Run Time Error 6197 Word
Finnis Springer
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The paper focusses on the description of the algorithms which are not
new but when applied to this specific model setup may have potential
to investigate specific issues of the formulation, setup, tuning and
characteristics of data assimilation systems. Studies of simplified
models can provide considerable insight into the performance of data
assimilation algorithms under specific conditions and thus I think it
is worth describing the system in a scientific paper.
The description of the implementation is outlined very clearly and
detailed and is reproducible. Indeed I think that some passages
may be shortened without loss of information. Maybe the authors could
try to strengthen the text in this sense.
The performance of the system is outlined by example of a simulation
encountering tropical convection. This is certainly a very specific
application and in order to allow the reader to grasp the situation it
would be nice to give more information on the case and the setup:
Good, the described data assimilation algorithms algorithms are not
new but there implementation in this specific toy-model setup has
potential to study details of the data assimilation setup and
application to specific situations.
Fair, The methods are well described. The description experimental
setup would improve with some more details given. The setup of the
illustrative test case could gain from further informations and
discussion of the tuning parameters involved.
The authors state that it is possible to achieve inter-variable
localisation within this setup. I think it should be mentioned that
the strength of ensemble systems is to provide reasonable
time-dependent inter-variable correlations and that therefore one
should have good reasons to apply inter-variable localisation in
praxis.
The author state that L_horiz has been found to be not positive
definite if the length scale is too large (localisation functions
exceeds the cycling domain). The fix applied by the authors (setting
negative eigenvalues of U^alfa seems problematic to me as the shape of
the resulting L at the origin is not smooth). There are better ways to
handle this problems:
1) The original article of Gaspari and Cohn shows how positive
definite correlation functions can be designed on the sphere. This
also works on a cycled domain.
2) another option is to specify U^alfa as a Gaspari Cohn function with
half the length scale as L. Then U^a*U^aT will again approximate a
Gaussian with the required length scale.
When first introducing the EBV method the authors just mention that
"the method .. is uninformed about the observational method". I think
this issue should be discussed a little bit further, maybe when the
ensemble spread is compared to the rmse error. Only if observation
density and observation error are properly accounted for in the
ensemble generation process (as done in some other ensemble generation
processes mentioned in this section) it can be expected that ensemble
spread and rmse matches.
The same discussion applies to the estimation of the climatological
matrix B_c. Also here as far as I see only possible balances are taken
into account, but not the actual variance which actually depends on
the data assimilation setup.
I thing the normalisation factor E_tot deserves more discussion. This
is basically a tuning factor which fixes the ensemble spread. Deriving
it from the mean energy norm of the ensemble of differences of
independent realisations of the state vector (eq. 7b) would represent
the climatological variance, not the uncertainty of the analysis.
I think the covariances shown in Figure 3 would deserve some more
discussion. It is mentioned that balances and multi-variate
relationships will be explored in a separate study but some more
information would be helpful here.
The (time dependent) B_e covariances could be contrasted
with physical fields at the respective time. Can the vertically
alternating patterns in the B_c correlations be explained ?
Figure 4 shows that the contribution of J_e to the total cost function
is very small, even only 20% in case of only B_e used (and 80%
contribution of J_o). Doesn't this indicate some insufficient tuning of
the variances? It means that the contribution of the background in
this experiment is quite limited.
If the RMSE values of analysis errors are compared to the nominal
observational errors the former appear to be very large. It would be
illustrative to show the distribution of observations to better
understand the performance of the data assimilation procedure. What
are the forecast (background) errors.
It is stated that B_c was re-calibrated using other training data after
the spin-up process. Wouldn't it be appropriate to show the covariances
for this matrix in figures 3, as they are actually used in the
assimilation experiment ?
It should be stated how exactly the length scale h for the
localisation function is defined, there a several options: There the
Gaspari?Cohn function goes to zero, based on the second derivation at
the origin (as defined by Daley, ... .
The main aspect that is currently lacking, in my opinion, is a description of this study's importance, and the motivation. I think this is a critical part of any manuscript, and currently it is too much left for the reader to guess.
1. As stated in the general comments above, I think the main change that is needed here is a clear description of this study's importance, and the motivation. It is needed in both the Abstract and Introduction.
A reader might guess, from what is currently written, that hybrid ensemble-variational DA algorithms are promising but relatively new, and that more studies are needed to understand implementation choices, properties, and performance. Any additional documentation of studies is then a valuable contribution to the literature.
Is that correct? If so, could you please add some description like this to the Abstract and Introduction? If not, could you please describe what, in your view, is the importance of this study, and the motivation for it?
The Summary section seems to include some statements along these lines, at Lines 626-630: "Given the rapid adoption and broad shift towards hybrid ensemble-variational methods in convective-scale numerical weather prediction, we hope that the ABC-DA system can prove useful in providing further insights and highlight other potential issues that may arise in such methods. Particularly for the tropics, further work is required to better understand the characteristics of the ensemble-derived background errors, such as disentangling its flow-dependency or designing the localisation to isolate or identify important multi-variate relationships."
That type of information from the Summary section should be made very clear to the reader in the Abstract and Introduction. Do not make your reader guess. Tell the reader exactly what you have in mind for the importance and motivation of your study.
2. I would not refer to your ABC model as a "toy" model. When I hear the phrase "toy" model, especially in the context of forecasing, I think of very low-degree-of-freedom models, often just ordinary differential equations, such as the Lorenz 63 system.
Because of the word "toy" in the Abstract and Introduction, I did not even realize that you were using the equations of two-dimensional fluid dynamics, until I saw the equations themselves in Section 2.
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