\section{Discussion}
\label{sec:Discussion}
In this chapter we will discuss the results that we presented in the previous chapter. We will first compare the results of MSW\textsubscript{C} and P\textsubscript{O} and assess implications. We then compare our main results with findings from the literature. This includes our estimated MSW\textsubscript{C} rates as well as the estimated P\textsubscript{O} by riverine sources and in total. Following, we propose methods to assess the error of our estimates. Then we show how the RF model error might affect our estimates and propose suggestions for how this could be changed. In the end we evaluate if the goal we presented in the introduction were reached.

\subsection{Implications of the Results}
Here we compare the results of MSW\textsubscript{C} and P\textsubscript{O} as presented in the previous chapter. We show trends and implications and present possible explanations. We suggest possible solutions to tackle the problem of marine plastic debris. We start by describing the regional and temporal changes of P\textsubscript{O}. Following we discuss the influence of the income on P\textsubscript{O}. Then we compare the effect of increasing F\textsubscript{collection} and decreasing losses from the waste collection system. In the end of this section we discuss the effect of the transport distance on P\textsubscript{O}.

	\subsubsection{Geographical Differences over Time}
	Our results show that the predicted P\textsubscript{O} has mostly increased from 1990 to 2015 in African, South Asian and South and Central American countries (Fig. \ref{fig:PO}). Eastern European countries show the largest decrease. These results align with the estimates of MSW\textsubscript{C} for 1990 and 2015 (table \ref{tab:MSW_RF}), where we predict increases in Africa, Asia and South America. For Europe, North America, and Oceania we predicted constant values. The decrease in Eastern Europe can be explained by the F\textsubscript{collection} rates which have increased from 63\% in 1990 to 82\% in 2015. Thus, the MSW\textsubscript{T} has decreased in Eastern Europe (by 11\%) and the decreased losses from uncollected waste have lead to lower P\textsubscript{O}.
		
	\subsubsection{Influence of the Income on P\textsubscript{O}}
	We predict that in 2015, the middle income countries (58\% of the global population) account for 90\% of the global plastic input to the oceans (compare Fig. \ref{fig:Projections}). This is in agreement with Jambeck et al. \cite{Jambeck2015} who also identify 16 of the 20 countries with the highest plastic inputs to the ocean as middle-income \cite{Jambeck2015}. This could be explained by fast economic growth in these countries while the waste management system lags behind the increasing MSW production \cite{Hoornweg2012}. When comparing our predictions for 2030 and 2050, the input of the current upper middle-income countries could reach their "peak waste" in this time period (compare Fig. \ref{fig:Projections}). On the other hand, the input from the current lower middle and low-income countries will continuously increase. Assuming further economic growth, the countries could rise in their income classification and follow the same trend as today's high-income countries. This implies that P\textsubscript{O} will further increase in the next 30 years if no changes in either policy measures or no improvements in the waste collection system occur.
		
	\subsubsection{Influence of F\textsubscript{collection} and the Losses from the Waste Collection System on P\textsubscript{O}}
	We predict that a F\textsubscript{collection} of 100\% would decrease the 2015 P\textsubscript{O} by 1.7 MT, which equals 10\% of the global P\textsubscript{O} (section \ref{sec:PolicyResults}. This is mainly due to reduced plastic waste emissions in Asian and middle-income countries (1.5 Mt). This result implies that an increase of F\textsubscript{collection} in Asian middle-income countries can have a significant effect on the global P\textsubscript{O}. On average, the F\textsubscript{collection} of all Asian countries is 65\% and reaching the average level of European countries (88\%) would thus result in a decrease of P\textsubscript{O} of 0.5 Mt. For the scenario where no plastic is lost from the collection system, we predicted that the P\textsubscript{O} could be reduced by 60\% (section \ref{sec:PolicyResults}). Thereof, Asia and middle income countries contribute 90\%. Thus, we predict that reducing the losses of the waste management system is the more efficient waste reduction measure compared to an increased rate of collection. As the collection of MSW is often the costliest step in the whole waste treatment process \cite{Kaza2018}, the reduction of losses should be preferred over the increase of F\textsubscript{collection}. Together, policy measures to increase  waste collection rates as well as minimize losses from the waste collection system that target the Asian middle-income countries could reduce the global P\textsubscript{O} by up to 70\%. This assumes that these countries reach a 100\% F\textsubscript{collection} and 0\% losses from the waste collection system. However, already reaching levels close to European countries would reduce the global P\textsubscript{O} significantly. Even slight improvements in these countries can therefore have a large effect on the global P\textsubscript{O}.
	
	\subsubsection{Influence of the Transport Distances on P\textsubscript{O}}
	We predict that reduced transport probabilities of plastic waste to the ocean would decrease the coastal input of P\textsubscript{O} by 28\% while the riverine input could decrease by 55\% (section \ref{sec:PolicyResults}). This implies that a reduction of the riverine fraction of P\textsubscript{O} is easier to achieve by clean-ups than a reduction of the coastal input. However, the effect of the reduced riverine load on the global P\textsubscript{O} are marginal (3\%).

\subsection[Comparison of our Results with Literature \newline Values]{Comparison of our Results with Literature Values}
In this section we compare our results (as presented in the previous chapter) to estimates found in the literature. We begin with comparing our MSW\textsubscript{C} estimates (presented in section \ref{sec:PredictedMSW}) as predicted by the RF model. This is followed by the comparison of our P\textsubscript{O} estimates that we presented in section \ref{sec:PredictedPO}.
	\subsubsection{Comparison of the MSW\textsubscript{C} estimates}
	We compare or estimates of MSW\textsubscript{T} (in t/person/year) to Jambeck et al. \cite{Jambeck2015} who provide waste generation rates (in kg/person/day). Their data is based on rates of 128 countries in 2005 presented by Hoornweg\&Bhada-Tata \cite{Hoornweg2012} and extended for a total of 192 countries. We first needed to make our 2010 estimates of MSW\textsubscript{T} comparable to their waste generation rates. Thus, the estimates of Jambeck et al. were multiplied by 365 days/year and 1'000 kg/t to obtain t/person/year. Figure \ref{fig:compare_Jambeck} shows the difference in our estimates of the waste generation rates and Jambeck et al. estimates for 58 countries where enough data was available to compare the estimates. A positive difference indicates that our prediction is higher than Jambeck et al. The mean (0.005 t/person/year) and median (-0.07 t/person/year) of the differences are close to zero. However, the estimates for some countries differ up to 2 t/person/year. We investigated the reasons for the large differences for the countries that are highlighted in Figure \ref{fig:compare_Jambeck}. Our RF model predicts an MSW\textsubscript{C} that is significantly higher or lower for the following countries: Qatar (+1.0 t/person/year), Brunei Darussalam (+0.35 t/person/year), Monaco (+0.36 t/person/year), Belize (-0.87 t/person/year), and Guyana (+1.89 t/person/year). When we furthermore apply the F\textsubscript{collection} to estimate MSW\textsubscript{T}, the error even increases (compare \ref{fig:WFM}). While the error of the RF estimates are moderate for Qatar (6\%), Brunei Darussalam (-8\%) and Monaco (4\%), the error of the RF estimate of Belize (-39\%) can explain the difference to some extent (compare Fig. \ref{fig:MSW_RF}). No prediction error is available for Guyana. The difference of our estimates and those from Jambeck et al. for Qatar, Brunei Darussalam and Monaco can thus be explained by the difference in our available MSW\textsubscript{C} data (obtained from \cite{UnitedNations2018MSWcollected}, compare section \ref{sec:DataSources}) and the estimates of Jambeck et al. In the case of Russia and Angola, the MSW\textsubscript{C} estimates of the RF model are close to the estimates of Jambeck et al. (\textless 0.1 t/person/year difference). However, the low F\textsubscript{collection} of these countries (19\% and 18\% respectively) result in a 5-fold increased estimate of MSW\textsubscript{T}. These F\textsubscript{collected} values are among the lowest of the 58 countries that we compare here. Values closer to the average F\textsubscript{collection} would decrease our estimated MSW\textsubscript{T} and thus the observed difference in the estimates. Additionally, the RF estimates of Russia and Angola are also erroneous (Russia: 182\%, Angola: 37\%). Thus, the RF error might again explain part of the observed difference. As the error of the other countries is smaller and Jambeck et al. include estimates for countries which were not included in our model training data, this comparison gives us further confidence of the model accuracy and prediction of unseen data.\\

	\begin{figure}[tbp]
		\renewcommand{\arraystretch}{1.2}
		\centering
		\includegraphics[width=\columnwidth]{img/compare_Jambeck.pdf}
		\caption{Difference of the MSW creation rates from Jambeck et al. \cite{Jambeck2015} and our predicted MSW\textsubscript{C} combined with averaged MSW\textsubscript{collection}. A positive difference indicates that our prediction is higher than Jambeck et al.}
		\label{fig:compare_Jambeck}
	\end{figure}

	\subsubsection{Comparison of the P\textsubscript{O} estimates}
	Jambeck et al. \cite{Jambeck2015} predict 4.8-12.7 Mt of plastic entering the ocean in 2010 while our models predicts 17.5 Mt in 2010 (table \ref{tab:RF_fluxes}). However, the results of Jambeck et al. are assuming that only the population within 50 km of the coast (35.6\% of the worldwide population in 2010) produce plastic waste that enters the ocean while our model calculates the waste flux to the ocean by considering the population within 100 km from the shore (44.6\% in 2010). While Jambeck et al used conversion rates (15\%, 25\% and 40\%) to estimate the fraction of this waste that enters the ocean, we predicted P\textsubscript{O} using our WFM and distance based probabilities for P\textsubscript{E} (section \ref{sec:ProbabilityOfTransport}). A comparison is thus difficult as Jambeck et al. assume the same conversion rate for each country while our estimates include the waste management system of each country (compare Fig. \ref{fig:WFM}). Additionally, we include transport by rivers (6\% of P\textsubscript{O} in 2015) which is neglected in Jambeck et al. estimates. However, down-scaling our results by the represented population (-21\%, 3.5 Mt in 2010) as well as subtracting the riverine input (1.07 Mt in 2010), would change our estimate to 12.9 Mt in 2010, which accords to the highest estimate of Jambeck et al. for the same year.\\
	Jambeck et al. furthermore provide an estimate of 31.9 Mt of mismanaged plastic waste in 2010. This represents plastic waste produced in a distance of \textless 50 km from the shore which is not adequately disposed (defined as waste in open, uncontrolled landfills) or littered. Our estimate of 49.4 Mt of P\textsubscript{E} in 2010 includes plastic waste that we expect to be lost from the waste collection system (27.1 Mt) or uncollected waste (22.3 Mt, compare table \ref{tab:MSW_RF}) but on a worldwide scale. It is therefore difficult to compare these estimates. Again, down-scaling our estimates by the represented population results in 39.8 Mt of inadequately disposed waste within 50 km of the shore in 2010, which is 8 Mt higher than the estimate of Jambeck et al. for the same year.\\
	Overall, our 2010 estimates are similar to Jambeck et al. in both the quantity of plastic waste streams (Jambeck et al.: 4.8-12.7 Mt, our estimate: 17.5 Mt) as well as in the distribution among countries. Nine of our ten countries that contribute the most to P\textsubscript{O} (table \ref{tab:Ocean_input}) ranked by their 2010 input appear in Jambeck et al. top 20 list for 2010 \cite{Jambeck2015}. The only exception is Timor-Leste, for which we predict 965 kt in 2010 while it does not appear in Jambeck et al. top 20 list. While our predicted waste generation rate (0.05 t/person in 2010) is even lower than Jambeck et al. (0.29 t/person in 2010), our population is considerably higher (1.49 millions in 2010) than Jambeck et al. (0.67 millions in 2010). Additionally, Timor-Leste is among the countries with the highest fraction of MSW that is treated in dumps (49\%) and only 41\% of the produced MSW is collected (table \ref{tab:DataCompleteness}). Thus, our estimated impact of Timor-Leste on P\textsubscript{O} for 2010 is higher than the 2010 estimates of Jambeck et al.\\

	\subsubsection{Comparison of Riverine Plastic Fluxes}
	Lebreton et al. \cite{Lebreton2017} estimate that rivers annually transport 1.15 to 2.41 Mt of plastic to the oceans. They were using the MSW production estimates of Jambeck et al. for the year 2010, which we discussed in the previous section. Thus, we compare the results of Lebreton et al. to our 2010 estimates where we predict 1.07 Mt or riverine plastic input. Our estimate is thus slightly lower than the estimate of Lebreton et al. However, it has to be considered that Lebreton et al. include the size of the river catchment, drainage patterns, topography and dams, while we only consider a uniform catchment size of 20 km and a distance based probability of transport in the river (compare section \ref{sec:ProbabilityOfTransport}). Thus, a comparison of the estimates is again difficult. Because Lebreton et al. used the MSW production estimates of Lebreton et al., we would expect that our estimates are larger (as our estimates of MSW production are larger than the estimates of Jambeck et al.). However, our estimates of riverine inputs are similar to Lebreton et al., which implies that our distance based probability approach results in lower estimates than the more detailed approach of Lebreton et al. Furthermore, we only include major rivers in our model (N=342) while Lebreton et al. included 40'760 watersheds worldwide. This again leads to smaller estimates of our estimates compared to Lebreton et al.\\
	Lebreton et al. estimate that Asian rivers account for 86\% of the global input while our model estimates that 69\% of the global riverine input originates in Asia. However, Lebreton et al. state that Indonesian rivers account for 14.2\% (200 kt) of the total global river emissions. Our model only includes four rivers in Indonesia and its fraction of the worldwide riverine input is only 0.6\% (6.9 kt). This discrepancy explains the lower estimates of our model in both the total flux as well as the lower input of Asian rivers.\\
	Schmidt et al. \cite{Schmidt2017} estimate the global riverine plastic input from 0.47 Mt to 2.75 Mt. They used non linear relationships between measured plastic concentrations in rivers and the mismanaged plastic waste obtained from Jambeck et al. \cite{Jambeck2015} for the year 2010. Again, our estimate for 2010 lies in the lower ranges of their prediction. Again, we explain this with the higher number of rivers used by Schmidt et al. (N=1'494 compared to our 342 rivers) as well as the lower estimates of our distance based probability approach.\\
	For eight of our ten rivers with the highest plastic loads, our estimates are within the range of the predictions of Schmidt et al. and/or Lebreton et al. (table \ref{tab:River_compare}). However, we underestimate the Yangtze by at least a factor of 2 and for the Red River our estimates are three times higher. Yet, comparing the estimates of Schmidt et al. and Lebreton et al. shows that they do not agree in three out of six cases where estimates are available. This shows the high uncertainties we are still facing in riverine plastic input estimates.
	\begin{table}[tbp]
		\renewcommand{\arraystretch}{1.2}
		\rowcolors{30}{}{color2!10}
		\caption{Comparison of our 10 rivers with the highest estimates of plastic input to the ocean in 2010 (as in table \ref{tab:River_input}) with the estimates of Schmidt et al. \cite{Schmidt2017} and Lebreton et al. \cite{Lebreton2017}.}
		\begin{tabularx}{\columnwidth}{X >{\raggedleft\arraybackslash}p{1.2cm} *{2}{>{\raggedleft\arraybackslash}p{1.5cm}}}
			\toprule 
			\multirow{2}{3cm}{\textbf{Name}} & \multicolumn{3}{c}{\textbf{Input 2010 [t/year]}} \\ \cline{2-4}
			 & \raggedright{Our estimate} & \raggedright{Schmidt et al. \cite{Schmidt2017}} & Lebreton et al. \cite{Lebreton2017} \\ \toprule
			Ganges-Brahmaputra & 145'691 & 79'075 - 12'269 & 172'000 - 105'000 \\
			Yellow River (Huang He) &  104'282 & 133'810 - 19'239 & \\ 
			Nile & 99'924 & 91'835 - 13'962 & \\ 
			Yangtze (Yangzi Jiang) & 89'358 & 1'538'763 - 154'722 & 480'000 - 310'000\\ 
			Indus & 77'087 & 176'309 - 24'355 & \\ 
			Pearl River (Zhujiang) & 62'684 & 57'781 - 9'400 & \\ 
			Red River (Yuang Jiang) & 60'430 & 4'805 - 1'114 & 23'100 - 10'900 \\ 
			Irrawaddy & 42'556 & 5'627 - 1'276 & 56'900 - 29'700 \\ 
			Mekong & 34'997 & 36'761 - 6'374 & 37'600 - 18'800 \\ 
			Congo & 30'202 & 15'052 - 2'969 & \\ \bottomrule
		\end{tabularx}
		\label{tab:River_compare}
	\end{table}

\subsection{Error Estimation}
While we present estimates of waste production and plastic fluxes, we do not give an estimate of the error. As it has already been stated, the error of the model prediction is known from the CV but there is no estimate for the other predictions that were performed. Here we discuss possible techniques to get an error estimate.\\
While the prediction error of the RF and NNET models helps to see how well the model performs on the unseen test dataset, it does not provide information regarding the variance among the models. Therefore, the distribution of the country-level predictions of multiple models could be compared (e.g. one standard deviation) to get an error of the overall prediction of the NNET and RF models. This would result in an estimate of the variability of the predictions and thus the robustness of the models. Additionally to the CV error, this would also yield errors for countries where no MSW\textsubscript{C} data is available.\\
A possible way to give an estimate of the errors produced in the waste flow modelling would be to create scenarios. While we do not know how accurate the data of MSW\textsubscript{collection} is, we could create two scenarios where the reported values are reduced or increased. This would give an idea of the influence of this parameter. The same could be done with the values of fluxes to the environment from collected and uncollected MSW. This has already be partially done with the distance where we assessed the effect of a reduced probability of transport from the shore and by rivers (compare table \ref{tab:Scenario_fluxes}). An upper and lower estimate could be created by implementing all these scenarios together.\\
Even though we did not yet perform these steps to provide an overall error estimate, we will present further thoughts on how to improve the accuracy of our results in the following section.\\


\subsection{Accuracy of the Estimates}
As described above, our approach predicts MSW\textsubscript{C} and P\textsubscript{O} accordingly to previously published estimates. Our RF model has low prediction errors for many countries. However, for several countries, our estimated MSW\textsubscript{C} are erroneous (compare Fig. \ref{fig:RF_summary} A). As our results suggest, the overall P\textsubscript{O} estimate is largely determined by the estimate of the countries with a big influence on the global P\textsubscript{O}. The errors of prediction of the RF model are high for several high-input countries, including China, Indonesia, Myanmar and the Philippines (compare Fig. \ref{fig:RF_summary} A). This produces a significant error of the global estimate. We predict that 47\% of all marine plastic debris originates from China. As the RF model over-predicts China by 69\%, the global plastic input in 2015 reduces by 3.6 Mt to 15.1 Mt (-19\%) if the input of China is reduced by its error. Correcting the top 10 countries, who together account for 80\% of the global plastic input to the oceans, results in an estimate of 14.0 Mt in 2015 (-25\%). When we correct all countries by their error, the global plastic input reduces to 13.7 Mt (-27\%) in 2015 and to 12.9 Mt in 2010 (-26\%), which is close to Jambeck et al. \cite{Jambeck2015} estimate of 4.8-12.7 Mt. This again demonstrates the high impact of the top 10 countries on the global waste flux.\\
Unfortunately, none of the trained RF models was able to predict these countries with an error \textless20\% (compare table \ref{tab:ModelErrors}). Even tough we took the impact of each country into consideration when choosing the best model, it was thus not possible to select a model that adequately predicts the top 10 countries. This implies, that it is challenging to create a globally valid model with the available data and/or the chosen methodology. This is supported by the fact that both NNET and RF models have their lowest prediction errors in Europe while predictions for Asia are generally multiple times larger (compare Fig. \ref{fig:NNET_summary} and \ref{fig:RF_summary}). Also, both NNET and RF models have a lower error the higher the income of the country is. Following, we will discuss the model performance of both the RF and NNET models. We show possible sources of the errors and propose possible improvements for future projects.\\

	\subsubsection{Causes of Uncertainty}
	\textbf{Overfitting and missing data of poor countries}\\
	There are indications that our RF model is overfitting as there are 879 branches for the 1'394 data  points. The RF is thus clinging strongly to the available data and its performance on generalizing for unseen data presumably not satisfactory. Our prediction errors are low for countries where more data is available (e.g. high-income countries). As mentioned previously, out of the 1'394 data points where all PVs as well as the MSW\textsubscript{C} were available, 898 (64\%) belonged to high-income countries and 309 (22\%), 151 (11\%) and 36 (3\%) to upper-middle, lower-middle and low-income countries respectively. However,this does not represent the global reality where 34\% of all countries are rated as high-income and upper-middle, lower-middle and low-income countries account for 16\%, 24\% and 25\% respectively. In other words, when predicting lower-middle and low-income countries, who together represent 50\% of all countries, we rely on models that could only use 14\% of the available data. The models could thus be biased towards high-income countries. This could help to explain why the predictions for low-income countries are generally more erroneous. We investigated the effect of training biases in he income classes (compare \ref{fig:TrainingData} A \& B) and found that the error significantly differs among the training data subsets. Thus, an improved accuracy could be obtained by using multiple models. For both NNET and RF, one model could be trained on high-income and upper middle-income countries, where the error was similar (Fig. \ref{fig:NNET_summary} D), and one trained on lower middle and low-income countries. For the RF, one model could be could be trained on data for each income class.\\
	
	\noindent\textbf{Variation of MSW\textsubscript{C} in the PV range}\\
	Additionally to the above mentioned missing data, errors could also occur due to a limited variation of the target variable MSW\textsubscript{C} in the range of the PVs. In Figure \ref{fig:Scatterplots} we show scatterplots of the PVs versus MSW\textsubscript{C}. We marked countries with an prediction error of \textgreater30\% in red. It can be seen that these countries show very little variation in MSW\textsubscript{C} over the whole range of the PVs. The Figures \ref{fig:3DPredictors} and \ref{fig:PredictorComparison} show the countries with an error in prediction of \textgreater30\% (N=18) compared to the whole dataset. Often, the erroneous countries are outside the normal range where most countries accumulate. This is especially apparent in \ref{fig:PredictorComparison} C,E\&F: most of the erroneous countries have very low MSW\textsubscript{C} values (\textless0.2 t/person/year) resulting in very steep slopes when compared to the PVs. The only country that does not follow this trend is Argentina. However, out of the five data points available for Argentina in the years 2008-2012, four are approximately 0.14 t/person/year while for the year 2011, 1.2 t/person/year are reported, which results in the visible spike as well as in the large error in the estimate. When neglecting this outlier, Argentina also falls in the class of erroneous countries with low reported MSW\textsubscript{C} values of \textless0.2 t/person/year. The countries Angola, Belize and Russia each have 2 data points and each country has one reported MSW\textsubscript{C} value of \textgreater 0.2 t/person/year.\\
	Besides having low reported MSW\textsubscript{C} values, the erroneous countries are also accentuated in their PV range (Fig. \ref{fig:3DPredictors} and \ref{fig:PredictorComparison} C,E\&F). In the three-dimensional space, many of the erroneous countries have a high fraction of young population coupled with a low fraction of urban population and sometimes strong greenhouse gas production and are thus outside the normal range of most countries. When comparing the slopes in Figure \ref{fig:PredictorComparison} A, several of the erroneous countries show a slope that differs compared to the other countries. In these countries, a fast rate of urbanization meets either a decrease in birth rates or a prolonged life expectancy. These fundamental changes in the socio-economic situation of the countries might be a reason why a prediction is difficult. Especially China shows a rapid urbanization rate whilst its PV range is often less extreme than for the other erroneous countries. Furthermore, several countries show strong fluctuations in the PV \textit{greenhouse gas} which seems to have less effect on the prediction performance. Thus, many of the erroneous countries have values in the PVs that are outside the range of most other countries and all of them have low reported MSW\textsubscript{C} values. However, the countries Argentina, Russia and Ukraine appear in the normal range in plot \ref{fig:3DPredictors}. While Argentina, as already stated, has an outlier in its data, the Ukraine has an unusual combination of a low fraction of young population and low MSW\textsubscript{C} (compare Fig. \ref{fig:PredictorComparison} C) which might explain the error in prediction. However, the error of Russia cannot be explained with unusual values in its PVs. Here, a possible explanation lies in the data availability. As Russia has only two reported MSW\textsubscript{C} values, one for 2000 (0.30 t/person/year) and one for 2012 (0.07 t/person/year) it is possible that the data was collected using different methodologies.\\
	
	\noindent\textbf{Data quality}\\
	As mentioned above, the initial data includes several countries with spikes or "jumps" (e.g. Argentina or Russia). Hoorn-weg\&Bhada-Tata \cite{Hoornweg2012} note, that the MSW data should be considered with caution as data collection methodologies and definitions contain inconsistencies. Thus, the MSW\textsubscript{C} data we used to train might have been collected slightly differently among the countries. Additionally, several countries do not provide continuous data over several years and the information could thus be collected at a non-representative moment \cite{Hoornweg2012}. The same issue has to be considered for each of our variables used in the MSW production modelling or the waste flow modelling. Generally, the data completeness is highest for high-income countries and the consistency is thus higher as outliers can be recognized. Additionally, the data for many low and middle-income countries is further compromised due to limited technological possibilities to accurately measure MSW\textsubscript{C} \cite{Hoornweg2012} or lacking funds to accurately characterize the waste composition and characteristics. Thus, these countries often provide estimates rather than actual measurements \cite{Hoornweg2012}. Furthermore, a changing economic situation in low and middle-income countries often leads to large variations in waste quantities which not necessarily represent increased waste production but a changed collection rate due to increased values of recoverable secondary materials in the waste (e.g. metals or high-value plastics) \cite{Hoornweg2012}.\\
	
	\noindent\textbf{Small scale effects}\\
	Besides the data quality, effects on a local scale could also effect the model prediction performance. Possible income gaps between rural and urban population or between regions within a country are not represented in our models. Neither do we include topography, weather and climate, locations of known large deposition sites nor data on river run-off or dams, which could possibly have severe effects on the local conditions and thus the release of plastic waste to the environment. Thus, using country-averaged data might lead to a discrepancy in MSW\textsubscript{C} within countries. This effect possibly affects large or highly populated countries more than small and sparsely populated countries. However, as data availability is already an issue on country level, including information on sub-national regions is especially difficult for socio-economic factors that cannot be measured using remote sensing. However, geographical and climatological data is available and could be used to get more detailed waste flows. This has already been done by Lebreton et al. \cite{Lebreton2017} who used hydrological data coupled with the location of dams to estimate riverine inputs.\\
	
	\noindent\textbf{Missing information of the waste flow}\\
	As stated in section \ref{sec:CalculatingPlasticEnteringEnvironment} and figure \ref{fig:WasteFlow}, the losses from the collected and uncollected waste to the natural environment are unknown for most countries. For the middle-income countries we used the known fluxes from China and the Philippines and scaled each country with its waste management system compared to the reference countries. However, for high and low-income countries, no data was available and we estimated these fluxes assuming a linear trend of losses and income. This could possibly result in erroneous estimates for high and low-income countries. However, our models estimate that only 10\% of the global input to the ocean originates from these countries (compare table \ref{tab:ocean_flux_total}). Thus, the uncertainty in the losses does only marginally affect the global estimates and the large error in predicting the MSW\textsubscript{C} in China has a much larger effect. Nonetheless would literature based loss estimates further increase the confidence in our estimates.\\
	
	\noindent\textbf{Predictor variable selection}\\
	The three variables selected to predict the MSW (\textit{urban population}, \textit{greenhouse gas} and \textit{young population}) were important in all analyses (compare table \ref{tab:VariableSelection}). When comparing the correlations between these variables (Fig. \ref{fig:Correlation}), it can be seen that they are not strongly correlated using either the Pearson or Spearman correlations. Additionally, the correlations of each selected PV to the non-selected PVs is often stronger. Furthermore, the selected variables are often almost complete and almost no extrapolation is needed (compare table \ref{tab:DataModification}). As the the different selection processes agreed on the same three PVs and their data is often available without interpolation, we expect only marginal uncertainty arising in the models due to the selected models. However, as the scatterplots of MSW\textsubscript{C} versus the PVs (Fig. \ref{fig:Scatterplots} shows, the explanatory power for several countries is low. Furthermore, it might be that the MSW\textsubscript{collection} in low-income countries is governed by other factors than our seven PVs. As it has already been noted in section \ref{sec:PredictorVariableSelection}, parameters such as policy factors or public attitudes  that are known to affect MSW\textsubscript{C} are not included in our PV set. Thus, the model performance in low-income countries could maybe be increased by adding such parameters.\\
	
	\noindent\textbf{Bias in the training data}\\
	As Figure \ref{fig:TrainingData} shows, training the models on a selected subset can have a huge effect. Surprisingly, training solely on data from European countries triples the error compared to training on high-income countries (Fig. \ref{fig:TrainingData} A\&B). As 34 of the total 45 European countries are classified high-income, we expected similar error for Europe and high-income countries. This might be caused by autocorrelation as the time series data of European countries was mostly complete (compare table\ref{tab:DataCompleteness}. Additionally to the 34 European countries, the 59 countries classified as high-income include 14 Asian, three Oceanian, one African, four Northern American, and two South American countries and the Caribbean islands. Thus, as this training dataset includes all continents and 5 out of 7 GDP clusters (compare Fig. \ref{fig:Clusters}), the diversity might explain why training on high-income countries yields the best results. On the other hand, the 28 countries classified as low-income only include 26 African and two Asian countries, that are all in the cluster 1 and the dataset is thus more uniform, which might explain the tripled error compared to high-income country trained models. However, training on Oceanian countries results also in relatively small errors despite the small dataset (17 points) and low diversity (only three countries) resulting in an uniform training dataset.\\
	To minimize the effect of biases in the training data, we trained 10'000 models on randomly selected training and test data and performed a 10-fold CV. A stricter selection in the CV might prefer models with a higher prediction power for unseen data. However, if this significantly lowers the prediction error needs to be tested.
	
	
\subsection{Limitations of the Model}
While the above mentioned measures could help to improve our estimates, we now want to highlight the main limitations of our model.\\
Our approach predicts the waste production on a 0.1x0.1° global raster. We include several assumptions that do not fully represent the reality. First of all we assume that the waste is produced where people live. This completely ignores the effect of tourism, where waste is produced away from home. Thus, the waste production in popular tourist destinations might be underestimated by our approach. Tourism has been found to increase the marine litter in the Mediterranean Sea by +40\% in the summer caused by \textgreater 200 million tourists visiting the areas each year \cite{WWF2018}. Similar effects might be observed in other popular tourist destinations. Including tourism as a variable in the model might help to account for this fact.\\
Furthermore, we assume that the waste produced in each cell is also treated in the same location and we do not account for the trade of waste and recycling material. This results in two limitations of our model. First, this might result in erroneous predictions of fluxes to the oceans. If waste produced far from the shore is transported to a dump site closer to the sea, its chances of reaching the ocean rise. Similarly, waste produced in large cities at the shore of rivers might be discarded outside the city's boundaries further from the river and with a lower chance of transport. Such effects are not included in our model. Secondly, if waste is exported to another country, the treatment will occur in a system that is different than in the original country. The European Union accounted for 34\% of the global export of non-hazardous waste in 2014, of which 60\% are transported to non-OECD countries of which 31\% went to China \cite{EuropeanCommission2015}. On the other hand, the European Union also accounts for 20\% of the global imports of non-hazardous waste. If the trade of waste has an influence on the losses to the environment and thus influxes to the ocean, it is not represented in our models.\\

\subsection{Evaluations of the Goals of this Thesis}
Here we reflect if the goals presented in the introduction have been reached. Our first hypothesis is that \textit{modelling MSW\textsubscript{C} is 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.}\\
Using the PVs \textit{urban population}, \textit{energy consumption}, and \textit{young population} we were able to predict MSW\textsubscript{C} for 173 countries. We compared our results to the estimates of Jambeck et al. \cite{Jambeck2015}) and found similar results. However, the model performance is significantly better the higher the country's income is. Especially countries classified as low-income were erroneous. This can to some degree be explained by the low variance of the PVs for these countries. However, the NNET and RF model might not be ideal with the data we used. Simpler models such as multiple linear regression could result in less error-prone estimates. Creating multiple models and focusing on countries with a high impact on P\textsubscript{O} might also help to improve the overall error of the predictions.\\
Our second hypothesis is that \textit{trends in the global production and disposal of MSW are expected to affect the plastic waste that enters the environment}. The increase in MSW production can be seen in our prediction of P\textsubscript{E} and P\textsubscript{O}. We predict an increase of P\textsubscript{E} from 31.8 Mt in 1990 to 51.0 Mt in 2015 (+60\%) and a growth of P\textsubscript{O} from 13.4 Mt in 1990 to 18.7 Mt in 2015 (+40\%). The faster growth of P\textsubscript{E} compared to P\textsubscript{O} can be explained by an increase of plastic waste production in regions without direct access to the sea. P\textsubscript{E} in these regions can only reach the ocean by riverine transport.\\
Our third hypothesis is that \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}. Our estimates of P\textsubscript{E} and P\textsubscript{O} are strongly influenced by the income. We predict that middle-income countries account for 90\% of P\textsubscript{O} while representing only 58\% of the world's population. Using a scenario where all waste is collected we could show that P\textsubscript{O} would sink by 10\%. Again, the effect of middle-income countries accounts for 90\% of this reduction. However, a scenario where no waste is lost from the waste collection system predicted even higher decreases in P\textsubscript{O} (59\%). Thus, the effect of the income class on P\textsubscript{O} is manly explained due to losses from the waste treatment system and not due to the fraction of waste collection.\\
Our fourth hypothesis is that \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}. We could show that the PARCELS model using the Eulerian total current and our predicted plastic inputs to the ocean is able to recreate the known aggregation zones. However, comparing these results with measurements is difficult because we did not include any degradation processes on the plastic particles. These can strongly affect the behaviour of floating plastic debris. Thus, our simulation could be used as benchmark to compare the relative effects of changing plastic inputs on the spatio-temporal level.\\

In the following chapter we will provide a short conclusion of the main findings of this thesis and provide further research questions.
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