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.. 8 2004 .
A one-dimensional model of shallow reservoir thermodynamics either describing physical processes in underlying soil layer is constructed. The model simulates seasonal dynamics of lake (including ice and snow layer formation) and year to year variability. A number of numerical experiments is performed; model and natural data are compared. It is shown, that the model performs satisfactory agreement of some parameters, modeled and observed, for lakes in Western Siberia and Yakutat.

1.
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2

..

. , , , , ( , , ), , .

2.
(., , [5], [6]) . . , . , (, , , ).

2.1.

.

. z , [0, h], h -- . h -- , , z = h . ( , t) : c T 1 =2 t h T + c dh T 1 dh0 T 1 S - c - + M. dt h h dt h (1)

c -- , -- , - ( -- ), T -- , t -- , dh0 -- dt [/], , S -- , M -- , . («») (. ), («-») -- . (. ). : S ( ) = S (0) exp(-e h ), e -- . h : dh = r - E - Rs - Rb . dt r -- , E -- , Rs -- , Rb -- . .

«-»

3

M . , , . . , 0 , 1 . (1), , (.. (1) ); «» M . - 0 . . , .

2.2. .
, . - . (z , t) : T T = sn + sn LFf r , csn sn t z z (2) W =- - Ff r . t z L -- , Ff r -- , W -- , -- . : =h W/z - W - Whc
hc

,

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2.3.

.

[8]. : , , . ( -- ) ,

4

..

, . , , . . , , 1 , [8] : s c T T = s + s LFf r , t z z W W = W - - Ff r , t z z z I = Ff r . t
s

(3)

W -- . , , , / . , , -- T , W , I . ( ) , , . ( - 100 ) .

2.4.

« - ».

. : S (1 - ) + Ea - Es - H - LE = - T . h (4)

S -- , Ea -- , Es -- , H LE -- , , , -- (, ). , , , (4) , . (4) . [9]: S= S (1 - csh n), 1 + / sinh0

-- , -- , 0.105, n -- , csh = 0.5607 -- . : S = S0 (sin cos + cos cos cos ).
1

,

«-»
: S0 , -- . 2 , . : Ea

5

-- , -- , -- -

4 = a T2 (1 + clg cld2 ), 350 1/7 a = c e2 exp , T2 clg = 0.22,

c =

0.15, T2 < 273.15, 0.14, T2 > 273.15

T2 -- 2 , e2 -- 2 , -- . . , . : H = -cp a CH |V2 | (2 - s ) , LE = -a LCE |V2 | (q2 - qs ) , (5)

cp -- , a -- , CH CE -- , 2 q2 -- 2 , s qs -- , V2 -- 2 . (5) ( )[10], .

3.

; , , . (1) : Tij
+1 j +1 j +1 j +1 j +1 j +1 Ti+1 - 2Ti + Ti-1 h Ti+1 - Ti-1 - Tij = + c - t 2 t hj 2 (hj )2

j +1 j +1 h0 1 Ti+1 - Ti-1 1 Sj -c - (6) t hj 2 h . 4). :

D + Q (1 - A) -

4 Tsj +1

-H

(Tsj +1

,

Ta

) - LE (q

j +1 s

(Tsj +1

),

qa

+1 Tsj+1 - Tsj ) = - hj

+1

(7)

6

..

; s , (s + 1) -- , , a -- 2 , , , .. . (7) Tsj +1 . :
+1 1. - s+1j s . - shj s ; h (7) Tsj +1 , ,

T

j +1

-T

j +1

T

j

-T

j

- s .

T

j +1 j +1 +1 -Ts j h

, , .. T
j +1

2. Tsj +1 (7) - s+1j s . h (7) 4 4 3 (Tsj +1 ) (Tsj ) + 4 (Tsj ) (Tsj +1 - Tsj ). . 3. H , LE (7) Tsj +1 (5). . 1) 2), 2) 3). [11]. [11]; : Tsj
+1 k k

-T

j +1

= Tsj

+1 k -1 k -1

+ k + k

Tsj

+1 k k

- Tsj

+1 k -1 k -1

, , (8)

+1 Tsj+1

+1 = Tsj+1

+1 Tsj+1

+1 - Tsj+1

k = 1, N . k -- , k -- , N -- ; (Tsj +1 )k : D + Q (1 - A) - Tsj
+1 4 k

-H

Tsj
k -1

+1 k

, Ta - LE q

s,j +1

Tsj

+1 k

, qa =

-
+1 Tsj+1 k

+1 Tsj+1

- (Tsj +1 )k

-1

hj

,

(6).

4.

( , . ) [12],[13]. . (20 , . ).

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7

4.1. . .
2 . , . , , , -- . , ( ) ( ). . 1. . 0.5 . , . , ( 2 ), , , . , , , ( , ), , , .

4.2.

. .

-- , , , , « ». . : 2 , 1 , 2 2 . 4.5, -- 12 . , . 280320 . [5]. . 19701980 ., . (19761977 .)[5]. , . 2. [5],[14] : · , , , -- . ; · ( ) 0.71.5 , ; · , , ;

8

..

. 1.

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9

. 2. / .

10

.. · 400 , (450 ).

. (. 3). , 20 (19651984 .). 1.2 2.0 . . , .

5.

. , , , , . , , , () () . . , : , , . , , . . ( ) . , , , , . .-. .., , . . .. . .. . 01-06-64150 01-2132.

[1] .., .. . . , . 333. .: , 1988, 152 . [2] .. . .: . . : - , 2002, C. 8387.

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11

. 3. .

12

.. [3] .., .. . .: . . - : - , 2002, C. 98103. [4] .., .. . .: . . : - , 2002, C. 8897. [5] .., .. . .: ; , «», 1981. [6] MALM J., TERZHEVIK A., BENGTSSON L., BOYARINOV P., GLINSKY A., PALSHIN N., PETROV M. Temperature and salt content regimes in three shallow ice-covered lakes //Nordic Hydrology, 28, 1997, P. 99128. [7] ., ., .. . - , 2000, 5, C. 5-14. [8] .., .. - . 1. . -- . , 1998, 34, C. 453465. [9]

.. . .-.: , 2000, 778 .

[10] .., .. // . . - . - 1954. - 24(151). - . 163187. [11] .. .: . - 4- , . . - .: , 2000. - 296 . - ISBN 5-9221-0092-0. [12] RAZUVAEV, V. N., E.G. APASOVA, AND R.A. MARTUGANOV. 1993. Daily Temperature and Precipitation Data for 223 USSR Stations. ORNL/CDIAC-56, NDP-040. Carbon Dioxide Information Analysis Center, Oak Ridge National Laboratory, Oak Ridge, Tennessee. [13] V R.S., R.L. SCHMOYER, P.M. STEURER, T.C. PETERSON, R. HEIM, T.R. KARL, AND J.K. EISCHEID. 1992. The Global Historical Climatology Network: Long-term monthly temperature, precipitation, sea level pressure, and station pressure data. ORNL/CDIAC-53, NDP-041. Carbon Dioxide Information Analysis Center, Oak Ridge National Laboratory, Oak Ridge, Tennessee.
OSE,

[14] PAVLOV A.V. Regularities in Thermal Regime of Lakes in Permafrost Areas// Russian Geocryological Research, V. 1, 1995.