>
> Jerry Avins wrote:
>
> >
> > Other things being equal, clustering should follow a Poisson
> > distribution. If you measure flow -- a quantity that can be heavily
> > influenced by rainfall -- only twice a week, how do you bill equitably?
> >
> > Jerry
>
> Jerry,
>
> I don't imagine that we bill entirely "equitably" - more like "agreeably".
>
> We measure flow continuously to get the volume and concentration once or
> twice a week.
>
> The concentration is assumed to apply for the entire measured volume
> between concentration samples. So, one may say that we sample loading
> in that fashion.
>
> I think I answered my own question to the point where I can deal with it:
>
> We have the weekly or twice-weekly samples and have computer monthly
> averages - as the latter have some regulatory importance.
> You might consider these monthly averages to be lowpassed versions of
> the samples.
> Then, one can compute the distribution of outcomes and infer(?) the
> amount of loading.
The volume measurement is accurate and the accuracy of the load
measurement is unknown due to aliasing. And your question appears to be
-> what method to use to determine the inaccuracy that aliasing might be
introducing to the Load measurement?
Seems like the only solution is to either sample at a higher rate or
filter out higher frequencies before taking a sample.
For instance, would it be possible for a valve controlled by a timer be
set up so that it diverted a quart of flow into a holding tank every 6
hours? Then at the end of a week you would have 7 gallons in the tank
that could be thoroughly mixed and then a sample taken from that. That
would be a crude anti-alias filter in front of the sampler.
-jim
>
> My "backwards" sort of reasoning goes like this:
> We take a set of samples.
> We determine the distribution of those sample values over a suitably
> long time such that daily and even annual variations are included in the
> distribution.
> The caution here is that trends get wiped out - so a suitable time frame
> or set of them needs to be selected that has some meaning where gross
> trends are concerned.
> If we assume that the distribution represents a reasonable estimate of
> ground truth, then we can infer in quantitative terms what's happening -
> such as over-loading (i.e. loading that's above some determined threshold).
> It's surely not "perfect" but it's better than nothing ... I think.
>
> Fred
Reply by Jerry Avins●July 14, 20102010-07-14
On 7/14/2010 1:30 PM, Mark wrote:
> On Jul 14, 6:34 am, Jerry Avins<j...@ieee.org> wrote:
>> On 7/14/2010 5:55 AM, Greg Heath wrote:
>>
>> > ... what's, I& I?
>>
>> Infiltration and inflow, which force sewage plants to process rainwater.
>> Infiltration occurs when leaky mains are lower than the water table.
>> Inflow is often illegal pump connections to the sanitary sewer. When
>> streets become submerged, rainwater can pour in through manhole covers.
>>
>> Jerry
>> --
>> Engineering is the art of making what you want from things you can get.
>> �����������������������������������������������������������������������
>
> I think the answer to the OPs questions are in the details of this
> statment made by the OP:
>
> "We measure flow continuously to get the volume and concentration once
> or
> twice a week."
>
> What does that means exactly,....
>
> Does it mean you measure __FLOW__ continuously and integrate flow
> continously and once or twice a week you read the integrated value to
> calculate __VOLUME__ during the last measurment period (integration
> period) and then rest the integrator?
I start knowing that he is eminently rational, so that an interpretation
that makes no sense is the wrong interpretation. His utility measures
flow continuously to get volume by integration (as does mine) and
samples the flow once or twice a week to assess its average
concentration. (Higher concentration of components that create
biological oxygen demand --a.k.a BOD-- increase processing cost.
Jerry
--
Engineering is the art of making what you want from things you can get.
�����������������������������������������������������������������������
Reply by Mark●July 14, 20102010-07-14
On Jul 14, 6:34�am, Jerry Avins <j...@ieee.org> wrote:
> On 7/14/2010 5:55 AM, Greg Heath wrote:
>
> �> ... what's, I& �I?
>
> Infiltration and inflow, which force sewage plants to process rainwater.
> Infiltration occurs when leaky mains are lower than the water table.
> Inflow is often illegal pump connections to the sanitary sewer. When
> streets become submerged, rainwater can pour in through manhole covers.
>
> Jerry
> --
> Engineering is the art of making what you want from things you can get.
> �����������������������������������������������������������������������
I think the answer to the OPs questions are in the details of this
statment made by the OP:
"We measure flow continuously to get the volume and concentration once
or
twice a week."
What does that means exactly,....
Does it mean you measure __FLOW__ continuously and integrate flow
continously and once or twice a week you read the integrated value to
calculate __VOLUME__ during the last measurment period (integration
period) and then rest the integrator?
Mark
Reply by Jerry Avins●July 14, 20102010-07-14
On 7/14/2010 5:55 AM, Greg Heath wrote:
> ... what's, I& I?
Infiltration and inflow, which force sewage plants to process rainwater.
Infiltration occurs when leaky mains are lower than the water table.
Inflow is often illegal pump connections to the sanitary sewer. When
streets become submerged, rainwater can pour in through manhole covers.
Jerry
--
Engineering is the art of making what you want from things you can get.
�����������������������������������������������������������������������
Reply by Jerry Avins●July 14, 20102010-07-14
On 7/14/2010 5:55 AM, Greg Heath wrote:
> ... what's, I& I?
Infiltration and inflow, which force sewage plants to process rainwater.
Infiltration occurs when leaky mains are lower that the water table.
Inflow is often illegal pump connections to the sanitary sewer. When
streets become submerged, rainwater can pour in through manhole covers.
Jerry
--
Engineering is the art of making what you want from things you can get.
�����������������������������������������������������������������������
Reply by Greg Heath●July 14, 20102010-07-14
On Jul 13, 9:29�pm, Jerry Avins <j...@ieee.org> wrote:
> On 7/13/2010 8:28 PM, Fred Marshall wrote:
>
>
>
>
>
> > Jerry Avins wrote:
>
> >> Other things being equal, clustering should follow a Poisson
> >> distribution. If you measure flow -- a quantity that can be heavily
> >> influenced by rainfall -- only twice a week, how do you bill equitably?
>
> >> Jerry
>
> > Jerry,
>
> > I don't imagine that we bill entirely "equitably" - more like "agreeably".
>
> > We measure flow continuously to get the volume and concentration once or
> > twice a week.
>
> > The concentration is assumed to apply for the entire measured volume
> > between concentration samples. So, one may say that we sample loading in
> > that fashion.
>
> > I think I answered my own question to the point where I can deal with it:
>
> > We have the weekly or twice-weekly samples and have computer monthly
> > averages - as the latter have some regulatory importance.
> > You might consider these monthly averages to be lowpassed versions of
> > the samples.
> > Then, one can compute the distribution of outcomes and infer(?) the
> > amount of loading.
>
> > My "backwards" sort of reasoning goes like this:
> > We take a set of samples.
> > We determine the distribution of those sample values over a suitably
> > long time such that daily and even annual variations are included in the
> > distribution.
> > The caution here is that trends get wiped out - so a suitable time frame
> > or set of them needs to be selected that has some meaning where gross
> > trends are concerned.
> > If we assume that the distribution represents a reasonable estimate of
> > ground truth, then we can infer in quantitative terms what's happening -
> > such as over-loading (i.e. loading that's above some determined threshold).
> > It's surely not "perfect" but it's better than nothing ... I think.
>
> If your samples are taken at times of unusually high I&I, the dilution
> can make the measured concentrations uncharacteristically low.
Duh, what's, I & I?
Greg
Reply by Fred Marshall●July 14, 20102010-07-14
Jerry Avins wrote:
> If your samples are taken at times of unusually high I&I, the dilution
> can make the measured concentrations uncharacteristically low.
>
> Jerry
Yes, I know but the sample times are set for a number of reasons.
Actually, our concern right now is why the concentrations are so darned
high! So, in these parts where there's nearly 100 inches of rain each
year, we're used to seeing and fixing I&I. Right now it's not a big
concern.
Fred
Reply by Jerry Avins●July 13, 20102010-07-13
On 7/13/2010 8:28 PM, Fred Marshall wrote:
> Jerry Avins wrote:
>
>>
>> Other things being equal, clustering should follow a Poisson
>> distribution. If you measure flow -- a quantity that can be heavily
>> influenced by rainfall -- only twice a week, how do you bill equitably?
>>
>> Jerry
>
> Jerry,
>
> I don't imagine that we bill entirely "equitably" - more like "agreeably".
>
> We measure flow continuously to get the volume and concentration once or
> twice a week.
>
> The concentration is assumed to apply for the entire measured volume
> between concentration samples. So, one may say that we sample loading in
> that fashion.
>
> I think I answered my own question to the point where I can deal with it:
>
> We have the weekly or twice-weekly samples and have computer monthly
> averages - as the latter have some regulatory importance.
> You might consider these monthly averages to be lowpassed versions of
> the samples.
> Then, one can compute the distribution of outcomes and infer(?) the
> amount of loading.
>
> My "backwards" sort of reasoning goes like this:
> We take a set of samples.
> We determine the distribution of those sample values over a suitably
> long time such that daily and even annual variations are included in the
> distribution.
> The caution here is that trends get wiped out - so a suitable time frame
> or set of them needs to be selected that has some meaning where gross
> trends are concerned.
> If we assume that the distribution represents a reasonable estimate of
> ground truth, then we can infer in quantitative terms what's happening -
> such as over-loading (i.e. loading that's above some determined threshold).
> It's surely not "perfect" but it's better than nothing ... I think.
If your samples are taken at times of unusually high I&I, the dilution
can make the measured concentrations uncharacteristically low.
Jerry
--
Engineering is the art of making what you want from things you can get.
�����������������������������������������������������������������������
Reply by Fred Marshall●July 13, 20102010-07-13
Jerry Avins wrote:
>
> Other things being equal, clustering should follow a Poisson
> distribution. If you measure flow -- a quantity that can be heavily
> influenced by rainfall -- only twice a week, how do you bill equitably?
>
> Jerry
Jerry,
I don't imagine that we bill entirely "equitably" - more like "agreeably".
We measure flow continuously to get the volume and concentration once or
twice a week.
The concentration is assumed to apply for the entire measured volume
between concentration samples. So, one may say that we sample loading
in that fashion.
I think I answered my own question to the point where I can deal with it:
We have the weekly or twice-weekly samples and have computer monthly
averages - as the latter have some regulatory importance.
You might consider these monthly averages to be lowpassed versions of
the samples.
Then, one can compute the distribution of outcomes and infer(?) the
amount of loading.
My "backwards" sort of reasoning goes like this:
We take a set of samples.
We determine the distribution of those sample values over a suitably
long time such that daily and even annual variations are included in the
distribution.
The caution here is that trends get wiped out - so a suitable time frame
or set of them needs to be selected that has some meaning where gross
trends are concerned.
If we assume that the distribution represents a reasonable estimate of
ground truth, then we can infer in quantitative terms what's happening -
such as over-loading (i.e. loading that's above some determined threshold).
It's surely not "perfect" but it's better than nothing ... I think.
Fred
Reply by Jerry Avins●July 13, 20102010-07-13
On 7/13/2010 12:31 PM, Fred Marshall wrote:
> Perhaps I should post this elsewhere but we speak the same language
> here. I may have asked a similar question some time ago but now I have
> a new perspective and want to investigate.
>
> I have a wastewater process that's being sampled periodically (uniform
> sampling for what it's worth).
> The sample rate is way too low to avoid aliasing but the samples are
> real enough and the data is continuously available and very likely not
> amenable to being sampled more often (economics).
>
> It's a bit like sampling a random series except that I "know" there is
> an underlying pattern that repeats each day with variable amplitude no
> doubt. That, plus transients, would be the highest frequency content and
> seasonal things are the lowest frequency content which I'm not too
> worried about. And, while I'd like to know when transients happen and
> how big they are, I'm afraid that's out of the question.
>
> In fact, what's of value here is to estimate how much plant capacity is
> being "used up". By my reckoning, 6 months of data during our peak
> months is a good averaging period - as it's the peak months that
> determine our capacity "use" for regulatory purposes.
> In the shorter term, the numbers are used for determining charges for
> overly high concentrations, shared use, etc.
>
> To make things a bit more complicated, the regulatory agency has us
> report the weekly data on a monthly basis (actually here there are 2
> samples per week) and average it for the month.
> If there are 3 contiguous months with these averages exceeding our
> "capacity" or some large fraction of it, then we are put on notice that
> planning for future capacity must begin. So, this is one "measure"
> that's in concrete. But, I digress a bit .....
>
> Here is my question:
>
> Instead of worrying about aliasing which is where I go to first of
> course, is there a statistical measure that might help me better
> understand the "quality" of our numbers or how much variation is
> "expected" given those numbers?
> For example, given 4 to 8 weeks of data (4 to 8 samples), what can be
> said the data set in a statistical sense? How might one best put the
> answer to use in a case like this?
>
> Where should I be looking?
Other things being equal, clustering should follow a Poisson
distribution. If you measure flow -- a quantity that can be heavily
influenced by rainfall -- only twice a week, how do you bill equitably?
Jerry
--
Engineering is the art of making what you want from things you can get.
�����������������������������������������������������������������������