Upper-layer soil moisture (JJA)

Rainfall (JJA)

EN

SO

IO

D

Tri

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nd

ex

SON JJA

EN

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1

( )N

n n

n

w t x a t

1

N

n nt

1

n nx an nn n

11 12 131

1

21 22 232

2

3

1 2 3M M MM

a a awx

a a awx

xa a aw

2 13a a11 12 1311 12 131w1 a11 111 12 1311 12 1311 12 13a11 1

1x1w1 11 1a11 1

1x

21 22 23a a21 22 2321 22 23a a1

2w2w aaa21 221 221 2a21 2x2x2xx

3xx

MwMw 1 2 31 2 31 2 3a a1 2 31 2 31 2 31 2 31 2 3a a

3x

1 2 3M M M1 2 3a 1 2 3M M M1 2 3aa

2x2

w A x

2ErrorTT

w Ax w Ax

1T T

1T T

1T TT T

x A A A w

diagonalcolumn- column-orthonormal orthonormal

T

M NM M N NM NM N M M NM NM M N NM NM NM M NM N

dia alcolumn- column-diagonaldia alM M NM M N NM NM M NM N

gondiagonalcolumn- column-diagonalorthonormal orthonormalorthonormal orthonormal

M M NM M N

A U W V

1 TT1x VW U w

1 1,T TM M,M M,1 1T T1 11 1M M

1 11 11 11 1C A A b A w

11x C b