ArticlePDF Available

Refereed Papers: Uncertainty in the Global Average Surface Air Temperature Index: A Representative Lower Limit

Authors:

Abstract and Figures

Sensor measurement uncertainty has never been fully considered in prior appraisals of global average surface air temperature. The estimated average ±0.2 C station error has been incorrectly assessed as random, and the systematic error from uncontrolled variables has been invariably neglected. The systematic errors in measurements from three ideally sited and maintained temperature sensors are calculated herein. Combined with the ±0.2 C average station error, a representative lower-limit uncertainty of ±0.46 C was found for any global annual surface air temperature anomaly. This ±0.46 C reveals that the global surface air temperature anomaly trend from 1880 through 2000 is statistically indistinguishable from 0 C, and represents a lower limit of calibration uncertainty for climate models and for any prospective physically justifiable proxy reconstruction of paleo-temperature. The rate and magnitude of 20th century warming are thus unknowable, and suggestions of an unprecedented trend in 20th century global air temperature are unsustainable.
Content may be subject to copyright.
MULTI-SCIENCE PUBLISHING CO. LTD.
5 Wates Way, Brentwood, Essex CM15 9TB, United Kingdom
Reprinted from
ENERGY &
ENVIRONMENT
VOLUME 21 No. 8 2010
UNCERTAINTY IN THE GLOBAL AVERAGE SURFACE AIR
TEMPERATURE INDEX:
A REPRESENTATIVE LOWER LIMIT
by
Patrick Frank (USA)
969
UNCERTAINTY IN THE GLOBAL AVERAGE SURFACE AIR
TEMPERATURE INDEX: A REPRESENTATIVE LOWER
LIMIT
Patrick Frank
Palo Alto, CA 94301-2436, USA
Email: pfrank830@earthlink.net
ABSTRACT
Sensor measurement uncertainty has never been fully considered in prior appraisals
of global average surface air temperature. The estimated average ±0.2 C station error
has been incorrectly assessed as random, and the systematic error from uncontrolled
variables has been invariably neglected. The systematic errors in measurements from
three ideally sited and maintained temperature sensors are calculated herein.
Combined with the ±0.2 C average station error, a representative lower-limit
uncertainty of ±0.46 C was found for any global annual surface air temperature
anomaly. This ±0.46 C reveals that the global surface air temperature anomaly trend
from 1880 through 2000 is statistically indistinguishable from 0 C, and represents a
lower limit of calibration uncertainty for climate models and for any prospective
physically justifiable proxy reconstruction of paleo-temperature. The rate and
magnitude of 20th century warming are thus unknowable, and suggestions of an
unprecedented trend in 20th century global air temperature are unsustainable.
1. INTRODUCTION
The rate and magnitude of climate warming over the last century are of intense and
continuing international concern and research [1, 2]. Published assessments of the
sources of uncertainty in the global surface air temperature record have focused on
station moves, spatial inhomogeneity of surface stations, instrumental changes, and
land-use changes including urban growth.
However, reviews of surface station data quality and time series adjustments, used
to support an estimated uncertainty of about ±0.2 C in a centennial global average
surface air temperature anomaly of about +0.7 C, have not properly addressed
measurement noise and have never addressed the uncontrolled environmental
variables that impact sensor field resolution [3-11]. Field resolution refers to the ability
of a sensor to discriminate among similar temperatures, given environmental exposure
and the various sources of instrumental error.
In their recent estimate of global average surface air temperature and its uncertainties,
Brohan, et al. [11], hereinafter B06, evaluated measurement noise as discountable,
writing, "The random error in a single thermometer reading is about 0.2 C (1σ) [Folland,
et al., 2001] ([12]); the monthly average will be based on at least two readings a day
throughout the month, giving 60 or more values contributing to the mean. So the error
in the monthly average will be at most = 0.03 C and this will be
uncorrelated with the value for any other station or the value for any other month."
Paragraph [29] of B06 rationalizes this statistical approach by describing monthly
surface station temperature records as consisting of a constant mean plus weather
noise, thus, "The station temperature in each month during the normal period can be
considered as the sum of two components: a constant station normal value (C) and a
random weather value (w, with standard deviation
σ
i)." This description plus the use
of a reduction in measurement noise together indicate a signal averaging
statistical approach to monthly temperature.
1.1. The scope of the study
This study evaluates a lower limit to the uncertainty that is introduced into the
temperature record by the estimated noise error and the systematic error impacting the
field resolution of surface station sensors.
Basic signal averaging is introduced and then used to elucidate the meaning of the
estimated ±0.2 C average uncertainty in surface station temperature measurements as
described by Folland, et al. [12]. An estimate of the noise uncertainty in any given
annual temperature anomaly is then developed. Following this, the lower limits of
systematic error in three temperature sensors are calculated using previously reported
ideal field studies [13].
Finally, the average measurement noise uncertainty and the lower limit of
systematic error in a Maximum–Minimum Temperature System (MMTS) sensor are
combined into a total lower limit of uncertainty for an annual anomaly, referenced to
a 30-year mean. The effect of this lower-limit uncertainty on the global average
surface air temperature anomaly time series is described. The study ends with a
summary and a brief discussion of the utility of the instrumental surface air
temperature record as a validation target in climate studies.
2. SIGNAL AVERAGING
The error in an observable due to random noise can be made negligible by averaging
repetitive measurements [14, 15]; a technique that is exploited to excellent effect in
spectroscopy [16]. Three cases below show when noise reduction by signal averaging
is appropriate, and when it is not. The statistical model in B06 is then appraised in light
of these cases.
2.1. Case 1
In signal-averaging repetitive measurements of a constant temperature, the
measurement in a random noise model is,
, (1)
where tiis the measured temperature,
τ
cis the constant "true" temperature, and niis the
tn
ici
=+
τ
160/
02 60./
970 Energy & Environment · Vol. 21, No. 8, 2010
random noise associated with the ith measurement. When the noise is stationary, it has
a constant average intensity and a mean of 0. The mean temperature is ,
and the ‘mean temperature ± mean noise’ is,
.(2)
When N is large and the noise is stationary, and
, where
σ
2
nis the variance of the noise intensity, and "" signifies
‘approaches equality with.’ Finally,
.(3)
That is, given a constant temperature and stationary random noise, averaging repetitive
measurements of any constant temperature reduces the impact of noise as , and
at large N, and [15, 17, p. 53ff]. Noise reduction by signal
averaging is thus entirely appropriate when data fall within Case 1.
2.2. Case 2
Now suppose the conditions of Case 1 are changed so that the N true temperature
magnitudes,
τ
i, vary inherently but the noise variance remains stationary and of constant
average intensity. Thus, , while .
Then,
, (4)
where tiis again the measured temperature,
τ
iis the "true" instantaneous temperature,
and niis again the noise intensity associated with the ith measurement. This case may
reflect a series of daily temperatures from any well-sited and maintained surface
station sensor. In this case the ‘mean temperature ± mean noise’ will again be,
.(5)
Tn NtNnT
N
ii
i
N
i
N
n
__ _
()±= ±
==
11 2
11
σ
tn
iii
=+
τ
σσσσ
1
2222
=====... ...
ij n
σ
nN0
Tc
_
τ
1N
Tn NtNNT
N
in
i
N
n
__ _
±= ±
=
11
2
1
σσ
()nN
i
i
N
n
=
2
1
2
σ
()
_
tT
i
i
N
−=
=
2
1
tTn
ii
−=
_
Tn NtNtT
ii
i
N
i
N
__ _
()±= ±
==
11 2
11
TNti
i
N
_
=
=
1
1
Uncertainty in the global average surface air temperature index: 971
a representative lower limit
However, a further source of uncertainty now emerges from the condition .
The mean temperature, , will have an additional uncertainty, ±s, reflecting the fact
that the
τ
imagnitudes are inherently different. The result is a scatter of the inherently
different temperature magnitudes about the mean, because now ,
where represents the difference between the "true" magnitude of
τ
iand , apart
from noise. The magnitudes of the niand the
τ
i,are physically independent and
uncorrelated, and niand are statistically independent. Therefore the uncertainties
due to these factors can be calculated separately:
, but [17,p. 9ff] (6)
The condition of noise stationarity means that the nihave a true constant mean of zero
(i.e.,
µ
noise = 0). However, the second part of eqn. (6) shows that use of the empirical mean
temperature, , in calculating , removes a degree of freedom from s2.
Following from eqns. (5) and (6), although the impact of random noise on diminishes
with , the magnitude uncertainty in , given by, [17, p. 9ff],
does not.
For Case 2 measurements the noise variance, , and the magnitude uncertainty,
±s, must enter into the total uncertainty in the mean temperature as .
Therefore under Case 2, the uncertainty never approaches zero no matter how large
N becomes, because although ±
σ
nshould automatically average away, ±sis never
zero.
The usual way to represent the uncertainty in averages of inherently varying
magnitudes is with the standard deviation (SD) of the total scatter about the mean [17,
p. 11], e.g., . If the sensor ±
σ
nhas been measured
independently, then ±scan be extracted as because
measurement noise and magnitude scatter are statistically independent. The magnitude
uncertainty, ±s, is a measure of how well a mean represents the state of the system. A
large ±s relative to a mean implies that the system is composed of strongly
heterogeneous sub-states poorly represented by the mean state [18]. This caution has
bearing on the physical significance of mean temperature anomalies (see below).
2.3. Case 3
Finally, suppose a series of N temperature measurements of inherently unique
magnitudes but now also with unique and unequal noise variances. Thus as in Case 2,
±=±sSD N
n
()
σ
SD t T N
i
i
N
=− −
=
()()
_2
1
1
TNs
n
_
()±±
σ
σ
n
2
±=
=
sN
i
i
N
()
τ
2
1
1
T
_
1N
T
_
ττ
ii
T=−
T
_
sNi
i
N
22
1
1
1
==
()
τ
σσ
noise i
i
N
noise
NnN
22
1
1
=→±
=
()
τ
i
T
_
τ
i
()( )tT n
iii
−= +
τ
T
_
ττ
ij
972 Energy & Environment · Vol. 21, No. 8, 2010
, but now both and .
This condition could arise from a time-dependent shift in the magnitude of the
measurement noise of a single sensor, or when averaging temperatures from multiple
sensors that each exhibits an independent and unique noise variance. The latter
situation is closest to a real-world spatial average, in which temperature measurements
from numerous stations are combined.
2.3.1. Case 3a
If the unequal noise variances from each and all of the station sensors are known to be
stationary and uncorrelated, then and the variance of the mean is
[17, p. 57]. One can simplify analysis by scaling all the variances
to a single variance, thus , where
are the coefficients of scale. Each of the N unequal variances entering a
mean can now be transformed into an average variance of uniform magnitude as,
(7)
where , and is a constant stationary
variance. On combining N measurements, the variance of the mean becomes,
(8)
The average noise uncertainty in is then , and if
σ
2
iwas the minimum of variances, then . Thus, with stationary noise variances
of known but uneven magnitude, an average noise uncertainty can be found,
, that again diminishes as . It is important to notice that
of Case 2, a variance of noise, is calculationally and conceptually distinct from of
Case 3, an average of variances.
2.3.2. Case 3b
When sensor noise variances have not been measured and neither their stationarity nor
their magnitudes are known, an adjudged average noise variance must be assigned
using physical reasoning [19]. For multiple sensors of unknown noise provenance, or
for a time series from a single sensor of unknown and possibly irregular variance, an
σ
n
2
σ
n
2
1N
±=±
σσ
noise c
q
q>1
T
_
σ
σσ
σ
µ
2
2
1
2
2
1
1
1
===
=
()
q
N
q
q
N
c
i
n
c
c
σσ
ic
22
qN cc c
jk n
++++()( ... )11
11
1
222 2
Ncc c Ncc c
ijiki ni jk n
( ... ) ( ...
σσσ σ
++++ =++++))
σσσ
iic
qq
222
==
cc c
jk n
,,...,
σσσ σσ σ σ σ
iijjikki nni
cc c
222 22 2 2 2
== = =; ; ; ...;
σσ
µ
22
1
11=
=
()
i
i
n
TNti
i
N
_
=
=
1
1
σσσσ
1
2222
≠≠≠... ...
ij n
ττττ
1≠≠ ≠ ≠≠... ...
ij n
tn
iii
=+
τ
Uncertainty in the global average surface air temperature index: 973
a representative lower limit
adjudged estimate of measurement noise variance is implicitly a simple average,
, where each is of unknown provenance and nominally represents
the unique noise variance of one of the N measurements. The primed sigma indicates
an adjudged estimate and distinguishes Case 3b noise uncertainty from those of Cases
1-3a.
In the case of an adjudged average noise uncertainty, each temperature
measurement must be appended with the constant uncertainty estimate as, .
The mean of a series of N measurements is the usual , but the average
noise uncertainty in the measurement mean is [17, p. 58,
wi = 1], with one degree of freedom lost because the estimated noise variance in each
measurement is an implied mean.
Thus when calculating a measurement mean of temperatures appended with an
adjudged constant average uncertainty, the uncertainty does not diminish as .
Under Case 3b, the lack of knowledge concerning the stationarity and true magnitudes
of the measurement noise variances is properly reflected in a greater uncertainty in the
measurement mean. The estimated average uncertainty in the measurement mean,
, is not the mean of a normal distribution of variances, because under Case 3b the
magnitude distribution of sensor variances is not known to be normal.
The condition in Case 3 also produces a magnitude uncertainty, ±s, in
analogy with Case 2. When the magnitudes and stationarities of measurement noise
variances are both unknown, the total uncertainty in a measurement mean is
. In Case 3b, does not diminish as , and ±s
cannot be separated from .
3. RESULTS AND DISCUSSION
3.1. The average noise uncertainty estimate
It is now possible to evaluate the ±0.2 C uncertainty estimate of Folland, et al. [12],
who "estimated the two standard error (2σ) measurement error to be 0.4 °C in any
single daily [land air-surface temperature] observation." This estimate was not based
on a survey of sensors nor followed by a supporting citation. The temperature sensor
at each station will exhibit a unique and independent noise variance, and the context
in Ref. [12] provides that the ±0.2 C is from the estimated average variance of the
ensemble of variances of the individual surface station sensors entering measurements
into a global average surface air temperature. This estimated uncertainty thus falls
under Case 3, above.
Following this identification, the question next becomes whether the relevant
station sensor noise variances are stationary and of known magnitude. In general,
detailed examinations of errors in station histories have focused principally on
inhomogeneities due to instrumental changes and station moves [3, 9, 20-24], but have
±
σ
µ
1N
±
σ
µ
±= −
=
σ
total i
i
N
tT N()()
_2
1
1
ττ
ij
±
σ
µ
1N
±
σσ
µ
NN
noise
21()
TNti
i
N
_
=
=
1
1
tinoise
±
σ
σ
i
2
=
=
σσ
noise i
i
N
N
22
1
1
974 Energy & Environment · Vol. 21, No. 8, 2010
not mentioned appraisals of station sensor variance. Reviews of time series quality
control and homogeneity adjustments do not discuss sensor evaluation [7-10], and the
methodological report of USHCN data quality [25] does not describe validation or
sampling of noise stationarity in temperature sensors. The surface station sensor
diagnostics, available in the online reports of the new USCRN National Climatic Data
Center network, include standard deviations calculated from the twelve temperatures
recorded hourly (http://www.ncdc.noaa.gov/crn/report; see the "Air Temperature
Sensor Summary," under "Instruments"). But despite the set of ~8640 monthly
standard deviations from individual CRN sensor data streams, which should give some
measure of the magnitude and stationarity of variance, no extensive survey of station
sensor variance is evident in published work.
The quality of individual surface stations is perhaps best surveyed in the US by way
of the commendably excellent independent evaluations carried out by Anthony Watts
and his corps of volunteers, publicly archived at http://www.surfacestations.org/ and
approaching in extent the entire USHCN surface station network. As of this writing,
69% of the USHCN stations were reported to merit a site rating of poor, and a further
20% only fair [26]. These and more limited published surveys of station deficits [24,
27-30] have indicated far from ideal conditions governing surface station
measurements in the US. In Europe, a recent wide-area analysis of station series
quality under the European Climate Assessment [31], did not cite any survey of
individual sensor variance stationarity, and observed that, "it cannot yet be guaranteed
that every temperature and precipitation series in the December 2001 version will be
sufficiently homogeneous in terms of daily mean and variance for every application."
Likewise, sensor variance was not mentioned in recent studies of data quality from
surface stations in Canada [32, 33], where it was noted in 2002 that, "adjustments have
only been carried out for identified step changes and the homogenized monthly
temperatures have not been adjusted for artificial trends at this time." The authors
stated further that, "The preferred methodology would be to develop procedures based
on each cause of inhomogeneity. However, this would be a very site-specific task that
would be nearly impossible to implement on a Canada-wide basis." Station
evaluations for sensor variance are also not mentioned in the climate normals report of
Environment Canada [34].
Thus, there apparently has never been a survey of temperature sensor noise
variance or stationarity for the stations entering measurements into a global
instrumental average, and stations that have been independently surveyed have
exhibited predominantly poor site quality. Finally, Lin and Hubbard have shown [35]
that variable field conditions impose non-linear systematic effects on the response of
sensor electronics, suggestive of likely non-stationary noise variances within the
temperature time series of individual surface stations (see Section 3.2.2).
These considerations indicate that an assumption of stationary noise variance in
temperature time series cannot be presently justified, and that the assumption of
random station errors is not empirically tenable. Therefore, the ±0.2 C estimate in Ref.
[12] is the assessed of Case 3b above, namely an adjudged assignment taken
to represent the average uncertainty from an ensemble of surface station measurement
±
σ
noise
Uncertainty in the global average surface air temperature index: 975
a representative lower limit
noise variances of unknown magnitude and stationarity. It does not represent the
magnitude of random noise for any specific measurement, nor does it represent the
noise variance of any specific sensor, nor is it an average of known stationary
variances. Following Case 3b, the ±0.2 C estimate of Ref. [12] is ; an adjudged
constant average uncertainty that attaches to each surface temperature measurement
and that must therefore be carried into a spatial average of N station measurements as
. This uncertainty does not decrement as
when calculating a mean, and will constitute a significant part of the total uncertainty
in any global average surface air temperature index. Therefore the noise
reduction model in B06 is in error.
Clearly, a different statistical approach to uncertainty in air temperature averages is
warranted; one that reflects the true empirical uncertainties. This approach is shown next.
3.2. An empirical approach to temperature uncertainty
Tmax and Tmin are typically measured many hours apart under physically opposing
irradiance conditions. Although they may have an identical instrumental noise
structure, they are experimentally independent measurements of physically different
observables, each measured separately.
3.2.1. Uncertainty due to estimated noise
Following from Case 3b and the discussion in Section 3.1 above, the estimated per-
measurement uncertainty = ±0.2 C from Ref. [12] must enter as a constant
applied to each temperature measurement. This value also represents the achievable
uncertainty recommended by the World Meteorological Organization [36]. Using this
value, and including normalization to a 30-year mean, the noise uncertainty in an
annual anomaly is now stepwise calculated.
In order to maximally reduce the uncertainty, the annual temperature and the 30-year
mean temperature were calculated directly, as though from individual
measurements, as , where is annual mean temperature, is a 30-year
mean reference, tiis an individual measurement, and N is the number of measurements
(twice the number of days entering each mean). Applying the estimated average per-
measurement uncertainty, , the total noise uncertainty in any
measurement average is
(9)
where N is the number of measurements entering the mean. This calculation yields
= ±0.200 for both an annual mean temperature and a 30-year mean, and this
uncertainty enters separately into each mean.
In calculating the uncertainty in an annual anomaly referenced against a multi-
decadal mean, , the uncertainties in each mean value are combined in
TTT
a=−
ˆ
±
σ
n
±=×
σσ
n
n
N
N
2
1
±
σ
nC02.
ˆ
T
T
_
TorT Nti
i
N
ˆ=
=
1
1
±
σ
n
1N
1N
±
σ
µ
±
σσ
µ
NN
noise
21()
±
σ
noise
976 Energy & Environment · Vol. 21, No. 8, 2010
quadrature [17, p. 48]. The average noise uncertainty in the annual anomaly is then,
= ±0.283 C, where , are
the average noise uncertainties in the annual mean temperature, or the 30-year mean
temperature, respectively. The represents the minimal noise-derived uncertainty
in an annual temperature anomaly, referenced to a 30-year mean, for any given surface
station when using the per-measurement estimated = ±0.20 C of Folland, et al. [12].
It is also possible to obtain an annual anomaly by normalizing an annual
temperature series to a fitted mean obtained by regression against a 30-year annual
temperature time series. However, a regression mean introduces the uncertainty of the
fit into the total uncertainty. This new uncertainty is the numerical estimated standard
deviation (e.s.d.) of the fit, further scaled to reflect the reduced degrees of freedom
induced by autocorrelation of the residuals [37]. The average uncertainty of each
annual anomaly magnitude is then,
,(10)
where (e.s.d.)i is the numerical estimated standard deviation per point, N is the number
of points, and
ν
is the number of degrees of freedom lost through autocorrelation of
the residuals.
Finally, in every case, a magnitude uncertainty, ±s, must also be included as part of
the uncertainty in an annual anomaly. The magnitude uncertainty in an annual
anomaly, ±sa, can be estimated as , where ±sis the magnitude
uncertainty in a yearly average temperature, is the average annual temperature
anomaly, referenced to a 30-year mean, and is the average temperature for that
same year. This uncertainty transmits the confidence that may be placed in an anomaly
as representative of the state of the system.
3.2.2. Uncertainty due to systematic impacts on instrumental field resolution
The degraded instrumental resolution due to the systematic error from uncontrolled
variables [38, 39] has apparently never found its way into any published assessment
of the uncertainties in the global average surface air temperature index. The systematic
measurement errors originating from the field exposure of the Min-Max Temperature
System (MMTS), Automated Surface Observing System (ASOS), the Gill shield, and
other commonly used electronic temperature sensors and shields have been
investigated in excellent detail by Lin and Hubbard [35] and found to originate
principally from solar radiation loading and wind speed effects. Other sources of error
were enumerated as, "originating with the sensing element, analog signal
conditioning, and data acquisition system [and] include the sensor interchangeability
error, polynomial and linearization errors, self-heating error, voltage or current
reference (excitation) error, total offset and drift in the amplifiers and ADC (associated
T
_
Ta
±=±×ssTT
aa
()
±=+× −
ˆ()[ (...) ( )]
σσ ν
n
T
i
Nesd N
22
σ
n
±
ˆ
σ
n
±
σ
n
T
ˆ
±
σ
n
T
±=+=+
ˆ()() (. )(. )
ˆ
σσ σ
nn
T
n
TCC

22 2 2
02 02
Uncertainty in the global average surface air temperature index: 977
a representative lower limit
with stability), and lead wire error." All these systematic errors, including the
microclimatic effects, vary erratically in time and space [40-45], and can impose non-
stationary and unpredictable biases and errors in sensor temperature measurements
and data sets. These uncontrolled experimental variables degrade instrumental field
resolution, and must be included in assessments of uncertainty in spatially and
chronologically averaged temperatures.
Under ideal site conditions Hubbard and Lin recorded thousands of air
temperatures using MMTS, ASOS, Gill, and other sensors and shields [13, 35, 42],
and compared them to temperatures simultaneously measured using a calibrated high-
resolution R. M. Young temperature probe with an aspirated shield. For each recorded
temperature, the measurement rate was 6 min.-1 integrated across 5 min., reducing the
random noise in each aggregated temperature measurement by . The
temperature data thus consisted primarily of a bias and a resolution width relative to
the "true" temperature provided by the R. M. Young probe. Figure 1 shows the ideal
day time field resolution envelopes of the MMTS, ASOS temperature sensors and Gill
shield [13], fitted with the Gaussian ,
where ais a vertical offset, bis an intensity scaler, σis the Gaussian (intensity)/e1/2
half-width (the standard deviation), and µis the Gaussian mean. The results of the fits
are shown in Table 1.
Analogous fits to the 24-hour average data yielded, (sensor, µ(C), 1σ(±C), r2):
MMTS, (0.29, 0.25, 0.995); ASOS, (0.18, 0.14, 0.993), and; Gill, (0.21, 0.19, 0.979).
These values are somewhat different from those originally reported in Ref. [13], which
were not obtained from Gaussian fits.
The sensor evaluations were carried out under conditions of ideal siting and
excellent maintenance [13]. Therefore, the field resolutions listed above approximate
best achievable values and represent an attainable lower limit of instrumental
resolution under field use conditions. Instrumental resolution by itself constitutes the
minimum uncertainty in any temperature measurement, and the response of ideally
sited and maintained sensors provides an empirical lower limit of field resolution.
Table 1: Lower Limit Temperature Sensor Resolutions from Gaussian fits
ab x − −()exp{ [( )( ) ]}12 12 2
σπ µσ
130/
978 Energy & Environment · Vol. 21, No. 8, 2010
Figure 1. Daytime (a) and nighttime (b) resolution of: (o), MMTS; (), ASOS, and;
() Gill temperature sensors. The points were derived from Figure 2a,b of Ref. [13],
using the program Digitizeit (www.digitizeit.de). The curves were normalized to unit
area and each temperature bias relative to the R. M. Young probe was removed to
yield a common mean of 0 C. The lines are Gaussian fits to the points. The ASOS
and Gill data were vertically shifted 1 and 2 units, respectively, for clarity.
Temperature sensor resolution can, however, be significantly improved by application
of a real-time empirical filtering algorithm to minimize the systematic error due to
uncontrolled micro-climate variables [13, 46], as shown in Figure 2.
Uncertainty in the global average surface air temperature index: 979
a representative lower limit
From the fits in Figure 2, the improved resolution of filtered MMTS data yields an
uncertainty of ±0.093 C in daily mean temperature (cf. Figure 2, Legend). Using the
equations gathered in Table 2, a minimum adjudged average ±0.1 C noise uncertainty
and the ±0.093 C filtered resolution from a well-maintained MMTS sensor in an ideal
site location, alone, yield a r.m.s. uncertainty in a per-station yearly temperature
anomaly of = ±0.193 C. However, the field resolution of
surface station temperature sensors is not yet commonly improved using the Hubbard-
Lin filter.
Figure 2. Gaussian fits to algorithmically filtered MMTS temperature resolution
data, digitized as in Figure 4 and extracted from Ref. [46]. a. Daytime and b.
nighttime, normalized to unit area and with the temperature bias again removed to
produce a common mean of 0 C. The fit parameters are: a. σ = ±0.093±0.002 C,
r2 = 0.993, and; b. σ = ±0.029±0.001 C, r2= 0.987.
(. ) (. )0 141 0 132
22
+
980 Energy & Environment · Vol. 21, No. 8, 2010
3.2.3. The lower limit uncertainty in an annual temperature anomaly
Appropriate statistics are now used to combine the average noise uncertainty of
Section 3.2.1 and the ideal lower limit of systematic error from Section 3.2.2, into a
composite lower limit of measurement uncertainty in surface station air temperature
anomalies.
The equations used to propagate an appended per-measurement uncertainty into an
annual anomaly, due to the entry of systematic error into field resolution, are
analogous to those used to propagate the constant average noise uncertainty. One
degree of freedom is lost in the statistical uncertainty mean because every
determination of systematic error in a temperature data set is an average of the effects
of uncontrolled variables. Each determination of field resolution uncertainty is also
unique in terms of bias and width, because uncontrolled variables fluctuate in time and
space. The idealized field resolutions for MMTS, ASOS sensors and the Gill shield
referenced to a 30-year mean are shown in Table 2. For an MMTS sensor under ideal
site conditions these equations yielded ±σ
r= ±0.36 C, which represents a lower limit
of resolution uncertainty from each such station entering into a global average
anomaly. Table 2 also includes the analogous Case 3b average noise uncertainties from
Section 3.2.1.
Table 2: Uncertainty in an Annual Anomaly Due to Noise or Resolutiona
a. Rows are, top: uncertainty in a yearly mean temperature; bottom: uncertainty in yearly anomaly
referenced to a 30 year mean. b. Uncertainty Equation. c. 1σ(±C; day, night): MMTS=(0.23, 0.17);
ASOS=(0.16, 0.11), and Gill=(0.22, 0.12); see Table 1.
Figure 1 and Table 2 reflect average noise, and the resolution uncertainties currently
expected from the ideal placement and maintenance of conventional surface station
temperature sensors. For any one surface-station deploying a modern MMTS sensor,
the minimal measurement uncertainty will be the average noise plus the ideal
resolution uncertainties combined in quadrature [39, Section 5, 47]. From Table 2, for
an MMTS sensor the total noise plus resolution lower-limit 1σmeasurement
uncertainty in an annual temperature anomaly referenced to a 30-year mean is
= ±0.46 C.
The meaning of an ideal lower limit of measurement uncertainty provides that it is
of lower magnitude than the uncertainty in each and all of the other homologous
single-station measurements, worldwide. Thus, liquid-in-glass (LIG) thermometers in
±= +
ˆ(. ) (. )
σ
0 283 0 359
22
Uncertainty in the global average surface air temperature index: 981
a representative lower limit
Cotton Regional Shelters are reckoned to be of lower field resolution than the MMTS
sensor [3, 41, 48]. Further, precision comparisons have shown that the systematic error
introduced into surface station temperatures by the Cotton Regional Shelter is about
twice that of the MMTS aspirated shield [42]. Thus, the ±0.46 C lower limit
uncertainty of a modern MMTS sensor underestimates the uncertainty in the
measurements from LIG thermometers in CRS shields that constitute the bulk of the
20th century global surface air temperature record.
The ±0.46 C lower limit of MMTS uncertainty is therefore applicable to every
measurement in the global land surface record, because of the very high likelihood that
it is of lower magnitude than the unknown uncertainties produced by surface station
sensors that are generally more poorly maintained, more poorly sited, and less accurate
than the reference sensors. The ideal resolutions of Figure 1 and Table 2 thus provide
realistic lower-limits for the air temperature uncertainty in each annual anomaly of
each of the surface climate stations used in a global air temperature average. This
lower limit of measurement uncertainty for each surface station annual temperature
anomaly is propagated into a global average as,
,(11)
to produce the total lower limit of uncertainty in a global temperature anomaly. Here
σ
2
iis the lower limit mean noise plus resolution annual temperature uncertainty at the
ith station, and N is the number of stations. For example, the lower limit of sensor
uncertainty propagates into a global surface average air temperature anomaly as
, when, e.g., N = 4349 as in Ref. [11].
This uncertainty enters each anomaly in a global annual time series, and will be in
addition to the commonly discussed uncertainties resulting from weather noise, step
discontinuities, incomplete station coverage, land-use changes, siting artifacts [26],
and albedo changes [49]. It seems likely that the new USCRN stations [50] will not
significantly improve on the lower limit uncertainty any time soon [51].
3.2.4. The representative lower limit uncertainty in a global average air temperature
anomaly time series
In independent calculations of global average surface air temperature anomalies,
[52-54], the major source of uncertainty was assigned to incomplete station
coverage, 2σ= ±0.07 C [55], with most of the remaining uncertainty assigned to
the temporal inhomogeneity of temperature records [5]. These estimates of the global
surface air temperature index did not include the instrumental uncertainties present in
the surface station temperature measurements themselves, however. Therefore, the
effect of the ideal lower limit uncertainty illustrated above on the reliability of the
global average surface air temperature index is briefly considered below.
±=±× −=±
σ
global NCN C(. ) ( ) . 046 1 046
2
±=
=
ˆ
ˆ
σ
σ
total
i
i
N
N
2
1
1
982 Energy & Environment · Vol. 21, No. 8, 2010
The uncertainties due to average noise and instrumental resolution in maritime
temperature sensors remain to be evaluated and propagated into marine air
temperature anomalies [11]. However, assessments of instrumental uncertainties in
marine air and sea-surface temperatures have revealed evidence of significantly large
systematic errors [56, 57], which both bias marine temperature measurements and
imply an instrumental resolution degraded by uncontrolled environmental variables
throughout the 20th century. Uncertainties in marine temperatures are thus not likely
to be less than appraised here for land surface stations [4, 58, 59]. Therefore, the lower
limit uncertainty in an MMTS land surface anomaly, σ= ±0.46 C, can be credibly
applied to the global land + ocean anomalies.
Figure 3 shows the global average surface air temperature anomaly index as
compiled from surface and maritime meteorological stations and provided by the
Goddard Institute for Space Studies, as updated on 18 February 2010. The lower limit
±0.46 C uncertainty in an annual surface anomaly is plotted on Figure 3 to illustrate a
credible lower limit of uncertainty in the current surface air temperature anomaly
series.
Figure 3. (), the global surface air temperature anomaly series through 2009, as
updated on 18 February 2010, (http://data.giss.nasa.gov/gistemp/graphs/). The grey
error bars show the annual anomaly lower-limit uncertainty of ±0.46 C.
Uncertainty in the global average surface air temperature index: 983
a representative lower limit
Figure 3 shows that the trend in averaged global surface air temperature from 1880
through 2000 is statistically indistinguishable from zero (0) Celsius at the 1σlevel
when this lower limit uncertainty is included, and likewise indistinguishable at the 2σ
level through 2009. Thus, although Earth climate has unambiguously warmed during
the 20th century, as evidenced by, e.g., the poleward migration of the northern tree line
[60-62], the rate and magnitude of the average centennial warming are not knowable.
4. SUMMARY AND CONCLUSIONS
The assumption of global air temperature sensor noise stationarity is empirically
untested and unverified. Estimated noise uncertainty propagates as ,
rather than as . Future noise uncertainty in monthly means would greatly
diminish if the siting of surface stations is improved and the sensor noise variances
become known, monitored, and empirically verified as stationary.
The persistent uncertainty due to the effect of uncontrolled microclimatic variables
on temperature sensor resolution has, until now, never been included in published
assessments of global average surface air temperature. Average measurement noise
and the lower limit of systematic sensor errors combined to yield a representative
lower limit uncertainty of ±0.46 C in a 30-year mean annual temperature anomaly. In
view of the problematic siting record of USHCN sensors, a globally complete
assessment of current air temperature sensor field resolution seems likely to reveal a
measurement uncertainty exceeding ±0.46 C by at least a factor of 2.
The ±0.46 C lower limit of uncertainty shows that between 1880 and 2000, the
trend in averaged global surface air temperature anomalies is statistically
indistinguishable from 0 C at the 1σlevel. One cannot, therefore, avoid the conclusion
that it is presently impossible to quantify the warming trend in global climate since
1880.
Finally, the relatively large uncertainty attending the global surface instrumental
record means that the centennial temperature trend is not a precision target for
validation tests of climate models. Likewise, the current surface instrumental record
cannot credibly be used to train or renormalize any physically valid proxy
reconstruction of paleo-temperature with sufficient precision to resolve any
temperature difference less than at least 1 C, to 95% confidence. It is thus impossible
to know whether the rate of warming during the 20th century was climatologically
unprecedented, or to know the differential magnitude of any air temperature warmer
or cooler than the present, within ±1 C, for any year prior to the satellite era. Therefore
previous suggestions, that the rate or magnitude of present climate warming is recently
or millennially unprecedented, must be vacated.
ACKNOWLEDGEMENTS
The author thanks Prof. David Legates, University of Delaware, Dr. David Stockwell,
University of California San Diego, and Prof. Demetris Koutsoyiannis, Athens
NTUA, for critically reviewing a previous version of this manuscript.
±
σ
nN
±NN
n
σ
21()
984 Energy & Environment · Vol. 21, No. 8, 2010
REFERENCES
1. Cicerone, R., Barron, E.J., Dickenson, R.E., Fung, I.Y., Hansen, J.E., Karl, T.R., Lindzen,
R.S., McWilliams, J.C., Rowland, F.S., Sarachik, E.S. and Wallace, J.M., Climate Change
Science: An Analysis of Some Key Questions, The National Academy of Sciences, USA,
http://books.nap.edu/openbook.php?record_id=10139&page=1, Last accessed on: 28
March 2010.
2. Bernstein, L., Bosch, P., Canziani, O., Chen, Z., Christ, R., Davidson, O., Hare, W., Huq,
S., Karoly, D., Kattsov, V., Kundzewicz, V., Liu, J., Lohmann, U., Manning, M., Matsuno,
T., Menne, B., Metz, B., Mirza, M., Nicholls, N., Nurse, L., Pachauri, R., Palutikof, J.,
Parry, M., Qin, D., Ravindranath, N., Reisinger, A., Ren, J., Riahi, K., Rosenzweig, C.,
Rusticucci, M., Schneider, S., Sokona, Y., Solomon, S., Stott, P., Stouffer, R., Sugiyama,
T., Swart, R., Tirpak, D., Vogel, C. and Yohe, G., Climate Change 2007: Synthesis Report.
Contribution of Working Groups I, II and III to the Fourth Assessment Report of the
Intergovernmental Panel on Climate Change, in, Pachauri, R.K. & Reisinger, A., eds.
IPCC, Geneva, Switzerland, 2007, pp. 104 pp.
3. Karl, T.R., Tarpley, J.D., Quayle, R.G., Diaz, H.F., Robinson, D.A. and Bradley, R.S., The
Recent Climate Record: What it Can and Cannot Tell Us, Rev. Geophys., 1989, 27(3),
405-430.
4. Trenberth, K.E., Christy, J.R. and Hurrell, J.W., Monitoring Global Monthly Mean
Surface Temperatures, J. Climate, 1992, 5, 1405-1423; doi: 10.1175/1520-
0442(1992)005.
5. Hansen, J. and Lebedeff, S., Global Trends of Measured Surface Air Temperature, J.
Geophys. Res., 1987, 92(D11), 13345-13372.
6. Easterling, D.R., Peterson, T.C. and Karl, T.R., On the Development and Use of
Homogenized Climate Datasets, J. Climate, 1996, 9(6), 1429-1434; doi: 10.1175/1520-
0442(1996)009<1429:OTDAUO>2.0.CO;2.
7. Jones, P.D., Osborn, T.J. and Briffa, K.R., Estimating Sampling Errors in Large-Scale
Temperature Averages, J. Climate, 1997, 10(10), 2548-2568; doi: 10.1175/1520-
0442(1997)010<2548:ESEILS>2.0.CO;2.
8. Peterson, T.C., Easterling, D.R., Karl, T.R., Groisman, P., Nicholls, N., Plummer, N.,
Torok, S., Auer, I., Boehm, R., Gullet, D., Vincent, L., Heino, R.T., H., Mestre, O.,
Szentimrey, T., Salinger, J., Førland, E., Hanssen-Bauer, I., Alexandersson, H., Jones, P.
and Parker, D., Homogeneity adjustments of in situ atmospheric climate data: a review,
Int. J. Climatol., 1998, 18(13), 1493-1517.
9. Peterson, T.C., Vose, R., Schmoyer, R. and Razuvaëv, V., Global historical climatology
network (GHCN) quality control of monthly temperature data, Int. J. Climatol., 1998,
18(11), 1169-1179; doi: 10.1002/(SICI)1097-0088(199809)18:11<1169::AID-
JOC309>3.0.CO;2-U.
10. Peterson, T.C. and Sun, B., Estimating temperature normals for USHCN stations, Int. J.
Climatol., 2005, 25(4), 1809-1817; doi: 10.1002/joc.1220.
Uncertainty in the global average surface air temperature index: 985
a representative lower limit
11. Brohan, P., Kennedy, J.J., Harris, I., Tett, S.F.B. and Jones, P.D., Uncertainty estimates in
regional and global observed temperature changes: A new data set from 1850, J. Geophys.
Res., 2006, 111 D12106 1-21; doi:10.1029/2005JD006548; see
http://www.cru.uea.ac.uk/cru/info/warming/.
12. Folland, C.K., Rayner, N.A., Brown, S.J., Smith, T.M., Shen, S.S.P., Parker, D.E.,
Macadam, I., Jones, P.D., Jones, R.N., Nicholls, N. and Sexton, D.M.H., Global
Temperature Change and its Uncertainties Since 1861, Geophys. Res. Lett., 2001, 28(13),
2621-2624.
13. Hubbard, K.G. and Lin, X., Realtime data filtering models for air temperature
measurements, Geophys. Res. Lett., 2002, 29(10), 1425 1-4; doi:
10.1029/2001GL013191.
14. Aunon, J.I., McGillum, C.D. and Childers, D.G., Signal Processing in Evoked Potential
Research: Averaging and Modeling, CRC Crit. Rev. Bioeng., 1981, 5(4), 323-367; cf. eqs.
10-18.
15. Leski, J., New Concept of Signal Averaging in the Time Domain, in, Nagel, J.H. & Smith,
W.M., eds. Vol. 13: Proc. Annu. Int. Conf. IEEE Eng. Med. Biol. Soc., IEEE, Orlando,
FL, 1991, pp. 367-369.
16. Mark, H. and Workman jr., J., Statistics in Spectroscopy, 2nd edn., Elsevier; cf. Chapter
11, Amsterdam 2003.
17. Bevington, P.R. and Robinson, D.K., Data Reduction and Error Analysis for the Physical
Sciences, 3rd edn., McGraw-Hill, Boston 2003.
18. Esper, J. and Frank, D., The IPCC on a heterogeneous Medieval Warm Period, Climatic
Change, 2009, 94 267-273; doi: 10.1007/s10584-008-9492-z.
19. Gleser, L.J., Assessing uncertainty in measurement, Statist. Sci., 1998, 13 (3), 277-290;
doi: 10.1214/ss/1028905888.
20. Guttman, N.B. and Plantico, M.S., Climatic Temperature Trends, J. Clim. Appl.
Meteorol., 1987, 26 1428-1435; doi: 10.1175/1520-
0450(1987)026<1428:CTN>2.0.CO;2.
21. Reek, T., Doty, S.R. and Owen, T.W., A Deterministic Approach to the Validation of
Historical Daily Temperature and Precipitation Data from the Cooperative Network, Bull.
Amer. Met. Soc., 1992, 73(6), 753-762; doi:10.1175/1520-
0477(1992)073<0753:ADATTV>2.0.CO;2.
22. Easterling, D.R. and Peterson, T.C., A new method for detecting undocumented
discontinuities in climatological time series, Int. J. Climatol., 1995, 15 (4), 369-377; doi:
10.1002/joc.3370150403.
23. Sun, B. and Peterson, T.C., Estimating temperature normals for USCRN stations, Int. J.
Climatol., 2005, 25(14), 1809-1817; doi: 10.1002/joc.1220.
24. Pielke Sr., R., Nielsen-Gammon, J., Davey, C., Angel, J., Bliss, O., Doesken, N., Cai, M.,
Fall, S., Niyogi, D., Gallo, K., Hale, R., Hubbard, K.G., Lin, X., Li, H. and Raman, S.,
Documentation of Uncertainties and Biases Associated with Surface Temperature
Measurement Sites for Climate Change Assessment, Bull. Amer. Met. Soc., 2007, 913-
928; doi: 10.1175/BAMS-88-6-913.
986 Energy & Environment · Vol. 21, No. 8, 2010
25. NCDC, Environmental Information Summaries C-23; United States Climate Normals,
1971-2000 Inhomogeneity Adjustment Methodology, National Climatic Data
Center/NESDIS/NOAA, http://lwf.ncdc.noaa.gov/oa/climate/normals/normnws0320.pdf,
Last accessed on: 28 March 2010.
26. Watts, A., Is the U.S. Surface Temperature Record Reliable?, The Heartland Institute,
Chicago, IL 2009
27. Davey, C.A. and Pielke Sr., R.A., Microclimate Exposures of Surface-Based Weather
Stations, Bull. Amer. Met. Soc., 2005, 86(4), 497-504; doi: 10.1175/BAMS-86-4-497.
28. Runnalls, K.E. and Oke, T.R., A Technique to Detect Microclimatic Inhomogeneities in
Historical Records of Screen-Level Air Temperature, J. Climate, 2006, 19(6), 959-978.
29. Pielke Sr., R.A., Davey, C.A., Niyogi, D., Fall, S., Steinweg-Woods, J., Hubbard, K., Lin,
X., Cai, M., Lim, Y.-K., Li, H., Nielsen-Gammon, J., Gallo, K., Hale, R., Mahmood, R.,
Foster, S., McNider, R.T. and Blanken, P., Unresolved issues with the assessment of
multidecadal global land surface temperature trends, J. Geophys. Res., 2007, 112 D24S08
1-26; doi: 10.1029/2006JD008229.
30. Fiebrich, C.A. and Crawford, K.C., Automation: A Step Toward Improving the Quality
of Daily Temperature Data Produced by Climate Observing Networks, Journal of
Atmospheric and Oceanic Technology, 2009, 26(7), 1246-1260.
31. Klein Tank, A.M.G., Wijngaard, J.B., Können, G.P., Böhm, R., Demarée, G., Gocheva,
A., Mileta, M., Pashiardis, S., Hejkrlik, L., Kern-Hansen, C., Heino, R., Bessemoulin, P.,
Müller-Westermeier, G., Tzanakou, M., Szalai, S., Pálsdóttir, T., Fitzgerald, D., Rubin, S.,
Capaldo, M., Maugeri, M., Leitass, A., Bukantis, A., Aberfeld, R., van Engelen, A.F.V.,
Forland, E., Mietus, M., Coelho, F., Mares, C., Razuvaev, V., Nieplova, E., Cegnar, T.,
Antonio López, J., Dahlström, B., Moberg, A., Kirchhofer, W., Ceylan, A., Pachaliuk, O.,
Alexander, L.V. and Petrovic, P., Daily dataset of 20th-century surface air temperature
and precipitation series for the European Climate Assessment, Int. J. Climatol., 2002,
22(12), 1441-1453; doi: 10.1002/joc.773.
32. Vincent, L.A. and Gullett, D.W., Canadian historical and homogeneous temperature
datasets for climate change analyses, Int. J. Climatol., 1999, 19(12), 1375-1388.
33. Vincent, L.A., Zhang, X., Bonsal, B.R. and Hogg, W.D., Homogenization of Daily
Temperatures over Canada, J. Climate, 2002, 15 (11), 1322-1334; doi: 10.1175/1520-
0442(2002)015<1322:HODTOC>2.0.CO;2.
34. Allsop, D. and Morris, R., Calculation of the 1971 to 2000 Climate Normals for Canada,
Meteorological Service of Canada,
http://www.climate.weatheroffice.ec.gc.ca/prods_servs/normals_documentation_e.html,
Last accessed on: 28 March 2010.
35. Lin, X. and Hubbard, K.G., Sensor and Electronic Biases/Errors in Air Temperature
Measurements in Common Weather Station Networks, J. Atmos. Ocean. Technol., 2004,
21 1025-1032.
36. Rüedi, I., WMO Guide to Meteorological Instruments and Methods of Observation:
WMO-8 Part I: Measurement of Meteorological Variables, 7th Ed., Chapter 1, World
Meteorological Organization, Geneva 2006
http://www.wmo.int/pages/prog/www/IMOP/IMOP-home.html.
Uncertainty in the global average surface air temperature index: 987
a representative lower limit
37. Santer, B.D., Wigley, T.M.L., Boyle, J.S., Gaffen, D.J., Hnilo, J.J., Nychka, D., Parker,
D.E. and Taylor, K.E., Statistical significance of trends and trend differences in layer-
average atmospheric temperature time series, J. Geophys. Res., 2000, 105(D6), 7337-
7356.
38. Eisenhart, C., Expression of the Uncertainties of Final Results, Science, 1968, 160 1201-
1204.
39. Taylor, B.N. and Kuyatt., C.E., Guidelines for Evaluating and Expressing the Uncertainty
of NIST Measurement Results, National Institute of Standards and Technology,
Washington, DC 1994 http://www.nist.gov/pml/pubs/tn1297/index.cfm.
40. Ishida, H., Seasonal variations of spectra of wind speed and air temperature in the
mesoscale frequency range Boundary-Layer Meteorology, 1990, 52(4), 335-348.
41. Wendland, W.M. and Armstrong, W., Comparison of Maximum-Minimum Resistance
and Liquid-in-Glass Thermometer Records, J. Atmos. Oceanic Technol., 1993, 10(2),
233-237.
42. Hubbard, K.G., Lin, X. and Walter-Shea, E.A., The Effectiveness of the ASOS, MMTS,
Gill, and CRS Air Temperature Radiation Shields, J. Atmos. Oceanic Technol., 2001,
18(6), 851-864.
43. Snyder, R.L., Spano, D., Duce, P. and Cesaraccio, C., Temperature data for phenological
models, Int. J. Biometeorol., 2001, 45(4), 178-183.
44. Lin, X., Hubbard, K.G. and Meyer, G.E., Airflow Characteristics of Commonly Used
Temperature Radiation Shields, J. Atmos. Oceanic Technol., 2001, 18 (3), 329-339.
45. Tarara, J.M. and Hoheisel, G.-A., Low-cost Shielding to Minimize Radiation Errors of
Temperature Sensors in the Field, Hort. Sci., 2007, 42(6), 1372-1379.
46. Hubbard, K.G., Lin, X., Baker, C.B. and Sun, B., Air Temperature Comparison between
the MMTS and the USCRN Temperature Systems, J. Atmos. Ocean. Technol., 2004, 21
1590-1597.
47. Lira, I.H. and Wöger, W., The evaluation of standard uncertainty in the presence of
limited resolution of indicating devices, Meas. Sci. Technol., 1997, 8 441-443; doi:
10.1088/0957-0233/8/4/012.
48. Quayle, R.G., Easterling, D.R., Karl, T.R. and Hughes, P.Y., Effects of Recent
Thermometer Changes in the Cooperative Station Network, Bull. Amer. Met. Soc., 1991,
72 (11), 1718-1723; doi: 10.1175/1520-0477(1991)072<1718:EORTCI>2.0.CO;2.
49. Lin, X., Hubbard, K.G. and Baker, C.B., Surface Air Temperature Records Biased by
Snow-Covered Surface, Int. J. Climatol., 2005, 25 1223-1236; doi: 10.1002/joc.1184.
50. Karl, T., U. S. Climate Reference Network: Site Information Handbook, National Climate
Data Center, National Oceanic and Atmospheric Administration (NOAA), Asheville, NC
2002
51. Hubbard, K.G., Lin, X. and Baker, C.B., On the USCRN Temperature system, J. Atmos.
Ocean. Technol., 2005, 22 1095-1101.
988 Energy & Environment · Vol. 21, No. 8, 2010
52. Hansen, J., Johnson, D., Lacis, A., Lebedeff, S., P., L., Rind, D. and Russell, G., Climate
Impact of Increasing Atmospheric Carbon Dioxide, Science, 1981, 213 (4511), 957-966.
53. Hansen, J. and Lebedeff, S., Global Surface Air Temperatures: Update through 1987,
Geophys. Res. Lett., 1988, 15(4), 323-326.
54. Hansen, J., Ruedy, R., Sato, M., Imhoff, M., Lawrence, W., Easterling, D., Peterson, T.
and Karl, T., A closer look at United States and global surface temperature change, J.
Geophys. Res., 2001, 106(D20), 23947-23963; see http://data.giss.nasa.gov/gistemp/.
55. Hansen, J. and Wilson, H., Commentary on the significance of global temperature
records, Climatic Change, 1993, 25(2), 185-191; doi: 10.1007/BF01661206.
56. Kent, E.C., Taylor, P.K., Truscott, B.S. and Hopkins, J.S., The Accuracy of Voluntary
Observing Ships' Meteorological Observations-Results of the VSOP-NA, J. Atmos.
Oceanic Technol., 1993, 10(4), 591-608; doi: 10.1175/1520-
0426(1993)010<0591:TAOVOS>2.0.CO;2.
57. Berry, D.I., Kent, E.C. and Taylor, P.K., An Analytical Model of Heating Errors in Marine
Air Temperatures from Ships, Journal of Atmospheric and Oceanic Technology, 2004,
21(8), 1198-1215.
58. Kent, E.C. and Berry, D.I., Quantifying random measurement errors in Voluntary
Observing Ships' meteorological observations, Int. J. Climatol., 2005, 25(7), 843-856;
doi: 10.1002/joc.1167.
59. Berry, D.I. and Kent, E.C., The effect of instrument exposure on marine air temperatures:
an assessment using VOSClim Data, Int. J. Climatol., 2005, 25(7), 1007-1022; doi:
10.1002/joc.1178.
60. Nichols, H., Historical Aspects of the Northern Canadian Treeline, Arctic, 1976, 29(1),
38-47.
61. Elliot-Fisk, D.L., The Stability of the Northern Canadian Tree Limit, Annal. Assoc. Amer.
Geog., 2005, 73(4), 560-576.
62. MacDonald, G.M., Kremenetski, K.V. and Beilman, D.W., Climate change and the
northern Russian treeline zone, Phil. Trans. Roy. Soc., 2008, B363 2285-2299;
doi:10.1098/rstb.2007.2200.
Uncertainty in the global average surface air temperature index: 989
a representative lower limit
... Until recently, 39,40 systematic temperature sensor measurement errors were neither mentioned in reports communicating the origin, assessment, and calculation of the global averaged surface air temperature record, nor were they included in error analysis. 15,16,[39][40][41][42][43][44][45][46] However, systematic temperature sensor errors are neither randomly distributed nor constant in time, space, or instrument. There is no theoretical reason to expect that these errors follow the Central Limit Theorem, 47,48 or that such errors are reduced or removed by averaging multiple measurements; even when measurements number in the millions. ...
... A complete inventory of contributions to uncertainty in the surface air temperature record must include, indeed must start with, the systematic measurement error of the temperature sensor itself. 39 The World Meteorological Organization (WMO) offers useful advice regarding systematic error. 20 "Section 1. 6.4.2.3 Estimating the true value-additional remarks. ...
... Combined in quadrature, bucket and engine-intake errors constitute the SST uncertainty prior to 1990. Over the same time interval the systematic error of the PRT/CRS sensor, 39,49 constituted the uncertainty in land-surface temperatures. Floating buoys made a partial contribution (0.25 fraction) to the uncertainty in SST between 1980-1990. ...
Conference Paper
Full-text available
Systematic measurement errors of surface air and sea surface temperature (SST) sensors are surveyed. Field-calibrations reveal that the traditional Cotton Regional Shelter (Stevenson screen) and the modern Maximum-Minimum Temperature Sensor (MMTS) shield suffer daily average 1σ systematic measurement errors of ±0.44°C or ±0.32°C, respectively, stemming chiefly from solar and albedo irradiance and insufficient windspeed. Marine field calibrations of bucket or engine cooling-water intake thermometers revealed typical SST measurement errors of 1σ = ±0.6°C, with some data sets exhibiting ±1°C errors. These systematic measurement errors are not normally distributed, are not known to be reduced by averaging, and must thus enter into the global average of surface air temperatures. Modern floating buoys exhibit proximate SST error differences of ±0.16°C. These known systematic errors combine to produce an estimated lower limit uncertainty of 1σ = ±0.5°C in the global average of surface air temperatures prior to 1980, descending to about ±0.36°C by 2010 with the gradual introduction of modern instrumentation. At the 95% confidence interval, the rate or magnitude of the global rise in surface air temperature since 1850 is unknowable.
... The work of Brohan, et al. [1], hereinafter B06, exemplifies the commonly accepted signal-averaging approach to uncertainty [2] in the global average surface air temperature record. In a previous publication [2], it was shown that this approach had incorrectly incorporated the statistics of random measurement error and had entirely neglected systematic error. ...
... The work of Brohan, et al. [1], hereinafter B06, exemplifies the commonly accepted signal-averaging approach to uncertainty [2] in the global average surface air temperature record. In a previous publication [2], it was shown that this approach had incorrectly incorporated the statistics of random measurement error and had entirely neglected systematic error. ...
... The total uncertainty in the measurement mean of a physical variable, such as air temperature, involves measurement error and magnitude uncertainty [2]. Measurement error includes both instrumental error and systematic error [3]. ...
Article
Full-text available
The statistical error model commonly applied to monthly surface station temperatures assumes a physically incomplete climatology that forces deterministic temperature trends to be interpreted as measurement errors. Large artefactual uncertainties are thereby imposed onto the global average surface air temperature record. To illustrate this problem, representative monthly and annual uncertainties were calculated using air temperature data sets from globally distributed surface climate stations, yielding ±2.7 C and ±6.3 C, respectively. Further, the magnitude uncertainty in the 1961-1990 global air temperature annual anomaly normal, entirely neglected until now, is found to be ±0.17 C. After combining magnitude uncertainty with the previously reported ±0.46 C lower limit of measurement error, the 1856-2004 global surface air temperature anomaly with its 95% confidence interval is 0.8±0.98 C, Thus, the global average surface air temperature trend is statistically indistinguishable from 0 C. Regulatory policies aimed at influencing global surface air temperature are not empirically justifiable.
... At the present time, the available observational data do not support subjective assignments of multi-decadal τ 's. (Frank, 2010). Solid line is the least squares best-fit straight line (λ obs 2Xo = 2.3 • C; R = 0.88) for the post-1970 data (ln(X/X o ) > 0.13). ...
... The time scale of the exponential line is τ obs T ≈ 32 years. Uncertainties in the individual ∆T s ( • C) data are circa +/-0.5 • C (Frank, 2010). ...
... It was founded in 1780 from Elector Count Karl Theodor from Mannheim, Germany. Its daily mean value is calculated according to formula (2). (2) where t in is the local temperature measured at day at n = 7, 14 and 21.00 hrs. ...
... Its daily mean value is calculated according to formula (2). (2) where t in is the local temperature measured at day at n = 7, 14 and 21.00 hrs. ...
Article
Full-text available
Existing uncertainty assessments and mathematical models used for error estimation of global average temperature anomalies are examined. The error assessment model of Brohan et al 06 [1] was found not to describe the reality comprehensive and precise enough. This was already shown for some type of errors by Frank [2];[3] hereinafter named F 10 and F 11. In addition to the findings in both papers by Frank a very common but new systematic error was isolated and defined named here “algorithm error” This error was so far regarded as self canceling or corrected by some unknown and unnamed homogenization processes. But this was not the case. It adds therefore a minimum additional systematic uncertainty of + 0,3 °C and – 0,23°C respectively to any global mean anomaly calculation. This result is obtained when comparing only the most used algorithms against a “true” algorithm of measuring the daily temperature continuously.
... To that end, we consider the inputs of the MiCES model as random variables and analyzed the ensembles of simulations with distributions of emission and temperature. According to Gütschow et al. [24], we consider the uncertainty range of emissions as 14%, and the uncertainty range of temperature comes from Frank [25] as ±0.46 • C. Then we run the model multiple times with randomly picked N emissions and N temperatures in their uncertainty range to obtain the parameter uncertainty. As shown in Figure 3, temperature samples produced by getting each time point as a random temperature, while the emission samples are produced by changing the whole series to a random rate. ...
Article
Full-text available
Climate change, induced by human greenhouse gas emission, has already influenced the environment and society. To quantify the impact of human activity on climate change, scientists have developed numerical climate models to simulate the evolution of the climate system, which often contains many parameters. The choice of parameters is of great importance to the reliability of the simulation. Therefore, parameter sensitivity analysis is needed to optimize the parameters for the model so that the physical process of nature can be reasonably simulated. In this study, we analyzed the parameter sensitivity of a simple carbon-cycle energy balance climate model, called the Minimum Complexity Earth Simulator (MiCES), in different periods using a multi-parameter sensitivity analysis method and output measurement method. The results show that the seven parameters related to heat and carbon transferred are most sensitive among all 37 parameters. Then uncertainties of the above key parameters are further analyzed by changing the input emission and temperature, providing reference bounds of parameters with 95% confidence intervals. Furthermore, we found that ocean heat capacity will be more sensitive if the simulation time becomes longer, indicating that ocean influence on climate is stronger in the future.
... The minimal uncertainty in an individual land-surface temperature measurement coming from a standard temperature sensor, even while operating under ideal field conditions, has been evaluated as ±0.46 C. [125] Combining this ±0.46 C with the estimated ±0.2 C uncertainty due to site inhomogeneities [115,127], the root-meansquare (r.m.s.) minimum uncertainty in the averaged global land-surface air temperature is 1σ = ±0.50 C. ...
Article
The purported consensus that human greenhouse gas emissions have causally dominated the recent climate warming depends decisively upon three lines of evidence: climate model projections, reconstructed paleo-temperatures, and the instrumental surface air temperature record. However, CMIP5 climate model simulations of global cloud fraction reveal theory-bias error. Propagation of this cloud forcing error uncovers a r.s.s.e. uncertainty 1 sigma approximate to +/- 15 C in centennially projected air temperature. Causal attribution of warming is therefore impossible. Climate models also fail to reproduce targeted climate observables. For their part, consensus paleo-temperature reconstructions deploy an improper 'correlation = causation' logic, suborn physical theory, and represent a descent into pseudoscience. Finally, the published global averaged surface air temperature record completely neglects systematic instrumental error. The average annual systematic measurement uncertainty, 1 sigma = +/- 0.5 C, completely vitiates centennial climate warming at the 95% confidence interval. The entire consensus position fails critical examination and evidences pervasive analytical negligence.
... The application of statistics in current climate variability research has indeed been subject to criticism by statistics specialists. [6,7] Discussions on trends are generally restricted to the assumed linear relationship between variables rather than on the fact that a variety of sinusoidal oscillations can be observed at time scales ranging between decades and 100.000s of years. [8] ...
Article
The strong climate-forcing effect of rising atmospheric CO2 concentrations advocated by the IPCC, is at odds with climate developments during geological, historical and recent times. Although atmospheric CO 2 concentrations continuously increased during industrial times, temperatures did not increase continuously to the present level but stagnated or even declined slightly during 1880 to 1900, 1945 to1977 and again since 1998. Total solar irradiation rose from a low in 1890 to a first peak in 1950 that was followed by a sharp decline ending in 1977, giving way to a period of rapidly increasing radiation peaking in 2002 when solar activity started to decrease, possibly declining to a new Little-Ice-Age type low. The Greenhouse Effect of increasing atmospheric CO2 concentrations, claimed and widely propagated by IPCC, is particularly vexing as it is widely over-estimated without adequate scientific justification. Large observed climate variations documented for geological and historical times, as well as the lack of insight into the behaviour of complex systems, seriously question the Anthropogenic Global Warming (AGW) concept propagated by the IPCC. The climate variability during industrial times was essentially governed by changes in solar activity with increasing atmospheric CO2 content playing a subordinate role. The climate controlling effect attributed by the IPCC to increasing atmospheric CO2 concentrations is rejected since supporting models are not compatible with observations. Lastly, the authors consider from a historical and philosophical science point of view why current mainstream climate change research and IPCC assessments may have been on an erring way for several decades.
Thesis
Full-text available
ABSTRACT: The instrumental temperature record is a key indicator in the analysis of global climate change. This research dealt with the verification and quantification of the effects of heterogeneities (errors) in air temperature series obtained from a climatological station located in Itirapina, SP, Brazil. The main causes of heterogeneity studied were: changes on the times of observation and on the daily mean air temperature calculation; changes on the types of instruments (conventional and automatic); and changes in thermometer screens. The methodology consisted of comparing, at different time scales, several series of air temperature series in relation to a reference series, assumed to be more reliable. The differences obtained, in terms of deviations, resulted in the following orders of magnitude, according to each scale: 10.0ºC in the range of hourly measurements, 5.0ºC in the range of daily mean, 2.0°C in monthly scale, 1.0°C in the annual scale and 1.5°C in the climatological normal scale (30 years). It follows that at small scales (hourly and daily) exist errors of high magnitude of change, but low frequency of occurrence. With increasing scale, the magnitude of the deviations decreases. The causes of heterogeneity, according to the observed deviations, are ranked in order of lowest to highest extent of influence: changes on screens, changes on daily mean air temperature calculation, and changes of the instruments. In the context of the discussion of global warming, on the order of 0.6ºC over the last century, the occurrence of errors and uncertainties in same or greater magnitude can compromise the use of air temperature as a reliable evidence of climate changes, since non-climatic changes significantly interfere the measurements. The use of evidence is discussed in the context of the interaction between Science, Politics, Media and Economics. It was identified that, outside the scientific environment context, the uncertainties are reduced and neglected, both due to the simplification process for the information dissemination, as due to concerns that guide the intentional and biased manipulation on the subject. Due to the competition of different interests, there was held a brief discussion of some controversial aspects, permeating the work of skeptical scientists on the belief of the significant human contribution to the climate change. RESUMO: O registro da temperatura terrestre é um indicador fundamental nas análises de mudanças do clima global. A presente investigação tratou da verificação e quantificação dos efeitos de heterogeneidades (erros) em séries da temperatura do ar obtidas em estação climatológica localizada em Itirapina, SP, Brasil. As principais causas de heterogeneidades estudadas foram: mudanças dos horários de observação e cálculos da temperatura média diária; mudanças dos tipos de instrumentos utilizados (convencionais e automáticos) e mudanças nos abrigos meteorológicos. A metodologia aplicada consistiu em comparar, em diferentes escalas temporais, várias séries de temperatura do ar em relação a uma série de referência, assumida como mais confiável. As diferenças obtidas, em termos de desvios, resultaram em valores nas seguintes ordens de grandeza, de acordo com cada escala: 10,0ºC na escala das medições horárias; 5,0ºC na escala das médias diárias; 2,0ºC, na escala mensal; 1,0ºC na escala anual; e 1,5ºC na escala de normal climatológica (30 anos) de exibição dos valores médios da temperatura do ar. Conclui-se que em escalas reduzidas (horárias e diárias) existem erros de alta magnitude de variação, porém de baixa frequência de ocorrência. Com o aumento da escala, a magnitude dos desvios diminui. As causas de heterogeneidades, de acordo com os desvios observados, ficam classificadas, na ordem de menor para a maior intensidade de influência: mudanças dos abrigos; mudanças dos cálculos das médias diárias; e mudanças dos instrumentos. No contexto da discussão do aquecimento global, na ordem de 0,6ºC no último século, a ocorrência de erros e incertezas de mesma ou maior magnitude pode comprometer o uso da temperatura do ar como uma evidência confiável de mudanças do clima, uma vez que mudanças não-climáticas interferem significativamente nas medições. O uso da evidência é discutido no contexto da interação entre a Ciência, Política, Mídia e Economia. Foi identificado que, neste âmbito externo ao meio científico, as incertezas são diminuídas e ignoradas, tanto devido ao processo de simplificação da informação para sua difusão, quanto devido a interesses que norteiam a manipulação intencional e tendenciosa do tema. Devido à disputa de diferentes interesses, foi feita uma breve discussão de alguns aspectos controversos, permeando a atuação de cientistas céticos à crença da contribuição humana significativa nas mudanças climáticas.
Article
Historical evidence shows that the mean temperatures in the main cities in New Zealand have not changed significantly since records began in the 1860s 1–4 . Recently, the New Zealand Institute for Water and Air Research ¹¹ , after a thorough Review, has presented a revised temperature anomaly chart for the average temperatures of seven of the major urban centres in New Zealand which shows that there has been an increasing temperature trend of 0.91°C per century since 1909. This paper analyses the Review and concludes that the results are compatible with the historic view of no significant change since records began. Although the trends found are explained by natural causes their statistical significance is very low because of the unsuitability of the “neighbour station” comparison used, and the inaccuracy of the measured and processed temperature measurements.
Article
The residual fraction of anthropogenic CO2 emissions which has not been captured by carbon sinks and remains in the atmosphere, is estimated by two independent experimental methods which support each other: the 13C/12C ratio and the temperature-independent fraction of d(CO2)/dt on a yearly scale after subtraction of annual fluctuations the amplitude ratio of which reaches a factor as large as 7. The anthropogenic fraction is then used to evaluate the additional warming by analysis of its spectral contribution to the outgoing long-wavelength radiation (OLR) measured by infrared spectrometers embarked in satellites looking down. The anthropogenic CO2 additional warming extrapolated in 2100 is found lower than 0.1°C in the absence of feedbacks. The global temperature data are fitted with an oscillation of period 60 years added to a linear contribution. The data which support the 60-year cycle are summarized, in particular sea surface temperatures and sea level rise measured either by tide gauge or by satellite altimetry. The tiny anthropogenic warming appears consistent with the absence of any detectable change of slope of the 130-year-long linear contribution to the temperature data before and after the onset of large CO2 emissions.
Article
Full-text available
The air temperature radiation shield is a key component in air temperature measurement in weather station networks; however, it is widely recognized that significant errors in the measured air temperature exist due to insufficient airflow past the air temperature sensor housed inside the shield. During the last several decades, the U.S. National Weather Service has employed a number of different shields in air temperature measurements. This paper focuses on the airflow characteristics inside air temperature shields including the Maximum-Minimum Temperature System (MMTS), the Gill shields, and the Cotton Region Shelter (CRS). Average airspeed profiles and airflow efficiency inside the shields are investigated in this study under both windtable and field conditions using an omnidirectional hot-wire sensor. Results from the windtable measurements indicate that the average airspeeds inside the shields oscillated along the center line of the Gill and MMTS shields as the "windtable air" speed was changed from 1.03 to 2.62 m s-1; the MMTS airflow efficiency demonstrated a nearly constant value, but the Gill's airflow efficiency increased. A linear transfer equation between the airspeed measured at the normal operating position for the temperature sensor inside the shield and the ambient wind speed was found under field conditions for all three nonaspirated air temperature radiation shields (CRS, Gill, and MMTS). Results indicate that the naturally ventilated temperature radiation shields are unable to provide sufficient ventilation when the ambient wind speed is less than 5 m s-1 at the radiation shield height.
Article
Full-text available
A new U.S. Climate Reference Network (USCRN) was officially and nationally commissioned by the Department of Commerce and the National Oceanic and Atmospheric Administration in 2004. During a 1-yr side-by-side field comparison of USCRN temperatures and temperatures measured by a maximum-minimum temperature system (MMTS), analyses of hourly data show that the MMTS temperature performed with biases: 1) a systematic bias-ambient-temperature-dependent bias and 2) an ambient-solar-radiation- and ambient-wind-speed-dependent bias. Magnitudes of these two biases ranged from a few tenths of a degree to over 1°C compared to the USCRN temperatures. The hourly average temperatures for the USCRN were the dependent variables in the development of two statistical models that remove the biases due to ambient temperature, ambient solar radiation, and ambient wind speed in the MMTS. The model performance was examined, and the results show that the adjusted MMTS data were substantially improved with respect to both systematic bias and the bias associated with ambient solar radiation and ambient wind speed. In addition, the results indicate that the historical temperature datasets prior to the MMTS era need to be further investigated to produce long-term homogenous times series of area-average temperature.
Article
Full-text available
A technique to identify inhomogeneities in historical temperature records caused by microclimatic changes to the surroundings of a climate station (e.g. minor instrument relocations, vegetation growth/removal, construction of houses, roads, runways) is presented. The technique uses daily maximum and minimum temperatures to estimate the magnitude of nocturnal cooling. The test station is compared to a nearby reference station by constructing time series of monthly "cooling ratios". It is argued that the cooling ratio is a particularly sensitive measure of microclimatic differences between neighbouring climate stations. Firstly, because microclimatic character is best expressed at night in stable conditions. Secondly, because larger-scale climatic influences common to both stations are removed by the use of a ratio and, because the ratio can be shown to be invariant in the mean with weather variables such as wind and cloud. Inflections (change points) in time series of cooling ratios therefore signal microclimatic change in one of the station records. Hurst rescaling is applied to the time series to aid in the identification of change points, which can then be compared to documented station history events, if sufficient metatdata is available. Results for a variety of air temperature records, ranging from rural to urban stations, are presented to illustrate the applicability of the technique.
Article
Clear statements of the uncertainties of reported values are needed for their critical evaluation.
Article
Statistics in Spectroscopy, Second Edition, is an expanded and updated version of the original title. The aim of the book is to bridge the gap between the average chemist/spectroscopist and the study of statistics. The book introduces the novice reader to the ideas and concepts of statistics and uses spectroscopic examples to show how these concepts are applied. Several key statistical concepts are introduced through the use of computer programs.
Article
From palynological studies it appears that northernmost dwarf spruces of the tundra and parts of the forest-tundra boundary may be relicts from times of prior warmth, and if felled might not regenerate. This disequilibrium may help explain the partial incongruence of modern climatic limits with the present forest edge. Seedlings established as a result of recent warming should therefore be found within the northernmost woodlands rather than in the southern tundra.
Article
Marine air temperature reports from ships can contain significant biases due to the solar heating of the instruments and their surroundings. However, there have been very few attempts to derive corrections. The biases can reverse the sign of the measured air-sea temperature differences and cause significant errors in the sea surface latent and sensible heat flux estimates. In this paper a new correction for the radiative heating errors is presented. The correction is based on the analytical solution of the heat budget for an idealized ship, using empirical coefficients to represent the physical parameters. For the first time heat storage is included in the correction model. The heating errors are estimated for the Ocean Weather Ship Cumulus and the coefficients determined. When the correction is applied to the Cumulus data the average estimated error is reduced from 0.32° to 0.04°C and the diurnal cycle in the error is removed. The rms error is reduced by 30%. The correction technique, although not the coefficients derived here that are specific to the Cumulus, can be applied to air temperature data from any type of ship, or to data from groups of ships such as the Voluntary Observing Ships.
Article
A method to homogenize daily maximum and minimum temperatures over Canada is presented. The procedure is based on previously defined monthly adjustments derived from step changes identified in annual Canadian temperature series. Daily temperatures are adjusted by incorporating a linear interpolation scheme that preserves these monthly adjustments. The temperature trends and variations present in the homogenized monthly and annual datasets are therefore preserved. Comparisons between unadjusted and adjusted daily temperatures at collocated sites show that the greatest impact of the adjustments is on the annual mean of the daily maximum and minimum temperatures with little effect on the standard deviation. The frequency and distribution of the extremes are much closer to those provided by the target observations after adjustments. Furthermore, the adjusted daily temperatures produced by this procedure greatly improve the spatial pattern of the observed twentieth century extreme temperature trends across the country.