Significant wave height
The median significant wave height (H
s) during the period 2003–2008 is 0.55 m. Lower values occur in spring (0.48 m) and summer (0.53 m) and higher ones in autumn (0.62 m) and winter (0.60 m). The median H
s during the tripod measurements at MOW1 was 0.58 m and at the Kwintebank 0.47 m. The median during MOW1 measurements is thus slightly higher than the median over 2003–2008, but significant wave heights >1.5 m have occurred less frequently (7% in MOW1 tripod data compared to 10% during the period 2003–2008).
During tidal cycle measurements, the median H
s was 0.49 m; these measurements are limited to rather good weather, with H
s not exceeding 1.5 m. The median H
s during satellite overpass in clouded weather is 0.60 m. During a clear sky condition, when SPM concentration data are available from MODIS, the median reduces to 0.44 m. This indicates that satellite SPM concentration data are biased towards good weather conditions (i.e. low wave condition) and that a significant wave height smaller than 0.44 m can be used as proxy for cloud-free conditions.
Some examples of measured and fitted profiles from tidal cycle measurements are shown in Fig. 3. Two types can be distinguished, which can both be approximated by a logarithmic function. The first one consists of well-mixed profiles with small vertical stratification (the vertical averaged to SPM concentration ratio is smaller than 2) and the second one is characterised by strong vertical gradient (the vertical averaged to surface SPM concentration is >2). The latter type of profile is typically occurring around high and low water (Fig. 4), when the increasing current velocity has reached a critical value for resuspending the fluffy layer. Maximum current velocity occurs at about 1 h before high and low water. The first type of profile occurs when bed erosion flux is low because no erodable material is left on the bottom or because bed shear stress drops below a critical value for erosion. It thus reflects periods of vertical mixing or relaxation phases during slack waters. In the offshore location (Kwintebank) and at MOW1, 88% and 74%, respectively, of the profiles fit this type. The correlation coefficient between the fitted and the measured data is high at both locations (MOW1: R
2 = 0.77; Kwintebank: R
2 = 0.98).
The fitted profiles have been used to calculate a correlation between the log-transformed SPM concentration at the surface, at 2 and 0.2 mab and vertically averaged (Fig. 5 and Table 3). The correlations are large for type 1 profiles at both locations and type 2 profiles at the Kwintebank (R
2 > 0.8), but weaker for type 2 profiles at MOW1 (R
2 = 0.4–0.6). The lowest correlation occurs with the near-bed data (0.2 mab), indicating that the extrapolation of near-bed values towards the surface is probably not accurate especially for the type 2 profiles.
A third type of profiles in the near-bed layer (<2 mab) has been observed in the tripod data. It is characterised by very high SPM concentration in the near bed layer, which is possibly the result of the formation of ephemeral fluid mud layers or high concentrated benthic suspension (HCBS) layers, resulting in a weak correlation between the near bed and the 2 mab SPM concentration. They are typically associated with storm conditions (Fettweis et al. 2010). These HCBS layers cannot be fitted with the above profiles since near bed and water dynamics is uncoupled under these conditions.
The relation between the tidal averaged data at 2 and 0.2 mab has been calculated after log transformation of the data (see Fig. 6). For SPM concentrations ranging from 100 to 1,000 mg l−1, the near the bed concentration is 1.5–1.7 times higher than at 2 mab (R
2 = 0.69). Note that from the same range and during two time series (MOW1-4 and MOW1-8), near-bed SPM concentrations were 1.4–5.6 times higher than the SPM concentration at 2 mab. The correlation coefficient for these series is low (R
2 = 0.33).
Matchups between in situ and satellite data
Nineteen matchups between satellite and tripod data are available during the period 2004–2006 at MOW1. The correlation—after log transformation of the data—between surface SPM concentration from MODIS and near-bed SPM concentration has a coefficient of R
2 = 0.8 for the 2 mab and R
2 = 0.7 for the 0.2-mab data. Remark that the difference between the surface and near-bed SPM concentrations is huge (15–30 times lower; see Fig. 7a). Based on the relation between the surface and near-bed SPM concentration derived from the fitted profiles (obtained from the tidal cycle measurements), a depth correction of the MODIS surface data has been applied. When the correction factors for all profiles are considered (Table 3), then a relatively good match (R
2 = 0.5) between MODIS and 2-mab tripod data is obtained (Fig. 7b), with an underestimation of the MODIS corrected data (see Section 5).
Frequency distribution of SPM concentrations
By using frequency distributions of different datasets, we can determine if two distributions are drawn from the same distribution function by use of standard statistic tests (Χ
2 test, Kolmogorov–Smirnov test). If the data collected with different sampling methods have similar log-normal distributions, means and standard deviations, then we could conclude that—within the range of uncertainties—the methods provide similar subsamples from the whole population. From the three different types of SPM concentration data (tidal cycle, long term and satellite), probability distributions have been constructed (Figs. 8, 9 and 10). The data could be fitted with log-normal distributions. The distributions from the tidal cycle data are set for three depths, corresponding to the measuring depth of satellite (surface) and tripod data (2 and 0.2 mab). The probability of the Χ
2 test was computed, hypothesising that the SPM concentration data fit a log-normal distribution. The geometric mean (x*, further called mean) and multiplicative standard deviation (s*) of these distributions, together with the X
2 test results, are shown in Table 4. In general, values of s* vary between 1.5 and 2.8; hence, they fall within the most frequent range of approximately 1.4–3, observed in various branches of natural sciences (Limpert et al. 2001). If the test probability is low (p < 0.05), then the null hypothesis should be rejected. Low probability occurs only in the tidal cycle surface data at Kwintebank and the 0.2-mab data at MOW1. The deviations from the log-normal distribution (Fig. 9) for the surface samples from the Kwintebank are possibly due to some high errors in SPM concentration (see Section 3). For the near-bed data at MOW1, such deviations are related to some unrealistic high values obtained from log extrapolation of the vertical profiles from tidal cycle measurements to 0.2 mab. We can therefore argue that a type I error has occurred in these two populations and that SPM concentrations also have a log-normal distribution in these cases.
MOW1 is situated in shallow waters where wave effects are important. Excluding samples from the tripod measurements where the bottom wave orbital velocity, U
w, is higher (respectively lower) than a certain value allows calculating the geometric mean and multiplicative standard deviation of a population representing stormy (respectively good) weather conditions (Table 5). The bottom wave orbital velocity has been calculated based on the significant wave height (H
s), the water depth and the JONSWAP spectrum of waves (Soulsby 1997). A U
w of 0.03, 0.3 and 0.5 m s−1 correspond to a significant wave height of about 0.5, 1.5 and 2.5 m in a water depth of 10 m. The results at MOW1 show that the distributions are very similar for the data collected during periods with U
w > 0.03 m s−1 and U
w < 0.3 m s−1. The mean SPM concentration at MOW1 increases from 145 mg l−1 (U
w < 0.03 m s−1) to 338 mg l−1 (U
w > 0.5 m s−1) at 2 mab and from 263 mg l−1 (U
w < 0.03 m s−1) to 617 mg l−1 (U
w > 0.5 m s−1) at 0.2 mab; this confirms the nonlinear behaviour of the system. The SPM concentration distribution from the tidal cycle data at 2 mab corresponds well—but still with significant differences—with the good weather tripod data (U
w < 0.03 m s−1; x* = 81 versus 145 mg l−1). Similar results are found for the 0.2-mab tidal cycle data and the good weather tripod data (93 versus 263 mg l−1).
Surface correction of tripod data
By extrapolating the Kwintebank and MOW1 tripod data towards the surface, the three datasets (tripod, tidal cycle and MODIS) can be compared to each other. The surface extrapolation has been calculated for the 2- and 0.2-mab tripod data using the relations obtained from all profiles in Table 3. This results in slightly higher surface values from 0.2 mab (Table 4). The difference between satellites, tidal cycle and tripod surface data is more significant. The lowest mean SPM concentrations are found for the satellite data (Kwintebank, 6 mg l−1; MOW1, 23 mg l−1) and the highest for the tripod data (Kwintebank, 19 mg l−1; MOW1, 59 mg l−1 for 2-mab extrapolation).
The results show that the mean SPM concentration of the satellite data at the Kwintebank is included within 1 standard deviation of the tidal cycle data and vice versa. The tidal cycle and satellite data are not included in the tripod data within 1 standard deviation. This is possibly linked to the fact that the tripod data are restricted to March 2004 and thus not representative for a whole year (Table 1 and Fig. 2). When only winter satellite data are selected, then a higher mean SPM concentration of 12 mg l−1 is obtained, which is, however, still very low compared to the mean of tripod data. At MOW1, the mean SPM concentration from the tidal cycle dataset is included within 1 standard deviation of the mean from the tripod and the satellite datasets. The mean SPM concentrations from the tripod and satellite datasets are not included within 1 standard deviation.