The procedure described so far actually refers to a single cycle of ANIDAS (Figure 17). However, importantly, the system can be used in an iterative manner in order to generate more accurate analysis for each time step (Figure 23).
Figure 23. Simplified diagram of the principal components of ANIDAS scheme used in an iterative manner.
The letter 𝐭 indicates time step.
The key point to note is the re-initialisation of the system which corresponds to the initialisation of ANIMo. This is done by feeding ANIMo at the current time step with the analysis produced at
82 the previous one. ANIMo can then produce a new background term for the current time and therefore trigger a new cycle. Because ANIMo is based on the solution of the 𝑂+ continuity equation (Eq. (5.11)) it has to be initialised with an ionospheric reconstruction in terms of 𝑂+. Given that method A is used, it is possible to retrieve all the coefficients that were applied to the vertical basis function to obtain the final analysis. These coefficients can be seen as scaling factors of the background model. As described in Chapter 5 ANIMo is able to provide 𝑂+, 𝑂2+, and 𝑁𝑂+ density values which are assumed to give electron density when summed. Hence, by saving the realization for the background state also in terms of 𝑂+, the latter can be scaled in order to find the analysis in terms of 𝑂+. The 𝑂+ analysis is then ready to be used to initialize ANIMo. In the next time step the background model will be more accurate as it corresponds to the modelled evolution of the previous analysis. At any time the system can perform forecasting by using the initialization to run ANIMo forward in time (routine forecasting in Figure 23).
7.3.1 Theoretical comparison between methods A and B and their usage in now-casting mode of ANIDAS
Method A, where the vertical constraint corresponds to the respective profile from the background realization, works better when the model is close to reality. Because method A uses a scaled version of the background, the resulting analysis profile can assume inaccurate profile’s shapes when the model is very far from the true state. In contrast, method B is more flexible as it uses ensembles of possible profiles generated by tuning model input parameters, hence can cope better when the background is not very accurate. In addition, the way of generating the ensemble compensates for the uncertainty in setting the model forcing parameter. The disadvantage of method B is that it must rely on data to estimate the profile even if they are generated by a physics-based model; by contrast method A relies solely upon the physical model itself. Approach B can be therefore problematic when there is no data coverage. In these cases the inversion is likely to be not reliable and therefore method B could generate misleading profile shapes. Method A also requests less computational load as it adopts the same model realization used in the DA approach as background information. In method B, the model is asked to create a series of different reconstructions which require multiple runs. This is inconvenient when ANIDAS is used in now-casting. In addition to the computational effort issue, method B is problematic in model initialization phases. Because ANIMo is based on the continuity equation of the monoatomic oxygen ion, the density of the latter is required to initialise the model in the following time step.
As mentioned in the previous section, this means that it is necessary to extract the 𝑂+ density information from the resulting DA analysis which is expressed in terms of electron density. If method A is adopted, this can be easily done by scaling ion density profiles generated by ANIMo according to the electron density analysis. The same thing cannot be performed as easily when
83 using method B because the analysis does not correspond to a scaled version of the background state.
Summary
The general aim of the presented project was to use a physics based model to support ionospheric tomography. In particular, the idea was to use the ionospheric model ANIMo to overcome the issue of the lack of data and poor vertical resolution. The first problem is due to an uneven distribution of GPS ground-based receivers on the Earth surface. In addition, there are locations where there is no data coverage, such as in the middle of the ocean. The second issue is related to the receivers-satellite arrangements, which cannot provide a surrounding scan geometry. For these specific reasons ANIMo was developed and implemented as a background model into MIDAS through a DA scheme. The scheme was created by modifying MIDAS algorithms. In this case, MIDAS cost function takes into account the modelled information generated by ANIMo (background state). In contrast with MIDAS, the DA scheme is working with residual, in other words, the minimization of the new cost function is solved for a gain value. This gain represents the correction that has to be added to the background state to have the final analysis. Working with residual raised an issue related to the handling of the GPS measurements offsets with residual values. The presented DA scheme uses MIDAS calibration that is entangled with the calculation of the final solution. It was demonstrated that MIDAS can work with residual values. An important aspect of the presented DA scheme is also the usage of a background covariance matrix. This is built by a time-dependent function that extrapolates horizontal correlation distances and coefficients from ionosonde historical data series. ANIMo is used to not only provide the background state but also for generating vertical basis functions. Their purpose is to constrain the reconstruction of the vertical electron density profiles during the inversion. This allows it to shape each profile by following the physics information of the model. Two different approaches to generate vertical basis function were developed in this project. One extrapolates them directly from the background state; the other performs a SVD over an ensemble of profiles produced by ANIMo by tuning its forcing parameters in order to simulate different possible states of the ionosphere.
Since the implementation of ANIMo involves a DA method, the presented set up can be used iteratively for performing ionospheric now-casting and eventually forecasting. This is possible by re-initializing ANIMo at every current time step of scheme with the analysis from the previous time step. At a given time, ANIMo can be initialized to run forward in the future for producing forecasting. The presented set-up in its entirety is called ANIDAS and it represents the evolution of MIDAS towards a more physic driven imaging tool and forecasting system.
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