input variables, which include bankfull water discharge, Q (5,000-50,000 m 3 s -1 ); bankfull channel width and depth, B ( m) and H (15-5 m), respectively; and grain diameter, D ( mm). These input variables also change the calculated Chezy friction coefficients, C z, and β adjustment factors (Table 1). As shown in Table 1, after 600 years, the model produces minimum (35.6 Mt/yr) and maximum (8.9 Mt/yr) values for total sand load reduction at Knox Landing (i.e., the head of the Mississippi River delta), which are equal to 10% and 7% of the initial sand load, respectively. Alternatively, calculating the minimum and maximum time to reach a sand load value of 3.9 Mt/yr at the delta (i.e., a 17% reduction, and equal to the value calculated for the base input variables) produces times of 410 and 800 years, respectively. Therefore, even when calculating minimum and maximum years for a reduced sand load to reach the head of the Mississippi River delta, the model consistently produces time scales of multiple centuries. We argue that, because the model is robust in simplifications and errors, the results are inescapable: sand load delivered to the Mississippi River delta has yet to 6

7 decrease and likely will not decrease of the next several centuries, as a result of dams placed many thousands of kilometers upstream of the delta. We emphasize that the novel result of this model is not necessarily in its ability to precisely calculate timing and magnitude for sand load reduction to the delta, but is that the timescale for the dams influence on sand load is on the order of multiple centuries. Indeed, this time scale is far longer than has been suggested by any studies to date. Methods for calculating suspended-sediment loads Suspended-sediment loads are calculated at Thebes, IL, and Tarbert Landing, MS, based on water discharge and sediment concentration data collected by the United States Geological Survey (USGS, survey station ID: and , respectively). At both locations, we focus on the suspended-sediment data that partition sand (>6.5 µm grain size) and mud (<6.5 µm) as a fraction of the overall sample (determined by sample sieving), and this detail of record keeping initiated in Suspended-sediment concentration measurements, reported as mg L -1, are converted to daily suspended-sediment discharge (T day -1 ) as per conventional USGS methods that use the daily water discharge (m 3 s -1 ) measured for the same day as when the sediment sample was collected. While water discharge is measured daily, sediment-concentration measurements are much more limited, and are typically collected times per year. To calculate sediment flux over a time duration of interest (e.g., annual sediment flux), water discharge versus sediment discharge data are plotted and used to develop a sediment rating curve, whereby a regression function is fit to the data (typically a power function, to minimize the residuals). Measured water discharges are then used with the regression function to calculate sediment flux, and these calculations are 7

8 summed over the time duration of interest to produce total sediment flux. Sediment rating curves are produced for both sand and mud fractions. For the Mississippi River, yearly sediment concentration measurements are too sparse to produce reliable yearly sediment rating curves; therefore, we combine the data over four decadal intervals: ; ; ; , and construct sediment rating curves for each decade (n = 74, 84, 66, 175, respectively). Binning the yearly data by decades has the added advantage of minimizing interannual variability that arises due to changing hydrodynamic conditions, such as prolonged droughts or periods of intense rainfall (i.e., floods) that typically last for 1-3 years, while still producing meaningful average-annual values over decadal periods. For example, the regression trends for the decadal data, shown in Fig., closely match those for the yearly data, shown in SI Figs. and 3. Flow duration curves are generated for each decade, by binning all daily discharge measurements (1500 m 3 s -1 bins) within the decade and then calculating the frequency of occurrence for each discharge bin within the respective decadal period. The water-discharge value of the bin is combined with the respective decadal sand and mud rating-curve regression functions to produce sand and mud loads, and this value is multiplied by the bin s respective frequency of occurrence. Sand and mud loads for each bin are then summed, and the resulting value is converted to annual sand and mud for each decadal interval (Fig., manuscript). Total load is produced by summing the mud and sand load calculations. To calculate yearly values of sand and mud loads (Supplementary Figs. and 3), daily discharges for every year are used with the respective decadal interval regression functions. These daily sediment-load (mud and sand) values are summed within each year to produce yearly sand and mud loads; the sum of yearly sand and mud loads yields yearly total load. The 8

9 high and low yearly values calculated for each decadal interval are used to establish the range bars for the mean annual sediment loads (Fig., manuscript). As a point of comparison between the methods used to calculate yearly sediment loads and the method used to calculate mean yearly sediment load for each decadal interval (detailed above), the average of yearly sediment load values (sand and mud) within each decadal interval match the mean yearly decadal values to within 10%. Thus, the two methods produce consistent values of yearly sediment load. Statistical methods for evaluating sand load at Tarbert Landing 16 Here we show that within a confidence of 95%, sand load at Tarbert Landing is constant over the period of observation The 38 estimates of annual sand load, Q s, at Tarbert Landing (data from 1973 to 011, with a data point missing for 1978) represent a sample of the population of annual sand loads at that gaging station. The population of annual sand loads at a station can be considered to be composed of the infinite values that the annual sand load has attained in the past and can attain in the future. Since the population is infinite, its composition and its cumulative probability function, P{Q s }, do not change from one sample of size n to the other. Consequently, cumulative probability functions estimated from different samples, F{Q s }, should all reproduce the cumulative probability function of the population with an accuracy that depends on the size of the samples, such that the accuracy increases with the dimension of the samples. The differences between the results for F{Q s } are largest for the tails of the distributions, i.e. where the probability density values are smallest. In the analysis presented below, a) the cumulative frequencies F i of each data point are estimated as 9

10 (6) where i denotes the order of the data point in the sample, ordered from smallest to highest value, and n is the dimension of the sample, i.e. 38, or as (7) when the sample is divided in a number K of classes bounded by the values Q sb,j-1 and Q sb,j with Q sb,j = Q sb,j-1 + Q s, with ν i denoting the number of data in the i-th class; b) when the sample is divided in K classes, the frequency of each class, f j, is estimated as (8) c) the estimated mean of the population, Q s,av, is (9) where Q s,i denotes the generic data point in the sample. d) the estimated standard deviation of the population, S Qs, is (10) where n is the number of elements in the sample, equal to 38. First hypothesis: the annual sand load at a station is normally distributed The annual sand load at a station is the sum of increments that are functions of a large number of factors and events. We can thus assume that each increment of the annual sand load from x i-1 to x i during a hydrologic year is largely independent of the value x i-1 attained by the 10

11 beginning of the i-th incremental event. In other words, we assume that the annual sand load at a station is normally distributed. For the record at Tarbert Landing, this hypothesis is tested by means of displaying the data in the normal probabilistic charts represented in Figures 4-6 below. In Figures 4-6, the continuous line represents the normal distribution, and the dashed lines denote the 95% confidence interval for the central part of the distribution, i.e. for 0.15 < P{Q s } < Our hypothesis should not be accepted if more than 1 point out of every 0 happens to be outside the confidence interval. In Figure 4, the entire sample is represented in normal probabilistic chart format. In Figures 5a and 5b, samples representing the and the periods are plotted in the normal probabilistic chart format. Finally, in Figures 6a, 6b, 6c, and 6d samples representing the time intervals ; ; ; are similarly analyzed. Figures 4-6 show that the hypothesis that the annual sand load at Tarbert Landing is normally distributed can be accepted with 95% confidence. In particular, Figures 4 and 5 show that for samples of size n = 19 and n = 38, the normal distribution reasonably approximates the distribution of the annual sand load. However, the analysis of the smaller samples reported in Figure 6 clearly shows that although the samples are within the 95% confidence interval, the normal distribution does not always reasonably represent the distribution of the subsamples (Figures 6b, 6c, and 6d). On the one hand, this can be attributed to the small subsample sizes (9 and 10 elements only), or it can be an indication that there has been some significant change in the annual sand load at Tarbert Landing in the period of observation. 11

12 To further test the hypothesis that the population can be reasonably described with a normal distribution with mean value Q s,av = 7 Mt/yr and standard deviation S Qs = 15 Mt/yr estimated with equations (4) and (5), we perform a χ test. Here χ is defined as (11) where K is the number of classes in which the sample is divided, f j is the frequency of each class estimated with equation (8). p j is the probability density of the generic class j for the normal distribution with mean Q s,av and standard deviation S QS, and the degrees of freedom, df, of the distribution are K-1. The hypothesis that the annual suspended annual sand load at a station is normally distributed is accepted if χ χ 0.95, where 0.95 is the relevant probability: (1) The χ test for K = 7 and K = 1 is reported in Tables and 3 In both the tests χ is smaller than the 95 th percentile of the distribution. Thus we can confidently accept the hypothesis that the annual suspended sand load is normally distributed. Test of the null hypothesis: sand load at Tarbert Landing is not changing in time We test the null hypothesis the data at Tarbert Landing are all from the same population, which is not changing in time in three different ways. We first perform a test on the deviation within the sample, we then perform a test on the estimates of the coefficient of variation, and finally we test the estimates of the variance for different sample dimensions (i.e. the samples of Figures 5 and 6). 1

13 If the samples of Figures 5 and 6 are samples from the same population, i.e. if the annual suspended sand load at Tarbert Landing is not changing in time, the χ computed with equation (11) should be smaller than χ The difference between this test and the test performed above is that this time we do not assume a normal distribution for the population, because we want to test the hypothesis that the annual sand load at Tarbert Landing is not changing in time regardless of its distribution. We thus compare the frequencies of each class estimated in the same way as for each sample k, as f j,k =ν j,k /n k - equation (8) - with the frequencies of the sample, f av,j, defined as (13) where N is the number of samples, n k is the number of data in each sample, and ν j,k is the number of data in the generic class j of the k-th sample. Equation (11) is thus rewritten as (14) The results of the χ tests on the samples of Figures 5 and 6 are reported in Tables 4 and 5. In the tests of Tables 4 and 5 the χ is always smaller than χ 0.95; thus our null hypothesis can be accepted at 95% confidence level. Since the distribution of the annual suspended sand load at Tarbert Landing can be reasonably approximated as normal, the null hypothesis is further tested with the distributions of the estimated coefficient of variation and variance from the samples of Figures 5 and 6. When the distribution can be approximated as normal, the estimated coefficients of variation, g nqs, are functions of the coefficient of variation of the population, γ, estimated from the entire sample (γ = 0.6), and the size of the sample n: 13

14 (15) where u p is the value of the argument of the standard normal distribution for the probability P of acceptance of the test, and df = degree of freedom = n -1. The test of the null hypothesis is represented in Figure 7 at a confidence level of 95%. The confidence intervals for the coefficient of variation are represented with different colors depending on the size of the samples, i.e. n = 38 (the population), n = 19, n = 10 and n = 9. In Figure 7, the points corresponding to the six samples of Figures 5 and 6 are well within the confidence interval for the variation of the estimated coefficients of variation, further confirming that the null hypothesis cannot be rejected at a 95% confidence level. Finally, when the population is reasonably approximated by a normal distribution, the distribution of the ratio between the estimated variance of the population, s Qsk, and the variance of the population, s Qs corresponds to χ /df, with df = n-1. The points representing the whole population (n = 38) and the samples of Figures 5 and 6 are represented at the 95% confidence interval in Figure 8. All the sample points in Figure 8 are well within the 95% confidence interval, further confirming that we can accept the null hypothesis. We can thus conclude that the hypothesis that the annual suspended sand load at Tarbert Landing is constant in time can be accepted with 95% confidence. 14

15 References, Supplementary Information 1: Parker, G. 1D Sediment Transport Morphodynamics with applications To Rivers and Turbidity Currents. This is an e-book with PowerPoint presentations, Excel worksheets with embedded working programs in Visual Basic for Applications, Word files with extended explanation and video clips. (004). : Engelund, F. and Hansen, E. A monograph on sediment transport in alluvial streams. Technisk Vorlag, Copenhagen, Denmark, (1967). 3: Paola, C., and Voller, V.R. A generalized Exner equation for sediment mass balance. Journal of Geophysical Research 110, (005). F04014, doi:10.109/004jf : Fisk, H.N. Geological Investigation of the Alluvial Valley of the Lower Mississippi River conducted for the Mississippi River Commission, Vicksburg Mississippi, U.S. Army Corps of Engineers, Mississippi River Commission, 78 p, (1944). 5: Meade, R. H and Moody, J. A. Causes for the decline of suspended-sediment discharge in the Mississippi River system, Hydrological Processes 4, 35-49, (010). 6: Wright, S., and Parker, G. Modeling downstream fining in sand-bed rivers. I: formulation, J. Hydraulic Res., 43(6), , (005). 15

16 7: Paola, C., Heller, P. L. and Angevine, C. L. The large-scale dynamics of grain-size variation in alluvial basins. I: Theory. Basin Research 4, 73-90, (199). 8: Kim, W., Mohrig, D., Twilley, R., Paola, C., and Parker, G. Is it feasible to build new land in the Mississippi River Delta? Eos Transactions AGU 90, , (009). 9: Nittrouer, J. A., Mohrig, D., & Allison, M.A. Punctuated sand transport in the lowermost Mississippi River. Journal of Geophysical Research Earth Surface, 116, (011). 10: Copeland, R.R., Biedenharn, D.S., and Fischenich, J.C. Channel Forming Discharge. US Army Corps of Engineers Report ERDC/CHL CHETN-VIII-5, 10 p, (000). 11: Nittrouer, J. A., Allison, M. A., & Campanella, R. Bedform transport rates for the lowermost Mississippi River. Journal of Geophysical Research Earth Surface, 113, (008). 1: Thorne, C., Harmar, O., Watson, C., Clifford, N., Biedenharn, D., Measures, R. Current and historical sediment loads in the lower Mississippi River. Final Report to the United States Army European Research Office, London, England; Contract Number: 1106-EN-01, (008). 13: Nittrouer, J. A., Shaw, J., Lamb, M. P., and Mohrig, D. Spatial and temporal trends for water-flow velocity and bed-material sediment transport in the lower Mississippi River. Geological Society of America Bulletin 14, , (01). 16

17 14: Wilkerson, G. V. and Parker, G. Physical basis for quasi-universal relations describing bankfull hydraulic geometry of sand-bed rivers. Journal of Hydraulic Engineering, 137(7), , (011). 15: Nordin, C.F., Queen, B.S. Particle Size Distributions of Bed Sediments along the Thalweg of the Mississippi River, Cairo, Illinois to Head of Passes, September U.S. Army Corps of Engineers Lower Mississippi Valley Division Office, Vicksburg, MS, (199). 16: Viparelli, C., Idrologia applicata all ingegneria. Parte I, Quaderno 1, Fondazione Politecnica per il Mezzogiorno d Italia, Napoli,(1964). Supplementary Figure Captions Supplementary Figure 1: Flow-duration curves. a, Flow-duration curve for Memphis and Tarbert Landing, based on data collected over the respective duration. b, Flow-duration curves for Memphis ( ), pre-dam installment ( ), and post-dam installment ( ). c, Flow-duration curves for Tarbert Landing ( ), pre-dam installment ( ), and post-dam installment ( ). d, e, Flow-duration curves for Memphis and Tarbert Landing (respectively) for decadal increments. Supplementary Figure : Mean annual sediment-transport measurements, Thebes. a, Total sediment load. b, mud load. c, Sand load. All three demonstrate a decreasing trend. 17

18 Supplementary Figure 3: Mean annual sediment-transport measurements, Tarbert Landing. a, Total sediment load. b, mud load. c, Sand load. While total and mud loads decline, sand load shows an increase over the time period of measurement. It is seen from Figure c, however, that when the lowest of the four decadal averages is excluded, Tarbert Landing reveals a sand load that is essentially constant. Supplementary Figure 4: Normal probabilistic chart for the sample. 38 elements, and no data for Supplementary Figure 5: Normal probabilistic charts. a, sample, 19 elements. b, sample, 19 elements. Supplementary Figure 6: Normal probabilistic charts. a, sample, 9 elements. b, the sample, 10 elements. c, sample, 10 elements. d, sample, 9 elements. Supplementary Figure 7: Test of the null hypothesis in terms of coefficient of variation with a confidence interval at 95%. The points and the intervals are representative of the population (n= 38) and of the samples with 19, 10 and 9 data points. Supplementary Figure 8: Test of the variance with a confidence interval at 95%. The points are representative of the population (n= 38) and of the samples with 19, 10 and 9 data points. 18

19 Supplementary Table 1: Model sensitivity analysis. Model runs, input variables, respective reductions in sand load after 600 years, and time in years to reduce load by 17% of the initial (modern) sand load measured at Tarbert Landing. Supplementary Table : χ test for K = 7 classes. Supplementary Table 3: χ test for K = 1 classes. Supplementary Table 4: χ test for K = 7 classes for the samples and the samples. Supplementary Table 5: χ test for K = 7 classes for the , , , and samples. 19

20 Supplementary Figure 1 a Flow discharge (m 3 s -1 ) 100,000 35,000 10,000 1, Memphis Tarbert Landing b c d Flow discharge (m 3 s -1 ) Flow discharge (m 3 s -1 ) Flow discharge (m 3 s -1 ) 100,000 35,000 10,000 1, ,000 35,000 10,000 1, ,000 35,000 10,000 Memphis Tarbert Landing Memphis s 1970s 1980s 1, e Flow discharge (m 3 s -1 ) 100,000 35,000 10,000 1, Probability of exceedance Tarbert Landing s 1970s 1980s 1990s 000s

21 Supplementary Figure Thebes, yearly sediment load, (A) (B) Mean annual total load (Mt/yr) Mean annual mud load (Mt/yr) y=-0.98x y=-0.59x (C) Mean annual sand load (Mt/yr) y=-0.38x

22 Supplementary Figure 3 Tarbert Landing, yearly sediment load, (A) (B) (B) Mean annual total load (Mt/yr) Mean annual mud load (Mt/yr) Mean annual sand load (Mt/yr) y=-0.53x+1169 y=-0.8x y=0.9x

23 Supplementary Figure P{Q s } Q s (Mt/yr)

24 Supplementary Figure a) P{Q s } b) P {Q s } Q s (Mt/yr) Q s (Mt/yr)

25 Supplementary Figure a) P{Q s } c) P{Q s } Q s (Mt/yr) b) P{Q s } d) P{Q s } Q s (Mt/yr) Q s (Mt/yr) Q s (Mt/yr)

26 Supplementary Figure s Qsk / s Qs df = n-1 sample n = 38 sample n = 19 sample n = 10 sample n = 9

27 Supplementary Figure g nqs n=38 n=10 n=9 n=19 sample n = 38 sample n =19 sample n = 10 sample n = 9

28 Supplementary Table 1: Input values used for model sensitivity analysis. *KL is Knox Landing, the downstream end of the model domain. Run Q (m 3 s -1 ) H (m) B (m) D (mm) Cz β sand load reduction, (total sand load), KL* after 600 yrs years to reach 17% reduction in sand load base %, (3.9 Mt/yr) %, (3.9 Mt/yr) %, (3.9 Mt/yr) %, (3.0 Mt/yr) %, (33.9 Mt/yr) %, (8.9 Mt/yr) %, (35.6 Mt/yr) %, (3.9 Mt/yr) %, (3.9 Mt/yr) 600

29 Supplementary Table : test for K = 7 classes. K 7 df 6 n 38 Classes j f j p j Q s < < Q s < < Q s < < Q s < < Q s < < Q s < < Q s

30 Supplementary Table 3: test for K = 1 classes. K 1 df 11 n 38 Classes j f j p j Q s < < Q s < < Q s < < Q s < < Q s < < Q s < < Q s < < Q s < < Q s < < Q s < < Q s < < Q s

31 Supplementary Table 4: samples. test for K = 7 classes for the samples and the K 7 df n k 19 n k 19 Classes j,k f j,k j,k f j,k f av,j Q s < < Q s < < Q s < < Q s < < Q s < < Q s < < Q s

32 Supplementary Table 5: test for K = 7 classes for the , , , and samples." K 7 df n k 9 n k 10 n k 10 n k 9 Classes j,k f j,k j,k f j,k j,k f j,k j,k f j,k f av,j Q s < < Q s < < Q s < < Q s < < Q s < < Q s < < Q s