Decompose annual time series in R
Seasonal decomposition doesn't make sense in this situation. You're sampling frequency needs to be greater than 1 for this to work!
I know this changes your model, but just for the sake of example:

&gt; dat=c(37.2,37,37.4,37.5,37.7,37.7,37.4,37.2,37.3,37.2,36.9,36.7,36.7,36.5, 36.3,35.9, 35.8,35.9,36,35.7,35.6, 35.2, 34.8, 35.3,35.6,35.6, 35.6, 35.9,36,35.7, 35.7, 35.5, 35.6, 36.3, 36.5)
&gt; whts &lt;- ts(dat, frequency=2, start=1966, end=2000)
&gt; decompose(whts)
$x
Time Series:
Start = c(1966, 1) 
End = c(2000, 1) 
Frequency = 2 
 [1] 37.2 37.0 37.4 37.5 37.7 37.7 37.4 37.2 37.3 37.2 36.9 36.7 36.7 36.5 36.3 35.9 35.8 35.9 36.0 35.7 35.6
[22] 35.2 34.8 35.3 35.6 35.6 35.6 35.9 36.0 35.7 35.7 35.5 35.6 36.3 36.5 37.2 37.0 37.4 37.5 37.7 37.7 37.4
[43] 37.2 37.3 37.2 36.9 36.7 36.7 36.5 36.3 35.9 35.8 35.9 36.0 35.7 35.6 35.2 34.8 35.3 35.6 35.6 35.6 35.9
[64] 36.0 35.7 35.7 35.5 35.6 36.3

$seasonal
Time Series:
Start = c(1966, 1) 
End = c(2000, 1) 
Frequency = 2 
 [1] -0.007141266  0.007141266 -0.007141266  0.007141266 -0.007141266  0.007141266 -0.007141266  0.007141266
 [9] -0.007141266  0.007141266 -0.007141266  0.007141266 -0.007141266  0.007141266 -0.007141266  0.007141266
[17] -0.007141266  0.007141266 -0.007141266  0.007141266 -0.007141266  0.007141266 -0.007141266  0.007141266
[25] -0.007141266  0.007141266 -0.007141266  0.007141266 -0.007141266  0.007141266 -0.007141266  0.007141266
[33] -0.007141266  0.007141266 -0.007141266  0.007141266 -0.007141266  0.007141266 -0.007141266  0.007141266
[41] -0.007141266  0.007141266 -0.007141266  0.007141266 -0.007141266  0.007141266 -0.007141266  0.007141266
[49] -0.007141266  0.007141266 -0.007141266  0.007141266 -0.007141266  0.007141266 -0.007141266  0.007141266
[57] -0.007141266  0.007141266 -0.007141266  0.007141266 -0.007141266  0.007141266 -0.007141266  0.007141266
[65] -0.007141266  0.007141266 -0.007141266  0.007141266 -0.007141266

$trend
Time Series:
Start = c(1966, 1) 
End = c(2000, 1) 
Frequency = 2 
 [1]     NA 37.150 37.325 37.525 37.650 37.625 37.425 37.275 37.250 37.150 36.925 36.750 36.650 36.500 36.250
[16] 35.975 35.850 35.900 35.900 35.750 35.525 35.200 35.025 35.250 35.525 35.600 35.675 35.850 35.900 35.775
[31] 35.650 35.575 35.750 36.175 36.625 36.975 37.150 37.325 37.525 37.650 37.625 37.425 37.275 37.250 37.150
[46] 36.925 36.750 36.650 36.500 36.250 35.975 35.850 35.900 35.900 35.750 35.525 35.200 35.025 35.250 35.525
[61] 35.600 35.675 35.850 35.900 35.775 35.650 35.575 35.750     NA

$random
Time Series:
Start = c(1966, 1) 
End = c(2000, 1) 
Frequency = 2 
 [1]           NA -0.157141266  0.082141266 -0.032141266  0.057141266  0.067858734 -0.017858734 -0.082141266
 [9]  0.057141266  0.042858734 -0.017858734 -0.057141266  0.057141266 -0.007141266  0.057141266 -0.082141266
[17] -0.042858734 -0.007141266  0.107141266 -0.057141266  0.082141266 -0.007141266 -0.217858734  0.042858734
[25]  0.082141266 -0.007141266 -0.067858734  0.042858734  0.107141266 -0.082141266  0.057141266 -0.082141266
[33] -0.142858734  0.117858734 -0.117858734  0.217858734 -0.142858734  0.067858734 -0.017858734  0.042858734
[41]  0.082141266 -0.032141266 -0.067858734  0.042858734  0.057141266 -0.032141266 -0.042858734  0.042858734
[49]  0.007141266  0.042858734 -0.067858734 -0.057141266  0.007141266  0.092858734 -0.042858734  0.067858734
[57]  0.007141266 -0.232141266  0.057141266  0.067858734  0.007141266 -0.082141266  0.057141266  0.092858734
[65] -0.067858734  0.042858734 -0.067858734 -0.157141266           NA

$figure
[1] -0.007141266  0.007141266

$type
[1] "additive"

attr(,"class")
[1] "decomposed.ts"