Numerical Simulation of Water Renewal Timescales in the Mahakam Delta, Indonesia

Abstract

Water renewal timescales, namely age, residence time, and exposure time, which are defined in accordance with the Constituent-oriented Age and Residence time Theory (CART), are computed by means of the unstructured-mesh, finite element model Second-generation Louvain-la-Neuve Ice-ocean Model (SLIM) in the Mahakam Delta (Borneo Island, Indonesia). Two renewing water types, i.e., water from the upstream boundary of the delta and water from both the upstream and the downstream boundaries, are considered, and their age is calculated as the time elapsed since entering the delta. The residence time of the water originally in the domain (i.e., the time needed to hit an open boundary for the first time) and the exposure time (i.e., the total time spent in the domain of interest) are then computed. Simulations are performed for both low and high flow conditions, revealing that (i) age, residence time, and exposure time are clearly related to the river volumetric flow rate, and (ii) those timescales are of the order of one spring-neap tidal cycle. In the main deltaic channels, the variation of the diagnostic timescales caused by the tide is about 35% of their averaged value. The age of renewing water from the upstream boundary of the delta monotonically increases from the river mouth to the delta front, while the age of renewing water from both the upstream and the downstream boundaries monotonically increases from the river mouth and the delta front to the middle delta. Variations of the residence and the exposure times coincide with the changes of the flow velocity, and these timescales are more sensitive to the change of flow dynamics than the age. The return coefficient, which measures the propensity of water to re-enter the domain of interest after leaving it for the first time, is of about 0.3 in the middle region of the delta.

Consistent Boundary Conditions for Age Calculations

“…In general, the open boundaries are believed to be the most problematic ones. To estimate water renewal of semi-enclosed domains, many authors resorted to Dirichlet boundary conditions [62,120] on open boundaries. This approach is undoubtedly the easiest one.…”

Tracers and Timescales: Tools for Distilling and Simplifying Complex Fluid Mechanical Problems

“…Using consistent boundary conditions, Pham Van et al [15] apply the water renewal assessment strategy of de Brye et al [20] to the delta of the Mahakam River (Indonesia). Water renewal timescales (i.e., age, residence, and exposure times) are quite short (i.e., a few days to a couple of weeks) and crucially depend on the river discharge in spite of the large influence of tides on the hydrodynamics.…”

“…For example, a number of the papers in this Special Issue describe studies in which transport timescales such as age, residence time, and exposure time are computed from the solution of partial differential problems ("PDPs", which include partial differential equations plus initial and boundary conditions). These PDPs describe the evolution of numerical tracers and tracer-like quantities, including tagged water types or masses, which are treated as passive tracers (e.g., [2,[15][16][17]).…”

Residence Time Analysis in the Albufera of Valencia, a Mediterranean Coastal Lagoon, Spain

“…This is the case of the Venice Lagoon (Italy), where the cleaning capacity of the basin is influenced by the renewal mechanism produced by the tidal exchange [6]. Moreover, the starting instant of a tidal cycle has a greater effect on the residence time of a water parcel than the duration of the cycle, as observed in Mahakam Delta (Borneo, Indonesia) [7]. In general, in coastal lakes connected to the sea, the water renewal rate of the lake depends not just on the tidal exchanges between the outer sea and the aquatic system but also on the combination of other factors such as wind, topography, bathymetry, density stratification and the freshwater runoff [8].…”

“…Depending on the size of the inputs and the volume of the water body, the variation in renewal can be significant [14]. The way to estimate the time of renewal is variable, and can be done with hydrodynamic models, used to simulate water surface elevation, exchanged flows and velocities [7,15], or by the use of tracers, such as the stable isotope ratios of hydrogen and oxygen or tritium-helium-3 isotope, among others [4,16], or by means of water balance when it is possible to make measurements of inflows or outflows.…”