EMPIRICAL PREDICTION AND PREDICTABILITY ... - Semantic Scholar

EMPIRICAL PREDICTION AND PREDICTABILITY OF DRY AND WET SPELLS OF THE INDIAN SUMMER MONSOON

A thesis submitted for the award of the degree of

Master of Science (Engineering) in the

Faculty of Engineering by PRINCE K. XAVIER

Centre for Atmospheric and Oceanic Sciences Indian Institute of Science Bangalore 560 012

July 2002

Dedicated to my family...

Contents

Acknowledgments

iii

Abstract

v

List of Tables

vii

List of Figures

viii

1

Introduction

1

1.1

5

Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.1.1

1.2 2

3

4

Empirical prediction of dry and wet spells in monsoon precipitation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

9

Objectives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

12

Data and Preparation

14

2.1

Precipitation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

14

2.2

Reanalysis Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

16

Relation between dry and wet spells and intraseasonal variability

22

3.1

Intraseasonal rainfall variability over India in CMAP . . . . . . . .

22

3.2

A circulation criteria for monsoon ISOs . . . . . . . . . . . . . . . .

24

3.3

Relation between the circulation index and rainfall . . . . . . . . . .

26

Empirical prediction of dry and wet spells of rain

33

4.1

34

Methodology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . i

ii

Contents

4.1.1

5

Stepwise regression . . . . . . . . . . . . . . . . . . . . . . . .

36

4.2

Dependency of the forecasts on the state of initial condition . . . . .

42

4.3

Model skill estimation for selected regions . . . . . . . . . . . . . . .

45

Summary and Conclusions

Bibliography

53 62

Acknowledgments

A journey is easier when you travel together. Interdependence is sometimes more valuable than independence. This thesis is the result of two years of work whereby I have been accompanied and supported by many people. It is a pleasant aspect that I have now the opportunity to express my gratitude for all of them. The first person I would like to thank is my research supervisor Prof. B. N. Goswami. His enthusiasm and integral view on research and his mission for providing ’only high-quality work and not less’, has made a deep impression on me. I owe him lot of gratitude for having shown me this way of research. The guidance, encouragement and motivation provided by him in the course of this work is greatly acknowledged. His enormous knowledge, understanding nature and a calm and collective approach helped me to keep my perspective throughout the crises. I would like to thank Prof. J. Srinivasan for permitting the full use of facilities in this centre. I Thank Prof. Debasis Sengupta, Prof. R. Narayana Iyengar, Prof. G. S. Bhat, Prof. G. Rangarajan for the courses they have offered to us. I express my sincere sense of gratitude to Prof. P. V. Joseph who has always provided a persistent inspiration for my research career. I thank Dr. V. Krishnamurthy (COLA) for a few constructive discussions during his visit to our centre. My thanks are due to the office staff, Mrs. Padma, Mrs. Rama and Mr. Mohan. Retish and Francis were constant sources of encouragement and support for iii

Acknowledgments

iv

me and they made the life here more enjoyable. Thanks to both of them. Thanks to Simi and Anitha not only for carefully going through the thesis manuscript but also for giving a wonderful company along with Ajayan, Anoop, Arindam, Asha, Beena, Hiren, Jaison, Kaustav, Pallav, Raju, Saurav, Semeena, Shivasankar, Sukanya, Vidya, Vinay, Vinoj and Vinu. I am indebted to my friends in CochinAshraf, Bindu, Jossia, Madhusoodanan, Madhu, Manu, Neema, Pappu, Prabha, Ranjit, Rajeev, Sandhya, Sanju, Sankar, Sathiyamoorthy (SAC), Siji, Sindu, Smitha, Sooraj and last but not the least, Sreedevichechi and the list goes on... Finally, my deepest sense of gratitude goes to my parents, without their care, love and understanding, this work would not have been materialised. I am indebted to them forever...

Abstract

An active (break) phase of intraseasonal oscillation (ISO) of the Indian summer monsoon is associated with a wet (dry) spell over the monsoon trough region and a dry (wet) spell over the equatorial Indian Ocean. Prediction of the dry and wet spells (break or active phases) of the Indian summer monsoon two to three weeks in advance is of great importance for food production and water management of the country, but is currently unavailable. While the last two decades have seen considerable advancement in our understanding of the basic characters of the monsoon ISO, the same has not been translated into predictive tools. The objective of this study is to develope a method for predicting the dry and wet spells of the monsoon about two weeks in advance. Prior to getting into the technical aspects of the prediction technique, potential for predictability of these spells is established by demonstrating that the intraseasonal fluctuations in circulation and precipitation of the Indian summer monsoon are integral parts of a low frequency large scale convectively coupled oscillation. We emphasise that the day-to-day fluctuations of rainfall have predictability limited only to 2-3 days as they are governed by synoptic systems. The intraseasonal component may have predictability upto 2-3 weeks as they are part of a large scale low frequency oscillation. Thus, our aim is to predict only the intraseasonal envelope of rainfall variations. For this purpose we use Climate Prediction Center Merged Analysis of Precipitation (CMAP) pentad data for the period 1979-2001. We show that CMAP pentad rainfall represents intraseasonal rainfall variability over the Indian monsoon region (including continental India) v

Abstract

vi

reasonably well. The first four Principal Components (PCs) are used as predictants as the first four Empirical Orthogonal Functions (EOFs) of CMAP contain most of the low frequency large scale component (predictable component) of rainfall variability. In addition to CMAP rainfall we also use daily 850 hPa vorticity and surface pressure from NCEP/NCAR reanalysis for developing the prediction model. The potential for prediction of the monsoon ISO is explored by developing a multiple linear regression model that predicts the first four principal components (PCs) of CMAP. The first four PCs of rainfall, the first four PCs of 850 hPa vorticity and the first two PCs of surface pressure are used as predictors. The model is developed in a step wise manner by adding the PCs of 15-90 day filtered precipitation, vorticity and surface pressure one by one on data over 17 northern hemisphere summers (1 June to 30 September of 1979-1995) and tested over recent 5 summers. The model gives optimum performance with the above mentioned 10 predictors. Skillful predictions of intraseasonal component of rainfall over most of the Indian monsoon region are possible up to a lead time of 15-days. The phase and northward propagation of the precipitation ISO are well predicted by the model. Predictions are found to be dependent on initial conditions. The predictions made from transition states (from dry to wet or from wet to dry) are only marginally skillful while those made from either active (wet) or weak (dry) initial conditions are significantly skillful. Predictions of area averaged rainfall over three regions, the monsoon trough (70◦ -95◦ E, 15◦ -25◦ N), the equatorial central Indian Ocean (70◦ -95◦ E, 5◦ S-5◦ N) and the equatorial eastern Indian Ocean including islands (95◦ -110◦ E, 5◦ S-5◦ N) show that the 15 day predictions starting from an active phase of the monsoon ISO (i.e. wet spell over the monsoon trough) and the 12 day predictions starting from a break phase (i.e. dry spell over the monsoon trough) are significantly skillful in all three regions. The correlation between predictions and observations during the verification period is better than 0.7 (sample size 68). The skill shows potential for application of these predictions in real-time.

List of Tables

4.1

Errors and Skill of model forecasts and persistance . . . . . . . . . . . . . . .

vii

52

List of Figures

1.1

Climatological seasonal mean (June-September) rainfall in the Asian monsoon region. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

1.2

Climatological seasonal mean (June-September) 850 hPa winds (m s−1 ) and relative vorticity (10−6 s−1 ) in the Asian monsoon region. . . . . . . . . . . . . .

1.3

2

4

Coefficient of variation (%) of a) unfiltered daily rainfall anomalies and b) intraseasonally filtered rainfall anomalies for the monsoon seasons (1 June-30 September) of 1979-1988. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

2.1

11

(a) The time series (thin line) and annual cycle (thick line) of 850 hPa relative vorticity at a point (90◦ E, 20◦ N), for the year 2000. (b) The concatenated 850 hPa vorticity anomalies (thin line) and 15-90 day filtered anomalies (thick line) for three summer monsoon season (1997-2000). . . . . . . . . . . . . . . . . . .

2.2

17

(a) The time series (thin line) and annual cycle (thick line) of precipitation at a point (90◦ E, 20◦ N), for the year 1999. (b) The concatenated precipitation anomalies (thin line) and 15-90 day filtered anomalies (thick line) for three summer monsoon season (1997-2000). . . . . . . . . . . . . . . . . . . . . . . . . .

2.3

18

(a) The unfiltered daily 850 hPa vorticity (10−6 s−1 ) averaged over the region(85◦ 95◦ E), for a typical period of three monsoon seasons. (b) The 15-90 day bandpass filtered daily anomalies of 850 hPa vorticity (10−6 ) for three summer monsoon seasons.

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . viii

19

List of Figures

2.4

ix

(a) The unfiltered daily rainfall (mm day−1 ) averaged over the region(85◦ -95◦ E), for the a typical period of three monsoon seasons. (b) The 15-90 day bandpass filtered anomalies for three summer monsoon seasons. . . . . . . . . . . . . .

3.1

20

Time series of anomalies of CMAP interpolated to daily values (thick line) and gridded station precipitation (thin line) averaged over central India (73◦ -85◦ E, 18◦ -25◦ N) during the monsoon season (1June-30September) for 11 years (19791989). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

3.2

23

Scatter plot of 15-90 day bandpass filtered daily anomalies of CMAP and gridded station precipitation averaged over central India (73◦ -85◦ E, 18◦ -25◦ N) during the monsoon season (1June-30September) for 11 years (1979-1989). . . . . .

3.3

24

EOF1 (a) and EOF2 (b) (arbitrary units are multiplied by 100) filtered 850 hPa vorticity during the monsoon period, for 1979-2001. The principal components (PCs) are shown in (c) for a typical period of three years. Thick line is PC1 and thin line is PC2. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

3.4

Correlation between PC1 and PC2 of 850 hPa relative vorticity for a period 19792001 at different lags. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

3.5

25

26

An index of the monsoon intraseasonal variability constructed using Equation 3.1 for a typical period of 3 years. Different phases (marked as 1, 2, 3 and 4) of the normalized index, to be chosen as initial conditions for the forecast model (see Chapter 4). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

3.6

27

The active minus weak phase composite of rainfall (mm day−1 ) from the gridded rain gauge data. Composite of active and weak phases of the monsoon are constructed using the dates when the normalized index is > 1.0 and < -1.0 respectively. Contour interval is 2 mm day−1 . . . . . . . . . . . . . . . . . .

3.7

27

The active minus weak phase composite of CMAP (mm day−1 ). Composite of active and weak phases of the monsoon are constructed using the dates when the normalized index is > 1.0 and < -1.0 respectively. Positive values are shaded and negative are contoured. . . . . . . . . . . . . . . . . . . . . . . . . . .

28

x

List of Figures

3.8

Temporal correlation of filtered CMAP anomalies at each grid point with the ISO index. The spatial pattern over the Indian subcontinent is similar to the classical pattern of rainfall variability from the rain guage data [Singh and Kriplani, 1990; Krishnamurthy and Shukla, 2000]. . . . . . . . . . . . . . . . . . . . . . . . .

3.9

29

Lead-lag correlations of ISO filtered CMAP (positive values shaded and negative values contoured) and 850 hPa zonal (u) and meridional (v) (represented as vectors) with a reference time series of the ISO filtered CMAP averaged over 85◦ -95◦ E, 14◦ -18◦ N for 1 June to 30 September, 1979-2001. Contour interval is 0.1. The thick line in each panel is the approximate position of TCZ. . . . . . .

4.1

30

(a) EOF1 and (b) EOF2 (arbitrary units are multiplied by 100) filtered precipitation during the monsoon period, for 1979-2001 (contour interval is 3). (c) Corresponding PCs plotted for a typical period of 3 years. Thick line is PC1 and thin line is PC2. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

34

. . . . . . . . . . . . . . . . . .

36

4.2

Same as Figure 4.1 but for surface pressure

4.3

Correlations between the predicted and observed values as a function of lead times for a) PC1, b) PC2, c) PC3 and d) PC4. The correlations are computed by generating predictions of each PC every day during the test period, 1996-2001. The thick line in each panel is the correlation between persistence forecast for the respective PC and corresponding observations. . . . . . . . . . . . . . . .

4.4

37

Normalized RMSE (NRMSE) of the predicted values as a function of lead times for a) PC1, b) PC2, c) PC3 and d) PC4. The thick line in each panel is the NRMSE of the persistence forecast for the respective PC. . . . . . . . . . . . . . . . .

4.5

Time-latitude plot of 15 day (a) predictions and (b) corresponding verification anomalies for a period of 5 years averaged over a longitudinal belt 85◦ -95◦ E. . .

4.6

39

The Standard deviation of all 15 day predictions and verifications of rainfall at all grid points. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

4.7

38

40

Temporal correlations between predictions of filtered anomalies and their corresponding verification at each grid point for a) 6 day, b) 9 day, c) 12 day and d) 15 day predictions during the validation period. . . . . . . . . . . . . . . . . .

41

xi

List of Figures

4.8

Mean of all 15 day predictions and their corresponding verifications for phase 1 (a) and phase 2 (b) of the monsoon as initial conditions. The phases are chosen as shown in fig. 3.5. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

4.9

43

Mean of all 15 day predictions and their corresponding verifications for phase 3 (a) and phase 4 (b) of the monsoon as initial conditions. The phases are chosen as shown in fig. 3.5. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

44

4.10 Three regions (marked as I, II and III) selected for comparing the predictions with observations.

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

46

4.11 Comparison of 15 day predictions with phase 2 initial conditions for the three regions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

47

4.12 Comparison of 12 day predictions with phase 4 initial conditions for the three regions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

48

4.13 Scatter plots of predicted and observed rainfall averaged over three regions (Reg.I, II and III). Number of predictions are 68. Comparisons of 15 day predictions from phase 2 initial conditions and the corresponding observations are on the left (a,c and e) while those of 12 day predictions from phase 4 are on the right (b, d and f). Units are mm day−1 .

. . . . . . . . . . . . . . . . . . . .

49

List of Figures

xii

Chapter 1

Introduction

The monsoons which return with remarkable regularity each summer provides rainfall needed for 60% of the global population. Over India, agriculture, power generation and industrial production depend substantially on the monsoon rainfall during the summer (June-September) which contributes more than 75% of the annual rainfall over most parts of the country. A weak or late monsoon can have disasterous consequences on productivity of the crops upon which millions of people rely on for sustenance [Swaminathan, 1987]. The seasonal mean Indian summer monsoon rainfall is characterized by high rainfall in the north eastern India, west of Western Ghats, moderate to heavy rainfall over central India, and low rainfall over north-western parts and southeastern tip of peninsular India (Figure 1.1). The large scale distribution of precipitation during northern summer over the monsoon region is characterized by two regions of maximum precipitation, one over the north Bay of Bengal and the other slightly south of the equator. These are the locations where the winds converge and are the most favorable positions of the Tropical Convergence Zone (TCZ) (Figure 1.2). The seasonal mean condition is not steady but fluctuates within the season between periods of enhanced rainfall activity over the central India and north Bay of Bengal (often referred to as a ‘wet’ spell) and a suppressed rainfall period - a ‘dry’ spell, a typical spell being 7-10 days long. Dry and wet spells are also known as ‘break’ and ‘active’ phases of the monsoon respectively. The dry spells could extend upto three weeks in extreme cases. The duration and 1

Chapter 1. Introduction

2

Figure 1.1: Climatological seasonal mean (June-September) rainfall in the Asian monsoon region.

the number of occurrences of these dry and wet spells eventually determine the seasonal mean rainfall. Major drought years have more frequent and/or longer dry spells. The statistics of the dry and wet spells, therefore, plays an important role in the agrarian economy of the region as the food production of the country is closely related to the seasonal monsoon rainfall [Gadgil, 1996; Webster et al., 1998]. Moreover, prolonged dry spells during critical growth period cause major damage to food production [Abrol and Gadgil, 1999; Lal et al., 1999]. Therefore prediction of dry and wet spells two to three weeks in advance could be of immense help in agricultural planning and water management. The intraseasonal variability between these dry and wet spells have been studied extensively using rain guage data over India [Ramamurthy, 1969; Singh et al., 1992; Hartmann and Michelson, 1989; Krishnamurthy and Shukla, 2000]. The spatial structure of an active spell is such that there is enhanced precipitation over central and western parts of the country while the rainfall activity is suppressed in the east and southeastern peninsula. The pattern typically reverses during a break. The active/break spells of the monsoon are associated with fluctuations of the tropical convergence zone (TCZ) [Yasunari, 1979, 1980, 1981; Sikka


3

and Gadgil, 1980]. The TCZ represents the ascending branch of the Hadley circulation. Intraseasonal Oscillations (ISOs) are, therefore, manifestations of fluctuations of the regional Hadley circulation. These fluctuations were initially observed in station data [Keshavamurthy, 1973; Dakshinamurthy and Keshavamurthy, 1976] and were later shown to be related to coherent fluctuations of the regional Hadley circulation. The transitions between these two situations (ISO) have two major periodicities. One between 10 and 20 days and another between 30 and 60 days. The 30-60 day mode has a northward and eastward propagation over the monsoon region and the 10-20 day mode has a clear westward and weak northward propagation. The seasonal mean (June-September) monsoon precipitation and circulation are resulting from the shift of the seasonal mean position of TCZ to about 25◦ N during the Boreal summer season from a mean position south of equator during Boreal winter. Recent global rainfall data sets [Xie and Arkin, 1996, 1997] show that there are two major zones of precipitation, one over the monsoon trough and head Bay of Bengal. The secondary zone of maximum precipitation is south of equator between equator and 10◦ S over the warm waters of tropical Indian Ocean. These two maxima in precipitation are the favored locations of the TCZ during monsoon season [Sikka and Gadgil, 1980; Goswami, 1994]. The ISOs are fluctuations of TCZ between these two favored locations within the monsoon season. In the intraseasonal time scales, the TCZ form repeatedly over the ocean and moves northward, persists for a period over the monsoon trough before decaying and reestablishing over the ocean. The tendency of the TCZ to persist over the monsoon trough results in larger residence time over the continent leading to slightly larger seasonal mean precipitation over the monsoon trough region compared to that over the ocean. The low frequency variability during the summer monsoon are observed in circulation and cloudiness as well [De et al., 1988; De and Natu, 1994; Sikka and Gadgil, 1980; Yasunari, 1979, 1981; Gadgil and Asha, 1992; Krishnamurti and Ardunay, 1980; Krishnamurti and Subrahmanyam, 1982; Mehta and Krishnamurti, 1988]. The intraseasonal variations in circulation have large scale


4

Figure 1.2: Climatological seasonal mean (June-September) 850 hPa winds (m s−1 ) and relative vorticity (10−6 s−1 ) in the Asian monsoon region.

structure similar to the seasonal mean (Figure 1.2) and enhances (weakens) the mean flow during the active (break) phase. A typical active (break) is also associated with enhanced (suppressed) low level cyclonic vorticity and convection anomalies. ISOs in circulation are associated with repeated northward propagation of the TCZ. This northward propagation is also observed in the rainfall [Hartmann and Michelson, 1989]. The origin of these quasi-periodic oscillations and its northward propagating characteristics have been studied by several authors [Webster, 1983; Goswami and Shukla, 1984; Nanjundiah et al., 1992; Keshavamurthy et al., 1986]. Some insight into the dynamics of initiation of ’breaks’ in the monsoon was provided by Krishnan et al. [2000] based on Rossby wave dynamics. Both observations as well as modeling experiments reveal that rapid northwest propagating Rossby waves are triggered in response to a large strengthening of the convectively stable anomalies over Bay of Bengal 2-3 days prior to commencement of ’break’ over India. Abrupt movement of anomalous Rossby waves from the Bay of Bengal into northwest and central India marks the initiation of a ’break’ monsoon spell. These represent higher frequency wave activity within the ’ac-


5

tive’ and ’weak’ phases of the low frequency ISO. While the transition to an ’active’ or a ’weak’ phase may be initiated by such high frequency synoptic events, the existence of the ISO itself does not depend on the HF synoptic activity. In fact, in a recent study, we use 40 years of data on genesis of low pressure systems (lows and depressions) and show that the large scale circulation associated with the ISO modulate the frequency of occurrence of the synoptic activity [Goswami et al., 2002]. How the spatial pattern and temporal characteristics of the monsoon ISOs influence the seasonal mean circulation and precipitation have also been studied recently [Sperber et al., 2000; Krishnamurthy and Shukla, 2000; Goswami and Ajayamohan, 2001]. It has been further shown [Sengupta et al., 2001] that the Indian Ocean has significant sea surface temperature (SST) fluctuations in the same time scale and that the intraseasonal SST fluctuations evolve coherently with the intraseasonal fluctuations of the surface wind and Outgoing Longwave Radiation (OLR).

1.1

Background

There has been growing interest on the tropical precipitation predictions upto two weeks in advance, especially over India, where the monsoon rainfall has a major impact on its economy. The dynamical extended range weather prediction models such as NMC DERF II and ECMWF global operational model provide useful skill for precipitation forecasts only at lead times less than 5 days [White et al., 1993; Arpe, 1988; Paegle et al., 1992]. Krishnamurti et al. [1992] used a low resolution AGCM and demonstrated that prediction of low frequency modes in the 850 hPa flow field and 500 hPa height over the central China region can be extended beyond the usual numerical weather prediction (NWP) predictability limit of 6-7 days. They showed that if the contamination from high frequency modes is suppressed by an initial filtering, then the prediction of low frequency motion through one cycle (a period of about one month) is possible. But the forecasts were shown to be sensitive to the definition of the initial time-mean state


6

and the sea surface temperature anomaly. Thus extracting the low frequency modes can improve the predictability to a certain limit. The extended range forecast of rainfall was, however not attempted either over China or over Indian region. In this study, our objective is to develop an empirical technique to predict the amplitude and phase of the ISOs about two weeks in advance. Our confidence in empirical techniques to achieve this objective stems from some recent studies [Waliser et al., 1999; Lo and Hendon, 2000; Mo, 2001; Wheeler and Weickmann, 2001] that have shown that skillful forecasts of the Madden-Julian Oscillation (MJO) [Madden and Julian, 1971, 1994], upto three weeks in advance could be made using empirical technique, where the dynamical models have very little skill. The MJO is an eastward propagating, equatorially trapped, wave number 1-3 baroclinic oscillation with a period of 40-50 days and accounts for most of the intraseasonal variability in the tropics during northern winter. Interactions between MJO-related anomalies in convection and the large scale circulation are strongest in the Eastern Hemisphere, over the Indian and western Pacific Oceans, where the oscillation exhibits its greatest variability and typically reaches its maximum amplitude. Such interactions strongly influence the onset and activity of the Asian-Australian monsoon system [Yasunari, 1979, 1980; Hendon and Liebmann, 1990a, b]. Waliser et al. [1999] used a field to field singular value decomposition (SVD) technique to explore the slow evolution of the MJO and predict the OLR using previous and present pentad values of OLR. The model was developed using 3070 day bandpass filtered data over a period 1979-1989 and validated on data from 1990-1996. They could get significant temporal correlations (0.5-0.9) of predictions with observed band passed anomalies at lead times 5-20 days over a significant region of the eastern hemisphere, after which the correlation drops rapidly with lead time. Correlations with the observed unfiltered anomalies were found to be of the order of 0.3-0.5 over a smaller region in the Eastern Hemisphere. The statistical model results were compared with the National Centers for Environmental Prediction’s (NCEP) Dynamical Extended Range Forecasts (DERF)


7

and showed that the statistical model performs considerably better at lead times greater than one week. The prediction of MJO in the OLR and 200 hPa streamfunction was attempted by Lo and Hendon [2000] using a simple multiple linear regression model. The predictors were OLR and 200 hPa streamfunction themselves. The predictants were two leading Principal Components (PC) of OLR and three leading PCs of 200 hPa streamfunction with the assumption that MJO can be well represented by a pair of empirical orthogonal functions (EOFs) of OLR, which represents the eastward propagation of anomalous convection across the Indian and western Pacific Oceans, and three EOFs of streamfunction, which depict the subtropical Rossby gyres and the zonally symmetric component related to the angular momentum fluctuations produced by the MJO. The predictant PCs were advanced in time using a simple multiple linear regression and the future values of anomalies were constructed with the EOFs and predicted PCs. The model was developed on 11 winters and validated with five winters of independent data and also compared to NCEP DERFs. The predictors were added in a stepwise manner. Skillful forecasts of the MJO in OLR and 200 hPa streamfunction were achieved out to about 15 days. The model performed well when the MJO is active at the initial condition but not so well when it is inactive. They also found that the empirical forecasts were better than the DERFs for lead times longer than one week. Mo [2001] uses a combination of Singular Spectrum Analysis (SSA) and Maximum Entropy Method (MEM) to monitor and forecast OLR on the intraseasonal time scale. When the method is applied to the Pacific and Pan-American region using 5 day mean OLR anomalies, the average correlation between the predicted and the observed anomalies is 0.65 at lead times of four pentads (20 days). Wheeler and Weickmann [2001] has developed a technique for near-real-time monitoring and prediction of various modes of coherent synoptic to intraseasonal zonally propagating tropical variability. This involved Fourier filtering of daily updated global OLR data set in a zonal wavenumber-frequency domain. The data is padded with zeros for a period of more than one year at the end point and the filtering is performed. The filtered fields for times before


8

the end point of the data set was used for monitoring MJO and the filtered fields obtained after the endpoint was used as forecast. This technique demonstrates good skill for the MJO and detectable skill for other convectively coupled equatorial modes. The skill of the MJO OLR field is comparable to that of the other techniques mentioned above. The skill shown by the model on the equatorial wave like oscillations in OLR, although considerably less than the MJO, was high enough when compared with NCEP MRF model.

Large volume of research on the summer monsoon ISO during the last two decades has enriched our knowledge about the spatial and temporal characteristics of these oscillations. However, only few attempts have been made to make use of the knowledge base to produce forecasts beyond the capability of the numerical models. The large spatial scale of the monsoon ISO, its quasi-periodic character with period between 30 and 60 days and coupling with the ocean indicate a high potential for useful prediction with 12-15 days lead time [van Den Dool and Saha, 1990]. The experience of empirical prediction of Madden-Julian Oscillation (MJO) indicates that this potential may be achievable. However, the monsoon ISO is different from the MJO in more than one way. Firstly, the summer monsoon ISO’s contain a higher frequency component with period between 10 and 20 days that is absent in the winter time MJO. Secondly, as the monsoon ISO move upto 25◦ N, land-surface processes also contribute to the internal variability of the monsoon ISO. As a result, there is a considerable amount of event to event variability and year to year variability in the frequency and northward propagation characteristics of the monsoon ISO. These processes would set a limit on the predictability of the monsoon ISO. However, the monsoon ISO has an underlying spatial pattern that is invariant from event to event and from year to year [Goswami and Ajayamohan, 2001]. This provides hope that even with all the variability, the monsoon ISO contain an element of quasi-periodicity that may yield a certain degree of predictability of the ISO.


1.1.1

9

Empirical prediction of dry and wet spells in monsoon precipitation

The low frequency character of intraseasonal oscillations in circulation and rainfall provides a potential for useful prediction of dry and wet spells at least two weeks in advance. Results of some studies [Ramasastry et al., 1986; Singh and Kriplani, 1990; Krishnamurti and Ardunay, 1980; Cadet and Daniel, 1988] that attempted to explore this potential in the past have been rather inconclusive. For example, Ramasastry et al. [1986] examined weekly rainfall data over four zonal belts spanning from the southern tip of India to the northern one for five years (1979-1983). They concluded that the year to year variability of the 40-day mode is quite large and it fluctuates from one area to another in the same year. Based on this observation they concluded that potential for long range prediction of rainfall is rather small. Singh and Kriplani [1990] studied interannual variability of the 30-40 day oscillation of rainfall utilizing daily rainfall data of 290 stations over the Indian continent for a period of 80 years. They also concluded that the 30-40 day oscillation has significant interannual variability. They found that pentad rainfall/OLR averaged over certain key regions have lag correlation of 0.3 to 0.4 with pentad rainfall over the central India and west coast upto a lag of 2 pentads. The correlations indicated potential for useful prediction 10 days in advance as the sample size was quite large,. However, no forecasts were made and verified. These studies used rainfall itself as predictor and used rainfall data only over the Indian subcontinent. Some other studies used circulation data to predict phases of rainfall activity. Krishnamurti and Ardunay [1980] used the steady variations of phase of the 10-20 day westward propagating mode in surface pressure over India to forecast the break phase 10 days in advance. They were successful in predicting the increased surface pressure over the central India in over 70% of the cases examined during the period 1943-1972. Cadet and Daniel [1988] used the low-frequency relationship between the surface meteorological parameters over the southern Bay of Bengal along the shipping route from Sri Lanka


10

to Sumatra and the summer monsoon rainfall activity at a number of stations in India to forecast the occurrence of active and inactive periods. They fitted an auto-regressive moving average process (AR model) to the filtered data at a box along the shipping lane for the first 4-month period of the year (January to April) and extrapolated the AR model for the next 30, 40 or 50 days. The four month window was moved by one day and the process was repeated. The phase of monsoon activity at stations were predicted using the average lag with the predicted variable over the shipping lane. During years when 30-50 day mode is well defined, good quality forecasts were obtained while the forecasts failed during years when the phase of the low frequency mode varies rapidly during spring and summer. On the average, peak of active/inactive phase of monsoon could be predicted with an accuracy of about a week. Although they tried to make predictions more than 30 days in advance, the predictions may not be useful due to large errors in timing of the phases. Chen et al. [1992] proposed a modification to Cadet and Daniel [1988] approach to reduce the phase skewness of the filtered data time series. This modification was accomplished by extending the real-data time series from the end data point with real data backtracked from that point posing a mirror image of the filtered data time series at the end date. They used 850 hPa streamfunction to predict the northward propagation or locations of the transient monsoon troughs/ridges and yielded relatively skillful performance in the long range forecast experiment for a few years. There were many drawbacks for the studies mentioned above. None of the above studies attempted quantitative forecast of rain spell. Some of the rainfall prediction studies in the past did not carefully separate the predictable component of the rainfall variability from the unpredictable one. Others used circulation but did not attempt quantitative prediction of rainfall. Daily rainfall variability at a given station may have predictability of only 2-3 days while the large scale low frequency (intraseasonal) envelope of rainfall variability may have predictability of 2-3 weeks. In order to get an idea about potential for prediction, let us examine the amplitude of daily and intraseasonal variability. The variability in the daily rainfall anomalies and


11

Figure 1.3: Coefficient of variation (%) of a) unfiltered daily rainfall anomalies and b) intraseasonally filtered rainfall anomalies for the monsoon seasons (1 June-30 September) of 1979-1988.

that of the intraseasonal components over the the Indian subcontinent can be expressed as the coefficient of variability (COV, defined as the ratio between the standard deviation and the mean expressed in percentage) and are shown in Figure 1.3. This is based on daily rain guage data for 11 monsoon seasons from 365 stations [Singh et al., 1992]. The pattern of variability for both the daily anomalies as well as the intraseasonal components are similar with high value of COV over the places where the mean rainfall itself is small (parts of Rajastan, Gujrat and southeastern parts of the peninsular India) and smaller values over the eastern zone and west coast where the mean rainfall is high. The maximum COV of the daily anomalies can go upto 300 % while that of the intraseasonally filtered anomalies go upto 100 %. The variability in the daily rainfall anomalies are varying from 75-300% compared to the mean over most parts of the country, whereas, the slowly varying intraseasonal component (15-90 day band pass filtered, described in chapter 2) is less variable compared to the mean (about 10-90 % over most parts of the country). The large variations of the daily rainfall anomalies make it less predictable compared to the underlying intraseasonal component.


12

Our objective in this study is not to attempt to predict the daily rainfall but to predict the intraseasonal envelope. Therefore, we shall attempt to predict the temporally filtered rainfall averaged over a relatively large region, e.g. central India. Eventhough we may not make quantitative daily precipitation forecasts, we believe that accurate forecasts of the dry and wet spells will be quite useful for the agricultural planning and water management in a country like India. The reason for this optimism is due to the fact that the daily rainfall is governed by the synoptic activity and that the synoptic activity tends to cluster together in space and time during wet spells [Goswami et al., 2002]. Thus, prediction of the wet (dry) spells would also provide higher (lower) probability of occurrence of high amount of daily rainfall.

1.2

Objectives

The background presented above leads us to the conclusions that the low frequency oscillations with periods 10-20 days and 30-60 days are integral parts of the Indian summer monsoon. The extreme phases and amplitude of the ISOs are coincident with the major active or break spells and the predictions of these phase are extremely important. Recent studies show that empirical models predict the tropical variability such as MJO with reasonable skill in the extended range, where the dynamical models show little skill. The large scale nature and the quasi-periodic slow evolution makes the monsoon ISOs similar to MJO and so there is potential for predicting monsoon ISOs two weeks in advance. This study basically addresses the question of how to exploit this potential. The objectives of the present study are described below.

• The objective is to establish the basis for predictability of ISO of rainfall. For this purpose, the relationship between the monsoon circulation and rainfall will be established and shown that they are integral parts of a large convectively coupled oscillation. With this view in mind, a circulation index that represents the


13

monsoon ISO will be constructed and shown that the circulation index depicts the right phase of monsoon precipitation. This index may be used to classify the phases of monsoon in examining the predictability of monsoon rainfall for different phases of the monsoon. • The main objective of the present study is to make an attempt to predict dry and wet spells of monsoon with 12-15 day lead time using a simple multiple linear regression technique similar to the one used by Lo and Hendon [2000] for MJO prediction. The model will be developed on 17 summer seasons and will be tested on recent 5 years of monsoon. The dependency of the model with different phases of monsoon classified according to the circulation index will also be thoroughly examined. The ultimate goal of the present study is the application of the empirical model on a real-time basis. The data used and preparation of intraseasonal anomalies are described in Chapter 2. The foundation for predictability of ISO of precipitation is laid in Chapter 3, where the ISO of precipitation and ISO of circulation are shown to be integral components of a convectively coupled intraseasonal oscillation. The empirical model for prediction is developed and tested in Chapter 4 and the results are summarized in Chapter 5.

Chapter 2

Data and Preparation

A detailed description of the data used for this study and their preliminary preparation is given in this chapter.

2.1

Precipitation

This study uses Climate Prediction Center Merged Analysis of Precipitation (CMAP) pentad rainfall data [Xie and Arkin, 1997] for the years 1979-1997 and 1999-2001. CMAP is a technique which produces pentad and monthly analyses of global precipitation in which observations from rain guage are merged with precipitation estimates from several satellite-based algorithms (infrared and microwave). The analyses are are on a 2.5◦ ×2.5◦ latitude/longitude grid and extend back to 1979. The input data sources to make these analyses are not constant throughout the period of record. Special Sensor Microwave/Imager (SSM/I) (passive microwave - scattering and emission) data became available in July of 1987; prior to that the only microwave-derived estimates available are from the Microwave Sounding Unit (MSU) algorithm [Spencer, 1993] which is emissionbased. Thus precipitation estimates are available only over oceanic areas. Furthermore, high temporal resolution IR data from geostationary satellites (every 3-hr) became available during 1986; prior to that, estimates from the OLR based Precipitation Index (OPI) technique [Xie and Arkin, 1997] are used based on OLR from polar orbiting satellites. The process of merging is a two-step process. First, 14

Chapter 2. Data and Preparation

15

the random error is reduced by linearly combining the satellite estimates using the maximum likelihood method, in which case the linear combination coefficients are inversely proportional to the square of the local random error of the individual data sources. Over global land areas the random error is defined for each time period and grid location by comparing the data source with the rain guage analysis over the surrounding area. Over oceans, the random error is defined by comparing the data sources with the rain guage observations over the Pacific atolls. Bias is reduced when the data sources are blended in the second step using the blending technique of Reynolds [1988]. Here the data output from step 1 is used to define the ”shape” of the precipitation field and the rain gauge data are used to constrain the amplitude. This results in a merged data that is of improved quality over individual data sources. There are gaps in the data during the summer of 1998 and towards the end of 2001. As the primary objective of our study is to predict intraseasonal rainfall variability over the Indian continent, and as we plan to use CMAP for this purpose, it is natural to ask, ’does CMAP represent intraseasonal rainfall variability over India?’ Therefore, we plan to compare the CMAP data with rain guage observations over India. For this purpose, we use daily gridded rainfall over Indian subcontinent for the period 1979-1989. The daily rainfall data was originally compiled by Singh et al. [1992] at 2.5◦ × 2.5◦ boxes based on daily rainfall at 365 rain guage stations distributed uniformly over the country and was later extended to 1990 and regridded to 1.25◦ × 1.25◦ . Due to unavailability of the gridded rainfall data for the recent years, we restrict ourselves to the period 1979-1989 for comparison with CMAP data. For the purpose of comparison with daily guage rainfall data, CMAP pentad data has been linearly interpolated to daily values. The daily interpolated CMAP is the base data for our forecast studies.


2.2

16

Reanalysis Data

The National Centers for Environmental Prediction/National Center for Atmospheric Research (NCEP/NCAR) 40 year reanalysis data is a research quality data set suitable for weather and short-term climate research. The NCEP/NCAR reanalysis project uses a Global Data Assimilation System (GDAS), along with the observations from 1957 to the present to produce global meteorological fields through dynamically thermodynamically consistent interpolations to support the needs of climate research community [Kalnay et al., 1996; Kistler et al., 2001]. The project began in 1991 and involves the recovery and quality control of historical land surface, ship, rawinsonde, aircraft, pibal, satellite and other data. These data are then assimilated with a GDAS that is kept unchanged over the reanalysis period 1957-1996, to avoid spurious climate jumps or trends. The project uses a frozen state-of-the-art global data assimilation system and a database as complete as possible. The model used here is a T62 spectral model (equivalent to a horizontal resolution of 210 km) with 28 vertical levels. Thus, any output variable in the reanalysis is a blend of observations and model. The fidelity of any variable to reality depends on the accuracy and density of observations as well as on the performance of the analysis scheme itself. The reliability of the parameters have been increased with the addition of delayed observations provided by different countries and organizations. Output variables are classified into four categories; A, B, C and D; depending on the relative influence of the observations and/or model. Variables belong to category ’A’ (e.g. winds, upper-air temperature) if they are strongly influenced by observed data and hence, reliable. The class ’B’ (e.g. SST, air temperature at 2 m, specific humidity at 2 m, relative humidity) indicates that although the variable is directly affected by observational data, the model also has strong influence on it. Variables like cloud, precipitation, latent heat flux, sensible heat flux fall into class ’C’ since there are no observations directly affecting these variables, so they are solely derived from the model. The category ’D’ (e.g. ice concentration, plant resistance, land sea mask) represents


17

Figure 2.1: (a) The time series (thin line) and annual cycle (thick line) of 850 hPa relative vorticity at a point (90◦ E, 20◦ N), for the year 2000. (b) The concatenated 850 hPa vorticity anomalies (thin line) and 15-90 day filtered anomalies (thick line) for three summer monsoon season (1997-2000).

fields that are fixed from climatological values and do not depend on the model. Relative vorticity derived from the zonal (u) and meridional (v) winds at 850 hPa and surface pressure from NCEP/NCAR reanalysis for the period 1979-2001 to match with the precipitation data are used in this study.

The circulation,

precipitation and surface pressure over Indian monsoon region are characterized by a strong annual cycle. Examples of the annual cycle embedded on the 850 hPa vorticity and precipitation shown in Figures 2.1a and 2.2a as thick lines. The annual cycle is defined as the sum of mean, annual and semi-annual harmonics. The annual cycle, which is basically driven by the external conditions, has year to year variations that manifest in the interannual variations of the seasonal mean. Traditionally daily anomalies are constructed by removing the climatolog-


18

Figure 2.2: (a) The time series (thin line) and annual cycle (thick line) of precipitation at a point (90◦ E, 20◦ N), for the year 1999. (b) The concatenated precipitation anomalies (thin line) and 15-90 day filtered anomalies (thick line) for three summer monsoon season (1997-2000).

ical mean of each day from the daily observations. In a particular year, the annual cycle may be significantly different from climatological mean annual cycle. This would introduce a bias in the daily anomalies and thus contaminate the analysis. The annual cycle is computed for every year independently and subtracted from the daily analysis to yield daily anomalies. Daily anomalies for the monsoon period (1 June-30 September) is extracted for each year for the domain 40◦ E-110◦ E, 20◦ S-30◦ N and are concatenated (thin lines in Figures 2.1b and 2.2b). To extract the intraseasonal variability, we need to extract the Fourier amplitudes that describe the intraseasonal variability. In this study, we use a Lanczos filter to accomplish this by modifying the given data sequence with a set of weights, called the filter weight function, to produce a new data sequence. The


19

Figure 2.3: (a) The unfiltered daily 850 hPa vorticity (10−6 s−1 ) averaged over the region(85◦ 95◦ E), for a typical period of three monsoon seasons. (b) The 15-90 day bandpass filtered daily anomalies of 850 hPa vorticity (10−6 ) for three summer monsoon seasons.

filter weight function is related to the variation with frequency of the ratio of the Fourier amplitude of the modified data sequence (response function). In practice, a finite or truncated Fourier series is used, with the result that if a response function with a step change in response were desired, the computed response function would exhibit an oscillation called ’Gibbs phenomenon’. The fewer the number of weights, the larger the oscillation. The principal feature of the Lanczos filter is the use of ‘sigma factors’ that significantly reduce the amplitude of Gibbs oscillation [Duchon, 1979]. A 15-90 day bandpass Lanczos filter with 51 weights is applied at every grid point on the concatenated data. An example of the intraseasonally filtered time series at a location 90◦ E, 20◦ N is shown in Figures 2.1b and 2.2b. The daily anomalies contain high frequency fluctuations of periodicity which have maximum power in less than 10 days. We consider them as noise or the


20

Figure 2.4: (a) The unfiltered daily rainfall (mm day−1 ) averaged over the region(85◦ -95◦ E), for the a typical period of three monsoon seasons. (b) The 15-90 day bandpass filtered anomalies for three summer monsoon seasons.

less predictable component. Since our interest is in the intraseasonal time scale (periodicity ranging from 15-90 days), filtering of the daily anomalies would be a right approach to bring out the important intraseasonal periodicities as well as their propagation characteristics. The daily unfiltered anomalies of 850 hPa relative vorticity and the rainfall for a typical period of three monsoon seasons are shown in Figures 2.3a and 2.4a. The corresponding 15-90 day intraseasonally filtered anomalies are shown in Figures 2.3b and 2.4b. The filtered anomalies removes the high frequency noise effectively and bring out the propagation characteristics of both the 850 hPa vorticity and rainfall. There is a reduction of about 20% in amplitude from unfiltered to filtered anomalies, which is the characteristic of any filter. The difference between filtered and unfiltered anomalies of rainfall are rather small. The rainfall anomalies are interpolated to daily from pentad data, as we have discussed above. Since the original data is a pentad data, it is already devoid of high frequency fluctuations to some extent. This study addresses


21

the predictability of intraseasonal fluctuations which are less noisy compared to the unfiltered daily anomalies which have lesser degree of predictability.

Chapter 3

Relation between dry and wet spells and intraseasonal variability

The primary objective of this section is to show that the dry and wet spells of the Indian summer monsoon are integral parts of the convectively coupled monsoon intraseasonal oscillation (ISO). For this purpose, first we show that CMAP represents the intraseasonal variability of the rainfall over India reasonably well. Then we demonstrate the large scale ISO of circulation and that of CMAP are coupled. To achieve this goal we also introduce a circulation index of the monsoon ISO.

3.1

Intraseasonal rainfall variability over India in CMAP

The strength of CMAP is that it provides large scale features of the precipitation variability on the intraseasonal time scale. This is partially why we plan to use CMAP for our prediction studies. However, for CMAP to be useful for this purpose, it must represent the observed intraseasonal variability of Indian rainfall reasonably well. To test this, we compare the time series of CMAP and 5 day running mean of gridded station rainfall averaged over a box 18◦ -25◦ N, 70◦ -85◦ E from 1 June-30 September every year for a period of 11 years (1979-1989). This area has been chosen based on the dominant empirical orthogonal function (EOF) of daily rainfall (Figure 3 of Krishnamurthy and Shukla [2000]) representing a large region of uniform intraseasonal variability. The long term mean (1979-1989) of the 22

Chapter 3. Relation between dry and wet spells and intraseasonal variability

23

Figure 3.1: Time series of anomalies of CMAP interpolated to daily values (thick line) and gridded station precipitation (thin line) averaged over central India (73◦ -85◦ E, 18◦ -25◦ N) during the monsoon season (1June-30September) for 11 years (1979-1989).

area averaged rainfall from the gridded station data is 7.9 mm day−1 while that of the CMAP is 7.2 mm day−1 . Thus, there is no serious bias in the CMAP. The daily anomalies of station precipitation and CMAP (interpolated to daily values) averaged over the same region as above for the monsoon period (1June-30September) for 11 years (1979-1989) are shown in Figure 3.1. The Low frequency component of rainfall variability over central India are well represented by CMAP, the correlation between the two time series being 0.7. The variance of anomalies (after removing the annual cycle) from CMAP is 7.2 mm2 day−2 while that of the station data is 11.5 mm2 day−1 . Thus, CMAP underestimates observed intraseasonal rainfall variability over India explaining only about 65% of the same and do not capture some of the shortlived intense events. However the phases of the intraseasonal oscillations are captured well by CMAP. This point may be better illustrated if both the time series are filtered to keep only the intraseasonal oscillations. This is seen in Figure 3.2 where a scatter plot of 15-90 day bandpass filtered CMAP and station precipitation averaged over central India are plotted. The correlation coefficient of 0.81 between the two indicates that CMAP is successful in representing the phase of the observed intraseasonal variability and our use of CMAP for the intraseasonal variability studies even over India is justified.


24

Figure 3.2: Scatter plot of 15-90 day bandpass filtered daily anomalies of CMAP and gridded station precipitation averaged over central India (73◦ -85◦ E, 18◦ -25◦ N) during the monsoon season (1June-30September) for 11 years (1979-1989).

3.2

A circulation criteria for monsoon ISOs

Next, we demonstrate that the intraseasonal oscillations of rainfall during the Indian summer monsoon season are closely related to the intraseasonal fluctuations of circulation and convection. We have chosen relative vorticity at 850 hPa to represent intraseasonal variability in circulation as it is known to be a good indicator of monsoon intraseasonal variability [Goswami and Ajayamohan, 2001; Annamalai et al., 1999]. We construct an index of large scale monsoon intraseasonal variability based on relative vorticity at 850 hPa. Towards this end, an Empirical Orthogonal Function (EOF) analysis of 850 hPa 15-90 day bandpass filtered vorticity is carried out using data during the monsoon season for the period 19792001. The EOF analysis is the method of choice for analyzing the variability of a single field. The method finds the spatial patterns of variability, their time variation and gives a measure of the importance of each pattern. The spatial patterns referred to as empirical orthogonal functions (EOFs) are orthogonal spatial patterns that can be thought of as empirically derived basis functions. The low-order EOFs can be interpreted as natural modes of variability in the system. The time coefficients or time evolution referred to as principal components (PCs) are ob-


25

Figure 3.3: EOF1 (a) and EOF2 (b) (arbitrary units are multiplied by 100) filtered 850 hPa vorticity during the monsoon period, for 1979-2001. The principal components (PCs) are shown in (c) for a typical period of three years. Thick line is PC1 and thin line is PC2.

tained by projecting the observed field onto the EOFs. They are orthogonal to each other and represent the variability of the fields efficiently [von Storch and Zwiers, 1999; Venegas, 2001]. Figures 3.3a and 3.3b shows the first and second EOFs, that together explain 15% of the total variance of 850 hPa relative vorticity. EOF1 is a pattern that corresponds to an active monsoon situation. It may be noted that the spatial pattern of EOF2 is similar to that of EOF1 but shifted to the north. Figure 3.3c shows the first two principal components corresponding to the leading EOFs.The length of the PC time series is the same as that of the number of time points in the field, namely 2616 days. To have a bird’s eye view of the relationship between PC1 and PC2, we have plotted them for a typical period of only three monsoon seasons in Figure 3.3c. The PCs are uncorrelated simultaneously, but they bear correlations at different lead/lag times. Figure 3.4 shows the lead-


26

Figure 3.4: Correlation between PC1 and PC2 of 850 hPa relative vorticity for a period 1979-2001 at different lags.

lag correlation between the two leading Principal Components (PC1 and PC2) with a maximum correlation of about 0.5 at lead times of 8-9 days. The leadlag relationship between PC1 and PC2 and the spatial structures of EOF1 and EOF2 together represent the northward propagation characteristics of the monsoon ISOs. Taking this into consideration an index to represent the monsoon intraseasonal variations may be defined as ISO(t) = P C1(t) +

P C2(t + 8) + P C2(t + 9) 2

! (3.1)

The time series of the index normalized by its standard deviation is shown in Figure 3.5. The monsoon activity is said to be normal when the normalized index value is between +1.0 and -1.0 and said to be in an active phase when the index value is > +1.0 and in a weak phase when the index value is < -1.0.

3.3

Relation between the circulation index and rainfall

To examine how this index of monsoon intraseasonal variations of circulation is related to intraseasonal rainfall variations over the monsoon region, we constructed active and weak phase composites of filtered gridded station precipitation anomalies and CMAP anomalies using circulation index to define active and


27

Figure 3.5: An index of the monsoon intraseasonal variability constructed using Equation 3.1 for a typical period of 3 years. Different phases (marked as 1, 2, 3 and 4) of the normalized index, to be chosen as initial conditions for the forecast model (see Chapter 4).

weak days. The difference between active and weak composite based on data for ten years (1980-1989) is shown in Figures 3.6 and 3.7.

The positive values

Figure 3.6: The active minus weak phase composite of rainfall (mm day−1 ) from the gridded rain gauge data. Composite of active and weak phases of the monsoon are constructed using the dates when the normalized index is > 1.0 and < -1.0 respectively. Contour interval is 2 mm day−1 .

over central India and west coast are indications of the enhancement of precipitation over these regions and the suppression of precipitation over the northeastern


28

Figure 3.7: The active minus weak phase composite of CMAP (mm day−1 ). Composite of active and weak phases of the monsoon are constructed using the dates when the normalized index is > 1.0 and < -1.0 respectively. Positive values are shaded and negative are contoured.

parts and southeastern peninsula during an active phase of the monsoon. During a weak phase, the situation typically reverses with decreased rainfall over central India and west of Western Ghats and increased rainfall over northeastern India and southeast peninsula. We note that the spatial distribution of rainfall anomalies associated with the active minus weak conditions from CMAP (Figure 3.7) correspond well with that from station data (Figure 3.6) within the Indian continent. The spatial pattern of active minus weak composites based on the circulation index corresponds well with the known distribution of rainfall anomalies during active and weak phases or wet and dry spells of Indian monsoon [Ramamurthy, 1969; Singh et al., 1992; Krishnamurthy and Shukla, 2000]. The spatial pattern shown in Figure 3.7 essentially represents the large scale pattern of rainfall variability associated with monsoon active/break conditions. The increase (decrease) in precipitation over the central India monsoon trough during an active (break) condition is also associated with large enhancement (decrease) of precipitation over the north Bay of Bengal. Moreover, the large scale intraseasonal precipitation variability is characterized by a meridional dipole, the


29

Figure 3.8: Temporal correlation of filtered CMAP anomalies at each grid point with the ISO index. The spatial pattern over the Indian subcontinent is similar to the classical pattern of rainfall variability from the rain guage data [Singh and Kriplani, 1990; Krishnamurthy and Shukla, 2000].

increase (decrease) in precipitation over the monsoon trough being associated with a decrease (increase) over the eastern equatorial Indian Ocean. The circulation index is, therefore, successful in identifying the wet and dry spells over the continent as well as the the large scale precipitation variability in the monsoon domain. Having established the fidelity of the index in representing the rainfall activity over the continent, we try to bring out the large scale patterns of rainfall variability associated with the dry and wet spells using CMAP. Simultaneous correlation of CMAP at all grid points with the circulation index is shown in Figure 3.8. The number of time points during the period under consideration (excluding the gaps) is 2616 and a correlation value of 0.0643 is significant at 99.9% level. The Figure 3.8 shows significant positive correlations over the continent, and negative correlations over the southeastern tip and northeastern parts. This is consistent with the classical pattern of intraseasonal rainfall variability over the continent observed from the rain guage data [Krishnamurthy and Shukla, 2000]. The positive correlation region has a maximum over the head Bay of Bengal and extends


30

Figure 3.9: Lead-lag correlations of ISO filtered CMAP (positive values shaded and negative values contoured) and 850 hPa zonal (u) and meridional (v) (represented as vectors) with a reference time series of the ISO filtered CMAP averaged over 85◦ -95◦ E, 14◦ -18◦ N for 1 June to 30 September, 1979-2001. Contour interval is 0.1. The thick line in each panel is the approximate position of TCZ.

upto South China Sea. The classical pattern observed over the continent from rain guage data is part of a large dipole like spatial pattern with a large area of negative correlation south of the continent with a negative maximum at few degrees north of the equator. This dipole pattern of correlation suggests that the rainfall fluctuates in phase with the index over most parts of the country, over the


31

head Bay of Bengal extending upto the South China Sea, while it fluctuates out of phase with the index over most parts of the eastern equatorial Indian Ocean. Thus, the intraseasonal oscillations of rainfall and circulation are integral parts of a large scale convectively coupled oscillation. The fact that large scale precipitation associated with active and break phases of the Indian summer monsoon fluctuate coherently with intraseasonal oscillation of circulation (Figures 3.6 and 3.8) indicates that the ISO of precipitation and circulation are coupled. The coupling between the precipitation and circulation of monsoon ISO is further illustrated by the coherence in northward propagation of ISOs in precipitation and circulation. A reference time series of the ISO filtered CMAP averaged over 85◦ -95◦ E, 14◦ 18◦ N for 1 June to 30 September, 1979-2001 is created and lead-lag correlations of ISO filtered CMAP at all grid points with respect to the reference time series are calculated. Spatial pattern of correlation corresponding to 10, 5 and 0 day lag and 5 day lead are shown in Figure 3.9 as shaded contours. Lead-lag correlation of ISO filtered zonal (u) and meridional (v) winds with respect to the reference rainfall time series are also calculated. The correlations of u and v for corresponding lead-lag is shown in Figure 3.9 as vectors. The vectors represent pattern of circulation anomaly associated with precipitation in each case. At any lag/lead, the regions of high positive correlations suggest that the rainfall or winds at these regions are in phase with the reference time series. The elongated band of positive correlation in precipitation is seen to propagate north from around 5◦ N at a lag of about 10 days to the monsoon trough region at lag 0 and moves further north with the advancement of time. Lag 0 is the simultaneous correlation. As the precipitation anomaly move north, the large scale cyclonic circulation (the tropical convergence zone) associated with it also move coherently northward. Both precipitation and circulation evolve coherently throughout the ISO cycle. Thus, the intraseasonal oscillations of rainfall and circulation are integral parts of a large scale convectively coupled oscillation. Having identified CMAP as a good representative of the monsoon intraseasonal rainfall variability, our next attempt is to explore the potential for pre-


32

dictability of these low frequency large scale oscillations in the following chapter.

Chapter 4

Empirical prediction of dry and wet spells of rain

The main objective of this study is to exploit the potential for predictability of the monsoon intraseasonal oscillations which has a large scale structure and slow evolution. Eventhough there are some attempts to predict the monsoon ISOs using different techniques [Ramasastry et al., 1986; Singh and Kriplani, 1990; Krishnamurti and Ardunay, 1980; Cadet and Daniel, 1988], there has been only limited success in predicting the ISOs with lead times of two weeks or more. Due to its large spatial and temporal fluctuations, a quantitative prediction of the evolution of daily rainfall is a formidable task. The results in chapter 3 show that the monsoon intraseasonal rainfall variability is a large scale low frequency variability and hence contain certain predictable elements in it. The main motivation for this study comes from the skillful prediction of Madden-Julian oscillation [Waliser et al., 1999; Lo and Hendon, 2000; Mo, 2001; Wheeler and Weickmann, 2001] two weeks in advance. In this section, we develop a multiple linear regression model to predict the intraseasonal component of rainfall using rainfall, 850 hPa vorticity and surface pressure as predictors over the spatial domain 40◦ -110◦ E, 20◦ S-30◦ N. The model is developed on 17 monsoon seasons (1June-30September) and tested on the recent 5 monsoon seasons. 33

Chapter 4. Empirical prediction of dry and wet spells of rain

34

Figure 4.1: (a) EOF1 and (b) EOF2 (arbitrary units are multiplied by 100) filtered precipitation during the monsoon period, for 1979-2001 (contour interval is 3). (c) Corresponding PCs plotted for a typical period of 3 years. Thick line is PC1 and thin line is PC2.

4.1

Methodology

Due to the similarity in low frequency character of the monsoon ISO and the MJO, we attempt to explore the predictability of the monsoon ISO using a linear regression technique similar to the one used by Lo and Hendon [2000]. An EOF based method would identify the dominant patterns, and the first few EOFs may be sufficient to represent the variability associated with the ISO. Figure 4.1a and 4.1b show the first two EOFs of the 15-90 day bandpass filtered daily rainfall anomalies for the monsoon period (1 June-30 September) from 1979 to 1995. Their corresponding PCs are shown in Figure 4.1c. Similarity between EOF1 and spatial pattern of rainfall during active-weak conditions (Figure 3.8) is noteworthy. However, there are differences between the two patterns as part of the pattern shown in Figure 3.8 may come from higher EOFs. First four EOFs together ex-


35

plain about 40% of the total variability. Here, we identify that the first four EOFs of rainfall represent a significant amount of variability and our effort would be to predict the first four PCs of rainfall using a multiple linear regression model. The philosophy behind choosing the first four PCs for prediction is that these EOFs contain most of the large scale low frequency component of variability. Most of the predictable signal is expected to be associated with these EOFs. The higher EOFs contain smaller scale higher frequency component of the ISO and would be less predicatble. The prediction scheme we employ is of the form ∗

P C (t + τ ) =

N X

βi (τ )P Ci (t)

(4.1)

i=1

where P C ∗ (t + τ ) are the PCs of rainfall predicted at a lead time τ , P Ci (t) are the predictor PCs at the initial time t, N is the number of different predictors used for the prediction and βi (τ ) are the multiple linear regression coefficients at different lags and are determined by least squares estimation. The predictors have to be independent each other to be used in multiple linear regression calculation. PCs, by definition are independent of each other due to their orthogonality. Their simultaneous correlation is zero but they correlate at different lead/lag times. Separate regression is done for each forecast lead time. This technique is essentially similar to the one used by Lo and Hendon [2000] where they used it to predict the slow evolution of MJO in OLR and 200 hPa streamfunction. The 850 hPa vorticity bears a good relationship with convection over the monsoon region which in turn is a measure of precipitation [Goswami and Ajayamohan, 2001]. We have also shown in chapter 3 that intraseasonal oscillations of 850 hPa relative vorticity and rainfall are strongly linked. We identify 850 hPa vorticity to be a possible candidate as predictor for rainfall other than rainfall itself. The first four PCs of 850 hPa vorticity along with the four PCs of CMAP are used in the linear regression model to generate forecasts. Surface pressure is also strongly associated with the active and weak phases of the monsoon. The EOF analysis of the intraseasonally filtered surface pressure anomalies is carried out (Figure 4.2) and the first two


36

Figure 4.2: Same as Figure 4.1 but for surface pressure EOFs together explain 60% of the total varience. This is attributed to the slow evolution of surface pressure compared to other parameters. The first and second EOFs are similar to a typical active monsoon surface pressure pattern with the monsoon trough extending from the heat low over Pakistan to the low pressure area over head Bay of Bengal and comparatively higher pressure south of the equator (Mascarene high). The first two PCs of surface pressure are also used as predictors. Individual predictors are added in a stepwise fashion described below.

4.1.1

Stepwise regression

The multiple linear regression model is employed to predict the first four PCs of rainfall. The model is developed on 17 monsoon seasons (1979-1995) and they are tested on the next 5 years. The regression coefficients are recomputed on ad-

37


Correlation

a) PC1

b) PC2

1

1

0.9

0.9

0.8

0.8

0.7

0.7

0.6

0.6

0.5

0

5

10

15

c) PC3

0.5

0

1

Correlation

0.9

5

d) PC4

10

15

PC1−4 P PC1−4 P + PC1−4 ζ PC1−4 P + PC1−4 ζ + PC1−2 SP persistance

0.8

0.8 0.6

0.7 0.6

0.4

0.5 0.2

0.4 0.3

0 0

5

10 Days

15

0

5

10

15

Days

Figure 4.3: Correlations between the predicted and observed values as a function of lead times for a) PC1, b) PC2, c) PC3 and d) PC4. The correlations are computed by generating predictions of each PC every day during the test period, 1996-2001. The thick line in each panel is the correlation between persistence forecast for the respective PC and corresponding observations.

dition of new predictors and predictions are made upto 15 days of lead times. We add the first 4 PCs of rainfall, first 4 PCs of 850 hPa vorticity,and the first two PCs of surface pressure one by one. 15-day predictions are generated everyday starting from the first day throughout the test period. The correlations between predictions of different PCs of rainfall and observations at different lead times are shown in Figure 4.3 on addition of each predictors. Inclusion of all four PCs of rainfall and four PCs of vorticity as predictors clearly improved correlations between prediction and observation of PC2 and marginally improved prediction of PC1. Eventhough they have not much effect on predictions of PC3 and PC4, we chose the four PCs of rainfall and four PCs of vorticity as optimal combination

38


NRMSE

a) PC1 1

0.9

0.9

0.8

0.8

0.7

0.7

0.6

0.6

0.5

NRMSE

b) PC2

1

0

5

c) PC3

10

15

0.5

0

1

1

0.9

0.8

0.8

0.6

0.7

0.4

0.6

0.2

0.5

0 0

5

10 Days

15

5

d) PC4

10

15

PC1−4 P PC1−4 P + PC1−4 ζ PC1−4 P + PC1−4 ζ + PC1−2 SP persistance

0

5

10

15

Days

Figure 4.4: Normalized RMSE (NRMSE) of the predicted values as a function of lead times for a) PC1, b) PC2, c) PC3 and d) PC4. The thick line in each panel is the NRMSE of the persistence forecast for the respective PC.

for predicting the first four PCs of rainfall. Initial skill (out to about one week) is seen to arise from autocorrelation. Subsequent skill arises from the cross correlation of the predictors which peaks at about 10-12 days lag. The thick lines in Figure 4.3 are the correlations of persistence forecasts for all the four PCs. The comparison shows clearly the superiority of the model forecasts over the persistence forecasts on the extended range. Figure 4.4 gives the Normalized RMS Error (NRMSE) of the predictions with the addition of each predictors, for different lead times. NRMSE of PC1, PC2 and PC3 are well below 0.8 at the 15th day and it is approaching 1 for PC4. Having generated the predicted values of the first four PCs of rainfall, the


39

Figure 4.5: Time-latitude plot of 15 day (a) predictions and (b) corresponding verification anomalies for a period of 5 years averaged over a longitudinal belt 85◦ -95◦ E.

predicted rainfall anomalies (P ) are reconstructed using P (x, y, t + τ ) =

4 X

P Cip (t + τ )Ei (x, y)

(4.2)

i=1

As the first four EOFs of P account for about 40% of the total variance, the predicted anomalies will also account for at most 40% variance of the data. Therefore, both positive and negative predicted anomalies are going to be systematically weaker than the observed intraseasonal anomalies. To compensate for this systematic bias in predictions are multiplied by a constant factor. The propagation characteristics of the rain band over the monsoon region predicted by the model 15 days in advance and their corresponding verifications averaged over the band 85◦ -95◦ E for a typical period of five monsoon seasons are shown in Figure 4.5 as a time-latitude diagram. A notable feature is that the model captures the larger rainfall anomalies and their northward propagation, eventhough the predicted


40

Figure 4.6: The Standard deviation of all 15 day predictions and verifications of rainfall at all grid points.

rainfall is slightly weaker than the observed. The standard deviation, which gives the amplitude of the predictions and corresponding observations are calculated and are shown in Figure 4.6. Model predicts the natural variability in precipitation as it captures the regions of high and low temporal variability in the monsoon system, with a reasonable degree of accuracy. However, there are some differences in the simulations and observations. The important features to be noted are that the amplitude of fluctuations of the predicted anomalies are more compared to the observations over the west coast of India where it reaches a maximum of 7 mm day−1 slightly off the coast. The standard deviation of predicted rainfall anomalies in the Bay of Bengal are about 10-20% weaker than observed. Further, the amplitude of rainfall variations over the central India is somewhat unpredicted. The rain shadow regions where the amplitude of rainfall variability is small also predicted by the model. To identify the regions where the predictions give better correlations with the observations, temporal correlation at each grid point between the predictions and the corresponding verification for lead times 6 days, 9 days, 12 days and 15 days are generated (Figure 4.7). It may be noted that there are 528 predictions and corresponding verifications. Thus the magnitude of correlations greater than 0.11


41

Figure 4.7: Temporal correlations between predictions of filtered anomalies and their corresponding verification at each grid point for a) 6 day, b) 9 day, c) 12 day and d) 15 day predictions during the validation period.

are significant at 99% level. The regions of significant temporal correlations are found to cover most parts of the subcontinent, especially the west coast and the central parts, a large portion of the Bay of Bengal with a maximum value of above 0.6 over the equatorial east Indian Ocean which are the important areas as far as the summer monsoon is concerned. The spatial pattern of significant correlation is maintained upto lead times of 15 days. The conclusion that can be derived from this picture is that eventhough quantitative prediction of rainfall during the dry and wet spells of the monsoon may


42

not be exact, the phases of rainfall fluctuations over most parts of the Indian monsoon region, equatorial Indian ocean and west coast of India in particular, are predictable upto 15 days lead time. The behavior of the model with different initial conditions is discussed in detail in the following section.

4.2

Dependency of the forecasts on the state of initial condition

There is some indication from Figure 4.5 that the skill of the forecasts depends on the initial state of the monsoon ISO. In this section, we examine how the model forecasts depend on the initial state of the monsoon ISO. In the case of MJO forecasts [von Storch and Baumhefner, 1991; Lo and Hendon, 2000] forecasts of MJO were found to be more skillful when the MJO is active in the initial condition. A typical monsoon ISO period could be divided into a number of phases. We make use of the normalized circulation index defined in (1) to identify four major phases of the monsoon ISO as indicated in Figure 3.5. Phase 1: A transition from a subdued phase to an active phase - days when the index is between -1 and +1 on the rising limb of the index. Phase 2: A typical active period - days when the index is greater than +1. Phase 3: A transition from an active to a subdued phase - days when the index is between -1 and +1 on the decreasing limb of the index. Phase 4: A typical subdued phase - days when the index is less than -1. We identify four days in each phase and predictions are made with all initial conditions corresponding to all days in a given phase. The predicted anomalies are reconstructed using (3) and composites (mean) of predictions and corresponding verifications for all four sets of initial conditions and are shown in Figure 4.8 and 4.9. Each of these composite is an average of more than 68 predictions or verifications. The spatial pattern as well as magnitude of the mean of all predictions starting from phase 2 and 4 agree well with those of corresponding verifications (Figure 4.8b and 4.9b). It may be recalled that phase 2 and 4 represent active and


43

Figure 4.8: Mean of all 15 day predictions and their corresponding verifications for phase 1 (a) and phase 2 (b) of the monsoon as initial conditions. The phases are chosen as shown in fig. 3.5.

break conditions respectively over the Indian continent. Thus, 15 day predictions from three initial conditions essentially attempt to predict a break and an active condition respectively. It may be noted that a typical break situation over the continent and a strong rain band in the equatorial Indian Ocean (Figure 4.8b) are well predicted 15 days in advance from initial conditions corresponding to phase 2. Similarly, predictions starting from phase 4 (Figure 4.9b) represents an active condition and are also in good agreement with the observations. An important


44

Figure 4.9: Mean of all 15 day predictions and their corresponding verifications for phase 3 (a) and phase 4 (b) of the monsoon as initial conditions. The phases are chosen as shown in fig. 3.5.

feature to be noted is that the enhanced rainfall over the monsoon trough and the west coast and the rain shadow region over the southeastern peninsula. The negative anomalies over the equatorial Indian Ocean are also predicted with sufficient skill. On the other hand the spatial pattern of the predictions starting from the initial conditions corresponding to phase 1 and phase 3 (Figure 4.8a and 4.9a) do not match very well with corresponding verifications.


4.3

45

Model skill estimation for selected regions

As we mentioned earlier, the 15 day predictions and verifications starting from phase 2 and 4 tend to represent a weak and an active condition respectively. However, the mean rainfall anomalies in the monsoon trough region in predictions as well as the verifications are of the order of 2-3 mm day−1 which are somewhat smaller then the composite anomalies corresponding to peak active or weak phases (3-4 mm day−1 , see Figure 3.7 that shows active-weak phase composite). This is due to the fact that there is considerable event to event variability. To get an idea about this variability and how the model tries to predict this variability, we have compared the predicted and observed anomalies of rainfall averaged over three key regions (Figure 4.10) namely RegionI : The monsoon trough (70◦ -95◦ E, 15◦ -25◦ N) including the north Bay of Bengal. RegionII : The equatorial central Indian Ocean (70◦ -95◦ E, 5◦ S-5◦ N). The equatorial central Indian Ocean is equally important as the monsoon trough as far as the monsoon rainfall variability is concerned due to the dipole like structure of monsoon ISO variability with a positive (negative) maximum over the monsoon trough region and negative (positive) maximum over the central equatorial Indian Ocean during a typical active (break) phase (see Figure 3.8). RegionIII : Parts of the equatorial eastern Indian Ocean (95◦ -110◦ E, 5◦ S-5◦ N), covering Sumatra islands and parts of Malaysia where rainfall varies similar to that in region II. Useful prediction of the dry and wet spells 12-15 days in advance could be useful in these countries as well. Comparison of correlations between predicted and observed anomalies starting from phase 2 and phase 4 initial conditions for all the three regions indicate that the 15 day predictions from phase 2 initial conditions and the 12 day predictions from phase 4 initial conditions are generally better compared with corresponding verifications. The 15 day predictions with phase 2 initial conditions for the three regions are plotted in Figure 4.11. The predictions are in good agreement


46

Figure 4.10: Three regions (marked as I, II and III) selected for comparing the predictions with observations.

with the observations when the 15 day outcome is weak monsoon phase over the region I, while it gives positive anomalies over the equatorial Indian Ocean due to the large meridional dipole like structure (see Figure 3.7). The 12 day predictions with phase 4 initial conditions turn out to positive anomalies over region I and negative anomalies over region II and III most of the time. The comparison of 12 day predictions with phase 4 initial conditions are shown in Figure 4.12. Important feature to be noted from Figure 4.11 and 4.12 are that the model predicts the major active and weak phases with reasonable accuracy, while it does not predict the right phase of the monsoon during near normal conditions. This number is quite small (less than 20%) compared to the right phase predictions. To gain further insight on the quality of the model predictions, the 15 day predictions from phase 2 initial conditions and 12 day predictions from phase 4 initial conditions and their corresponding observations averaged over the three regions are shown as scatter plots in Figure 4.13. The correlations between predictions and verifications are also indicated in the figure. It may be noted that a majority of predictions and observations are in phase (note that most of the dots

47

Chapter 4. Empirical prediction of dry and wet spells of rain Phase 2, 15 day Predictions a) Region I 4 r=0.68

Observation Prediction

2 0 −2 −4 0

10

20

30 40 b) Region II

50

60 r=0.75

5

0

−5 0

10

20

30 40 c) Region III

50

60

6 r=0.70 4 2 0 −2 −4

0

10

20

30

40

50

60

Figure 4.11: Comparison of 15 day predictions with phase 2 initial conditions for the three regions.

fall in first and third quadrants) eventhough there is a certain amount of scatter. A small fraction of the predictions goes out of phase (in second and fourth quadrants). However, most of these happen to be cases where the corresponding verifications are near the transition from a break to active or vice-versa. Thus model proves to be useful in predicting the right phase of the monsoon 12 to 15 days in advance. We have noted (not shown) that the 12 or 15 day prediction over the monsoon trough region starting from transition initial conditions from phase 1 and phase 3 have much less skill (correlation with verification ≈ 0.2-0.3) compared with those made from peak phases. This is due to the fact that the 12 or 15 day evolution from the transition are much more variable.

48

Chapter 4. Empirical prediction of dry and wet spells of rain Phase 4, 12 day Predictions a) Region I 6 r=0.75 4 2 0 −2 0 5

10

20

30 40 b) Region II

50

60 r=0.85

Observation Prediction

0

−5 0

10

20

30 40 c) Region III

50

60

4 r=0.80 2 0 −2 −4 −6

0

10

20

30

40

50

60

Figure 4.12: Comparison of 12 day predictions with phase 4 initial conditions for the three regions.

It is evident from Figure 4.13 that eventhough there is a good correspondence between the observed and predicted anomalies in terms of their phase, there is a good deal of scatter of points even if they are in the same phase. So it is worth estimating a quantitative nature of the errors and the skill of the forecasts over persistence (which is the only available reference forecast). The mean absolute error (M AbsE) and the root mean square error (RM SE) computed for both the model predictions and persistence. The M AbsE and RM SE for both the model (M AbsEm and RM SEm ) and for the persistence (M AbsEp and RM SEp ) and are normalized with the corresponding standard deviation of observations over each region for the entire test period. i.e, region I, II and III have observed standard

49


a) Phase 2, Reg I, 15 Day

b) Phase 4, Reg I, 12 Day

2

8 r=0.66

r=0.73

4

−2

0

Predictions

0

−4 −4

−2

0

2

−4 −4

c) Phase 2, Reg II, 15 Day

0

4

8

d) Phase 4, Reg II, 12 Day 8

8

r=0.75

r=0.88

Predictions

4 4

0

0

−4

−8 −4 −4

0

4

−12 −12

8

−8

−4

0

4

8

f) Phase 4, Reg III, 12 Day

e) Phase 2, Reg III, 15 Day 8

4 r=0.79

Predictions

r=0.64 4 0

0 −4

−4 −4

0 4 Observations

8

−4

0 Observations

4

Figure 4.13: Scatter plots of predicted and observed rainfall averaged over three regions (Reg.I, II and III). Number of predictions are 68. Comparisons of 15 day predictions from phase 2 initial conditions and the corresponding observations are on the left (a,c and e) while those of 12 day predictions from phase 4 are on the right (b, d and f). Units are mm day−1 .

50


deviations of precipitation anomalies 2.09, 3.35 and 2.11 mm day−1 respectively. Table. 4.1 gives the distributions of Absolute error (AbsE) at different ranges and the values of normalized M AbsE (N M AbsE) and RM SE (N RM SE), the correlation coefficients of observations and model predictions for each case and the Brier skill score defined by

! Brier Skill Score (%) =

1−

2 RM SEm RM SEp2

× 100

The frequency distribution of absolute errors (AbsE) falling in different ranges show that most of the errors fall within 3 mm day−1 range which are considered as small errors. Eventhough there are a few large errors in region II, they do not spoil the skill of the predictions since the persistence errors are also considerably large in region II. The N M AbsE as well as N RM SE are found to be less than 1 standard deviation of the observed precipitation anomalies which is considered to be the upper limit of errors for useful prediction. While the N M AbsE and N RM SE of the persistence forecasts cross this limit and most of the errors are above 2 standard deviation. This sets limit on the use of persistence forecasts in the extended range. The skill score values are mostly above 90% except for three cases. The poorest skill is for 12 day predictions with phase 2 initial conditions in region III (82.22%).

The correlation coefficients suggest that there is a good agreement between observations and 15 day predictions in terms of their phase with phase 2 initial conditions except for region I where 15 day predictions are equally skillful with both phase 2 and phase 4 initial conditions. While 12 day predictions with phase 4 initial conditions agree well for all three regions with observations and these show reasonable skill for useful extended range rainfall predictions. All these correlation values are significant at 99.99% level. Thus the model does a good job of predicting major breaks 15 days in advance and active phases 12 days in advance.


51

In this study we have done a hindcast experiment in which the data beyond the initial condition is also considered for filtering. Of course, some modifications are necessary to apply this technique in real-time. We are planning to use a filtering technique similar to the one used by Wheeler and Weickmann [2001]. The anomalies created by removing first three harmonics and the seasonal cycle are subject to removal of mean and linear trend. The end of the dataset is padded with over one year of zeros. This allows the maximum amount of information to be retained at the end of the dataset. This method appears to work well in their forecast scheme.

12

day

38

17

12

1

0

0

0.56

0.68

2.19

2.53

0.70

92.68

AbsE Range

(mm day−1 )

0-1

1.1-2

2.1-3

3.1-4

4.1-5

>5

NMAbsE(M)

NRMSE(M)

NAbsE(P)

NRMSE(P)

Corr. Coeff.

Skill (%)

95.28

0.68

2.67

2.30

0.58

0.47

0

0

0

9

19

40

day

15

92.08

0.75

2.79

2.31

0.79

0.64

0

2

4

10

26

26

day

12

90.17

0.54

2.92

2.39

0.91

0.78

0

0

9

13

23

23

day

15

Phase 4

88.50

0.67

2.49

1.91

0.84

0.73

4

5

12

21

19

7

day

12

93.86

0.75

2.67

2.01

0.66

0.47

4

0

7

10

15

32

day

15

Phase 2

93.63

0.85

3.09

2.52

0.78

0.65

4

2

14

18

10

20

day

12

92.78

0.66

2.96

2.46

0.79

0.71

0

9

11

22

16

10

day

15

Phase 4

[70◦ -95◦ E, 5◦ S-5◦ N]

[70◦ -95◦ E, 15◦ -25◦ N]

Phase 2

Region II

Region I

82.22

0.56

1.90

1.36

0.80

0.68

0

1

4

11

27

25

day

12

86.04

0.70

2.41

1.64

0.89

0.66

1

6

1

7

21

32

day

15

91.15

0.80

2.67

2.20

0.79

0.65

0

0

6

10

29

23

day

12

90.08

0.73

2.65

2.17

0.83

0.66

0

0

8

10

21

29

day

15

Phase 4

[95◦ -110◦ E, 5◦ S-5◦ N]

Region III

Phase 2

Table 4.1: Errors and Skill of model forecasts and persistance


52

Chapter 5

Summary and Conclusions

The daily monsoon rainfall has high temporal and spatial variability. This daily variability is due to synoptic events and thus predictability of daily rainfall is limited by the predictability of synoptic events. Therefore, quantitative prediction of daily rainfall more than 3-5 days in advance may be formidable. However, monsoon precipitation and circulation have low frequency intraseasonal oscillations (ISO) with dominant periods between 30 and 60 days. The amplitude of variability of the daily rainfall anomalies and that of the intraseasonal anomalies are estimated. The variability of the intraseasonal component is less compared to the daily anomalies and hence a potential for predicting the monsoon ISOs, 12-15 days in advance, exists. This potential is explored in this study using a simple regression technique. The active and break phases of the monsoon ISOs are the wet and dry spells of the monsoon. These dry and wet spells have major impact on water management and food production of the country. Therefore, prediction of these spells even 12-15 days in advance would be of immense help. To bring out the intraseasonal oscillations of rainfall, some pre-filtering is required to remove the high frequency component. We use CMAP pentad rainfall linearly interpolated to daily values for this purpose. It is shown that CMAP represents the intraseasonal variability of the rainfall over the Indian continent (as documented by station data) well. In addition, it provides a large scale view of the intraseasonal rainfall variability. An index of monsoon intraseasonal variability in circulation is constructed in terms of relative vorticity at 850 hPa. An active 53

Chapter 5. Summary and Conclusions

54

phase is defined as when the normalized index value is above +1 and a weak monsoon phase is defined when the normalized index value is below -1. The feasibility of using this index in classifying the different phases of the monsoon are also examined. It is shown that the active and weak phases of monsoon can be defined using the circulation index. It is then shown that the intraseasonal variability in circulation and rainfall are strongly coupled. The evolution of intraseasonal oscillation of rainfall (dry and wet spells) is spatially and temporally coherent with that of circulation. As dry and wet spells are two phases of Indian summer monsoon ISO, this analysis establishes the potential predictability of the dry and wet spells and indicates that 850 hPa relative vorticity could be used as a potential predictor. The first four EOFs of CMAP precipitation together explain about 40% of the total variance. We choose the first four PCs of CMAP rainfall as the predictand as these EOFs represent most of the large scale low frequency signal. The higher EOFs are associated with small scale higher frequency component of ISO and hence are likely to be less predictable. The predictors are chosen to be the first four PCs of rain itself together with first four PCs of 850 hPa relative vorticity and two PCs of surface pressure. The regression model is developed over data for a period of 17 years (1979-1995) and tested over a period of 5 years (1996-1997 and 1999-2001). The model is developed stepwise by adding additional predictors one at a time and by comparing the skill of the predictions. It is found that all four PCs of rainfall, four PCs of relative vorticity at 850 hPa and two PCs of surface pressure together give optimum performance of the model. The rainfall anomalies predicted by the empirical model are compared with the intraseasonally filtered rainfall anomalies. The rainfall anomalies reconstructed from the four predicted PCs are generally weaker than the observed by a constant factor almost everywhere in the spatial domain. The bias is corrected empirically. The skill of the correlation are good upto 15 days. The correlation between 528 predictions generated during the test period and corresponding verifications is high (0.5-0.6) over the entire Indian monsoon region. The phase of the northward propagation of the rainfall anoma-

Chapter 5. Summary and Conclusions

55

lies are also generally well predicted. The model captures the extreme events with sufficient skill. Examination of these predictions indicate that predictions initiated from some initial conditions had more skill than others. To investigate the dependence of the predictions on the initial conditions, they were seperated into four phases of the ISO, namely the active phase, weak phase and two transition phases (active to weak and weak to active). This classification is done based on the circulation index defined in chapter 3. It is found that 15 day predictions made from active or break conditions agreed much better with observations than those made from the transition initial conditions. In a detailed comparison of predictions and observations over three key regions over the monsoon domain namely over the monsoon trough region, the equatorial central Indian Ocean and the eastern Indian Ocean alongwith the Sumatra Islands, we have found that 15 day predictions starting from an active phase and 12 day predictions from a break like phase predicts the right phase of the monsoon variability over the entire domain well with significant skill. Our simple technique indicates a significant predictability of the dry and wet spells of the monsoon with 12-15 days lead time. The correlation between the 12-15 day predicted and corresponding observed intraseasonal rainfall range between 0.6 and 0.85. The skill is significant and likely to be useful for practical purposes. In real-time applications of this technique, we have the index value at the initial condition and one can see whether it falls in the active, weak or transitional phase. The philosophy behind examining the skill of the model at different initial condition is that, once we identify the state of the initial condition it also gives the level of reliability of the model forecasts.

The technique used here is simple and could be extended to generate realtime predictions 12-15 days in advance and provide outlook for large scale dry and wet spells. Such forecasts could then be translated to advisories for farmers and water management authorities. Only constraint is the availability of CMAP data and NCEP/NCAR reanalysis on almost real-time.

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