Appendix C A COMPARISON OF RESULTS DERIVED FROM ANALYZES USING DIFFERENT MODELS FOR 1 DAILY VARIATION OF BIRETS. The first goal was to determine how the distribution of clouds (as they occur now) in the Earth's atmosphere affects the radiation budget of the surface and atmosphere. Finally, empirical relationships between various meteorological parameters (at shorter time ~ and smaller spatial scales of GCMs) and top-of-the-atmosphere radiation have been determined.
For each orbital pass, the range and mean solar zenith angle for the STA are reported. From December 1978 to December 1979, the countries of the world worked together on the First GARP Global Experiment (FGGE). Most of the data I analyzed covered a period during the second SOP (mid-June).
1 gives an idea of the distribution of radiation data (in the upper hemisphere) obtained during daylight hours (solar angle Z'eni th less than 85 degrees) by the Nimbus 7 satellite for several typical target areas (regions of 500 km per side). Another change I made to the corner container map was to increase the size of the containers. Thus, they were able to average together data from very different regions (and most importantly, latitudes) of the Earth.
The result was to cover most of the range of solar zenith angles for the various models.
MU SUN
0 is the declination of the sun (latitude of the sub-solar point on Earth), then the cosine of the sun's zenith angle is given by. Then the daily average of the cosine of the sun's zenith angle is given by I used a linear least-squares fit of the additive model to the Stowe-Taylor ADMs to determine the model parameters, g and h.
Some of the weather variables are simply taken directly from the EFL3Ts as is. Many of the variables I used involve values of FGGE variables calculated on the Earth's surface. Thus, if the original temperature of the packet (at level j) was then (assuming that cp remains relatively constant) inequality gives 4 .4 us.
23, and ak is the albedo of the surface under investigation in the kth solar zenith angle bin. For a fuller explanation of the data, the reader should consult the original publications. The sums were placed in the elements of the matrices corresponding to one of the small bins that were combined.
The exact form of the statistical relationships examined in these appendices is explained in the appendices themselves. Interestingly, the correlation coefficients of the additive data set are slightly higher than for the constant or multiplicative data sets. The first source consists of the systematic and random errors in the measurements used as the basic data set in this thesis.
The probability that the absolute value of a measurement of the correlation coefficient of two uncorrelated variables. However, there are no measurements of top-of-the-atmosphere radiative flux (at least of the kind and scale discussed here). The first aim of this thesis was to determine the effect of clouds, as they currently occur in the Earth's atmosphere, on the net radiation flux at the top of the atmosphere.
VARIABLE
In this table, I compare the results of the 6DAY 49BA and 6DAY 19BA analyzes to determine the effect of using different angular bin models in analyzing the visible data. The table is set up in the same way as Table B.l and includes the same type of data from the 8 LATITUDES geographic grouping, analyzed in the same way. I used ratios of 6DAY 19BA results to 6DAY 49BA results in determining these statistics.
Unlike the comparison in Table B.1, h~ver, the 19 angled bin pattern was used by averaging the results in the summation matrices of different bins in the 49 angled bin pattern together, thereby making summation matrices appropriate for the 19 angular bin patterns. pattern. LATITUDE # 1 AVERAGE RATIO RATIO STD DEV MINIMUM RATIO MAXIMUM RATIO LATITUDE # 2 AVERAGE RATIO RATIO STD DEV MINIMUM RATIO MAXIMUM RATIO LATITUDE # 3 GEN. In this table (as in Table B.3), I compare the results of the 6DAY 49BA and 6DAY 19BA analyzes to determine the effect of using different patterns of angled bins to analyze the visible data.
2 and includes the same type of data (from the 8 LOCAL, CONTINENTAL, OCEANIC and HEMISPHERIC geographical groupings) analyzed in the same way. I used ratios of 6DAY 19BA results to 6DAY 49BA results in determining these statistics. Unlike the comparison in Table B.2, however, the angular bin model 19 was used by averaging the results in the summary matrices for the different bins in the angular model 49 together, and fitting the summary matrices to the angular bin 19. model.
A COMPARISON OF RESULTS FROM ANALYZES USING DIFFERENT MODELS FOR BIDIRECTIONAL DIURNAL VARIATION. The statistical results I investigate include apparent flux means, covariances of .__this variable with other variables I investigated, and correlation coefficients of apparent flux with other variables. The purpose of the comparison is to determine whether the choice of model for the diurnal variation of bidirectional reflectance (for regions of the land surface–atmosphere system) is relevant to the outcome of my analysis and, if relevant, whether any g · iven model appears to work better than others.
In this table I compare the results of the 49BIN CON, 49BIN MUL and 49BIN ADD analyzes to determine the effect of using different daily correction techniques on the visible data. I looked at the mean visible flux and the covariances and correlation coefficients of visible flux with non-radiative variables for the geographic grouping of 8 LATITUDES. I took the ratio of the MUL score to the CON score and the ratio of the ADD score to the CON score and used these ratios to determine the mean, minimum and maximum ratios and standard deviations of the ratios for each latitude band.
In each latitude band, the ratios related to the 49BIN MUL analysis are presented first and those from the 49BIN ADD analysis second. At the beginning of each latitude band, I present the number of 49BIN CON correlation coefficients (out of 40) that were greater than or equal to 0.15, as only these cases were examined for the ratios of the covariances and correlation coefficients. In this table (as in Table C.l), I compare the results of the 49BIN CON, 49BIN MUL, and 49BIN ADD analyzes to determine the effect of using different daily correction techniques on the visible data.
I looked at mean visible flux and the covariances and correlation coefficients of visible flux with all variables for each of the geographic groupings. I took the ratio of the MUL result to the CON result and the ratio of the ADD result to the CON result and used these _;:atios to determine mean, minimum and maximum ratios and standard deviations for the mean visible flux ratios and for each of the visible flux covariances and correlation coefficients. The conditions involving the 49BIN MUL assay are presented first, and the conditions for the 49BIN ADD assay are presented second.
Then the covariance results for each variable (with which visible flux is correlated) are tabulated followed by the number of 49BIN CON correlation coefficients (out of 20) that were greater than or equal to 0.15 (since, as in the last table, only these cases were examined for the ratios of the covariances and correlation coefficients) followed by the ratio results for the correlation coefficients.
AVERAGE 1.1864 STAND DEV 0.1578
The statistical results I examine include the means for the visible flux, the covariances of this variable with the other variables I. examine, and the correlation coefficients of the .. visible fluxes with the other variables. The purpose of this comparison is to determine the extent of error by analyzing only a small portion of the available data. In this table I compare the results of the 6DAY 49BA and 49BIN ADD analyzes to determine the effect of using different amounts of data on the resulting statistics.
I took the ratios of the 49BIN ADD results to the 6DAY 49BA results and used these ratios in determining the mean, minimum, and maximum ratios, and standard deviations of the ratios, for each latitude band. At the beginning of each latitude band, I present the number of 6DAY 49BA correlation coefficients (out of 40) that were greater than or equal to 0.15, as only these cases were examined for the ratios of the covariances and correlation coefficients.
