||Human activities cause flow of nitrogen (N) from terrestrial to aquatic systems. This has many serious consequences that need to be alleviated. Understanding and anticipation of N flow to aquatic systems can be achieved by modeling. Several models have been developed but one of their major weaknesses is the use of inappropriate scales. Therefore, the objective of this thesis is to increase our ability to identify appropriate spatial and temporal scales for N-flow models in a transparent and comprehensive way. In order to meet this objective, the following sub-objectives are addressed:
I. To model of global N flows from land to water in a spatially explicit way.
II. To develop aframeworkfor identifying the appropriate spatial and temporal scales of N-flow models.
III To apply this framework to a model of global N flow.
IV To assess the applicability of this framework to models of N flow between floodplains and rivers.First, a spatially explicit, global model for predicting dissolved inorganic nitrogen export (DIN) by rivers to coastal waters (NEWS-DIN) is developed. NEWS-DIN models DIN export from watersheds to coastal waters as a function of N inputs to watersheds including manure N, fertilizer N, atmospheric N deposition, and biological N 2 fixation, as well as sewage. NEWS-DIN also includes retention and loss terms, including N retention in river networks, N retention in dammed reservoirs, N loss via consumptive water use,denitrificationin rivers, and N loss via harvesting and grazing. For global watersheds DIN yields are calculated ranging from 0.0004 to 5217 kg N km -2 y -1 with the highest DIN yields occurring in Europe andSouth East Asia. The calculated global DIN export to coastal waters is 25TgN y -1 ,with 16TgN y -1 from anthropogenic sources. Biological N 2 fixation is the dominant source of exported DIN. And globally, and on every continent exceptAfrica, N fertilizer is the largest anthropogenic source of DIN export to coastal waters. NEWS-DIN is a global model, calculating annual DIN flows for 540 basins, while resolving equations at the scale of individual basins and sub-basins as well as a grid of 0.5 x 0.5°. These scales were mainly chosen for pragmatic reasons.Next, a framework (FAMOS) is described to identify the appropriate spatial and temporal scales for N-flow models. FAMOS has been developed for models that predict N export from large watersheds. With FAMOS, modelers can identify the appropriate scale for model predictions and other Scalable Model Parts (SMPs). Different measures of model scale are distinguished in FAMOS. These are support, stream length, extent, and stream order. Spatial support is a measure of the size of the areas represented by single values of input variables. Temporal model support is a measure of the duration of the times represented by single values of input variables. Stream length is the length of river sections represented by single values of input variables. Model extent is the total range of time or space within which processes are modeled. Stream order is a measure of the size of river reaches that are modeled. Using twelve indicators, FAMOS determines the appropriateness of model scales. Indicators are to be specified by the modeler and are associated with four criteria. The criteria require modeling scales to correspond with (A) data and scenarios, (B) model assumptions, (C) available resources for modeling, and (D) appropriately scaled predictions.The applicability of FAMOS is assessed for NEWS-DIN. Ranges of appropriate scales are determined for model output and fiveSMPs, which model the (1) surface N balance, (2) point sources, (3) N flow in sediments and small streams, (4) retention in dammed reservoirs, and (5)riverineDIN retention. Indicators of appropriateness of modeling scale are quantified based on existing data and knowledge. A comparison is made between the scale at which NEWS-DIN was applied and the identified appropriate scale. Based on this, recommendations can be made for improvement of application of the model. The results indicate that most of the scales used in the original application of NEWS-DIN are appropriate. FAMOS identified that spatial support and temporal extent of someSMPsare inappropriate. For theSMPsmodelingriverineretention and predictedriverineDIN export no appropriate values of temporal support were found. The applied scales for NEWS-DIN were for practical reasons chosen such that they agreed with the available data. We conclude that the modeling scale of NEWS-DIN could be improved if (1) knowledge or data sufficient to modelriverineprocesses on a smaller temporal support is obtained, or if (2) if NEWS-DIN is used tohindcastor model scenarios of the future.The applicability of FAMOS is also assessed for models of N-flow from rivers to aquatic systems in reconnected floodplains. Floodplain models describe smaller systems than the ones for which FAMOS was originally developed. We conclude that FAMOS can be applied to floodplain models, if three phenomena affecting appropriate scales of these models are considered. This requires an extension with three new indicators for the appropriateness of modeling scale: (1) the reliability with which empirical relations can model the aggregated effect of an intermittent process on N flow, (2) the validity of particular nonlinear model equations, and (3) the reliability of modeling past N inflows. These new indicators are applied to a hypothetical model of an existing reconnected floodplain to illustrate their use, output and effect on appropriate scales. It is shown that inclusion of the new indicators in FAMOS provides a feasible basis for a comprehensive identification of appropriate scales of N flow from rivers to aquatic systems in reconnected floodplains.Novel aspects of our approach for identifying appropriate scales for N-flow models can be summarized as follows. First, the most appropriate scale results in an optimal balance between the use of available data and scenarios, validity of model assumptions, effort needed for modeling, and the usefulness of model output. Second, different indicators can be used to assess these criteria. Third, appropriate scales need to be identified for scalable model parts, not for complete models. Fourth, several interactions in affecting scale appropriateness can be identified between values of different measures of modeling scale. SMP scales affect the appropriateness of scales of otherSMPs. And the appropriateness of a value of a measure of model scale is usually affected by the value chosen for another measure of model scale within the same SMP. Finally, the modeled system and the type of model equations affect the methods that are suitable to indicate if there is an optimal balance between agreement with available data, model assumptions, resources and end users. This thesis shows that FAMOS is a promising tool that can be applied to a wide range of models.