Climate
Climate is the statistical description of the atmosphere and the parts of the Earth system coupled to it, over periods long enough for the statistics to be meaningful. The conventional standard period is thirty years, which is a compromise rather than a physical constant — long enough to average out interannual variability, short enough to remain relevant.
The compact version, that climate is what you expect and weather is what you get, is genuinely useful, but it flattens the point that actually matters. Climate is not the mean. It is the whole distribution: the variance, the shape of the tails, the seasonal cycle, the persistence, and the correlations between variables. A statement about mean temperature is a small part of a climate, and frequently not the important part. Most impacts come from the tails, and the tails can move independently of the mean.
The problem with the definition
Defining climate as a distribution assumes there is a stable distribution to describe. Under a changing climate that assumption fails, and the failure is not a technicality — it removes the ground the standard method stands on.
A thirty-year normal computed over a period of trend is not an estimate of a stationary distribution. It is an average over a moving one, which describes the middle of the period and misrepresents both ends. Every application built on climate normals — engineering design values, agricultural planning, insurance pricing, flood standards — inherits this. The infrastructure assumption that the past is a guide to the future is precisely what has stopped holding.
There is no clean replacement. Shorter periods reduce the trend problem and increase the noise. Trend-adjusted normals require assuming a trend form. Model-based projections carry model error. Each option trades one difficulty for another, and I do not think the field has settled this.
Scales, and why they are not separable
Climate is studied from global down to the urban and the micro-scale, and the scales are coupled in both directions. Large-scale circulation sets the regional context; the surface modifies it locally; and the local modifications aggregate. Dynamical downscaling exists to bridge that, and its central limitation — a regional model cannot correct errors it inherits at its boundaries — is a direct consequence of the coupling running one way in the method and both ways in reality.
Climate and weather as one problem
The separation is a matter of what question is being asked, not a physical boundary. The same equations generate both, and the same models are used for each with different configurations and run lengths. The distinction is whether the initial condition or the boundary condition dominates the answer — weather prediction is an initial-value problem, climate projection is a boundary-value problem — and the middle ground between them, seasonal to decadal prediction, is genuinely hard because neither framing is adequate.
See also: physical climatology for the process-based approach, applied climatology for the decision-facing one, climate variables for the quantities involved, and regional climate modeling.