Hybrid Rainfall Estimates from Satellite, Lightning and Ground Station Data in West Africa Nederbördsestimat Från Satellit Och Blixtar I Västafrika

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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

GEOVETENSKAPER

DEPARTMENT OF EARTH SCIENCES

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 Published at Department of Earth Sciences, Uppsala University (www.geo.uu.se), Uppsala, 2015 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 molntoppstemperaturen 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 necessary. 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 temperature 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.

1 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 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.

3 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−1 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

4 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

5 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−1. 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 × 10−9 Cm−2 and the global fair weather charge is approximately −5.1 × 105 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, respectively. 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/r2, 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−4.52z + 38.6e−0.375z + 10.27e−0.121z (1)

where z is the height. Using the permittivity of vacuum, ε0, and Gauss law:

∇ ·~E = ρ/ε0 (2) eq. (1) can be expressed as:

ρ = 20.4e−4.52z + 0.8e−0.375z + 0.069e−0.121z (3)

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

6 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 × 10−12 Am−2 and globally a value of 1,500 A. Based on the average value, it would take approximately 6.5 minutes for the global current to neutralize the total fair weather charge of −5.1 × 105 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, Tc.

7 If T < Tc, the graupel will be charged negatively while on the contrary for T > Tc. The value of Tc 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.

8 (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: 6 f ≈ Rw ~Vi (4) where f is the lightning frequency, R the cloud radius, w the up-draft speed and ~Vi 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.

9 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 environment). 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 105 km2. 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 different 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.

10 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.

11 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 measurements 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

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

3 S = ∑Wi × Si (5) i−1

Where Si is the individual satellite rainfall estimate and Wi 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:

σ −2 W = i (6) i 3 −2 ∑ σi i−1

Where σ 2 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

13 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 resolution 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 orbiting 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

14 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.

15 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 measurements 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 between 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 comparison 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

16 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 & Bergstrom¨ (2009).

1 N Bias = ∑ (xs,t − xo,t ) (7) N t=1

The bias is used to see whether there is an underestimation or overestimation of the observations. xs is the satellite estimated rainfall, xo is the observed rainfall and N the number of measurements.

1 N Absolute bias = ∑ |xs,t − xo,t | (8) N t=1

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

v u N u 2 u ∑ (xs,t − xo,t ) RMSE = tt=1 (9) N

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

17 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:

v u 2 u N u ∑ (xs,t − xs) − (xo,t − xo) tt=1 CRMSE = (10) N xs is the mean of satellite estimated rainfall and xo is the mean of observed rainfall.

N ∑ (xs,t − xs) ∗ (xo,t − xo) Correlation coe f ficient = r = t=1 (11) N ∗ std(xs) ∗ std(xo) 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(xs) is the standard deviation of satellite series and std(xo) is the standard deviation of observation series.

s N (x − x¯)2 std = ∑ i (12) i=1 N

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:

2 1 − (x−µ) f (x) = √ e 2σ2 (13) σ 2π

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,

18 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:

1 − 1 (log(x)−µ)2 f (x) = √ e 2σ2 (14) x · σ 2π 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:

1/n n ! ∗ x¯ = ∏xi (15) i=1 " #1/2 n 2 ∗ 1 h xi i s = exp ∑ log( ∗ )  (16) n − 1 i=1 x¯ 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.

19 Figure 4: A map showing the satellite regime where the yellow line separating the coastal regime from the continental. 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.

20 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 further 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 Nino˜ 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

21 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 coordinates 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

22 5 Results

5.1 Satellite Results

5.1.1 Dataset Comparison

In figure 5, a comparison between the three satellite datasets (RFE2.0, ARC2 and MPE) and observations from the GTS-station data, for rainfall amounts of >0-100 mm, is seen. The figure shows that RFE2.0 has the best correlation to the observation values (0.62). RFE2.0 also has the best values for CRMSE (12.94 mm) and, although the ARC2-dataset has the closest standard deviation (12.82) to the observations, the conclusion is that the RFE2.0-dataset best estimates rainfall amounts for the total rainfall range >0-100 mm. The ARC2-dataset has a slightly smaller correlation (0.56) and a higher CRMSE (13.85) compared to the RFE2.0. The reason for that is probably the lack of PM-data to the input in the ARC2 algorithm and the poor temporal sampling. The MPE-data shows the poorest correlation (0.26) to observation data, likely due to no observation gauge measurements as an input to its algorithm. In figure 6, a comparison between the three satellite datasets and observed rainfall, for each rainfall amount category, is shown. In 6a the comparison is for rainfall range >0-10 mm, in 6b the comparison is for the range >10-50 mm and in 6c for >50-100 mm. All figures show the same pattern as for the whole dataseries (i.e. RFE2.0-data best estimate the observations from GTS-stations). From the figures it is also seen that the best correlation between satellite data and observations of rainfall is in the >10-50 mm span (for all satellite datasets). The fact that larger rainfall amounts (>50- 100 mm) is more poorly caught by the satellites is probably due to the poor number of observations of such rainfall amounts and it is hence hard to draw any conclusions from this.

23 Figure 5: A Taylor diagram comparing RFE2.0, ARC2 and MPE with observations from GTS-station data. This is done for rainfall amounts of >0-100 mm and the time period of 01/08/2012-30/09/2013. Included in this comparison is the correlation coefﬁcient, CRMSE and standard deviation.

24 (a) >0-10 mm (b) >10-50 mm

Figure 6: The Taylor diagrams comparing satellite data (RFE2.0, ARC2 and MPE) with observations from the GTS-station network. The comparison is divided in each rainfall amount subcategory and the time period 01/08/2012-30/09/2013. Included in the comparison are the correlation coefﬁcient, CRMSE and the standard deviation for th rainfall amount between > 0 and 100 mm.

5.1.2 Satellite Regimes

Table 5 shows the correlation coefﬁcients and RMSE values for the RFE2.0-dataset divided into the different satellite regimes, compared to observations. From the table it is seen that there is a better correlation and smaller RMSE for the continental regime compared to the coastal regime, concerning rainfall in the >0-50 mm range. The poorer capture of rainfall in the coastal regime is likely due to the change in upper cloud structure for coastal regimes compared to continental. For rainfall amounts of >50-100 mm, the opposite is seen; it seems to be a better correlation and smaller RMSE for the coastal regimes. No explanation for this behaviour was found and it is probably due to the lack of observations, making the results more uncertain, in this span of rainfall amounts

25 Table 5: Correlation coefﬁcients and RMSE values for the RFE2.0-dataset in comparison with the observations from GTS-stations is shown. This is done for each satellite regime the time period of 01/08/2012-30/09/2013.

Rainfall [mm] >0-10 >10-50 >50-100 Statistical variable r RMSE [mm] r RMSE [mm] r RMSE [mm] Whole 0.263 6.51 0.448 14.09 0.122 44.76 Coast 0.234 8.69 0.329 18.76 0.259 40.22 Continental 0.281 5.84 0.508 12.95 0.021 46.15

5.1.3 Linear Adjustment

Figure 7 shows in 7a) the relation between the median of the estimated rainfall amount by RFE2.0 for each unique rainfall amount value of the observation (y-axis) and the unique observations values from the GTS-dataset (x-axis). Each integer value in mm is presented and this plot is only for the continental regime since it showed the best correlation between satellite data and observation data. It is seen from the graph that the median values of RFE2.0 deviate more from the observed values as the rainfall amounts increases (>10 mm). A perfect match would be a 45◦ line, signifying 1:1 correspondence. In an attempt to get a better precipitation estimate, a linear adjustment was formed on the median. One relation for each rainfall amount domain was made and they can be seen in table 6. The result of this linear adjustment is seen in ﬁgure 7b). In order to estimate whether this is a good approximation some statistical analysis was made on the datasets, both the unadjusted RFE2.0 and the adjusted one. The results are shown in table 7. It is seen that even if the bias is reduced, the RMSE and the absolute bias are increased for the adjusted dataset in comparison with the original RFE2.0-dataset. This tells us that the dataset has a too large amount of extreme values for the adjustment to be proper and will probably not be a better estimate of rainfall than the original RFE2.0-dataset. A quick scan through a number of correction functions point to that the RFE2.0 seeks to minimize RMSE. This would imply that any alteration of original data will cause an increase in RMSE.

26 (a) Unadjusted

(b) Adjusted

Figure 7: Showing in (a) the median for estimated rainfall for each unique observation value (blue stars) and in (b) the linearly adjusted median. The blue line in both ﬁgures is the 1:1 correspondence line.

Table 6: The linear functions used to bias correct the RFE2.0-dataset for the different rainfall intervals are shown. x is the unadjusted rainfall amount from the RFE2.0 dataset and y is the adjusted amount of the rainfall.

Rainfall [mm] Linear dependence >0-10 y=0.66x+1.57 >10-50 y= 0.56x+2.37 >50-100 y=0.16x+18.11

27 Table 7: The bias, absolute bias, RMSE and the correlation coefﬁcient are shown for the RFE2.0-dataset and the linearly adjusted RFE2.0-dataset compared to observations from GTS-stations. This is shown for each rainfall amount regime for the time period 01/08/2012-30/09/2013.

Dataset RFE2.0 RFE2.0 adjusted Rainfall [mm] >0-10 >10-50 >50-100 >0-100 >0-10 >10-50 >50-100 >0-100 r 0.28 0.49 0.03 0.62 0.27 0.5 0.12 0.62 Bias [mm] 1.45 -7.71 -41.05 -3.32 2.29 0.48 15.95 2.09 |Bias| [mm] 3.67 9.96 41.23 7.22 4.90 11.68 76.10 9.77 RMSE [mm] 5.84 13.31 47.55 12.69 8.33 16.66 91.21 20.54

5.1.4 Reference Data

In figure 8a, a comparison between the reference observations and RFE2.0 and MPE is demonstrated for the time period 01/03/2013-30/06/2013. The same is seen in figure 8b, but compared to the observations from GTS-stations. These figures show that the MPE-dataset has the same skill in catching rainfall for the GTS-observations as for the reference observations. The RFE2.0-dataset, on the other hand, does not. In figure 8a, there is a much smaller correlation with the observations in comparison to figure 8b. There is also a somewhat bigger CRMSE for the reference observation. Results show that, even if the RFE2.0 shows a better correlation close to GTS-stations, it does not work as well on places away from these stations in West Africa. Rather, it behaves much like MPE, except from smaller CRMSE and standard deviation.

(a) Reference observations. (b) GTS-observations.

Figure 8: Taylor diagrams for the MPE- and RFE2.0-datasets compared to observation data are shown. In (a) the satellite datasets are compared to the reference dataset and in (b) they are compared to the GTS-observations. Included in the comparison are the correlation coefﬁcient, CRMSE and the standard deviation for rainfall amounts between >0 and 100 mm. The time period the comparisons are made is 01/03/2013-30/06/2013.

5.1.5 Annual Comparison

Figure 9 shows the annual amount of rainfall for a set of ground stations, the RFE2.0-dataset, the ARC2- dataset and the MPE-dataset. This is shown for ﬁve different places in Ghana; Navrongo, Tamale,

28 Wenchi, Kumasi and Accra, for the years 2010-2012 (except Accra which only has observations the years 2010 and 2012). The graph shows that the best estimator of the observed annual precipitation amount is, in most cases, the RFE2.0-dataset. Also a comparison of the cumulative rainfall amount for the time period 01/03/2013-30/06/2013 was made, shown in ﬁgure 10. The comparison is made for the location of the 31 reference observing stations. This comparison is made between the reference observation set and the RFE2.0 and MPE. In this comparison, shown in ﬁgure 10, the RFE2.0-dataset strongly underestimates the amount of rainfall. The MPE-dataset does not show any skill of estimating rainfall amounts either, sometimes overestimating it and sometimes underestimating it.

29 (a) Navrongo (b) Tamale

(e) Accra

Figure 9: The annual precipitation amount for Observations, RFE2.0, ARC2 and MPE are shown. This is shown for ﬁve different locations. Navrongo, Tamale, Wenchi, Kumasi and Accra .

30 Figure 10: The cumulative rainfall amount is shown for the months March to June 2013 at 31 different locations in Ghana. This is shown for the reference observations, the RFE2.0-dataset and the MPE-dataset.

5.2 Lightning Results

5.2.1 Lightning Compared to GTS-Station Data

Due to the lack of station data, only general tendencies of the relations between GLD360 and precipitation from GTS-stations are presented. Figure 11 shows the total rainfall amount per station compared to detected number of CG-lightning during the most intense hour of the day and within a radius of 10 km from the station. Figure 11a shows the wet period and ﬁgure 11b the dry period where zone 1 is blue, zone 2 is green and zone 3 is orange. When comparing the different zones, a trend is seen where more lightning strikes per amount of rainfall are seen for zone 3 than for zones 2 and 1, where the latter have less occurrence of lightning with precipitation. This distinction is especially seen during the wet period.

31 (a) Wet period. (b) Dry period.

Figure 11: The total amount of precipitation per GTS-station compared to the total amount of lightning strikes within a radius of 10 km for the wet (a) and the dry (b) period, respectively. Note the scale difference in the amount of precipiation between the periods.

5.2.2 The Distribution of Lightning

When GLD360 was compared to RFE2.0, a log-normal distribution was seen between the rainfall intensity and the LD. The likelihood of heavy precipitation increased with denser lightning, as seen in figure 12, which shows an example for zone 1 during the wet period. Similar trends were seen for all the zones during both the wet and the dry period. The chosen statistical tools to probabilistically relate precipitation intensity to LD were the median and the geometric average. Figure 13a shows an example when taking the geometric average of the amount of precipitation per LD on the linear scale. The figure regards zone 1 during the wet period. The relatively large increase in the amount of precipitation at LD< 10 suggests a linear relation on the logarithmic scale, shown in figure 13b. Similar trends are shown for the other zones, periods etc., and will be presented on the logarithmic scale in order to better see a linear relation between the amount of precipitation and LD.

32 (a) 1-5 lightning strikes. (b) 6-10 lightning strikes.

Figure 12: The precipitation distribution for different LD during 24 hours for every RFE2.0 grid-point. The likelihood of heavy precipitation increases with denser lightning activity.

(a) Linear scale. (b) Logarithmic scale.

Figure 13: The geometric average for the rainfall for different LD on a linear (a) and a logarithmic (b) scale for zone 1 during the wet period. The relatively large increase at the low LD suggests a linear relation on the logarithmic scale.

33 5.2.3 GLD360 Compared to RFE2.0 Rainfall Estimates for Wet and Dry Period

Figure 14 and 15 show how the geometric average and the median of the estimated precipitation vary with LD on a logarithmic scale for the dry and the wet period, respectively. The number of pixel estimates for each LD are also shown. A logarithmic linear dependence between the amount of precipitation and LD is seen where the calculated rainfall-lightning (RL) functions (black lines) are shown and tabulated in tables 8 and 9. The RL-functions follow the pixel estimates well for LD < 50 but deviate for LD > 50, where a larger variation appears. A large difference between the number of pixel estimates is seen where LD < 50 have an order of 103 pixel estimates while LD > 50 have an order of 102 and LD > 100 an order of 101. Thus, with less pixel estimates, the precipitation varies more between different LD making the RL-functions to deviate. The earlier the variation starts, the larger the likelihood of deviating functions. Furthermore, no larger differences between the median and the geometric average are seen except that the latter show slightly less variation in precipitation for larger LD. This is especially true for the wet period where the RL-functions based on the median deviate quicker from the actual precipitation than the geometric average. The largest difference are seen for zones 2 and 3 which have also the lowest amount of pixel estimates. Less difference in the amount of precipitation between zones is seen for the dry period than in the wet period. The distributions are the same, nevertheless. The RL-functions show a better ﬁt for the dry period for all zones whereas it tends to deviate from the estimated precipitation during the wet period at lower LD. Due to less pixel estimates for zones 2 and 3, the variation in precipitation between LD starts early. Thus, it is more clearly seen for zone 1 that the RL-functions tend to deviate from the precipitation already at lower LD, compared to the dry period.

34 (a) The geometric average, zone 1. (b) The geometric average, zone 2. (c) The geometric average, zone 3.

(d) The median, zone 1. (e) The median, zone 2. (f) The median, zone 3.

(g) Pixel estimates per LD, zone 1. (h) Pixel estimates per LD, zone 2. (i) Pixel estimates per LD, zone 3.

Figure 14: The variation in precipitation amount for different LD during the dry period. The logarithmically linear ﬁtted RL-functions are shown as well (black lines). As the number of pixel estimates decreases, more variation in precipitation is seen, appearing as intermittancy spikes.

Table 8: The estimated RL-functions, r(n), for the different zones during the dry period, where n is the number of lightning strikes. The functions have been estimated using the geometric average and the median, respectively. Little variation in the slope is seen whereas the starting value differs both between the zones and the statistical measures.

Zone Geometric average Median 1 r(n) = 0.6log(n) + 4.1 r(n) = 0.8log(n) + 4.5 2 r(n) = 0.7log(n) + 5.2 r(n) = 0.9log(n) + 6.2 3 r(n) = 0.8log(n) + 6.3 r(n) = 1.0log(n) + 7.4

35 (a) The geometric average, zone 1. (b) The geometric average, zone 2. (c) The geometric average, zone 3.

(d) The median, zone 1. (e) The median, zone 2. (f) The median, zone 3.

(g) Pixel estimates per LD, zone 1. (h) Pixel estimates per LD, zone 2. (i) Pixel estimates per LD, zone 3.

Figure 15: The variation in precipitation amount for different LD during the wet period. The logarithmically linear ﬁtted RL-functions are shown as well (black lines). As the number of pixel estimates decreases, more variation in precipitaiton is seen, appearing as intermittency spikes. The RL-functions for zone 1 tend to overestimate the estimated precipitation.

Table 9: The estimated RL-functions, r(n), for the different zones during wet period, where n is the number of lightning strikes. The functions have been estimated using the geometric average and the median. Less variation in the slope value is seen between the different statistical measures whereas differences exist between zones. Larger starting values are seen for the median compared to the geometric average as well as zone 3 compared to zone 1. Compared to the dry period, the starting value for the wet period is larger.

Zone Geometric average Median 1 r(n) = 1.1log(n) + 7.3 r(n) = 1.2log(n) + 8.6 2 r(n) = 2.4log(n) + 9.8 r(n) = 2.5log(n) + 12.4 3 r(n) = 3.3log(n) + 12.0 r(n) = 3.5log(n) + 15.3

36 Figure 16 shows the RL-functions for the different zones and periods. There is a clear difference between the dry and the wet period, both in the amount of precipitation per LD and the variation between zones. Less variation is seen for the dry period where a tendency for more precipitation per LD is seen over zones 2 and 3 than over zone 1. The differences are more pronounced during the wet period when most amount of precipitation occurs over zone 3 while the least amount of precipitation for zone 1. Furthermore, the little difference in the slope value between the geometric average and the median results in similar functions for small LD but differ more for larger LD. Comparing table 8 and 9 the starting value is larger for all respective functions during wet period and is less for zone 1 than for zone 2 and 3. Moreover, higher starting values are seen for the median compared to the geometric average.

(a) Wet period. (b) Dry period.

Figure 16: The RL-functions for the wet (a) and the dry (b) period. Larger variation between the zones is seen for the wet period where zone 1 tends to have least amount of rainfall per LD and zone 3 the most. More rainfall per LD is seen during the wet period compared to the dry period. Note that, for the dry period, the slope of the RL-function based on the median for zone 1 is the same as for the geometric average for zone 3 and is not seen in the ﬁgure.

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

To see further trends in the temporal regimes, two smaller time periods have been analysed. Figure 17 and 18 show the AM and JJAS period, respectively, and how the geometric average and the median of the precipitation vary for different LD for each zone. The number of pixel estimates for each LD is shown as well. Similar trends as for the comparison between the dry and the wet period are seen where less pixel estimates results in larger variation, and the RL-functions based on the geometric average show less variation than the ones based on the median. The RL-functions, tabulated in table 10 and 11, show a better fit for JJAS and tends to overestimate the precipitation for AM, except for zone 2 where the RL-functions show a better fit. For JJAS, the functions based on the geometric average show a better fit for zone 2 and 3 than the median. Furthermore, a higher amount of precipitation occurs during JJAS than AM. The increase is larger for zone 2 and 3 than for zone 1. For both periods, more precipitation per LD

37 occurs for zone 3 while the opposite is seen for zone 1.

(a) The geometric average, zone 1. (b) The geometric average, zone 2. (c) The geometric average, zone 3.

(d) The median, zone 1. (e) The median, zone 2. (f) The median, zone 3.

(g) Pixel estimates per LD, zone 1. (h) Pixel estimates per LD, zone 2. (i) Pixel estimates per LD, zone 3.

Figure 17: The variation in the amount of precipitation for different LD during AM. The logarithmically linear ﬁtted RL-functions are shown as well (black lines). As the number of pixel estimates decreases, more variation in precipitation is seen, appearing as intermittency spikes. The RL-functions tend to overestimate the precipitation except for zone 2 which functions show good ﬁts.

Table 10: The estimated RL-functions, r(n), for the different zones for AM, where n is the number of lightning strikes. The functions have been estimated using the geometric average and the median. Little variation in the slope value between the geometric average and the median is seen as well as between zones 2 and 3. Zone 1 tends to deviate from zone 2 and 3. Smaller starting values are seen for the median and for zone 1 compared to the geometric average and the other zones, respectively.

Zone Geometric average Median 1 r(n) = 0.9log(n) + 6.6 r(n) = 1.0log(n) + 7.8 2 r(n) = 1.3log(n) + 7.7 r(n) = 1.4log(n) + 9.5 3 r(n) = 1.2log(n) + 7.4 r(n) = 1.4log(n) + 9.2

38 (a) The geometric average, zone 1. (b) The geometric average, zone 2. (c) The geometric average, zone 3.

(d) The median, zone 1. (e) The median, zone 2. (f) The median, zone 3.

(g) Pixel estimates per LD, zone 1. (h) Pixel estimates per LD, zone 2. (i) Pixel estimates per LD, zone 3.

Figure 18: The variation in precipitation intensity for different LD for JJAS. The logarithmically linear ﬁtted RL-functions are shown as well (black lines). As the number of pixel estimates decreases, more variation in precipitation is seen, appearing as intermittency spikes. The RL-functions based on the geometric average tends to ﬁt better with the precipitation, especially for zones 2 and 3.

Table 11: The estimated RL-functions for the different zones for JJAS. The functions have been estimated using the geometric average and the median. Less difference in the slope value between the statistical tools are seen as well as between zones. Smaller starting value for the geometric average and for zone 1 compared to the median and the other zones, respectively.

Zone Geometric average Median 1 r(n) = 2.7log(n) + 9.7 r(n) = 3.2log(n) + 11.8 2 r(n) = 3.6log(n) + 12.8 r(n) = 3.7log(n) + 16.2 3 r(n) = 3.3log(n) + 12.0 r(n) = 3.5log(n) + 15.3

Figure 19 shows the RL-functions for the different zones and periods. The RL-functions for each period show little variation between zones where the RL-functions for zone 1 tend to deviate from the rest with less precipitation per LD. This is true for both the geometric average and median for both AM and JJAS where the geometric average for zone 1 for the latter period tends to deviate more from the

39 other functions. More precipitation per LD occurs for JJAS compared to AM and is larger for zone 3 and less for zone 1. When comparing table 10 and 11, the starting values of all respective functions are larger for JJAS compared to AM. The RL-functions of zone 2 have the largest rainfall amount per LD whereas RL-functions for zone 1 have the least.

(a) AM. (b) JJAS.

Figure 19: The RL-functions for the AM (a) and JJAS (b) period. Less variation is seen between the different zones where zone 1 deviates more from zone 2 and 3, especially for AM. More rainfall per lightning density is seen for JJAS than for AM. Note that, for AM, the slope of the RL-function based on the median for zone 2 is the same as for the median for zone 3 and is not seen in the ﬁgure.

5.3 Lightning Correction to Satellite Data

Figure 20 shows an example of how lightning data can be used to improve satellite estimates of the precipitation. The example considers the 24 hour amount of rainfall for 14/08/2012. The RL-functions based on the geometric average have been used to estimate the amount of rainfall from lightning strikes. Due to the poor correlation between RFE2.0 and rain gauge station data, no details of how accurate the amount of estimated precipitation from the lightning strikes is, can be made. Nevertheless, the beneﬁts of using lightning strikes in order to erase e.g. the false precipitation from cirrus clouds as well as locating the trajectory of convective cells are clearly shown.

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

Figure 20: The estimated amount of precipitation from RFE2.0 (a) compared to the converted rainfall amount from GLD360 using the RL-functions based on the geometric average (b). The total amount of precipitation during 14/08/2012 is presented as an example of how lightning can contribute to improve satellite estimates of rainfall.

41 6 Discussion

6.1 The Lack of Station Data

The lack of station data both affects the satellite and lightning comparison. For the comparison with satellite dataset, this mainly affects the analysis for larger amounts of rainfall. As seen in table 2, the number of observations of rainfall for amounts between >50 and 100 mm are less compared to smaller amounts. Therefore, the conclusions are more uncertain for larger rainfall amounts than for smaller. As for the lightning data, no continuous relationship between lightning and rainfall can be made. Two things are affecting this: the little amount of measurements from stations and the narrow time period when both GLD360 and GTS-station data are available. For instance, no relation between lightning and rainfall can be made for June since both of the datasets are non-existing. Furthermore, as seen in ﬁgure 11 the number of stations is small and, as described in the method, when stations fail to report precipitation during a day, the amount of rainfall is set to zero. The common outages in the GLD360 also have a large impact on the already small number of measurements. Even though these measurements have been discarded in the analysis, it still affects the result when comparing GLD360 to GTS-station data. For instance, if a station has failed to report the amount of precipitation on days with lightnings or vice versa, the monthly relation between precipitation and lightning will be misleading for that station. The same discussion can be made for the outages in GLD360. The coarse resolution of stations in West Africa makes this matter even worse since the dependence of the few existing stations increases. Nevertheless, some trends can be seen when looking at ﬁgure 11, where more rainfall amount per lightning strike occurs for zone 3 than in zone 1. Furthermore, more variation between the zones is seen for their respective wet period compared with their dry period, suggesting that a RLR is harder to establish for the maritime environment and depends on the monsoon, as e.g. Petersen & Rutledge (1998) concluded.

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

The assumption made when using IR-data for rain rate retrieval, that cloud top temperatures is directly coupled to rain rates, is a far too basic assumption even in an area dominated by convective activity (as in West Africa). This can be seen by looking at ﬁgure 6a and 6b. Comparing these two ﬁgures it is seen that rain rates between >10 and 50 mm shows a better correlation than rain rates between >0 and 10 mm (for all datasets). Smaller amounts of rainfall (>0-10 mm) is harder to detect from IR-data due to the plethora of cloud types it can emerge from. If rain falls from warm clouds (clouds with a lower cloud top, such that coalescence processes dominate without ice crystals), the temperature is often too high in the cloud top to be regarded as rain by the IR-channels and therefore an underestimation of rain rates occurs. An overestimation can also occur due to that higher clouds, with very low cloud top temperatures, do

42 not always correspond to cumulonimbus clouds (CB). For example, if cirrus clouds or anvils from CB clouds are present, which is a normal state of affairs in areas dominated by convective activity, the rain amount is often overestimated. This over- and underestimation also occurs for high rain rates but is more pronounced for low. In figure 21, an example of how the MPE-dataset sometimes estimates rain from cirrus clouds is seen. The fact that IR-data are poor estimates of rainfall by its own has been seen before (Heinemann et al. 2002) and therefore two of the datasets investigated in this report (RFE2.0 and MPE) also have PM-data from polar orbiting satellites as an input to the dataset. The idea with the PM-data is that it will correct poor estimates from the IR-data but due to its poor temporal sampling it fails in doing so consistently. In figure 21, it is seen what can happen with the rainfall estimation due to poor temporal sampling of the PM-data for the MPE-dataset. To the left in the figure, as previously mentioned, an overestimation occurs due to the presence of cirrus clouds. If the temporal sampling of the PM-sensor would have been better, this would have been corrected. Also, the figure shows another of the MPE-dataset disadvantages regarding the resolution of the PM-sensor. Due to lack of data from the PM-sensor, a look up table for a grid can not be created, hence estimating all clouds as dry in that grid (explained in section 3.2.3). This is most likely what happens at the sharp border in the picture. CB- clouds present in this grid are therefore not correctly estimated. Out of the two datasets using PM-data, MPE is most affected by this since it does not have input from station data, correcting the errors in the satellite data. It is a real-time product, being refreshed every 15 minutes, so it is therefore difficult to correct before being provided to the user community.

Figure 21: The IR-image and the MPE satellite estimation for rainfall intensity, deﬁned by the color bar, over West Africa 2015/02/22 at 21:15 UTC is shown. [Source: EUMETSAT]

43 The fact that coastal regimes show different results compared to the continental regime is due to the difference in cloud characteristics over sea and over land (see section 2.1.1). Since less CAPE is built up over the sea, clouds will have lower cloud tops, hence lower cloud top temperatures compared to continental clouds with the same rainfall rate. In table 5, where the RFE2.0-dataset is compared to observations from GTS-stations, the coastal regions have a poorer correlation and a higher RMSE for rainfall amounts between 0-50 mm compared to the continental regime. This is probably due to that the calibration of cloud top temperatures against rain rates is done for the whole region of West Africa and the main part of it is continental. If a calibration would have been done against coastal regimes an overestimation of rainfall in continental regimes would most likely have been seen. Note also that the coastal regimes can receive more rain due to abundance of moisture and warm cloud rainfall, than what IR-sensors would be able to tell.

6.3 Satellite Datasets Using GTS-stations for Calibration

From figure 6 it is seen, when compared to the GTS-stations, that RFE2.0 shows a better correlation and smaller RMSE values than the MPE-dataset. By looking at figures 8a and 8b it is also seen that, even if the MPE-dataset shows the same skill of capturing the reference observation as the GTS- observations, the RFE2.0-dataset has a lower correlation to the reference observations compared to the GTS-observations. Also figures 9 and 10 show the same pattern. The annual value of rainfall, which is estimated in GTS-observation points, is in general best estimated with the RFE2.0-dataset. When using the reference dataset to estimate the cumulative rainfall amount during the measuring period, RFE2.0 strongly underestimates rainfall. Since GTS-stations are used in the creation of the RFE2.0-dataset, the good result comparing this dataset to GTS-stations is somewhat misleading since it is, to some extent, a self-correlation. Away from the GTS-stations, the estimation of rainfall is more influenced by satellite data (explained in section 3.2.1). The estimations in these points will therefore be less accurate due to the poor ability of IR-algorithms to estimate rainfall amounts, as discussed in section 6.2.

6.4 The ”Best” Satellite Dataset

By looking at ﬁgures 5 and 6, it is seen that RFE2.0 shows better skill in estimating rainfall compared to ARC2. As already mentioned in chapter 3.2.2, the difference in the algorithms between ARC2 and RFE2.0 is the lack of PM-data as an input to the ARC2-dataset. Since PM-data is better at estimating rainfall amounts compared to IR-data, this is why ARC2 is poorer at estimating rainfall than RFE2.0. In addition, the ARC2-dataset is derived from 3-hourly IR images (as compared to the half hour sample of RFE2.0), hence missing what occurs in between. This result was expected since the ARC2-dataset is created for climatological purposes rather than for estimating the exact amount of daily rainfall. Figure

44 5 also indicates that RFE2.0 is a better estimator of rainfall compared to MPE since both the correlation and CRMSE are better for the RFE2.0-dataset. However, to verify these results, comparisons with the reference dataset have to be done since the RFE2.0-dataset is calibrated to measurements from GTS- stations. The difference between RFE2.0 and MPE in the comparison with the reference dataset (seen in ﬁgure 8b) is the values of the CRMSE. MPE has a higher CRMSE value than RFE2.0, indicating that the RFE2.0-dataset has a smaller spread of rainfall amount from the observations compared to the MPE-dataset. The explanation to this could be that the input of station measurements in the RFE2.0- dataset corrects the spread even outside of the points of the measurements. Another explanation for this is that the merging of IR- and PM-data is done in a better way for the RFE2.0-dataset compared to the MPE-dataset. The conclusion is, however, that even in places outside the GTS-observation network, the RFE2.0-dataset estimates rainfall amounts better compared to MPE. However, all satellite datasets show a poor correlation to the observations, hence they are poor at estimating rainfall amounts. Taking this into consideration, the satellite datasets cannot be seen as an optimal replacement of rain gauge measurements in West Africa. For satellite datasets to be able to do that, better instruments need to be installed on satellites and/or better algorithms to capture rainfall need to be developed.

6.5 Expected Value for The Probabilistic Lightning Distribution

As already suggested in the theory, the geometric average is usually the best estimator as the scale parameter (expected value) for a log-normal distribution. For comparison, though, the median was used in the analysis as well. Little difference of the slope value between their RL-functions was seen. Generally, the median showed a higher amount of precipitation per LD than the geometric average. Whichever correlates best with the actual precipitation will remain unanswered in this report. However, smaller variation in precipitation between different LD was seen for the geometric average suggesting it is more stable, and thus more accurate, than the median.

6.6 Rainfall-Lightning Regime Dependence

When comparing the amount of precipitation from the estimates of RFE2.0 with the corresponding number of CG-lightning detected by GLD360, the results show a regime dependence, especially a temporal one. For the dry period, the slope value of the RL-functions was similar between zones as well as between the geometric average and the median. For their respective wet period, the geometric average and the median had similar slope value in their RL-functions, but differed more between the zones. This is most likely due to the complex mesoscale weather systems in West Africa which makes the occurrence and frequency of rainfall during the wet period not as straightforward as for e.g. southern Asia. For instance, because of the strong sea breeze during the monsoon period, the southern part of West Africa

45 experiences a small dry period in the monsoon period. Furthermore, during a part of the monsoonal period, the subsidence at the outskirts of the ITCZ will cause stable stratiﬁcation for zone 2 inhibiting convection and thus less rain. Due to these aspects, the temporal regime dependence was further investigated with a comparison between two smaller time periods, April to May and June to September. Indeed, when divided into shorter time periods, the slope of the RL-functions differed less between the zones whereas variations between the temporal regimes still were seen. A tendency of less rainfall per LD still existed for zone 1 in comparison to zones 2 and 3 due to less CAPE in the coastal environment. Because of the, in general, smaller slope of the RL-functions for zone 1 in comparison to zones 2 and 3, a tendency can be seen where the likelihood of precipitation without lightning are greater over zone 1. The same holds when looking at the starting value of the RL-functions where less precipitation are seen for zone 1 compared to zones 2 and 3, for respective temporal period and statistical measure. An accurate RL-function was harder to make for zone 1 during the wet period and for all zones for AM. This suggests that the probabilistic distribution is more dependent on a smaller temporal regime during the beginning, i.e. the build up, of the monsoon when the ITCZ starts to move northward causing disturbances in the easterly ﬂow. Hence the importance of mapping the beginning of the monsoon period.

6.7 Proposed Solutions and Suggestions for Improvements

As already mentioned, satellite derived rainfall estimations using IR-data as an input show poor skills in estimating the actual rainfall. The major disadvantage is the false rainfall estimation from the cold cirrus clouds as well as locating the trajectory of convective cells. As seen in ﬁgure 20, improvements of such errors can be done using lightning data. A combination between lightning and satellite could, however, not be analysed in this report, since no robust relation between GLD360 and GTS-stations could be established due to the lack of data. Better rainfall/lightning relations can be made if the lightning data are compared to other rainfall measurements. Unfortunately, no such measurements could be retrieved for this report. Overall, in order to estimate the rainfall amount in West Africa more accurately, other measuring techniques and improvements of the already existing ones are needed. Examples of such techniques and improvements are listed below.

6.7.1 The Launch of New Satellites

In the year 2019, METEOSAT will start their launching of six new geostationary satellites. There are two sounding satellites and four imaging satellites which will operate until at least 2030. The Meteosat Third Generation imaging satellites (MTG-I) will contain the ﬂexible combined imager (FCI) and the lightning imager (LI). The FCI will replace the spinning enhanced visible and infrared imager (SEVIRI) on the METEOSAT second generation satellites and will have better spatial, temporal

46 and radiometric resolution. Thanks to this, improvements in the meteorological information of rapid processes in the atmosphere’s water cycle can be retrieved and also the daytime column of precipitable water. The cloud microphysics is also better represented, all this resulting in better rainfall retrievals. Thanks to the LI, total lightning over the hemisphere can be observed continuously and simultaneously. With this instrument, active convective areas can be detected and monitored (MTG 2015). The sounding satellites will carry the infrared sounder (IRS) and the ultraviolet visible near-infrared (UVN) spectrometer. The IRS provides information of horizontally, vertically and temporally resolved water vapor and temperature structures of the atmosphere. This is the first time that the METEOSAT satellites are able to analyze the atmosphere layer by layer and better precipitation forecasts are expected using this data in models. The UVN instrument is designed for chemistry applications (MTG 2015). Also EUMETSAT’s polar orbiting satellites will be replaced into a second generation version. The two satellites (metop A and metop B) will be launched in 2020. Their primary mission is to improve numerical weather prediction but they will also contribute to climate monitoring, marine meteorology and oceanography. This system will be part of a joint polar system with NOAA’s satellites. Since these two satellites will have the same orbit as the first generation, this will make it easier with the continuity of the dataset. The satellites will hold nine different instruments and the ones most beneficial for rainfall estimations are the microwave imaging (MWI) and the ice cloud imaging (ICI) (EPS 2015).

6.7.2 Telecommunication Network

With the ongoing worldwide trend with a decreasing number of weather observing stations, new tech- nologies to measure precipitation are needed, especially in areas with an already coarse density of ground measurements. One proposed solution for this is to take advantage of the growing telecommunication network, which has microwave links between the antennas. The idea is to have an antenna transmitting a radio signal that will be received by a sensor on another antenna. When precipitation occurs, an atten- uation of the radio signal will be seen, and by using algorithms it can be transformed to represent the rainfall intensity in real time (Doumounia et al. 2014). Indeed, studies have proven the method to be useful to monitor precipitation. Doumounia et al. (2014) concluded that even in West Africa, with a coarse density of telecommunication towers, the method estimated the actual rainfall well when compared to a nearby ground station.

6.7.3 Radar

The possible installation of a radar network in West Africa would help to improve the estimated precipitation, as both the temporal and, within a certain area, spatial resolution increases. A radar, especially when combining X- and C-band, gives more information about the structure of the cloud as well as the

47 intensity and location of precipitation. Furthermore, the radar measures precipitation in real time making it easier to monitor the development and movement of a convective cell. With this information, more accurate results are received for both how well a satellite estimates the amount of rainfall, as well as to relate the amount of rainfall to the number of lightning strikes (Xu et al. 2012). A radar will provide continuous information about rainfall in a certain area and thus more data will be available for analysis, compensating for the lack of station data.

48 7 Conclusions

The assumption made using IR-data for rainfall retrieval, that the cloud-top temperature is directly coupled to rain is a far too basic assumption even in an area dominated by convective activity. PM-data better estimate the rainfall amount but, because of its coarse spatial and temporal resolution, a complete picture of the rainfall amount is not obtained. Comparing the different datasets, RFE2.0 is the best rainfall estimator analysed in this report. This statement is valid for comparison with both GTS-stations and the reference stations, although a better correlation is seen with the measurements from GTS-stations, probably due to the use of them in the build up of the RFE2.0-dataset. However, all satellite datasets show a poor correlation to the observations, hence they are poor at estimating rainfall amounts in West Africa. Taking this into consideration, the satellite datasets cannot be seen as an optimal replacement for the rain gauge measurements in West Africa. From the comparison between GLD360 and GTS-stations, only tentative conclusions could be made due to the lack of station data. A more comprehensive analysis could be made when comparing GLD360 to RFE2.0. The comparison between the two datasets showed that the likelihood of heavy precipitation increased with denser lightning activity, suggesting a log-normal distribution and a linear relation on the logarithmic scale. Between the median and the geometric average, the latter was shown to be the most stable one. The rainfall/lightning relation was more dependent on the temporal regime than the spatial one, pointing at the need of smaller temporal regimes especially during the build-up of the monsoon period when the ITCZ starts to move northward. It was also shown that the use of lightning data is a good tool to erase false precipitation from satellite estimates as well as locating the trajectory of convective cells. With the ongoing improvement of instruments on satellites as well as the ground-based remote sens- ing systems, complementing the traditionally in-situ-stations, more accurate rainfall measurements can be made.

49 8 Acknowledgements

We would like to thank Ignitia and especially our supervisor Andreas Vallgren for the opportunity of writing this thesis for you. Also thanks to our supervisor at Uppsala University, Anna Rutgersson. Last but not least the Biology Education Centre who made it possible for us to go to Ghana.

50 9 Contributions of Authors

Below is listed which parts each author has been writing.

Henrik: 2.1.1 Convection 2.1.5 West African Squall Lines 2.1.6 Madden-Julian Oscillation 2.2 Lightning 2.3.2 Lightning 3.3 Lightning 4.1.2 Lightning to GTS and RFE2.0 Data 4.2.2 Probabilistic Distribution 5.2 Lightning Result 6.5 Expected Value for The Probabilistic Lightning Distribution 6.6 Rainfall/Lightning Regime Dependence 6.7.2 Telecommunication Network 6.7.3 Radar

Charlotta: 2.1.2 ITCZ and The Monsoon 2.1.3 Sea Breeze 2.1.4 The African Easterly Jet and the African Easterly Wave 2.3.1 Satellite 3.1 Station data 3.2 Satellite data 4.1.1. Satellite to GTS- and Reference Observation Data 4.2.1 Statistical Variables 5.1. Satellite Results 6.2 The Ability of IR- and PM-data to Estimate Rainfall Amount 6.3 Satellite Datasets Using GTS-stations for Calibration 6.4 The ”Best” Satellite Dataset 6.7.1 The Launch of New Satellites

51 Together: Abstract Sammanfattning 1. Introduction 4.4 Regimes 5.3 Lightning Correction to Satellite Data 6.1 The Lack of Station Data 6.7 Proposed Solutions and Suggestions for Improvements 7 Conclusions 8 Acknowledgement

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