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There certainly other teleconnection patterns that influence western U.S. precipitation, but most of them have little to no connection with sea surface temperatures. For example, we can see a list of teleconnection patterns monitored by CPC, and I believe that only the PNA and TNH have a strong connection to ENSO among that list. That means that most teleconnection patterns that influence U.S. climate are what we consider "internal to the atmosphere" and tend to grow and decay on time scales of a couple of weeks. These sorts of patterns occur in the simulations I described, but they are part of the "weather noise" that gets averaged out among the 30 simulations. 

So, that gets to the main point of the post. There are many patterns that influence U.S. weather, but only a few have a strong connection to slowly varying (and seasonally predictable) sea surface temperatures. Understanding what teleconnection patterns we can and cannot predict on these seasonal time scales remains a big research topic.