Feature: StormSim: LCS Storm Sampling Scheme Upscaling

[fgarcia0128]

Some Context:

• LCS sampling scheme only has a yearly resolution.
• Increasing the sampling resolution would allow for more robust/accurate methods to add things such as: tides and sea level rise.

Considerations:

• Solution must be something we can automate through the contents of CHS Files (i.e timestamp for PROS).
• Up-scaling the sampling scheme ultimately boils down to recomputing the underlying storm statistics from a yearly basis to a monthly or daily basis.
• XC peak responses are sampled from historical distributions and not whats reported on the Peaks file for Storm ID X.

Discussion Point:

• Can we automate this process with the files that we have currently?
• 1. TC Storm Recurrence Rates [stm/ yr * Km] -> At 1025 Coastal Reference Locations along the Atlantic Basin (3 intensities)
• 2. TC Discrete Storm Weights -> Likelihood of occurrence in a year
• 3. XC Rate [stm/yr]

@jmelby @KHodgens @astehno @Piro628 @rustypermenter

Inside look at sampling scheme appended below:

All files can be found at: https://github.com/Coastal-Hazards-System/StormSim-Library/tree/b909bb3a237b9bc2e21c1f9b06700e914cad82a8/StormSim_Library/Forcing_Generation/Life_Cycle_Simulation

---

Estimate How Many Events Get Sampled Per Year (Poisson Distribution)

• Process applies to both storm types.
• Dictates how many events get sampled per year.
• TC_SRR -> 1 x 4 array containing TC Storm Recurrence Rates [stm/yr] | [ SRR_low, SRR_mid, SRR_high, SRR_Total ]
• For XC Poisson distribution is created by using historical rate (StormSim computes it automatically) instead of the SRR's. (See: https://github.com/Coastal-Hazards-System/StormSim-Library/blob/b909bb3a237b9bc2e21c1f9b06700e914cad82a8/StormSim_Library/Forcing_Generation/Life_Cycle_Simulation/sample_xc_storm.m)
  https://github.com/Coastal-Hazards-System/StormSim-Library/blob/b909bb3a237b9bc2e21c1f9b06700e914cad82a8/StormSim_Library/Forcing_Generation/Life_Cycle_Simulation/sample_tc_storm.m#L130-L143

---

Core Sampling Loop

• With a given rate of events per year, we can proceed with sampling random events to populate the life cycles.
• The core loop is the same for both storm types. The main differences are:
• • TC: We have an extra step to determine from what intensity population to sample from. Additionally, each intensity has a specific probability tied to it. (randsample(storm_peaks_at_intensity, 1, true, DSW))
• • XC: We make all XC events equally as probable to occur and randomly sample from the historical set. randsample(storm_peaks(:,1), 1)
    https://github.com/Coastal-Hazards-System/StormSim-Library/blob/b909bb3a237b9bc2e21c1f9b06700e914cad82a8/StormSim_Library/Forcing_Generation/Life_Cycle_Simulation/sample_xc_storm.m#L140-L160

---

TC Sampling Scheme:

• Core Loop Contains extra step to randomly sample what intensity bin to use.
• TC sampling steps are as follows:
• 1. Compute Yearly Rate (Poisson Distribution)
• 2. Compute Cumulative Probability cumulativeProb = cumsum(TC_SRR / TC_SRR_Total);
• 3. Randomly sample intensity bin to use as storm population. (Core Loop Starts)https://github.com/Coastal-Hazards-System/StormSim-Library/blob/b909bb3a237b9bc2e21c1f9b06700e914cad82a8/StormSim_Library/Forcing_Generation/Life_Cycle_Simulation/sample_tc_storm.m#L160-L169
• 4. Randomly sample TC from sampling population randsample(storm_peaks_at_intensity, 1, true, DSW) (Core Loop Ends)
• 5. Pull storm data associated to sampled events by matching storm IDs for all LCs.

---

XC Sampling Scheme:

• XC have an extra step when it comes to sampling Peak responses (SWL, Hm0, Tp, wDir). (Step 3)
• Peak responses are sampled form a set of historical distributions. (storm ID to Peak response relationship is lost) (This is only for Peaks datasets)
• When populating LCs with timeseries, storm data is pulled according to sampled storm IDs. (i. e. copula sampler outputs don't matter)
• XC sampling steps are as follows:
• 1. Compute Historical Yearly Rate (Poisson Distribution)
• 2. Randomly sample XC from historical population. (All just as likely) randsample(storm_peaks, 1) (Core Loop Start/End)
• 3. Randomly sample XC event peak responses from historical distributions (See: copula_sampler.m)
     https://github.com/Coastal-Hazards-System/StormSim-Library/blob/b909bb3a237b9bc2e21c1f9b06700e914cad82a8/StormSim_Library/Forcing_Generation/Life_Cycle_Simulation/copula_sampler.m#L1-L24
• If populating with Timeseries
• 4. Pull storm data associated to sampled events by matching storm IDs for all LCs.

---

Timeseries LC Creation:

• storm -> n_storm x 2 cell array | Cols: storm ID, storm_data
• • storm_data -> For each cell in storm m_tstp x x_cols [ swl, hm0, tp, wDir, ....]
• Notice we are pulling a hydrograph from a randomly sampled storm ID
  https://github.com/Coastal-Hazards-System/StormSim-Library/blob/b909bb3a237b9bc2e21c1f9b06700e914cad82a8/StormSim_Library/Forcing_Generation/Life_Cycle_Simulation/stormsim_lcs.m#L213-L233

---