First of all, thank you for providing such helpful feedback and taking the time to present all your questions in detail.

> 1. Terminology: Instead of referring to 'particles,' using 'phytoplankton

cells' would better align with the biological focus of their study.

We had a similar discussion when we were writing the paper, so we particularly

value this input.

In the end, we chose "particle" to emphasise the abstraction that takes place in

our model when representing a phytoplankton cell, as our model is of course not

able to fully capture their behaviour and dynamics.

Ideally, therefore, these two concepts should not be confused by the reader.

However, as you suggested, the term "particle" might be more confusing,

especially for non-modeling readers, as it obscures the biological implications,

and we have changed the term "particle" to "phytoplankton cell" where

appropriate, as you suggested.

E.g. we changed the paragraph introducing the concept of a lagrangian model to

read:

    [...] [Eulerian models] lack temporal consistency, meaning that the life

    history and trajectory of a phytoplankton cell cannot be tracked.

    Previous modeling studies have attempted to overcome this problem using a

    Lagrangian approach.

    A Lagrangian model does not try to track e.g. concentrations at fixed

    positions, but rather follows the motion of individual particles that

    can be used to represent e.g. water parcels or organisms.

    Their ability to resolve the interactions of individual phytoplankton cells

    or aggregates with the bathymetry, e.g. through settling or stranding,

    while maintaining temporal consistency, is essential for investigating

    retention mechanisms.

> 2. Model Validation: Including aspects related to model validation, such as

capturing the seasonal cycle, the duration of bloom events, the spatial

distribution of blooms in relation to distance from the estuary, and other

relevant parameters, would enhance the biological relevance of their research

and provide a more comprehensive understanding of the dynamics at play.

We agree that model validation is important, but it seems to us that there may

be a misunderstanding about the type of model presented, its implications and

purpose.

Our model can be interpreted (in part) as a post-processing or further analysis

of the model presented by Pein et al. (2021).

The model of Pein et al. is a Eulerian model that captures both hydrodynamics

and biology. The biology is modelled using ECOSMO. This model includes several

planktonic compartments (diatoms, flagellates, cyanobacteria and two zooplankton

compartments) and has been successfully applied in several areas (Schrum et al.,

(2006), Daewel and Schrum (2013)).

In the model of the Elbe estuary that we use, it is calibrated and validated

with observational data from both long-term measuring stations and cruises that

take transects in the centre of the channel.

The Pein et al. model is able to predict population dynamics at the

concentration level reasonably well. It captures both the seasonal cycle, i.e.

the bloom events, and the spatial distribution.

Our model does not attempt to predict population dynamics.

We use our model to shed light on physical processes that are largely ignored in

Eulerian models such as that of Pein et al. (2021) - in particular, the process

of stranding and other interactions with the bathymetry.

Our focus is therefore, in a sense, to help understand the loss term induced by

outwashing to high salinity waters or dry shores.

These processes are not directly represented in the differential equation of the

Eulerian model that predicts ecosystem dynamics and therefore can not be easily

studied with such models.

For this purpose, we have chosen a Lagrangian approach, which allows us to model

phytoplankton stranding in a simple and (computationally) inexpensive way, with

a temporal consistency that is crucial for modelling the processes studied and

that cannot be achieved with Eulerian models.

Because of this narrow focus, we have simplified the biological processes as

much as possible to allow for high interpretability of our results.

We agree that it would be desirable for our model to predict the full ecosystem

dynamics, as this would potentially improve the interpretability of the effects

of the processes studied, i.e. to make quantitative rather than just qualitative

predictions.

However, not only would this greatly increase the cost of building, running and

evaluating such models, it is not currently possible due to technical

constraints and lack of calibration and validation data, neither in our

Lagrangian model nor in any other model to our knowledge.

We this paragraph to emphasize the already validated hydrodynamical and

ecostsystem model on which our study is based:

    Nevertheless, there are sophisticated estuarine models that are able to

    reproduce the complex dynamics of estuaries reasonably well. This

    includes currents and water levels on the physical side, but also

    chlorophyll concentrations and other biologically driven properties

    (Pein et al. (2021), Schoel et al (2014)).

    However, these are Eulerian models.

    This means that they are based on a fixed grid and calculate the

    concentration of a tracer, such as phytoplankton, at each grid cell.

    This makes it difficult to study concepts such as retention times, as they

    lack temporal consistency, meaning that the life history and trajectory

    of a phytoplankton cell cannot be tracked.

    Previous modeling studies have attempted to overcome this problem using a

    Lagrangian approach.

    A Lagrangian model does not try to track e.g. concentrations at fixed

    positions, but rather follows the motion of individual particles that

    can be used to represent e.g. water parcels or organisms.

    The ability to resolve the interactions of individual phytoplankton cells or

    aggregates with the bathymetry, e.g. through settling or stranding,

    while maintaining temporal consistency, is essential for investigating

    retention mechanisms.

and the following section in the "model limitations" section:

    In this study, we aimed to thoroughly investigate different possible

    retention mechanisms in a complex Lagrangian model system with a highly

    resolved bathymetry.

    Due to this computational and spatial complexity, the complexity of the

    biological particle properties needed to remain simple to keep

    computational cost manageable and due to a lack of high resolution

    validation data.

    

    Our model design does not resolve more complex ecosystem dynamics such as

    nutrient limitation and grazing by higher trophic levels.

    The Lagrangian model is performed offline, meaning it is not coupled to the

    Eulerian model that calculates the hydrodynamics and is performed after

    the fact.

    Therefore, modeling the advection and dispersal of changes in concentration

    fields e.g. nutrients due to growth or remineralization was not easily

    possible.

    Future modeling efforts could couple the Lagrangian model to a Eulerian

    model that disperses changes in concentrations fields by biotic activity

    throughout the model domain. [...]

> 3. The aspect that phytoplankton cells survive in the dry grid cell (without

water) needs to be justified. Otherwise, this should be corrected in the method,

post-processing (without redoing all the tests) – these cells can be excluded

from the final count, and further conclusions should be corrected.

We agree that pythoplankon cannot survive indefinitely in dry conditions.

To contextualise their ability to survive, we would like to highlight two

things:

First, the areas where phytoplankton strand are typically frequently flooded by

the tide.

The vast majority of phytoplankton in our model are stranded for less than one

tidal cycle, i.e. less than 12 hours.

Secondly, cells that are considered 'dry' by the model are not necessarily

devoid of water.

The cell resolution in these areas is typically between 50 and 100m.

Cells are considered dry if the water level falls below 0.1m over the majority

of their area.

Therefore, a lot of sub-resolution structure can be expected.

These include sand ripples, tidal creeks or small pools that hold water where

phytoplankton could survive for several days before drying out.

In addition, the low marsh that surrounds most of the estuary contains a lot of

vegetation, typically tall reeds.

This is thought to improve the survivability of the phytoplankton around it by

increasing soil moisture long enough for most cells to survive through a tidal

cycle.

The stranding and resuspension of phytoplankton and microphytobenthos has been

shown to be an important process for primary production under eastuarine

conditions (Carlson et al (1984), De Jonge et al (1992), Kromkamp et al (1995),

Savelli et al (2019)).

While this process is particularly well established for microphytobenthos

(Savelli et al), Semcheski et al (2016) showed that the distinction between

'phyoplankton' and 'microphytobenthos' is fuzzy with a large overlap.

To our knowledge, no study has investigated the survival of stranded

phytoplankton under estuarine conditions.

We therefore tested a range of parameter choices before publication and have now

added a sensitivity analysis in the appendix to show that time to dry-out is not

a particularly sensitive parameter.

Testing parameters from 1 to 30 days showed no regime shift in our results.

We chose the 7 day cut-off because we felt it was a reasonable time frame under

the conditions observed in the tidal marshes, and there were no observational

data to suggest a better choice.

We have also added the following first paragraphs and adjusted the second in the

methods section to better contextualise this choice for the reader:

    We consider phytoplankton cells that are stranded out of the water by the

    receding tide, and lie dry for more than 7 consecutive days to be dead

    and remove them.

    Note that these dry cells are not necessarily completely devoid of water,

    but are considered dry if the majority of its area has a water level

    below 0.1 m.

    Additionally, in nature these areas typically contain small sub-resolution

    structures like tidal ripples or small puddles and vegetation.

    There are currently no studies investigating the time range for survival of

    stranded phytoplankton on tidal-flats or marshes in estuaries.

    Therefore, we performed a sensitivity analysis to determine the effect

    of this parameter on the retention success of the phytoplankton

    population (see appendix section A).

    We include a settling and resuspension model to represent tidal stranding

    and phytoplankton cells settling on the bed of the estuary. Stranding

    phytoplankton and microphytobenthos have been shown on several occasions

    to be a major driver of estuarine primary production (Carlson et al.,

    1984; De Jonge and Van Beuselom, 1992; Kromkamp et al., 1995; Savelli et

    al.,

    2019). Phytoplankton cells become stranded when the current grid cell

    becomes dry and stay in place until they are resuspended

    or dry-out. They are not allowed to move from wet cells to dry cells, by the

    random walk diffusion applied to all phytoplankton

    cells. A grid cell is considered dry based on the flag given in the SCHISM

    hydrodynamic model output. Once this cell is flooded again, all the

    stranded phytoplankton cells are resuspended and able to move again.

> Page 2, lines 30-35: It appears that the author may be conflating two distinct

diel migration behaviors observed in planktonic species. One type of diel

migration is exhibited by phytoplankton, which is primarily driven by the

availability of sunlight for photosynthesis. This behavior is solely dependent

on the sun's position in the sky, as phytoplankton are primary producers that

rely on light for their metabolic processes. On the other hand, carnivorous

planktonic species, like certain zooplankton and dinoflagellates, exhibit a

different diel migration pattern. Their vertical movements are not directly

driven by the sun but are instead motivated by the distribution of their prey,

mainly phytoplankton, which, in turn, is influenced by sunlight-driven

photosynthesis. These species engage in diel migration as a survival strategy,

often to avoid predators or to exploit variations in food availability. In this

context, it is essential to emphasize the distinction between these two types of

diel migration patterns to provide a more accurate and biologically informed

account of the behaviors of planktonic organisms. Recognizing the ecological

drivers behind these migrations is crucial for a comprehensive understanding of

aquatic ecosystems.

We agree that the reason why diel migration is beneficial for autotrophs,

mixotrophs and heterotrophs is different.

As we study phytoplankton, we focus on autotrophic and mixotrophic plankton.

Therefore, all model organisms benefit from diel migration by maximising light

capture while potentially avoiding grazing, while the mixotrophs may

additionally benefit by following food or nutrient sources.

In all cases, however, the consequence remains the same: an upward movement

during the day and a downward movement at night.

While there may be two reasons for the diurnal migration, whatever the cause,

the purpose of this paper is to examine the effect of this migration on

retention.

We changed the mentioned paragraph to make this clearer. It now reads:

    Diel vertical migration is a process where organisms move up and down in the

    water column in response to the sun. This

    movement may favors retention by allowing plankton to reduce the time in the

    faster downstream currents at the water surface.

    A study by Anderson and Stolzenbach (1985) showed that diel migrating

    dinoflagellates were able to out compete other

    non-motile phytoplankton in an embayment environment and even compensate for

    outwashing losses through reproduction

    increasing their abundance. However, this also implies that the growing part

    of the population is somehow retaining their

    position. If the regrowing population is also continuously drifting

    downstream they will not able to sustain their population

    in that area and ultimately die out due to unfavorable salinity conditions

    in marine waters (Admiraal, 1976; von Alvensleben

    et al., 2016; Jiang et al., 2020). The presence of diel migration has mostly

    been demonstrated for motile phytoplankton such

    as dinoflagellates (Hall et al., 2015; Crawford and Purdie, 1991; Hall and

    Paerl, 2011) and zooplankton species (Kimmerer

    et al., 2002). While the motivation for diel migration for autotrophic,

    mixotrophic, and heterotrophic differs, the consequence

    remains the same, an upward movement during the day and a downward movement

    during the night.

> Page 4, lines 83-84: What is the spatial resolution of the three-dimensional

unstructured grid used to represent the Elbe estuary in this model, and how does

it vary within the dataset?

We added more detailed information on the gridding of the model domain in the

methods sections as requested. It now reads:

    The unstructured mesh is three-dimensional and consists of 32k nodes using

    terrain-following coordinates based on the LSC2 technique (Zhang et al.,

    2016) for the vertical grid, allowing a maximum number of 20 levels.

    Regions with depths less than 2 m are resolved by only one vertical level.

    The bathymetric data were provided by the German Federal Maritime and

    Hydrographic Agency (Bundesamt fuer Seeschifffahrt und Hydrographie,

    BSH) and the German Waterways Agency (Wasserstraßen- und Schiffahrtsamt,

    WSA) with a horizontal resolution of 50 m in the German Bight, 10 m in

    the Elbe estuary and 5 m in the Hamburg port \cite{Stanev2019}. [...]

    The model provides us with a node-based mesh containing a range of

    information [...] and a dynamically varying spacial resolution with

    distance between nodes ranging from 5 to 1400 m with a median distance

    of approximately 75 m

> Page 5 lines 107-110: The statement, "A particle starts its life with a light

budget of 28 days, and each minute below 1m reduces this budget by one minute,

while the opposite applies when they are above 1m. Children of light-limited

parents inherit the remaining light budget of their parents," should be

supported by relevant laboratory studies or evidence. Additionally, the

terminology used, such as "children" and "parents" for phytoplankton, might be

confusing and should be rephrased for clarity.

We changed the paragraph as suggested to better explain the choice and avoiding

the term "children" and "parents". We also fixed a typo incorrectly stating the

light budget used in the model in this section.

The mentioned paragraph now reads:



    Phytoplankton cells will also die if they are light-limited for 14 days.

    This value is based on measurements presented in (Walter et al., 2017)

    which imply

    that the majority of phytoplankton is dead after 14 days of light

    limitation. A sensitivity analysis for this parameter is presented

    in sec. B suggesting no strong influence on the retention success. They are

    considered light-limited below a depth of 1m based

    on SPM data presented in (Stanev et al., 2019). The initial batch of

    phytoplankton cells starts their life with a full light budget

    of 14 days, and each minute below 1m reduces this budget by one minute,

    while the opposite applies if they are above 1m.

    When a cell splits both inherit the same remaining light budget.

> Page 5 lines 118-122: The statement that "particles become stranded when the

current grid cell becomes dry, and once this cell is rewetted, all stranded

particles resuspend and are able to move again" should be justified based on

ecological principles and the behavior of phytoplankton. It's important to

explain the reasoning behind this choice, as phytoplankton typically cannot

survive when completely dry.

We justified this choice in our answer to 3.) above as requested.

In short grid cells are typically not completely dry and phytoplankton cells

typically rewettet in less then 12 hours.

We added a paragraph in the paper to reflect our arguments and updated the

mentioned paragraph as also presented in our response to 3.).

It now reads:

    We consider phytoplankton cells that are stranded out of the water by the

    receding tide, and lie dry for more than 7 consecutive days to be dead

    and remove them.

    Note that these dry cells are not necessarily completely devoid of water,

    but are considered dry if the majority of its area has a water level

    below 0.1 m.

    Additionally, in nature these areas typically contain small sub-resolution

    structures like tidal ripples or small puddles and vegetation.

    There are currently no studies investigating the time range for survival of

    stranded phytoplankton on tidal-flats or marshes in andTherefore, we

    performed a sensitivity analysis to determine the effect of this

    parameter on the retention success of the phytoplankton population (see

    appendix section A).

    We include a settling and resuspension model to represent tidal stranding

    and phytoplankton cells settling on the bed of the estuary. Stranding

    phytoplankton and microphytobenthos have been shown on several occasions

    to be a major driver of estuarine primary production (Carlson et al.,

    1984; De Jonge and Van Beuselom, 1992; Kromkamp et al., 1995; Savelli et

    al.,

    2019). Phytoplankton cells become stranded when the current grid cell

    becomes dry and stay in place until they are resuspended

    or dry-out. They are not allowed to move from wet cells to dry cells, by the

    random walk diffusion applied to all phytoplankton

    cells. A grid cell is considered dry based on the flag given in the SCHISM

    hydrodynamic model output. Once this cell is flooded again, all the

    stranded phytoplankton cells are resuspended and able to move again.

> Page 6, line 150: Please provide an explanation for the choice of population

doubling times in idealized conditions ranging from 40 to 404 days. This choice

should be based on scientific rationale and may require further clarification.

Under ideal conditions, phytoplankton doubling times are much lower than the

range tested in our model, with doubling times of less than one day.

These ideal cases are of course rare, as phytoplankton are almost always

strongly limited in nature, e.g. by light or nutrient availability.

In our study we are examining the impact of a range of physical drivers, most

importantly losses due to outwashing of phytoplankton and are trying to decouple

the biological drivers as much as possible to achieve a better interpretability

of the results.

Hence, we chose our doubling times not to accuratley represent fission rates

observed in nature but such that they allow us to estimate the losses due to

physical drivers, which in our case are light limitation, outwashing to the

shores and to the sea.

The presented doubling times in our study can be interpreted as potential

average net-doubling-times in the presence of predation and mortality, nutrient

availability.

We are not trying to representing the ecosystem dynamics by natural growth and

mortality of phytoplankton as this is already done in the cited study Pein et

al. (2021) where they include a full ecosystem model but lack the possibility to

represent the process (e.g. stranding) simulated and studied here.

We added a comment to clarify this to the mention paragraph. It now reads:

    Each vertical velocity is examined for a range of different reproduction

    rates, expressed as population doubling times ranging from 40 to 404

    days with a logarithmic scaling.

    In the following, we will use reproduction rate to refer to the prescribed

    population growth rate under idealized conditions and use growth rate

    whenever we describe population growth in nature.

    The prescribed population growth rate can be interpreted as potential

    average net-doubling-times in the presence of predation and mortality,

    nutrient availability while testing the effect of outwashing.

> Page 7, Section "Results": Before analyzing the retention success, it's

advisable to perform some form of model validation. Consider whether your model

or specific scenarios with their parameters successfully reproduce the seasonal

cycle of phytoplankton, including the duration of bloom events and the number of

particles over distance from the North Sea. Model validation is crucial to

ensure the reliability of your results.

This request is similar to point 2.) where we explained why this model does not

attempt to predict population dynamics.

We agree that model validation is important to ensure the reliability of model

results, which is why we use the hydrodynamics of an ecosystem model with

validated population dynamics.

However, to our knowledge, no observational studies have been conducted to

investigate the mechanism of phytoplankton retention under estuarine conditions

and spatial distribution at finer scales.

In fact, the lack of field studies was the main motivation for this modelling

study, as we try to emphasise the importance of these processes and suggest that

such experiments should be carried out.

Quantifying the importance of these processes in the field is essential before

they can be added to the current state of the art models to better represent

phytoplankton losses, which are currently fitted to observational data mainly

using natural mortality and grazing parameters.

We have added the following paragraph, as previously stated in our response to

2.) above:

We added this paragraph to emphasise the already validated hydrodynamic and

ecosystem model on which our study is based:

    [...] there are sophisticated estuarine models that are able to reproduce

    the complex dynamics of estuaries reasonably well. This includes

    currents and water levels on the physical side, but also chlorophyll

    concentrations and other biologically driven properties (Pein et al.

    (2021), Schoel et al (2014)).

    However, these are Eulerian models.

    This means that they are based on a fixed grid and calculate the

    concentration of a tracer, such as phytoplankton, at each grid cell.

    This makes it difficult to study concepts such as retention times, as they

    lack temporal consistency, meaning that the life history and trajectory

    of a phytoplankton cell cannot be tracked.

    [...]

and the following section in the "model limitations" section:

    In this study, we aimed to thoroughly investigate different possible

    retention mechanisms in a complex Lagrangian model system with a highly

    resolved bathymetry.

    Due to this computational and spatial complexity, the complexity of the

    biological particle properties needed to remain simple to keep

    computational cost manageable and due to a lack of high resolution

    validation data.

    

    Our model design does not resolve more complex ecosystem dynamics such as

    nutrient limitation and grazing by higher trophic levels.

    The Lagrangian model is performed offline, meaning it is not coupled to the

    Eulerian model that calculates the hydrodynamics and is performed after

    the fact.

    Therefore, modeling the advection and dispersal of changes in concentration

    fields e.g. nutrients due to growth or remineralization was not easily

    possible.

    Future modeling efforts could couple the Lagrangian model to a Eulerian

    model that disperses changes in concentrations fields by biotic activity

    throughout the model domain. [...]

And further emphasised the point that this study suggest and shall work as a

foundation for future field measurements in the outlook. It now reads:

    Our results clearly suggest the importance of tidal flats and shallow areas

    along the river banks for the persistence of primary production in the

    Elbe estuary. However, their effect can currently not be quantified due

    to the lack of validation data.

    Chlorophyll data with a sufficient temporal and spacial resolution is only

    gathered in the center of the river. Future monitoring efforts should

    therefore also include data along the river shores on tidal flats or

    shore-to-shore to quantify the effect of potential future changes by

    dredging, diking or restoration attempts.

    Frequently stranded plankton have been shown to be essential to the survival

    of populations in our model. However, data on their ability to survive

    under these conditions are scarce. Our results suggest that these

    conditions may be as important as their ability to quickly regrow under

    more favorable conditions, and we suggest further research on plankton

    survivability when stranded.

> Page 7, line 171: Please clarify the intention behind looking at the state of

phytoplankton after one year in terms of estimating areas where they

"successfully retain."

This is a reference to our 'retention metric' defined on line 158ff.

Conceptually, we consider a population to be successfully maintained if it shows

long-term growth.

We consider one year to be a reasonable "long-term" time frame for this, firstly

because it is much longer than the typical outwash period (see newly added

Figure 6) of up to 3 weeks, and secondly because it represents all the major

seasonal cycles, in particular the upstream seasonal runoff cycle and the

downstream seasonal and tidal cycles.

We have modified the "retention metric" paragraph as you suggested to reflect

the reasoning presented here.

It now reads:

    Conceptually,

    we consider a population to be successfully retained if it is able to

    sustain itself long term or even shows growth. Practically,

    this is evaluated by comparing the population size at the end of the year to

    the size after release. The choice of one year is

    considered reasonable because it covers the full seasonal cycle and is also

    much longer than the average exit or flushing time

    of the estuary (see fig. 6).



and added a paragraph to the outlook:

    Our hydrodynamics data set was limited to the year 2012. Therefore, we were

    not able to study different release times with the same methodology.

    While we do not expect the general dynamics to change, future research

    could examine the effect of varying discharge throughout the seasons on

    retention and could address the very long term success (>1 year) of the

    population,

    as it affected by inter-annual variability and climate change.

> Page 7, line 177: When stating "approximately 3 months," consider providing

supporting evidence or references to confirm the accuracy of this time frame

based on relevant observations or studies.

This is not based on other studies but is a reference to our results presented

in fig. 3 where the break even point between physically induced loses and growth

lies in between 81-101 days. which are approximatly 3 months.

The mentioned paragraph now references this:

    Our simulations show that the population is able to successfully retains

    itself under certain conditions. Passively drifting

    phytoplankton is able to sustain themselves in the estuary if they have a

    reproduction rate that doubles their population size

    within approximately 3 months (see fig. 3)

> Page 9, Figure 4: The positive depths shown in Figure 4 may be related to

tidal oscillations. It would be valuable to describe the tide variabilities or

free surface level variability in the site section to help explain these depth

variations.

Yes, the positive values are caused by tidal oscillations that lift

phytoplankton cells into areas where they become stranded during ebb tides.

We have added a contextualising comment to the tidal range to make this clearer

to the reader:

    Fig. 4 compares two box plots showing the average water depth at

    the location of each phytoplankton cell between those cells that remained

    alive for less than three months (short-living) and

    for more than three months (long-living). Depth is measured relative to the

    current water surface. Therefore, a value greater

    than zero indicates that the phytoplankton cell is stranded on the shore

    during ebb tide. For reference, the water level varies

    on average by about 5 m due to the tides. (Stanev et al., 2019; Schöl et

    al., 2014).

> Page 9, line 196: Please clarify which tests or scenarios were chosen to be

plotted on Figure 5. Explain whether this is an average over all the tests

conducted and provide justification for this choice.

Since we have no reason to favour or emphasise any particular case, we use an

average calculated over all cases, or tests as you call them here.

Furthermore, all cases follow the same spatial pattern when plotted

individually, with no significant shift in the structure of the average age map,

as they all rely on stranding processes to retain themselves, as shown in Figure

4.

In order to make this clear to the reader, we have modified the referenced

paragraph, which now reads

    We moreover analyzed the horizontal spacial distribution of long and short-

    living phytoplankton in fig. 5. To do this, we

    divide the model domain into equally sized hexagons. The color of each

    hexagon indicates the average age of the phytoplankton

    cells within it calculated across all cases. Note, that the spatial age

    structure is similar for all cases. Hexagons with a yellow

    color indicate an average age of over three months. These yellow areas are

    mainly found along the river banks in shallow

    waters or tidal flats.

> Page 9, line 195: The statement regarding the parameterization of drifting

particles as phytoplankton and their tendency to strand near riverbanks should

be approached with caution. Phytoplankton typically cannot survive away from

water. To provide a more accurate assessment of phytoplankton behavior, consider

excluding particles that become stranded in dry grid cells and correlating their

behavior with currents over the coasts and tides, as these factors are usually

lower near the coasts, favoring retention.

As discussed in our response to point 3), we do indeed remove

particles/phytoplankton aggregates that become stranded after a period of time,

and cells flagged as 'dry' have a lot of sub-resolution structure. Perhaps a

better name for this scihsm flag would have been 'not-flooded' as these cells

are in most cases quite moist.

Regarding your comment after "To provide [...]", we are not quite sure what you

are referring to.

If you are asking how the currents are calculated and how they affect the

movement of the phytoplankton: The trajectory of a phytoplankton is driven by

currents and tides. They move almost instantaneously with the currents and

follow them, ignoring diffusion for the moment.

They are therefore correlated.

Advection and diffusion were calculated by Pein et al. (2021) using SCHISM

solving the Navier-Stokes equations, and their behaviour, which in our case is a

kind of vertical motion, is added by us.

This implies that we represent the currents and tides along the coast as

accurately as possible in our model resolution. This is discussed in more detail

in the Pein paper, where the validation process with tides and currents is

shown.

The currents in shallow water are also slower in our model than in deeper water,

as you suggested. This is mainly due to friction between the water layer and the

river or sea bed.

Alternativly, if you are referring to the inclusion of a dynamic behaviour:

During the early conceptual development of this model we also considered

including a vertical migration process of the phytoplankton depending on their

velocity, e.g. that they move up and down depending on their speed relative to

the coast.

However, we couldn't find any observations showing that pytoplankton exhibit

such a migration behaviour or any other behaviour that would suggest that they

are somehow able to feel their speed, only their acceleration.

One could consider acceleration as a driver for migratory behaviour.

However, we did not find any study showing that phytoplankton also exhibit

acceleration-dependent migratory behaviour either.

We therefore decided to include only light-dependent migration, i.e. moving up

and down with the sun.

A phytoplankton cell is moved by three processes: Advection (currents influenced

by tides), Diffusion (e.g. turbulence) and their behavior.

> Page 10, Figure 5: If possible, mark the important sites labeled as "a," "b,"

"c," etc., on Figure 1 to provide a clearer reference for readers.

The areas labelled in Figure 5 are not visible in Figure 1.

Figure 1 only shows the port area, which is the far right part of Figure 5.

We have added a comment to the figure description to help the reader to align

these to maps.

> Page 10, lines 210-220: Please cite relevant observations or studies where

phytoplankton survival without water is documented to support the statement made

in this section. If it cannot be supported, all conclusions about retention in

tidal flats should be rewritten.

We added citations to relevant observations or studies where phytoplankton

survival without water is documented to support the statement made in this

section and as described in our response to 3.)

In short they are:

    [...]. Stranding phytoplankton and microphytobenthos have been shown on

    several occasions to be a major driver of

    estuarine primary production (Carlson et al., 1984; De Jonge and Van

    Beuselom, 1992; Kromkamp et al., 1995; Savelli et al.,2019).

> Conclusion section is very poor and need to be revised.

We reworked the conlusion as suggested and it now reads:

    In this study, we investigated the role of different retention strategies

    for phytoplankton organisms to persist in an estuarine

    environment. We showed that stranding in shallow nearshore areas is

    essential for phytoplankton retention, and that phyto-

    plankton that do not strand are rapidly washed away. Our model simulations

    suggest that growth rates much lower than those

    observed in nature may be sufficient for populations to prevent their

    decline due to outwashing, implying that stranding may

    be sufficient to maintain the population. Moreover, buoyancy and strong diel

    vertical migration enhance retention within the

    estuary. These results highlight the importance of shallow nearshore areas

    in maintaining the productivity of estuarine ecosys-

    tems. Our results suggest that current state-of-the-art models of estuarine

    ecosystems may overlook an important process and

    emphasize the need for informed ecosystem-based management to avoid the

    degradation of estuarine ecosystems by dredging

    and diking activities.

> On the numerical velocity fields: boundary conditions, resolution, vertical

components, explicit bathymetry, etc...

We added the requested information to the description of the hydrological in the

introduction. It now reads:

    We use the hydrodynamic data generated by the latest SCHISM model of the

    Elbe estuary (Pein et al., 2021) from the

    weir at Geesthacht to the North Sea, including several side channels and the

    port area (see figure 2). SCHISM solves the

    Reynolds-averaged Navier-Stokes equations on unstructured meshes assuming

    hydrostatic conditions with a time step of 60 s.

    The unstructured mesh is three-dimensional and consists of 32k nodes using

    terrain-following coordinates based on the LSC2

    technique (Zhang et al., 2016) for the vertical grid, allowing a maximum

    number of 20 levels. Regions with depths less than 2 m

    are resolved by only one vertical level. The bathymetric data were provided

    by the German Federal Maritime and Hydrographic

    Agency (Bundesamt fuer Seeschifffahrt und Hydrographie, BSH) and the German

    Waterways Agency (Wasserstraßen- und

    Schiffahrtsamt, WSA) with a horizontal resolution of 50 m in the German

    Bight, 10 m in the Elbe estuary and 5 m in the

    Hamburg port Stanev et al. (2019). The boundary conditions on the seaward

    side include sea surface elevation, horizontal

    currents, salinity and temperature Stanev et al. (2019) and discharge and

    temperature from the Elbe river on the land-ward side.

    Atmospheric forcing includes wind, air temperature, precipitation, shortwave

    and longwave radiation Stanev et al. (2019).

    Model validation is based on tide gauge stations and long-term stationary

    measurements of salinity, water temperature, and

    horizontal currents. Biochemical variables, including chlorophyll, are based

    on long-term measurements at the Seemannshöft

    and Grauerort stations Pein et al. (2021). The model provides us with a

    node-based mesh containing a range of information such

    as water velocity, salinity, water level and dispersion. The year

    represented in that dataset is 2012 with a temporal resolution

    of 1 hour and a dynamically varying spacial resolution with distance between

    nodes ranging from 5 to 1400 m with a median

    distance of approximately 75 m.

> On the Lagrangian transport model: interpolation schemes, use of eddy

diffusion?, sticking of particles to land, etc... You may also compute other

Lagrangian quantities to show like exit times, retention times, or accumulation

zones (vertical and horizontal).

We modified the section describing the interpolation scheme, use of eddy

diffusion and how they stick to the land to be clearer.

Thank you very much for the suggestion to include "exit-times". We added a

figure showing average exit times in the results.

The section describing eddy diffusivity now reads:

    Phytoplankton cells are not only advected but also diffused based on eddy

    diffusivity which is crucial

    to represent tidal-pumping processes. Diffusion was modeled using a random

    walk using a random number generator with a

    normal distribution. Horizontally the standard distribution of the random

    walk is set to 0.1 ms−1. The vertical displacement of

    a phytoplankton cell ∂z i is calculated by

    ∂zi = K′_v (z_i(n))∂t + N (0, 2K_v (z_i)) (2)

    based on Yamazaki et al. (2014) where zi is the vertical position of the

    phytoplankton cell, K′_v is the vertical eddy diffusivity gradient,

    K_v is the vertical eddy diffusivity and N is the normal

    distribution. The term based K′_v is needed to avoid

    phytoplankton accumulation on the top and bottom of the water column from

    the hydrodynamic model output.

The section describing the interpolation scheme now reads:

    Flow velocities, like any other hydrodynamic data, were

    interpolated linearly in time, linearly in space on the vertical axis and on

    the horizontal axis using barycentric coordinates, with175

    the exception of water velocity in the bottom model cell, where logarithmic

    vertical interpolation is used.

The section describing sticking to land now reads:

    Phytoplankton cells become stranded when the current grid cell becomes dry

    and stay in place until they are resuspended

    or dry-out. They are not allowed to move from wet cells to dry cells, by the

    random walk diffusion applied to all phytoplankton

    cells. A grid cell is considered dry based on the flag given in the SCHISM

    hydrodynamic model output. Once this cell is

    becomes flooded again all stranded phytoplankton cells resuspend and are

    able to move again

> On the "population dynamics": how particles divide, die (is it a Gillespie

simulation)? number of particles, density, etc...

We do not use a Gillespie simulation. Phytoplankton cells die independent off

the presence of other cell but only based on enviromental conditions.

Hence we do not need to enforce a mass balance as required in a Gillespie

simulation.

We updated the paragraph describing the particle division, mortality and the

paragraph describing particle density.

The section regarding reproduction now reads:

    Reproduction is represented as a fission process, where each phytoplankton

    cell has a probability to split effectively produc-

    ing a copy. This is a novel feature  [...]

    We perform multiple

    simulations for a range of reproduction rates, implemented as a fission

    probability evaluated every minute, that are constant

    over the lifetime of the cell. While a fixed reproduction rate is a

    simplification that does not allow for more realistic simulation115

    of the population dynamics of a particular species, it does allow us to

    investigate the general mechanisms that enable plankton

    retention.

The section regarding mortality now reads:

    Mortality is induced by one of three processes: high salinity, when they dry

    out while stranded, or due to long term light

    limitation. When particles cells are exposed to high salinity water above

    20PSU, a mortality probability of 0.5% per minute is

    applied removing dead phytoplankton cells from the simulation (see salinity

    map in fig. C1 ).

    [...] # reasoning

    We consider phytoplankton cells that are

    stranded out of the water by the receding tide, and lie dry for more than 7

    consecutive days to be dead and remove them.

    [...] # reasoning

    Phytoplankton cells will also die if they are light-limited for 14 days.

    This value is based on measurements presented in (Walter et al., 2017)

    [...] # reasoning

    They are considered light-limited below a depth of 1m based

    on SPM data presented in (Stanev et al., 2019). The initial batch of

    phytoplankton cells starts their life with a full light budget

    of 14 days, and each minute below 1m reduces this budget by one minute,

    while the opposite applies if they are above 1m.

    When a cell splits both inherit the same remaining light budget.

The section on particle counts now reads:

    In both sets of experiments, we release 10,000 individuals representing the

    studied phytoplankton population at the be-

    ginning of the year. This results in over 1 billion individual particles

    simulated for each case with approximately 1 million

    particles active simultaneously counted over all cases over 500,000 time

    steps. This corresponds approximately to a one to one

    ratio of simulated phytoplankton cells to mesh nodes in the hydrodynamic

    model at each time step

> Provide a sensitivity analysis of the many parameters of the model, in

particular those concerning phytoplankton demography like mortality,

reproduction rates, etc...

We have added a sensitivity analysis for the mortality conditions of

phytoplankton dry-out and light limitation to the sensitivity analysis already

performed for growth rates and vertical velocities in the appendix.

Varying these parameters changes the break-even point of growth and loss as

expected but no regime shift occurs and the observed trends remain the same.

It seems to have broken the formatting of my previous reply.

I have attached it as a text file to this reply for better readability.

I hope this makes it easier to read.

Additionally, we attached figures added to the manuscript that you requested.

These are the sensitivity analysis and flush times.

• Figure "retention_success_sa_dryout_1_day.png" and ""retention_success_sa_dryout_14_day.png"" show a sensitivity analysis for mortality due to stranding i.e. drying out showing the retention success similar to fig. 3 (relative pop. changes) with a threshold of 1 and 14 days without resuspension compared to the 7 days in fig 3 before phytoplankton are culled
• Figure "retention_success_sa_light_deficit_7_days.png" and "retention_success_sa_light_deficit_28_days.png" shows a sensitivity analysis for mortality due to light limitation showing the retention success similar to  fig. 3 with a light deficit threshold of 7 and 28 days compared to the 14 days in fig 3 before phytoplankton are culled
• Figure "flush_times_hexbin.png" shows a hex-bin heatmap of  average exiting times of the Elbe estuary with Hamburgs port area, as shown in \ref{fig:bathymetry}, in the bottom right without reproduction, light-limitation, stranding and settling on the riverbed. Colors indicate the time of a phytoplankton cell or water parcel to reach the 20 PSU isohaline from its origin hexagon.
  
  Thank you particularly for this suggestion!
• Figure  "average_salinity_with_20PSU_isohaline.png" shows a salinity map of the Elbe estuary with Hamburgs port area, as shown in fig. 1, in the bottom right.
  
  Salinity is averaged in depth and over the whole year. 20 PSU isohaline is marked with a black line. that this plotted area has been extended downstream compared to fig. 5. Further note that the color map has been capped at 25 PSU for better visibility in low salinity areas.