Simulate sugar kelp as a function of depth, interpolate across transects

[zhrandell]

Overview

We would like to formally evaluate two questions: the first centers around evaluating / optimizing ROV field methods sampling design, and the second revoles around evaluating methods of data interpolation to create spatial layers from our ROV-derived benthic community data. To evaluate both of these questions we will utilize empirical data to simulate sugar kelp across a seascape of depth, and we'll use empirical ROV transects to evaluate how well our surveys captured simulated sugar kelp pattern.

In summer 2025 our team conducted 23 perpendicular ROV transects offshore of Centennial Park in Elliott Bay, Seattle, with each transect starting at a depth of approximately 16m depth and terminating at a depth of approximately 1m depth. As you can see below, summer 2025 we completed 23 of these two perpendicular transects offshore of Centennial Park in Elliott Bay, Seattle, and we split these into two halves (to test the ability to differentiate two "sub-regions" of interpolated layers).

The intent with these perpendicular transects was to capture pattern across depth, i.e., capture the lack of sugar kelp at 16m, and then its emergence towards around 9m, and peak density around 6m.

As noted above, we'd ultimate like to be able to extract empirical sugar kelp data from all our spatially explicit survey photos and use those data to interpolate and create ArcGIS layers for, in this case, sugar kelp. First however, we need to better understand the relationship between the number of ROV transects completed, and the ability to generate minimally effective interpolated layers.

Files / data available

We have the following information:

• percent-cover_abundances.csv contains earlier Port of Seattle survey data with sugar kelp information across a broad depth gradient
• GLMM.R contains initial code used to conduct generalized linear mixed effects modeling
• Extract_Cent_1.tif contains depth information for the sampling region shown above (left)
• perpendicular_transects.csv contains ROV telemetry information (including lat/lon) for our 2025 perpendicular transects

nestled within our standard repo structure:

• data - raw data input
• results - files resulting from analyses here
• code - scripts utilized
• figs - output figures, files

Proposed approach

• let's first recover a probability function for sugar kelp as a function of depth (figure depicted below). We need to analyze sugar_kelp within percent-cover_abundances via GLMM and extract the probability function.
• with a sugar kelp vs depth probability function, we can then simulate sugar kelp across the entire seascape of depth values deliniated via Extract_Cent_1.tif.
• with a seascape of simulated sugar kelp, we can then use the lat/lon information from perpendicular_transects to extract the simulated sugar kelp values "surveyed" by our real transects (across a 1m width, with lat/lon used to deliniate transect length).
• we can then interpolate the simulated sugar kelp captured by our transects to the broader (original) spatial extent of the full Extract_Cent_1.tif file.
• now we have (1) a layer of simulated sugar kelp, and (2) a layer of interpolated simulated sugar kelp captured by our transects. We can now calculate the delta between the two layers, and evaluate how well our real transects captured the "true" (simulated) underlying pattern of sugar kelp.
• from here, there may well be calculations / further simulations to identify how many transects are necessary to optimize the interpolation. Reworded: what is the minimum number of transects necessary to generate a useful interpolation?

Subsequent empirical step

Now that we have workflows to process imagery at scale (via https://github.com/Seattle-Aquarium/underwater-auto-image-encoder) and can extract Toolbox data at scale, a separate and subsequent Issue will follow utilizing real-world sugar kelp values that have been extracted from the real images. To provide a speedy initial investigation, we will rely upon unverified Toolbox output, i.e., we will not review the model's predictions via Kelp Quest, and will instead simply apply the algorithm and analyze the output.