There's a ton physics in the models, a lot of it correct
with parameters estimated with high precision.
All these studies depend on inferring the statistical properties of the time - series from an assumed noise model
with parameters estimated from the residuals.
Forecasting confidence intervals for trend stationary and stochastic trend specification over 1885 - 2008,
with parameter estimates based on 1881 - 1935 sample, here, with accompanying figures here.
Not exact matches
We therefore performed each simulation 2,000 times, drawing key
parameters at random from triangular distributions covering the range of
estimates available in the literature associating breastfeeding
with maternal health outcomes, centered on the point
estimate provided in the literature and a distribution width of four standard errors.
For example, data on royalties for licensing drugs may be collected along
with other market information (e.g., market sizes,
estimated drug price, patent life) and used to develop a ranking system based on a certain set of market
parameters.
While some of these
parameters are difficult to
estimate, they show that there exists a lower bound to crosstalk
with respect to these
parameters.
Where climate sensitivity is
estimated in studies involving comparing observations
with values simulated by a forced climate model at varying
parameter settings (see Appendix 9.
Rather, they tested a range of potential values for key
parameters of their model and retained those consistent
with the paleo - sea level
estimates, but they did not explore the full space of possible values within their ranges.
New paper mixing «climate feedback
parameter»
with climate sensitivity... «climate feedback
parameter was
estimated to 5.5 ± 0.6 W m − 2 K − 1» «Another issue to be considered in future work should be that the large value of the climate feedback
parameter according to this work disagrees
with much of the literature on climate sensitivity (Knutti and Hegerl, 2008; Randall et al., 2007; Huber et al., 2011).
We find that our
estimates and their associated uncertainties are comparable to the results of other methods, but
with the additional benefit of being able to explore many more stellar
parameters while using much less computation time.
Comparisons
with stellar
parameter estimates from the literature show good agreement within uncertainties.
Summary
estimates were calculated using a general variance - based method (random - effects model)
with 95 % CIs.19 Because the potential confounders considered in multivariate analyses vary across studies, we used the
parameter estimates in the most complex model, which typically include demographic, lifestyle, and dietary factors.
This survey should provide an updated list of breeding sites, a good
estimate of the size of the population, and data about survival rate of different age classes: together
with the high resolution data from our intensive study of Sea Lion Island this new information should provide the
parameters needed to determine the current status of the population and forecast its future.
This is visualized in figure 4 where ensemble members from the CCSM4 AR4 runs are fit
with S - shaped (Gompertz) functions using the 1979 - 2011 period to
estimate the
parameters.
The point
estimates are roughly Weibull distributed
with shape
parameter ~ 2.
If the modeled results from scenario c (
with best possible
parameter estimates and counterfactual CO2 assumptions) continue for a sufficient time to be closer to actual data than the modeled results from scenarios a and b (
with best possible
estimates of
parameters and accurate CO2 assumptions), then the model that produced the computed results will have been disconfirmed.
A detailed reanalysis is presented of a «Bayesian» climate
parameter study (Forest et al., 2006) that
estimates climate sensitivity (ECS) jointly
with effective ocean diffusivity and aerosol forcing, using optimal fingerprints to compare multi-decadal observations
with simulations by the MIT 2D climate model at varying settings of the three climate
parameters.
Anyone reading our paper may or may not agree
with our choice of
parameters and hence
with our revised
estimates of climate sensitivity, which are very much lower and very much closer to observed reality than those of the more complex models.
In recent years one of the most important methods of
estimating probability distributions for key properties of the climate system has been comparison of observations
with multiple model simulations, run at varying settings for climate
parameters.
The most popular observationally - constrained method of
estimating climate sensitivity involves comparing data whose relation to S is too complex to permit direct estimation, such as temperatures over a spatio - temporal grid,
with simulations thereof by a simplified climate model that has adjustable
parameters for setting S and other key climate properties.
And as I've pointed out in my response to Mike Jonas, 99.992 % is not much of an improvement over 99.99 % if
with nothing but a little more precision in
estimating my original
parameters 99.997 % is easily achieved.
(b) Correlation coefficient between [E] n and test
parameter [Ttest] n is shown
with corresponding number of variables used for
estimating the [Ttest] n.
What I demonstrated was that Earth's 140 year GAST, which I'd
estimate might require roughly 30
parameters to represent (the number will depend on the efficiency of the orthogonal function set), can be represented as accurately as IPCC's smoothed estimator itself
with a linear transfer function
with just 5
parameters.
The same is true for any
estimate of a physical
parameter based on a method
with a large range of uncertainty and no well defined theory or earlier data to define the prior.
Significant uncertainties in the process
parameters result in a wide, asymmetric range associated
with this
estimate,
with higher values being more likely than lower ones.
Condition 2: k − m < Cm,
with a
parameter Cm
estimated using the equation (see Eq.
The climate models have gotten more complex, for sure,
with thousands of
estimated parameters for warming potential, vorticity, circulation patterns, absorption of heat, pressure, energy, and momentum by various layers or atmosphere, land, ocean, and sea - ice.
It would be interesting if the model outputs and the TLTs were related back to a stochastic emulation
with specifed model
parameters given
estimated values and ranges.
Only the final model (5f in Fig. 2) returns a statistically significant climate
parameter estimate; apparently, major civil war years (i.e., years
with at least 1,000 battle deaths) are more frequent in years following unusually wet periods — a result that directly contradicts the notion of scarcity - induced conflicts.
At a recent debate at Oxford University, organized by the OU Engineering Society, I gave the undergraduates an argument from process engineering (which you will find in outline in my Union College presentation, and in more detail in my Hartford College lecture) to the effect that the closed - loop temperature - feedback gain in the climate system (i.e., the product of the Planck
parameter and the net sum of all unamplified feedbacks) can not much exceed 0.1, implying at most 1.3 K of warming per CO2 doubling, compared
with the IPCC's central
estimate of 3.3 K.
For each model, there is an ad hoc change to this
parameter that produces the best fit — but the confidence interval on the
parameter estimate is extremely large, and correlated
with all other
parameter estimates.
In such cases, the matrix has a determinant which is close to zero, which makes it «ill - conditioned» so the matrix can't be inverted
with as much precision as we'd like, there's uncomfortably large variance in the final
parameter estimates.
It is shown that this
estimate is based on a wrong interpretation of the literature, a confusion of short - term
with long - run costs, and a selection of worst - case assumptions and
parameters.
Like all omitted variables, it biases
estimated parameters for included variables if the selection criterion is correlated
with variables included in the analysis.
By comparing values of these
parameters from the mid-19 century to now, they can
estimate how much the earth warmed in association
with human greenhouse gas emissions.
Some people may prefer to say that no - feedback climate sensitivity is
estimated, I used calculated, as that fits well
with the fact that it's a value defined true some formulas rather than by specifying a real physical
parameter to be
estimated.
In physical sciences, where an OLS regression model
with normally distributed errors is validly used to
estimate a slope
parameter between two variables
with observational data, errors in the regressor variable contributing a small part of the total uncertainty, it is usual to accept the uniform prior in the slope
parameter (here Y) implied by the regression model.
Estimates of natural variability from an AOGCM provide a critical input in deriving, by comparing temperature estimates from the simple model with observations, a likelihood function for the parameters jointly at each possible combination of parameter settings (and in one or two cases AOGCMs provide surrogates for some of the observation
Estimates of natural variability from an AOGCM provide a critical input in deriving, by comparing temperature
estimates from the simple model with observations, a likelihood function for the parameters jointly at each possible combination of parameter settings (and in one or two cases AOGCMs provide surrogates for some of the observation
estimates from the simple model
with observations, a likelihood function for the
parameters jointly at each possible combination of
parameter settings (and in one or two cases AOGCMs provide surrogates for some of the observational data).
That said,
with some simple
estimates (length for one) and some well - determined
parameters for air (viscosity, and density) the Reynolds number is easily determined.
Carefully designed and executed interventional experiments are required to determine which representation is best (e.g. most accurate
with the same number of
estimated parameters.)
General Introduction Two Main Goals Identifying Patterns in Time Series Data Systematic pattern and random noise Two general aspects of time series patterns Trend Analysis Analysis of Seasonality ARIMA (Box & Jenkins) and Autocorrelations General Introduction Two Common Processes ARIMA Methodology Identification Phase
Parameter Estimation Evaluation of the Model Interrupted Time Series Exponential Smoothing General Introduction Simple Exponential Smoothing Choosing the Best Value for
Parameter a (alpha) Indices of Lack of Fit (Error) Seasonal and Non-seasonal Models
With or Without Trend Seasonal Decomposition (Census I) General Introduction Computations X-11 Census method II seasonal adjustment Seasonal Adjustment: Basic Ideas and Terms The Census II Method Results Tables Computed by the X-11 Method Specific Description of all Results Tables Computed by the X-11 Method Distributed Lags Analysis General Purpose General Model Almon Distributed Lag Single Spectrum (Fourier) Analysis Cross-spectrum Analysis General Introduction Basic Notation and Principles Results for Each Variable The Cross-periodogram, Cross-density, Quadrature - density, and Cross-amplitude Squared Coherency, Gain, and Phase Shift How the Example Data were Created Spectrum Analysis — Basic Notations and Principles Frequency and Period The General Structural Model A Simple Example Periodogram The Problem of Leakage Padding the Time Series Tapering Data Windows and Spectral Density
Estimates Preparing the Data for Analysis Results when no Periodicity in the Series Exists Fast Fourier Transformations General Introduction Computation of FFT in Time Series
I think it is fair to say that a lot of readers agree that you have a model
with a high correlation to the data from which the
parameters have been
estimated.
The model needs to properly reflect the underlying physical structure in order to have any chance at an end result that is meaningful
with properly
estimated parameters and measures of uncertainty for those
parameters.
Rather, they tested a range of potential values for key
parameters of their model and retained those consistent
with the paleo - sea level
estimates, but they did not explore the full space of possible values within their ranges.
However, climates at high latitude are known to be very sensitive to orbital
parameters affecting insolation (Ravelo et al., 2004), and thus proxy
estimates with uncertain age constraints are not directly comparable to model simulations that typically span hundreds of years.
Essentially, Clegg finds that it's hard to
estimate the Hurst
parameter even for artificial time series where the answer is known ahead of time, even when working
with 100,000 data points.
So yes, you don't know the changes in the tails
with the same confidence as the middles, and you never will, but you can have some pretty strong and defensible clues based on the totality of the evidence coming from the
estimated changes in various
parameters of the distribution.
Where climate sensitivity is
estimated in studies involving comparing observations
with values simulated by a forced climate model at varying
parameter settings (see Appendix 9.
The mean is not a good central
estimate for a
parameter like climate sensitivity
with a highly skewed distribution.
Secondly, as many have said in different ways above, the error
estimate is derived as I understand it mainly by multiple runs of the model
with variations in the initial conditions and
parameters.