Publications by Hannah Christensen


Machine Learning for Stochastic Parameterization: Generative Adversarial Networks in the Lorenz’96 Model

Journal of Advances in Modeling Earth Systems American Geophysical Union 12 (2020) e2019MS001896

DJ Gagne, HM Christensen, AC Subramanian, AH Monahan

Stochastic parameterizations account for uncertainty in the representation of unresolved subgrid processes by sampling from the distribution of possible subgrid forcings. Some existing stochastic parameterizations utilize data‐driven approaches to characterize uncertainty, but these approaches require significant structural assumptions that can limit their scalability. Machine learning models, including neural networks, are able to represent a wide range of distributions and build optimized mappings between a large number of inputs and subgrid forcings. Recent research on machine learning parameterizations has focused only on deterministic parameterizations. In this study, we develop a stochastic parameterization using the generative adversarial network (GAN) machine learning framework. The GAN stochastic parameterization is trained and evaluated on output from the Lorenz '96 model, which is a common baseline model for evaluating both parameterization and data assimilation techniques. We evaluate different ways of characterizing the input noise for the model and perform model runs with the GAN parameterization at weather and climate time scales. Some of the GAN configurations perform better than a baseline bespoke parameterization at both time scales, and the networks closely reproduce the spatiotemporal correlations and regimes of the Lorenz '96 system. We also find that, in general, those models which produce skillful forecasts are also associated with the best climate simulations.


Constraining stochastic parametrisation schemes using high-resolution simulations

Quarterly Journal of the Royal Meteorological Society Wiley 146 (2020) 938-962

H Christensen

Stochastic parametrisations can be used in weather and climate models to improve the representation of unpredictable unresolved processes. When compared with a deterministic model, a stochastic model represents “model uncertainty”, that is, sources of error in the forecast due to the limitations of the forecast model. A technique is presented for systematically deriving new stochastic parametrisations or constraining existing stochastic approaches. A high‐resolution model simulation is coarse‐grained to the desired forecast model resolution. This provides the initial conditions and forcing data needed to drive a single‐column model (SCM). Comparing the SCM parametrised tendencies with the evolution of the high‐resolution model provides an estimate of the error in the SCM tendencies that a stochastic parametrisation seeks to represent. This approach is used to assess the physical basis of the widely used stochastically perturbed parametrisation tendencies (SPPT) scheme. Justification is found for the multiplicative nature of SPPT, along with some evidence for the use of spatio‐temporally correlated stochastic perturbations. Evidence that the stochastic perturbation should be positively skewed is found, indicating that occasional large‐magnitude positive perturbations are physically realistic. However, other key assumptions of SPPT are less well justified, including coherency of the stochastic perturbations with height, coherency of the perturbations for different physical parametrisation schemes, and coherency for different prognostic variables. Relaxing these SPPT assumptions allows for an error model that explains a larger fractional variance than traditional SPPT. In particular, it is suggested that independently perturbing the tendencies associated with different parametrisation schemes is justifiable and would improve the realism of the SPPT approach.


Machine learning and artificial intelligence to aid climate change research and preparedness

Environmental Research Letters IOP Publishing 14 (2019) 12

C Huntingford, ES Jeffers, M Bonsall, H Christensen, T Lees, H Yang


The impact of stochastic physics on the El Niño Southern Oscillation in the EC-Earth coupled model

Climate Dynamics Springer Berlin Heidelberg 53 (2019) 2843–2859-

C Yang, H Christensen, S Corti, J Von Hardenberg, P Davini

The impact of stochastic physics on El Niño Southern Oscillation (ENSO) is investigated in the EC-Earth coupled climate model. By comparing an ensemble of three members of control historical simulations with three ensemble members that include stochastics physics in the atmosphere, we find that in EC-Earth the implementation of stochastic physics improves the excessively weak representation of ENSO. Specifically, the amplitude of both El Niño and, to a lesser extent, La Niña increases. Stochastic physics also ameliorates the temporal variability of ENSO at interannual time scales, demonstrated by the emergence of peaks in the power spectrum with periods of 5–7 years and 3–4 years. Based on the analogy with the behaviour of an idealized delayed oscillator model (DO) with stochastic noise, we find that when the atmosphere–ocean coupling is small (large) the amplitude of ENSO increases (decreases) following an amplification of the noise amplitude. The underestimated ENSO variability in the EC-Earth control runs and the associated amplification due to stochastic physics could be therefore consistent with an excessively weak atmosphere–ocean coupling. The activation of stochastic physics in the atmosphere increases westerly wind burst (WWB) occurrences (i.e. amplification of noise amplitude) that could trigger more and stronger El Niño events (i.e. increase of ENSO oscillation) in the coupled EC-Earth model. Further analysis of the mean state bias of EC-Earth suggests that a cold sea surface temperature (SST) and dry precipitation bias in the central tropical Pacific together with a warm SST and wet precipitation bias in the western tropical Pacific are responsible for the coupled feedback bias (weak coupling) in the tropical Pacific that is related to the weak ENSO simulation. The same analysis of the ENSO behaviour is carried out in a future scenario experiment (RCP8.5 forcing), highlighting that in a coupled model with an extreme warm SST, characterized by a strong coupling, the effect of stochastic physics on the ENSO representation is opposite. This corroborates the hypothesis that the mean state bias of the tropical Pacific region is the main reason for the ENSO representation deficiency in EC-Earth.


Correction to: The impact of stochastic physics on the El Niño Southern Oscillation in the EC-Earth coupled model (Climate Dynamics, (2019), 10.1007/s00382-019-04660-0)

Climate Dynamics (2019)

C Yang, HM Christensen, S Corti, J von Hardenberg, P Davini

© 2019, The Author(s). The article The impact of stochastic physics on the El Niño Southern Oscillation in the EC-Earth coupled model, written by Chunxue Yang, Hannah M. Christensen, Susanna Corti, Jost von Hardenberg and Paolo Davini, was originally published electronically on the publisher’s internet portal (currently SpringerLink) on 07 February 2019 without open access.


From reliable weather forecasts to skilful climate response: A dynamical systems approach

Quarterly Journal of the Royal Meteorological Society Wiley 145 (2019) 1052-1069

H Christensen, J Berner

While weather forecasting models can be tested by performing and evaluating many hindcasts, the limited observational record restricts the degree to which climate projections can be evaluated. Therefore a question of interest is: to what degree can we evaluate the potential skill of a climate model's response to forcing by assessing the reliability of short‐range weather and seasonal forecasts produced by the same model? We address this question using a dynamical systems framework. We use linear response theory to provide the mean climate response of a general dynamical system to a small external forcing. We relate this response to the reliability of initial value forecasts. We find that, in order to capture the mean climate response, the forecast model must correctly represent the slowest evolving modes of variability in the system. The reliability of forecasts on seasonal and longer time‐scales, which is sensitive to the representation of these slow modes, could therefore indicate if the forecast model has the correct climate sensitivity and so will respond correctly to an applied external forcing. In this way, the skill of initialized forecasts could act as an ‘emergent constraint’ on climate sensitivity. However, we also highlight that unreliable seasonal forecasts do not necessarily indicate an incorrect climate projection. This is because correctly representing rapidly evolving modes is also necessary for reliable seasonal forecasts.


Stochastic parameterization of subgrid-scale velocity enhancement of sea surface fluxes

Monthly Weather Review American Meteorological Society 147 (2019) 1447-1469

J Bessac, AH Monahan, H Christensen, N Weitzel

Subgrid-scale (SGS) velocity variations result in gridscale sea surface flux enhancements that must be parameterized in weather and climate models. Traditional parameterizations are deterministic in that they assign a unique value of the SGS velocity flux enhancement to any given configuration of the resolved state. In this study, we assess the statistics of SGS velocity flux enhancement over a range of averaging scales (as a proxy for varying model resolution) through systematic coarse-graining of a convection-permitting atmospheric model simulation over the Indian Ocean and west Pacific warm pool. Conditioning the statistics of the SGS velocity flux enhancement on 1) the fluxes associated with the resolved winds and 2) the precipitation rate, we find that the lack of a separation between “resolved” and “unresolved” scales results in a distribution of flux enhancements for each configuration of the resolved state. That is, the SGS velocity flux enhancement should be represented stochastically rather than deterministically. The spatial and temporal statistics of the SGS velocity flux enhancement are investigated by using basic descriptive statistics and through a fit to an anisotropic space–time covariance structure. Potential spatial inhomogeneities of the statistics of the SGS velocity flux enhancement are investigated through regional analysis, although because of the relatively short duration of the simulation (9 days) distinguishing true inhomogeneity from sampling variability is difficult. Perspectives for the implementation of such a stochastic parameterization in weather and climate models are discussed.


Progress Towards a Probabilistic Earth System Model: Examining The Impact of Stochasticity in EC-Earth v3.2

Geoscientific Model Development European Geosciences Union 12 (2019) 3099-3118

K Strommen, H Christensen, D Macleod, S Juricke, T Palmer

We introduce and study the impact of three stochastic schemes in the EC-Earth climate model: two atmospheric schemes and one stochastic land scheme. These form the basis for a probabilistic Earth system model in atmosphere-only mode. Stochastic parametrization have become standard in several operational weather-forecasting models, in particular due to their beneficial impact on model spread. In recent years, stochastic schemes in the atmospheric component of a model have been shown to improve aspects important for the models long-term climate, such as El Niño–Southern Oscillation (ENSO), North Atlantic weather regimes, and the Indian monsoon. Stochasticity in the land component has been shown to improve the variability of soil processes and improve the representation of heatwaves over Europe. However, the raw impact of such schemes on the model mean is less well studied. It is shown that the inclusion of all three schemes notably changes the model mean state. While many of the impacts are beneficial, some are too large in amplitude, leading to significant changes in the model's energy budget and atmospheric circulation. This implies that in order to maintain the benefits of stochastic physics without shifting the mean state too far from observations, a full re-tuning of the model will typically be required.


The benefits of global high-resolution for climate simulation: process-understanding and the enabling of stakeholder decisions at the regional scale.

Bulletin of the American Meteorological Society (2018)

MJ Roberts, PL Vidale, C Senior, HT Hewitt, C Bates, S Berthou, P Chang, HM Christensen, S Danilov, M-E Demory, SM Griffies, R Haarsma, T Jung, G Martin, S Minobe, T Ringler, M Satoh, R Schiemann, E Scoccimarro, G Stephens, MF Wehner


Systematic Errors in Weather and Climate Models: Nature, Origins, and Way Forward

Bulletin of the American Meteorological Society (2017)

A Zadra, K Williams, A Frassoni, M Rixen, Á Adames, J Berner, F Bouyssel, B Casati, HM Christensen, MB Ek, G Flato, Y Huang, F Judt, H Lin, E Maloney, W Merryfield, A van Niekerk, T Rackow, K Saito, N Wedi, P Yadav


The impact of stochastic parametrisations on the representation of the Asian summer monsoon

Climate Dynamics Springer 50 (2017) 2269-2282

KJ Strømmen, HM Christensen, J Berner, T Palmer

The impact of the stochastic schemes Stochastically Perturbed Parametrisation Tendencies (SPPT) and Stochastic Kinetic Energy Backscatter Scheme (SKEBS) on the representation of interannual variability in the Asian summer monsoon is examined in the coupled climate model CCSM4. The Webster–Yang index, measuring anomalies of a specified wind-shear index in the monsoon region, is used as a metric for monsoon strength, and is used to analyse the output of three model integrations: one deterministic, one with SPPT, and one with SKEBS. Both schemes show improved variability, which we trace back to improvements in the El Niño-Southern Oscillation (ENSO) and the Indian Ocean Dipole (IOD). SPPT improves the representation of ENSO and through teleconnections thereby the monsoon, supporting previous work on the benefits of this scheme on the model climate. SKEBS also improves monsoon variability by way of improving the representation of the IOD, in particular by breaking an overly strong coupling to ENSO.


Forcing single column models using high-resolution model simulations

Journal of Advances in Modeling Earth Systems Wiley 10 (2018) 1833-1857

HM Christensen, A Dawson, CE Holloway

To use single column models (SCMs) as a research tool for parametrisation development and process studies, the SCM must be supplied with realistic initial profiles, forcing fields and boundary conditions. We propose a new technique for deriving these required profiles, motivated by the increase in number and scale of high-resolution convection-permitting simulations. We suggest that these high-resolution simulations be coarse-grained to the required resolution of an SCM, and thereby be used as a proxy for the ‘true’ atmosphere. This paper describes the implementation of such a technique. We test the proposed methodology using high-resolution data from the UK Met Office’s Unified Model (MetUM), with a resolution of 4 km, covering a large tropical domain. This data is coarse grained and used to drive the European Centre for Medium-Range Weather Forecast’s (ECMWF) Integrated Forecasting System (IFS) SCM. The proposed method is evaluated by deriving IFS SCM forcing profiles from a consistent T639 IFS simulation. The SCM simulations track the global model, indicating a consistency between the estimated forcing fields and the ‘true’ dynamical forcing in the global model. We demonstrate the benefits of selecting SCM forcing profiles from across a large-domain, namely robust statistics, and the ability to test the SCM over a range of boundary conditions. We also compare driving the SCM with the coarse-grained dataset to driving it using the ECMWF operational analysis. We conclude by highlighting the importance of understanding biases in the high-resolution dataset, and suggest that our approach be used in combination with observationally derived forcing datasets.


On the dynamical mechanisms governing El Niño-Southern Oscillation irregularity

Journal of Climate American Meteorological Society 31 (2018) 8401-8419

J Berner, PD Sardeshmukh, H Christensen

This study investigates the mechanisms by which short-timescale 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 20th-century reanalysis in having lower inter-annual 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 timescale 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 (that is, 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 LIMs could provide useful insight into model sensitivities, uncertainties, and biases also in those cases.


Stochastic representations of model uncertainties at ECMWF: state of the art and future vision

Quarterly Journal of the Royal Meteorological Society Wiley 143 (2017) 2315-2339

M Leutbecher, S-J Lock, P Ollinaho, STK Lang, G Balsamo, P Bechtold, M Bonavita, HM Christensen, M Diamantakis, E Dutra, S English, M Fisher, R Forbes, J Goddard, T Haiden, R Hogan, S Juricke, H Lawrence, S Malardel, S Massart, I Sandu, P Smolarkiewicz, A Subramanian, F Vitart, N Wedi

Members in ensemble forecasts differ due to the representations of initial uncertainties and model uncertainties. The inclusion of stochastic schemes to represent model uncertainties has improved the probabilistic skill of the ECMWF ensemble by increasing reliability and reducing the error of the ensemble mean. Recent progress, challenges and future directions regarding stochastic representations of model uncertainties at ECMWF are described in this paper. The coming years are likely to see a further increase in the use of ensemble methods in forecasts and assimilation. This will put increasing demands on the methods used to perturb the forecast model. An area that is receiving a greater attention than 5 to 10 years ago is the physical consistency of the perturbations. Other areas where future efforts will be directed are the expansion of uncertainty representations to the dynamical core and to other components of the Earth system as well as the overall computational efficiency of representing model uncertainty.


Climate SPHINX: evaluating the impact of resolution and stochastic physics parameterisations in the EC-Earth global climate model

Geoscientific Model Development Copernicus Publications 10 (2017) 1383-1402

P Davini, J von Hardenburg, S Corti, HM Christensen, S Juricke, A Subramanian, PAG Watson, A Weisheimer, TN Palmer

The Climate SPHINX (Stochastic Physics HIgh resolutioN eXperiments) project is a comprehensive set of ensemble simulations aimed at evaluating the sensitivity of present and future climate to model resolution and stochastic parameterisation. The EC-Earth Earth system model is used to explore the impact of stochastic physics in a large ensemble of 30-year climate integrations at five different atmospheric horizontal resolutions (from 125 up to 16 km). The project includes more than 120 simulations in both a historical scenario (1979–2008) and a climate change projection (2039–2068), together with coupled transient runs (1850–2100). A total of 20.4 million core hours have been used, made available from a single year grant from PRACE (the Partnership for Advanced Computing in Europe), and close to 1.5 PB of output data have been produced on Super- MUC IBM Petascale System at the Leibniz Supercomputing Centre (LRZ) in Garching, Germany. About 140 TB of postprocessed data are stored on the CINECA supercomputing centre archives and are freely accessible to the community thanks to an EUDAT data pilot project. This paper presents the technical and scientific set-up of the experiments, including the details on the forcing used for the simulations performed, defining the SPHINX v1.0 protocol. In addition, an overview of preliminary results is given. An improvement in the simulation of Euro-Atlantic atmospheric blocking following resolution increase is observed. It is also shown that including stochastic parameterisation in the low-resolution runs helps to improve some aspects of the tropical climate – specifically the Madden–Julian Oscillation and the tropical rainfall variability. These findings show the importance of representing the impact of small-scale processes on the large-scale climate variability either explicitly (with highresolution simulations) or stochastically (in low-resolution simulations).


Stochastic parameterization and El Niño–Southern Oscillation

Journal of Climate American Meteorological Society 30 (2016) 17–38-

H Christensen, TN Palmer, J Berner, DRB Coleman

El Niño–Southern Oscillation (ENSO) is the dominant mode of interannual variability in the tropical Pacific. However, the models in the ensemble from phase 5 of the Coupled Model Intercomparison Project (CMIP5) have large deficiencies in ENSO amplitude, spatial structure, and temporal variability. The use of stochastic parameterizations as a technique to address these pervasive errors is considered. The multiplicative stochastically perturbed parameterization tendencies (SPPT) scheme is included in coupled integrations of the National Center for Atmospheric Research (NCAR) Community Atmosphere Model, version 4 (CAM4). The SPPT scheme results in a significant improvement to the representation of ENSO in CAM4, improving the power spectrum and reducing the magnitude of ENSO toward that observed. To understand the observed impact, additive and multiplicative noise in a simple delayed oscillator (DO) model of ENSO is considered. Additive noise results in an increase in ENSO amplitude, but multiplicative noise can reduce the magnitude of ENSO, as was observed for SPPT in CAM4. In light of these results, two complementary mechanisms are proposed by which the improvement occurs in CAM. Comparison of the coupled runs with a set of atmosphere-only runs indicates that SPPT first improve the variability in the zonal winds through perturbing the convective heating tendencies, which improves the variability of ENSO. In addition, SPPT improve the distribution of westerly wind bursts (WWBs), important for initiation of El Niño events, by increasing the stochastic component of WWB and reducing the overly strong dependency on SST compared to the control integration.


Introducing independent patterns into the Stochastically Perturbed Parametrisation Tendencies (SPPT) scheme

Quarterly Journal of the Royal Meteorological Society Wiley 143 (2017) 2168-2181

HM Christensen, S-J Lock, I Moroz, TN Palmer

The Stochastically Perturbed Parametrisation Tendencies (SPPT) scheme is used at weather and climate forecasting centres worldwide to represent model uncertainty that arises from simplifications involved in the parametrisation process. It uses spatio-temporally correlated multiplicative noise to perturb the sum of the parametrised tendencies. However, SPPT does not distinguish between different parametrisation schemes, which do not necessarily have the same error characteristics. A generalisation to SPPT is proposed, whereby the tendency from each parametrisation scheme can be perturbed using an independent stochastic pattern. This acknowledges that the forecast errors arising from different parametrisations are not perfectly correlated. Two variations of this ‘independent SPPT’ (iSPPT) approach are tested in the Integrated Forecasting System (IFS). The first perturbs all parametrised tendencies independently while the second groups tendencies before perturbation. The iSPPT schemes lead to statistically significant improvements in forecast reliability in the tropics in medium range weather forecasts. This improvement can be attributed to a large, beneficial increase in ensemble spread in regions with significant convective activity. The iSPPT schemes also lead to improved forecast skill in the extra tropics for a set of cases in which the synoptic initial conditions were more likely to result in European ‘forecast busts’. Longer 13-month simulations are also considered to indicate the effect of iSPPT on the mean climate of the IFS.


Stochastic parameterization: Towards a new view of weather and climate models

Bulletin of the American Meteorological Society American Meteorological Society 98 (2017) 565–588-

J Berner, U Achatz, L Batté, L Bengtsson, A De la Cámara, HM Christensen, M Colangeli, DRB Coleman, D Crommelin, SI Dolaptchiev, CLE Franzke, P Friederichs, P Imkeller, H Järvinen, S Juricke, V Kitsios, F Lott, V Lucarini, S Mahajan, TN Palmer, C Penland, M Sakradzija, J-S Von Storch, A Weisheimer, PD Williams

The last decade has seen the success of stochastic parameterizations in short-term, medium-range, and seasonal forecasts: operational weather centers now routinely use stochastic parameterization schemes to represent model inadequacy better and to improve the quantification of forecast uncertainty. Developed initially for numerical weather prediction, the inclusion of stochastic parameterizations not only provides better estimates of uncertainty, but it is also extremely promising for reducing long-standing climate biases and is relevant for determining the climate response to external forcing. This article highlights recent developments from different research groups that show that the stochastic representation of unresolved processes in the atmosphere, oceans, land surface, and cryosphere of comprehensive weather and climate models 1) gives rise to more reliable probabilistic forecasts of weather and climate and 2) reduces systematic model bias. We make a case that the use of mathematically stringent methods for the derivation of stochastic dynamic equations will lead to substantial improvements in our ability to accurately simulate weather and climate at all scales. Recent work in mathematics, statistical mechanics, and turbulence is reviewed; its relevance for the climate problem is demonstrated; and future research directions are outlined.


Decomposition of a New Proper Score for Verification of Ensemble Forecasts

MONTHLY WEATHER REVIEW 143 (2015) 1517-1532

HM Christensen


Stochastic and Perturbed Parameter Representations of Model Uncertainty in Convection Parameterization*

JOURNAL OF THE ATMOSPHERIC SCIENCES 72 (2015) 2525-2544

HM Christensen, IM Moroz, TN Palmer

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