Re: [ferret_users] Using xbox and zbox to find total transport

To: Russ Fiedler <russell.fiedler@xxxxxxxx>

Subject: Re: [ferret_users] Using xbox and zbox to find total transport

From: Ryo Furue <furue@xxxxxxxxxx>

Date: Tue, 15 Aug 2017 01:02:03 +0900

Arc-authentication-results: i=4; mx.google.com; dkim=pass header.i=@hawaii-edu.20150623.gappssmtp.com header.s=20150623 header.b=cNIXcFKt; arc=pass (i=2 dkim=pass dkdomain=hawaii-edu.20150623.gappssmtp.com); spf=softfail (google.com: domain of transitioning furue@xxxxxxxxxx does not designate 52.222.5.176 as permitted sender) smtp.mailfrom=furue@xxxxxxxxxx

Arc-authentication-results: i=3; mx.google.com; dkim=pass header.i=@hawaii-edu.20150623.gappssmtp.com header.s=20150623 header.b=cNIXcFKt; arc=pass (i=2 dkim=pass dkdomain=hawaii-edu.20150623.gappssmtp.com); spf=softfail (google.com: domain of transitioning furue@xxxxxxxxxx does not designate 52.222.5.176 as permitted sender) smtp.mailfrom=furue@xxxxxxxxxx

Arc-authentication-results: i=2; mx.google.com; dkim=pass header.i=@hawaii-edu.20150623.gappssmtp.com header.s=20150623 header.b=cNIXcFKt; arc=pass (i=1 spf=pass spfdomain=hawaii.edu dkim=pass dkdomain=hawaii-edu.20150623.gappssmtp.com); spf=softfail (google.com: domain of transitioning furue@xxxxxxxxxx does not designate 65.127.216.226 as permitted sender) smtp.mailfrom=furue@xxxxxxxxxx

Arc-authentication-results: i=1; mx.google.com; dkim=pass header.i=@hawaii-edu.20150623.gappssmtp.com header.s=20150623 header.b=cNIXcFKt; spf=pass (google.com: domain of furue@xxxxxxxxxx designates 2607:f8b0:400c:c08::22e as permitted sender) smtp.mailfrom=furue@xxxxxxxxxx

Arc-message-signature: i=4; a=rsa-sha256; c=relaxed/relaxed; d=google.com; s=arc-20160816; h=list-archive:list-help:list-post:list-id:mailing-list:precedence:cc :to:subject:date:from:references:in-reply-to:mime-version :arc-authentication-results:arc-message-signature :arc-authentication-results:arc-message-signature:message-id :arc-authentication-results:arc-message-signature:dkim-signature :arc-authentication-results; bh=WJywYkxPDrlFKAgdJGOLJclOwmDoG/vjIMwU/7zSTMA=; b=mzYX6iUAbDpLtIDxNrhELK0iHP6P3hBf41zjnWXR7Hk389iAm9+oleki8v6zZA/xtr ++uGK0NLjZH75jOLZEtX2IAXSGN9dSVItYcIiLkoP06fU2zGUB2TtFJhCOR62DqvMATi fIf3tznT9tZcCBA84AdOH4rqx0tbZ4b1mbnRiSSfIZ3nvsSDwk7W10RniHbiz0K/eSnp FpAekt2qGJh3XQCR10ON71+IaP3sEr5i8g1ywDfaFspPBe6VN7RsO9lMFI6Po9T66B1C 4jQxHUW57jTa8FxIRunZHRhlxuLpInko1qRRKvDEcYtnd7ehqxeAVAYE+6RtTKsYsHxF fWGw==

Arc-message-signature: i=3; a=rsa-sha256; c=relaxed/relaxed; d=google.com; s=arc-20160816; h=cc:to:subject:date:from:references:in-reply-to:mime-version :dkim-signature:arc-authentication-results:arc-message-signature :arc-authentication-results:arc-message-signature:message-id :arc-authentication-results; bh=WJywYkxPDrlFKAgdJGOLJclOwmDoG/vjIMwU/7zSTMA=; b=tKhMtbRjNmkN2Ykk8A5WZFeb5FD6NfRyEAd8Xdf42iKvkc2d1I/ZGU+H7QEynVPAy8 PV6h7rtIt/G3WaVio4PO6ItzP7R/G04LvUCTLAURCArnpbzXrl+XdpJ4tuQhs1abL4Sa uhp8W6ce1Exb4SnoBjubAbfNxAl98ol5fcAQg9rs09ydDp+5N+UqnHtAE4pW6NsuNWDg D3o//4Zi9gxxY/uPPsGhp0dz6xjYG1YTFoQK78J6kvHuGrOOWwSTB9Ol+ebLlqmloFw3 ZGn0KqeWVbuDymEvPxTGK1N+B1iMRRX3623gPJ1jtACZgUOEcJVZWWAUfVDoPgDDMscL FQmw==

Arc-message-signature: i=2; a=rsa-sha256; c=relaxed/relaxed; d=google.com; s=arc-20160816; h=cc:to:subject:message-id:date:from:references:in-reply-to :mime-version:dkim-signature:arc-authentication-results :arc-message-signature:arc-authentication-results; bh=WJywYkxPDrlFKAgdJGOLJclOwmDoG/vjIMwU/7zSTMA=; b=YNKtRNBgFz3So8NNsk/8fBek6BQVUJuy10951sMDVEpSnRaE1RbZk6nEJKIl8AIu// Hr+sQuZX3k6cpHlai7JleWg5xRreh9EBJNQ6BMQaT0ajeH2xCRnjQnWHsJFcB0OnWJAP kMLABm/wdzvI3L3qnZ6OfRcdyDGeHzVjiKngdAZnnXZMUl85OPhUgp61Ktket6Uc4tKi T5Hh7076tzsHW6kDcGkBBiLQJWZHJ7GzRt45bFWacJX/FacDDw/nhHSsRnfViZCP+gWL 5a1Xh82QZere1qpLlRE1wje/px0qB2UEe17zKiVcNTJZRMgN5sOEHHjFy2czkNRSyV29 wd7Q==

Arc-message-signature: i=1; a=rsa-sha256; c=relaxed/relaxed; d=google.com; s=arc-20160816; h=cc:to:subject:message-id:date:from:references:in-reply-to :mime-version:dkim-signature:arc-authentication-results; bh=WJywYkxPDrlFKAgdJGOLJclOwmDoG/vjIMwU/7zSTMA=; b=bQ/g76Y43Gm+5gVcYLm3cvsb80xB8rWBfnhK5WeVoa4tF2vI99eZ1aj4ex7YUWuFC/ Rv1bsmUG2aLnqONEOErpc2zm0I6WgI5nkTQ+T432fl4jjZy5Njp6brnl2dggDk2s1kM/ a3a9e5lZd0TcwLl0DAJYuxXhFdLf4sBEpXTrQABoIF+N1IueAKB57c4zuEm54XbEgPoY d81IUsQeHARkHNgeQEezD65tXW26zbv2Ec9zrp+pR+VVlxnUygCUtS0gmK/LG74q7MkP 5W6nOb6xAv3eOG8yterygWn7saAaj/jkEyqzN0KVzYKjieAQQw+gxVOzWRBK4BGlXnuq iblg==

Arc-seal: i=4; a=rsa-sha256; t=1502726532; cv=pass; d=google.com; s=arc-20160816; b=qJc6rWzguJe8tMd7egqonfwQ63Fl1NTHQ92Ej7g8QKpfZaEshfkOJPgZVeVCyxq332 WNYdTRkebb+mnS09eQRPQHbw81dJ6HyYXRF47WBfXtxdFL18D6j57luwjdqchdQDyYUA EN0Yez8dzRoUIz6/pFiAGLAaJpVPjM5ikUMQsUDDC0H0Kib4m7XpwOP8mrS15CfoylVP 6Of3lGs+HUtTip4E9ZT6f/IovbuWp5YREOcG/Xt497pfECIE7v5c8rpMvpsILYzL/aXq stO4U/V1+spp9PpKSsRPUYVobyUJPQgrAQdfaVpD+xzA6SxtsDTh9TYgRhid79RDfNjH bmCQ==

Arc-seal: i=3; a=rsa-sha256; t=1502726531; cv=pass; d=google.com; s=arc-20160816; b=zPSN3n/w+WEC6oGRnRUC2L3gOYVyitbunHP+xnHsmJr7urQzttZvshqreMROYZI1tV wa1WZ8ijxVtPntdimeiY3mhiCDUR3IV5atmi1dwX6HyQG/xTYqpdNHV1PJ4v3Ufm8GR8 fjPjY9cml2n5j0PPrjwibmjKD5QrevnacnFVjBsxkuzRtlZ9hhSq2kA9muWXKEWADZop h9A2/XR3LJAUjNgnNJTAKsN/LbSo1Kr8C6Mwge8h1d0w60fZVdHATNIoVaW2L1vjZyCn 3dbtlsrC5ORN0KjZF/VTjN30CzzHIeZxkz05vvoi3GbyFJ3HIzpog3eFAn7gLsmv1hiH UlPA==

Arc-seal: i=2; a=rsa-sha256; t=1502726528; cv=pass; d=google.com; s=arc-20160816; b=gNk754yEslO6E56fML8dtpTmwLV/h1qeIk9gouGlZSlSxaK6BVFbtowrM+Nl3oePRE 6BKIwXQYNDLhkGkmpLJwZMUgT1yvw9t4446VaXy9tAFb0TtKZVMjJX37uyfmt1C1TSIt 0rvNMaPL+z4kTIElnDJRXISCjnIGQSe4WUDHOYj88Qc9lHw4vqSK5HQ/PhRCpj1V6ofY UdR1DKfelaG+VQrBwkd0aGmW7olXYf4G2KWGvui2Yhu+hl1lzX7U4YDaCE/TvPv3bSS4 iAXkwm+H7DbcMAh/6aDSOfWG0L7AhTRE+mPVEMJecen6ffC1ZYmMiT9crC7eW2I1uOlc mGVQ==

Arc-seal: i=1; a=rsa-sha256; t=1502726524; cv=none; d=google.com; s=arc-20160816; b=MkT46nFNc+FBACg7BQtw4eUH0jI4E3OVamTHTqE7gVeZc2ahsyoxD5ZVVdmHbbAl8y Cpma6oqw8eIcyfnuTsqlWD79ubSEJ/yIpZGl2yKTdVr8cFmsAK2jFiq3VaCpVX7zu5fz Dif5XXKv7w4iXMWceFNPcrCw3K4uLzgJz+J1V9mHq+kpfj7zCtTs/OWob24VJ+UaTnT8 mVf2oG/lR7+2boQrXMBmcw32zSwSzGQBLkcUN8biHr1w5SDIX7IUEPPJYnARFDK3GRCj s2jENyZ0IzdwvXCO9qD5DhAmR9MP/Pwtx2Kao9ppZ8fXmrpK8ZAkREFVRRyaJCiZy7G9 OvSg==

Cc: ferret users <ferret_users@xxxxxxxx>

Dkim-signature: v=1; a=rsa-sha256; c=relaxed/relaxed; d=noaa-gov.20150623.gappssmtp.com; s=20150623; h=message-id:mime-version:in-reply-to:references:from:date:subject:to :cc:x-original-sender:x-original-authentication-results:precedence :mailing-list:list-id:list-post:list-help:list-archive; bh=WJywYkxPDrlFKAgdJGOLJclOwmDoG/vjIMwU/7zSTMA=; b=b2DLuUgZ61RICHnW5RWQSBTBohJW5mB9CxqK7RvCVHOPZfA/hXqt72thOJVzhga2+p Ko0j2Np5Jy3q5hBlCzQEwTPM4vQYlZCB+HilXqrq5t9FeTFbx6yO/m7Bag7tFLb9dtg2 xc4hk+y+smrdFqMcbnKEe+wBXnFFKe1c1o8gzQvd0iOcbdQ1r52+67fJUAiS7Z8PHIvq D/kvFllmD4QqzaDa0KJOmDrlAQtQUxV7Wb5yViX1GEx0XcIO9ETLrdyeltAfQx/K2yOP Pn8zVTgYlniwxia4qufQgSZzTF0uroQ2Ws3bH2lJaVh3PBc8FPajyhDomB0uDXpDcsqD rV8A==

In-reply-to: <71b74d20-bc6a-d224-4f82-2fa837afd29c@csiro.au>

List-archive: <https://groups.google.com/a/noaa.gov/group/ferret_users/>

List-help: <https://support.google.com/a/noaa.gov/bin/topic.py?topic=25838>, <mailto:ferret_users+help@noaa.gov>

List-id: <ferret_users.noaa.gov>

List-post: <https://groups.google.com/a/noaa.gov/group/ferret_users/post>, <mailto:ferret_users@noaa.gov>

Mailing-list: list ferret_users@xxxxxxxx; contact ferret_users+owners@xxxxxxxx

References: <CAJMBgoPvP1A-dfx13ePX-ONwKp4SwUUDanvrz6Peb1ZhXAnftg@mail.gmail.com> <CAEwQpaKGiTdhqXwM5aDU6ofnOK8vQBT4hWgOam54rBC3gRYEJQ@mail.gmail.com> <CAJMBgoPvZErVYz4CC3-sp=hS+rv5Nzpyg8ZB1uQnp_VQYPnwQg@mail.gmail.com> <CAEwQpa+dAZ01DSk9ciz_NC3zEP5bPVrASZL5vZrj=-s1jOZgPw@mail.gmail.com> <CAJMBgoNjt_QBO+cBWGwi-rMUgAw-6Bcm4R9VZjkHs6jqEBSSZQ@mail.gmail.com> <71b74d20-bc6a-d224-4f82-2fa837afd29c@csiro.au>

Sender: owner-ferret_users@xxxxxxxx

Hi James and Russ,

I think the version of SODA you are using is based on POP and grid cell centres are at the middle of the cell. So let Z(k) be the centre of cell k and ZB(k) be the base of the cell. We have all the Z(k) and set ZB(0) to zero

ZB(0) = 0
Z(k)=0.5*(ZB(k-1)+ZB(k))

=> ZB(k) = 2*Z(k)-ZB(k-1) for k=1...

Same answer from me. Although I don't know the SODA grid, ZB(0) = 0 is most likely correct. If so, you can solve our coupled equations as Russ shows above.

Note there may be partial cells involved which complicates transport calculations. There's also the free surface to consider. Also I think the results are interpolated from a mercator grid to evenly spaced in latitude so beware. I'd suggest contacting the original providers for further info.

I second. (In so doing, you can ask them to include the cell boundary information in the netCDF files they provide.)

I hope the SODA people interpolated the velocity field considering volume conservation. The free surface and partial cells can be a problem depending on the accuracy you pursue.

Cheers,

Ryo