Reply on RC2

Some could be included in the abstract about the case study used in the paper.

The Introduction Section focuses on three existing techniques to forecast VCI: Auto-Regression, Gaussian Processes and Artificial Neural Networks. A longer revision of the techniques used in last years to develop EWS for droughts could be included in this section, as well as other papers that develop similar tools. For example, stochastic algorithms based on different types of Markov Chains, autoregressive moving-average (ARMA), autoregressive integrated moving average (ARIMA) techniques, support vector machines, Kalman filters, multiple regression tree techniques, among others, have been used in last years to forecast droughts.
Response: Comment well noted, the section on existing works that use similar tools will be updated with cited papers.
While the BARDL algorithm supplies a probability distribution, the AR model supplies a deterministic value. Therefore, the comparison between the two models is not straightforward. In the paper, a confidence interval for the AR model is estimated from RMSE and z-score. However, this is a simplified way to estimate the prediction uncertainty, supplying a constant confidence interval regardless the magnitude of both VCI and the explanatory variables. This step is very important to compare BARDL results with AR results in a proper way. In addition, the methodology to compare both models should be clarified in the paper, as it is not clear how most of measures used to quantify accuracy and precision have been applied to the probabilistic forecast supplied by BARDL.
Response: Thanks for this comment, the results from the AR model was compared to the means (average) of the forecast distribution obtained from the Bayesian model. We realise this explanation is missing in the paper and will be addressed accordingly together with additional comments.
The Discussion Section should be rewritten, as in its current form it is mostly a mixture of conclusions with some additional results considering seasonality.
The Conclusions Section could be extended to summarise the main findings of the study.
Response: Comment accepted and well noted, the discussion will be restructured so it does not come across as being incoherent. The conclusion will also be rewritten.

Specific comments:
Abstract: Some sentences could be included in the abstract about the case study used in the paper.

14:
The acronym AR has not been introduced in the paper at this point yet.
Response: Comment noted and will be fixed 30: The acronym USAID is not introduced in the paper and could be explained at this point.

Response: Comments noted and will be fixed
46: The ARDA model has been applied to assess droughts previously, such as Zhu et al. (2018). References to previous studies in which the ARDA technique is applied to droughts should be included in the paper.
Response: Well noted will be considered, however, the paper focused on Hydrological Droughts in river basins and not vegetation conditions. 51: The paper proposes the use of a Bayesian framework in the ARDA model to incorporate the prior knowledge about model parameters in the analysis, obtaining a probability distribution for VCI results. Bayesian networks have been also applied to develop a long-term drought forecast (Shin et al., 2019), supplying probabilistic results that can assess forecast uncertainties. A discussion could be included in the paper, stating the benefits of a BARDL model compared to Bayesian networks.
Response: Comment noted and will be considered however, the results in this paper are also for Hydrological drought and not comparable to agricultural drought indicators.
Section 2.1: Some information about the number of counties considered in the study could be included in this section, as well as the number of counties that are arid and semi-arid. In addition, some information about the area in km2 that is considered in the study could be useful for the reader.
Response: Comment accepted and well noted, more details on this will be included 70: 'estimates' should be changed to 'estimate.
Response: Comment well noted and will be fixed 98-99: The description of NVIi and NDVIi variables should be included in this paragraph too.
Response: Comment well noted and will be fixed 103-104: 'long term' should be changed to 'long-term'.
Response: Comment well noted and will be fixed 111: The acronym AR has been introduced in the paper above.

Response: Comment well noted and will be fixed
118: A discussion could be included about the selection of the OLS method for estimating parameters of ARDL. Some other methods are also available.

Response: Comment not too clear because OLS was not used for the ARDL in this paper.
131 -Eq. 3: The variable subscripts should be revised in Eq. 3. Dt-q seems to be the drought indicator in a constant time step t-q, which seems to be constant in the first summation regardless the value of i. Similarly, Pt-p and St-p seem to be constant values in the summations. In addition, the regression coefficients are also constant values in the summation, though they could change in terms of i. A discussion should be included about the use of constant values in summations. 214: R2 is not a good measure of forecast accuracy. RMSE is more adequate than R2. Therefore, the gain in performance metrics could be assessed with RMSE. However, the BARDL model supplies a probability distribution of VCI. How do you obtain a RMSE value from the comparison between probability distributions and deterministic values of observations?
Response: We used the R2 because we needed to test the goodness of fit and the variation in dependent variables captured or explained by our model. The R2 and RMSE values were determined with the means (Average) of the forecast probability distribution.  Response: Comment noted, and will be considered.

229-231:
The table in Appendix A could be summarised in a figure and included in the main text of the paper, in order to analyse the comparison between the two models. The results included in Table 1 show that PICP values are smaller for AR than for BARDL, meaning that a greater number of observations are out of the confidence intervals for BARDL. This result should be discussed in the paper. In addition, most of PCIP values for the BARDL model are smaller than 94-96 %, in contrast to the statement of line 229.
Response: Comment noted, the details will be discussed Figure 5: Please use the same y-axis scale in each row to compare the AR and BARDL results. The dashed line of the left column differs from the dashed line of the right column, though observations do not change. The green line represents the forecast. What is such a forecast for the BARDL model given that it supplies a probability distribution?
Response: Comment well noted, the y-axis will be set to the same scale. The difference in the dashed line is due to the shift in time-series data when creating observed led time datasets.
235: A drought is forecasted when VCI3M values are smaller than 35. This is straightforward for the AR model, as it is deterministic. However, how do you apply this criterion to the BARDA outputs considering probability distributions?
Response: Comment noted, the criterion was applied to the mean of the forecast distribution from the bayesian model.
We have noted that details on the use of the mean forecast distribution model evaluation are missing the narrative and will be addressed.

251-253:
The BARDL lines lie above the main diagonal of the reliability diagram. This means that the probabilities supplied by the BARDL model tend to underestimate droughts. A comment about this point should be included in the paper.
Response: Comment noted, this was an omission in the paper and the details on this have now been outlined in the paper.
253-256: The sharpness diagrams are mostly flat for 10 and 12 weeks. The low values close to 1 means that the BARDL model is not able to forecast droughts. Therefore, the BARDL model is useful to forecast droughts with 6 weeks ahead but it is not for 10 and 12 weeks. A comment about this point should be included in the paper.