Karl,
I think there are two issues here. One is a general representational issue,
the other is a particular processing issue. I'm curious to find out if we
are on the same page. As I understand it, CF directs that the reported
bounds of the interval should cover the leading edge time of the first
acquisition to the trailing edge time of the last acquisition, regardless
of the time coordinate value you associate with the mean value (or
integral, or whatever function), with the trailing edge value treated as
exclusive (everything up to but not including, the value). If you are
treating the input measurements to the mean as instantaneous (first
acquisition at 23:10:00 exactly and the last one at 23:20:00 exactly) it
appears to me that there is no problem with representing the upper bound as
23:20:00, as the moment that is infinitesimally close to 23:20:00 is
included. If I understand you correctly, you are suggesting giving half the
weight of each instantaneous boundary point to the intervals on either
side. Are we on the same page, or are am I confused?
Grace and peace,
Jim
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On Tue, Mar 27, 2018 at 1:08 PM, Karl Taylor <taylor13 at llnl.gov> wrote:
> Hi again,
>
> I think we've been thinking about this wrong. You apparently want to
> report the mean for the period 23:10:00 - 23:20:00 from 1-second samples
> (sampled on the second). This amounts to integrating over the 10-minute
> period (multiply each sample by the time interval it represents) and
> dividing by 10 minutes.. For a case like this, elementary approaches to
> estimating the integral make use of *both* end points. The Trapezoid Rule,
> for example, weights each of the samples equally except the two end points,
> which get half the weight.
>
> So, your bounds should define the interval represented by the mean you
> are reporting (23:10:00 - 23:20:00), and you should estimate that mean
> using 601 samples, but weighting the first and last sample half as much as
> the others.
>
> best regards,
> Karl
>
>
> On 3/26/18 9:00 AM, Karl Taylor wrote:
>
> Dear Erik,
>
> I think one could argue that a "sample" taken *on* the second is most
> representative of an interval extending from half a second prior to the
> sample time and half a second following the sample time, so, for example, a
> sample at 1 sec represents the interval from 0.5 to 1.5 seconds. In that
> case if your 1st sample is at 23:10:00 and last sample is at 23:19:59, you
> might want to set the bounds on your 10-minute mean as 23:09:59.5 and
> 23:19:59.5.
>
> On the other hand, if there is some finite response response time of your
> instrument (say, of order 1 sec), you could argue that a sample taken at
> time t really represents an average over some preceding interval, and then
> you might say your 10-minute mean extends from 23:09:59 to 23:19:59. In
> this case I would be tempted to compute 10-minute means from samples
> starting with 23:10:01and ending with 23:20:00, so the bounds would be
> 23:10:00 and 23:20:00.
>
> In any case the bounds should span exactly 10 minutes, I think.
>
> These suggestions come from someone unfamiliar with observational
> protocols, so take them for what they're worth.
>
> regards,
> Karl
>
> On 3/26/18 7:26 AM, Jim Biard wrote:
>
> Erik,
>
> Bounds are always inclusive lower / exclusive upper. That's [low, high) in
> common notation. If the cells abut one another, the upper bound for one
> should be identical to the lower bound for then next.
>
> Grace and peace,
>
> Jim
>
> [image: CICS-NC] <http://www.cicsnc.org/>Visit us on
> Facebook <http://www.facebook.com/cicsnc> *Jim Biard*
> *Research Scholar*
> Cooperative Institute for Climate and Satellites NC <http://cicsnc.org/>
> North Carolina State University <http://ncsu.edu/>
> NOAA National Centers for Environmental Information
> <http://ncdc.noaa.gov/>
> *formerly NOAA?s National Climatic Data Center*
> 151 Patton Ave, Asheville, NC 28801
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>
>
> On Mon, Mar 26, 2018 at 4:29 AM, Erik Quaeghebeur <
> E.R.G.Quaeghebeur at tudelft.nl> wrote:
>
>> Dear list,
>>
>>
>> Is there a standard way to indicate which bounds are included in a bounds
>> variable?
>>
>> Context: I have 10-min. statistics, e.g., the mean of 600 per-second
>> samples from 23:10:00 to 23:19:59. Currently, in my bounds variable for
>> time, I have, essentially, [23:10:00, 23:20:00]. I list my time in seconds
>> since 1970-01-01. Should I use [23:10:00, 23:19:59] instead?
>>
>>
>> Best,
>>
>> Erik
>>
>> --
>> https://ac.erikquaeghebeur.name
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