A Survey Design Performance 

Analysis Examining Linkages 

between Reef Fish Assemblages and 

Benthic Morphologies in the Main 

Hawaiian Islands

Kelvin D. Gorospe

Tomoko S. Acoba

U.S. DEPARTMENT OF COMMERCE

National Oceanic and Atmospheric Administration

National Marine Fisheries Service

Pacific Islands Fisheries Science Center

NOAA Technical Memorandum NMFS-PIFSC-64 

https://doi.org/10.7289/V5/TM-PIFSC-64 

November 2017
2
A Survey Design Performance

Analysis Examining Linkages

between Reef Fish Assemblages

and Benthic Morphologies in the

Main Hawaiian Islands

Kelvin D. Gorospe

Tomoko S. Acoba

Joint Institute for Marine and Atmospheric Research

University of Hawaii

1000 Pope Road

Honolulu, Hawaii 96822

NOAA Technical Memorandum NMFS-PIFSC-64 

November 2017

U.S. Department of Commerce

Wilbur L. Ross, Jr., Secretary

National Oceanic and Atmospheric Administration

RDML Tim Gallaudet, Ph.D., USN Ret., Acting NOAA Administrator

National Marine Fisheries Service

Chris Oliver, Assistant Administrator for Fisheries
ii

Recommended citation:

Gorospe, K.D., and T. Acoba. 2017. A survey design performance analysis examining linkages 

between reef fish assemblages and benthic morphologies in the main Hawaiian Islands. NOAA 

Tech. Memo. NMFS-PIFSC-64, 35 p. https://doi.org/10.7289/V5/TM-PIFSC-64.

Copies of this report are available from:

Science Operations Division

Pacific Islands Fisheries Science Center

National Marine Fisheries Service

National Oceanic and Atmospheric Administration

1845 Wasp Boulevard, Building #176 

Honolulu, Hawaii 96818 

Or online at:

https://www.pifsc.noaa.gov/library/

Cover: Photo courtesy of NOAA Fisheries
iii

Table of Contents

List of Tables ................................................................................................................................. iv

List of Figures................................................................................................................................. v

Introduction..................................................................................................................................... 1

Materials and Methods.................................................................................................................... 2

Geomorphologic Benthic Characteristics................................................................................... 2

Fish Variables ............................................................................................................................. 6

Design Performance.................................................................................................................... 6

Results............................................................................................................................................. 8

Discussion..................................................................................................................................... 13

Acknowledgements....................................................................................................................... 14

References..................................................................................................................................... 15
iv

List of Tables

Table 1. List of benthic geomorphology variables derived from LiDAR. The base imagery shows 

Kaneohe Bay, Oahu ............................................................................................................ 3

Table 2. List of all combinations of geomorphological metrics, spatial scales, and summary 

metrics tested as potential stratification variables. ............................................................. 5

Table 3. Strata boundaries for various geomorphology metrics based on inspection of loess 

curves. ................................................................................................................................. 9

Table 4. A comparison of n* (CV = 20%) for depth only vs. depth and standard deviation of 

profile curvature at 50 m for various fish biomass indicators and four main Hawaiian 

Island complexes............................................................................................................... 12

Table 5. A list of geomorphology metrics and spatial scales found to produce the greatest total 

sample reduction across all islands for individual fish biomass indicators. ..................... 12
v

List of Figures

Figure 1. Fish biomass for total reef fish biomass vs. slope of slope (A) and aspect (B) for sites in 

the main Hawaiian Islands.................................................................................................. 9

Figure 2. Slope, as an example of how for a given geomorphology, the assignment of strata 

bounds (green line) was consistent across different spatial scales. .................................. 10

Figure 3. Slope at the 50-m scale shown as an example of how, for a given geomorphology, the 

assignment of strata bounds (green line) was consistent across different fish indicators. 11

Figure 4. Top row: Illustration of profile curvature; Bottom row: Illustration of plan curvature. 13

1

Introduction

Coral reefs are structurally complex and heterogeneous marine ecosystems whose physical 

structure is known to influence ecological processes such as predation, competition, and 

recruitment (Hixon and Beets, 1993). Many species of reef fish depend on coral reefs for food, 

shelter, and habitat and are thus behaviorally influenced by the geomorphological structure of 

coral reefs (Sutton, 1985). A number of studies have demonstrated associations between fish 

assemblages and geomorphological benthic structure (e.g., Friedlander and Parrish, 1998; 

Richards et al., 2012; Williams et al., 2015), however these relationships appear to vary widely 

across studies, likely due to biogeographical differences and the different spatial scales being 

considered (Mellin et al., 2009). 

Understanding the relationships that link reef fish assemblages with their underlying habitats is 

important to conservation practitioners and managers. For example, it can also be used in 

assessing the relative importance of environmental features and provide insight as to which 

habitat areas should be prioritized for conservation purposes (i.e., marine spatial planning, 

Pittman and Brown, 2011). From a fisheries management perspective, developing an improved 

understanding of linkages between fishes and their habitat is important for identifying 

legislatively defined ‘essential fish habitat’ and for reducing habitat-related uncertainty in stock 

assessments (National Marine Fisheries Service, 2010). Furthermore, habitat-biota relationships 

are important for informing the design of stratified random surveys, whereby the environment 

(i.e., survey domain) is partitioned into discreet strata, and the amount of survey effort (e.g., the 

number of surveys) allocated to each stratum is based on its area and variance. 

The latter is most related to the Coral Reef Ecosystem Program (CREP) and its implementation 

of the Pacific Reef Assessment and Monitoring Program (Pacific-RAMP). CREP uses a stratified 

random survey design, but currently, only depth and reef zone are typically used as 

environmental correlates. Here, we derive several geomorphologic characteristics from 

bathymetric LiDAR data and investigate their relationship to different fish assemblage summary 

metrics collected from underwater visual census surveys. Specifically, we explore the possibility 

of adding geomorphological strata to the CREP reef fish survey design. We do this by comparing 

survey design efficiency of depth-only stratification vs. depth and geomorphology stratification. 

Overall, our goal is to use this enhanced understanding of habitat-biota relationships to improve 

future reef fish survey designs. 
Materials and Methods

Geomorphologic Benthic Characteristics

Two bathymetric data sets were initially considered for deriving the geomorphologic benthic 

habitat characteristics. A synthesis of bathymetric data gridded at 5-m spatial resolution was 

provided by the University of Hawaii, Hawaii Mapping Research Group (HMRG). Geometric 

distortions were observed across these bathymetric data. These distortions were likely generated 

due to spatial interpolation of multiple sources of data points at various spatial resolution 

producing local extrema at data points (Appendix A). The distortions were exacerbated on

derivation of the geomorphologic features. Therefore, the 5-m bathymetric synthesis was 

excluded from our analysis.

The aerial topographic and bathymetric LiDAR collected in 2013 by Joint Airborne LiDAR

Bathymetry Technical Center of Expertise with funding provided by the US Army Corps of 

Engineers (USACE) National Coastal Mapping Program (NCMP) (USACE NCMP, 2016) 

around most of the main Hawaiian Islands was used to derive geomorphologic benthic 

characteristics. The data were adjusted to the local mean sea level (LMSL). The bathymetric 

LiDAR points were gridded at 2-m pixel resolution. The cell values in this data set represent the 

minimum depth measurement found within each cell, or if there were no values in the cell, a 

value have been interpolated from surrounding cells with data values using Inverse Distance 

Weighting method.

We derived a series of benthic geomorphology variables for the nearshore environment of Kauai, 

Oahu, Molokai, Lanai, Maui and Hawaii Islands where the 2013 bathymetric LiDAR is 

available. The open source GIS software, System for Automated Geoscientific Analysis (SAGA) 

version 2.1.4 (Conrad et al., 2015) was used for the processing. A total of nine geomorphology 

variables were derived for this study: depth, aspect, rugosity, plan curvature, profile curvature, 

slope, slope of slope, real surface area, and terrain surface convexity. Each variable and tools to 

derive them is described in Table 1. Watkins (2015) describes further details on calculating each 

of these benthic geomorphology variables.
3

Table 1. List of benthic geomorphology variables derived from LiDAR. The base imagery 

shows Kaneohe Bay, Oahu

Geomorphology Variables Description

Depth (m) Depth is distance from the sea surface to the bottom 

of the ocean. The bathymetric LiDAR data collected 

around the main Hawaiian Islands in 2013 were 

used in the analysis. The data were adjusted to local 

mean sea level, and gridded at 2-m pixel resolution.

The cell values in the data represent the minimum 

depth measurement found in each cell. 

Aspect (°) Aspect shows the compass direction that the surface 

faces at a cell. It can be thought of as slope 

direction. It is derived with the Slope, Aspect, 

Curvature tool using the nine parameter secondorder polynomial method (Zevenbergen and Thorne, 

1987). Values range from 0 to 360 degrees.

Plan Curvature Plan curvature is perpendicular to the direction of 

the maximum slope. A positive value indicates the 

surface is horizontally convex at that cell, while a 

negative value indicates horizontally concave at that 

cell. A value of zero indicates the surface is linear. It 

is derived with the Slope, Aspect, Curvature tool 

using the nine parameter second-order polynomial 

method (Zevenbergen and Thorne, 1987). 

Profile Curvature Profile curvature is parallel to the direction of the 

maximum slope. A negative value indicates that the 

surface is upwardly convex; a positive value, 

concave. Zero indicates a linear surface. It is derived 

with the Slope, Aspect, Curvature tool using the 

nine parameter second-order polynomial method 

(Zevenbergen and Thorne, 1987).

Slope (°) Slope is the maximum change in depth over distance 

between the cell and its neighboring cells. It is 

derived with the Slope, Aspect, Curvature tool using 

the nine parameter second-order polynomial method 

(Zevenbergen and Thorne, 1987). Values range 

from 0 to 90 degrees.
Geomorphology Variables Description

Slope of Slope Slope of slope is maximum rate of maximum slope 

change between the cell and its neighboring cells 

(Pittman et al., 2009). It is a second derivative of 

bathymetry. Unit is degrees of degrees. It is derived 

with the Slope, Aspect, Curvature tool using the 

nine parameter second-order polynomial method 

(Zevenbergen and Thorne, 1987).

Surface Area (m2) Real surface area (Grohmann et al., 2009) is derived 

using Real Surface Area tool. This is a measure of 

surface roughness. Rougher surfaces have greater 

surface areas.

Rugosity Rugosity (or surface area ratio) is derived by 

dividing real surface area by the geometric surface 

area (or planimetric area). This is a unitless measure 

of surface roughness. The minimum value is 1 and 

indicates flat surface.

Terrain Surface Convexity Terrain surface convexity is measured as the 

percentage of convex-upward cells within a constant 

radius of ten cells (Iwahashi and Pike, 2007). It is 

derived using Terrain Surface Convexity tool.

Sources: Esri, DigitalGlobe, GeoEye, Earthstar Geographics, CNES/Airbus DS, USDA, USGS, AEX, 

Getmapping, Aerogrid, IGN, IGP, swisstopo, and the GIS User Community. The scale bar for each image 

shows the range of values within the extent of the map.

For each of the benthic geomorphology variables described above, site-specific values were 

extracted for each fish survey location in the main Hawaiian Islands using ESRI’s ArcToolbox. 

In addition, it has long been recognized that different metrics of fish communities respond to 

different scales of their environment (Mellin et al., 2009). Since we do not know the specific 

spatial scale that would be most important for our study, we employ a multi-scale approach and 

calculate the average and standard deviation of all geomorphology values within radii of 15, 25, 

and 50 m (i.e., diameters of 30, 50, and 100 m) of each input cell location and extract this 

information for each GPS location of fish survey. This was conducted to characterize the 

geomorphology of each survey location at four spatial scales: one that is based on the sitespecific geomorphology value for each fish survey (0 m), and three that are based on averaging

all cells within 15, 25, and 50 m of the survey site. Thus, this framework allowed us to 
5

investigate linkages between fish biomass and multiple scales of benthic structure. A list of all 

geomorphological variables tested here can be found in Table 2. 

Table 2. List of all combinations of geomorphological metrics, spatial scales, and 

summary metrics tested as potential stratification variables.

Geomorphological Variable Spatial Scale Summary metric

Aspect 0 Point-value

30 Mean

Standard Deviation

50 Mean

Standard Deviation

100 Mean

Standard Deviation

Plan Curvature 0 Point-value

30 Mean

Standard Deviation

50 Mean

Standard Deviation

100 Mean

Standard Deviation

Profile Curvature 0 Point-value

30 Mean

Standard Deviation

50 Mean

Standard Deviation

100 Mean

Standard Deviation

Rugosity 0 Point-value

30 Mean

Standard Deviation

50 Mean

Standard Deviation

100 Mean

Standard Deviation

Slope 0 Point-value

30 Mean

Standard Deviation

50 Mean

Standard Deviation

100 Mean

Standard Deviation

Slope of Slope 0 Point-value

30 Mean

Standard Deviation

50 Mean

Standard Deviation

100 Mean

Standard Deviation
Geomorphological Variable Spatial Scale Summary metric

Surface Area 0 Point-value

30 Mean

Standard Deviation

50 Mean

Standard Deviation

100 Mean

Standard Deviation

Terrain Surface Convexity 0 Point-value

30 Mean

Standard Deviation

50 Mean

Standard Deviation

100 Mean

Standard Deviation

Fish Variables

Fish data were collected around islands in main Hawaiian Islands in the years 2010, 2012, 2013, 

2015, and 2016 using identical methods as part of Pacific RAMP. Prior to each field season, fish 

survey sites were randomly selected at hard-bottom depths between 0 and 30 m, with effort (i.e., 

the number of survey sites) allocated proportionally to the amount of reef area found at 3 depth 

strata (shallow or 0–6 m; mid-depth or > 6–18 m; and deep or > 18–30 m). At each survey site, 

paired divers collected replicate data on fish sizes and counts using a stationary point count 

(SPC) method. The surveys consisted of: (i) a 5-min enumeration period when divers recorded 

all fish species that passed through a visually estimated cylinder of 7.5-m radius and (ii) a 

tallying period when divers recorded all sizes and counts of all fish species listed during the 

enumeration period. For more information of fish survey methodology, details are available at 

Ayotte et al. 2011. Count and size data were then converted to fish biomass (g m-2

). Fish biomass

were summarized at an island-level spatial scale by first pooling across sites within strata, and 

then summing across strata weighted by reef area. For this project, we used a total of 9 fish 

biomass indicators, including 4 trophic groups (primary consumers, secondary consumers, 

planktivores, piscivores), three size classes (0–20 cm; 20–50 cm; and 50+ cm), as well as 

parrotfishes and total fish biomass. All fish biomass indicators are deemed priority indicators by 

the NOAA National Coral Reef Monitoring Plan (NOAA Coral Program, 2014; Heenan et al., 

2015; McCoy et al., 2017; McCoy et al., 2016).

Design Performance

A total of 803 fish surveys with benthic geomorphology data were used in this analysis (195 

deep strata, 387 mid-depth strata, and 221 shallow strata surveys). The first step was to look for 

trends between each of the 9 fish biomass indicators and each of the 8 geomorphological metrics

(each of which was listed in Table 1. For each fish-geomorphological pairing, we calculated the 

mean biomass of all fish surveys in the data set, and used local polynomial regression fitting 

(loess, α = 1.5) to fit a smoothed curve and 95% confidence intervals (estimated using standard 

error) to the data. The loess model works by fitting a low-degree polynomial using weighted 

least squares, meaning that when fitting the curve, the amount of weight given to any point is 

inversely proportional to its distance from the point being estimated (Cleveland et al., 1992). 
7

This was done for all geomorphological variables (e.g., slope, aspect, convexity, etc.) and for all 

moving averages and standard deviations (e.g., 0-, 30-, 50-, and 100-m spatial scale). The 

purpose of these loess curves is to help in determining potential strata boundaries in a 

stratification scheme. Once potential strata boundaries were decided, all fish sites were assigned 

to new strata that were now based on geomorphology and depth (i.e., post-stratification), thus 

allowing us to compare each new stratification design to the original design based only on depth. 

Finally, our framework for evaluating design performance is based on examining the trade-off 

between enhancing the precision of fish biomass estimates and increasing the overall survey 

effort (i.e., cost) by adding additional sample sizes (Smith et al., 2011; Ault and Smith, 2008). To 

do this, we calculated for each data set, n*, or the number of primary units (i.e., survey sites) 

required to achieve a specified coefficient of variation, CV (here, we use a CV of 20%; Equation 

1 below). The resulting n* for each sampling scheme assumes that the allocation of survey sites 

among strata places more surveys in more variable strata and fewer surveys in less variable 

strata. 

Equation 1: n* 

whereby

= ,

and wh is the stratum h weighting factor, or the proportion of the stratum area relative to the 

total survey area

sh is the stratum h standard deviation in fish biomass,

is the target variance for future surveys of fish biomass

is the target coefficient of variation for future surveys of fish biomass

is the domain-wide estimate of biomass,

N is the total number of primary unit samples, and

sh

2 is the stratum h variance in fish biomass.

Due to gaps in the geomorphological layers described above, the number of fish survey sites with 

associated geomorphological data varies across the different spatial scales of averaging buffers. 

Thus, in order to accurately compare n* for the various data sets, we only include fish survey 

sites that had geomorphological data for all spatial scales. Luckily, the Pacific RAMP reef fish 

dataset is relatively large with 1185 sites surveys conducted between 2010 and 2016; even after 

filtering out fish surveys with incomplete geomorphological metrics, a total of 804 fish surveys 

were retained for our analysis.
Finally, a separate synthesis bathymetric data set available from HMRG (from here on, 

“synthesis maps”) was used to derive the same geomorphology metrics at a coarser spatial scale. 

These synthesis maps are integrated into CREP’s current survey design, which stratifies effort 

based only on depth. The advantage of these maps is they have greater spatial coverage of our 

target domain (hard-bottom habitats between 0 and 30 m). The disadvantage, however, is that 

they are much coarser (50-m × 50-m resolution). The purpose of this final step was to 

demonstrate whether this approach of stratifying based on depth and geomorphology could be 

put into practice, even for areas of the Pacific where we do not have high-resolution LiDAR data. 

Results

Based on visually inspecting the loess curves of all geomorphological metrics, we determined 

that mean rugosity, mean slope, mean slope of slope, and standard deviation of profile curvature 

showed the most promise for improving fish survey design. For each of their loess curves, we see 

that low measures of the geomorphology metric are significantly less than (based on 95% 

confidence intervals) the global mean for fish biomass, while high measures of the 

geomorphology metric are significantly greater than the global mean. In other words, the loess 

curves for each of these geomorphologies displayed clear trends with total reef fish biomass

(e.g., Figure 1A; Appendix B), as well as with several other indicator groups of fish biomass as 

opposed to a flat line (Figure 1B). 

Conversely, the following metrics were not considered further, either because their loess curve 

showed no trend with fish biomass (i.e., displayed a flat line; Appendix C), or if the metric’s 

distribution was overly skewed (e.g., mean surface area; Appendix C): mean aspect, mean 

convexity, mean planar curvature, mean profile curvature, and mean surface area, as well as all 

standard deviation metrics except that for profile curvature. 

The remaining analyses focused on these four candidate geomorphology metrics: mean rugosity, 

mean slope, mean slope of slope, and standard deviation of profile curvature. Furthermore, in 

terms of spatial scale, we found increasing correlations between fish biomass at larger scales (50 

and 100 m) as opposed to smaller scales. The difference in correlation between spatial scales was 

relatively small (e.g., for slope of slope, correlation with total reef fish biomass increased from 

0.15 at 0 m to 0.28 at 100 m), however, this pattern of increasing correlation for larger scales was 

consistent for all four candidate geomorphology metrics. One possible explanation is that large, 

roving predators, which tend to add stochastic noise to reef fish data, are correlated more with 

these larger scale geomorphologies, thus driving this pattern of increased correlation at larger 

scales. Others have suggested that the home range of a fish species is an important factor in 

determining to what environmental spatial scale the species will respond, but it is difficult to 

generalize across species due to the limited number of species with information on home-ranging 

behavior (Pittman and Brown, 2011). Since the final step in our analysis was to compare 

LiDAR-derived metrics with metrics derived from the coarser 50-m × 50-m synthesis maps, we 

focused our analysis of LiDAR metrics at the 50-m spatial scale. 

To determine the strata boundaries for each geomorphological metric, we looked for regions in 

the loess curve that tended to be less than, equal to, or greater than the mean biomass. For 

example, for slope of slope, total fish biomass is generally below the mean for lower slope of 

slope values and above the mean for higher slope of slope values, corresponding to two strata. 
9

The point at which the loess curve intersects the mean biomass line was used to identify strata

boundaries (Figure 1A; green line). 

Figure 1. Fish biomass for total reef fish biomass vs. slope of slope (A) and aspect (B) for 

sites in the main Hawaiian Islands.

Displayed on each graph are the site-level survey data (points), global mean (black dotted line), loess 

curve (red solid line), and 95% confidence intervals (red dotted line). Total reef fish biomass appears to 

trend with slope of slope, justifying the delineation of strata with regards to slope of slope. The green line 

represents the boundary between low and high slope of slope. On the other hand, total reef fish biomass 

appears to have no relationship with aspect. 

For a given geomorphology metric, we found relatively broad agreement in strata boundaries 

across different spatial scales as well as across fish biomass indicators. For example, for slope, 

the strata boundary between low slope and high slope was similar across all spatial scales (Figure 

2) as well as for various fish biomass indicators (Figure 3). Strata boundaries for mean rugosity, 

mean slope, mean slope of slope, and standard deviation of profile curvature can be found in 

Table 3.

Table 3. Strata boundaries for various geomorphology metrics based on inspection of 

loess curves.

Geomorphology Strata Boundary

Mean Rugosity 1.025

Mean Slope 8

Mean Slope of Slope 50

Profile Curvature Standard Deviation 0.1
Loess curves for the geomorphology metrics that displayed a trend with total reef fish biomass 

based on visual inspection of loess curves as described above (i.e., mean rugosity, mean slope, 

mean slope of slope, standard deviation of profile curvature) can be found in Appendix B. A total 

of 640 loess curves were created for this study, each displaying patterns between each variable in 

Table 1 and each of the 9 fish biomass indicators. Because of the sheer number of graphs, we 

only show the mean metric of each geomorphology variable at 50-m spatial scales as examples 

in Appendix B. Examples of geomorphology metrics that did not display clear trends with fish 

biomass can be found in Appendix C.

Figure 2. Slope, as an example of how for a given geomorphology, the assignment of 

strata bounds (green line) was consistent across different spatial scales.

Clockwise from top left: 0 m, 30 m, 100 m, and 50 m.
11

Figure 3. Slope at the 50-m scale shown as an example of how, for a given 

geomorphology, the assignment of strata bounds (green line) was consistent across 

different fish indicators.

Based on these strata boundaries, each fish survey site was assigned to a stratum based on its

depth and geomorphology characteristic (i.e., post-stratification). For each stratification scheme, 

the number of samples (n*) required in a future survey to achieve a CV of 20% was calculated. 

Next, n* for depth only vs. depth and geomorphology stratification were compared. Overall, the 

geomorphology metric that resulted in the greatest reduction in n* (i.e., the stratification scheme 

with the most efficient sampling) across all fish biomass indicators and across all islands was 

standard deviation of profile curvature at the 50-m scale (Table 4). Finally, the most efficient 

sampling scheme for each fish biomass indicator is listed in Table 5.
Table 4. A comparison of n* (CV = 20%) for depth only vs. depth and standard deviation 

of profile curvature at 50 m for various fish biomass indicators and four main Hawaiian 

Island complexes. 

Total sample reduction was calculated as the difference in n* between depth only vs. depth and profile 

curvature summed across all islands.

Indicator Stratification Scheme Hawaii Kauai

Maui 

Nui Oahu

Total Sample 

Reduction

Total Fish Depth Only 11.82 26.96 30.39 26.73 12.62 Depth + Profile Curvature 11.56 21.00 29.25 21.46

Primary Depth Only 14.70 25.10 34.65 39.52 19.37 Depth + Profile Curvature 13.75 18.21 30.11 32.54

Secondary Depth Only 21.44 20.73 32.34 23.17 21.09 Depth + Profile Curvature 18.97 16.39 24.13 17.10

Planktivore Depth Only 44.17 52.22 111.79 86.93 27.36 Depth + Profile Curvature 43.34 45.43 108.93 70.05

Piscivore Depth Only 47.56 38.77 52.22 74.64 17.45 Depth + Profile Curvature 40.52 28.09 52.29 74.84

0–20 cm Depth Only 18.57 16.33 27.10 24.32 5.18 Depth + Profile Curvature 14.87 15.85 28.21 22.22

20–50 cm Depth Only 19.48 25.67 37.91 46.89 19.43 Depth + Profile Curvature 19.56 21.38 30.98 38.59

50 cm+ Depth Only 98.14 36.21 124.35 117.78 136.41 Depth + Profile Curvature 67.71 25.88 77.30 69.18

Parrots Depth Only 46.68 46.73 61.15 104.35 58.49 Depth + Profile Curvature 41.50 28.26 59.90 70.75

Table 5. A list of geomorphology metrics and spatial scales found to produce the 

greatest total sample reduction across all islands for individual fish biomass indicators.

Indicator Optimal Geomorphology Strata

Total Sample 

Reduction

Total Fish Mean Slope of Slope at 100 m 13.85

Primary Profile Curvature Standard Deviation at 50 m 19.37

Secondary Profile Curvature Standard Deviation at 100 m 22.67

Planktivores Mean Slope at 50 m 39.95

Piscivores Mean Slope of Slope at 0 m 24.45

0–20 cm Profile Curvature Standard Deviation at 30 m 6.42

20–50 cm Mean Slope of Slope at 100 m 19.88

50+ cm Profile Curvature Standard Deviation at 100 m 140.83

Parrotfishes Profile Curvature Standard Deviation at 50 m 58.49

OVERALL Profile Curvature Standard Deviation at 50 m 317.38
13

Discussion

We found several geomorphological characteristics (e.g., mean slope, mean slope of slope, mean 

rugosity, and standard deviation of profile convexity) for a variety of spatial scales, which if 

added as a second stratum variable, enhanced our survey design efficiency when compared to 

depth-only stratification.

Slope (Pittman and Brown, 2011), slope of slope (Pittman et al., 2009), as well as remotely

sensed rugosity (Kuffner et al., 2007), were found to be important predictors of fish biomass, 

abundance, and/or diversity in numerous other studies (Mellin et al., 2009). In our analysis, 

standard deviation of profile curvature produced the most efficient survey design when combined 

with depth stratification. As far as we know, however, this geomorphology variable has not been 

emphasized in previous studies of reef fish distributions. 

Profile curvature (Figure 4, top row) is measured in the parallel direction of the maximum slope, 

while planform curvature (Figure 4, bottom row) is measured perpendicular to the direction of 

the maximum slope. Large values of curvature represent complex terrain, and positive or 

negative values are indicative of either upwardly concave or convex surface in the vertical 

(profile) and horizontal (planform) direction relating to slope. The importance of profile 

curvature standard deviation in our survey efficiency analysis indicates that variation in 

upwardly convex and concave environments (i.e., complex benthic terrain) may be an 

overlooked geomorphological variable that can aid in reef fish biomass survey design. That 

planform curvature was not found to be an important geomorphological variable suggests that 

horizontal or sideward convexity/concavity has less influence on reef fish distributions. This 

makes sense if one considers that reef fish distributions and the oceanographic environment, in 

general, are vertically as opposed to horizontally patterned. 

Figure 4. Top row: Illustration of profile curvature; Bottom row: Illustration of plan 

curvature. 

Graphic credit: Esri, https://blogs.esri.com/esri/arcgis/2010/10/27/understanding-curvature-rasters/
While other studies (Chitarro, 2004) have shown that spatial scale had little influence with regard 

to predictive power, we found increasing predictive power with broader spatial scales. When 

looking at individual fish biomass indicators (Table 4), the most efficient survey designs mainly 

included larger (e.g., 50 and 100 m), as opposed to smaller, spatial scale predictors. One should 

exercise caution, however, in making generalizations of patterns across the different fish 

indicator groups. Previous attempts to compare across studies found that the relationships 

between remotely-sensed geomorphology and fish assemblages were widely varied, with 

biogeography and reef types being among some of the confounding factors (Mellin et al., 2009). 

We also demonstrate in our analysis the importance of spatial resolution when initially deriving 

the geomorphologies. Of the LiDAR-derived geomorphologies that were found to increase 

survey efficiency (i.e., mean slope, mean slope of slope, mean rugosity, and profile curvature 

standard deviation), none of them were found to produce the same effect when derived from 

coarser “synthesis” maps (see Materials and Methods). Although we used the 50-m spatial scale 

to calculate sampling efficiency (i.e., n*) for each of our candidate geomorphology metrics, the 

original data came from much finer (i.e., 2-m) resolution LiDAR maps. Thus, even though we 

summarize the geomorphology metrics at a 50 m spatial scale, there is additional fine-scale 

information in the 2-m resolution LiDAR data that is presumably lost when we move to the 50-m 

“synthesis” maps.

In the future, we intend to explore more systematic possibilities for visualizing fishgeomorphology trends and determining strata boundaries. The strategy of using loess curves to 

explore overall trends in the data was mainly used as a first pass. There are likely more 

sophisticated techniques for exploring fish biomass trends with benthic morphology (e.g., 

GAMs) as well as optimization algorithms for stratifying data with the goal of lowering variance 

in each strata (e.g., R package SamplingStrata; Barcaroli 2014). Furthermore, a better test of 

design performance would be to derive the geomorphology stratas using a portion of the Pacific 

RAMP fish data set (e.g., only certain years or islands) and then testing its effect on design 

performance on the remaining portion. Overall, the analytical framework described here (i.e., n*

calculation) forms the basis for continuing to explore how to improve the efficiency of future 

reef fish monitoring efforts under Pacific RAMP.

Acknowledgements

This report was made possible with funding support from NOAA’s Coral Reef Conservation 

Program. Numerous people helped at various stages of the project. Russell Watkins and John 

Rooney helped to get the initial funding. Feedback was provided by Ivor Williams, Annette 

DesRochers and Rhonda Suka. Technical data support was provided by Ross Winans. 
15

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APPENDIX	A	–	Example	of	distortions	observed	in	the	5-m	bathymetric	data,	exacerbated	upon	

derivation	of	geomorphology	features	(the	focus	of	this	project),	thus	causing	us	to	turn	to	

other	mapping	data	sources.

A-1
APPENDIX	B	–	Geomorphology metrics with loess curves that trend with fish biomass (i.e.,

low measures of the geomorphology metric are significantly less than (based on 95% 

confidence intervals) the global mean for fish biomass, while high measures of the 

geomorphology metric are significantly greater than the global mean

STANDARD	DEVIATION	OF	PROFILE	

CURVATURE	AT	50	m

0.05 0.10 0.15 0.20 0.25 0.30

0 100 200 300 400

Total Fish

std

g m

−

2

B-1
MEAN	RUGOSITY	AT	50	m

1.00 1.10 1.20 1.30

0 100 200 300 400

Total Fish

rugosity

g m

−

2

B-2
MEAN	SLOPE	AT	50	m

5 10 15 20 25 30

0 100 200 300 400

Total Fish

slope

g m

−

2

B-3
MEAN	SLOPE	OF	SLOPE	AT	50	m

20 30 40 50 60 70

0 100 200 300 400

Total Fish

slope_of_slope

g m

−

2

B-4
APPENDIX	C	–	Geomorphology	metrics	with	loess	curves	that	show	no	significant	trend	

with	total	fish	biomass	based	on	loess	curves	whose	95%	confidence	intervals	overlap	with	

the	global	mean	for	fish	biomass	throughout	the	full	range	of	biomasses.

MEAN ASPECT AT 50 m	

100 150 200 250 300

0 100 200 300 400

Total Fish

aspect

g m

−

2

C-1
MEAN	CONVEXITY	AT	50	m

0.40 0.45 0.50 0.55 0.60

0 100 200 300 400

Total Fish

convexity

g m

−

2

C-2
MEAN	PLANAR	CURVATURE	AT	50	m	

−0.4 −0.2 0.0 0.2 0.4

0 100 200 300 400

Total Fish

plan_curvature

g m

−

2

C-3
MEAN	PROFILE	CURVATURE	AT	50	m

−0.02 −0.01 0.00 0.01 0.02

0 100 200 300 400

Total Fish

profile_curvature

g m

−

2

C-4
MEAN	SURFACE	AREA	AT	50	m

4.0 4.2 4.4 4.6 4.8 5.0 5.2 5.4

0 100 200 300 400

Total Fish

surface_area

g m

−

2

C-5