In 2011, Lake Erie experienced the largest harmful algal bloom in its recorded history, with a peak intensity over three times greater than any previously observed bloom. Here we show that long-term trends in agricultural practices are consistent with increasing phosphorus loading to the western basin of the lake, and that these trends, coupled with meteorological conditions in spring 2011, produced record-breaking nutrient loads. An extended period of weak lake circulation then led to abnormally long residence times that incubated the bloom, and warm and quiescent conditions after bloom onset allowed algae to remain near the top of the water column and prevented flushing of nutrients from the system. We further find that all of these factors are consistent with expected future conditions. If a scientifically guided management plan to mitigate these impacts is not implemented, we can therefore expect this bloom to be a harbinger of future blooms in Lake Erie.

Predictions of the Earth system, such as weather forecasts and climate projections, require models informed by observations at many levels. Some methods for integrating models and observations are very systematic and comprehensive (e.g., data assimilation), and some are single purpose and customized (e.g., for model validation). We review current methods and best practices for integrating models and observations. We highlight how future developments can enable advanced heterogeneous observation networks and models to improve predictions of the Earth system (including atmosphere, land surface, oceans, cryosphere, and chemistry) across scales from weather to climate. As the community pushes to develop the next generation of models and data systems, there is a need to take a more holistic, integrated, and coordinated approach to models, observations, and their uncertainties to maximize the benefit for Earth system prediction and impacts on society.

High-resolution Weather Research and Forecasting Model (WRF) simulations are used to explore the sensitivity of Great Lakes lake-effect snowfall (LES) to changes in lake ice cover and surface temperature. A control simulation with observed ice cover is compared with three sensitivity tests: complete ice cover, no lake ice, and warmer lake surface temperatures. The spatial pattern of unfrozen lake surfaces determines the placement of LES, and complete ice cover eliminates it. Removal of ice cover and an increase in lake temperatures result in an expansion of the LES area both along and downwind of the lake shore, as well as an increase in snowfall amount. While lake temperatures and phase determine the amount and spatial coverage of LES, the finescale distribution of LES is strongly affected by the interaction between lake surface fluxes, the large-scale flow, and the local lake shore geography and inland topography. As a consequence, the sensitivity of LES to topography and shore geometry differs for lakes with short versus long overwater fetch. These simulations indicate that coarse-resolution models may be able to realistically reproduce the gross features of LES in future climates, but will miss the important local-scale interactions that determine the location and intensity of LES.

This study explores the functional relationship between model physics parameters and model output variables for the purpose of 1) characterizing the sensitivity of the simulation output to the model formulation and 2) understanding model uncertainty so that it can be properly accounted for in a data assimilation framework. A Markov chain Monte Carlo algorithm is employed to examine how changes in cloud microphysical parameters map to changes in output precipitation, liquid and ice water path, and radiative fluxes for an idealized deep convective squall line. Exploration of the joint probability density function (PDF) of parameters and model output state variables reveals a complex relationship between parameters and model output that changes dramatically as the system transitions from convective to stratiform. Persistent nonuniqueness in the parameter–state relationships is shown to be inherent in the construction of the cloud microphysical and radiation schemes and cannot be mitigated by reducing observation uncertainty. The results reinforce the importance of including uncertainty in model configuration in ensemble prediction and data assimilation, and they indicate that data assimilation efforts that include parameter estimation would benefit from including additional constraints based on known physical relationships between model physics parameters to render a unique solution.

This paper explores the temporal evolution of cloud microphysical parameter uncertainty using an idealized 1D model of deep convection. Model parameter uncertainty is quantified using a Markov chain Monte Carlo (MCMC) algorithm. A new form of the ensemble transform Kalman smoother (ETKS) appropriate for the case where the number of ensemble members exceeds the number of observations is then used to obtain estimates of model uncertainty associated with variability in model physics parameters. Robustness of the parameter estimates and ensemble parameter distributions derived from ETKS is assessed via comparison with MCMC. Nonlinearity in the relationship between parameters and model output gives rise to a non-Gaussian posterior probability distribution for the parameters that exhibits skewness early and multimodality late in the simulation. The transition from unimodal to multimodal posterior probability density function (PDF) reflects the transition from convective to stratiform rainfall. ETKS-based estimates of the posterior mean are shown to be robust, as long as the posterior PDF has a single mode. Once multimodality manifests in the solution, the MCMC posterior parameter means and variances differ markedly from those from the ETKS. However, it is also shown that if the ETKS is given a multimode prior ensemble, multimodality is preserved in the ETKS posterior analysis. These results suggest that the primary limitation of the ETKS is not the inability to deal with multimodal, non-Gaussian priors. Rather it is the inability of the ETKS to represent posterior perturbations as nonlinear functions of prior perturbations that causes the most profound difference between MCMC posterior PDFs and ETKS posterior PDFs.

Uncertainty in cloud microphysical parameterization—a leading order contribution to numerical weather prediction error—is estimated using a Markov chain Monte Carlo (MCMC) algorithm. An inversion is performed on 10 microphysical parameters using radar reflectivity observations with vertically covarying error as the likelihood constraint. An idealized 1D atmospheric column model with prescribed forcing is used to simulate the microphysical behavior of a midlatitude squall line. Novel diagnostics are employed for the probabilistic investigation of individual microphysical process behavior vis-à-vis parameter uncertainty. Uncertainty in the microphysical parameterization is presented via posterior probability density functions (PDFs) of parameters, observations, and microphysical processes. The results of this study show that radar reflectivity observations, as expected, provide a much stronger constraint on microphysical parameters than column-integral observations, in most cases reducing both the variance and bias in the maximum likelihood estimate of parameter values. This highlights the enhanced potential of radar reflectivity observations to provide information about microphysical processes within convective storm systems despite the presence of strongly nonlinear relationships within the microphysics model. The probabilistic analysis of parameterization uncertainty in terms of both parameter and process activity PDFs suggest the prospect of a stochastic representation of microphysical parameterization uncertainty—specifically the results indicate that error may be more easily represented and estimated by microphysical process uncertainty rather than microphysical parameter uncertainty. In addition, these new methods of analysis allow for a detailed investigation of the full nonlinear and multivariate relationships between microphysical parameters, microphysical processes, and radar observations.