Edge effect causes apparent fractal correlation dimension of uniform spatial raindrop distribution

Lovejoy and Schertzer (1990a) presented a statistical analysis of blotting paper observations of the (twodimensional) spatial distribution of raindrop stains. They found empirical evidence for the fractal scaling behavior of raindrops in space, with potentially far-reaching implications for rainfall microphysics and radar meteorology. In particular, the fractal correlation dimensions determined from their blotting paper observations led them to conclude that “drops are (hierarchically) clustered” and that “inhomogeneity in rain is likely to extend down to millimeter scales”. Confirming previously reported Monte Carlo simulations, we demonstrate analytically that the claims based on this analysis need to be reconsidered, as fractal correlation dimensions similar to the ones reported (i.e. smaller than the value of two expected for uniformly distributed raindrops) can result from instrumental artifacts (edge effects) in otherwise homogeneous Poissonian rainfall. Hence, the results of the blotting paper experiment are not statistically significant enough to reject the Poisson homogeneity hypothesis in favor of a fractal description of the discrete nature of rainfall. Our analysis is based on an analytical expression for the expected overlap area between a circle and a square, when the circle center is randomly (uniformly) distributed inside the square. The derived expression ( r2−8r3/3+r4/2, where r denotes the ratio between the circle radius and the side of the square) can be used as a reference curve against which to test the statistical significance of fractal correlation dimensions determined from spatial point patterns, such as those of raindrops and rainfall cells.Postprint (published version

Drought in the Anthropocene

Drought management is inefficient because feedbacks between drought and people are not fully understood. In this human-influenced era, we need to rethink the concept of drought to include the human role in mitigating and enhancing drought

Drought in a human-modified world: reframing drought definitions, understanding, and analysis approaches

In the current human-modified world, or Anthropocene, the state of water stores and fluxes has become dependent on human as well as natural processes. Water deficits (or droughts) are the result of a complex interaction between meteorological anomalies, land surface processes, and human inflows, outflows, and storage changes. Our current inability to adequately analyse and manage drought in many places points to gaps in our understanding and to inadequate data and tools. The Anthropocene requires a new framework for drought definitions and research. Drought definitions need to be revisited to explicitly include human processes driving and modifying soil moisture drought and hydrological drought development. We give recommendations for robust drought definitions to clarify timescales of drought and prevent confusion with related terms such as water scarcity and overexploitation. Additionally, our understanding and analysis of drought need to move from single driver to multiple drivers and from uni-directional to multi-directional. We identify research gaps and propose analysis approaches on (1) drivers, (2) modifiers, (3) impacts, (4) feedbacks, and (5) changing the baseline of drought in the Anthropocene. The most pressing research questions are related to the attribution of drought to its causes, to linking drought impacts to drought characteristics, and to societal adaptation and responses to drought. Example questions include: (i) What are the dominant drivers of drought in different parts of the world? (ii) How do human modifications of drought enhance or alleviate drought severity? (iii) How do impacts of drought depend on the physical characteristics of drought vs. the vulnerability of people or the environment? (iv) To what extent are physical and human drought processes coupled, and can feedback loops be identified and altered to lessen or mitigate drought? (v) How should we adapt our drought analysis to accommodate changes in the normal situation (i.e. what are considered normal or reference conditions) over time? Answering these questions requires exploration of qualitative and quantitative data as well as mixed modelling approaches. The challenges related to drought research and management in the Anthropocene are not unique to drought, but do require urgent attention. We give recommendations drawn from the fields of flood research, ecology, water management, and water resources studies. The framework presented here provides a holistic view on drought in the Anthropocene, which will help improve management strategies for mitigating the severity and reducing the impacts of droughts in future

Drought in a human-modified world: reframing drought definitions, understanding, and analysis approaches

In the current human-modified world, or Anthropocene, the state of water stores and fluxes has become dependent on human as well as natural processes.Water deficits (or droughts) are the result of a complex interaction between meteorological anomalies, land surface processes, and human inflows, outflows, and storage changes. Our current inability to adequately analyse and manage drought in many places points to gaps in our understanding and to inadequate data and tools. The Anthropocene requires a new framework for drought definitions and research. Drought definitions need to be revisited to explicitly include human processes driving and modifying soil moisture drought and hydrological drought development. We give recommendations for robust drought definitions to clarify timescales of drought and prevent confusion with related terms such as water scarcity and overexploitation. Additionally, our understanding and analysis of drought need to move from single driver to multiple drivers and from uni-directional to multi-directional. We identify research gaps and propose analysis approaches on (1) drivers, (2) modifiers, (3) impacts, (4) feedbacks, and (5) changing the baseline of drought in the Anthropocene. The most pressing research questions are related to the attribution of drought to its causes, to linking drought impacts to drought characteristics, and to societal adaptation and responses to drought. Example questions include (i) What are the dominant drivers of drought in different parts of the world? (ii) How do human modifications of drought enhance or alleviate drought severity? (iii) How do impacts of drought depend on the physical characteristics of drought vs. the vulnerability of people or the environment? (iv) To what extent are physical and human drought processes coupled, and can feedback loops be identified and altered to lessen or mitigate drought? (v) How should we adapt our drought analysis to accommodate changes in the normal situation (i.e. what are considered normal or reference conditions) over time

Перспективи інформаційної економіки

Метою доповіді є дослідження впливу інформаційних технологій на розвиток таких категорій сучасності як перехід сучасної економіки до інформаційного етапу, а також становлення інформаційного суспільства на основі сучасного пост промислового суспільства споживання

The importance of hydraulic groundwater theory in catchment hydrology: The legacy of Wilfried Brutsaert and Jean-Yves Parlange

Based on a literature overview, this paper summarizes the impact and legacy of the contributions of Wilfried Brutsaert and Jean-Yves Parlange (Cornell University) with respect to the current state-of-the-art understanding in hydraulic groundwater theory. Forming the basis of many applications in catchment hydrology, ranging from drought flow analysis to surface water-groundwater interactions, hydraulic groundwater theory simplifies the description of water flow in unconfined riparian and perched aquifers through assumptions attributed to Dupuit and Forchheimer. Boussinesq (1877) derived a general equation to study flow dynamics of unconfined aquifers in uniformly sloping hillslopes, resulting in a remarkably accurate and applicable family of results, though often challenging to solve due to its nonlinear form. Under certain conditions, the Boussinesq equation can be solved analytically allowing compact representation of soil and geomorphological controls on unconfined aquifer storage and release dynamics. The Boussinesq equation has been extended to account for flow divergence/convergence as well as for nonuniform bedrock slope (concave/convex). The extended Boussinesq equation has been favorably compared to numerical solutions of the three-dimensional Richards equation, confirming its validity under certain geometric conditions. Analytical solutions of the linearized original and extended Boussinesq equations led to the formulation of similarity indices for baseflow recession analysis, including scaling rules, to predict the moments of baseflow response. Validation of theoretical recession parameters on real-world streamflow data is complicated due to limited measurement accuracy, changing boundary conditions, and the strong coupling between the saturated aquifer with the overlying unsaturated zone. However, recent advances are shown to have mitigated several of these issues. The extended Boussinesq equation has been successfully applied to represent baseflow dynamics in catchment-scale hydrological models, and it is currently considered to represent lateral redistribution of groundwater in land surface schemes applied in global circulation models. From the review, it is clear that Wilfried Brutsaert and Jean-Yves Parlange stimulated a body of research that has led to several fundamental discoveries and practical applications with important contributions in hydrological modeling.Keywords: Parlange, hillslope, catchment, groundwater, Brutsaert, Boussines

Satellite and in situ observations for advancing global Earth surface modelling: a review

In this paper, we review the use of satellite-based remote sensing in combination with in situ data to inform Earth surface modelling. This involves verification and optimization methods that can handle both random and systematic errors and result in effective model improvement for both surface monitoring and prediction applications. The reasons for diverse remote sensing data and products include (i) their complementary areal and temporal coverage, (ii) their diverse and covariant information content, and (iii) their ability to complement in situ observations, which are often sparse and only locally representative. To improve our understanding of the complex behavior of the Earth system at the surface and sub-surface, we need large volumes of data from high-resolution modelling and remote sensing, since the Earth surface exhibits a high degree of heterogeneity and discontinuities in space and time. The spatial and temporal variability of the biosphere, hydrosphere, cryosphere and anthroposphere calls for an increased use of Earth observation (EO) data attaining volumes previously considered prohibitive. We review data availability and discuss recent examples where satellite remote sensing is used to infer observable surface quantities directly or indirectly, with particular emphasis on key parameters necessary for weather and climate prediction. Coordinated high-resolution remote-sensing and modelling/assimilation capabilities for the Earth surface are required to support an international application-focused effort

Twenty-three unsolved problems in hydrology (UPH) – a community perspective

This paper is the outcome of a community initiative to identify major unsolved scientific problems in hydrology motivated by a need for stronger harmonisation of research efforts. The procedure involved a public consultation through on-line media, followed by two workshops through which a large number of potential science questions were collated, prioritised, and synthesised. In spite of the diversity of the participants (230 scientists in total), the process revealed much about community priorities and the state of our science: a preference for continuity in research questions rather than radical departures or redirections from past and current work. Questions remain focussed on process-based understanding of hydrological variability and causality at all space and time scales. Increased attention to environmental change drives a new emphasis on understanding how change propagates across interfaces within the hydrological system and across disciplinary boundaries. In particular, the expansion of the human footprint raises a new set of questions related to human interactions with nature and water cycle feedbacks in the context of complex water management problems. We hope that this reflection and synthesis of the 23 unsolved problems in hydrology will help guide research efforts for some years to come