The manuscript is presented as a review paper on multivariate extremes, specifically flood, and drought. The multivariate aspect of such extremes is intended in space, in time, and in their characteristics. The topic is relevant for preparedness and risk management in the current and future climates. However, the manuscript in its current form presents some limitations.

The introduction on the drawbacks of the univariate approach seems in contrast with the types of multivariate extremes identified. The regional and temporal extremes fall back on a univariate approach. Indeed, they are defined based on whether, e.g., flood magnitude is above a given threshold or with a given return period at one single location. When does an extreme in one location become a multivariate extreme? How many locations should be flooded? Is the regional extent of the univariate floods an indicator of whether an extreme is multivariate or not? How so? These kinds of questions are difficult to answer from the definitions of multivariate extremes provided and it makes questioning whether it is necessary to move away from the univariate approach.

In my opinion, more emphasis should be given to the descriptors of multivariate extremes, as defined by the Author, their differences, and the implication of using one descriptor rather than another. As a matter of fact, the definition of an extreme cannot be decoupled from the descriptor used. In the manuscript, they are simply listed in tables without further implications on their use.

Section 3 on modeling multivariate extremes is about models for assessing the frequency and magnitude of multivariate hydrologic extreme events (as summarized by the Author in lines 241-243). In this section, bivariate copula models are described way more extensively compared to other methods. However, it is unclear why such a detailed description and how copula models differ from the descriptors of hydrological extremes with multiple characteristics. As a matter of fact, copulas model the dependence between two variables, where the dependence between the variables is measured by the correlation between two variables (descriptors in Table 3). It would be useful to discuss whether bivariate copulas can be applied also to regional and temporal multivariate extremes and how. Moreover, limiting the description of multivariate models to bivariate statistical methods in a review paper on multivariate extremes is not enough. I encourage the Authors to add studies and methods for higher dimensions.  

Point-by-point comments:

Line 28 and Line 280: my suggestion is to cite textbooks or the original journal papers where these concepts are first defined. For example, G. Salvadori and C. De Michele earlier works.

Line 88: “precipitation dependence” dependence to what?

Figure 4: it would help to have more information on how drought is defined

Lines 182 – 200: discussion about variables dependence is a bit vague. Which variables? Is it a bi-variate dependence? The example of dependence between peak and volume for hydraulic design should be elaborated further.

Line 321: studies in higher dimensions should be added to the manuscript

This manuscript presents a review of some hydrological problems that can be characterized in terms of a multivariate extreme value distribution. The identified hydrological conditions that require a probabilistic estimation in terms of event magniture and occurrence are listed and briefly discussed along with the metrics that can be generally used to determine the dependence among the variables. Further, copula for multivariate frequency analysis and continuous time serie simulation are introduced as strategies for modeling those phenomena. Due to the variety and complexity of the problems mentioned in the review paper, each of them is only hinted at, missing an in-depth discussion about several important issues. Further, many interesting works about multivariate statistical modeling are not mentioined at all; indeed, also the most recent literature on the topic is very rich. Based on these consideration, I suggest the Author to revise her work trying to improve the description of the phenomena, especially those problems that are still unsolved, and enlarge the state of the art description referring the interested readers to the most recent papers (and books) that provide well established and innovative solutions with a deeper insight into the mentioned problems.