LONG-TERM PREDICTION OF LONGSHORE SEDIMENT TRANSPORT IN THE CONTEXT OF CLIMATE CHANGE

Due to climate change impacts on atmospheric circulation, global and regional wave climate in many coastal regions around the world might change. Any changes in wave parameters could result in significant changes in wave energy flux, the patterns of coastal sediment transport, and coastal evolution. Although some studies have tried to address the potential impacts of climate change on longshore sediment transport (LST) patterns, they did not sufficiently consider the uncertainties arising from different sources in the projections. In this study, the uncertainty associated with the choice of model used for the estimation of LST is examined. The models were applied to a short stretch of coastline located in Northern Gold Coast, Australia, where a huge volume of sediment is transported along the coast annually. The ensemble of results shows that the future mean annual and monthly LST rate might decrease by about 11 %, compared to the baseline period. The results also show that uncertainty associated with LST estimation is significant. Hence, it is proposed that this uncertainty, in addition to that from other sources, should be considered to quantify the contribution of each source in total uncertainty. In this way, a probabilistic-based framework can be developed to provide more meaningful output applicable to long-term coastal planning.

the existence of a wide range of coastal sediment transport models developed under different assumptions. Variability of climate systems can be considered as aleatory/intrinsic uncertainty. Figure 1 illustrates the potential sources of uncertainty in the projection of LST patterns.

Figure 1. Potential sources of uncertainty in the projection of wave-driven LST
There have been some efforts to estimate future LST patterns for different case studies around the world (e.g., West Africa (Almar et al., 2015), Vietnam (Dastgheib et al., 2016), India (Chowdhury et al., 2020)). Nonetheless, they mainly addressed the uncertainty associated with global circulation models and/or emission scenarios, and they overlooked other sources of uncertainty. A reliable prediction of future LST rates requires addressing uncertainty associated with all sources. One of the main sources of uncertainty is the choice of LST estimation method. Two conventional models for estimation of LST are simplified (bulk transport formulae) and process-based models. In recent decades, many researchers endeavored to develop or modify formulas for the prediction of the LST rate (e.g., Mil-Homens et al., 2013;Shaeri et al., 2020). Along with the simplified models, process-based models such as LITPACK and UNIBEST have been used to simulate LST patterns. The long-term net annual LST rate is typically estimated using hydrographic surveys and sediment budget analysis. Although these rough approaches do not provide any information on LST variations in time, they can be used to calibrate sediment transport models. Then the calibrated sediment transport models can be employed to estimate long-term patterns of LST.
This paper provides a preliminary investigation of the uncertainty associated with choice of LST model by comparing the intra-and inter-annual variability of LST patterns projected by a range of models for a short stretch of coastline close to the Gold Coast Seaway (QLD, Australia).

STUDY AREA
The Gold Coast (GC) is a coastal city located in southeast Queensland, Australia (Figure 2a). The GC beaches are social places where people interact, exercise, and relax. The beaches are also a major driver of the local tourism economy. The GC has a 35 km sandy coast (with medium to fine sand-sized grain) backed by a primary dune system. Coastal profiles along the shoreline typically show multiple bars (Figure 2c). The littoral system is interrupted by three natural headlands and four river/creek inlets ( Figure 2a). Offshore waves in the region are typically one of five wave climate types (Splinter et al., 2012): long period swells from the S-SE direction, medium-period swells (generated in the Tasman Sea), wind waves from different directions, tropical cyclones (generated in the Coral Sea), and East Coast Lows (ECL) from the NE to SE direction. Coastal erosion along the coast occasionally occurs due to the highly developed coastline lacking a sufficient buffer for major storm events. Hence, to mitigate erosion problems in this region, periodic beach nourishment has been recommended and carried out. Additionally, two sand bypassing systems have been installed at the south and north of the Gold Coast. The sand bypassing systems mitigate the interruption of longshore drift caused by the extension of the training walls of the river entrances, as well as the construction of groins and two artificial reefs. The predominance of waves from the south-easterly direction is recognizable in the offshore wave rose of GC ( Figure 2b). The average long-term net northward littoral drift has been estimated to be 500,000 m 3 /year at the southern GC (DHL, 1992) and 635,000 m 3 /year at the northern GC (Patterson, 2007). It is worth mentioning that the changes in the LST rate can have significant influences on the rate of beach nourishment and artificial sand bypassing (or sand back-passing) in this study area. The focus of this paper is a 3-km stretch of coastline close to GC Seaway at the northern end of GC ( Figure 2a).

METHODOLOGY
In this study, the uncertainty associated with choice of LST estimation model was investigated. In this regard, an ensemble of LST models, including Kamphuis (Kamphuis,1991; hereafter K1), modified Kamphuis (Mil-Homens et al., 2013;hereafter K2), CERC (USACE, 1984; hereafter C), Van Rijn (van Rijn, 2014; hereafter V), two new formulas (hereafter S1 and S2) proposed by Shaeri et al. (2020), as well as a process-based model (LITPACK, hereafter DHI) have been used to project the LST rate. Table  1 indicates the dependency of the used transport formulae to different parameters. To set-up LITPACK, a representative mean coastal profile, through analyzing the shape of measured profiles and the corresponding wave climate of northern Gold Coast, was chosen ( Figure 2c). To this end, fully recovered coastal profiles (a rare condition for northern GC) or completely erosive ones (one immediately measured after extreme conditions), were excluded from analysis as they could not be representative of long-term shape of coastal profiles.
All offshore waves of this study were extracted from the CSIRO's CMIP5 global future wave projections databases Hemer and Trenham, 2016). Nearshore wave forcing conditions were first obtained by applying a simple, low-computational-cost wave transformation method (e.g., Battjes andStive, 1985, Larson et al., 2010) to the hindcast datasets (CFSR-driven waves) for the period of 1979 to 2005. The depth-induced breaking wave height was estimated using the breaker index ( ) of Kamphuis (2010): where Hsb is breaker height, db is the water depth at break point, and m is the average surf zone bed slope. All LST models were then calibrated to reproduce the estimated rate of average long-term annual net LST in the area (i.e., 635,000 m 3 /year, Patterson, 2007). For calibration of the bulk transport formulas, simple adjustment factors were applied (Table 2); while for calibration of the process-based model, its free parameters were tuned (Table 3). Since shoreline orientation in northern GC has remained in an equilibrium condition in recent decades, it was assumed that shoreline orientation does not change in the future.

Description:
Hsb is the significant wave height at breaker point (in m); Tp is peak wave period; αb is the angle of waves at breaker point (in degree or radian); mb is the beach slope within surf zone, and D50 is the median size of sediment particles (m).
To project future LST patterns, offshore waves projected with surface wind forcing from the MRI-CGCM3 GCM was used. This GCM was selected from the eight available GCMs as it provided the best comparison with the wave rose of the CFSR-driven hindcast (not shown). Nearshore wave conditions (the forcing conditions of LST models) for the baseline  and future (2081-2100, under RCP 8.5) periods were obtained using the simple wave transformation method. The ensemble of LST projections was then analyzed to examine the intra-and inter-annual variability of LST and to establish the range of uncertainty corresponding to the choice of LST model. The projected change for each LST model was computed as follows: Where LSTFmo and LSTBmo are the LST rates estimated by the LST model 'mo' for future and baseline periods, respectively, and n is the number of ensemble members (LST models).

RESULTS AND DISCUSSION
The boxplots of CFSR-driven waves (Figure 3, left panel) imply that for the historical period 1979-2005, wave height distribution (i.e., first quartile, median and third quartile) varies monthly. Additionally, the occurrence of storms during February to April intensifies compared to other months. The statistical distribution of wave direction varies considerably from month to month. The rotation of waves direction toward the southeast, from May to August, is recognizable (Figure 3, right panel). This pattern was also observed in MRI-CGCM3-driven waves for the baseline period 1979-2005 (not shown).

Figure 3. Monthly offshore wave height (left panel) and mean wave direction (right panel) for baseline period 1979-2005 from CFSR-driven waves data
Projected future wave climate of MRI-CGCM-driven waves indicates ~ 5% decrease in mean significant wave height (Figure 4), and 2% decrease in mean peak wave period compared to the baseline period (not shown). Rotation of future wave direction towards the east, particularly from June to September (5 to 10 degrees), is recognizable (Figure 4). Besides, the GCM-driven waves data shows that the Hs95 and Hs99 of future waves decrease by 6.5% and 7%, respectively, compared to the baseline period. Therefore, the projected changes in the wave climate could lead to changes in the future patterns of LST. The offshore waves of the studied area are a combination of modal and stormy conditions so each of models were applied during stormy and modal conditions ( Figure 5). During stormy conditions, the K1 formula results in the lowest LST rates whilst the process-based model (DHI) and the V formula provide the highest estimates. During modal conditions, the DHI model provides the smallest LST estimates rates. As the process-based model considers sediment transport processes in the forms of both bedload and suspended load, it is conceivable that the relative contributions of bedload and suspended load to the total load are different during extreme and modal conditions. Under extreme wave forcing, the model simulates the separation of more sediments from bed, and as a result, more sediments become available in water column that eventually are transported by strong wave-driven longshore currents. In contrast to the other bulk formulae, the V formula was initially developed based on field measurements, experimental data, and numerical modeling. That is probably why its behavior is closer to that of the process-based model. Nonetheless, since all models were calibrated by long-term average net annual LST rate, instead of relying on the results of a specific model for the prediction of long-term patterns of LST, the mean ensemble of results was considered for projections.  Figure 6 shows the intra-annual variation of monthly LST amounts for baseline and future periods associated with the forcing of MRI-CGCM3-driven waves. Seasonal variations in LST are observed due to seasonal changes in wave direction, and somehow, due to variations in the wave height. The highlighted gray area shows the range of uncertainty associated with the choice of LST models (intermodel uncertainty). The range of the uncertainty during February to April is really high (~50,000 m 3 /month difference in LST rate), whereas during November to January the uncertainty range is meager. The cycle for the baseline period indicates an increase in the LST rate from January to March and a decrease from March to December. This pattern changes slightly in the future period, as the duration of the seasonal cycle of LST is extended to April. The projected future LST rate shows a decrease in almost all months, compared to the baseline period (variation of LST calculated by each model has been presented in Figure 7 and Figure 8 ). Each LST model has projected a different magnitude of variations in LST rates. For instance, the DHI model

COASTAL ENGINEERING PROCEEDINGS 2020
7 projected a 19 % decrease in the annual rate of LST, while the S2 formula projected only a 9 % decrease. The mean of results (ensemble mean) shows ~ 11% decrease (compared to the baseline period) in annual and monthly mean LST rate. Intra-and inter-annual variability of the LST rates were also determined based on normalized standard deviations of the results (i.e., intra-annual variability: standard deviation of the monthly means/time slice mean, inter-annual variability: standard deviation of the annual means/time slice mean); see Table 4. It seems that the DHI and the V models show higher inter-annual variability, compared to other models. But, all model, in the timescale of months, show relatively close intra-annual variability. Whilst there is variance amongst the LST models they are all in qualitative agreement with a projected increase in intraannual variability and a decrease in the inter-annual variability. Understanding the impact of such variabilities (estimated by different LST models) on prediction of coastal evolution, and the corresponding countermeasures (e.g., sand bypassing) requires more investigation.

LIMITATIONS AND THE WAY FORWARD
In this study, inter-model uncertainty was addressed by be employing an ensemble of LST models that were calibrated against a long-term average estimate of the annual LST for the historical period. Choosing the members of the ensemble can be a challenging task. Because forming an ensemble with more transport formulae than process-based models can bias the results of ensemble toward transport formulae limitations. A simple low-computational cost wave transformation method was applied to the offshore forcing as northern GC is far away from headlands and the bathymetry is not complicated. Using the simple wave transformation for other coastal regions of GC (e.g., southern GC) is not justifiable. Hence, a spectral-based wave transformation/hybrid method (e.g., Antolínez et al., 2016Antolínez et al., , 2018 is preferred at the expense of considerably higher computational costs. Another limitation of this preliminary study is that the uncertainty associated with the choice of parameters incorporated within each LST model (e.g., beach slope, shoreline orientation, sediment grain diameter, the shape of coastal profiles) have not been considered. Moreover, uncertainties arising from other sources such as emission scenarios, GCMs, and wave transformation methods should be addressed. In this way, the overall reliability (robustness) of projections can be determined. Hence, some other investigations should be conducted to a more sophisticated framework that yields probabilistic results. Such a framework could be developed within coastal management and adaptation plans of the study area.

CONCLUSION
In this paper, a preliminary investigation of the uncertainty associated with the choice of LST model was presented. In this regard, an ensemble of models, including bulk transport formulae and a processbased model, was employed. The forcing conditions of the LST models were obtained from the projected waves of one GCM-forced wave simulation (under one RCP) that were transferred to nearshore using a simple wave transformation method. The results showed that whilst there is variance amongst the results of LST models they are all in qualitative agreement with a projected increase in intra annual variability and a decrease in the inter-annual variability. The mean of results (ensemble mean) shows ~ 11% decrease (compared to the baseline period) in annual and monthly mean LST rate. It should be noted that the results of this study are not still applicable to coastal planning, as other sources of uncertainty should also be considered to find the robustness of projections.