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Determining the optimal grid resolution for topographic analysis on an airborne lidar dataset
(2019)

Digital elevation models (DEMs) are a gridded representation of the surface of the Earth and typically contain uncertainties due to data collection and processing. Slope and aspect estimates on a DEM contain errors and uncertainties inherited from the representation of a continuous surface as a grid (referred to as truncation error; TE) and from any DEM uncertainty. We analyze in detail the impacts of TE and propagated elevation uncertainty (PEU) on slope and aspect.
Using synthetic data as a control, we define functions to quantify both TE and PEU for arbitrary grids. We then develop a quality metric which captures the combined impact of both TE and PEU on the calculation of topographic metrics. Our quality metric allows us to examine the spatial patterns of error and uncertainty in topographic metrics and to compare calculations on DEMs of different sizes and accuracies.
Using lidar data with point density of ∼10 pts m−2 covering Santa Cruz Island in southern California, we are able to generate DEMs and uncertainty estimates at several grid resolutions. Slope (aspect) errors on the 1 m dataset are on average 0.3∘ (0.9∘) from TE and 5.5∘ (14.5∘) from PEU. We calculate an optimal DEM resolution for our SCI lidar dataset of 4 m that minimizes the error bounds on topographic metric calculations due to the combined influence of TE and PEU for both slope and aspect calculations over the entire SCI. Average slope (aspect) errors from the 4 m DEM are 0.25∘ (0.75∘) from TE and 5∘ (12.5∘) from PEU. While the smallest grid resolution possible from the high-density SCI lidar is not necessarily optimal for calculating topographic metrics, high point-density data are essential for measuring DEM uncertainty across a range of resolutions.

Determining the optimal grid resolution for topographic analysis on an airborne lidar dataset
(2019)

Identifying abrupt transitions is a key question in various disciplines. Existing transition detection methods, however, do not rigorously account for time series uncertainties, often neglecting them altogether or assuming them to be independent and qualitatively similar. Here, we introduce a novel approach suited to handle uncertainties by representing the time series as a time-ordered sequence of probability density functions. We show how to detect abrupt transitions in such a sequence using the community structure of networks representing probabilities of recurrence. Using our approach, we detect transitions in global stock indices related to well-known periods of politico-economic volatility. We further uncover transitions in the El Nino-Southern Oscillation which coincide with periods of phase locking with the Pacific Decadal Oscillation. Finally, we provide for the first time an 'uncertainty-aware' framework which validates the hypothesis that ice-rafting events in the North Atlantic during the Holocene were synchronous with a weakened Asian summer monsoon.

High Mountain Asia (HMA) - encompassing the Tibetan Plateau and surrounding mountain ranges - is the primary water source for much of Asia, serving more than a billion downstream users. Many catchments receive the majority of their yearly water budget in the form of snow, which is poorly monitored by sparse in situ weather networks. Both the timing and volume of snowmelt play critical roles in downstream water provision, as many applications - such as agriculture, drinking-water generation, and hydropower - rely on consistent and predictable snowmelt runoff. Here, we examine passive microwave data across HMA with five sensors (SSMI, SSMIS, AMSR-E, AMSR2, and GPM) from 1987 to 2016 to track the timing of the snowmelt season - defined here as the time between maximum passive microwave signal separation and snow clearance. We validated our method against climate model surface temperatures, optical remote-sensing snow-cover data, and a manual control dataset (n = 2100, 3 variables at 25 locations over 28 years); our algorithm is generally accurate within 3-5 days. Using the algorithm-generated snowmelt dates, we examine the spatiotemporal patterns of the snowmelt season across HMA. The climatically short (29-year) time series, along with complex interannual snowfall variations, makes determining trends in snowmelt dates at a single point difficult. We instead identify trends in snowmelt timing by using hierarchical clustering of the passive microwave data to determine trends in self-similar regions. We make the following four key observations. (1) The end of the snowmelt season is trending almost universally earlier in HMA (negative trends). Changes in the end of the snowmelt season are generally between 2 and 8 days decade 1 over the 29-year study period (5-25 days total). The length of the snowmelt season is thus shrinking in many, though not all, regions of HMA. Some areas exhibit later peak signal separation (positive trends), but with generally smaller magnitudes than trends in snowmelt end. (2) Areas with long snowmelt periods, such as the Tibetan Plateau, show the strongest compression of the snowmelt season (negative trends). These trends are apparent regardless of the time period over which the regression is performed. (3) While trends averaged over 3 decades indicate generally earlier snowmelt seasons, data from the last 14 years (2002-2016) exhibit positive trends in many regions, such as parts of the Pamir and Kunlun Shan. Due to the short nature of the time series, it is not clear whether this change is a reversal of a long-term trend or simply interannual variability. (4) Some regions with stable or growing glaciers - such as the Karakoram and Kunlun Shan - see slightly later snowmelt seasons and longer snowmelt periods. It is likely that changes in the snowmelt regime of HMA account for some of the observed heterogeneity in glacier response to climate change. While the decadal increases in regional temperature have in general led to earlier and shortened melt seasons, changes in HMA's cryosphere have been spatially and temporally heterogeneous.

We propose a RAndom Interacting Network (RAIN) model to study the interactions between a pair of complex networks. The model involves two major steps: (i) the selection of a pair of nodes, one from each network, based on intra-network node-based characteristics, and (ii) the placement of a link between selected nodes based on the similarity of their relative importance in their respective networks. Node selection is based on a selection fitness function and node linkage is based on a linkage probability defined on the linkage scores of nodes. The model allows us to relate within-network characteristics to between-network structure. We apply the model to the interaction between the USA and Schengen airline transportation networks (ATNs). Our results indicate that two mechanisms: degree-based preferential node selection and degree-assortative link placement are necessary to replicate the observed inter-network degree distributions as well as the observed inter-network assortativity. The RAIN model offers the possibility to test multiple hypotheses regarding the mechanisms underlying network interactions. It can also incorporate complex interaction topologies. Furthermore, the framework of the RAIN model is general and can be potentially adapted to various real-world complex systems.