The shaded region envelops the ± 2
standard deviation uncertainty as derived from the validation period.
Not exact matches
I figure that the
uncertainty in a sample of 4 counts is ± 2, which means that the expected value of 1 is well within 2
standard deviations.
Fustey's takeaway message is that
standard deviation can't model
uncertainty.
I strongly suspect (and I admit to not having done this analysis — this is just my opinion «by eye») that the records are indistuinguishable within their one -
standard -
deviation uncertainties in the 19th century.
There is significant
uncertainty in the forecast; Zhang and Lindsay point out that the
standard deviation in the model ensemble is high in this area (Figure 2b).
[13] Of course, although averages across
standard deviations are not
standard deviations themselves, they enable us to quantify the
uncertainty associated with the five probability distributions used to estimate the SCC.
The average
standard deviations are also interesting, quantifying the
uncertainty associated with these probability distributions.
Double their joint
standard deviation and you get a reasonable figure for the
uncertainty of a prediction in any given year.
5.1 The combined
standard uncertainty of a measurement result, suggested symbol uc, is taken to represent the estimated
standard deviation of the result.
No. 0.1 cm is the
standard deviation of the
uncertainty, so there is a probability that
deviations will be larger than 0.1 cm.
It is obtained by combining the individual
standard uncertainties ui (and covariances as appropriate), whether arising from a Type A evaluation or a Type B evaluation, using the usual method for combining
standard deviations.
(A-3)-RSB-, is often called the law of propagation of
uncertainty and in common parlance the «root - sum - of - squares» (square root of the sum - of - the squares) or «RSS» method of combining
uncertainty components estimated as
standard deviations.
The
standard deviation across the ensemble mean ice extents is an estimate of the
uncertainty of our projection given we do not know the atmospheric conditions that will occur this summer.
The
standard deviation of the ensemble is 0.38 million km2 which we provide as
uncertainty estimate of the prediction.
where σc is the calibration
uncertainty standard deviation, which in general will be a function of ti.
I've assumed an error
standard deviation of 30 14C years, to include calibration curve
uncertainty as well as that in the 14C determination.
The radiocarbon determination will be more than two
standard deviations (of the combined radiocarbon and calibration
uncertainty level) below the exact calibration curve value for the true calendar date in 2.3 % of samples.
There is significant
uncertainty in the forecast; Zhang and Lindsay point out that the
standard deviation in the model ensemble is high in this area (Figure 2, right).
The very high significance levels of model - observation discrepancies in LT and MT trends that were obtained in some studies (e.g., Douglass et al., 2008; McKitrick et al., 2010) thus arose to a substantial degree from using the
standard error of the model ensemble mean as a measure of
uncertainty, instead of the
standard deviation or some other appropriate measure of ensemble spread.
Given»n' measurements and a measurement error with a
standard deviation of»S», the
uncertainty scales with the number of measures by:
After 10000 rolls the
uncertainty in the estimate of the mean will 100 times smaller than the
standard deviation of a single die roll, far below the single digit resolution of the die faces.
«Our estimate of LGM global cooling is thus 4.5 ± 0.5 °C, where 0.5 °C is our estimated one
standard deviation (σ)
uncertainty.
As the submitted
uncertainty standard deviations are about 0.4 million square kilometers, most of the Outlook estimates overlap.
The only difference between the two panels is the degree of
uncertainty associated with climate sensitivity: The mean sensitivity is identical, but the spread (
standard deviation) of the sensitivity distribution is greater in Panel B (
standard deviation 2.5) than in Panel A (
standard deviation.5).
The grey IPCC
uncertainty envelope about the 20th century simulation is ± one
standard deviation about the multi-model mean.
The very high significance levels of model — observation discrepancies in LT and MT trends that were obtained in some studies (e.g., Douglass et al., 2008; McKitrick et al., 2010) thus arose to a substantial degree from using the
standard error of the model ensemble mean as a measure of
uncertainty, instead of the ensemble
standard deviation or some other appropriate measure for
uncertainty arising from internal climate variability... Nevertheless, almost all model ensemble members show a warming trend in both LT and MT larger than observational estimates (McKitrick et al., 2010; Po - Chedley and Fu, 2012; Santer et al., 2013).
To illustrate, whereas expected (mean) damage increases by «only» around 50 % between the two panels, the associated
standard deviation (
uncertainty) of the damage increases 10-fold.
Plus, note that Seitz is using the range to quantify the
uncertainty in ECS estimates, rather than, say, the
standard deviation.
But I do know the difference between a simple linear interpolation and principal component analysis, and I can calculate the two
standard deviations range of
uncertainty on a white noise linear trend.
We fixed climate sensitivity at a constant mean but varied the
uncertainty of that sensitivity, expressed as its
standard deviation in 6 steps from 0.26 °C to 1.66 °C
The lightest gray shading shows the 5 — 95 %
uncertainty in the estimates, and the medium gray shading denotes the one
standard deviation error estimate.
Good points all — but one wonders how you could even «define the
uncertainty of an «ensemble mean» as the «average of the within - model
standard deviations over all the models»» in this case.
I mean you could define the
uncertainty of an «ensemble mean» as the «average of the within - model
standard deviations over all the models», but comparing that with observed range wouldn't tell you anything about the proportion of models whose range of
uncertainty falls outside the
uncertainty of observations.
If the claim is that the ensemble mean represents all models then the
uncertainty in that ensemble mean needs to represent the
uncertainty of all models, not the «average of the within - model
standard deviations over all the models» as McIntyre put it.
It should be noted that the formula can be used for any level of
uncertainty, not just one
standard deviation (1 sigma), provided the same level of
uncertainty is used for each term.
The ensemble prediction from the PIOMAS model submitted by Zhang and Lindsay is still showing an open Northwest Passage (Figure 1a), as in the June Outlook, but there has been a notable drop in the
uncertainty of the estimate with a low
standard deviation in the model ensemble (Figure 1b).
Given an ensemble of models from which an observable variable takes the mean value m 1 = 0 (without loss of generality) and
standard deviation s 1, and an observation of this variable which takes the value m 2 with associated
uncertainty s 2, the observation is initially at a normalised distance m 2 / s 1 from the ensemble mean.
The total AF
uncertainty estimate of ± 0.87 W / m ² in Table 8.7 equates to an error
standard deviation of 0.44 W / m ², which is taken as applying for 2002 — 2011.
That implies a change in OHU of 0.353 W / m ², with a
standard deviation of 0.075 W / m ², adding the
uncertainty variances.
Adding the relevant years» total
uncertainty estimates for the HadCRUT4 21 - year smoothed decadal data (estimated 5 — 95 % ranges 0.17 °C and 0.126 °C), and very generously assuming the variance
uncertainty scales inversely with the number of years averaged, gives an error
standard deviation for the change in decadal temperature of 0.08 °C (all
uncertainty errors are assumed to be normally distributed, and independent except where otherwise stated).
Almost all the SOD's 10.2 % error
standard deviation for greenhouse gas AF relates to the AF magnitude that a given change in the greenhouse gas concentration produces, not to
uncertainty as to the change in concentration.
Finally, I add an error
standard deviation of 0.05 W / m ² for
uncertainty in volcanic forcing in 1871 — 1880 and a further 0.05 W / m ² for
uncertainty therein in 2002 — 2011, small though volcanic forcing was in both decades.
The WGI TAR made some effort at consistency, noting in the SPM that when ranges were given they generally denoted 95 % confidence intervals, although the carbon budget
uncertainties were specified as ± 1
standard deviation (68 % likelihood).
But when I compute a mean as my estimate and a
standard deviation as its
uncertainty, I'm assuming that each model is producing independent data, and I'm relying on the expectation that their errors will cancel each other out.
However, given the similarity between most of the forcing time series — which apart from volcanoes and solar variation all increase smoothly over time — the estimation
uncertainty will be greater than appears from the coefficient
standard deviation values.
Summing the
uncertainties, the total AF change error
standard deviation is 0.45 W / m ².
Kohler et al. (2010; doi: 10.1016 / j.quascirev.2009.09.026) estimate total forcing at the LGM to be — 9.5 W / m2 relative to preindustrial, with Gaussian
uncertainty having a
standard deviation of between 0.9 and 1.9 W / m2.
Figure 1: (a) Ensemble prediction of September 2011 sea ice thickness in the Northwest Passage region and (b) ensemble
standard deviation (SD) of ice thickness, which shows the
uncertainty of the prediction.