SUPPLEMENTARY INFORMATION

Transcription

1 SUPPLEMENTARY INFORMATION DOI: /NCLIMATE1664 Climate-change impact assessment for inlet-interrupted coastlines ROSHANKA RANASINGHE 1,2,3*, TRANG MINH DUONG 1,3, STEFAN UHLENROOK 1,2, DANO ROELVINK 1,2, MARCEL STIVE 2 1. Department of Water Engineering, UNESCO-IHE, PO ox 3015, 2610 DA Delft, The Netherlands. R.Ranasinghe@unesco-ihe.org (Ph: ), T.Duong@unesco-ihe.org, S.Uhlenbrook@unesco-ihe.org, D.Roelvink@unesco-ihe.org 2. Civil Engineering & Geosciences, Technical University of Delft, PO ox 5048, 2628 CN Delft, The Netherlands. M.J.F.Stive@tudelft.nl 3. Harbour, Coastal and Offshore Engineering, Deltares, PO ox 177, 2600 MH Delft, The Netherlands. NATURE CLIMATE CHANGE 1

2 SUPPLEMENTARY METHODS (1): Derivation of the co-efficient representing the lag effect between SLR and resulting basin infilling for the basin infilling term; (Eqn 2) in the model. The starting point for this derivation is the scale aggregated model ASMITA (Stive et al., 1998), which is based on the conservation of sediment within a domain comprising a three element inlet system (ebb delta, channel, and basin) and the 'outside world' (which represents the adjacent nearshore area). The two main assumptions in ASMITA is that morphological interaction between the three system elements take place due to diffusive sediment transport and that the 'outside world' is always in a state of equilibrium. When the system is perturbed (e.g. by introducing SLR), the three elements and the outside world interact such that each of the 3 system elements evolve towards an empirically specified dynamic equilibrium state. Van Goor et al. (2003) present a simplified single-element version of ASMITA. In the singleelement model, it is assumed that morphological evolution of one system element (e.g. the basin) is dominated by the sediment transport between that element and the outside world, which, in this case, includes not only the adjacent nearshore area but also the other two possible system elements (i.e. channel and ebb delta). Such a single-element version of the ASMITA model is appropriate to investigate (to first order) the process of basin infilling due to SLR in the small inlet-basin systems (barrier estuaries with little or no intertidal flats, backwater marshes, or ebb tidal deltas) that are considered in the present study. The absence of pronounced ebb tidal deltas at these systems, enables the simplifying assumption that the infill volume will be borrowed from the adjacent coastline. The linearised single-element ASMITA model can be expressed as: dv dt V V T AR (A1.1) Page 2 of 9

3 where, V t V = wet volume of the basin below the changing sea level = time = equilibrium volume in case that sea level does not change (taken to be the present day basin volume) T = morphological time scale of the inlet/basin system A = horizontal surface area of the basin, and R = rate of sea-level rise. The second term on the right hand side represents the change of the basin volume due to sealevel rise, while the first term represents the basin volume change due to erosion. Thus, the sediment import into the basin is given by: Q bi V V T (A1.2) When R is constant, the solution of equation (A1.1) is t V V0 Ve exp V T e (A1.3) In which V 0 is the initial value of V, i.e. V(t = 0), and V e is the dynamic equilibrium volume, i.e. the basin volume after a long time of sea level rise at a constant rate of R. When dynamic equilibrium is reached, the rate of volume change should be zero (i.e dv/dt = 0) and thus by susbstituting V = V e in (A1.1): Ve V A RT (A1.4) Therefore, the linear model correctly reproduces the basic system behaviour where the basin at dynamic equilibrium gets deeper with sea level rise. Page 3 of 9

4 In case sea level rise suddenly accelerates from rate R 1 to R 2 at t = 0 (e.g. at the beginning of the 21st century as projected by IPCC (2007) ) the solution is: t t V V V exp V A T R R exp V A TR T T e1 e2 e (A1.5) y substituting (A1.5) for V in (A1.2), the sediment import into the basin (or the sand eroded from the adjacent coast to satisfy the demand of SLR induced basin infilling) is obtained as: t Q A R R exp A R T bi (A1.6) Equation (A1.6) indicates that the sediment import into the basin gradually increases from the import needed for compensating sea level rise at the old rate to that needed at the new increased rate. This derivation can also be done for the general case where R is a function of time. An analytical solution is possible if R can be written in the form of a polynomial of t. From (A1.6), the total sediment import during a given time period (t = t 1 to t=t 2 ) can be calculated by integrating within those limits of t as: t2 t1 AT R1 R2 exp exp T T (A1.7) The above expression is the same quantity described by Eqn 2 for basin infilling in the manuscript, and therefore, t2 t1 CI LAChDoC M SA AT R1 R2 exp exp T T (A1.8) Page 4 of 9

5 where M is the lag coefficient being sought (representing the lag between SLR and basin morphological response); L AC is the length of inlet affected coastline (m); and h DoC is the depth of closure (m). Due to the very slow rate of SLR (~1.8mm/yr) in the 20th century, R 1 can be assumed to be zero (Stive et al., 2010). This reduces (A1.8) to: t2 t1 M S TR2 exp exp T T (A1.9) The Morphological time scale T still needs to be defined. As (A1.1) is essentially a linearised version of the single element ASMITA model, the expression given by Stive and Wang (2003) for the morphological time scale in ASMITA can be directly used here: T 1 VE V E nce wsa (A1.10) where DA c L n = an empirical coefficient, between 3 and 5 (Wang et al., 2007), C E = representative (long-term average) volumetric sediment concentration in the system. w s = vertical exchange velocity of sediment D = diffusion coefficient A c = cross sectional area at the mouth of the basin L = a length scale representing the distance between inside and outside of the basin Assuming typical values of the above variables for the small inlet-basin systems considered in the present study (n = 5; C E = 3.14x10-4 ; V E = 200 x10 6 m 3 ; A = 75 x10 6 m 2 ; w s = 0.001m/s; D = 200m 2 /s; Ac = 2000 m 2 ; L = 10,000m), the morphological time scale T is estimated as ~ 100 Yrs. Page 5 of 9

6 Now substituting t 1 =0; t 2 = 100 yrs, T = 100 yrs, and S = R 2 t 2 (assuming a linear rate of SLR) in (A1.9) yields M = 0.63 (i.e. M ~ 0.5). Thus, a coefficient of 0.5 is used to represent the lag effect in Eqn 2 of the model presented in the manuscript. Note that the above derivation is based on the following assumptions: (a) the rate of SLR increases sharply at the beginning of the 21st century, as predicted by the IPCC, (b) the inlet cross-sectional area and the tidal prism remains more or less constant, which is a valid assumption for the small inlet/basin systems considered herein (see system description in manuscript), especially at the 100yr time scales considered. References: IPCC. (2007). "Climate Change 2007: The Physical Science asis, Summary for Policy Makers, Fourth Assessment Report of the Intergovernmental Panel on Climate Change (IPCC)", Cambridge University Press, Cambridge, UK. Stive, M.J.F., Capobianco, M., Wang, Z.., Ruol, P. and uijsman, M.C. (1998). "Morphodynamics of a tidal lagoon and the adjacent Coast". In: Physics of estuaries and coastal seas (Eds: J. Dronkers and M. Scheffers), alkema, Rotterdam, pp Stive, M. J. F., and Wang, Z.. (2003). "Morphodynamic modelling of tidal basins and coastal inlets", In: Advances in Coastal Modelling (Ed. C. Lakhan). Elsevier Science. V. pp Stive, M. J. F., Ranasinghe, R., and Cowell, P. (2010). "Sea level rise and coastal erosion", In: Handbook of Coastal and Ocean Engineering (Ed. Y. Kim). World Scientific. pp Van Goor, M.A., M.J.F. Stive, Z.. Wang, T.J. Zitman. (2003). "Impact of sea level rise on the morphological stability of tidal inlets". Marine Geology (202: 3-4), pp Page 6 of 9

7 SUPPLEMENTARY METHODS (2): Derivation of the term to describe basin volume change due to CC driven variations in average annual riverflow; (Eqn 3) in the model. A basin/inlet system will always strive to maintain cross-sectional equilibrium velocities (O'rien, 1931; van der Wegen et al., 2010). Therefore, here the main assumption is that the mean velocity through any cross-section remains unchanged in time: Vel present = Vel future (A2.1) Furthermore, for the small inlet-basin systems (barrier estuaries) located in wave dominated, microtidal environments considered here, it can also be safely assumed that the tidal prism remains unchanged in time. This is mainly because this type of systems generally have little or no intertidal flats, backwater marshes, or ebb tidal deltas (Kjerfve, 1994; Woodroffe, 2002). To satisfy (A2.1) and taking into consideration the riverflow modified ebb flow, at a given time in the future (say year 2100) P Q P Q Q W h W h h) R R R (A 2.2) where Q R = CC driven variation (relative to present) in riverflow (per ebb tide), h = average basin depth change related to the CC driven variation in riverflow, P = mean ebb tidal prism (m 3 ), Q R = present day riverflow volume during ebb tide (m 3 ), W = width of the basin (m), and h = present day average basin depth (m). Simplifying (A2.2) yields: P Q W h Q W h (A2.3) R R Page 7 of 9

8 If the length of the basin = L, then the sediment demand/supply (m 3 ) to the coast due to this process is given by: hl W ` (A2.4) Multiplying both sides of (A2.3) by L and using similarity with (A2.4): Q W L h Q V hlw P Q P Q R R R R (A2.5) where V = present day basin volume ( = W L h). References: Kjerfve,. (1994). "Coastal lgoon processes", In: Coastal lagoon process (Ed.. Kjerfve). Elsevier Science V, pp 1-7. O rien, M.P. (1931). "Estuary and Tidal Prisms Related to Entrance Areas". Civil Engineering, 1(8), Van der Wegen. M., Dastgheib, A., and Roelvink, J. (2010). "Morphodynamic modelling of tidal channel evolution in comparison to empirical PA relationship". Coastal Engineering, 57, Woodroffe, C. D. (2002). "Coasts: Form, process and evolution". Cambridge university press, 623pp. Page 8 of 9

9 SUPPLEMENTARY TALE 1: Location Coordinates, and wave, tide and riverflow conditions at the study sites. System name Coordinates Annual ave. wave height (m), and period (s) Mean Oceanic Tidal range (m) Mean estuarine tidal range (m) Approx. Annual riverflow (10 6 m 3 ) Wilson Inlet Swan River Tu Hien Inlet Thuan An Inlet 35 o S; 117 o 19,53 E 1m, 13s 0.7 (diurnal) o S; 115 o E 1.5m, 8s 0.7 (diurnal) o N; 107 o E 1m, 4s 0.4 (semi-diurnal) o N; 107 o E 1m, 4s 0.4 (semi-diurnal) Page 9 of 9