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Many definitions have been proposed for climate in the literature \citep[e.g.,][]{Lorenz1997,Werndl2015,Lovejoy2013,IPCC5.1,WMOno100}. For many of the central concepts in climate science, there do not appear to be any widely accepted definitions \citep{Todorov1986, JoePhD, Werndl2015}. One might argue that definitions used are broadly similar, that there appears to be consensus on the intuitive idea of climate \citep{Leith1985} and that the descriptions used are generally ``good enough'' for the specific contexts in which they are applied. However, \citet{Lorenz1997} notes that ``certain questions regarding climate may be answered either affirmatively or negatively, according to the precise [definition of climate used]''. Furthermore, \citet{Lorenz1997} suggests that in different contexts---across which the nature of the available data varies---the definition that would lead to the most meaningful characterisation of a given climatic state, may differ \citep[see also][]{Schneider1974}. In particular, definitions of climate which are applicable in observational studies, are not necessarily the most useful in theoretical or modelling studies \citep{Lorenz1997, Schneider1974, Leith1978}.
Of particular interest in this work are various climate quantifications---definitions which, when applied, provide a quantitative characterisation of a ``model climate'' (also referred to as a ``model climatic state''). In an observational context, one must consider quantifications applicable to individual climate variable trajectories sampled over time; however, in ensemble modelling studies collections of such trajectories can either be sampled at a particular ``instant'' or over a period of time. In this work, ensembles considered are initial condition (IC) ensembles (the value of which is argued for in,
e.g. e.g., \citet{Hawkins2015}), but definitions involving perturbed physics and multi-model ensemble output could also be proposed; in particular, it could be argued that the \citet{IPCC5.1} apply a multi-model ensemble definition in quantifying projected future climates.
Following, Following \citet{Werndl2015}, we focus on probability distributions
(more precisely, probability density functions (PDFs) and empirical cumulative density functions (ECDFs)) as a means of capturing the mean state, variability and extremes of a local, regional or global climatic state. For a particular variable, over a particular domain, three such quantifications are considered here:
\cite{Gent2011}\cite{IPCC5.1}\cite{Leith1978}\cite{Leith1985}\cite{Lovejoy2013}\cite{Massey1951}\cite{Schneider1974}\cite{Todorov1986}\cite{Werndl2015}\cite{WMOno100}
\subsubsection*{Climate Quantifications}\label{ClimQuants}
\begin{description}
\item[Temporal (TCQs):] {the
corresponding distribution sampled from a series of consecutive ``points in time'' of a single model trajectory. In this study, annual averages are considered as ``points in time'', thus avoiding complexities involved with the diurnal and seasonal cycles. Note, furthermore, that in
a an observational setting, rather than a model setting, only TCQs are
available to us, applicable, as there is only one realisation of the planetary climate that occurs over a given period.}
\item[Ensemble (ECQs):] {the
corresponding distribution sampled at a particular ``point in time'', from all members of an IC ensemble
(this could conceivably be generalised to include other types of ensembles) at the $n^{\textrm{th}}$ year of the ensemble duration.}
\item[Ensemble-temporal (ETCQs):] {the
distribution, distribution sampled from all members of an IC ensemble over a series of consecutive points in time (in this case, thus, several years).}
\end{description}
Understanding of the differences in climatic characterisations that could be produced by different approaches to defining climate, should be explored and considered in experimental design and interpretation of results. This study aims to contribute to the discussion on preferable future approaches to climate model experimental design, following.
