What is El Niño Modoki?
Here is a nice picture from Ashok &amp; Yamagata (2009):

It seems like the Kelvin wave is held back for some reason that I am not familiar with. From the figure below it looks analogous to a standing wave vs a freely propagating wave.  Interestingly, some authors argue that the frequency of these events has increased in recent years for anthropogenic reasons. i.e. climate change.




  a, An El Niño event is produced when the easterly winds weaken; sometimes, in the west, westerlies prevail. This condition is
  categorized by warmer than normal sea surface temperatures (SSTs) in
  the east of the ocean, and is associated with alterations in the
  thermocline and in the atmospheric circulation that make the east
  wetter and the west drier. b, An El Niño Modoki event is an
  anomalous condition of a distinctly different kind. The warmest SSTs
  occur in the central Pacific, flanked by colder waters to the east and
  west, and are associated with distinct patterns of atmospheric
  convection. c, d, The opposite (La Niña) phases of the El Niño
  and El Niño Modoki respectively. Yeh et al.3 argue that the increasing
  frequency of the Modoki condition is due to anthropogenic warming, and
  that these events in the central Pacific will occur more frequently if
  global warming increases.


The most concise definition i found is:


  The peak warming of the sea surface temperature anomaly (SSTA) is confined to the  central equatorial Pacific until boreal winter instead of propagating to the east.


You may already be familiar with this paper, but I found this passage interesting:


  Because of the obvious distinction from the traditional El Niño
  [Rasmusson and Carpenter, 1982] and even from that defined by NOAA in
  2003, we refer to the SSTA pattern observed in 2004, namely, warming
  in the central Pacific (∼NINO4 region) flanked by colder SSTA to the
  west and east, as an El Niño Modoki (pseudo-El Niño) event; this term
  is now popular in Japan and east Asia. (The word Modoki was introduced
  by T. Yamagata during 2004 while explaining a probable cause behind
  the abnormal summer climatic conditions over Japan. It has been often
  used since then by various Japanese Mass Media. “Modoki” is a
  classical Japanese word which means “similar but different.” A news
  article also appeared in The Japan Times on 24 July 2004 under the
  heading “'Mock El Niño' culprit behind heat wave, floods: Professor,”
  which follows: “The heat wave and floods in various parts of Japan are
  being caused by an El Niño-like phenomenon in the central Pacific
  Ocean, a Japanese researcher said Friday. Toshio Yamagata, a professor
  at the University of Tokyo specializing in climate dynamics, said an
  increase in the sea surface temperature has activated convection
  currents and promoted a high-pressure ridge in the Pacific, bringing a
  hot summer to Japan …”


(Ashok et al. 2007)