# Publications by Fenwick Cooper

## Oceanic stochastic parametrizations in a seasonal forecast system

Monthly Weather Review American Meteorological Society **144** (2016) 1867-1875

Stochastic parametrization provides a methodology for representing model uncertainty in ensemble forecasts. Here we study the impact of three existing stochastic parametrizations in the ocean component of a coupled model, on forecast reliability over seasonal timescales. The relative impacts of these schemes upon the ocean mean state and ensemble spread are analyzed. The oceanic variability induced by the atmospheric forcing of the coupled system is, in most regions, the major source of ensemble spread. The largest impact on spread and bias came from the Stochastically Perturbed Parametrization Tendency (SPPT) scheme - which has proven particularly effective in the atmosphere. The key regions affected are eddy-active regions, namely the western boundary currents and the Southern Ocean where ensemble spread is increased. However, unlike its impact in the atmosphere, SPPT in the ocean did not result in a significant decrease in forecast error. Whilst there are good grounds for implementing stochastic schemes in ocean models, our results suggest that they will have to be more sophisticated. Some suggestions for next-generation stochastic schemes are made.

## Optimisation of an idealised ocean model, stochastic parameterisation of sub-grid eddies

OCEAN MODELLING **88** (2015) 38-53

## The character of polar tidal signatures in the extended Canadian Middle Atmosphere Model

Journal of Geophysical Research: Atmospheres Wiley **119** (2014) 5928-5948

The characteristics of the diurnal, semidiurnal, and terdiurnal tides (zonal wave numbers -5 to +5 in temperature and zonal wind) in the polar mesosphere and lower thermosphere region as simulated by the extended Canadian Middle Atmosphere Model are examined. The most significant diurnal, semidiurnal, and terdiurnal tides in the polar regions are Ds0, Dw1, and De1; Sw3, Sw2, Sw1, Ss0, Se1, and Se2; and Tw3, Ts0, and Tw1, respectively, and their latitudinal structures, seasonal variations, and hemispheric asymmetries noted. Of these components, Ds0, Tw1, Ts0, and Tw3 exhibit a seasonally symmetric variation with both hemispheres strengthening simultaneously. On the other hand, Dw1 strengthens asymmetrically so that when one hemisphere is strong, the other is weak. The remainder show no seasonal tendency but vacillate on shorter than seasonal time scales in a symmetric or antisymmetric manner at different times of the year. Global-scale correlations of the amplitudes of the migrating tides Dw1/Sw2 and the stationary planetary wave 1 and the assumed “child” nonmigrating tides are also examined. The results indicate that the correlations are highly time scale-dependent and the significant correlations seen with the original time series are mainly due to longer-term variations (>18 days). There are no consistent global correlations associated with the short-term variations (<18 days) among these waves.

## Estimation of the local response to a forcing in a high dimensional system using the fluctuation-dissipation theorem

Nonlinear Processes in Geophysics **20** (2013) 239-248

The fluctuation-dissipation theorem (FDT) has been proposed as a method of calculating the response of the earth's atmosphere to a forcing. For this problem the high dimensionality of the relevant data sets makes truncation necessary. Here we propose a method of truncation based upon the assumption that the response to a localised forcing is spatially localised, as an alternative to the standard method of choosing a number of the leading empirical orthogonal functions. For systems where this assumption holds, the response to any sufficiently small non-localised forcing may be estimated using a set of truncations that are chosen algorithmically. We test our algorithm using 36 and 72 variable versions of a stochastic Lorenz 95 system of ordinary differential equations. We find that, for long integrations, the bias in the response estimated by the FDT is reduced from ∼75% of the true response to ∼30%. © 2013 Author(s).

## Statistical analysis of global variations of atmospheric relative humidity as observed by AIRS

Journal of Geophysical Research: Atmospheres American Geophysical Union (AGU) **117** (2012) n/a-n/a

## Climate Sensitivity via a Nonparametric Fluctuation–Dissipation Theorem

Journal of the Atmospheric Sciences American Meteorological Society **68** (2011) 937-953

<jats:title>Abstract</jats:title> <jats:p>The fluctuation–dissipation theorem (FDT) has been suggested as a method of calculating the response of the climate system to a small change in an external parameter. The simplest form of the FDT assumes that the probability density function of the unforced system is Gaussian and most applications of the FDT have made a quasi-Gaussian assumption. However, whether or not the climate system is close to Gaussian remains open to debate, and non-Gaussianity may limit the usefulness of predictions of quasi-Gaussian forms of the FDT. Here we describe an implementation of the full non-Gaussian form of the FDT. The principle of the quasi-Gaussian FDT is retained in that the response to forcing is predicted using only information available from observations of the unforced system, but in the non-Gaussian case this information must be used to estimate aspects of the probability density function of the unforced system. Since this estimate is implemented using the methods of nonparametric statistics, the new form is referred to herein as a “nonparametric FDT.” Application is demonstrated to a sequence of simple models including a stochastic version of the three-component Lorenz model. The authors show that the nonparametric FDT gives accurate predictions in cases where the quasi-Gaussian FDT fails. Practical application of the nonparametric FDT may require optimization of the method set out here for higher-dimensional systems.</jats:p>

## Transverse waves in a post-flare supra-arcade

Astronomy & Astrophysics EDP Sciences **430** (2005) L65-L68

## Short period fast waves in solar coronal loops

Astronomy & Astrophysics EDP Sciences **409** (2003) 325-330