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\title{Unnamed Article}


\author[ ]{Dmitry}

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\date{}

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\section{Introduction}

%Martian climate is mainly determined by the processes occurring in its atmosphere such as air mass movement, convective mixing, radiative and impurities transport. The problem of experimental measurements, for example, the full velocity field in the planet atmosphere is not completely solved because of the strong nonlinearity of the task. As a result to determine the unknown parameters obtained in the experiments one should build general or global climate models (GCMs). The water cycle plays a significant role in the Martian climate, mostly manifested through radiative effects of water ice clouds. Water in its different phase states is a very sensitive marker of transport processes on Mars, able to challenge 3D climate models.

Water in its different phases is a very sensitive marker of transport processes
in the atmosphere of Mars. It also affects the Martian climate, mostly 
manifested through radiative effects of water ice clouds.
Water was first detected in the Martian atmosphere more than a half century 
ago \citep{spinrad1963letter}. The next generation of studies broadly utilized
data from orbital and reentry space vehicles, e.g. from Mars Atmospheric Water
Detector (MAWD) onboard the Viking Orbiter \citep{jakosky1982seasonal}. To date,
the main sources of information about the water vapor distribution in the 
Martian atmosphere are the Thermal Emission Spectrometer (TES) onboard Mars 
Global Surveyor (MGS) \citep{smith2001thermal, smith2004interannual}, the Mars
Climate Sounder (MCS) and the Compact Reconnaissance Imaging Spectrometer for 
Mars (CRISM) onboard Mars Reconnaissance Orbiter \citep{smith2009compact}, and 
the Planetary Fourier Spectrometer (PFS), the Visible and Infrared 
Mineralogical Mapping Spectrometer (OMEGA) and the Spectroscopy for 
Investigation of Characteristics of the Atmosphere of Mars (SPICAM) instruments 
onboard Mars Express \citep{fedorova2006mars, melchiorri2007water, 
tschimmel2008investigation, sindoni2011observations, maltagliati2011annual}.

The history of modeling the water cycle using Martian global circulation models (MGCMs) starts from the work of \citet{richardson2002investigation}. Later, 
a more sophisticated model that included transport, phase transitions and 
microphysical processes was described in detail by \citet{montmessin2004origin}.
Although several MGCMs of sufficient complexity have been developed to date, 
the water cycle was most closely reproduced by two models that share physical
parameterizations: the Laboratoire de M\'et\'eorologie Dynamique (LMD) MGCM 
\citep{montmessin2004origin, navarro2014global} and the Oxford University MGCM 
\citep{steele2014seasonal}.

To successfully reproduce water clouds formation in the atmosphere of Mars, 
the microphysical modeling requires a correct prediction of the distribution 
of aerosol particles, which serve as cloud condensation nuclei (CCN). Several 
observations have provided the evidence that this distribution is bimodal 
\citep{montmessin2006stellar, maattanen2013complete, fedorova2014evidence}.\SH{TEST} 
\AM{A sentence clarifying what is the bimodal distribution is required here!}
%In spite of this for a long time GCMs ignored the bi-modality, using a mono-modal dust distribution. 
\citet{montmessin2002new} implemented a bimodal distribution into the model, 
specifying two peaks with stationary effective radii and variance for small 
and large modes utilizing a ratio of populations 25. They indicated that this 
distribution have had some positive effects on the modeling. For instance, it 
decreased the effective radii of ice particles that condensed on the CCN. 
In our study, we focus on the effects of the bimodal dust distribution on the 
whole hydrological cycle and demonstrate that it significantly improves 
simulations with respect to available observations.

%\subsection{MAOAM model}
To do that, we present a new hydrological scheme and its implementation into 
the Max Planck Institute (MPI) MGCM (also known as MAOAM). This model with a 
spectral dynamical core and the employed physical parameterizations have been
described in detail in the works of \citet{hartogh2005description, 
hartogh2007middle} and \citet{medvedev2007winter}. The most recent applications
of this MGCM along with the current setup are presented in the works of 
\citet{medvedev2016comparison,medvedev2015cooling} and \citet{yiugit2015gravity}.
The hydrological scheme represents a further development of the earlier
version [\AM{Include the reference (Shaposhnikov et al., 2016)}]
%model resented below includes a realistic two-moment microphysics, advection, and sedimentation according to particle sizes. We are using specially parameterized bimodal dust distribution with a variable effective radius for the large mode to reproduce the dust scenario more accurate, and to obtain a more realistic distribution of the water ice particles.

The structure of this paper is as follows.
In section~\ref{sec:MGCM}, we outline the newly developed hydrological scheme,
discuss its main parameters and importance.

%As a result, the model successfully reproduces seasonal variations of water vapor, in both latitude and longitude. We employed Mars Express/SPICAM-IR nadir dataset \citep{trokhimovskiy2015mars} collected during Martian years 27–31 for comparison with the GCM. More detailed consideration of the water vapor lateral distribution shows discrete peaks in longitude during the aphelion season at $L_s$ = 90 – 150$^{\circ}$.

%\subsection{Work structure}
%In the first sections we will briefly review the structure of the new hydrological block, define the main parameters and emphasize their importance. Then we will move to the comparison of modeling results with experiments and, as a last point, remark the difference between climate modeling of Mars with mono-modal and bimodal aerosol distributions.

\section{Martian General Circulation Model}
\label{sec:MGCM}

\subsection{Transport}

The MPI-MGCM employs a spectral dynamical core to solve the primitive equations
of hydrodynamics on a sphere. The physics and tendencies are calculated on a
three-dimensional grid, and then are transformed into spectral coefficients at
every time step. In vertical, the grid uses the hybrid $\eta$~coordinate 
\citep{simmons1981energy} discretized into 50 evolving in time levels, 
terrain-followig near the surface and pressure based near the top, which was
located at $\sim$100 km in our simulations.
The horizontal grid is based on the Gauss-Kruger map projection with 32 and 64 
bins in latitude and longitude, respectively. This discretization corresponds 
to a T21 triangular spectral truncation.

The spectral dynamical core is not well suited for describing transport of 
minor species like water ice and vapor. Instead, we employ a semi-Lagrangian 
advection based on the explicit monotone second-order hybrid scheme and on the 
splitting method in three spatial directions \citep{mingalev2010generalization}.
\AM{A sentence about how good the scheme is, or/and a reference? Something like "Our simulations showed..."}
Besides the advection, transport includes diffusion and mixing associated with
subgrid-scale processes.
The importance of vertical turbulent diffusion or eddy mixing for modeling the 
water cycle was emphasized by \citet{richardson2002investigation}. In our
simulations, we use the Crank-Nicolson implicit method with the Richardson
number-based diffusion coefficients \citep{becker2007nonlinear} to solve the  
vertical diffusion equation. 
\AM{Reference to the diffusion paper in MathPhys Journal? Is there any news?}

%\subsection{Particle bins}
The hydrological cycle includes a transport of water vapor and ice particles, 
the sizes of which are subdivided into bins. Each bin has its own size of dust 
condensation nuclei. We use 4 bins with radii 0.03, 0.1, 0.3, 1 $\mu$m. 
A two-moment scheme is used for every bin while maintaining separately the ice 
mass and number of particles \citep{rodin2002moment}.
\AM{Bins for ice particle sizes or for nuclei?}
%\subsection{Sedimentation}
The size of ice particles determines their sedimentation velocity.
It is accounted for through corrections to the vertical velocity for every 
particle bin according to the formula obtained by \citet{korablev1993vertical} 
with the Cunningham correction. The latter depends on the effective radius of 
the bin. \AM{What is the ``effective radius of the bin"??}

\subsection{Bimodal dust distribution}

We employ a predetermined dust scenario that represents a seasonal evolution 
of the zonally averaged aerosol optical depth in the thermal IR based on MGS-TES
and MEX-PFS measurements with the global dust storms removed. Then, the number 
of aerosol particles (serving as nuclei) in each bin can be calculated from 
the bimodal log-normal dust distribution \citep{fedorova2014evidence}, as
shown in Figure~\ref{fig:bimodal_scheme}. 
This procedure includes the following step. First, one has to prescribe the 
number of large particles and the dust mass in the cell \AM{How?}. Then, 
the effective radius for large particles is calculated. \AM{``Effective" is 
not defined.} Next, using constant values for the effective variance of 
small/large particles and for the radius of small ones, the probability 
density function of the bimodal distribution is obtained. Having CCN sizes and 
number density of small particles, it is straightforward to calculate the 
\adel{real} number of particles in each bin and use it in the microphysical equations.
\AM{I would describe it in more definite steps: 1), 2),3)... Such that anybody
would be able to reproduce if wanted}

Unlike in the work of \citet{montmessin2002new}, we use the bimodal 
distribution with much smaller particles (effective radius of small mode is 
only 0.03 $\mu$m) and number density ratio up to 10$^3$-10$^4$ \alex{compared
to ... and ...}. \AM{Why? Because of the observational constraints?}
In addition, our distribution has a variable effective radius for large mode
\AM{sizes}?, 
This allows for taking into account a variation of distribution of large 
particles and its decrease with the height \AM{descrease of distribution?}. 
Figure~\ref{fig:maoam_bimodal_evolution} demonstrates that the second peak 
corresponding to the large mode shifts to the left with height. As the result, 
at altitudes above 40-60 km (depends on a latitude and season), the 
distribution becomes a mono-modal only with small particles. 
Some studies claimed that the source of such particles can be a micrometeoric 
smoke \citep{bardeen2008numerical}, and that particle lifting can be caused by 
electrical forces \citep{kok2006enhancement}.

\subsection{Saturation and Nucleation}

The water vapor saturation \alex{pressure} in a given spatial bin provides an 
information about the water amount \AM{i.e. vapor+ice??} that the parcel holds. 
In the model, the saturation pressure is expressed as a function of temperature
with a modification of the August-Roche-Magnus formula 
\citep{curry1998thermodynamics}. \AM{Give the formula here}

%\subsection{Nucleation}

Ice clouds are formed when water vapor nucleates on CCN. Unlike in the earlier 
version \citep{shaposhnikov2016water}, where water vapor turned instantaneously
into ice (or vice versa) reaching the saturation pressure, we use a two-moment 
scheme with 4 bins for different mean nuclei core sizes. For quantification of
water ice condensation on dust nuclei, a heterogeneous nucleation rate is
required. For this, we obtain the homogeneous (without aid of a pre-existing 
surfaces) homomolecular (nucleation of high molecular weight) nucleation rate 
first, and then relate it to its heterogeneous counterpart 
\citep{jacobson2005fundamentals}. The number of active CCN also depends on the
parameter $m_h = \cos{\theta}$, where $\theta$ is the "contact angle" (for the 
liquid phase, it is the angle of the interface between the droplet and its 
nucleus). We use in calculations the value $m_h = 0.95$, which is consistent 
with the typical range between 0.97 and 0.93 for Martian dust 
\citep{trainer2008measurements}. There are indications that the value of this 
parameter significantly affects the distribution of water in simulations
\citep{navarro2014global}. Our numerical experiments show that the constant 
contact angle produces more realistic results for the hydrological cycle 
compared to the existing parameterizations, like those described by \citet{maattanen2014estimating}.

\subsection{Particle Growth and Sublimation}

Once water vapor condensed, the ice particles are prone to growth determined 
by various factors. The rate of growth depends on the current water vapor 
saturation ratio, the saturation pressure ratio over a curved surface, the 
molecular diffusion resistance and the heat \AM{What heat?}
\citep{kong2014water, montmessin2002new}. In the model, we take into account 
the dependence of the molecular diffusion resistance from the Knudsen number 
and the accommodation coefficient. \AM{Needs either the formula or reference}

%\subsection{Sublimation}
The hydrological cycle in the Martian atmosphere is driven by the water 
sublimating from the surface. The model accounts for this with the turbulent 
flux at the bottom of the atmosphere, where the drag coefficient is assumed to 
be $0.005$ \citep{montmessin2004origin}. The north polar cap is the only 
permanent source of water in the atmosphere. We assume in the simulations that 
there is an infinite reservoir of surface ice above 85$^{\circ}$N. 
The initial shape of the ice cap is a disc, but the following condensation and 
sublimation can change it.

\section{Numerical Simulations}

%To compare the calculation results of the GCM with the experimental data one needs to perform calculations over a several Martian years. The special computer cluster with 64 processors was used for the task. One Martian year with PGI Acceleration, MPICH and Cuda parallelization, enabled microphysics, 4 ice bins and 20 seconds time step required approximately a week of calculations.

The model was initialized with the distribution of water vapor in the atmosphere
obtained from our previous simulations \citep{shaposhnikov2016water}. Note that
in the latter, a linear latitudinal gradient of water vapor (from 0 in the 
south to 200 ppm in the north) and no ice wer prescribed everywhere in the 
atmosphere as initial conditions, and then runs have been performed for several
Martian years. Results to be presented here are based on the second model year 
of simulations

\subsection{Annual water cycle}
\label{sec:annual}

Figure~\ref{fig:compare_h2o_sum} presents the comparison of the simulated 
column water density and that observed with SPICAM over a whole Martian year. 
It is seen that the model reproduces both the seasonal asymmetry of the 
hydrological cycle and the general amount of the water vapor in the atmosphere. 
The differences between the observed and simulated quantities do not exceed 
$\sim$10 precipitable microns, and vary with the season. 
The maximum amount of vapor occurs near the north pole between $L_s=90^\circ$ 
and 140$^{\circ}$. The model also reproduces the specific southward tail 
afterwards. Some excess of the simulated water vapor in the season of 
$L_s=170^\circ - 180^\circ$ at 0$^\circ$N -- 45$^\circ$N can be explained by an 
overly strong turbulent diffusion. Note also that the SPICAM data presents a
compunded cycle based on data average over 4 Martian years (MY27--30) and, thus,
devoid of differences in meteorological conditions for individual years. 
Another deficiency of the model results compared to SPICAM is the smaller
amount of vapor after $L_s \sim$270$^\circ$. Near the south pole, this can be 
related to the restriction imposed on the surface temperature. There (southward 
of 85$^{\circ}$S), CO$_2$ ice is assumed constantly on the surface, thus 
preventing temperature increase. It is also seen that the modeled cycle is 
somewhat delayed compared to the observations. This may be due to a relatively
short spinup, during which the model did not form a sufficient water ice cap 
in the north. The simulated scarcity of water in middle latitudes can be 
related to the ``mean" dust scenario used in the MGCM. Despite the mentioned 
differences, the the simulated cycle, generally, reproduces the observation
better. \alex{The comparison of the results for the bi- and monomodal
size distributions will be given in section~\ref{sec:mono}}.
\AM{Need to add more positive discussion, otherwise it looks like a list of
deficiencies }

Further comparison of the simulated water vapor with the SPICAM data is shown
in Figure~\ref{fig:maoam_h2o_lat_compar}. It presents observations for
individual Martian years rather than a composite plot based on the 4-year
average. The upper panel displays the comparison at 70$^{\circ}$N, where 
the amount of water vapor is strongly affected by sublimation from the north
pole cap. It illustrates the time lag of the simulated vapor in the atmosphere
with respect to the observations mentioned above. The middle panel (at the
equator) demonstrates a reasonably good agreement of the simulations and 
observations. The lower panel (at 55$^{\circ}$S) shows the lack of the
vapor in the simulations during the season of $L_s=270^{\circ} - 360^{\circ}$.
Note that it is very similar to the observations in MY28, when the Martian
atmosphere was affected by the global dust storm.
The periodic waves in the simulated vapor between $L_s$=220$^{\circ}$ and 
260$^{\circ}$ are caused by sublimation of ice in the finite size model cells.

Because SPICAM measurements of water ice are not as plentiful as of vapor,
we compare the simulated annual cycle of ice with that based on the TES data.
Figure~\ref{fig:TES_MAOAM_h2o_4_op} (left column) presents the seasonal 
variations of zonally averaged water vapor and ice from TES data (MY24-26).
The simulated quantities are shown on the right panels. It is seen that
the TES-observed vapor is very similar to that measured by SPICAM. 
The bottom panels present the opacity of water ice clouds in the atmospheric 
column. To calculate the cloud opacity for ice particles, we use the equation
\AM{Either give here the number or eqn itself} from the work of
\citet{warren2006visible}, in which the absorption efficiency depends on 
ice particle sizes and the wavelength (12 $\mu$m for TES observations).
\AM{I didn't fully understand this question. Why 12 mkm?}
The simulated and observed clouds are in a good agreement. Most of
the simulated ones are located near the border of observationally available 
data and at higher latitudes. The model reproduced the slightly displaced to
the north equatorial cloud belt. The MGCM successfully produces correct winds 
that eliminate the extra clouds formation at the north pole during the season 
$L_s=90^{\circ} - 130^{\circ}$.

\subsection{Horizontal Distributions}

The amount of the collected SPICAM data allows for comparing not only the 
zonally averaged water cycle, but also horizontal distributions of the vapor. 
The latitude-longitude cross-sections of the simulated and observed by SPICAM 
(and averaged over 4 Martian years) water vapor are shown in 
Figure~\ref{fig:compare_h2o_lon-lat_interp}. Leaving aside the mentioned 
in Section~\ref{sec:annual} quantitative differences, one can immediately
notice the similar wave structures between $L_s$=90$^{\circ}$ and 150$^{\circ}$.
These structures are present at other seasons as well, although are less clear. 
For example, on the first panel (averaged over the season $L_s$=0$^{\circ}$ -- 
30$^{\circ}$), the structures are located near the equator between 90$^{\circ}$W
and 140$^{\circ}$W (see also the Figure~\ref{fig:h2o_lon_lat_globe_ls120}) and 
northward between 0$^{\circ}$E and 50$^{\circ}$E. 
%On the panel averaged over the season $L_s$ 240$^{\circ}$ - 270$^{\circ}$ some maximum is too presented but located northwest.
They represent a water vapor imprint on the wave structure of temperature in
the lower atmosphere.

These quasi-symmetric \alex{with respect to the equator?} peaks are associated 
with the stationary planetary waves. They are formed dynamically, and not 
caused by the shape of the northern polar cap, which we specifically prescribed
axially symmetric with respect to the pole. The numerical experiments show 
that the peaks start to form near the season $L_s\sim 90^\circ$ and disappear
later (around $L_s\sim 150^{\circ}$. The main peak is located near 
140$^{\circ}$W, in a good accordance with the observations. It should be 
recalled that the main mountain massif on Mars (Olympus Mons and Tharsis Montes)
is located at the same longitudes. The other two wave peaks are less stable, 
and migrate between 0$^{\circ}$E and 130$^{\circ}$E. Further examination of
the horizontal distributions reveals also wave imprints in water vapor around 
$L_s$=90$^{\circ}$ to 150$^{\circ}$. They consist of three quasi-symmetric 
peaks tightly related to stationary planetary waves in temperature.

\subsection{Vertical Distributions}
\label{sec:vertical}

%Moving from the lateral distribution to the vertical one briefly highlight the observation method. 
In the solar occultation mode, SPICAM IR (1.38 $\mu$m-band) channel has 
conducted measurements of 82 vertical water profiles during MY28. 
The eclipse orbits were recorded from $L_s \sim 255^{\circ}$ to $L_s\sim 
300^{\circ}$, 49 of them in the northern hemisphere and 33 in the southern one. 
Each orbit corresponds to its time and coordinates. \AM{Didn't understand the
last sentence}.
We have chosen the period from $L_s$=255$^{\circ}$ to $L_s$=270$^{\circ}$ for 
comparison with the model output to exclude the period with the major dust 
storm of MY28. The results for 6 randomly chosen orbits from that period are 
shown in Figure~\ref{fig:ProfilesComparison} (see also Table~\ref{table:spicam_orbits}).

The left column presents the comparison of the water vapor density from 
observations and simulations. The plots show a good agreement (within the
error \alex{of observations} between the observed and simulated profiles. 
The central column compares the same for the water ice density. Different $N_s$
denote different CCN bins for the MGCM and diverse recovery scenario for SPICAM.
It can be seen that the ice density is systematically underestimated by the 
model. As the result, the simulated particle radii are too large compared to
observations for some orbits and altitudes (the last column). The reason for 
this discrepancy is not fully understood. It can be associated with the 
insufficient number of CCN in the model, the slow nucleation rate, or too 
rapid growth. Another source of errors is the fact that the model data were 
averaged over a Martian day, while the orbits correspond to well-defined local 
times. Numerical experiments indicate that the discrepancy is observed around 
12 am at the north close to onset of the dust storm. Despite of that, the results, 
generally, look perfectly acceptable. Especially interesting is that the model 
tends to reproduce the shape of the profiles. Disagreements in particle sizes 
occur mostly for cells with a small amount of water, and have very little effect
on the whole cycle.

\AM{This paragraph is not suited for the vertical distribution section. Where
to put it?}
Finally, to complete our comparison with observations, we focus on the ice 
opacity retrievals. For that, we use 410 assembled limb-viewing observations 
from 
%the Compact Reconnaissance Imaging Spectrometer for Mars (i
CRISM \citep{smith2013vertical, guzewich2014vertical} to verify the compliance 
of the MGCM simulations with the experiment. In Figure~\ref{fig:CRISM_mix_full},
weighted ice mixing ratios from the surface up to 60 km averaged over longitude
and seasons $L_s\sim 40^{\circ} - 110^{\circ}$ are plotted. It is seen that
the model produces slightly thinner ice clouds, and they are located lower 
than the CRISM shows. The main reason for that is some excess of the ice 
particle sizes, as was mentioned before. The large size of ice particles leads 
to the enhanced sedimentation (and clouds lowering), as well as to a reduced
transparency. Nevertheless, the shape and location of the clouds agree well
with the observations. Interesting that the model produces some low clouds 
above the south pole, which are not visible from CRISM.

%===================================================

\section{Comparison With the Mono-modal Distribution}
\label{sec:mono}

Having compared the simulations versus the available observation and verified 
the ability of the model to reproduce the hydrological cycle, we turn to the 
comparison of two model scenarios: with mono-modal and bimodal particle size
distributions. The former is characterized by $r_\mathrm{eff} = 0.8$~$\mu$m 
decreasing exponentially with the scale height $\sim$18 km. The CCN initial 
\AM{lower boundary?}
sizes for this scenario have been modified to fit the log-normal function. 
There \AM{They?} are 0.1, 0.5, 1 and 5 $\mu$ m. The bimodal distribution has 
been described above.

The comparison of the annual water cycle was done in a similar manner as in 
Figure~\ref{fig:TES_MAOAM_h2o_4_op}. For that, we plotted the seasonal
dependence of the zonally averaged water vapor and ice in Figure~\ref{fig:maoam_bimodal_h2o_4_op}). 
It is seen that the water vapor distributions are very similar for both scenarios. 
The mono-modal simulation \alex{also} has the secondary maximum of vapor clouds 
near $L_s$=200$^{\circ}$, which agrees with the SPICAM observations. 
This occurs because the vapor strongly depends on temperature. Therefore, 
changing the modality of dust scenario has a slight overall effect on it.
On the other hand, the occurence of ice strongly depends on the amount and 
distribution of CCN. This influence can be clearly seen in the bottom panels. 
First, the mono-modal scenario leads to an insufficient amount of CCN in the 
atmosphere and, thus, to an overly rapid growth of ice particles. As the result,
strong sedimentation results in a very thin and too low ice clouds. 
In addition, because MPI-MGCM has a very weak numerical dissipation, this can 
cause numerical instabilities in some grid points, especially over the mountains. 
An example of it is seen at the equator from $L_s$=100$^{\circ}$ to 
190$^{\circ}$ over the Tharsis region. \AM{I don't see it. Where? Can you describe more?}

Figure~\ref{fig:maoam_bimodal_profiles} presents the vertical profiles of 
(averaged over a Martian year) water ice characteristics simulated using the 
mono-modal and bimodal dust particle size scenarios. The top two panels 
illustrate the fact that CCN have not enough time (\AM{may be "cannot"?})
to capture water mass in mono-modal scenario. \AM{Need to elaborate here: 
We see that amount of ice is much less than in bimodal, etc.}
Herewith the CCN with average size 0.3 $\mu$m become the main source of the mass for the bimodal scenario. And it is not surprising because this CCN corresponds to the second peak of the bimodal distribution (see for example the Figure~\ref{fig:maoam_bimodal_evolution}). The second panels show the ice number densities, and again the small amount of CCNs leads to the very low ice densities. The bimodal scenario shows some growth of the amount of ice particles with the greatest masses on the altitudes 30-40 km. And finally the last panels give a clear understanding of the need to use the bimodal scenario, because the mono-modal one produces huge ice particles with unrealistic radii. It should be noted that our model still has some excess of ice particle sizes, and the future development should fix it.
\AM{I did not understand and could not modify the above part. Can you extend
and rewrite it for dummies?}

The comparison of latitude-altitude distributions of the ice clouds simulated
with mono- and bimodal scenarios is presented in Figure~\ref{fig:moaoam_modal_bimodal_clouds}). 
It is seen that the clouds are located in the same latitude region, but, in 
the mono-modal scenario, they are thinner \AM{Are they?}, tend to occur lower and
their distribution is tilted. Note also that local instabilities occur more 
often near the surface \alex{and there are less clouds over the north pole}
for the monomodal scenario. The reasons for such behavior were discussed 
previously. \AM{Need some more discussion! Even repeat, but with a new wording.}

%===================================================

\section{Conclusion}

In this paper we described the recent version of the hydrological scheme of the MPI-MGCM. The new scheme includes a real two-moment microphysics, transport, 4 different sizes of ice particles, condensation, sublimation and sedimentation according to the average radius of particles, the surface microphysics. The simulations have been compared with SPICAM, TES and CRISM observations. The comparison shows a good agreement between the observed and simulated water vapor and ice distribution and abundance, including seasonal dynamics and mesoscale features.

We have shown the influence of a bi-modality of aerosol particle distribution on the annual hydrological cycle and on such parameters as ice clouds mass, opacity, numerical density, particle radius and etc. There is no strong effect of the small particles on the water vapor. Their deficiency changes the amount of available CCN resulting in small nucleation rate. This leads to appearance of large-sized ice particles. Strong sedimentation than presses clouds to the surface, as well as causes the numerical instabilities. The small nucleation rate and giant radii produce thin and unstable clouds. Interesting that even using the mono-modal scenario more or less realistic annual cycle (averaged over the height) could be obtained in some cases due to the parameters selection. But a more detailed consideration reveals the problems mentioned above.

Based on our research we can confidently recommend the inclusion of small particles in the GCM dust scenarios. The open questions are their sources and the mechanisms of their lifting. The next steps of our work will be an addition of the mobile dust and a consideration of radiation effects of water.

%The results of simulations can be seen in more detail, plotted and/or downloaded from the site \underline{mars.mipt.ru}.

\acknowledgments
The data supporting MPI-MGCM simulations can be found at https://\-mars.mipt.ru/.
\AM{Need to give either address where the observational data can be found, or
the email of a person, from whom they can be obtained. For example, Dima's address}

We express our deep gratitude to Anna Fedorova, Alexander Trokhimovskiy, Scott 
Guzewich and Takeshi Kuroda for the assistance with the observational data and
helpful discussions.

This work has been performed at the Laboratory of Applied Infrared Spectroscopy
of MIPT and at Max Planck Institute for Solar System Research. The work was
partially supported by the Russian Science Foundation grant 100027.07.32.RSF27
and German Science Foundation (DFG) grant ME2752/3-1.

%% After you run BibTeX, Copy in the contents of the .bbl file here:
\bibliography{maoam-jgr}

%%%
\listofchanges
%%%\selectlanguage{english}
\begin{figure}[h]
\centerline{\includegraphics[width=30pc]{fig/bimodal_scheme}}
\caption{{The operation scheme of the bimodal dust distribution. 
$N$ is the number density of large/small particles, $\tau$ is the dust optical 
depth in a vertical column (``MGCM dust scenario"), $H$ is the altitude of the 
cell, $r_\mathrm{eff}$ is the effective radius, $v_\mathrm{eff}$ is the 
effective variance, $n(r)$ and $n(r)_*$ are is the probability density 
functions for the bimodal  and mono-modal distributions, correspondingly.}}
\label{fig:bimodal_scheme}
\end{figure}\selectlanguage{english}
\begin{figure}[h]
\centerline{\includegraphics[width=30pc]{fig/maoam_bimodal_evolution}}
\caption{{Evolution of the probability density function of the bimodal aerosol 
particles distribution with altitude in the MPI-MGCM averaged over latitude 
and longitude around the season of $L_s$ 250$^{\circ}$. Different curves 
correspond to different altitudes (see the legend).}}
\label{fig:maoam_bimodal_evolution}
\end{figure}\selectlanguage{english}
\begin{figure}[h]
\centerline{\includegraphics[width=40pc]{fig/compare_h2o_sum}}
\caption{{Annual water cycle on Mars from the SPICAM data \citep{trokhimovskiy2015mars} 
and simulated with the MPI-MGCM. The upper panels shows water vapor column 
density observed with SPICAM averaged over 4 Martian years and zonally. 
The middle panel displays the same but for the MGCM output. The lower panel 
presents the difference between the SPICAM data and the simulations. 
%Horizontal axis is one Martian year in $L_s$. Vertical axis is latitude.
\AM{Put the labels (a), (b), (c) to the panels. Add the ihorizontal axis label 
"Solar longitude,  $L_s$,  [deg]" below } }}
\label{fig:compare_h2o_sum}
\end{figure}\selectlanguage{english}
\begin{figure}[h]
\centerline{\includegraphics[width=40pc]{fig/maoam_h2o_lat_compar}}
\caption{{Annual water cycle measured by SPICAM (markers) and simulated with 
the MGCM (red lines) at three characteristic latitudes (70$^{\circ}$N, 
0$^{\circ}$N and 55$^{\circ}$S). Color and shape of markers indicate the 
Martian year of observations (see the annotations) }} 
\label{fig:maoam_h2o_lat_compar}
\end{figure}\selectlanguage{english}
\begin{figure}[h]
\centerline{\includegraphics[width=40pc]{fig/TES_MAOAM_h2o_4_op}}
\caption{{Comparison of the simulated annual water cycle with TES observations
\citep{smith2001thermal} averaged zonally and over 3 Martian years (MY24--26).
The upper panels are for the precipitable water vapor from TES (left) and 
from the model (right). The bottom panels are for the column opacity at
12 $\mu$m of water ice particles with the same conditions (absorption 
efficiency depends on mean particle radius and is parametrized). 
\AM{I did not understand the last sentence}}}
\label{fig:TES_MAOAM_h2o_4_op}
\end{figure}\selectlanguage{english}
\begin{figure}[h]
\centerline{\includegraphics[width=40pc]{fig/compare_h2o_lon-lat_aved}}
\caption{{Horizontal distributions of water vapor column density observed with
SPICAM (upper parts of each panel) and simulated with MPI-MGCM. In each pair 
of plots, the measured by SPICAM water vapor is averaged over 4 Martian years.}}
\label{fig:compare_h2o_lon-lat_interp}
\end{figure}\selectlanguage{english}
\begin{figure}[h]
\centerline{\includegraphics[width=30pc]{fig/h2o_lon_lat_globe_ls120}}
\caption{{Water vapor column density in precipitable microns (log-scale) 
averaged diurnally in orthographic projection over the season 
$L_s$$\sim$120$^{\circ}$ (northern hemisphere summer). 
%More detailed matching of the water vapor lateral distribution shows interesting wave effects in seasons $L_s$ 90$^{\circ}$ - 150$^{\circ}$ with three quasi-symmetric peaks associated with stationary planetary waves.
}}
\label{fig:h2o_lon_lat_globe_ls120}
\end{figure}\selectlanguage{english}
\begin{figure}[h]
\centerline{\includegraphics[width=40pc]{fig/ProfilesComparison}}
\caption{{Vertical profiles of water vapor number density in cm$^{-3}$ (left 
column), water ice density in cm$^{-3}$ (middle column) and effective ice radii 
(in $\mu$m) from SPICAM (MY28, markers) and the MGCM simulations (solid lines) 
for several orbits given in Table~\ref{table:spicam_orbits}). 
%In the mode of solar occultations SPICAM IR has conducted measurements of 82 vertical water profiles on the band 1.38 $\mu$ m. Each orbit corresponds to its time and coordinates (see the Table~\ref{table:spicam_orbits}). 
Different ice effective radii (R1, R2...) correspond to different number 
densities (N1, N2...). \alex{Errorbars denote...}}}
\label{fig:ProfilesComparison}
\end{figure}\selectlanguage{english}
\begin{table}
\caption{{Characteristics of the SPICAM orbits}}
\centering
\begin{tabular}{*{5}{c}}
Orbit & Longitude (E) & Latitude (N) & Local time (h) & $L_s$ \\
\hline
4407A3 & 54.19 & -25.75 & 5.14 & 254.94 \\
4409A2 & 215.82 & -28.63 & 5.03 & 255.30 \\
4421A1 & 168.45 & 41.52 & 7.55 & 257.41 \\
4428A1 & 207.70 & 46.97 & 7.92 & 258.65 \\
4435A1 & 247.16 & 51.49 & 8.31 & 259.89 \\
4461A2 & 109.05 & -60.03 & 2.34 & 264.53 \\
\hline
\end{tabular}
\label{table:spicam_orbits}
\end{table}\selectlanguage{english}
\begin{figure}[h]
\centerline{\includegraphics[width=40pc]{fig/CRISM_mix_full}}
\caption{{Comparison of the observed by CRISM (left) \citep{smith2013vertical, 
guzewich2014vertical} and simulated (right) weighted ice mixing ratios from 
the surface up to 60 km averaged over longitude and seasons $L_s\sim 40^\circ 
- 110^{\circ}$. }}
\label{fig:CRISM_mix_full}
\end{figure}\selectlanguage{english}
\begin{figure}[h]
\centerline{\includegraphics[width=40pc]{fig/maoam_bimodal_h2o_4_op}}
\caption{{Comparison of the annual water cycle using mono-modal (left) and 
bimodal (right) \alex{CCN} scenarios. The top panels illustrate the water 
vapor in precipitable $\mu$m. The bottom ones illustrate the column opacity 
of water ice particles at 12 $\mu$m. \AM{Do you account only 
particles larger than 12 mkm in the model? I didn't get it.}}}
\label{fig:maoam_bimodal_h2o_4_op}
\end{figure}\selectlanguage{english}
\begin{figure}[h]
\centerline{\includegraphics[width=30pc]{fig/maoam_bimodal_profiles}}
\caption{{Vertical profiles of the water ice mass mixing ratio (in mg/kg,
upper row), number density (in cm$^{-3}$, central row) and ice particle 
radii (in $\mu$m, lower row) simulated with the mono-modal (left column)
and bimodal (right column) dust scenarios.
All the profiles are based on the output averaged over latitude, longitude 
and season. Solid color lines denote the results for 4 different bins: 
with CCN 0.1, 0.5, 1 and 5 $\mu$m for mono-modal distribution, and
with 0.03, 0.1, 0.3 and 1 $\mu$m for the bimodal one (see also legend for
notations).}}
\label{fig:maoam_bimodal_profiles}
\end{figure}\selectlanguage{english}
\begin{figure}[h]
\centerline{\includegraphics[width=40pc]{fig/moaoam_modal_bimodal_clouds}}
\caption{{Latitude-altitude cross-sections of the \adel{weighted} ice mixing 
ratios simulated with the mono-modal (left) and bimodal (right) dust size 
distribution scenarios. Results are averaged over longitudes and 
$L_s$=40$^{\circ}$ to 110$^{\circ}$. }}
\label{fig:moaoam_modal_bimodal_clouds}
\end{figure}

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