Center for Massive Data Algorithmics

Estimating the geographical flood extent is a key element in impact-based flood forecasting and crucial for countries with long coastlines, and places where storm surges pose a significant risk, such as Denmark. For local flood mitigation measures and climate adaptation strategies, inundation mapping is often performed using physical models. However, in the context of flood forecasting and early warning, these are computationally demanding and therefore may not be able to provide timely forecasts and effective warnings.The Danish Meteorological Institute (DMI) has developed a real-time flood forecasting system for storm surge events in Denmark together with the company SCALGO. This system couples the HBM regional oceanic storm surge forecasting model, developed by DMI, with a rapid inundation mapping, developed by SCALGO, using a 0.4 m resolution Digital Elevation Model (DEM). All inland pixels in the DEM are connected to a coastline pixel through pre-computed hydrological flow paths. The predicted water level from the storm surge model at each coastline pixel is then instantaneously projected inland through the pre-mapped flow paths. This study evaluates the performance of the flood forecasting system on the Oct. 20-21 (2023) storm surge event, with an estimated return period of over 100 years and affecting large parts of southern Denmark (and northern Germany).This flood forecasting system creates a simple inundation mapping based on forecasted sea levels based on a high-resolution DEM modified to account for hydrological flow processes. This real-time flood mapping allows for a visualization of full five-day ocean model forecasts updated continuously at 6h intervals and has been operational for flood warning since October 2022, to supplement DMIs operational ocean forecasting system [1]. The evaluation is performed by comparing the inundation map from the flood forecasting system with media reports, photographs, and other data sources to get an overview of spatial and temporal accuracy and accuracy of the severity of the event. We see a large overlap between areas with forecasted flood risks and actual flooded areas. In some cases, the extent of the flooding differs from the area at risk due to errors in the DEM or local emergency services mitigation strategies.We conclude that the flood forecasting system is useful for identifying coastal areas at risk. While it does not account for detailed physics of flow on land, it is able to reflect the effects of, even very local, geographical variations in sea level that determine the distributions of local-scale flood risk. The current inundation mapping does not currently include the impact of waves, which resulted in larger differences between predictions and actual flooded areas, for easterly-facing locations exposed to large waves. Proposed activities to include the effect of waves will therefore improve the flood forecasting system. [1] Andrée, E., Su, J., Larsen, M. A. D., Madsen, K. S., & Drews, M. (2021). Simulating major storm surge events in a complex coastal region. Ocean Modelling, 162, 101802.

Urban residence is associated with a higher risk of some psychiatric disorders, but the underlying drivers remain unknown. There is increasing evidence that the level of exposure to natural environments impacts mental health, but few large-scale epidemiological studies have assessed the general existence and importance of such associations. Here, we investigate the prospective association between green space and mental health in the Danish population. Green space presence was assessed at the individual level using high-resolution satellite data to calculate the normalized difference vegetation index within a 210 × 210 m square around each person's place of residence (∼1 million people) from birth to the age of 10. We show that high levels of green space presence during childhood are associated with lower risk of a wide spectrum of psychiatric disorders later in life. Risk for subsequent mental illness for those who lived with the lowest level of green space during childhood was up to 55% higher across various disorders compared with those who lived with the highest level of green space. The association remained even after adjusting for urbanization, socioeconomic factors, parental history of mental illness, and parental age. Stronger association of cumulative green space presence during childhood compared with single-year green space presence suggests that presence throughout childhood is important. Our results show that green space during childhood is associated with better mental health, supporting efforts to better integrate natural environments into urban planning and childhood life.

Predicting floods caused by the rise of the sea level is a critical task for preventing large scale catastrophes. Such predictions can potentially be made using a forecast of the sea level and a detailed model of the terrain. However, since available terrain datasets can easily exceed the size of the main memory of a standard computer, I/O (rather than internal computation time) can often become the bottleneck when computing such predictions. Thus to perform predictions efficiently we need an I/O-efficient approach, which minimizes the transfer of data blocks between main memory and disk. Given a terrain raster T and a sea-level forecast raster S of N cells each, we examine the problem of computing the water level of the induced flood for each cell in T. We introduce an I/O-efficient algorithm for this problem that uses O((N/B) logM/B (X/B)) I/Os after O((N/B) logM/B (N/B)) I/Os of preprocessing, where X is the number of local minima in T, and M and B are the size of main memory and data block, respectively. When X < M (which holds in practice) our algorithm requires optimal O(N/B) I/Os after preprocessing. We have implemented our algorithm and put considerable effort into engineering it. We present experiments that illustrate the efficiency and practicality of the algorithm, which is so efficient that work is underway to incorporate our results in the forecast services of the Danish Meteorological Institute.

An important problem in terrain analysis is modeling how water flows across a terrain and creates floods by filling up depressions. In this paper we study the flooding query problem: Given a rain region R and a query point q on the terrain, quickly determine how much rain has to fall in R so that q is flooded. Available terrain data is often subject to uncertainty which must be incorporated into the terrain analysis. For instance, the digital elevation models of terrains have to be refined to incorporate underground pipes, tunnels, and waterways under bridges, but there is often uncertainty in their existence. By representing the uncertainty in the terrain data explicitly, we can develop methods for flood risk analysis that properly incorporate terrain uncertainty when reporting what areas are at risk of flooding.

Many species assemblages represent a nonrandom subset of a larger species pool. When an assemblage tends to contain close evolutionary relatives or species with similar functional traits, it can be described as phylogenetically or functionally clustered. Clustering is often interpreted as evidence for filtering by some combination of environmental and biotic factors. At sufficiently large spatial extents, however, biogeographic barriers can also lead to strong clustering. Here, we suggest that the breakdown of biogeographic barriers associated with human introductions of exotic species can be used as an unintentional experiment to assess their importance in driving phylogenetic and functional structure. An important role of biogeographic barriers would be revealed by a breakdown in clustering, particularly phylogenetic clustering, following species introductions. On the other hand, a role of filtering can be supported by similar patterns of clustering in the native and exotic assemblages along environmental gradients. We test these predictions using the grasses of California, a diverse group including many introduced species. Native grass assemblages in the state are highly clustered with respect to the global grass species pool, both phylogenetically and functionally. Within the state, variation in the strength of clustering is well explained by climatic variables, suggesting an important role for environmental-biotic filtering. Further, subregions within the state with highly clustered native assemblages also contain highly clustered exotic assemblages. Contrary to expectation, though, the introduction of exotic species led to even more strongly clustered assemblages. We conclude that biogeographic barriers have generally not excluded the major grass lineages (e.g., tribes) from the state and likely act only on finer taxonomic scales (for example, excluding particular genera). Our approach should prove broadly applicable and contribute to improved understanding of broad-scale patterns of assemblage structure.

One of the important tasks in the analysis of spatio-temporal data collected from moving entities is to find a group: a set of entities that travel together for a sufficiently long period of time. Buchin et al. [JoCG, 2015] introduce a formal definition of groups, analyze its mathematical structure, and present efficient algorithms for computing all maximal groups in a given set of trajectories. In this paper, we refine their definition and argue that our proposed definition corresponds better to human intuition in certain cases, particularly in dense environments. We present algorithms to compute all maximal groups from a set of moving entities according to the new definition. For a set of n moving entities in R^1, specified by linear interpolation in a sequence of tau time stamps, we show that all maximal groups can be computed in O(tau^2 n^4) time. A similar approach applies if the time stamps of entities are not the same, at the cost of a small extra factor of alpha(n) in the running time. In higher dimensions, we can compute all maximal groups in O(tau^2 n^5 log n) time (for any constant number of dimensions). We also show that one tau factor can be traded for a much higher dependence on n by giving a O(tau n^4 2^n) algorithm for the same problem. Consequently, we give a linear-time algorithm when the number of entities is constant and the input size relates to the number of time stamps of each entity. Finally, we provide a construction to show that it might be difficult to develop an algorithm with polynomial dependence on n and linear dependence on tau.

In this paper, we look at the complexity of designing algorithms without any bank conflicts in the shared memory of Graphical Processing Units (GPUs). Given input of size n, w processors and w memory banks, we study three fundamental problems: sorting, permuting and w-way partitioning (defined as sorting an input containing exactly n/w copies of every integer in [w]).

Abstract In this paper, we propose streaming algorithms for approximating the smallest intersecting ball of a set of disjoint balls in \(\mathbb {R}^d\). This problem is a generalization of the \(1\)-center problem, one of the most fundamental problems in computational geometry. We consider the single-pass streaming model; only one-pass over the input stream is allowed and a limited amount of information can be stored in memory. We introduce three approximation algorithms: one is an algorithm for the problem in arbitrarily dimensions, but in the other two we assume \(d\) is a constant. The first algorithm guarantees a \((2+\sqrt{2}+\varepsilon ^*)\)-factor approximation using \(O(d^2)\) space and \(O(d)\) update time where \(\varepsilon ^*\) is an arbitrarily small positive constant. The second algorithm guarantees an approximation factor \(3\) using \(O(1)\) space and \(O(1)\) update time (assuming constant \(d\)). The third one is a \((1+\varepsilon )\)-approximation algorithm that uses \(O(1/\varepsilon ^{d})\) space and \(O(1/\varepsilon ^{(d-1)/2})\) amortized update time. They are the first approximation algorithms for the problem, and also the first results in the streaming model.KeywordsDisjoint BallsStreaming ModelApproximation FactorBalanced InputFactor Analysis EstimationThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.