A simple, rapid method for mapping bathymetry

of small wetland basins

Chris Wilcox*, Marc Los Huertos

Department of Environmental Studies, University of California, Santa Cruz, CA 95064, USA

Received 25 July 2002; revised 28 May 2004; accepted 15 June 2004

Abstract

Many tools exist for determining and mapping the bathymetry and topography of aquatic systems, such as freshwater

wetlands. However, these tools often require time-consuming survey work to produce accurate maps. In particular, the large

quantity of data necessary may be prohibitive for projects where determining bathymetry is not a central focus, but instead a

necessary step in achieving some other goal. We present a method to produce bathymetric surface maps with a minimum

amount of effort using global positioning system receiver and laser transit survey data. We also demonstrate that this method is

surprisingly accurate, given the small amount of data we use to generate the bathymetry maps.

q 2004 Elsevier B.V. All rights reserved.

Keywords: Bathymetry; Wetland; Map; Vernal pool

1. Introduction

Many tools exist for determining and mapping the

bathymetry and topography of aquatic systems, such

as freshwater wetlands (Barrette et al., 2000;

Cruz-Orozco et al., 1996; Gardner et al., 1998;

Roberts and Anderson, 1999). However, many of

these tools require large amounts of data on basin

elevations at fine scales across the landscape to be

mapped (Kavanagh and Bird, 2000; Wright, 1982).

This quantity of data may make mapping prohibitive

0022-1694/$ - see front matter q 2004 Elsevier B.V. All rights reserved.

doi:10.1016/j.jhydrol.2004.06.027

* Corresponding author. Present address: Department of Zoology

and Entomology, University of Queensland, St Lucia, QLD 4072,

Australia.

E-mail addresses: c.wilcox@uq.edu.au (C. Wilcox), marcos@

cats.ucsc.edu (M.L. Huertos).

for projects where determining bathymetry is not a

central focus, but instead a necessary step in some

other process. For instance, determining population

sizes of aquatic species using subsamples requires an

estimate of the water volume in the habitat. In this

case the primary objective in developing bathymetric

maps might be to determine the approximate volume

of water present in the basin at the time of sampling

using the depth at some known location. As such,

detailed bathymetry may not be necessary, however,

due to potentially complex basin shapes it may not be

possible to use a simple approximation, such as a cone

with similar depth and surface area, to estimate basin

volume.

We describe a method for generating bathymetry

using a combination of transit survey points

Journal of Hydrology 301 (2005) 29–36

www.elsevier.com/locate/jhydrol

C. Wilcox, M.L. Huertos / Journal of Hydrology 301 (2005) 29–3630

and locations generated using a global positioning

system. We have been studying a system of vernal

pools, seasonal wetlands that form in shallow basins

underlain by an impervious soil layer. These features

often occur in large complexes with many basins areas

where the soils and climate are appropriate. While

there is some disagreement over how vernal pools are

formed, it is generally assumed to be through

weathering of soil in low lying areas and uplift of

soil in other area by the activity of burrowing

mammals. The resulting basins are relatively shallow,

filling directly from rainfall and drying by evapo-

transpiration. While some overland flow into the

basins occurs, it is generally limited to spillover from

adjoining basins at higher elevations and limited

contributions from upland areas around the basin

itself. There is little transport of sediments into the

basins, and their dimensions remain stable for

decades, perhaps centuries.

Our goal was to develop bathymetric surfaces for

over 120 vernal pools as background for a study on the

population dynamics of several endangered crus-

tacean species that utilize these basins as habitat. As

such, we needed a method that: (1) required minimum

field time; (2) that could be applied to a wide variety

of basin shapes; and (3) would provide reasonably

accurate maps of the basins. We decided on a process

combining direct measurements of spatial coordinates

in the basins and indirect measurements of the basin

topography using high and low water levels in the

basins. Using regression techniques we were then able

to extend the usefulness of these basic measurements

to accurately predict the bathymetry of the basins.

2. Methods

2.1. Study system

Our work was conducted on the West Bear Creek

unit of the San Luis National Wildlife Refuge, Merced

County, California. This site is composed of an

elevated clay lens, bounded on the west by Salt

Slough and on the east by the San Joaquin River. The

site is bisected by numerous small seasonal channels,

or swales that drain overland water flow from upland

areas. Vernal pools are seasonal wetlands that form on

the uplands between these swales. These wetlands are

underlain by an impermeable clay layer and dry by

evapotranspiration. The basins vary in size, with

surface areas ranging from less than 10 m2 to more

than 21,000 m2. The basins are gentle in relief, their

depth is proportional to their surface area, and none

of the basins hold standing water deeper than 75 cm

(C. Wilcox personal observation). Adjoining basins

are generally connected, and the gentle slope across

the uplands results in directional flow from the

spillway of one basin into the next and so on until

the excess flow reaches one of the swales that drains

the site.

2.2. Indirect basin measurements using GPS

We were able to gain some information on the

topography of the basins indirectly using observations

on the hydrology of the basins. We followed the

drying process in all of the basins during 1997 to

determine the deepest point in each basin. Although

several isolated pools of water were present during the

drying phase in some basins, standing water persisted

the longest in the deepest part of the basins. We

assumed that the last point with standing water was

the deepest point in the basin. This point was

permanently marked by pounding a steel stake into

the sediment to a depth of 50 cm, leaving 10 cm above

the surface. We will refer to this point as the pool

center (Fig. 1a). By following these locations as water

first began filling the pools in the two proceeding wet

seasons, we confirmed that they were the lowest

points in each basin.

We used a Trimble Pathfinder Pro XR GPS to map

the permanent center stake in each pool. We also

mapped the high water mark around the perimeter of

each basin (Fig. 1a). We determined the location of

the high water mark using a combination of vegetation

changes and other evidence, such as matted vegetation

or algae. The transition from the basin to the

surrounding upland is generally abrupt in these

systems, and based on observations during subsequent

wet seasons our initial mapping of the basin perimeter

was accurate. Finally, we surveyed points along the

boundary of the water in the basin at the time of the

survey. The GPS survey was conducted during April

1998, when most pools had standing water, but had

dried to levels well below their high water mark. GPS

data was differentially corrected using data from

Fig. 1. Empirical data collected to map a vernal pool basin, (a) Initial measurement of the basin boundary using GPS. Laser transit data points at

the pool center and along the initial 4 transects (transects at 908 intervals, 3 points each: one in the interior of the basin, one at the boundary, and

one exterior) are also displayed. (b) Prediction of depths at points along the transects using linear interpolation. Each shade change in the

interpolated data points represents a 0.01 m increase in elevation from 0 at the pool center to 0.16 at the basin boundary.

C. Wilcox, M.L. Huertos / Journal of Hydrology 301 (2005) 29–36 31

Trimble Company’s base station (ftp://ftp.trimble.

comlpub/cbsfiles/), located in San Jose, CA.

2.3. Laser surveys of pool basins

We used a laser transit (Sokia total station, model

SDM3F, supplied by Lietz, 9111 Barton, Overland

Park, KS) to survey 4 transects radiating out from the

center stake in the pool toward the perimeter at 908

intervals (Fig. 1a). Along each transect, we surveyed 3

points, midway between the pool boundary and the

center stake, at the highest water mark, and a third in

the adjoining upland area (Fig. 1a). If the pool was

significantly asymmetric, we added additional trans-

ects to better specify the shape of the pool (Fig. 1b).

We were attempting to minimize effort, so we added

the minimum number of transects that were required

to specify the shape of the pool. In some cases, this

required adding additional points in the interior of the

pool. We followed a simple set of rules in adding

these points: (1) transects should follow the lowest

elevation path possible to reach the pool boundary;

and (2) transects should be added only until there is a

direct line of sight possible between interior points in

neighboring transects (Fig. 1b). For example, for the

pool shown in Fig. 1, we added three additional

transects characterize the shape of the basin. Note that

these transects share a common interior point.

2.4. Interpolating transect points

In order to increase the density of the points along

each transect, we assumed a linear change in elevation

between adjoining points along each transect. We

calculated the slope of this transition by dividing the

increase in elevation between points by the horizontal

distance. Using this slope and one of the points as the

intercept we then predicted the coordinates of points

along the transect line in between the two known

points (Fig. 1b). We scaled the spacing between these

points to be similar to the points that were taken along

the pool boundary using GPS.

Fig. 2. Bathymetry of a vernal pool basin predicted based on our

mapping method. (a) The relationship between relative altitude and

relative distance for this pool used to generate additional point data

in the basin. The elevation changes from 0 m at the pool center to

0.162 m at the basin boundary, and is resealed by the boundary

elevation. The length of the transects, from the center to the

surrounding upland, is different for each transect, ranging from 8.7

to 41.9 m. The regression line is a third order polynomial regression

(yZ1.33x3K0.95x2C0.60x, R2Z87.6). (b) The predicted bathy-

metry for the pool basin using both empirical data and predicted

values for elevations. The data points used to create the map are

shown as lines of shaded shapes. The shading indicates the elevation

of the data points, with each shade change denoting an increase in

elevation of 0.01 m. This figure includes the initial 4 transects at 908

angles, 3 additional transects (although note that the interior point

C. Wilcox, M.L. Huertos / Journal of Hydrology 301 (2005) 29–3632

2.5. Creating boundary points

We estimated the elevation of the boundary for

each pool as the mean of the elevations for all of the

laser transit transects at the pool boundary. We then

assigned this mean elevation to all of the GPS

coordinates taken at the pool boundary (highest

water mark). In cases where our laser survey point

at the boundary did not match the boundary mapped

using GPS, we used the linear interpolation described

above to predict the elevation of the transect at the

point where it crossed the pool boundary. We used

this predicted point in our calculation of the mean

elevation at the boundary.

2.6. Generating additional point data

within the basins

In cases where the pools had complex shapes, our

field data and interpolated points would provide

only a rough approximation of the basin shape

(Fig. 1b). In order to more completely specify the

shape of the basins we predicted coordinates along a

number of paths running from the pool center to the

boundary. We did this by first scaling all of the

points along each transect by the transect length and

the total elevation change (Fig. 2a). After rescaling,

transects were used as replicate profiles of the

transition from the basin center to the boundary. We

used regression to generate a predictive relationship

between the relative distance from the center to the

pool boundary and the relative elevation from the

deepest point to the boundary height (Fig. 2a). In

most cases a second order regression equation

adequately fit the profile data, although in some

cases a third order was used when there was a

marked improvement in the R2. We used this

regression equation and coordinates of the pool

center and a point on the boundary to interpolate

additional points in the basin along paths running

from the center to the boundary (Fig. 2b). Again we

for the additional transects is the same and points have not been

interpolated between it and the pool center point), and data points

predicted along 6 additional transects using the relationship in panel

a, above. Isolines are at 0.025 m intervals. For additional

explanation of the regression models see Section 2: Generating

Additional Bathymetry Data.

Table 1

Sizes of 24 basins used to check the mapping method

Basin Mean depth

(m)

Coefficient

of variation

Number of

GPS points

Basin size

(m2)

A 0.059 0.0021 107 301.0

B 0.138 0.0219 550 8123.0

C 0.109 0.0078 182 1796.0

D 0.256 0.0022 501 11659.0

E 0.136 0.0034 167 2744.0

F 0.087 0.0038 109 1288.0

G 0.070 0.0455 197 6818.0

H 0.151 0.0063 144 1389.0

I 0.017 0.0073 82 219.0

J 0.087 0.0075 66 229.0

K 0.034 0.0031 34 92.0

L 0.025 0.0304 92 3302.0

M 0.038 0.0031 84 319.0

N 0.123 0.0047 95 691.0

O 0.066 0.0039 111 526.0

P 0.033 0.0033 53 1362.0

Q 0.013 0.0242 16 58.0

R 0.016 0.0157 17 55.0

S 0.092 0.0068 177 1005.0

T 0.010 0.0049 35 140.0

U 0.029 0.0027 49 1217.0

V 0.034 0.0307 42 152.0

W 0.054 0.0060 20 31.0

X 0.041 0.0084 42 137.0

Mean elevation is the average of the elevations found by querying

the basin map using GPS points at the edge of water standing in the

basin as the basin dried. Basin size is the surface area of water in the

basin when it is filled to the high water mark.

C. Wilcox, M.L. Huertos / Journal of Hydrology 301 (2005) 29–36 33

scaled these points to be similar to the spatial scale

of the GPS points taken around the basin boundary.

Fig. 3. Variance in the predicted elevations around an unknown

constant value across 24 vernal pool basins.

2.7. Generating bathymetric surfaces

We created a triangulated irregular network (TIN)

using a combination of ARCVIEW and ARC/INFO.

An ARCVIEW shape file was created from the interior

transect points, interpolated transect points, and

additional interpolated points. We converted the file

to ARC/INFO coverage and processing each pool

separately using a script (AML—arc macro language).

Although some of the TINs we created had long narrow

triangles, which reduces the accuracy of the maps, we

found that the effect was not significant at the spatial

scale of these vernal pool basins.

2.8. Comparing predicted basin bathymetry

with observed conditions

We tested the accuracy of the maps by comparing

the elevations at a large number of points in the basins

that have an unknown, but constant value. We

Fig. 4. Variance in the predicted elevations at the edge of standing

water versus sample size. Sample size is the number of GPS points

collected at the boundary of the standing water in each basin. GPS

points were collected at a roughly constant interval thus the number

of points is proportional to the perimeter of the standing water.

Fig. 5. Variance in the predicted elevations at the edge of standing

water versus the size of the basin. Basin size is measured as the

surface area of water in the basin when the basin is filled to its high

water mark.

C. Wilcox, M.L. Huertos / Journal of Hydrology 301 (2005) 29–3634

generated points with a constant elevation by survey-

ing the location of the edge of the water in the pool

late in the season, when water levels were well below

the high water mark, using a GPS. We compared the

elevations predicted by our basin maps at each of

these points with the expectation that they should have

some mean value and no variance. The error in the

map is then measured by the spread of the elevations

at these points around the mean value. We can

generate a measure of the accuracy of the map by

calculating a confidence interval around the mean

elevation.

We hypothesized that more-irregularly shaped

basins might be less accurately mapped using our

method. As a simple measure of irregularity we

calculated the tortuosity of the basin boundary. We

calculated tortuosity using the variance in the turning

angle between successive pairs of points along the

pool boundary. For instance, a very regularly shaped

pool would have some mean turning angle between

pairs of points, with a very small variance around this

mean. If the pool was nearly a circle, the most

symmetric shape possible; the mean turning angle

would be 3608/n where n is the number of points taken

along the boundary of the pool. In this case the turning

angle would be constant, resulting in no variance

around the mean. As the boundary of a pool becomes

more complex the turning angle will vary more

between successive pairs of points, thus while the

mean may not change, the variance would increase.

3. Results

We compared elevations predicted at the boundary

of the observed standing water for 24 vernal pool

basins with a surface area ranging in size from 31 to

11659 m2 (Table 1). The range of mean elevations

predicted across the basin maps ranged from 1 to

Fig. 6. Standard deviation of the predicted elevations with pools of

increasingly complex shape. Pool shape complexity is measured as

the variance in the turning angle between successive pairs of GPS

data points taken at the pool boundary.

C. Wilcox, M.L. Huertos / Journal of Hydrology 301 (2005) 29–36 35

25.6 cm. The standard deviation of the elevations

within each basin was small, with a maximum of

0.056 m for any basin (Fig. 3). The variation in

elevations was small in comparison with the mean, the

maximum coefficient of variation observed was 0.044

and the maximum 95% confidence interval on any of

the mean elevations was G1 cm (Table 1). There was

no relationship between the number of GPS points

(i.e. the length of the perimeter of the water remaining

in the pool) and the variance in the predicted elevation

(Fig. 3). There was also no relationship between the

size of the basin, measured as the water surface area

when the basin is filled to its high water mark and the

variance in predicted elevations (Fig. 4). Finally, there

was no relationship between the complexity of the

basin shape, as measured by the tortuosity of the basin

boundary, and the variation in elevations predicted in

the basins (Figs. 5 and 6).

4. Discussion

The method we used for creating bathymetric

surfaces for seasonal wetland basins is surprisingly

accurate, given the very small amount of field data we

collected. We found only a small deviation in

predicted elevations along a known isoline in the

basins. In fact, the largest coefficient of variation in

elevation for any pool was only 0.0455 cm, and the

maximum 95% confidence interval on any of our

mean elevations was only 1 cm.

While we did not test the accuracy of our maps in

predicting the exact elevation at various points in the

basins, we tested the maps for consistency in

predicting an unknown, constant elevation at many

points in the basin. Directly testing our maps by

comparing them with measured elevations at many

known points would be difficult. First, collecting

transit data at many locations is time consuming. In

addition point measurements are probably not repre-

sentative of the shape of the basin due to localized

relief, for instance due to irregularities in the basin

floor from livestock hoof prints. Because the total

vertical differential across the vernal pool basins we

worked with was often less than 0.5 m, small

undulations or irregularities could have introduced

significant error into surveyed coordinates that might

used to verify our maps. While using water levels to

generate isolines does not completely avoid this

problem it does provide an opportunity to generate a

large number of known points rapidly, overcoming

the problem of errors introduced by locally varying

relief in the basin floor. In addition, since the water

level in the basins varies seasonally, we were able to

test our maps at a variety of locations across the 24

basins.

In some basins we surveyed as few as 13 laser

transit data points in the basin, including 4 transects of

3 points each and a point at the steel pin in the pool

center. These data, in combination with GPS locations

taken at the high water mark and at the center pin in

the basin were used to create the maps for simple

(oval) shaped basins. The total time required to collect

this data less than 15 min per basin. The most time

consuming part of the field work was the laser

survey work.

This method may not be applicable to all types of

wetland basins. One essential feature that allowed us

to maximize the information we gained from our data

is that we knew the location of the deepest point and

general shape of the basin, and thus were able to orient

our transects from this point along the deepest path to

a perpendicular intersection with the basin perimeter

(Fig. 1a). This allowed us to quantify the general

profile of the basin and thus predict points outside the

transects. This uniformity of shape likely results from

the absence of significant in or outflow, which limits

the effect of erosion, leaving wind driven sediment

movement and weathering as the main processes

C. Wilcox, M.L. Huertos / Journal of Hydrology 301 (2005) 29–3636

shaping these closed basins. We believe this method is

widely applicable to basins that have smooth

transitions between the bottom and the perimeter,

where the slope of the transition is relatively constant

in proportion to the distance from the bottom to the

perimeter.

Given that a basin has smooth transitions, it should

be possible to generate reasonably accurate bathy-

metric maps by following these steps: (1) find the

deepest point of the basin; (2) survey transects from

the basin bottom to outside the perimeter of the basin

along the shortest line of sight; (3) If a line a site

between the basin bottom and perimeter cannot be

used, the establish additional points in the interior of

the basin, following the lowest elevation path until it

is possible to survey along a line of sight to the basin

perimeter; and (4) Survey the perimeter of the basin at

its highest water mark.

We only tested this method for shallow vernal

pools, given the constraints outlined above, this

methods seems to be appropriate for many appli-

cations. Our method remained accurate even for

basins with more complex shapes (Fig. 2b). For

researchers who need a rapid and simple method

for developing maps of aquatic systems this method

can provide a simple and quick alternative to more

data intensive methods for determining bathymetry.

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