Tidal mixing of estuarine and coastal waters in the Western English Channel is a control on spatial and temporal variability in seawater CO 2

. Surface ocean CO 2 measurements are used to compute the oceanic air–sea CO 2 flux. The CO 2 flux component from rivers and estuaries is uncertain. Estuarine and coastal water carbon dioxide (CO 2 ) observations are relatively few compared to observations in the open ocean. The contribution of these regions to the global air–sea CO 2 flux remains uncertain due to systematic under-sampling. Existing high-quality CO 2 instrumentation predominantly utilise showerhead and percolating style equilibrators optimised for open ocean observations. The intervals between measurements made with 15 such instrumentation make it difficult to resolve the fine-scale spatial variability of surface water CO 2 at timescales relevant to the high frequency variability in estuarine and coastal environments. Here we present a novel dataset with unprecedented frequency and spatial resolution transects made at the Western Channel Observatory in the south west of the UK from June to September 2016, using a fast response seawater CO 2 system. Novel observations were made along the estuarine–coastal continuum at different stages of the tide and reveal distinct spatial patterns in the surface water CO 2 fugacity (fCO 2 ) at 20 different stages of the tidal cycle. Changes in salinity and fCO 2 were closely correlated at all stages of the tidal cycle and suggest that the mixing of oceanic and riverine end members partially determines the variations in fCO 2 . The observations demonstrate the complex dynamics determining spatial and temporal patterns of salinity and fCO 2 in the region. Spatial variations in observed surface salinity were used to validate the output of a regional high resolution hydrodynamic novel estimate of the CO 2 flux in the estuarine–coastal CO 2 flux variability is state of strong CO 2 from the river The observations and model output demonstrate that undersampling the complex tidal and mixing processes characteristic of estuarine and bias quantification of air-sea CO 2 fluxes in coastal waters. The results provide a mechanism to support critical national and regional policy implementation by reducing uncertainty in carbon budgets.

Estuaries are net heterotrophic and thus typically oversaturated with pCO 2 with respect to the atmosphere (Laruelle et al., 2017a). The global air-water CO 2 flux from estuaries is thus into the atmosphere and this flux is currently perceived to roughly offset the CO 2 uptake by the continental shelves (Cai, 2011;Borges et al., 2006). However, the global estuarine airwater CO 2 flux remains highly uncertain, with estimates ranging from 0.09 to 0.78 Pg C yr -1 (Cai, 2011;Laruelle et al., 45 2010;Chen and Borges, 2009;Chen et al., 2013;Resplandy et al., 2018).
Many estuaries and rivers such as those around major ports and harbours are deep and are easily accessed with large research vessels. However, there are many estuaries which are shallow or have irregular topography that are either fully or partially inaccessible to many research ships with large drafts. Observations of pCO 2 included in SOCAT from upper estuarine waters come from a limited number of research vessels that are typically small (~25 m long) and have shallow (~3 m) drafts. This 50 restriction on large vessels means that mapping the pCO 2 of many estuaries is challenging. Transects of many large rivers and estuaries by shallow-bottom boats identify a CO 2 concentration gradient between the mouth and source, with high pCO 2 (~10,000 ppm) upriver and pCO 2 levels similar to seawater close to the river mouth (Borges et al., 2018;Joesoef et al., 2015;Macklin et al., 2014;Bozec et al., 2012;Volta et al., 2016;Cai, 2011;Jeffrey et al., 2018b). Assessment of pCO 2 in inland waters, determined from measurements of total alkalinity (TA) and dissolved inorganic carbon (DIC), is also highly 55 uncertain, due to limited carbonate buffering capacity at low pH, and because acids in terrestrial organic matter make an unknown contribution to the TA anions (Abril et al., 2015).
The zone where estuarine waters meet coastal waters is a physically dynamic system influenced by riverine outflow, winds, waves, and tidal cycles, hence pCO 2 is likely to vary where estuarine water and continental shelf water interact, yet there has been relatively little attention given to air-water CO 2 fluxes in this zone (Cai, 2011). One holistic modelling study has tried 60 to understand the coastal system in Eastern North America, encompassing tidal wetlands, estuaries and continental shelves (Najjar et al., 2018). The study demonstrated that, despite estuaries representing <10 % of the domain area, interactions with shelf seas must be considered as the estuarine waters gave off more CO 2 than the shelves drew down. Eulerian studies in the estuarine zone have identified large tidal signals in pCO 2 with data collected from research vessels (Borges and Frankignoulle, 1999;Jeffrey et al., 2018a) and from moorings or fixed sites (Dai et al., 2009;Jeffrey et al., 2018a;Li et al., 65 2018;Bakker et al., 1996;Call et al., 2015;Ferrón et al., 2007;Santos et al., 2012). pCO 2 levels at the mouth of different rivers have been observed to co-vary with changes in river flow rate and with the tidal cycle (Ribas-Ribas et al., 2013;Canning et al., 2021;Najjar et al., 2018;Frankignoulle et al., 1996). Transects underway CO 2 measurements have not been regularly repeated through the transitional zone where estuaries connect with continental shelf waters.
Here we present weekly surface water fCO 2 observations along a transect from estuarine waters into continental shelf waters 70 in the English Channel between April and September 2016 (Figure 1). The CO 2 measurement system was capable of high spatial (~0.2 km) and temporal resolution (~ 48 s) revealing substantial variations in surface fCO 2 . Our aim was to examine in detail the transition zone between rivers, estuaries and the coastal zone in order to investigate variations in surface CO 2 and potential drivers of this variation.
We then used the observed relationship in the CO 2 and salinity data together with the output of a high resolution 75 hydrodynamic model of the estuary and nearshore region to estimate the spatial heterogeneity in fCO 2 and air/water CO 2 flux.

Study location and physical setting
This study was conducted in the English Channel off the coast of Plymouth (south-west UK) at the Western Channel Observatory (WCO, see Figure 1a), which includes the oceanographic station L4 (50.251°N, 4.221°W; (Smyth et al., 2010a) 80 and the Penlee Point Atmospheric Observatory (PPAO, 50.319°N, 4.193°W;(Yang et al., 2019;Yang et al., 2016) among other routine monitoring activities and assets. The PPAO is a coastal land-based observatory on the Rame Head peninsula at the entrance to the Plymouth Sound. Station L4 is a coastal site ~8 km from PPAO and is a focal point of the ongoing WCO time series.
L4 is seasonally stratified between late April and early October (Smyth et al., 2010b). The onset of stratification typically 85 drives a diatom dominated spring bloom in early April. Nitrogen limitation later in the year favours a summertime dominance of smaller plankton (Widdicombe et al., 2010). High river discharge rates in July 2006 were caused by several days of high rainfall and resulted in ~0.5 psu reduction in surface salinity at L4 (Rees et al., 2009). A prominent feature of the coastal region around WCO is the coastal/tidal current that entrain buoyant freshwater from the River Tamar outflow with prominent frontal features (Uncles and Torres, 2013). The River Tamar is a large source of freshwater to the region 90 despite being a relatively small river (Uncles et al., 2015). The coastal current moves along the west coast of Plymouth Sound adjacent to the Plymouth Breakwater and toward PPAO before following the coastline towards Rame Head peninsula (Uncles et al., 2015;Siddorn et al., 2003).
The annual cycle of L4 surface water pCO 2 is mainly determined by biological activity, with the spring bloom depleting pCO 2 in April and May . Seawater pCO 2 increases to pre-bloom levels throughout the summer and is at 95 equilibrium or slightly oversaturated with respect to the atmosphere in the autumn and winter (Kitidis et al., 2012;Marrec et al., 2013). Surface water pCO 2 decreases with distance offshore at all times of the year, with the greatest variability within 10 km of the coast (Kitidis et al., 2012). Changes in surface pCO 2 >40 ppm have been observed during a 24 hour eulerian study at L4 (Litt et al., 2010). Direct methane flux measurements made at the PPAO indicate that the waters around the Rame Head peninsula are influenced by the interaction between tidal cycles and the Tamar freshwater outflow (Yang et al., 100 2016).

Sampling approach:
Transects between the Breakwater in the Plymouth Sound and Station L4 were conducted weekly where possible during the study period (Figure 1b). Transects took place between 09:00 and 15:00 hrs local time using the RV Plymouth Quest. 15 105 transects were conducted on 12 non-sequential days between 10 th June and 21 st September 2016. RV Plymouth Quest takes ~40 minutes to travel directly to L4 during transects, except during a number of voyages when the ship was redirected into Cawsand Bay and/or closer to the PPAO. The underway seawater system on the ship has an intake at 3 m depth, supplying seawater for measurements of pCO 2 , sea surface temperature (SST) and surface salinity (SBE45; Seabird Scientific, USA).
The underway system is turned off when the ship is shore side of the Breakwater to reduce the risk of heavy biofouling and 110 the intake of large quantities of sediment and coastal debris.

Seawater CO2 and carbonate system analyses:
Two independent CO 2 systems with different equilibrator designs were used to measure seawater CO 2 on the RV Plymouth Quest. The PML-Dartcom Live pCO 2 system (Dartcom systems Inc, UK) is permanently installed to measure ocean surface 120 CO 2 at L4, and utilises a vented showerhead equilibrator with an equilibration time of 8 minutes (4 e-folding times). This was setup with a sampling frequency of 27 minutes (Kitidis et al., 2012). The showerhead system also measured atmospheric pCO 2 every 27 minutes. Additionally, a high-frequency and high-resolution membrane CO 2 system (Sims et al. (2017) was installed during the study period. This system utilises a membrane equilibrator with a fast response time of 48 seconds (2 efolding times) and has a high sampling frequency (1 Hz). Both CO 2 systems were calibrated with the same secondary 125 standards (263.04 and 483.36ppm), traceable to WMO standards by cross-calibration at PML against National Oceanic and Atmospheric Administration Global Monitoring Laboratory (NOAA GML, USA) certified standards (244.91, 388.62 and 444.40 ppm). The membrane system was calibrated pre-and post-voyage (~4-5 hours apart) and the showerhead system calibrated hourly while the underway system was running.
The membrane and Dartcom systems used non-dispersive infrared gas analysers (Model 840B and 7000,respectively;Licor,130 Inc., USA) to measure gas phase CO 2 mixing ratio (xCO 2 ) in the equilibrated gas exiting the membrane or shower-head equilibrators. The fugacity of CO 2 inside the equilibrator (fCO 2(eq) ) and the fugacity of CO 2 in seawater (fCO 2(sw) ) were calculated using measured SST, surface salinity, equilibrator pressure and equilibrator temperature, using equations listed in SOP 5 (Dickson et al., 2007). Lag-time correlation analysis between SST and the equilibrator temperature identified that a -79 sec adjustment should be made to the fCO 2 measurement time. The fCO 2 time adjustment accounted for the time taken 135 for water to enter the seawater intake beneath the hull of the ship and arrive at the showerhead and membrane equilibrators.
The flux (F) of CO 2 (mmol m -2 d -1 ) is computed following (Wanninkhof, 2014b): (1) k w is the water phase gas transfer velocity (cm hr -1 ; Equ. 2), k 0 is the solubility of CO 2 in seawater (mol L -1 atm -1 ) from Weiss (1974), ΔfCO 2 is the difference in fugacity between the atmosphere and ocean (μatm; Equ. 3), and SF is a scaling 140 factor of 0.24 to express the result flux F in units of (mmol m -2 d -1 ).
The gas transfer velocity is computed following Nightingale et al. (2000): k W = (0.222 (U 10 ) 2 + 0.333 (U 10 )) (Sc/660) -1/2 (2) where U 10n is the mean wind speed at 10m height and for neutral conditions, Sc is the scaling by unitless Schmidt number of 660 (Wanninkhof, 2014a). U 10n measurements were taken from the L4 buoy (Smyth et al., 2010a). 145 ΔfCO 2 is here defined as the difference between the seawater interface fugacity and the fugacity of air: To account for the cool and salty layer at the atmosphere ocean interface, -0.17°C and +0.1 PSU were added to the in situ temperature and salinity when calculating seawater fCO 2 at the interface and for the estimation of air-sea CO 2 flux (Woolf et al., 2019). 150 TA samples were measured by open cell potentiometric titration with 0.1M hydrochloric acid on a Total Alkalinity Titrator (Model AS-ALK2; Apollo SciTech, Inc. USA) following SOP 3b in Dickson et al. (2007). DIC was measured using an Apollo SciTech DIC analyser (Model AS-C3; Apollo SciTech, Inc., USA) following SOP 2 in Dickson, Sabine et al. (2007), by acidifying samples with excess 10% phosphoric acid and using nitrogen gas to transfer liberated CO 2 to an infrared gas analyser (Model Licor 7000, Licor Inc., USA). These two measurement systems are described in more detail in 155 (Kitidis et al., 2017). fCO 2 was calculated from TA and DIC using CO2SYS in Matlab (Van Heuven et al., 2011) with the carbonic acid dissociation constants of Mehrbach (1973) refit by Dickson and Millero (1987) and the hydrogen sulphate dissociation constant of Dickson (1990).

Numerical model:
The hydrodynamics of the WCO were modelled following Uncles et al. (2020) using an implementation of the Finite-160 Volume Community Ocean Model (FVCOM; (Chen et al., 2003)). The model domain (~ 49.7° to 50.6° N and ~ 4.8° to 3.8° W) encompasses station L4, PPAO, Plymouth Sound, and the estuary of the River Tamar including its major tributaries.
FVCOM utilises an unstructured grid consisting of a mesh of variable resolution triangles, which allows the representation of complex coastlines and higher resolution in areas of interest whilst remaining computationally feasible. The resolution of the model is ~600 m at L4, becoming finer towards the PPAO and Plymouth Sound (~85 m), with highest resolution around the 165 upper River Tamar channel (~40 m). The vertical system is terrain following sigma coordinates with 24 equally spaced layers. Horizontal mixing is parameterised through the (Smagorinsky, 1963) scheme and vertical turbulence closure through an updated version of the MY 2.5 scheme (Mellor and Yamada, 1982), with mixing coefficients of 0.2 and 1x10 -5 respectively.
Water depth within the model domain uses the EMODNET bathymetry product with a nominal resolution of 1/16 degree. In 170 the estuary and nearshore areas (< 20 m depth) the data have been complemented with local data sources of Lidar, single and multi-beam surveys accessed through the Coastal Channel Observatory (CCO, https://www.channelcoast.org/). The CCO data was re-projected from its original projection (OSGB) to WGS84 and concatenated and averaged into a 20 m regular grid using the Generic Mapping Tools (GMT 5.3.2) software (http://gmt.soest.hawaii.edu/). The merged dataset was processed using the ROMS toolbox for bathymetry processing downloaded from https://github.com/dcherian/tools. The scattered 175 bathymetry was interpolated to 25 m and smoothed iteratively to achieve a Haney number less than 2 (Haney, 1991).
Lateral boundary conditions are provided as a one-way direct nesting at hourly resolution from a larger FVCOM model covering the west UK shelf (Cazenave et al., 2016). The surface atmospheric forcing is from the NCEP GFS 6 hourly historical product, which is downscaled to ~3 km resolution using a triple nested implementation of the Weather Research and Forecasting (WRF) model (Skamarock et al., 2008). The freshwater input flux for 11 rivers in the domain was obtained 180 from daily river gauge data from the National River Flow archive (https://nrfa.ceh.ac.uk). The temperature of freshwater inputs was determined using a regression model on the WRF 2m air temperature, which was trained on temperature records from the UK Environment Agency's Freshwater River Temperature Archive (Orr et al., 2010) and data from the Westcountry river trust.
The model was run for the period between March 2016 and November 2016, with instantaneous values output hourly. Only 185 the uppermost layer of the FVCOM output is used in the analysis below. The thickness of this layer varies between 0.05 m and 5m across the domain (because the model uses terrain-following coordinates), and the significance of this and how it relates to the 3 m underway measurement and air-sea CO 2 fluxes is discussed below.

Results 190
Showerhead vs membrane comparison: Surface fCO 2 was measured for several hours while RV Plymouth Quest was stationary at L4 in between outbound and return transects. The showerhead system sampled continuously from the fixed seawater intake (3 m depth). The membrane equilibrator system was switched to sample via tubing from a near surface ocean profiler (Sims et al., 2017) when at L4 ( Figure S1). The two CO 2 systems showed good agreement when the surface ocean profiler was between 2.5m and 3.5m, 195 despite sampling slightly different water through different tubing ( Figure 2). The mean residual was 2.77 μatm and the RMSE was 6.9 μatm when sampling on station (Figure 2), this is similar to the ±2 μatm difference that has been observed during other seawater CO 2 intercomparison exercises (Körtzinger et al., 2000;Ribas-Ribas et al., 2014). The CO 2 systems both sampled from the underway seawater supply of the ship during the L4 to Breakwater transects, and fCO 2 was estimated from pCO 2 using the underway SST and salinity. The 11 coincident fCO 2 measurements during the transects had a mean 200 residual of 2.88 μatm and a RMSE of 27.1 μatm ( Figure 2). The largest differences between the CO 2 systems tend to occur when the ship was not on station at L4.

Spatial and temporal variation in salinity, SST and fCO 2 :
Sea surface salinity at L4 during the June to October study period does show small variation (mean ±SD = 35.15±0.08 psu; Figure 3a). The L4 salinity range during the study period is within the range of previous years (Smyth et al., 2010b). L4 205 salinity decreased intermittently, with a maximum reduction of 0.68 psu on 9 th August. The salinity measurements at L4 contrast with the large variability in Breakwater salinity during the study period (34.17-35.23 psu). The average salinity difference between the Breakwater and L4 is 0.36 psu. The salinity ranges observed at L4 and at the Breakwater are similar to model results during a tidal cycle (Uncles et al., 2015).
Coastal SSTs (Figure 3b) followed the seasonal warming pattern slowly increasing from 13.9°C on 10 th June to 16.7°C on 210 21 st September. The warming trend was in broad agreement with SST trends observed during previous years (Smyth et al., 2010b). The SST variation along each transect was typically small (<1°C) compared to the SST change over the study period (2.8°C). The smallest temperature difference between L4 and the Breakwater (0.025°C) occurred on 15 th September. The largest temperature differences occurred during early summer (1.20°C, 0.63°C, 0.59°C and 0.65°C on 10 th , 15 th , 22 nd and 30 th June, respectively). 215 L4 surface fCO 2 increased from 355 μatm to 420 μatm between 10 th June and 21 st September (Figure 3c). The average fCO 2 difference between L4 and the Breakwater was 20 μatm. Abrupt changes in fCO 2 were observed along the transects, generally close to the Breakwater (>4 km from the L4 station). fCO 2 in waters within 4 km of the Breakwater ranged between 338 and 440 μatm during the study period. fCO 2 measurements within 2 km of the PPAO also varied considerably during some of the transects; for example, fCO 2 varied between 337 and 434 μatm during the transect past the PPAO on 7 th 220 July. The variability in membrane equilibrator fCO 2 measurements agreed with previous observations in the region (Kitidis et al., 2012) . When transects were ordered by stage along the 12 hour tidal cycle, the spatial variability in salinity transects ( Figure S2) appeared to correspond to the different stages of the tidal cycle. Temperature and fCO 2 transects can be found in the supplementary materials ( Figure S3-4). We divided our transect data according to the stage in the tidal cycle (determined 225 from the Devonport tidal gauge station; 50.368°N, -4.185°W, Figure 1b). Transects were characterised by the time elapsed since the last period of low water (i.e. LW + X hrs) using the time at the midpoint of each transect.
Four categories were used, corresponding to 3 hr tidal periods: Low water (LW+0 hrs); Flooding tide (LW+3 hrs); High water (LW+6 hrs); and Ebbing tide (LW+9 hrs). Four transects are used below to exemplify the relationship between the different stages of the tidal cycle and the spatial variation in fCO 2 (Figures 4-7). 230

Example transects:
The transect on 7 th July (low water, LW+0 hrs) began at L4 and headed inland (Figure 4). Salinity was 35.1 psu close to L4 and declined along the transect. The low salinity was directly North of PPAO (34.7 psu), and in the shallow waters of Cawsand Bay (North of PPAO, 35.5 psu). SST was warmest near L4 and in the relatively shallow Cawsand Bay. The river water was cooler than the L4 seawater and there was a negative gradient (0.55°C) into Cawsand Bay. fCO 2 was lowest (~360 235 μatm) when near to L4 and highest (~430 μatm) immediately South of PPAO. fCO 2 to the North of PPAO in Cawsand Bay was ~390 μatm, lower than waters South of PPAO.
The data collected on 15 th June is an example from a flooding tide transect (LW+3 hrs, Figure 5). Salinity was 35.1 psu in waters close to L4 and decreased toward PPAO and the Breakwater (34.7 psu minimum). The Tamar river plume was warmer than coastal waters in July. SST was highest (~14.1°C) close to the Breakwater and the coldest water along the 240 transect (13.3°C) was near to L4. The difference in fCO 2 between L4 and the Breakwater was ~18 μatm, with higher fCO 2 (353 μatm) in the warm, low salinity water close to the Breakwater.
Data collected on 30 th June is an example of a transect at high water (LW+6 hrs, Figure 6). High salinity (>35 psu) water was observed much closer to PPAO during the LW+6 hr transect than on transects during low water periods in the tidal cycle (Figures 4&5). Salinity reduces rapidly to 34.1 psu in between the PPAO and the Breakwater. Spatial patterns similar to 245 surface salinity are seen in SST and fCO 2 , with the gradients the inverse of the salinity gradient. The low salinity water close to the Breakwater has higher SST and fCO 2 (14.8°C and 385 μatm) than the observations South of PPAO. The fCO 2 range on this transect was ~38 μatm, and the majority of the change was close to the PPAO. The fCO 2 difference between L4 and the water just South of PPAO was only ~12 μatm. These data suggest that the Tamar plume during LW+6 hrs was restricted near to the coast and did not make a big impact upon the waters in between PPAO and L4. 250 Data on 10 th June show a transect during an ebbing tide (LW+9 hrs) (Figure 7). Salinity near to L4 was 35.15 psu and declined toward the coast, interrupted by a patch of water due east of PPAO with salinity levels similar to L4. Two patches of low salinity water (34.8 psu) were encountered along the transect. One low salinity patch was just South of PPAO and the other patch was close to the Breakwater. Spatial variation in SST and fCO 2 coincide with the variations in salinity, with higher SST (~14.2°C) and fCO 2 (~365 μatm) in the patches of low salinity water. The fCO 2 difference between L4 surface 255 waters and the fresh, warm waters influenced by the River Tamar plume is ~25 μatm.
In summary: The variations in salinity observed in all transects (i.e. examples above and those in Supplementary Figure S2) qualitatively agreed with output from a previous physical model of the Plymouth Sound (Siddorn et al., 2003). The freshwater plume at low water extends out past the PPAO, whereas the plume at high water (LW+6 hrs) is restricted to close to the breakwater (Siddorn et al., 2003). The same model on an ebbing tide predicts that two plumes of river water exit via 260 the channels at the east and west ends of the Breakwater.

Relationship between salinity and fCO 2 :
The changes in salinity and fCO 2 during the example transects suggest that the changes in fCO 2 are driven by conservative mixing of salt and fresh water end members. Robust fCO 2 and salinity relationships have been observed in large rivers like the Amazon and Mississippi (Lefèvre et al., 2010;Cai et al., 2013). The relationship between salinity and fCO 2 is 265 complicated by the seasonal variability in fCO 2 and the constantly changing position of the tidally-controlled freshwater plume. We calculated the difference between in situ data from transects and from measurements at L4 to account for seasonal variations in seawater CO 2 : ξfCO 2 = Transect fCO2 -L4 fCO2 (4) ξS = Transect Salinity -L4 Salinity (5) 270 ξfCO 2 and ξS displayed an apparent relationship throughout different seasons and stages of the tidal cycle ( Figure 8). ξS was a stronger predictor of ξfCO 2 than location along the transect (distance from L4).
The fCO 2 and salinity data diverged from the general trend when the RV Plymouth Quest travelled into Cawsand Bay (West of the Breakwater) on 7 th July (Figure 8). Uncles and Torres (2013) showed that the seawater residence time increases as you approach the Breakwater, following that methodology the FVCOM model used here also shows this is true for Cawsand 275 Bay. A long residence time and a shallow water column mean that the waters in Cawsand Bay are likely to be closer to equilibrium with the atmosphere due to relatively higher turbulent mixing from bottom stress and surface waves (Upstill-Goddard, 2006). As Cawsand Bay is a micro-environment, the bay could be a biological hotspot driving the changes in CO 2 .
Excluding the 7 th July transect that went into Cawsand Bay, the linear fit to the ξfCO 2 and ξS data gives ξfCO 2 = -39.83 ξS + 5.50 (R 2 =0.2165, N=22262, p=<0.001). The fit explained 21.6% of the variability in the data, with a RMSE of 18.95 μatm. 280 fCO 2 calculated from TA and DIC bottle data from the River Tamar on 1 st October 2014 show a qualitatively similar relationship between salinity and fCO 2 ( Figure S5) for stations T3-T9. The trend continues for stations furthest upstream (T1 and T2), but does not follow the same linear relationship. A linear fit between ξS and ξfCO 2 for stations T3-T9 suggests a 42.24 μatm change per unit of salinity. The bottle data indicates that the ξfCO 2 and ξS relationship can be extrapolated to lower salinities and that the relationship begins to break down at ξS < -4 psu. Note that the TA/DIC data and fCO 2 data were 285 collected at different times (years and stages of seasonal cycle) and with different sampling and analytical approaches. The apparent linear relationship between ξfCO 2 and ξS suggested that it can be applied to the wider coastal region. The next section assesses the utility of the high resolution model  to predict coastal fCO 2 .

Using FVCOM to estimate coastal air-sea CO 2 fluxes:
Extrapolation of the relationship between ξS and ξfCO 2 across the coastal domain required that FVCOM accurately 290 replicates available surface salinity observations at different stages of the tidal cycle. FVCOM compares very well with the spatial and temporal variability in the four example transects at different stages of the tidal cycle (Figure 9) Modelled spatial variations in coastal surface salinity are shown in Figure 10a, which focuses on the 7 th July transect.
Equivalent plots for the other three example transects on 30 th June, 15 th June and 10 th June ( Figures S7 to 9). The 7 th July transect was at low water (LW +0 hrs), and when low salinity water was exiting from either side of the Breakwater and wrapping around the Rame Head Peninsula (Figure 10a). give an uncertainty due to ξS (8.48 μatm). The standard combined uncertainty in fCO 2 includes the uncertainty in the ξfCO 2 and ξS relationship (18.95 μatm), uncertainty due to ξS (8.48 μatm) and the uncertainty in the fCO 2 observations (L4 fCO 2 = 315 6.9 μatm, in the on station comparison, Figure 2). These uncertainties add in quadrature to give a standard combined uncertainty of 21.88 μatm.
The FVCOM model enables simulation of a full tidal cycle so that the impact on air-sea CO 2 flux can be visualised throughout 7 th July (Figure 11, equivalent figures for the examples on 30 th June, 15 th June and 10 th June are in Figures S10 to S12). A constant wind speed equal to the mean across the period is applied across the model domain (surface area = 132 320 km 2 ) for simplicity. The flux signal co-varies with tidal height (Figure 11a-b). The flux integrated across the model domain changes substantially throughout the tidal cycle (~9.3% change). If the region of the integration is restricted further to include just the region due north of PPAO (>50.32°N) then the magnitude of the flux changes substantially, it was a weak sink (~-65 mol hr -1 ) at low tide whereas at high tide there was a substantially larger sink (~-1113.23 mol hr -1 ).
Three configurations were used to calculate the flux (Figure 12) to establish whether the tidal plume had a net effect on the 325 regional air-sea fluxes calculated on seasonal timescales between March and November 2016. In the first configuration (L4), L4 measurements were scaled by surface area. The second configuration (this study) used the L4 measurements with the fCO 2 and salinity relationship determined above, applied to the spatially varying salinity field from the FVCOM model. In the third configuration (Landschützer coastal product), the closest node (50.125°N, 4.125°W) in the widely used Landschützer coastal product (Landschützer et al., 2020) is scaled by surface area. Fluxes were computed for a fixed region 330 of 128 km 2 (a slight modification of the region in Figures 10b and 11a-d) encompassing the river plume and the region behind the Breakwater. Regions met the depth and salinity criteria in the region (depth >10m, ξS > -4 psu and >50.24°N) for > 80% of the period included. Whilst fCO 2 is typically measured weekly at L4 by the showerhead system, instrument downtime in 2016 meant that the measurements were less frequent than expected, the requirement to interpolate between measurements to construct a non-fragmented timeseries of seasonal fCO 2 in 2016 is therefore an unavoidable limitation of 335 this approach. The average regional fCO 2 (i.e. including using the spatially varying salinity) showed undersaturation in the summer and oversaturation in the spring and autumn. The regional concentration was ~30 μatm greater than the observed concentrations at L4, which is larger than the uncertainty in our estimate of fCO 2 (Figure 12). The pCO 2 in the Landschützer coastal product was much lower than the observed fCO 2 values at L4 in 2016 ( Figure 12). L4 pCO2 saturations ( Figure 12) indicate that fluxes follow the same trend as previous measurements at the site: CO 2 uptake 340 in the region throughout the summer and a short period of outgassing in late September (Kitidis et al., 2012;Marrec et al., 2013). The Landschützer product suggests that the region is a larger sink than indicated by the measurements at L4, and does not suggest that the region is ever a source of CO 2 to the atmosphere. This study calculates fluxes calculated with the fCO 2 values predicted from salinity and suggests that the near coastal region (128 km 2 ) was a weaker sink in the summer, increasing the discrepancy with the Landschützer product. This study also suggests weak outgassing of CO 2 from the near 345 coastal region in March, April and October, which would not be the case if the L4 measurements are taken as representative of the near coastal region. Salinity is the variable driving the differences between this study and the L4 measurements in spring, it can be surmised that this is due to increased low salinity water inputs from rivers input in the spring.

Discussion
Here we show large variations in fCO 2 in the estuarine zone using a high-frequency membrane equilibrator which could not 350 be detected using a showerhead equilibrator. Seawater fCO 2 is assumed to be relatively homogeneous over large spatial scales in the open ocean (Takahashi et al., 2009). Temporal variability in open ocean waters is also typically slow, with the most rapid variations occurring over hourly or slower timescales (e.g. diurnal, (Torres et al., 2021)). The measuring frequency of a typical showerhead seawater CO 2 system (~8 min) is thus sufficient to determine open ocean fCO 2 variability.
The difference between the underway fCO 2 measurements made by the two systems used in this study (Figure 2) is caused 355 by the different response times of the showerhead and membrane equilibrators and their ability to resolve the considerable horizontal variability in coastal and shelf waters (Kitidis et al., 2012). The membrane and showerhead systems agreed well when the ship was on station (RMSE = 6.9 µatm), because both systems had sufficient time to equilibrate. When the ship was moving through heterogeneous coastal surface waters, the showerhead system cannot fully equilibrate, and the agreement with the fast-response membrane equilibrator system is worse (RMSE = 27.1 µatm). 360 Single seawater CO 2 observations are representative of CO 2 integrated across the region that the ship transits through whilst equilibrating. The RV Plymouth Quest typically travels at ~9 knots (4.6 m/s), which is equivalent to 0.22 km in 48 s (2 times the e-folding response time of the membrane system) and 1.1 km in 4 minutes (2 times the e-folding response time of the showerhead system). However, the showerhead system also switches between seawater CO 2 , CO 2 gas standards and atmospheric CO 2 , hence seawater measurements are not continuous. Routines of seawater fCO 2 measurements are 27 min 365 apart, which equates to a distance of ~7.5 km when the RV Plymouth Quest is moving.
We found an inverses linear relationship between salinity and fCO 2 and that salinity measurements also agreed well with model salinity output. The FVCOM model output confirms that the river plume extent is highly variable in time and space, and that oceanographic features in the region such as the river plume are ~1 km or smaller. The highly dynamic nature of the plume means that a showerhead CO 2 system cannot be expected to resolve the spatial dynamics. A showerhead fCO 2 system 370 design can also be biased toward the end of the equilibration period, which may generate some measurement bias if seawater fCO 2 changes rapidly during the 8 min full equilibration time (e.g. (Ribas-Ribas et al., 2014)). Complete characterisation of fCO 2 in coastal waters within 10 km of land and with highly variable fCO 2 requires a system with a fast response equilibrator or slower steaming.
Mixing of estuarine and continental shelf water masses partially determines the fCO 2 levels observed in this near shore study 375 region. Shelf waters exhibit a seasonal surface fCO 2 trend associated with a) cooling-enhanced solubility in late winter, b) net phytoplankton uptake in spring/summer , c) partial re-equilibration with the atmosphere and d) mixing with CO 2 -rich bottom waters in autumn (Kitidis et al., 2019). The River Tamar is the other mixing end member and is typically oversaturated with fCO 2 with respect to the atmosphere (Frankignoulle et al., 1998). The results presented in this paper also suggest that riverine fCO 2 may have a strong influence on the spatial and temporal patterns in coastal waters off Plymouth. It 380 is important to note that the relationship between salinity and fCO 2 determined in this paper only explains 21.6% of the variability, was derived with summer data only (due to sampling constraints), and further work is needed to confirm if the relationship stands during the remaining period of the year (i.e. October through to May). The fCO 2 variability that is not explained by our relationship could be driven by other factors including gas exchange in shallow waters, river runoff during storms, upwelling and increased nutrient runoff in the Tamar leading to plankton blooms. 385 The confluence of estuarine and continental shelf waters near the PPAO/Breakwater and the local circulation of surface waters are dominated by the semi diurnal tidal cycle (Uncles et al., 2015). The rising tide after low water pushes shelf water toward the Breakwater, whereas a falling tide after high water encourages riverine-influenced water to extend south. The tidal influence upon coastal fCO 2 is evident in the 15 transects during this study, with changes of 20-40 μatm relative to L4 ( Figure 8). Timeseries data presented by Borges and Frankignoulle (1999) indicate a similar magnitude (20-25 μatm) tidal 390 signature in coastal Belgian and Dutch waters.
Accurate fCO 2 data are essential when comparing ∆fCO 2 with direct eddy covariance CO 2 flux observations and trying to estimate the gas transfer velocity (Dong et al., 2021). Well-resolved seawater fCO 2 observations are needed within a coastal eddy covariance flux footprint when the flux observations are made from a fixed platform such as the PPAO (Yang et al., 2016). The RV Plymouth Quest transects through the PPAO flux footprint once a week, but the exact timing of this within a 395 tidal cycle is determined by when the vessel is able to exit and enter the tidally restricted harbour lock. Flux footprint sampling is thus restricted to certain stages of the tidal cycle and it is not possible to characterise the full extent of estuarine/shelf water mixing at all stages of the tide. Autonomous platforms (moored or otherwise) instrumented with highfrequency seawater CO 2 sensors would make a crucial contribution to the current observational gap (Chavez et al., 2018;Manning et al., 2020) and achieve high resolution fCO 2 mapping in the coastal zone. 400 The salinity field from the FVCOM model is used to estimate the surface fCO 2 features over a complete tidal cycle and shows that the flux can change by a non-trivial amount (~10%) over a short period of time ( Figure 11). These data also show that using a hydrodynamic model can extend the spatial and temporal coverage of CO 2 uptake and outgassing estimates in the coastal region surrounding Plymouth made with weekly L4 measurements ( Figure 12). If similar relationships can be developed for other estuarine zones, then operational dynamic models may be able to add information to flux estimates for 405 these zones, too. The spatial resolution of the model at the surface means that it is possible that near surface features such as fresh water lenses are being overlooked by this analysis. Higher resolution modelling of the surface ocean would make future coastal products more applicable to air sea flux studies.

Conclusions
Here we show for the first time dynamic and large variations in the coastal zone using a fast response membrane equilibrator 410 system. These gradients between estuarine waters and shelf waters were not resolved by a co-located showerhead CO 2 system. The gradients in salinity and fCO 2 fields show strong tidal influence. Changes in fCO 2 after accounting for the seasonal trend, are linked with salinity variations, with the highest regions of fCO 2 coinciding with the lowest salinity regions and vice versa. The inverse linear relationship between salinity and fCO 2 variations (Figure 8) suggests that mixing of estuarine and shelf water end members is a control on the surface water distribution of fCO 2 . Measured salinity agrees 415 well with FVCOM model surface salinity fields at different stages of the tidal cycle. FVCOM output is used to estimate the temporal and spatial variations of fCO 2 in coastal waters. The model output demonstrates that neglecting the river plume leads to an overestimation of the magnitude of the CO 2 sink in the summer. The region may also be misidentified as a sink for atmospheric CO 2 in the spring and autumn when it could be a weak source, as suggested .
Measurements from L4 are not fully representative of the estuarine zone and caution should be used when scaling them over 420 this region.
The surface flux from estuaries and coastal waters has proven difficult to assess comprehensively (Borges et al., 2006). The high resolution fCO 2 data presented in this study show that tidal and estuarine-influenced coastal waters can quickly transition from a strong source to a strong sink depending on the state of the tide (Figure 11). Inland and coastal waters are a large uncertainty in global fluxes (Chen et al., 2013). The high resolution observations presented in this paper show that the 425 head of the river/estuarine plume for this region is linked to the tidal state. This is critical for the accurate calculation of airwater flux from the region. Further studies are required to evaluate the wider applicability of this method to similar coastal regions. Distinctly different estuarine/coastal zones such as lagoons, river deltas and fjords will have their own distinct fCO 2 signatures and patterns driven in part by surface water circulation and mixing. High-resolution models that can resolve tides and surface salinity in estuarine/coastal waters with high confidence, are a useful tool in ongoing and future efforts to 430 constrain coastal air-sea CO 2 fluxes.

Acknowledgements
This research was supported by UK NERC via studentship (NE/L000075/1), the Shelf Sea Biogeochemistry pelagic research programme (NE/K002007/1), RAGNARoCC (NE/K002473/1), single centre national capability (CLASS; NE/R015953/1), the Land Ocean Carbon Transfer project (LOCATE; NE/N018087/1), NERC grant NE/L007010 and the NERC LTSS 435 National Capability Program that underpins numerical modelling work at PML. This research was also supported by EU projects MyCoast (EU Interreg Atlantic Area Program project MYCOAST (EAPA_285/2016)), IMMERSE (H2020 821926), AtlantOS (H2020 633211), FixO3 (FP7 312463) and RINGO (H2020 730944). We thank the captain and crew of the RV Plymouth Quest for all their assistance. We also thank Tim Smyth and Ming Yang for insightful discussions and data relating to the WCO and PPAO time series and John Stevens and Rachel Beale for their help on the PML Explorer. 440