Dear reviewer, 

We thank you for the valuable comments that you provided us. We have addressed the points mentioned, and our response to each of them will be detailed below.

In response to general comments:

The case study chosen at first indeed is a rather intense mostly convective rainfall event. Despite the quantitative verification representing the average performance of the model across a diverse corpus of events, we added a second case study, which concerns a rather different stratiform large-scale precipitation event. There, we found many of the same features that were found with the first case study, and we believe that the addition of this case study gives a better general view of how the model performs in different scenarios to the reader. 

To address the concerns about the data distribution, we added a histogram of the dataset reflectivity, highlighting the fact that those reflectivity values that are the most likely to represent precipitation are normally distributed, motivating the modeling method of the predictive distribution

In response to specific comments: 

We attempted to clarify the notation in subsection 2.1. What was meant by real was observed, or ground-truth. Next, the symbols x, y, ŷ were clarified to mean tensors, and Θ a list of tensors . We hope that these changes will make the sentences concerned more clear and understandable. 

Line 190: 

We expanded the KL-divergence D_KL to its definition in Eq. 1.

Line 280:

It is correct to note that precipitation is not normally distributed (but log-normally). However, in this work we are applying the model to reflectivity and not precipitation rates. Radar reflectivity is known to follow a normal distribution because rain rate follows a log-normal distribution [1], and we verified whether this is in addition the case for our input data specifically with histograms of the data reflectivity of the dataset. We found that the part of the reflectivity distribution corresponding most likely to precipitation and not clutter or noise has indeed a Gaussian shape. Tangentially, we clarify the language used to make it clear that we are approaching precipitation nowcasting through working with radar reflectivity values, which may further be used to make actual quantitative precipitation rate or accumulation predictions.  

1. Kedem, B. and Chiu, L. S.: On the lognormality of rain rate, Proceedings of the National Academy of Sciences, 84, 901–905,  https://doi.org/10.1073/pnas.84.4.901, publisher: Proceedings of the National Academy of Sciences, 1987

Dear reviewer, 

We thank you for the valuable comments that you provided us. We have addressed the points mentioned, and our response to each of them will be detailed below.

In response to major comments: 

We addressed the comments by adding discussion relating to the two facets mentioned from a machine learning perspective. Since what was asked is minor revisions, we did not include any supplementary experiments in the manuscript. We still carried some experiments exploring the suggestions made, and our findings were:

1. We tried training for more epochs (60 in total) but did not find that increasing the number of training epochs improves validation performance in the present case. However we cannot exclude the potential effect of external factors such as our learning rate schedule. 

2. We tried to weight the likelihood part of the loss according to the inverse of the density of the pixel reflectivity value in the dataset distribution. Unfortunately, this did only result in considerable over-forecasting and oddly-behaving aleatoric uncertainties. Despite of this type of weighting being difficult to get right, we acknowledge the data imbalance problem in precipitation nowcasting giving rise to the importance of weighting samples such that all, even rare occurrences, can reasonably contribute to the gradients.  

The discussion section was modified such that the paragraph on small-scale variability was reworked, and a new paragraph was added next to it describing potential ways to mitigate the underforecasting and lack of small-scale variability problems together from a machine learning perspective. We presented the two methods which you suggested together with some of our own ideas. 

In response to minor comments: 

L7:

This was fixed. 

L75:

To the extent of our knowledge, all of the models presented above L75 are discriminative, as they only model the conditional probability of predicted outputs given input frames, maximizing its likelihood through the MSE loss. In contrast, generative models such as GANs model the joint probability distribution of the outputs and inputs. We have however removed the word "discriminative" from the sentence such as to reduce possible confusion, because the same point can be made without its explicit usage. 

L240-252:

After some thought, we indeed came by a possible method to better incorporate the correlated noise sampling procedure into the network, which was detailed in the conclusions section  :

    - "We could also think of directly appending the post-processing sampling with spatially correlated noise to the neural network, or even learning context-dependent spatiotemporal correlation structures. The sampled outputs could then be, e.g., fed to a GAN-like discriminator module, which would drive the processed outputs to be more realistic while retaining the uncertainty decomposition. "

L324-325: 

We fixed that.

L353:

This has been fixed too.

L421:

"...keeps open the possibility for..." rephrased to "...means that we cannot exclude... ".

L423:

Rephrased to "Such dependencies are...".

L426:

This has been fixed. 

L431:

This has been fixed. 

L503:

We meant "breadth of the ensemble" and replaced "variety" here, acknowledging the ambiguity of the meaning of "variety" in this context.

L507-509:

The paragraph containing was restructured in an attempt to separate and make clearer the different points made. See major comment modifications. 

Dear reviewer,

We have here attached a supplement illustrating the points made in our response to the major comments 1 and 2. The supplement is a figure illustrating the predictive mean and standard deviation of a base DEUCE checkpoint, a checkpoint with longer training, and a checkpoint trained with the loss weighting scheme described on a case taken from the prediction split (2019-05-25 13:00:00 UTC).

For this run, we slightly modified the training procedure as we found that the original DEUCE checkpoint sometimes experienced instabilities (NaN loss) in training for longer. The base DEUCE checkpoint here did not experience the same issues but had similar performance to the original one and was trained for 37 epochs with a batch size of 8, a sample size of 4, using 256x256px random crops from the 512x512px area, with learning rate decay after 5 epochs of non-improving validation loss (start at 1e-4). The "long" version started from the base checkpoint but was trained until 60 epochs. In the visualization, we show it after 57 epochs, as that was where its validation performance peaked. The "weighted" version was again trained from scratch with the same hyper-parameters except for the loss function. It achieved its peak validation performance after 28 epochs, which is the checkpoint shown in the figure.