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Artifacts and limitations in the plots

We have already noted some of the limitations of the DREAM electron flux output. They include:

  • Use of an assumed isotropic pitch angle distribution for the GOES data
  • Limits due to fitting a spectrum to only two GOES integral energy channels
  • A simplifying assumption of dipole L in converting from PSD to flux which is inconsistent with the T89 model L* used when converting the initial flux measurements to PSD.
  • Limits on the range of L-shells for which flux can be calculated. This is due to the limited range of µ and K values chosen for the assimilations
  • None of these limitations is a fundamental limitation of the DREAM model. The choice of the range of µ and K values can be changed as can the number of µ-K pairs (currently 25). Since a separate assimilation needs to be done for each µ-K pair there are computational limits but it should be possible to increase the range and number of µ and K values significantly while still fitting the computational limitations of a simple desktop computer.

    Other limitations and artifacts come from the use of a single satellite as a source of data for the assimilation. Because of the asymmetry of the magnetic field, a geosynchronous satellite at fixed altitude still samples different drift shells (denoted by L*) on the day side and night side of the Earth. This diurnal variation of the L* sampled by GOES is most readily seen in the Phase Space Density plots but ruminants extend to the Flux plots also.

    It is almost always true that the phase space density across the range of L-shells sampled by GOES in a single orbit is not constant but, rather, exhibits a radial gradient. When higher PSDs are measured their effects diffuse inward and outward in the model. When lower PSDs are measured their effects also propagate. This often creates “stripes” of higher or lower PSD that propagate to higher or lower L-shells. What it means physically is that radial diffusion cannot reproduce the PSD gradient that exists between the L*-shells measured at noon and midnight. In fact the existence of these artifacts provides important information on the sign and the magnitude of PSD gradients near geosynchronous orbit. We also note that the actual PSD gradients can be a function of µ and/or K and therefore the diurnal artifacts can appear differently for different values of µ and K.

    We note that assimilating data from multiple geosynchronous satellites that sample different L-shells simultaneously reduces or eliminates these diurnal artifacts. Two (or more) geosynchronous satellites can measure the PSD gradient directly and include it properly in the model.

    The artifacts of diurnal variations can still be seen in the flux data even at energies (i.e. 2 MeV) that were measured in the original input. There are two reasons for this. One is the current mismatch between the magnetic field model used to convert flux to PSD and the field model used to convert back from PSD to flux. The other is more subtle. At any point in space the flux at fixed energy and fixed pitch angle must be reconstructed from interpolated values of discrete µ and K values. Since the artifacts in the PSD calculations can be different for different µ-K pairs and the flux at any given time and location needs to interpolate between different µ and K values, the artifacts do not “cancel out”.

    Future versions of the DREAM web services will use the same magnetic field model in all calculations. Some artifacts will remain if flux is calculated at an arbitrary position but if we calculate flux at the location of the input GOES data we should be able to reproduce the original measurements with high accuracy. A measure of this accuracy tests the numerics but also tests the effects of spectral fitting or the assumption of isotropic pitch angle distributions.

    It is also possible to use a single GOES satellite as input and a different GOES satellite as a validation data set. Using the LANL-GEO observations we assimilate multiple geosynchronous satellites (reducing diurnal artifacts) and still have one or more geosynchronous satellites for validation. With proper validation data sets we can quantitatively test the errors introduced by different simplifying assumptions or by limited data availability.

    Figure 6:This figure shows PSD values from the DREAM assimilation using geosynchronous and GPS observations (top) and compares it with an assimilation using only geosynchronous observations (panel 2). The remaining panels show the ratio of PSD values obtained from the two model runs, and the Dst index. This figure is illustrative of the types of tests that can be conducted to determine where and when the models perform best. Similar tests can quantify the uncertainties (or errors) in the model as a function of energy, pitch angle, spatial location, and/or geomagnetic activity. Such studies will be conducted in the near future.

    An example of one quantitative test using PSD values is shown in the figure above. In the top panel we have used three geosynchronous satellites and one GPS satellite in the assimilation. We show near-equatorial K values which GPS samples only close to 4 RE. In the second panel we conduct the same assimilation with the same assumptions but without GPS observations. Next we show the ratio of the two assimilation results for this µ-K pair on a log scale. Geomagnetic activity (Dst) is plotted in the bottom panel. As we can see, using geosynchronous observations alone produces PSD values that can be too high by a factor of 100 or too low by a factor of 10.

    We have done similar tests for larger K values (which also extends the L* range of available GPS observations) and found that using geosynchronous data alone generally produces the largest errors inside L≈5. We have also done similar comparisons of assimilations with and without POLAR observations outside geosynchronous orbit and find that the assimilations reproduce PSD values outside geosynchronous orbit surprisingly well.

    It is important to note that true validation should be done on flux values rather than on PSD values. These initial comparisons are illustrative of what could be done and where the largest errors are expected. Some initial, quantitative validations of fluxes from DREAM has been published in the AMOS conference proceedings [Reeves et al., 2008].

    The DREAM beta web service also has limitations on times that are available. The beta web service was developed specifically for real time data and real time specifications (nowcasts). This means that it is not currently simple to request a specific period of time or to store a database of values that spans many years. We are currently re-working the codes in order to make it possible to run a DREAM assimilation for a user-selectable period of time and a user-selectable set of available satellite data sets as either input or validation. We are currently working with the Air Force Space Weather Forecast Laboratory (SWFL) and NASA’s Community Coordinated Modeling Center (CCMC) to perform more extensive validations once the greater flexibility is available.

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