Once the pair-wise distances between
observation and model ensemble members defined in Eq.
The analysis methods include the explanation of the calculation of rank histogram and the statistical test for the reliability (2 — 2), the formulation of EDoF (2 — 3), and the distances between
observation and model ensemble members (2 — 4).
MSTs (minimum sum of distances between ensemble members, Table 5) and the averages of the distances between
the observations and model ensemble members (Fig. 6) are calculated.
For this reason, in the next section we investigate the relationship between
the observations and model ensembles based on their distances.
Not exact matches
Knutti, R., T.F. Stocker, F. Joos,
and G.K. Plattner, 2002: Constraints on radiative forcing
and future climate change from
observations and climate
model ensembles.
The analysis of processes contributing to climate feedbacks in
models and recent studies based on large
ensembles of
models suggest that in the future it may be possible to use
observations to narrow the current spread in
model projections of climate change.
A large
ensemble of Earth system
model simulations, constrained by geological
and historical
observations of past climate change, demonstrates our self ‐ adjusting mitigation approach for a range of climate stabilization targets ranging from 1.5 to 4.5 °C,
and generates AMP scenarios up to year 2300 for surface warming, carbon emissions, atmospheric CO2, global mean sea level,
and surface ocean acidification.
«We use a massive
ensemble of the Bern2.5 D climate
model of intermediate complexity, driven by bottom - up estimates of historic radiative forcing F,
and constrained by a set of
observations of the surface warming T since 1850
and heat uptake Q since the 1950s... Between 1850
and 2010, the climate system accumulated a total net forcing energy of 140 x 1022 J with a 5 - 95 % uncertainty range of 95 - 197 x 1022 J, corresponding to an average net radiative forcing of roughly 0.54 (0.36 - 0.76) Wm - 2.»
Although a useful process to see which
models should have more weight,
and which ones should be discarded all together, the average that the
ensemble produces will automatically have a higher correlation with
observation data simply because of how far a set of numbers are spread out from each other.
Global climate
model projections (in CMIP3 at least) appear to underestimate sea ice extent losses with respect to
observations, though this is not universally true for all
models and some of them actually have
ensemble spreads that are compatible with PIOMAS ice volume estimates
and satellite
observations of sea ice extent.
As I pointed out on another thread (http://tinyurl.com/yntbat), Douglass et al. did something silly with the
ensemble of climate
models — apply computations that assume that they're raw
observations,
and treat them as «independent»
models (*)-- see Section 2.3.
A new assimilation system (CERA) has been developed to simultaneously ingest atmospheric
and ocean
observations in the coupled Earth system
model used for ECMWF's
ensemble forecasts.
The meeting will mainly cover the following themes, but can include other topics related to understanding
and modelling the atmosphere: ● Surface drag
and momentum transport: orographic drag, convective momentum transport ● Processes relevant for polar prediction: stable boundary layers, mixed - phase clouds ● Shallow
and deep convection: stochasticity, scale - awareness, organization, grey zone issues ● Clouds
and circulation feedbacks: boundary - layer clouds, CFMIP, cirrus ● Microphysics
and aerosol - cloud interactions: microphysical
observations, parameterization, process studies on aerosol - cloud interactions ● Radiation: circulation coupling; interaction between radiation
and clouds ● Land - atmosphere interactions: Role of land processes (snow, soil moisture, soil temperature,
and vegetation) in sub-seasonal to seasonal (S2S) prediction ● Physics - dynamics coupling: numerical methods, scale - separation
and grey - zone, thermodynamic consistency ● Next generation
model development: the challenge of exascale, dynamical core developments, regional refinement, super-parametrization ● High Impact
and Extreme Weather: role of convective scale
models;
ensembles; relevant challenges for
model development
Because the
models are not deterministic, multiple simulations are needed to compare with
observations,
and the number of simulations conducted by
modeling centers are insufficient to create a pdf with a robust mean; hence bounding box approaches (assessing whether the range of the
ensembles bounds the
observations) are arguably a better way to establish empirical adequacy.
Sylvain, one of the main challenges of verifying climate
models on a time scale of 1 - 2 decades is that natural forcing (solar
and volcanic) is unknown plus the decadal ocean cycles are not deterministic
and will not be simulated in a way that matches
observations unless a very large
ensemble is used.
It costs little to field the
observations — the satellites
and the radars, the surface in situinstruments, etc. to monitor conditions
and their changes; to assimilate the data into variety of numerical
models, to run these
and form
ensemble averages; to disseminate the findings.
The
model's
ensemble - mean EOF accounts for 43 % of the variance on average across the 40
ensemble members,
and is largely similar to
observations although the centers - of - action extend slightly farther east
and the southern lobe is weaker (maximum amplitude of approximately 2 hPa compared to 3 hPa in
observations; Fig. 3c).
«We use a massive
ensemble of the Bern2.5 D climate
model of intermediate complexity, driven by bottom - up estimates of historic radiative forcing F,
and constrained by a set of
observations of the surface warming T since 1850
and heat uptake Q since the 1950s... Between 1850
and 2010, the climate system accumulated a total net forcing energy of 140 x 1022 J with a 5 - 95 % uncertainty range of 95 - 197 x 1022 J, corresponding to an average net radiative forcing of roughly 0.54 (0.36 - 0.76) Wm - 2.»
Wang, 5.0 (± 0.27),
Modeling A projected September Arctic sea ice extent of 5.0 million km2 is based on a NCEP
ensemble mean CFSv2 forecast initialized from the NCEP Climate Forecast System Reanalysis (CFSR) that assimilates observed sea ice concentrations
and other atmospheric
and oceanic
observations.
The method is a sea ice - ocean
model ensemble run (without
and with assimilation of sea - ice / ocean
observations); the coupled ice - ocean
model NAOSIM has been forced with atmospheric surface data from January 1948 to 7 July 2015.
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.
Simulations by regional climate
models show good agreement with
observations in the seasonal
and spatial variability of the joint distribution, especially when an
ensemble of simulations was used.
Right now I don't see a good fit between the
model ensemble and the
observations in the period 1910 to 1945.
Likewise, to properly represent internal climate variability, the full
model ensemble spread must be used in a comparison against the
observations (e.g., Box 9.2; Section 11.2.3.2; Raftery et al. (2005); Wilks (2006); Jolliffe
and Stephenson (2011)-RRB-.
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).
Arguing against the
model vs real world comparison «Here Judith is (I think) referring to the mismatch between the
ensemble mean (red)
and the
observations (black) in that period... However, the
observations are well within the spread of the
models and so could easily be within the range of the forced trend + simulated internal variability.»
I would bet that while the mean of the
observations shifts upward to near the
ensemble mean of the
models, the uncertainty of the mean of
observations would be hardly reduced at all: these time series are very strongly correlated as they all contain the same forced
and unforced natural variations, see their Figure.
In Sect. 2, we describe the
model ensembles and the application of the rank histogram approach, including a description of the statistical method used to define the reliability of
model ensembles from the rank histogram,
and a method for handling uncertainties in the
observations.
C / decade
and the simulated
ensemble mean over the
models, calculated from the grid boxes of the
models where
observations exist (which is flawed in my opinion, since excluding of mostly the high latitudes from the
model data may emphasize a warm bias in lower latitudes in the
models making them appear warmer than they are, but a possible cold bias of the global
observations data set is not excluded in this way) had a trend of 0.3 deg.
Then, at each grid point, we compared the value of the
observation with the
ensemble of
model values at each grid point, evaluating the rank of the
observation in the ordered set of
ensemble values
and observed value.
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.
Knutti et al. (2010a) investigated the behaviour of the state - of - the - art climate
model ensemble created by the World Climate Research Programme's Coupled Model Intercomparison Project Phase 3 (CMIP3, Meehl et al. 2007), and found that the truth centred paradigm is incompatible with the CMIP3 ensemble: the ensemble mean does not converge to observations as the number of ensemble members increases, and the pairwise correlation of model errors (the differences between model and observation) between two ensemble members does not average to zero (Knutti et al. 2010a; Annan and Hargreaves 2010; hereafter A
model ensemble created by the World Climate Research Programme's Coupled
Model Intercomparison Project Phase 3 (CMIP3, Meehl et al. 2007), and found that the truth centred paradigm is incompatible with the CMIP3 ensemble: the ensemble mean does not converge to observations as the number of ensemble members increases, and the pairwise correlation of model errors (the differences between model and observation) between two ensemble members does not average to zero (Knutti et al. 2010a; Annan and Hargreaves 2010; hereafter A
Model Intercomparison Project Phase 3 (CMIP3, Meehl et al. 2007),
and found that the truth centred paradigm is incompatible with the CMIP3
ensemble: the
ensemble mean does not converge to
observations as the number of
ensemble members increases,
and the pairwise correlation of
model errors (the differences between model and observation) between two ensemble members does not average to zero (Knutti et al. 2010a; Annan and Hargreaves 2010; hereafter A
model errors (the differences between
model and observation) between two ensemble members does not average to zero (Knutti et al. 2010a; Annan and Hargreaves 2010; hereafter A
model and observation) between two
ensemble members does not average to zero (Knutti et al. 2010a; Annan
and Hargreaves 2010; hereafter AH10).
He points out that the range of values for 2xCO2 ECS goes from 0.6 ºC (low end of Lindzen & Choi, 2011,
observation - based on CERES satellite data)
and 9.2 ºC (upper end of range of Knutti, 2002, based on a large
ensemble of
model simulations).
I don't know about Antarctica,
and CMIP5 is definitely an improvement over CMIP3, but almost two thirds of the
ensemble models do not agree «reasonably well» with
observations.
The rank histogram analysis discussed in Sect. 2.2 only considers the rank ordering of
models and observations,
and thus information on the distances between
observation and ensemble members is missing.
In addition to the rank histogram we explore other ways of evaluating the
ensemble, analysing the distances between
models and observational data by calculating the minimum spanning trees (e.g., Wilks 2004)
and the average of the distances between the
observation and the
models for all the
ensembles.
If a
model ensemble was perfect such that the true observed climatic variable can be regarded as indistinguishable from a sample of the
model ensemble, then the rank of each
observation lies with equal probability anywhere in the
model ensemble,
and thus the rank histogram should have a uniform distribution (subject to sampling noise).
Here we count the rank of
observation among
model ensemble members
and create histogram, so the number of rank in horizontal axis is from one to the number of
ensemble plus one.
Among the various techniques, the AR4 AOGCM
ensemble provides the most sophisticated set of
models in terms of the range of processes included
and consequent realism of the simulations compared to
observations (see Chapters 8
and 9).