Gradient free descent: Shadowing, and state estimation using limited derivative information

Physica D: Nonlinear Phenomena 190 (2004) 153-166

K Judd, L Smith, A Weisheimer

Shadowing trajectories can play an important role in assessing the reliability of forecasting models, they can also play an important role in providing state estimates for ensemble forecasts. Gradient descent methods provide one approach for obtaining shadowing trajectories, which have been shown to have many useful properties. There remains the important question whether shadowing trajectories can be found in very high-dimensional systems, like weather and climate models. The principle impediment is the need to compute the derivative (or adjoint) of the system dynamics. In this paper we investigate gradient descent methods that use limited derivative information. We demonstrate the methods with an application to a moderately high-dimensional system using no derivative information at all. © 2003 Elsevier B.V. All rights rserved.

Radar-echo tracking by use of invariant moments.

Appl Opt 42 (2003) 5891-5896

M Andrejczuk, S Moszkowicz, KE Haman, T Szoplik

A number of techniques to track rainfall patterns by use of radar observations have been developed over the years. We present a method for radar-echo tracking based on Hu invariant moments. The method has been tried on several sequences of test images, and the derived displacement fields were in good agreement with the real motions of the tested objects. For the real data obtained from the conventional meteorological radar in Legionowo the method occasionally failed when changes in the radar echo between observations were too large.

Predictability of weather and climate: From theory to practice - From days to decades


TN Palmer

Extratropical low-frequency variability in a three-level quasi-geostrophic atmospheric model with different spectral resolution

Journal of Geophysical Research D: Atmospheres 108 (2003)

A Weisheimer, MV Kurgansky, K Dethloff, D Handorf

Apart from variations of external forcing components and interactions between climate subsystems, natural atmospheric fluctuations with periods of years, decades and centuries can also be generated by inherent atmospheric dynamical instabilities of the flow. The objective of this study is to investigate the spatial and temporal structure of internal low-frequency atmospheric variability of the Northern Hemisphere using a minimum-complexity model of the extratropical circulation. Here, the main focus is the influence of varying spectral horizontal resolution on the formation of dominant patterns of variability. For this purpose, a three-level quasi-geostrophic atmospheric model with idealized thermal and orographic forcing has been integrated over 1,000 years under perpetual winter conditions with T5, T10, T15, and T21 resolutions. It has been shown that for the crude resolution T5 a rather strong bias occurs, whereas starting with T1O resolution, the nonlinear feedback between large- and small-scale features is reasonably well described. At this resolution a sort of plateau in the model performance has been reached, in respect to both the model climatology and the spatiotemporal structure of variability. Ultralow-frequency variability is most pronounced in the model's stratosphere and is associated with changes in the polar vortex strength and shape caused by vertically propagating planetary waves. Rossby wave trains in the lee of the model large-scale orography are the most dominant structures of long-period fluctuations in the middle troposphere. The results show that interannual- and decadal-scale variations can, in substantial part, be considered as a manifestation of the natural variability of the extratropical atmosphere. The inclusion of a seasonal cycle of the model's diabatic heating increases the interannual and interdecadal variability.

Validation of water vapour profiles from GPS radio occultations in the Arctic


M Gerding, A Weisheimer

Forcing singular vectors and other sensitive model structures


J Barkmeijer, T Iversen, TN Palmer

Benefits of increased resolution in the ECMWF ensemble system and comparison with poor-man's ensembles


R Buizza, DS Richardson, TN Palmer

Potential improvement to forecasts of two severe storms using targeted observations


M Leutbecher, J Barkmeijer, TN Palmer, AJ Thorpe

The economic value of ensemble forecasts as a tool for risk assessment: From days to decades


TN Palmer

Quantifying the risk of extreme seasonal precipitation events in a changing climate.

Nature 415 (2002) 512-514

TN Palmer, J Räisänen

Increasing concentrations of atmospheric carbon dioxide will almost certainly lead to changes in global mean climate. But because--by definition--extreme events are rare, it is significantly more difficult to quantify the risk of extremes. Ensemble-based probabilistic predictions, as used in short- and medium-term forecasts of weather and climate, are more useful than deterministic forecasts using a 'best guess' scenario to address this sort of problem. Here we present a probabilistic analysis of 19 global climate model simulations with a generic binary decision model. We estimate that the probability of total boreal winter precipitation exceeding two standard deviations above normal will increase by a factor of five over parts of the UK over the next 100 years. We find similar increases in probability for the Asian monsoon region in boreal summer, with implications for flooding in Bangladesh. Further practical applications of our techniques would be helped by the use of larger ensembles (for a more complete sampling of model uncertainty) and a wider range of scenarios at a resolution adequate to analyse average-size river basins.

Model error in weather forecasting

Nonlinear Processes in Geophysics 8 (2001) 357-371

D Orrell, L Smith, J Barkmeijer, TN Palmer

Operational forecasting is hampered both by the rapid divergence of nearby initial conditions and by error in the underlying model. Interest in chaos has fuelled much work on the first of these two issues; this paper focuses on the second. A new approach to quantifying state-dependent model error, the local model drift, is derived and deployed both in examples and in operational numerical weather prediction models. A simple law is derived to relate model error to likely shadowing performance (how long the model can stay close to the observations). Imperfect model experiments are used to contrast the performance of truncated models relative to a high resolution run, and the operational model relative to the analysis. In both cases the component of forecast error due to state-dependent model error tends to grow as the square-root of forecast time, and provides a major source of error out to three days. These initial results suggest that model error plays a major role and calls for further research in quantifying both the local model drift and expected shadowing times.

Dynamical seasonal predictability of the Asian summer monsoon

MONTHLY WEATHER REVIEW 129 (2001) 2226-2248

KR Sperber, C Brankovic, M Deque, CS Frederiksen, R Graham, A Kitoh, C Kobayashi, T Palmer, K Puri, W Tennant, E Volodin

A nonlinear dynamical perspective on model error: A proposal for non-local stochastic-dynamic parametrization in weather and climate prediction models


TN Palmer

Tropical singular vectors computed with linearized diabatic physics


J Barkmeuer, R Buizza, TN Palmer, K Puri, JF Mahfouf

A probability and decision-model analysis of a multimodel ensemble of climate change simulations

JOURNAL OF CLIMATE 14 (2001) 3212-3226

J Raisanen, TN Palmer

On the structure and variability of atmospheric circulation regimes in coupled climate models


A Weisheimer, D Handorf, K Dethloff

Ensemble prediction of tropical cyclones using targeted diabatic singular vectors


K Puri, J Barkmeijer, TN Palmer

On the structure and variability of atmospheric circulation regimes in coupled climate models

Atmospheric Science Letters 2 (2001)

A Weisheimer, D Handorf, K Dethloff

In order to investigate whether climate models of different complexity have the potential to simulate natural atmospheric circulation regimes, 1000-year-long integrations with constant external forcing have been analysed. Significant non-Gaussian uni-, bi-, and trimodal probability density functions have been found in 100-year segments. © 2001 Royal Meteorological Society.

Arctic and Antarctic ozone layer observations: Chemical and dynamical aspects of variability and long-term changes in the polar stratosphere

Polar Research 19 (2000) 193-204

M Rex, K Dethloff, D Handorf, A Herber, R Lehmann, R Neuber, J Notholt, A Rinke, P von der Gathen, A Weisheimer, H Gernandt

The altitude dependent variability of ozone in the polar stratosphere is regularly observed by balloon-borne ozonesonde observations at Neumayer Station (70°S) in the Antarctic and at Koldewey Station (79°N) in the Arctic. The reasons for observed seasonal and interannual variability and long-term changes are discussed. Differences between the hemispheres are identified and discussed in light of differing dynamical and chemical conditions. Since the mid-1980s, rapid chemical ozone loss has been recorded in the lower Antarctic stratosphere during the spring season. Using coordinated ozone soundings in some Arctic winters, similar chemical ozone loss rates have been detected related to periods of low temperatures. The currently observed cooling trend of the stratosphere, potentially caused by the increase of anthropogenic greenhouse gases, may further strengthen chemical ozone removal in the Arctic. However, the role of internal climate oscillations in observed temperature trends is still uncertain. First results of a 10 000 year integration of a low order climate model indicate significant internal climate variability, on decadal time scales, that may alter the effect of increasing levels of greenhouse gases in the polar stratosphere.

North Atlantic oscillation: Diagnosis and simulation of decadal variability and its long-period evolution

Izvestiya - Atmospheric and Ocean Physics 36 (2000) 555-565

II Mokhov, AV Eliseev, D Handorf, VK Petukhov, K Dethloff, A Weisheimer, DV Khvorost'yanov

Two 1000-year numerical experiments based on the IFA RAN global climate model, the first with completely interacting atmosphere and ocean and the second with a fixed climatic mean annual cycle of sea surface temperature, are analyzed. In both cases, a quasi-decadal cyclicity (QDC), but with substantially different amplitude-frequency characteristics, is detected for the North Atlantic Oscillation (NAO) in winter. Significant changes in the QDC regimes from one century to another are observed in the model. A comparison of the numerical results with empirical data and reconstructions reveal a fairly good agreement of the QDC amplitude and periods for winter NAO regimes in the model with completely interacting atmosphere and ocean for individual model subperiods on the order of a century. The model results suggest that interdecadal NAO variations of natural origin can be noticeably strengthened in the climate system without any influence of external, in particular, anthropogenic factors. In the case of a fixed annual cycle of SST, the QDC amplitudes are underestimated several times by the model, and no positive correlation is observed between the amplitudes and periods of the NAO QDC in contrast to the empirical data, reconstructions, and the model with completely interacting atmosphere and ocean.