3. See comments (line 100 -112) in m.file
4. The observations were made more during winter (53 %) than during summer (47 %). This is
why the mean temperature value based on observation time series is lower than the mean
climatological temperature and interpolated temperatures, both of which have temperature at
regular time intervals.
See comment (line 131 – 149) for explanation of TVC, TV, tv, tva, and rest.
TVC
TV
tv
tva
rest
18.18
20.03
19.83
7.95
18.17
16 % (tva^2/tv^2) of total variance of interpolated time series is explained by observation, and
84 % (rest^2/tv^2) of total variance is explained by climatology
5. Time range for Figure 2 is from 1998/3/17 to 1998/4/1. There are gaps around 3/22 and 3/2425. The predictions during the gap period were made by adding climatology (model) to the
model error determined at the last time step when both observation and climatology values are
available. For other periods, basically, if current model error (difference between climatology
and observation) is small, next error is similar to previous, and similar amount of error value is
added to climatology to come up with predicted temperature. If current error is big, larger
amount of error is produced by kalman filter and added, resulting in larger departure of predicted
value (vector v) from observation. For this code, used observed temperature during the time
when observation is available.
6. This harmonic analysis used two harmonics (diurnal and annual), and equation is
T (t )  T  A1 cos(
2πk1t
2πk1t
2πk 2 t
2πk 2 t
)  B1 sin(
)  A2 cos(
)  B2 sin(
)
T
T
T
T
T is 9*365 day, k1 = 9*365 wave number, k2 = 9 wave number, and t is in unit of day (increment
for each step is hour given by fraction of a day). After the regression coefficients are determined,
diurnal cycle terms (2nd and 3rd terms) and annual cycle terms are combined separately. The
amplitudes for diurnal and annual cycle are Ck  Ak2  Bk2 , and phases are φk 
T2
B
tan1 k
2π
Ak
(k = 1 or 2 for diurnal, annual, respectively). See comments in m.file for explanation for fy and
fd
7. It seems like amplitude of diurnal cycle is underestimated, though amplitude of annual cycle
comparable to climatology, but overall magnitude is lower.
8. See in m.file
9. If interpolated time series is used for harmonic analysis, noise variance is slightly reduced (by
1 %), meaning annual and diurnal cycle more explain the variance of temperatures time series
(tables below). During fall season (around October and November), harmonic fits agree with
climatology best, but for the other seasons, there is discrepancy between harmonic fit and
climatology in terms of amplitude of diurnal cycle. Also mean value over the annual cycle from
harmonic fit is lower than climatology.
From observed time series
Annual
Diurnal
“Noise”
Amplitude(F)
24.03
7.11
Std dev (F)
17.00
5.02
9.34
% total variance
72
6.3
21.7
Phase
Day 200 (Jul 19)
22 UTC
% total variance
72.9
7.3
20.0
Phase
Day 200 (Jul 19)
22 UTC
From interpolated time series
Annual
Diurnal
“Noise”
Amplitude(F)
23.94
7.60
Std dev (F)
16.93
5.37
8.82
Fig 2
Fig 3