Physical controls and a priori estimation of raising land surface elevation across the southwestern Bangladesh delta using Tidal River Management

The Ganges-Brahmaputra-Meghna delta in Bangladesh is one of the largest and most populated deltas in the world and threatened by relative sea level rise (RSLR). Renewed sediment deposition through tidal river management (TRM), a 10 controlled flooding with dike breach, inside the lowest parts of the delta polders (so-called 'beels') can potentially counterbalance RSLR. The potential of TRM application in different beels across southwestern Bangladesh, however, still remains to be determined. We used a 2D morphodynamic model to explore the physical controls of five variables on total sediment deposition inside the beels during TRM: river tidal range (TR), river suspended sediment concentration (SSC), inundation depth (ID), width of the inlet (IW) and surface area of the beel (BA). Non-linear regression models (NLMs) were 15 developed using the results of 2D models to quantify how sediment deposition inside the beels depends on these variables. The NLMs have an average coefficient of determination of 0.74 to 0.77. Application of the NLMs to 234 beels of southwestern Bangladesh indicates that TRM operation in beels located closer to the sea will retain more sediment as a result of decreasing SSC further inland. Beels in the western part retain more sediment because of lower average land surface elevation. Smaller beels have higher potential to raise land surface elevation due to nonlinear increase of sediment deposition 20 per day (SPD) with beel area. Compartmentalization of larger beels may increase their potential to raise land surface elevation. Thus, the length of time of TRM application in cyclic order will need to vary across the delta to counterbalance RSLR, depending on current beel land surface elevation and local TRM sediment accumulation rates. We found that operating TRM only during the monsoon season is sufficient to raise land surface in 96% and 80% of all beels by more than 3 and 5 times the yearly RSLR, respectively. Applying TRM only seasonally offers huge advantages as to keeping the land 25 available for agriculture during the rest of the year. The methodology presented here applying regression models based on 2D morphodynamic modeling may be used for the low-lying sinking deltas around the world to provide an a-priori estimation of sediment deposition from controlled flooding to counterbalance RSLR. https://doi.org/10.5194/hess-2021-300 Preprint. Discussion started: 29 June 2021 c © Author(s) 2021. CC BY 4.0 License.


Introduction
Bangladesh contains one of the largest and most populated deltas in the world (Darby et al., 2015). The coastal areas of 30 Bangladesh are low-lying and flat: 62% of the coastal zone lies less than 3 m above mean sea level (AMSL) (Mohal et al., 2007). Sea level rise (SLR) is an imminent threat to the livelihood of millions of people and Bangladesh can lose one fourth of its livable land due to flooding (Ericson et al., 2006). Sea level projections for the year 2050 indicate a rise by 0.17-0.32 m under the RCP 2.6 scenario and 0.23-0.40 m for the RCP 8.5 scenario (Oppenheimer et al., 2019). Goodwin et al. (2018) analyzed the effect of the Adjusting Mitigation Pathway (AMP) on global warming and SLR in the future and projected that 35 the sea level rise can be 0.21 m by 2050 for the AMP4.5 scenario. The average rate of land subsidence for the Ganges-Brahmaputra-Meghna (GBM) delta is 2-3 mm/year (Krien et al., 2019). This increases the vulnerability of the low-lying delta to SLR (Brown et al., 2018). Therefore, the rate of relative SLR (RSLR) for the GBM delta can range from 7.6 mm/year for AMP4.5 to 10 mm/year for RCP8.5 in 2050.
To protect the low-elevation coastal zone from tidal flooding and to increase food productivity, polders with earthen dikes 40 were constructed in the 1960s and 1970s (Van Staveren et al., 2017). Initially, these polders increased food production (Nowreen et al., 2014). However, the rivers in the GBM delta carry more than a billion tons of sediment per year (Islam et al., 1999) and the constructed polder dikes interrupted the sediment flow from the tidal rivers to the former floodplain. This obstruction of sediment flow to the floodplains in combination with reduction of water flow from upstream areas due to anthropogenic changes silted-up the rivers. Sediments are now deposited in the river channel itself leading to bed levels 45 being higher than the low elevation areas inside the polders. This causes drainage congestion inside those polders especially during the monsoon season with intense rainfall and high water levels in the rivers. Moreover, being starved from the yearly inflow of sediment, the land surface elevation of the polders decreased by as much as 1.5 m due to compaction, whereas the elevation of the nearby unprotected and regularly flooded Sundarbans mangrove forest remained unchanged (Auerbach et al., 2015). 50 within polders through sedimentation inside the polders (Shanmpa and Pramanik, 2012;Gain et al., 2017). Tidal river management (TRM) has been applied to several polders by the Bangladesh Water Development Board (BWDB) since the late 1990's (Van Staveren et al., 2017).
Sediment deposition inside a beel through TRM is determined by its surface area, inlet width and lay-out, as demonstrated 65 by Gain et al. (2017) who evaluated previous TRM operation in Bhaina Beel, Khuksia Beel and Pakhimara Beel.
Furthermore, deposition patterns within the beels showed large spatial differences (Amir and Khan, 2019). Satellite image analyses and field surveys indicated that sediment deposition is larger close to the inlet of Pakhimara Beel, while one third of the beel situated farthest from the inlet hardly experienced any sedimentation (Islam et al., 2020). Uneven sedimentation inside Bhaina resulted in water logging in some parts of the beel after TRM was implemented (Gain et al., 2017). An 70 additional inlet was introduced through dike breach of the Khuksia Beel, which increased the spatial uniformity of sedimentation inside the beel (Van Minnen, 2013). Amir and Khan (2019) proposed to achieve a more equal sedimentation over a beel through compartmentalization, thereby first feeding the more distal parts of a beel. Through stepwise removal of embankments along the feeding canal inside the beel towards the compartment near the inlet, sufficient sediment deposition can be achieved over the entire beel over a period of 4 years. However, this compartmentalization likely requires large 75 investments and an adequate regulation scheme. Islam et al. (2020) demonstrated how regulation of flow into a beel combined with multiple inlets connecting different river channels may increase the rate of sedimentation and enhance spatial uniformity of sediment distribution. Finally, Talchabhadel et al. (2018) suggested multiple inlets for effective utilization of Khuksia Beel and inferred that the tidal basin size should be limited depending on tidal prism. These studies indicate that a better understanding of the physical controls of TRM sediment dynamics inside the beel is needed for effective and efficient 80 TRM operation.
The boundary conditions provided by the river channel to which a beel is connected are major, external factors for deposition (e.g., Talchabhadel et al. (2017;Islam et al., 2020Islam et al., , 2021. The river flow, flood stage, tidal range, inundation depth of a beel and suspended sediment concentrations in the feeding tidal channels together determine the amount of suspended matter that can enter and settle inside the beel. Since these external boundary conditions may vary across the southwestern (SW) 85 Ganges-Brahmaputra delta in Bangladesh, these may result in considerable regional variation in potential success of TRM application. Islam et al. (2021) explored the applicability of TRM in southwestern Bangladesh for different river flow regimes. The tidal-dominated river zone near the sea in the south and the mixed tidal-river flow regime about 60 km inland were found to be most suitable for raising land level with TRM. Adnan et al. (2020) determined the effect of geomorphological variables on sediment deposition for 234 beels in the 90 southwestern region of Bangladesh. They selected 14 flood conditioning factors to derive a flood susceptibility map and identified through regression analysis five predictive geomorphological variables for sediment deposition inside a beel, which are: land elevation, distance from the canal, topographic wetness index, topographic slope and curvature of the land. Although their regression model had a coefficient of determination (R 2 ) of 0.88, it remarkably did not include tidal range (TR), suspended sediment concentration (SSC) and surface area of the beel. Tidal range (TR) and SSC vary seasonally and spatially and directly affect the amount of sediment delivered and deposited inside the beel (Islam et al., 2020). Another problem of this regression is its linear character and the positive residual, suggesting sediment deposition under conditions of zero value for all variables.
To evaluate how TRM may help to raise the land in polders in southwestern Bangladesh, a quantitative understanding is needed on how different boundary conditions and beel lay-outs determine sediment deposition, and how these vary across 100 the SW Ganges delta. In this study we aim to determine the effect of physical controls related to the hydrodynamics of the river and how geo-morphodynamics of beels control the sediment deposition in those beels using TRM. We hereby evaluate the potential of the beels in the southwestern region of Bangladesh to raise land surface elevation through sediment deposition using TRM to counterbalance yearly RSLR. We explore the effect of five parameters on the total sediment deposition inside a beel using a calibrated 2D hydro-morphodynamic model: river tidal range (TR), river suspended 105 sediment concentration (SSC) are the two physical controls related to hydrodynamics of the river, inundation depth (ID), the width of the inlet (IW) and the surface area of the beel (retention basin, BA) are the three physical controls related to geomorphodynamics of the beel. Through multiple-regression analysis we correlate beel characteristics and boundary conditions to total sediment deposition as calculated by the hydro-morphodynamic model, and subsequently apply the regression model obtained to the 234 beels identified by Adnan et al. (2020) to produce a priori assessment of the potential of raising the land 110 surface elevation in beels inside the polders across the southwestern Bangladesh delta using Tidal River Management.

Study area
The southwestern GBM delta of Bangladesh is a 41,900 km 2 large delta plain bounded by the Ganges and Padma Rivers in 115 the north, the Meghna River in the east, the Bay of Bengal in the south, and the international border between Bangladesh and India in the west (Fig. 1). The southwestern region comprises 64 polders, located in the southern part of the study area ( Fig.   1). The average land elevation of the polders of the southwestern delta obtained from the Coastal DEM (Kulp and Strauss, 2018) is 0.58 m AMSL and 45% of the areas within polders are below 1 m AMSL. The average land elevation of polders of southwestern GBM delta located east of Pasur River ( Fig. 1) is about 0.62 m higher than the polders located in the west. 120 https://doi.org/10.5194/hess-2021-300 Preprint. Discussion started: 29 June 2021 c Author(s) 2021. CC BY 4.0 License.

General approach
The approach to evaluate the potential of raising land surface elevation of the beels in southwestern Bangladesh by sedimentation through controlled flooding is presented in Fig. 2 and described in the following sections.

Beel template for 2D hydro-morphodynamic model simulations
To estimate total sediment deposition in beels resulting from TRM operation, we used a two-dimensional (2D) hydromorphodynamic numerical model that was implemented and calibrated for Pakhimara Beel by Islam et al. (2020) as a reference. Tidal river management (TRM) has been operational since 2015 in Pakhimara Beel and monitoring data on water 130 level, discharge and suspended sediment concentration have been collected by Institute of Water Modelling (IWM) (IWM, 2017), which makes it an appropriate reference situation (cf. Islam et al. 2020). Here, this model was used as a template for beels across southwestern Bangladesh by adapting the surface area of the beel and the boundary conditions to different local conditions that occur within the SW delta. The area of Pakhimara Beel is about 700 ha, which is comparable to the average surface area of the beel (656 ha) as described by Adnan et al. (2020). Model simulations were carried out using Mike 21FM 135 in which hydrodynamic processes and sediment transport are simulated dynamically to account for hydro-morphological interactions (DHI, 2012a). The three-dimensional incompressible Reynolds-averaged Navier-Stokes equations are solved by https://doi.org/10.5194/hess-2021-300 Preprint. Discussion started: 29 June 2021 c Author(s) 2021. CC BY 4.0 License.
Mike 21FM (DHI, 2012a). The tool uses an approximate Riemann solver to calculate the convective fluxes at the interface of the cells of the 2D mesh (DHI, 2012a). The MT module uses the advection-dispersion equation (ADE). The ADE is solved using the third-order finite difference scheme, known as the ULTIMATE scheme, which is based on the QUICKEST scheme 140 (DHI, 2012b). For morphological simulation, the bathymetry is updated for each time step according to net sedimentation (DHI, 2012b).
To represent the bathymetry of Pakhimara Beel, a flexible cell size was used. A finer mesh was opted to represent the canal inside the beel, and a coarser mesh was used for the flood plain to reduce calculation costs (Islam et al., 2020). The surface area of the mesh cells varied from 170.5 m 2 to 5000 m 2 (Islam et al., 2020). The model of Pakhimara Beel was supplied by 145 time varying water levels and SSC data. As the grain size of the sediment is fine (less than 63 µm) for the study area (Datta and Subramanian, 1997;IWM, 2010), the MT (mud transport) module of Mike 21FM for cohesive sediment transport was used. Islam et al. (2020) calibrated the 2D hydro-morphodynamic model for Pakhimara Beel by comparing the observed water level, discharge and SSC with simulated ones. Manning's coefficient, shear stress and settling velocity were the primary 150 parameters for calibrating the hydrodynamic and morphodynamic models. Sensitivity analysis of the model was carried out with varying Manning's coefficient from 0.1 s m -1/3 to 0.01 s m -1/3 , shear stress from 0.01 N m -2 to 0.1 N m -2 and settling velocity from 0.0001 m s -1 to 0.001 m s -1 . To understand the uncertainty of the model, the coefficient of determination (R 2 ) and the normalized root mean square error (NRMSE) were calculated by comparing the modelled results with the observed data for the different input variables. Best model performance was obtained using a spatial average value of 0.032 s m -1/3 for 155 the Manning's coefficient, shear stress of 0.08 N m -2 and settling velocity of 0.0005 m s -1 . The related R 2 for water level, discharge and sediment concentration were 0.87, 0.88 and 0.84, respectively. The NRMSE (%) for water level, discharge and sediment concentration were 9.7, 16.6 and 18.3, respectively (Islam et al., 2020). Islam et al. (2020) used the model to simulate three sets of consecutive 14 days to capture the effect of spring and neap tide during different seasons. For this study, we carried out similar 14 days simulations and similar parameterizations to capture the full range of tidal cycles for 160 three flow seasons. The resulting sediment deposition in a beel was calculated in tons per day.

Scenario matrix for hydro-morphodynamic modelling
For our analysis, we adjusted the hydro-morphodynamic model of Pakhimara Beel with different values for the input parameters that represent the physical control variations across the SW delta. A scenario matrix of those boundary conditions was developed considering varying inlet width (IW), surface area of the beel (BA), tidal range (TR) and suspended sediment 165 concentration (SSC). Inundation depth (ID) was determined for each scenario as the difference between the average land level inside the beel and the average water level from 2D hydro-morphodynamic model results for each scenario. The land elevation data were obtained from the coastal DEM generated by Kulp and Strauss (2018).
The inlet width of beels of previous TRM projects reported by Gain et al. (2017) varied from 30 m to 60 m. We, therefore, used inlet widths of 30 m, 60 m and 120 m for the scenarios. The study of Adnan et al. (2020) was used to determine a relevant range in surface areas of the beels (Fig. 1). The average area of the beels of southwestern Bangladesh is about 656 ha (Adnan et al., 2020), and 90% of the beels are smaller than 1400 ha. The beels are located within the catchments of Pasur, Shibsa, Kobadak and Kholpetua rivers and their tributaries (Fig. 1). For our scenarios, 230 ha, 460 ha, 700 ha and 1400 ha were considered as the surface area of the beel.  (Islam et al., 2021). Tidal range is generally higher for the rivers in the TDF region than for the rivers in the RDF region of the 180 southwestern delta. Suspended sediment concentration (SSC) in the river is highest during the monsoon and lowest during the dry season for RDF and MF regions. For the TDF region, SSC in the river is highest during the pre-monsoon and lowest during the dry season (Islam et al., 2021). For the scenarios, we used the TR and the SSC that occur within the three flow regime regions during the different seasons as defined by Islam et al. (2020Islam et al. ( , 2021 (Table 1). Islam et al. (2021) used sediment rating curves when measured SSC were not available. 185 To simulate and analyze the effect of different scenarios, the calibrated model of Pakhimara Beel developed by Islam et al. (2020) was adjusted for different inlet widths and surface areas of the beel (Fig. 3), and for different TR, SSC and inundation depth where the last results from the flood water level in the feeding river channel. It was assumed that the adjusted models represent the sediment dynamics inside the beel as if the beels were located within different parts of the delta. Ground level of the model was adjusted for different regions within the delta following Islam et al. (2021). The average altitude of the 190 RDF region is 5.6 m AMSL which is higher than the average river water level for pre-monsoon and dry seasons. During the monsoon season, the average water level in the rivers of the RDF region is high enough to flood the land. Therefore, only the monsoon season is considered for the RDF region in the scenario matrix. In total we developed 84 scenarios considering the seasonality of water level and SSC, different inlet width and the surface area of the beel (Table 1) TD11  TP11  TM11  MD11  MP11  MM11  RM11  460  TD12  TP12  TM12  MD12  MP12  MM12  RM12  700  TD13  TP13  TM13  MD13  MP13  MM13  RM13  1400  TD14  TP14  TM14  MD14  MP14  MM14  RM14   60   230  TD21  TP21  TM21  MD21  MP21  MM21  RM21  460  TD22  TP22  TM22  MD22  MP22  MM22  RM22  700  TD23  TP23  TM23  MD23  MP23  MM23  RM23  1400  TD24  TP24  TM24  MD24  MP24  MM24  RM24   120   230  TD31  TP31  TM31  MD31  MP31  MM31  RM31  460  TD32  TP32  TM32  MD32  MP32  MM32  RM32  700   TD33  TP33   TM33   MD33   MP33   MM33  RM33   1400   TD34  TP34  TM34  MD34  MP34 MM34 RM34

Identifying the effect of TR, SSC, ID, IW and BA on sediment deposition 200
The calculated amounts of sediment deposition per day (SPD) in the beel using the 2D hydro-morphodynamical model for all scenarios were compared with each other to determine and understand how these depend on the five parameters studied (TR, SSC, ID, BA and IW). Using an analysis of variance (ANOVA), we identified which of these five parameters and their interconnectivity significantly correlate to sediment deposition per day (SPD). A Pearson correlation matrix was calculated to determine the strength of the correlations among the variables. 205

Non-linear regression analysis
Previous studies (Islam et al. 2020;Islam et al., 2021, Talchabhadel et al., 2017Gain et al., 2017) indicated that the relations are non-linear between SPD and TR and between BA and IW. Moreover, linear multivariate regressions (LMs) usually include a residual term, which would predict sediment deposition even when all variables have zero value, such as in https://doi.org/10.5194/hess-2021-300 Preprint. Discussion started: 29 June 2021 c Author(s) 2021. CC BY 4.0 License. the empirical equation used by Adnan er al. (2020). We, therefore, applied a non-linear multivariate regression (NLM) 210 analysis between the beel characteristics (BA, IW), boundary conditions (TR, SSC, ID) and sediment deposition in the beel (SPD, in tons per day) calculated by the hydro-morphodynamic model for these inputs (Fig. 2). The regression equation has the following form as Eq. (1): where a, b, c, d, e and f are statistically obtained coefficients. 215 The results of the model simulations for the 84 scenarios were divided into two groups, 56 (70%) of them were used as training set and 28 (30%) as testing set for the regression analysis (Fig. 2). The regression coefficients were determined from the training set, after log-transformation of the equation and correction for bias resulting from this transformation. In accordance with the way Mike 21FM simulates sediment deposition from suspended sediments, SSC affects sediment deposition linearly (DHI, 2012b). Therefore, the exponent for SSC in the regression analysis was fixed to "1". We calculated 220 the coefficient of determination (R 2 ) and normalized root mean square error (NRMSE) for different combinations of predictive variables to identify which predictors should be included to estimate sediment deposition per day. To explore the sensitivity of regression analysis related to dividing the results of the model simulations to training and testing samples, 10 sets of training and testing samples were randomly generated.

Application of the regression model to estimate potential sediment deposition and land surface elevation in the 225 beels of southwestern Bangladesh
The regression model established was applied to estimate sediment deposition per beel under TRM using IW, BA, ID, average SSC and average TR for the 234 beels identified by Adnan et al. (2020). For each beel, we first determined the associated flow regime of the feeding river branch (cf. Islam et al., 2021). To estimate sediment deposition for the beels using the regression model, we used the TR and SSC for the flow regions and different seasons defined by Islam et al. 230 (2021). Inundation depth (ID) was determined from the difference between the average local land surface elevation and the average water level inside the beel. The surface area (BA) was determined for all beels, and a standard inlet width (IW) of 60 m was used. To estimate the total sediment deposition for each of the 234 beels, sediment deposition per day (SPD) was multiplied for each season by the number of days per season, and the results were summed to obtain the annual deposition.
From these estimated seasonal and annual sediment depositions, land elevation increase was calculated using the beel area 235 and sediment dry bulk density of 1300 kg m -3 as suggested by Allison and Kepple (2001) and Rogers and Overeem (2017) for the GBM delta. The estimated land elevation increase was compared with the relative sea level rise (RSLR) per year to define the potential of raising land surface elevation to counteract RSLR. The potential is considered as "low" when the land height increase is lower than maximum anticipated RSLR of 10 mm yr -1 for RCP8.5 in 2050; as "medium" when the land elevation increment is between 1 and 3 times RSL; "high" with increment between 3 and 5 times RSLR and "very high" 240 when elevation increment is more than 5 times RSLR. In the latter case TRM can potentially be applied to the beel once every five years to counteract RSLR. https://doi.org/10.5194/hess-2021-300 Preprint. Discussion started: 29 June 2021 c Author(s) 2021. CC BY 4.0 License.

Sediment deposition for different beel lay-outs and boundary conditions
The results obtained by the hydro-morphodynamic models for the different scenarios indicate that average sediment 245 deposition per day (SPD) varies seasonally and spatially with varying tidal range (TR) and suspended sediment concentration (SSC) (Fig. 4). Highest SPD occurs during the monsoon season along river branches with a mixed flow (MF) regime. During the dry and the pre-monsoon seasons, the highest SPD occurs in the tide-dominated flow (TDF) region.
During the dry and pre-monsoon seasons, deposition cannot occur in the river-dominated flow (RDF) region, and even during the monsoon season the SPD in the RDF region is substantially lower than in the other two regions. 250 Sediment deposition per day (SPD) generally increases for larger beels, but the increase varies among the regions and seasons (Fig. 4). For the monsoon season, the beels with surface area (BA) of 1400 ha have 1.5, 5.2 and 5.4 times higher SPD compared to the SPD of 230 ha BA in the TDF, MF and RDF regions, respectively. For the pre-monsoon, this ratio is about 2 in the TDF region and about 4 in the MF region. The results of the morphodynamic model also indicate that inlet width (IW) of the beel has very little effect on SPD (Fig. 4). According to the morphodynamic model results the considered 255 inlet widths are apparently not a limiting factor for deposition, the channel capacity becomes the limiting factor to convey the larger flow of water towards the beel for the wider inlets.  With larger tidal range, larger volumes of water and sediment become transported inside the beels. Moreover, the effect of TR on SDP is highest close to the inlet and the effect decreases when moving away from the inlet. The effect of tide also decreases further inwards the beel as those beel sections are much wider and the tidal energy dissipates. For the subareas 265

IW
where the effect of TR is high especially near the inlet, the flow remains dynamic and active which results in lower SPD.
Furthermore, the velocity inside the beel decreases with increasing distance from the inlet. Therefore, water flow velocities in the distal areas located farthest from the inlet of larger beels are considerably lower than those in the distal parts of smaller beels. Sediment deposition rates increase at lower flow velocity. Combining the effect of having larger volumes of sediment delivered into a beel and lower flow velocities in the distal areas of the beel results in higher sediment trapping efficiency 270 and higher SPD for larger beels (Fig. 4). However, sediment deposition per unit area is generally higher for smaller beels. As TR and SSC govern the sediment load delivered by the river, the seasonality of TR and SSC results in seasonal and spatial variation of SPD inside the beel. Sediment deposition per day (SPD) is higher when TR and SSC are higher. The velocity and shear stress are higher close to the inlet for narrow inlets which prevent sedimentation near the inlet. Therefore, https://doi.org/10.5194/hess-2021-300 Preprint. Discussion started: 29 June 2021 c Author(s) 2021. CC BY 4.0 License.
suspended sediment tends to settle close to the inlet with increasing inlet width resulting in different spatial distribution of 275 sediment deposition for different IW even though IW has minimal effect on SPD.

Controls of sedimentation
The ANOVA test demonstrated a significant effect of TR, SSC, BA, IW and ID on modelled SPD (Table 2). Also, most of the interactions between TR, SSC, ID, BA and IW are significant for SPD as the p-value is smaller than 0.05 (Table 2).  Tidal range (TR), SSC, ID and BA positively correlate with SPD, with highest correlations for SSC and BA (Table 3). These 285 correlations reflect the higher TR and SSC in the TDF region (Table 1) resulting in high SPD, when compared to the other flow regions (Fig. 4). Conversely, the lowest SPD in the RDF region reflects its lower SSC and TR (Table 1; Fig. 4). The strong correlation of SSC with SPD is evident for the MF region during the monsoon season because SSC is higher in this region than in the TDF region (Fig. 4). TR is higher during the monsoon season in the TDF region than that in the MF region, while SSC is lower (Table 1). Similar to TR and SSC, larger BA and ID result in larger volumes of water and 290 sediment entering a beel, and hence higher SPD (Fig. 4), which is reflected in their positive correlation with SPD ( Table 3).
The large ID in the MF region during the monsoon season results in the positive correlation of ID with SPD. The correlation matrix also indicates that TR and ID have a very strong negative correlation (Table 3). Tidal range (TR) is lowest during the monsoon season when water level in the river is highest and TR is high during the dry and the pre-monsoon season when water level in the river is low (Table 1). This results in the negative correlation between TR and ID. Suspended sediment 295 concentration (SSC) and BA have stronger effect on SPD as the correlation of SPD with these are highest. Tidal range (TR) and ID have moderate effect on SPD and IW has minimal to no effect of SPD.

Multivariate regression model for prediction of sediment deposition 300
Based on the correlation between the controlling factors and SPD as well as the significance of the controlling factors for SPD (Table 2 and Table 3), we set-up a multivariate regression model to estimate SPD. Sediment deposition per day (SPD) has strong to moderate positive correlation with SSC, BA, TR and ID, and weak negative correlation with IW (Table 3).
Although IW has minimal effect on SPD, IW is found as statistically significant for SPD ( Table 2). The interconnectivities between TR, SSC, ID and BA are also identified as statistically significant for SPD (Table 2). Therefore, we considered all 305 the control factors (TR, SSC, ID, BA and IW) as variables for the regression analysis to estimate SPD and compared the results to identify the most suitable empirical equation for the regression model.
Since the interconnectivities between TR, SSC, ID and BA are significant for SPD (Table 2) and since the effect of TR and BA on SPD is non-linear (Fig. 4), we developed three non-linear multivariate (NLM) regressions with increasing number of variables. Suspended sediment concentration (SSC) and BA were considered as variables for NLM1 as SSC and BA have 310 higher correlation with SPD (Table 3). Tidal range (TR) and ID were included as variables along with SSC and BA for NLM2 as TR and ID have moderate correlation with SPD (Table 3) Table 4. Note that the exponential coefficient for suspended sediment concentration was fixed to 1.
The variation in regression coefficients obtained using the different training sets is generally low, with higher variation for 315 the scaling factor a and the exponential coefficient f related to IW. Figure 5 shows the estimated SPD by Mike 21FM models versus the calculated SPD by regression models for both the training and testing datasets. NLM1 shows a larger spread and seems to overestimate SPD for low and higher values when compared to the other two regression models. The coefficient of determination (R 2 ) of the three regression models ranges between 0.61 to 0.84 for the training sets and 0.29 to 0.94 for the testing sets ( Table 5). The averages for the two sets are, 320 however, highly comparable. The predictive skill of the models generally increases with increasing number of variables. NLM1 using only BA and SSC as predictors for SPD, results in relatively moderate average R 2 of 0.61 and 0.71 for the training and testing data sets, respectively (Table 5). NLM2 using TR, SSC, ID and BA and NLM3 using TR, SSC, ID, BA and IW produce better results. The mean R 2 for NLM2 are 0.77 and 0.74 for training and testing data sets respectively and the mean R 2 for NLM3 are 0.77 and 0.76 for training and testing data sets respectively (Table 5). Although IW correlates 325 statistically significant with SPD in the ANOVA test (Table 2), it hardly contributes to better prediction of SPD with exponential coefficients of 0.02 -0.14 ( Table 4). The normalized root mean square error (NRMSE) ranged between 0.3 to 0.5 for the training datasets and 0.15 to 0.49 for the testing datasets (Table 5). The mean of NRMSE for NLM1 for the training samples is higher than obtained for NLM2 and NLM3. The mean NRMSE obtained for the testing dataset is almost similar for all three NLMs. 330 Since NLM3 yielded the highest mean R 2 and the lowest mean NRMSE for both the training and testing dataset (Table 5), it was selected as most suitable regression model to estimate SPD for the beels of southwestern Bangladesh. As a separate test, we applied NLM3 to the Bhaina Beel and the Khuksia Beel where TRM was operated previously. Van Minnen (2013) reported that 6.45 million m 3 and 8.2 million m 3 of sediment were deposited in Bhaina Beel and Khuksia Beel, respectively, after five years of TRM operation. Sediment deposition per day (SPD) estimated with the NLM3 regression models for 335 Bhaina Beel and Khuksia Beel had an average error of about 12-17% relative to the observed value which can be considered as moderate. This supported our confidence that the regression model NLM3 can be applied as a simple regression model for evaluating TRM potential on the basis of estimated sediment deposition in beels in the southwestern GBM delta.

Estimation of potential of the beels to stay above sea level through renewed sedimentation using the regression model 350
The potential of sediment deposition to raise the land surface of the beels of southwestern Bangladesh was assessed using the empirical equation of the NLM3 regression model, assuming a beel inlet width of 60 m for all cases. The estimated potential of raising land surface elevation shows considerable seasonal and spatial variability (Fig. 6). Seasonal estimated SPD for all beels varies from 4 mm yr -1 (0,4 times RSLR) during the dry season to 150 mm yr -1 (15 times RSLR) during the monsoon https://doi.org/10.5194/hess-2021-300 Preprint. Discussion started: 29 June 2021 c Author(s) 2021. CC BY 4.0 License.
season. Spatially the beels located west of the Pasur River of the study area have a high potential for TRM for all scenarios, 355 while the beels east of the Pasur River generally have lower potential (Fig. 6). Generally, smaller beels have higher potential to raise land surface elevation than larger beels (Fig. 6). Out of the 234 beels, 32, 31 and 35 have high, and 115, 120 and 187 have very high potential to raise the land surface elevation during the dry season, pre-monsoon and monsoon, respectively. This means TRM operation during the monsoon season only is sufficient to raise the land surface by more than 3 times yearly RSLR (> 30 mm yr -1 ) for 96% of all beels and by more than 5 times the RSLR (>50 mm yr -1 ) for 80% of all beels. 360 Applying TRM around the year increases the potential to raise land surface elevation from high to very high in 22 additional beels.
A number of beels located east of the Pasur River remain having low to medium potential even with around the year operation of TRM. The beels within the MF region have low to medium potential to raise land surface elevation when TRM is operated during the dry and pre-monsoon seasons ( Fig. 6a and Fig. 6b).

The effect of physical controls on sediment deposition per day (SPD)
We explored how sediment deposition per day (SPD) in beels within the southwestern GBM delta of Bangladesh under active operation of Tidal River Management (TRM) depends on boundary conditions associated with flow regime of the 370 feeding river and season (tidal range (TR) and suspended sediment concentration (SSC)), and on various beel dimensions (surface area (BA), width of the inlet channel (IW) and inundation depth (ID)).
The physical controls TR and SSC which are related to hydrodynamics of the river have a positive correlation with SPD.
SPD depends on the sediment load in the feeding rivers for which TR and SSC are primary drivers resulting in positive correlation of SPD with TR and SSC (Table 3). This is similar to the findings of Islam et al. (2020;. Of the two 375 physical controls TR and SSC, SSC has the highest correlation with SPD (Table 3). This means that sediment deposition in beels depends mostly on suspended sediment concentrations (SSC) in the feeding river, which in turn shows a high correlation with TR (0.57). The physical controls TR and SSC are deemed statistically significant by the ANOVA test pvalues (Table 2). Islam et al. (2021) found that seasonal and spatial variation of SSC and TR in the rivers result in a large seasonal and spatial variation of sediment deposition in beels indicating that TR and SSC are primary physical controls of 380 SPD. The scientific document provided by DHI for Mike 21FM indicates that SPD increases linearly with increasing SSC (DHI, 2012b). Talchabhadel et al. (2017) indicated that high sediment deposition occurs inside the beel with stronger tide in the river. According to Talchabhadel et al. (2017) and DHI (2012b), SPD will vary seasonally with seasonality for SSC and TR, which is confirmed by our findings.
Statistical analysis of our 2D hydro-morphodynamic model results indicates that among the physical controls BA, ID and IW 385 which are related to geo-morphodynamics of the beels, SPD has highest correlation coefficient with BA (0.56) ( Table 3).
SPD increases with larger beel surface area, which is in accordance with Van Minnen (2013) who reported 6.45 million m 3 of sediment deposited in Bhaina Beel (600 ha) compared to 8.2 million m 3 in the larger Khuksia Beel (1100 ha) during 4 years of TRM operation. With larger surface area (BA) of a beel, a larger volume of suspended sediment can be delivered inside. We found that SPD has positive correlation with ID and BA (Table 3) which is similar to Talchabhadel et al. (2017) 390 who indicated that more sediment deposition occurs when larger volumes of water enter the beel with tide. We found low correlation between IW and SPD (Table 3) which is consistent with the findings of Talchabhadel et al. (2017). They suggested IW has minimal effect on SPD, although the spatial distribution of sediment deposition varies between different IWs, which is similar to the results of our 2D hydro-morphodynamic model. As BA and ID vary among the beels of SW Bangladesh, this causes variations in SPD among the beels. All three physical controls related to geo-morphodynamics of the 395 beels, BA, ID and IW, and their interactions are statistically significant for SPD as indicated by the ANOVA test p-values (Table 2). https://doi.org/10.5194/hess-2021-300 Preprint. Discussion started: 29 June 2021 c Author(s) 2021. CC BY 4.0 License.

Estimation of SPD with multivariate non-linear regression models (NLMs)
We developed non-linear regression models from the 2D morphodynamic model results to provide an a priori estimation of sediment deposition inside the beels of southwestern Bangladesh if they would be subjected to TRM practice. Adnan et al. 400 (2020) used linear regression modelling with geomorphological variables which were mostly related to land elevation to calculate sediment deposition. They did not consider TR and SSC to estimate sediment deposition, but Islam et al. (2020) found sedimentation inside the beel depends strongly on the SSC and TR in the rivers. The coefficient of determination (R 2 ) of the linear regression model of Adnan et al. (2020) is stated as 0.88 even though their empirical equation had a residual which will yield sediment deposition with all the variables set to zero. We used non-linear regression models to include the 405 effects of non-linearity between SPD and the steering physical factors TR, BA, ID and IW and their interaction as described by Islam et al. (2020), Talchabhadel et al. (2017), Gain et al. (2017), Van Minnen (2013 and DHI (2012b). The accuracy and uncertainty analysis of our regression models for 10 sets of training and testing samples indicates that the regression model NLM3 may be applied to estimate sediment deposition.

Estimated sediment deposition, potential to raise land surface elevation and their implication for the beels of 410 southwestern GBM delta
Our estimation of potential sediment deposition and associated land surface elevation increment inside beels using the regression models indicates that TRM shows high potential to counterbalance RSLR in southwestern Bangladesh. When operated year-round, in 228 out of 234 beels (97%), the land surface elevation can be raised by more than 3 times the RSLR as predicted under the RCP 8.5 scenario (10 mm yr -1 ) for southwestern Bangladesh (Oppenheimer et al., 2019). When 415 operated only during monsoon, land surface elevation can be raised in 96% of all beels by more than 3 times RSLR and in 80% of all beels by more than 5 times RSLR, indicating that TRM operation only during monsoon is almost as effective as year round operation.
Beels close to sea and to the west of the Pasur River in the tide dominated flow region show highest potential for sediment deposition and raising their land surface elevation by means of TRM. However, Adnan et al. (2020) indicated that the beels 420 close to the sea have a low potential to reduce flood susceptibility. The tidal range (TR) and suspended sediment concentrations (SSC) are high in the rivers close to the sea all around the year (Islam et al. 2021) resulting in a high potential to raise the land surface elevation with sediment deposition for the beels of southwestern Bangladesh. Thus, our results indicate the natural flood vulnerability of these polders may be sustainably reduced by application of TRM using controlled flooding. 425 According to our estimation smaller beels generally have higher potential to raise land surface elevation than larger beels.
Van Minnen (2013) reported that 6.45 million m 3 and 8.2 million m 3 of sediment deposited in Bhaina Beel and Khuksia Beel during TRM operation, with surface areas of 600 and 1100 ha respectively (Gain et al., 2017). Although surface area of Khuksia Beel was 1.8 times that of Bhaina Beel, sediment deposition was only 1.3 times higher. Therefore, the average land https://doi.org/10.5194/hess-2021-300 Preprint. Discussion started: 29 June 2021 c Author(s) 2021. CC BY 4.0 License. elevation increment was higher in smaller Bhaina Beel which is in line with our findings. As suggested by Amir et al. 430 (2019), the rise of land surface elevation in larger beels may be achieved by compartmentalizing the beel into smaller part.
The land elevation east of the Pasur River is higher (Fig. 1), resulting in lower inundation depth (ID) for the beels even within the same flow regions. Suspended sediment concentration (SSC) and Tidal range (TR) are generally lower for the mixed flow (MF) region when compared to the TDF region during dry and pre-monsoon seasons (Islam et al., 2021).
Therefore, SPD and potential to raise land surface elevation with sediment deposition are also generally lower for beels in 435 the MF region during dry and pre-monsoon seasons when TR and SSC for the river stretches in the MF region are lowest.
However, the water level in the rivers is generally higher during the monsoon season (Islam et al., 2021), increasing the ID and consequently the SPD and potential to raise land surface elevation is high for almost all the beels. The beels having low to medium potential to raise land surface elevation during monsoon season and annual operation of TRM, have high average land level (Fig. 1) reducing the ID and causing low SPD. 440 Adnan et al. (2020), Amir and Khan (2019) and Talchabhadel et al. (2018) considered uninterrupted operation of TRM for several years. In addition to annual operation of TRM we have considered seasonal operation of TRM as well. Our analysis shows that the potential is higher when TRM is operated during monsoon than during pre-monsoon and dry seasons (Fig. 6).
Monsoon season is longer and sediment load is higher in the rivers compared to the pre-monsoon and dry seasons resulting in higher sediment deposition and higher potential to raise land surface elevation than in other seasons. This is an important 445 finding as continuous and lengthy operation of TRM may not be accepted by local communities. Farmers living in Khuskshia Beel where TRM was operated continuously for 7 years have a negative impression of TRM due to such a long period of operation and lack of compensation, and questioned its effectiveness (Gain et al., 2017). When TRM is only operated in the monsoon season, the land inside the beel will remain available to local stakeholders for the rest of the year. This may potentially increase the acceptability of TRM to the local stakeholders. 450

Using tidal river management (TRM) as a way to keep up with relative sea level rise (RSLR)
Controlled flooding like TRM can potentially be applied in rotation to the beels with high potential to counteract yearly RSLR through sediment deposition and thus raise the coastal areas of the GBM delta. This would entail two main phases.
First, the land surface in the beels, as well as the polders they are in, should be raised to get equal to the current average sea level of the region. After that TRM should be applied such that the land surface is raised at least at the pace of RSLR to 455 remain equal or above to sea level. TRM may be operated once in every few years to achieve these goals and keep the land available for agriculture in between. Gain et al. (2017) indicated that rotational operation of TRM is suggested by experts and local communities. Talchabhadel et al. (2020) explored the rotation of TRM in 4 beels of southwestern Bangladesh and concluded that TRM can be applied sequentially in one beel at once continuously for 4 years. They also suggested that TRM should initially be applied in beels located downstream and gradually shift towards the beels located upstream, regardless of 460 the surface area of the beels. IWM (2017) also proposed sequential operation of TRM in the beels along the Teka-Hari-Teligati River system of southwestern Bangladesh where TRM can be applied in one beel at once and continuously for 7 https://doi.org/10.5194/hess-2021-300 Preprint. Discussion started: 29 June 2021 c Author(s) 2021. CC BY 4.0 License. years in each beel. At this point in time however, there is no master plan indicating how a rotational scheme should be devised to raise the BGM delta effectively with TRM against RSLR.
Our study may present a method to work out such a plan in future to raise the land with sedimentation and to offset yearly 465 RSLR. However, it must be noted in our study only total sedimentation inside the beel was explored and spatial distribution of sediment deposition was not considered. As Islam et al. (2020), Talchabhadel et al. (2017) and Gain et al. (2017) indicated, spatial distribution of sediments inside the beel is also important for the operation of TRM. For this more location specific detailed studies will be required to understand the effect of TRM inside a specific beel. Next to these physical considerations the social acceptability of TRM should get ample attention in order to fully reap the potential of this method. 470 https://doi.org/10.5194/hess-2021-300 Preprint. Discussion started: 29 June 2021 c Author(s) 2021. CC BY 4.0 License.

Conclusion
We present a method to estimate the potential of Tidal River Management for the beels in southwestern Bangladesh to raise the land through renewed sedimentation in order to counterbalance the relative sea level rise (RSLR) in the coming decades.
Our 2D hydro-morphodynamic modelling indicates that sediment deposition inside beels (expressed as sediment deposition per day (SPD)) shows a strong seasonal variability, due to seasonally varying suspended sediment concentration (SSC) and 475 tidal range (TR) in the feeding river channel, and inundation depth (ID) in the beel. Sediment deposition also varies across the delta, depending on the surface area of the beel (BA) and spatial differences in TR, SSC, ID and (Fig. 4). The inlet width (IW) of a beel has negligible effect on SPD. Using a multivariate non-linear regression model developed from the results of the 2D hydro-morphodynamic model, we estimated potential to raise land surface elevation with sediment deposition in 234 beels across the southwestern delta, based on the local TR, SSC, BA, IW and ID. The analysis with the morphodynamic 480 model and the regression model indicates that: -Suspended sediment concentration (SSC) and beel area (BA) are primary drivers of sediment deposition as they have the highest positive correlation with SPD among the physical controls. Tidal range (TR) and ID affect SPD moderately and IW has minimal to no impact on SPD. However, all of TR, SSC, BA, ID and IW are statistically significant for SPD. So are the interactions between TR, SSC, ID and BA. 485 -Sediment deposition is non-linearly related with TR, ID, BA and IW and linearly with SSC. The non-linear multivariate (NLM) regression model NLM3 which consists of all five physical controls (TR, SSC, BA, ID and IW) appeared the most suitable to estimate SPD showing highest average of coefficient of determination (R 2 ) and moderate average of normalized root mean square (NRMSE) among the NLMs for the randomly selected 10 sets of the training and the testing data sets. 490 -The estimated SPD with the regression model for the beels of southwestern Bangladesh indicates that sediment deposition and potential to raise land surface elevation is high for 97% of the beels when TRM is operated round the year, but almost as effective (96% of all beels) when operated only during monsoon. High potential means land surface elevation inside the beels can be raised more than 3 times the yearly RSLR (Fig. 6). 80% of all beels have very high potential to raise the land surface elevation more than five time the RSLR (>50 mm yr -1 ) when operated 495 only during monsoon.
-Smaller beels have higher potential to raise the land surface elevation than larger beels. Higher land surface increments in larger beels may be achieved by compartmentalizing the larger beels into smaller compartments.
-For a few beels east of Pasur River the sediment deposition and potential to raise the land surface elevation is low to medium for annual and monsoonal TRM operation. There the average land surface elevation is relatively high 500 resulting in lower ID, SPD and potential to raise the land surface elevation. The beels within the mixed flow region have low to medium potential when TRM is operated only during dry and pre-monsoon seasons (Fig. 6). TRM operation during monsoon shows virtually the same high potential as year round operation. This is an important finding since restricting TRM to the monsoon season means that the land will remain available for agriculture during the rest of the year. This may increase acceptability to stakeholders of the beels and polders. The regression model presented here 505 can provide a priori estimation of sediment deposition and potential to raise land surface elevation for the beels. This can assist the decision makers to prioritize the location of TRM operation. However, TRM operation is complex and contains socio-economic aspects as well. Therefore, sediment deposition as well as socio-economic aspects of TRM should be considered to determine an optimum flood rotation scheme for the beels of the southwestern Bangladesh. The methodology presented here can be used for the low-lying sinking deltas around the world to provide a preliminary estimation whether 510 sediment deposition with controlled flooding can counter the RSLR. The regression model provides an opportunity for stakeholders including decision makers to explore the effect of sedimentation with controlled flooding.

Data availability.
The data used in this research were provided by the Institute of Water Modelling (IWM) for research purposes only. IWM is the owner of the data. Therefore, the authors do not have the authority to share the data publicly.