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.

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

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


A Weisheimer, D Handorf, K Dethloff

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.

Niederfrequente Variabilität großräumiger atmosphärischer Zirkulationsstrukturen in spektralen Modellen niederer Ordnung. Reports on Polar Research.

AWI (2000) 356

A Weisheimer

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.