Climate Change and Predictability of the Indian Summer Monsoon B. N. Goswami (goswami@tropmet.res.in) Indian Institute of Tropical Meteorology, Pune
Annual mean Temp. over India 1875-2004 Kothawale, Roopakum ar, 2005, GRL Trend in temp. is similar to global temp. trend. Much faster during past 50 years
1 0.8 TREND=+0.56 0 C/100 YEARS 9 POINT BINOMIAL FILTER 0.6 Annual Mean Temp Anomalies 0.4 0.2 0-0.2-0.4-0.6-0.8 1901 1911 1921 1931 1941 1951 1961 1971 1981 1991 2001 Y E A R S Courtesy : India meteorological Department
All India Rainfall (AIR) Interannual Variability No increasing trend in Monsoon rainfall past 100 yrs.
Questions : Why is the mean Indian Summer Monsoon rainfall not increasing with increasing temperature due to Climate Change? Is there some aspects of the Indian monsoon clearly affected by Climate Change?
Time series of count over CI Low & Moderate events Heavy events (>10cm) Goswami et al. 2006, Science,, 314, 1442 V. Heavy events (>15cm)
Increase in intensity of extreme events Time series of av. Intensity of four largest events in a year
Evidences of responses in the monsoon region to global change Seasonal mean CAPE and CINE averaged over central India (using ERA 40 reanalysis from 1958-2001)
Higher level of saturation of errors in the high frequency events would cascade larger errors to weather scale and could decrease the predictability of monsoon weather Could Global Warming make Indian Monsoon Weather Less Predictable?
Recently, it has been shown that monsoon ISOs (active-break spells) have potential predictability of about 3 weeks (Goswami and Xavier,2003). As the ISOs arise from a feedback between convection, radiation and large scale background flow, change in the background flow (climate change) could influence the potential predictability of the monsoon ISOs How does Global Warming influence Potential Predictability of Monsoon ISOs?
Change in predictability of Indian summer monsoon on weather scales Neena Joseph Mani, E. Suhas and B. N. Goswami Geophys.Res. Letts (2009)
Data and Methodology India Meteorological Department s 104 (1901-2004) years daily gridded rainfall data (1 1 ) based on daily accumulated rainfall from about 1384 stations (Rajeevan et al 2008). The May to October part of the rainfall anomalies are taken as representative of the Indian summer monsoon season. We examined the change in character of predictability of ISM weather over the 104 year period (1901-2004) by estimating the error doubling time for four separate quarters (each of 26 years) Q1(1901-1926), Q2(1927-1952), Q3(1953-1978) 1953-1978),, Q4(1979-2004 1979-2004) giving more emphasis to the last two quarters.
The rainfall time series is representative of the evolution of the trajectories of monsoon atmosphere. Using nonlinear dynamical techniques of embedding, we reconstruct the phase space of evolution of the trajectories. Following Zeng et al, 1991 methodology we estimate the spectrum of Lyapunov exponents (LE) - which measure the average rate of exponential convergence or divergence of nearby trajectories in the phase space. LE s were estimated using the combined rainfall time series in each 3 4 boxes over central India. Invariably two positive Lyapunov exponents were obtained and error doubling time was computed as ln (2) / (Sum of positive Lyapunov exponents)
Used the daily gridded data set prepared by Rajeevan et al. 2008, Geophys. Res. Lett. Between 1901-2004 And calculated the Lyapunov Exponents over different 26 year periods
Steps for computing Lyapunov exponents from the Time series ( Zeng et.al 1991 algorithm ) 1) Phase space Reconstruction. Time series from a dynamical system having an attractor, when embedded in sufficiently large phase space, would preserve its dynamical invariants like Lyapunov exponents.takens (1981). X m ( t) = [ x( t), x( t + τ ),... x( t + ( m 1) τ )] 2) Estimating correlation dimension (Grassberger and Proccacia, 1983). From the set of vectors, we find the number of vector pairs separated by distance less than a small value r. Correlation integral is defined as: C( r) = 1 N 2 { number of vector pairs ( i, j) whose dis tan ce X i X j < r}
C(r) = r D For deterministic dynamical systems, the correlation exponent saturates at some value of embedding dimension. The saturated value of correlation exponent gives the correlation dimension. 3) Lyapunov exponents : Selecting neighbors. After embedding the time series in a k dimensional phase space,, we determine the set of vectors X j which fall within a short distance r from each vector X i X j X i k 1 = l = 0 ( x j + lm x i+ lm ) 1/ 2 r
4) Least square fit and T matrix construction. As the system evolves, the trajectories diverge and small vectors X j X i evolve to vectors X j+n X i+n after m time steps of evolution. X j + n X i+ n = T i ( X j X i ) 5) QR decomposition of T matrix. Each of the T i matrix is decomposed into an orthogonal matrix Q i and an upper triangular matrix with diagonal elements, R i. T Q 1 (0) = Q (1) R (1) T 1+ n Q (1) = Q (2) R (2), T 1+ jn Q ( j) = Q ( j+ 1) R ( j+ 1),
6) Calculation of Lyapunov exponents from the diagonal elements of upper triangular matrix. λ κ 1 1 l = ln ( R j ) ll l = 1,2,... k. τ κ j= 0 Where к is the available number of Ti matrices. 7) Error doubling time Td = ln (2) / (λ1( 1 + λ2) Even though Zeng s algorithm is designed for short noisy time series, we checked the robustness of the estimate by increasing the length of the time series by combining close by grid points. Error doubling time Number of grid points
Error doubling Time for the last two quarters (1953-1978 and 1979-2004) (18N-27N, 73E -85E) Long Time series ----combined time series of all the grid points in the 3 4 boxes. That is, for each quarter we used a time series of length 57408
Lyapunov exponents for the periods 1953-1978 and 1979-2004 First Lyapunov exponent Second lyapunov exponent Most of the contribution to decrease in error doubling time is from the increase in the first lyapunov exponent.
Average error doubling time during the four quarters Average frequency of extreme events 20 18 16 14 12 10 8 6 1901-1926 1927-1952 Quarters 1953-1978 4.5 4.0 3.5 3.0 2.5 2.0 1.5 1.0 1979-2004 Average error doubling time (days) The average error doubling time is almost constant at 3-3.5days during the first three quarters and then decreases to 1.5 days
Change in predictability of Indian summer monsoon on intraseasonal timescales J. M. Neena and B. N. Goswami* Extension of potential predictability of Indian summer monsoon dry and wet spells in recent decades Q. J. R. Meteorol. Soc. 136: 000 000, January 2010 Part A
It has been demonstrated that the potential predictability of monsoon weather has decreased significantly during the past couple of decades as compared to earlier periods. There exists complex interactions among the different scales of variability of the monsoon. The seepage of errors to the synoptic scales from high frequency scales may influence the predictability in the subseasonal scales also The increasing SST trends in the Indian Ocean may also have an effect on the low frequency variability of the monsoon system. Using the same gridded rainfall data we estimate the potential predictability of active and break phases through a fifteen year sliding window in the period 1901-2004, using the empirical method proposed by Goswami and Xavier, 2003.
Goswami and Xavier, 2003 empirical method to estimate the potential predictability of active and break spells from the observed data 10-90 day filtered precipitation (IMD) averaged over central India normalized by its own standard deviation for 15 summers (1 June- 30 Sept.). Red circles peak wet spells (active conditions); green squares peak dry spells (break in monsoon).
2 CMAP Box-I 2 2
Change in potential predictability of rainfall ISO -------through a 15 year sliding window Evolution from active to break Evolution from break to active The predictability of active as well as break phases show a phenomenal increase after the seventies..
Change in potential predictability of 850hPa vorticity ISO -------through a 15 year sliding window Evolution from active to break Evolution from break to active The signature of such predictability changes are also evident in large scale circulation parameters as well.
Changes in Initial error A B B ------green, B A A ------blue There is lesser event to event variability in the magnitude of ISO peak phases. Thus, monsoon ISO s seem to have become increasingly more similar in recent years.
Changes in error growth characteristics A B B -----green, B to A -----blue The changes in error growth is different from that of initial error, implying some other control mechanism.
Variability in evolutions from active to break and from break to active The mode of evolution is another factor determining potential predictability. A slower evolving event is considered to have higher potential predictability than a faster evolving event. Along with the reduced initial errors, the slower rate of evolution from break to active would also favor an increase in potential predictability of the active phases.
An apparent Dichotomy? The changing climate seems to have decreased the predictability of monsoon weather, but Increased the predictability of monsoon ISOs (active-break spells) Is the upscale cascade of errors from small scale to large scales non-uniform? To test this, we carried an extensive study of interactions between different scales using nonlinear triad interactions
Synoptic - ISO scale interactions In the recent decades, the kinetic energy transfer is downscale i.e, from ISO to synoptic scales!!! Thus the synoptic scale errors may not be actually affecting the ISO timescales. Rate of kinetic energy exchange (15 year running mean) between ISO and synoptic scale over 60-110E, 5S-27.5N. Positive values indicate that ISO gains Kinetic energy from the synoptic scale.
Kinetic energy exchange between 30-60 day mode and 10-20 day. Kinetic energy exchange between 10-20 day mode and synoptic. Positive values indicate that the 30-60 day mode gains energy from the 10-20 day mode Negative values indicate that the 10-20 day mode loses energy to the synoptic modes in recent years
Conclusions and Discussions Convective instability is increasing (CAPE) and becoming increasingly easier to realize (decreasing trend in CINE). The increasingly unstable atmosphere favors extreme events, which eventually decrease the error doubling time. The error doubling time during the recent quarter has significantly decreased compared to that during the previous quarters from 2-3 days to 1-2 days. A lower error doubling time means decrease in the potential predictability of monsoon weather. The potential predictability on subseasonal scales on the other hand is showing an increasing trend. The potential predictability of active spells has shown an increase from one week to two weeks while that for break spells increased from two weeks to three weeks.
The main contribution to the increase in predictability of active/break phases comes from the decrease in initial error or the variance among different ISO events. The ISO phases are becoming more similar. The mean evolution from break to active also show an increase after the seventies. An unprecedented increase in IO SSTs has been observed after the mid eighties. The rapid increase in break predictability is also around the same time. The role of SST variability on predictability needs to be explored. Increased phase locking of ISO to the annual cycle has been observed in recent decades. This too points at a certain regularity in the ISO.
The increasing ISO predictability in spite of the decreasing weather predictability was understood from nonlinear kinetic energy exchange studies. It shows that in recent decades, the energy transfer is downscale, ie, from ISO to synoptic scale, whereas, prior to 1980s, ISO was drawing energy from synoptic scale. It was also found that in recent decades the 30-60 day mode is gaining energy while 10-20 day mode is losing energy and their energy exchange pattern has also undergone a phase reversal. The energized 30-60 day mode may have also favored the increase in potential predictability. All these results suggest that the monsoon atmosphere is sensitive to the changes in the large scale environment and its intrinsic properties such as predictability are affected.
Kinetic Energy at 850 hpa of 30-60day mode ----- solid line 10-20day mode ------dashed line Kinetic energy exchange between 30-60 day mode and 10-20 day. Positive values indicate that the 30-60day mode gains energy from the 10-20 day mode The mean KE and KE exchange analysis indicate that in recent decades, ISO is dominated by the more periodic 30-60 day mode which is drawing energy from the more chaotic 10-20 day mode