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MERRA Multiple Stream Investigation

• Overlapping Experiments tested
• Differences between Overlapping Streams
• Other reanalyses with multiple streams
• Methodology: Student's T-Test for Climate Models

Overlapping Experiments Tested

GEOS4-CERES has been run for multiple streams of analysis, producing overlapping periods. The overlaps occur at the end of an older stream and the beginning of a newer stream. Thus, the older stream effectively has many years of time to spin up land states, while the newer stream has had only a few months of spin up before the overlap period. We are evaluating the spin-up issues encountered by the land and atmosphere components of the assimilation, in order to assess and minimize the impact of data discontinuities.

In this demonstration, the overlapping analyses are labeled CERES_1 and CERES_2. The overlap period is 15 months, starting in Jan 2000. The first experiment has been processing for several years, whereas the second had a month and a half spin-up. The GEOS4-CERES reprocessing was performed to support the CERES instrument team research efforts and is not publicly available.

Differences between Overlapping Streams

Figure 1. Sea Level Pressure

These two figures compare monthly means of Sea Level Pressure (SLP) between the two experiments during Feb 2000 (left) and Jul 2000 (right). The color of the image shows the size of the difference between the two experiments, but what is of interest are the contours around statistically significant differences. Notice that in Feb 2000 there are substantial areas with differences that have confidence levels of 90% and 95% significance, wheras by Jul 2000 the two streams have converged and there are no notable regions of difference. In the case of SLP, the early differences were particularly notable in the Tropical Pacific and inland Africa.

Figure 2. Skin Temperature

These two figures compare monthly means of Skin Temperature (Tskin) between the two experiments during Feb 2000 (left) and Jul 2000 (right). The color of the image shows the size of the difference between the two experiments, but what is of interest are the contours around statistically significant differences. Notice that in Feb 2000 there are substantial areas with differences that have confidence levels of 90% and 95% significance, whereas by Jul 2000 the two streams have converged and there are no notable regions of difference. In the case of SLP, the early differences were particularly notable in Polar Regions, including all of Siberia, and in Mongolia.

Other reanalyses with multiple streams

The use of multiple overlapping streams is a convenient tool for parallel programming of long-term climate reanalyses.

• NARR: North American Regional Reanalysis
• JRE-25: Japanese 25-year Reanalysis Project

Methodology: Student's T-Test for Climate Models

We have applied the Student's T-Test to evaluate the statistical significance of differences between overlapping model streams. For a given climate parameter, global maps of the monthly mean are differenced and the Student's T-Test is applied to the mean and distribution of the differences.

The conventional statistic for measuring the significance of a difference between means is called Student's t-test ("Student" is actually a pseudonym for the inventor, W.S. Gossett, 1876--1937). When the two distributions are climate models which are thought to have the same variance, but possibly different means, the Student's t-test is computed as follows:

1. First, the standard error of the difference of the means, s_D, is computed from their pooled variance.
2. Second, compute t = [(mean x_A) - (mean x_B)]/s_D
3. Finally, the signifiance of this value of t is evaluated for Student's distribution with (References:by Press, W.H., Teukolsky, S.A., Vetterling, W.T., and Flannery, B.P. c. 1992 Cambridge University Press

References:
Numerical Recipes in Fortran 77, The Art of Scientific Computing, by Press, W.H., Teukolsky, S.A., Vetterling, W.T., and Flannery, B.P. c. 1992 Cambridge University Press