Instability Indices and Heavy Rainfall Forecast in a Maritime Environment

Home , Atmospheric instability, Instability, Lifted index

Ram Kumar DHURMEA

Dissertation Submitted in Partial Fulﬁlment For a Master in Applied Meteorology with Climate and Management to The University of Reading

Department of Meteorology, Faculty of Physical and Mathematical Sciences

September 2015

Supervisor:

Dr. Pete Inness Contents

List of Figures iv

List of Tables viii

Acknowledgements x

List of Acronyms xi

Abstract xiii

1 Introduction 1 1.1 Problem Statement ...... 1 1.2 Study Objectives ...... 4 1.3 Strength and Limitations ...... 5 1.4 Outline of Thesis ...... 6

2 Literature Survey 7 2.1 Topography and Rainfall of Mauritius ...... 7 2.1.1 Location, climate and topography ...... 7 2.1.2 Rainfall in Mauritius ...... 9 2.2 An Overview of Indices ...... 10 2.2.1 Potential instability indices ...... 11 2.2.2 Temperature and humidity indices ...... 12 2.2.3 Advanced derived indices ...... 14 2.2.4 Wind shear indices ...... 16 2.2.5 Conclusions ...... 16

i CONTENTS

3 Local Convection In Mauritius 18 3.1 Introduction ...... 18 3.2 Spatial Distribution of Local Convection in Mauritius ...... 19 3.3 Indices and Local Convection Forecast ...... 23 3.4 Where Indices Fail ...... 24 3.4.1 Stable indices - heavy rainfall event ...... 24 3.4.2 Unstable indices - light rainfall events ...... 26 3.4.3 Unstable indices - nil convection events ...... 27 3.5 Inﬂuence of Upper Level Synoptic Situation ...... 28 3.6 Conclusions ...... 33

4 Data analysis and Index Development 34 4.1 Introduction ...... 34 4.2 Data ...... 35 4.2.1 Rainfall data ...... 35 4.2.2 Radiosonde data ...... 36 4.2.3 Categorisation of events ...... 36 4.2.4 Filtering of convective events ...... 37 4.3 Proposed Indices ...... 37 4.3.1 Modiﬁcation of traditional indices ...... 37 4.3.2 Lapse-rate and moisture based indices ...... 38 4.3.3 Wind shear based indices ...... 39 4.4 Indices Thresholds and Evaluation ...... 40 4.5 Validation of Indices ...... 41

5 Results and Discussions 45 5.1 Exploratory Analysis ...... 45 5.2 Evaluation of Traditional Indices ...... 47 5.3 Evaluation of Modiﬁed Indices ...... 47 5.4 Evaluation of Lapse-Rate and Moisture Based Derived Indices ...... 50 5.5 Evaluation of the Wind Shear Indices ...... 51 5.6 Validation of Indices ...... 54 5.6.1 Performance of individual indices ...... 55

ii CONTENTS

5.6.2 Performance of forecast schemes ...... 57

6 Conclusions and Recommendations for Future Works 63

Bibliography 66

Appendices i

A Correlation Between Rainfall Events and Indices ii A.1 Traditional indices ...... ii A.2 Modiﬁed indices ...... iv A.3 Lapse-rate and moisture indices ...... vi A.4 Wind shear indices ...... viii

B More Examples of Indices Failures x

C Cross Validation Statistics xiii

iii List of Figures

2.1 Location of Mauritius in the South West Indian Ocean (Atlas of Mauritius). . . . 8 2.2 Topography of Mauritius. The Vacoas Synoptic Station, located on the western slope of the Central Plateau at a height of 425 m, is shown by the white arrow (http://mauritiusattractions.com/)...... 8

3.1 MeteoSat-7 visible imagery at 0600 UTC and 1200 UTC showing local convection over different region of Mauritius (http : //www.sat.dundee.ac.uk/geobrowse). 20 3.2 MeteoSat-7 visible imagery at 0600 UTC and 1200 UTC showing intensity of local convection over Mauritius (http : //www.sat.dundee.ac.uk/geobrowse). . 21 3.3 MeteoSat-7 visible imagery at 0600 UTC and 1200 UTC showing convection due to forcing from a frontal system (top) and a meso low (bottom) (http : //www.sat.dundee.ac.uk/geobrowse)...... 22 3.4 Domain of the ALADIN limited area model over the SWIO showing a 12 hour forecast of accumulated precipitation (mm) for a convective event on 30 March 2013. The model analysis is at 30 @ 0000 UTC and is valid for 30 @ 1200 UTC (http : //www.meteo.fr/extranets/)...... 23 3.5 Skew-T plots of soundings at Vacoas synoptic station @ 1200 UTC showing temperature and dew point proﬁle with (a, b) moist mid-troposphere (c, d) dry mid-troposphere. Calculated indices are shown on top right corner (http : //weather.uwyo.edu/upperair/sounding.html)...... 25 3.6 Skew-T plots of soundings at Vacoas synoptic station @1200 UTC showing temperature and dew point proﬁle (a) dry low level (b) moist low level. Calculated indices are shown on top right corner (http : //weather.uwyo.edu/upperair/sounding.html). 26

iv LIST OF FIGURES

3.7 MeteoSat-7 visible imagery t 0600 UTC and 1200 UTC showing evolution of a meso scale system in the vicinity of Mauritius dampening any local convection. 27 3.8 Skew-T plots of soundings at Vacoas synoptic station @1200 UTC showing temperature and dew point proﬁle of a rather dry atmosphere. Calculated indices are shown on top right corner (http : //weather.uwyo.edu/upperair/sounding.html). 28 3.9 500 hPa geopotential height (m) composite mean over the SWIO for the days with stable indices and heavy rainfall (H: high, L: Low) (http : //www.esrl.noaa.gov/). 29 3.10 500 hPa air temperature (K) composite anomaly (1981-2010) over the SWIO for the days with stable indices and heavy rainfall (W: warm pool, C: cold pool). . 30 3.11 500 hPa geopotential height (m) composite mean over the SWIO for the days with unstable indices and light rainfall (H: high, L: Low) (http : //www.esrl.noaa.gov/). 31 3.12 500 hPa air temperature (K) composite anomaly (1981-2010) over the SWIO for the days with unstable indices and light rainfall (W: warm pool, C: cold pool) (http : //www.esrl.noaa.gov/)...... 31 3.13 500 hPa geopotential height (m) composite mean for the days with unstable indices without convection (H: high, L: Low) (http : //www.esrl.noaa.gov/). . . 32 3.14 500 hPa air temperature (K) composite anomaly (1981-2010) over the SWIO for the days with unstable indices without convection (W: warm pool, C: cold pool) (http : //www.esrl.noaa.gov/)...... 32

4.1 Location of the 20 AWS (A) and 20 manned stations (M))used in this study. The site of radiosonde launch (Vacoas synoptic station) is encircle in red...... 35

5.1 Box plots of (a) HgRr60 (b) HgAcRr (c) Drtn and (d) relationship between

HgRr60 and HgAcRr for the 64 rainfall events from 2003 to 2009...... 46

5.2 Scatter plots showing relationship between HgRr60 and (a) CAP E (b) P rpW tr (c) KI (d) DCI. The uneven scattering of the different category of events with CAP E and P rpW tr is quite discernible...... 48

5.3 Scatter plots of HgRr60 and modiﬁed K indices showing only 3 overlapping o o weak events in Ksfc−850 ≥28 C and Ksfc−500 ≥50 C...... 49

5.4 Scatter plot of HgRr60 and mixing ratios calculated between surface and (a) 925 hPa (b) 850 hPa (c) 700 hPa (d) 500 hPa. Note the absence of weak events

beyond certain threshold in rsfc−850 ≥ 16, rsfc−700 ≥ 14 and rsfc−500 ≥ 12. . . . . 51

v LIST OF FIGURES

5.5 Scatter plots of rainfall event categories and conjunction between mixing ratios and lapse rate in different layers showing most weak events conﬁned in

(rΓd)sfc−500 < 0.07...... 52

5.6 Scatter plot showing an ambiguous relationship between HgRr60 and directional and speed shear and shear vector calculated for the layer 850-500 hPa and 700-500 hPa...... 53 5.7 Hourly rainfall intensities of 48 selected cross validation events...... 54 5.8 Schematic using traditional indices to forecast rainfall of ≥ 20 mmh−1 over Mauritius. A better CSI and lower F AR is achieved by applying the Θ ≥ 299.5. 58 5.9 Schemes with less complexity and better score using traditional indices. . . . . 58 5.10 Schemes to forecast rainfall of ≥ 20 mmh−1 using modiﬁed indices ...... 59 5.11 Schemes showing combined traditional indices, modiﬁed indices and 500 hPa variables scores in forecasting rainfall of ≥ 20 mmh−1 over Mauritius...... 59

A.1 Scatter plots HgRr60 against traditional indices. The uneven scattering of the

different category of events with TTI, Ko, PII, CII and LCLpp is quite discernible ...... iii

A.2 Scatter plots of HgRr60 against modiﬁed indices. Most of the plots show uneven scattering of the different category of events with the indices ...... v

A.3 Scatter plots of HgRr60 against lapse-rate and moisture based indices. Most of the plots show uneven scattering of the different category of events with the indices ...... vii

A.4 Scatter plot showing an ambiguous relationship between HgRr60 and directional shear, speed shear and shear vector calculated for the layer 850-500 hPa and 500-250...... ix

B.1 500 hPa geopotential height (m) composite mean over the SWIO for the days with stable indices and heavy rainfall. The island is under the inﬂuence of a trough on 27 Feb 2004 and 19 Feb 2005 and high geopotential height on 26 and 27 Feb 2005(http : //www.esrl.noaa.gov/)...... x B.2 Skew-T plots of soundings at Vacoas synoptic station @1200 UTC showing unstable proﬁle with (a, b) moist mid-troposphere (c, d) dry mid-troposphere (http : //weather.uwyo.edu/upperair/sounding.html)...... xi

vi LIST OF FIGURES

B.3 500 hPa geopotential height (m) composite mean over the SWIO for the days with unstable indices and light rainfall (http : //www.esrl.noaa.gov/)...... xii B.4 Skew-T plots of soundings at Vacoas synoptic station @1200 UTC showing unstable proﬁle with (a, b) moist mid-troposphere (c, d) dry mid-troposphere (http : //weather.uwyo.edu/upperair/sounding.html)...... xii

vii List of Tables

4.1 Contingency table of a dichotomous veriﬁcation scheme ...... 42

5.1 Percentiles of HgRr60, HgAcRr and Drtn for the period November to April 2003-2009...... 45 5.2 Comparison of the correlations of traditional and modiﬁed K and TT indices

with HgRr60, HgAcRr and Drtn...... 48

5.3 Comparison of the correlations of r and modiﬁed r with HgRr60, HgAcRr and Drtn...... 50

5.4 Correlation of HgRr60, HgAcRr and Drtn with directional shear, speed shear and shear vector for different layers...... 52 5.5 Scores of selected traditional indices in forecasting rainfall intensity≥ 20mmh−1. 56 5.6 Scores of selected modiﬁed indices and lapse rate-moisture indices in forecasting rainfall intensity of ≥ 20 mmh−1...... 56 5.7 Scores of individual 500 hPa variables in forecasting rainfall intensity of ≥20 mmh−1...... 60

A.1 Correlation between traditional indices and rainfall for all the events...... ii A.2 Correlation between modiﬁed indices and rainfall for all events ...... iv A.3 Correlation between rainfall and lapse rate and moisture based derived indices for all events ...... vi A.4 Correlation between rainfall and directional shear for all events...... viii A.5 Correlation between rainfall and speed shear for all events...... viii A.6 Correlation between rainfall and shear vector for all events...... viii

C.1 Scores for different threshold associated with different traditional indices. . . . xiii

viii LIST OF TABLES

C.2 Scores for different threshold associated with different modiﬁed and lapse rate- moisture based indices...... xiv

ix LIST OF TABLES

Acknowledgements

This was a much needed study which has eventually materialise. But this achievement would have been harder without full support from my supervisor, Dr. Pete Inness, who accepted to guide me through this endeavour.

It is a pleasure to acknowledge the support of Mauritius Meteorological Service, particularly the Director, in providing the necessary data for this project. As such, the credit also goes to all those colleagues who have spared no effort in collecting and archiving the data.

I am also thankful to Mrs Jane Lewis for her constant help in the Python Programming and my friend Philip Craig for helping me with the spell checks.

Last but not the least, I will remain ever thankful to my wife my daughters Kirti and Eesha for humbly accepting my absence and endure the hardship for over a year .

x LIST OF TABLES

List Of Acronyms

CAP E : Convective Available Potential Energy.

CSI : Critical Success Index

CT : Cross Total.

DCI : Deep Convective Index.

Drtn : Duration.

EL : Equilibrium Level.

EPS : Equivalent Percentage Success.

F AR : False Alarm Ratio.

F low500 : ﬂow curvature at 500 hPa.

Γ : Lapse rate

HgRr60 : Highest hourly rainfall intensity.

HgRr30 : Highest 30 minutes rainfall intensity.

HgRr6 : Highest 6 minutes rainfall intensity.

HgAcRr : Highest accumulated rainfall amount.

HR : Hit Rate.

KI : K-Index.

LI : Lifted Index.

LCL : Lifting Condensation Level.

LCLtt : Lifting Condensation Level Temperature.

LCLpp : Lifting Condensation Level Temperature.

LF C : Level of Free Convection.

PC : Percent Correct.

xi LIST OF TABLES

P rpW tr : Precipitable Water. r Mean mixing ratio. r Mixing ratio.

ShwI : Showalter Index.

SW EAT : Severe Weather Threat.

T : Temperature

Θ : Mean Potential Temperature.

VT : Vertical Total.

P rpW tr : Precipitable Water.

Z500 : 500 hPa geopotential height.

AWS : Automatic weather stations.

MRU : Mauritius.

SWIO : South West Indian Ocean.

ITCZ : Inter Tropical Convergence Zone.

xii ABSTRACT

Forecasting heavy rainfall associated with in-situ convective cloud development over small island states is a challenge in operational forecasting as not all numerical models are able to resolve convection at such small scales. Forecasting of such phenomena is mainly based on prevailing local conditions and the use of a plethora of thermodynamic indices derived from the local sounding. This study is an effort to assess the suitability of the different available indices, hereafter referred as traditional indices, to forecast heavy rainfall from local convection, commonly known as pure sea breeze, over Mauritius. An attempt is also made to improve the forecast through modiﬁcations of the traditional indices, to include lower boundary layer temperature and moisture parameters. Suitable thresholds of all these indices are also determined via scatter plots of the events which are categorised into weak, moderate and severe based on hourly rainfall intensity.

It is found that the most commonly used Convective Available Potential Energy (CAP E) and the Total Total Index (TTI) is not the best indicators of heavy rainfall for Mauritius and can even be misleading in some instances. The Precipitable Water (P rpW tr) is found to be more related to the impending amount of rainfall than the intensity and better performance is achieved with the mean mixing ratio (r). Analysis also shows that the Deep Convective Index (DCI) is a better indicator of moderate to heavy rainfall than is CAP E and TTI. Some of the modified indices such as K-index and mixing ratio (r) give better correlation with the hourly rainfall intensity compared to their traditional counterparts. The cross validation is based on a dichotomous verification scheme and the Hit Rate (HR), False Alarm Ratio (F AR), Criti- cal Success Index (CSI) and the Yule’s Index (YI) are used as verification statistics/score. No better scores are achieved with the use of only one index. and any attempt to improve a particular score leads to worsening of others. As such the final choice of index is not based on only one score but rather a conjunction of scores. Better results are achieved through combinations of indices and decision trees/schemes are devised for that purpose. However, adding too much complexity to the decision tree, through blending of lots of indices, leads to a decline in the verification score. Modified indices lead to better scores and further improvements are achieved by its combination with traditional indices. Good performances from DCI and KI make them potential individual indices for use in Mauritius and the forecast is further improved through the use of the decision schemes.

xiii Chapter 1

Introduction

1.1 Problem Statement

Forecasting and issuing warnings of severe weather is the concern of every operational meteorologist as disaster managers rely heavily on these forecasts to save lives and properties. With the advent of technology and development of novel numerical weather prediction (NWP) systems, forecasting severe weather has became relatively less tedious. But still, as new tools have emerged, the influence of global warming on behaviour of severe weather has made the task of operational meteorologists slightly more difficult. Models are presently dealing well with synoptic scale convection and nowadays with powerful parameterisation techniques meso-scale convection are also resolved. The plethora of basic and derived meteorological variables and products available from models has enabled the construction of a 3 dimensional picture of the atmosphere at various point in time and project its future behaviour within a certain degree of accuracy. Nevertheless, these models still have some limitations as they are not able to provide good diagnosis of convection in regions where there are dearths of observations and also in situations where the physics are still not well understood, particularly in the tropics (Birch et al., 2014). A model may also fail because of its resolution. Usually, with other conditions satisfied, the higher the resolution the better the output. For instance, many small island states, like Mauritius, are at sub-grid scale and convective activity over these islands is hardly resolved even by regional models. In the absence of high resolution limited area models, resolving small or micro scale convective processes will remain a challenge. Even if a high resolution limited area models may resolve local convective cloud developments over small islands, it may still not give a estimate of the severity of that convection.

1 1.1 Problem Statement

As such in-situ synoptic and upper air observations can be important tools for short term forecasts, at least for the next 12-24 hours for such islands. Among these observations, the upper air observations obtained from radiosondes have stood as a powerful tool since its invention. Following the pioneering work of Showalter (1953), several indices have since been developed using data from radiosondes and these indices are still used to diagnose the likelihood of severe weather namely heavy rainfall, thunderstorms and tornadoes (Showal- ter, 1953; Galway, 1956; Jefferson, 1963a,b; Andersson et al., 1989). These indices have been verified for both large-scale weather systems and local convective activity. Even if all the instability indices are precursors of severe or non-convective showers and thunderstorms, their reliability is still a function of geographical locations (Sanchez et al., 2009) and seasons (Hak- lander and Delden, 2003) or both (Marinaki et al., 2006) and synoptic situations (Doswell et al., 1981). In his work on the evaluation of sounding parameters in different latitudes (region spread over Spain, France and Argentina), Sanchez et al. (2009) found that there are no single indices that give a very good performance in all the regions. The only common ingredients they found to begin convection were the atmospheric instability and low level moist layers but the sounding data on its own cannot detect the third ingredient which is the triggering mechanism. In their study in Netherland, Haklander and Delden (2003) found that threshold of the ”K” index for detecting thunderstorms is lower in summer than in winter. In a study over Greece, Marinaki et al. (2006) found that for the same summer months,the optimum thresholds of the ”Jefferson” index were not the same for the Thessaly region and the Crete Islands. Furthermore, for other months such as April and May, the ”K” index was found to be more satisfactory for the Crete Islands. Doswell et al. (1981) and Maddox and Doswell (1982) stipulated that it is not necessary that all indices is suitable for one and the same region because thunderstorms are also influenced by the prevailing synoptic situations, and it important for operational meteorologists to be aware of such limitations. Even for a particular location it is not uncommon to find one index outperforming another one making the choice of an appropriate index a challenge in itself (Monteverdi et al., 2003; Jacovides and Yonetani, 1990). For Central and Northern California region, Monteverdi et al. (2003) found that Convective Available Potential Energy (CAP E) was of little value in discriminating between tornadic and non-tornadic thunderstorm while the 0-1 km shear in the wind was able to make such discrimination. For the Greater Cyprus area Jacovides and Yonetani (1990) found that the ”Humidity” and ”K” indices were unsuccessful in forecasting air mass thunderstorms and their newly derived index, called the Yonetani Index, performed better. Even more intriguing, different indices can be tied to particular aspect of convection. For

2 1.1 Problem Statement example, in Spain Lopez et al. (2001) found CAP E to be useful in distinguishing between thunderstorm with and without hail. In a study in Netherland, Groenemeijer and Delden (2006) found CAP E not to be very useful in discriminating between an environment that is conducive for tornadoes from that of thunderstorm only but found high CAP E values to be associated with large hails. Similarly for Switzerland, Huntrieser et al. (1996) found the ShwI to be better indicator of a thunderstorm day while a modiﬁed version of CAP E was the best in discriminating between the occurrence of isolated or widespread thunderstorm.

Another good approach is then to use a blend of sounding data with NWP products such as vertical velocity, relative humidity at mid to upper levels, divergence field and wind shear to mention a few (Colquhoun, 1987). For example, using a decision tree Colquhoun (1987) determined some threshold minimum for thunderstorm formation and he found that a vertical velocity larger than 0.5 m s−1 at 800 hPa and a relative humidity of 75% are favourable thresholds for thunderstorm formation. Other authors have developed systematic methods and checklists that could aid in diagnosing conditions conducive for severe convection (Gordon and Albert, 2000; Miller, 1972). The dynamic influence of the atmosphere on the threshold of the indices has been investigated by Hales (1996) and he found that if this influence is strong a lifted index (LI) as low as 0 oC is sufficient to produce severe weather while if the upper air transport is very weak the LI must be as high as -8 oC . Other scientists are still developing new indices using the novel approaching of retrieving information from the atmosphere. For example, Walker et al. (2008) used selected spectral bands from remotely sensed radiomet- ric data to construct temperature profiles of the atmosphere from which they developed an instability index, called the shape factor, based on the sign and magnitude of the gradient of equivalent potential temperature. Temperature profiles for both the clear weather and severe weather were derived and the shape factor differs significantly for the two weather conditions in agreement with other well established instability indices. The shape factor distinguishes itself from other indices based on the fact that it is calculated from the entire temperature profile rather than just selected levels.

The above issues show the importance of evaluating and testing the performance of various indices for a particular region to identify the synoptic conditions under which each of them perform better. Such studies have been performed in many different regions of the world such as Cyprus (Jacovides and Yonetani, 1990), Greece (Marinaki et al., 2006), Netherlands (Groenemeijer and Delden, 2006), Sweden (Andersson et al., 1989), Switzerland (Huntrieser

3 1.2 Study Objectives et al., 1996). Others have ventured in tuning and developing new indices more adaptable for their own local context (Fontana, 2008; Korologou et al., 2014; Sanchez et al., 2001; Walker et al., 2008). However, to the author’s knowledge, no studies have been conducted in a purely maritime environment free from continental and orographic influences. Also, most of the above-mentioned studies have focused on events involving thundery activities rather than considering heavy rainfall alone. Although it is widely accepted that these two are inextrica- bly linked but still heavy rainfall is possible without occurrence of thunderstorm (Doswell, 2001). Furthermore, local convective cloud development is not only a phenomenon of large land masses but can also impact land masses as small as 65 km × 45 km, which is the size of Mauritius. Over Mauritius a bright sunny day can turn into a hazardous afternoon with localised thundery showers and flash floods associated with local convection that develops by midday and last for 2-4 hours thereon. The task becomes even more delicate as usually only a small region of the island suffers from the severe weather, the heavy showers being very localised. If heavy rainfall from larger scale weather system such as fronts and easterly waves can be easily foreseen and warning issued to the public, forecasting rainfall intensities from such local convective cloud development remains a big challenge and added to this difficulty is determining its spatial distribution.

1.2 Study Objectives

Among the plethora of indices, operational meteorologists in Mauritius use only some selected indices for making 12-24 hour forecasts while others are not considered or simply ig- nored. The use of indices in day to day forecasting over a particular region call for a prior veriﬁcation on their performance (Doswell and Schultz, 2006) and this leads to some pertinent questions, namely:

• Has there been a systematic study in Mauritius to evaluate the performance of the actual indices that are being used?

• Have there been any attempts to investigate into the possibility of identifying more suitable indices?

• Is it possible to modify the existing indices or develop an index that blends better with the maritime environment in which the island is located?

However, until now the above could not be investigated because of the unavailability of suf- ﬁcient appropriate data. But now the state of the meteorological observations in Mauritius

4 1.3 Strength and Limitations has reached a point where sufﬁcient data is available providing the opportunity to undertake such studies. The aim of this study is to attempt to answer the above questions. It focuses only on local convection, commonly known as pure sea breeze development, and considers only rainfall irrespective of the occurrence of thunderstorms, though these two are usually intertwined, particularly in severe events. The main objectives are as follows:

1. Categorise the convective events into weak, moderate and severe events based on the rainfall intensities and amounts.

2. Assess the performance of available traditional indices for the different rainfall events.

3. Establish appropriate forecast thresholds of the indices that suit the afternoon (1200 UTC) soundings and appropriate ones for the early morning (2300 UTC) soundings.

4. Modify the traditional indices and investigate their performances compared to their traditional counterparts.

5. Assess impact of prevailing synoptic situation in the mid to upper level on the convection, for example wind shear, temperature, divergence or geopotential heights. Investi- gate into their use in conjunction with the other indices in order to improve the forecast.

6. Devise a decision scheme/tree that include thermodynamic indices and model output products to forecast heavy rainfall. The decision scheme must constitute a good compromise between accuracy and complexity as in an operational environment time is an important factor. As such devising a complex forecast scheme that requires lots of time to interpret may not be that useful.

1.3 Strength and Limitations

Most experimental studies have associated with them some strengths and limitations and this work is not an exception. Some of the major limitations are as follows:

1. Availability of radiosonde data is rather adhoc i.e. no continuous data are available. However, by selecting events over a long time period this issue is smoothed out to some extent.

2. Radiosonde data are available at only one station. But given the size of the island it could be considered to be representative of the whole island.

5 1.4 Outline of Thesis

3. The spatial distribution of the automatic weather stations are sparse and some heavy localised showers could have been missed. However, the severity of the event can be counterchecked with available satellite pictures and in case of doubtful rainfall the event is simply discarded.

The major strengths are as follows:

1. The availability of automatic weather station data that enable to identify rainfall events associated speciﬁcally with sea breeze development.

2. Mauritius as a tiny island with a maximum peak height of only 828 m provides a good environment to rigorously test the suitability of the different indices in a maritime environment with limited inﬂuence of topography.

1.4 Outline of Thesis

After introducing the motivation behind this study in this Chapter 1, the Chapter 2 gives a literature survey which includes description of the rainfall distribution, topography and weather systems over the island of Mauritius as well as an overview of the various existing instability indices that are suitable for forecasting heavy rainfall and thunderstorms; instability indices used for forecasting tornadoes are not considered. Chapter 3 give some further insights into local convection over Mauritius. The methodology, which involves data analysis and index development and associated theory applied, follows in Chapter 4. Results and discussions as well as critical analysis with respect to other studies are presented in Chapter 5. Conclusions and future works follow in Chapter 6. Any extra table of values and plots, theories and equations not presented inside the main chapters are shown in the Appendices.

6 Chapter 2

Literature Survey

2.1 Topography and Rainfall of Mauritius

2.1.1 Location, climate and topography

Mauritius is a small island, covering a surface area of slightly over 2000km2, located in the Southwest Indian Ocean (SWIO) basin. It forms part of the commonly known Mascarene Is- lands and lies between latitudes 19.98oS and 20.53oS and longitudes 57.3oE and 57.78oE, near the edge of the southern tropical belt (Fig. 2.1), and has mainly a maritime climate. It is quite far from large land masses and hence practically free from the inﬂuence of continents. Two seasons prevail over the island, a wet summer from November to April and drier winter from May to October though May and October are usually considered as transition months. The mean annual precipitation over the island is about 2100 mm, varying from 1500 mm on the east coast to 4000 mm on the central plateau and 900 mm on the west coast and about 70% of this rainfall occurs during summer. Climatological rainfall shows that February is the wettest month, while October is the driest one (AnnualReports − MauritiusMeteorologicalService). Throughout most of the year the island is swept by the southeasterly trade winds which are stronger and more persistent in winter while during summer they could be occasionally very light (Padya, 1989). Wind blows from different directions whenever tropical depressions or the Inter Tropical Convergence Zone (ITCZ) are centered very near. Most of the island con- sists of terrains which rise to an irregular central plateau, surrounded by mountain ranges, except for the low-lying coastal plains to the North. The maximum elevation is about 828 m in the southwest and is the height of the tallest mountain Fig. 2.2(b).

7 2.1 Topography and Rainfall of Mauritius

Figure 2.1: Location of Mauritius in the South West Indian Ocean (Atlas of Mauritius).

Figure 2.2: Topography of Mauritius. The Vacoas Synoptic Station, located on the western slope of the Central Plateau at a height of 425 m, is shown by the white arrow (http://mauritiusattractions.com/).

8 2.1 Topography and Rainfall of Mauritius

2.1.2 Rainfall in Mauritius

There are three dominant patterns of rainfall observed over the island:

• frontal rain caused by the usual interaction between warm air and cold air,

• relief (or orographic) rainfall occurring when moist-air cools as it is forced to rise over hills or mountains,

• convective rainfall caused by excessive warming of the land surface.

Given that Mauritius is located on the periphery of the subtropical belt it comes under the inﬂuence of both subtropical and tropical weather systems. This leads to different weather systems bringing the rainfall over the island and varies between seasons.

Winter rainfall

During winter the island is mostly under subtropical weather systems including cold fronts, easterly disturbances and other minor clouds in the trades associated with the anticyclone known as the Mascarene High. Most of the time the island is under the inﬂuence of moderate to strong inﬂuxes of cold and relatively drier air from the southeast associated with the Mas- carene High. As the trades start to blow more from the east, the air becomes laden with more moisture and this moist air interacts with relief of the island leading to rainfall mainly over the regions exposed to the wind. In its most active form the easterly disturbances almost have the characteristics of easterly waves and lead to widespread showers while minor disturbances will precipitate mainly over the central plateau, eastern and southern slopes aided by orographic lifting. Occasionally cold fronts also bring some short duration rainfall mostly over the southern, western and central plateau region of the island. Rainfall from these weather systems can be accentuated by the presence of mid-tropospheric troughs which increases the instability leading to formation of clouds with greater vertical extent compared to the mostly stratiform clouds. On average about 7 anticyclones pass south of the region during every winter months. Occasionally, this number reduces to 4 due to slow moving or quasi-stationary anticyclones but of higher intensity. The central pressure of the migrating anticyclones varies from 1030 to 1035 hPa, though central pressures may be as low as 1025 hPa or occasionally may reach 1040 hPa, but located further south at about 40oS compared to the normal position which is around 32oS (Padya, 1989).

9 2.2 An Overview of Indices

Summer rainfall

During summer the island comes under the influence of a relatively warm and moist north- easterly airstream. Beside this moisture laden airstream, other active cloud systems associated with tropical storm and meso-scale convective systems can give rise to significant rainfall even over the leeward side and flatter regions of the islands. Summer rainfall includes those from tropical storms or cyclones, ITCZ, meso-scale convective systems and other amorphous cloud clusters with no identifiable synoptic-scale. For instance, cloud bands associated with a tropical cyclone hundreds of kilometers away can bring heavy extended period of rainfall over the island. Very unstable conditions prevail with the presence of mid and upper tropospheric depressions and troughs. When any of the above mentioned systems come in phase with these upper level features it results into heavy thundery showers. Another cause of rainfall is from air mass thunderstorm where convection is triggered by local heating. Such local convective cloud developments, commonly known as sea breeze development, peak usually in the afternoon and has oftentimes led to heavy rainfall and flash floods in some regions, irrespective of their elevation. This study in fact focuses on this type of local convective rainfall and it is analysed in greater details in Chapter 3.

2.2 An Overview of Indices

Presently there are many thermodynamic parameters and derived indices, particularly those from radiosondes, that are being used as diagnostic variables or precursors of thunderstorms and heavy rainfall. The work by Showalter (1953) was just a breakthrough, and since then several indices have followed namely Lifted Index (LI) (Galway, 1956), K-Index (KI) (George, 1960), Totals Total Index (TTI) (Miller, 1972), CAPE (Moncrieff and Miller, 1976), Boyden Index (Boyden, 1963) and Jefferson Index (Jefferson, 1963a,b) to mention a few. More complex indices have been elaborated from these basic indices for other speciﬁc purposes. A common example is the Severe Weather Threat Index (SWEAT) (Miller, 1972) which includes wind shear parameters combined with the TTI and the temperature at 850 hPa. The power of these indices lie in their capabilities to integrate various thermodynamic and kinematic parameters of the atmosphere into a single parameter that can give an indication of the stability of the atmosphere. Such indices simplify the tedious task of analysing and assessing the complex three-dimensional structure of the atmosphere and as such are a very beneﬁcial tool for operational meteorologists who usually have to work under prescribed deadlines (Doswell and Schultz, 2006). The most commonly used indices, thereon referred to as ”traditional” in-

10 2.2 An Overview of Indices dices interchangeably, to forecast heavy rain and thunderstorm include KI, LI, TTI and the CAP E amongst others. Other indices used in some part of the world affected by tornadoes include the Showalter Stability index (ShwI) and the SW EAT . A description of the whole set of available indices is beyond the scope of this thesis. Interested readers are referred to the review by Grieser (2012) for a more exhaustive list of available convective indices. How- ever, some of the indices that are going to be considered in this study are elaborated on in the sections that follow.

2.2.1 Potential instability indices

Showalter Index

The Showalter Index (Showalter, 1953) is based on the potential instability of the 850 hPa and 500 hPa layer as it measures the buoyancy at 500 hPa of an air parcel lifted at that level. As such it gives an indication of the latent instability of the layer. A negative value is equivalent to the existence of positive buoyancy above the Level of Free Convection (LF C) and as such the chances of free convection. A value of ShwI of ≤ +3 is associated to showers with possibility of thundery activity and a value of ≤ −3 to severe convection.

ShwI = T500 − Tp500 (2.1)

where Tp500 is the 500 hPa temperature a parcel would achieve if it is lifted dry adiabatically from 850 hPa to its condensation level and then moist adiabatically to 500 hPa. Common thresholds are as follows:

  −3K < SW I ≤ 3K : thunderstorm possible;  SWI ≤ −3K : severe thunderstorms likely.

Lifted Index

Developed by Galway (1956), the lifted index (LI) assesses the degree of stability of the atmosphere between the surface and 500 hPa. It is similar to the ShwI except that the parcel is lifted from surface rather than 850 hPa. It is the temperature difference of a parcel that is lifted from the surface to its lifting condensation level (LCL) dry adiabatically and further moist adiabatically to 500 hPa. Furthermore, Galway (1956) assigned to the parcel the mean mixing ratio of the lowest ﬁrst kilometers and the potential temperature corresponding to the forecasted afternoon maximum temperature. As such, contrary to the ShwI which is a static

11 2.2 An Overview of Indices index, the LI is a forecast index. A negative LI represents an unstable boundary layer compared to the middle troposphere. A value of −2 has been used as an upper limit for severe convection, but this varies from location to location. Galway (1956) established the following thresholds:

 LI ≥ 0K :  stable atmosphere-no thunderstorm possible;   0K > LI ≥ −2K : thunderstorm possible;  −2K > LI ≥ −6K : thunderstorms likely;    −6K > LI : severe thunderstorm likely.

2.2.2 Temperature and humidity indices

Vertical Totals, Cross Totals and Total Totals

These are used as a ﬁrst guess indices to identify the potential for severe convection (Miller, 1972). The Vertical Total (VT ) gives an indication of the vertical temperature gradient of a layer of the atmosphere which includes the top of the boundary layer up to 500 hPa level. It is calculated as the temperature difference between the 850 hPa and the 500 hPa levels.

VT = T850 − T500 (2.2)

Humidity is an important element in the process of deep moist convection in addition to strong vertical temperature gradient. In order to consider the humidity in the calculation, Miller (1972) devised the Cross Total (CT ) which uses the dewpoint temperature at the 850 Pa instead of the temperature and is given by

CT = Td,850 − T500 (2.3)

However, in the presence of a steep temperature lapse rate the CT and TT can have large values even if the low level moisture is not high. As such indices must be used with care else they are bound to overestimate the potential of convection. To account for both for the depth of moisture in the low level and vertical temperature gradient in the layer , the Total Total (TT ) was proposed as a sum of the CT and VT and is given by

TT = VT + CT = T850 + Td,850 − 2T500 (2.4)

12 2.2 An Overview of Indices

The TT has shown a high degree of success (Huntrieser et al., 1996) and the thunderstorm threshold varies between 45 and 50 depending on the geographical location and also the sea- son and synoptic situation (Marinaki et al., 2006). The higher the value of TT the higher the probability of thunderstorm.

K-Index

Derived by George (1960), the K index (KI) has been found to be very helpful at forecasting air mass thunderstorms. It combines the vertical temperature gradient between 850 hPa and 500 hPa, the 850 hPa dewpoint (as a direct measure of low level moisture) and the 700 hPa dewpoint depression. Since a drier atmosphere at a slightly higher level, namely at 700 hPa, might compromise the severity of the convection, the dewpoint depression at that level gives an indication of the vertical intrusion of the low level moisture or the extent of the depth of the moist layer. This index essentially quantiﬁes the probability of thundery activity and is given as

K = (T850 − T500) + Td,850 − (T700 − Td,700) (2.5)

When all temperatures are provided in oC the thresholds for thunderstorm potential, as per George (1960), are as follows:  20 ≥ KI ≥ 0 :  0%-20%;   25 ≥ KI > 20 :  20%-40%;   30 ≥ KI > 25 : 40%-60%;

 35 ≥ KI > 30 : 60%-80%;    40 ≥ KI > 35 : 80%-90%;   KI > 40 : 90%-100%.

Humidity Index

The humidity index (HI), developed by Litynska et al. (2005), includes moisture depth at 3 standard levels, namely 850 hPa, 700 hPa and 500 hPa and its main use is to predict air mass thunderstorms. It is given by

HI = (T850 − Td,850) + (T700 − Td,700) + (T500 − Td,500) (2.6)

A value of 30K has been suggested as a threshold for thunderstorm with the chance increasing as the value of HI decreases.

13 2.2 An Overview of Indices

Deep Convective Index

The Deep Convection Index (DCI) (Barlow, 1993) is a combination of temperature and humidity at 850 hPa as well as the LI and is given by:

DCI = T850 + Td,850 − LI (2.7)

Usually a DCI higher than 30 oC indicates likelihood of thunderstorm.

2.2.3 Advanced derived indices

Convective Available Potential Energy

CAP E is a concept that is based on a parcel that accelerates vertically upward on its own once it becomes warmer than its surrounding, i.e. positively buoyant. The parcel is said to have CAP E after being lifted by some mechanism, such as heating or by orography, up to its point where it becomes positively buoyant, called the Level of Free Convection (LF C). Beyond the LF C the parcel rises until it becomes cooler than its surrounding at the Level of Neutral Buoyancy (LNB) (also called the equilibrium level (EL)) where it starts sinking back. The CAP E is numerically calculated as the integration of the buoyancy force from the LF C to the EL which represents the work done by this force. This also represents the amount of kinetic energy generated from the CAP E and is given by

Z EL Z LNB T − T 0 BT dz = g 0 dz (2.8) LF C LF C T where BT is the thermal buoyancy, T is the parcel temperature perturbation deﬁned with respect to its environment , T 0 is temperature of the surrounding and g is the acceleration due to gravity. It has been suggested that instead of actual temperatures the virtual temperatures be used and Doswell (2001) gave the following relationship

Z LNB Z LNB 0 Tv BT dz = g dz (2.9) LF C LF C Tv

0 where Tv is the parcel virtual temperature perturbation deﬁned with respect to its environment, Tv is the mean virtual temperature.

Hence occurrence of deep moist convection requires at least the presence of CAP E and a forcing large enough to induce release of that CAP E (Groenemeijer and Delden, 2006). However,

14 2.2 An Overview of Indices it has been shown that convective storms may occur even if little or no CAP E is present and in such cases strong vertical wind shear was found to play a more important role in sustaining convection. In such a case, Groenemeijer and Delden (2006) suggested that dynamical insta- bilities triggered the convection rather than release of CAP E. In most cases the following thresholds of CAP E apply:  0JKg−1 < CAP E < 1000JKg−1 :  weak instability;   1000JKg−1 < CAP E ≤ 2500JKg−1 : moderate instability;  2500JKg−1 < CAP E ≤ 4000JKg−1 : strong instability;    4000JKg−1 < CAP E : extreme instability.

Convective Inhibition Energy

The Convective Inhibition Energy (CIN) is the energy needed to lift an air parcel from the surface to its LF C, i.e. it is an energy needed to overcome any initial resistance to convection. It is given by Z LF C T − T 0 CIN = g 0 dz (2.10) 0 T Usually a strong CIN will compromise the triggering of convection. However, as stipulated by Emanuel (1994), accumulation of CAP E is a pre-requisite for strong convection and to accomplish this it is important to have some negative area (CIN) in the sounding that will prevent the instantaneous release of the instability. Hence, a low CIN will lead to minor convection at a quite early stage of instability. On the other hand if is too strong, it is likely to dampen any convection, except if there is another mechanism that can force the lifting such as the orography or large scale dynamic forcing. The following threshold has been found to apply:  CIN ≤ 15JKg−1 :  minor cumuli develop;   0JKg−1 < CIN ≤ 50JKg−1 : single cell thunderstorm possible;  50JKg−1 < CIN ≤ 200JKg−1 : multi cell thunderstorms possible;    200JKg−1 < CIN : no thunderstorm develop.

Total Precipitable Water

The total precipitable water (P rpW tr) is calculated from the speciﬁc humidity q of the air in a column of the atmosphere. In a layer between height z1 and z2 and pressure p1 and p2, if

15 2.2 An Overview of Indices the density of the air is ρ, the precipitable water is given by

Z z2 P rpW tr = ρqdz (2.11) z1

dp r and applying the hydrostatic equation dz = −ρg and deﬁnition of speciﬁc humidity q = 1+r , where r is the mixing ratio, gives

1 Z p1 P rpW tr = qdp (2.12) g p2 1 Z p1 r P rpW tr = ( )dp (2.13) g p2 1 + r

Using from a tephigram, the atmosphere can be divided into several suitable layers and the mean r of each layer determined and used to calculate the precipitable water of each layer . The P rpW tr then the sum of the precipitable water of the sub layers. Usually the higher the precipitable water the higher the volume of precipitation could be expected.

2.2.4 Wind shear indices

Beside the availability of moisture, which accounts for the thermodynamic factor affecting atmospheric instability, the dynamical effect of wind has also an important role to play in convection. Wind affects convective activities at all levels of the atmosphere in terms of wind shear. At the surface the impact of wind is in terms of orographic lifting which can enhance the rainfall associated with convective clouds. In the case convection from sea breeze, low level wind and wind shear play a great role in determining the spatial distribution and depth of the convection. Wind shear largely inﬂuences convection, particularly deep convection, because it leads to perturbations in dynamic pressure that impact on the organisation of convective clouds/storms (Emanuel, 1994; Groenemeijer and Delden, 2006). Weak vertical wind shear usually leads to short lived single or ordinary cells with no severe weather associated. As wind shear increases so does the storm’s size and the multicell storms usually lead to severe weather.

2.2.5 Conclusions

This chapter has considered some of the most commonly used indices commonly known as ”traditional indices”. Nevertheless based on these, several other indices have been derived for speciﬁc purposes, such as tornadoes, hail and downdrafts and for particular locations.

16 2.2 An Overview of Indices

The environment in which Mauritius is located has also been highlighted as well as the less complex topography. This makes the island a suitable study area for convection in a purely maritime environment free from orographic and continental inﬂuences.

17 Chapter 3

Local Convection In Mauritius

3.1 Introduction

The sea breeze effect is a phenomenon observed worldwide, be it over coastal areas of large continents or over islands as small as Mauritius. A sea breeze circulation is triggered once a temperature difference between land and the sea is developed. During the day, particularly summer, the land surface warms up faster than the sea surface being greatest around mid- afternoon. A simple description of the process is that as the air over a land surface warms it rises and a local circulation commences, with cooler air from the sea being drawn in over the land. At the same time the ascending air returns seaward in what is known as the upper return current and this process goes in a loop until the land cools down by the evening. In some instances when the earth’s surface gets much warmer the updraft becomes stronger such that the sea breeze becomes more active with clouds covering a large area. Over large continents the sea breeze front can penetrate tens or over even a hundred kilometres inland leading to heavy precipitation. The duration of the convection from sea breeze development also varies. Over Mauritius, it oftentimes last for at most 2-3 hours and dies by late afternoon but on some occasions it can last for several hours with thundery activities up to up 7 or 8 p.m. The spatial and temporal distribution of the sea breeze is largely driven by its intensity which in turn depends on the 3 major ingredients that are required to trigger and sustain the convection (Johns and Doswell, 1992) and these are:

1. An adequate deep layer of moisture in the low and/or mid troposphere

2. Conditional instability

3. A mechanism that triggers the convection.

18 3.2 Spatial Distribution of Local Convection in Mauritius

The triggering mechanisms could be synoptic/meso scale forcing, orographic uplift or local heating. Surrounded by the sea, low level moisture is not a limiting factor over the island. All that is needed is a triggering mechanism. The absence of large extent of elevated areas, Fig. 2.2, leads to rather negligible contribution from orographic uplift. Actually, during local convective cloud development it is not uncommon to have rainfall of higher amount and intensity over ﬂatter areas. The major triggering mechanism is the heating of the land surface and this study considers only those events arising from surface heating which is referred to as pure sea breeze, i.e. convection free from the inﬂuence of synoptic scale or orographic forcing.

3.2 Spatial Distribution of Local Convection in Mauritius

A pure sea breeze front will develop on the opposite direction of the prevailing wind and the extent of inland penetration of this front is largely inﬂuenced by the strength of the prevailing wind. With weak prevailing wind circulations a pure sea breeze will commence over the coastline soon after the land temperature starts to exceed the sea surface temperature and this could be by late morning to early afternoon. Increase of this temperature gradient strengthens the sea breeze which extends farther inland gaining in vertical depth at the same time. Being most of the time swept by easterly winds, sea breeze is more frequent on the west side of the island, Fig. 3.1(a), (b). During the month of January and February, when the wind occasionally blow from the west and north, the region of convection develops over the eastern and southern sectors respectively, Fig. 3.1(c), (d) and Fig. 3.1(e), (f). On some occasions, with the presence of a meso-scale system, the prevailing wind back towards the south and in such a case the clouds develop to the north, Fig. 3.1(g), (h).

No studies exists as such, but observations show that low level winds (surface to 850 hPa) of ≤ 8 knots are conducive for local convection. Oftentimes, with low level wind speed of >10 knots the convection gets carried offshore Fig. 3.2(a), (b). Sometimes such moderate surface wind either delay the onset of the sea breeze, such that it forms in the late afternoon, or simply prevent the sea breeze from developing at all. If the prevailing wind is light, usually ≤ 5 knots, the convection spreads further inland over the Central Plateau, Fig. 3.2(c), (d). When the wind is very light and variable in direction an island low is formed due to convergence of winds from all directions leading to widespread cloud development, Fig. 3.2(e), (f).

19 3.2 Spatial Distribution of Local Convection in Mauritius

(a) West-23 Dec 2005@0600z (b) West-23 Dec 2005@1200z

(e) South-23 Feb 2012@0600z (f) South-23 Feb 2012@1200z

(g) North-12 Jan 2009@0600z (h) North-12 Jan 2009@1200z

Figure 3.1: MeteoSat-7 visible imagery at 0600 UTC and 1200 UTC showing local convection over different region of Mauritius (http : //www.sat.dundee.ac.uk/geobrowse).

20 3.2 Spatial Distribution of Local Convection in Mauritius

(a) 27 Dec 2008@0600z (b) 27 Dec 2008@1200z

(e) 18 Nov 2005@0600z (f) 18 Nov 2005@1200z

(g) 19 Feb 2012@0600z (h) 19 Feb 2012@1200z

Figure 3.2: MeteoSat-7 visible imagery at 0600 UTC and 1200 UTC showing intensity of local convection over Mauritius (http : //www.sat.dundee.ac.uk/geobrowse).

21 3.2 Spatial Distribution of Local Convection in Mauritius

The event on 19 Feb 2012 is of particular interest as it involves thunderstorms development at various locations perfectly driven by the backing of winds in the low levels, Fig. 3.2(g), (h). On 19 February 2012 the wind directions at 925 hPa, 850 hPa, 800 hPa, 750 hPa, 700 hPa and 650 hPa were 55o, 30o, 27o, calm, 155o and 190o respectively. The ﬁrst cell formed to the southwest (in response to the northeasterlies from surface to 800 hPa), then to the northwest (driven by the southeasterly at 700 hPa) and then eventually to the northeast (due to the southwesterly at and above 650 hPa). This is a pertinent example of directional shear on the spatial distribution of the convection. It is worth noting that the speed shear was rather negligible with the winds varying between 1 to 7 knots from surface to 700 hPa, a calm condition at 750 hPa, and varying between 10-12 knots between 650 hPa and 550 hPa.

(a) 08Sep2013@0600z (b) 08Sep2013@1200z

Figure 3.3: MeteoSat-7 visible imagery at 0600 UTC and 1200 UTC showing convection due to forcing from a frontal system (top) and a meso low (bottom) (http : //www.sat.dundee.ac.uk/geobrowse).

Not all the convection that forms in the afternoon is due to pure sea breeze. The local con-

22 3.3 Indices and Local Convection Forecast vection is also triggered by large scale systems such as an approaching cold front, Fig. 3.3(a), (b) or meso-scale system such as a meso-low, Fig. 3.3(c), (d). Such events are omitted in this study.

3.3 Indices and Local Convection Forecast

Far from forecasting the location of heavy rainfall, forecasting occurrence of such convection at such small scale is a challenge even for numerical models. The highest resolution limited area model available for the region is the ALADIN which is run by Meteo France and has a resolution of 8 km×8 km. On some occasions this model is able to capture the local convection but not the intensity or spatial extent. The 12-hour accumulated precipitation as forecast by ALADIN, which was associated with one such convective event in the afternoon of 30 March 2013 is shown in Fig. 3.4. This was not a pure sea breeze type convection by rather one triggered by synoptic scale system. The model analysis is at 0000 UTC and forecasted some 18-20 mm of accumulated rainfall to the southeast of the island by 1200 UTC (i.e. in 12 hours). On that particular day the bulk of the rain fell to the northwest of the island with some stations recording over 150 mm in just 2 hours.

Figure 3.4: Domain of the ALADIN limited area model over the SWIO showing a 12 hour forecast of accumulated precipitation (mm) for a convective event on 30 March 2013. The model analysis is at 30 @ 0000 UTC and is valid for 30 @ 1200 UTC (http : //www.meteo.fr/extranets/).

23 3.4 Where Indices Fail

Even though the above was a synoptically forced convective event the model was not able to achieve a good forecast. In the case of pure sea breeze type convection this ability is even more reduced. Hence forecasts of these convective events are mostly based on local prevailing conditions such as wind strength, temperature and moisture in the low levels as well as in the mid-level. The temperature of the sea and land surface are also important as these influence the horizontal and vertical temperature gradients. Here the experience of an operational meteorologist is crucial and he can use the available thermodynamic indices as a complementary tool. But in spite of the plethora indices, at the Mauritius Meteorological Service, meteorologists use only on few common indices and these are the TTI, CAP E and the P rpW tr. The first two are mostly used to forecast likelihood of thunderstorms and heavy rainfall while the last one is specifically used as an indication of the amount of rain that could be expected, but it must be admitted that these indices are not always on target. Local convection has become a high impact weather event over the island and the need of better forecasts is strongly felt. One way to achieve this is through a more coherent use of the available indices. This calls for a systematic study on the suitability of other existing indices and the possibility for adapt- ing these indices to the local context. The ultimate aim is to limit the misses and reduce the false alarms in the forecast as both of these disrupt the socio-economic activities as well as endanger the lives of people. Special cases of failures of the traditional indices during pure sea breeze events are highlighted in the section that follows.

3.4 Where Indices Fail

There have been several occasions when the conventional indices have totally failed to give indication of the actual severity of the local convection, sometimes leading to overestimation or underestimation of the events. In some instances, even if all the ingredients were available and the indices point towards unstable conditions, no cloud formation was observed at all. Some of these events are analysed below and some additional ones shown in Appendix B.

3.4.1 Stable indices - heavy rainfall event

Heavy rainfall events associated with low TTI and CAP E are not uncommon. Some of these events are shown in Fig. 3.5 where hourly rainfall intensities of 53 mm, 50.4mm, 34.4mm and 30 mm were recorded on 29 February 2004, 28 December 2004, 25 February 2005 and 10 March 2006 respectively. For these events, most of the indices which have been calculated from the meteorological parameters when the convection was already occurring or peaking, i.e. at

24 3.4 Where Indices Fail around 1100UTC (15hr00 LT), show a stable atmosphere. The only pertinent observation shown by all the proﬁles in Fig. 3.5is the presence of a super adiabatic lapse rate in the lower strata of the boundary layer given that the launch is around the time of maximum temperature.

(a) 29 Feb 2004 (b) 28 Dec 2004

Figure 3.5: Skew-T plots of soundings at Vacoas synoptic station @ 1200 UTC showing temperature and dew point proﬁle with (a, b) moist mid-troposphere (c, d) dry mid-troposphere. Calculated indices are shown on top right corner (http : //weather.uwyo.edu/upperair/sounding.html).

This super-adiabatic heating of the lower boundary layer is what traditional indices ignore, a

25 3.4 Where Indices Fail factor that contributes to the steepening of the lapse rate in the lower level. It’s consideration in the Normand’s point construction is expected to alter the value of a series of indices including the CAP E and TTI. Furthermore, two types of proﬁles are readily discernible, some which are moist and some relatively drier. Fig. 3.5(a), (b) shows occasions during which the layer up to almost the mid-troposphere is moist, characterised by the closeness of the temperature and dewpoint curve. Heavy rainfall from these proﬁles can be expected given the deep moisture content as captured by the high P rpW tr even if the TTI and CAP E are quite low. However, in some events, the atmosphere suddenly dries up at around 850 hPa as shown by a large departure between temperature and dewpoint curves in Fig. 3.5(c), (d). In these two events all the indices point towards a rather stable and dry atmosphere. The only difference if the built up of moisture again at around 300 hPa.

3.4.2 Unstable indices - light rainfall events

Sometimes the indications of unstable atmospheric conditions do not materialise into the expected rainfall. Such examples are shown in Fig. 3.6. In some cases this could be explained by a relatively dry low level, Fig. 3.6(a) but in others light rainfall is observed even though the low level is very moist, Fig. 3.6(b).

(a) 01 Feb 2005 (b) 10 Dec 2008

Figure 3.6: Skew-T plots of soundings at Vacoas synoptic station @1200 UTC showing temperature and dew point proﬁle (a) dry low level (b) moist low level. Calculated indices are shown on top right corner (http : //weather.uwyo.edu/upperair/sounding.html).

26 3.4 Where Indices Fail

3.4.3 Unstable indices - nil convection events

The evolution of meso-scale or synoptic scale features can have a signiﬁcant impact on the local atmospheric conditions. Depending on their proximity and large scale circulation, they can either enhance the convection, Fig. 3.3 or dampen it, Fig. 3.7 where a meso-scale system moved from the north east of the island towards the south. Hence, in such cases, in spite of the light wind conditions and available moisture and heating, the descending air induced by the meso scale system impeded any vertical motion over the island.

(a) 25 Dec 2008@0600z (b) 25 Dec 2008@1200z

Figure 3.7: MeteoSat-7 visible imagery t 0600 UTC and 1200 UTC showing evolution of a meso scale system in the vicinity of Mauritius dampening any local convection.

During these two days some moisture is available in the low level (surface to 950 hPa) but the

27 3.5 Inﬂuence of Upper Level Synoptic Situation atmosphere is dry aloft, Fig. 3.8. Besides the indices, the wind shear also gives an indication of some severe weather with both the directional and speed shear being favourable.

(a) 25 Dec 2008 (b) 26 Dec 2008

Figure 3.8: Skew-T plots of soundings at Vacoas synoptic station @1200 UTC showing temperature and dew point proﬁle of a rather dry atmosphere. Calculated indices are shown on top right corner (http : //weather.uwyo.edu/upperair/sounding.html).

3.5 Inﬂuence of Upper Level Synoptic Situation

The above cases are viewed through a diagnosis of the synoptic situation at the mid-level using the 500 hPa mean geopotential height and temperature anomaly fields. The temperature anomaly is the difference of observed temperature and 1981-2010 climatological mean. The NCEP-NCAR re-analysed data of the different fields are obtained from the NOAA/ESRL website, http : //www.esrl.noaa.gov/ and these fields are retrieve for the above cases as follows:

• Case I: stable index-heavy rainfall,

• Case II: unstable index-light rainfall and

• Case III: unstable index-no convection.

The 500 hPa mean geopotential height ﬁelds, for the above 3 cases, are shown in Fig. 3.9, Fig. 3.11 and Fig. 3.13. The 500 hPa temperature anomaly ﬁelds are shown in Fig. 3.10, Fig. 3.12 and Fig. 3.14. High geopotential height is represented by blue H, low geopotential by red L,

28 3.5 Inﬂuence of Upper Level Synoptic Situation cold anomaly by blue C and warm anomaly by red W.

As explained earlier, for Case I two distinct soundings are observed, one with a moist mid- troposphere, Fig. 3.5(a), (b) and the other with a drier one, Fig. 3.5(c), (d). In the former, the island is under the inﬂuence of a trough and low geopotential height as shown in Fig. 3.9(a) and Fig. 3.9(b) respectively. This cyclonic ﬂow certainly contributed in enhancing the convection in spite of the stable conditions shown by the indices.

(a) 29 Feb 2004 (b) 28 Dec 2004

Figure 3.9: 500 hPa geopotential height (m) composite mean over the SWIO for the days with stable indices and heavy rainfall (H: high, L: Low) (http : //www.esrl.noaa.gov/).

The cyclonic ﬂow at 500 hPa is in fact an important element in the Pickup Index and has proved to be a successful index in forecasting thunderstorms (Pickup, 1982). The ﬂow curvature at 500 hPa has also been found to improve the performance of other indices (Michalopou-

29 3.5 Influence of Upper Level Synoptic Situation los and Jacovides, 1987; Jacovides and Yonetani, 1990). The events with dry mid-troposphere perfectly tally with the high or ridge of geopotential height as shown in Fig. 3.9(c), (d), which indicates mainly sinking air over the region. But in spite of this subsiding air, the low level heating and moisture was enough to force the convection with some moderate to heavy rainfall. The temperature anomaly field is simply a reflection of the geopotential height field. A cold anomaly is associated with the low geopotential height (Fig.3.10(b)) and a warm anomaly is associated with the high geopotential height (Fig. 3.10(c)). The temperature anomaly associated with the trough and the ridge lie in between the warm and cold as shown in Fig. 3.10(a) and Fig. 3.10(d). Thus with a cold pool in the mid-level, which is indicative of a buoyant atmosphere, moderate to heavy rainfall can be forecasted even if the indices show otherwise. But, with an anomaly in between, the forecast might not be straightforward.

(a) 29 Feb 2004 (b) 28 Dec 2004

Figure 3.10: 500 hPa air temperature (K) composite anomaly (1981-2010) over the SWIO for the days with stable indices and heavy rainfall (W: warm pool, C: cold pool).

30 3.5 Inﬂuence of Upper Level Synoptic Situation

For Case II, mostly stable conditions are observed at 500 hPa with ridge of high geopotential height inﬂuencing the region as shown in Fig. 3.11(a) and (b). After the passage of the trough in Fig. 3.11(b) stable conditions starts to set in but this does not necessarily lead to spontaneous change in the values of the indices. Furthermore, the stable conditions are further reﬂected by the warm temperature anomaly at 500 hPa, i.e. a less buoyant atmosphere as shown in Fig. 3.12(a) and (b).

(a) 01 Feb 2005 (b) 10 Dec 2008

Figure 3.11: 500 hPa geopotential height (m) composite mean over the SWIO for the days with unstable indices and light rainfall (H: high, L: Low) (http : //www.esrl.noaa.gov/).

(a) 01 Feb 2005 (b) 10 Dec 2008

Figure 3.12: 500 hPa air temperature (K) composite anomaly (1981-2010) over the SWIO for the days with unstable indices and light rainfall (W: warm pool, C: cold pool) (http : //www.esrl.noaa.gov/).

31 3.5 Inﬂuence of Upper Level Synoptic Situation

The events in Case III are more ambiguous with unstable conditions shown both by the indices and the situation at 500 hPa. A trough and a low geopotential height is discernible on the 25 and 26 as shown in Fig. 3.13(a) and Fig. 3.13(b) respectively. This is further sup- ported by a negative temperature anomaly on the 25 though it becomes slightly less negative on the 26. In such situations only the sounding proﬁle (Fig. 3.8), which shows a rather dry atmosphere, can give a clue to the observed damped convection.

(a) 25 Dec 2008 (b) 26 Dec 2008

Figure 3.13: 500 hPa geopotential height (m) composite mean for the days with unstable indices without convection (H: high, L: Low) (http : //www.esrl.noaa.gov/).

(a) 25 Dec 2008 (b) 26 Dec 2008

Figure 3.14: 500 hPa air temperature (K) composite anomaly (1981-2010) over the SWIO for the days with unstable indices without convection (W: warm pool, C: cold pool) (http : //www.esrl.noaa.gov/).

32 3.6 Conclusions

3.6 Conclusions

The analysis in this chapter shows that, in spite of being a small island, convection of several spatial extent can occur even over a small area and these are largely driven by the prevailing winds in the low levels. It has also been demonstrated how difficult it is even for a limited area model capture both the spatial extent and intensity of convection over such a small island. In- dices can be used as a complementary tool but it has been shown that in some instances they may be misleading because the convection may be largely influenced by synoptic situation in the higher levels. But still, due to unusual atmospheric processes, there are instances when both the indices or the upper level conditions are not able to account for the actual observed weather only a thorough look through the sounding profile can help.

As such there is a need for a complete assessment of the traditional indices as well as their modiﬁcations to include lower boundary layer parameters so that they better adapt to the local context as well as taking onboard some model output products. The next chapter deals with the methodology for identifying better traditional indices and modiﬁcations of some indices as well as their validation.

33 Chapter 4

Data analysis and Index Development

4.1 Introduction

It has been observed that not all heavy downpours over the island are necessarily associated with thundery activity. This observation has also been made by Doswell (2001), where he preferred to use the term ’Deep Moist Convection’ instead of ’ thunderstorm’ simply because hazardous weather, such as heavy rainfall, may be associated with non-thundering convection. Furthermore, a high amount of rainfall may not necessarily be hazardous, what really makes the event severe is a high amount in a very short time, ie. a high rainfall intensity.

This chapter elaborates on the methodology towards development of a new index and a decision tree to forecast heavy rainfall. It involves the following

1. Evaluation of selected traditional (existing) indices.

2. Modiﬁcation of certain traditional indices through inclusion of low level parameters and compare their performances.

3. Investigation of the impact of wind shear at different levels on severity of events.

4. validation of the various indices (traditional and modiﬁed) and construction of decision tree (scheme).

5. Identiﬁcation of the best traditional and/or modiﬁed indices through a stepwise regression process.

34 4.2 Data

4.2 Data

4.2.1 Rainfall data

Rainfall data were obtained from the Mauritius Meteorological Service which is the ofﬁcial national institution responsible to collect, archive and quality control rainfall data over the island. Rainfall data from 20 automatic weather stations (AWS) were used. These stations measure rainfall at 6 mins intervals. This enabled extraction of rainfall associated solely with sea breeze events, for instance night and early morning rainfall are easily discarded. The stations used are shown in Fig.4.1(a), (b). Five types of rainfall were considered in the analysis as well as the duration of the total rainfall and these include the:

• The highest accumulated rainfall (HgAcRr)

• The highest hourly (60 minutes) rainfall (HgRr60)

• The highest 30 minutes rainfall (HgRr30)

• The highest 6 minutes rainfall (HgRr6)

• The mean duration(Drtn)

• The mean hourly rainfall (AvgRr60)

Figure 4.1: Location of the 20 AWS (A) and 20 manned stations (M))used in this study. The site of radiosonde launch (Vacoas synoptic station) is encircle in red.

35 4.2 Data

The duration (Drtn) of the rainfall is that associated with the station reporting the highest accumulated rainfall or in some cases taken as an average of all the stations rainfall duration. The rainfall data include those available from 21 AWS from 2003 to 2014. A further 19 manned stations were used to verify any possibility of heavy rainfall that may have been missed by the AWS.

4.2.2 Radiosonde data

Upper air soundings are done only at one station in Mauritius, the Vacoas synoptic station located at a height of 425 m above sea level and about 12 km from the coast ( Fig.4.1). Sound- ings are launched either at 2300z (0300 hours local time) or 1100z (1500 hours local time). The timing is as such in order to broadcast the data on the Global Telecommunication System (GTS) by 0000z and 1200z respectively. This is also appropriate for local use as the two main weather forecast are issued not later than 0100z and 1300z everyday. But given the small size of the island one radiosonde is well representative of the air mass characteristics over the whole island at a particular time. The only major issue could be the drifting of the balloon as it moves with height (Laroche and Sarrazin, 2013).

Archived upper air soundings from the Vacoas synoptic station (Station Code 61995) were retrieved from the website of University of Wyoming’s Department of Atmospheric Science (http : //weather.uwyo.edu/upperair/sounding.html). This web site provides plotted vertical proﬁles as well as the raw data with calculated value of different instability indices. From 2011 to 2014 radiosondes were launched mainly in the early morning at around 2300UTC (available at 0000 z) and these will be used for cross validation purpose. The aim is to optimise the use of the available morning proﬁle to make a short term forecast, i.e. for the next 12 hours particularly focusing on the likelihood of convective rainfall during the day.

4.2.3 Categorisation of events

As mentioned in Section 4.2 six elements of the rainfall data could be analysed. But, since in an operational environment one is more interested in forecasting the type of events that could be expected rather than the exact amount, the events are categorised into weak, moderate and severe based on the percentiles of either the HgRr60 or the HgAcRr. Use of shorter time scale rainfall intensities such as the 30 mins or 6 mins are not considered at this stage. Most results and discussions provided in the main section will include those associated with the HgRr60,

36 4.3 Proposed Indices

HgAcRr and Drtn. Other detailed results, such as correlation of indices with HgRr30, HgRr6 and mean hourly rainfall (AvgRr60) are provided in the Appendices.

4.2.4 Filtering of convective events

Given afternoon convection occurs particularly in summer over the island, radiosonde data for the summer months of November to April were used in the analysis. For afternoon convection to take place the winds in the low levels, from surface to 700 hPa, must be light and usually not more than 8-10 knots and as such only these days were selected. The occurrence of afternoon convection (cloud development) was cross checked with satellite pictures (0600 UTC and 1200 UTC) available from the Dundee Satellite Receiving Station website (http : //www.sat.dundee.ac.uk/geobrowse/geobrowse.php). Any convection involving meso-scale or synoptic scale systems were discarded. The aim was to retrieve clouds development arising solely from local convection triggered by heating (pure sea breeze). Based on the extent and thickness of clouds a ﬁrst guess of the intensity of the convection could be deduced. These were then cross checked with the rainfall data from the available AWS and manned stations.

The reason for using 1100UTC radiosonde for the purpose of analysis is that it is during this time the convection starts to develop or reaching its peak depending on the time it started. As such radiosonde data for that particular time provides meteorological parameters which give an actual diagnosis of the atmosphere during the occurring convection. In all 64 convective rainfall events were identiﬁed from Summer 2003 to 2009. More events have occurred during that period but soundings are not available for all of them. For instance no events during the Year 2010 could be used as radiosondes launches were sporadic and the available soundings did not coincide with days when pure sea breeze events were observed.

4.3 Proposed Indices

4.3.1 Modiﬁcation of traditional indices

As mentioned earlier traditional indices mostly involve meteorological parameters between 850 hPa and 500 hPa. Since the type of convection under investigation is those triggered by surface heating, the traditional indices are modiﬁed to include low boundary layer parameters, i.e. those below 850 hPa down to the surface. The following were tested:

37 4.3 Proposed Indices

1. Vertical Totals (VT ) are calculated as the temperature gradient between different layers as follows:

(VT )z1−z2 = Tz1 − Tz2 (4.1)

Here z1 and z2 are interchanged between the surface (sfc), 925 hPa, 850 hPa, 700 hPa and 500 hPa. Similarly, the Cross Totals CT are calculated for respective layers as follows:

(CT )z1−z2 = Td,z1 − Tz2 (4.2)

Finally the respective Total Totals TTz1−z2 are calculated as the sum of respective VT s and CT s

2. The traditional TT which is calculated based solely on level 850 hPa and 500 hPa is

modiﬁed, (TTm), whereby the temperature and dewpoint at the 850 hPa are replaced by the average temperatures and dew-point in the lower layers from surface (sfc) to 850

hPa. This modiﬁed TT is calculated between surface and 500 hPa (TTm500 ) and 700 hPa

(TTm700 ):

1 1 TT = (T + T + T ) + (T + T + T ) − 2T (4.3) m500 3 sfc 925 850 3 d,sfc d,925 d,850 500 1 1 TT = (T + T + T ) + (T + T + T ) − 2T (4.4) m700 3 sfc 925 850 3 d,sfc d,925 d,850 700

3. The K-Index is also modiﬁed and calculated for different layers and is given by :

KIsfc−500 = Tsfc − T500 + Td,sfc − (T700 + Td,700) (4.5)

KIsfc−850 = Tsfc − T850 + Td,sfc − (T700 + Td,700) (4.6)

KI925−500 = T925 − T500 + Td,925 − (T700 + Td,700) (4.7)

KI925−850 = T925 − T850 + Td,925 − (T700 + Td,700) (4.8)

4.3.2 Lapse-rate and moisture based indices

For a better representation of the moisture and the level at which it is more critical, the mixing ratios ((r)z1−zn ) are calculated in different layers as follows

n 1 X (r) = r (4.9) z1−z2 n z z=1

38 4.3 Proposed Indices

where z1 and z2 are the lower and upper levels in the layer and n is the number of levels in a particular layer.

The dry adiabatic lapse rate in these different layers is also considered and is simply the ratio of the VT and the height (4z) (m) separating these two layers.

VT Γ = (4.10) d 4z

However, since beyond a certain level the air becomes saturated the dry adiabatic lapse rate no longer holds but rather the pseudo-adiabatic lapse rate (Γp) must be considered and this is given by equation 4.11 below

Lvrv (1 + rv)(1 + RT ) Γp = g( 2 ) (4.11) Lvrv(+rv) Cpd + rvCpv + RT 2

The actual lapse rate between the layer surface to 500 hPa is therefore the sum of the dry adiabatic lapse rate between surface and 850 hPa, 850 hPa and 500 hPa minus the the pseudo adiabatic lapse rate at 850 hPa. This is referred to as the effective lapse rate (Γe) given as follows

Γe = Γdsfc−850 + Γd850−500 − Γp850 (4.12)

The extent and rate of of penetration of this moisture in the vertical is largely inﬂuenced by the temperature lapse rate. As such, it is worth considering the conjunction of the lapse rate and moisture as an index of convection, particularly for the maritime environment where moisture is most of the time abundant but heating may not be sufﬁcient.

4.3.3 Wind shear based indices

The impact of wind change in the vertical on the rainfall is analysed for different levels in terms of the directional, speed and wind vector shear separately. The absolute directional and speed shear is given by

ddz1−z2 = |ddz1 − ddz2 | (4.13)

ffz1−z2 = |ffz1 − ffz2 | (4.14) where dd and ff represents the wind direction and force respectively and the absolute value is considered.

39 4.4 Indices Thresholds and Evaluation

The shear vector (ShrV ec) is given by the difference of the wind vector w between layers. The wind vector in a particular layer is the resultant of the horizontal component(u) and vertical component(v) of the winds in each layer given by:

p 2 2 wz = (u + v ) (4.15) where  u = −ffsinθ, v = −ffcosθ : 0o ≤ θ ≤ 90o    u = −ffsinθ, v = ffcosθ : 90o < θ ≤ 180o o o  u = ffsinθ, v = ffcosθ : 180 < θ ≤ 270   u = ffsinθ, v = −ffcosθ : 270o < θ ≤ 360o where θ is the direction of the wind measured clockwise from north and wind is +ve in a direction away from origin. Then the shear vector between two layers is given by

ShrV ecz1−z2 = wz1 − wz2 (4.16)

4.4 Indices Thresholds and Evaluation

A straightforward method to evaluate the efﬁcacy of the indices is through correlations with the rainfall, where the hourly rainfall intensity is mostly considered. Another aim is to establish appropriate thresholds which might not be readily available from a correlation matrix. As such scatter plots of the rainfall against the different indices are plotted. These enabled the visualisation of the relationship between indices and different categories of the events which are shown in different colours. Ideally, for a well behaving index showing positive correlation with the rainfall, the severe events (shown in red) are expected to cluster on the top right corner while weaker events (shown in green) on the bottom left corner of the scatter plots. For an index negatively correlated the opposite is expected in terms of clustering position. Additionally a scatter plot will clearly show the range of an index for which weak, moderate (shown in blue) or heavy rainfall events could be expected and as such appropriate thresholds for speciﬁc categories could be determined.

Forecast Thresholds

The threshold of the different indices is determined from the scatter plots. However, since these thresholds are from 1100 UTC (1500 LT) soundings, some adjustments are necessary

40 4.5 Validation of Indices before they are used for the 2300 UTC (0300 LT)soundings because the temperature and humidity is usually higher in the afternoon than in the early morning. This intrinsic diurnal variations of the indices, due changes in the boundary layers, is in fact one of their major limitations. As such some adjustments must be made to the afternoon thresholds before it is used for the morning soundings, particularly for the modiﬁed indices which includes lower boundary layer temperature and humidity variables. The adjustment is based on the forecast of the expected afternoon temperature and dew point mainly in the lower layers, surface to 850 hPa at most, and here model based outputs and climatology of the location are of great use. Adjustment of the surface parameters is easily made using the synoptic observations but for the 850 hPa, model outputs can be used as support. Similar adjustments are also important and carried out to account for seasonal variations in the indices, Huntrieser et al. (1996); Sanchez et al. (2009).

From the climatology of the Vacoas synoptic station the difference between the maximum and the minimum temperature is about 7oC and this varies from month to month (http : //metservice.intnet.mu/climate − services). Given that the temperature at 2300 UTC is warmer by about 2oC than the minimum, which occurs at around 0300 UTC, an adjustment of the order of 5oC is made in the temperature. Similarly for the dew point a difference of about 3oC is observed at Vacoas. As such an adjustment (substraction) of this order is made to the thresholds of the indices determined from the scatter plots for use in the validation process where 2300 UTC sounding data are used. In fact one of the main objective of this study is actually to determine appropriate forecast thresholds to optimise the use of the morning radiosondes. As at now, meteorologists are still using the standard thresholds, irrespective of time of launch, for their inferences and this oftentimes lead to misses and false alarms.

4.5 Validation of Indices

The validation process includes those radiosondes launched at around 2300UTC during the summer months of year 2011-2014. The basis of the validation is simple. Since most of the indices’ values increase with increasing instability, so once the determined threshold is ex- ceeded, a certain correct forecast must be expected. For some indices which show decreasing value with increasing instability, a correct forecast is expected once the index is below the determined threshold. The dichotomous veriﬁcation scheme is used to validate the indices, i.e. assessing the outcomes of the forecast made using these indices. There exists a plethora

41 4.5 Validation of Indices of veriﬁcation statistics for validating the success of a forecast based on the ”Y es/No” forecast. For the purpose of this study the commonly used ”Percent of Correct forecast” (PC), ”Hit Rate”(HR), ”False Alarm Ratio”(F AR) and ”Critical Success Index”(CSI) will be used. However, with the exception of (PC), all these veriﬁcation formulae only evaluate the performance of the indices when the event has/has not occurred when it had been forecast, but do not cater for correctly forecast non-occurrences. Since in this study the forecast is based solely on using the instability indices, and as stipulated in Section 3.4 indices can lead to overforecast, a measure of correctly forecasting non-occurrences may be important. For that purpose a more rigorous statistic, compared to the PC, called the the ”Yule’s Index” is used (Jacovides and Yonetani, 1990). A dichotomous (Y es/No) forecast is summarised in a contingency table, Table 4.1, the elements of which are used to compute a large variety of categorical statistics to describe particular aspects of forecast performance.

Table 4.1: Contingency table of a dichotomous veriﬁcation scheme Observed Total Yes No Forecast Yes Hits (h) False Alarms (f) Forecast Yes No Misses (m) Correct Negatives (n) Forecast No Total Observed Yes Observed No Total

From Table 4.1, the different veriﬁcation statistics, expressed as percentage, can be written as follows:

h + n PC = 100( ) (4.17) T otal h HR = 100( ) (4.18) h + m f F AR = 100( ) (4.19) h + f h + f BIAS = 100( ) (4.20) h + m h CSI = 100( ) (4.21) h + m + f

The following is worth noting:

• The PC (0 to 100%), indicates the accuracy of the forecast and is the simplest and most intuitive statistics. However, it should be interpreted with care as it could be misleading since it is strongly inﬂuenced by the ”Correct Negatives”. In some events analysis,like the rare/severe weather, the ”correct negative” is the most common category.

42 4.5 Validation of Indices

• The HR (0 to 100%), also termed as ”Probability of Detection” (POD) in other literature, is sensitive to hits and ignores false alarms. It is very sensitive to the climatological frequency of the event and a good statistics for severe events. For example in Mauritius, rainfall during the month of February is more likely to be heavy, as climatologically this is the wettest month. However, it must be noted that the HR can be easily increased by issuing more ”yes” forecasts and this is likely to lead to a higher F AR. As such it must be used in conjunction with the F AR.

• The F AR (0 to 100%) ignores misses and is also very sensitive to the climatological frequency of the event. For example, in Mauritius, forecasting heavy rainfall event during the month of October is likely to yield more false alarms rather than hits as climatologically October is a dry month.

• The BIAS gives an indication of the tendency of the forecast scheme to underforecast (BIAS < 1) or overforecast (BIAS > 1) a particular event. It does not actually measure how well the forecast corresponds to the observations but rather only measures relative frequencies, i.e. frequency of forecast events to the frequency of observed events.

• The CSI (0 to 100%), also commonly known as the ”Threat Score”, assesses the fraction of observed and/or forecast events that were correctly predicted such that it is sensitive to hits while penalizing misses and false alarms. It can be considered as the accuracy when correct negatives are discarded. It is strongly inﬂuenced by the climatology of the events and a poor score is unavoidable for rare events as some of the hits may be purely by chance.

• Since the aim is to maximise HR and minimise F AR, the difference between HR−F AR can also be used as a quick indicator. If this difference is negative, i.e. F AR > HR, then the index can be considered as very poor. The higher the value of HR − F AR, the better is the index.

As stipulated earlier it might be worth considering the correct negatives in the present context and the Yule’s Index YI is used for that purpose, (Jacovides and Yonetani, 1990; Marinaki et al., 2006). As highlighted in Jacovides and Yonetani (1990), the YI can be further modiﬁed to give a linear correlation coefﬁcient between forecast and observed events. This is achieved by denoting ”occurrences” by +1 and ”non-occurrences” by -1. Then adding 1 to YI and dividing it by 2, yields a value called the ”Equivalent Percentage Success” (EPS), which can be expressed in percentage. For a perfect/(totally wrong forecast) YI and EPS take values

43 4.5 Validation of Indices

+1/(-1) and 100%/(0) respectively. These are given below:

(hn − fm) YI = 100( ) (4.22) p(h + n)(h + f)(f + n)(m + n) YI + 1 EPS = 100( ) (4.23) 2

Decision trees/schemes are devised where combinations of indices is made used and their scores computed. The approach is that to combine indices with a high HR but this is also likely to increase the F AR. In such cases indices with a low F AR could be used to reduce the latter. Care is also taken not to combine indices whose equations share common terms, an example being DIC and LI given the former is a modiﬁed version of the latter. The overall score of the decision scheme is as follows:

• If HgRr60 ≥ 20 mm is observed and all indices show a h then the overall score is a ”hit”.

• If HgRr60 ≥ 20 mm is observed and at least one index shows a m then the overall score is a ”miss”.

• If HgRr60 ≤ 20 mm is observed and all indices show a h then the overall score is a ”false alarm”.

• If HgRr60 ≤ 20 mm is observed and at least one index shows a n then the overall score is a ”correct negative”.

As a ﬁnal step a stepwise regression is run using the best indices identiﬁed in devising the decision tree. They are assesses based on their R2-value, which gives an indication of the amount of variance in the rainfall which could be explained by the indices. The higher the R2-value the more appropriate the index is expected to be. It must be noted that the regression equation is not meant to be used to calculate the amount of rainfall using the indices.

44 Chapter 5

Results and Discussions

5.1 Exploratory Analysis

A total of 64 events with convection triggered by local heating (pure sea breeze) were identi- ﬁed during summer months (November to April) of 2003 to 2009. The percentiles of highest rainfall amount (HgAcRr), highest hourly intensity (HgRr60) and duration (Drtn) are shown in Table 5.1. The box plots show rather symmetric for the rainfall data(Fig. 5.1(a), (b)) except for the duration which is left-skewed, i.e. the events tend to last slightly longer than the me- dian value of 2.5 hours as shown in Fig. 5.1(c). The distribution of rainfall events in the lower quartile, inter-quartile and upper quartile is the same in both the HgRr60 and HgAcRr with the exception of an outlier in the latter agreeing with the close correlation between them as shown by the scatter plot in Fig. 5.1(d). This indicates the possibility of using either of these two rainfall parameters in categorisation of the events.

Table 5.1: Percentiles of HgRr60, HgAcRr and Drtn for the period November to April 2003- 2009. Percentiles

Parameters Q10 Q25 Q50 Q75 Q90 Highest Hourly Rainfall (mmh−1 3 7.2 22.1 33.9 48.8 Maximum Total Rainfall (mm) 3.8 10 27.8 39.7 59.9 Duration (hours) 1.2 1.5 2.5 3.0 4.0

Over Mauritius, it has been observed that ﬂash ﬂoods occur mainly from high rainfall intensities, usually exceeding 20 mm in 30 minutes, rather than a high amount of rainfall spread over a longer time period. As such the events are rather categorised based on HgRr60 and this is used for further analysis.

45 5.1 Exploratory Analysis

(a) Highest hourly rainfall (b) Highest accumulated rainfall

Figure 5.1: Box plots of (a) HgRr60 (b) HgAcRr (c) Drtn and (d) relationship between HgRr60 and HgAcRr for the 64 rainfall events from 2003 to 2009.

As a ﬁrst guess two consecutive spells of 20 mm in 30 minutes or 40 mm in one hour can be categorised as a severe event, i.e. approximately the 85th percentile. But, given the low sample size available in this category (10 events), the events are categorised as follows:

1. severe events: highest hourly rain > 75th percentile (16 events),

2. moderate events: 25th < highest hourly rain ≤ 75th percentile (32 events),

3. weak events: highest hourly rain ≤ 25th percentile (16 events).

46 5.2 Evaluation of Traditional Indices

5.2 Evaluation of Traditional Indices

The correlation between all traditional indices and different rainfall parameters are shown in Table A.1. The overall correlations between the indices and HgRr60, as well as the other parameters, are quite low. The highest correlations include those with derived indices such as DCI, CAP E, LI and ShwI as well as with some basic meteorological parameters such as mean mixing ratio (r) and mean potential temperature (Θ) in the column of air. It is worth noting that the LI is included in the DCI and hence need not be considered separately. As expected the rainfall is negatively correlated with EL and positively correlated with r and Θ in the column. No higher correlations are observed using the indices calculated from virtual temperature, as suggested by Doswell and Schultz (2006).

The scatter plots of HgRr60 against the panoply of indices are shown in Fig. A.1. Some selected examples are shown in Fig. 5.2. The following observations can be made:

1. Traditional indices such as CAP E and P rpW tr hardly show any close relationship with

the HgRr60 with an uneven scattering of the different categories of events, i.e. no clus- terings are observed towards the high end of the plot (Fig. 5.2(a), (b)). P rpW tr only gives an indication of higher total rainfall with longer duration, but not necessarily a high intensity, Table A.1. This may sound obvious as for a certain amount of rainfall spread over a longer period of time a high hourly rate may not be expected. Hence, it is very difﬁcult to depict an appropriate threshold for these indices as an indication of heavy rainfall.

2. The KI and the DCI show the expected positive relationship with the HgRr60, whereby the heavy rainfall events are mostly clustered towards the higher values of the indices. Moreover, overlapping of the moderate and weak rainfall events within that range are inevitable. Nevertheless, these two indices provide optimum threshold for forecasting heavy rainfall and these are 35oC and 37 K for DCI and KI respectively.

5.3 Evaluation of Modiﬁed Indices

The correlations between the modiﬁed indices and the different rainfall parameters are shown in Table A.2. Overall the correlations remains rather low in spite of inclusion of low level parameters. Nevertheless, some modiﬁed indices, such as KI and TT , show a better relationship with HgRr60 or HgAcRr when compared to their traditional counterparts (Table 5.2).

47 5.3 Evaluation of Modiﬁed Indices

(a) (b)

Figure 5.2: Scatter plots showing relationship between HgRr60 and (a) CAP E (b) P rpW tr (c) KI (d) DCI. The uneven scattering of the different category of events with CAP E and P rpW tr is quite discernible.

Table 5.2: Comparison of the correlations of traditional and modiﬁed K and TT indices with

HgRr60, HgAcRr and Drtn. K-indices TT - indices

KI Ksfc−850 Ksfc−500 TTI TTsfc−700 TTsfc−500 T T m500

HgRr60 0.19 0.28 0.32 0.16 0.22 0.21 0.21 HgAcRr 0.22 0.33 0.37 0.17 0.2 0.23 0.25 Drtn 0.23 0.24 0.26 0.17 0.02 0.1 0.15

48 5.3 Evaluation of Modiﬁed Indices

(a) (b)

Figure 5.3: Scatter plots of HgRr60 and modiﬁed K indices showing only 3 overlapping weak o o events in Ksfc−850 ≥28 C and Ksfc−500 ≥50 C.

The scatter plots of the four modified KI are shown in Fig. 5.3. Ksfc−850 and Ksfc−500 with thresholds above approximately 28oC and 50oC respectively stand as good indices to filter out weak events. Hence, use of these two modified indices, with appropriate thresholds, is expected to give a better probability of detection of moderate to heavy rainfall. Remaining scatter plots of HgRr60 against the modified indices are shown in Fig. A.2.

49 5.4 Evaluation of Lapse-Rate and Moisture Based Derived Indices

5.4 Evaluation of Lapse-Rate and Moisture Based Derived Indices

Given that the local convection under consideration is triggered mainly by surface heating it is bound to be inﬂuenced by the lapse rates at different levels in the lower layer of the atmosphere. The traditional indices consider lapse rate in terms of temperature gradient, but most of them consider the layer 850 hPa and above. It is oftentimes observed that on days of severe convection a super-adiabatic lapse rate exists (Fig. 3.5). Thus, considering the temperatures and moisture only above 850 hPa partly omits the destabilising effect of such heating in the boundary layer. As such, it is plausible to investigate the effect of the lapse rate and the associated moisture in the layers below 850 hPa with the rainfall.

The correlations of these indices with the rainfall are shown in Table A.3. Unlike expected, the lapse rate in the lower layers of the atmosphere, i.e. between surface and 850 hPa do not yield good correlations. However, the mixing ratios computed in the various layers do perform well when compared to r as shown in Table 5.3.

Table 5.3: Comparison of the correlations of r and modiﬁed r with HgRr60, HgAcRr and Drtn.

rv rsfc−925 rsfc−850 rsfc−700 rsfc−500 (rΓd)sfc−700 (rΓd)sfc−500

HgRr60 0.28 0.37 0.38 0.37 0.35 0.33 0.38 HgAcRr 0.29 0.26 0.3 0.32 0.35 0.19 0.33 Drtn 0.23 0.24 0.22 0.18 0.13 0.24 0.2

The various scatter plots of HgRr60 against the lapse-rate moisture based indices are shown in Fig. A.3. Those of the mixing ratios are shown in Fig. 5.4 where some satisfactory clustering of the heavy rainfall events in the top right hand corner can be observed except for the persistent −1 overlapping of few weak events. But still beyond certain threshold, like 16 gkg for rsfc−850 , −1 −1 14 gkg for rsfc−700 and 12 gkg for rsfc−500 , most of the weak events are ﬁltered out (Fig.

5.4(b), (c), (d)). The conjunction of dry adiabatic lapse rate (Γd) and mixing ratios (r) do not improve the correlation by much. For the layer between the surface and 700 hPa, (rΓd)sfc−700 results in a decrease of about 5% in the correlation. However, the combination of lapse rate and moisture between surface and 500 hPa ((rΓd)sfc−500 ) increases the correlation by about 3% and is a potential index to ﬁlter out most weak events for threshold ≥ 0.07 (Fig.5.5(b)).

50 5.5 Evaluation of the Wind Shear Indices

(a) (b)

Figure 5.4: Scatter plot of HgRr60 and mixing ratios calculated between surface and (a) 925 hPa (b) 850 hPa (c) 700 hPa (d) 500 hPa. Note the absence of weak events beyond certain threshold in rsfc−850 ≥ 16, rsfc−700 ≥ 14 and rsfc−500 ≥ 12.

5.5 Evaluation of the Wind Shear Indices

It is now well established that the vertical shear of the ambient horizontal wind can play a vital role in the organisation of convection from single cell to super cell thunderstorm (Emanuel, 1994). The scatter plots of the different shears calculated for the layer 850-700 hPa and 700-500 hPa are shown in Fig. 5.6. Most of the rainfall, all categories inclusive, are found to be clustered towards the lower end of shears. Nevertheless, the directional shear,

51 5.5 Evaluation of the Wind Shear Indices

o o dd850−700 ≥100 and dd850−500 ≥120 show some possibility of ﬁltering weak events, though the rate of misses is likely to be high. But against all expectations, the speed shear as well as the shear vector is negatively correlated with HgRr60, an outcome that cannot be explained at this stage of analysis (Table 5.4).

(a) (b)

Figure 5.5: Scatter plots of rainfall event categories and conjunction between mixing ratios and lapse rate in different layers showing most weak events conﬁned in (rΓd)sfc−500 < 0.07.

Table 5.4: Correlation of HgRr60, HgAcRr and Drtn with directional shear, speed shear and shear vector for different layers. Directional Shear Speed Shear Shear Vector

Layer HgRr60 HgAcRr Drtn HgRr60 HgAcRr Drtn HgRr60 HgAcRr Drtn 850 − 700 0.25 0.28 0.35 -0.10 -0.12 -0.17 -0.14 -0.18 -0.21 850 − 500 0.34 0.33 0.07 0.01 0.00 -0.06 -0.19 0.02 -0.04 850 − 300 0.25 0.22 0.01 -0.16 -0.19 -0.13 -0.21 -0.20 -0.23 700 − 500 0.21 0.22 0.00 -0.05 -0.06 -0.03 -0.23 -0.10 -0.15 500 − 300 0.19 0.18 -0.01 -0.26 -0.27 -0.18 -0.20 -0.27 -0.28

52 5.5 Evaluation of the Wind Shear Indices

(a) (b)

(e) (f)

Figure 5.6: Scatter plot showing an ambiguous relationship between HgRr60 and directional and speed shear and shear vector calculated for the layer 850-500 hPa and 700-500 hPa.

53 5.6 Validation of Indices

The whole set of correlations between HgRr60 and the directional shear, speed shear and shear vector are shown in Table A.4, Table A.5 and Table A.6 respectively and the scatter plots for the layer 850-500 hPa and 500-250 hPa in Fig.A.4.

5.6 Validation of Indices

The validation data includes those radiosondes launched at around 2300 UTC during the summer months of year 2011-2014 and 48 events with pure sea breeze were identiﬁed. The magnitude of the highest hourly rainfall intensities (HgRr60) for the 48 events are shown in Fig. 5.7.

Figure 5.7: Hourly rainfall intensities of 48 selected cross validation events.

−1 Most of the HgRr60 is less than 15 mmh and only 7 events have rainfall intensities above 30 mmh−1. The initial aim of this study was to evaluate the performance of the indices in forecasting heavy rainfall events, i.e. with hourly intensities of at least 33.9 mmh−1 as per Table 5.1, but only 5 such events are available in the cross validation sample. The scatter plots also show lots of overlapping between moderate and severe events and focusing only on severe events are likely to result in a lower HR. As such it may be justifiable to merge part of the moderate rainfall intensities with the heavy ones. Considering the local context of the island, forecast for rainfall intensities of at least 20 mmh−1 is justifiable since such moderate intensities can equally disturb the socio-economic activities, though it might not necessarily lead to life threatening flash floods. Hence, rainfall intensity of ≥ 20 mmh−1 is considered for the validation process. In operational meteorology, issuing a forecast of moderate to heavy rainfall with a higher HR is certainly more useful than a specific heavy rainfall forecast with lower HR, even though the F AR may be slightly higher in the former.

54 5.6 Validation of Indices

5.6.1 Performance of individual indices

The scores for several traditional instability indices, with different thresholds, are summarised in Table C.1. Some selected indices with associated thresholds are shown in Table 5.5 as examples. In line with other studies (Marinaki et al., 2006), different thresholds of a particular index gives different scores. As such the performance of any index cannot be inferred from only one veriﬁcation statistic, but rather it must be looked upon in conjunctions with other veriﬁcation statistics. For the purpose of this study maximising the HR with a minimising F AR as well as targeting a high CSI is the main focus and this can be achieved by choosing the most appropriate index and also its optimum threshold. For example, from Table 5.5, a P rpW tr ≥ 35, KI ≥ 32 and DCI ≥ 28 could be the best indices as the difference between the HR and F AR is the highest and even the YI is high showing a good correlation between the forecast and observed events.

CAP E is commonly used in Mauritius to forecast thundery showers but it is found to have a rather low HR and a BIAS indicating a tendency to underestimate the rainfall. Hence, lots of events are likely to be missed if the forecast rely solely on CAP E and this is a hazard in itself since when it comes to severe weather and safety of life, false alarms are more desirable than misses. Similar results have been reported by Monteverdi et al. (2003) who found that CAP E was unable to discriminate between tornadic and non-tornadic thunderstorms and Groenemeijer and Delden (2006) reported that CAP E was unable to distinguish between en- vironments supportive of tornadoes or simply thunderstorms. Without sanctioning the use of this commonly-used index worldwide and in Mauritius, it is suggested to be used in combination with other indices rather than in isolation.

The verification statistics for the different modified instability indices and lapse rate-moisture based indices, with different thresholds, are summarised in Table C.2. Some of the selected modified indices are shown in Table 5.6.

55 5.6 Validation of Indices

Table 5.5: Scores of selected traditional indices in forecasting rainfall intensity≥ 20mmh−1. Indices Thresholds HR F AR CSI HR − F AR PC YI EPS BIAS CAP E CAP E ≥ 800 50.00 17.86 40.00 32.14 68.75 0.34 67.09 0.75 CAP E ≥ 1200 15.00 7.14 13.64 7.86 60.42 0.13 56.34 0.25 TTI TTI ≥ 40 90.00 67.86 46.15 22.14 56.25 0.26 62.99 1.85 TTI ≥ 42 75.00 39.29 48.39 35.71 66.67 0.35 67.67 1.30 P rpW tr P rpW tr ≥ 35 85.00 42.86 53.13 42.14 68.75 0.42 71.24 1.45 P rpW tr ≥ 40 50.00 28.57 35.71 21.43 62.50 0.22 60.91 0.90 KI KI ≥ 28 70.00 42.86 43.75 27.14 62.50 0.27 63.43 1.30 KI ≥ 32 57.14 22.22 44.44 34.92 68.75 0.36 67.89 0.86 DCI DCI ≥ 28 90.00 53.57 51.43 36.43 64.58 0.39 69.37 1.65 DCI ≥ 30 75.00 39.29 48.39 35.71 66.67 0.35 67.67 1.30 r r ≥ 14 75.00 53.57 42.86 21.43 58.33 0.22 60.91 1.50 r ≥ 15 65.00 35.71 43.33 29.29 64.58 0.29 64.45 1.15

Table 5.6: Scores of selected modiﬁed indices and lapse rate-moisture indices in forecasting rainfall intensity of ≥ 20 mmh−1. Modiﬁed Indices HR F AR CSI HR − F AR PC YI EPS BIAS

Ksfc−850 ≥ 18 70.00 35.71 46.67 34.29 66.67 0.34 66.90 1.20

Ksfc−500 ≥ 42 65.00 35.71 43.33 29.29 64.58 0.29 64.45 1.15

K925−850 ≥ 16 70.00 32.14 48.28 37.86 68.75 0.37 68.68 1.15

K925−500 ≥ 36 80.95 44.44 51.52 36.51 66.67 0.37 68.52 1.38

rsfc−850 ≥ 12 95.00 75.00 46.34 20.00 54.17 0.26 63.23 2.00

rsfc−700 ≥ 11 90.00 57.14 50.00 32.86 62.50 0.36 67.82 1.70

rsfc−500 ≥ 10 65.00 35.71 43.33 29.29 64.58 0.29 64.45 1.15

rΓdsfc−700 ≥ 0.05 95.00 60.71 51.35 34.29 62.50 0.39 69.52 1.80

dd850−500 ≥ 120 36.84 51.72 20.59 -14.88 43.75 -0.15 42.70 1.16

Slightly better performances are observed from some of the modiﬁed indices. For instance, for a similar HR of 70%, Ksfc−850 and K925−850 yield a lower F AR (Table 5.6) compared to its traditional counterpart KI (Table 5.5). Similarly, compared to r, the rsfc−700 gives a much higher HR than the F AR where the difference (HR − F AR) > 32% whilst in the former this difference is only about 22% for a similar F AR. This better performance from mixing ratios evaluated in the low levels show the importance of low level moisture compared to that found in the mid-level (Korologou et al., 2014). Low level moisture increases instability through the provision of more latent heat to the lower atmosphere. While high moisture content in the mid-levels may decrease the instability since moist air can hinder the evaporation of precipitation at or beneath cloud base. Such evaporation, usually present with dry air in

56 5.6 Validation of Indices the mid-level, leads to the cooling of the air at this level increasing the buoyancy. In some cases, depending on the thresholds, it is not unusual to see the performance of both the mod- iﬁed indices and that of their traditional counterparts coinciding, for example rsfc−500 ≥ 10 and r ≥ 15.

5.6.2 Performance of forecast schemes

In the process of optimising a particular score, through the change of thresholds, it is observed that other scores tend to get worse, for example the F AR or the BIAS increasing with increase in the HR or CSI. This suggests that an optimum forecast may be difﬁcult to achieve through the use of only one index (Blanchard, 1998; Schultz, 1989). It is therefore proposed to use a blend of different indices in improving the performance and as such forecasting schemes/trees, thereon referred as Scheme, are devised. It is proposed to combine indices, with appropriate thresholds, that have high HR at the top of the decision tree as shown by SchemeI (Fig. 5.8(a)). This increases the probability of identifying most of the impending rainfall events with intensity≥ 20 mmh−1, but the F AR is also bound to be higher. One way to bring down the F AR is to apply an index with a low F AR at the bottom of the tree (Fig. 5.8(b)). As such in the schemas shown in Fig. 5.8 a decrease of the F AR by about 7% is achieved simply by replacing the KI ≥ 28 and DCI ≥ 32 in SchemeI by a DCI ≥ 30 and a Θ ≥ 299.5 to yield SchemeII. The DCI ≥ 30 has a higher HR than DCI ≥ 32 and any increase in the F AR is removed by the Θ ≥ 299.5. The better performance from SchemeII is also shown by the gain in the YI which reﬂects a better correlation between the forecast and the observed event.

Having a decision tree with a lot of indices does not imply a better forecast. Some indices can be actually redundant and their removal not only simpliﬁes the scheme but also improves the results. For instance removing the TTI from SchemeII increases the HR by about 5% but the F AR also increases by 7% while the gain in CSI is negligible as shown by SchemeIII (Fig. 5.9(a)). SchemeIII may not the best decision tree in terms of performance because the increase in F AR is higher than the gain in HR, but it may be more acceptable as it constitutes a lower number of indices. A far better and simpler decision tree is obtained by removing the TTI and KI from the SchemeI to yield SchemeIV as shown in Fig. 5.9(b). SchemeIV shows an all round improvement in the scores, for instance a gain of 20% in the HR is only associated with an increase of 10.7% in the F AR and the increase in CSI is over 9%.

57 5.6 Validation of Indices

ShwI ≤ 3 ShwI ≤ 3 HR = 55 % HR = 55 % FAR = 21.4 % FAR = 14.3 % CSI = 42.3 % CSI = 45.8 % PC = 68.8 % PC = 72.9% TTI ≥ 40 YI = 0.35 TTI ≥ 40 YI = 0.43 EPS = 67.3 % EPS = 71.7 % BIAS = 0.85 BIAS = 0.75

PrpWtr ≥ 35 PrpWtr ≥ 35

KI ≥ 28 DCI ≥ 30

DCI ≥ 32 Θ ≥ 299.5

(a) SchemeI (b) SchemeII

Figure 5.8: Schematic using traditional indices to forecast rainfall of ≥ 20 mmh−1 over Mau- ritius. A better CSI and lower F AR is achieved by applying the Θ ≥ 299.5.

Note: In the decision tree the arrows shows the steps to be undertaken. When the condition is satisfied, the next step is verified (arrows on the right). When the condition is not satisfied the occurrence of rainfall intensity of ≥ 20 mmh−1 is not envisaged (blank arrow on the left).

ShwI ≤ 3 ShwI ≤ 3 HR = 60 % HR = 75 % FAR = 21.4 % FAR = 32.1 % CSI = 46.2 % CSI = 51.7 % PC = 70.8% PC = 70.8 % PrpWtr ≥ 35 YI = 0.39 PrpWtr ≥ 35 YI = 0.42 EPS = 69.6 % EPS = 71.1 % BIAS = 0.90 BIAS = 1.2

DCI ≥ 30 DCI ≥ 32

Θ ≥ 299.5

(a) SchemeIII (b) SchemeIV

Figure 5.9: Schemes with less complexity and better score using traditional indices.

Similarly, using the modiﬁed indices, forecasting schemes are devised as shown in Fig. 5.10. When compared to the SchemeIV , SchemeV shown in Fig. 5.10(a) is better in all aspects.

58 5.6 Validation of Indices

There is a gain in HR by 5% while the F AR increases only by 3.6%. This F AR can be brought down to 32% by applying a low F AR index such as rΓdsfc−700 down the tree to yield SchemeV I (Fig. 5.10(b)). But adding complexity for a reduction of only about 3.6% in F AR may defeat the purpose in an operational environment.

rsfc-850 ≥ 12 rsfc-850 ≥ 12 HR = 80 % HR = 80 % FAR = 35.7 % FAR = 32.1 % CSI = 53.3 % CSI = 55.1 % PC = 70.8 % PC = 72.9% rsfc-500 ≥ 9 YI = 0.44 rsfc-500 ≥ 9 YI = 0.47 EPS = 71.9 % EPS = 73.6 % BIAS = 1.3 BIAS = 1.25

K925-850 ≥ 13 K925-850 ≥ 13

K925-500 ≥ 36 K925-500 ≥ 36

rΓsfc-700 ≥ 0.05

(a) SchemeV (b) SchemeV I

Figure 5.10: Schemes to forecast rainfall of ≥ 20 mmh−1 using modiﬁed indices .

r ≥ 9 r ≥ 9 sfc-500 HR = 90 % sfc-500 FAR = 39.3 % HR = 65 % CSI = 58.1 % FAR = 3.6 % PC = 72.9 % CSI = 61.9 % rΓsfc-700 ≥ 0.05 YI = 0.51 rΓsfc-700 ≥ 0.05 PC = 83.3 % EPS = 75.6 % YI = 0.67 BIAS = 1.45 EPS = 83.3 % BIAS = 0.70

DCI ≥ 28 DCI ≥ 28

Flow500 ≤ 5855

(a) SchemeV II (b) SchemeV III

Figure 5.11: Schemes showing combined traditional indices, modiﬁed indices and 500 hPa variables scores in forecasting rainfall of ≥ 20 mmh−1 over Mauritius.

59 5.6 Validation of Indices

Given that better results can be obtained from selected modiﬁed or traditional indices, a better decision tree may be expected through a combination of these two. This is actually achieved by the combination of DCI with SchemeV I. In SchemeV I the two modiﬁed indices K925−850 and K925−500 are removed and a DCI ≥ 28 is applied at the bottom. In so doing the rsfc−850 ≥ 12 becomes redundant and is removed and this is shown by SchemeV II in Fig. 5.11(a). SchemeV II and SchemeIV are similar in simplicity but the former gives much better scores with a gain in of 15% in the HR and 6.4% in CSI while the F AR increases only by 7.2%. The correlation between forecast and observed event also increases by 9% (YI = 0.51).

The ﬂow curvature (F low500) and the temperature at the 500 hPa (tt500) give rather low CSI and HR and high F AR as shown in Table 5.7. Furthermore, the combination of the F low500 to SchemeV II lead to poorer scores with the HR and CSI dropping to 52.6% and 43.4% respectively but this is also accompanied by a drop of 13.8% in the F AR. But missing 9 moderate to heavy events out of 19 is not desirable when it comes to safety of the people. Contrary to the

ﬂow and temperature at 500 hPa, the geopotential height value Z500 is a better indicator for

Mauritius (Table 5.7). Combination of the Z500 ≤ 5855 m to the decision tree leads to a drop in the F AR by over 35% though the HR also drop by 25%, Fig. 5.11(b). But with a HR − F AR of over 61%, a CSI of almost 62% and a YI of 0.67, the contribution of Z500 has not only superseded the ﬂow curvature or temperature at 500 hPa but also yielded the best overall score when all the Schemes presented are considered. As such the 500hPa can be tagged as one of the best variable to remove false alarms and must be considered in forecasting of the moderate to severe events.

Table 5.7: Scores of individual 500 hPa variables in forecasting rainfall intensity of ≥20 mmh−1. HR FAR HR-FAR CSI PC YI EPS BIAS

Z500 ≤ 5860 70.00 46.43 23.57 42.42 60.42 0.23 61.71 1.35

Z500 ≤ 5855 70.00 32.14 37.86 48.28 68.75 0.37 68.68 1.15

Z500 ≤ 5850 65.00 25.00 40.00 48.15 70.83 0.40 70.00 1.00

tt500 ≤ 0 50.00 39.29 10.71 32.26 56.25 0.11 55.32 1.05

tt500 ≤ -0.5 50.00 39.29 10.71 32.26 56.25 0.11 55.32 1.05

tt500 ≤ -1 40.00 17.86 22.14 32.00 64.58 0.25 62.28 0.65

F low500 50.00 25.00 25.00 37.04 64.58 0.26 62.89 0.85

The stepwise regression performed using the traditional indices shows that the variance in

60 5.6 Validation of Indices the hourly rainfall intensity was better explained by the KI (15.5%) followed by the P rpW tr

(13.8%) and DCI (13.2%). Similar regression with the modiﬁed indices shows the rΓdsfc−700 to explain 22.3% of the variance in the hourly rainfall, followed by K925−500 (19.2%) and K925−850

(16.3%). This better performance of rΓdsfc−700 conﬁrms the importance of the inclusion of low level moisture coupled with the respective lapse rate.

The weak performance of the commonly used indices like CAP E and TTI in discriminating between heavy and weak rainfall over Mauritius by no means imply that they are poor indices. It simply means that they cannot be used for every purpose as these two indices are mostly used for thunderstorm prediction. This affirms the fact that, within the plethora of indices, some are meant for specific detection of a particular characteristic of convection (Huntrieser et al., 1996; Lopez et al., 2001; Sanchez et al., 2009). For example, Sanchez et al. (2009) found the K-Index to be useful in identifying air masses conducive for thunderstorm activity but not to ascertain the occurrence of thunderstorm. Similarly, Huntrieser et al. (1996) found the ShwI to be a better indicator of a thunderstorm day while a modified version of CAP E was able to discriminate between spatial extent of the thunderstorm. Furthermore, Lopez et al. (2001) showed that CAP E is able to discriminate between thunderstorm with and without hail. Similarly, in Mauritius it is important to identify indices which can discriminate between presence of instability and occurrence of heavy rainfall, a study not done so far. The results so far shows that the KI and DCI can be used to evaluate the stability of the atmosphere while the P rpW tr and rΓdsfc−700 to assert the occurrence of moderate to heavy rainfall. Similar studies include that of Monteverdi et al. (2003) who found CAP E to be unable in discriminating between tornadic and non-tornadic thunderstorm while (Lopez et al., 2001) found it to be of great help in distinguishing between thunderstorm bearing hail and those that does not. It is very likely that if the present study over Mauritius considered the occurrence/non-occurrence of thunderstorms, CAP E and TTI would have been good indicators. Flow curvature at 500hPa has been successfully used by Pickup (1982) and this parameter has been used to improve effectiveness of other indices Jacovides and Yonetani (1990). Such results are not obtained for Mauritius where either as a stand alone index or in combination with other indices, the cyclonic/anticyclonic flow at 500 hPa does not lead to satisfactory scores. It is worth pointing out that, to achieve better scores with the inclusion of the F low500, Jacovides and Yonetani (1990) had to alter thresholds of other indices and select less restraining ones, showing that the use of this parameter is not straightforward. Instead, for Mauritius, the geopotential height of the 500hPa emerge as a better parameter, particularly

61 5.6 Validation of Indices useful in avoiding false alarms.

Given the range of indices available and their range of suitable thresholds a panoply of decision schemes can be devised, one better than the others, either in terms of HR, F AR or CSI or other veriﬁcation statistics. It is important to adhere to the same statistics for all the indices or combination of indices irrespective of their successes or failures. It will be purely irrational to hide failures of supposedly better indices or their combinations behind an armour of sta- tistical inferences. Rather, it must be ascertained that any index or combination of indices used have a meteorological meaning behind it (Doswell, 1996). For instance, SchemeV II highlights the importance of a deep level of moisture else a moist mid-level overlaying a dry low level may lead to more stability. Any moisture available in the low level need sufﬁcient heating to move it vertically up and this is determined by the conjunction of lapse rate and mixing ratio between surface and 700 hPa. To continuously rise, in the absence of other forcing except heating, a parcel must at all times be warmer than its surroundings and this is catered for by the DCI. Furthermore, SchemeV II add the importance of rising or sinking air at the mid level, for instance a high Z500, which is usually associated with sinking air from upper troposphere, is likely to prevent deep cloud formation.

This study has brought forward some indices (traditional or modified) as well as schemes in an attempt to better the forecasts of moderate to heavy rainfall. However indices remain as mathematical artefacts and using them uncritically is likely to lead unexpected failures as exemplified in Section 3.4. There are so many unconventional processes in the atmosphere which are difficult to understand and inferred only from indices. Better clues can be obtained from a thorough analysis of the whole sounding profile where the complexity of the atmosphere is better illustrated, Doswell (1996), as shown in Fig. 3.5, Fig. 3.6 and Fig. 3.8.

62 Chapter 6

Conclusions and Recommendations for Future Works

Literature reviews show that no index is better that the others or works equally well in different places as their performances vary with locations, seasons, weather types and prevailing synoptic situations. Even for a particular region not all indices perform equally well. The performance are influenced by various factors such as time of year (months or seasons) and also the weather types. Such factors have also been found to influence the optimum thresholds of a particular index making it an important criteria that must be considered. The various studies also converge towards the conclusions that sounding data and associated indices are only able to give an indication of two ingredients of convection, namely instability of the atmosphere and the extent of the moist low level layers but not the triggering mechanism which is the third ingredient of convection. In most cases only one index does not suffice to give a good forecast and combinations several indices must be considered or even some model outputs may be considered in conjunction.

A thorough study of the local convection over Mauritius shows that in some cases indices may be misleading. The impact of synoptic scale weather systems on enhancing and dampening of local convection has also been illustrated. It has also been shown that, even the sea breeze phenomenon is a low level circulation, mid-level circulation, particularly at 500 hPa can impact the intensity of the event. The importance of the low level wind strength in determining the spatial distribution of the convective clouds has also been scrutinised.

Similar to other regions, it has been shown that, for Mauritius also, not all the traditional

63 indices might be a good indicator of different categories of rainfall events. For instance, compared to TTI, the P rpW tr is able to give a better indication of the impending rainfall. The

P rpW tr is mainly correlated with HgAcRr while the correlation with HgRr60 is is only 0.19. A simpler index, such as r, is able to capture both these two parameters giving a correlation of 0.28 with HgRr60. Of all the traditional indices considered, the DCI has been shown to be the most promising one. Modification of the existing indices, to include temperature and moisture parameters below 850 hPa, leads to better results particularly the modified K-index and r. For instance, the modified mixing ratios show correlations higher by 10% with HgRr60 compared to the mean mixing ratio over the whole column showing the importance of low level moisture in driving the convection. A much unexpected result is the low correlation between rainfall and the lapse rate below 850 hPa.

Results show that CAP E alone is likely to lead to lots of misses with a HR of only 50% associated with a threshold of as low as 800 JKg−1. The TTI alone gives a high HR reaching 90% but is tied to a high F AR reaching over 67.8% and when compared to the DCI, a similar HR is associated with a F AR which is 20% lower. Better results/scores are achieved through combination of the indices, but blending lots of indices does not necessarily leads to better scores. As an example, using SchemeV III a CSI of 58.1% is achieved, but the indices namely rΓsfc−500 , rΓdsfc−700 , DCI and Z500, when used alone, have CSI of 47.7%, 51.6%, 51.4% and 48.2% respectively. This shows that better result could be achieved from simpler decision schemes as long as the scheme is able to capture the underlying meteorological processes. A pertinent result of this study is the better performances from decision schemes involving modiﬁed indices with further improvements following their combination with traditional indices. The 500 hPa geopotential height turn out to be a good index to remove false alarms. So far, the ﬂow curvature at 500 hPa is of little use compared to what has been found in other studies (Jacovides and Yonetani, 1990; Pickup, 1982).

The better performance from DCI and modiﬁed K and r show them as potentially better indices to forecast moderate to heavy rainfall in Mauritius. Optimum thresholds for the DCI is around 30oC and 35oC for the morning and afternoon soundings respectively while that −1 −1 for the KI is 32 K and 37 K respectively. A rsfc−500 ≥ 9 gkg and rsfc−500 ≥ 12 gkg are optimum thresholds for the morning and afternoon soundings respectively. Combining these indices into a simple forecast scheme is most likely to lead to even better results.

64 As a ﬁnal word, it is worth pointing out that forecasting is the job of an operational meteorologist and requires lots of experience and knowledge about the environment. It would be a mistake to expect any index to replace this expertise. As such indices must not be relied upon as a substitute for meteorologist but rather used as a complementary tool. As stipulated by Doswell (1996) ”the day a perfect index for a particular weather is found, i.e. giving no misses and no false alarms, forecasters of such weather phenomenon will be out of a job”.

Recommendations for Future Works This is a very ﬁrst study that has been undertaken to relate instability/stability indices and heavy rainfall for a maritime environment in which Mauritius is located. The results presented here cannot be taken for face value but, with the availability of more data and better time factor, the analysis can be further improved with more rigorous testing and the following can constitute follow up works:

1. A more rigorous check of the daily rainfall with other available manned stations to ascertain that no modearte to heavy rainfall have been missed. This will deﬁnitely have an impact on the event categorisation and its correlation with the several indices.

2. Use the highest accumulated rainfall amount as an alternative criteria to categorise the events. This will provide an opportunity to use rainfall data from manned station and thus events prior to the year 2003. A larger data set will certainly improve the analysis and cross validation. For example, radiosonde launch at the same time, i.e 2300 UTC or 1100 UTC, could be used for both analysis and validation process. This will allow comparisons of the behaviour of the indices in the early morning and in the afternoon.

3. This study has focussed only on local convection , a typical summer type weather. A similar study could be done to include other events during summer and also for winter weather systems. This will enable establishing the monthly and seasonal performance of these indices.

4. Against all expectations, a negative correlation between the speed shear and shear vector, between the low level and mid-level, is observed. This result cannot be explained at this stage and call for further in-depth studies. For instance, an in-depth analysis might consider the impact of veering and backing of the winds with height instead of considering only the absolute value of the directional shear.

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Appendices

i Appendix A

Correlation Between Rainfall Events and Indices

A.1 Traditional indices

Table A.1: Correlation between traditional indices and rainfall for all the events. HgRr60 HgAcRr Drtn AvgRr60 HgRr30 HgRr6 ShwI -0.22 -0.24 -0.25 -0.10 -0.24 -0.28 LI -0.23 -0.22 -0.15 -0.16 -0.23 -0.35 LIVT -0.24 -0.23 -0.14 -0.18 -0.24 -0.35 SW EAT 0.16 0.20 0.24 -0.02 0.18 0.21 KI 0.19 0.22 0.23 0.01 0.20 0.19 CT 0.14 0.16 0.20 0.03 0.16 0.18 VT 0.16 0.16 0.11 0.14 0.16 0.23 TTI 0.16 0.17 0.17 0.09 0.17 0.22 CAP E 0.26 0.25 0.22 0.18 0.27 0.37 CAP EVT 0.27 0.25 0.21 0.19 0.27 0.38 CIN 0.06 0.07 -0.05 0.03 0.03 0.04 CINVT 0.07 0.05 -0.09 0.07 0.07 0.10 EL -0.37 -0.39 -0.23 -0.34 -0.40 -0.47 ELVT -0.28 -0.24 -0.23 -0.18 -0.32 -0.38 LF C 0.16 0.15 -0.04 0.11 0.14 0.14 LF CVT 0.13 0.12 -0.04 0.12 0.15 0.18 BRN 0.12 0.10 0.08 0.06 0.11 0.17 BRNVT 0.09 0.07 0.03 0.05 0.08 0.15 LCLtt 0.26 0.26 0.21 0.12 0.30 0.39 LCLpp 0.04 0.04 0.09 -0.08 0.12 0.13 Θ 0.27 0.28 0.14 0.26 0.23 0.33 r 0.28 0.29 0.23 0.15 0.31 0.42 THICK500−100 0.00 0.04 0.11 -0.10 0.00 0.04 P rpW tr 0.19 0.24 0.35 0.01 0.25 0.29 DCI 0.39 0.42 0.30 0.28 0.40 0.51

* subscript VT show indices which have been calculated using virtual temperature.

ii A.1 Traditional indices

(a) LF C (b) EL (c) CIN

(d) ShwI (e) LI (f) TTI

(g) Θ (h) LCLtt (i) LCLpp

(j) Ko (k) CII (l) PII

Figure A.1: Scatter plots HgRr60 against traditional indices. The uneven scattering of the different category of events with TTI, Ko, PII, CII and LCLpp is quite discernible

iii A.2 Modiﬁed indices

A.2 Modiﬁed indices

Table A.2: Correlation between modiﬁed indices and rainfall for all events HgRr60 HgAcRr Drtn AvgRr60 HgRr30 HgRr6 VTsfc−850 -0.04 -0.05 -0.11 0.07 -0.08 -0.15 CTsfc−850 0.17 0.16 0.07 0.13 0.20 0.22 TTsfc−850 0.06 0.04 -0.06 0.13 0.04 0.00 VTsfc−700 0.13 0.10 -0.04 0.18 0.09 0.03 CTsfc−700 0.28 0.27 0.09 0.23 0.30 0.30 TTsfc−700 0.22 0.20 0.02 0.23 0.21 0.17 VTsfc−500 0.13 0.14 0.03 0.20 0.07 0.09 CTsfc−500 0.25 0.28 0.16 0.23 0.25 0.33 TTsfc−500 0.21 0.23 0.10 0.24 0.17 0.23 VT925−850 -0.08 -0.11 -0.16 0.02 -0.15 -0.09 CT925−850 0.03 0.05 0.05 -0.03 0.07 0.12 TT925−850 -0.01 -0.01 -0.03 -0.01 0.00 0.06 VT925−700 0.19 0.16 -0.02 0.20 0.15 0.16 CT925−700 0.18 0.18 0.07 0.11 0.21 0.22 TT925−700 0.21 0.19 0.04 0.16 0.20 0.21 VT925−500 0.15 0.17 0.07 0.19 0.10 0.20 CT925−500 0.17 0.21 0.14 0.13 0.18 0.27 TT925−500 0.18 0.21 0.12 0.17 0.16 0.26 Ksfc−500 0.32 0.37 0.26 0.18 0.29 0.30 K925−500 0.26 0.32 0.24 0.12 0.25 0.28 Ksfc−850 0.28 0.33 0.24 0.14 0.26 0.25 K925−850 0.23 0.28 0.22 0.08 0.22 0.23 T T m500 0.21 0.25 0.15 0.20 0.19 0.27 T T m700 0.16 0.14 0.03 0.11 0.15 0.11

iv A.2 Modiﬁed indices

(a) CTsfc−850 (b) CTsfc−700 (c) CTsfc−500

(d) VTsfc−850 (e) VTsfc−700 (f) VTsfc−500

(g) TTsfc−850 (h) TTsfc−700 (i) TTsfc−500

(j) T T msfc−700 (k) T T msfc−500

Figure A.2: Scatter plots of HgRr60 against modiﬁed indices. Most of the plots show uneven scattering of the different category of events with the indices v A.3 Lapse-rate and moisture indices

A.3 Lapse-rate and moisture indices

Table A.3: Correlation between rainfall and lapse rate and moisture based derived indices for all events Indices HgRr60 HgAcRr Drtn AvgRr60 HgRr30 HgRr6

Γdsfc−925 0.01 -0.04 0.08 0.02 0.01 -0.08

Γdsfc−850 -0.05 -0.11 0.08 -0.03 -0.07 -0.13

Γdsfc−700 0.10 -0.05 0.17 0.13 0.09 0.04

Γdsfc−500 0.13 0.01 0.20 0.12 0.07 0.08

Γd925−850 -0.13 -0.17 0.01 -0.09 -0.16 -0.11

Γd925−700 0.14 -0.03 0.18 0.18 0.14 0.14

Γd925−500 0.15 0.05 0.17 0.13 0.08 0.17

Γd850−700 0.21 0.05 0.18 0.22 0.22 0.20

Γd850−500 0.20 0.12 0.17 0.17 0.14 0.22

Γd700−500 0.02 0.05 0.01 -0.01 -0.03 0.04

Γp850 0.13 0.02 0.19 0.15 0.12 0.21

Γesfc−700 0.01 -0.08 0.13 0.02 -0.03 -0.07

Γesfc−500 0.07 -0.07 0.16 0.09 0.06 0.00

rsfc−925 0.37 0.26 0.24 0.36 0.39 0.50

rsfc−850 0.38 0.30 0.22 0.35 0.39 0.48

rsfc−700 0.37 0.32 0.18 0.33 0.37 0.42

rsfc−500 0.35 0.35 0.13 0.30 0.34 0.41

(rΓ)dsfc−925 0.08 0.02 0.11 0.08 0.08 0.01

(rΓ)dsfc−850 0.13 0.04 0.16 0.13 0.11 0.08

(rΓ)dsfc−700 0.33 0.19 0.24 0.32 0.32 0.31

(rΓ)dsfc−500 0.38 0.33 0.20 0.32 0.33 0.40

(rΓ)esfc−700 0.15 0.09 0.13 0.13 0.11 0.07

(rΓ)esfc−500 0.14 0.13 0.09 0.12 0.11 0.07

vi A.3 Lapse-rate and moisture indices

(a) Γdsfc−850 (b) Γdsfc−700 (c) Γdsfc−500

(d) Γd850−700 (e) (rΓ)esfc−700 (f) (rΓ)esfc−500

(g) (rΓ)dsfc−850 (h) (rΓ)esfc−700 (i) (rΓ)esfc−500

Figure A.3: Scatter plots of HgRr60 against lapse-rate and moisture based indices. Most of the plots show uneven scattering of the different category of events with the indices

vii A.4 Wind shear indices

A.4 Wind shear indices

Table A.4: Correlation between rainfall and directional shear for all events. HgRr60 HgAcRr Drtn AvgRr60 HgRr30 HgRr6 dd850−700 0.25 0.28 0.35 0.10 0.22 0.22 dd850−500 0.34 0.33 0.07 0.43 0.37 0.31 dd850−400 0.27 0.25 -0.04 0.35 0.31 0.27 dd850−300 0.25 0.22 0.01 0.31 0.27 0.26 dd850−250 0.23 0.17 0.01 0.24 0.25 0.24 dd700−500 0.21 0.22 0.00 0.31 0.20 0.17 dd700−400 0.21 0.24 0.14 0.20 0.20 0.25 dd700−300 0.06 0.07 -0.03 0.15 0.03 0.08 dd700−250 0.00 -0.02 -0.15 0.10 -0.04 -0.01 dd500−400 0.25 0.25 -0.02 0.32 0.27 0.31 dd500−300 0.19 0.18 -0.01 0.20 0.18 0.18 dd500−250 0.17 0.12 -0.09 0.18 0.17 0.16

Table A.5: Correlation between rainfall and speed shear for all events. HgRr60 HgAcRr Drtn AvgRr60 HgRr30 HgRr6 ff850−700 -0.10 -0.12 -0.17 -0.04 -0.16 -0.11 ff850−500 0.01 0.00 -0.06 -0.03 -0.10 -0.16 ff850−400 -0.16 -0.16 -0.08 -0.18 -0.22 -0.33 ff850−300 -0.16 -0.19 -0.13 -0.13 -0.22 -0.30 ff850−250 -0.15 -0.16 -0.10 -0.14 -0.20 -0.24 ff700−500 -0.05 -0.06 -0.03 -0.11 -0.13 -0.19 ff700−400 -0.20 -0.19 0.00 -0.24 -0.23 -0.36 ff700−300 -0.17 -0.20 -0.10 -0.16 -0.22 -0.30 ff700−250 -0.14 -0.16 -0.06 -0.15 -0.19 -0.24 ff500−400 -0.43 -0.41 -0.15 -0.40 -0.40 -0.49 ff500−300 -0.26 -0.27 -0.18 -0.16 -0.24 -0.32 ff500−250 -0.13 -0.15 -0.12 -0.08 -0.15 -0.19

Table A.6: Correlation between rainfall and shear vector for all events. HgRr60 HgAcRr Drtn AvgRr60 HgRr30 HgRr6 ff850−700 -0.10 -0.12 -0.17 -0.04 -0.16 -0.11 ff850−500 0.01 0.00 -0.06 -0.03 -0.10 -0.16 ff850−400 -0.16 -0.16 -0.08 -0.18 -0.22 -0.33 ff850−300 -0.16 -0.19 -0.13 -0.13 -0.22 -0.30 ff850−250 -0.15 -0.16 -0.10 -0.14 -0.20 -0.24 ff700−500 -0.05 -0.06 -0.03 -0.11 -0.13 -0.19 ff700−400 -0.20 -0.19 0.00 -0.24 -0.23 -0.36 ff700−300 -0.17 -0.20 -0.10 -0.16 -0.22 -0.30 ff700−250 -0.14 -0.16 -0.06 -0.15 -0.19 -0.24 ff500−400 -0.43 -0.41 -0.15 -0.40 -0.40 -0.49 ff500−300 -0.26 -0.27 -0.18 -0.16 -0.24 -0.32 ff500−250 -0.13 -0.15 -0.12 -0.08 -0.15 -0.19

viii A.4 Wind shear indices

(a) (b)

(e) (f)

Figure A.4: Scatter plot showing an ambiguous relationship between HgRr60 and directional shear, speed shear and shear vector calculated for the layer 850-500 hPa and 500-250.

ix Appendix B

More Examples of Indices Failures

BI: Stable indices - heavy rainfall event

(a) 19 Feb 2005 (b) 27 Feb 2004

Figure B.1: 500 hPa geopotential height (m) composite mean over the SWIO for the days with stable indices and heavy rainfall. The island is under the inﬂuence of a trough on 27 Feb 2004 and 19 Feb 2005 and high geopotential height on 26 and 27 Feb 2005(http : //www.esrl.noaa.gov/).

x (a) 19 Feb 2005 (b) 29 Feb 2004

Figure B.2: Skew-T plots of soundings at Vacoas synoptic station @1200 UTC showing unstable proﬁle with (a, b) moist mid-troposphere (c, d) dry mid-troposphere (http : //weather.uwyo.edu/upperair/sounding.html).

xi BII: Unstable indices - light rainfall events

(a) 08 Mar 2005 (b) 12 Dec 2008

Figure B.3: 500 hPa geopotential height (m) composite mean over the SWIO for the days with unstable indices and light rainfall (http : //www.esrl.noaa.gov/).

(a) 08 Mar 2005 (b) 12 Dec 2008

Figure B.4: Skew-T plots of soundings at Vacoas synoptic station @1200 UTC showing unstable proﬁle with (a, b) moist mid-troposphere (c, d) dry mid-troposphere (http : //weather.uwyo.edu/upperair/sounding.html).

xii Appendix C

Cross Validation Statistics

Table C.1: Scores for different threshold associated with different traditional indices. Indices Thresholds HR F AR CSI HR − F AR PC YI EPS BIAS CAP E ≥ 800 50.00 17.86 40.00 32.14 68.75 0.34 67.09 0.75 CAP E CAP E ≥ 1000 30.00 14.29 25.00 15.71 62.50 0.19 59.54 0.50 CAP E ≥ 1200 15.00 7.14 13.64 7.86 60.42 0.13 56.34 0.25 CAP E ≥ 1400 10.00 7.14 9.09 2.86 58.33 0.05 52.55 0.20 TTI ≥ 40 90.00 67.86 46.15 22.14 56.25 0.26 62.99 1.85 TTI TTI ≥ 42 75.00 39.29 48.39 35.71 66.67 0.35 67.67 1.30 TTI ≥ 44 60.00 25.00 44.44 35.00 68.75 0.35 67.64 0.95 P rpW tr ≥ 30 95.00 71.43 47.50 23.57 56.25 0.30 64.89 1.95 P rpW tr P rpW tr ≥ 35 85.00 42.86 53.13 42.14 68.75 0.42 71.24 1.45 P rpW tr ≥ 40 50.00 28.57 35.71 21.43 62.50 0.22 60.91 0.90 KI ≥ 28 70.00 42.86 43.75 27.14 62.50 0.27 63.43 1.30 KI KI ≥ 30 55.00 35.71 36.67 19.29 60.42 0.19 59.58 1.05 KI ≥ 32 57.14 22.22 44.44 34.92 68.75 0.36 67.89 0.86 KI ≥ 34 50.00 10.71 43.48 39.29 72.92 0.44 71.79 0.65 ShwI ShwI ≤ 3 95.00 64.29 50.00 30.71 60.42 0.36 68.01 1.85 ShwI ≤ 2 80.00 46.43 48.48 33.57 64.58 0.34 66.92 1.45 LI LI ≤ −2 60.00 21.43 46.15 38.57 70.83 0.39 69.64 0.90 LI ≤ −1 75.00 32.14 51.72 42.86 70.83 0.42 71.13 1.20 DCI ≥ 28 90.00 53.57 51.43 36.43 64.58 0.39 69.37 1.65 DCI DCI ≥ 30 75.00 39.29 48.39 35.71 66.67 0.35 67.67 1.30 DCI ≥ 32 55.00 25.00 40.74 30.00 66.67 0.31 65.28 0.90 DCI ≥ 34 50.00 14.29 41.67 35.71 70.83 0.39 69.37 0.70 r ≥ 14 75.00 53.57 42.86 21.43 58.33 0.22 60.91 1.50 r r ≥ 14.5 70.00 42.86 43.75 27.14 62.50 0.27 63.43 1.30 r ≥ 15 65.00 35.71 43.33 29.29 64.58 0.29 64.45 1.15 r ≥ 15.5 55.00 28.57 39.29 26.43 64.58 0.27 63.32 0.95 LCLpp LCLpp ≥ 910 70.00 46.43 42.42 23.57 60.42 0.23 61.71 1.35 LCLpp ≥ 915 55.00 39.29 35.48 15.71 58.33 0.16 57.77 1.10 LCLtt LCLtt ≥ 292 55.00 35.71 36.67 19.29 60.42 0.19 59.58 1.05 LCLtt ≥ 293 35.00 10.71 30.43 24.29 66.67 0.29 64.74 0.50 LF C LF C ≥ 850 45.00 39.29 29.03 5.71 54.17 0.06 52.86 1.00 LF C ≥ 880 20.00 17.86 16.00 2.14 56.25 0.03 51.35 0.45 EL EL ≤ 200 30.00 21.43 23.08 8.57 58.33 0.10 54.88 0.60 EL ≤ 250 50.00 32.14 34.48 17.86 60.42 0.18 59.00 0.95 Θ ≥ 298 80.00 89.29 35.56 -9.29 39.58 -0.13 43.51 2.05 Θ Θ ≥ 299 65.00 60.71 35.14 4.29 50.00 0.04 52.18 1.50 Θ ≥ 299.5 65.00 42.86 40.63 22.14 60.42 0.22 60.93 1.25 Θ ≥ 300 50.00 21.43 38.46 28.57 66.67 0.30 64.94 0.80

xiii Table C.2: Scores for different threshold associated with different modiﬁed and lapse rate- moisture based indices. Modiﬁed Indices Thresholds HR F AR CSI HR − F AR PC YI EPS BIAS

Ksfc−850 Ksfc−850 ≥ 18 70.00 35.71 46.67 34.29 66.67 0.34 66.90 1.20

Ksfc−850 ≥ 19 66.67 33.33 46.67 33.33 66.67 0.33 66.55 1.10

Ksfc−500 Ksfc−500 ≥ 42 65.00 35.71 43.33 29.29 64.58 0.29 64.45 1.15

Ksfc−500 ≥ 44 52.38 22.22 40.74 30.16 66.67 0.31 65.64 0.81

K925−850 K925−850 ≥ 13 80.95 51.85 48.57 29.10 62.50 0.30 65.09 1.48

K925−850 ≥ 16 70.00 32.14 48.28 37.86 68.75 0.37 68.68 1.15

K925−500 K925−500 ≥ 36 80.95 44.44 51.52 36.51 66.67 0.37 68.52 1.38

K925−500 ≥ 38 70.00 35.71 46.67 34.29 66.67 0.34 66.90 1.20

rsfc−850 rsfc−850 ≥ 12 95.00 75.00 46.34 20.00 54.17 0.26 63.23 2.00

rsfc−850 ≥ 14 65.00 39.29 41.94 25.71 62.50 0.25 62.68 1.20

rsfc−700 rsfc−700 ≥ 11 90.00 57.14 50.00 32.86 62.50 0.36 67.82 1.70

rsfc−700 ≥ 12 65.00 35.71 43.33 29.29 64.58 0.29 64.45 1.15

rsfc−500 rsfc−500 ≥ 9 90.00 64.29 47.37 25.71 58.33 0.29 64.64 1.80

rsfc−500 ≥ 10 65.00 35.71 43.33 29.29 64.58 0.29 64.45 1.15

rΓd rΓdsfc−850 ≥ 0.06 70.00 50.00 41.18 20.00 58.33 0.20 60.00 1.40

rΓdsfc−700 ≥ 0.05 95.00 60.71 51.35 34.29 62.50 0.39 69.52 1.80

rΓdsfc−500 ≥ 0.05 80.00 39.29 51.61 40.71 68.75 0.40 70.23 1.35

dd850−700 ≤ 60 57.14 55.56 33.33 1.59 50.00 0.02 50.79 1.29

ddl1−l2 dd850−500 ≥ 120 36.84 51.72 20.59 -14.88 43.75 -0.15 42.70 1.16

dd700−500 ≥ 120 15.79 34.48 10.34 -18.69 45.83 -0.21 39.71 0.68

dd500−250 ≤ 60 73.68 55.17 40.00 18.51 56.25 0.19 59.35 1.58

xiv