Models Methods Software

Dan Hughes

Climate is not the Average of Weather

The climate at a location is fundamentally determined by the radiative energy output of the Sun, the relationships between the geometry of the earth, the geometry of the revolution of the earth around the Sun ( the yearly cycle ), the relationship between Earth’s axis of rotation and the plane of Earth’s orbit ( the seasons ), and the rotation of the earth about its axis ( the daily cycle ).

The climate at a location is determined to first order by these factors and the latitude and altitude of the location. The climate also can be influenced by significant, more-or-less thermally stable, bodies of liquid or solid water, primarily near the oceans but including also other large bodies of liquid or solid water.

Meso-scale ( larger than local, smaller than global ) topology of Earth’s surface can also affect local climate. Mountain ranges that significantly affect specific regions relative to precipitation are an example; rain shadows, monsoon

Weather at a location is the time-varying thermodynamic and hydrodynamic states of the atmosphere. Weather can be viewed as perturbations, deviations from some kind of norm, in the local climate. In this sense, one could argue that climate is some kind of temporal average of the weather at a location. Note, however, the descriptions in the previous three paragraphs of the basic factors that determine the climate at a location. These factors are independent of the temporal variations of the states of the atmosphere.

The climate at a location is not determined by the weather. Local climate is determined by factors outside the domain of the states of the atmosphere.

Weather and Climate are Local
Climate and weather are both local and neither is global. There is no need to focus on any aspects of “global climate”: such averages are useless for decision support. Primary focus should be on the advantages and dis-advantages, if any, of the status and changes in local weather. It cannot be over-emphasized the extent to which focus on global-average changes in the “global climate” is mis-guided. Local decision support demands solely local information. It also cannot be over-emphasized that the complete lack of focus on local states is a major failing.

The hour-by-hour, day-to-day, and month-by-month variations in local weather are determined by the effects of the net of the radiative energy into the physical phenomena and processes occurring within and between the thermodynamic and hydrodynamic sub-systems. All phenomena and processes, ( thermodynamic, hydrodynamic, chemical, biological, all ), occurring within the Earth’s systems of interest are driven by this net energy. Basically, weather is the distribution, and internal redistribution, of the energy supplies of sensible and latent thermal energy within Earth’s thermodynamic and hydrodynamic systems.

The solar-system and Earth’s geometric relationships, and local altitude/latitude, are the primary reasons that we can know that the temperature, and the weather in general, at a location will be different, for example, at January and July. The degree of differences between the seasons primarily is determined by the local latitude and altitude. The degree of differences over the seasonal / yearly cycle is a strong function of location. Variations over the seasonal cycle are more or less distinct; the variations are either small or large depending on the location.

Weather and Chaos
Weather is thought to be chaotic. And the numerical solutions of the mathematical models for both weather (NWP) and climate (GCM) are classified as ill-posed, in the sense of ¬†Hadamard, initial-value problems; lack of continuous dependence on the initial data. The average of a chaotic response is itself chaotic. Thus, if climate is the average of weather, then climate is also chaotic. Again, the descriptions of climate given in the first three paragraphs above preclude the chaotic nature of weather being a part of chaotic climate. It is the Earth-Sun geometry and the axis of Earth’s rotation that determines that January and July are easily differentiated. That differentiation is independent of, is not a function of, the chaotic nature of weather.

Chaotic is not random. Chaotic is the antithesis of random. Random fills phase space, whereas temporal chaotic trajectories are limited to the attractor and so by definition, cannot fill phase space. Weather is not random and is not noise; neither pink or white. Especially not white noise which has equal power at all frequencies. Averaging the trajectories from multiple runs of a single GCM, or one or more runs from several GCMs, does not in any way ensure that the so-called noise will be ‘averaged away’. The averaging is instead an averaging of different trajectories. Additionally, there is no way to ensure that the different trajectories are associated with ‘an attractor’ for the real-world case of spatio-temporal chaotic response, which is the case of finite-difference approximations to partial differential equations.

If it is insisted that climate is the average of weather, then projections of the climate into future times demands that weather be correctly simulated by mathematical models that are used for the projections. The statement that, Weather is chaotic and can’t be projected with high fidelity to the physical domain, but climate can be, simply makes no sense.

GCM Validation
Validation, fidelity of simulations relative to the physical domain, of GCMs thus firstly requires that the calculations be shown to be correctly simulating the distribution and internal redistribution of the internal variations; that are responsible for the local weather. Validation relative to effects of increasing concentrations of CO2 must then require that the GCMs are correctly simulating how the distribution and internal redistribution of the internal variations have been altered by the increasing concentration of CO2 in the atmosphere. This is a very difficult problem.

A first major difficulty will be in devising and development of procedures and processes that can be used to determine that changes in the phenomena and processes that are responsible for changes in local weather are in fact due primarily or solely to changes in CO2 concentration. A third order delta that will be exceedingly difficult to (1) observe and (2) model and calculate.

The case of extreme weather events requires the same series of accounting if climate change is invoked as the fundamental cause. Extreme weather events are generally very localized. Thus if the invoked driving source of the event is a significant distance away from the observed occurrence, the effects of changes in the composition of the atmosphere are required to be shown to obtain over the distance of the course from the source to the location of occurrence. If the event is a mighty downpour of rain and the source of the rain is said to be the Oceans far away from the location of the downpour, it must be shown that the changes in the composition of the atmosphere are directly related to the fact that the water vapor survived its path from the Oceans to the downpour location, and that the previous composition of the atmosphere would have prevented the water vapor from surviving its journey. Sounds very difficult to me.

Global Metrics are Useless
Global metrics for assessing GCMs fidelity to the real world are of no use whatsoever relative to assessing the correctness of simulations of local weather. The changes in local weather are required for decision support. Additionally, none of the fundamental laws describing weather and climate can be usefully expressed in terms of global quantities. The state of the atmosphere and the state of liquid and solid phases of water, and changes in these states, are determined by local conditions. No physical phenomena and processes, governed by the fundamental natural laws, have been demonstrated to scale with global averages of anything.

The temperature of the atmosphere, which has been chosen to represent changes in climate due to increasing concentrations of CO2 in the atmosphere, on the other hand, is determined by the path of the thermodynamic processes that the atmosphere experiences at the locations of interest. As the initial states are different, and the changes in weather are different, so will the temperature be different.  Again, no dependency on the global-average state.

Climate is local, weather is local. Weather is the variations in local climate. For decision support, the variations in local weather are what must be correctly simulated by GCMs. The models are required to be able to correctly simulate the changes in the weather variations due to changes in the concentration of CO2.

Based on my comment here.

January 14, 2015 Posted by | Uncategorized | 3 Comments