General Comments

This manuscript proposes treating positioning errors in ensemble forecasts by aggregating ensemble members across time. This method was then applied to improve the analysis and forecasts of dust storm events. The results are interesting and this is an exciting avenue of research. 

However, I have grave concerns about this study (detailed below) that will require several months of work to treat. As such, I recommend rejecting the paper for now and encourage resubmission. I will be happy to review this particular study again. 

Grave concern 1: Contrary to the authors' claims, the Neighbouring Time approach to aggregating ensemble members is not novel.

The authors claim that their neighbouring time approach to increase ensemble sizes is novel. Unless I am missing some detail in their manuscript, that claim is incorrect.  In fact, that method has been extensively tested. The common name for that method is "valid time shifting" (VTS). A similar, but extremely popular, variant of this method is "time-lagged ensembles".

This concern is particularly grave for this study because this ensemble size increasing method is a huge part of this study's supposed novelty.

Here is a sampling of papers that employed those methods. 

• Gasperoni, N. A., X. Wang, and Y. Wang, 2023: Valid Time Shifting for an Experimental RRFS Convection-Allowing EnVar Data Assimilation and Forecast System: Description and Systematic Evaluation in Real Time. Mon. Wea. Rev., 151, 1229–1245, https://doi.org/10.1175/MWR-D-22-0089.1.
• Huang, B., and X. Wang, 2018: On the Use of Cost-Effective Valid-Time-Shifting (VTS) Method to Increase Ensemble Size in the GFS Hybrid 4DEnVar System. Mon. Wea. Rev., 146, 2973–2998, https://doi.org/10.1175/MWR-D-18-0009.1.
• Xu, Q., L. Wei, H. Lu, C. Qiu, and Q. Zhao, 2008: Time-expanded sampling for ensemble-based filters: Assimilation experiments with a shallow-water equation model. J. Geophys. Res., 113, D02114, https://doi.org/10.1029/2007JG000450.
• Van den Dool, H. M., and L. Rukhovets, 1994: On the weights for an ensemble-averaged 6–10-day forecast. Wea. Forecasting, 9, 457–465, https://doi.org/10.1175/1520-0434(1994)009<0457:OTWFAE>2.0.CO;2.

To address this concern, please remove all claims that the Neighboring Time approach is novel in your manuscript.

Grave concern 2: Their EnKF's struggle with positioning error is highly contrived.

The EnKF's struggle with positioning errors is likely simply due to their choice of meteorological forcing. Specifically, they failed to account for uncertainties in meteorological forcing. This could have been avoided by using the ECMWF's ensemble forecasts instead of the operational forecast. With an ensemble of forecasts, there should be more ensemble spread in the positioning of the dust storms, thus ameliorating the EnKF's issue with positioning error.

To address this concern, the authors need to rerun all of their experiments using the ECMWF's ensemble forecast data. This will likely take months of effort. The ECMWF has archived some of its ensemble forecasts on MARS. The ERA5's 10-member ensemble is also available through the Climate Data Store.

Grave concern 3: The authors did not satisfactorily demonstrate that the NTEnKF's improved performance over EnKF is purely due to NTEnKF's ability to handle positioning errors. The fact that the NTEnKF has less sampling error-related under-dispersion is likely playing a role. 

To address this concern, run an experiment with the NTEnKF that uses the same number of members as the EnKF (i.e., run a 32-member NTEnKF experiment). I suspect that the NTEnKF's performance will be comparable to the EnKF's in such a situation. Remember to use the ECMWF ensemble forecasts as your meteorological forcings. 

Major concern: The authors did not explore the statistical problems that surround the use of Neighbourhood time ensembles. The primary issues are 

1. the ensemble members are correlated with each other (i.e., the ensemble is no longer i.i.d.), causing the estimated ensemble variance to be biased from the true forecast variance, and,
2. the ensemble becomes non-Gaussian, especially if time points far apart are used, strengthening the possibility that the EnKF creates suboptimal biased analyses

Minor comments: 

1) The authors' writing seem to imply that the Pf matrix does not normally account for position errors. That is incorrect. The Pf matrix accounts for both intensity and position uncertainties if the forecast ensemble has both kinds of uncertainty. However, note that the Pf matrix only adequately represents position uncertainties if it is sufficiently small -- position uncertainties result in non-Gaussian statistics if those uncertainties are large.

2) Line 64: Please acknowledge that the EnKF is suboptimal for non-Gaussian problems. Though the EnKF can be employed in such situations, the EnKF is probably injecting some kind of bias because it is designed specifically for Gaussian problems. 

3) Given the centrality of the EnKF to the paper, it seems unusual that only 3 papers are cited between lines 60-67. In particular, the sentences in lines 66 and 67 are missing supporting references. Here's a good review paper about the EnKF that you can use to find more EnKF references:

• Houtekamer, P. L., and F. Zhang, 2016: Review of the Ensemble Kalman Filter for Atmospheric Data Assimilation. Mon. Wea. Rev., 144, 4489–4532, https://doi.org/10.1175/MWR-D-15-0440.1.

Also, the stochastic EnKF scheme you are using is not the one that Geir Evensen formulated. It is the one Burgers formulated. Here's the paper:

• Burgers, G., P. Jan van Leeuwen, and G. Evensen, 1998: Analysis Scheme in the Ensemble Kalman Filter. Mon. Wea. Rev., 126, 1719–1724, https://doi.org/10.1175/1520-0493(1998)126<1719:ASITEK>2.0.CO;2.

Peter Jan van Leeuwen of Colorado State University (Evensen's good friend), recently published a much more satisfactory explanation of the stochastic EnKF than Burgers et al (1998):

• van Leeuwen PJ. A consistent interpretation of the stochastic version of the Ensemble Kalman Filter. QJR Meteorol Soc. 2020; 146: 2815–2825. https://doi.org/10.1002/qj.3819

4) Eq. 9 -- The notation can be mistaken as summing up matrices containing the ensemble members at different time points. Please find another way to mathematically express the idea that you are concatenating ensembles across time. Perhaps you can refer to the valid time shifting papers that I referenced earlier.

 

The authors have provided a clear description of the background and motivation behind their study, pointing out the limitations faced by current models and the ensemble Kalman filter (EnKF) in predicting dust events with precision. The authors have pinpointed that these systems often fail due to position errors during the long-distance movement of dust. In response, they introduced an innovative data assimilation approach called the neighboring time ensemble Kalman filter. This technique hinges on the generation of extra ensembles at neighboring time to the current one and then rebuilding the ensemble-derived background covariance. This approach has the potential to tackle errors concerning both the strength and location of dust events. Their methodology was validated with several dust storms occurring in spring 2021. The outcomes affirm that this new method enhances the quality of both dust event analysis and forecast, outperforming the conventional EnKF. There are also a few major concerns need to be addressed before it can be accpted.

1)As the other referee pointed out, similar techniques have been proposed before as the “valid time shifting” in other applications. The authors should reconsider their novelty about the method and refer to the proper papers.

2)The authors have confined their consideration to the issue of dust emission uncertainty in the EnKF’s P matrix, as detailed in Section 3.1. However, given that the introduction highlights the emergence of position errors as a result of meteorological input, Why not incorporate meteorological uncertainty within the process of ensemble generation?

3)The decision to merge information from five distinct time points, centering around the central time, is mentioned, yet the rationale behind selecting these specific time points for combination is not fully explained. Could you please elaborate on the relevance of this choice?

4)It would be helpful to clarify the methodology for detecting the occurrence of position error, especially in light of the rapid evolution of dust storms. Is it automatically detected or manually chosen? What criteria do the authors employ to determine the appropriate timing for implementing the NTEnKF?

5)In both Figure 4 (b.2) and Figure 7 (b.2), there are conspicuously high values located to the west of the dust plumes following the NTEnKF analysis. I’m curious if, in the absence or scarcity of observations, applying the NTEnKF could lead to the generation of false or overly extensive dust plumes, potentially exacerbating the inaccuracies of the original model simulation.

6)The scatters depicted in all the figures are too small to recognize, making it challenging for readers to quickly grasp the information being conveyed. Consider magnifying these visuals or narrowing the focus of the map to enhance the visibility of the dust shapes and allow for a more immediate and clear interpretation.