Simulating the three-dimensional circulation and hydrography of Halifax Harbour using a multi-nested coastal ocean circulation model

Abstract

Halifax Harbour is located on the Atlantic coast of Nova Scotia, Canada. It is one of the world’s largest, ice-free natural harbours and of great economic importance to the region. A good understanding of the physical processes controlling tides, flooding, transport and dispersion, and hydrographic variability is required for pollution control and sustainable development of the Harbour. For the first time, a multi-nested, finite difference coastal ocean circulation model is used to reconstruct the three-dimensional circulation and hydrography of the Harbour and its variability on timescales of hours to months for 2006. The model is driven by tides, wind and sea level pressure, air-sea fluxes of heat, and terrestrial buoyancy fluxes associated with river and sewage discharge. The predictive skill of the model is assessed by comparing the model simulations with independent observations of sea level from coastal tide gauges and currents from moored instruments. The simulated hydrography is also compared against a new monthly climatology created from all available temperature and salinity observations made in the Harbour over the last century. It is shown that the model can reproduce accurately the main features of the observed tides and storm surge, seasonal mean circulation and hydrography, and wind driven variations. The model is next used to examine the main physical processes controlling the circulation and hydrography of the Harbour. It is shown that non-linear interaction between tidal currents and complex topography occurs over the Narrows. The overall circulation can be characterized as a two-layer estuarine circulation with seaward flow in the thin upper layer and landward flow in the broad lower layer. An important component of this estuarine circulation is a relatively strong, vertically sheared jet situated over a narrow sill connecting the inner Harbour to the deep and relatively quiescent Bedford Basin. Local wind driven variability is strongest in winter as expected but it is also shown that a significant part of the temperature and salinity variability is driven by physical processes occurring on the adjacent inner continental shelf, especially during storm and coastal upwelling events.

Appendix A: Barnes’ Algorithm

Point observations of temperature and salinity made in Halifax Harbour over the last century have been interpolated onto a regular grid (∼110 m and 1 m grid spacing in the horizontal and vertical respectively) using Barnes’ Algorithm (Barnes 1964). The value of the analyzed field at a given grid point is a weighted sum of the observations within a specified radius of influence. The algorithm is iterative and the weight function can be changed with each iteration. If the number of iterations increases without bound the analyzed field will converge to the observation at the observation location (or the mean if there is more than one observation at the same point).

To provide more detail on the algorithm, assume that the analyzed field at grid point r _i is required. At iteration j the analyzed value at the ith grid point is given by

$$\begin{array}{lll} f^{j}_{A}(\mathbf{r}_{i}) \\ \;\;= \begin{cases} \sum_{k=1}^{K_i} W_{ik}f_{O}(\mathbf{r}_{k}) &\quad j = 1 \\ f^{j-1}_{A}(\mathbf{r}_{i})+\sum_{k=1}^{K_i} W_{ik}[f_{O}(\mathbf{r}_{k})-f^{j-1}_{A}(\mathbf{r}_{k})] &\quad j > 1 \end{cases} \end{array}$$

(3)

The subscripts A and O in Eq. 3 denote analyzed and observed quantities respectively, r _k is the position vector of the kth observation, K _i is the number of observations within the region of influence centred on the ith grid point. W _ik is the weight applied to the kth observation in order to estimate the field at the ith grid point. It is defined by (Geshelin et al. 1999; Spencer et al. 1999)

$$ W_{ik}=\frac{w_{ik}}{\sum{_{k=1}^{K_i}w_{ik}}}$$

(4)

where

$$ w_{ik}=\exp\left[-\frac{R^{2}_{xy}}{\lambda^{2}}-\frac{R^{2}_{z}}{\beta^{2}}-\frac{R^{2}_{t}}{\tau^{2}}\right] $$

(5)

and R _xy , R _z and R _t are the horizontal, vertical and temporal distances between the ith grid point at mid-month and the kth observation, and λ, β and τ are the corresponding decorrelation scales.

To construct the new monthly climatology of Halifax Harbour, the number of iterations was set to three, and the decorrelation scales as a function of iteration number were

 

Scale	Iteration $(j)$
	1	2	3
λ (km)	7.5	5	4.5
β (m)	5	5	5
τ (day)	15	15	15

An illustration of the effectiveness of Barnes’ algorithm is provided by Fig. 7 which shows vertical profiles of temperature and salinity at two locations in the Harbour based on (i) direct observation, and (ii) the new climatology. Clearly the algorithm has performed well in mapping the irregular and sparse observations onto a regular grid.