<html><head><meta http-equiv="Content-Type" content="text/html; charset=utf-8"></head><body style="word-wrap: break-word; -webkit-nbsp-mode: space; line-break: after-white-space;" class="">Hi Lily,<div class=""><br class=""></div><div class="">That’s very interesting. Just out of interest, did you define all of the flags?</div><div class=""><br class=""></div><div class="">Martin<br class=""><div><br class=""><blockquote type="cite" class=""><div class="">On 19. Apr 2022, at 12:53, Lily Greig <<a href="mailto:l.greig@pgr.reading.ac.uk" class="">l.greig@pgr.reading.ac.uk</a>> wrote:</div><br class="Apple-interchange-newline"><div class=""><meta charset="UTF-8" class=""><div style="font-style: normal; font-variant-caps: normal; font-weight: 400; letter-spacing: normal; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; word-spacing: 0px; -webkit-text-stroke-width: 0px; text-decoration: none; font-family: Calibri, Arial, Helvetica, sans-serif; font-size: 12pt;" class="">Hi Martin, </div><div style="font-style: normal; font-variant-caps: normal; font-weight: 400; letter-spacing: normal; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; word-spacing: 0px; -webkit-text-stroke-width: 0px; text-decoration: none; font-family: Calibri, Arial, Helvetica, sans-serif; font-size: 12pt;" class=""><br class=""></div><div style="font-style: normal; font-variant-caps: normal; font-weight: 400; letter-spacing: normal; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; word-spacing: 0px; -webkit-text-stroke-width: 0px; text-decoration: none; font-family: Calibri, Arial, Helvetica, sans-serif; font-size: 12pt;" class="">An update on this which could be of interest. With the updated code and using the KPP regularisation you suggested below, there is noticeable smoothing of the noise in the flow fields of the simulation. <span style="margin: 0px; font-size: 12pt;" class=""><span style="margin: 0px; background-color: rgb(255, 255, 255);" class="">I'm attaching 2D Y-Z snapshots of the flow fields, with (left) and without (right) the regularisation</span><span style="margin: 0px; background-color: rgb(255, 255, 255);" class="">. It is a clean comparison so there are no other changes between the simulations other than these suggested regularisations (</span><span style="margin: 0px; background-color: rgb(255, 255, 255);" class="">both simulations use viscosity vicA4Grid=0.01 as per your previous suggestion). </span></span><br class=""><span style="margin: 0px; font-size: 12pt;" class=""></span></div><div style="font-style: normal; font-variant-caps: normal; font-weight: 400; letter-spacing: normal; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; word-spacing: 0px; -webkit-text-stroke-width: 0px; text-decoration: none; font-family: Calibri, Arial, Helvetica, sans-serif; font-size: 12pt;" class=""><br class=""></div><div style="font-style: normal; font-variant-caps: normal; font-weight: 400; letter-spacing: normal; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; word-spacing: 0px; -webkit-text-stroke-width: 0px; text-decoration: none; font-family: Calibri, Arial, Helvetica, sans-serif; font-size: 12pt;" class="">The smoothing is most obvious in the Northern half of the domain, which is initially sea-ice covered (Southern half initially open ocean). Although there is also ice forming over time in the initially open ocean, the regularisation has less of an impact here. </div><div style="font-style: normal; font-variant-caps: normal; font-weight: 400; letter-spacing: normal; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; word-spacing: 0px; -webkit-text-stroke-width: 0px; text-decoration: none; font-family: Calibri, Arial, Helvetica, sans-serif; font-size: 12pt;" class=""><br class=""></div><div style="font-style: normal; font-variant-caps: normal; font-weight: 400; letter-spacing: normal; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; word-spacing: 0px; -webkit-text-stroke-width: 0px; text-decoration: none; font-family: Calibri, Arial, Helvetica, sans-serif; font-size: 12pt;" class="">It was also noted that it seems that the appearance of noise is in general is related to the onset of sea ice formation. </div><div style="font-style: normal; font-variant-caps: normal; font-weight: 400; letter-spacing: normal; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; word-spacing: 0px; -webkit-text-stroke-width: 0px; text-decoration: none; font-family: Calibri, Arial, Helvetica, sans-serif; font-size: 12pt;" class=""><br class=""></div><div style="font-style: normal; font-variant-caps: normal; font-weight: 400; letter-spacing: normal; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; word-spacing: 0px; -webkit-text-stroke-width: 0px; text-decoration: none; font-family: Calibri, Arial, Helvetica, sans-serif; font-size: 12pt;" class="">Best wishes, </div><div style="font-style: normal; font-variant-caps: normal; font-weight: 400; letter-spacing: normal; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; word-spacing: 0px; -webkit-text-stroke-width: 0px; text-decoration: none; font-family: Calibri, Arial, Helvetica, sans-serif; font-size: 12pt;" class=""><br class=""></div><div style="font-style: normal; font-variant-caps: normal; font-weight: 400; letter-spacing: normal; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; word-spacing: 0px; -webkit-text-stroke-width: 0px; text-decoration: none; font-family: Calibri, Arial, Helvetica, sans-serif; font-size: 12pt;" class="">Lily</div><div id="appendonsend" style="caret-color: rgb(0, 0, 0); font-family: Helvetica; font-size: 12px; font-style: normal; font-variant-caps: normal; font-weight: 400; letter-spacing: normal; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; word-spacing: 0px; -webkit-text-stroke-width: 0px; text-decoration: none;" class=""></div><hr tabindex="-1" style="caret-color: rgb(0, 0, 0); font-family: Helvetica; font-size: 12px; font-style: normal; font-variant-caps: normal; font-weight: 400; letter-spacing: normal; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; word-spacing: 0px; -webkit-text-stroke-width: 0px; text-decoration: none; display: inline-block; width: 1025.078125px;" class=""><span style="caret-color: rgb(0, 0, 0); font-family: Helvetica; font-size: 12px; font-style: normal; font-variant-caps: normal; font-weight: 400; letter-spacing: normal; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; word-spacing: 0px; -webkit-text-stroke-width: 0px; text-decoration: none; float: none; display: inline !important;" class=""></span><div id="divRplyFwdMsg" dir="ltr" style="caret-color: rgb(0, 0, 0); font-family: Helvetica; font-size: 12px; font-style: normal; font-variant-caps: normal; font-weight: 400; letter-spacing: normal; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; word-spacing: 0px; -webkit-text-stroke-width: 0px; text-decoration: none;" class=""><font face="Calibri, sans-serif" style="font-size: 11pt;" class=""><b class="">From:</b><span class="Apple-converted-space"> </span>Lily Greig <<a href="mailto:l.greig@pgr.reading.ac.uk" class="">l.greig@pgr.reading.ac.uk</a>><br class=""><b class="">Sent:</b><span class="Apple-converted-space"> </span>10 March 2022 10:44<br class=""><b class="">To:</b><span class="Apple-converted-space"> </span><a href="mailto:mitgcm-support@mitgcm.org" class="">mitgcm-support@mitgcm.org</a><span class="Apple-converted-space"> </span><<a href="mailto:mitgcm-support@mitgcm.org" class="">mitgcm-support@mitgcm.org</a>><br class=""><b class="">Subject:</b><span class="Apple-converted-space"> </span>Re: [MITgcm-support] Noise in vertical velocity field with ocean cooling/sea ice</font><div class=""> </div></div><div dir="ltr" style="caret-color: rgb(0, 0, 0); font-family: Helvetica; font-size: 12px; font-style: normal; font-variant-caps: normal; font-weight: 400; letter-spacing: normal; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; word-spacing: 0px; -webkit-text-stroke-width: 0px; text-decoration: none;" class=""><div style="font-family: Calibri, Arial, Helvetica, sans-serif; font-size: 12pt;" class="">Hi Martin, </div><div style="font-family: Calibri, Arial, Helvetica, sans-serif; font-size: 12pt;" class=""><br class=""></div><div style="font-family: Calibri, Arial, Helvetica, sans-serif; font-size: 12pt;" class="">Indeed, the problem persists without KPP! </div><div style="font-family: Calibri, Arial, Helvetica, sans-serif; font-size: 12pt;" class=""><br class=""></div><div style="font-family: Calibri, Arial, Helvetica, sans-serif; font-size: 12pt;" class="">Ah yes, my code is a couple of years old, so did not have these updates. Thanks. </div><div style="font-family: Calibri, Arial, Helvetica, sans-serif; font-size: 12pt;" class=""><br class=""></div><div style="font-family: Calibri, Arial, Helvetica, sans-serif; font-size: 12pt;" class="">Best wishes, </div><div style="font-family: Calibri, Arial, Helvetica, sans-serif; font-size: 12pt;" class=""><br class=""></div><div style="font-family: Calibri, Arial, Helvetica, sans-serif; font-size: 12pt;" class="">Lily </div><div id="x_appendonsend" class=""></div><hr tabindex="-1" style="display: inline-block; width: 1025.078125px;" class=""><div id="x_divRplyFwdMsg" dir="ltr" class=""><font face="Calibri, sans-serif" style="font-size: 11pt;" class=""><b class="">From:</b><span class="Apple-converted-space"> </span>MITgcm-support <<a href="mailto:mitgcm-support-bounces@mitgcm.org" class="">mitgcm-support-bounces@mitgcm.org</a>> on behalf of Martin Losch <<a href="mailto:Martin.Losch@awi.de" class="">Martin.Losch@awi.de</a>><br class=""><b class="">Sent:</b><span class="Apple-converted-space"> </span>08 March 2022 15:55<br class=""><b class="">To:</b><span class="Apple-converted-space"> </span>MITgcm Support <<a href="mailto:mitgcm-support@mitgcm.org" class="">mitgcm-support@mitgcm.org</a>><br class=""><b class="">Subject:</b><span class="Apple-converted-space"> </span>Re: [MITgcm-support] Noise in vertical velocity field with ocean cooling/sea ice</font><div class=""> </div></div><div class="x_BodyFragment"><font size="2" class=""><span style="font-size: 11pt;" class=""><div class="x_PlainText">Hi Lily,<br class=""><br class="">viscA4Grid=0.5 is clearly too high to be useful.<br class=""><br class="">Do you have these issues also without KPP?<br class=""><br class="">Are you using more or less recent code? The KPP flags are all described in the pkg/kpp/KPP_OPTIONS.h file (in fact I just copy-pasted them from there into the email).<br class=""><br class="">Martin<br class=""><br class="">> On 8. Mar 2022, at 16:31, Lily Greig <<a href="mailto:l.greig@pgr.reading.ac.uk" class="">l.greig@pgr.reading.ac.uk</a>> wrote:<br class="">><span class="Apple-converted-space"> </span><br class="">> Hi Martin & all,<span class="Apple-converted-space"> </span><br class="">><span class="Apple-converted-space"> </span><br class="">> Thanks very much for your help, I have tried your suggestions however am still unfortunately having the noise issues, so am just prying for any further thoughts. I forgot to mention in my original email, but I am using a 2D set-up here (Nx=1), although an analogous 3D set-up with eddies also has noise.<span class="Apple-converted-space"> </span><br class="">><span class="Apple-converted-space"> </span><br class="">> Following your recommendations with viscA4Grid, what I found is a similar picture to my previous experiments, in that I had to increase the value of viscA4Grid a lot, from 0.01 up to around 0.5 in order for the noise in the vertical velocity field to reduce. At such high values of viscosity, the zonal jet is also damped an undesirable amount.<span class="Apple-converted-space"> </span><br class="">><span class="Apple-converted-space"> </span><br class="">> I have tried your suggestions with viscC2leith+D which also didn't reduce the noise much. I also ran using non-hydrostatic dynamics, which made only a very small difference to the noise.<br class="">><span class="Apple-converted-space"> </span><br class="">> Also just to mention for the KPP options you described, I could not find a KPP_SCALE_SHEARMIXING flag anywhere in the code.<span class="Apple-converted-space"> </span><br class="">><span class="Apple-converted-space"> </span><br class="">> If you did have any further recommendations, it would be great to hear. Thanks a lot.<span class="Apple-converted-space"> </span><br class="">><span class="Apple-converted-space"> </span><br class="">> Best wishes,<span class="Apple-converted-space"> </span><br class="">><span class="Apple-converted-space"> </span><br class="">> Lily<span class="Apple-converted-space"> </span><br class="">> From: Lily Greig <<a href="mailto:l.greig@pgr.reading.ac.uk" class="">l.greig@pgr.reading.ac.uk</a>><br class="">> Sent: 17 February 2022 18:02<br class="">> To:<span class="Apple-converted-space"> </span><a href="mailto:mitgcm-support@mitgcm.org" class="">mitgcm-support@mitgcm.org</a><span class="Apple-converted-space"> </span><<a href="mailto:mitgcm-support@mitgcm.org" class="">mitgcm-support@mitgcm.org</a>><br class="">> Subject: Re: [MITgcm-support] Noise in vertical velocity field with ocean cooling/sea ice<br class="">> <span class="Apple-converted-space"> </span><br class="">> Thank you Martin,<span class="Apple-converted-space"> </span><br class="">><span class="Apple-converted-space"> </span><br class="">> I will give this a try :)<span class="Apple-converted-space"> </span><br class="">><span class="Apple-converted-space"> </span><br class="">> Best wishes,<span class="Apple-converted-space"> </span><br class="">><span class="Apple-converted-space"> </span><br class="">> Lily<span class="Apple-converted-space"> </span><br class="">><span class="Apple-converted-space"> </span><br class="">> From: MITgcm-support <<a href="mailto:mitgcm-support-bounces@mitgcm.org" class="">mitgcm-support-bounces@mitgcm.org</a>> on behalf of Martin Losch <<a href="mailto:Martin.Losch@awi.de" class="">Martin.Losch@awi.de</a>><br class="">> Sent: 17 February 2022 17:31<br class="">> To: MITgcm Support <<a href="mailto:mitgcm-support@mitgcm.org" class="">mitgcm-support@mitgcm.org</a>><br class="">> Subject: Re: [MITgcm-support] Noise in vertical velocity field with ocean cooling/sea ice<br class="">> <span class="Apple-converted-space"> </span><br class="">> Hi Lily,<br class="">><span class="Apple-converted-space"> </span><br class="">> hydrostatic simulations will always have noise issues in the vertical velocity (as the vertical velocity is the vertical integral of the horizontal velocity divergence, so any noise accumulates, and C-grids tend to have noisy horizontal fields), unless you have very smooth horizontal velocities.<br class="">><span class="Apple-converted-space"> </span><br class="">> I would use viscA4Grid to tune this noise away, also I would use a smaller viscAXGridMax of maybe 0.5 (1 is the limit; X=h,4). I wouldn’t use smag and leigth simultaneously, as the do the same thing, also the Smagorinsky parameterisation is for 3D isotropic turbulence, which you don’t have in your set up.<span class="Apple-converted-space"> </span><br class="">> I suggest to start with this:<br class="">><span class="Apple-converted-space"> </span><br class="">> # viscC4leith = 2,<br class="">> #viscC4leithD = 2,<br class="">> viscA4Grid = 0.01,<br class="">> viscA4GridMax = 0.5,<br class="">> # only necessary if you use harmonic viscosity<br class="">> viscAhGridMax = 0.5,<br class="">><span class="Apple-converted-space"> </span><br class="">> and vary viscA4Grid until you are happy. Alternatively I would try viscC2leith+D in addition to constant backround (or you can use viscC2leith+D = 2 + viscAhMin = 0.01.)<br class="">><span class="Apple-converted-space"> </span><br class="">> A trick is to use non-hydrostatic dynamics (with very few cg3d iterations O(40) to not make too expensive), because that introduces horizontal viscosity for vertical velocity.<br class="">><span class="Apple-converted-space"> </span><br class="">> There are a few regularization in KPP, but in experience they don’t do much, but maybe worth a try:<br class="">><span class="Apple-converted-space"> </span><br class="">> # personally, I think this should be default, but it isn't<br class="">> C o reduce shear mxing by shsq**2/(shsq**2+1e-16) according to<br class="">> C Polzin (1996), JPO, 1409-1425), so that there will be no shear mixing<br class="">> C with very small shear<br class="">> #undef KPP_SCALE_SHEARMIXING<br class="">><span class="Apple-converted-space"> </span><br class="">> # this improves things sometimes at high resolution.<br class="">> #undef KPP_DO_NOT_MATCH_DIFFUSIVITIES<br class="">> #ifndef KPP_DO_NOT_MATCH_DIFFUSIVITIES<br class="">> C only makes sense if the diffusitivies are matched<br class="">> # undef KPP_DO_NOT_MATCH_DERIVATIVES<br class="">> #endif /* KPP_DO_NOT_MATCH_DIFFUSIVITIES */<br class="">><span class="Apple-converted-space"> </span><br class="">> C o Include/exclude smooth regularization at the cost of changed results (maybe useful for AD-simulations)<br class="">> C With this flag defined, some MAX(var,phepsi) are replaced by var+phepsi<br class="">> #undef KPP_SMOOTH_REGULARISATION<br class="">><span class="Apple-converted-space"> </span><br class="">><span class="Apple-converted-space"> </span><br class="">> Hope that helps,<br class="">><span class="Apple-converted-space"> </span><br class="">> Martin<br class="">><span class="Apple-converted-space"> </span><br class="">> > On 17. Feb 2022, at 18:06, Lily Greig <<a href="mailto:l.greig@pgr.reading.ac.uk" class="">l.greig@pgr.reading.ac.uk</a>> wrote:<br class="">> ><span class="Apple-converted-space"> </span><br class="">> > Hi MITgcm community,<span class="Apple-converted-space"> </span><br class="">> ><span class="Apple-converted-space"> </span><br class="">> > I'm using MITgcm with set-up similar to Horvat et al. 2016 (75 by 75 km at 2 km resolution, zonally re-entrant channel, northern half sea ice covered, hydrostatic). The ocean is cooling everywhere, sea ice forming with thsice package. I am having some issues with grid scale noise and large values of the vertical velocity field. I have tried a few adjustments so far: I turned KPP smoothing options on, to no effect, and next I tried using different viscosities/tuning the viscosity constants using examples in the MLAdjust tutorial. Using modified Leith & Smagorinsky, noise reduction only happens in the model when I increase the viscosity constants by up to 2 orders of magnitude, but increasing them this much also dampens the dynamics, reducing magnitude of the zonal jet.<span class="Apple-converted-space"> </span><br class="">> ><span class="Apple-converted-space"> </span><br class="">> > For reference, I've attached an image with snapshots of zonal & vertical velocity fields, model day 105, for a range of viscosity constant values from 1.85 -> 250, all using modified Leith & Smagorinsky. The subplot titles e.g 'UVEL LS30' stand for velocity field + viscosities used (all Leith and Smag. here, or LS) + the value used for every viscosity constant. I've also attached an example data file to this email. Increasing the viscosity constants reduces the vertical velocity from ~ 4e-4 m/s to 1e-4 m/s, but also the zonal jet by ~ factor 2.<span class="Apple-converted-space"> </span><br class="">> ><span class="Apple-converted-space"> </span><br class="">> > I have also tried also using Leith & Smagorinsky individually, QGLeith, harmonic/biharmonic but all to little avail unfortunately. Any help would be much appreciated, if anyone has an idea of what could be the issue, or further adjustments to try.<br class="">> ><span class="Apple-converted-space"> </span><br class="">> > Many thanks,<span class="Apple-converted-space"> </span><br class="">> ><span class="Apple-converted-space"> </span><br class="">> > Lily<span class="Apple-converted-space"> </span><br class="">> > <data><UVEL_WVEL_snap.png>_______________________________________________<br class="">> > MITgcm-support mailing list<br class="">> ><span class="Apple-converted-space"> </span><a href="mailto:MITgcm-support@mitgcm.org" class="">MITgcm-support@mitgcm.org</a><br class="">> ><span class="Apple-converted-space"> </span><a href="https://eur03.safelinks.protection.outlook.com/?url=http%3A%2F%2Fmailman.mitgcm.org%2Fmailman%2Flistinfo%2Fmitgcm-support&data=04%7C01%7Cl.greig%40pgr.reading.ac.uk%7Cf5323f8d024c443358eb08da011c250e%7C4ffa3bc4ecfc48c09080f5e43ff90e5f%7C0%7C0%7C637823517632184418%7CUnknown%7CTWFpbGZsb3d8eyJWIjoiMC4wLjAwMDAiLCJQIjoiV2luMzIiLCJBTiI6Ik1haWwiLCJXVCI6Mn0%3D%7C3000&sdata=vdk%2BHTXeEM5i9u%2Bmth6lM9ErK%2BZ9ph5nBVne7P5NkLs%3D&reserved=0" class="">https://eur03.safelinks.protection.outlook.com/?url=http%3A%2F%2Fmailman.mitgcm.org%2Fmailman%2Flistinfo%2Fmitgcm-support&data=04%7C01%7Cl.greig%40pgr.reading.ac.uk%7Cf5323f8d024c443358eb08da011c250e%7C4ffa3bc4ecfc48c09080f5e43ff90e5f%7C0%7C0%7C637823517632184418%7CUnknown%7CTWFpbGZsb3d8eyJWIjoiMC4wLjAwMDAiLCJQIjoiV2luMzIiLCJBTiI6Ik1haWwiLCJXVCI6Mn0%3D%7C3000&sdata=vdk%2BHTXeEM5i9u%2Bmth6lM9ErK%2BZ9ph5nBVne7P5NkLs%3D&reserved=0</a><br class="">><span class="Apple-converted-space"> </span><br class="">> _______________________________________________<br class="">> MITgcm-support mailing list<br class="">><span class="Apple-converted-space"> </span><a href="mailto:MITgcm-support@mitgcm.org" class="">MITgcm-support@mitgcm.org</a><br class="">><span class="Apple-converted-space"> </span><a href="https://eur03.safelinks.protection.outlook.com/?url=http%3A%2F%2Fmailman.mitgcm.org%2Fmailman%2Flistinfo%2Fmitgcm-support&data=04%7C01%7Cl.greig%40pgr.reading.ac.uk%7Cf5323f8d024c443358eb08da011c250e%7C4ffa3bc4ecfc48c09080f5e43ff90e5f%7C0%7C0%7C637823517632184418%7CUnknown%7CTWFpbGZsb3d8eyJWIjoiMC4wLjAwMDAiLCJQIjoiV2luMzIiLCJBTiI6Ik1haWwiLCJXVCI6Mn0%3D%7C3000&sdata=vdk%2BHTXeEM5i9u%2Bmth6lM9ErK%2BZ9ph5nBVne7P5NkLs%3D&reserved=0" class="">https://eur03.safelinks.protection.outlook.com/?url=http%3A%2F%2Fmailman.mitgcm.org%2Fmailman%2Flistinfo%2Fmitgcm-support&data=04%7C01%7Cl.greig%40pgr.reading.ac.uk%7Cf5323f8d024c443358eb08da011c250e%7C4ffa3bc4ecfc48c09080f5e43ff90e5f%7C0%7C0%7C637823517632184418%7CUnknown%7CTWFpbGZsb3d8eyJWIjoiMC4wLjAwMDAiLCJQIjoiV2luMzIiLCJBTiI6Ik1haWwiLCJXVCI6Mn0%3D%7C3000&sdata=vdk%2BHTXeEM5i9u%2Bmth6lM9ErK%2BZ9ph5nBVne7P5NkLs%3D&reserved=0</a><br class=""><br class=""></div></span></font></div></div><span id="cid:BF94157B-3781-40B2-AEE9-4F1933412A95"><UVW_comp.png></span><span style="caret-color: rgb(0, 0, 0); font-family: Helvetica; font-size: 12px; font-style: normal; font-variant-caps: normal; font-weight: 400; letter-spacing: normal; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; word-spacing: 0px; -webkit-text-stroke-width: 0px; text-decoration: none; float: none; display: inline !important;" class="">_______________________________________________</span><br style="caret-color: rgb(0, 0, 0); font-family: Helvetica; font-size: 12px; font-style: normal; font-variant-caps: normal; font-weight: 400; letter-spacing: normal; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; word-spacing: 0px; -webkit-text-stroke-width: 0px; text-decoration: none;" class=""><span style="caret-color: rgb(0, 0, 0); font-family: Helvetica; font-size: 12px; font-style: normal; font-variant-caps: normal; font-weight: 400; letter-spacing: normal; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; word-spacing: 0px; -webkit-text-stroke-width: 0px; 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