\section{Introduction}
The worldwide production of plastic goods rose exponentially since its introduction to the public after World War II, from 2 Mt in 1950 to 380 Mt in 2015 (average yearly growth rate of 8.4\%) \cite{Geyer2017}. Properties such as light weight, durability, bio-inertness, oxygen/moisture barrier and low costs make plastic an ideal packaging material \cite{Andrady2011}. Thus, 44.8\% of the worldwide plastic resin production is used for packaging materials which have a mean lifetime of half a year \cite{Geyer2017}. Almost half of the 302 Mt of plastic waste produced in 2015 \cite{Geyer2017} was therefore single-use plastic. With increasing plastic waste production, an increasing contamination of plastic waste in the natural environment can be expected \cite{Thompson2004}.\\
Over the past five decades, the plastic waste input to the oceans has continuously risen \cite{Andrady2011,Jambeck2015}. While the first report of plastic in the oceans dates back to 1972 \cite{Carpenter1972}, estimates for 2010 suggest that 4.8-12.7 Mt entered the ocean from the coast \cite{Jambeck2015}. As of today, plastic has been found in the most remote areas of the ocean and in various sizes \cite{Kooi2018}, ranging from the nano (\textless 100 nm) to the micro (\textless 5 mm) and meso (\textgreater5 mm) scale \cite{Andrady2011,Kooi2018}. This global distribution of marine plastic debris has severe effects on marine biota.\\
It is estimated that over 90\% of the damage caused to marine animals by human waste is due to plastic pollution \cite{WWF2018}. Mesoplastics, including lost fishing gear, six-pack drink holders or balloons, can entangle animals. This makes them more vulnerable to predators or can lead to starvation, strangulation or drowning due to exhaustion \cite{Kuhn2015}. Animals such as sharks, sea turtles, sea mammals and birds are especially vulnerable to entanglement \cite{Kuhn2015}. Furthermore, mesoplastics are often ingested by various types of animals. Kühn et al. \cite{Kuhn2015} documented ingestion of plastics in 44\% of 446 observed birds, turtles and sea mammals and Auman et al. \cite{Auman1997} found plastic in 97.6\% of stomachs of chicks of the Laysan albatross. Plastic ingestion can block or damage the gastrointestinal track, which may lead to death \cite{Kuhn2015}. Additionally, plastic pieces can block parts of the stomach, which can lead to reduced digestive processes and a feeling of satiation, which results in malnourishment, dehydration and, eventually, death \cite{Kuhn2015}. In addition to the threats of mesoplastics, micro- and nanoplastics can have deleterious effects on many organisms. Due to their small size they can be ingested, as observed in zooplankton such as \textit{calanus helgolandis} \cite{Cole2015} or \textit{daphnia magna} \cite{Canniff2018, Besseling2014}, algae such as \textit{scenedesmus obliquus} \cite{Besseling2014}, invertebrates such as the fiddler crab (\textit{uca rapax}) \cite{Brennecke2015}, sea urchins such as \textit{paracentrotus lividus} \cite{Martinez-Gomez2017}, sea cucumbers (\textit{holothuroidea}) \cite{Wright2013} or corals such as \textit{acropora}, \textit{pocillipora} and \textit{porites} \cite{Reichert2017}. Besides these direct physiological and physical effects on biota, plastic also poses a chemical risk.\\
Marine plastic debris consists of a complex mixture of chemicals, including by-products such as polycyclic aromatic hydrocarbons (PAHs) or absorbed compounds such as polychlorinated biphenyls (PCBs), polybrominated diphenyl ethers (PBDEs) and heavy metals such as Ni and Pb \cite{Rochman2015}. 78\% of the priority pollutants (a list containing 126 well known toxic pollutants in water which is often used for regulations) as listed by the United States Environmental Protection Agency were associated with marine plastic debris \cite{Rochman2013}. Bioavailability upon ingestion has been shown in several marine animals such as whales, sharks, seabirds and fish \cite{Rochman2015}. The ingestion of plastic particles can furthermore lead to the accumulation of deleterious pollutants in the animal itself and the food chain \cite{Rochman2015}. This can cause various sub-lethal effects in smaller animals or poisoning of marine mega fauna and apex predators such as sharks \cite{Rochman2015, Rochman2013, Kuhn2015, Prata2018, Chen2018, Gallo2018}. Additionally, plastic particles may also create an ecological problem by acting as vectors for invasive species \cite{Koelmans2016}. The global economic cost due to damage in marine ecosystems caused by plastic pollution has been estimated to amount to 13 billions USD per year \cite{WWF2018}. Because of the mentioned risk and threats of marine plastic debris, the increasing marine pollution has risen awareness. In the scientific community and among the politicians and the public, efforts are made to understand and solve the problem of plastic pollution.\\
\begin{figure*}[tbp]
	\renewcommand{\arraystretch}{1.2}
	\centering
	\includegraphics[width=\textwidth]{img/publications_1990-2017.pdf}
	\caption{Number of publications listed on Thomson Reuters Web of Science when searching for the terms "ocean" and "plastic" in both title and topics (search query: \textit{TI=(ocean AND plastic*) OR TS=(ocean AND plastic*)}). As of 30. May, 122 publications were listed in 2018 that are not included in the graph. In total, 2'001 publications have been listed from 1968 until 30. May 2018.}
	\label{fig:Publications1990-2017}
\end{figure*}
Political efforts to reduce plastic pollution include plans for product bans and for a 90\% collection rate of single-use drink bottles in the EU \cite{EuropeanComission2018} or the recent total ban of plastic bags in Kenya \cite{Wakhungu2017}. Meanwhile, the scientific community tries to gain further insight on the governing processes of plastic pollution. The number of publications on marine plastic debris were exponentially increasing in the last decade (compare Fig. \ref{fig:Publications1990-2017}). However, the sources, sinks, amount and distribution of plastic particles in the ocean are still barely constrained. Open research questions include the limited understanding regarding the pathways of terrestrial plastic to the marine environment \cite{Cozar2014}, the effects of wind and currents on the floating behaviour of litter items \cite{Kiessling2015}, the degradation processes of plastics in the ocean \cite{Cozar2014,Kiessling2015}, or the missing understanding of (future) trends of plastic debris \cite{Thompson2015}. Nonetheless, several studies have created insights by providing estimates of plastic input to the ocean and current amount of marine plastic debris (compare table \ref{tab:PaperSummary}). However, there is a large difference in the modelled estimates and measurements.\\
\begin{table*}[tbp]
	\renewcommand{\arraystretch}{1.2}
	\rowcolors{2}{}{color2!10}
	\centering
	\caption{Summary of estimates on the amount of plastic debris in the worlds oceans. We present predictions based on measurements and predictions based on model approaches. It is obvious that the modelling approaches predict higher plastic masses in the ocean that what the measurements suggest. This difference is known as the \textit{missing plastic problem}.}
	\begin{tabularx}{\textwidth}{>{\centering\arraybackslash}p{0.3cm} p{2.2cm} p{2.5cm} p{2.5cm} X >{\centering\arraybackslash} p{1cm}}
		\toprule
		& \textbf{Location} & \multicolumn{2}{l}{\textbf{Estimate of plastic in the ocean}} & \textbf{Description} & \textbf{Source} \\ \cline{3-4}
		& & Particles & Mass & & \\ \toprule
		\cellcolor{white} & All oceans & $5.25\cdot10^{12}$  \newline $4.85\cdot10^{12}$ (microplastic) & 268.9 kt \newline 35.5 kt (microplastic) & Estimate based on 24 expeditions in 2007-2013 & \cite{Eriksen2014} \\
		\cellcolor{white} & All oceans & & 6.6-35.2 kt & Estimates based on 2010 Malaspina circumnavigation measurements & \cite{Cozar2014} \\ 
		\cellcolor{white} & All oceans & 15-$51\cdot10^{12}$ (microplastic) & 93-236 kt (microplastic) & Estimates on microplastic particles based on a statistical model incorporating \textgreater 11'000 observation (including \cite{Eriksen2014} and \cite{Cozar2014}) & \cite{VanSebille2015} \\
		\cellcolor{white} & Southern Ocean &  100'000 particles/km\textsuperscript{2} & & Measurements from 5 net tows on an expedition in 2016 & \cite{Isobe2017} \\
		\cellcolor{white} \multirow{-9}{*}{\rotatebox[origin=c]{90}{Measurements}} & North Pacific Central Gyre & 334'271 particles/km\textsuperscript{2} & & Measurements from 11 net tows in August 1999 & \cite{Moore2001} \\ \midrule
		\cellcolor{white} & Coastal regions & & 4.8-12.7 Mt/year & Model including mismanaged MSW of coastal populations in 192 coastal countries & \cite{Jambeck2015} \\
		\cellcolor{white} & All oceans & 1.1-$3.6\cdot10^{18}$ & 45-129 kt & Model based on multiple boat and aircraft surveys & \cite{Lebreton2018} \\
		\cellcolor{white} & All oceans & & 1.15-2.41 Mt/year & Modelled yearly riverine inputs based on mismanaged MSW and river flow model & \cite{Lebreton2017} \\ 
		\cellcolor{white} \multirow{-5}{*}{\rotatebox[origin=c]{90}{Model estimates}} & All oceans & & 0.41-4 Mt/year & Modelled yearly riverine inputs based on mismanaged MSW data from \cite{Jambeck2015} extended with river catchment sizes & \cite{Schmidt2017} \\ \bottomrule
	\end{tabularx}
	\label{tab:PaperSummary}
\end{table*}
Modelling approaches to predict the amount of marine plastic debris based on the total plastic production \cite{Geyer2017} or on the municipal solid waste (MSW) production \cite{Jambeck2015,Lebreton2017,Schmidt2017} estimate yearly plastic inputs on the order of millions of tons. On the other hand, estimates based on ocean surveys predict the total amount of plastic floating at the surface only on the order of thousands of tons. This difference between modelled estimates and measured concentrations is known as the \textit{missing plastic problem} \cite{Cressey2016} and has been discussed since 2004 \cite{Thompson2004}. Furthermore, several ocean regions (including the Eastern Pacific and the North Sea) do not show an increase in surface plastic concentrations since the 1980's \cite{Cozar2014,VanFraneker2015}. This is surprising because the production of plastic waste has increased drastically since and we thus could expect an increased flux to the ocean and thus higher oceanic plastic concentrations \cite{Thompson2004,Geyer2017,Hoornweg2012}. The \textit{missing plastic problem} and the lacking increase in the concentrations thus imply that the ocean surface is not the ultimate destination of plastic that enters the ocean and that unknown sinks exist, that rapidly remove plastic debris from the ocean surface \cite{Eriksen2014,Cozar2014,VanFraneker2015}.\\
Possible removal process of plastic from the ocean surface include degradation, mineralization and sedimentation \cite{Andrady2011,Cozar2014}. As already mentioned above is our understanding of the removal processes of marine plastic debris still limited. However, several mechanisms that could remove plastic from the surface have been suggested. Here we present an overview of these removal processes and their mode of action:
\begin{itemize}[noitemsep,topsep=0pt]
	\item \textbf{UV degradation:} The UV-B radiation in sunlight initiates a photo-oxidative degradation in many common plastics \cite{Andrady2011}. UV degradation is orders of magnitude faster compared to other types of degradation such as hydrolysis \cite{Andrady2011}. The process adds oxygen rich functional groups to the plastic and lowers its molecular weight \cite{Andrady2011} which makes the plastic less stable. Degraded plastics are more prone to be fragmented by physical forces such as waves. However, the light-induced oxidative degradation is severely less effective on plastics floating in water due to lower temperatures and a decreased oxygen availability compared to plastics out of the water \cite{Andrady2011}. Furthermore, UV radiation is rapidly absorbed by the water column and the process is thus only relevant at the water surface \cite{Andrady2011}. Thus, UV degradation can decrease the size of plastic particles.
	\item \textbf{Beaching:} As UV degradation is hindered in water and other degradation processes such as hydrolysis are much slower, UV degradation on beaches likely plays an important role in breaking down mesoplastics \cite{Andrady2011}. Due to the low specific heat of sand, plastic on beach surfaces can reach temperatures of around 40°C \cite{Andrady2011}. As the rate of the oxidative degradation doubles when rising the temperature by 10°C (Arrhenius equation), plastics on the beach will degrade even more rapidly \cite{Andrady2011}. Additionally, the mechanical damage of waves can break down mesoplastics \cite{Galgani2015}. Thus, beaching can also decrease the size of plastic particles.
	\item \textbf{Biofouling:} Plastic floating in the water will rapidly be colonized by bacteria, diatoms or barnacles. This process is called biofouling and increases the density of the particle \cite{Andrady2011}. An increased density will result in sinking of the plastic particle. Thus, biofouling removes plastic from the ocean surface. Additionally, a colonization by microbes can also start the process of biodegradation \cite{Andrady2011}. This describes the breakdown or mineralization by organisms \cite{Andrady2011}. As the rate of biodegradation is dependant on the molecular weight of the plastic, already UV degraded microplastic particles will be faster biodegraded than mesoplastics \cite{Andrady2011}. Thus, colonization can also lead to removal of microplastics due to mineralization. However, by blocking the light, biofilms also reduce UV degradation which is the faster degradation process on the ocean surface than biodegradation \cite{Andrady2011}. As the rate of biodegradation is dependant on the molecular weight of the plastic, already UV degraded microplastic particles will be faster biodegraded than mesoplastics \cite{Andrady2011}. However, UV degradation will only decrease the molecular weight down to $10^3$-$10^4$ g/mol whereas microbial biodegradation requires molecular weight of 500 g/mol or lower to be efficient \cite{Andrady2011}. Thus, many plastics are relatively fast degraded to the microplastic range but will not be mineralized at similar rates. Estimated mineralization rates vary from 10-20 years for plastic bags, 50 years for styrofoam cups and up to 600 years for fishing lines \cite{NOAA2014}. Thus, biofouling can lead to fast rates of removal due to increased densities as well as to slow rates due to mineralization. On the other hand, biofouling decreases UV degradation.
	\item \textbf{Grazing:} Digestion and excretion of plastic particles can further degrade them. Microplastic particles ingested by the Antarctic krill (\textit{Euphausia superba}) were found to be fragmented into pieces of less than 1 \textmu m, small enough to cross physical barriers \cite{Dawson2018}. Additionally, plastic fragments can be bound in faeces and sink \cite{Law2017}. Also in the case of death of these organisms, the plastic will sediment together with the biological material \cite{Eriksen2014,Cozar2014,Law2017}.
\end{itemize}
These processes could help to explain the sinks of marine plastic debris from the ocean surface. However, due to the several mechanisms and their influence on each other, estimates on the longevity of floating plastic are still unreliable and include high uncertainties \cite{Kiessling2015}. Estimates of the degradation rates of marine plastic debris (based on drift trajectories of plastic particles, stage of the rafting community, size of rafting organisms and the degradation stage) range from several weeks to centuries, depending on the type of plastic and the environmental conditions \cite{Kiessling2015}. However, by combining measured plastic concentration data and modelled plastic input with quantitative process descriptions, Koelmans et al. \cite{Koelmans2017} estimate that floating plastic gets removed from the ocean surface layer in about three years due to the processes mentioned above. This implies that 99.8\% of all plastic that entered the ocean from 1950-2016 has settled \cite{Koelmans2017} which could help to explain the \textit{missing plastic problem}.\\
Additionally to the unknown sinks, the methodology used to quantify the amount of floating plastic debris in the ocean might accentuate the \textit{missing plastic problem}. Andrady \cite{Andrady2011} highlights that the common quantification of floating plastic debris using nets neglects plastic particles in sediment and mid-water and thus seriously underestimates the total plastic in the ocean. Brunner et al. \cite{Brunner2015} suggest a multiplication factor of 3-13 to estimate the total buoyant microplastic marine debris from measurements using nets tows. Additionally, measurements often focus on the known aggregation zones in the subtropical gyres and large parts of the ocean surface outside these zones remain unsurveyed \cite{VanSebille2015}. \\
In order to better understand the sources and sinks of marine plastic debris, there is a need to gather more information on the plastic input (quantity, location and temporal variations), the possible degradation and mineralization mechanisms and mechanisms that lead to settling of the particles. These insights could help to better explain the \textit{missing plastic problem}. With this thesis, we aim to create a spatio-temporal prediction of plastic fluxes from land based sources to the oceans. We furthermore want to couple this model with an ocean current simulation to predict the dispersal of the marine plastic debris. To reach this goal, we predict the total production of MSW (MSW\textsubscript{T}) on country-level for the years 1990-2015. We therefore use machine-learning models (MLM) trained on socio-economic predictor variables (PV) such as greenhouse gas production or the fraction of urban population and test it on known MSW collection data (MSW\textsubscript{C}) from 78 countries. We then further process this data by applying information on the waste collection system (F\textsubscript{collection}), the fraction of plastic in MSW\textsubscript{C} (F\textsubscript{plastic}) and the MSW treatment to estimate the amount of plastic waste that enters the environment (P\textsubscript{E}). By further applying gridded population density data and a waste flow model (WFM) for the inadequately managed plastic waste, we create a geospatial estimate of plastic waste entering the ocean (P\textsubscript{O}) on a global scale. This is then coupled with a Lagrangian particle advection simulator to predict the dispersal pathways of the floating plastic debris entering the ocean as well as to predict plastic concentrations in the known aggregation zones. These include the subtropical gyres as well as highly populated and enclosed seas, gulfs, and seas \cite{Eriksen2014}. \\
This approach includes several assumptions for which we will present reasoning in the following paragraphs. We also indicate hypotheses and open research question that we will investigate in this thesis.\\
%\begin{itemize}[noitemsep,topsep=0pt]
%	\item The same drivers of MSW production are valid for each country.
%	\item The production of plastic waste is linked to the production of MSW.
%	\item The flux of plastic to the oceans is linked to the production of plastic waste.
%\end{itemize}

By creating a model that is valid for each country, we assume that the selected set of PVs includes all the drivers that explain the MSW generation. Therefore, it is important that this set of PVs includes the drivers that have been found to affect the MSW production. Next, we introduce our selection of six PVs. We indicate for which PVs we found links to MSW production in the literature or we explain, why we expect the PV to influence the MSW production.\\
\textbf{GDP per person:} MSW generation is known to be monotonically rising with increasing GDP per capita \cite{Karousakis2006}. Additionally, countries with higher GDP also show a lower fraction of MSW deposition in landfills and a higher recycling rate of cardboard and paper \cite{Karousakis2006}. Therefore, GDP does not only include the tendency of industrialized countries to produce more MSW but also the capacities for a more efficient MSW management system compared to non-industrialized countries \cite{Karousakis2006}.\\
\textbf{Share of urban population:} The urbanization of a country was found to have a positive effect on MSW generation rates \cite{Karousakis2009}. People living in cities have a better access to services and thus consume more goods, which increases MSW production \cite{Karousakis2009}.\\
\textbf{Fraction of population aged 0-14 years}: The proportion of children in a population was found to have a negative influence on MSW generation \cite{Karousakis2009}. This could be explained by the fact that children negatively affect the amount of the households income spent on consumer goods.\\
\textbf{Fraction of households with access to electricity:} We assume that households without electricity access produce less MSW compared to households with access to electricity. While the fraction is usually 100\% in high-income countries, Sub-Saharan low-income countries show fractions \textless50\% which indicates either the remoteness and/or poverty of many households. We thus expect a positive link between higher electricity access and MSW production.\\
\textbf{Energy consumption per person:} We assume that the amount of energy that is consumed is positively linked to MSW generation. We reason that people who consume more energy likely are wealthier and can thus consume more goods than people that use energy more sparsely.\\
\textbf{Greenhouse gas production per person:} In addition to the energy consumption (which accounts for $\sim$25\% of the global CO\textsubscript{2} production \cite{IPCC2014}), the greenhouse gas production includes further processes of the society, such as transportation of people and goods, manufacturing or agriculture \cite{IPCC2014}. Here, we use this PV as an indicator of the economic strength of a country. We assume that a higher greenhouse gas production is positively linked to MSW production.\\

Figure \ref{fig:Scatterplots} in the appendix shows that the described trends between these PVs and MSW\textsubscript{C} was also found in our data. The data is further described in the sections \ref{sec:DataSources} and \ref{sec:TrendsAndCorrelations}. Additional PVs such as policy factor or public attitudes are reported to have a significant effect on MSW generation \cite{Karousakis2009,Karousakis2006}. However, these predictors are hard to quantify and data is sparsely available on the temporal scale. Furthermore, the effectiveness of the same policy measure might be different among countries \cite{Karousakis2009}. Thus, these parameters are not included in our PV set.\\

The selection of the PVs, as described above, led us to our \textbf{first hypothesis}:\\
\textit{Modelling the amount of MSW production of each country is expected to be possible using the PVs GDP, share of urban population, fraction of population aged 0-14 years, fraction of households with access to electricity, energy consumption and greenhouse gas emissions.}\\

By predicting the plastic waste production using the MSW generation, we assume that the production of plastic waste is linked to the production of MSW. Next we provide reasoning for this relationship by showing the trends in MSW productions and the MSW disposal practices and their effect on plastic waste production.\\
As both the worldwide affluence and population have risen continuously in the last decades, the production of MSW has followed this trend \cite{Hoornweg2015,Hoornweg2012} and reached a total of 3.5 Mt/day in 2012 \cite{Hoornweg2012}. For 2025, estimates of the World Bank predict a total of 6.1 Mt/day \cite{Hoornweg2012}. With the total MSW production rising, a peak in global waste production is expected to occur likely after 2100 at up to 10.9 Mt/day \cite{Hoornweg2015}. Nonetheless, several high-income countries could have already reached their peak waste production and the future MSW production is strongly dependant on the economic and population growth in Asia and Africa \cite{Hoornweg2015} as well as on other developmental factors such as legislation or education \cite{Karousakis2009}. The increase in these regions might be problematic as the growth of MSW production in countries with high fractions of inadequately disposed waste might lead to higher loads of MSW entering the environment.\\
MSW is often adequately managed in high-income countries using a efficient waste collection system and treatments using incineration, recycling, composting or deposition in controlled landfills \cite{Hoornweg2012}. On the other hand, many low-income and mid-income countries have a less efficient MSW collection system and can not afford to manage their MSW in an environmentally sound way \cite{Hoornweg2012}. Thus, a high percentage of waste is not adequately disposed but discarded into uncontrolled landfills or open dump sites \cite{Geyer2017}. Where MSW collection systems are not available at all or can not be afforded and regulations are absent or not enforced, the waste will be disposed the most cost efficient way, which often results in local burning or deposition in open dump sites \cite{Waste2015}. Such inadequately managed MSW has a strong impact on the environment and public health \cite{Hoornweg2012, Karousakis2006}. Detrimental effects on public health include higher congenital anomalies in the population close to dumps and landfill sites or a higher risk factor for cancer due to airborne pollutants \cite{Karousakis2006}. Furthermore, inadequately managed MSW produces more leachates and greenhouse gases than adequately managed MSW \cite{Waste2015} and is therefore contributing to climate change. Estimates range from a 10-15\% reduction of global greenhouse gases if solid waste management is improved. However, the impact of inadequately managed MSW is highly dependent of its composition, which varies strongly among countries \cite{Hoornweg2012}.\\
While MSW in low-income to middle-income countries consists mainly of organic material (64\% and 54\% respectively), MSW in high-income countries consists mainly of paper (31\%) \cite{Hoornweg2012}. While the organic and paper fraction of MSW will readily decompose and valuable parts such as metals are often recollected, the low value plastics in MSW will remain \cite{Waste2015}. As plastic is one of the most environmentally persistent types of MSW \cite{Kooi2018} it can thus easily accumulate in the environment if the MSW is inadequately disposed \cite{Kooi2018,Eriksen2014}. The fraction of plastic in MSW is between 8\% and 12\%, independent of the country's income \cite{Hoornweg2012}. We can therefore expect that trends in global MSW production and treatment also have a high impact on plastic waste in the environment.\\

Our \textbf{second and third hypotheses} are thus:\\
\textit{Trends in the global production and disposal of MSW are expected to affect the plastic waste that enters the environment.}\\

\textit{The income class of each country is expected to influence the amount of plastic waste due to decreased effectiveness of the waste collection system with decreasing income.}\\

Finally, by coupling our prediction of plastic flux to the ocean with a Lagrangian particle advection simulation including sinks of particles, we can create estimates of the distribution of plastic particles. Circulation models have already been used to estimate plastic concentrations \cite{VanSebille2015}. By performing this analysis we can compare if our predicted concentration patterns of plastic are realistic by comparing the simulation results to measurements.\\

Our \textbf{fourth hypothesis} is thus:\\
\textit{Advecting our predicted plastic fluxes to the ocean in an Lagrangian particle advection model will result in similar plastic concentration patterns as in the observed aggregation zones.}\\

In the following chapter we will present the methodology used to reach the set goals and check our hypotheses.