Process Contribution to the Time-Varying Residual Circulation in Tidally Dominated Estuarine Environments

In tide-dominated environments, residual circulation is the comparatively weak net flow in addition to the oscillatory tidal current. Understanding the 3D structure of this circulation is of importance for coastal management as it impacts the net (longer term and event-scale) transport of suspended particles and the advection of tracer quantities. The Dee Estuary, northwest Britain, is used to understand which physical processes have an important contribution to the time-varying residual circulation. Model simulations are used to extract the time-varying contributions of tidal, riverine (baroclinicity and discharge), meteorological, external and wave processes, along with their interactions. Under hypertidal conditions, strong semi-diurnal interaction within the residual makes it difficult to clearly see the effect of a process without filtering. An approach to separate the residual into the isolated process contribution and the contribution due to interaction is described. Applying this method to two hypertidal estuarine channels, one tide dominant and one baroclinic dominant, reveals that process interaction can be as important as the sub-tidal residual process contributions themselves. The time variation of the residual circulation highlights the impact of different physical process components at the event scale of tidal conditions (neap and spring cycles) and offshore storms (wind, wave and surge influence). This gives insight into short-term deviation from the typical estuarine residual. Both channels are found to react differently to the same local conditions, with different short-term change in process dominance during events of high and low energy.


Introduction 37
This research continues from earlier studies of the 3D circulation within the channels of this 38 hypertidal estuary system (Bolaños et al. 2013) and coastal wave impact across Liverpool Bay 39 ). Bolaños Komen et al. 1994), modified for coastal applications (see Monbaliu et 170 al. 2000) and the generation of radiation stress (using Mellor 2003Mellor , 2005, enabled 3D wave-171 induced currents and enhanced bottom friction and surface roughness to be included. The 172 modelling system was coupled such that a 2-way exchange of information occurred between the 173 component models and was configured to include wetting and drying, making it apt for this 174 estuarine application. The wave coupling was initiated on the 21 st February 00:00, when the 175 conditions were no longer considered calm and the waves exceed 0.6 m (> 168 hrs Fig. 2c), to 176 reduce computational cost. No wave induced residual is therefore shown in later figures during the 177 calm period. Prior to this time wave activity is assumed to be minimal within the estuary. Details 178 of the modelling system setup and validation of this period confirming this approach is acceptable 179 are given by Bolaños et al. (2013). Previous studies have also shown it to give good multi-year 180 tide-surge hindcast across the eastern Irish Sea ) and within Liverpool Bay 181 (Brown et al. 2011). 182 Operational atmospheric forcing from the UK Met Office was used to drive the local Liverpool 184 Bay model. The full set of ~12 km resolution atmospheric conditions (3 hourly air temperature 185 and specific humidity, with hourly pressure and 10 m wind components) are used to include air-186 sea heat and momentum fluxes. Freshwater input is considered using daily mean gauged discharge 187 at all available river sources around the Irish Sea. The offshore (Liverpool Bay) model boundary 188 have been compared with observation ( Fig. 3 a and b). Taking the depth-average enables the full 201 water column to be considered at each time instance, and does not incur problems relating to the 202 volume conservation of sigma co-ordinates when time-averaged. The comparison is performed 203 using the ADCP measurements in the Hilbre Channel for the full period of observation at the 204 fixed mooring. Both the model results and observations are filtered (see Section 3.2) to obtain the sub-tidal residual. This technique causes a loss of data at the ends of the time series. It is clear that 206 the model over predicts the depth-mean currents and has less accuracy during the stormier period 207 (around hour 300). Generally the model shows less fluctuation than the observations. The wave 208 conditions are also compared using a wave buoy deployed in the Hilbre Channel close to the 209 ADCP mooring (Fig. 1). The modulation in the wave properties over the tidal cycle in response to 210 depth change is captured (Fig. 3 c and  In hypertidal estuaries the tide has a strong modulating influence on the other non-tidal physical 232 processes, not only due to fast currents (~1.2 ms -1 during spring tide in the Dee, Fig. 2b), but also 233 due to the wetting and drying of banks, which modifies the bathymetric cross-sectional estuary 234 profile. The model can be used to simulate circulation due to user chosen inputs, for example 235 whether the atmospheric forcing is turned on or not in the model. In this model application the 236 physical processes available for user selection are: meteorological forcing (M), baroclinicity (B), 237 river flow (R), external residual (E), tides (T) and waves (W). Filtering methods are also applied 238 to the model data to remove all energy at tidal frequencies to isolate the tidally-interactive residual 239 component. Here the Chebyshev Type II filter is used as a low-pass filter with a stop-band of 26 240 hours and a pass-band of 30 hours to remove all energy at tidal frequencies. A standard 3 decibels 241 pass-band amplitude was applied with a stop-band attenuation of 30 decibels, which is an 242 attenuation factor of 1000. This leaves only the low frequency (≥ 30 hours, sub-tidal) residual 243 without any tidal energy or tidal interaction, which is removed as it has a similar frequency to the 244 tide. Tidal harmonics with a period ≥ 30 hours will not be removed by this filter design, but within 245 an estuary environment their contribution is expected to be small. A 2-way filtering process was 246 applied so no phase shift occurred in the residual, however the start and end of the residual cannot 247 be accurately obtained, hence a shorter time series is later presented. When applied to the total 248 modelled current velocity more data are lost to filter error, at the ends of the time series, than 249 when applied to the weaker residual current velocities obtained from model simulations. This is 250 because the length of the erroneous period is a percentage of the input signal magnitude. Later 251 figures for the filtered tidal and total current simulations are therefore shorter than those for the 252 filtered (much weaker) residual current. This filter setup has previously been show to successfully 253 remove the tidal energy within surface elevations compared with harmonic tidal analysis methods 254 within this estuary ), so has been used again in this study. The results presented consider the total residual circulation and its component parts, a sub-tidal 294 (≥30 hour period) process driven component and an interactive component due to intra-tidal (< 30 295 hour period) process interaction for all (i) processes modelled: 296 total residual = Ʃ i (sub-tidal process residual + intra-tidal process residual).

…(1) 297
From the model simulation the full sub-tidal residual for all processes can be obtained by filtering: 298 where < > denote filtering has been applied. The difference between modelling experiments 300 considering different processes, are used to obtain the time-varying residual circulation due to 301 isolated processes including interactive effects (Table 2). For a single process the process residual 302 obtained from model simulation is: 303 process residual = full simulationreduced simulation.

…(3) 304
The sub-tidal residual and intra-tidal residual for that process are then defined as: 305 sub-tidal process residual = <full simulationreduced simulation>,

…(4) 306
intra-tidal process residual = (full simulationreduced simulation) -<full simulationreduced simulation>, …(5) 307 For example, the Metrological residual (M in Table 2, row 4) is the difference between a full 308 process model simulation (PGW_MBRET) and a reduced process simulation that does not include 309 Meteorology (PGW_BRET). Filtering this model residual removes any component with a 310 coherent phase, thus removing interaction with intra-tidal frequency between the residual process 311 itself and all other processes considered, mainly the tide. This method extracts the sub-tidal 312 residual induced by the non-tidal process and its nonlinear interactions with other non-tidal 313 forcing. The intra-tidal residual for meteorology is then obtained by subtracting the sub-tidal 314 residual (< PGW_MBRET -PGW_BRET>) from the process residual (PGW_MBRET -315 PGW_BRET). To obtain the non-tidal sub-tidal residual (Table 1, row 3, Fig. 4 and 5) the 316 difference between a model full physics simulation containing all processes (PGW_MBRETW) 317 and that of the tide only (PG_T) is filtered to remove all intra-tidal iteration. 318 In Section 4 the total (sub-tidal and intra-tidal) residual for one or more selected processes is 320 obtained by subtracting a model simulation without the processes in question from one which 321 includes them. The sub-tidal residual is obtained by filtering the total residual and the intra-tidal 322 residual calculated as the difference between the total and sub-tidal residual. By filtering the tide-323 alone (PG_T, Residual 1) and the fully coupled (PGW_MBRETW, Residual 2) model simulations 324 the sub-tidal (≥30 hours) tide-only and full process residual is obtained. This gives an idea of how 325 the tide behaves within the modelled estuary and how it contributes compared with the non-tidal 326 processes to the total residual circulation within the estuary channels. 327 The modelled tide only (PG_T) and total circulation (PGW_MBRETW) are filtered to remove all 338 semi-diurnal interaction to give the sub-tidal (≥ 30 hrs) residuals. For these two cases, the much 339 larger input signal to the filter causes the data loss at the ends of the time series to be over a longer 340 period than for the weaker residual currents presented later (refer to section 3.2). Comparison of 341 these sub-tidal residuals determines the importance of the tide relative to the non-tidal processes in influencing the total residual circulation. Filtering the tide-alone simulation (PG_T) enables the 343 tidal residual, generated by asymmetries and bathymetric constraint, to be obtained from the 344 model. In both channels the tide causes a long-term (time-averaged) 2-layer horizontal structure 345 (see Bolaños  and also to the weakening of the seaward sub-tidal tidal residual in the Welsh Channel during 359 neap tides. In this channel the tidal residual (Fig. 4a) is about half the magnitude of the sub-tidal 360 residual generated by the combined non-tidal processes (Fig. 6a), considered in the next section. 361 The influence of non-tidal processes on the total (tide plus non-tidal) residual is therefore clearly 362 seen (Fig. 4b). 363 In the Welsh Channel a strong seaward flow occurs during spring tide, weakening to zero residual 365 during neap tides (Fig. 4c). The seaward direction of this flow is related to mooring being located 366 on the right side of the channel, when facing out to sea. The time-mean residual within the Welsh 367 Channel has net out flow to the right and net inward flow to the left (Bolaños et al. 2013), with 368 flow speeds more than double that modelled in the Hilbre Channel. At spring tide the magnitude 369 of the Welsh tidal residual is much larger than that due to the non-tidal processes considered, thus, 370 greatly influences the total (tide plus non-tidal) residual at this time (Fig. 4d). However, during 371 neap tide stronger stratification and therefore baroclinicity determines the residual pattern and not 372 the tide, especially during calm atmospheric conditions (> 75 hrs, Fig. 4d). Storm impact, 373 coinciding with neap tide, weakens the stratification modifying the total residual, which becomes 374 storm process driven (~375 -450 hrs, Fig. 4d). 375

376
The same effects as those seen in the major channel axis component occur in the minor channel 377 axis component of both channels (Fig. 5). The Hilbre Channel has a complex sub-tidal residual in 378 the minor channel axis component (Fig. 5b). The surface flow varies in direction from westerly 379 due to baroclinic processes (see Section 4.2) to intense easterly during storm conditions; however The non-tidal sub-tidal residuals (3 -8 given in Table 2) are analysed to determine the importance 388 of different physical non-tidal process, in contributing to the total residual circulation. In the 389 Hilbre Channel comparison of the non-tidal sub-tidal residual (Figs 6a and 7a) with the total sub-390 tidal residual (Figs 4b and 5b) column, in addition to influence over the full depth at neap tide, which is particularly strong 396 during the storm event. 397 398 Figures 6 and 7 show that the non-tidal processes (considered in Table 2, rows 3 -8) have greater 399 influence in the Hilbre Channel, except for the external surge which has a similar influence in 400 both. Baroclinicity (Figures 6c, and 7c,) is the dominant process at generating sub-tidal residual 401 circulation when all of the considered non-tidal processes are simulated together (Figures 6a and  402 7a). This is seen clearly by the similarity in time-varying pattern. It is important to recall that 403 baroclinicity in this model application represents any process driven by density gradients and their 404 straining. This creates a seaward surface flow and landward bottom flow in the major channel axis 405 component (Fig. 6c). Even at high water, when the water column becomes mixed, straining 406 continues to drive this circulation due to modifications in the flood tide velocity profile and 407 turbulent mixing (Burchard and Baumert 1998), which interacts with the vertical profile of both 408 the river flow and the seaward mass transport in response to Stoke's drift. The tidal straining 409 induced residual therefore has similar characteristics to the classical density-driven flow 410 (Burchard et al. 2011). In the major channel axis the baroclinic residual component (Fig. 6c) is 411 weakened following waves enhancing the seaward flow under windy conditions from the west, 412 both processes reducing stratification (e.g. 300 -320 hrs), or when the wind is southerly (e.g. 460 413 hrs) and therefore opposing estuarine circulation. The depth of the baroclinic residual surface 414 layer is also found to deepen during the extreme storm once the initially south-westerly winds 415 have veered more westerly (e.g. 380 -460 hrs).  Fig 6i), even though the river 419 discharge is low and decreasing. Under these conditions stratification is able to form and is 420 strengthened by wind straining. During the extreme storm event the waves (359 -447 hrs, Figs. 6l 421 and 7l), external surge (captured in the external residual ~400 hrs, Figs. 6k and 7k) and local 422 meteorology ( Fig. 6h and 7h) have greatest influence. These processes weaken the stratification in 423 the Welsh Channel and therefore also weaken the persistent density-driven flow pattern (Fig. 6i). 424

425
In both channels the river discharge has the least influence (note the different color scale in Fig.  426 6d, j and 7d, j) creating a weak offshore flow in both channels. The strength of this residual 427 component is related to the river discharge entering the upper estuary from the catchment (Fig. 2e)  428 and not the local storm event itself. Non-regular quasi-period oscillation is seen in the river flow 429 at the mouth (≥ 30 hrs) due to interaction with the atmospheric forcing and possibly the long-430 period variability in the channel cross-sectional area due to the surge component influencing the 431 total water elevation over the intertidal shoals. The local meteorological (wind) forcing and the 432 external surge seem to have counteractive effects at the event-scale (compare Fig. 6b, h and 7b, h  433 with Fig. 6e, k and 7e, k). The external surge acts to increase water levels causing flow into the 434 estuary during southwest storm events, while the local southwest wind promotes seaward flow for 435 the Hilbre Channel alignment. In the Welsh Channel, these two processes cause opposing 436 bidirectional 2-layer vertical residual flow structures. Finally waves (Fig. 6f, l), when present (> 437 168 hrs, Fig. 2c The general pattern (Fig. 7a, g) in the minor channel axis residual component is driven by 446 baroclinicity (Fig. 7c, i)  The interactions within this hypertidal estuary are predominantly controlled by the tide. The intra-454 tidal residuals produced by tidal interactions are similar in magnitude to the sub-tidal residuals 455 induced by the non-tidal processes; they are therefore equally as important in contributing to the 456 total (sub-tidal plus intra-tidal) time-varying residual circulation. 457

458
The non-tidal processes (3 -8 given in Table 2), which have greater influence in the Hilbre 459 Channel also cause a greater intra-tidal (interaction driven) residual within this channel ( Fig. 8 and  460   Fig. 9). The interactions generating the intra-tidal residual within Figures 8 and 9 are given in 461 Table 2 (column 4), and are not just due to the tide. Bolaños et al. (2013) shows the importance of 462 tide-stratifiction interaction within this estuary, which enables periodic stratification to develop at 463 low water followed by its break down creating a well mixed water column at high water. 464 Compared with the non-tidal sub-tidal residuals ( Fig. 6 and 7), the intra-tidal residual ( Fig. 8 and  465 9), although intermittent, is a significant contribution (at least double at times) to the total residual 466 circulation generated by that process. The intra-tidal residual is of similar magnitude in both the 467 major and minor channel axis components. During the storm event the local meteorology (wind, Residual 4) interacts to create a seaward 478 surface flow at high water elevations and landward surface flow at low water elevation (Fig. 8b  479 and 9b). This interaction is clearly the result of wind straining. At high water slack the estuarine 480 stratification is weakest, but the wind fetches are greatest producing larger wind induced currents. 481 At low water slack stratification is at its strongest, the high wind speeds act to break down the 2- where the river discharge is strongest (e.g. intermittent red and blue stripes in Fig. 8d and 9d,  493 around 300 -500 hrs). sections. They compare equal periods of calm and stormy conditions to identify process 527 dominance over the longer-term, due to the cumulative effect of event-scale process contribution 528 (in magnitude and duration) presented here. The study period (Fig. 2) consists of calm and stormy 529 conditions with a mean river discharge (32 m 3 s -1 ), which is equivalent to the long-term mean (31 530 m 3 s -1 ). This period therefore gives good representation of the typical conditions within the Dee 531 Estuary. 532

533
The dynamically evolving bathymetry within the Dee Estuary (Moore et al. 2009) and lack of 534 bathymetric data at the time of observation prevents the time-varying modelled circulation from 535 being perfect at a point observation. In a hypertidal estuary the large tidal prism means inter-tidal 536 shoals in addition to the sub-tidal channels will have an important role influencing the accuracy of 537 the estuarine processes. In Section 3.1 POLCOMS-GOTM is shown to give acceptable 538 simulations of the residual circulation for the given input data (Fig. 3). Previously, the model has 539 been found to be robust at modelling the 3D current patterns within Liverpool Bay (Brown et al. period. Extreme storms have a strong, but short-term influence during the event. In Liverpool 625 Bay extreme storm surges are often associated with southwest winds, under which conditions the 626 local wind counteracts the influence of the external surge at this estuary mouth. The influence of 627 storm events on the residual circulation is different within the two channels due to their 628 orientation relative to wind direction. This is an example of how the complexity of the channel-629 bank system within an estuary prevents a consistent pattern in circulation occurring across the 630 estuary. For sediment dynamics the volume flux during such short-term events (e.g. storm events) 631 of atypical circulation may have high impact for the long-term net transport. The short-term 632 deviations in residual circulation demonstrate that time-scales longer than seasonal influence (due 633 to changes in storminess and river discharge) must be considered to truly define the long-term 634 process dominance. 635

636
In addition to the sub-tidal residual the interactions between tide and stratification are found to 637 create a strong intra-tidal residual, influencing the time-variation of the total residual. In hypertidal conditions the interactions must also be included when considering residual circulation 639 as they can be as important as the sub-tidal process contribution itself. The periodic (semi-diurnal 640 for the Hilbre Channel and during calm neap conditions for the Welsh Channel) formation of the 641 vertical 2-layered water column structure can have an important role in longer-term transport 642 pathways. It is therefore suggested that the net transport of suspended and dissolved particles 643 within a hypertidal estuary system can be dependent on the baroclinicity despite low river flow. supplementing the meteorological forcing with air temperature, humidity, and cloud cover to 661 enable full atmospheric forcing. River data has also been supplied by the Centre for Ecology and for the residual generated by the river discharge (R, case 6 in Table 2). 853