\section{Results}
\label{sec:Results}
% Fabio: show best model first, then the calculations of this model, then show how good the model is (errors, fit, etc)
In this chapter we present the results of our MLM and the estimates for P\textsubscript{E} and P\textsubscript{O} for the time period 1990-2015 as well as for our scenarios. We start with presenting the selected NNET and RF model in section \ref{sec:PerformanceOfTheMLM}. This is followed by estimates of MSW\textsubscript{C} for each country in the years 1990-2015 derived from these MLM (section \ref{sec:PredictedMSW}). We then show the estimated P\textsubscript{E} and P\textsubscript{O} (including riverine and coastal inputs) for this same time period in the sections \ref{sec:PredictedPE} and \ref{sec:PredictedPO} respectively. This is followed by the comparison of P\textsubscript{E} and P\textsubscript{O} of 2015 to the future projections and policy change scenarios (section \ref{sec:ScenarioResults}). We then present the estimated densities of marine plastic from the PARCELS particle advection model \ref{sec:PARCELSResults}. In the end of this chapter, we present the results of the machine learning model stability tests in section \ref{sec:ModelStability}.

\subsection{Performance of the Machine Learning Models}
\label{sec:PerformanceOfTheMLM}
\begin{figure*}[htbp]
	\renewcommand{\arraystretch}{1.2}
	\centering
	\includegraphics[width=\textwidth]{img/NNET_summary.pdf}
	\caption{Summary of the selected NNET model. A: Map including the mean error of the predicted versus observed MSW\textsubscript{C} in percent Grey countries had no data available. B: Comparison of the predicted versus observed  MSW\textsubscript{C} for all available data. Red circles represent the test data which was not used in training the RF. C: Boxplot showing the MSE of the 10-fold CV that was performed after training the model. The grey circles represent training data and the red circles represent test data. D: Median error per region and income.}
	\label{fig:NNET_summary}
\end{figure*}
\begin{figure*}[htbp]
	\renewcommand{\arraystretch}{1.2}
	\centering
	\includegraphics[width=\textwidth]{img/RF_summary.pdf}
	\caption{Summary of the selected RF model. A: Map including the mean error of the predicted versus observed MSW\textsubscript{C} in percent. Grey countries had no data available. B: Comparison of the predicted versus observed  MSW\textsubscript{C} for all available data. Red circles represent the test data which was not used in training the RF. C: Boxplot showing the MSE of the 10-fold CV that was performed after training the model. The grey circles represent training data and the red circles represent test data. D: Median error per region and income.}
	\label{fig:RF_summary}
\end{figure*}
\begin{table}[bp]
	\renewcommand{\arraystretch}{1.2}
	\rowcolors{42}{}{color2!10}
	\caption{Error of prediction versus observation of the selected NNET and RF models for the countries that contribute the most to marine plastic pollution according to Jambeck et al. \cite{Jambeck2015} as well as the MSE and r\textsuperscript{2}. The error of prediction of these eleven countries with a high impact on P\textsubscript{O} was used to select the NNET and RF models that have the best overall performance (section \ref{sec:SelectionOfBestModel}). The column \textit{range} indicates the minimum and maximum error of all 10'000 generated models for that country. An estimate of P\textsubscript{O} for our top 10 countries can be found in table \ref{tab:Ocean_input}.}
	\begin{tabularx}{\columnwidth}{p{1.4cm} >{\raggedleft\arraybackslash}p{0.6cm} >{\raggedleft\arraybackslash}p{1.5cm} l >{\raggedleft\arraybackslash}p{0.8cm} >{\raggedleft\arraybackslash}p{1.7cm} }
		\toprule
		& \multicolumn{2}{c}{\textbf{NNET error [\%]}} & & \multicolumn{2}{c}{\textbf{RF error [\%]}} \\ \cline{2-3} \cline{5-6}
		& Used & Range & & Used & Range \\ \toprule
		China & 119 & 94\textminus-352 & & 49 & 41\textminus116\\
		Indonesia & 654 & 211\textminus1'340 & & 216 & 180\textminus422\\
		Philippines & 94 & 0\textminus269 & & 25 & 10\textminus103\\
		Sri Lanka & 129 & 0\textminus2'116 & & 294 & 241\textminus861\\
		Egypt & -63 & -19\textminus-85 & & -4 & 0\textminus-18\\
		Malaysia & -5 & 0\textminus-41 & & -2 & 0\textminus-8\\
		Algeria & 14 & 0\textminus54 & & 11 & 0\textminus23\\
		Turkey & -32 & -5\textminus-57 & & -8 & -6\textminus-14\\
		Brazil & 44 & -2\textminus98 & & 10 & 6\textminus17\\
		Morocco & 28 & 0\textminus83 & & 1 & 0\textminus55\\
		USA & -2 & 0.0\textminus-35 & & 0 & 0\textminus-1 \\ \midrule
		MSE & 0.04 & 0.03\textminus0.08 & & 0.004 & 0.003\textminus0.009\\
		r\textsuperscript{2} & 0.88 & 0.92\textminus0.80 & & 0.99 & 0.99\textminus0.98\\ \bottomrule
	\end{tabularx}
	\label{tab:ModelErrors}
\end{table} 
\begin{figure}[htbp]
	\renewcommand{\arraystretch}{1.2}
	\centering
	\includegraphics[width=\columnwidth]{img/model_comparison.pdf}
	\caption{Difference of the NNET and RF model prediction error for each country. Negative values indicate countries that are better predicted by the NNET model, positive values indicate countries that are better predicted by the RF model. Grey indicates countries where no MSW\textsubscript{C} data was available. }
	\label{fig:model_comparison}
\end{figure}

Here we present the MLM that we selected as described in section \ref{sec:SelectionOfBestModel}). We first present the NNET model,then the RF model. This is followed by a comparison of both models.\\

\textbf{NNET}\\
The error of prediction of the unseen test data of the selected NNET model is presented per country in Figure \ref{fig:NNET_summary} A. For two out of the eleven countries with the highest plastic input, the error of the prediction is \textless= 10\% (compare table \ref{tab:ModelErrors}). From the four countries with the highest plastic input, only the Philippines (94\%) have prediction errors below 100\%. While the errors of China (119\%) and Sri Lanka (129\%) are slightly above 100\%, the model predicted 6.5 times higher MSW\textsubscript{C} for Indonesia (654\%) than observed. Additionally, none of the 10'000 NNET models was able to predict China an Indonesia with an error of less than 94\% and 211\% respectively. In total, 24 countries have errors \textgreater100\% and an additional eleven have errors \textgreater 50\% (Fig. \ref{fig:NNET_summary} A). 19 countries have an error of less than 10\%. The NNET model has an average MSE of 0.04 t/person/year and an R\textsuperscript{2} of 0.88 (table \ref{tab:ModelErrors} and Figure \ref{fig:NNET_summary} B). The MSE of the unseen test data in the CV is 0.045 (Fig. \ref{fig:NNET_summary} C). No country in South America can be predicted with an error of less than 23\% (Ecuador) and no low-income country has a prediction error of less than 317\% (Senegal) (Fig. \ref{fig:NNET_summary} D). Additionally, the prediction error of a country usually decreases with increasing income.\\

\textbf{RF}\\
The error of prediction of the selected RF model is presented per country in Figure \ref{fig:RF_summary} A. For six out of the ten countries with the highest plastic input, the prediction error is \textless= 10\% (compare table \ref{tab:ModelErrors}). From the four countries with the highest plastic input (compare table \ref{tab:ModelErrors}), China (49\%) and the Philippines (25\%) have prediction errors below 50\% and Indonesia (215\%) and Sri Lanka (294\%) have errors between 200-300\%. However, none of the 10'000 RF models was able to predict these two countries with an error less than 180\% and 241\% respectively. In total nine out of 125 countries have errors \textgreater100\% and an additional four have errors \textgreater 50\%. 39 countries have an error of less than 10\%. The RF model has an average MSE of 0.0036 and an r\textsuperscript{2} of 0.99 (compare table \ref{tab:ModelErrors} and Figure \ref{fig:RF_summary} B). The MSE of the unseen test data in the CV is 0.0063 t/person/year (Fig. \ref{fig:RF_summary} C). For each continent there are several countries with an prediction error \textless 10\% (Fig. \ref{fig:RF_summary} D). Also, for each income class, there is at least one country with a prediction error of less than 10\%. However, the prediction error of a country usually decreases with increasing income.\\

\textbf{Comparison of the NNET and RF model}\\
After describing the selected NNET and RF model we now compare them. Figure \ref{fig:model_comparison} shows the difference of the NNET and RF prediction error. The RF model is more successful in predicting the MSW\textsubscript{C} than the NNET model in 100 out of 106 countries where MSW\textsubscript{C} data was available. The six countries where the NNET model has the smaller error in prediction include Andorra, Belize, Costa Rica, Georgia, Russia and Sri Lanka. However, for Andorra, Costa Rica and Georgia, the difference in the NNET and RF prediction error is below 6\%. The error is bigger for Belize, Russia and Sri Lanka, where the NNET model has an error of 15\%, 76\% and 129\% respectively while the RF model has an error of 38\%, 182\% and 293\% respectively. Thus, the RF model prediction is always significantly more accurate than the NNET, except in 3 out of 106 countries where the NNET error is significantly lower. We therefore dropped the NNET model for the final analysis and only used the RF model to calculate MSW\textsubscript{C} and thereof P\textsubscript{E} and P\textsubscript{O}. In the next section we will present the estimates of MSW\textsubscript{C} derived from the RF model.

\subsection{Predicted MSW\textsubscript{C}}
\label{sec:PredictedMSW}
\begin{figure*}[bp]
	\renewcommand{\arraystretch}{1.2}
	\centering
	\includegraphics[]{img/MSW_pp.pdf}
	\caption{Predicted MSW\textsubscript{C} from the RF model averaged from 1990 - 2015 for each country and the relative change in 2015 compared to 1990. Please note the tenfold difference in the scale of the change plots. Countries with a MSW\textsubscript{C} \textgreater1 t/person/year (Singapore, Qatar, Monaco, Bermuda and Kuwait) or a relative change \textgreater1'000\% (Lesotho and Bangladesh) are marked in violet to keep the colour gradients in scale.}
	\label{fig:MSW_RF}
\end{figure*}
Here we present our estimates for MSW\textsubscript{C} which we derived using the RF model presented in the previous section. We dropped the NNET model because the RF model was superior in the prediction performance (Fig. \ref{fig:model_comparison}).\\
The RF models predicts an increase in the average worldwide MSW\textsubscript{C} from 0.28 t/person/year in 1990 to 0.35 t/person/year in 2015 (table \ref{tab:MSW_RF}). Of all countries, Kuwait is predicted to collect the highest amount of MSW in 2015 (3.29 t/person) and Burundi collected the least MSW with 6 kg/person in 2015. The 20 countries with the highest predicted MSW\textsubscript{C} in 2015 are located on all continents except Africa and South America (Fig. \ref{fig:MSW_RF} A). All of these are high-income countries, where the median error of prediction is 2\% (Fig. \ref{fig:RF_summary} D). Only two of the 20 countries with the lowest predicted MSW\textsubscript{C} are not located in Sub Saharan Africa (Laos and Afghanistan) and 14 of them are low-income countries.\\
The USA collect the most MSW (0.65 t/person) and Indonesia the least (0.10 t/person) from the 20 countries that have the highest impact on marine plastic debris according to Jambeck et al. \cite{Jambeck2015}. China, the country with the highest impact on marine plastic debris \cite{Jambeck2015}, has a predicted MSW\textsubscript{C} of 0.22 t/person and 0.26 t/person in 1990 and 2015 respectively.\\
Figure \ref{fig:MSW_RF} A shows the averaged predicted values of MSW\textsubscript{C} from the RF model for the years 1990-2015. In all countries in Western Europe (except Portugal), North America and Oceania, the amount of MSW\textsubscript{C} has remained constant or decreased slightly. At least 0.4 t of MSW\textsubscript{C} per capita and year are predicted in these countries. The average MSW\textsubscript{C} in these continents has remained almost constant during this time period (compare table \ref{tab:MSW_RF} and Fig. \ref{fig:MSW_RF} B). In Africa, no country collected more than 0.4 t MSW per person in 1990 and most countries are predicted to have a collection of no more than 0.1 t per person and year. The continental average is thus by far the lowest at 0.09 t/person (table \ref{tab:MSW_RF}). However, several countries in Sub-Saharan Africa are predicted to have increases of MSW\textsubscript{C} in the time period 1990-2015 (Fig. \ref{fig:MSW_RF} B). This is also apparent in the 2015 continental average which has increased to 0.15 t/person (table \ref{tab:MSW_RF}). A similar trend can be seen in South America, where average MSW\textsubscript{C} has risen from 0.23 t/person in 1990 to 0.32 t/person in 2015 and all countries except Colombia collect the same amount or more waste in 2015 compared to 1990 (Fig. \ref{fig:MSW_RF} B). Asia has the strongest increase in the average MSW\textsubscript{C}, from 0.29 t/person in 1990 to 0.47 t/person in 2015 (table \ref{tab:MSW_RF}). However, while many countries in South Asia, including the Arabian Peninsula, have rising MSW\textsubscript{C} rates, Russia and Laos (-0.20 kg/person/year and -0.22 kg/person/year respectively) are predicted to have a declining rate (Fig. \ref{fig:MSW_RF} B). However, the prediction error of Russia is 182\% (Fig. \ref{fig:RF_summary} A) and this result has to be considered with caution. \\
From all 174 countries, 12 exhibit a decrease in MSW\textsubscript{C} of at least 0.1 t/person/year between 1990 and 2015 (Fig. \ref{fig:MSW_RF} B). Eight of these are high-income countries, three and one are upper and lower middle-income countries respectively. In total, 53 countries show a decrease (Fig. \ref{fig:MSW_RF} B). Thereof, 38 show a decrease of \textless1\%. Monaco exhibits the largest decrease by 43\% from 1.32 t/person/y in 1990 to 0.89 t/person/y in 2015.

\begin{table}[tbp]
	\renewcommand{\arraystretch}{1.2}
	\rowcolors{32}{}{color2!10}
	\caption{Summary of the modelled MSW\textsubscript{C} in 1990 and 2015 for the three countries with the highest collection as well as averaged for the income classes, the continents and worldwide.}
	\begin{tabularx}{\columnwidth}{>{\centering}p{0.3cm} X >{\raggedleft\arraybackslash}p{1cm} >{\raggedleft\arraybackslash}p{1cm} }
		\toprule 
		 & \multirow{2}{5cm}{\textbf{Subset}} & \multicolumn{2}{c}{\begin{minipage}{1.8cm}\textbf{MSW\textsubscript{C} [t/person/year]}\end{minipage}} \\ \cline{3-4}
		 & & 1990 & 2015 \\
		\toprule
		& World & 0.28 & 0.35 \\ \hline
		\cellcolor{white} & Kuwait & 2.13 & 3.29\\
		\cellcolor{white} & Qatar & 0.65 & 1.50\\
		\cellcolor{white} \multirow{-3}{0.3cm}{\rotatebox[origin=c]{90}{ Top 3}}  & Bermuda & 1.26 & 1.22\\ \midrule
		\cellcolor{white} & High-income & 0.54 & 0.60\\
		\cellcolor{white} & Upper middle-income & 0.24 & 0.32 \\
		\cellcolor{white} & Lower middle-income & 0.12 & 0.23 \\
		\cellcolor{white} \multirow{-4}{0.3cm}{\rotatebox[origin=c]{90}{Income}} & Low-income & 0.05 & 0.09 \\ \midrule
		\cellcolor{white} & Africa & 0.09 & 0.15 \\
		\cellcolor{white} & Asia & 0.29 & 0.47 \\
		\cellcolor{white} & Europe & 0.47 & 0.47 \\
		\cellcolor{white} & North America \& Caribbean & 0.38 & 0.37 \\
		\cellcolor{white} & South America & 0.23 &  0.32 \\
		\cellcolor{white} \multirow{-6}{0.3cm}{\rotatebox[origin=c]{90}{Continents}} & Oceania & 0.52 & 0.49 \\ \bottomrule
	\end{tabularx}
\label{tab:MSW_RF}
\end{table}

\subsection[Predicted Plastic Fluxes to the Environment \newline and the Oceans]{Predicted Plastic Fluxes to the Environment and the Oceans}
In this section we present our predictions for P\textsubscript{E} and P\textsubscript{O}, derived from the WFM presented in section \ref{sec:WFM} and Figure \ref{fig:WFM}. We start with the estimates of P\textsubscript{E} and then present the estimates of P\textsubscript{O} broken down to riverine and coastal inputs.

\begin{table*}[htbp]
	\renewcommand{\arraystretch}{1.2}
	\rowcolors{2}{}{color2!10}
	\caption{Summary of the modelled fluxes of plastic to the environment and the ocean for the years 1990, 1995, 2000, 2010 and 2015. We separate the P\textsubscript{E} by inputs from the waste collection system and from uncollected waste. The P\textsubscript{O} is separated by inputs from coastal areas and from riverine sources.}
	\begin{tabularx}{\textwidth}{X *{6}{>{\raggedleft\arraybackslash}p{1.5cm}}}
		\toprule
		& \textbf{1990} & \textbf{1995} & \textbf{2000} & \textbf{2005} & \textbf{2010} & \textbf{2015} \\ \toprule
		Flux from MSW\textsubscript{C} to P\textsubscript{E} [Mt] & 15.9 & 17.5 & 20.0 & 21.6 & 27.1 & 29.5 \\
		Flux from uncollected MSW to P\textsubscript{E} [Mt] & 15.9 & 17.3 & 19.4 & 19.8 & 22.3 & 21.5 \\
		Total P\textsubscript{E} [Mt] & 31.8 & 34.9 & 39.5 & 41.4 & 49.4 & 51.0 \\ \midrule
		Flux from P\textsubscript{E} to P\textsubscript{O} by rivers [Mt] & 0.47 & 0.55 & 0.72 & 0.81 & 1.07 & 1.1 \\
		Flux from P\textsubscript{E} to P\textsubscript{O} by coastal areas [Mt] & 13.0 & 13.8 & 15.7 & 15.1 & 16.5 & 17.7 \\
		Total P\textsubscript{O} [Mt] & 13.4 & 14.4 & 16.4 & 15.9 & 17.5 & 18.7 \\ \bottomrule
	\end{tabularx}
	\label{tab:RF_fluxes}
\end{table*}

	\subsubsection{Predicted P\textsubscript{E}}
	\label{sec:PredictedPE}
	% Which cities/countries/regions emit the most MSW? Is there an effect of high GDP/good waste management v. low GDP/bad waste management?
	The WFM suggests that the amount of worldwide P\textsubscript{E} has continuously risen from 31.8 Mt in 1990 to 51.0 Mt in 2015 (table \ref{tab:RF_fluxes}). While the plastic that entered the environment in 1990 originated in equal amounts from collected and uncollected MSW (15.9 Mt each), this fraction has changed over time. In 2015, 58\% originated from MSW that entered the collection system while 42\% originated from MSW that was not collected.

	\subsubsection{Predicted Plastic Fluxes to the Oceans}
	\label{sec:PredictedPO}
	Here we present the estimates for P\textsubscript{O} separately for riverine and coastal inputs and as a total.\\
	
	\begin{figure*}[htbp]
		\renewcommand{\arraystretch}{1.2}
		\centering
		\includegraphics[width=\textwidth]{img/Plastic_input.pdf}
		\caption{Predicted marine plastic input averaged for the years 1990 - 2015 and the relative change in 2015 compared to 1990. A) Modelled input from riverine sources per country. B) Modelled input from coastal sources per country. C) Modelled input from both coastal and riverine sources per country. Please note the log-scale in the average input and the tenfold difference in the scale of the change plots. Countries with a relative change \textgreater1'000\% are marked in violet to keep the colour gradient in scale.}
		\label{fig:PO}
	\end{figure*}

	\textbf{Fluxes from rivers}\\
	The WFM (compare Fig. \ref{fig:WFM}) predicts that 0.47 Mt (3\%) of the plastic that enters the ocean in 1990 (13.4 Mt) originated from riverine sources (table \ref{tab:RF_fluxes}). The fraction of riverine sources is predicted to double (6\%) until 2015. Figure \ref{fig:PO} A shows the evolution of riverine plastic flux to the ocean from 1990 to 2015. In 1990, rivers in Asia and Europe are predicted to have released 225 kt (48\%) and 162 kt (34\%) respectively into the oceans. All the other rivers accounted for 95 kt. In 2015, the highest fluxes are predicted in Asia with a total of 739 kt (70\%), followed by Africa and Europe with 135 kt (13\%) and 114 kt (11\%) respectively and 73 kt are released in the remaining continents combined. Europe is the only continent where the riverine input decreased in the study period (by 51\%). However, the input in Asia and South America tripled while input in Africa and North America doubles during the same time period. Table \ref{tab:River_input} shows the input of the top 10 ranked rivers in 2015. Eight of these ten rivers are located in Asia and five flow through China (Yellow River, Yangtze, Xi River, Red River and Mekong). Figure \ref{fig:River_input} shows the global riverine input in 2015. It can be seen that the rivers with the highest plastic loads (\textgreater10 kt/year) are located in Asia, Africa and Europe while no rivers in the Americas or Oceania has loads \textgreater10 kt/year. Furthermore, a North-South gradient can be seen. Rivers that flow to the Arctic Sea carry \textless100 t/year. The river Ob in Russia is the only exception with \textgreater100 t/year. Also rivers in Australia and New Zealand as well as Alaska and Canada usually carry \textless100 t/year. All other estimated river loads are \textgreater100 t/year. In 1990, 61\% (295 kt) of all riverine plastic waste originated from lower middle-income countries. This fraction has remained constant until 2015 (60\%, 638 kt). However, while the input from high-income and low-income countries has only risen from 73 kt to 95 kt and from 22 kt to 35 kt respectively, the input from upper middle-income countries has tippled from 92 kt to 292 kt. Together, upper and lower middle-income countries account for 88\% of the global riverine marine plastic input in 2015.\\
	
	\begin{table}[tbp]
		\renewcommand{\arraystretch}{1.2}
		\rowcolors{2}{}{color2!10}
		\caption{List of the 10 rivers with the largest estimated plastic input to the ocean in kt in 2015, ranked by their 2015 plastic input. The number in the column \textit{world} represent the fraction of the total riverine plastic input in 2010. }
		\begin{tabularx}{\columnwidth}{X >{\raggedleft\arraybackslash}p{2.5cm} >{\raggedleft\arraybackslash}p{1cm}}
			\toprule 
			\textbf{Name} & \textbf{Input 2010 [kt]} & \textbf{World} \\ \toprule
			Ganges-Brahmaputra & 145'691 & 13.5\% \\
			Yellow River (Huang He) &  104'282 & 9.7\%\\ 
			Nile & 99'924 & 9.3\% \\ 
			Yangtze (Yangzi Jiang) & 89'358 & 8.3\% \\ 
			Indus & 77'087 & 7.2\% \\ 
			Pearl River (Zhujiang) & 62'684 & 5.8\% \\ 
			Red River (Yuang Jiang) & 60'430 & 5.6\% \\ 
			Irrawaddy & 42'556 & 3.9\% \\ 
			Mekong & 34'997 & 3.2\% \\ 
			Congo & 30'202 & 2.8\% \\ \bottomrule
		\end{tabularx}
		\label{tab:River_input}
	\end{table}

	\begin{figure*}[htbp]
		\renewcommand{\arraystretch}{1.2}
		\centering
		\includegraphics[width=\textwidth]{img/river_input.pdf}
		\caption{Predicted riverine plastic input to the oceans in 2015. In total, 342 rivers transported 1.1 Mt of plastic to the ocean (compare table \ref{tab:RF_fluxes}). Please note the log-scale. A more detailed description can be found in section \ref{sec:ProbabilityOfTransport}}
		\label{fig:River_input}
	\end{figure*}
	%
	\textbf{Fluxes from the coast}\\
	The input from coastal sources (compare Fig.\ref{fig:PO} B) is predicted to increase from 13.0 Mt to 17.7 Mt while accounting for 97\% and 94\% respectively of P\textsubscript{O} in the years 1990 and 2015 (table \ref{tab:RF_fluxes}). Predictions for countries in Europe, North America an Oceania remained relatively constant over time, but many African, Asian and South American countries have increased their plastic input (Fig. \ref{fig:MSW_RF} B). African countries emitted 279 kt (2\% of global coastal input) in 1990 and 728 kt (4\% of global coastal input) in 2015 and thus doubled their fraction of global coastal inputs (table \ref{tab:ocean_flux_shore}). The total coastal plastic input from South American countries increased from 213 kt (2\%) to 592 kt (3\%), North America from 331 kt (3\%) to 587 kt (3\%) while Europe decreased from 900 kt (7\%) to 732 kt (4\%). The coastal plastic input from Asian countries rose from 11'217 kt (86\%) to 15'015 kt (85\%). China releases 8'539 kt and is thus accountable for more than half of the Asian coastal plastic input and 48\% of the global coastal input in 2015.\\
	All low-income countries (representing 11\% of the global population in 2015) combined account for 1\% of the coastal plastic waste flux to the ocean in 2015 and high-income countries (31\% of the global population) account for 9\% (table \ref{tab:ocean_flux_shore}). Thus, upper and lower middle-income countries account for 55\% and 35\% respectively (while representing 14\% and 44\% of the global population respectively). However, the total fluxes from low-income and lower middle-income countries have tripled since 1990 while the upper middle-income countries have remained relatively constant (9'319 kt in 1990 and 9'762 kt in 2015).\\
	
	\textbf{Total plastic influx to the oceans}\\
	We predict an increase in total marine plastic input from 13.4 Mt in 1990 to 18.7 Mt in 2015 (table \ref{tab:RF_fluxes}). Table \ref{tab:Ocean_input} shows the ten countries that we estimate to produce the most marine plastic litter in 2015. This tables also shows the evolution of the marine plastic litter input of these countries. China alone produces 8'770 Mt of marine plastic debris in 2015, which accounts for 47\% of the worldwide input in 2015. Compared to the country with the second highest input (Indonesia), China accounts for six times more marine plastic litter. From the top ten countries, only Brazil and the USA are not located in Asia and out of the Asian countries, only Bangladesh and India are not in South East Asia. Combined, the top 10 emitters account for 11.1 Mt in 1990 and 15.1 Mt in 2015 which represents 83\% and 81\% of the worldwide input. From 1990 to 2015, only the input of Europe decreased from 1'063 kt to 847 kt (table \ref{tab:ocean_flux_total}). In Africa (1990: 240 kt, 2015: 864 kt) and North America (1990: 359 kt, 2015: 637 kt) the input roughly doubled while South America (1990: 220 kt, 2015: 615 kt) tripled its plastic flux. The input of Oceania increased from 31 kt to 37 kt, which represents 0.2\% of the worlds input.\\
	As with the coastal plastic inputs, all low-income countries combined account for 1\% of the total plastic waste flux to the ocean in 2015 and high-income countries account for 9\% (table \ref{tab:ocean_flux_total}). Thus, upper and lower middle-income countries account for 53\% and 37\% respectively. However, the total fluxes from low-income and lower middle-income countries have tripled since 1990 while the upper middle-income countries have remained relatively constant (9'410 kt in 1990 and 10'055 kt in 2015).\\
	
	After describing the results of our estimates of P\textsubscript{O} for the time period 1990-2015, we present the estimates of P\textsubscript{O} we made for the future projections and the policy change scenarios in the next section.
	
	\begin{table}[tbp]
		\renewcommand{\arraystretch}{1.2}
		\rowcolors{2}{}{color2!10}
		\caption{Summary of the modelled P\textsubscript{O} from 1990 to 2015 for the ten countries with the highest plastic input to the oceans in 2015, ranked by the 2015 values. A detailed description can be found in section \ref{sec:WFM}.}
		\begin{tabularx}{\columnwidth}{X *{6}{>{\raggedleft\arraybackslash}p{0.7cm}}}
			\toprule
			\multirow{2}{*}{\textbf{Country}} & \multicolumn{6}{c}{\textbf{Total marine plastic input [kt]}} \\ \cline{2-7}
			& 1990 & 1995 & 2000 & 2005 & 2010 & 2015 \\ \toprule
			China & 8'854 & 8'888 & 9'512 & 8'067 & 8'632 & 8'770 \\
			Indonesia & 395 & 634 & 605 & 427 & 783 & 1'431 \\
			Vietnam & 369 & 473 & 704 & 1'115 & 1'220 & 1'197 \\
			Timor-Leste & 529 & 648 & 800 & 896 & 965 & 1'096 \\
			Philippines & 231 & 358 & 609 & 785 & 769 & 782 \\
			India & 122 & 220 & 258 & 322 & 293 & 404 \\
			Brazil & 135 & 131 & 250 & 433 & 402 & 377 \\
			Myanmar & 270 & 293 & 335 & 162 & 291 & 372 \\
			Bangladesh & 16 & 48 & 191 & 223 & 312 & 357 \\
			USA & 232 & 245 & 287 & 300 & 312 & 328 \\ \bottomrule
		\end{tabularx}
		\label{tab:Ocean_input}
	\end{table}

\subsection{Scenarios}
\label{sec:ScenarioResults}
Besides the P\textsubscript{O} estimates for the years 1990-2015, we also used the MLM to predict future projections and the WFM to predict policy change scenarios. This includes projections for the years 2030 and 2050 as well as scenarios including a 100\% collection rate of MSW, no losses of plastic to the environment and a decreased transport distance of plastic litter (as described in section \ref{sec:FutureProjections}). Here we first present the estimates of the future projections, followed by the predictions for the policy change scenarios.

	\subsubsection{Future projections}
	Here we present the projections for the years 2030 and 2050 (assuming business as usual) and compare them to the year 2015. These were created by extrapolation the population density and the PVs used in the RF model presented in section\ref{sec:PerformanceOfTheMLM}. The PVs and the population density were extrapolated as described in section \ref{sec:FutureProjections}.\\
	\vfill\null
	\textbf{Projection for 2030}\\
	For 2030, the RF model predicts a P\textsubscript{O} of 19.7 Mt, which is a 5\% increase compared to 2015 (table \ref{tab:Scenario_fluxes}). This increase mostly originates from Africa, which increases its input by 50\% to 1'210 kt (+346 kt) and Asia, whose input increases by 1.7\% (+282 kt). Nine of the ten countries with the highest input are still the same as in 2015 (compare table \ref{tab:Ocean_input}). The input of the USA decreases from 238 kt in 2015 to 203 kt in 2030. Meanwhile, Pakistan increases its input from 149 kt to 369 kt and thus replaces the USA in the list of the biggest emitters in 2030. Also China decreases its input by 51\% (8'770 kt in 2015) to 5'816 kt. Nevertheless, China is till on the higher rank than Indonesia, whose input increased by 39\% to 1'995 kt. We project a 41\% increase in riverine input (from 739 kt in 2015 to 1043 kt in 2030) in Asia while the fluxes in South America decrease (from 21.9 kt in 2015 to 9.6 kt in 2030). Riverine transport from lower middle-income countries could double (to 1'169 kt) compared to 2015 while the input from upper middle-income countries might increase 1.5 times (to 173 kt). The flux from the shore is predicted to remain constant for Asia (15'015 kt in 2015 ad 14'993 kt in 2030), while it increases by 39\% (from 723 kt to 1'013 kt) in Africa and by 23\% (733 kt to 900 kt) in Europe. The other continents change by \textless10\%.\\

	\textbf{Projection for 2050}\\
	For 2050, we predict a P\textsubscript{O} of 21.6 Mt, which is a 16\% increase compared to 2015 (table \ref{tab:Scenario_fluxes}). This increase mostly originates from Asia, which increases its input by 12\% (+1'868 t) and Africa, whose input increases by 60\% to 1'382 kt (+ 518 kt).The same countries are atop of the top 10 list as in 2030. While China is still leading with 6'403 kt (decrease of 27\% compared to 2015), the Philippines are second with 2'137 kt (increased by 173\% compared to 2015). The riverine fluxes increase in Africa (from 135 kt in 2015 to 209 kt in 2050) and Asia (from 739 kt in 2015 to 1'279 kt in 2030) the input of the other continents changes \textless10\%. The plastic input from the shore increases in Africa (+445 kt to 1174 kt), Asia (+1'337 kt to 16'342 kt) and North America (+155 kt to 578 kt). We project that the rise from 2015 to 2050 in the total worldwide marine plastic input (2.9 Mt) mostly originates from Asia (+1'868 kt) and Africa (+518 kt) the other continents only show moderate increases. In the income classes, a shift from the upper middle-income countries (-2'764 kt) towards lower middle-income countries (+4'961 kt) might arise.\\
		
	\textbf{Comparison of the 2030 and 2050 projections}\\
	We project an increase of P\textsubscript{O} for the years 2030 and 2050 (table \ref{tab:Scenario_fluxes}). The increase in the period 2030-2050 (+1.7 Mt total, +85 kt/year) is larger than in the period 2015-2030 (+1 Mt total, +67 kt/year ). Figure \ref{fig:Projections} shows that we project a strong increase in P\textsubscript{O} originating from lower middle-income countries between 2015 and 2030. However, in the same time period we also predict a decrease in P\textsubscript{O} originating from upper middle-income countries. Thus, the total P\textsubscript{O} increase is subdued. In the time period 2030-2050, we project increasing P\textsubscript{O} for both lower and upper middle-income countries. Thus, the global P\textsubscript{O} shows a larger increase in this period. Figure \ref{fig:Projections} also shows that the P\textsubscript{O} inputs of the low-income and high-income countries only make up a small fraction of the global input. 
	
	\begin{figure*}[htbp]
		\renewcommand{\arraystretch}{1.2}
		\centering
		\includegraphics[width=\textwidth]{img/future_projections.pdf}
		\caption{Estimated marine plastic input for the years 1990-2015 (solid lines) including projections for 2030 and 2050 (marked with points). The estimates are provided for the four income classes and for the whole world. The dashed lines represent the trends between 2015 and 2030 and between 2030 and 2050 but are not based on estimates for the years in-between.}
		\label{fig:Projections}
	\end{figure*}

	\subsubsection{Policy change scenarios}
	\label{sec:PolicyResults}
	Here we present the estimates for the scenarios. We created three scenarios, simulating policy measures that aim to collect all waste, decrease losses to the environment and reduce the transport to the ocean. These scenarios were created by changing parameter values of the WFM presented in section\ref{sec:WFM}. We used the MSW\textsubscript{C} predictions of 2015 and thus compare to this year. A detailed description can be found in section \ref{sec:FutureProjections}.\\
	
	\textbf{No uncollected MSW}\\
	In this scenario we assume that 100\% of the MSW is collected (MSW\textsubscript{C} = MSW\textsubscript{T}). Table \ref{tab:Scenario_fluxes} shows, that we predict a reduction of P\textsubscript{E} by 15\% to a total of 43.4 Mt (as compared to the regular value of 51.0 Mt in 2015). We predict that P\textsubscript{O} is reduced by 10\% to 16.9 Mt (18.7 Mt in 2015). A decrease can be seen in both riverine transport (-0.3 Mt) and influx from the shore (-1.7 Mt). Thus, we predict that collecting all the MSW produced in 2015 would only decrease the P\textsubscript{E} by 15\% and the P\textsubscript{O} by 10\%. Comparing the continents reveals that the biggest change in P\textsubscript{O} is predicted in Asia (-1.5 Mt) while the other continent show reductions of less than 0.1 Mt. Considering the income classes, both upper and lower middle-income countries could reduce their predicted marine input by 0.8 Mt while high and low-income countries have lower decreases. Thus, increasing the F\textsubscript{collection} might only have a significant result on the amount of P\textsubscript{O} in Asian middle-income countries.\\
		
	\textbf{No losses}\\
	In this scenario we assume that no flux to P\textsubscript{E} occurs from either the waste collection system or from uncollected waste.\\
	In the case that no losses occur from the waste collection system, we predict a P\textsubscript{E} of 21.5 Mt and a P\textsubscript{O} of 7.7 Mt (table \ref{tab:Scenario_fluxes}). This represents a reduction of 58\% and 59\% respectively compared to the regular 2015 values.
	In the case where no losses occur from uncollected waste, we predict a P\textsubscript{E} of 29.5 Mt and a P\textsubscript{O} of 11.1 Mt. This represents a reduction of 42\% and 41\% respectively compared to the regular 2015 values. Furthermore, our predictions indicate that 40\% (0.4 Mt) of the riverine plastic waste originates from MSW\textsubscript{C} while 60\% (0.6 Mt) originate from uncollected waste. From the coastal fraction of P\textsubscript{O}, 41\% (7.2 Mt) originate from MSW\textsubscript{C} while 59\% (10.5 Mt) originate from uncollected waste. Again, the biggest effect of this measure can be seen in Asia, which contributes to 90\% (6.9 Mt) of the reduced plastic inputs. Also reducing the losses in the middle-income countries would result in an 90\% reduction. Worldwide, minimizing the losses from the waste collection system could reduce the worldwide P\textsubscript{E} and P\textsubscript{O} by up to 60\%.\\
	
	\textbf{Halved transport distances}\\
	In this scenario we assume that the probability of transport of plastic is halved (e.g. due to collection of P\textsubscript{E}). Table \ref{tab:Scenario_fluxes} shows that this could lead to a reduction of P\textsubscript{O} by 29\% to 13.3 Mt (compared to the regular value of 18.7 Mt in 2015). Efforts in removing plastic from the environment could reduce the riverine plastic input by 55\% (to 0.5 Mt), and the coastal input by 28\% (to 12.8 Mt). This policy measure shows no major differences among the continents for riverine and coastal inputs.
	
	\begin{table*}[htbp]
		\renewcommand{\arraystretch}{1.2}
		\rowcolors{2}{}{color2!10}
		\caption{Summary of the modelled fluxes of P\textsubscript{O} and P\textsubscript{O} for the future projections of the years 2030 and 2050 as well as for the policy change scenarios. We include the year 2015 as a comparison. The future projections are derived using the MLM with projected PVs and population density and the 2015 WFM. The policy change scenarios are derived using the 2015 MLM estimates and changes in the WFM (see section \ref{sec:FutureProjections}).}
		\begin{tabularx}{\textwidth}{X *{2}{>{\raggedleft\arraybackslash}p{0.6cm}} >{\raggedleft\arraybackslash}p{1.2cm} *{2}{>{\raggedleft\arraybackslash}p{0.6cm}} >{\raggedleft\arraybackslash}p{1.5cm} >{\raggedleft\arraybackslash}p{1cm}}
			\toprule
			& \textbf{2030} & \textbf{2050} & \textbf{All coll.} & \multicolumn{2}{c}{\textbf{No loss in}} & \textbf{Distance} & \textbf{2015}\\ \cline{5-6}
			& & & & uncoll. & coll. & & \\ \toprule
			Plastic flux from collected MSW to the environment [Mt] & 32 & 36.8 & 43.4 & 29.5 & 0.0 & 29.5 & 29.5 \\ \hline
			Plastic flux from uncollected MSW to the environment [Mt] & 22.4 & 26.5 & 0.0 & 0.0 & 21.5 & 21.5 & 21.5 \\ \hline
			Total plastic input to the environment [Mt] & 54.4 & 63.3 & 43.3 & 29.5 & 21.5 & 51.0 & 51.0 \\ \hline
			Plastic flux from rivers to the ocean [Mt] & 1.5 & 1.7 & 0.8 & 0.6 & 0.4 & 0.5 & 1.1 \\ \hline
			Plastic flux from coastal areas to the ocean [Mt] & 18.2 & 19.9 & 16.0 & 10.5 & 7.2 & 12.8 & 17.7 \\ \hline
			Total plastic input to the ocean [Mt] & 19.7 & 21.6 & 16.9 & 11.1 & 7.7 & 13.3 & 18.7 \\ \bottomrule
		\end{tabularx}
		\label{tab:Scenario_fluxes}
	\end{table*}

\subsection{Predicted Concentrations of Floating Marine \newline Plastic}
\label{sec:PARCELSResults}
Here we present the estimated changes for the concentrations of marine plastic debris in the years 1996 and 2015. Figure \ref{fig:DensityDifference} A shows the yearly averaged plastic concentrations in the oceans have changed from 1996 to 2015. Oceans that show no difference include the South Pacific and the Southern Ocean. All other oceans show zones of changed concentrations. In the North Pacific, North and South Atlantic and the Indian Ocean, zones of increase are related to the known aggregation zones of the gyres. These oceans also include minor zones of decrease. The largest increases can be seen in the southern Indian Ocean, in the North Atlantic, in the Arctic Sea near Scandinavia and western Russia and in the Seas around Japan. We predict a major decrease of plastic concentrations in the the North Sea, the Baltic Sea and in the western North Atlantic (Bay of Biscay). Comparing the mean concentration of the years 1996 and 2015 (Fig. \ref{fig:DensityDifference} B\&C) reveals that the shape of the aggregation zones have changed from 1996 to 2015. This results in the small zones of decrease found in most Oceans. The change of the shape of the aggregation zones can be explained by slightly different currents in these years. Overall, the only major decrease in plastic concnetrations is predicted for the North Sea and the Baltic Sea. As no current data is available for the Mediterranean, we excluded plastic particles in this Ocean.
\begin{figure*}[htbp]
	\renewcommand{\arraystretch}{1.2}
	\centering
	\includegraphics[width=\textwidth]{img/density_diff_1996-2015.pdf}
	\caption{Results of the PARCELS simulation. A: Predicted difference in the concentrations [kg/km\textsuperscript{2}] of marine plastic debris from 1996 until 2015. B: Predicted concentrations for 1996. C: Predicted concentrations for 2015. See section \ref{sec:SimulationofPlasticDistribution} for further details.}
	\label{fig:DensityDifference}
\end{figure*}


\subsection{Model Stability}
\label{sec:ModelStability}
%\textbf{Training data size}\\
Here we present the results of the stability test performed on the NNET and RF models as described in section \ref{sec:MLMStability}. We tested both the bias of the training data size and the bias of in the training data selection.\\
Both models have a better prediction performance the bigger the training dataset is (Fig. \ref{fig:TrainingData} A\&B). Generally, the more data is used for training, the better is the model performance. Both MLM perform best when the training data consists of 90\% of the available data (white lines). Additionally, the RF is more sensitive to the size of the training dataset than the NNET. However, the effect on the error is relatively low when varying the size between 80\% and 50\% compared to the models trained on 40\% or less.\\
%\textbf{Bias in the training data}\\
A strong variation in the error of the NNET and RF model prediction (MSE) is observed when the training data is biased (Fig. \ref{fig:TrainingData} C\&D). Both MLM perform best when trained on the high-income countries and perform worst when trained on the lower middle and low-income countries. Overall, both models behave similarly when trained on the same data. While the size of the training data is between 1\% (Oceania dataset) and 64\% (high-income dataset), the MSE is always lager than for randomly sampled training data (Fig. \ref{fig:TrainingData} A\&B). Thus, MLM trained on biased data will have a larger MSE compared to MLM trained on randomly sampled training data.
The effect of the cluster (where C1 represents countries with the lowest GDP and C7 those with the highest GDP) does not follow the trend observed with the income where "rich" countries perform better. When the models are trained on data from Europe, the prediction is worse than when the training is performed on other continents.\\
Contrary to the above described bias in the training data size, the effect of the size of the training data is of less importance. Training on the 17 data points from Oceania results in an overall better prediction for worldwide data than training on 773 points from the countries in Europe.\\

In the following chapter we will discuss the results that were described in this chapter.
\vfill\null

\begin{figure*}[htbp]
	\renewcommand{\arraystretch}{1.2}
	\centering
	\includegraphics[width=\textwidth]{img/Model_stability.pdf}
	\caption{Results of the Model stability tests as described in section \ref{sec:MLMStability}. A and B show the MSE for different sized training data. C and D show the MSE of the MLM trained on data selected by income, continent, or cluster. The numbers in brackets indicate how many data points were included in each training dataset (total N=1'394). The white lines indicate the MSE of the model when the training data is randomly selected and training is done on 90\% of the available data. Abbreviations: H,UM,LM,L: high, upper middle, lower middle and low-income countries, OC: Oceania, AS: Asia, AF: Africa, AM:Americas, EU: Europe, C\textit{n}: GDP-cluster \textit{n} (compare Fig. \ref{fig:Clusters}).}
	\label{fig:TrainingData}
\end{figure*}