Analysis of the Ozone Profile Specifications in the Wrf-arw Model and Their Impact on the Simulation of Direct Solar Radiation

Although ozone is an atmospheric gas with high spatial and temporal variability, mesoscale numerical weather prediction (NWP) models simplify the specification of ozone concentrations used in their shortwave schemes by using a few ozone profiles. In this paper, a two-part study is presented: (i) an evaluation of the quality of the ozone profiles provided for use with the shortwave schemes in the Advanced Research version of the Weather Research and Forecasting (WRF-ARW) model and (ii) an assessment of the impact of deficiencies in those profiles on the performance of model simulations of direct solar radiation. The first part compares simplified data sets used to specify the total ozone column in six schemes (i.e., Goddard, New God-dard, RRTMG, CAM, GFDL and Fu–Liou–Gu) with the Multi-Sensor Reanalysis data set during the period 1979– 2008 examining the latitudinal, longitudinal and seasonal limitations in the ozone profile specifications of each param-eterization. The results indicate that the maximum deviations are over the poles and show prominent longitudinal patterns in the departures due to the lack of representation of the patterns associated with the Brewer–Dobson circulation and the quasi-stationary features forced by the land–sea distribution, respectively. In the second part, the bias in the simulated direct solar radiation due to these deviations from the simplified spatial and temporal representation of the ozone distribution is analyzed for the New Goddard and CAM schemes using the Beer–Lambert–Bouguer law and for the GFDL using empirical equations. For radiative applications those simplifications introduce spatial and temporal biases with near-zero departures over the tropics throughout the year and increasing poleward with a maximum in the high middle latitudes during the winter of each hemisphere.

This document provides a detailed point-by-point response to all referee comments and specifies all changes on the revised manuscript.
First of all, we would like to express thanks for the suggestions, comments and ideas provided by our Editor and both referees.
The paper entitled Analysis of the ozone profile specifications in the WRF-ARW model and their impact on the simulation of direct solar radiation was published in the Atmospheric Chemistry and Physics Discussion in 6 th August 2014.During the Open Discussion period, the paper was reviewed by two anonymous referees.
The first review was received in 29 th August 2014 by the Anonymous Referee #2 while the second one was published in 3 rd August 2014 by the Anonymous Referee #1.
In 12 th November 2014, we submitted two documents as a response to referees reviews: Response to "Reviewer Comments", Anonymous Referee #1 and Response to "Referee Comment for ACP Manuscript acp-2014-143", Anonymous Referee #2.
With this document, we submit the revised version of the paper based on the aforementioned responses.The document is divided in four blocks.The first one is composed of these paragraphs.Through each one, we will explain the structure and we will define the used nomenclature that will be useful for the next sections.
The following three sections show all the responses again.The idea is to make easier the revision of the changes.In general, the text is the same that the submitted in 12 th November 2014.However, some parts have been updated after the revision and others have been summarized.Some points are common for both referees or they have a full impact to the entire paper.For this reason, we will present firstly a common block and then we will discuss each review point by point.Hereinafter, we will use R#1 and R#2 such as 35 Referee #1 and #2, respectively.
In order to contextualize the response, the referee's commentary appears before our answer.Each review is quoted in gray.Our response appears with A: (from Authors) at the beginning and in black color.Each one is identified with a label 40 composed with a number and a tag: GC (General Comments) and SC (Specific Comments).For example, SC4 refers to the 4 th specific comment.During the discussion, the reader can find some cross-references between responses for R#1 and R#2.For example, SC7 R#1 means the 7 th specific comment 45 of R#1.
The last part of the document refers to the new version 50 of the article.The old text appears in red and crossed out while the new parts are typed in blue and underline.The parts in black indicate the same text for both versions.In order to compare easier the document changes and the responses, the label of each response (e.g.SC14 R#2) appears always

Introduction
We have concluded that we can improve the introduction in two aspects: i) a better contextualization of the interest of the paper and ii) a better explanation of the presented ideas.
Further information is presented in SC4 R#2 and GC1 R#1.

Methodology
Based on the ideas from both referees, we propose a set of updates in the methodology in order to increase the scientific significance of the results.Two of them have an important impact in the paper structure and the others introduce small improvements or clarifications in the current text.Through the following paragraphs, we will present a small overview of these modifications.You can find further details in the full text at the particular responses (referred in the following explanation).
In his review, R#2 suggested that excluding the GFDL scheme from the analysis deprives the readers from the opportunity to understand its accuracy relative to the other methods (see SC12 R#2).We agree about this consideration and we have decided to add this parameterization to the discussion, thus giving a global vision of WRF.As a consequence, we propose to add some changes on section 2 (providing further details about this parameterization), on sections 3 and 4 (adding this scheme to the discussion) and on the figures (adding the respective maps).
On the other hand, from the commentaries of R#1 (see GC1 R#1 and GC2 R#1), we have concluded that we could show and discuss the vertical profiles provided by each scheme.Moreover, this discussion could be linked with the current results and conclusions.As we understand it, this small study could be interesting to the scientific community as well as for the WRF users because it is missing in the state-of-the-art.

Results
After reading the review from R#1, we have concluded that the used metrics are useless for a good paper understanding (see GC4 R#1 and SC8 R#1).We would like to improve this point.

120
In the first part (sections 2.2 and 3.1), our discussion was based on the relative error (equation 5 in the paper) without including any figure as a baseline (e.g.monthly maps for the MSR data-sets).We concluded that this way of showing the results is useless if the reader does not have a background 125 about the ozone spatial and seasonal distributions.In order to correct this point, without adding new figures, we propose to replace the relative error by the bias (in Dobsons).As a consequence, equation 5 in the paper, section 3.1, Conclusions and Figures 1 and 2 must be updated accordingly.

130
In the second part (sections 2.3 and 3.2), we computed the bias in the ozone absorption (equation 22 in the paper) normalized with respect to the radiation at the top of the atmosphere.As a result, we compared two percentages and we lost the physical sense of the results.To improve this point, 135 we propose to show the results as W m −2 multiplying the previous results by the incoming radiation at the top of the atmosphere.Sections 2.3 and 3.2, Conclusions and Figure 3 must be updated accordingly.

Figures 140
Both referees noted that the quality of the images could be improved.We agree about these considerations.The original figures were created using the R language.We have been testing the NCAR Command Language and it clearly improves the quality of the results.
2 Response to "Reviewer Comments", Anonymous Referee #1 Response to general comments GC1 R#1: In this paper, the authors aim at analyzing i) the ozone representation in the shortwave (SW) radiative transfer schemes of WRF, and ii) the impact of the biases in this representation on the predicted direct solar radiation.Three different ozone representations have been analyzed: one which is shared by the Goddard, New-Goddard and Fu-Gu-Liou SW schemes, and two more used in the CAM and RRTMG SW schemes, respectively.The two objectives are clearly set out at the beginning of the paper but, to my view, the interest of the study is not sufficiently well motivated.
The methods used are appropriate to achieve the proposed objectives.However, I have concerns regarding how the second objective was addressed.In my opinion, the interest of the paper has not been clearly set out.This work deals with stratospheric ozone.Thus, in principle, it has high interest for WRF's applications in the stratosphere.However, only total ozone has been verified and nothing is said regarding how the vertical profile of ozone is represented in WRF.This limits the interest of the study for "stratospheric" applications.In any case, authors should add comments on how important is a correct vertical distribution for the vertical distribution of heating rate, and the coincidences and differences in this with respect in the analyzed data bases.It is claimed that this study has interest for solar energy, more specifically, for solar energy forecasting.However, in my opinion, this importance should be better contextualized.
A: Regarding to the second objective issue, we will provide a full explanation about the ideas and procedures to address in the GC1 R#2 response.In the following lines, we will focus our discussion on your commentaries about the stratosphere and the solar energy forecasting.We agree that the work deals with stratospheric ozone.
However, it also deals with solar modeling.In its travel throughout the atmosphere, a solar beam is absorbed and scattered by atmospheric gases (e.g.water vapor, ozone) and particles (e.g.aerosols, cloud droplets).Therefore, to compute the solar radiation reaching the surface is requires understanding all these physical processes that occur in the atmosphere.
In a clear sky atmosphere, basically two gases absorb the solar radiation: water vapor and ozone.In the troposphere, water vapor absorbs solar radiation in some near-infrared (near-IR) spectral bands.
On the other hand, ozone is located in two atmospheric regions with a different impact on the radiative transfer.Most ozone (∼90%) is located in the stratosphere while the remaining ozone (∼10%) is found in the troposphere.The stratospheric ozone absorbs solar energy in a few bands of ultraviolet (UV) and photosynthetic active region (PAR) whereas the impact of the tropospheric ozone on the radiative transfer is negligible.
Hence, all approximations assumed on modeling these 200 contributions have an impact on the accuracy.Of course, other elements such as aerosols or clouds have a higher impact and, at the same time, they are more difficult to be improved.In contrast, as we presented in the paper, ozone introduces smaller errors that, moreover, could be easily reduced.

205
From our perspective, an understanding of the physical processes is significant per se, beyond the impact on the output accuracy.
When we started to work on this study, we were worried because the lack of literature analyzing the impact of the 210 ozone modeling on radiative codes and we decided to introduce a scientific discussion about that.In the first part, we presented a detailed information of the ozone treatment in the radiative parameterizations of the WRF-ARW that we considered that could be of interest to many WRF-ARW users 215 and solar modeling researchers.
In addition to this, the shortwave radiation absorbed by ozone in the stratosphere is the primary physical process in maintaining its thermal structure.Thus, the stratosphere is a parallel topic but it is not the focus of the analysis.Never-220 theless, from your considerations, we recognize that the paper can be enhanced if we introduce more details about the stratosphere on the discussion.
A validation of the vertical profiles is not feasible under the structure of the presented work because a global and cli-225 matic ozone profile dataset with a reasonable horizontal resolution does not exist.The ozone-soundings are provided generally from balloon and aircraft campaigns at several sites and for limited periods.Furthermore, many of these sites are located in the United States.We searched this kind of 230 data in the NOAA Earth System Research Laboratory server (ESRL), the Climate Prediction Center (CPC) and the National Climatic Data Center (NCDC) without success.
In contrast, satellite data provide global and climate measurements with good spatial resolution.However, these data 235 are vertically integrated such as in the Total Ozone Mapping Spectrometer (TOMS) Data or the MSR used in the present analysis.For this reason, we decided to use the MSR dataset as a baseline for our analysis.
In order to include your ideas, we propose the following 240 improvements: -A better contextualization of the paper in the introduction following the aforementioned ideas.
-Add new figures plotting the ozone profiles for each scheme and a description in section 2.1.
Moreover, we consider that this type of figures can increase the scientific significance of the paper because similar plots do not exist in the state-of-the-art.
GC2 R#1: I miss some comments on the average absorption due to ozone in typical conditions, so that the reader receives a clearer message on the importance of ozone for solar energy.Since it is claimed that "high spatial and temporal variability" of ozone occurs in the stratosphere, it would be helpful if some figures were given of the expected range of seasonal variability in a point and spatial variability for a fixed season and how they translate to solar radiation extinction.These simple numbers would help to advance the reader the order of magnitude of the corrections that could be achieved with an improved representation of ozone.This could be compared with the typical errors of WRF in solar energy forecasting applications.
A: The response to these considerations is linked to the previous one.The new figures related to the ozone profiles can be useful for the reader to understand the order of magnitude of the ozone variability.
In addition, we agree about the idea of including some numbers to help the reader to understand the paper.
Finally, as we detail in SC8 R#1, we propose to show the bias in W m −2 instead of percentages.This improvement will be useful in order to clarify some ideas.
GC3 R#1: One application that is not even mentioned is the modeling of shortwave irradiance in the UV part of the spectrum.The SW schemes analyzed make spectral computations.Could have been this analyzed somehow?Moreover, the latest WRF versions provide broadband direct and diffuse irradiance with RRTMG and New-Goddard.Could they be used to investigate the impact of ozone misrepresentation on irradiance fluxes?A: Regarding the application for modeling of shortwave irradiance in the UV part of the spectrum, we agree with the reviewer that it is important from the point of view of the radiative transfer models.Nevertheless, we did not mention this application because this is not the "natural" usage of solar parameterizations in mesoscale NWP models and particularly, in WRF.
In general, the shortwave schemes in WRF divide the spectrum in a few bands (from 1 in Dudhia's case to 8-16 in the other schemes).Upward and downward fluxes are computed at each band in terms of different contributions.Some contributions are specific of that band (e.g.ozone in the UV or water vapor in the near-IR) and others are general for all of them (e.g.clouds or aerosols).The total upward and downward fluxes are the sum over all the bands (i.e.spectral integration).In order to reduce computational memory, the intermediate values are generally stored in temporal arrays that are removed at each computation step.
Moreover, note that the shortwave schemes in the model are not designed for spectral applications.In the past, the 300 shortwave schemes were necessary to set the day-night behavior on NWP simulations.Therefore, the greatest interest of this kind of parameterizations was the total absorbed energy (i.e. the heating rate) profile and the total global horizontal irradiance at surface for the land model.A full treat-305 ment of the radiative problem was computationally expensive (even nowadays).Therefore, the general methodology was to reduce the computational time by reducing the complexity of the methods (e.g. using a few bands instead of line-by-line computations).With this usage of the radiative codes, accu-310 racy was not a matter of concern because other sources of error had a higher impact.
In recent years, the interest for modeling the solar resource by using NWP models has increased and, as a result, also the interest for a good accuracy on global, direct and diffuse 315 irradiances.Nevertheless, the radiative codes are the same as in the past.
Thus, from our perspective, the radiative codes in WRF are not good tools to be used for spectral purposes.There are other external codes more complex that are ready to perform 320 this type of studies.
Setting aside these set of considerations, note that we are actually analyzing the UV and PAR regions.Let us simplify the problem and imagine a scheme with three bands: UV, PAR and near-IR.Since ozone absorption occurs in the UV 325 and PAR bands, we can write the total direct flux as when we use the scheme ozone data, and when we use the MSR dataset.

330
If we only consider the ozone contribution, then the atmosphere is transparent in the near-IR.Thus, both terms F sch dir,nearIR and F M SR dir,nearIR are mutually canceled when we compute the bias.
Regarding the second question, we agree with the reviewer 335 when he says that the RRTMG and New Goddard parameterizations provide spectrally integrated direct and diffuse irradiance components.However, this is not required as we detailed in GC1 R#2.
In short, ozone does not have an explicit contribution on 340 the diffuse component.The molecular scattering is considered in the Rayleigh's term and it assumes dry air mass without considering any kind of species.Therefore, the ozone dataset does not play any role on the scattering computation.
On the other hand, in the computation of the Beer-Lambert 345 law, we can consider each contribution to the optical thickness (e.g.water vapor, ozone, ...) independent one another.
Hence, we can analyze the ozone impact on the direct flux without considering the other elements.

GC4 R#1:
To my view, the study of the impact of the ozone misrepresentation on the computed direct irradiance has not been totally addressed.This analysis has been done showing maps and numbers of absorption biases, instead of the expected irradiance biases.However, the irradiance biases can be very easily computed by including the effect of solar geometry.Unless these maps are included in the paper and the results analyzed in terms of irradiance biases I don't agree that this paper addresses the impact of ozone errors on the direct solar irradiance.I would encourage the authors to address these issues and the specific comments detailed below.
A: The radiative schemes use the ozone data to compute the direct flux (see GC1 R#1) while the molecular scattering (i.e.diffuse component) of these molecules is considered in the Rayleigh term without any consideration about the gas species.Therefore, since this paper is focused on the ozone profiles, we only validate the direct flux because the diffuse one does not depend on the ozone data.
In a non-scattering medium, when a solar beam travels throughout a layer, one part of the energy is absorbed A by the medium and the other part is transmitted T to the next layer (energy conservation).In other words, if we consider normalized values (3) Therefore, when we compare the outcomes using the MSR dataset and the ozone data provided by each scheme, the biases on the absorption and transmission are the same but with opposite sign.
As we normalized the results with respect to the radiation at the top of the atmosphere (TOA), we plotted the absorption because it was more understandable.All this information appears in the equations.Furthermore the nomenclature is coherent during all the paper.Thus, from our point of view the ozone misrepresentation on the computed direct irradiance has been well addressed.
In the response at point SC10 R#1, we propose to show the results with physical units (i.e.W m −2 ).Hence, we can plot the direct radiation instead of the absorption if the Editor thinks that it is better.Nevertheless, from our understanding, this type of plots will not add any new information.
GC5 R#1: I would also suggest the authors to use the knowledge acquired in this work to improve the current representation of ozone in WRF (for instance, by including the MSR dataset in WRF and making it available for the SW schemes).WRF is public and freely available for anyone and I am sure that the WRF's community would be thankful.
A: This idea sounds good but is not be feasible with the MSR dataset.The MSR considers the total ozone amount instead of the vertical profiles that are required by the WRF model to compute the heating rate profile at each grid-point 400 (see GC1 R#1).
As the dataset provided in CAM shows the best accuracy when it was compared with the MSR data, it could be used for the other schemes.
In fact, from version 3.5 the RRTMG can utilize the ozone 405 profiles available in the CAM scheme with the option o3input in the namelist.inputfile (as we commented in the paper).This improvement could be added in the other parameterizations with some code modifications.
We will add this suggestion on the Conclusions and we 410 will explore this idea as a future work (see GC5 R#2).
Response to specific comments Title: Analysis of the ozone profile specifications in the WRF-ARW model and their impact on the simulation of direct solar radiation 415 SC1 R#1: I don't see the title appropriate for a threefold reason: R#1: i) only the total ozone amount has been analyzed, but not the "ozone profile" (i.e., the vertical distribution of ozone); 420 A: It is true that we are analyzing the total ozone amount.However, the main idea of the paper is to offer to the scientific community a description about the simplifications that are assumed in the ozone treatment within the radiation options of the WRF model and a quantification of the impact of 425 these assumptions.
In section 2.1 we provide a full description of the ozone datasets that can be improved as we suggest in GC1 R#1.In section 2.2, we compute and validate the total ozone amount because 4D (spatial and temporal) ozone datasets are not 430 available (further details in GC1 R#1).
Therefore, from our perspective, this part of the title is correct because the ozone profile datasets are the subject at matter in which the study is developed.
R#1: ii) the impact of the ozone misrepresentation is an-435 alyzed, and not the impact of the ozone profile "specifications"; and A: From our point of view, what we have done is analyzing the ozone profile specifications to asses the impact of the ozone misrepresentation.Moreover, as we referred in the 440 previous paragraph, we also provide a full analysis of the profiles in section 2.1 that can be improved after this revision.
R#1: iii) the impact on the solar radiation absorption is analyzed, and not the "impact on the direct solar radiation" A: We believe that "direct solar radiation" is justified following our discussion in GC4 R#1 regarding the relationship between absorption and transmission.
Probably the title could be improved but, from our point of view, it is a good representation of the paper's content.
Section 2.1 SC2 R#1: I don't think you have necessarily to distinguish always between the Goddard and New-Goddard SW schemes.The new SW Goddard is essentially the Goddard scheme (Chou and Suarez, 1999) with only few minor modifications (http://www.atmos.umd.edu/∼martini/wrfchem/ppt/WRFToshi.ppt).You can mention you are using the new version implemented in WRF and from there on just talk about Goddard SW scheme.
A: We understand your point of view and it is true that New Goddard is an updated version of Goddard.However, we think that is better to distinguish both schemes because: i) they are different model options (i.e.Goddard was not overwritten by New Goddard).Hence, the paper can be more useful for the WRF's users (see SC12 R#2), ii) the source code of New Goddard was rewritten with many differences at computational level.These code changes lead to significant differences in the applicability.For example, New Goddard can not be coupled to the WRF-CHEM, while Goddard can.Concluding, both assume the same approximations but the differences in the code are significant to be distinguished in the paper.
SC3 R#1: One more thing is that the reference Chou et al. (2001) is not appropriate because it is for the longwave Goddard scheme only.
A: We included this reference in terms of the available literature that is listed in the code of the New Goddard scheme (module ra goddard.F).
The code referring to the physical processes in the UV and PAR bands is based on Chou et. al. (1999), while the code referred to the near-IR is based on Chou et. al (2001).Therefore, we chose both references as relevant to the scheme.
Since the WRF-ARW User's Guide lists the primary references of each parameterization, we have decided to follow that nomenclature to avoid misunderstandings on the readers.A complementary explanation is given in SC13 R#2.SC4 R#1: Could you provide details and/or references on the origin of the ozone profiles used in each SW scheme?
A: Sorry, we can not.We tried to search this information when we wrote the paper, but without success.In general, this information does not appear on the source code or in the based papers.Finally, we decided that this information was not mandatory for the paper.However, we could try to contact the authors to ask them if the Editor thinks that it could be valuable to enhance the paper.

495
SC5 R#1: I don't understand: "The RRTMG scheme includes two ozone profiles as a function of the season (winter and summer).Nevertheless, this granularity is useless due to the fact that the final used profile is computed as a composition of both, without considering the day of the year.There-500 fore, only one profile is considered for any latitude and season."Could you please explain better?Why is it useless?Is it not used in RRTMG?
A: As we summarized in Table 1, the ozone data of this parameterization is stored in a subroutine O3DATA located 505 in a file denoted module ra rrtmg lw.F (note that the letters lw are not a mistake).
Given one grid-point, this routine has three inputs: the pressure at the relative ETA levels of that point, the starting index for the vertical levels (in all the cases, 1) and the 510 ending index for the vertical levels (in all cases, the number of vertical levels).In order to reduce the discussion, we will disregard the difference between full and half levels.
As output, this routine returns the ozone profile interpolated to the ETA levels.

515
When you begin to read the code, you find 4 arrays with a dimension of 31 elements each one: O3SUM, O3WIN, PP-SUM and PPWIN where O3 denote the ozone mixing ratio (kg/kg), PP the pressure (hPa), SUM summer and WIN winter.

520
These arrays store two ozone profiles: one for summer and one for winter.
In the next step, two new arrays are built: PPANN and O3ANN, both with a dimension of 31 elements.
In the PPANN is stored the PPSUM array (this process is 525 completely arbitrary).Given one element K, the O3ANN(K) is computed as Finally, this array is interpolated to the ETA levels and returned to the main code flow.
You can note that, although this scheme contains two ozone profiles, this information is not actually used.As a result, we have a single profile that is invariant on latitude and 535 time.
When we prepared that paper, we decided to summarize this information because we believed it was not important for the purpose of this study.The key point it is that this parameterization only uses one scheme.As we indicated in 540 the paper, this scheme can work with the CAM dataset but we chose the original settings.
The paragraph has been reworded to be more clear.
Section 2.2 SC6 R#1: How did you re-grid the datasets to 1 deg x 1 deg ?A: As both MSR and ERA-Interim are defined in a regular lat-lon grid, we used a simple bi-lineal interpolation.
Section 3 SC7 R#1: Why can you validate the RRTMG's ozone amount but not the impact of its misrepresentation on direct solar irradiance?Why do you only validate the impact using the Goddard and CAM ozones?I don't understand this point.
A: We can validate the RRTMG's ozone amount because we can isolate the vertical profile (see SC5 R#1) and integrate vertically from the surface to the top.
In contrast, we can not validate the impact of its misrepresentation on direct solar irradiance as we will argue in the following lines.
From equation 20 (in the paper), we know that the absorption can be computed as where the optical thickness τ λ from the TOA to a level z may be expressed as where k λ denotes the mass absorption cross section and ρ is the dry air density.
This integral requires the vertical information of the ozone mixing ratio and the dry air density.
The mass absorption cross section is the ability of one molecule to absorb a photon given a particular wavelength.Nevertheless, in the atmosphere, the molecules are not isolated and they interact the ones with the others.As a consequence, monochromatic absorption is rarely observed because the energy levels during energy transitions are changed due to the external influences.Therefore, the radiation absorbed during consecutive energy transition is nonmonochromatic and the spectral lines are broadened.
In virtue of the kinetic theory of gases, the dependence of the k λ on temperature and pressure can be demonstrated.
Hence, as τ λ is a function of the height and this is a function of the temperature and pressure, the integral can not be computed without a detailed information about k λ .
Regarding the spectral integration, the best method to compute equation 4 is the line-by-line (LBL) calculation.
However, this method is not computationally feasible because would require many thousands of computations at each grid-point.Instead of this, some approximations are assumed in terms of the gas and its spectral behavior.For example, the water vapor absorption has a high variation with the wave-590 length and the K-distribution method is required (see Liou (1980)).
Other gases as the ozone show a lower variation with the wavelength and an effective k λ is used for each spectral band.This coefficient is previously computed using the LBL at 595 a reference value of pressure and temperature.Finally, this value is scaled to the pressure and temperature of each layer in order to consider the dependency on these magnitudes.
In WRF, New Goddard and CAM use this second approximation while the RRTMG uses the K-distribution method.

600
Moreover, the dependency of the ozone absorption with pressure and temperature is small and New Goddard and CAM do not scale this magnitude (see, for example, Chou and Suarez(1999)).
Therefore, in New Goddard and CAM, k λ can be assumed 605 as a constant with height and τ λ is or using the hydrostatic equation and considering the entire atmosphere 610 The integral is directly the ozone amount described by equation 3 (in the paper).Therefore, we can evaluate the radiative absorption without any information about the vertical distribution.
In contrast, the RRTMG considers the dependence of k λ 615 on height and we need to know the vertical structure of the atmosphere to solve τ λ .
Since the vertical profile from the MSR dataset is not available, we can not compute this integral for the baseline dataset.For this reason, we did not include the analysis of 620 the RRTMG scheme.

Results
SC8 R#1: It would be interesting to add annual results, not only monthly.As mentioned earlier, direct solar irradiance biases (in W m −2 , and in % would be also interesting) should 625 be shown instead of absorption biases.
A: We think that, the annual results are a good way to summarize the results but they do not contribute with new information since ozone shows a well-defined seasonal pattern.Then, in our opinion, it is not necessary.Regarding the direct solar irradiances, we agree about your consideration.We propose to update all the figures to show the results in W m −2 .This update involves some modifications in the Methodology (section 2.3) and in the Results discussion (section 3.2).SC9 R#1 A: We agree about this point.We will wait until the Editor's decision.

Figures and Tables
Others 640 SC10 R#1: Technical Corrections Needs careful proofreading for English grammar and style.
A: We have tried to address and to improve this point.

645
Response to general comments GC1 R#2: This paper describes the specification of ozone profiles used within most of the WRF-ARW radiation options, compares these to the MSR total ozone dataset, and reviews the impact of the differing ozone amounts on the cal-650 culation of the direct solar radiation in two of the WRF radiation options.The first part of the analysis, which compares the various WRF ozone specifications to the MSR data, is a very useful demonstration of the degree to which the ozone concentrations vary spatially and temporally among the radi-655 ation codes.While the worthwhile goal of the second part of the analysis is to illustrate the isolated impact of the ozone differences using a consistent, if simplified, radiative transfer method, this result does not relate directly to how the ozone variations contribute to actual radiation calculations 660 within WRF.The paper would be more useful to the WRF user community if the authors added an analysis using one or more of the WRF radiation codes so that the full complexity of the radiative processes involved were represented.For example, the two models applied in the second part could be 665 run within WRF for a single time step for some region or globally.In different experiments, each radiation code could be run with its own ozone specification and then run again with the ozone concentration from the other radiation code.This might be an insightful way to demonstrate the impact of 670 the ozone changes within the context of actual WRF calculations.
A: As we understand it, full WRF simulations are not necessary in the second part of the paper (this answer links with point SC35 R#2).We will argue this idea through the follow-675 ing lines.
The general approach in all the radiative codes is to assume independent columns at each grid-point.In brief, the upward and downward solar fluxes are solved at each column considering the vertical profile information provided by the 680 model (e.g.air density, water vapor or hydrometeors) and a set of auxiliary information that is not explicitly solved by the NWP model such as the ozone or the other trace gases (e.g.oxygen, carbon dioxide).Forgetting Dudhia's parameterization that is a special case, the downward component is split 685 in two contributions: direct and diffuse.The first component is solved by using the Beer-Lambert law, while the diffuse contribution requires solving the radiative transfer equation (RTE) assuming different approximations.
Given one wavelength interval, two variables are neces-690 sary to solve the Beer-Lambert law: the optical thickness and the cosine of the solar zenith angle.The first one is a function of the absorption/extinction coefficient (intrinsic magnitude of the material) and the mass amount traversed by the solar beam.The second one is a result of positional astronomy.
The RTE is solved in terms of the same variables, the single scattering albedo and the asymmetry factor.Both last describe how the light is scattered.
In the atmosphere, there are many elements that contribute to the absorption and the scattering processes (e.g.ozone and water vapor absorption or the molecular scattering among others).Thus, the total optical thickness, τ t , the total single scattering albedo, ω 0t , and the total asymmetry factor, g t , are a function of those contributions.
As a first order approximation (widely used in the radiative codes), we can assume that all these contributions are independent one another.Following this assumption, the radiative variables may be split as the sum of contributions as where N is the number of elements (e.g.ozone, aerosols, ice crystals, molecular scattering, water vapor, etc).
In virtue of the exponential form of the Beer-Lambert law, the total transmission of the direct beam through a layer is the product of each contribution.Thus, each one of them can be analyzed independently and we can consider the ozone impact without the other elements.
Regarding the diffuse component in the ozone's case, the radiative parameterizations do not consider explicitly this gas as an scatter element (i.e.ω O3 = 0 and g O3 =1).The molecular scattering of ozone molecules is parameterized in the Rayleigh scattering term without any differentiation of the gas species.Therefore, the ozone profile is useless in that computation and it can be omitted for the purposes of this paper.
The idea of this reviewer related on real WRF simulations is interesting but the analysis of the problem becomes more complex.In a real simulation, new sources of error are overlapped due to the number of vertical levels, the distribution of the ETA levels and the top of the model.Vertical ozone profiles are interpolated to the domain's ETA levels, thus the ozone information can be smoothed of even lost.Moreover, the radiative codes approximate the atmosphere composition between the top of the model and the top of the atmosphere (TOA) losing the details in those layers.
Moreover, real simulations add a part of particularism (region, domain settings, etc) that was not desired in our work.Although the regional particularism could be solved using global simulations (see SC35 R#2), this part of the code is not commonly-used and it must be used with caution as it is indicated in the User's Guide: Note: since this is not a commonly-used configuration in the model, use it with caution.Not all physics and diffusion options have been tested with 745 it, and some options may not work well with polar filters.Also, positive-definite and monotonic advection options do not work with polar filters in a global run because polar filters can generate negative values of scalars.This implies, too, that 750 WRF-Chem cannot be run with positive-definite and monotonic options in a global WRF setup.
Therefore, we think that the derived conclusions could be useless for the scientific community because we could not be sure about the output reliability.

755
Concluding, we believe that the proposed methodology is valid because -We reduce a complex problem in a simpler one based on well supported physics.
-The ozone absorption is independent of the other phys-760 ical processes.
-We are rigorous and transparent in the derivation of the equations.
-The results are useful as a baseline to quantify the impact of the ozone profile simplifications on the direct 765 flux computation.
-The results and conclusions are general.
However, as a self-criticism this part of the paper should be better explained and contextualized.
GC2 R#2: Furthermore, from this reviewer's perspective, 770 the differing specification of trace gas amounts within each radiation option is a fundamental flaw in the design of WRF-ARW itself rather than the radiation codes.These quantities should be provided to each radiation option in a consistent and sufficiently detailed manner from the host model, rather 775 than be defined haphazardly as presently done.In some cases the radiation codes were extracted from other global models, which define their own ozone specification, while in other cases the radiation codes were provided for WRF independently of any existing dynamical model and without a pre-780 defined ozone specification.The authors are encouraged to consider addressing this perspective by using this paper not simply to compare the various ozone approaches but to provide guidance to the community on a better way forward; that is, to provide evidence for the advantages of improving WRF by adopting a unified and accurate approach to atmospheric specification for all of the radiation options.
A: We agree about these ideas.When somebody start to work with the source code, the first difficulties appear.The most relevant is in the nomenclature.In general, each scheme 790 uses a different nomenclature to refer to the same physical magnitudes (e.g.temperature, pressure, height, ozone, absorption coefficient, etc).As a consequence, the time to work with the codes increases because each one requires starting from zero.
Linked with this, another incoherence is in the physical constants.All these magnitudes are defined in the module share/module model constants.F.Nevertheless, these variables are redefined with other names in each code.
Moreover, some processes are similar for all the schemes (e.g.prepare the vertical profiles).All of the common processes could be shared using new subroutines or they could be run in the module radiation driver.F and shared as input arguments.
Furthermore, there are more physical differences similar to the ozone profile.For example, the carbon dioxide concentration.
In our opinion, this makes more difficult read the source code and it increases the sources of bugs.However, we understand that it is difficult to deal with the code structure and with the outside contributions.
We will put an emphasis on these issues.

Introduction
SC2 R#2: Page 20232, Line 23: The first sentence of the Introduction uses a somewhat awkward analogy.The shortwave absorption is more the "fuel" than the "engine".A bet-ter start may be "The absorption of shortwave radiation by the surface and atmosphere is the primary source of energy that drives the atmospheric system."

840
A: We agree that the analogy is not suitable and the language was misused.Nevertheless, we do not fully agree with this proposal because it seems that the "absorption of shortwave radiation" is the unique source of energy.This is not really true because both terrestrial and solar radiation have 845 this role.
In the new introduction, this sentence is not necessary and it has been omitted.SC3 R#2: Page 20233, Line 2: Specify the peak level of ozone heating in the stratosphere.The authors might also 850 specify here the top pressure level required to simulate the stratospheric ozone heating effectively.
SC4 R#2: Page 20233, Line 24: The phrase "defining a region denoted by ozone layer" is unclear and should be reworded.
A: We agree with you.However, we will wait to the Editor's decision.A: This sentence has been reworded accordingly.

Methodology
SC12 R#2: Page 20236, Line 8-9: Excluding the GFDL shortwave code from the analysis deprives the readers, especially those who may be using this parameterization in WRF, from the opportunity to understand its accuracy relative to the other methods.It is arguable that the community would be better served by including results from all of the available SW options.
A: We agree about this reviewer's suggestion and we have been working to include this parameterization in the discussion.
As a consequence, we need to update some parts of the paper: -After reading in depth the source code, we have improved our knowledge about the ozone treatment in this radiation scheme.Therefore, we can improve the description of section 2.1.
-Following the same procedure that was described in section 2.2, we can include the analysis of the errors in the total ozone column.
-Finally, this scheme can be added in the analysis presented in section 2.3.However, this scheme does not consider the Beer-Lambert law and it computes the ozone absorption following an empirical relationship proposed by Lacis and Hansen (1974).
SC13 R#2: Page 20236, Line 10: The WRF-ARW user's guide lists the reference for the original Goddard scheme as Chou and Suarez (NASA, 1994), for the GFDL SW model as Fels and Schwarzkopf (JGR, 1981), and for RRTMG SW as Iacono et al. (JGR, 2008).
A: We chose these references because we considered that they were representative of the approximations used in each scheme.However, we agree that it is better to use the references listed in the WRF-ARW User's Guide.They have been updated.
This review is linked with SC3 R#1.
SC14 R#2: Page 20236, Line 12: This reviewer's understanding of the RRTMG SW code is that the number of sub-intervals (i.e.quadrature points) used to integrate the kdistributions in each spectral band is variable among the four-teen bands, not fixed at 16, and totals 112.This is a time saving feature of that code relative to the RRTM SW model, which does use a fixed set of 16 quadrature points in each 930 spectral band for a total of 224.
A: We agree about this consideration.We tried to give a simple description of the scheme but the result was a simplistic and inaccurate view.This part will be improved.A: We agree with you that it is not clear.It has been re-940 placed as "In section 3.1," SC17 R#2: Page 20237, Line 10: Replace "composed by 37 levels" with "defined at 37 levels" A: It has been replaced.Moreover, after during the analysis of the GFDL we found typing error.There are 81 vertical 945 levels and 37 latitudes.The text has been checked accordingly.

950
SC19 R#2: Page 20237, Line 25: A better word than "assigned" in this sentence would be "distributed" A: It has been updated accordingly.
SC20 R#2: Page 20238, Line 3: Add "with" before "respect"   5) suggests that the resulting error term on the left hand side is a function of ozone method in addition to the spatial dimensions.
A: Your are right, the nomenclature was not well defined.Equation 5 in the paper has been updated.SC34 R#2: Page 20240, Line 23: Replace "previous" with "previously" A: It has been updated.SC35 R#2: Page 20240, Line 25: While it's insightful to examine the ozone method of each radiation model using a similar, simplified radiative method as described in Section 2.3, it isn't clear how this result relates to the effectiveness of 1010 each model to simulate the radiative effects of ozone within WRF.For example, are the differences in the ozone absorption related to the radiative transfer method used by each model larger, smaller or comparable to the differences caused by the ozone specification?Perhaps global calculations for a 1015 single time step with each radiation model (or at least New-Goddard and CAM) using its own ozone specification and the ozone specification of the other model would also be insightful.
A: In virtue of the Beer-Lambert law, we can analyze the 1020 ozone contribution independently of the others (see GC1 R#2).Moreover, real model simulations introduce other sources of error and some particularisms that were not desired for the purposes of our study.We understand your concern when you say that it is un-1025 clear how the presented results relate to the effectiveness of each scheme to simulate the radiative effects of ozone within WRF.Nevertheless, note that, given one scheme (e.g.New Goddard), we compare two scheme outcomes (equation 22 in the old version).Variables A sch,ij (m) and A M SR,ij (m) are 1030 computed using equation 21 where W (λ) and k λ are provided by the scheme and T O 3 is the total ozone using the scheme ozone data and the MSR dataset, respectively.Therefore, we intrinsically did your proposal but using the MSR as a baseline instead of permuting all the ozone 1035 datasets.
From our perspective, this is a valid procedure because the MSR dataset has been accepted by the scientific community whereas the ozone profiles in WRF do not appear in the literature and they have not been validated until our work.

1040
In our opinion, we can include a discussion about the effectiveness of each model to simulate the radiative effects of ozone within WRF using the MSR outcomes as a baseline (i.e.A M SR,ij (m) from New Goddard and A M SR,ij (m) for CAM).This new discussion could be valuable for the readers 1045 and it is in the line of your suggestion.These considerations link with GC2 R#1.
We will keep in stand-by this point during the discussion of the revised version.From our point of view, this improvement implies important modifications on the structure (e.g.A: The sentence refers to the spring and summer of each Hemisphere.

1110
In Figure 1 (G-NG-FLG), you can see negative departures in NH mid-latitude regions during April, May and June.These values drift to positive in July and August.
In contrast, you can note the reversed pattern in the SH.In October, November and December, we have negative de-1115 viations while in January and February they drift to positive values.
We have clarified the sentence to avoid any confusion.

1125
A: In our opinion, we preferred using the geographical nomenclature.However, this sentence has been updated to avoid any confusion.SC51 R#2: Page 20247, Line 5: Regarding the statement ". ..while the largest errors are observed in the RRTMG", 1130 are the authors referring to a globally weighted RMS error, or to the extreme errors?The prior text refers to larger extreme biases in the G-NG-FGL ozone method.In addition, it is recommended that this sentence be revised to refer to the biases of the ozone method used with RRTMG rather than 1135 the model itself, since the ozone specification defined in the interfacing is not strictly part of the RRTMG code itself.
A: In that paragraph we referred globally while in the G-NG-FLG we considered the extreme errors.After your review, we agree that this part must be reworded to avoid any 1140 misunderstanding.
SC52 R#2: Page 20247, Line 9: Clarify the phrase ". ..during the ending Southern Hemisphere winter and the near Southern Hemisphere spring due to the ozone hole is smoothed. .."

35
The shortwave radiation absorption by the surface and the atmosphere is the basic engine that starts the atmospheric system.In a cloudless and clear (i.e.without aerosols) sky, the most important absorbers of the solar radiation in the 40 Earth's atmosphere are water vapor and ozone.Water vapor absorption occurs mainly in the troposphere because water sources are located on the surface.In contrast, ozone absorbs the shortwave radiation in the stratosphere becoming the major source of heating in that layer .In a dynamic frame, the 45 ozone profile should be well detailed in numerical weather prediction (NWP) models which include vertical levels above ∼ 50.
From the point of view of the radiative transfer, the optical properties of the atmosphere (i.e.optical thickness, single 50 scattering albedo, asymmetry factor and back-scattering) are defined as a function of the atmospheric composition (i.e.gas species, aerosols, water drops or ice particles among others).Thus, the vertical characterization for the entire atmosphere arises as a critical point.For example the absorption due to 55 the ozone in the stratosphere determines the radiative input energy in the troposphere.
(SC2R#1) The Goddard and the New Goddard schemes (SC3R#1) (Chou andSuarez, 1994, 1999;Chou et al., 2001) are similar because the second is an update of the first.The ozone treatment is common for both schemes and is based on Chou and Suarez (1999).From now, both schemes will be denoted as G-NG.In these schemes the solar spectrum is divided into eleven spectral bands (seven in the ultraviolet, UV, one in the visible or photosynthetic active region, PAR, and three in the near-infrared, near-IR).In the UV+PAR spectral regions, G-NG neglect the pressure and temperature (i.e.height) (SC11R#2) :::::::::: dependence ::: of effects over the ozone absorption assuming a constant absorption coefficient in each spectral interval.These coefficients are obtained dividing each band into 127 narrow sub-bands with a width of ∼ 0.003 µm and using the ozone absorption coefficient given in WMO (1986).The absorption in the near-IR is added by enhancing the absorption in the PAR region, reducing the computational time.The New Goddard scheme introduces a small correction for the ozone absorption coefficient in the PAR region, from 0.0539 (cm-atm) stp −1 to 0.0572 (cm-1 ECMWF ERA-Interim data used in this study have been obtained from the ECMWF data server.(SC10R#2)atm) stp −1 .The effect of this correction can be neglected for the purposes of this paper considering both schemes as one.

220
All results are based on New Goddard values since it is the newest version.
The CAM scheme (Collins et al., 2004) splits the spectrum into nineteen bands (seven for the ozone, one in the visible or PAR, seven for the water vapor, three for the carbon dioxide 225 and one for the near-IR).The ozone absorption is computed over the seven ozone bands and over the PAR region as well.As in the previous scheme, the CAM parameterization assumes a constant ozone absorption coefficient for each band.The procedure to compute these coefficients is described in 230 Briegleb (1992).

365
Under the assumption of a well-stratified atmosphere, the pressure and the geometric height are related by the hydrostatic equation given by where g is the gravity acceleration, assumed as a constant 370 value.
Because (SC23R#2) :: the : of available ozone profiles in the shortwave schemes are not ::::::::: analytical : analytic functions, Eq. ( 3) in practice must be solved using a numerical integration scheme such as Simpson's method.Further, for an ozone profile composed by N vertical levels, Eq. ( 3) may be discretized such as where q O3,k and p k are the ozone mixing ratio and the pressure at a level k.This vertical integration requires two boundary conditions: the ozone mixing ratio at the TOA and the (SC24R#2) :::::: surface :::::::: pressurepressure at surface .The first one is assumed as zero (i.e.without ozone between the last available level and the TOA).The (SC25R#2) ::::::: surface :::::::: pressure pressure at surface requires a complex treatment since it (SC26R#2) ::::: varies ::: by :::::::: location :::: and : shows a dependence on the location and the season.This boundary is computed using the ERA-Interim reanalysis covering the climate period :::: from : since 1979 until 2008 (i.e.thirty years).This period is not arbitrary since it (SC27R#2) : is : has been consistent with the baseline data described below.Based on this period, monthly surface pressure averages are computed and used as surface conditions for the vertical integration of the ozone profiles.From this procedure, the total ozone column for any location of the world and season can be computed.To (SC28R#2) ::::::: quantify : discuss about the geographical distribution of the errors, a global 1 • per 1 • grid is built using the latitudinal thresholds fixed in each shortwave scheme as described in Sect.2.1.(SC29R#2) :: In ::::: order ::: to ::::::: examine : For the discussion about the seasonal variability, values are computed throughout the twelve months of a year.Ozone profiles in some shortwave schemes like the New Goddard or the FLG are defined as a : function of the day of the year instead of the month.In this (SC30R#2) :::::::: situationsituations, months are (SC31R#2) :::::::: identified : summarized by the 15th day of the month.This means that January is the 15th day of the year, February is the 46th day of the year, etc.
These gridded results are compared with real data.The data used as a baseline derive from the Multi-sensor reanalysis, MSR (van der A et al., 2010) during the period 1979-430 2008 and are monthly averaged (this dataset is provided with a monthly resolution).
The MSR was created from all available ozone column data measured by fourteen polar orbiting satellites in the near-ultraviolet Huggins band since November 1978 to December 2008, including TOMS (on the satellites Nimbus-7 and Earth Probe), SBUV (Nimbus-7, NOAA-9, NOAA-11 and NOAA-16), GOME (ERS-2), SCIAMACHY (Envisat), OMI (EOS-Aura), and GOME-2 (Metop-A).The dataset processing includes two steps.In the first one, a bias correc-440 tion scheme is applied over all satellite observations based on independent ground-based total ozone data from the World Ozone and Ultraviolet Data Center.In the second step, a data assimilation process is applied using a sub-optimal implementation of the Kalman filter method and based on a chemi-445 cal transport model driven by ECMWF meteorological fields.This dataset shows a bias departure less than 1 % with a root mean square standard deviation of around 2 % as compared to the corrected satellite observations used.
Therefore, for each node i (west-east direction) and j 460 This metric will be used to discuss the simplifications assumed within the ozone column by the shortwave schemes.
Extending the integral over the entire atmosphere and assuming the hydrostatic equilibrium given by Eq. ( 2), Eq. ( 22) 590 may be written as In virtue of Eq. ( 3), the optical thickness may be expressed as 595 Substituting Eq. ( 24) into Eq.( 19), the total absorption may be written as

A(τ λ,O3
::: (25) The necessary information to compute the A(τ /µ 0 ) in Eq. ( 25) are the T O 3 , W (λ), k λ and µ 0 .Information about 600 the T O 3 can be obtained from Sect.2.2.The W (λ), k λ are data available in the source code of each shortwave scheme (i.e.New Goddard and CAM).Finally, the cosine of the solar zenith angle µ 0 may be computed as a function of the latitude, the longitude, the hour and the day of the year.

605
From the expression 25, we can conclude that, given a fixed wavelength, there are two variables that may change the ozone absorption over the globe.On the one hand, the cosine of the solar angle increases the absorption as solar beams travel throughout a longer path when the Sun is near 610 to the horizon than when is normal to the surface.On the other hand, the total ozone column increases or decreases the opacity of the atmosphere, absorbing more or less energy.20 DU 2with a tendency to underestimate the total ozone 700 column values.Seasonally, positive and negative departures are observed over the summer and winter hemispheres, respectively.Mid-latitudes and high latitudes show a high seasonal variability due to the ozone profiles (SC44R#2) ::::: being are limited to winter or summer (Table 1).The mid-latitude :: In : Finally, in the CAM case, E).In November and December, an overestimated region (+ : 0 : 15 to +20 DU) is observed over the Mediterranean basin and over the Sahara.

Arctic. :
(SC51R#2) Latitudinally and seasonally, the distribution of the departures shows a logical coherence with the quality of the ozone profiles available in each shortwave scheme.790 Thus, the ozone dataset in the CAM scheme shows the lowest deviations while the largest ::::: global : errors are observed in the RRTMG.Generally, the total ozone column is overestimated by all the analyzed schemes with the exception of some locations, especially, for the G-NG-FGL profiles.The largest weaken smoothed in all the ozone datasets.

800
Longitudinally, similar distribution patterns can be observed for all the shortwave schemes because all of them assume meridional averages in the ozone mixing ratio.Two zones may be discussed.Firstly, during the Northern Hemisphere fall and winter, (SC53R#2) it is observed an underes-805 timated region :: is :::::::: observed : between the north-eastern side of Asia and the north-western side of Canada as well as an overestimated region between Greenland and the Scandinavian Peninsula.This pattern reflects the quasi-stationary features of the upper-air circulation due to the sea-land distribution in the Northern Hemisphere as discussed in Dütsch (1974) or in Fusco and Salby (1999).Secondly, strong longitudinal gradients in the distribution of the errors are observed over Antarctica due to the ozone hole in September and October.In the other locations, the east-west distribution of the errors 815 may be neglected.In the New Goddard scheme :::: (Fig. ::: 8), the bias in the total absorption with respect to the radiation at TOA ranges from − : 3 : 1.0 to + : 3 Wm −2 1.0reaching peaks near + : 6 Wm −2 2.0values close to the poles.The absorption is slightly underestimated in the tropics for the entire year.(SC55R#2) ::::::::::: Mid-latitude : Mid-latitudes regions show overestimated values in winter, more homogeneous and higher in the Southern Hemisphere than in the Northern, ranging from +0 to + : 2 Wm −2 0.7.Near-zero values are observed over North America and Asia and extended over Europe in March.An exception of this winter pattern occurs over the eastern side of Asia where (SC56R#2) : a : bias greater than − : 1 Wm −2 0.4is observed.During the spring, negative and near-zero departures in the bias are observed over both hemispheres, higher in the Northern (from − :: 2 Wm −2 0.4in April to nearzero values in June) than in the Southern (from slightly negative in October to near-zero in December).In summer, the departures drift from near-zero biases during the early season to positive values at the end of the summer.As in the winter season, the bias is higher in the Southern Hemisphere.During the fall, the largest negative bias is observed over both hemispheres reaching the maximum during the first months.
(SC12R#2) :: In ::::::: GFDL ::::: (Fig. 6 :::: and :: 7Figs.?? (G-NG-FLG) and ??.Both schemes tend to overestimate the absorption with lower departures in the trop-890 ics than in the middle or high latitudes and a maximum over Antarctica during the early Southern Hemisphere spring.As opposed to the results in Sect.3.1, the impact of these errors on the simulation of the shortwave irradiance at the surface is linked to the Sun's position.The highest ozone biases 895 in the poles are masked by their coincidence with the polar night.However, the low solar elevation angles at high latitudes results in a higher sensitivity to the ozone datasets in these latitudes.These factors combine to produce the largest meridional gradients in the errors in the modeling of direct 900 solar radiation in the high latitudes during the winter season of each hemisphere.

Conclusions
Two sets of conclusions can be derived from the results of the analysis presented in this paper.The first set is related to the 905 quality of the ozone concentration datasets available to the WRF-ARW mesoscale model and the second set is associated with the impact of these deficiencies in representing the spatial and temporal variations of the ozone profiles on the performance of the shortwave radiation schemes available to 910 WRF-ARW model users.
The key point is that the analysis indicates that the ozone profiles available :: to in the WRF-ARW package are a poor representation of the ozone distribution over the planet during a typical year.These datasets assume zonal averages in 915 the ozone mixing ratio and describe the anomalies in latitude and in time with a low resolution.
In general, the largest deviations are observed over the polar latitudes during the winter of each hemisphere due to the ozone depletion, greater in Antarctica than in Arctic.

920
All the WRF-ARW ozone datasets that were analyzed in this study exhibited similar longitudinal error patterns.The error patterns were more prominent in the Northern Hemisphere due to the quasi-stationary features associated with the land-sea distribution that are not captured in the ozone 925 profiles.As consequence, a systematic underestimation of the total ozone column is observed in a region between the east of Asia (i.e.eastern Russia) and the west of North Amer-ica (i.e.Alaska and Western Canada) during the (SC59R#2) :::::::: Northern : Southern Hemisphere winter and near spring.In contrast, a systematic overestimation occurs in a region defined between Greenland and the Scandinavian Peninsula during the Southern Hemisphere fall and near winter.
The ozone profiles used by the Goddard, New Goddard and the Fu-Liou-Gu consider five ozone profiles: tropical, mid-latitude (winter/summer) and Arctic (winter/summer) for both hemispheres.This discretization ::::: shows : show better results in the Northern Hemisphere than in the Southern ::::::::::: Hemisphere.The tropical profile shows a systematic underestimation of the ozone amount over any longitude, greater in the summer hemisphere, near-zero in the winter hemisphere and practically homogeneous during the equinoxes.This underestimation pattern is directly linked to the obliquity of the ecliptic and the available insolation ::::::::: producing which produce more ozone in summer than in winter.Positive departures are observed over the mid-latitudes in winter and in summer, better ::: for ::: the ::::::: second ::: one ::: in in the second for both hemispheres.Negative deviations are observed during spring while the worst results of the year are obtained during fall.A similar pattern is observed in the polar regions with greater differences between the northern and the southern as discussed at the beginning of this section.
Finally, the CAM shortwave parameterization shows the lowest departures in the total ozone column.This scheme, composed (SC62R#2) :: of by 64 ozone profiles with a monthly temporal resolution, captures a great part of the ozone variations over the globe.The largest deviations are observed throughout the longitudes because of the zonal averages in the profile datasets.The highest zonal gradients in the errors are observed over the poles during the winter season of each hemisphere.
The second set of conclusions (SC63R#2) ::::::::: addresses address the impact of the deficiencies in the specification of the ozone distribution on the simulation of the shortwave radiation.A key point is that the impact of errors in the representation of the spatial and temporal distribution of ozone on the model's simulation of shortwave radiation is determined by multiple factors and : it : is not a simple function of the errors in the ozone profiles.For example, the largest errors in the ozone profiles were determined to be in the Polar Regions during winter.However, the impact of these errors on the simulation of shortwave radiation are masked by the coincidence of these errors with the polar night.On the other hand, the low solar elevation angles at high latitudes result in a higher sensitivity of the shortwave radiation schemes to the ozone profiles in these latitudes.These factors combine to produce the largest meridional gradients in the errors in the simulations of shortwave radiation in the high latitudes 985 during the winter season of each hemisphere.
The lowest biases in the absorption of the solar direct beam occur over the tropics (Fig. : 8, :: 9 :::: and ::: 10??) with near-zero departures.In contrast, the largest biases are observed poleward during the winter of each hemisphere.Longitudinally, 990 (SC64R#2) :: the : underestimated ozone region over the northern Pacific produces important biases in the absorption.

8A.
Montornès et al.: Analysis of the ozone profile specifications in the WRF-ARW model

:
Split both Fig. 1 and Fig. 3 in two figures.

955A:
It has been updated.SC21 R#2: Page 20238, Line 12: This sentence has to be reworded.The phrase ". ..individual gas species loss progressively the hydrostatic equilibrium. .." doesn't communicate the intended meaning.

960A:
This sentence has been reworded.SC22 R#2: Page 20238, Line 16: Reword the end of this sentence to read ". ..and are monotonically decreasing" A: It has been updated.SC23 R#2: Page 20238, Line 19: Reword "Because of 965 available ozone profiles. .." as "Because the available ozone profiles. .."SC33 R#2: Page 20240, Line 18: Equation ( 1050adding a new block).SC36 R#2: Page 20241, Line 3: Replace "we" with "be" A: It is a typing error.It has been updated.SC37 R#2: Page 20241, Line 6: Reword the phrase "discussed by many literature such as" 1055 A: The sentence has been reworded.SC38 R#2: Page 20242, Line 3: The provided definition of W(λ) is unclear.Is this the ratio of the energy in a band dλ to the total integrated energy?A: Yes, it is.We have tried to clarify the definition of W(λ) writing the equation explicitly in the paper.SC39 R#2: Page 20242, Line 9: Suggest replacing "with the wavelength throughout the interval" with "on wavelength in the interval" A: This sentence has been replaced.SC40 R#2: Page 20244, Line 17: Reword the phrase "the minimum slant respect the normal. .."A: This phrase has been rewritten.SC41 R#2: Page 20244, Line 22: Suggest rewording "using as TO3, the original and MSR datasets" as "using TO3 from the model and the MSR datasets" A: We have updated this sentence.SC42 R#2: Page 20245, Line 4: Clarify and reword the phrase "due to total absorptions are normalized respect. .."A: We agree about the inaccuracy of this sentence.In equation 11 (in the paper), we normalized the fluxes with respect to the solar radiation at the top of the atmosphere.Thus, the results from equation 21 range from 0 to 1.In equation 22, we compared two outcomes from equation 21 and, as a consequence, the bias is dimensionless.With this sentence, we tried to clarify this point to avoid any misunderstanding related to the relative error.As we detail in SC8 R#1, we propose to use physical units (i.e.W m −2 ) instead of dimensionless values.Results SC43 R#2: Page 20245, Line 12: Move the first comma so that the sentence reads "In the RRTMG scheme, shown in Fig. 1, the lowest. ..)A: The comma has been shifted.SC44 R#2: Page 20246, Line 2: Replace ". ..due to the ozone profiles are limited to winter. .." with ". ..due to the ozone profiles being limited to winter. .."A: It has been updated.SC45 R#2: Page 20246, Line 4: Suggest replacing ". ..larger in the Southern during the Southern Hemisphere fall. .." with "larger in the Southern Hemisphere from March to May. .."SC46 R#2: Page 20246, Line 5: Suggest replacing ". ..lower in the Northern Hemisphere during the Northern Hemisphere winter. .." with "lower in the Northern Hemisphere from December to February. .."A: Your suggestions make the sentence simpler.They have been replaced.SC47 R#2: Page 20246, Line 7: Remove "the" after "around 1105 A: It has been replaced.SC48 R#2: Page 20246, Line 9: Does this sentence refer to boreal spring and summer?

3. 2
Part two: an analysis of the uncertainties added to the computation of the direct solar radiation As previously noted in Sect.2.3, the errors in the (SC54R#2) ::::::::::: specification : determination of the ozone profiles are propa-820 gated in the shortwave radiation results.In this section, sys-A.Montornès et al.: Analysis of the ozone profile specifications in the WRF-ARW modeltematic biases introduced in the modeling of the direct solar radiation are discussed focusing on ::::: three two schemes: New Goddard, :::::: CAM :::: and :::::: GFDLand CAM .First, a detailed description of the uncertainties over the globe is shown.Then, a general view of those limitations and their implications is discussed.

Table 1 .
Description of the ozone profiles in the shortwave schemes in the WRF-ARW model.Dudhia (SC12R#2) :::::: scheme :: is and GFDL schemes are not analyzed in this study for the reasons mentioned in the text.