Scale is a fundamental concept that has attracted persistent attention in geography literature over the past several decades. However, it creates enormous confusion and frustration, particularly in the context of geographic information science, because of scale-related issues such as image resolution and the modifiable areal unit problem (MAUP). This paper argues that the confusion and frustration arise from traditional Euclidean geometric thinking, in which locations, directions, and sizes are considered absolute, and it is now time to revise this conventional thinking. Hence, we review fractal geometry, together with its underlying way of thinking, and compare it to Euclidean geometry. Under the paradigm of Euclidean geometry, everything is measurable, no matter how big or small. However, most geographic features, due to their fractal nature, are essentially unmeasurable or their sizes depend on scale. For example, the length of a coastline, the area of a lake, and the slope of a topographic surface are all scale-dependent. Seen from the perspective of fractal geometry, many scale issues, such as the MAUP, are inevitable. They appear unsolvable, but can be dealt with. To effectively deal with scale-related issues, we present topological and scaling analyses illustrated by street-related concepts such as natural streets, street blocks, and natural cities. We further contend that one of the two spatial properties, spatial heterogeneity, is de facto the fractal nature of geographic features, and it should be considered the first effect among the two, because it is global and universal across all scales, which should receive more attention from practitioners of geography.

In comprehending flood model results, we performed sensitivity analyses and evaluated how different combinations of digital elevation model (DEM) resolution and Manning’s roughness affect flood maps produced from a 2D hydraulic model. Moreover, we analysed how the estimation of accuracy can further be influenced by the performance measure and the area’s topography. Various combinations of DEM and Manning’s $n$ produced different results, in terms of quantified performance in relation to actual flood extent and the generated flood boundaries. High-resolution DEMs performed better with higher Manning’s $n,$ while lower $n$ values were better for lower resolution DEMs. Furthermore, although lower resolution DEMs (25 and 50 m) received higher quantified performances, there are more discrepancies in the flood maps and water surface elevations (WSE) produced by them. The current statistical estimators of model performance do not necessarily provide an accurate estimate of which combination of DEM resolution and roughness are more suitable for application to modelling. Different statistical estimates have different assumptions, which can affect the model selection. Therefore, a more holistic approach towards model selection should be adopted that gives equal importance to statistical estimators, as well as the quality of flood inundation extents.

A literature survey on methods of computing stable river-channel geometry, demanding a small amount of work effort and few input data, has been made and is presented. Besides the use of empirical regime equations and the use of an extremal hypothesis in conjunction with a sediment-transport and a flow-friction theory, new regression equations have been formulated which are used together with a sedimenttransport equation. These methods may prove efficient when predicting changes, such as after dam and reservoir construction, on an alluvial river. Calculations using the different methods have been exemplified on a natural river.