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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 variance 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.

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.

 

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 ofBI,the Entropic Braiding Index (eBI), which augments the information content inBIby using Shannon Entropy to encode the diversity of channels in each cross section.eBIis interpreted as the number of “effective channels” per cross‐section, allowing a direct comparison with the traditionalBI. We demonstrate the potential of the ratioBI/eBIto 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.

 

As droughts have widespread social and ecological impacts, it is critical to develop long‐term adaptation and mitigation strategies to reduce drought vulnerability. Climate models are important in quantifying drought changes. Here, we assess the ability of 285 CMIP6 historical simulations, from 17 models, to reproduce drought duration and severity in three observational data sets using the Standardized Precipitation Index (SPI). We used summary statistics beyond the mean and standard deviation, and devised a novel probabilistic framework, based on the Hellinger distance, to quantify the difference between observed and simulated drought characteristics. Results show that many simulations have less thanerror in reproducing the observed drought summary statistics. The hypothesis that simulations and observations are described by the same distribution cannot be rejected for more thanof the grids based on ourdistance framework. No single model stood out as demonstrating consistently better performance over large regions of the globe. The variance in drought statistics among the simulations is higher in the tropics compared to other latitudinal zones. Though the models capture the characteristics of dry spells well, there is considerable bias in low precipitation values. Good model performance in terms of SPI does not imply good performance in simulating low precipitation. Our study emphasizes the need to probabilistically evaluate climate model simulations in order to both pinpoint model weaknesses and identify a subset of best‐performing models that are useful for impact assessments.

 

Precipitation prediction at seasonal timescales is important for planning and management of water resources as well as preparedness for hazards such as floods, droughts and wildfires. Quantifying predictability is quite challenging as a consequence of a large number of potential drivers, varying antecedent conditions, and small sample size of high‐quality observations available at seasonal timescales, that in turn, increases prediction uncertainty and the risk of model overfitting. Here, we introduce a generalized probabilistic framework to account for these issues and assess predictability under uncertainty. We focus on prediction of winter (Nov–Mar) precipitation across the contiguous United States, using sea surface temperature‐derived indices (averaged in Aug–Oct) as predictors. In our analysis we identify “predictability hotspots,” which we define as regions where precipitation is inherently more predictable. Our framework estimates the entire predictive distribution of precipitation using copulas and quantifies prediction uncertainties, while employing principal component analysis for dimensionality reduction and a cross validation technique to avoid overfitting. We also evaluate how predictability changes across different quantiles of the precipitation distribution (dry, normal, wet amounts) using a multi‐category 3 × 3 contingency table. Our results indicate that well‐defined predictability hotspots occur in the Southwest and Southeast. Moreover, extreme dry and wet conditions are shown to be relatively more predictable compared to normal conditions. Our study may help with water resources management in several subregions of the United States and can be used to assess the fidelity of earth system models in successfully representing teleconnections and predictability.

 

The Madden‐Julian Oscillation (MJO) is the leading mode of intraseasonal climate variability, having profound impacts on a wide range of weather and climate phenomena. Here, we use a wavelet‐based spectral Principal Component Analysis (wsPCA) to evaluate the skill of 20 state‐of‐the‐art CMIP6 models in capturing the magnitude and dynamics of the MJO. By construction, wsPCA has the ability to focus on desired frequencies and capture each propagative physical mode with one principal component (PC). We show that the MJO contribution to the total intraseasonal climate variability is substantially underestimated in most CMIP6 models. The joint distribution of the modulus and angular frequency of the wavelet PC series associated with MJO is used to rank models relatively to the observations through the Wasserstein distance. Using Hovmöller phase‐longitude diagrams, we also show that precipitation variability associated with MJO is underestimated in most CMIP6 models for the Amazonia, Southwest Africa, and Maritime Continent.

 

Fire emissions of gases and aerosols alter atmospheric composition and have substantial impacts on climate, ecosystem function, and human health. Warming climate and human expansion in fire‐prone landscapes exacerbate fire impacts and call for more effective management tools. Here we developed a global fire forecasting system that predicts monthly emissions using past fire data and climate variables for lead times of 1 to 6 months. Using monthly fire emissions from the Global Fire Emissions Database (GFED) as the prediction target, we fit a statistical time series model, the Autoregressive Integrated Moving Average model with eXogenous variables (ARIMAX), in over 1,300 different fire regions. Optimized parameters were then used to forecast future emissions. The forecast system took into account information about region‐specific seasonality, long‐term trends, recent fire observations, and climate drivers representing both large‐scale climate variability and local fire weather. We cross‐validated the forecast skill of the system with different combinations of predictors and forecast lead times. The reference model, which combined endogenous and exogenous predictors with a 1 month forecast lead time, explained 52% of the variability in the global fire emissions anomaly, considerably exceeding the performance of a reference model that assumed persistent emissions during the forecast period. The system also successfully resolved detailed spatial patterns of fire emissions anomalies in regions with significant fire activity. This study bridges the gap between the efforts of near‐real‐time fire forecasts and seasonal fire outlooks and represents a step toward establishing an operational global fire, smoke, and carbon cycle forecasting system.

 

The effective characterization of topographic surfaces is a central tenet of geomorphology. Differences in land surface properties reveal variations in structural controls and the nature and efficacy of Earth‐shaping processes. In this paper, we employ the Hölder exponents,α, characterizing the local scaling behavior of topography and commonly used in the study of the (multi)fractal properties of landscapes and show that the joint probability distribution of the area of the terrain with a given elevation andαcontains a wealth of information on topographic structure. The conditional distributions of the hypsometric integrals as a function ofα, that is,I_hyp|α, are shown to capture this structure. A multivariate analysis reveals three metrics that summarize these conditional distributions: Strahler's original hypsometric integral, the standard deviation of theI_hyp|α, and the nature of any trend of theI_hyp|αagainstα. An analysis of five digital elevation models (DEMs) from different regions of the United States shows that only one is truly described by the hypsometric integral (Mettman Ridge from central Oregon). In the other cases, the new metrics clearly discriminate between instances where topographic roughness is more clearly a function of elevation, as captured by the conditional variables. In a final example, we artificially sharpen the ridges and valleys of one DEM to show that while the hypsometric integral and standard deviation ofI_hyp|αare invariant to the change, the trend ofI_hyp|αagainstαcaptures the changes in topography.

 

Due to its importance for water availability in the tropics and subtropics, efficient tracking of the seasonal and long‐term shifts of the intertropical convergence zone (ITCZ) is of great value. Current approaches, which are based on tracking changes in the annual mean of single variables, ignore the intra‐annual dynamics, while more sophisticated methods are computationally intensive. Here we propose a new probabilistic framework to track the ITCZ, which is based on tracking the location of maximum precipitation and minimum outgoing longwave radiation in overlapping longitudinal windows. Our framework is seasonally and longitudinally explicit, allows for joint consideration of multiple variables to define the ITCZ, and is flexible in its implementation, thus, it can be used in analyses of different scales and scopes. We apply our framework to analyze the recent climatology of the ITCZ and report a southward trend in its location over central Pacific in the late twentieth century.

 

We expose the statistical foundations of deep learning with the goal of facilitating conversation between the deep learning and statistics communities. We highlight core themes at the intersection; summarize key neural models, such as feedforward neural networks, sequential neural networks, and neural latent variable models; and link these ideas to their roots in probability and statistics. We also highlight research directions in deep learning where there are opportunities for statistical contributions. 

Abstract Changing wildfire regimes in the western US and other fire-prone regions pose considerable risks to human health and ecosystem function. However, our understanding of wildfire behavior is still limited by a lack of data products that systematically quantify fire spread, behavior and impacts. Here we develop a novel object-based system for tracking the progression of individual fires using 375 m Visible Infrared Imaging Radiometer Suite active fire detections. At each half-daily time step, fire pixels are clustered according to their spatial proximity, and are either appended to an existing active fire object or are assigned to a new object. This automatic system allows us to update the attributes of each fire event, delineate the fire perimeter, and identify the active fire front shortly after satellite data acquisition. Using this system, we mapped the history of California fires during 2012–2020. Our approach and data stream may be useful for calibration and evaluation of fire spread models, estimation of near-real-time wildfire emissions, and as means for prescribing initial conditions in fire forecast models.