Hybrid Rainfall Estimates from Satellite, Lightning and Ground Station Data in West Africa

Examensarbete vid Institutionen för geovetenskaper

Degree Project at the Department of Earth Sciences

ISSN 1650-6553 Nr 316

Hybrid Rainfall Estimates from Satellite, Lightning and Ground Station Data in West Africa

Nederbördsestimat från satellit och blixtar i Västafrika

Henrik Enbäck Charlotta Eriksson

INSTITUTIONEN FÖR

Examensarbete vid Institutionen för geovetenskaper

Degree Project at the Department of Earth Sciences

ISSN 1650-6553 Nr 316

Hybrid Rainfall Estimates from Satellite, Lightning and Ground Station Data in West Africa

Nederbördsestimat från satellit och blixtar i Västafrika

Henrik Enbäck

Charlotta Eriksson

ISSN 1650-6553

Copyright © Henrik Enbäck, Charlotta Eriksson and the Department of Earth Sciences, Uppsala

University

Abstract

Hybrid Rainfall Estimates from Satellite, Lightning and Ground Station Data in West Africa

Henrik Enbäck & Charlotta Eriksson

Most of the working population in Ghana are farmers. It is of importance for them to know where and when precipitation will occur to prevent crop losses due to droughts and floodings. In order to have a sustainable agriculture, improved rainfall forecasts are needed. One way to do that is to enhance the initial conditions for the rainfall models. In the mid-latitudes, in-situ rainfall observations and radar data are used to monitor weather and measure rainfall. However, due to the lack of station data and the present absence of a radar network in West Africa, other rainfall estimates are needed as substitutes.

The rainfall amount in convective systems, dominating in West Africa, is coupled to their vertical structure. Therefore, satellite measurements of cloud top temperatures and microwave scatter, as well as the number of lightning, can be used to estimate the amount of rainfall. In this report, derived rainfall estimates from satellites and the use of lightning data are analysed to see how well they estimate the actual rainfall amount. The satellite datasets used in this report are NOAA RFE2.0, NOAA ARC2, and the EUMETSAT MPE. The datasets were compared to in-situ measurements from GTS- and NGO- collaborating observation stations in order to verify which satellite dataset that best estimates the rainfall or, alternatively, if a combination between two or all the datasets is a better approach. Lightning data from Vaisala GLD360 have been compared to GTS-station data and RFE2.0 to see if a relation between the number of lightning and rainfall amount could be found. It was also tested whether a combination between the satellite- and lightning data could be a better estimate than the two approaches separately.

Rainfall estimates from RFE2.0 alone showed the best correlation to GTS- and the NGO- collaborating station data. However, a difference in how well RFE2.0 estimated rainfall at GTS-stations compared to reference stations was seen. Comparing RFE2.0 to GTS-stations showed a better correlation, probably due to the use of these observations in the build up of RFE2.0. Even though RFE2.0 showed the best correlation compared to other datasets, satellite estimates showed in general poor skill in catching the actual rainfall amount, strongly underestimating heavy rainfall and somewhat overestimating lighter rainfall. This is probably due to the rather basic assumptions that the cloud top temperature is directly coupled to rain rate and also the poor temporal resolution of the polar orbiting satellites (carrying microwave sensors). Better instruments and algorithms need to be developed to be able to use satellite datasets as an alternative to rainfall measurements in West Africa. Furthermore, due to the lack of station data, only tentative results between GLD360 and GTS-stations could be made, showing a regime dependence. When further analysed to RFE2.0, a stronger temporal dependence, i.e.

seasonal variation, rather than a spatial one was seen, especially during the build up of the monsoon.

However, due to poor rainfall estimates from RFE2.0, no accurate rainfall-lightning relation could be made but trends regarding the relation were seen. The use of GLD360 showed to be an effective way to erase false precipitation from satellite estimates as well as locating the trajectory of convective cells. To be able to further analyse rainfall/lightning relation, more measurements of the true rainfall is needed from e.g. a radar.

Keywords: Rainfall estimates, West Africa, lightning, satellite

Degree Project E in Meteorology, 1ME422, 30 credits Supervisors: Anna Rutgersson and Andreas Vallgren

Department of Earth Sciences, Uppsala University, Villavägen 16, SE-752 36 Uppsala (www.geo.uu.se) ISSN 1650-6553, Examensarbete vid Institutionen för geovetenskaper, No. 316, 2015

The whole document is available at www.diva-portal.org

Sammanfattning

Nederbördsestimat från satellit och blixtar i Västafrika Henrik Enbäck & Charlotta Eriksson

Majoriteten av Ghanas befolkning arbetar inom jordbrukssektorn. Det är viktigt för jordbrukarna att veta när och var nederbörd kommer att falla för att deras skörd inte ska bli förstörd av till exempel torka eller översvämningar. Det behövs därför bättre nederbördsprognoser för ett hållbart jordbruk. Ett sätt att få mer noggranna prognoser är att förbättra initialvärden till nederbördsmodellerna. Vid de mellersta breddgraderna på norra halvklotet används nederbördsmätningar från in-situ stationer samt data från radarsystem som initialvärden, men på grund av få mätstationer och inget radarsystem i västra Afrika behövs alternativa nederbördsestimater.

Nederbörden i västra Afrika domineras av konvektiva system, vars regnmängd är kopplad till dess vertikala struktur. Satellitmätningar av molntoppstemperaturen och mikrovågornas spridning och absorption, liksom antalet blixtar är också relaterat till molnets struktur och kan därför användas för att estimera nederbördsmängden. I den här rapporten analyserades nederbördsestimater från satellitdata samt användning av blixtdata för att undersöka hur bra metoderna är på att estimera den verkliga nederbördsmängden. Satellitdataseten som analyserades var NOAA RFE2.0, NOAA ARC2 och EUMETSAT MPE. Dataseten jämfördes med in-situ mätningar från GTS-stationer samt observationer från NGO-samarbetande jordbrukare för att verifiera vilket satellitdataset som ger det bästa nederbördsestimatet, alternativt att en kombination mellan två eller alla dataset ger det bästa estimatet.

Vidare har blixtdata från Vaisala GLD360 jämförts med GTS-stationer och RFE2.0 för att se om antalet blixtar är relaterat till nederbördsmängden. Slutligen har det också undersökts om en kombination mellan satellit- och blixtdata är ett bättre än de två metoderna separat.

Nederbördsestimater från RFE2.0 visade på bäst korrelation med både GTS- och NGO-stationer. En tydlig skillnad noterades dock i RFE2.0:s förmåga att estimera nederbörd vid jämförelse mellan de två stationsdataseten. En bättre korrelation mellan RFE2.0 och GTS-stationerna påvisades, troligen för att RFE2.0 använder dessa observationer i uppbyggnaden av datasetet. Även om RFE2.0 visade på bäst korrelation i jämförelse med ARC2 och MPE var samtliga satellitdataset dåliga på att estimera den verkliga nederbördsmängden. De underestimerar starkt stora mängder nederbörd samtidigt som de överestimerar små mängder. Anledningen är troligen det relativt enkla antagandet att molntopps- temperaturen är direkt kopplad till molnets regnmängd samt den dåliga tidsupplösningen på de polära satelliterna som är utrustade med mikrovågssensorer. För att satellitdataseten ska kunna användas som ett alternativt nederbördsestimat i Västafrika behövs bättre mätinstrument och algoritmer. Vid analysen mellan GLD360 och GTS-stationer kunde, på grund av för få stationsdata, endast övergripande resultat erhållas. Ett områdesberoende gick dock att urskilja som vid en ytterligare analys mellan GLD360 och RFE2.0 visade på ett större säsongsberoende, särskilt under uppbyggnaden av monsunperioden i april och maj. Eftersom RFE2.0 visade sig ha dåliga nederbördsestimat kunde ingen noggrann koppling hittas, utan resultatet visade på trender samt möjligheter att kunna använda blixtdata som ett alternativt nederbördsestimat. Till exempel visade det sig att GLD360 kunde användas som ett verktyg för att sålla bort falsk nederbörd från satellitestimat samt identifiera trajektorien för ett konvektivt system. För en djupare analys i att relatera blixtar och nederbörd i Västafrika krävs bättre tekniker för att estimera nederbörd eller fler in-situ observationer.

Nyckelord : Nederbördsestimat, Västafrika, blixtar, satellit

Examensarbete E i meteorologi, 1ME422, 30 hp Handledare: Anna Rutgersson och Andreas Vallgren

Institutionen för geovetenskaper, Uppsala universitet, Villavägen 16, 752 36 Uppsala (www.geo.uu.se) ISSN 1650-6553, Examensarbete vid Institutionen för geovetenskaper, Nr 316, 2015

Hela publikationen finns tillgänglig på www.diva-portal.org

Abbreviations

AEJ African Easterly Jet

AEW African Easterly Waves

AM April and May

AMSU Advanced Microwave Sounding Unit

ARC2 African Rainfall Climatology version 2

BBT Blending Brightness Temperatures

CAPE Convective Available Potential Energy

CC Cloud-to-Cloud

CG Cloud-to-Ground

CRMSE Centred Root Mean Square Error

CWC Cloud Water Content

DMSP Defence Meteorological Satellite Program

EUMETSAT European Organization for the Exploitation of Meteorological Satellites

FSI Flexible Combined Imager

ICI Ice Cloud Imaging

IRS InfraRed Sounder

ITCZ Intertropical Convergence Zone

JJAS June, July, August and September

GLD360 Vaisala Global Lightning Dataset

GTS Global Telecommunication System

LD Lightning Density

LI Lightning Imager

LLS Local Lightning System

MJO Madden-Julian Oscillation

MPE Multi-sensor Precipitation Estimate

MTG-I Meteosat Third Generation

MWI MicroWave Imaging

NGO Non-Governmental Organisation

NOAA National Oceanic and Atmospheric Administration

PDF Probability Density Function

RDE Relative Detection Efficiency

RFE2.0 African Rainfall Estimation Algorithm Version 2

RL Rainfall/Lightning

RLA Relative Location Accuracy

RLR Rainfall/Lightning Ratio

RMSE Root Mean Square Error

SEVIRI Spinning Enhanced Visible and InfraRed Imager

SL Squall Line

SSM/I Special Sensor Microwave/Imager

TRMM Tropical Rainfall Measuring Mission

U.S. United States

UVN Ultraviolet Visible Near-infrared

WAM The West African Monsoon

WMO World Meteorological Organisation

Table of Contents

1 Introduction 1

2 Theory 2

2.1 The Weather and Climate of West Africa . . . . 2

2.1.1 Convection . . . . 2

2.1.2 ITCZ and The Monsoon . . . . 3

2.1.3 Sea Breeze . . . . 4

2.1.4 The African Easterly Jet and African Easterly Waves . . . . 4

2.1.5 West African Squall Lines . . . . 5

2.1.6 Madden-Julian Oscillation . . . . 5

2.2 Lightning . . . . 6

2.2.1 The Electric Charges in the Atmosphere . . . . 6

2.2.2 Cloud Electrification in Relation to Cloud Microphysics . . . . 7

2.3 Rainfall Estimation Techniques . . . . 9

2.3.1 Satellite . . . . 9

2.3.2 Lightning . . . . 10

3 Datasets 12 3.1 Station Data . . . . 12

3.1.1 GTS Station Data . . . . 12

3.1.2 Reference Data . . . . 12

3.2 Satellite Data . . . . 12

3.2.1 RFE2.0 . . . . 12

3.2.2 ARC2 . . . . 13

3.2.3 MPE . . . . 14

3.3 Lightning . . . . 14

3.3.1 GLD360 . . . . 14

4 Method 16 4.1 Comparisons Between The Different Datasets . . . . 16

4.1.1 Satellites to GTS-Station and Reference Observation Data . . . . 16

4.1.2 Lightning to GTS-Station and RFE2.0 Data . . . . 16

4.2 Statistical Methods . . . . 17

4.2.1 Statistical Variables . . . . 17

4.2.2 Probabilistic Distributions . . . . 18

4.3 Regimes . . . . 19

4.3.1 Spatial . . . . 19

4.3.2 Filtering of Data . . . . 20

4.3.3 Temporal . . . . 21

5 Results 23

5.1 Satellite Results . . . . 23

5.1.1 Dataset Comparison . . . . 23

5.1.2 Satellite Regimes . . . . 25

5.1.3 Linear Adjustment . . . . 26

5.1.4 Reference Data . . . . 28

5.1.5 Annual Comparison . . . . 28

5.2 Lightning Results . . . . 31

5.2.1 Lightning Compared to GTS-Station Data . . . . 31

5.2.2 The Distribution of Lightning . . . . 32

5.2.3 GLD360 Compared to RFE2.0 Rainfall Estimates for Wet and Dry Period . . . . 34

5.2.4 GLD360 Compared to RFE2.0 Rainfall Estimates for AM and JJAS . . . . 37

5.3 Lightning Correction to Satellite Data . . . . 40

6 Discussion 42 6.1 The Lack of Station Data . . . . 42

6.2 The Ability of IR- and PM-data to Estimate Rainfall Amount . . . . 42

6.3 Satellite Datasets Using GTS-stations for Calibration . . . . 44

6.4 The ”Best” Satellite Dataset . . . . 44

6.5 Expected Value for The Probabilistic Lightning Distribution . . . . 45

6.6 Rainfall-Lightning Regime Dependence . . . . 45

6.7 Proposed Solutions and Suggestions for Improvements . . . . 46

6.7.1 The Launch of New Satellites . . . . 46

6.7.2 Telecommunication Network . . . . 47

6.7.3 Radar . . . . 47

7 Conclusions 49

8 Acknowledgements 50

9 Contributions of Authors 51

10 References 53

1 Introduction

Approximately 55% of the working population in Ghana are farmers and therefore very dependent on the weather. It is of importance for the farmers to know where and when precipitation will occur to prevent crop losses due to extreme rainfall or droughts. If early warnings can be made for these events, the farmers can better plan and sustain their agriculture, and the risk of crop losses decreases. Thus, a need of more accurate rainfall forecasts are important for the development of a sustainable food production (Ignitia 2014).

In order to improve rainfall estimations, better initial conditions to the forecasting models are neces- sary. In the mid-latitudes, the rainfall observations and radar measurements are effective tools for this.

However, due to the sparse, as well as decreasing amount of observation stations in West Africa, new techniques to measure precipitation are needed. For instance, radars are effective and useful substitutes for the rain-gauge measurements, but due to the present absence of a radar network in West Africa, other rainfall estimates have to be used (Seyyedi 2010; Doumounia et al. 2014). Examples of such methods are satellite measurements and detection of lightning strikes. From satellites, the cloud top tempera- ture and microwave scatter can be derived in order to determine the amount of rainfall from a certain cloud system. Furthermore, in parts of the world, a correlation between rainfall amount and lightning strike density/amount has been seen, why also this is of interest to study (Blackmore et al. 2007, Xu et al. 2012). This report investigates how well satellite derived rainfall datasets and lightning detection systems, or a combination of them, estimate and represent the amount of rainfall over West Africa.

Three different satellite datasets will be used, EUMETSAT MPE, NOAA RFE2.0 and NOAA ARC2.

The datasets will be compared with in-situ measurements from synoptic weather stations to find out advantages and drawbacks with the different datasets and to see if there is an optimum satellite to use in rainfall estimation. Alternatively, it might be more preferable to use statistical corrections or weighted combinations between the datasets. The Vaisala global lightning system (GLD360) is compared to in- situ measurements and the RFE2.0-dataset to see correlations between the amount of rainfall and the number of lightning strikes. From this, an attempt to find a relation between the two parameters will be made. The two methods will then be compared with each other in order to see if they can be combined to improve rainfall estimates over West Africa.

The report will begin with some fundamental information about the weather and climate in West

Africa in order to understand the underlying mechanisms behind rainfall in the region. Further, the

datasets and how they are derived will be explained, followed by the methods of investigating the

datasets. Finally, the results are presented followed by a discussion concerning the most important com-

ponents of the results. In the section Contributions of Authors, the division of which parts each author

has written in the report is presented.

2 Theory

2.1 The Weather and Climate of West Africa

2.1.1 Convection

The precipitation occurring in West Africa, as well as in most other tropical areas, mainly originates from convection. The severity of the convective precipitation is significantly modulated by the convective available potential energy (CAPE), i.e. the potential energy available for up-draft intensity in an area. In general, higher CAPE is seen over land areas than over the ocean due to the higher heat capacity of water that makes the surface temperature heating much smaller than over most land surfaces, as seen in figure 1. Because of this, differences in the cloud microphysics exist where the likelihood of a more robust ice-phase is present over continents, while warm-rain processes contribute to more of the precipitation over the oceans. Moreover, the presence of less cloud condensation nuclei over oceans also affect the microphysical properties in the clouds. These differences will affect the vertical structure of the cloud as well as its ice content and thus affecting the cloud top temperature and lightning discharge (Wang 2013;

Xu et al. 2012).

Mesoscale systems also affect convection which causes variations in space and time, and are also seasonally and topographically modulated. Therefore, because of the complexity of convection and its small time and length scales, it is important to have a comprehensive understanding of the mesoscale systems to be able to forecast where and when the convective precipitation will occur (Lafore et al.

2008). In the following sections, examples of tropical mesoscale systems in West Africa are described.

Figure 1: Example of the diurnal CAPE distribution over parts of West Africa for 26/10/2014. Less CAPE occurs

over ocean than over land [Source: Ignitia].

2.1.2 ITCZ and The Monsoon

By definition, a monsoon is a large scale wind flow that originates in one hemisphere affecting the circulation at the other geographical hemisphere (Leroux 2001). The West African monsoon is driven by the thermal differences between sea and land (just like a sea breeze) and is characterized by summer rainfall and winter drought over the continent. It is predominantly present at the longitudinal range from 10

W to 5

E and corresponds to the south-north-south movement of the Intertropical Convergence Zone, ITCZ (Janicot et al. 2010). The onset of the monsoon is characterized by a jump of the ITCZ between 5

N and 10

N (Sultan & Janicot 2003). This jump normally occurs in the end of June and it is noticeable due to the decrease of convective activity, hence less rainfall, that temporally occurs over West Africa as a response to it (Sultan & Janicot 2003). The ITCZ stays at its northernmost location until late August and then moves back southwards again. This period defines the singular rainy season of the Sahel regions whereas the coastline (at about 5

N) experiences two rainy seasons during the year, as a result of the ITCZ passing this area twice (Laux et al. 2007). In figure 2, the rain pattern over West Africa the years 2001-2013 is seen, based on the moving average rainfall per 5 days and latitude band between 10

W and 10

E (from NOAA RFE2.0). In the figure, the jump of the ITCZ is seen in the discontinuous jump of the rain maxima.

Figure 2: The 5-days moving average of rainfall for each latitude between 10

S and 15

N and averages of longitudes between 10

E and 10

W, the years 2001-2013. The different colours show the precipitation amount in millimetres, as defined by the bar. The blue dotted line is where the maximum latitudinal rainfall occurs each day.

The red dotted line is the spatial centroid, which is the center of mass of the rainfall.

During the dry period in West Africa (i.e. winter time for the northern hemisphere), the area is governed by dry and hot north-easterly trade winds arriving from the Sahara, instead of the more humid southwesterly winds. These winds are called the Harmattan (Leroux 2001). The Harmattan often carries dust from the Sahara desert, creating a haze in the sky which inhibits incoming solar radiation and therefore further inhibits convection, resulting in an even drier winter climate.

2.1.3 Sea Breeze

A sea breeze arises due to the difference in heat capacity between sea and land surfaces. Since the water surface has a greater heat capacity compared to land surfaces, temperature does not change as much over the sea as compared to over land during the day. As a response to the differential heating, a pressure gradient builds up, causing a local wind circulation system, i.e. a sea breeze, blowing onshore during the day and offshore during the night. Since there are such high temperatures in West Africa (and generally in the Tropics) sea breezes are relatively strong and a breeze can penetrate 50-100 km inland, sometimes even more. The onshore breeze also creates a convergence zone (onshore breeze front) which builds near the shore in the early morning and reaches its maximum inland position when the temperature reaches its maximum during the day or slightly after. At night, when the offshore breeze is established, the front dissolves and can be set up over the sea again, albeit less marked (Leroux 2001).

2.1.4 The African Easterly Jet and African Easterly Waves

The African Easterly Jet (AEJ) is a jet stream over West Africa that is created during summer as a response to the strong heat gradient between land and sea with the dry and hot Harmattan winds and the cooler and more humid south westerly monsoon winds, respectively (Janicot et al. 2010). It is located around 600 hPa, between the latitudinal limits of the Guinean coast in the south and the Harmattan winds in the north (Lafore et al. 2008). According to Janicot et al. (2010), the AEJ influences the creation of African Easterly Waves (AEW) which are regarded as the major type of synoptic weather system in the African monsoon. The AEW most often originate west of 20

E and travel westward, with a speed of about 8 ms

and a wave length of 200-400 km, along the AEJ at around 600 hPa. The spectral periodicity of the AEW normally ranges between 3 and 5 days and the life cycle of them can be divided into three phases (Diedhiou et al. 1999, Janicot et al. 2010). The first phase is the initiation of the wave.

The initiation is, according to Janicot et al (2010), a response to mesoscale convective systems being

triggered in the highlands of Darfur (25

E) in southwestern Sudan. This outbreak of convection close to

the AEJ leads to downstream development of baroclinicity, and from that an AEW develops. The second

phase is the baroclinic development. In this stage the waves grow to their full potential, both north and

south of the AEJ, and start to affect convective activity (hence rainfall) over West Africa. This is affected

in such a way that ahead and in the troughs of the wave, convection at ITCZ is enhanced (Diedhiou et al. 1999). The third phase is the West Coast development of the AEW. When the wave reaches the west coast, convection is triggered over the Guinea highland. The potential vorticity in the AEW and from the convection in the Guinean highland creates a structure ideal for the genesis of tropical cyclones as the waves move out over the Atlantic (Janicot et al. 2010).

2.1.5 West African Squall Lines

When a flow is disturbed by topography or when a flow of relatively cooler air is advected southwards in northern parts of Africa, a perturbation in the AEJ occurs. This perturbation accelerates a part of the AEJ and has a west or south-west flux with an anticyclonic flow field. When in collision with the opposite monsoonal flow, the AEJ works as an obstacle, forcing parts of the monsoon winds to move northward and upward. As the AEJ penetrates deeper into the monsoon, the north will be separated from the southern part. Meanwhile, the very humid monsoonal flow is forced upward in the atmosphere above the easterly obstacle. The humid air will condensate in its upward movement and clouds will form. This formation of clouds is known as the squall line (SL). If strong enough to break through the monsoon, the perturbed AEJ may reach the westernmost coast where the North-Atlantic high pressure ridge area finally will stop its movement (Leroux 2001).

The real cause of the fluctuations leading to the appearance of an SL yet remains uncertain, and is subject to scientific discussion. The above description is from Leroux (2001) who assumes neutral conditions, preventing the development of clouds to begin with. Notwithstanding the real cause of an SL, the upward lift of the monsoonal air may create heavy precipitation and strong down-drafts, depending on the amount of moisture in the monsoonal air. Furthermore, the depth of the monsoonal air mass affects the intensity of the SL where deeper layers have a more intense precipitation but shorter lifetime than shallow layers (Leroux 2001).

2.1.6 Madden-Julian Oscillation

The Madden-Julian Oscillation (MJO) is an intraseasonal wave in the Tropics with a cycle of 30-60 days

resulting in changes of several atmospheric parameters, such as wind and precipitation. The MJO can

be monitored by its eastward propagation of enhancing or suppressing of the tropical rainfall over the

Pacific and Indian ocean. Even though these areas are the most affected ones by the MJO, other areas

are influenced by it as well. Studies have shown that the Kelvin and Rossby waves originating from the

Pacific and Indian ocean increase the convection in West Africa during the monsoon period. The MJO is

also hypothesised to somewhat affect the ITCZ movement over the West Africa region. Since the MJO

can be predicted a few weeks ahead, it is of importance to understand its influence on West Africa in

order to better predict the start of the monsoon period (Ghassan & Maloney 2011).

2.2 Lightning

2.2.1 The Electric Charges in the Atmosphere

In general, during a fair weather day, the surface of the Earth has an average electric field, ~ E , of about 120 Vm

. This value varies depending on location and is generally larger over land than over oceans.

Furthermore, ~ E is a vector field which by convention points from a positive to a negative direction.

Studies have shown that the vector field points downward, suggesting that an overall negative net charge exists at the Earth’s surface. The average charge density, σ , is −1.1 × 10

Cm

and the global fair weather charge is approximately −5.1 × 10

C (Wang 2013).

Both positive and negative charges occur in the atmosphere. The two main driving mechanisms for producing these charges are the radioactive emanation from the Earth’s surface and the cosmic rays.

These two mechanisms are both related to the ionization of neutral molecules producing both negative and positive ions. In this way, some ions disappear from the atmosphere through neutralization whereas other attach themselves to neutral molecules or to aerosol particles and create small or large ions, respec- tively. These ions are the reason for the different charges of the atmosphere where the positive charge is approximately 20% larger than the negative charge (Wang 2013).

At the surface, the Earth’s emanation and the cosmic rays each contributes with one half of the total charge while cosmic rays will dominate with increasing height from the surface. As already mentioned, there exists a negative σ at the surface. According to Coulomb’s law, the charge magnitude will decrease with a rate of 1/r

, where r is the distance from the Earth’s centre. Due to the cosmic rays, however, a source of positive space charge, ρ, is supplied from above which will attenuate the negative σ at the ground more quickly (Wang 2013, Pruppacher & Klett 1997). Gish (1944) described this empirically as:

E(z) = 81.8e

+ 38.6e

+ 10.27e

(1)

where z is the height. Using the permittivity of vacuum, ε

, and Gauss law:

∇ · ~ E = ρ/ε

(2)

eq. (1) can be expressed as:

ρ = 20.4e

+ 0.8e

+ 0.069e

(3)

Inserting values to eq. (3), ρ will be about four times less at 1 km height compared to the surface. Thus,

because of the existence of the positive space charges, the magnitude of the negative average electric field at the ground will decrease more rapidly with height than explained by Coulomb’s law (Wang 2013, Pruppacher & Klett 1997).

Due to the average negative charge at the Earth’s surface during fair weather, the positive ions will have a direction downward while the negative ions will be directed upward. This leads to an electric current in the atmosphere where the positive ions will have a down-flow, trying to neutralize the negative fair weather charge at the ground. Since the larger ions have more mass and thus are resistant to move, the electric current consists basically of the smaller ions. The current density has an average value of 3 × 10

Am

and globally a value of 1,500 A. Based on the average value, it would take approx- imately 6.5 minutes for the global current to neutralize the total fair weather charge of −5.1 × 10

C at the surface. However, since the fair weather electric field is always present, other mechanisms must contribute transporting negative charges to the surface (Wang 2013, Pruppacher & Klett 1997). More- over, the lower atmosphere works as an insulator between the Ionosphere and the Earth’s surface which potential difference is 200-300 kV. Since a leakage current of 1,500 A exists, the lower atmosphere is not a perfect insulator which is why thunderstorms are generated to compensate for these losses (Wang 2013).

2.2.2 Cloud Electrification in Relation to Cloud Microphysics

Several mechanisms exist to electrify a cloud. Many of them are, however, not alone sufficient to separate charged particles and generate lightning. Presently, the most acceptable charge separation mechanism is the riming electrification (Wang 2013).

Reynold et al. (1957) noticed in laboratory experiments that when graupels collide with ice crystals, the graupel received a negative charge while the ice crystal had a positive charge. Because of gravity, the graupel will fall and have its highest concentration in the cloud base whereas the positive ice crystals will be located at the top. Because of this, the cloud receives a bipolar structure with a positive charge centre at the top and a negative charge centre at the bottom.

Takahashi (1978) and Jayaratne et al. (1983) developed this theory further and noticed that both a negative and a positive charge could be deposited on the graupel. They saw that the sign and magnitude of the charge depended much on the cloud temperature and the cloud water content (CWC). If too little CWC, meaning little ice, the less likelihood for electrification to be produced. Hence, a robust ice-phase in the cloud is needed for storms to have lightning discharges. On the other hand, too large amount of CWC would inhibit the charging magnitude on a graupel as well, which relates to the lack of lightning in certain storms in the Tropics (Wang 2013; Saunders 2008).

Moreover, the sign of the charge deposit on the graupel depends on a certain cloud temperature, T

.

If T < T

, the graupel will be charged negatively while on the contrary for T > T

. The value of T

depends on the CWC. By this, when ice crystals and graupels collide at higher altitude the graupel will get a negative charge and fall down in the cloud due to gravity while the positive ice crystals will be concentrated at the top. At lower altitudes, where the temperature is warmer, the graupel will more likely get a positive charge. This leads to a positive charge centre at the cloud top, a negative charge centre at the lower part of the cloud and a slightly positive charge centre at the very bottom. This tripolar structure simplification coincides well with what is also observed in reality. The slightly positive charge centre at the bottom is thought to enhance the cloud-to-ground (CG) lightning from the negative charge centre (Wang 2013; Saunders 2008).

Even though the structure of the cloud as well as its charge separation are necessary for a lightning discharge to occur, other meteorological parameters such as temperature, humidity and air density are important as well. For example, in arid or semi-arid areas where the troposphere is deep, i.e. warm, and the air is dry, lightning discharges can occur but the precipitation will evaporate before reaching the ground. Thus, no precipitation will reach the ground even though lightning has been produced as well as a strong down-draft. Moreover, the likelihood of a lightning discharge increases if the resistance in the air is small (Rakov & Uman 2003).

For a cloud to be electrically charged, to begin with, the presence of considerable CAPE is needed,

contributing to strong up-drafts to separate the particles and thus the charges. By looking at figure 3,

showing a comparison between the rainfall estimates from RFE2.0 and the lightning strikes detected by

GLD360 between 2012/03/01 and 2013/02/28 over parts of West Africa, it is seen that more lightning

occurs over land than over ocean due to the difference in CAPE, seen in figure 3. The figure also shows

some of the mesoscale systems occurring in West Africa such as the sea breeze effect along the coasts

resulting in less precipitation and lightning over the area. Furthermore, the warm-rain process over

oceans resulting in less lightning discharges is also visible.

(a) RFE2.0. (b) GLD360.

Figure 3: The total precipitation amount from RFE2.0 (a) compared to the total lightning strikes from GLD360 (b) between 2012/03/01 and 2013/02/28 over parts of West Africa. Each grid-point has a spatial resolution of 0.1

× 0.1

. Less lightning occurs over ocean compared to land because of less CAPE. Due to the warm-rain processes, less lightning occurs over the ocean when still heavy precipitation is seen. The sea breeze resulting in less rainfall and lightning along the coasts is also visible and provides an example of the mesoscale systems in the area.

Besides the up-draft speed, two other parameters are important for lightning to occur: the cloud radius and the ice volume in the cloud (Wang 2013, Pruppacher & Klett 1997). Baker et al. (1995) made a simple model to show this relation:

f ≈ Rw

~ V

(4)

where f is the lightning frequency, R the cloud radius, w the up-draft speed and ~ V

is the ice volume. As seen from eq. (4) the up-draft has the biggest impact on the lightning frequency. Indeed, a non-lightning storm cloud does not need a high up-draft speed for precipitation to occur nor does it need a robust ice- phase i.e. large volume of ice. This is why, for instance, less lightning occur over oceans than over land and also why the rainfall/lightning ratio (RLR) is different to establish in the Tropics than for e.g. the mid-latitudes (Wang, 2013).

2.3 Rainfall Estimation Techniques

2.3.1 Satellite

Determination of rainfall by the aid of satellites can be done in several different ways. The main types are, according to Blackmore et al. (2007):

•

Algorithms that primarily use infra-red (IR) data from geostationary satellites.

•

Algorithms that primarily use passive microwave (PM) data from polar orbiting satellites.

•

Algorithms that use a combination of IR- and PM-data.

The algorithms that use IR-data work under the assumption that colder pixels represent higher cloud tops, which are more likely to produce precipitation than warm clouds (in the same synoptic environ- ment). The benefits of using geostationary satellites in rainfall estimation are the high temporal and spatial resolutions. However, the accuracy of this approach is limited due to the rather basic assumption that rain rates and cloud top temperatures show a negative correlation. This assumption is only valid for convective cloud systems and only partly true for frontal and orographic cloud systems. For warm fronts, this is not valid since the rain in such cloud systems is not associated with the highest clouds but occurs much later (Heinemann 2003). Even in areas dominated by convective activity, cloud types which are non-convective occur, for example cirrus clouds, resulting in errors for IR rainfall estimation also here.

The use of PM-data in rainfall estimation is a more direct method. Rainfall over land and sea can be estimated by looking at the absorption of microwave radiation by liquid water and the scattering of it caused by ice particles (Heinemann et al. 2002). According to Blackmore et al. (2007), algorithms that primarily uses PM-data in Africa overestimates rainfall. The reason for that could possibly be the poor temporal sampling of the polar orbiting satellites (carrying the PM-sensors).

By using a combination of both IR- and PM-data, a possible improvement of rainfall estimation can be done, using the PM-sensor more accurate rainfall estimation with the IR-sensor resolution advantage (Heinemann et al 2002). Two of the datasets analysed in this report uses both IR- and PM-data, RFE2.0 and MPE. This approach is also limited by the temporal resolution of the PM-data, relying only on IR-data when no PM-data is available.

2.3.2 Lightning

Several studies have been made in finding correlation between the amount of convective precipitation and the number of lightning strikes. The majority of these studies have been case studies for a single or an ensemble of thunderstorms in a mid-latitude region. Petersen & Rutledge (1998) estimated the amount of precipitation from CG-lightning by studying specific thunderstorms. They observed the warm-season rain yield for several domains during one-month periods over an area of 10

km

. Two domains, divided into several subdomains, were chosen for their study. One over the United States (U.S.) and the other one over northern Australia i.e. the mid-latitudes and the Tropics, respectively. By comparing the amount of rainfall, specifically caused by deep convection, with number of lightning strikes, they proposed an RLR hypothesis.

In the study by Petersen & Rutledge (1998), they concluded that the RLR depended much on differ-

ent regimes and generally increased with a more humid or tropical maritime climate. For instance, more

rainfall per CG-lightning was produced over the tropical continent than over the mid-latitude continent.

However, better correlation between the CG-lightning and rainfall was seen in the mid-latitudes than in the Tropics and questions arose whether the same technique can be used to make an RLR in the Tropics, since a robust ice-phase is not needed for precipitation to occur. They studied this problem further by analysing the annual and diurnal cycles of lightning and rainfall data for French Guyana and northern Australia. Correlations between rainfall and CG-lightning strikes were seen but with more dependence on the type of regime. For example, the RLR differed whether there was a monsoon period or in-between monsoons, or if it was a continental or a maritime environment. More pronounced positive correlations between rainfall and CG-lightning were seen for in-between monsoons than monsoon regimes. Further- more, poorer correlations were seen in the maritime environments than for the continental due to the differences in convective properties.

Xu et al. (2012) did a comprehensive study looking at different approaches to correlate the amount of precipitation to lightning. The study used measurements from the Tropical Rainfall Measuring Mission (TRMM) satellite’s precipitation radar (PR) and lightning image sensor (LIS) during 1998-2010. When comparing precipitation from radar reflectivity with detected lightning, positive correlations could be seen where either linear or power law functions could be made to relate the two parameters. However, when comparing precipitation intensity with lightning frequency for different spatial resolutions, poor correlations were seen. The correlation coefficients were 0.2-0.3 and decreasing with finer resolutions, hence no continuous functions could be estimated. Instead, as connections between the intensity in precipitation and lightning density still could be seen, a probabilistic approach was implemented where the probability for heavy rain increased with denser lightning frequency, especially for spatial resolutions of around 15 km. The probability distribution for this had a significance level of 95%.

In their study, Xu et al. (2012) concluded that lightning detection is a good tool to improve the

estimates from geostationary satellites. The use of lightning can better locate convective cloud cores

which sometimes are hard to trace by the satellites’ IR-sensors as well as filtering out false precipitation

estimates from cold cirrus clouds.

3 Datasets

3.1 Station Data

3.1.1 GTS Station Data

The observation data used in this report are taken from the Global Telecommunication System (GTS).

Station reports of rainfall in this system are provided by the member countries of the World Meteorolog- ical Organization (WMO) and consist of daily rainfall measurements from all over the world. In total, daily rainfall observations are available for about 6000 stations, but in Africa the observation network is sparse (Chen et al. 2008). The GTS-station data used in this report cover the period between 01/08/2012 and 30/09/2013 and the area from 5

N to 15

N and from 9

E to 15

W. The number of stations in this dataset is 112, although every station does not provide measurements every day.

3.1.2 Reference Data

In order to verify the results from the comparison between the satellite datasets and the GTS-station data, another independent and limited dataset of observed rainfall has been collected from non-governmental organisations (NGO) collaborating with farmers. This reference dataset consists of daily rainfall mea- surements for the time period between 01/03/2013 and 30/06/2013. The number of stations in this dataset are 31 and they are spread in the area from 5.87

N to 11.02

N and from 2.52

E to 0

E.

Annual rainfall measurement data are also used in this report. These data are collected from Ghana’s Meteorological Institute for five different locations in Ghana: Navrongo (10.9

N, 1.1

W), Tamale (9.41

◦

N, 0.85

W), Kumasi (7.75

N, 2.1

W), Wenchi (6.67

N, 1.62

W) and Accra (5.57

N, 0.2

W). The measurements cover the year 2010-2012, except for Accra where no data for the year of 2011 exist.

3.2 Satellite Data

3.2.1 RFE2.0

The RFE2.0-dataset, provided by NOAA, delivers 24-hour rainfall data for the whole of Africa (from

40

S to 40

N and from 20

W to 55

E). The data are provided in a resolution of 0.1

× 0.1

, and

this high gridded spatial resolution is unique for this kind of product (Novella et al. 2012). The dataset

consists of input from satellite observations by two passive microwave instruments, the Advanced Mi-

crowave Sounding Unit (AMSU) and the Special Sensor Microwave/Imager (SSM/I). It also uses half

hour samples of cloud top temperatures from IR-data from the geostationary satellites Meteosat 5 & 7

and daily rainfall gauge data. Since there are different measurement periods for the data from the polar

orbiting satellites (PM-data) and the data that come from the geostationary satellites (IR-data), they are

combined by using linear interpolation. The equation used to do this is:

S =

3 i−1

∑

W

× S

(5)

Where S

is the individual satellite rainfall estimate and W

is the weighting coefficient for the different satellite rainfall estimations. The weighting coefficient of the satellite sets are determined from their random errors by using the following equation:

W

= σ

3 i−1

∑

σ

(6)

Where σ

is the random error. The random error, in its turn, is calculated by comparing the estimated precipitation to actual rain gauge data (NOAA CPC 2003). These results are then merged with gridded rainfall gauge measurements to obtain the final product (Laws et al. 2003). The merging works in such a way that close to the gauge measuring point, the dataset relies more heavily on the observed value, while further away from the measuring point it relies more heavily on satellite measurements (NOAA CPC 2003). In this report, RFE2.0-data from the period 01/01/2010-31/12/2013 and the geographical coverage from 5

N to 15

N and from 9

W to 15

E are used.

3.2.2 ARC2

The African Rainfall climatology, version 2 (ARC2) is a 29 year precipitation estimation dataset centred over Africa. The dataset uses input from two sources, EUMETSAT’s 3 hourly geostationary IR-data centred over Africa and quality controlled GTS-station data. The merging of these two inputs works the same way as the merging between satellite input and GTS-station data for RFE2.0 (see section 3.2.1).

The spatial resolution of the ARC2-dataset is 0.1

× 0.1

. The ARC products (ARC1 and ARC2) was

constructed due to the temporal brevity of the dataset record of the RFE2.0-dataset. The RFE2.0-dataset

does not allow users to see trends and changes in rainfall on long enough periods of time in order to

assess the current state and evolution of the climate in Africa. The reason that ARC2 only has two inputs

(IR-data and gauge measurements) is due to the availability and consistency of these two over time. Both

rain gauge measurements and IR-data can be accessible over a long period of time whereas PM-data

can not. The advantages with ARC2 compared to other satellite precipitation datasets is, as already

mentioned, its long consistency in time but also its spatial resolution (as for RFE2.0), which allows users

to see rainfall phenomena on a local scale. The drawbacks with this dataset is that it is failing at capturing

locally heavy precipitation events, most likely to do with the exclusion of microwave rainfall retrievals

and the 3 hour temporal gap (Novella et al. 2012). In this report, ARC2 data between 01/01/2010 and

31/12/2013, with a geographical coverage from 5

N to 15

N and from 9

W to 15

E are used.

3.2.3 MPE

The MPE (Multi-sensor Precipitation Estimate) is an instantaneous rain rate product. The spatial resolu- tion is 3×3 km (Heinemann 2003). It is derived from the blending brightness temperatures (BBT’s) by IR-data from the geostationary EUMETSAT satellites and with passive rain rate data from polar orbit- ing microwave sensors. The sensor is the SSM/I which is located on Defence Meteorological Satellite Program (DMSP) satellites. The conversion of microwave radiance to rain rates is formed with the NOAANESDIS scheme. Calibration between IR-data from the geostationary satellites and the PM-data from the polar orbiting satellites is done by first co-locating them in time and in space. The spatial co-location is when a METEOSAT pixel has its geographical centre in an SSM/I pixel. The temporal co-location corresponds to the spatial, and the largest difference between a measurement of the SSM/I and a METEOSAT scan is 30 minutes. In tropical regions (including West Africa) the average time difference is ten minutes, but a temporal floating average of rain rate is applied to reduce the effects of the time difference. When the co-location is done, BBT and rain rates from microwave radiance are statistically matched, resulting in look up tables that describe the relation between the datasets. This is done in order to get rain rates from BBT’s. For each spatial grid of 5

× 5

, one look up table is created.

Each IR-pixel in this grid is ascribed its rain fall intensity adjusted by the grid’s specific look up table.

For the border pixels of each grid, a mix of the look up tables surrounding this pixel determines the rain rate for it. Using the MPE algorithm, some limitations and errors arise. First of all, the algorithm is only valid for convective clouds, other forms of precipitation will be incorrectly estimated. Secondly, the bad temporal resolution of the polar orbiting satellites sometimes makes it impossible to create a look up table for each 5

× 5

grid. When this happens, the rainfall amounts for all pixels in the grid concerned is put to zero. The same thing also occurs when the grid box is ”too dry”, meaning not enough rainfall data are present to derive a look up table (Heinemann et al 2002). In this report, MPE-data for the period of 01/01/2010-31/12/2011 and 01/08/2012-30/09/2013 are used.

3.3 Lightning

3.3.1 GLD360

The Vaisala Global Lightning Dataset (GLD360) has a worldwide band of sensors detecting abnormality in the magnetic field, i.e. when a lightning discharge occurs. The dataset consists mainly of CG-lightning with a detection efficiency of at least 70% and with a median location accuracy of 5-10 km (Vaisala 2015).

In this work, the time period of the dataset is from 01/03/2012 to 30/06/2013 and covers an area with the

coordinates from 3.55

N to 11.15

N and from 8.05

W to 3.05

E.

Pohjola et al. (2011) compared the GLD360 to the NORDLIS lightning detection network in northern Scandinavia (59

N-70

N, 21

E-31

E) to investigate the performance of GLD360. Although it is not perfect, they considered NORDLIS to be an accurate and stable network, i.e. when compared to GLD360 the NORDLIS data were seen as true values.

By dividing the number of lightning locations from GLD360 by the first CG-stroke location detected by NORDLIS in the area, Pohjola et al. (2011) made a relative detection efficiency (RDE) for GLD360.

From this, GLD360 had an average RDE of 78% for a daily comparison. However, large variation was seen for the RDE, ranging from a few percent for some days to above 100% for other days. The reason for this variation was thought to be dependent on (1) the storm characteristics, (2) when the storm pass during the day and (3) the sensor redundancy in the region. When Pohjola et al. (2011) made an hourly comparison, the RDE showed little variation with an average of 78%. However, a drop to 30% was seen around 9 UTC which might explain the large day-to-day variation.

Furthermore, Pohjola et al. (2011) studied the relative location accuracy (RLA) of GLD360 by comparing temporal matched events with NORDLIS most accurate first stroke. They stress that the uncertainty of the absolute accuracy of NORDLIS makes the comparison less interpretable. Also, a systematic sensor error in the GLD360 corrupted the comparison. Despite this, the average location difference was 9.4 km and the median difference 7.5 km. Table 1 shows how many events of GLD360 that were within different radii from the NORDLIS location.

Table 1: Below is listed how many CG-events from GLD360 occurred within different radii from the NORDLIS stroke location. Values are taken from Pohjola et al. (2011).

Radius [km] No. of events [%]

1 5

2 15

5 37

16 90

Pohjola et al. (2011) concluded that the detection efficiency of CG-lightning by GLD360 is 70%

with some diurnal variations and with a location accuracy of 5-10 km. Their result is similar to when

GLD360 was compared to the National Lightning Detection Network (NLDN) data in the U.S. In overall,

GLD360 performs less accurately compared to a local lightning system (LLS). The results are, however,

good enough for GLD360 to be used in areas without an LLS.

4 Method

4.1 Comparisons Between The Different Datasets

4.1.1 Satellites to GTS-Station and Reference Observation Data

The ability of the satellite datasets to estimate rainfall amounts, two datasets of observation measure- ments were used for comparison on a daily basis. The first one is observations from the GTS-station data (explained in section 3.1.1). These daily comparisons were made for the time period of 01/08/2012- 30/09/2013. Since two of the satellite datasets (RFE2.0 and ARC2) used in this report already have been calibrated to this observation data network, a reference dataset (explained in 3.1.2) is used to verify the result of the initial comparison. The reason why the reference observation dataset is not the only dataset used to compare the satellite datasets with is, partly, the sparse observations and the short time this dataset captures. However, the main reason is the interest of validating its performance, and to see how the observations correspond to the datasets and influence the estimates, both in GTS observation points and at other locations in West Africa. The comparisons with the reference dataset stretches be- tween 01/03/2013 and 30/06/2013. Comparisons for the three satellite datasets were also made on an annual accumulation basis, comparing the estimated annual amount of rainfall to observed rainfall totals gathered from Ghana’s Meteorological Institute, further explained in section 3.1.2. The annual compar- ison is for the years 2010-2012, with exception of the year 2011 for Accra and the year 2012 for the MPE-dataset due to lack of data. In addition, also the cumulative rainfall amount for the reference period was analysed for the reference observations and the satellite datasets. To compare the different satellite datasets with observations, the pixel in the datasets closest to the latitudinal and longitudinal position of the observation station was used. If a station is positioned in such a way that there are several pixels which have the same minimum distance to it, the rainfall amount that will be compared to the station data is the mean value of all those pixels.

4.1.2 Lightning to GTS-Station and RFE2.0 Data

Two approaches were made to estimate the precipitation amount from lightning. First, the GLD360 was

compared to daily precipitation from the GTS-station data to see whether any tentative relations could be

seen. For the comparison between GLD360 and GTS-station data, the time period was from 01/08/2012

to 30/06/2013 when both datasets were available. Different lightning detection radii from the stations

were compared as well as different time periods where either the total lightning during 24 hours was

used or the hour when most of the lightning occurred. The latter was too see whether better correlation

could be made, since the time period for a storm cell affecting an area is usually an hour or less. In the

results, data from the hour with the highest lightning frequency of the day will be presented. However, little difference in trends were seen between using the hour with most lightning frequency and the total amount during a 24-hour period. The differences between different radii were small as well. When less than 2 km, too little amount of lightning data were available for an analysis and radii larger than 20 km was thought to be too large and unrepresentative when compared with the amount of precipitation from the station. In the result, a radius of 10 km is presented as this area is matching well with the typical cloud cell size and had enough measurements for an analysis.

The second approach was to compare the GLD360 to rainfall estimates from RFE2.0 to check if the intensity of precipitation correlates with the lightning density (LD). For this analysis, the complete time period of the GLD360 could be used with a temporal resolution of 24 hours where the total amount of lightning was compared with the corresponding grid-point in RFE2.0. This dataset was used because it is generally known to be the most accurate one in Africa as its estimate uses both IR- and PM-data and has been weighted with GTS-station data. To see a trend between the precipitation and lightning, the precipitation distribution for different LD was analysed.

4.2 Statistical Methods

4.2.1 Statistical Variables

The datasets are compared with observation data using standard statistics presented below. If nothing else is expressed, the reference in this chapter is Alexandersson & Bergstr¨om (2009).

Bias = 1 N

N

∑

t=1

(x

− x

) (7)

The bias is used to see whether there is an underestimation or overestimation of the observations. x

is the satellite estimated rainfall, x

is the observed rainfall and N the number of measurements.

Absolute bias = 1 N

N

∑

t=1



|x

− x

|



(8)

The absolute bias does not show the direction of the error, but the average magnitude of it.

RMSE = v u u u t

N

∑

t=1

(x

− x

)

N (9)

The Root Mean Square Error (RMSE) also gives the average magnitude of error but since it is weighted

to the square of the error (as seen in the formula), the RMSE gives a greater weight to the large errors in the sample (Sayyedi 2010). Also the Centered Root Mean Square Error (CRMSE) is used in the report, since some of the results are best illustrated in a Taylor diagram:

CRMSE = v u u u t

N

∑

t=1



(x

− x

) − (x

− x

)



N (10)

x

is the mean of satellite estimated rainfall and x

is the mean of observed rainfall.

Correlation coe f f icient = r =

N

∑

t=1



(x

− x

) ∗ (x

− x

)



N ∗ std(x

) ∗ std(x

) (11) The correlation coefficient investigates the linear dependence between two dataseries. The coefficient ranges between (-1) and 1, values close to one indicates a high linear dependence whereas values close to zero indicates low linear dependence. std(x

) is the standard deviation of satellite series and std(x

) is the standard deviation of observation series.

std = s

∑

i=1

(x

− ¯x)

N (12)

The standard deviation tells more about the spread in the values of a dataset. For a dataset to be a good proxy of another, they should have standard deviations of the same size.

4.2.2 Probabilistic Distributions

Since nature generally shows a stochastic pattern rather than continuous, statistical and probabilistic tools are used to interpret mathematical descriptions of it. Describing reality with probability distributions gives a fundamental description of how a system works. Normal distributions are the most common ones where a variable, x, can be described by a probability density function (PDF), which normally is parameterised with a scale and shape parameter (expected value), denoted µ and σ , respectively:

f (x) = 1 σ

√ 2π e

(x−µ)2

2σ 2

(13)

Usually, the arithmetic average, ¯ x, is used as the scale parameter and the shape parameter denoted by the standard deviation, s. In a perfectly normal distribution, the median and the arithmetic average is the same value (Limbert et al. 2001).

Many systems in nature are not normally distributed and many parameters in meteorology often show

a positively skewed distribution. Furthermore, if the arithmetic average is low with a large variability,

a log-normal distribution is often a better option. The main difference between the two distributions is whether their symmetry is additive or multiplicative, where the latter is log-normal. Mathematically, x is log-normally distributed if log(x) has a normal distribution. The parameterised log-normal PDF of x is expressed as:

f (x) = 1 x · σ √

2π e

(14)

The most efficient estimators for the two parameters in eq. (14) are the geometric average, ¯ x

, and the multiplicative standard deviation, s

, generally expressed as:

¯ x

=

n

∏

i=1

x

!

(15)

s

= exp





"

1 n − 1

n

∑

i=1

h log( x

¯ x

)

i

#



 (16)

where n is the number of measurements. Hence the additive and multiplicative differences between the normal and log-normal distributions (Limbert et al. 2001).

4.3 Regimes

4.3.1 Spatial

The area analysed for satellite comparisons with the observations in this report stretches between 1

N to 15

N and between 9

W to 15

E. Due to the area restriction in the GLD360, the comparison between lightning and relevant datasets are 5

N-13

N and 3.05

W-8.05

E.

Since there is a difference in coastal and continental climate and hence the cloud building (see section 2.1.1), a division between these regimes was made during the analysis for all datasets. For the satellite datasets, the coastal regime stretches between the latitudes of 1

N-6

N whereas the range is 5

N - 7

N for the GLD360. The latitudinal difference in coastal regimes for satellite- and lightning datasets is due to the different longitudinal range. The continental regime of the satellite datasets is between 6

-15

N.

Since lightning are more dependent on the humidity, the continental regime has been divided into two, 7

◦

N-9

N and 9

N-13

N, for these comparisons. This will further be explained in section 4.3.3. Figure

4 shows the spatial regimes for satellite and lightning comparisons.

Figure 4: A map showing the satellite regime where the yellow line separating the coastal regime from the conti- nental. The large blue box shows the lightning regimes which is divided into three smaller boxes with one coastal regime and two continental regimes.

4.3.2 Filtering of Data

For the analysis on how well the satellite datasets estimate rainfall, a subdivision of amount of rainfall

is also made in the analysis. Rainfall observations over 100 mm were considered too few for a robust

statistical analysis to be made and is therefore not analysed in this report. Observations with rainfall

amounts equal to zero are also not considered in this report. This is done to avoid the errors in station

reports when no measurements are done. It is then sometimes reported as 0 mm rainfall, even if there

was heavy rainfall on the reported date (Laws et al. 2003). Concerning rainfall amounts between 0 and

100 mm, three subgroups were created for statistical analysis: >0-10 mm, >10-50 mm and >50-100

mm. Farmers in West Africa are more interested in the ability to monitor and predict heavy rainfall

than smaller amounts of rainfall, due to the risk of crop losses connected to it. Since the number of

observations of 0-10 mm is by far dominant, these were analysed separately to be able to see trends in

the estimation of heavy rainfalls outside that range. For rainfall observations over 50 mm, the amount

of observations decreases rapidly, making it harder to rely on the results, and therefore a division at

50 mm was done. In table 2 and 3 the amounts of observations of the GTS- and the reference dataset,

respectively, for each geographic satellite regime are presented.

Table 2: The number of GTS-observations that exists in each satellite regime during the time period 01/08/2012- 30/09/2013.

Rainfall [mm] >0-10 >10-50 >50-100

Whole 3428 2165 220

Coast 684 363 54

Continental 2744 1802 166

Table 3: The number of reference observations that exists in each satellite regime during the time period 01/03/2013-30/06/2013.

Rainfall [mm] >0-10 >10-50 >50-100

Whole 390 359 34

Coast 59 27 2

Continental 331 332 32

For the analysis on the relation between lightning and rainfall, only CG-lightning from the GLD360 has been used, even though cloud-to-cloud (CC) lightning also is detected. However, the number of detected CC-lightning is low in relation to CG-lightning and has been discarded for this analysis. From previous studies, better correlations between CG-lightning and precipitation have been seen, which fur- ther motivates why CC-lightning have not been used. Furthermore, when no precipitation is registered, the corresponding lightning data have not been used and vice versa. Thus, the results regarding the rainfall/lightning trends only show when both precipitation and lightning have been registered and no information whether the likelihood of e.g. precipitation with or without lightning.

4.3.3 Temporal

To find relationships between GLD360 and rainfall, the data have been divided into temporal regimes to find better correlations, as seen from previous studies. A distinction between the wet and the dry period has been made to see whether the monsoon has a large impact on the RLR. The wet and the dry period are of different length depending on the spatial regime. The reason for this is the movement of ITCZ where the front of it can be regarded as the start of the wet period. To further analyse the differences in temporal regimes, two smaller time periods, same for all zones, have been chosen as well, one from April to May (AM) and the other one from June to September (JJAS). Note that the latter period is equal to the wet period of the lightning regime between 9

N and 13

N.

Keep in mind that the chosen temporal periods, denoted wet and dry, in this analysis are general and

the beginning and end of the wet period may vary between years because of the atmospheric oscillations

such as El Ni˜no and Madden-Julian etc. However, as this analysis is a first approach to see trends between

seasons and zones, a general distinction of the wet and dry period is acceptable, as it will be dominated

by data from the relevant conditions. Table 4 shows which latitudinal coordinates that have been used to

separate the spatial zones as well as their respective length of the wet period.

Table 4: The chosen spatial zones for the lightning/rainfall comparison with their corresponding latitudinal coor- dinates and wet period time. The longitude coordinates are the same for all zones, 8.05

W-3.05

E.

Zone Spatial coordinates Wet period length

1 5

N-7

N 1st April - 31st October

2 7

N-9

N 1st May - 31st October

3 9

N-13

N 1st June - 30th September