Two-way Nested Model Research Articles

Transport dynamics in a complex coastal archipelago

Abstract. The Archipelago Sea (in the Baltic Sea) is characterised by thousands of islands of various sizes and steep gradients of the bottom topography. Together with the much deeper Åland Sea, the Archipelago Sea acts as a pathway to the water exchange between the neighbouring basins, Baltic proper and Bothnian Sea. We studied circulation and water transports in the Archipelago Sea using a new configuration of the NEMO 3D hydrodynamic model that covers the Åland Sea–Archipelago Sea region with a horizontal resolution of around 500 m. The results show that currents are steered by the geometry of the islands and straits and the bottom topography. Currents are highest and strongly aligned in the narrow channels in the northern part of the area, with the directions alternating between south and north. In more open areas, the currents are weaker with wider directional distribution. During our study period of 2013–2017, southward currents were more frequent in the surface layer. In the bottom layer, in areas deeper than 25 m, northward currents dominated in the southern part of the Archipelago Sea, while in the northern part southward and northward currents were more evenly represented. Due to the variation in current directions, both northward and southward transports occur. During our study period, the net transport in the upper 20 m layer was southward. Below 20 m depth, the net transport was southward at the northern edge and northward at the southern edge of the Archipelago Sea. There were seasonal and inter-annual variations in the transport volumes and directions in the upper layer. Southward transport was usually largest in spring and summer months, and northward transport was largest in autumn and winter months. The transport dynamics in the Archipelago Sea show different variabilities in the north and south. A single transect cannot describe water transport through the whole area in all cases. Further studies on the water exchange processes between the Baltic proper and the Bothnian Sea through the Archipelago Sea would benefit from using a two-way nested model set-up for the region.

Transport of Microplastics From the Daugava Estuary to the Open Sea

This study considers the transport of microplastics (MPs) from inland waters (rivers and lakes) to coastal waters and then to the open sea. A three-dimensional MP Eulerian tracer model based on the HIROMB-BOOS model (HBM) with wave-induced transport and biofouling process is used. Multilayer two-way nested model grids with 3–0.5–0.25–0.05 nautical mile resolutions are applied to resolve relevant riverine–estuarial–coastal hydrodynamics with a focus on the southern waters in the Gulf of Riga. The major river of the Gulf of Riga, Daugava, is governed by the Riga Hydro Power Station (RHPS) with high daily and weekly variability of the runoff creating more intense outflows during its working hours. This gives additional complexity when calibrating this model. The model results are validated against MP observations that are collected on various cruises in the summer of 2018 in the Gulf of Riga. There exists a strong synoptic variability in the observations, which are also reproduced. As the rivers are the primary source of MPs, a special backtracking algorithm was developed to find the most possible source of pollutants at a given location and time. The backtracking algorithm includes optimization with respect to salinity in order to prefer trajectories coming from freshwater and, consequently, MP sources. Lagrangian drift studies are performed for events with high precipitation in the estuary domain when sewer overflow at wastewater treatment plants (WWTPs) can occur, and the results are compared with different MP components in observations.

ROMS configuration of a two-way nested model of the Mid-Atlantic Bight and Delaware Bay.

ROMS configuration of a two-way nested model of the Mid-Atlantic Bight and Delaware Bay.

Modeling Transit Flow Through Port Gates and Connecting Channel in Baltic Sea—Liepaja Port—Liepaja Lake System

This study investigates a water transport features by extending Copernicus Marine Environment Service (CMEMS) to the Liepaja coast-port-channel-lake system with a two-way nested model. The Liepaja lake and Liepaja port are connected by Trade channel. The Liepaja port has three gates—the openings in wave breakers connecting the port aquatory with the Baltic sea. Each of gates has a corresponding dredged channel for securing the navigation. A hydrodynamic model is set up to study the flow and water level in this system. The area of the port gates, port and Trade channel are resolved by 33 m grid. The model results are verified against currents and sea level observations inside/outside port, Trade channel and Liepaja lake. Results and observations show that strong currents occur in the Trade channel in case of rapid sea level change in Baltic sea despite the Trade channel is rather shallow at the connection with Liepaja lake. The northern part of the Liepaja lake gets filled with brackish water during storm surge events. The channel has notable alternating current also during a relatively calm weather due to the port seiches. Long and narrow shape of the channel implies the Helmholtz type oscillations between the lake and the port with a period in approximately semidiurnal range. Hydrodynamic simulations describe well these oscillations but the phase of hourly scale oscillations in the port may differ in case of weak external forcing. Water exchange is significantly increased by the transit (gate to gate) sea currents. This transit flow usually occurs between South or Central gate and the North gate carrying sea water into the port. Northward flow of the surface layer is more characteristic in the port aquatory due the prevailing south-western winds. There are intense morphological processes at the coastline and underwater slope near the Liepaja port due to a sandy western coastline of Latvia, long fetch of the waves and strong currents at the port gates. Liepaja port is one of the Latvian ports in HywasPort operational service of hydrodynamics, waves and siltation.

Closed-form approximate tolerance intervals for some general linear models and comparison studies

The problems of constructing tolerance intervals (TIs) in random effects model and in a mixed linear model are considered. The methods based on the generalized variable (GV) approach and the one based on the modified large sample (MLS) procedure are evaluated with respect to coverage probabilities and expected width in various setups using Monte Carlo simulation. Our comparison studies indicate that the TIs based on the MLS procedure are comparable to or better than those based on the GV approach. As the MLS TIs are in closed-form, they are easier to compute than those based on the GV approach. TIs for a two-way nested model are also derived using the MLS method, and their merits are evaluated using simulation. The procedures are illustrated using a practical example.

Island shadow effects and the wave climate of the Western Tuamotu Archipelago (French Polynesia) inferred from altimetry and numerical model data

To implement a numerical model of atoll lagoon circulation, we characterized first the significant wave height (Hs) regime of the Western Tuamotu Archipelago and the local attenuation due to the protection offered by large atolls in the south Tuamotu. Altimetry satellite data and a WAVEWATCH III two-way nested wave model at 5km resolution from 2000 to 2010 were used. Correlation between altimetry and model was high (0.88) over the period. According to the wave model, the archipelago inner seas experienced attenuated Hs year-long with a yearly average Hs around 1.3m vs a minimum of 1.6m elsewhere. The island shadow effect is especially significant in the austral winter. In contrast with southern atolls, Western Tuamotu experienced only few days per year of Hs larger than 2.5m generated by very high Hs southern swell, transient western local storms, strong easterly winds, and during the passage of distant hurricanes.

Flux comparison of Eulerian and Lagrangian estimates of Agulhas leakage: A case study using a numerical model

Estimating the magnitude of Agulhas leakage, the volume flux of water from the Indian to the Atlantic Ocean, is difficult because of the presence of other circulation systems in the Agulhas region. Indian Ocean water in the Atlantic Ocean is vigorously mixed and diluted in the Cape Basin. Eulerian integration methods, where the velocity field perpendicular to a section is integrated to yield a flux, have to be calibrated so that only the flux by Agulhas leakage is sampled. Two Eulerian methods for estimating the magnitude of Agulhas leakage are tested within a high-resolution two-way nested model with the goal to devise a mooring-based measurement strategy. At the GoodHope line, a section halfway through the Cape Basin, the integrated velocity perpendicular to that line is compared to the magnitude of Agulhas leakage as determined from the transport carried by numerical Lagrangian floats. In the first method, integration is limited to the flux of water warmer and more saline than specific threshold values. These threshold values are determined by maximizing the correlation with the float-determined time series. By using the threshold values, approximately half of the leakage can directly be measured. The total amount of Agulhas leakage can be estimated using a linear regression, within a 90% confidence band of 12 Sv. In the second method, a subregion of the GoodHope line is sought so that integration over that subregion yields an Eulerian flux as close to the float-determined leakage as possible. It appears that when integration is limited within the model to the upper 300 m of the water column within 900 km of the African coast the time series have the smallest root-mean-square difference. This method yields a root-mean-square error of only 5.2 Sv but the 90% confidence band of the estimate is 20 Sv. It is concluded that the optimum thermohaline threshold method leads to more accurate estimates even though the directly measured transport is a factor of two lower than the actual magnitude of Agulhas leakage in this model.

Tolerance intervals in a two-way nested model with mixed or random effects

We address the problem of deriving a one-sided tolerance interval in a two-way nested model with mixed or random effects. The generalized confidence interval idea is used in the derivation of our tolerance limit, and the results are obtained by suitably modifying the approach in Krishnamoorthy and Mathew [Krishnamoorthy, K. and Mathew, T., 2004, Generalized confidence limits and one-sided tolerance limits in balanced and unbalanced one-way random models. Technometrics, 46, 44–52], for the one-way random model. Our proposed tolerance limit can be estimated by Monte Carlo simulation. We have also been able to develop closed form approximations in some cases. The performance of our tolerance interval is numerically investigated and found to be satisfactory. The results are illustrated with an example.

A two-way nested coupled tide-surge model for the Taiwan Strait

A two-way nested coupled tide-surge prediction model was established and applied in the Taiwan Strait and adjacent sea area in this study. This two-dimensional (2D) model had a fine horizontal resolution and took into account the interaction between storm surges and astronomical tides, which made it suitable for depicting the complicated physical properties of storm surges in the Taiwan Strait. A two-way nesting technique and an open boundary condition developed from Flather's radiation condition and Røed and Smedstad's local mode idea, were successfully implemented in the model. A simulation experiment showed that the open boundary condition could be used in the coupled tide-surge model and that the performance of the two-way nested model was slightly superior in accuracy to that of the one-way nested one. The fluctuations of storm surge residuals with tidal period at Sansha and Pingtan tide stations during the period of typhoon Dan in 1999 were well reproduced by the model, with the coupling effect between storm surges and tides indicating that the effect of astronomical tides upon typhoon surges should be considered in a storm-surge prediction model for the Taiwan Strait. The forecast experiment during typhoon Talim in 2005 showed that the storm surge prediction outputs by the model were better in the early 20 h of the forecast period of each model run than those in the later period due to the prediction accuracy of the typhoon track, maximum winds, and central air pressures.

Multigrid state vector for data assimilation in a two-way nested model of the Ligurian Sea

A system of two nested models composed by a coarse resolution model of the Mediterranean Sea, an intermediate resolution model of the Provençal Basin and a high resolution model of the Ligurian Sea is coupled with a Kalman-filter based assimilation method. The state vector for the data assimilation is composed by the temperature, salinity and elevation of the three models. The forecast error is estimated by an ensemble run of 200 members by perturbing initial condition and atmospheric forcings. The 50 dominant empirical orthogonal functions (EOF) are taken as the error covariance of the model forecast. This error covariance is assumed to be constant in time. Sea surface temperature (SST) and sea surface height (SSH) are assimilated in this system.

Two-way nested model of mesoscale circulation features in the Ligurian Sea

A coarse resolution primitive equation model of 1/4° resolution is implemented covering the whole Mediterranean Sea. Within this grid a 1/20° resolution model of the Liguro-Provençal basin and the northern part of the Tyrrhenian Sea is embedded. A third fine resolution model of 1/60° is nested in the latter one and simulates the dynamics of the Ligurian Sea. Comparisons between one-way and two-way nesting in simulating the Northern Current (NC) are made. The properties of the Eastern and Western Corsican Current and the Northern Current are investigated with this nesting system. Special attention is given to the variability of the NC. Meanders and interactions with Winter Intermediate Water lenses are shown. Topographic features also lead to a highly variable NC.

Application of a two-way nested model to the seamount problem

A two-way nested model has been constructed and applied to the idealized ocean where a uniform mean flow impinges on the isolated Gaussian-shaped seamount and produces two eddies (cold and warm) in the depths. The performance of the nested model has been evaluated subjectively and objectively. Both subjective and objective analyses confirm the traditional view that the nested model can well capture the performance of isolated eddies. Objective analysis, however, reveals some quantitatively important features of a two-way nested model. One is penetration of improved features into the coarse domain and another is the deterioration of mean flow field inside the nested area, neither of which is clear from subjective analysis. With successful application of two-way nested model to the seamount problem, we expect that such a nested model will also be applicable to other oceanic phenomena, particularly to some coastal problems whose time scale is short and where the topographic effects are dominant.

A two-way nested-grid ocean-circulation model for the Meso-American Barrier Reef System

A two-way nested-grid ocean-circulation model is developed for the Meso-American Barrier Reef System (MBRS), using a newly developed two-way interactive nesting technique. The unique feature of this new nesting technique is its use of the semi-prognostic method (Sheng et al. 2001) to exchange information between different grids through the model momentum equations. The nested-grid model for the MBRS has a fine-resolution inner model embedded in a coarse-resolution outer model. The outer model is the western Caribbean Sea model developed by Sheng and Tang (2003), with a horizontal resolution of roughly 19 km. The inner model domain covers the northwest Caribbean Sea (NWCS) between 79°W and 89°W and between 15.5°N and 22°N, with a horizontal resolution of roughly 6 km. The nested-grid ocean model is initialized with the January mean temperature and salinity and forced by the monthly mean COADS (comprehensive ocean-atmosphere data set) wind stress and surface heat flux. The model sea-surface salinity is restored to the monthly mean climatology. The nested-grid model is integrated for 2 years and the second-year model results are presented in this paper. The model-calculated annual-mean near-surface currents over the NWCS agree reasonably well with the time-mean near-surface currents inferred by Fratantoni (2001) from trajectories of the satellite-tracked 15-m drogued drifters in the 1990s. The two-way nested model is also used to quantify the role of local wind stress, local density gradients and boundary forcings of the outer model in driving the annual-mean circulation in the region.

Variance Components in the Two-Way Nested Model with Incomplete Nesting Information

When part of the nesting information in a two-way nested model is missing, there has been no way to use all of the data in the analysis of variance components. Discarding the data with missing nesting information loses useful information, and in some circumstances, this approach cannot separate variance components from one another. To make use of the data with missing nesting information, computable sums of squares for the data with missing nesting information can be linearly combined with sums of squares for the data with complete nesting information. Prespecified weights are needed for the combination. Different estimates are obtained by using different weights. Because all of these estimators are unbiased, variances and covariances of these estimators are derived and used to compare these estimators. In addition, a simulation study is conducted to provide evidence for the reliability of the variances and covariances formulas. Finally, as an application, the proposed methods are applied to the analysis of a proficiency testing program.

Variance Components in the Two-Way Nested Model With Incomplete Nesting Information

When part of the nesting information in a two-way nested model is missing, there has been no way to use all of the data in the analysis of variance components. Discarding the data with missing nesting information loses useful information, and in some circumstances, this approach cannot separate variance components from one another. To make use of the data with missing nesting information, computable sums of squares for the data with missing nesting information can be linearly combined with sums of squares for the data with complete nesting information. Prespecified weights are needed for the combination. Different estimates are obtained by using different weights. Because all of these estimators are unbiased, variances and covariances of these estimators are derived and used to compare these estimators. In addition, a simulation study is conducted to provide evidence for the reliability of the variances and covariances formulas. Finally, as an application, the proposed methods are applied to the analysis of a proficiency testing program.