4404138.pdf [Levina Tatyana Borisovna]
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0.4 . . . ...!.. 0.3 "-'-':":'--:"~~~~~~~' . 0.2
: : : , 0.1
o Figure 2-13: The estilnated mean cloud cover value and standard deviation of the estimate as a function of the length of transition period (Thlsa,
104
4 6 10 2 4 8 4 4 6 N(t-1 ) a 2 N t-1 = 7 a 2 N(t-1)=5 a 2 N(t-1)=3 2 ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . -4 -2 a N(t-1) = 9 2 : :- . 3 a a -6 -4 -2 a 10 Statisticsof transformed beta-variables a -2 N(t-1) = 1 1 .... 2 . a -2 0.6 0.4 a -2 0.4 0.4 :0 0.1 RO.2
:0 0. 0.2 :0 0. 0.2 6 2 4 N(t-1)=2 January: N(t-1) = a a .. . . . . . . . . . . . . . . . . . . . . . . . . . 2 a :0 1 0. :0 0. 0.5 . . .
. . . .. a -2 a 2 4 N(t-1)=4 0.3
:0 0.2
0. 0.1
a -2 a 2 4 N(t-1) = 6 0.4 .. . . 0.' • . . RO.2 a -4 -2 a 2 N(t-1) = 8 0.6 . . . . . . . . . . :0 0.4 .. . . . . . . . . . . 0. 0.2 a -4 -2 a 2 2 N(t-1) = 10 :0 1 . . . . . . ... 0. a -6 -4 -2 a Value of random term Figure 2-17: A histogralll of deviates c ( t)
and the corre- sponding probability density function (solid line) approximated with the Beta
distri- bution. The cloud cover N(t -
1) for the lllonth of January
is given on a [0, 10] basis (Albuquerque, NM). 111 6 10 2 4 8 2 4 6 N(t-1 ) 2 4 N(t-1)=3 o N(t-1) = 7 o 2
-2 0 N(t-1)=9 2 -2 -5 o 1 . N(t-1) = 1 o -4 1.5 0.4 . :0 0- 0.5 0 0 0.6 0.4
:0 0- 0.2 0 -2 1 RO.5 0 0.6 :0 0- 0.2 :0 0-
. 5 o 2 -4 -2 0 Statisticsof transformed beta-variables 10 4 4 4 123 N(t-1) = 2 July: N(t-1) = 0 o 2
-4 -2 0 Value of random term
o , , , =:=1
o -1 1 2 o -2 o o -6 0.4 0.4
:01 0- :01 0- RO.2 -2 0 2 N(t-1)=8
0.4 :0 0- 0.2 0 -4 -2 0 2 N(t-1) = 10 :0 0- 0.2 R 0.5 Figure 2-18: A histograrll of deviates c(t) in the cloud cover lllodel and the correspond- ing probability density function (solid line) approxilllated with the Beta distribution. The cloud cover
for the lllonth of July is given on a [0, 10] basis (Albuquerque, NlvI). 112
a) Parameter "a" of the Beta distribution (random term in AR(1) model of cloudiness) 4 3 «l '0 0>2 ::J Cii
> Comput~d after cor1ditioning by cloudines~ at (t-1) hqur for each: month (diff~rent curve~) Means ~nd stds of ~he param~ter for all curves are shown o 2 3 4 5 N(t-1 ) 6 7 8 9 10 4 b) Parameter "a" of the Beta distribution (random term in AR(1) model of cloudiness) 0 -
-.. - ....... - ......
- .. -. ".---. 1 2 3 4 5 6 7 8 9 10 11 12 Month Figure 2-19: The parameter
of the
Beta distribution for different months (Albu- querque, NM) as a function of a.) N (t -
1) and b.) month of the year. The mean parameter values and the corresponding standard deviations are shown as the error bar plot. 113
5 a.) Parameter "b" of the Beta distribution (random term in AR(1) model of cloudiness) 10 9
7 6 5 N(t-l ) 4 3 2 Computed after conditionlng by cloudiness at (t~ 1) hour fo~ each month (different :Curves) .. .................. Means ahd stds of the parameter for all curves are shown 4 o o 5 b.) Parameter "b" of the Beta distribution (random term in AR(1) model of cloudiness) 0---- 1 2 3 4 5 6 7 Month 8 9 10 11 12 Figure 2-20: The parameter b of the Beta distribution for different months (Albu- querque,
NM) as a function of a.) N (t - 1) and b.) month of the year. The mean parameter values and the corresponding standard
deviations are shown as the error bar plot. 114
0.8 0.8
0.8 0.8
0.8 0.8
5 =0.3913 : 5 0.4 0.6
June 0.4
0.6 October
0.4 0.6
December 0.4
0.6 Cloudiness 5=0.4104; 5=0.41136 .0 .
5 =0.3891; .0 5 =0.354: 5 =0.34653 .0 5 0.2 0.2
0.2 0.2
0.2 0.2
~0=0.3447; 55=0.34189 . '"
. 5 =0.349; : 5 =0.34968 .0 5 0.4 0.6
April m =0.3913; m :(').42674 : .. '. ,0, : 5 '.' ' . February m =0.4243; m =0.43556 : ..
: ..• 5 . '.'
' . m =0.302;: m =0.32875 .. '. '0' : 5 . 0.4 0.6
August m =0.3230; m =0.32663 . .. '. '0' : ..
'5' . '.'
' . ... m =0.2276; m =0.22442 . . .. '0' 5' , - . .. rtl =0.2752; m =0.28824 : . . '. '0' .... : ..
"5' . '.'
••.•. '.••••..
5 =0.3841;
5 =0.38546 .0 . 5 . 0.4 o o o o 0.2
0.6 0" (]) -= 0.2
0.4 o o 0.6 o o o o 0.4 0.4 o o 0.2 0" (]) -= 0.2
0" (])
-= 0.2
0" (])
-= 0.2
0" 0.4
~ 0" 0.4 ~ 0.8
0.8 0.8
0.8 0.8
0.8 5 =0.40632 5 .
5 . 0.4 0.6 July
0.4 0.6
November 0.4
0.6 Cloudiness 0.4 0.6
September ~o =0.3758~ 55=0:36827 5 =0.3998; .0 . 5 =0.3216; .0 0.2 0.2 0.2
0.2 0.2
0.2 January
.ry10~0:~~3.;. ~5:=q.~E?~~ -t-
Simul. 5 ::::0.4075; :5 =0.4069 0 Obs.
o .. 5 . 0.4 0.6
March m =0.4022; m =0.4299 . . . '. '0' ,5, '.' ' . 0.4 0.6
May m =0.3813; m =0.37824 .. '. '0' 5.. ' . m=0.2881; m=O.31121 . . . '. '0' : .. '5'
. '.' ' . m =0.2105;
m =0;19819 : .. "'0' s . ~0=0.3286; 55=0.;30353 . '"
rtl =0.2570; m =0.25996 : ..
: s . '.'
' . 5 =0.3574:; 5 =0.35619 .0 5
0" ~ 0.2 0 0 0.4 0" ~ 0.2 0 0 0.4 0" ~ 0.2 0 0 0.4 0" ~ 0.2 0 0 0.6 0" 0.4
~ 0.2
0 0 0.6 0" 0.4
~ 0.2
0 0 Figure 2-23: Observed and silllulated cloud cover distribution (Albuquerque, N:NI). SYlnbols
Tn and
s are the lllean and standard deviation values, correspondingly, for the observed (sub-index "0") and sinllllated (sub-index "8") data. 132
0.8 0.8
0.8 0.8
0.8 0.4
0.6 December
0.4 0.6
October 0.4
0.6 August
0.4 0.6
June 0.4
0.6 April
S =0.35634 s =0.35223 .,? 5 .. .. s =0.38135 s =0.3654
'0 5 0.2 0.2 0.2
0.2 0.2
5 =0.31907
s =0.31579
.. '? : s ' : . 5 =0.29692 s =0.32833 . . ,? , s ' . S =0.33124 s =0.35163
. . ,? , s ' . February ri1 =0.18419
m =0:17857 : . . " '0' .... ; ...
s. '.' ..... '.....
rtl =0.18227 m =0;24761 . . . '. '0' : s ' . .. . . . . . . .
. . . . . . . .
. . . . . . . . . rtl =0.20342 m =0;23332 , . . '. '0' : s. '.'
' . .... . . . -
. . . . . m =0.28479 m =0:2475 . .. '. '0' ; s. '.'
' . . . ~0:=9.~~??~ . r.ns=:,q;??~q8.. .. .. . . . . . . . . . . . . . .
. .. . . . o o 0.6 0.6
o o o o 0.2
o o 0.6 o o 0.6 0.6 K 0.4 0.2 CT 0.4 ~ K 0.4 0.2 K 0.4 0.2 K 0.4 0.2 j • 0.8
0.8 0.8
0.8 0.8
0.4 0.6
November 0.4
0.6 July
0.4 0.6
May 0.4
0.6 March
0.4 0.6
September ...
. . . . . . . . . . . . . . . . . .
. . . ...
5 =0.29386 s =0.30744 ,0 ...
, ... s...
', . . s =0.38769
s =0.38415
'0 5 . . . s =0.37767 s =0.37538 '0 5 . 0.2 0.2
0.2 0.2
0.2 S =0.33984 s =0.347
.. ,? s ' .. S =0.35797 s =0.35957 .. ,? .....•.. ,5 ' . January
m =0.29766
m =0:26794
. ...
: '0' ~ s .. : : . m =0.21041 m =0:21436 ...
: '0' ~ s .. : ~ . ri1 =0.17637 m =0;19801 . ..
: s. '.'
' . ... ............................ . . . m =0.30061 m =0:2876 . .. '. '0' , ; s .. " , '
. . . . ... .. ............ -t- Sim .
m =0.26345
m =0:25
~ Obs.
I' '0'
, ; s. '.' ' . o o o o o o CT 0.4 ~ o o 0.2
CT 0.4
~ 0.6
o o 0.6 0.2 0.6
0.6 0.6
K 0.4
0.2 K 0.4 0.2 K 0.4 0.2 , . , ............................. . .
. 0.8
0.4 0.6
Cloudiness 0.2
5 =0.37009 s =0.37107 . . ,? .....•... s ' . ri1
=0.259: m =0;2522 . . . " '0' : s. '.'
' . . " . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 0.6
o o K 0.4 0.2
0.8 0.4
0.6 Cloudiness 0.2 5 =0.34931 s =0.33597
.. ,? .....•... s ' . ri1
=0.22516 m =0;20058 : ..
: s' '.'
' . 0.6 o o K 0.4 0.2
Figure 2-24: Observed and simulated cloud cover distribution (Thcson, AZ). SYlnbols m and s are the lnean and standard deviation values, correspondingly, for the observed (sub-index "0") and simulated (sub-index "s") data. 133
0.8 0.8
0.8 0.8
0.8 0.4
0.6 December
0.4 0.6
October 0.4
0.6 August
0.4 0.6
June 0.4
0.6 April
. . 5 =0.3932 5 =0.3924 '0 . 5 . . . . 5 =0.31832 5 =0.33743 '0 . 5 . . . . 5 =0.40787 5 =0.41259 '0 . 5 • 0.2 0.2 0.2
0.2 0.2
. . . ~o =0.32404
55=0.~2718 . .
' - . - . '" ~ . February
m =0.25428
m =0:27031
: .. '.'0' : 5' '.' ' . .. s =0.36605
5 =0.37391 ,0 5 . . . . m =0.27023 m =0:28327 . . "'0'
....•... s .. '
. ....
. . . . . . . . . .
. . .
. . . . . . . . . . . . . . . . . .. . . . . m =0.24973 m =0:30029 ' . . . ' '0' ....•... s, .' ......•...... . . . . . m =0.38564 m =0:38101 . . "'0, ....•...
s .. ' ......•...... . . . . . . . . m =0.37827 m =0:38648 . .
0 s .. '
. o o o o o o o o o o 0.4 0.6 0.4
0.2 0.2
0.2 0.4
0.2 0.4
0.2 0.4
0.8 0.8
0.8 0.8
0.8 5 =0.40409 5 .
0.6 November
0.4 0.6
July 0.4
0.6 September 0.4 0.6
,May 0.4
0.6 March
. . . 5 =0.3573-1 5 =0.36262 '0 5
S =0.4011: o . . . 5 =0.41235 5 =0.4098 '0 '5'
0.2 0.2
0.2 0.2
0.2 January
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