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Investigating satellite radiance data assimilation at different scales in an idealised convective modelling framework

Prof. Onno Bokhove (SOM), Prof. Steve Tobias

Project partner(s): Met Office (potential CASE)

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Satellite radiance assimilation has proved its worth in recent decades, contributing to many improvements in numerical weather prediction (NWP) performance. Improvements in data assimilation techniques in turn enable the maximum value to be extracted from the significant investment being made in current and future satellite instruments. Recent advances mean that large-scale features are generally well represented and attention is turning now to the less-accurate small-scale features that are critical to the success of convective-scale NWP. This leads to the strategically important question of whether it is more beneficial to focus on correcting the remaining small errors in the large scales of the “dry ” analysis (the model state obtained by merging recent observational data with a previous forecast that is used to start the next forecast) or whether attention should instead focus on the larger errors in the small-scale features of the moist flow. The large-scale errors influence the arrival time of low-pressure and frontal systems and directly affect the model’s ability to retain the benefits of assimilated information, particularly humidity. The small-scale errors, on the other hand, affect the initiation of convection and rainfall events.

The expense and complexity of operational NWP and radiative transfer computer codes limits the number of research experiments that can be conducted into finding improved modelling and assimilation approaches. Idealised models, on the other hand, are much less expensive and can be run on desktop computers [1,3].

Idealised model: Recent PhD work [2,3,4] at the University of Leeds by Thomas Kent, supervised by Onno Bokhove and Steve Tobias (University of Leeds) with Gordon Inverarity (Met Office), has demonstrated the potential of a shallow-water model, modified to simulate convection and precipitation, to assimilate simulated conventional observations within an ensemble Kalman filter. The model exhibits slow and fast timescales associated with frontal dynamics and inertia-gravity waves, respectively, and the shock and non-negativity preserving (of rain mass fraction and density) numerical solver [2,4,5] allows convective-scale processes to be modelled without the problems usually associated with numerical dissipation in NWP models. We now propose extending this forecast/assimilation system to assimilate simulated satellite radiance observations at different length-scales. In addition, to facilitate the transfer and the use of the software developed, we have obtained EPSRC Impact-accelerator funding for four months, through the University of Leeds, for Thomas Kent to embed his model within the open EMPIRE data assimilation environment at the University of Reading.


An idealised radiative transfer model will be constructed based on the modified shallow water equations’ geopotential height, horizontal velocity and rainfall. This will use the fact that the equations are incompressible so the temperature is proportional to the geopotential height. The brightness temperature can then be modelled by treating the fluid as a black body using the Rayleigh-Jeans law. Large- and small-scale observations can then be generated by adding random and/or systematic noise to simulated observations from a nature run using a truth configuration of the model and averaging the resulting high-resolution simulated observations to simulate the pixel size of interest.

Potential for high impact outcome

The effect of observing different length-scales and different variables will be investigated by examining the idealised model’s large-scale geopotential height variable and small-scale rain mass fraction variable. As well as using the large- and small-scale simulated observations described above, the impact of observing large-scale variables, such as the diagnosed temperature, on the rain mass fraction via the ensemble covariance can be compared with the impact of directly observing rain. The model can be configured to exhibit both large-scale frontal rain with suitable forcing or initial conditions as well as small-scale convection, cloud and rainfall to study the benefits of the different approaches in a variety of weather conditions. A possible further extension would be to address the question of how best to treat biases in the radiance observations at different length scales

Having an idealised experimental framework that allows different modelling and assimilation techniques to be tested and tuned by running multiple combinations of parameter choices simultaneously will allow viable techniques to be sifted to inform the Met Office’s choice of experiments to be run in an operational NWP configuration.

Work Plan

In the first year, the student will become familiar with the theory of ensemble Kalman filtering and satellite radiance assimilation and replicate Thomas Kent’s idealised ensemble Kalman filter experiments assimilating simulated conventional observations using the modified shallow water equations. The second year will focus on developing an idealised radiative transfer model, extending the software to assimilate simulated satellite radiance observations and tuning a suitable observational configuration. In the third year, experiments will be run to compare the impact of assimilating different observation types on different scales in a variety of simulated weather conditions. The final (half) year will focus on the preparation and submission of the PhD thesis. The student will  collaborate with staff in the Data Assimilation and Ensembles and Satellite Applications teams in Weather Science.


The School of Mathematics in Leeds is strongly committed to ensuring that all PhD students receive a broad and sound subject-related and generic skills training, maintained as an indispensible part of a PhD degree complementing first-class quality research. This approach is vital in order to keep the PhD programmes competitive in the national and international arena, and to ensure that a PhD awarded in the School of Mathematics at Leeds is a recognised guarantee of an independent and highly qualified researcher.

Policy & Arrangements. Within one month of arrival, each student must agree a one-year training plan with their supervisor(s) at Leeds and the Met Office, which includes academic (subject-related) courses as well as generic skills training. An agreed plan is signed and kept on an online monitoring system, along with subsequent records of completion of training, and is reviewed/updated at each assessment meeting with the student (e.g., 6- and 12-month viva). Moreover, the student will acquire transferable skills such as presentation techniques and writing skills.

Knowledge transfer: Regular contact with Met Office staff will enable the academic partners to understand their work from a more operational and user-oriented point of view.

Student profile

The student should have a strong background in a quantitative science (math, physics, engineering, environmental sciences) and a flair for, and good familiarity with, programming and scientific computing.

CASE Partner

The proposal has been agreed as a “Partnership Project” (a potential CASE project) with the UK Met Office. Until CASE funding is obtained, the Met Office will give indirect contribution to the project by providing facilities and equipment and supervision time by its staff.


[1] G.W. Inverarity 2015: Quasi-static estimation of background-error covariances for variational data assimilation. Q. J. R. Meteorol. Soc., 141, 752–763.

[2] T. Kent, O. Bokhove, and S. Tobias 2016: A modified shallow water model for investigating convective scale data assimilation. Under revision prior to resubmission.

[3] T. Kent, O. Bokhove, S. Tobias, and G. Inverarity 2016:  Ensemble Kalman filter data assimilation for a modified shallow water model with convection. In preparation.

[4] T. Kent, S. Tobias, and O. Bokhove 2016: On a non-negativity preserving flux solver for a modified shallow water model with a rain mass fraction. Technical note. In preparation for a computational journal.

[5] S. Rhebergen, O. Bokhove, and J. van der Vegt, 2008: Discontinuous Galerkin finite element methods for hyperbolic nonconservative partial differential equations. J. Comp. Phys., 227 (3), 1887-1922.

Related undergraduate subjects:

  • Engineering
  • Meteorology