| 05 Jan 2026
Along-channel Variability of Total Exchange Flow in a Narrow, Well-mixed Estuary: Influence of the M4 Tide
Abstract. This study provides preliminary estimates of Total Exchange Flow (TEF) along the Guadalquivir River Estuary (Spain) at notable cross-sections during low river flows. The analysis combines observations recorded during 3 years by a real time monitoring network and analytical model output for a well-mixed M2+M4 tidal flow with oscillating salinity. Exchange profiles and volume and salinity transports sorted by salinity classes are computed. The results indicate that bulk along-channel TEF estimates decrease upstream.
The largest net incoming water volume transport, viz. approx. 300 m3 s-1, is attained at the lower part of the estuary, near where the largest salinity gradient is observed. This value is about 12-fold the normal river flow from the head dam at Alcalá del Río. Knudsen-consistent bulk quantities evidence the weakly-stratified character of the Guadalquivir estuary, whose mixing completeness is larger than 67 % at all cross-sections. The covariance between salinity and current seems to play a more important role in exchange flow in the Guadalquivir estuary than the effects due to tidal asymmetry.
Overall, the inclusion of the M4 improves TEF estimates in ∼ 10 % in the Guadalquivir estuary. A sensitivity analysis shows that in other estuaries and semi-enclosed basins the effects of the M4 could be even larger. The inclusion of the M4 constituent changes thickness and magnitude of the bi-layer exchange flow by salinity class. A remarkable inflow could be obtained at low salinity classes when the estuary exhibits large M4 current amplitude and M4 current phases close to 160°.
Review of “Along-channel Variability of Total Exchange Flow in a Narrow, Well-mixed Estuary: Influence of the M4 Tide” by Manuel Díez-Minguito and Hans Burchard
General
This article deals with the calculation of the Total Exchange Flow (TEF) from observations in the Guadalquivir estuary, and focuses on the role of the M4 tide. I think the article could be a nice contribution to the knowledge of the dynamics of the Guadalquivir estuary and similar systems, the computation of the TEF from observations and the role of different tidal constituents in the exchange of an estuary with the adjacent sea. However, I have some suggestions for improvements, see below.
Major
What I miss in the introduction is a clear motivation why to do this study. The methodology is discussed in the introduction. But, what is the knowledge gap that this study is trying to address? And what is the context of that knowledge gap?
In section 3.2, the mixing completeness is 67%, which is framed as evidence for the poorly-stratified character of the Guadalquivir estuary. However, in order to obtain this result, it was assumed that the cross-sections are well-mixed laterally and vertically. So to me it appears that this is input to the analysis, and can therefore not be framed as a result.
The article often refers to the Knudsen (1900) paper: Knudsen relations, Knudsen-bulk estimates, Knudsen-consistent... , without explaining this terminology. I suggest to limit the different variations of this to a minimum, and explain these terms when introduced, because their exact meaning is not that trivial to me.
Minor
The article states (line 3) that an analytical model’ is used. The model consists of an expressions of the salinity and along-channel velocity at x,t. I would not so rather call this a model, but merely a set of two analytical equations. See also line 44.
Line 9: “covariance between salinity and current”. I think, when this is used in the text, it applies to the M2 salinity and current, that is, that of the main tidal constituent. I suggest to add this, to be specific. Is this the same quantity as in line 115? Same for lines 237, 316.
Line 25: It may be good to specify here what is meant with “exchange flow”, as different definitions are possible. See also line 116.
Line 35: it is a bit unclear to me why the M4 tide is considered as extension of the tidal module, and not for instance the S2 tide, which has a stronger amplitude. I assume this is because the M4 tide is the overtide of the M2, which makes the analysis simpler? But I think the article would benefit from some elaboration on this important choice.
Line 41 and later: “notable” cross-sections: what is meant with ‘notable’.
Line 75: “volume-integrated” → over which volume is integrated?
Line 85: “mean salinity”. I suppose tidally-averaged is meant here?
Line 105: I assume the subscript means one standard deviation, but this is nowhere specified.
Equation 11: this is a simplification of the real profiles. Can you comment on how large the error is that you are making with this assumption?
Line 125: If I understand correctly, there is one value for along-channel current and salinity for the entire cross-section (this becomes clear later in the text, I suggest to stress it here). In reality, there will be variations over depth and the lateral direction. Can you comment on the magnitude of the error that you are making here? In general, I think the article would benefit from some more explicit (if possible quantitative) reflection on the uncertainty of the results in terms of volume transports, dividing salinity classes and mixing completeness.
Line 154: To me, this phrasing suggest two layers in the vertical are observed. However, that seems not to be the case. I suggest to phrase this differently, to avoid confusion with an exchange flow consisting of two vertical layers.
Line 160-161: But this is a different quantity than in Reyes-Merlo et al. (2013), because there only gravitational circulation is considered, while the current results also include tidal flow if I understand correctly. I suggest to make this more clear to avoid confusion (also for example in line 179). Also, since transport of salt by tidal currents is thought to be large in this estuary (Diez-Minguito et al., 2013, Biemond et al, 2024), wouldn’t you expect a larger value than 10%?
Line 178: larger than what?
Line 196: small with respect to what?
Figure 5: why use an inset here? I suggest to plot the two lines in the same graph, with the y-axis for MC[%] on the right of the figure.
Line 226: ‘increases the thickness of the upper outflowing layer’ I found this confusing, because it suggests that it refers to a surface layer. I suggest to use something like “increases the range of salinities of the seaward flow”
Line 227: “except at CS2 and CS5 where the lower inflowing layer thickness increases”. Can you explain this?
In line 275: Differences between the different values of R are impossible to see in Figure 7. I suggest another way to visualize this, or alternatively, just state in the text that the results are practically independent of the value of R in the range 10-40, as evidenced by the numbers given in lines 277-279.
Section 3.3.2: In general, I think the added value of this analysis needs somewhat better motivation. It would be good to have reference values to compare the results with. For instance, how big are the changes in the numbers when vertical stratification would be considered? Or irregular bathymetry? In that manner, the interpretation of the quantitative results in this section would have a better context.