Data assimilation in operator algebras.

We develop an algebraic framework for sequential data assimilation of partially observed dynamical systems. In this framework, Bayesian data assimilation is embedded in a nonabelian operator algebra, which provides a representation of observables by multiplication operators and probability densities by density operators (quantum states). In the algebraic approach, the forecast step of data assimilation is represented by a quantum operation induced by the Koopman operator of the dynamical system. Moreover, the analysis step is described by a quantum effect, which generalizes the Bayesian observational update rule. Projecting this formulation to finite-dimensional matrix algebras leads to computational schemes that are i) automatically positivity-preserving and ii) amenable to consistent data-driven approximation using kernel methods for machine learning. Moreover, these methods are natural candidates for implementation on quantum computers. Applications to the Lorenz 96 multiscale system and the El Niño Southern Oscillation in a climate model show promising results in terms of forecast skill and uncertainty quantification.

Spatial patterns of climate change across the Paleocene-Eocene Thermal Maximum.

The Paleocene-Eocene Thermal Maximum (PETM; 56 Ma) is one of our best geological analogs for understanding climate dynamics in a "greenhouse" world. However, proxy data representing the event are only available from select marine and terrestrial sedimentary sequences that are unevenly distributed across Earth's surface, limiting our view of the spatial patterns of climate change. Here, we use paleoclimate data assimilation (DA) to combine climate model and proxy information and create a spatially complete reconstruction of the PETM and the climate state that precedes it ("PETM-DA"). Our data-constrained results support strong polar amplification, which in the absence of an extensive cryosphere, is related to temperature feedbacks and loss of seasonal snow on land. The response of the hydrological cycle to PETM warming consists of a narrowing of the Intertropical Convergence Zone, off-equatorial drying, and an intensification of seasonal monsoons and winter storm tracks. Many of these features are also seen in simulations of future climate change under increasing anthropogenic emissions. Since the PETM-DA yields a spatially complete estimate of surface air temperature, it yields a rigorous estimate of global mean temperature change (5.6 ∘C; 5.4 ∘C to 5.9 ∘C, 95% CI) that can be used to calculate equilibrium climate sensitivity (ECS). We find that PETM ECS was 6.5 ∘C (5.7 ∘C to 7.4 ∘C, 95% CI), which is much higher than the present-day range. This supports the view that climate sensitivity increases substantially when greenhouse gas concentrations are high.

Convergence in simulating global soil organic carbon by structurally different models after data assimilation.

Current biogeochemical models produce carbon-climate feedback projections with large uncertainties, often attributed to their structural differences when simulating soil organic carbon (SOC) dynamics worldwide. However, choices of model parameter values that quantify the strength and represent properties of different soil carbon cycle processes could also contribute to model simulation uncertainties. Here, we demonstrate the critical role of using common observational data in reducing model uncertainty in estimates of global SOC storage. Two structurally different models featuring distinctive carbon pools, decomposition kinetics, and carbon transfer pathways simulate opposite global SOC distributions with their customary parameter values yet converge to similar results after being informed by the same global SOC database using a data assimilation approach. The converged spatial SOC simulations result from similar simulations in key model components such as carbon transfer efficiency, baseline decomposition rate, and environmental effects on carbon fluxes by these two models after data assimilation. Moreover, data assimilation results suggest equally effective simulations of SOC using models following either first-order or Michaelis-Menten kinetics at the global scale. Nevertheless, a wider range of data with high-quality control and assurance are needed to further constrain SOC dynamics simulations and reduce unconstrained parameters. New sets of data, such as microbial genomics-function relationships, may also suggest novel structures to account for in future model development. Overall, our results highlight the importance of observational data in informing model development and constraining model predictions.

China's Fossil Fuel CO2 Emissions Estimated Using Surface Observations of Coemitted NO2.

Accurate estimates of fossil fuel CO2 (FFCO2) emissions are of great importance for climate prediction and mitigation regulations but remain a significant challenge for accounting methods relying on economic statistics and emission factors. In this study, we employed a regional data assimilation framework to assimilate in situ NO2 observations, allowing us to combine observation-constrained NOx emissions coemitted with FFCO2 and grid-specific CO2-to-NOx emission ratios to infer the daily FFCO2 emissions over China. The estimated national total for 2016 was 11.4 PgCO2·yr-1, with an uncertainty (1σ) of 1.5 PgCO2·yr-1 that accounted for errors associated with atmospheric transport, inversion framework parameters, and CO2-to-NOx emission ratios. Our findings indicated that widely used "bottom-up" emission inventories generally ignore numerous activity level statistics of FFCO2 related to energy industries and power plants in western China, whereas the inventories are significantly overestimated in developed regions and key urban areas owing to exaggerated emission factors and inexact spatial disaggregation. The optimized FFCO2 estimate exhibited more distinct seasonality with a significant increase in emissions in winter. These findings advance our understanding of the spatiotemporal regime of FFCO2 emissions in China.

Global hydroclimatic response to tropical volcanic eruptions over the last millennium.

Large tropical volcanic eruptions can affect the climate of many regions on Earth, yet it is uncertain how the largest eruptions over the past millennium may have altered Earth's hydroclimate. Here, we analyze the global hydroclimatic response to all the tropical volcanic eruptions over the past millennium that were larger than the Mount Pinatubo eruption of 1991. Using the Paleo Hydrodynamics Data Assimilation product (PHYDA), we find that these large volcanic eruptions tended to produce dry conditions over tropical Africa, Central Asia and the Middle East and wet conditions over much of Oceania and the South American monsoon region. These anomalies are statistically significant, and they persisted for more than a decade in some regions. The persistence of the anomalies is associated with southward shifts in the Intertropical Convergence Zone and sea surface temperature changes in the Pacific and Atlantic oceans. We compare the PHYDA results with the stand-alone model response of the Community Earth System Model (CESM)-Last Millennium Ensemble. We find that the proxy-constrained PHYDA estimates are larger and more persistent than the responses simulated by CESM. Understanding which of these estimates is more realistic is critical for accurately characterizing the hydroclimate risks of future volcanic eruptions.

Intracounty modeling of COVID-19 infection with human mobility: Assessing spatial heterogeneity with business traffic, age, and race.

The COVID-19 pandemic is a global threat presenting health, economic, and social challenges that continue to escalate. Metapopulation epidemic modeling studies in the susceptible-exposed-infectious-removed (SEIR) style have played important roles in informing public health policy making to mitigate the spread of COVID-19. These models typically rely on a key assumption on the homogeneity of the population. This assumption certainly cannot be expected to hold true in real situations; various geographic, socioeconomic, and cultural environments affect the behaviors that drive the spread of COVID-19 in different communities. What's more, variation of intracounty environments creates spatial heterogeneity of transmission in different regions. To address this issue, we develop a human mobility flow-augmented stochastic SEIR-style epidemic modeling framework with the ability to distinguish different regions and their corresponding behaviors. This modeling framework is then combined with data assimilation and machine learning techniques to reconstruct the historical growth trajectories of COVID-19 confirmed cases in two counties in Wisconsin. The associations between the spread of COVID-19 and business foot traffic, race and ethnicity, and age structure are then investigated. The results reveal that, in a college town (Dane County), the most important heterogeneity is age structure, while, in a large city area (Milwaukee County), racial and ethnic heterogeneity becomes more apparent. Scenario studies further indicate a strong response of the spread rate to various reopening policies, which suggests that policy makers may need to take these heterogeneities into account very carefully when designing policies for mitigating the ongoing spread of COVID-19 and reopening.

Probabilistic Estimation and Control of Dynamical Systems Using Particle Filter with Adaptive Backward Sampling.

Estimating and controlling dynamical systems from observable time-series data are essential for understanding and manipulating nonlinear dynamics. This paper proposes a probabilistic framework for simultaneously estimating and controlling nonlinear dynamics under noisy observation conditions. Our proposed method utilizes the particle filter not only as a state estimator and a prior estimator for the dynamics but also as a controller. This approach allows us to handle the nonlinearity of the dynamics and uncertainty of the latent state. We apply two distinct dynamics to verify the effectiveness of our proposed framework: a chaotic system defined by the Lorenz equation and a nonlinear neuronal system defined by the Morris-Lecar neuron model. The results indicate that our proposed framework can simultaneously estimate and control complex nonlinear dynamical systems.

Progress and opportunities in advancing near-term forecasting of freshwater quality.

Near-term freshwater forecasts, defined as sub-daily to decadal future predictions of a freshwater variable with quantified uncertainty, are urgently needed to improve water quality management as freshwater ecosystems exhibit greater variability due to global change. Shifting baselines in freshwater ecosystems due to land use and climate change prevent managers from relying on historical averages for predicting future conditions, necessitating near-term forecasts to mitigate freshwater risks to human health and safety (e.g., flash floods, harmful algal blooms) and ecosystem services (e.g., water-related recreation and tourism). To assess the current state of freshwater forecasting and identify opportunities for future progress, we synthesized freshwater forecasting papers published in the past 5 years. We found that freshwater forecasting is currently dominated by near-term forecasts of water quantity and that near-term water quality forecasts are fewer in number and in the early stages of development (i.e., non-operational) despite their potential as important preemptive decision support tools. We contend that more freshwater quality forecasts are critically needed and that near-term water quality forecasting is poised to make substantial advances based on examples of recent progress in forecasting methodology, workflows, and end-user engagement. For example, current water quality forecasting systems can predict water temperature, dissolved oxygen, and algal bloom/toxin events 5 days ahead with reasonable accuracy. Continued progress in freshwater quality forecasting will be greatly accelerated by adapting tools and approaches from freshwater quantity forecasting (e.g., machine learning modeling methods). In addition, future development of effective operational freshwater quality forecasts will require substantive engagement of end users throughout the forecast process, funding, and training opportunities. Looking ahead, near-term forecasting provides a hopeful future for freshwater management in the face of increased variability and risk due to global change, and we encourage the freshwater scientific community to incorporate forecasting approaches in water quality research and management.

An ensemble data assimilation modeling system for operational outdoor microalgae growth forecasting.

Microalgae have received increasing attention as a potential feedstock for biofuel or biobased products. Forecasting the microalgae growth is beneficial for managers in planning pond operations and harvesting decisions. This study proposed a biomass forecasting system comprised of the Huesemann Algae Biomass Growth Model (BGM), the Modular Aquatic Simulation System in Two Dimensions (MASS2), ensemble data assimilation (DA), and numerical weather prediction Global Ensemble Forecast System (GEFS) ensemble meteorological forecasts. The novelty of this study is to seek the use of ensemble DA to improve both BGM and MASS2 model initial conditions with the assimilation of biomass and water temperature measurements and consequently improve short-term biomass forecasting skills. This study introduces the theory behind the proposed integrated biomass forecasting system, with an application undertaken in pseudo-real-time in three outdoor ponds cultured with Chlorella sorokiniana in Delhi, California, United States. Results from all three case studies demonstrate that the biomass forecasting system improved the short-term (i.e., 7-day) biomass forecasting skills by about 60% on average, comparing to forecasts without using the ensemble DA method. Given the satisfactory performances achieved in this study, it is probable that the integrated BGM-MASS2-DA forecasting system can be used operationally to inform managers in making pond operation and harvesting planning decisions.

Low-Cost Particulate Matter Sensors for Monitoring Residential Wood Burning.

Conventional monitoring systems for air quality, such as reference stations, provide reliable pollution data in urban settings but only at relatively low spatial density. This study explores the potential of low-cost sensor systems (LCSs) deployed at homes of residents to enhance the monitoring of urban air pollution caused by residential wood burning. We established a network of 28 Airly (Airly-GSM-1, SP. Z o.o., Poland) LCSs in Kristiansand, Norway, over two winters (2021-2022). To assess performance, a gravimetric Kleinfiltergerät measured the fine particle mass concentration (PM2.5) in the garden of one participant's house for 4 weeks. Results showed a sensor-to-reference correlation equal to 0.86 for raw PM2.5 measurements at daily resolution (bias/RMSE: 9.45/11.65 µg m-3). High-resolution air quality maps at a 100 m resolution were produced by combining the output of an air quality model (uEMEP) using data assimilation techniques with the network data that were corrected and calibrated by using a proposed five-step network data processing scheme. Leave-one-out cross-validation demonstrated that data assimilation reduced the model's RMSE, MAE, and bias by 44-56, 38-48, and 41-52%, respectively.

Hypothesis-driven modeling of the human lung-ventilator system: A characterization tool for Acute Respiratory Distress Syndrome research.

Mechanical ventilation is an essential tool in the management of Acute Respiratory Distress Syndrome (ARDS), but it exposes patients to the risk of ventilator-induced lung injury (VILI). The human lung-ventilator system (LVS) involves the interaction of complex anatomy with a mechanical apparatus, which limits the ability of process-based models to provide individualized clinical support. This work proposes a hypothesis-driven strategy for LVS modeling in which robust personalization is achieved using a pre-defined parameter basis in a non-physiological model. Model inversion, here via windowed data assimilation, forges observed waveforms into interpretable parameter values that characterize the data rather than quantifying physiological processes. Accurate, model-based inference on human-ventilator data indicates model flexibility and utility over a variety of breath types, including those from dyssynchronous LVSs. Estimated parameters generate static characterizations of the data that are 50%-70% more accurate than breath-wise single-compartment model estimates. They also retain sufficient information to distinguish between the types of breath they represent. However, the fidelity and interpretability of model characterizations are tied to parameter definitions and model resolution. These additional factors must be considered in conjunction with the objectives of specific applications, such as identifying and tracking the development of human VILI.

A methodology of phenotyping ICU patients from EHR data: High-fidelity, personalized, and interpretable phenotypes estimation.

OBJECTIVE: Computing phenotypes that provide high-fidelity, time-dependent characterizations and yield personalized interpretations is challenging, especially given the complexity of physiological and healthcare systems and clinical data quality. This paper develops a methodological pipeline to estimate unmeasured physiological parameters and produce high-fidelity, personalized phenotypes anchored to physiological mechanics from electronic health record (EHR). METHODS: A methodological phenotyping pipeline is developed that computes new phenotypes defined with unmeasurable computational biomarkers quantifying specific physiological properties in real time. Working within the inverse problem framework, this pipeline is applied to the glucose-insulin system for ICU patients using data assimilation to estimate an established mathematical physiological model with stochastic optimization. This produces physiological model parameter vectors of clinically unmeasured endocrine properties, here insulin secretion, clearance, and resistance, estimated for individual patient. These physiological parameter vectors are used as inputs to unsupervised machine learning methods to produce phenotypic labels and discrete physiological phenotypes. These phenotypes are inherently interpretable because they are based on parametric physiological descriptors. To establish potential clinical utility, the computed phenotypes are evaluated with external EHR data for consistency and reliability and with clinician face validation. RESULTS: The phenotype computation was performed on a cohort of 109 ICU patients who received no or short-acting insulin therapy, rendering continuous and discrete physiological phenotypes as specific computational biomarkers of unmeasured insulin secretion, clearance, and resistance on time windows of three days. Six, six, and five discrete phenotypes were found in the first, middle, and last three-day periods of ICU stays, respectively. Computed phenotypic labels were predictive with an average accuracy of 89%. External validation of discrete phenotypes showed coherence and consistency in clinically observable differences based on laboratory measurements and ICD 9/10 codes and clinical concordance from face validity. A particularly clinically impactful parameter, insulin secretion, had a concordance accuracy of 83%±27%. CONCLUSION: The new physiological phenotypes computed with individual patient ICU data and defined by estimates of mechanistic model parameters have high physiological fidelity, are continuous, time-specific, personalized, interpretable, and predictive. This methodology is generalizable to other clinical and physiological settings and opens the door for discovering deeper physiological information to personalize medical care.

Interpretable physiological forecasting in the ICU using constrained data assimilation and electronic health record data.

OBJECTIVE: Prediction of physiological mechanics are important in medical practice because interventions are guided by predicted impacts of interventions. But prediction is difficult in medicine because medicine is complex and difficult to understand from data alone, and the data are sparse relative to the complexity of the generating processes. Computational methods can increase prediction accuracy, but prediction with clinical data is difficult because the data are sparse, noisy and nonstationary. This paper focuses on predicting physiological processes given sparse, non-stationary, electronic health record data in the intensive care unit using data assimilation (DA), a broad collection of methods that pair mechanistic models with inference methods. METHODS: A methodological pipeline embedding a glucose-insulin model into a new DA framework, the constrained ensemble Kalman filter (CEnKF) to forecast blood glucose was developed. The data include tube-fed patients whose nutrition, blood glucose, administered insulins and medications were extracted by hand due to their complexity and to ensure accuracy. The model was estimated using an individual's data as if they arrived in real-time, and the estimated model was run forward producing a forecast. Both constrained and unconstrained ensemble Kalman filters were estimated to compare the impact of constraints. Constraint boundaries, model parameter sets estimated, and data used to estimate the models were varied to investigate their influence on forecasting accuracy. Forecasting accuracy was evaluated according to mean squared error between the model-forecasted glucose and the measurements and by comparing distributions of measured glucose and forecast ensemble means. RESULTS: The novel CEnKF produced substantial gains in robustness and accuracy while minimizing the data requirements compared to the unconstrained ensemble Kalman filters. Administered insulin and tube-nutrition were important for accurate forecasting, but including glucose in IV medication delivery did not increase forecast accuracy. Model flexibility, controlled by constraint boundaries and estimated parameters, did influence forecasting accuracy. CONCLUSION: Accurate and robust physiological forecasting with sparse clinical data is possible with DA. Introducing constrained inference, particularly on unmeasured states and parameters, reduced forecast error and data requirements. The results are not particularly sensitive to model flexibility such as constraint boundaries, but over or under constraining increased forecasting errors.

Developments of inverse analysis by Kalman filters and Bayesian methods applied to geotechnical engineering.

The present paper reviews recent activities on inverse analysis strategies in geotechnical engineering using Kalman filters, nonlinear Kalman filters, and Markov chain Monte Carlo (MCMC)/Hamiltonian Monte Carlo (HMC) methods. Nonlinear Kalman filters with finite element method (FEM) broaden the choices of unknowns to be determined for not only parameters but also initial and/or boundary conditions, and the use of the posterior probability of the state variables can be widely applied to, for example, the decision making for design changes. The relevance of the unknowns and the observed values and the selection of the best sensor locations are some of the considerations made while using the Kalman filter FEM. This paper demonstrates several real-world geotechnical applications of the nonlinear Kalman filter and the MCMC with FEM. Future studies should focus on the following areas: attaining excellent performance for long-term forecasts using short-term observation and developing a viable method for selecting equations that describe physical phenomena and constitutive models.

Pedestrian Positioning Using an Enhanced Ensemble Transform Kalman Filter.

Due to the unavailability of GPS indoors, various indoor pedestrian positioning approaches have been designed to estimate the position of the user leveraging sensory data measured from inertial measurement units (IMUs) and wireless signal receivers, such as pedestrian dead reckoning (PDR) and received signal strength (RSS) fingerprinting. This study is similar to the previous study in that it estimates the user position by fusing noisy positional information obtained from the PDR and RSS fingerprinting using the Bayes filter in the indoor pedestrian positioning system. However, this study differs from the previous study in that it uses an enhanced state estimation approach based on the ensemble transform Kalman filter (ETKF), called QETKF, as the Bayes filer for the indoor pedestrian positioning instead of the SKPF proposed in the previous study. The QETKF estimates the updated user position by fusing the predicted position by the PDR and the positional measurement estimated by the RSS fingerprinting scheme using the ensemble transformation, whereas the SKPF calculates the updated user position by fusing them using both the unscented transformation (UT) of UKF and the weighting method of PF. In the field of Earth science, the ETKF has been widely used to estimate the state of the atmospheric and ocean models. However, the ETKF algorithm does not consider the model error in the state prediction model; that is, it assumes a perfect model without any model errors. Hence, the error covariance estimated by the ETKF can be systematically underestimated, thereby yielding inaccurate state estimation results due to underweighted observations. The QETKF proposed in this paper is an efficient approach to implementing the ETKF applied to the indoor pedestrian localization system that should consider the model error. Unlike the ETKF, the QETKF can avoid the systematic underestimation of the error covariance by considering the model error in the state prediction model. The main goal of this study is to investigate the feasibility of the pedestrian position estimation for the QETKF in the indoor localization system that uses the PDR and RSS fingerprinting. Pedestrian positioning experiments performed using the indoor localization system implemented on the smartphone in a campus building show that the QETKF can offer more accurate positioning results than the ETKF and other ensemble-based Kalman filters (EBKFs). This indicates that the QETKF has great potential in performing better position estimation with more accurately estimated error covariances for the indoor pedestrian localization system.

Retrieving Soil Physical Properties by Assimilating SMAP Brightness Temperature Observations into the Community Land Model.

This paper coupled a unified passive and active microwave observation operator-namely, an enhanced, physically-based, discrete emission-scattering model-with the community land model (CLM) in a data assimilation (DA) system. By implementing the system default local ensemble transform Kalman filter (LETKF) algorithm, the Soil Moisture Active and Passive (SMAP) brightness temperature TBp (p = Horizontal or Vertical polarization) assimilations for only soil property retrieval and both soil properties and soil moisture estimates were investigated with the aid of in situ observations at the Maqu site. The results indicate improved estimates of soil properties of the topmost layer in comparison to measurements, as well as of the profile. Specifically, both assimilations of TBH lead to over a 48% reduction in root mean square errors (RMSEs) for the retrieved clay fraction from the background compared to the top layer measurements. Both assimilations of TBV reduce RMSEs by 36% for the sand fraction and by 28% for the clay fraction. However, the DA estimated soil moisture and land surface fluxes still exhibit discrepancies when compared to the measurements. The retrieved accurate soil properties alone are inadequate to improve those estimates. The discussed uncertainties (e.g., fixed PTF structures) in the CLM model structures should be mitigated.

Informer-Based Temperature Prediction Using Observed and Numerical Weather Prediction Data.

This paper proposes an Informer-based temperature prediction model to leverage data from an automatic weather station (AWS) and a local data assimilation and prediction system (LDAPS), where the Informer as a variant of a Transformer was developed to better deal with time series data. Recently, deep-learning-based temperature prediction models have been proposed, demonstrating successful performances, such as conventional neural network (CNN)-based models, bi-directional long short-term memory (BLSTM)-based models, and a combination of both neural networks, CNN-BLSTM. However, these models have encountered issues due to the lack of time data integration during the training phase, which also lead to the persistence of a long-term dependency problem in the LSTM models. These limitations have culminated in a performance deterioration when the prediction time length was extended. To overcome these issues, the proposed model first incorporates time-periodic information into the learning process by generating time-periodic information and inputting it into the model. Second, the proposed model replaces the LSTM with an Informer as an alternative to mitigating the long-term dependency problem. Third, a series of fusion operations between AWS and LDAPS data are executed to examine the effect of each dataset on the temperature prediction performance. The performance of the proposed temperature prediction model is evaluated via objective measures, including the root-mean-square error (RMSE) and mean absolute error (MAE) over different timeframes, ranging from 6 to 336 h. The experiments showed that the proposed model relatively reduced the average RMSE and MAE by 0.25 °C and 0.203 °C, respectively, compared with the results of the CNN-BLSTM-based model.

Analysis of COVID-19 in Japan with extended SEIR model and ensemble Kalman filter.

We introduce an extended SEIR infectious disease model with data assimilation for the study of the spread of COVID-19. In this framework, undetected asymptomatic and pre-symptomatic cases are taken into account, and the impact of their uncertain proportion is fully investigated. The standard SEIR model does not consider these populations, while their role in the propagation of the disease is acknowledged. An ensemble Kalman filter is implemented to assimilate reliable observations of three compartments in the model. The system tracks the evolution of the effective reproduction number and estimates the unobservable subpopulations. The analysis is carried out for three main prefectures of Japan and for the entire country of Japan. For these four communities, our estimated effective reproduction numbers are more stable than the corresponding ones estimated by a different method (Toyokeizai). We also perform sensitivity tests for different values of some uncertain medical parameters, like the relative infectivity of symptomatic/asymptomatic cases. The regional analysis results suggest the decreasing efficiency of the states of emergency.

Disentangling the role of virus infectiousness and awareness-based human behavior during the early phase of the COVID-19 pandemic in the European Union.

In this work, we manage to disentangle the role of virus infectiousness and awareness-based human behavior in the COVID-19 pandemic. Using Bayesian inference, we quantify the uncertainty of a state-space model whose propagator is based on an unusual SEIR-type model since it incorporates the effective population fraction as a parameter. Within the Markov Chain Monte Carlo (MCMC) algorithm, Unscented Kalman Filter (UKF) may be used to evaluate the likelihood approximately. UKF is a suitable strategy in many cases, but it is not well-suited to deal with non-negativity restrictions on the state variables. To overcome this difficulty, we modify the UKF, conveniently truncating Gaussian distributions, which allows us to deal with such restrictions. We use official infection notification records to analyze the first 22 weeks of infection spread in each of the 27 countries of the European Union (EU). It is known that such records are the primary source of information to assess the early evolution of the pandemic and, at the same time, usually suffer underreporting and backlogs. Our model explicitly accounts for uncertainty in the dynamic model parameters, the dynamic model adequacy, and the infection observation process. We argue that this modeling paradigm allows us to disentangle the role of the contact rate, the effective population fraction, and the infection observation probability across time and space with an imperfect first principles model. Our findings agree with phylogenetic evidence showing little variability in the contact rate, or virus infectiousness, across EU countries during the early phase of the pandemic, highlighting the advantage of incorporating the effective population fraction into pandemic modeling for heterogeneity in both human behavior and reporting. Finally, to evaluate the consistency of our data assimilation method, we performed a forecast that adequately fits the actual data. Statement of significance: Data-driven and model-based epidemiological studies aimed at learning the number of people infected early during a pandemic should explicitly consider the behavior-induced effective population effect. Indeed, the non-isolated, or effective, fraction of the population during the early phase of the pandemic is time-varying, and first-principles modeling with quantified uncertainty is imperative for an adequate analysis across time and space. We argue that, although good inference results may be obtained using the classical SEIR type model, the model posed in this work has allowed us to disentangle the role of virus infectiousness and awareness-based human behavior during the early phase of the COVID-19 pandemic in the European Union from official infection notification records.

Increased adoption of best practices in ecological forecasting enables comparisons of forecastability.

Near-term iterative forecasting is a powerful tool for ecological decision support and has the potential to transform our understanding of ecological predictability. However, to this point, there has been no cross-ecosystem analysis of near-term ecological forecasts, making it difficult to synthesize diverse research efforts and prioritize future developments for this emerging field. In this study, we analyzed 178 near-term (≤10-yr forecast horizon) ecological forecasting papers to understand the development and current state of near-term ecological forecasting literature and to compare forecast accuracy across scales and variables. Our results indicated that near-term ecological forecasting is widespread and growing: forecasts have been produced for sites on all seven continents and the rate of forecast publication is increasing over time. As forecast production has accelerated, some best practices have been proposed and application of these best practices is increasing. In particular, data publication, forecast archiving, and workflow automation have all increased significantly over time. However, adoption of proposed best practices remains low overall: for example, despite the fact that uncertainty is often cited as an essential component of an ecological forecast, only 45% of papers included uncertainty in their forecast outputs. As the use of these proposed best practices increases, near-term ecological forecasting has the potential to make significant contributions to our understanding of forecastability across scales and variables. In this study, we found that forecastability (defined here as realized forecast accuracy) decreased in predictable patterns over 1-7 d forecast horizons. Variables that were closely related (i.e., chlorophyll and phytoplankton) displayed very similar trends in forecastability, while more distantly related variables (i.e., pollen and evapotranspiration) exhibited significantly different patterns. Increasing use of proposed best practices in ecological forecasting will allow us to examine the forecastability of additional variables and timescales in the future, providing a robust analysis of the fundamental predictability of ecological variables.