1. LAND SURFACE AND AIR TEMPERATURE AT CLEAR AND OVERCAST SKIES
Konstantin Vinnikov, Yunyue Yu, Mitchell Goldberg, Dan Tarpley, Ming Chen, Chuck Long
Land Team Meeting, January 7, 2011

2. STATISTICAL DISTRIBUTION OF CLOUDINESS
CLR-clear sky. (Fractional amount) = 0.
OVC-overcast sky. (Fractional amount) ≥ 0.9.
OTHER or INT 0 < (Fractional amount) ≤ 0.9.
“Bin averaging” technique
Bin size= 1 hour x 1 month
It is known that fractional amount of total cloudiness has U- shaped statistical distribution with much larger occurrences of CLR and OVC sky conditions compared to other fractional amounts of cloudiness. Generally, CLR sky takes place in about 1/3 of all observations with relatively small diurnal/seasonal variations.
CLR sky occurrence is smaller during the spring/summer months with early afternoon minimum, and larger - in the autumn. At Desert Rock, NV stations clear sky conditions are prevailing because of very dry regional climate.
OVC sky occurrence has daytime maximum in the diurnal cycle and winter maximum in the seasonal cycle.
The most of selected stations display a sharp decreasing of OVC sky occurrence at sunset and a sharp increasing – at sunrise.
Occurrence of the INT fractional cloudiness, other than CLR and OVC, is also about 1/3 of all observations but it is largest during warm season with morning maximum that usually exceeds 50%.

3. LST –Land Surface Temperature; SAT- Surface Air Temperature;
ALL sky conditions (CLR & OVC & INT).
“Bin averaging” technique is applied to estimate Expected Value and Standard Deviation of LST and SAT at each
1 hour x 1 month bin.
LST and SAT, display regular seasonal and diurnal cycles in the expected value with significantly larger amplitudes for LST compared to SAT and relatively small differences (up to 2°C) between annual averages of LST, SAT, and their differences at ALL, CLR and OVC sky conditions in estimates for the same stations.
Annual cycle of standard deviations of LST and SAT have summer minimum. Cold season maximum is shifted to the spring.
Diurnal cycle of LST has a maximum close to noon time.
Maximum in diurnal cycle of SAT is shifted to ~3p.m. of local solar time.
Standard deviations of LST are only a little larger compared to those of SAT.

4. LST –Land Surface Temperature;
SAT- Surface Air Temperature;
CLR - Clear sky conditions.
“Bin averaging” technique.
At CLR sky, diurnal and seasonal amplitudes of LST are significantly larger than of SAT.
Annual cycle of standard deviations of LST and SAT have summer minimum and cold season maximum.
Diurnal cycle of LST has a maximum close to noon time.
Maximum in diurnal cycle of SAT is shifted to ~3p.m. of local solar time.
Standard deviations of LST are very close to those of SAT.

5. LST –Land Surface Temperature;
SAT- Surface Air Temperature;
OVC - Overcast sky conditions.
“Bin averaging” technique.
At OVC sky, diurnal and seasonal amplitudes of LST are noticeable larger than of SAT.
Annual cycle of standard deviations of LST and SAT have summer minimum and cold season maximum.
Diurnal cycle of LST has a maximum close to noon time.
Maximum in diurnal cycle of SAT is shifted to ~3p.m. of local solar time.
Standard deviations of LST are very close to those of SAT.

6. Annual Averages of LST, SAT and their Differences
for ALL, CLR, & OVC Skies, ºC.
ALL
CLR
OVC
LST
SAT
Diff
FPK
6.5
5.7
0.8
6.6
5.9
0.7
5.5
4.5
1.0
SXF
8.2
7.9
0.3
7.5
0.0
7.4
PSU
9.7
9.8
-0.1
8.0
8.6
-0.5
10.1
BON
10.8
11.2
-0.4
9.1
10.0
-0.9
11.1
DRA
20.3
18.3
1.9
20.6
18.6
2.0
17.8
16.2
1.6
GWN
16.9
16.7
0.2
15.2
15.1
0.1
16.4
0.5
The Differences of Annual Means <LST-SAT> at ALL, CLR & OVC skies,
and the Differences of LST or SAT at CLR and OVC, ALL and CLR, ALL and OVC skies are relatively small and do not exceed 2°C for most of SURFRAD stations.

7. Estimates of systematic difference <LST- SAT> are statistically significant for ALL, CLR & OVC sky conditions.
Daytime differences are much larger at CLR than at OVC skies.
Nighttime <LST- SAT> differences are close to ZERO at OVC sky, and they are about -2 to -4°C at CLR sky conditions.
At CLR sky , the systematic <LST- SAT> differences are mostly larger than their standard deviations.
At OVC sky, this systematic differences have the same order of value as their standard deviations.

8. Sensitivity of LST and SAT to changes in Cloudiness:
“Bin averaging technique” estimates of mean differences of LST at CLR and OVC skies , <LSTclr-LSTovc> , and the same for SAT, <SATclr-SATovc>.
Daytime LST is increasing with decrease of cloudiness.
Nighttime LST is decreasing with decrease of cloudiness.
LST is almost twice as sensitive to change in cloudiness compared to SAT.
<LSTclr-LSTovc> is almost mirror symmetric to noon time in the diurnal cycle. (Does it mean that thermal inertia of the vegitated “Land Surface” is negligible small?)
<SATclr-SATovc> is almost mirror symmetric to ~3 p.m. time in the diurnal cycle. (Is it shifted because of thermal inertia of surface air layer?)
Values |<LSTclr-LSTovc>|>2°C & |<SATclr-SATovc>|>2°C are statistically significant.

9. Empirical estimates of
LAG-CORRELATION FUNCTIONS of time series of standardized anomalies of LST (BLUE lines) and SAT (RED lines).
F(t) is LST or SAT, t is time.
is time
dependent Expected value of F(t).
F’(t)=F(t)-E[F(t)] is anomaly;
θ(t)=F’(t)/σF (t) is standardized anomaly.
is Lag-Correlation, τ is Lag.
Synoptic scale temporal variations prevail in Lag-Correlation functions of LST and SAT at ALL, CLR, & OVC skies.
Larger-scale, Interseasonal to Interdecadal, temporal variability of LST and SAT are much weaker compared to the synoptic-scale component. There is no statistically significant lag-correlation for lags above two weeks.

10. at CLR, INT, OVC, & ALL Sky Conditions.
Lag-Correlation Functions of Standardized Anomalies of LST (BLUE) and SAT (RED)
at CLR, INT, OVC, & ALL Sky Conditions.
CLR –clear skies.
INT - intermediate cloudiness.
OVC-overcast skies.
ALL - all skies.
ALL* - observated LST and SAT at different sky conditions are normalized and standardized using the time dependent expected value and time dependent standard deviation for relevant sky conditions.

11. The scales are the same at CLR, OVC, ALL, & OTHER sky conditions.
Empirical Estimates of CROSS-LAG-CORRELATION FUNCTIONS of LST and SAT at ALL, CLR, OVC & INT (OTHER) skies.
There is no significant difference between scales of temporal variability (autocorrelation) of LST and SAT.
The scales are the same at CLR, OVC, ALL, & OTHER sky conditions.
Temporal variations of LST and SAT are modulated by the same synoptic-scale weather processes and closely correlated.
0.93
0.92
0.95
0.93
0.93
0.93
0.97
0.94
0.92
0.92
0.96
0.93
0.94
0.93
0.97
0.94
0.90
0.93
0.92
0.90
0.91
0.93
0.95
0.90

12. Standard Deviations of LST & SAT (ºC) and
their Lag=0 Correlation Coefficients
for ALL, CLR, and OVC Skies
0≤ALL<0.9
CLR=0
OVC≥0.9
0<OTHER≤0.9
σLST ºC
σSAT
Lag=0
CORR
FPK
6.6
6.4
0.93
6.7
0.92
5.6
5.7
0.95
6.1
6.3
SXF
5.5
5.4
4.5
4.8
0.97
0.94
PSU
5.3
5.1
4.7
4.9
4.2
0.96
BON
5.0
DRA
4.0
0.90
3.6
3.9
4.3
GWN
0.91
4.1
Lag=0 correlation between LST and SAT is very stable and is the largest at OVC sky conditions.
Standard Deviations of LST and SAT at ALL, CLR, OVC, and OTHER skies are very close between themselves.

13. CONCLUSIONS:
Expected values of LST and SAT display strong diurnal and seasonal variations. They are significantly different at CLR and OVC sky conditions.
LST at CLR sky is warmer than at OVC sky at daytime and it is colder at nighttime. The same is true for SAT.
LST is warmer than SAT at daytime and colder than SAT at nighttime at CLR, OVC and ALL skies.
Scales of Lag-Correlation and Cross-Lag-correlation of LST and SAT are almost the same at CLR, OVC and ALL skies.
Moving mid-latitudinal weather systems are responsible for temporal variability of LST and SAT.
At arbitrary sky conditions, the observed temporal variations of LST and SAT carry the same weather-related signal.