This page contains a variance analysis of potential temperature in the oceans by latitude and depth. Observational data from the ARGO network will be compared against model realizations. The first plot is an image of the variance by latitude and depth. More precisely the percentile rank of the variances for each depth. For each gridbox's time series, the variance of the detrended potential temperature anomalies was calculated and then the longitudinal values were averaged. In order to provide a higher resolution image and also to facilitate comparisons with a selection of SRES A1B models, the calculated values were first intepolated (splined) by depth and then by latitude. The percentile rank was then calculated for each depth level. Percentile rank was used instead of a standard deviation scaling because there is a long tail distribution which gobbles up much of the color spectrum for the image. The sample is from 55N to 55S for all longitudes with a complete time series down to 1000M. Here is the result: This is a distinctive pattern, with the highest variances in the mid-latitude except for the red spot about 50 to 200M under the tropics. The northern mid-latitudes show larger variances than the southern mid-latitudes, which is probably expected with a higher land to ocean ratio.The following line plots show the variances at sample latitudes by depth. As I'm not qualified to interpret these plots I'll try to keep my speculations to a minimum as they could easily be wrong. I believe that the pattern in the tropics is due to the anti-phased signals of solar isolation vs. the upwelling of cooler waters in the "summer". Seasonal variations in the trade winds may be partially responsible for this. It is noteworthy that the ITCZ has an annualized center at about 7ºN. I would caution against interpreting the pattern in the extra-tropics as one resulting primarily from conduction. It could be that seasonal variations in the westerlies result in an in-phase signal. It is interesting that at both 35º North and South there is an increase in variance with depth. I should note that I've performed this analysis on different selections of time series. That is, four different 12 month series with ENSO 3.4 at a high average, a low average, the most positive slope, and the most negative slope. Aside from some subtle differences in the red spot under the tropics, the picture remains basically the same. I believe that this picture is a persistent one. I also wonder if the image plot exhibits Chladni patterns? Given that this plot arises from annual pulses, I wouldn't find it unreasonable to expect interference patterns to emerge. The following are a number of comparisons between ARGO and a sample of SRES A1B AR4 model realizations. The model data is from the first time series file available. Typically these times series run from 2000 to 2009, but there are a couple of exceptions. The ARGO dataset I used had six complete years of coverage from 2005 to 2010. It should also be noted that there are also spatial differences between the models. ARGO and most models have a 1x1 degree lat/lon gridbox. Others have less resolution, in particular GISS Model-ER which has a 4x3 gridbox. The depth levels of the models also varies. It appears to me that the models are having difficulty mimicking oceanic behavior with respect to seasonal temperature variances. I'm not sure if this is important or not. Hopefully this sort of analysis is being done by someone who does this for a living. I'd be surprised if it wasn't. Let's see if there is a mention of variances in AR5. If I understand it correctly, as per Parseval's Theorem, the variance in a signal equates to the power of the signal. I'm guessing that the the above calculations could easily be converted into watts, although interference might be a confounding issue. There are other ways to calculate the average power, Welch's Method being a notable alternative. The following link demonstrates a few alternatives: I have chosen the variance method as it is the easiest to understand, appears to be fairly accurate, and doesn't need any tuning of parameters. IIRC, the phase of the signal varies longitudinally, so I'm also guessing that this would aid in the accuracy of calculating the power via this method. Also note that the standard deviation can be calculated via the formula: stdev=sqrt(var). Using the stdev wouldn't impact the image plots above. Another interesting item is that if the signal is sinusoidal, then the amplitude of the signal can be calculated by the formula: amp=sqrt(2*var). The source code and an intermediate file are available here: |