Interactive comment on “An online trajectory module
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1. studies page 1241 bottom it is a limitation We will include this fact in the introduction Of course it is a limitation that only forward trajectories can be calculated but we think it is not really tremendously difficult to find a suitable starting region if one is interested in trajectories ending at a certain location 5 Issues related to details of the implementation Ulrich Blahak C199 200 Presentation of the Petterssen Scheme and its implementa tion in section 2 1 You present the Petterssen scheme in a way which is customary in the literature as a kind of predictor corrector method think your term iterative forward Euler timestep from page 1230 line 5 is wrong However in my view it would be more enlightening to present it slightly differently To solve the trajectory equation x Z t t numerically forward in time from time t to t 11 a second order semi implicit discretization in space and time is used which reads E te41 This is an implicit equation for Z t 1 because the last differential on the right hand Side ti Z ti 1 ti41 depends itself on x t 41 A common method to solve such a problem numerically is a fixpoint iteration The above equation is alread in fixpoint form so all we need is a starting value Zo ti 1 resp ti Zo ti 1 ti 1 Then the n th C678 Z t a AtA Ei tita Z t At EEEE ipa tie GMDD 6 C667 C698 2013 Interactive Comment BY iteration ste2. 2 2 vs 14 km is very interesting It deserves deeper investigation We agree that it is an interesting result but a deeper investigation is not in the scope of the article Petra Seibert C361 Discussion of error quantification at the end of Section 3 4 think one needs to define first which errors one wishes to quantify Investigation of differences between configurations has its justification Yes but we are not quite sure what we are supposed to change Petra Seibert C361 The word f hn can be written in lowercase like bora or mistral Most English language papers would spell foehn Note that mistral is spelt once with upper and once with lowercase And bora features interestingly are not discussed in the case study although present We used F hn whenever f hn winds along the Alpine ridge are considered in order to discriminate from the general term f hn used for warm downslope winds in general However we realized that is not common in literature and therefore we will change the spelling in the revised verison Petra Seibert C362 Section 3 3 list of variables which is written out probably is not specific to case study so it does not belong to Section 3 C688 GMDD 6 C667 C698 2013 Interactive Comment BY The list of variables written to the output file can be chosen by the user and therefore can vary from case study to case study depending on the focus of the study This is already mentioned in
3. Harr P A and Weissmann M The impact of Typhoon Jangmi 2008 on the midlatitude flow Part l Upper level ridgebuilding and modification of the jet Q J R Meteorol Soc doi 10 1002 qj 2091 2013 Gross G Vogel H and Wippermann F Dispersion over and around a steep obsta cle for varying thermal stratification numerical simulations Atmospheric Environment 21 483 490 1987 C691 GMDD 6 C667 C698 2013 Interactive Comment BY Kogan Y L Large eddy simulation of air parcels in stratocumulus clouds Time scales and spatial variability J Atmos Sci 63 952 967 2006 Lefohn A S Wernli H Shadwick D Limbach S Oltmans S J and Shapiro M Importance of stratospheric tropospheric transport in affecting surface ozone concentrations in the western and northern tier of the United States Atmospheric Environment 45 4845 4857 2011 Schemm S Wernli H and Papritz L Warm conveyor belts in idealized moist baroclinic wave simulations J Atmos Sci 70 627 652 2013 Seibert P Convergence and accuracy of numerical methods for trajectory calcula tions J Appl Meteorol 32 558 566 1993 Sodemann H Schwierz C and Wernli H Interannual variability of Greenland winter precipitation sources Lagrangian moisture diagnostic and North Atlantic Oscillation influence J Geophys Res 113 D03107 doi 10 1029 2007JD008503 2008 Stern D P and Zhang F How does the e
4. a big gain in physical accuracy if nontheless trajectories are interpreted as coherent air parcels over several days Therefore what miss is a more thorough discussion of the influence of diffusive processes Results of this module might be misleading for e g applications in high resolution dispersion modeling What is the advantage of doing online trajectories when one could use artificial tracers in the model to simulate advection and diffusion simultaneously Ulrich Blahak C198 While this may justify publication in GMD the comparatively simple numerical implementation e g no turbulent fluctuations on the trajectories could have some implications for some applications like dispersion modeling or analysis of strongly turbulent flows in convective clouds This fact should be elaborated more in the paper Ulrich Blahak C199 Consequences of the neglect of diffusive processes As men tioned above please add in section 1 and or in section 4 at places where you think it is appropriate short discussions on the influence of turbulent diffusive processes and the consequences if these are neglected and if the trajectories are interpreted as coherent air parcels over long times Discuss which kind of applications at which spatial temporal scales potentially could suffer from this neglect and to what extent One example of a paper applying an autoregressive Markov process to represent turbulent fluctuations on trajectories for high res
5. e P 1227 line 28 start new paragraph before More recently e P 1229 line 3 Change Deutscher Wetterdienst to German Meteorological Service DWD e P 1237 line 11 The sentence It appears that sounds strange please change C690 GMDD 6 C667 C698 2013 Interactive Comment BY e P 1239 line 23 Because instead of As in addition Again we want to thank the referees for reading the article so carefully We will implement all of your notes on readability spelling etc References Bellasio R Scarpato S Bianconi R and Zeppa P APOLLO2 a new long range Lagrangian particle dispersion model and its evaluation against the first ETEX tracer release Atmospheric Environment 57 244 256 2012 Cirisan A Spichtinger P Luo B P Weisenstein D K Wernli H Lohmann U and Peter T Microphysical and radiative changes in cirrus clouds by geoengineering the stratosphere J Geophys Res doi 10 1002 jgrd 50388 2013 Fierro A O Simpson J LeMone M A Straka J M and Smull B F On how hot towers fuel the Hadley Cell An observational and modeling study of line organized convection in the equatorial trough from TOGA COARE J Atmos Sci 66 2730 2746 2009 Gheusi F and Stein J Lagrangian description of airflows using Eulerian passive tracers Q J R Meteorol Soc 128 337 360 2002 Grams C M Jones S C Davis C A
6. not used at which resolution vertical grid spacing min mean max We will add a few more lines on the used coordinate specification and the parameteri zations The pole of the rotated grid is at 47 5 N 171 5 E the model resolution for COSMO14 is 0 125 for COSMO7 0 0625 and for COSMO2 2 0 02 The spacing of C686 GMDD 6 C667 C698 2013 Interactive Comment BY the model levels ranges from approximately 16 m 13 m to 2800 m 1190 m with an average of 582 m 388 m for COSMO14 and COSMO7 COSMO2 2 The model top is at about 23 km Turbulence soil processes and radiation are parameterized in all simulations For the COSMO14 and COSMO7 runs the Tiedtke convection scheme is used to rep resent convection but for COSMO2 2 only shallow convection is parameterized A two moment microphysics parameterization with 6 hydrometeor classes is used Ulrich Blahak C201 202 Case study in section 3 P 1239 line 18 statement Therefore it would be desirable But you did just that And sticking to the rigorous definition of trajectories as the solution of the trajectory equation do not see an immediate alternative other than comparing to the best possible reference solution which you tried to achieve by online computations Yes you are probably right We will remove this sentence from the paper Petra Seibert C359 Repeatedly we find the wording from a reanalysis data set or a numerical weather pred
7. the grid spacing and hence is different from LES to NWP applications While it may be inappropriate or impossible to study deep convection with a Lagrangian parcel model in a NWP model that does not resolve convective processes it is justified in convection resolving models Lagrangian particle models have been specifically developed to investigate the C670 GMDD 6 C667 C698 2013 Interactive Comment BY dispersion of pollutants in the turbulent boundary layer where subgrid scale velocity variations are particularly important Outside of the planetary boundary layer turbu lence becomes less important and therefore the solution of Lagrangian particle models and Lagrangian parcel models should converge Online trajectories aim to represent the motion of air parcels as accurately as possible according to the resolved scale wind field Thereby the air parcels are not regarded as closed boxes but as permeable for subgrid scale motions which they do not aim to represent explicitely If the latter is the objective of a study then Lagrangian particle models must be used The differentiation between sub grid scale processes and the resolved wind is fundamental although it relates to different scales and processes for different model resolutions We acknowledge that it is important to discuss the difference between the two approaches in the paper together with their advantages and disadvantages for certain scientific questio
8. 698 2013 Interactive Comment BY al 2011 Cirisan et al 2013 Schemm et al 2013 and Grams et al 2013 3 Terrain intersecting trajectories Ulrich Blahak C198 The authors honestly highlight one remaining technical problem of their new online trajectory module namely that too many trajectories intersect the ground especially in mountaneous regions Currently this problem is mitigated by the standard method of simply reinitializing grouna hitting trajectories 10 m above the ground However the deeper reasons for this behaviour are not very well explained and this should be improved in the manuscript This is important for future users of the module to decide whether this fact is acceptable for their application or not Without beeing a detailed expert would presume that there can be found something in the literature on this topic Ulrich Blahak C 203 204 Issue with too many trajectories hitting the ground starting at p 1242 line 9 Although can follow your argument with linear interpolation smoothing the wind field presumably especially the vertical compontent and beeing responsible for curving down your example trajectories in figure 6 towards the surface the exact behaviour near the surface should depend on details of what is assumed for the wind field close to the surface and how this interplays with a possible violation of the vertical CFL criterion see above in this case with Az vert distance to
9. Geosci Model Dev Discuss 6 C667 C698 2013 Geoscientific 8 www geosci model dev discuss net 6 C667 201 3 3 Author s 2013 This work is distributed under the Creative Commons Attribute 3 0 License Model Development F D Discussions Interactive comment on An online trajectory module version 1 0 for the non hydrostatic numerical weather prediction model COSMO by A K Miltenberger et al A K Miltenberger et al annette miltenberger env ethz ch Received and published 29 May 2013 We thank both referees Ulrich Blahak and Petra Seibert for their extensive and very constructive reviews Both reviews were very useful for improving the module description as well as the discussion section of the paper As some aspects are discussed several times at different places in the two reviews we choose to bundle our reply to these comments C667 GMDD 6 C667 C698 2013 Interactive Comment BY 1 Neglect of diffusive processes Lagrangian parcel vs Lagrangian particle models Both referees allude to the aspect that our model does not consider subgrid scale turbulent processes for the calculation of the trajectories Ulrich Blahak C197 C 198 The authors strongly advocate the Lagrangian perspective also for very high resolution applications However diffusive processes are completely neglected in the new module Therefore it is questionable and will depend on the application if there is really
10. Wang and Xue 2012 trajectories based on one minute NWP output were em ployed to determine the origin of air parcels feeding initial convective cells The study investigates convective initiation cases associated with a cold front dryline system from the IHOP field project Fierro et al 2009 In idealized simulations of a nocturnal equatorial oceanic squall line online trajectories are used to investigate the hot tower hypothesis The study concludes based on the evolution of equivalent potential temperature and latent heating along the trajectories that most parcels experience mixing at low levels and that the associated loss of buoyancy is compensated by latent heat release from ice processes b Lagrangian parcel model applications with LES Yamaguchi and Randall 2012 This study of cloud top entrainment in ma rine stratocumulus boundary layer clouds employs a Lagrangian parcel tracking model online in a LES Though for this model a parameterization of sub gridscale velocities is available it is not used in the study as the authors found it to have negligible effect on the trajectories Stevens et al 1996 In this study of non precipitating stratocumulus clouds trajectory ensembles calculated with LES resolved winds were used as driving C672 GMDD 6 C667 C698 2013 Interactive Comment BY conditions for a microphysical parcel model Besides the illustration of the use fulness of the approach to investigate c
11. e CFL criterion etc Ulrich Blahak C201 Convergence criterion for the Petterssen Scheme As described in section 2 1 your scheme uses a fixed number of iterations for the Pet terssen Scheme The number of iterations required for convergence depends on the flow situation and the time step but we find that a default value of three iterations gives mostly satisfactory results However it is possible to alter this number via the namelist Here a convergence analysis of the fixpoint iteration would be helpful We propose to introduce as an alternative a termination criterion into the iteration so that the iteration stops if the trajectory increment Z ti 1 n 1 ti 1 from one step to the next falls be low a predefined threshold Then do a histogram after how many steps convergence was reached and mention if some instances did not converge at all i e iteration did not terminate after some maximum step number Thank you for this suggestion We performed the suggested analysis for the alpine flow casestudy The iteration stopped either after 50 iterations or if n ti 1 n 1 ti41 lt 0 1da Yn ti 1 Yn 1 tiz1 lt 0 1dy len ti 1 2n 1 ti41 lt 1m The prob ability distribution of the number of required iterations is shown in Fig 2 for the three spatial resolutions It is clearly visible that for all spatial resolutions used in the cas estudy three iterations are enough to receive a reasonably good convergence Mos
12. f the height difference of the trajectories between the southern and the northern side of the Alps and of the height of the trajectories on the southern side of the Alps L Jonine Ax 2 2km C Joniine Ax 7km online Ax 14km elevation change across the Alps m _Jonline ax 2 2km C Jotiine at 1h __ offline At 3h L Joftiiine At 6h 1000 0 elevation change across the Alps m 0 15 0 17 0 05 occurence frequency 0 500 1000 1500 2000 height south of the Alps m 0 15 0 1 0 05 occurence frequency 00 1500 2000 height south of the Alps m C698 GMDD 6 C667 C698 2013 Interactive Comment
13. for the sedimentation of hydrometeors if the vertical CFL criterion is violated and for the fast wave solver The trajectory time step is equal to the major time step of COSMO We will state this more clearly in section 2 1 Petra Seibert C360 Missing technical information presume that all is implemented in Fortran90 95 2003 it would be useful to explicitly say this Which implementation of the MPI library is used Also say at the beginning and in the abstract that it is an MPI distributed memory machine implementation The implementation is done in Fortran 90 as the entire COSMO model code We will state this in the introduction part of section 2 We use the implementation MPICH http Awww mpich org which will be added to the last line of section 2 2 Petra Seibert C362 Section 3 2 last line The jump flag needs to be explained by the way the wording is misleading it is not so much a flag indicator but rather an algorithmic feature The jump flag is already explained at the end of section 2 1 We refer to this feature of the algorithm as jump flag because it can be switched on and off by switch in the namelist In LAGRANTO it was an additional parameter in the call of the program and therefore a flag 6 Numerical costs Petra Seibert C360 Section 2 2 It would be very helpful to have a better idea of the numerical costs of the trajectories before this discussion but it comes only in Section 3 It is
14. g 1 Composite of the surface elevation trajectory height and lowest model level for all terrain intersecting trajectories in the COSMO7 simulation of our alpine case study C694 GMDD 6 C667 C698 2013 Interactive Comment 8 BY frequency of occurrence 10 Ax 14km Ax 7km Ax 2km 4 oF 107 10 0 10 number of iterations Fig 2 Distribution of the required number of iterations until the trajectory position changes less than one tenth of the horizontal gridspacing and 1m in the vertical C695 GMDD 6 C667 C698 2013 Interactive Comment GMDD 6 C667 C698 2013 10 Ax 14km Interactive Ax 7km Comment 2 g 10 F Phi Ax 2km C D 3 10 fo io S 10 5 o Dad QF T gt 10 10 aaao 10 10 10 vertical Courant number Fig 3 Distribution of occurrence of vertical Courant numbers during all iterations C696 Fig 4 The map shows potential vorticity on 320 K colours in pvu and sea level pressure blue contours every 2 hPa at 1800 UTC 26 July 1987 from the COSMO14 simulation C697 GMDD 6 C667 C698 2013 Interactive Comment BY kal a 2 e o D 0 04 occurence frequency nm 0 1 0 08 0 06 2 ro occurence frequency 2 fo N Fig 5 Histogram o
15. he gridspacing and the advection velocity the variation in a finite size box is well captured by the parcel model If subgrid scale variations and according timescales are the focus of the study then of course Lagrangian particle dispersion models are the tool of choice Note that then a much larger number of particles must be calculated compared to the number of parcels with our approach in order to statistically sample the subgrid scale variations For instance as illustrated in the Stevens et al 1996 study on timescales in non precipitating stratocumulus clouds a microphysical boxmodel driven with a Lagrangian parcel model may have problems at cloud edges as warming and drying rates of individual parcels may be too strong due to the neglect of subgrid scale variations in humidity and temperature Nevertheless parcel models are successfully used in the literature for Lagrangian analyses of LES simulations e g Yeo and Romps 2013 In contrast to LPDM they allow to study the influence of non resolved mixing be it from parameterizations or numerical diffusion on the mean properties of air parcels In addition as Yeo and Romps 2013 pointed out air parcel trajectories ensure a constant mass of dry air associated with the trajectory while this is not the case if subgrid scale velocities are additionally taken into account In addition it is important to keep in mind that the represented processes using mean wind trajectories strongly depend on
16. hitting the ground see below Which boundary conditions are assumed in other trajectory schemes from the literature We extrapolate the horizontal wind velocity below the lowest model level with the same algorithm used to determine the lower boundary condition for the vertical velocity in the dynamical core of COSMO Namely the velocity at some height z below the lowest model level is calculated by linear extrapolation of the difference between the two lowest model levels We will add this information in section 2 1 Ulrich Blahak C199 Please specify somewhere here that the COSMO model uses a C679 GMDD 6 C667 C698 2013 Interactive Comment BY staggered Arakawa C grid and is formulated in terrain following and rotated spherical coordinates because this is important for the spatial interpolation procedure and the portability of the module to other NWP or climate models We will add a sentence in the description of the COSMO model including these details In addition we add a paragraph on the portability of the module in section 2 Ulrich Blahak C199 At the end of this secion you mention the trace variables but this important part of the module is not explained further Please add a short paragraph on this aspect and on its applications starting perhaps on p 1229 line 8 Paragraph will be added Ulrich Blahak C204 Discussion on the properties of the new module and possible enhancements in the future You me
17. iction model This is a bit strange as reanalyses are carried out with NWP models see three categories operational forecasts operational analyses and reanalyses Yes of course that is true Will be changed to re analysis data set or a forecast Petra Seibert C359 Page 1226 error source 3 Wind field errors are not only due to prediction errors Also the initial condition contains errors One may also wish to either mention here or in a separate item the representativity error between wind field represented in the model and present in Nature The error source you describe here is actually what we meant with our point 3 of the list of error sources Petra Seibert C359 Page 1226 error source 4 don t understand this point and also C687 GMDD 6 C667 C698 2013 Interactive Comment BY not how this would depend on the forecasting system This error source is only relevant if point observations shall be compared to modeling results As the trajectory starting point e g the release location of a pollutant is often not exactly known or because there are differences between model and real topography discrepancies between observations and model results may occur However because this point is not important for the following discussion we will remove it in the revised version of the manuscript Petra Seibert C360 361 Figure 4 The result that transport differences are very similar for 2 2 vs 7 km and
18. l does not consider diffusive processes but this is also not the goal of our study For applications like dispersion modeling there are other better tools and methods like Lagrangian particle dispersion models and passive tracer models which aim to represent subgrid scale processes In the following we refer to trajectory models neglecting diffusive processes as Lagrangian parcel models while those representing subgrid scale velocity variations are named Lagrangian particle dispersion models LPDMs The two approaches Lagrangian parcel and particle dispersion models have different strengths and weaknesses and are therefore suitable to investigate different scientific questions Therefore we agree with the second referee Petra Seibert that the Lagrangian parcel model approach has its validity also for high resolution modeling and even LES C669 GMDD 6 C667 C698 2013 Interactive Comment BY The Lagrangian parcel model represents the average properties of an air parcel with a typical volume of a grid cell The motion of such an air parcel represent the mean of a particle plume starting within a grid box in a Lagrangian particle model As noted for instance by Stevens et al 1996 and utilized in trajectory based moisture source diagnostics Sodemann et al 2008 the time average result of mixing is represented on the scale of gridboxes along parcel trajectories Therefore on temporal scales that are in agreement with t
19. necessary to give at least some more information here It is not clear immediately why the simple trajectory integration should contribute significantly to the computational resources compared to the integration of a comprehensive NWP model C681 GMDD 6 C667 C698 2013 Interactive Comment BY Petra Seibert C360 Section 3 3 discussion of performance don t know whether it is justified to discuss the performance with a single case study Please explain if and why If not more case studies need to be done no need to discuss them in detail just for quantifying performance The relative runtime or runtime increase should be evaluated also as a function of the number of trajectories This will be important for future users As we performed only this one case study so far it is hard to make a general statement on the computational costs of the online trajectory calculation Because the perfor mance depends strongly on the number of trajectories the number of traced variables and also on the setup of the Eulerian part of the model we shifted the discussion of performance to section 3 The numerical costs of the trajectory calculation do actually not result from the trajec tory integration itself as this is really comparatively simple compared to the integration of the NWP model but has mainly three sources e Writing of output files COSMO has no asynchronous output so far and in addition all output is written by one p
20. ns As suggested we will add a note in the introduction and an additional paragraph on this issue in the discussion section 2 Representativity of literature in the introduction section Ulrich Blahak C 196 197 All in all the authors reference an adequate quantity of liter ature concerning applications in synoptic meteorology which is their field of expertise There are less citations of the more technical aspects of trajectory calculations as well as of applications in other fields like lagrangian dispersion modeling For the scope of this paper this should however be fine Petra Seibert C359 The list of possible applications of Lagrangian trajectory based analyses is obviously only meant to give some illustrations but in the light of my re marks above on applicability of this specific high resolution trajectory model they may want to give more consideration specifically to high resolution applications We will include a few more references on high resolution applications Specifically we C671 GMDD 6 C667 C698 2013 Interactive Comment BY want to include the following studies in the introduction as examples how trajectories have been successfully used in high resolution models a Lagrangian parcel model applications in high resolution NWP models Stern et al 2013 investigated the motion of parcels inside the eye of an ideal ized hurricane by calculating trajectories based on one to six minute NWP output
21. ntion that you apply tri linear interpolation in space p 1230 line 23 and this is perfectly fine presume this means that the interpolation is done between the 8 neighbours of an interpolation point in a way that horizontal interpolations in i and j direction are performed along the terrain following coordinates which is both efficient and accurate If such details would have been mentioned in the text things would be more easy to understand You could incorporate this into the required new description of the lower boundary conditions see above Yes the interpolation is performed along the terrain following coordinates We will add this in the description of the interpolation procedure Petra Seibert C360 Time step In section 3 2 time step durations are stated Are they specific to the case study If not move them up How is the time step determined in COSMO Are there different time steps for different processes How do they relate to the trajectory time step All this should be in Section 2 The time step for COSMO is specified by the user it depends on the grid spacing used and on the application In that sense the time step is specific for the case study though the values used here are the standard ones used at MeteoSwiss for the respective C680 GMDD 6 C667 C698 2013 Interactive Comment BY spatial resolution For some subroutines the time step is split into smaller steps For instance this applies
22. of height change across the Alpine ridge and of height south of the Alps are shown The general picture does not change compared to the non normalized distributions Therefore we want to stick with the non normalized figures in the paper C689 GMDD 6 C667 C698 2013 Interactive Comment BY 10 Other issues Petra Seibert C362 Some Figures are quite small hope they will appear larger in the final version Especially the legend inset of Fig 4 is much too small at print scale printer friendly version Petra Seibert C362 Same page shut on off write switch on off Petra Seibert C362 Starting a new paragraph with line 19 on page 1234 would improve the readability number of trajectories is important Petra Seibert C362 Page 1236 bottom The symbol for the number should be N instead of n to be consistent with the equation on p 1237 You are using three levels of round brackets you could use curly square round or a root symbol instead of the outermost brackets Ulrich Blahak C205 3 Technical corrections e COSMO COnsortium for Small scale MOdeling the model s correct name is COSMO model Please check everywhere e Please cite the COSMO model when it is first referenced There is a newer ref erence M Baldauf et al 2011 Operational convective scale numerical weather prediction with the COSMO model description and sensitivities Mon Wea Rev DOI 10 1175 MWR D 10 05013 1
23. olution Monte Carlo dispersion model ing would be Gross H Vogel F Wippermann 1987 Dispersion over and around a C668 GMDD 6 C667 C698 2013 Interactive Comment BY steep obstacle for varying thermal stratification numerical simulations Atmospheric Environment Volume 21 Pages 483 490 Petra Seibert C 358 Another reviewer has questioned the value of mean wind trajectories at the spatial scale covered by the model Also the authors allude to this issue in their discussion of the behaviour near ground My opinion is that a trajectory model this is the term that am using for a mean wind based model as opposed to a Lagrangian particle model which would simulate also the effects of subgrid scale motions does have its place also at high resolution even at LES scale as it allows to investigate atmospheric motion patterns represented explicitly in the model in a way that cannot be achieved e g by a Eulerian tracer carried unless a number of tracer species is used which is the same as the number of trajectories but even then diffusive properties of the numerical integration would deteriorate the result However think the authors could invest some additional work to include a survey of possible application types the set ups related to them and their merits and shortcomings This would be a significant benefit for users beyond their own group and enhance the value of the paper It is true that our trajectory mode
24. p is given by n ti 1 Z ti Atu x ti ti U n 1 ti41 ti 1 z which equals your second through n th equation on page 1230 The convergence properties of such an iteration depend on the properties of the flow field and the starting value In your case the starting value has been simply chosen as w z t t so that your Eq 1 is recovered However you would be basically free to choose different starting values For example near the ground amp To ti 1 ti 1 0 could help to reduce the problem of terrain hitting trajectories during the first iteration step We will change the naming of the numerical procedure We thank the reviewer for offering an alternative description of the scheme but since we regard our original presentation more intuitive we decided not to change it The result of both derivations is equivalent Ulrich Blahak C200 201 Detailed specification of the lower boundary condition s miss a detailed specification of the lower boundary condition s for computing the linear spatial interpolations of the velocity components near the ground These are decisive for the behaviour of trajectories near the ground and should be clearly mentioned so that future users may decide on the applicability of the module for their specific application Add a paragraph in section 2 1 or an own subsection whichever you feel Details of these lower boundary conditions could also be responsible for the problem of too many trajectories
25. ple in the original paper C675 GMDD 6 C667 C698 2013 Interactive Comment BY it supports our original hypothesis that the majority of ground intersections occur due to errors introduced by spatial horizontal interpolation Reducing the time step of the trajectory integration so strongly likely leads to a more frequent detection of terrain intersections and therefore leads to an increased percentage of terrain hitting trajecto ries The hypothesis linking the ground intersection to the spatial interpolation is also sup ported by our analysis of the vertical Courant number Fig 3 The vertical CFL criterium is never exceeded in the COSMO2 2 and COSMO14 simulations and in the COSMO7 simulation only very rare exceedances are registered Ulrich Blahak C204 On p 1243 starting in line 5 some possibilities for mitigating this problem are shortly mentioned Perhaps you could elaborate a little more on the possible changes to the integration scheme close to the surface in addition to adding turbulent fluctuations Could these be e Alternative starting value for the Petterssen iteration see above e Sub timestepping near the ground so as to keep the vertical CFL lt 1 see above using suitable time interpolation of u e Changes to the lower boundary condition s We will include some discussion of such a modification of the integration scheme close to the surface Petra Seibert C361 am surprised that conside
26. ration of turbulence is offered as possible way to overcome the ground intersection problem don t see why this should be effective On the other hand this would totally change the character of the model and transform it from a trajectory model to a dispersion model This would be a big step in concept but also in terms of algorithm and code Introducing turbulent diffusion in only a part of the boundary layer if this is meant would be quite unphysical C676 GMDD 6 C667 C698 2013 Interactive Comment BY After the further investigations we did we agree that adding turbulence is not the solution to the problem We will remove this point from our suggestion list 4 Structure of module description Petra Seibert C358 However the description of the module should be made more detailed and better structured It would also be useful to better explain and maybe explore certain decisions and their consequences Petra Seibert C359 Module description have the following suggestions for improving e First summarise the algorithms used in LAGRANTO and clearly point out where additional details if not included can be found is the Wernli and Davies paper fully comprehensive If not add other source or add corresponding document as supplementary material e Then give an overview where the COSMO module deviates from the off line version e Finally give the details on the COSMO specific features Unfortunatel
27. ritical timescales for droplet growth the paper provides a discussion of the representation of entrainment and its effect on microphysical modeling Kogan 2006 This study used the approach of Stevens et al 1996 for drizzling stratocumulus clouds The in cloud residence time is found to be 2 5 times longer than for non drizzling stratocumulus indicating that cycling of air parcels inside the cloud is important for drizzle formation Yeo and Romps 2013 computed trajectories with the resolved wind to study entrainment rates and residence times in convective clouds c Lagrangian Particle Dispersion models e Bellasio et al 2012 described a long range Lagrangian particle dispersion model developed for simulating radioactive clouds The paper comprises a com parison to the ETEX tracer release experiment e Weil et al 2012 coupled an LPDM to a LES for investigation of plume dispersion in a convective planetary boundary layer e Gross et al 1987 Description of the simulation of pollutant dispersion from a point source around a steep obstacle Petra Seibert C361 Page 1229 am wondering whether there are no more recent applications of LAGRANTO than 2005 Of course there are numerous more recent applications of LAGRANTO but the list was meant to indicate the spectrum of applications for which it has been used But of course we can in addition name a few more recent papers as for instance Lefohn et C673 GMDD 6 C667 C
28. rocessor In case the trajectory position together with a potentially large number of trace variables is written to a file after every model time step this adds significantly to the runtime of the model e Communication between the processors for trajectories passing between do mains This strongly depends on the distribution of trajectories across the entire computational domain e Excessive interpolation of trace variables Of course we plan to do more case studies in the future but we think it is not worth to compute other case studies only for assessing the performance of the module This would also not be very useful because the performance depends on the architecture of the supercomputer and the number of other integrations running on the same C682 GMDD 6 C667 C698 2013 Interactive Comment BY machine As we cannot control these factors easily the runtime increases given in the article are only thought as a rough estimate In our case study the runtime increase seems to scale approximately linearly with the number of trajectories taking only half of the trajectories reduces the runtime increase by approximately a factor two Decreasing the number of traced variables by a factor two leads in our simulation to a reduction of the runtime increase by approximately a factor three This indicates that the runtime increase on our machine is strongly determined by IO 7 Numerical properties of the module Convergenc
29. rson algorithm is of second order the truncation error is proportional to At and hence small timesteps are leading to smaller truncation error As stated by Seibert 1993 the truncation error should be kept about one order of magnitude smaller than the total uncertainty which is hard to quantify but probably does not too strongly limit the timestep as other uncertainties are also large In addition it has been shown by Seibert 1993 that fulfilling the CFL criterion is important for a convergent solution This constrains the timestep as a function of the horizontal and vertical resolution of the wind field data Assuming a maximum wind speed of 50m s and a horizontal grid spacing of 100km the timestep has to be smaller than 2000s for a grid spacing of 14km smaller than 280s and for a grid spacing of 2km smaller than 40s 8 Source code availability and user manual Petra Seibert C358 GMD guidelines call for supplementary material such as codes and user manuals The authors should give some consideration to this issue and explain at least why they don t think that they can or want to attach such material It would also be important to state the conditions for using their module whether it will be included in COSMO in general etc We will submit a user manual with the revised version of this paper At the moment C685 GMDD 6 C667 C698 2013 Interactive Comment BY there are some vague plans to introduce the online trajec
30. sed version we will include a section in the module description with an extended discussion of the problem As promised below we will also include a description of the lower boundary condition and we will improve the de scription of our idealized example However we do not think that the lower boundary condition itself is causing the terrain intersection problem In the meanwhile we did some further analysis to pin down the problem of ground inter secting trajectories For all trajectories that hit the surface in the COSMO7 simulation of our case study the surface elevation as well as the height of the lowest model level are traced along the trajectories in the last 200 time steps before ground intersection In addition the surface elevation that would be beneath the trajectory if it continued in the same direction and speed as during the last timesteps before the terrain inter section was computed for the next 200 time steps From this data a composite of the surface elevation the lowest model level height and the trajectory height was derived by normalizing and averaging the data This composite shows the average surface elevation 200 time steps before the ground intersection and its extrapolated behavior for the 200 time steps after the ground intersection Fig 1 The distance that the trajectories travel during these about 400 time steps corresponds to approximately 3 to 6 grid points As this composite closely resembles our hypothetical exam
31. t C683 GMDD 6 C667 C698 2013 Interactive Comment BY cases that require more iterations do probably not converge at all since no conver gence was achieved even after 50 iterations Ulrich Blahak C202 203 In section 4 page 1241 starting with line 24 you discuss some challenges problems associated with online trajectories in general and your im plementation in particular This is a very important topic for any future user of the module Here suggest to add modify the following points To reproduce all flow features present in the Eulerian NWP model in the trajectories the time step for trajectory calculations should obey the CFL criterion of the Eulerian model Seibert 1990 For your online trajectories keep in mind that the model time step At only guarantees that the horizontal CFL criterion is fulfilled But the vertical CFL criterion may become an issue when strong updrafts occur close to the ground where the vertical grid spacing in NWP models is usually strongly reduced but not nec essarily only there The numerics of most NWP models is robust in that respect For example in the COSMO model a fully implicit second order vertical advection scheme is used which is stable for vertical Courant numbers exceeding 1 To mitigate this problem for online trajectories one could control the timestep by a suit able vertical CFL criterion and if necessary do a local sub timestepping for some of the trajectory calc
32. the general module description in line 26 on page 1229 So it is specific and therefore we think it is appropriate to keep it in Section 3 Petra Seibert C362 Figure 5 One would expect Az z t2 z t1 but it was defined the other way round We choose to define Az z t1 z t2 because then a positive Az is associated with a warming of the trajectories and hence can explain foehn air warming on the downwind side of the Alps Ulrich Blahak C205 3 Technical corrections Figure 5 Based on this figure find it sometimes hard to identify shape differences of the histograms especially in the lower left figure This is because the total number of Fohn trajectories sum over the histogram seems to be more or less different for the different configurations Is that true and if yes why is that so In any case it would be better to normalize the histograms by their total number of trajectories and to be mathematically correct also by the class width to obtain a proper estimate of the probability density functions Then it would be easier to compare the shapes of the distributions The total number of foehn trajectories varies from configuration to configuration as the trajectories are always started in the same starting region over the British Isle but from there do not necessarily follow the same track Therefore the number of trajectories crossing the Alps varies with the data set used for the analysis In Fig 5 the normalized distributions
33. the ground However do not understand figure 6 because of missing information What are the axis labels what is the grid spacing of the Eulerian framework 1000 X units as sug gested by the crosses on the orography line What is the online timestep resp the typical online travel distance during 1 timestep What exactly is the windfield you only mention in the figure caption that it is linear But at which value does it start at the surface All this information is necessary to understand why the online trajectory can hit the ground And I do not understand why it can continue below the surface Should it not end on impact i e when its position first falls below the orography during the C674 GMDD 6 C667 C698 2013 Interactive Comment BY Petterssen scheme iteration From this I conclude that the surface normal wind compontent does not go to 0 towards the ground and that there is an artificial non zero velocity below the surface so that the iteration may continue there and eventually may converge to a final position above the surface ls that true If yes how is this calculated Constant extrapolation from the lowest model level Petra Seibert C361 The ground intersection problem should not be introduced as the second last paragraph of the whole paper It belongs into the module description We agree that it is probably not best to discuss the ground intersection problem in the discussion section In the revi
34. tory module in a future official release of the COSMO model However for research purposes the authors are happy to provide the code upon request 9 Other issues Ulrich Blahak C201 202 Case study in section 3 Although the presented case study in section 3 has been treated extensively in the literature before a simple weather chart on the case e g 500 hPa geopoential and surface pressure or whatever the authors feel appropriate would be very helpful for the reader in section 3 1 This chart could be taken e g from the 14 km run and could also contain the outlines of the smaller model domain for the 2 2 km runs If you do the plot in rotated spherical coordinates you can easily make the connection to Fig 2 where you only plot all trajectories starting south of 8 5 rotated North We will include such a chart in the new version of the article Fig 4 Ulrich Blahak C201 202 Case study in section 3 In section 3 2 again mention the fact that the COSMO model employs rotated spherical coordinates and specify the coordinates of the rotated North pole perhaps before We employ in line 7 Mention also the true model resolutions in degrees not only in km Few people know the standard model setup of the Swiss weather service p 1234 line 7 For the sake of clarity it would be good to mention at least some main things about these setups which are not mentioned at the moment e g which parameteriza tions are used
35. ulations Doing a first quick calculation a suitable criterion could be something like _ ae At where Az is the local vertical grid spacing w the vertical velocity the horizontal wind vector and VH 2 y the orography H gradient in local flow direction wl A t tand lt w lt N tand This is an interesting idea that would guarantee that on all occasions the trajectory timestep also fulfils the vertical CFL criterion which is of course important for numer ical stability However we think it is not really urgent to implement such a criterion and or a sub timestepping since in our case study the vertical Courant number remained smaller than 1 in almost all iterations of all timesteps in the COSMO14 and C684 GMDD 6 C667 C698 2013 Interactive Comment BY COSMO2 2 simulations Fig 3 For COSMO7 probably a time step of 40 seconds i e the same as the timestep of COSMO14 is not really appropriate as this leads to exceedance of the vertical CFL criterion in some rare cases We will implement a warning that is written to the logfile in case the vertical CFL criterion is hurt together with the number of the affected trajectory The user can than decide to either rerun the simulation with a smaller timestep or to exclude the trajectory from further analysis Petra Seibert C361 Page 1227 would not say that the Petterson algorithm requires specifically a short time step As the Pette
36. y though not fully comprehensive the Wernli and Davies paper is the only and latest technical reference for LAGRANTO However we describe all essential algorithms used in the section Physical Core There the numerical procedure to integrate the trajectory equation and the interpolation method are described This section corresponds to the first section suggested by Petra Seibert The COSMO module only deviates from the LAGRANTO algorithms in not using a temporal interpolation and in being parallelized see section Parallelization and Communication Both of these issues are discussed in the paper There are little COSMO specific features The code developed for this project should be applicable C677 GMDD 6 C667 C698 2013 Interactive Comment BY to any NWP model that has a spatial domain decomposition for the parallelization Only the technical details of writing the output file addressing of variables as well as probably the input structure have to be slightly adapted We will make this clearer in the revised paper Petra Seibert C360 Section 2 3 would call this selection of trajectory starting points instead of initialisation The fact that back trajectories are not easily possible for on line calculation needs to explained already in the introduction and then be discussed in the Section on applications that propose disagree with the statement that this limitation slightly complicates
37. ye warm Part Il Sensitivity to vertical wind shear and a trajectory analysis J Atmos Sci 2013 70 73 90 Stevens B Feingold G Cotton W R and Walko R L Elements of the microphys ical structure of numerically simulated nonprecipitating stratocumulus J Atmos Sci 53 980 1006 1996 Wang Q W and Xue M Convective initiation on 19 June 2002 during IHOP High resolution simulations and analysis of the mesoscale structures and convective initiation J Geophys Res 117 D12107 doi 10 1029 2012JD017552 2012 Weil J C and Sullivan P P Patton E G and Moeng C H Statistical variability of dispersion in the convective boundary layer Ensembles of simulations and observa tions Boundary Layer Meteorol 145 185 210 2012 C692 GMDD 6 C667 C698 2013 Interactive Comment BY Yamaguchi T and Randall D A Cooling of entrained parcels in a large eddy simulation J Atmos Sci 69 1118 1136 2012 GMDD Yeo K and Romps D M Measurement of convective entrainment using Lagrangian 6 C667 C698 2013 particles J Atmos Sci 70 266 277 2013 Interactive Comment Interactive comment on Geosci Model Dev Discuss 6 1223 2013 C693 0 8 0 6 0 4 normalized height 0 2 Zur taj 7 Z lowest model level 0 i i i 200 150 100 50 0 50 100 150 200 timestep relative to terrain intersection Fi
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