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This is a nice site about La Nina:

Review the Causes and Consequences of Cold Events: A La Nina Summit

Here's the teleconnections section. Note my emphases.

"George Kiladis (NOAA) opened the session on La Niña teleconnections by first loosely defining the term "teleconnections" as referring to "remote influences". More specifically, in the context of La Niña, it is the influence of SST variations in the tropical Pacific on regional and local climate regimes. He then provided a brief overview of the probable physical causes and effects of teleconnections during El Niño and La Niña (Figures 5, 6).

Physical scientists are researching how events in the tropical Pacific transmit a signal through the atmosphere and ocean to distant places on the globe. Since tropical convection represents the primary "heat engine" for the global circulation, changes in the location of this convection alters the global circulation, which in turn is manifested as climate anomalies. For example, as convection shifts westward from the tropical Pacific into the Indian Ocean during La Niña, the jet stream over the Pacific is weakened, thereby affecting the downstream wave activity (high and low pressure weather systems) moving into North America.

Kiladis provided a list of La Niña and El Niño years in order to identify statistically likely impacts of La Niña around the globe. This was done by the method of "compositing", or averaging the anomalous temperature and precipitation over all La Niña (or El Niño) events, regardless of their magnitude. In this way, the statistical likelihood of a particular teleconnection can be calculated, thereby giving a measure of the probable impact of a La Niña event where the signals are strongest.

Kiladis first showed how islands in the equatorial Pacific Ocean are affected by changes in SSTs. During La Niña, these islands experience drier than normal conditions due to the stabilizing effect of cold SSTs. It was pointed out that these signals might not really be considered teleconnections in sensu strictu, since they are directly influenced by the local SST, rather than remote forcing. He then introduced one measure of the robustness of the observed signals, which is based only on the percentage of time a meteorological station had above or below normal temperature or precipitation, compared to the "expected" sign of the teleconnection signal according to the composites. It was demonstrated that the equatorial Pacific islands had very robust signals, with nearly all La Niña events drier and all El Niño events wetter than normal at these locations.

Several maps were then presented depicting the global temperature and precipitation composites for both La Niña and El Niño events. It was suggested that there was some degree of linearity between El Niño and La Niña impacts over many regions, meaning that cold events in several locations produced the opposite climate anomalies to those occurring during warm events. However, the reliability of the teleconnection signals becomes less as one moves farther away from the tropical Pacific, the "center of action" of ENSO. Thus, even though a given teleconnection might still be defined as "statistically significant", and almost certainly related to the entire population of warm and cold events, the probability of that signal occurring during any one event may not necessarily be very high due to the large amount of climate "noise", or random fluctuations in the atmosphere. This is especially true in the extratropics, where large "internal climate variability" is dominant, as opposed to the tropics, which is to a much larger degree determined by SST. In addition, weak and moderate La Niña events might not be strong enough to generate climate anomalies in distant locations.

Kiladis then discussed what he considered to be among the more robust La Niña teleconnections. These included a tendency for wetter than normal conditions, with a risk for flooding, in southern Africa and the monsoon regions of India, Indonesia, and northern Australia, and drier than normal conditions, sometimes leading to drought, over eastern Africa, the western equatorial Indian Ocean, southern South America, and the southern Plains and southeastern portions of the U.S.. In general, tropical surface temperatures tend to be below normal, with robust signals even as far away from the tropical Pacific as Africa. The most pronounced extratropical temperature signals during La Niña are seen over North America, where there is a pronounced tendency for colder than normal conditions over Alaska, western Canada, and the central Plains of midwestern Canada and the northern United States, and warmer than normal tendencies over the southeastern United States.

Discussion was initiated concerning the tropical temperature signal. Kiladis showed that far-field tropical SST anomalies of the same sign as those in the Pacific developed in the Indian and Atlantic Oceans three to six months following the onset of both warm and cold event conditions. These remote SST anomalies were in phase with the observed tropical surface temperature anomalies, even over the tropical continents, which also lagged the equatorial Pacific SST by the same amount of time. Kiladis pointed out that, if one could explain the far-field SST signal, one could then also account for the tropical temperature signal, since over the ocean surface air temperature follows the SST very closely. He suggested that anomalous surface solar heating because of changes in cloudiness during warm and cold events was a probable factor. Peter Webster (University of Colorado, PAOS) then commented that the monsoon circulation was also a likely player, through observed changes in the intensity of its circulation during warm and cold events and the impact of these changes on the heat budget of the ocean, at least in the Indian sector. It was agreed that this was an important area for future research.

As a cautionary note, Kiladis cited a nearly 20-year-old article by Colin Ramage entitled "Teleconnections and the Siege of Time". Ramage referred to the fact that many of the time series used in teleconnection analyses are of relatively short duration, and that teleconnections identified as being robust during one epoch may fail completely during a later epoch. While some of this might be attributed to the statistical fragility of using short samples, there could also be long-term changes in the climate system itself which could alter the response of the atmosphere to SST anomalies. Thus, forecasts based on established La Niña teleconnections, even those considered highly statistically significant, could fail or even reverse sign in the future due to decadal time scale climate variability. Finally, Kiladis also noted that the linearity, or the reversal in the sign of anomalies in the same location between La Niña and El Niño, exists to some extent on the large spatial scale of his maps, but would likely break down with increased spatial resolution in many regions. This would result from, for example, the effect of mountains or of proximity to the ocean on the local climatic response to global-scale atmospheric circulation changes."

But despite the NOAA's daily graphics showing ALL the oceans cooling, at the end of the February the NOAA claimed the temperature anomaly increased

Watching the animation (and being wholly unable to perform a whole-ocean integration), I noted some very warm areas off South America and South Africa, and other warm areas (smaller) near Japan, and the U.S./Canadian East Coast. Perhaps these regions are why the anomaly increased.