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The seasonal movement of soil water through a deep vadose zone of a sandy hill was studied in the central part of The Netherlands. The behaviour of soil water was tracked by monitoring soil water fluctuations and changes in the environmental tracer lS 0 in vertical profiles at test sites with grassland, heathland and forest. In the temperate climate of the study area a soil moisture deficit develops during summer and a precipitation surplus prevails during winter. The 18 0 content in precipitation exhibits a distinct seasonal cycle with the highest (relatively enriched) values of c. -6%o vs V-SMOW occurring in summer and the lowest (relatively depleted) values of c. -9%o vs V-SMOW in winter. The influence of this cycle can be traced back in the subsurface to a depth of sometimes more than 6 m. This seasonal fluctuation moves around the average annual 18 0 content in rainfall, tending closer to the average as depth increases. In the saturated zone the same average value is observed. This suggests that, although the precipitation surplus is limited to the winter period, part of the summer precipitation also infiltrates to below the root zone and contributes to the groundwater recharge. The results of this study indicate that preferential flow dominates in the root zone. Below the root zone of low homogeneous vegetation covers, the soil water movement is dominated by diffuse flow. In forests, a more heterogeneous root pattern causes a more preferential type of flow, also at greater depths below the root zone.Mécanisme du mouvement des eaux souterraines d'après les conclusions des études de l'isotope stable ls O Résumé Nous avons réalisé une étude du mouvement saisonnier des eaux souterraines à travers une zone vadose profonde d'une colline sableuse, au centre des Pays-Bas. Le comportement des eaux souterraines a été suivi en contrôlant les modifications du traceur environnemental 18 0 selon des profils verticaux sur des sites d'essai situées dans des prairies, des landes et des forêts. La teneur en 1S 0 des précipitations présente un cycle saisonnier propre, avec des valeurs maximales (relativement enrichies) d'environ -6%o par rapport au V-SMOW l'été, et minimales (relativement appauvries) de -9%o par rapport au V-SMOW l'hiver. L'influence de ce cycle peut être retrouvée dans le sous-sol jusqu'à une profondeur parfois supérieure à 6 m. Cette fluctuation saisonnière est proche du pourcentage annuel moyen de 18 0 dans les précipitations, tendant à se rapprocher davantage de la moyenne lorsque la profondeur augmente. Dans la zone saturée, on observe la même valeur moyenne ce qui suggère qu'une partie des pluies estivales s'infiltre sous la couche d'enracinement et contribue à la réalimentation des nappes phréatiques, bien que l'excédent de précipitations se limite à la période hivernale. Il ressort des résultats de cette étude que l'écoulement préférentiel est dominant dans la couche

IntroductionCommuting has been the subject of increasing public attention and intensive research in recent decades (see Nijkamp and Rouwendal, 2004;Rouwendal and Nijkamp, 2004). The increasing role of commuting has far-reaching consequences for public policy concerning traffic, infrastructure, and spatial planning. Commuting flows connect labor and housing markets. Knowledge of the intensity and spatial range of this interaction is required to determine the accessibility of a location to centers of population and employment. Theoretical and applied research on commuting issues can help to clarify the relevant effects.The analysis of the sizes of commuting flows between cities or regions, and their effects on housing and labor markets, is part of the much wider area of spatial interaction modeling (Batten and Boyce, 1986;Fotheringham and O'Kelly, 1989;Nijkamp and Reggiani, 1992). Spatial interaction models are applied not only to commuting but also to migration, international trade, shopping behavior, and other topics related to origin^destination flows. An essential element of these models is that interaction decreases with distance or travel cost. This is described by a distance-decay function. However, distance is not the only factor affecting the intensity of the interaction. Also important are the sizes (however measured) of origin and destination. And it is increasingly recognized that additionally the positions of origin and destination in the spatial system are relevant. The research in this paper is an application of spatial interaction modeling, and the methodological issues are not limited to commuting.An important issue in spatial interaction modeling is the choice of the functional form of distance or travel cost. In the literature, the distance-decay function is usually assumed to be an exponential or a power function:`I n practice, the debate over the form of the cost function in spatial interaction models has evolved to a reasonably widespread consensus that the exponential function is more appropriate for analysing short distance interactions such as those that take place within an urban area. The power function, conversely, is generally held to be more appropriate for analysing longer distance interactions such as migration flows '' (Fotheringham and O'Kelly, 1989, pages 12^13 Abstract. In this paper we investigate the functional form of distance decay for commuting flows between municipalities in Denmark. Our inference is based on a single equation that includes variables to capture the effect of spatial structure. Special attention is given to a proper estimation method: we estimate the distance-decay parameters by nonlinear weighted least-squares with balancing factors. It appears that neither an exponential nor a power distance-decay function fits the data well. Using a spline regression we find a cost elasticity of À4 for distances around 20 km and a much smaller value for shorter and longer distances. It appears that the logarithm of distance decay can be described adequately as a (downwar...