On the modelling of wave breaking and set-up on coral reefs

An extended refraction-diffraction equation [Massel, S.R., 1993. Extended refraction-diffraction equation for surface waves. Coastal Eng. 19, 97-126] has been applied to predict wave transformation and breaking as well as wave-induced set-up on two-dimensional reef profiles of various shapes. A free empirical coefficient alpha in a formula for the average rate of energy dissipation [epsilon(b)] = (alpha rho g omega/8 pi)(root gh/C)(H-3/h) in the modified periodic bore model was found to be a function of the dimensionless parameter F-c0 = (g(1.25)H(0)(0.5)T(2.5))/h(r)(1.75), proposed by Gourlay [Gourlayl M.R., 1994. Wave transformation on a coral reef. Coastal Eng. 23, 17-42]. The applicability of the developed model has been demonstrated for reefs of various shapes subjected to various incident wave conditions. Assuming proposed relationships of the coefficient alpha and F-c0, the model provides results on wave height attenuation and set-up elevation which compare well with experimental data. (C) 2000 Elsevier Science B.V. All rights reserved.

Nonbreeding Eastern Curlews Numenius madagascariensis Do Not Increase the Rate of Intake or Digestive Efficiency before Long-Distance Migration because of an Apparent Digestive Constraint

The possibility of premigratory modulation in gastric digestive performance was investigated in a long-distance migrant, the eastern curlew (Numenius madagascariensis), in eastern Australia. The rate of intake in the curlews was limited by the rate of digestion but not by food availability. It was hypothesized that before migration, eastern curlews would meet the increased energy demand by increasing energy consumption. It was predicted that (1) an increase in the rate of intake and the corresponding rate of gastric throughput would occur or (2) the gastric digestive efficiency would increase between the mid-nonbreeding and premigratory periods. Neither crude intake rate (the rate of intake calculated including inactive pauses; 0.22 g DM [grams dry mass] or 3.09 kJ min(-1)) nor the rate of gastric throughput (0.15 g DM or 2.85 kJ min(-1)) changed over time. Gastric digestive efficiency did not improve between the periods (91%) nor did the estimated overall energy assimilation efficiency (63% and 58%, respectively). It was concluded that the crustacean-dominated diet of the birds is processed at its highest rate and efficiency throughout a season. It appears that without a qualitative shift in diet, no increase in intake rate is possible. Accepting these findings at their face value poses the question of how and over what time period the eastern curlews store the nutrients necessary for the ensuing long, northward nonstop flight.

Settling velocity of sediments at high concentrations

New data on the settling velocity of artificial sediments and natural sands at high concentrations are presented. The data are compared with a widely used semiempirical Richardson and Zaki equation (Trans. Inst. Chem. Eng. 32 (1954) 35), which gives an accurate measure of the reduction in velocity as a function of concentration and an experimentally determined empirical power n. Here, a simple method of determining n is presented using standard equations for the clear water settling velocity and the seepage flow within fixed sediment beds. The resulting values for n are compared against values derived from new and existing laboratory data for beach and filter sands. For sands, the appropriate values of n are found to differ significantly from those suggested by Richardson and Zaki for spheres, and are typically larger, corresponding to a greater reduction in settling velocity at high concentrations. For fine and medium sands at concentrations of order 0.4, the hindered settling velocity reduces to about 70% of that expected using values of n derived for spheres. At concentrations of order 0.15, the hindered settling velocity reduces to less than half of the settling velocity in clear water. These reduced settling velocities have important implications for sediment transport modelling close to, and within, sheet flow layers and in the swash zone.

Hindered settling of sand grains

The sedimentation rate of sand grains in the hindered settling regime has been considered to assess particle shape effects. The behaviour of various particulate systems involving sand has been compared with the widely used Richardson-Zaki expression. The general form of the expression is found to hold, in as much as remaining as a suitable means to describe the hindered settling of irregular particles. The sedimentation exponent n in the Richardson-Zaki expression is found to be significantly larger for natural sand grains than for regular particles. The hindered settling effect is therefore greater, leading to lower concentration gradients than expected. The effect becomes more pronounced with increasing particle irregularity. At concentrations around 0.4, the hindered settling velocity of fine and medium natural sands reduces to about 70% of the value predicted using existing empirical expressions for n. Using appropriate expressions for the fluidization velocity and the clear water settling velocity, a simple method is discussed to evaluate the sedimentation exponent and to determine the hindered settling effect for sands of various shapes.

Atoll lagoon flushing forced by waves

Water level and current measurements from two virtually enclosed South Pacific atolls, Manihiki and Rakahanga, support a new lagoon flushing mechanism which is driven by waves and modulated by the ocean tide for virtually enclosed atolls. This is evident because the lagoon water level remains above the ocean at all tidal phases (i.e., ruling out tidal flushing) and because the average lagoon water level rises significantly during periods with large waves. Hence, we develop a model by which the lagoons are flushed by waves pumping of ocean water into the lagoon and gravity draining water from the lagoon over the reef rim. That is, the waves on the exposed side push water into the lagoon during most of the tidal cycle while water leaves the lagoon on the protected side for most of the tidal cycle. This wave-driven through flow flushing is shown to be more efficient than alternating tidal flushing with respect to water renewal. Improved water quality should therefore be sought through enhancement of the natural wave pumping rather than by blasting deep channels which would change the system to an alternating tide-driven one.

Artificial pumping errors in the Kool-Parker scaling model of soil moisture hysteresis

Hysteresis models that eliminate the artificial pumping errors associated with the Kool-Parker (KP) soil moisture hysteresis model, such as the Parker-Lenhard (PL) method, can be computationally demanding in unsaturated transport models since they need to retain the wetting-drying history of the system. The pumping errors in these models need to be eliminated for correct simulation of cyclical systems (e.g. transport above a tidally forced watertable, infiltration and redistribution under periodic irrigation) if the soils exhibit significant hysteresis. A modification is made here to the PL method that allows it to be more readily applied to numerical models by eliminating the need to store a large number of soil moisture reversal points. The modified-PL method largely eliminates any artificial pumping error and so essentially retains the accuracy of the original PL approach. The modified-PL method is implemented in HYDRUS-1D (version 2.0), which is then used to simulate cyclic capillary fringe dynamics to show the influence of removing artificial pumping errors and to demonstrate the ease of implementation. Artificial pumping errors are shown to be significant for the soils and system characteristics used here in numerical experiments of transport above a fluctuating watertable. (c) 2005 Elsevier B.V. All rights reserved.

The cost of uniqueness in groundwater model calibration

Calibration of a groundwater model requires that hydraulic properties be estimated throughout a model domain. This generally constitutes an underdetermined inverse problem, for which a Solution can only be found when some kind of regularization device is included in the inversion process. Inclusion of regularization in the calibration process can be implicit, for example through the use of zones of constant parameter value, or explicit, for example through solution of a constrained minimization problem in which parameters are made to respect preferred values, or preferred relationships, to the degree necessary for a unique solution to be obtained. The cost of uniqueness is this: no matter which regularization methodology is employed, the inevitable consequence of its use is a loss of detail in the calibrated field. This, ill turn, can lead to erroneous predictions made by a model that is ostensibly well calibrated. Information made available as a by-product of the regularized inversion process allows the reasons for this loss of detail to be better understood. In particular, it is easily demonstrated that the estimated value for an hydraulic property at any point within a model domain is, in fact, a weighted average of the true hydraulic property over a much larger area. This averaging process causes loss of resolution in the estimated field. Where hydraulic conductivity is the hydraulic property being estimated, high averaging weights exist in areas that are strategically disposed with respect to measurement wells, while other areas may contribute very little to the estimated hydraulic conductivity at any point within the model domain, this possibly making the detection of hydraulic conductivity anomalies in these latter areas almost impossible. A study of the post-calibration parameter field covariance matrix allows further insights into the loss of system detail incurred through the calibration process to be gained. A comparison of pre- and post-calibration parameter covariance matrices shows that the latter often possess a much smaller spectral bandwidth than the former. It is also demonstrated that, as all inevitable consequence of the fact that a calibrated model cannot replicate every detail of the true system, model-to-measurement residuals can show a high degree of spatial correlation, a fact which must be taken into account when assessing these residuals either qualitatively, or quantitatively in the exploration of model predictive uncertainty. These principles are demonstrated using a synthetic case in which spatial parameter definition is based oil pilot points, and calibration is Implemented using both zones of piecewise constancy and constrained minimization regularization. (C) 2005 Elsevier Ltd. All rights reserved.

Swash-aquifer interaction in the vicinity of the water table exit point on a sandy beach

The coupling of sandy beach aquifers with the swash zone in the vicinity of the water table exit point is investigated through simultaneous measurements of the instantaneous shoreline (swash front) location, pore pressures and the water table exit point. The field observations reveal new insights into swash-aquifer coupling not previously gleaned from measurements of pore pressure only. In particular, for the case where the exit point is seaward of the observation point, the pore pressure response is correlated with the distance between the exit point and the shoreline in that when the distance is large the rate of pressure drop is fast and when the distance is small the rate decreases. The observations expose limitations in a simple model describing exit point dynamics which is based only on the force balance on a particle of water at the sand surface and neglects subsurface pressures. A new modified form of the model is shown to significantly improve the model-data comparison through a parameterization of the effects of capillarity into the aquifer storage coefficient. The model enables sufficiently accurate predictions of the exit point to determine when the swash uprush propagates over a saturated or a partially saturated sand surface, potentially an important factor in the morphological evolution of the beach face. Observations of the shoreward propagation of the swash-induced pore pressure waves ahead of the runup limit shows that the magnitude of the pressure fluctuation decays exponentially and that there is a linear increase in time lags, behavior similar to that of tidally induced water table waves. The location of the exit point and the intermittency of wave runup events is also shown to be significant in terms of the shore-normal energy distribution. Seaward of the mean exit point location, peak energies are small because of the saturated sand surface within the seepage face acting as a "rigid lid'' and limiting pressure fluctuations. Landward of the mean exit point the peak energies grow before decreasing landward of the maximum shoreline position.