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Judith Berner

Abstract

To link prominent nonlinearities in the dynamics of 500-hPa geopotential heights to non-Gaussian features in their probability density, a nonlinear stochastic model of atmospheric planetary wave behavior is developed. An analysis of geopotential heights generated by extended integrations of a GCM suggests that a stochastic model and its associated Fokker–Planck equation call for a nonlinear drift and multiplicative noise. All calculations are carried out in the reduced phase space spanned by the leading EOFs. It is demonstrated that this nonlinear stochastic model of planetary wave behavior captures the non-Gaussian features in the probability density function of atmospheric states to a remarkable degree. Moreover, it not only predicts global temporal characteristics, but also the nonlinear, state-dependent divergence of state trajectories. In the context of this empirical modeling, it is discussed on which time scale a stochastic model is expected to approximate the behavior of a continuous deterministic process.

The reduced model is then used to determine the importance of the nonlinearities in the drift and the role of the multiplicative noise. While the nonlinearities in the drift are crucial for a good representation of planetary wave behavior, multiplicative (i.e., state dependent) noise is not absolutely essential. It is found that a major contributor to the stochastic component is the Branstator–Kushnir oscillation, which acts as a fluctuating force for physical processes with even longer time scales, like those that project on the Arctic Oscillation pattern. In this model, the oscillation is represented by strongly correlated noise.

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Judith Berner and Grant Branstator

Abstract

To identify and quantify indications of linear and nonlinear planetary wave behavior and their impact on the distribution of atmospheric states, characteristics of a very long integration of an atmospheric general circulation model (GCM) in a four-dimensional phase space are examined. The phase space is defined by the leading four empirical orthogonal functions of 500-hPa geopotential heights.

First it is established that nonlinear tendencies similar to those reported in an earlier study of the phase space behavior in this GCM have the potential to lead to non-Gaussian features in the probability density function (PDF) of planetary waves. Then using objective measures it is demonstrated that the model’s distribution of states has distinctive non-Gaussian features. These features are characterized in various subspaces of dimension as high as four. A key feature is the presence of three radial ridges of enhanced probability emanating from the mode, which is shifted away from the climatological mean. There is no evidence of multiple maxima in the full PDF, but the radial ridges lead to three distinct modes in the distribution of circulation patterns.

It is demonstrated that these key aspects of non-Gaussianity are captured by a two-Gaussian mixture model fitted in four dimensions. The two circulation states at the centroids of the component Gaussians are very similar to those associated with two nonlinear features identified by Branstator and Berner in their analysis of the trajectories of the GCM. These two dynamical features are locally linear, so it is concluded that the behavior of planetary waves can be conceptualized as being approximately piecewise-linear, leading to a two-Gaussian mixture with three preferred patterns.

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Grant Branstator and Judith Berner

Abstract

To identify and quantify indications of linear and nonlinear planetary wave behavior, characteristics of a very long integration of an atmospheric general circulation model in a four-dimensional phase space are examined. The phase space is defined by the leading four empirical orthogonal functions of 500-hPa geopotential heights, and the primary investigated characteristic is the state dependence of mean phase space tendencies. Defining the linear component of planetary wave tendencies as that part which can be captured by a least squares fit linear operator driven by additive Gaussian white noise, the study finds that there are distinct linear and nonlinear signatures. These signatures are especially easy to see in plots of mean tendencies projected onto phase space planes. For some planes the mean tendencies are highly linear, while for others there are strong departures from linearity.

The results of the analysis are found to depend strongly on the lag time used to estimate tendencies with the linear component monotonically increasing with lag time. This is shown to result from the ergodicity of the system. Using the theory of Markov models it is possible to remove the lag-dependent component of the tendencies from the results. When this is done the projected mean dynamics in some planes is found to be almost exclusively nonlinear, while in others it is nearly linear.

In the four-dimensional space the linear component of the dynamics is largely a reflection of a westward propagating Northern Hemisphere pattern concentrated over the Pacific and North America. The nonlinear signature can be approximated by two linear functions, each operating in a different region of phase space. One region is centered around a Pacific blocking pattern while the other is centered on a state with enhanced zonal symmetry. It is concluded that reduced models of the planetary waves should strive to include these state-dependent dynamics.

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Steven M. Cavallo, Judith Berner, and Chris Snyder

Abstract

Accurate predictions in numerical weather models depend on the ability to accurately represent physical processes across a wide range of scales. This paper evaluates the utility of model time tendencies, averaged over many forecasts at a given lead time, to diagnose systematic forecast biases in the Advanced Research version of the Weather Research and Forecasting (WRF) Model during the 2010 North Atlantic hurricane season using continuously cycled ensemble data assimilation (DA). Erroneously strong low-level heating originates from the planetary boundary layer parameterization as a consequence of using fixed sea surface temperatures, impacting the upward surface sensible heat fluxes. Warm temperature bias is observed with a magnitude 0.5 K in a deep tropospheric layer centered 700 hPa, originating primarily from the Kain–Fritsch convective parameterization.

This study is the first to diagnose systematic forecast bias in a limited-area mesoscale model using its forecast tendencies. Unlike global models where relatively fewer time steps typically encompass a DA cycling period, averaging all short-term forecast tendencies can require potentially large data. It is shown that 30-min averaging intervals can sufficiently represent the systematic model bias in this modeling configuration when initializing forecasts from an ensemble member that is generated using a DA system with an identical model configuration. However, the number of time steps before model error begins to dominate initial condition (IC) errors may vary between modeling configurations. Model and IC error are indistinguishable in short-term forecasts when initialized from the ensemble mean, a global analysis from a different model, and an ensemble member using a different parameterization.

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Soyoung Ha, Judith Berner, and Chris Snyder

Abstract

Mesoscale forecasts are strongly influenced by physical processes that are either poorly resolved or must be parameterized in numerical models. In part because of errors in these parameterizations, mesoscale ensemble data assimilation systems generally suffer from underdispersiveness, which can limit the quality of analyses. Two explicit representations of model error for mesoscale ensemble data assimilation are explored: a multiphysics ensemble in which each member’s forecast is based on a distinct suite of physical parameterization, and stochastic kinetic energy backscatter in which small noise terms are included in the forecast model equations. These two model error techniques are compared with a baseline experiment that includes spatially and temporally adaptive covariance inflation, in a domain over the continental United States using the Weather Research and Forecasting (WRF) Model for mesoscale ensemble forecasts and the Data Assimilation Research Testbed (DART) for the ensemble Kalman filter. Verification against independent observations and Rapid Update Cycle (RUC) 13-km analyses for the month of June 2008 showed that including the model error representation improved not only the analysis ensemble, but also short-range forecasts initialized from these analyses. Explicitly accounting for model uncertainty led to a better-tuned ensemble spread, a more skillful ensemble mean, and higher probabilistic scores, as well as significantly reducing the need for inflation. In particular, the stochastic backscatter scheme consistently outperformed both the multiphysics approach and the control run with adaptive inflation over almost all levels of the atmosphere both deterministically and probabilistically.

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Judith Berner, Prashant D. Sardeshmukh, and Hannah M. Christensen

Abstract

This study investigates the mechanisms by which short time-scale perturbations to atmospheric processes can affect El Niño–Southern Oscillation (ENSO) in climate models. To this end a control simulation of NCAR’s Community Climate System Model is compared to a simulation in which the model’s atmospheric diabatic tendencies are perturbed every time step using a Stochastically Perturbed Parameterized Tendencies (SPPT) scheme. The SPPT simulation compares better with ECMWF’s twentieth-century reanalysis in having lower interannual sea surface temperature (SST) variability and more irregular transitions between El Niño and La Niña states, as expressed by a broader, less peaked spectrum. Reduced-order linear inverse models (LIMs) derived from the 1-month lag covariances of selected tropical variables yield good representations of tropical interannual variability in the two simulations. In particular, the basic features of ENSO are captured by the LIM’s least damped oscillatory eigenmode. SPPT reduces the damping time scale of this eigenmode from 17 to 11 months, which is in better agreement with the 8 months obtained from reanalyses. This noise-induced stabilization is consistent with perturbations to the frequency of the ENSO eigenmode and explains the broadening of the SST spectrum (i.e., the greater ENSO irregularity). Although the improvement in ENSO shown here was achieved through stochastic physics parameterizations, it is possible that similar improvements could be realized through changes in deterministic parameterizations or higher numerical resolution. It is suggested that LIMs could provide useful insight into model sensitivities, uncertainties, and biases also in those cases.

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Judith Berner, Hannah M. Christensen, and Prashant D. Sardeshmukh

Abstract

The impact of a warming climate on El Niño–Southern Oscillation (ENSO) is investigated in large-ensemble simulations of the Community Earth System Model (CESM1). These simulations are forced by historical emissions for the past and the RCP8.5-scenario emissions for future projections. The simulated variance of the Niño-3.4 ENSO index increases from 1.4°C2 in 1921–80 to 1.9°C2 in 1981–2040 and 2.2°C2 in 2041–2100. The autocorrelation time scale of the index also increases, consistent with a narrowing of its spectral peak in the 3–7-yr ENSO band, raising the possibility of greater seasonal to interannual predictability in the future. Low-order linear inverse models (LIMs) fitted separately to the three 60-yr periods capture the CESM1 increase in ENSO variance and regularity. Remarkably, most of the increase can be attributed to the increase in the 23-month damping time scale of a single damped oscillatory ENSO eigenmode of these LIMs by 5 months in 1981–2040 and 6 months in 2041–2100. These apparently robust projected increases may, however, be compromised by CESM1 biases in ENSO amplitude and damping time scale. An LIM fitted to the 1921–80 observations has an ENSO eigenmode with a much shorter 8-month damping time scale, similar to that of several other eigenmodes. When the mode’s damping time scale is increased by 5 and 6 months in this observational LIM, a much smaller increase of ENSO variance is obtained than in the CESM1 projections. This may be because ENSO is not as dominated by a single ENSO eigenmode in reality as it is in the CESM1.

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Felipe Tagle, Judith Berner, Mircea D. Grigoriu, Natalie M. Mahowald, and Gennady Samorodnitsky

Abstract

This paper evaluates the performance of the NCAR Community Atmosphere Model, version 4 (CAM4), in simulating observed annual extremes of near-surface temperature and provides the first assessment of the impact of stochastic parameterizations of subgrid-scale processes on such performance. Two stochastic parameterizations are examined: the stochastic kinetic energy backscatter scheme and the stochastically perturbed parameterization tendency scheme. Temperature extremes are described in terms of 20-yr return levels and compared to those estimated from ERA-Interim and the Hadley Centre Global Climate Extremes Index 2 (HadEX2) observational dataset. CAM4 overestimates warm and cold extremes over land regions, particularly over the Northern Hemisphere, when compared against reanalysis. Similar spatial patterns, though less spatially coherent, emerge relative to HadEX2. The addition of a stochastic parameterization generally produces a warming of both warm and cold extremes relative to the unperturbed configuration; however, neither of the proposed parameterizations meaningfully reduces the biases in the simulated temperature extremes of CAM4. Adjusting warm and cold extremes by mean conditions in the respective annual extremes leads to good agreement between the models and reanalysis; however, adjusting for the bias in mean temperature does not help to reduce the observed discrepancies. Based on the behavior of the annual extremes, this study concludes that the distribution of temperature in CAM4 exhibits too much variability relative to that of reanalysis, while the stochastic parameterizations introduce a systematic bias in its mean rather than alter its variability.

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Gregory Thompson, Judith Berner, Maria Frediani, Jason A. Otkin, and Sarah M. Griffin

Abstract

Current state-of-the art regional numerical weather forecasts are run at horizontal grid spacings of a few kilometers, which permits medium to large-scale convective systems to be represented explicitly in the model. With the convection parameterization no longer active, much uncertainty in the formulation of subgrid-scale processes moves to other areas such as the cloud microphysical, turbulence, and land-surface parameterizations. The goal of this study is to investigate experiments with stochastically-perturbed parameters (SPP) within a microphysics parameterization and the model’s horizontal diffusion coefficients. To estimate the “true” uncertainty due to parameter uncertainty, the magnitudes of the perturbations are chosen as realistic as possible and not with purposeful intent of maximal forecast impact as some prior work has done. Spatial inhomogeneities and temporal persistence are represented using a random perturbation pattern with spatial and temporal correlations. The impact on the distributions of various hydrometeors, precipitation characteristics, and solar/longwave radiation are quantified for a winter and summer case. In terms of upscale error growth, the impact is relatively small and consists primarily of triggering atmospheric instabilities in convectively unstable regions. In addition, small in situ changes with potentially large socio-economic impacts are observed in the precipitation characteristics such as maximum hail size. Albeit the impact of introducing physically-based parameter uncertainties within the bounds of aerosol uncertainties is small, their influence on the solar and longwave radiation balances may still have important implications for global model simulations of future climate scenarios.

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Jeffrey D. Duda, Xuguang Wang, Fanyou Kong, Ming Xue, and Judith Berner

Abstract

The efficacy of a stochastic kinetic energy backscatter (SKEB) scheme to improve convection-allowing probabilistic forecasts was studied. While SKEB has been explored for coarse, convection-parameterizing models, studies of SKEB for convective scales are limited. Three ensembles were compared. The SKMP ensemble used mixed physics with the SKEB scheme, whereas the MP ensemble was configured identically but without using the SKEB scheme. The SK ensemble used the SKEB scheme with no physics diversity. The experiment covered May 2013 over the central United States on a 4-km Weather Research and Forecasting (WRF) Model domain.

The SKEB scheme was successful in increasing the spread in all fields verified, especially mid- and upper-tropospheric fields. Additionally, the rmse of the ensemble mean was maintained or reduced, in some cases significantly. Rank histograms in the SKMP ensemble were flatter than those in the MP ensemble, indicating the SKEB scheme produces a less underdispersive forecast distribution. Some improvement was seen in probabilistic precipitation forecasts, particularly when examining Brier scores. Verification against surface observations agree with verification against Rapid Refresh (RAP) model analyses, showing that probabilistic forecasts for 2-m temperature, 2-m dewpoint, and 10-m winds were also improved using the SKEB scheme. The SK ensemble gave competitive forecasts for some fields. The SK ensemble had reduced spread compared to the MP ensemble at the surface due to the lack of physics diversity.

These results suggest the potential utility of mixed physics plus the SKEB scheme in the design of convection-allowing ensemble forecasts.

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