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Science by Images

Some of our older headers tell stories about inverse problems and data assimilation.

Engineering the World: Ove Arup and the Philosophy of Total Design (V&A London Nov 2016). Art and science do not need to live on different planets. Today, much art needs and is based on science, and science includes elements of beauty, elements of art, elements of creativity! The mathematician or physicist or biologist needs creativity which is close to those of the artists, and where ever the different worlds inspire each other, we find us in a stream of deep progress and change.

Today, there are 14 centers worldwide which run operational global numerical weather prediction. These models have a quite different setup and structure, with spectral or finite element type of approaches for the simulation of the atmosphere and with different variational or ensemble data assimilation methods run to determine the current state of the atmosphere through the so-called “data assimilation cycle”. We show prediction scores for global Numerical Weather Prediction (NWP) competing with each other to get the most acurate description of the planetary atmosphere, its uncertainty and future development.

We show a visualization for a thunderstorm and the task to prepare for desaster. The goal to understand and to prepare for risk of environmental hazards is a very important task which becomes more and more important with the growing complexity of modern societies. The task includes estimation of the uncertainty of model forecasts and based on the the state estimates and their uncertainty for natural processes, their dynamic states and underlying parameters and distributions.

We show several ground based remote sensing devices as they are used to monitor the atmosphere for climate monitoring and weather prediction. You see the Swiss radar station in Payerne, a radar wind profiler which measured a profile of atmospheric winds up to 11km height and several radiometers measuring electromagnetic radiation which is emitted and diffracted by the different atmospheric layers. All devices are key ingredients of inverse problems and data assimilation in meteorology.

Celebrating James-Clerk Maxwell and the Electromagnetic Waves in the Shanghai Museum of Science. Electromagnetic waves are fundamental for our life and our environment. Visible light is known to be a small part of this spectrum, with infrared, microwave, x-rays and many further wavelength bands as key parts of today's everyday-life.

The images show the Japanese K-Computer, #1 very recently on the supercomputer List. Data assimilation experiments for global or high-resolution numerical weather prediction with 10.000 ensemble members are being carried out on this machine. Such experiments are very important for further developing operational prediction algorithms for weather and climate, in particular for estimating the uncertainty of such predictions and the risk which society faces by weather related high impact phenomena such as storms, hurricanes and floods.

Markov Chain Monte Carlo Method (MCMC) generate sequences of points which sample some probability distribution. It can be used for calculating important quantities such as the mean or variance of an unknown distribution given some prior knowledge and various measurements. The image shows different realizations of an MCMC sequence with Metropolis-Hastings sampling strategy for the posterior distribution of some two-dimensional inverse problem with a bi-modal distribution of both the prior and posterior probability density.

The image shows a comparison of Shape Reconstruction by Born approximation versus the Ortho-Sampling Method. Both methods are based on measurements of the scattered field of the scatterer in a large distance (its so-called far field pattern). They use far field patterns for many different incident waves and sample the space to reconstruct the scatterer using the displayed indicator functions.

Inverse Problems at IOP - 30 Years Celebration, August 26-28, 2014, Bristol, UK: The journal “Inverse Problems” is celebrating 30 years since the start of the journal's regular publication in 1985. The journal would like to thank all of our authors, referees, board members and supporters across the world for their vital contribution to the work and progress of Inverse Problems. Browse its webpage for information on the journal, special issue and topical review collections and our upcoming 2014 conference. The page will be updated throughout the year with more free content: news, photos and highlights articles. The Inverse Problems Special issue collection is now free to read until the end of September 2014.


The World Weather Open Science Conference 2014 is held in Montreal, Canada, August 16-21. With more than 1000 participants a good crowd of scientists meets to talk about their research, to develop their interaction and network, and to share progress in the science of weather and climate. Data Assimilation, i.e. the use of measurements to calculate the state of the atmosphere and the whole earth system is one of the key parts of the conference. Many new measurement devices are in use in both atmospheric analysis, data assimilation and climate monitoring. More infos and the whole programme can be found on the webpage is

Global Temperature reconstruction from incomplete data. You cannot measure the global temperature at all places at the same time. But it is very important to calculate the temperature distribution on the whole globe - for climate monitoring as well as for weather forecasting. Only when we know the key global variables like pressure, wind, humidity and temperature, we can calculate a weather forecast, we are able to estimate the risk of high-impact events (like storms, hail, strong rain and floods) and we can monitor potential threads like nuclear desasters, which are distributed by atmospheric winds.

The world turned around - Exhibition in Marseille, France, Summer 2014. The world inversed. Calculating backwards. Inverting data. Calculating unknown quantities. That is what inverse problems is about. Looking into what is not directly accessible. Reconstructing sources. Reconstructing unknown causes of action. Reconstructing scatterers when waves are scattered. Can you hear the shape of a drum from its particular sound? Different examples of inverse problems - one of the most fascinating research areas currently.

Recent progress for mathematical and numerical analysis of inverse problems has been discussed at the mathematical research centre CIRM, Marseille, May 18-23, 2014 Web. With around 90 participants, covering important parts of the field of inverse problems, the meeting reflected the state of the art of the mathematical theory of inverse problems. It includes results on uniqueness, stability and algorithmic efficiency.

International Symposium on Data Assimilation, LMU Munich 24.-28.2.2014 Website at LMU. The Symposium had more than 200 Participants and combined four days of invited talks and discussions on Data Assimilation both on the global and the regional scale in the area of weather and climate with a workshop of the European COST Action ES1206 “GNSS4SWEC” (see on GPS/GNSS Data in Weather and Climate and a KENDA Mini-Workshop (Programme PDF) on kilometer-scale ensemble data assimilation.

Medical Imaging investigates processes in the brain by techniques like MRI, EEG, MEG and many more. Dynamical models based on finite element approaches are married with data by inversion and data assimilation. (Images by Ingo Bojak, Reading.)

Magnetic Tomography: we show a magnetic sensor recording the field of the current distribution within a fuel cell. The forward operator is given by the Biot-Savart integral \begin{equation} H(x) = \frac{1}{4\pi} \int_{\Omega} \frac{j(y) \times (x-y)}{|x-y|^3} \; dy, \;\; x \in \mathbb{R}^3 \end{equation} The reconstruction of the currents is shown in the right image. The inversion needs to solve an integral equation of the first kind, where $H(x)$ is measured on some outer surface and $j(y)$ is to be reconstructed.

Satellite remote sensing of the atmosphere is an indispensible tool today to monitor the atmosphere and calculate initial states which is used for weather predictions. Many different other remoste sensing techniques are used, for example radar based wind profiler, and cloud radar. In the third image, we show a weather radar operated by the University of Bonn. Also, networks of lidars are used today to monitor the atmospheric aerosol. We show a ceilometer profile of the atmospheric boundary layer (approx. 0-2km height), as recorded by the observatory in Hohenpeißenberg, sourthern Germany.

Reconstructions of scatterers using orthogonality sampling; simulation/reconstruction of a flow field, eigenfunctions of the Laplacian on the sphere.

Image reconstruction from noisy data is an important inverse problem. Here, we also show a picture taken on the Hannover Industrial Fair, where Electrical Impedance Tomography (EIT) on trees has been presented to a wider public. The last image displays a feasibility study of the “No Response Test” applied to Magnetic Tomography.

imag8852smsm.jpg imag8759smsm.jpg imag8853smsm.jpg

We show images taken during a special semester on “inverse problems” at the Isaak Newton Institute at Cambridge, UK, in 2011.

There is a growing number of meetings on both inverse problems and data assimilation. The different communities have their own interaction and language. But there is also some convergence, while techniques and tools are used both in mathematical and engineering communities and important application areas.

Various remote sensing data are used to control dynamical systems simulations and forecasts for atmospheric applications. The electromagnetic waves in the infrared and microwave range which are radiated by the atmosphere are measured on satellites. This leads to highly ill-posed inverse problems, which are treated by variational or ensemble methods and assimilated into atmospheric models. Radar measurements (indicated by the circles surrounding radar stations in central Europe) are used to measure precipitation and radial winds. The inverse scattering type measurements are used for atmospheric forecasting. The images on the right show a forecast by the COSMO-DE model over Germany, which is developed by Switzerland, Germany, Italy, Russia, Poland, Romania and Greece.

WMO Symposium on Data Assimilation Oct 7-11, 2013 at the University of Maryland, USA

Data assimilation is about using data in dynamical systems such as weather simulations. The field has grown from applications in meteorology and geophysics. Here, the World Meteorological Organization plays a key role, since it combines many national weather services which work together in sharing data on a global scale and running various programs to support the science as well as the operational work which provides services to all our states and communities.


The display of temperature fields in the atmosphere during deep convection (left). The distributions are simulated using numerical models on supercomputers as on the NEC SX9, shown in image no. 2. Sea surface temperature fields are calculated by inverse techniques over the oceans and used by data assimilation in numerical models (image 3). Scientific meetings are essential in developing these methods, image 4 shows a snapshot from the International Symposium on Data Assimilation in Offenbach in 2012. The distribution of temperature, winds and pressure (and other quantities) is simulated by data assimilation techniques and then forecasted (image 5). To this end various measurements such as radar measurements (last image; on the right) are employed.


misc.txt · Last modified: 2017/02/05 18:51 by potthast