Extreme Rainfall over Complex Terrain: An Application of the Linear Model of Orographic Precipitation to a Case Study in the Italian Pre-Alps

Round 1

Reviewer 1 Report

In general, the authors should frame their questions, the model they developed, and their results more in the context of the literature. They need to provide a nicer literature review and their current literature review doesn't sufficiently refer back to the literature. They need considerably better discussion and presentation. This article needs a number of corrections and emendations to make its central points clear to readers. Also, reading and understanding this paper were very hard. I advise the authors to find a native English speaker to proofread the ms. Significant improvement in the language of the paper must be addressed. Both in terms of the way the story is described and the way the sentences are structured.

General comments:

1- It is not so much the advanced analysis, using any rainfall-runoff model depends on the question. "when advanced analysis is required, rainfall-runoff models are adopted to investigate the dynamic of a hydrogeological event" (line 41)

2-"To avoid these problems, several authors have proposed some extensions of these interpolation techniques." What problem? Hard to understand and connect to it. 

3- You have to define any abbreviations you are using in your study. What is PRISM? I know it but you have to provide this information for the reader."One of them is the PRISM model"

4-"We reconstruct the real rainfall field following a hybrid approach that considers the power of meteorological models with the affordability of interpolation techniques. " - Why? What is unique about your method? You have to provide more information. Also, why you used only one case study? What was the importance of this one case study?

5- The labels in all the figures are hard to read. 

6- The title of this work really doesn't give any information about the motivation and objective of this study. "Extreme Orographic Rainfalls in Italian Pre-Alps: the case study of 11 -12 June 2019 " The title should have a taste of the article. What aspect of the extreme precipitation are you going to analyze.

7- "One of its worth points is the relatively small amount of input data for its implementation. Lack of data is generally a problem in mountain catchments, but, as we have seen in our case study, the linear model was able to interpret the convective rainstorm triggered by upslope air motion simply using sounding data and topographic elevation. " You are using only one case study. So how can you generalize your method? Is it a good method anywhere in the world? What would be the use of your model? And, linearity is not always the best solution. Whey you think with the data you used, you can always get accurate perceitation data? So, I'm comfuse about the novelty of this work.  

Author Response

REFEREE N°1

We would like to thank the reviewer for the time and effort he/she put into thoroughly reviewing this manuscript. We believe that the comments are constructive and would lead the considerable improvement of our work. Our point-by-point response is provided in italics.

In general, the authors should frame their questions, the model they developed, and their results more in the context of the literature. They need to provide a nicer literature review and their current literature review doesn't sufficiently refer back to the literature.

They need considerably better discussion and presentation. This article needs a number of corrections and emendations to make its central points clear to readers. Also, reading and understanding this paper were very hard.

I advise the authors to find a native English speaker to proofread the ms. Significant improvement in the language of the paper must be addressed. Both in terms of the way the story is described and the way the sentences are structured.

We have enlarged the literature review, focusing better on the description of rainfall interpolation techniques and Limited Area Models. All the paragraphs, especially the discussion, has been completely rewritten highlight and motivate better the aim and the outcomes of our analysis. An English Proof Reading has been carried out in order to improve the style of the overall paper.

General comments:

1- It is not so much the advanced analysis, using any rainfall-runoff model depends on the question. "when advanced analysis is required, rainfall-runoff models are adopted to investigate the dynamic of a hydrogeological event" (line 41)

That’s right, it is a redundant statement and we have reformulated it in the text.

2-"To avoid these problems, several authors have proposed some extensions of these interpolation techniques." What problem? Hard to understand and connect to it. 

The “problems” regards to the approximated results of interpolation techniques over complex terrain. We have reformulated it in the text, including some proofing and literature references.

3- You have to define any abbreviations you are using in your study. What is PRISM? I know it but you have to provide this information for the reader. "One of them is the PRISM model"

We have corrected it across all the text.

4-"We reconstruct the real rainfall field following a hybrid approach that considers the power of meteorological models with the affordability of interpolation techniques. " - Why? What is unique about your method? You have to provide more information.

We have reformulated this statement in this way: “The aim of our study is to try to overcome the poor accuracy of classical interpolation techniques, while avoiding the complexities of running a LAM.” Some comments about our choice are also reported in initial part of paper discussion: “As opposed to the classical interpolation techniques we have also gained a physical interpretation of the phenomena under twofold aspects. The first regard the analysis of soundings data that can depict the atmosphere state before and during the event, highlighting potential critical situations, as in the present case. The second consists in a better understanding of orographic rainfall mechanism in relation to several parameters that can influence it. We can say that LUM can be more “didactic” rather than complex LAM models and its simple implementation permit to make the problem more tractable.”

Also, why you used only one case study? What was the importance of this one case study?

The case study was considered because it was very recent, rather exceptional, and also because of the availability of field data. The importance is related to the large amount of rainfall triggered chain effect that has caused: the dam of Pagnona risked a collapse, and the town of Dervio was flooded. It was interesting to reproduce understand how such amount of rainfall poured in that precise location and if there was a direct correlation with orographic intensification.

5- The labels in all the figures are hard to read. 

We have checked and corrected them, following the Editor References about Layout.

6- The title of this work really doesn't give any information about the motivation and objective of this study. "Extreme Orographic Rainfalls in Italian Pre-Alps: the case study of 11 -12 June 2019 " The title should have a taste of the article. What aspect of the extreme precipitation are you going to analyze?

In the paper we analyzed and episode of orographic precipitation. We have modified the title as: “Extreme Rainfall over Complex Terrain: an application of the linear model of orographic precipitation to a case study in Italian Pre-Alps”

7- "One of its worth points is the relatively small amount of input data for its implementation. Lack of data is generally a problem in mountain catchments, but, as we have seen in our case study, the linear model was able to interpret the convective rainstorm triggered by upslope air motion simply using sounding data and topographic elevation. "

You are using only one case study. So how can you generalize your method?

We have reformulated this statement and we dedicated a paragraph in the Discussion:

“One of its strengths is the relatively small amount of input data required for its implementation. Lack of data is generally a problem in mountain catchments, but, as we have seen in our case study, LUM was correctly initialized simply using sounding data and topographic elevation. Unfortunately, even if the terrain elevation is available worldwide with good resolution, sounding data are typically single-point data. In this particular case, the radio soundings were taken some 60 km away from the starting point of the simulation. This approximation was considered acceptable for defining the initial conditions of the model, i.e. WVF0. The estimation of WFV0, could be a non-trivial task at some location or even not sufficiently precise to feed the linear model. In fact, it is more likely that the sounding is located too far away from the studied area, i.e. hundreds of kilometres. In that case, the atmosphere’s vertical profile should be inferred comparing different data sources, especially considering vertical atmosphere profiles retrieved form reanalysis models or using satellites.  The information detected by infrared sensors and LiDAR scanners from geostationary satellites are now providing encouraging results in terms of WVF estimation. These techniques are currently adopted for the study atmospheric rivers [58,59]. As a matter of fact, increasing data availability regarding atmospheric moisture flows may help in this way.”

Is it a good method anywhere in the world? What would be the use of your model? And, linearity is not always the best solution.

About “linearity” of the model we have reformulated this part adding a comment in the Discussion:

“Another point of discussion concerns the hypothesis of linearity under which the model operates. In fact, trying to represent or simulate a chaotic system such as the atmosphere with a liner model could sound as a nonsense. In our view, this is partially true. As described by the model authors, it contains strong simplification of the processes occurring in the atmosphere. Microphysics is completely neglected, and rainfall formation is reduced to a simple water mass balance of WVF flow. This is obviously not true in reality and the process is simulated by LAM. Nevertheless, the complexity of LAMs sometimes not permit to effectively control the solution especially over complex terrain and when orography abruptly influences rainfall generation. LUM permitted us to highlight the critical parameters that affect to final outcome of the model, neglecting second order influences. In the case study, the test of LUM moved on in this direction, accepting some simplification but sill pretending a reasonable rainfall field reconstruction.”

Why you think, with the data you used, you can always get accurate precipitation data? So, I'm comfuse about the novelty of this work.  

“We have reformulated this part in the Discussion, trying to explain also the limitation of the model applicability commenting on our experience:

“In the case study, the test of LUM moved on in this direction, accepting some simplification but sill pretending a reasonable rainfall field reconstruction. These simplifications are discussed here in detail:

         The mono-dimensional domain is a strong idealization of the event occurred. Nonetheless, sounding data compared to a local LAM depicted an event that developed northward following a narrow cone extension. The thunderstorm corridor had a clear starting point, an average width around 10-15 km but an extent of 100 km. Therefore, considering also the low-level wind convergence (Figure 3) a mono-dimensional reduction has been retained sufficiently realistic.

         The resampling of orography is an operation that is generally adopted in atmospheric model. For the Alps, a rectangular shape range with 2000 m average slope was considered in the past as a sufficient representation of the morphology in regional atmospheric-dynamic models [6,32,34,50]. Nowadays, LAMs can assimilate orography at higher resolution, but the smoothing operations are still necessary [58,59]. In our case, the high sensitivity of LUM to the terrain profile required that local morphology should have been smoothed for obtaining realistic simulations.

         Topographic influence on incoming airflow can generate some gravity waves and turbulences that can also perturb airflow dynamic along the vertical [5,34,60]. These secondary effects have probably played a significant role in a spatial redistribution of the rainfall, especially behind the peak of Mount Legnone where results have shown highest errors with underestimation around 40 mm. Using the linear model, the airmass uplift triggered by orography is the process predominantly simulated and the others are confined to the second order. For these reasons, downslope dynamics are poorly described due to high non linearities that may occur in these processes.

         The estimation of the boundary layer height cannot be computed explicitly, and this represents a significant uncertainty that should be treated carefully. However, in our opinion, this quantity should be considered when LUM is adopted. In fact, as we have experimented for this case study, BL is essential to determinate the portion of atmosphere that can contribute to the effective rainfall generation. The motivation is the following: due to surface friction, low atmosphere layers are maintained at rest and do not experience any upslope motion until the BL is completely eroded. In our case study, that evidence was confirmed looking at three sounding data where, for layers comprised in BL, wind velocities were sensibly reduced, and their directions were not aligned with WFV airflow. Furthermore, if these layers are included in the computation of WFV0 they could lead to a sensibly overestimation of the initial condition because of their high concentration in water vapour. For these reasons we have tested this BL adjustment and the results has demonstrated good improvements in LUM simulation.

Bearing in mind these necessary simplifications, the final result was rather encouraging. The model has highlighted how the orography has played a determinant role in enhancing the precipitation rate locally. As was observed analysing the reconstructed precipitation field, the critical value recorded at Premana rain gauge has been matched correctly. Also, in the upper part of Valchiavenna the model outcome was in good accordance with the rain gauges measurements. Probably, hidden errors were also contained in reference rain gauges, especially due to their relative distance from the cross section considered such as in the case of Barzio station. For this reason, an extension of LUM for working with 2D domain could be a further improvement of the analysis in order to fulfil these uncertainties. Nonetheless, we can conclude that the linear upslope model has turned out performant in a reliable reproduction of this exceptional rainfall event.”

Reviewer 2 Report

See the attached file.

Best Regards.

Comments for author File: Comments.pdf

Author Response

REFEREE N°2

We would like to thank the reviewer for the time and effort he/she put into thoroughly reviewing this manuscript. We believe that the comments are constructive and would lead the considerable improvement of our work. Our comments are privided in Italics.

Review of “Extreme Orographic Rainfalls in Italian Pre-Alps: the case study of 11 -12

June 2019” by Andrea Abbate, Monica Papini and Laura Longoni

The manuscript described the application of a linear model of orographic precipitation to a

case study in the Italian alps. The method used is based on the original model proposed by

Smith and Barstad (2004), which has been applied to several domains all over the world.

Standard statistical techniques are used for validation and verification. The study considers a

single case study, which is not enough to gain a complete understanding of the behaviour of

linear upscale models in the Alps but it might help other researchers interested in the same

topic. The study is valuable, but the manuscript is not ready for publication yet. The authors should

address the comments that follow before the manuscript should be considered for

publication.

We would like to thank the reviewer for the time and effort he/she put into thoroughly reviewing this manuscript. We believe that the comments are constructive and would lead the considerable improvement of our work.

We have enlarged the literature review, focusing better on the description of rainfall interpolation techniques and Limited Area Models. All the paragraphs, especially the discussion, has been completely rewritten highlight and motivate better the aim and the outcomes of our analysis. An English Proof Reading has been carried out in order to improve the style of the overall paper.

Comments:

- Introduction. The motivations are a better understanding of the precipitation

representation in complex terrain. In the conclusion or discussion sections, the

authors should describe what they actually learned on the precipitation field from

running the linear upslope model. New findings? Ideas leading to further tests ?

We have reformulated all the paper sections, stressing better the aims, findings, and learnings about our case study.

- Innovative and original part of this research. It is not clear if there is any significant

modification to the linear upslope model that is tested here. For instance, the

inclusion of BL may be an original contribution of this study. Please, explicitly state

the original part of your work in the Introduction.

We have included a proofing about BL problem threated in the model. In particular we have extended the hypothesis assumed, the result presentation and we made a specific paragraph in the discussion that highlight our final consideration about that.

- Sec. 2.1. This section must be revised because of inconsistencies in the

mathematical notation. If the authors decide to consider a vertical slice of the

atmosphere and to use a x-z reference system on this slice, this is fine with me, but

the mathematical notation must be consistent with this decision. For instance, h(x)

should be used instead of h(x,y).

- In its current state, this section is difficult to read because of the ambiguity in

the reference system chosen. The operator del, or nabla, is assumed to

operate in two or three dimensions?

- Eq.(4), why do you need to know w(x,y,z)? I assume that w(x,z) would be

enough. Mathematical notation:

- Eq.(1) states that WVF is a vector field, however this is contradicted by Eq.(2)

and Eq.(3) where WVF is defined as a scalar. Please, clarify it.

- Eq.(6) a scalar product of two vector fields is introduced, I guess. That should

be written explicitly.

- Eq.(7) clarify the notation of the operator |...|

We have adjusted this section correcting mistakes, reorganizing the formulae presentation, and specifying all the quantities in correct units of measures.

- Simulation setup. I believe your simulation setup makes sense. However, you have

made choices that are not well explained. For instance, you have decided to use a

South-North section. Have you decided to do so because of the data availability

(Milan is south of the Alps) or because of the atmospheric flow?

We have made this choice principally looking at the Milan sounding wind parameters (velocities and directions) where this fact was very well depicted. Milan sounding is the nearest soundings we have available for the western part of southern Alps. The motivation of our choice has been detailed in the Result section when the model has been applied:

“The first regards the mono-dimensional approximation of the domain geometry. The event analysis has depicted a clear south-north corridor followed by thunderstorms (Figure 1). That rectilinear path can ideally define a bidimensional domain that slices the atmosphere along horizontal and vertical coordinates x and z. Bearing in mind that the quantity WVF is vertically integrated, the problem has been reduced to one dimension.”

What if the flow was from North to South? Or in the east-west direction? This is an important point for

readers that may be interested in adapting the linear upslope model to their domains.

Following your question, we made an extended comment in the discussions:

“One of its strengths is the relatively small amount of input data required for its implementation. Lack of data is generally a problem in mountain catchments, but, as we have seen in our case study, LUM was correctly initialized simply using sounding data and topographic elevation. Unfortunately, even if the terrain elevation is available worldwide with good resolution, sounding data are typically single-point data. In this particular case, the radio soundings were taken some 60 km away from the starting point of the simulation. This approximation was considered acceptable for defining the initial conditions of the model, i.e. WVF0. The estimation of WFV0, could be a non-trivial task at some location or even not sufficiently precise to feed the linear model. In fact, it is more likely that the sounding is located too far away from the studied area, i.e. hundreds of kilometres. In that case, the atmosphere’s vertical profile should be inferred comparing different data sources, especially considering vertical atmosphere profiles retrieved form reanalysis models or using satellites.  The information detected by infrared sensors and LiDAR scanners from geostationary satellites are now providing encouraging results in terms of WVF estimation. These techniques are currently adopted for the study atmospheric rivers [58,59]. As a matter of fact, increasing data availability regarding atmospheric moisture flows may help in this way.”

- Precipitation efficiency (page 9) equal to 0.3 and smoothing parameter (page 12)

equal to 10 km. In my opinion, the two parameters are ad-hoc adjustments

introduced to better fit the rain gauge observations. The authors describe the reasons

leading to the introduction of the two parameters. The precipitation efficiency has

been used by others in scientific literature.

We agree with your statement. In fact, the precipitation we recorded on the ground is not the same produced in the atmosphere under the HP that all condensed water transforms into rain. Microphysics is neglected in this model therefore the efficiency parameter is a way to consider it.

On the other hand, the smoothing parameter does not have a concrete justification (10km? Why not 20 km? Or 5 km? They are both values in the meso-gamma scale, which is the scale of a single thunderstorm). Note that I think the authors are totally justified introducing parametrizations to make the linear upscale model better fitting the observed values. The linear upscale model is a useful approximation but it is not supposed to be perfect. However, I would prefer to read that in the text. Something like “We have used a smoothing parameter of 10 km to better fit the observed values. This also led us to think that 10 km was the length scale of the thunderstorms hitting the region in the case study considered”.

We agree with your statement. Yes, this what we have done. We have tried different “smoothing windows” and we have seen the best of these looking at the best fitting with rain gauges reference. We have extended this section in results and we have reformulated in this way:

“LUM results of P(x) and E(x) appear to be physically correct, but we have noticed that the rainfall amounts were too under/overestimated at some points and rather irregularly distributed. Therefore, to obtain a realistic representation of rainfall pattern, a smoothing function has been applied to P(x). We tested three different smoothing windows related to the meso-gamma scale of the studied phenomena: 5 km, 10 km and 20 km ranges, as reported in Figure 8. We considered a smoothing window of 10 km that turned out to better fit the observed values. This also led us to believe that 10 km was the length scale of the thunderstorms that stroke the region during the event [5,32,53]. The green continuous line in Figure 7 and Figure 8 represents the smoothed function for the precipitation P(x): the values of rainfall field are now more uniformly distributed with respect to the initial prediction (Figure 7).”

- Page 8. The study of the soundings is quite extensive, perhaps a bit too much. For

example, 7-8 parameters are introduced just to say that this was a convective case.

This part can be shortened.

Checked and Corrected: we have shortened the discussion in this paragraph, excluding the part relative to the precipitable water.

- Lines 315. Why are you introducing the BL? It is not clear how this information is

used in the linear upscale model, since this is not stated when you describe that

model. Is the use of BL in the linear upscale model an original part of this work?

That has better explained. We have introduced the BL to assess the real elevation that “was seen” by the airflow flux. In fact, inside the boundary layer the air is rather static (with negligible velocity) due to the surface roughness. If the velocity is around few meters per second cannot rise the mountain flank and generally non contributed into precipitation formation. This is particularly true for internal areas such as Val Padana basin where the BL formation has a daily cycle and can be well recognized from soundings.

We have adjusted this part in the Result section, and we have made a further comment in the discussion.

- Lines 38-39. Intensity-duration rainfall curves can be computed without data on landslides. In this sense, I think your statement here is misleading. Please reformulate it.

We have reformulated the statement in a more clearly way.

- Lines 55-56. Kriging works particularly well when a strong relationship between a

meteorological variable and elevation is present. The spatial interpolation of

temperature is an example of successful application of Kriging (or co-Kriging). In the

case of Kriging, the issue with precipitation is that precipitation does not follow

neither an additive error model or a Gaussian distribution. Both are prerequisites for

a rigorous application of most geostatistical methods. Instead, precipitation follows a

multiplicative error model (and this is the reason what efficiency is defined as a ratio)

and its distribution is positively skewed. Please, reformulate the statement.

We have reformulated the statement in a more clearly way and we have added some references:

“Interpolation techniques work well across flat areas where terrain elevation is nearly constant or very smooth [18]. In fact, the simplest ones, such as IDW, are geometry-based, where interpolated values depend only on rain gauge distance. In this case, the availability of a sufficient dense network is necessary to obtain a reasonable interpolation, but sometimes this is not possible in mountain environments. Moreover, the dependence of the rainfall field on elevation is not taken into account. In this light, geostatistical techniques such as Kriging External Driven (KED) may be a viable solution: the classical Kriging could be conditioned (driven) considering an external drift such as the elevation [18], [21] [22]. KED yields good results when a strong relationship between a meteorological variable and elevation is present. The spatial interpolation of temperature is an example of a successful application of KED [23,24] but this cannot be extended to precipitation. Precipitation does not follow neither an additive error model, nor a Gaussian distribution (typical of temperatures) that are both prerequisites for a rigorous application of most geostatistical methods [18,25]. Instead, precipitation follows a multiplicative error model and its distribution is positively skewed [25,26]. Therefore, the Kriging performances are rather low, especially in the reconstruction of daily and sub-daily rainfall fields.”

- Lines 68-70. I would not say that the main drawback for numerical models is the

parameterization of cloud microphysics, although it is one of the points that are in

need of improvement. I believe there are more significant weaknesses, however,

such as the lack of predictability after a few hours for small-scale precipitation events

(e.g. less than approximately 50 km). An overview of the topic is given by:

Frogner, I-L, Singleton, AT, Køltzow, MØ, Andrae, U. Convection-permitting

ensembles: Challenges related to their design and use. Q J R Meteorol Soc. 2019;

145 ( Suppl. 1): 90– 106. https://0-doi-org.brum.beds.ac.uk/10.1002/qj.3525

We have reformulated the statement in a more clearly way and we have added some references:

In these cases, Limited Area Models (LAMs) for local weather forecasting represent an important data source [5,14,31–33]. Their affordability is still increasing worldwide especially in now-casting meteorology and they are continuously updated and trained in the prediction of atmosphere dynamics [31,32]. Historically, one of the main drawbacks of these models has been the complexity of their parameterization regarding the cloud microphysics that is the “engine” responsible for precipitation formation [5,31,32]. Difficulties have risen especially across mountain areas where morphology could dramatically influence rainfall processes, even at a local level[34]. Result variability is also dependent on the microphysical scheme implemented inside the model [5]. Nowadays, according to [35], the lack of predictability after a few hours represents a current challenge aspect for small-scale precipitation events. In particular, for scales smaller than ∼60 km it is lost rapidly within the first 6 h of the forecast, that is, the typical scale length of the. intense precipitation phenomena. For this reason, the design and the use of a convection-permitting ensemble seems promising [35,36]. However, also in these cases, meteorological outputs should be always compared and validated through appropriate error analysis with rain gauges records on the ground [14], [25,26].

• Lines 95-103. What happens if there are two consecutive peaks along the trajectory of the thunderstorm? Is the linear model able to simulate the modified atmospheric conditions at the second peak because of the first peak? Please, elaborate on this point.

The model simulates along the path of thunderstorm. Of course, due to the airflow moisture balance, the amount of WFV is decreased on the second peak but the air flow re-raising with the same characteristics of the first one. There is not any further investigation about the possibility wind weakening or rain shadows area behind the first mountain peak due to the local turbulence generated from overpassing the obstacle. May be could be a further improving of the model because we know that the first range or peak is generally more critical than the second one regarding rainfall produced on the ground.

We have commented also this problem in results and in the discussion:

         Topographic influence on incoming airflow can generate some gravity waves and turbulences that can also perturb airflow dynamic along the vertical [5,34,60]. These secondary effects have probably played a significant role in a spatial redistribution of the rainfall, especially behind the peak of Mount Legnone where results have shown highest errors with underestimation around 40 mm. Using the linear model, the airmass uplift triggered by orography is the process predominantly simulated and the others are confined to the second order. For these reasons, downslope dynamics are poorly described due to high non linearities that may occur in these processes.

• Lines 125-128. Revise the units. I found Kg/s/m a weird way to write the units. Please

be more precise.

We have reconsidered that rewriting of the unit measure.

• Line 154. Specify the reference for the 200 yr return period.

We have specified the reference in the text. We have calculated it using IDF (Intensity-Duration-Frequency curves)

• Rain gauges in Sec. 2.2. Who is responsible for the observation you have used?

Where have you found them? Please add more detail and the website for your

observational data. The same holds true for the soundings too.

ARPA Lombardia for the Rain Gauge data and Wayoming University for Soundings. We have specified the reference in the text.

• Eq.(9a) Prain-gauge should be Pgauge (line 285)

We have corrected.

• Lines 308-314. What is the data source of your digital elevation model? Please

specify it. Minor comment on the resolution of the digital model: is it 5m or 500 m?

The starting model is 5m, downloaded from Regione Lombardia Geodatabase. It was then resampled at 500m resolution for decreasing the dependency of high-resolution elevation.

• Fig 6. I believe there is a mistake here. Two figures are reported while it should be

just one.

There was an error that we have corrected it

• Lines 340-342. Since there are soundings available before and after the one used at

00 UTC, why have you decided to use just that one? Would that be possible to

simulate the temporal evolution of the atmospheric conditions by considering more than one sounding?

We have considering all three soundings to address the correct initial value of WVF0. We have specified that calculation in the text:

“The continuity equation of LUM (Eq. 2 and Eq.3) requires an initial condition. As specified in the Materials and Methods section, we have described the model under two hypotheses: a steady state conditions and a mono-dimensional geometry along the x coordinate. Therefore, the initial condition for the incoming airflow is defined by the vector WVF0 calculated at location x = 0. Looking at Table 3, the WVF0 vector was retrieved for each sounding described previously plus a third one recorded on 12 June 2019 12 h UTC.

As reported in the Eq.4, the module of WVF vector is represented by the integral over an air column height. The integral limits have been assessed looking at sounding data: they were comprised between LCL (lower) and EL (upper) levels. For each sounding, validity windows have been defined as 6 h backward and 6 h forward from the central reference time. Then, considering that the rainfall event started at 8 p.m. of 11 June until 9 a.m. of 12 June, the two sounding of the 12 June 2019 00 h UTC and 12 June 2019 12 h UTC were selected for computing the average module of WVF0 at location x=0.”

Yes, in principle you can do it simply feeding the model but of course you need to interpolate data of soundings to define a continuous interpolation. 12h frequency is a rather large time interval, but data could be used as a proxy, as we have seen in their analysis, to discover the environment tendency to trigger or rainfall phenomena.

• Lines 360-362 and 431. Reformulate the statement without using “Unless” at the

beginning of the phrase.

Checked and Corrected

• Fig 8. This is perhaps the most significant result of your study. It is a pity that the

horizontal scales in the graphs of the two panels do not match. Please, re-plot the

graph such that there is a perfect overlap between the x-axes of both graphs.

Checked and Corrected

• Line 389. Thee -> the

Checked and Corrected

• Lines 400-405. Why is this paragraph here? I’d like it more in the Introduction or

conclusions.

We checked and moved in the introduction.

• Line 436. “Has been revelled” is a typo.

Checked and Corrected

• Conclusions. I think that you should write more about the findings of the present

manuscript. What have you learned from this case study?

We have reformulated the conclusion highlighting better what we have learned from this study:

The aim of this paper was to try to reconstruct a realistic rainfall field through the application of simple linear upslope model. In fact, over complex terrain, this task is required in many fields, in particular for hydrogeological risk assessment. Some interpolation techniques that consider only data recorded by rain gauge networks may fail as they do not consider orography as critical factor for precipitation intensification. On the other hand, LAMs offer a good solution to investigate rainfalls, but their complexity is highly data-demanding, and, especially in mountain environments, solutions could be often too approximate. For these reasons, we have attempted to apply the linear upslope model proposed by [37], that represents an intermediate alternative. To test the model application, a case study was chosen due its severity that was intensified by two main causes: the favourable meteorological conditions of the atmosphere and its interaction with the local orography. Considering its known limitations and the simplification adopted, LUM has turned out suitable for that purpose. The rainfall field reconstructed was able to fit well data obtained from reference rain gauges, and especially around the critical areas where the highest amount of rainfall was recorded. In addition, it has allowed us to increase the understanding of this type of complex meteorological phenomena, discovering the importance of BL for the assessment of initial condition related to WVF.

Round 2

Reviewer 2 Report

Dear Authors,

thank you for your revised version, that I think substantially improved over the original version and I am happy to acknowledge that you have successfully addressed my comments.