Results_uwnd_sst_Joni

__**UWIND vs. SST**__

1. Check

2. The GRAND (spacetime) **mean** of my x and y (including units): -1.7987 m/s, 27.5744 C The GRAND (spacetime) **variance** of my x and y (including units): 6.0236 m/s^2, 2.9326 C^2 The GRAND standard deviations are: 2.4543 m/s, 1.7125 C The SPATIAL variance of my TIME MEAN longitude section is: 4.54 m/s^2, 1.8427 C^2 The TEMPORAL variance of my LONGITUDE MEAN time series is: 0.0711 m/s^2, 0.3616 C^2

3. Confirm that the 20-year mean of the anomalies as defined above is 0: Yes. Is the spatial mean of the climate anomalies (as defined above) 0? Is it the same as the time series of the spatial mean of the raw data? Or is it a new object? See graphs below. In decending order: Spatial av. of Uwind, Spacial average of Uwind anomaly, difference in Uwind and Uwind anomaly, Spatial av. of SST, Spacial average of SST anomaly, difference in SST and SST anomaly.

Uwind:



SST:







My CLIMATOLOGICAL ANNUAL CYCLE has variance: 0.1921 (Uwind), 2.3864 (SST) My INTERANNUAL ANOMALY ARRAYS has variance: 6.2039 (Uwind), 0.5461 (SST) Fill out a variance decomposition table for field 1: j) h minus i (anomalies from both space and monthly-climatological means)
 * || Uwind || SST ||
 * a) total variance of x || 6.0236 || 2.9326 ||
 * b) purely spatial (variance of TIME mean at each lon) || 4.54 || 1.8427 ||
 * c) temporal anomalies (x minus its TIME mean at each lon) || 1.48 || 1.0899 ||
 * d) purely temporal (variance of LON mean at each time) || 0.0711 || 0.3616 ||
 * e) spatial anomalies (x minus its LON mean at each time) || 5.95 || 2.571 ||
 * f) remove both means (space-time variability) || 1.41 || 0.7283 ||
 * g) mean seasonal cycle || 0.1921 || 2.3864 ||
 * h) deseasonalized anomalies || 6.2039 || 0.5461 ||
 * i) variance of longitudinal mean of part h) || 4.5605 || 0.7016 ||
 * 1.6389 || -1.555 ||

Discuss your results: (a) = (g) + (h)

(a) = (d) + (e)

(a) = (b) + (c)

(a) = (b) + (d) + (f)

(a) = (c) + (e) - (f)

4. Further Decomposition

variance_by_scalefactor =

6.2039 5.8806 5.5010 5.0968 4.8765 4.6783 6.0673 5.7793 5.4336 5.0478 4.8351 4.6405 5.8322 5.5689 5.2502 4.8967 4.6944 4.5062 5.3204 5.0867 4.8060 4.4931 4.3074 4.1331 4.0974 3.9247 3.7066 3.4949 3.3518 3.2025 2.1879 2.1034 1.9942 1.9031 1.8459 1.7591



5. 1.Based on your data fields (which you've seen pictures of), **make subsets of your 2 variables** x and y and **make a scatter plot of these showing the strongest (positive or negative) correlation of one field with the other you can find**. The subset might simply be all (x,t) values if your fields are very similar (olr, precip), or maybe the 240 time values at one longitude, or 144 longitudinal values in the time mean, or time series at different longitudes if some variability is offset in your two fields (like pressure and wind).

2. Scatter Hist plots at 130lon





Correlation Coefficient:

rho =

1.0000 0.1661 0.1661 0.4868

Standard Dev: std(x) = 2.4543 std(y) = 1.7125

The fraction of variance of uwind is explained by rho^2: 0.2469 The explained variance of sst is std(x)^2*rh o.^2=1.4872

m is the slope of the least-squares fit line rho*std(y)/std(x)=0.1159

How did the variance of y change when this noise was added? var(y)=2.9326, var(noisey)=3.9302 var(x)=6.0238, var(noisex)=6.9700

How did the correlation change?

rho =

1.0000 0.9266 0.9266 1.0000

Variance of noisey subset: 3.9302

6. Lagged Correlation, Covariance