Existing water governance systems are proving to be quite ineffective in managing water scarcity, creating severe risk for many aspects of our societies and economies. Water markets are a relatively new and increasingly popular tool in the fight against growing water scarcity. They make a voluntary exchange possible between interested buyers and sellers of water rights. This paper presents direct evidence from seven water markets around the globe to document key economic and ecological challenges and achievements of water markets with respect to water scarcity. We specifically approach water markets as localized cap-and-trade systems, similar to those for carbon emissions. We examine whether water use remains within the set limits on use of water rights (i.e., under the cap), the degree to which water markets help protect the health of ecosystems and species, and whether (as predicted by economic theory) the explicit pricing of water is accompanied by improving efficiency, as less productive water users decide to sell water to more productive water users.

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Seafloor topography affects a wide range of physical and biological processes; therefore, collapsing the three‐dimensional structure of the bottom to roughness metrics is a common challenge in studies of marine systems. Here we assessed the properties captured by metrics previously proposed for the seafloor, as well as metrics developed to characterize other types of rough surfaces. We considered three classes of metrics: properties of the bottom elevation distribution (e.g., standard deviation), length scale ratios (e.g., rugosity), and metrics that describe how topography varies with spatial scale (e.g., Hölder exponents). The metrics were assessed using idealized topography and natural seafloor topography data from airborne lidar measurements of a coral reef. We illustrate that common roughness metrics (e.g., rugosity) can have the same value for topographies that are geometrically very different, limiting their utility. Application of the wavelet leaders technique to the reef data set demonstrates that the topography has a power law scaling behavior, but it is multifractal so a distribution of Hölder exponents is needed to describe its scaling behavior. Using principal component analysis, we identify three dominant modes of topographic variability, or ways metrics covary, among and within reef zones. Collectively, the results presented here show that coral reef topography is both multiscale and multifractal. While individual metrics that capture specific topography properties relevant to a given process may be suitable for some studies, many applications will require a set of metrics that includes statistics that capture how topography varies with spatial scale.