the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
| 30 May 2024
Modelling convective cell lifecycles with a copula-based approach
Abstract. This study proposes an algorithm designed to model convective cell lifecycles, for the purpose of improving the representation of convective storms in rainfall modelling and forecasting. We propose to explicitly model cell property inter-dependence and temporal evolution. To develop the algorithm, 165 effective convective storm events occurring between 2005 and 2017 in Birmingham, UK, were selected. A state-of-the-art storm tracking algorithm was employed to reconstruct convective cell lifecycles within each selected event. The investigation of these cell lifecycles proceeded in three stages. The initial stage involved statistically characterising individual properties of convective cells, including rainfall intensity, spatial extent at peaks, and lifespan. Subsequently, an examination of the inter-correlations amongst these properties was conducted. In the final stage, the focus was on examining the evolution of these cell properties during their lifetimes. We found that the growth and decay rates of cell properties are correlated with the cell properties themselves. Hence the need to incorporate this correlation structure into the process of sampling convective cells. To resolve the dependence structures within convective cell evolution, a novel algorithm based on vine copulas is proposed. We show the proposed algorithm's ability to sample cell lifecycles preserving both observed individual cell properties and their dependence structures. To enhance the algorithm's applicability, it is linked to an exponential shape model to synthesise spatial fields of rainfall intensity for each cell. This defines a model which can readily be incorporated into rainfall generators and forecasting tools.
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Status: open (until 31 Jul 2024)
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RC1: 'Comment on egusphere-2024-1540', Anonymous Referee #1, 27 Jun 2024
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General opinion:
The paper entitled “Modelling convective cell lifecycles with a copula-based approach” by Chien-Yu Tseng and co-authors proposes a new model for stochastic generation of convective rainfall cells. In my opinion the topic is relevant for the journal HESS, the proposed model is new and in general properly described, and the paper is well written.
I nevertheless have two major concerns that should be addressed before publication. First, several steps of the statistical model are not sufficiently justified or explained, and depending on how they have been actually implemented they may be improper and therefore should be improved. Second, the simulation of actual rainfall fields based on rain cells properties is a very important application of the model and is mentioned in many places of the manuscript, but it is not at all illustrated in this paper. I strongly encourage the authors to implement this step and show the corresponding results in this paper.
Major concerns:
Unclear statistical model
L 253-259: It seems that the marginal distribution models are selected based on the likelihood of each model in competition. However the different models may have different number of parameters, which makes a direct comparison of their likelihoods “unfair”. A more standard model selection approach (e.g., AIC or BIC) should be used instead.
L294-301: Based on this description, it is unclear to me how the TLL copula has been selected/chosen, and why it has been preferred to parametric copulas. This should be explained in more details. For instance an AIC procedure is mentioned L285 and L287 for model selection, but how is the “model complexity term” computed in the case of a non-parametric copulas (i.e., the 2k term with k the number of model parameters and AIC=2k-2ln(L))?
In addition, how the TLL copulas are fitted and used must be described in more details. For instance is there any hyperparameter involved? If yes how is it selected?
Simulation of rainfall fields
The simulation of more realistic rainfall fields during convective events is a major selling point for the proposed method. This is mentioned in many places of the manuscript, but unfortunately the reader cannot find much details about the method that could be used to generate actual rainfall fields from rain cells properties. In addition, there is no illustration about how such rainfall fields would look like (neither in the form of rain maps, nor in terms of rainfall statistics).
There is a brief mention and description of the EXCELL model that is envisioned to translate rain cells properties into rainfall fields (L 339-352), but many questions remain open. For instance: (1) are the rain cell advected, and if yes with which speed and direction? Should these parameters be linked to rain cell properties? (2) How do new rain cells enter the simulation domain? And in which stage of their development? (3) What is the rain cell density within the simulation domain? And what is the “birth rate” of new rain cells within the target area?
I invite the authors to address the question of how to simulate rainfall fields from the rain cell properties simulated by their current method, and to illustrate the results of this rainfall field simulation.
Minor comments:
L13: “synthesise spatial fields of rainfall intensity for each cell” → I find this phrasing a bit misleading since I assume that the final rainfall intensity fields are made by the juxtaposition of intensities coming from several rain cells.
L80-83: Be more specific and better situate your work in relation to the above literature review. In particular, I have the impression that the proposed approach is an improvement of the step 2 of a point-process based rainfall model as mentioned at line 35. If this is the case it would be nice to state it clearly. In addition here would be a good place to briefly explain how the simulated rain cell properties would be used to generate rainfall fields, and how to deal with “side issues” such as advection, rain cell occurrence, etc.
L97: It would be nice to show some data of these events, and in general of the dataset that will be used for application. Not necessarily in the main text, but maybe in supplementary material.
L127: Please provide a brief description of the WaPUG method.
L138-139: How to deal with rain cells with multiple cores as well as with cells splitting and merging seems an interesting future work. This may be mentioned in conclusion/perspectives.
L148-149: “preserve the observed statistical properties and inter-dependence of convective cells.” → Said like this I have the impression that the proposed method models dependencies between rain cells (which if I understood well is not the case). Maybe a word is missing? → "inter-dependence of convective cells properties". Otherwise please rephrase.
Sect 3.3 (starting L230): Please be more specific in the description of how the convective cell lifecycles are modeled. For instance: does the peak always occurs at Lifespan/2? Is the peak state “instantaneous” or does it last for a given duration? (if it is instantaneous please modify Fig. 3 accordingly). Are growth and decay linear? (at first I was sure that they were, but the dashed lines in Fig. 3 made me doubt)
L255-259: Implement a standard model selection approach (e.g., AIC or BIC) or justify why the log-Likelihood would be enough to select the best model.
L265-266: “do not adhere to a Gaussian distributions” → Do you mean “do not follow Gaussian distributions”?
L266: “resolving these dependencies analytically is practically unfeasible” → I do not understand this statement very well, and if I try to guess what it means I disagree. The fact that the rain cell properties do not follow Gaussian distributions do not impede an analytical (do you mean parametric?) modeling. This is even the main interest of the copulas approach that you are using afterwards (if parametric copulas are used).
L267: “utilise the theory of copulas to numerically model” : I think this is misleading about the copula approach (see my previous comment). Please rephrase.
Figure 5 (and its description L269-277): the bivariate dependence plots are unreadable and not very informative about the dependence structure between variables (because the scatter-plots are dominated by the marginal distributions of the variables). Please replace the scatter-plots by empirical densities to improve readability (this comment is also valid for Fig.9 and 11). In addition instead of showing the correlation between “raw” variables I would rather transform the data using the parametric distributions inferred in Sect 3.4.1, and plot the dependencies between transformed data (i.e., in the [0,1]x[0,1] square) to align with the framework of copulas. To make my comment more clear: I propose to show the empirical copulas instead of the correlations between variables.
L295-296: “Based on our analysis […] appears to be the most suitable model”. This is unclear what this analysis is. Please be more specific, and in particular explain in details why you prefer TLL instead of parametric copulas.
L294-301: I’m very confused about what you are doing here. Please provide more details, and if possible with references. You mention both parametric and non-parametric copulas, this is confusing.
L371 and Fig. 8, Fig. 10: Could you add q-q plots in order to better see which part of the pdf is well (or poorly) simulated?
L385: “sample unseen properties values” → unobserved properties?
L433: typo in “distributions”
Caption of Fig. 8: Remind what is Ce and Ct, and possibly also what are the cell properties.
Fig. 9 and 11: use empirical densities instead of scatter-plots. In contrast with Fig. 5, I think that for these two figures (Fig 9 and 11) showing correlations is fine since one want to evaluate the combined effects of the marginal distribution and the denpendencies encoded by the copulas.
L452: “can infer properties” → can simulate properties
Citation: https://doi.org/10.5194/egusphere-2024-1540-RC1
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