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Aneesh Subramanian
,
Stephan Juricke
,
Peter Dueben
, and
Tim Palmer

Abstract

Numerical weather prediction and climate models comprise a) a dynamical core describing resolved parts of the climate system and b) parameterizations describing unresolved components. Development of new subgrid-scale parameterizations is particularly uncertain compared to representing resolved scales in the dynamical core. This uncertainty is currently represented by stochastic approaches in several operational weather models, which will inevitably percolate into the dynamical core. Hence, implementing dynamical cores with excessive numerical accuracy will not bring forecast gains, may even hinder them since valuable computer resources will be tied up doing insignificant computation, and therefore cannot be deployed for more useful gains, such as increasing model resolution or ensemble sizes. Here we describe a low-cost stochastic scheme that can be implemented in any existing deterministic dynamical core as an additive noise term. This scheme could be used to adjust accuracy in future dynamical core development work. We propose that such an additive stochastic noise test case should become a part of the routine testing and development of dynamical cores in a stochastic framework. The overall key point of the study is that we should not develop dynamical cores that are more precise than the level of uncertainty provided by our stochastic scheme. In this way, we present a new paradigm for dynamical core development work, ensuring that weather and climate models become more computationally efficient. We show some results based on tests done with the European Centre for Medium-Range Weather Forecasts (ECMWF) Integrated Forecasting System (IFS) dynamical core.

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Sam Hatfield
,
Aneesh Subramanian
,
Tim Palmer
, and
Peter Düben

Abstract

A new approach for improving the accuracy of data assimilation, by trading numerical precision for ensemble size, is introduced. Data assimilation is inherently uncertain because of the use of noisy observations and imperfect models. Thus, the larger rounding errors incurred from reducing precision may be within the tolerance of the system. Lower-precision arithmetic is cheaper, and so by reducing precision in ensemble data assimilation, computational resources can be redistributed toward, for example, a larger ensemble size. Because larger ensembles provide a better estimate of the underlying distribution and are less reliant on covariance inflation and localization, lowering precision could actually permit an improvement in the accuracy of weather forecasts. Here, this idea is tested on an ensemble data assimilation system comprising the Lorenz ’96 toy atmospheric model and the ensemble square root filter. The system is run at double-, single-, and half-precision (the latter using an emulation tool), and the performance of each precision is measured through mean error statistics and rank histograms. The sensitivity of these results to the observation error and the length of the observation window are addressed. Then, by reinvesting the saved computational resources from reducing precision into the ensemble size, assimilation error can be reduced for (hypothetically) no extra cost. This results in increased forecasting skill, with respect to double-precision assimilation.

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Hajoon Song
,
Ibrahim Hoteit
,
Bruce D. Cornuelle
, and
Aneesh C. Subramanian

Abstract

A new approach is proposed to address the background covariance limitations arising from undersampled ensembles and unaccounted model errors in the ensemble Kalman filter (EnKF). The method enhances the representativeness of the EnKF ensemble by augmenting it with new members chosen adaptively to add missing information that prevents the EnKF from fully fitting the data to the ensemble. The vectors to be added are obtained by back projecting the residuals of the observation misfits from the EnKF analysis step onto the state space. The back projection is done using an optimal interpolation (OI) scheme based on an estimated covariance of the subspace missing from the ensemble. In the experiments reported here, the OI uses a preselected stationary background covariance matrix, as in the hybrid EnKF–three-dimensional variational data assimilation (3DVAR) approach, but the resulting correction is included as a new ensemble member instead of being added to all existing ensemble members.

The adaptive approach is tested with the Lorenz-96 model. The hybrid EnKF–3DVAR is used as a benchmark to evaluate the performance of the adaptive approach. Assimilation experiments suggest that the new adaptive scheme significantly improves the EnKF behavior when it suffers from small size ensembles and neglected model errors. It was further found to be competitive with the hybrid EnKF–3DVAR approach, depending on ensemble size and data coverage.

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Aneesh C. Subramanian
,
Ibrahim Hoteit
,
Bruce Cornuelle
,
Arthur J. Miller
, and
Hajoon Song

Abstract

This paper investigates the role of the linear analysis step of the ensemble Kalman filters (EnKF) in disrupting the balanced dynamics in a simple atmospheric model and compares it to a fully nonlinear particle-based filter (PF). The filters have a very similar forecast step but the analysis step of the PF solves the full Bayesian filtering problem while the EnKF analysis only applies to Gaussian distributions. The EnKF is compared to two flavors of the particle filter with different sampling strategies, the sequential importance resampling filter (SIRF) and the sequential kernel resampling filter (SKRF). The model admits a chaotic vortical mode coupled to a comparatively fast gravity wave mode. It can also be configured either to evolve on a so-called slow manifold, where the fast motion is suppressed, or such that the fast-varying variables are diagnosed from the slow-varying variables as slaved modes. Identical twin experiments show that EnKF and PF capture the variables on the slow manifold well as the dynamics is very stable. PFs, especially the SKRF, capture slaved modes better than the EnKF, implying that a full Bayesian analysis estimates the nonlinear model variables better. The PFs perform significantly better in the fully coupled nonlinear model where fast and slow variables modulate each other. This suggests that the analysis step in the PFs maintains the balance in both variables much better than the EnKF. It is also shown that increasing the ensemble size generally improves the performance of the PFs but has less impact on the EnKF after a sufficient number of members have been used.

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Hyodae Seo
,
Aneesh C. Subramanian
,
Arthur J. Miller
, and
Nicholas R. Cavanaugh

Abstract

This study quantifies, from a systematic set of regional ocean–atmosphere coupled model simulations employing various coupling intervals, the effect of subdaily sea surface temperature (SST) variability on the onset and intensity of Madden–Julian oscillation (MJO) convection in the Indian Ocean. The primary effect of diurnal SST variation (dSST) is to raise time-mean SST and latent heat flux (LH) prior to deep convection. Diurnal SST variation also strengthens the diurnal moistening of the troposphere by collocating the diurnal peak in LH with those of SST. Both effects enhance the convection such that the total precipitation amount scales quasi-linearly with preconvection dSST and time-mean SST. A column-integrated moist static energy (MSE) budget analysis confirms the critical role of diurnal SST variability in the buildup of column MSE and the strength of MJO convection via stronger time-mean LH and diurnal moistening. Two complementary atmosphere-only simulations further elucidate the role of SST conditions in the predictive skill of MJO. The atmospheric model forced with the persistent initial SST, lacking enhanced preconvection warming and moistening, produces a weaker and delayed convection than the diurnally coupled run. The atmospheric model with prescribed daily-mean SST from the coupled run, while eliminating the delayed peak, continues to exhibit weaker convection due to the lack of strong moistening on a diurnal basis. The fact that time-evolving SST with a diurnal cycle strongly influences the onset and intensity of MJO convection is consistent with previous studies that identified an improved representation of diurnal SST as a potential source of MJO predictability.

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Hajoon Song
,
Ibrahim Hoteit
,
Bruce D. Cornuelle
,
Xiaodong Luo
, and
Aneesh C. Subramanian

Abstract

A new hybrid ensemble Kalman filter/four-dimensional variational data assimilation (EnKF/4D-VAR) approach is introduced to mitigate background covariance limitations in the EnKF. The work is based on the adaptive EnKF (AEnKF) method, which bears a strong resemblance to the hybrid EnKF/three-dimensional variational data assimilation (3D-VAR) method. In the AEnKF, the representativeness of the EnKF ensemble is regularly enhanced with new members generated after back projection of the EnKF analysis residuals to state space using a 3D-VAR [or optimal interpolation (OI)] scheme with a preselected background covariance matrix. The idea here is to reformulate the transformation of the residuals as a 4D-VAR problem, constraining the new member with model dynamics and the previous observations. This should provide more information for the estimation of the new member and reduce dependence of the AEnKF on the assumed stationary background covariance matrix. This is done by integrating the analysis residuals backward in time with the adjoint model. Numerical experiments are performed with the Lorenz-96 model under different scenarios to test the new approach and to evaluate its performance with respect to the EnKF and the hybrid EnKF/3D-VAR. The new method leads to the least root-mean-square estimation errors as long as the linear assumption guaranteeing the stability of the adjoint model holds. It is also found to be less sensitive to choices of the assimilation system inputs and parameters.

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William E. Chapman
,
Aneesh C. Subramanian
,
Shang-Ping Xie
,
Michael D. Sierks
,
F. Martin Ralph
, and
Youichi Kamae

Abstract

Using a high-resolution atmospheric general circulation model simulation of unprecedented ensemble size, we examine potential predictability of monthly anomalies under El Niño–Southern Oscillation (ENSO) forcing and background internal variability. This study reveals the pronounced month-to-month evolution of both the ENSO forcing signal and internal variability. Internal variance in upper-level geopotential height decreases (~10%) over the North Pacific during El Niño as the westerly jet extends eastward, allowing forced signals to account for a greater fraction of the total variability, and leading to increased potential predictability. We identify February and March of El Niño years as the most predictable months using a signal-to-noise analysis. In contrast, December, a month typically included in teleconnection studies, shows little to no potential predictability. We show that the seasonal evolution of SST forcing and variability leads to significant signal-to-noise relationships that can be directly linked to both upper-level and surface variable predictability for a given month. The stark changes in forced response, internal variability, and thus signal-to-noise across an ENSO season indicate that subseasonal fields should be used to diagnose potential predictability over North America associated with ENSO teleconnections. Using surface air temperature and precipitation as examples, this study provides motivation to pursue “windows of forecast opportunity” in which statistical skill can be developed, tested, and leveraged to determine times and regions in which this skill may be elevated.

Free access
Karsten Haustein
,
Friederike E. L. Otto
,
Victor Venema
,
Peter Jacobs
,
Kevin Cowtan
,
Zeke Hausfather
,
Robert G. Way
,
Bethan White
,
Aneesh Subramanian
, and
Andrew P. Schurer

Abstract

The early twentieth-century warming (EW; 1910–45) and the mid-twentieth-century cooling (MC; 1950–80) have been linked to both internal variability of the climate system and changes in external radiative forcing. The degree to which either of the two factors contributed to EW and MC, or both, is still debated. Using a two-box impulse response model, we demonstrate that multidecadal ocean variability was unlikely to be the driver of observed changes in global mean surface temperature (GMST) after AD 1850. Instead, virtually all (97%–98%) of the global low-frequency variability (>30 years) can be explained by external forcing. We find similarly high percentages of explained variance for interhemispheric and land–ocean temperature evolution. Three key aspects are identified that underpin the conclusion of this new study: inhomogeneous anthropogenic aerosol forcing (AER), biases in the instrumental sea surface temperature (SST) datasets, and inadequate representation of the response to varying forcing factors. Once the spatially heterogeneous nature of AER is accounted for, the MC period is reconcilable with external drivers. SST biases and imprecise forcing responses explain the putative disagreement between models and observations during the EW period. As a consequence, Atlantic multidecadal variability (AMV) is found to be primarily controlled by external forcing too. Future attribution studies should account for these important factors when discriminating between externally forced and internally generated influences on climate. We argue that AMV must not be used as a regressor and suggest a revised AMV index instead [the North Atlantic Variability Index (NAVI)]. Our associated best estimate for the transient climate response (TCR) is 1.57 K (±0.70 at the 5%–95% confidence level).

Open access
Yassir A. Eddebbar
,
Keith B. Rodgers
,
Matthew C. Long
,
Aneesh C. Subramanian
,
Shang-Ping Xie
, and
Ralph F. Keeling

Abstract

The oceanic response to recent tropical eruptions is examined in Large Ensemble (LE) experiments from two fully coupled global climate models, the Community Earth System Model (CESM) and the Geophysical Fluid Dynamics Laboratory Earth System Model (ESM2M), each forced by a distinct volcanic forcing dataset. Following the simulated eruptions of Agung, El Chichón, and Pinatubo, the ocean loses heat and gains oxygen and carbon, in general agreement with available observations. In both models, substantial global surface cooling is accompanied by El Niño–like equatorial Pacific surface warming a year after the volcanic forcing peaks. A mechanistic analysis of the CESM and ESM2M responses to Pinatubo identifies remote wind forcing from the western Pacific as a major driver of this El Niño–like response. Following eruption, faster cooling over the Maritime Continent than adjacent oceans suppresses convection and leads to persistent westerly wind anomalies over the western tropical Pacific. These wind anomalies excite equatorial downwelling Kelvin waves and the upwelling of warm subsurface anomalies in the eastern Pacific, promoting the development of El Niño conditions through Bjerknes feedbacks a year after eruption. This El Niño–like response drives further ocean heat loss through enhanced equatorial cloud albedo, and dominates global carbon uptake as upwelling of carbon-rich waters is suppressed in the tropical Pacific. Oxygen uptake occurs primarily at high latitudes, where surface cooling intensifies the ventilation of subtropical thermocline waters. These volcanically forced ocean responses are large enough to contribute to the observed decadal variability in oceanic heat, carbon, and oxygen.

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Aneesh C. Subramanian
,
Markus Jochum
,
Arthur J. Miller
,
Raghu Murtugudde
,
Richard B. Neale
, and
Duane E. Waliser

Abstract

This study assesses the ability of the Community Climate System Model, version 4 (CCSM4) to represent the Madden–Julian oscillation (MJO), the dominant mode of intraseasonal variability in the tropical atmosphere. The U.S. Climate Variability and Predictability (CLIVAR) MJO Working Group’s prescribed diagnostic tests are used to evaluate the model’s mean state, variance, and wavenumber–frequency characteristics in a 20-yr simulation of the intraseasonal variability in zonal winds at 850 hPa (U850) and 200 hPa (U200), and outgoing longwave radiation (OLR). Unlike its predecessor, CCSM4 reproduces a number of aspects of MJO behavior more realistically.

The CCSM4 produces coherent, broadbanded, and energetic patterns in eastward-propagating intraseasonal zonal winds and OLR in the tropical Indian and Pacific Oceans that are generally consistent with MJO characteristics. Strong peaks occur in power spectra and coherence spectra with periods between 20 and 100 days and zonal wavenumbers between 1 and 3. Model MJOs, however, tend to be more broadbanded in frequency than in observations. Broad-scale patterns, as revealed in combined EOFs of U850, U200, and OLR, are remarkably consistent with observations and indicate that large-scale convergence–convection coupling occurs in the simulated MJO.

Relations between MJO in the model and its concurrence with other climate states are also explored. MJO activity (defined as the percentage of time the MJO index exceeds 1.5) is enhanced during El Niño events compared to La Niña events, both in the model and observations. MJO activity is increased during periods of anomalously strong negative meridional wind shear in the Asian monsoon region and also during strong negative Indian Ocean zonal mode states, in both the model and observations.

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