5. Model validation

For the modeling, the coordinate is shown in Figure 9a with the eastward as the positive x-axis and u velocity, the northward as the positive y-axis and v velocity, and the upward as the positive z-axis and w velocity. Since the PRE is generally along the meridional direction, we choose the u to represent the cross-estuary velocity and the v the along-estuary velocity.

The comparison of the cruise observations and FVCOM modeling salinity profiles at a number of stations (B3, D4, D6, F2, G2, G3, H3, H8, I5, J3, M3, and N7 illustrated in Figure 2) is shown in Figure 10. It reveals good agreements between the observations and modeled salinity profiles except at B3, D6, H8, J3, and N7, where the model underestimates the salinity profiles. B3, D6, and N7 were close to coastal land (or island), which may affect the simulation results. Another possible reason is that the river discharge used for the modeling is the climatological data that may not represent the actual discharges, which can cause biases in the salinity profiles between the modeling results and the observations.

The comparison of sea levels between the model results and observations at eight tide gauge stations from 1 to 30 May is shown in Figure 11. The locations of the tide gauge stations are shown in Figure 12. The hourly tide gauge sea level data during the period between May 1, 2014 and May 3, 2014 are provided by the Hong Kong Observatory (HKO) and Marine Department for the model validation. The

Circulations in the Pearl River Estuary: Observation and Modeling DOI: http://dx.doi.org/10.5772/intechopen.91058

Figure 10. Comparison of the modeling salinity profiles (blue lines) with the cruise observation (red lines).

modeled sea levels agree well with the observed records both at spring and neap tides for this period.

To further quantify the accuracy of model results, four statistical parameters are calculated, namely, root-mean-square (RMS) error, relative average error (RE), correlation coefficient, and the model skill parameter used by [30].

The RMS error is defined as:

$$\text{RMS} = \left\{ \frac{1}{\text{N}} \sum\_{i=1}^{\text{N}} \left( \eta\_{\text{mo}} \text{ - } \eta\_{\text{ob}} \right)^{2} \right\}^{1/2} \tag{1}$$

The relative average error (E) is defined as:

$$\mathbf{E} = \frac{\sum\_{i=1}^{N} (\eta\_{\rmmo} \cdot \eta\_{\rm obs})^2}{\sum\_{i=1}^{N} \left\{ (\eta\_{\rmmo} \cdot \overline{\eta}\_{\rmmo})^2 + (\eta\_{\rm obs} \cdot \overline{\eta}\_{\rm obs})^2 \right\}} \times 100\,\% \tag{2}$$

The correlation coefficient is defined as:

$$\mathbf{R} = \frac{\sum\_{i=1}^{N} \{ (\eta\_{\rmmo} \cdot \overline{\eta}\_{\rmmo}) (\eta\_{\rm ob} \cdot \overline{\eta}\_{\rm ob}) \}}{\left[ \sum\_{i=1}^{N} (\eta\_{\rmmo} \cdot \overline{\eta}\_{\rmmo})^2 \sum\_{i=1}^{N} (\eta\_{\rm ob} \cdot \overline{\eta}\_{\rm ob})^2 \right]^{1/2}} \tag{3}$$

The model skill parameter is:

$$\text{Skill} = 1 - \frac{\sum\_{i=1}^{N} (\eta\_{\text{mo}} \cdot \eta\_{\text{ob}})^2}{\sum\_{i=1}^{N} (|\eta\_{\text{mo}} \cdot \overline{\eta}\_{\text{ob}}| + |\eta\_{\text{ob}} \cdot \overline{\eta}\_{\text{ob}}|)^2},\tag{4}$$

Figure 11. Comparison of modeled (blue lines) and observed (red lines) sea surface elevations at eight tidal gauge stations.

where ηmo and ηob represent the model sea level data and the observations, respectively, and the overbar denotes the temporal average. N is the number of records.

Table 2 provides the validation results at the eight tidal gauge stations. The RMS errors are less than 0.15 m, and the relative average errors are less than 3% except at the Ko Lau Wan Station. The correlation coefficients are higher than 0.97, and the skill parameters reach 0.98. Based on the skill assessment results, the model works well in simulating the sea level variations.

Figure 13 presents the comparison of cross-estuary and along-estuary velocities between the cruise observations and FVCOM modeling for transects D and I. The observation duration of transect D was in the flood tide with the northeasterly wind. In the cross-estuary direction, for transect D, the modeled velocity agrees well with the observation, which reveals that the lateral current flows westward (negative) on the left side of the Lantau Channel and eastward

Circulations in the Pearl River Estuary: Observation and Modeling DOI: http://dx.doi.org/10.5772/intechopen.91058

Figure 12. The locations of the tide gauge stations.


Table 2.

The RMS error, RE, correlation coefficient (CC), and the skill assessment parameter (skill).

(positive) on the right, forming a divergence on the deep channel, although the modeled current speed has some biases from the observed speed, especially for the eastward flow in the Lantau Channel where the modeling underestimates the current (Figure 13a vs. Figure 13b). In the along-estuary direction for transect D, the modeled current flows northward with maximum velocity in the surface at the Lantau Channel location, in accordance with the observed current (Figure 13c vs. Figure 13d). For transect I with the southeasterly wind during the ebb tide, there was a velocity convergence occurred in the Lantau Channel in the cross-estuary direction as revealed in both observations and modeling (Figure 13e vs. Figure 13f). In the along-estuary direction, the modeled velocity agrees well with the observations, and both of the observations and modeling show that the exchange flows exist along the estuary with the strong seaward current in the surface and weak landward current in the bottom (Figure 13g vs. Figure 13h). Since the smoothed topography is applied to the modeling, the simulated velocity is spatially less varied than that from the observation; however, the general patterns of the modeling velocity and the observed velocity are similar and consistent, indicating that the FVCOM modeling can well simulate the estuarine water dynamics of the PRE.

Figure 13.

The cruise-observed cross-estuary (a for Transect D, e for Transect I) and along-estuary (c for Transect D, g for Transect I) velocities vs. the model cross-estuary (b for Transect D, f for Transect I) and along-estuary (d for Transect D, h for Transect I) velocities.
