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  1. Free, publicly-accessible full text available April 1, 2023
  2. Abstract. This paper presents the results of the ensemble Riemannian data assimilation for relatively high-dimensional nonlinear dynamical systems, focusing on the chaotic Lorenz-96 model and a two-layer quasi-geostrophic (QG) model of atmospheric circulation. The analysis state in this approach is inferred from a joint distribution that optimally couples the background probability distribution and the likelihood function, enabling formal treatment of systematic biases without any Gaussian assumptions. Despite the risk of the curse of dimensionality in the computation of the coupling distribution, comparisons with the classic implementation of the particle filter and the stochastic ensemble Kalman filter demonstrate that, with the same ensemble size, the presented methodology could improve the predictability of dynamical systems. In particular, under systematic errors, the root mean squared error of the analysis state can be reduced by 20 % (30 %) in the Lorenz-96 (QG) model.
  3. Abstract As more global satellite-derived precipitation products become available, it is imperative to evaluate them more carefully for providing guidance as to how well precipitation space-time features are captured for use in hydrologic modeling, climate studies and other applications. Here we propose a space-time Fourier spectral analysis and define a suite of metrics which evaluate the spatial organization of storm systems, the propagation speed and direction of precipitation features, and the space-time scales at which a satellite product reproduces the variability of a reference “ground-truth” product (“effective resolution”). We demonstrate how the methodology relates to our physical intuition using the case study of a storm system with rich space-time structure. We then evaluate five high-resolution multi-satellite products (CMORPH, GSMaP, IMERG-early, IMERG-final and PERSIANN-CCS) over a period of two years over the southeastern US. All five satellite products show generally consistent space-time power spectral density when compared to a reference ground gauge-radar dataset (GV-MRMS), revealing agreement in terms of average morphology and dynamics of precipitation systems. However, a deficit of spectral power at wavelengths shorter than 200 km and periods shorter than 4 h reveals that all satellite products are excessively “smooth”. The products also show low levels of spectral coherencemore »with the gauge-radar reference at these fine scales, revealing discrepancies in capturing the location and timing of precipitation features. From the space-time spectral coherence, the IMERG-final product shows superior ability in resolving the space-time dynamics of precipitation down to 200 km and 4 h scales compared to the other products.« less
  4. Abstract

    Satellite precipitation products, as all quantitative estimates, come with some inherent degree of uncertainty. To associate a quantitative value of the uncertainty to each individual estimate, error modeling is necessary. Most of the error models proposed so far compute the uncertainty as a function of precipitation intensity only, and only at one specific spatiotemporal scale. We propose a spectral error model that accounts for the neighboring space–time dynamics of precipitation into the uncertainty quantification. Systematic distortions of the precipitation signal and random errors are characterized distinctively in every frequency–wavenumber band in the Fourier domain, to accurately characterize error across scales. The systematic distortions are represented as a deterministic space–time linear filtering term. The random errors are represented as a nonstationary additive noise. The spectral error model is applied to the IMERG multisatellite precipitation product, and its parameters are estimated empirically through a system identification approach using the GV-MRMS gauge–radar measurements as reference (“truth”) over the eastern United States. The filtering term is found to be essentially low-pass (attenuating the fine-scale variability). While traditional error models attribute most of the error variance to random errors, it is found here that the systematic filtering term explains 48% of the error variancemore »at the native resolution of IMERG. This fact confirms that, at high resolution, filtering effects in satellite precipitation products cannot be ignored, and that the error cannot be represented as a purely random additive or multiplicative term. An important consequence is that precipitation estimates derived from different sources shall not be expected to automatically have statistically independent errors.

    Significance Statement

    Satellite precipitation products are nowadays widely used for climate and environmental research, water management, risk analysis, and decision support at the local, regional, and global scales. For all these applications, knowledge about the accuracy of the products is critical for their usability. However, products are not systematically provided with a quantitative measure of the uncertainty associated with each individual estimate. Various parametric error models have been proposed for uncertainty quantification, mostly assuming that the uncertainty is only a function of the precipitation intensity at the pixel and time of interest. By projecting satellite precipitation fields and their retrieval errors into the Fourier frequency–wavenumber domain, we show that we can explicitly take into account the neighboring space–time multiscale dynamics of precipitation and compute a scale-dependent uncertainty.

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  5. Bedload particle hops are defined as successive motions of a particle from start to stop, characterizing one of the most fundamental processes of bedload sediment transport in rivers. Although two transport regimes have been recently identified for short and long hops, respectively, there is still the lack of a theory explaining the mean hop distance–travel time scaling for particles performing short hops, which dominate the transport and may cover over 80 % of the total hop events. In this paper, we propose a velocity-variation-based formulation, the governing equation of which is intrinsically identical to that of Taylor dispersion for solute transport within shear flows. The key parameter, namely the diffusion coefficient, can be determined by hop distances and travel times, which are easier to measure and more accurate than particle accelerations. For the first time, we obtain an analytical solution for the mean hop distance–travel time relation valid for the entire range of travel times, which agrees well with the measured data. Regarding travel times, we identify three distinct regimes in terms of different scaling exponents: respectively, $\sim$ 1.5 for the initial regime and $\sim$ 5/3 for the transition regime, which define the short hops, and 1 for the Taylor dispersionmore »regime defining long hops. The corresponding distribution of the hop distance is analytically obtained and experimentally verified. We also show that the conventionally used exponential distribution, as proposed by Einstein, is solely for long hops. Further validation of the present formulation is provided by comparing the simulated accelerations with measurements.« less
  6. Abstract The quantitative estimation of precipitation from orbiting passive microwave imagers has been performed for more than 30 years. The development of retrieval methods consists of establishing physical or statistical relationships between the brightness temperatures (TBs) measured at frequencies between 5 and 200 GHz and precipitation. Until now, these relationships have essentially been established at the “pixel” level, associating the average precipitation rate inside a predefined area (the pixel) to the collocated multispectral radiometric measurement. This approach considers each pixel as an independent realization of a process and ignores the fact that precipitation is a dynamic variable with rich multiscale spatial and temporal organization. Here we propose to look beyond the pixel values of the TBs and show that useful information for precipitation retrieval can be derived from the variations of the observed TBs in a spatial neighborhood around the pixel of interest. We also show that considering neighboring information allows us to better handle the complex observation geometry of conical-scanning microwave imagers, involving frequency-dependent beamwidths, overlapping fields of view, and large Earth incidence angles. Using spatial convolution filters, we compute “nonlocal” radiometric parameters sensitive to spatial patterns and scale-dependent structures of the TB fields, which are the “geometric signatures”more »of specific precipitation structures such as convective cells. We demonstrate that using nonlocal radiometric parameters to enrich the spectral information associated to each pixel allows for reduced retrieval uncertainty (reduction of 6%–11% of the mean absolute retrieval error) in a simple k-nearest neighbors retrieval scheme.« less
  7. Abstract 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, revealingmore »spatially coherent patterns with robust propagation dynamics.« less
  8. Abstract Understanding the physical drivers of seasonal hydroclimatic variability and improving predictive skill remains a challenge with important socioeconomic and environmental implications for many regions around the world. Physics-based deterministic models show limited ability to predict precipitation as the lead time increases, due to imperfect representation of physical processes and incomplete knowledge of initial conditions. Similarly, statistical methods drawing upon established climate teleconnections have low prediction skill due to the complex nature of the climate system. Recently, promising data-driven approaches have been proposed, but they often suffer from overparameterization and overfitting due to the short observational record, and they often do not account for spatiotemporal dependencies among covariates (i.e., predictors such as sea surface temperatures). This study addresses these challenges via a predictive model based on a graph-guided regularizer that simultaneously promotes similarity of predictive weights for highly correlated covariates and enforces sparsity in the covariate domain. This approach both decreases the effective dimensionality of the problem and identifies the most predictive features without specifying them a priori. We use large ensemble simulations from a climate model to construct this regularizer, reducing the structural uncertainty in the estimation. We apply the learned model to predict winter precipitation in the southwesternmore »United States using sea surface temperatures over the entire Pacific basin, and demonstrate its superiority compared to other regularization approaches and statistical models informed by known teleconnections. Our results highlight the potential to combine optimally the space–time structure of predictor variables learned from climate models with new graph-based regularizers to improve seasonal prediction.« less