Update paper.md

joss_submission/paper.md

@@ -75,7 +75,7 @@ The `MultiHazard` R package is designed to enable practitioners to estimate the
 
 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 Figure 1. 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]. 
 
-![Caption for example figure.\label{fig:isolines}](Figure_1.png)
+![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)
 
 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.