Subseasonaldecadal linkage in Indian monsoon rainfall

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Subseasonal-decadal linkage in Indian monsoon
rainfall

• Arthur M. Greene, Andrew W. Robertson
• International Research Institute for Climate and
  Society
• Palisades, NY USA
• Sergey Kirshner
• University of Alberta, Canada
• amg_at_iri.columbia.edu

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Synopsis

• Homogeneous hidden Markov model is applied to a
  70-yr record of daily rainfall over a 13-station
  network in central-western India.
• Dianosed states correspond sensibly with
  large-scale circulation composites, a dry state
  associated with monsoon breaks.
• CCA indicates that interannual variability is
  associated with changes in frequency of
  occurrence (FO) of wet and dry states.
• CCA applied to decadally-smoothed data shows very
  similar patterns, leading to
• Conclusion Interdecadal variability also
  mediated by FO of wet and dry states, rather than
  by long-term changes in the character of the
  states themselves.

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Outline

• Data, model structure and assumptions.
• Character of the diagnosed states.
• Relationships to large-scale flow field.
• Subseasonal variability ISO.
• Interannual variability ENSO.
• CCA, extension to the multidecadal scale.
• Summary and conclusions

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Dataset

• Analysis based on a 70-yr record of daily JJAS
  rainfall data (GDCN).
• 13-station network, west-central India.
• Missing Only 11 days out of 8540 (average, no
  station missing more than 29 days).
• Mean seasonal rainfall well-correlated with ISMR
  index (r 0.86), based on 300 stations.
• Good agreement with a recent 1 gridded dataset
  produced by IMD.

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Climatological occurrence probability, mean
intensity
JJAS Climatological rainfall probability (left),
and mean amount on rainy days.
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Subseasonal cycle
Subeasonal cycle of occurrence frequency (left,
days/pentad) and mean intensity (precipitation
amount on rainy days).
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Non-homogeneous hidden Markov model

• Diagnostic tool (no external forcing).
• Patterns of daily rainfall associated with
  hidden states.
• States proceed in time according to a first-order
  Markov process.
• Like a clustering or classification scheme, but
  with added (serial) time dependence.

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HHMM schematic

• Rt is a vector describing rainfall over the
  network at time t, St the corresponding scalar
  sequence of states. The subscript on S takes
  values ranging from 1 to K, where K is the number
  of states in the model. Rainfall on a particular
  day is assumed to depend only on that days state
  (and not, e.g., on the previous days rainfall.
  Day-to-day memory resides only in the states).
  The states are assumed to follow a first-order
  Markov process, with todays S dependent on
  yesterdays, but not (directly) on that of any
  previous day.

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Station rainfall is described as a PDF
Rainfall amount on a particular day, conditional
on that days hidden state (St), depends on the
station (m). On wet days (r gt 0), station
rainfall is modeled as a mixture of two
exponentials (C 2). Parameters of the
exponential distributions (limc) are state- and
station-dependent, time-invariant.
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Optimal number of states depends on application
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Four-state decomposition
Top row shows occurrence probabilities for the
four states, bottom row the corresponding mean
daily intensities (average rainfall on wet days).
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Viterbi sequence of most-likely states

• Estimated state sequence, day by day.
• Climatology (left) shows early and late
  predominance of dry state, JA predominance of
  states 3 and 1.
• Aggregation (above) provides a perspective on
  interannual variability of state FO.
• Note occurrences of the dry state during the peak
  rainy season (JA).

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Monsoon breaks

• Good match found between days on which state 4 is
  diagnosed and historical breaks identified by
  Gadgil and Joseph (2003).
• Almost all (state-4) breaks are preceded by state
  1 no direct 3-4 or 4-3 transitions. Suggests
  dynamical processes at work
• which leads in turn to consideration of ISO.

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Climatological JJAS wind field (1951-1970)
Note Somali jet, centers of ascending motion in
Bay of Bengal, Eastern Arabian Sea.
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State-associated wind composites
Wet (dry) state 3 (4) exhibits anomalous cyclonic
(anticyclonic) flow, ascending (descending)
motion. In state 1, anomalous ascent impinges on
the Himalayan escarpment state 2 shows anomalous
inflow from Bay of Bengal.
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Vorticity composites suggest wavelike ISO
propagation
850-mb relative vorticity composities for
1951-1970. Most-likely state sequences (excluding
self-transitions) 4-2-3-1, 2-3-1, 3-1-3-1.
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ENSO monsoon coupling

• Expressed on the interannual time scale.
• Warm events associated with poor monsoons.
• Correlations between NINO3.4 index and the four
  FO time series are -0.18, -0.16, -0.45 and 0.56,
  respec-tively, the latter two values significant.
  Thus, there are fewer wet days, more dry ones,
  during warm ENSO events.
• FO of the four states not independent method
  that accounts for their joint variability
  required CCA.

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Canonical Correlation Analysis

• Identifies pairs of patterns across two fields,
  such that the temporal correlation between
  members of a pair is maximized.
• Useful, e.g., in the analysis of teleconnections.
• Utilized here (a) A pseudo-field, consisting
  of the four state FO series, (b) the
  teleconnected station rainfall data.
• Can reveal (a) how the state frequencies covary,
  and (b) how the canonical patterns of FO are
  related to rainfall patterns over the station
  network.

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CCA Interannual variability

• Applied here to high-passed series subdecadal
  frequencies filtered out.
• First canonical mode Alternation between wet and
  dry states predomi-nance of the former
  associated with increased rainfall at all
  stations.
• For this pattern, canonical correlation r 0.92,
  significant at 0.001.
• Correlation of first FO canonical variate with
  ISMR, r 0.81.
• First set of patterns explains 48 of variance in
  FO pseudofield, 33 in precipitation field.
• Next two modes (not shown) explain 14, 12 of
  variance, respectively.

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State FO at decadal scales
Here, the time series of state FO have been
low-pass filtered (11-yr moving average),
attenuating interannual variability. States 3 and
4 exhibit opposing long-term trends,
decadal-scale variations.
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CCA Multidecadal variability
Interannual
Interdecadal

• Applied to the smoothed series and rainfall
  records, CCA yields canonical patterns very
  similar to those of the annualized data.
  Amplitudes are smaller, but data is smoothed.
• First three patterns explain 52, 24 and 7 of
  station rainfall variance, respectively.
• Smoothed ISMR is well-correlated with first
  canonical FO variate r 0.85, p 0.015, on 5
  d.o.f.
• Conclusion Decadal variations in monsoon
  rainfall can largely be attributed to integrated
  variations in FO, number of break days.

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A few random notes

• Large-scale circulation patterns characteristic
  of the monsoon seem to have been well-captured
  using data from only a small network of stations.
  Still, the eastern portion of the monsoon zone
  is not sampled may be possible to extract more
  (or more detailed) information using a larger
  network.
• Large-scale nature of the monsoon may imply that
  most networks having adequate spatial sampling
  characteristics are capable of capturing the
  large-scale patterns of variability.
• CCA reveals decadal-scale cross-pattern
  correlations, even though the states were defined
  on daily data. Monsoon breaks would be lost if
  averaging were performed prior to fitting the
  HMM, but have not attemped to fit to
  decadally-smoothed data.
• Goswami and Mohan (2001) identify a linkage
  between intraseasonal and interannual scales, in
  which accumulated break/rainy days determine
  character of the years monsoon Similar to our
  decadal finding.
• Coupling the HMM to a GCM variable (field, PC)
  permits exogenous driving of the transition
  matrix. Such a non-homogeneous model could, in
  principle, be used to simulate station-level
  rainfall under climate change.

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Summary

• Decomposition of 70-yr daily rainfall record over
  a 13-station network, using HHMM.
• Reasonable relationship between diagnosed states
  and the large-scale wind fields.
• Good correspondence between dry state and
  independently identified monsoon breaks.
• CCA reveals linkage between state FO and station
  rainfall patterns.
• This linkage persists across intraseasonal-interde
  cadal scales Break days add up!

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Thank you!