To calculate
the surface
average
temperature
of our planet,
the Earth's surface
is divided into
5 degree longitude by
5 degree latitude grids.
( this divides the globe's surface
into 2592 grid cells )
( this divides the globe's surface
into 2592 grid cells )
Unfortunately, a majority
of the surface grids
have no thermometers,
or are missing some data
needed to compile
the global average.
For a majority of grids.
missing data are "infilled"
( wild guessed )
by government bureaucrats
with science degrees.
There is no way
to double check
(verify)
their guesses,
or to prove
them wrong
(falsify them.)
But ... the global
surface average,
with all that infilling,
can be compared
with two other
measurement
methodoloiges,
weather satellites
and weather balloons.
Weather satellites and balloons
show LESS warming than the
surface data.
They also correlate well
with each other.
That means surface
temperature data
are outliers,
so you'd expect
them to be rejected.
But not in
climate
junk "science",
where the
weather satellites
and weather balloons
are ignored
simply because
they show
less warming
than surface data !
A real scientist
would consider
surface temperature
data quality, with all
of that infilling,
and the lack of
correlation with
satellite and balloon
data, to be low quality !
But never mind that,
for now !
Surface temperature
data quality are low
for other reasons too
-- even if we deliberately
ignore all the infilling
and lack of correlation
with other methodologies !
The surface
temperature record
is built on
two measurements,
taken daily at each
monitoring station,
specifically the
maximum
temperature (Tmax),
and the
minimum
temperature (Tmin).
These daily readings
are then averaged
to calculate a daily
mean (average) temperature:
Tmean = ( Tmax + Tmin ) / 2.
The surface instrumental
temperature record
is the basis for all
the ( fake ) alarm
over climate change.
Therefore, the accuracy
of the surface temperature
record is important.
Are two daily measurements
of temperature sufficient
to accurately determine
the average temperature
of ouyr planet's surface,
and temperature trends?
The right answer is "no".
It is important to understand
that air temperature is a signal.
The process of measuring
a signal is known as sampling.
A rapidly changing signal
must be sampled
more frequently
than a slow
rate of change signal.
Exactly how frequently
a signal must be sampled,
was answered in 1928 ,
by Harry Nyquist,
a Swedish-born
American Electronics
Engineer.
A few years later,
with the help
of Claude Shannon,
the Nyquist-Shannon
Sampling Theorem
was published.
According to the
Nyquist-Shannon
Sampling Theorem,
we must
sample the signal
at a rate at least
two times
the highest frequency
component of the signal.
If we sample signals
less often than
the Nyquist Rate,
our samples
will contain error.
The Nyquist
Sampling Theorem
is essential science for
digital audio, digital video,
industrial process control,
medical instrumentation,
flight control systems,
digital communications,
etc.
Climate "science", and the
surface instrumental
temperature record,
completely ignore Nyquist.
The historical temperature data
use only two samples / day.
NOAA, in their USCRN
( US Climate Reference Network )
has determined that it is
necessary to sample
at 4,320-samples/day
to eliminate Nyquist errors.
4,320-samples/day
equates to 1-sample
every 20 seconds.
This rate can only be achieved
by automated sampling
with electronic instruments.
But most of the instrumental
surface temperature record
is comprised of
historical readings
of mercury max/min
thermometers,
taken long before
automation was an option.
Today, despite the
availability of automation,
the instrumental record
still uses Tmax and Tmin
( effectively 2- samples/day )
instead of a
Nyquist-compliant
sampling rate.
The reason for this
is to maintain
compatibility
with the older
historical record.
The maximum
and minimum
temperatures happen
whenever they happen,
not at exactly
the same time
of each day.
The fact that
Tmax and Tmin
happen at
irregular times
during the day
causes its own kind
of sampling error.
The instrumental
surface temperature
record uses
the worst method
of sampling possible
– resulting in
maximum error.
Calculating
mean temperature
with 2-samples/day
rarely yields
the correct mean
calculated with
five-minute samples.
The trend
sampling error
may be of a
similar magnitude
to the claimed
temperature trends!
It is certain that every
mean temperature,
and derived trend
in the record ,
contains
significant error,
if it was calculated
with two temperature
samples/day,
violating the
Nyquist-Shannon
Sampling Theorem,
known for over 80 years
and essential science
to every field
of technology
that involves
signal processing.
This calls
into question
the scientific value
of the instrumental
surface temperature
record and the
practice of using
Tmax and Tmin
to calculate
mean values
and long-term
temperature trends.