Research Projects

  • Representation of uncertainty in climate models.

Stochastic parametrisations are designed to represent uncertainty in atmospheric models due to the unpredictability of unresolved small-scale processed. While they are widely used in the weather and seasonal forecasting communities, their potential in climate prediction is only beginning to be explored. However, theory indicates that stochastic perturbations could influence the climate of a model due to the non-linear nature of the Earth-system.

I have performed some of the first analysis considering the impact of stochastic schemes from the weather forecasting community in a world-leading climate model. We find a substantial improvement in the representation of the El Niño-Southern Oscillation (ENSO) in the ‘CESM’ climate model, due to an improved response of the winds in that model to small changes in sea surface temperature. There has been widespread interest in this development: our paper was awarded the Lloyds ‘Science of Risk’ prize for its relevance to the insurance industry.

Through research carried out under the EU Horizon 2020 PRIMAVERA project, we have also identified a substantial improvement in ENSO in the European ‘EC-Earth’ model on including stochastic schemes. Stochastic parameterisations could be the breakthrough needed to accurately represent ENSO in the next generation of climate models.

Niño 3.4 power spectrum. (a) Observations. (b) Control (c) Model with stochastic parametrisation scheme. From Christensen et al, 2017, J. Climate

Relevant publications:
Roberts, M. J., et al (17 authors including Christensen, H. M.). ‘The benefits of global high-resolution for climate simulation: process-understanding and the enabling of stakeholder decisions at the regional scale’. Submitted to Bull. Amer. Met. Soc.
Davini, P., et al (9 authors including Christensen, H. M.), 2017, Geosci. Model Dev. 10, 1383-1401
Christensen, H. M., Berner, J., Coleman, D., and Palmer, T. N., 2017. J. Climate. 30, 17–38.

  • Idealised dynamical systems as an analogue for the Earth system

There are many benefits of performing proof of concept experiments using idealized dynamical systems. Simple chaotic systems are transparent and computationally cheap, but can mimic certain properties of the atmosphere. Simple dynamical systems provide a useful testbed for assessing new ideas in probabilistic forecasting or model development, such as new stochastic parametrisation schemes, or the use of machine learning to derive emulators for unresolved processes. Using simple dynamical systems in parallel with full Earth-system models can also provide important insight, enabling complex mechanisms to be unpicked. For example, a simple Delayed Oscillator model of the El Niño-Southern Oscillation (ENSO) can provide insight into the impact of stochastic perturbations on ENSO in a comprehensive coupled climate model.

Relevant publications:
Christensen, H. M., Berner, J., Coleman, D., and Palmer, T. N., 2017. J. Climate. 30 (1), 17–38
Christensen, H. M., Moroz, I. M. and Palmer, T. N., 2015b, Climate Dynamics. 44 (7-8) 2195–2214
Arnold, H. M., Moroz, I., and Palmer, T. N., 2013, Phil. Trans. Roy. Soc. A, 371 (1991).

  • Characterising uncertainty in Earth-system models

There are several sources of uncertainty when forecasting the future state of the Earth-system. I am particularly interested in model uncertainty, whereby limitations in the forecast model result in errors in the forecast. How can we characterise this source of uncertainty?

I have proposed a novel coarse-graining technique whereby very high resolution simulations are combined with a low-resolution single-column forecast model to explicitly measure the ‘error’ in the forecast model that any representation of model uncertainty must account for. Using such a technique led to a simple-to-implement but conceptually interesting improvement to the widely used “SPPT” stochastic parametrisation scheme. In the standard version of the scheme, each parametrised sub-grid process is treated the same, but my coarse-graining work suggests each scheme should be treated independently. This scheme is now an available feature in the operational ECMWF forecast model, where it leads to substantial improvements in weather forecasts in the tropics.

Relevant publications
Christensen, H. M., Dawson, A., and Holloway, C. ‘Forcing single column models using high-resolution model simulations.’ Submitted to JAMES.
Christensen, H. M., Lock, S.-J., Moroz, I. M. and Palmer, T. N., 2017, Q J Roy Meteor Soc, 143(706), 2168–2181
Leutbecher, M., et al. (28 authors, including Christensen, H. M.)., 2017, Q J Roy Meteor Soc, 143(707), 2315–2339

  • Verification of probabilistic forecasts.

Having produced a forecast for an event, the accuracy of the forecast must be verified. Scoring rules provide a statistical framework for forecast verification. While there are many ‘proper’ (or unbiased) scoring rules available for forecast verification, different scores are sensitive to different properties of the forecast. I developed a new proper score (the ‘Error-spread score’) for evaluation of ensemble forecasts. The score is particularly sensitive to forecast reliability, and so is useful when evaluating and comparing different representations of model uncertainty. ECMWF have recently adopted the Error-spread Score into their operational forecast verification suite.

Relevant publications
Christensen, H. M., 2016. J. R. Statist. Soc. B, 78 (3), 505–562.
Christensen, H. M., 2015. Mo. Weath. Rev., 143, 1517–1532.
Christensen, H. M., Moroz, I. M., and Palmer, T. N., 2015a. Q J Roy Meteor Soc, 141, 538–549.