Update paper.md

joss_submission/paper.md

@@ -73,15 +73,15 @@ The `MultiHazard` R package is designed to enable practitioners to estimate the
 
 # Statement of need
 
-The `MultiHazard` package was developed in collaberation with the South Florida Water Management District (SFWMD) to improve level of service assessments for coastal infrastructure affected by both inland and coastal drivers [@Jane:2020]. Initially, the package was created to implement the conditional sampling-copula theory approach. In two-sided conditional sampling a driver is conditioned to be extreme and paired with the maximum value of the other driver within a specified lag-time. The process is repeated with the drivers reversed yielding two conditional samples. The best fitting of 40 copulas are tested to model the dependence between drivers in each conditional sample. The isoline corresponding to a user specified return period is given by the outer envelope when overlaying the (conditional) contours from the copula model fit to each sample @Bender:2016, see \autoref{fig:isolines}. To obtain a single design event, the probability of events on the isolines is calculated using an empirical density estimate, selecting the event with the highest probability. Some experts recommend sampling an ensemble of events from the isoline to account for uncertainty in design event selection which is also possible in the package. The conditional sampling – copula theory approach has continued to gain traction [@Kim:2023; @Maduwantha:2024] and in a review of the best-available, actionable science was highlighted as an approach that Federal agencies in the United States may wish to develop detailed technical guidance on how to use it meet their needs [@FFRMS:2023]. 
+The `MultiHazard` package was developed in collaberation with the South Florida Water Management District (SFWMD) to improve level of service assessments for coastal infrastructure affected by both inland and coastal drivers [@Jane:2020]. Initially, the package was created to implement the conditional sampling-copula theory approach. In two-sided conditional sampling a driver is conditioned to be extreme and paired with the maximum value of the other driver within a specified lag-time. The process is repeated with the drivers reversed yielding two conditional samples. The best fitting of 40 copulas are tested to model the dependence between drivers in each conditional sample. The isoline corresponding to a user specified return period is given by the outer envelope when overlaying the (conditional) contours from the copula model fit to each sample @Bender:2016, see \autoref{fig:isolines}. To obtain a single design event, the probability of events on the isolines is calculated using an empirical density estimate, selecting the event with the highest probability. Some experts recommend sampling an ensemble of events from the isoline to account for uncertainty in design event selection which is also possible in the package. The conditional sampling – copula theory approach has continued to gain traction [@Kim:2023; @Maduwantha:2024] and in a review of the best-available, actionable science was highlighted as an approach that Federal agencies in the United States may wish to develop detailed technical guidance on how to use it meet their needs [@FFRMS:2023]. The package possesses the functionaity to obtain the desired isoline by interpolating oint return periods calculated over a user-defined grid which can result in smoother curves than overlaying the partial isolines [@Maduwantha:2024]. Also coded in the package are the methods proposed in @Barltrop:2023 to derive isolines using the @Heffernan:2004 and models along with the bootstrap procedure for caculating sample uncertainties.
 
-![The 100-year isoline at case study site derived using two methods. Overlaying method: (a) Partial isolines from the samples conditioned on rainfall (red line) and water level (blue line) whose outer envelopen when overlaid gives the full isoline (b). Rays method: The isoline derived derived using the Heffernan and Tawn model with ucertainties calculayed along 100 rays (c) eminating from the point comprising the mimum obseved values of both drivers. The Isoline (red line) and associated 90% confidence interval (dashed black lines) obtained via a block bootstrap procedure (d). \label{fig:isolines}](Figure_1.png)
+![The 100-year isoline at case study site derived using two methods. Two-sided consitoina sample - copula theory method: (a) Partial isolines from the samples conditioned on rainfall (red line) and water level (blue line) whose outer envelopen when overlaid gives (b) the full isoline. Heffernan and Tawn model method: (c) Sample uncertainties are calculated along 100 rays eminating from the point comprising the mimum obseved values of both drivers. (d) The Isoline (red line) and associated 90% confidence interval (dashed black lines) obtained via a block bootstrap procedure . \label{fig:isolines}](Figure_1.png)
 
 Compound events are increasingly concern for entities responsible for managing flood risk. `MultiHazard` is designed as a comprehensive user-friendly tool for copula-based joint probability analysis in R. As such the package provides functions for pre-processing data including imputing missing values, detrending and declustering time series as well as exploratory data analysis e.g., analyzing pairwise correlations over a range of time-lags between the two drivers/hazards. The package also contains an automated threshold selection method for the Generalized Pareto distribution [@Solari:2017] and approaches for robustly capturing the dependence structure when there are more than two relevant drivers/hazards,namely, standard (elliptic/Archimedean) copulas, Pair Copula Constructions (PCCs) and the conditional threshold exceedance approach of @Heffernan:2004. For the analysis undertaken for the SFWMD, the higher dimensional approaches enabled groundwater level to be included in the analysis.  More recently, an approach to generate time varying synthetic events, i.e., hyetographs and hydrographs was added. Time varying condition are a prerequisite for non-steady state hydrodynamic modeling. 
 
 # Related packages
 
-Several packages employ copula-based approaches to derive isolines. The MATLAB toolbox `MvCAT` (Multivariate Copula Analysis Toolbox) [@Sadegh:2017] utilizing up to 26 copula families to model the dependence structure between a pair of random variables. `MvCAT` includes fewer copula families than MultiHazard and does not consider the two-sided conditional sampling - copula theory methodology but rather uses a one-sided sampling approach. On the other hand, `MvCAT` adopts multiple criteria to select among the candidate copula families and a Bayesian framework to account for the uncertainty range for the copula parameters. `ReturnCurves` [@Andre:2024] is a recently released R package that generates bivariate isolines based on the angular dependence function [@Barltrop:2023]. The bootstrap procedure in the `ReturnCurve`package used to assess the sampling uncertainty of the estimated isolines is implemented in `MultiHazard`. 
+Several packages employ copula-based approaches to derive isolines. The MATLAB toolbox `MvCAT` (Multivariate Copula Analysis Toolbox) [@Sadegh:2017] utilizing up to 26 copula families to model the dependence structure between a pair of random variables. `MvCAT` includes fewer copula families than MultiHazard and does not consider the two-sided conditional sampling - copula theory methodology but rather uses a one-sided sampling approach. On the other hand, `MvCAT` adopts multiple criteria to select among the candidate copula families and a Bayesian framework to account for the uncertainty range for the copula parameters. `ReturnCurves` [@Andre:2024] is a recently released R package that generates bivariate isolines based on the angular dependence function (Wadsworth and Tawn (2013) model) [@Barltrop:2023]. The bootstrap procedure in the `ReturnCurve`package used to assess the sampling uncertainty of the estimated isolines is implemented in `MultiHazard`. 
 
 # Acknowledgements