Rotated Spectral Principal Component Analysis (rsPCA) for Identifying Dynamical Modes of Variability in Climate Systems.

Spectral PCA (sPCA), in contrast to classical PCA, offers the advantage of identifying organized spatiotemporal patterns within specific frequency bands and extracting dynamical modes. However, the unavoidable trade-off between frequency resolution and robustness of the PCs leads to high sensitivity to noise and overfitting, which limits the interpretation of the sPCA results. We propose herein a simple nonparametric implementation of sPCA using the continuous analytic Morlet wavelet as a robust estimator of the cross-spectral matrices with good frequency resolution. To improve the interpretability of the results, especially when several modes of similar amplitude exist within the same frequency band, we propose a rotation of the complex-valued eigenvectors to optimize their spatial regularity (smoothness). The developed method, called rotated spectral PCA (rsPCA), is tested on synthetic data simulating propagating waves and shows impressive performance even with high levels of noise in the data. Applied to global historical geopotential height (GPH) and sea surface temperature (SST) daily time series, the method accurately captures patterns of atmospheric Rossby waves at high frequencies (3-60-day periods) in both GPH and SST and El Niño-Southern Oscillation (ENSO) at low frequencies (2-7-yr periodicity) in SST. At high frequencies the rsPCA successfully unmixes the identified waves, revealing spatially coherent patterns with robust propagation dynamics

The Entropic Braiding Index (eBI): A Robust Metric to Account for the Diversity of Channel Scales in Multi-Thread Rivers

The Braiding Index (BI), defined as the average count of intercepted channels per cross-section, is a widely used metric for characterizing multi-thread river systems. However, it does not account for the diversity of channels (e.g., in terms of water discharge) within different cross-sections, omitting important information related to system complexity. Here we present a modification of BI, the Entropic Braiding Index (eBI), which augments the information content in BI by using Shannon Entropy to encode the diversity of channels in each cross section. eBI is interpreted as the number of “effective channels” per cross-section, allowing a direct comparison with the traditional BI. We demonstrate the potential of the ratio BI/eBI to quantify channel disparity, differentiate types of multi-thread systems (braided vs. anastomosed), and assess the effect of discharge variability, such as seasonal flooding, on river cross-section stability

Climate Signatures on Lake And Wetland Size Distributions in Arctic Deltas

Understanding how thermokarst lakes on arctic river deltas will respond to rapid warming is critical for projecting how carbon storage and fluxes will change in those vulnerable environments. Yet, this understanding is currently limited partly due to the complexity of disentangling significant interannual variability from the longer‐term surface water signatures on the landscape, using the short summertime window of optical spaceborne observations. Here, we rigorously separate perennial lakes from ephemeral wetlands on 12 arctic deltas and report distinct size distributions and climate trends for the two waterbodies. Namely, we find a lognormal distribution for lakes and a power‐law distribution for wetlands, consistent with a simple proportionate growth model and inundated topography, respectively. Furthermore, while no trend with temperature is found for wetlands, a statistically significant decreasing trend of mean lake size with warmer temperatures is found, attributed to colder deltas having deeper and thicker permafrost preserving larger lakes

Channel Network Control on Seasonal Lake Area Dynamics in Arctic Deltas.

The abundant lakes dotting arctic deltas are hotspots of methane emissions and biogeochemical activity, but seasonal variability in lake extents introduces uncertainty in estimates of lacustrine carbon emissions, typically performed at annual or longer time scales. To characterize variability in lake extents, we analyzed summertime lake area loss (i.e., shrinkage) on two deltas over the past 20 years, using Landsat-derived water masks. We find that monthly shrinkage rates have a pronounced structured variability around the channel network with the shrinkage rate systematically decreasing farther away from the channels. This pattern of shrinkage is predominantly attributed to a deeper active layer enhancing near-surface connectivity and storage and greater vegetation density closer to the channels leading to increased evapotranspiration rates. This shrinkage signal, easily extracted from remote sensing observations, may offer the means to constrain estimates of lacustrine methane emissions and to develop process-based estimates of depth to permafrost on arctic deltas

Channel Network Control on Seasonal Lake Area Dynamics in Arctic Deltas.

The abundant lakes dotting arctic deltas are hotspots of methane emissions and biogeochemical activity, but seasonal variability in lake extents introduces uncertainty in estimates of lacustrine carbon emissions, typically performed at annual or longer time scales. To characterize variability in lake extents, we analyzed summertime lake area loss (i.e., shrinkage) on two deltas over the past 20 years, using Landsat-derived water masks. We find that monthly shrinkage rates have a pronounced structured variability around the channel network with the shrinkage rate systematically decreasing farther away from the channels. This pattern of shrinkage is predominantly attributed to a deeper active layer enhancing near-surface connectivity and storage and greater vegetation density closer to the channels leading to increased evapotranspiration rates. This shrinkage signal, easily extracted from remote sensing observations, may offer the means to constrain estimates of lacustrine methane emissions and to develop process-based estimates of depth to permafrost on arctic deltas

Rotated Spectral Principal Component Analysis (rsPCA) for Identifying Dynamical Modes of Variability in Climate Systems.

Spectral PCA (sPCA), in contrast to classical PCA, offers the advantage of identifying organized spatiotemporal patterns within specific frequency bands and extracting dynamical modes. However, the unavoidable trade-off between frequency resolution and robustness of the PCs leads to high sensitivity to noise and overfitting, which limits the interpretation of the sPCA results. We propose herein a simple nonparametric implementation of sPCA using the continuous analytic Morlet wavelet as a robust estimator of the cross-spectral matrices with good frequency resolution. To improve the interpretability of the results, especially when several modes of similar amplitude exist within the same frequency band, we propose a rotation of the complex-valued eigenvectors to optimize their spatial regularity (smoothness). The developed method, called rotated spectral PCA (rsPCA), is tested on synthetic data simulating propagating waves and shows impressive performance even with high levels of noise in the data. Applied to global historical geopotential height (GPH) and sea surface temperature (SST) daily time series, the method accurately captures patterns of atmospheric Rossby waves at high frequencies (3-60-day periods) in both GPH and SST and El Niño-Southern Oscillation (ENSO) at low frequencies (2-7-yr periodicity) in SST. At high frequencies the rsPCA successfully unmixes the identified waves, revealing spatially coherent patterns with robust propagation dynamics

The Entropic Braiding Index (eBI): A Robust Metric to Account for the Diversity of Channel Scales in Multi-Thread Rivers

The Braiding Index (BI), defined as the average count of intercepted channels per cross-section, is a widely used metric for characterizing multi-thread river systems. However, it does not account for the diversity of channels (e.g., in terms of water discharge) within different cross-sections, omitting important information related to system complexity. Here we present a modification of BI, the Entropic Braiding Index (eBI), which augments the information content in BI by using Shannon Entropy to encode the diversity of channels in each cross section. eBI is interpreted as the number of “effective channels” per cross-section, allowing a direct comparison with the traditional BI. We demonstrate the potential of the ratio BI/eBI to quantify channel disparity, differentiate types of multi-thread systems (braided vs. anastomosed), and assess the effect of discharge variability, such as seasonal flooding, on river cross-section stability