Not exact matches
[25] Lemaitre's famous differential equation for cosmic expansion is: R [2] = C / R + 1 / 3AR [2]- k where R is the
scale factor for cosmic expansion which is proportional to the radius of the universe when that radius has
meaning; C > 0 and proportional to the average present - day density of non-relativistic matter in the universe; cosmological constant, - C [0] < A < C [0], which serves to create a cosmic repulsion that keeps galaxies from being drawn together by gravity when it is positive and adds to the attractive force of gravity when it is negative; and
spatial curvature, k = -1,0, +1.
Figure 1.4 http://cybele.bu.edu/courses/gg312fall02/chap01/figures/figure1.4.gif shows the natural variability of the annual
mean surface temperature on several different
spatial scales from a climate model simulation for 200 years.
The two former methods are dependent on the large -
scale circulation variables from GCMs, and their value as a viable
means of increasing the
spatial resolution of climate change information thus partially depends on the quality of the GCM simulations.
This
means that they should be on a
spatial scale covering rather large number of cells.
Of course, if a larger
spatial or shorter temporal
scale is the chaotic one, then hardly matters about the smaller space or longer time
scale when it might
mean the whole shebang is wiped out by a — non-cataclysmic, non-alarming, but mathematically fascinating — event.)
I assume you
mean here «whose
spatial scale of interest is often much SMALLER than current high resolution GCMs can capture».
Owing to the decreased number of
spatial degrees of freedom in the earliest reconstructions (associated with significantly decreased calibrated variance before e.g. 1730 for annual -
mean and cold - season, and about 1750 for warm - season pattern reconstructions) regional inferences are most meaningful in the mid 18th century and later, while the largest -
scale averages are useful further back in time.
Moreover, we suggest that accounting for any
spatial or seasonal biases in the stack would tend to reduce its variability because of the cancellation of noise in a large -
scale mean and the opposing nature of seasonal insolation forcing over the Holocene, causing the Holocene temperature distribution to contract.
Analyses of tide gauge and altimetry data by Vinogradov and Ponte (2011), which indicated the presence of considerably small
spatial scale variability in annual
mean sea level over many coastal regions, are an important factor for understanding the uncertainties in regional sea - level simulations and projections at sub-decadal time
scales in coarse - resolution climate models that are also discussed in Chapter 13.
And following from those two, there is a further question as to whether or not averaging local, daily «windy - calm» trends to larger
scales (temporal or
spatial) is a legitimate exercise at all, given the
meanings assigned to such trends.
«Climate variability refers to variations in the
mean state and other statistics (such as standard deviations, the occurrence of extremes, etc.) of the climate on all temporal and
spatial scales beyond that of individual weather events.
This
means that even if
spatial averaging were to reduce the error further, the best predictability would still occur for the global behaviour at the monthly
scale.
«Epistemology is here applied to problems of statistical inference during testing, the relationship between the underlying physics and the models, the epistemic
meaning of ensemble statistics, problems of
spatial and temporal
scale, the existence or not of an unforced null for climate fluctuations, the
meaning of existing uncertainty estimates, and other issues.
These range from simple averaging of regional data and
scaling of the resulting series so that its
mean and standard deviation match those of the observed record over some period of overlap (Jones et al., 1998; Crowley and Lowery, 2000), to complex climate field reconstruction, where large -
scale modes of
spatial climate variability are linked to patterns of variability in the proxy network via a multivariate transfer function that explicitly provides estimates of the spatio - temporal changes in past temperatures, and from which large -
scale average temperature changes are derived by averaging the climate estimates across the required region (Mann et al., 1998; Rutherford et al., 2003, 2005).