An Online-Learned Neural Network Chemical Solver for Stable Long-Term Global Simulations of Atmospheric Chemistry

A major computational barrier in global modeling of atmospheric chemistry is the numerical integration of the coupled kinetic equations describing the chemical mechanism. Machine-learned (ML) solvers can offer order-of-magnitude speedup relative to conventional implicit solvers, but past implementations have suffered from fast error growth and only run for short simulation times (<1 month). A successful ML solver for global models must avoid error growth over year-long simulations and allow for re-initialization of the chemical trajectory by transport at every time step. Here we explore the capability of a neural network solver equipped with an autoencoder to achieve stable full-year simulations of tropospheric oxidant chemistry in the global 3-D GEOS-Chem model, replacing its standard mechanism (228 species) by the Super-Fast mechanism (12 species) to avoid the curse of dimensionality. We find that online training of the ML solver within GEOS-Chem is essential for accuracy, whereas offline training from archived GEOS-Chem inputs/outputs produces large errors. After online training we achieve stable 1-year simulations with five-fold speedup compared to the standard implicit Rosenbrock solver with global tropospheric normalized mean biases of -0.3% for ozone, 1% for hydrogen oxide radicals, and -5% for nitrogen oxides. The ML solver captures the diurnal and synoptic variability of surface ozone at polluted and clean sites. There are however large regional biases for ozone and NOx under remote conditions where chemical aging leads to error accumulation. These regional biases remain a major limitation for practical application, and ML emulation would be more difficult in a more complex mechanism.

Recalculation of error growth models' parameters for the ECMWF forecast system

This article provides a new estimate of error growth models' parameters approximating predictability curves and their differentials, calculated from data of the ECMWF forecast system over the 1986 to 2011 period. Estimates of the largest Lyapunov exponent are also provided, along with model error and the limit value of the predictability curve. The proposed correction is based on the ability of the Lorenz (2005) system to simulate the predictability curve of the ECMWF forecasting system and on comparing the parameters estimated for both these systems, as well as on comparison with the largest Lyapunov exponent (λ=0.35 d−1) and limit value of the predictability curve (E∞=8.2) of the Lorenz system. Parameters are calculated from the quadratic model with and without model error, as well as by the logarithmic, general, and hyperbolic tangent models. The average value of the largest Lyapunov exponent is estimated to be in the < 0.32; 0.41 > d−1 range for the ECMWF forecasting system; limit values of the predictability curves are estimated with lower theoretically derived values, and a new approach for the calculation of model error based on comparison of models is presented.

Mesoscale Predictability in Moist Mid-Latitude Cyclones Is Not Sensitive to the Slope of the Background Kinetic Energy Spectrum

We investigate the sensitivity of mesoscale atmospheric predictability to the slope of the background kinetic energy spectrum E by adding initial errors to simulations of idealized moist midlatitude cyclones at several wavenumbers k for which the slope of E(k) is significantly different. These different slopes arise from 1) differences in the E(k) generated by cyclones growing in two different moist baroclinically unstable environments, and 2) differences in the horizontal scale at which initial perturbations are added, with E(k) having steeper slopes at larger scales. When small-amplitude potential temperature perturbations are added, the error growth through the subsequent 36-hour simulation is not sensitive to the slope of E(k) nor to the horizontal scale of the initial error. In all cases with small-amplitude perturbations, the error growth in physical space is dominated by moist convection along frontal boundaries. As such, the error field is localized in physical space and broad in wavenumber (spectral) space. In moist mid-latitude cyclones, these broadly distributed errors in wavenumber space limit mesoscale predictability by growing up-amplitude rather than by cascading upscale to progressively longer wavelengths. In contrast, the error distribution in homogeneous turbulence is broad in physical space and localized in wavenumber space, and dimensional analysis can be used to estimate the error growth rate at a specific wavenumber k from E(k). Predictability estimates derived in this manner, and from the numerical solutions of idealized models of homogeneous turbulence, depend on whether the slope of E(k) is shallower or steeper than k−3, which differs from the slope-insensitive behavior exhibited by moist mid-latitude cyclones.

Prediction Error Growth in a more Realistic Atmospheric Toy Model with Three Spatiotemporal Scales

This article studies the growth of the prediction error over lead time in a schematic model of atmospheric transport. Inspired by the Lorenz (2005) system, we mimic an atmospheric variable in 1 dimension, which can be decomposed into three spatiotemporal scales. We identify parameter values that provide spatiotemporal scaling and chaotic behavior. Instead of exponential growth of the forecast error over time, we observe a more complex behavior. We test a power law and the quadratic hypothesis for the scale dependent error growth. The power law is valid for the first days of the growth, and with an included saturation effect, we extend its validity to the entire period of growth. The theory explaining the parameters of the power law is confirmed. Although the quadratic hypothesis cannot be completely rejected and could serve as a first guess, the hypothesis’s parameters are not theoretically justifiable. In addition, we study the initial error growth for the ECMWF forecast system (500 hPa geopotential height) over the 1986 to 2011 period. For these data, it is impossible to assess which of the error growth descriptions is more appropriate, but the extended power law, which is theoretically substantiated and valid for the Lorenz system, provides an excellent fit to the average initial error growth of the ECMWF forecast system. Fitting the parameters, we conclude that there is an intrinsic limit of predictability after 22 days.

The Three-Cornered Hat Method for Estimating Error Variances of Three or More Atmospheric Data Sets – Part II: Evaluating Radio Occultation and Radiosonde Observations, Global Model Forecasts, and Reanalyses

We apply the three-cornered hat (3CH) method to estimate refractivity, bending angle, and specific humidity error variances for a number of data sets widely used in research and/or operations: radiosondes, radio occultation (COSMIC, COSMIC-2), NCEP global forecasts, and nine reanalyses. We use a large number and combinations of data sets to obtain insights into the impact of the error correlations among different data sets that affect 3CH estimates. Error correlations may be caused by actual correlations of errors, representativeness differences, or imperfect co-location of the data sets. We show that the 3CH method discriminates among the data sets and how error statistics of observations compare to state-of-the-art reanalyses and forecasts, as well as reanalyses that do not assimilate satellite data. We explore results for October and November 2006 and 2019 over different latitudinal regions and show error growth of the NCEP forecasts with time. Because of the importance of tropospheric water vapor to weather and climate, we compare error estimates of refractivity for dry and moist atmospheric conditions.

Error Growth Dynamics within Convection-Allowing Ensemble Forecasts over Central U.S. Regions for Days of Active Convection

Error growth is investigated based on convection-allowing ensemble forecasts starting from 0000 UTC for 14 active convection events over central to eastern U.S. regions from spring 2018. The analysis domain is divided into the NW, NE, SE and SW quadrants (subregions). Total difference energy and its decompositions are used to measure and analyze error growth at and across scales. Special attention is paid to the dominant types of convection with respect to their forcing mechanisms in the four subregions and the associated difference in precipitation diurnal cycles. The discussions on the average behaviors of error growth in each region are supplemented by 4 representative cases. Results show that the meso-γ-scale error growth is directly linked to precipitation diurnal cycle while meso-α-scale error growth has strong link to large scale forcing. Upscale error growth is evident in all regions/cases but up-amplitude growth within own scale plays different roles in different regions/cases.When large-scale flow is important (as in the NE region), precipitation is strongly modulated by the large-scale forcing and becomes more organized with time, and upscale transfer of forecast error is stronger. On the other hand, when local instability plays more dominant roles (as in the SE region), precipitation is overall least organized and has the weakest diurnal variations. Its associated errors at the γ– and β-scale can reach their peaks sooner and meso-α-scale error tends to rely more on growth of error with its own scale. Small-scale forecast errors are directly impacted by convective activities and have short response time to convection while increasingly larger scale errors have longer response times and delayed phase within the diurnal cycle.