Empirical relations to estimate underwater PAR attenuation in San Quintín Bay using Secchi depth and horizontal sighting range

Relaciones empíricas para estimar la atenuación subacuática de PAR en Bahía San Quintín utilizando la profundidad de Secchi y la distancia horizontal de desaparición de objetos

Martín A. Montes-Hugo¹ and Saúl Álvarez-Borrego²

¹ EOS Lab, College of Marine Science University of South Florida 140 7th Ave S St. Petersburg, FL 33701, USA. E-mail: mmontes@mail.usf.edu

Recibido en septiembre de 2004;
aceptado en agosto de 2005.

Abstract

Empirical relationships to estimate vertical attenuation coefficient of photosynthetically available radiation (K_PAR) using Secchi disk, vertical black disk, and horizontal sighting ranges for San Quintín Bay, Baja California, were developed. Radiometric PAR profiles were used to calculate K_PAR. Vertical (Z_D) and horizontal (HS) sighting ranges were measured with white (Secchi depth or Z_SD, HS_W) and black (Z_BD, HS_B) targets. The empirical power models K_PAR = 1.48 Z_SD^-116, K_PAR = 0.87 Z_BD^-152, K_PAR = 0.54 HS_W^-065 and K_PAR = 0.53 HS_B^-092 were developed for the corresponding relationships. The parameters of these models are not significantly different from those of models developed for Punta Banda Estuary, another Baja California lagoon, with the exception of the one for the K_PAR-HS_W relationship. Also, parameters of the K_PAR-Z_SD model for San Quintín Bay and Punta Banda Estuary are not significantly different from those developed for coastal waters near Santa Barbara, California. A set of general models is proposed that may apply to coastal water bodies of northwestern Baja California and southern California (K_PAR = 1.45 Z_SD^-110, K_PAR = 0.92 Z_BD^-145, and K_PAR = 0.70 HS_B^-110). While this approach may be universal, more data are needed to explore the variability of the parameters between different water bodies.

Key words: PAR attenuation, horizontal sighting range, Secchi disk, coastal lagoons, Baja California.

Resumen

Palabras clave: atenuación de PAR, disco de Secchi, distancia horizontal de desaparición de objetos, lagunas costeras, Baja California.

Introduction

Light appears as the major limiting variable of primary producers in most coastal water bodies. Autotrophic organisms are only able to use a portion of the electromagnetic radiation spectrum, 400-700 nm, which is known as photosynthetically available radiation (PAR). Temporal and spatial distribution of phytoplankton, macroalgae and seagrass in estuaries and coastal lagoons are greatly affected by PAR attenuation throughout the water column (Garza-Sánchez et al., 2000; Cabello-Pasini et al., 2003; Montes-Hugo and Álvarez-Borrego, 2003). PAR attenuation in coastal water bodies influences the larval settlement of many invertebrates, including bivalves of commercial interest (Baker and Mann, 1999), and the feeding success of various ichthyoplankton species (Breitburg, 1988). Water transparency is also a key parameter for monitoring water quality and can be used for detecting the anthropogenic impact due to dredging, erosion and eutrophication (Iannuzi et al., 1996; Ruffink, 1998; Wang et al., 1999). Visual water clarity (measured as Secchi or black disk visibility) has been recognized as the relevant variable to measure in water-quality monitoring programs, instead of the more traditional suspended solid concentration or turbidity measurements. Contrary to common perception, visual clarity measurement is not particularly subjective and is more precise than turbidity measurement (Davies-Colley and Smith, 2001).

The underwater PAR attenuation can be quantified with the vertical attenuation coefficient (KPAR). PAR readings are often obtained with a light meter. The vertical attenuation coefficient is sometimes estimated with Secchi depth (ZSD) in which a white disk is lowered into the water until it disappears from view (Tyler, 1968; Holmes, 1970; Smith, 2001; Steel and Neuhausser, 2002). Coastal lagoons often have strong tidal currents and large shallow areas that make the vertical sighting observation (ZD) difficult. Secchi disk readings cannot be performed when ZSD is greater than bottom depth (ZB). A possible solution to these methodological problems is presented by the horizontal sighting (HS) range or the maximum distance a target can be seen when viewed horizontally (Davies-Colley, 1988). In this case, the visual target can be positioned just below the water surface so as to avoid some of the drag effect of the water current.

Measurement of visual water clarity involves attenuation of contrast of an image with respect to background. According to Preisendorfer (1986), Z_SD = [ln(C₀/C_T)/(c + K_PAR)], where C₀ is the Secchi disk contrast at depth zero, CT is the threshold contrast where the maximum visual range occurs, and c is the beam attenuation coefficient, equal to the sum of the total absorption and scattering coefficients (c = a + b). The value of C₀ varies with water reflectanceóthe ratio of upwelling to downwelling irradiance (Davies-Colley and Vant, 1988). Reflectance is an apparent optical property and varies with the ambient light field, or angular distribution of light, and the optical components of water-organic detritus, inorganic suspended matter, phytoplankton, and gelbstoff (Kirk, 1994). Because the inherent contrast of the Secchi disk varies between waters, it is not possible to use the Secchi depth in any simple way to precisely estimate the optical properties c or K_PAR, or even their sum, c + KPAR (Preisendorfer, 1986). Many studies have attempted to estimate KPAR from visual water clarity measurements with a Secchi disk, using the simple inverse relationship KPAR = constant/ZSD; however, Davies-Colley and Vant (1988) have shown that the product KPAR-Z SD ^varies appreciably between waters.

In contrast to the bright Secchi disk, an all-black target (black body) reflects no light and thus is seen as a silhouette. Visibility depends only on the attenuation coefficients for the water and is independent of the ambient light field. The maximal vertical distance of visual extinction for a black body is Z_BD = [ln(-1/C_T)/(c + K_PAR)], and for horizontal sighting of a black target it is HS_B = ln(-1/C_T)/c (Davies-Colley, 1988).

Holmes (1970) performed radiometric measurements and Secchi disk readings in coastal waters near Santa Barbara, California, to obtain a simple KPAR-ZSD relationship (KPAR = 1.44 Z_SD^-1). Montes-Hugo et al. (2003) developed empirical power models for the KPAR-ZD and KPAR-HS relationships for Punta Banda Estuary, a coastal lagoon of the southern California Current System, ~100 km south of the US-Mexico border. Montes-Hugo et al. (2003) indicated that although their approach seems to be valid in other shallow coastal water bodies, more data are needed to explore the variability of the parameters between different water bodies. Nevertheless, it is interesting to note that their result for the KPAR-ZSD relationship for Punta Banda Estuary is not significantly different from that of Holmes (1970). To explore the possibility that the parameters of Montes-Hugo et al. 's (2003) empirical models may apply to other coastal water bodies of northwestern Baja California, simultaneous HS, ZD and KPAR measurements were performed in San Quintín Bay, a shallow coastal lagoon (mean depth ~ 2 m) 200 km south of Punta Banda Estuary. The underlying hypothesis is that these coastal water bodies have similar water reflectance ranges. The final objective was to explore the possibility of "regional" K_PAR-HS and K_PAR-Z_D empirical relationships for shallow coastal waters of northwestern Baja California and southern California. Since reflectance range is large in these coastal waters (Montes-Hugo et al., 2003), some scatter of data points is expected causing relatively low correlation coefficients of the regression models. Thus, the objective of this work is not to build models to predict instantaneous local values of KPAR, but rather models that can be used with several visibility readings (at least ten) covering a certain region and time period. This would allow an estimate of a more representative and precise average KPAR that may be used to characterize the light regime for that region and period.

Study area

San Quintín Bay is a coastal lagoon in the southern California Current System, located ~300 km south of the US-Mexico border (California) and ~200 km south of Ensenada, Baja California (fig. 1). According to Kjerfve's (1994) classification, it is a restricted lagoon, with a permanent single connection to the ocean and tides that co-oscillate with tides in the coastal ocean with little reduction of amplitude inside the lagoon. The lagoon is a 49-km² 7-shaped embayment. It is characterized by extensive intertidal flats, shallow subtidal shoals, and narrow tidal channels (Barnard, 1962). The lagoon is quite shallow, about 85% of the eastern arm lying in depths of 1.8 m or less at mean high water. Depths greater than this occur in channels that are strongly differentiated from the shallow bay flats by sharp depth changes. Maximum water depth is at the main channel and near the mouth (~15 m). The mouth, most of the western arm, and the Y base are characterized by sandy sediments. The rest of the lagoon, including the eastern arm and the inner part of the western arm, has a predominantly clay-silt sediment type (Gorsline and Stewart, 1962).

Vertical distribution of water properties is generally homogeneous due to turbulence caused by tidal currents (Martori-Oxamendi, 1989). Also, tidal currents produce large local changes of water properties, including optical properties (Álvarez-Borrego, 2004). Average KPAR values (main channel and shallows) are highest in the western arm and lowest at the mouth (Montes-Hugo, 2001). High turbidity in the western arm is caused by the effect of waves on the shallow bathymetry due to the wind action. Barnard (1962) reported Secchi disk readings of 2-2.7 m for the mouth, 1.2-1.5 m for the eastern arm, and ~1 m for the western arm. Osorno-Velázquez (2000) reported 3-3.5 m for the eastern arm and 1-3 m for the western arm. These Secchi disk readings are very low and imply a strong light attenuation, in some cases up to 50% in the first 0.5 m depth (Álvarez-Borrego, 2004). Fresh-water input to the bay is not considerable, and it is mainly derived from the San Simón stream during the rainy season (November to March) (Camacho-Ibar et al., 2003).

Field measurements

Measurements were carried out during 1999 and 2003. Underwater PAR was measured with a profiling PAR irradiometer PNF-300 (precision: ±1%, as quoted by the manufacturer, Biospherical Instr. Inc., Los Angeles, California) during the 1999 surveys, and with a PAR irradiometer LiCor (LI-190SB, LI-192SB) (precision: ±5%, as quoted by the manufacturer, LiCor Inc., Lincoln, Nebraska) during 2003. For each sampling, an average PAR profile was generated with at least ten consecutive PAR measurements for each water depth. Average values of radiometric vertical PAR attenuation (KPAR) were calculated for the water column. For the calculation of these averages we did not consider the first 0.5 m since PAR data for near-surface waters were noisy because of focusing and defocusing effects of small gravity waves. Linear regressions of ln(PAR_0.5m PAR_Z^-1) vs z were run to estimate the average of K_PAR as the slope (Lambert-Beer Law). Readings of Z_D were taken on the sunny side of the boat with a 30-cm diameter disk (white, Z_SD, and black, Z_BD), and each value was corrected for the wire angle caused by tidal current drag. Care was taken to avoid the effect of surface glitter (Preisendorfer, 1986) using a small cloth cover close to the water surface and waiting ~30 s for eye accommodation to the water light field. For the 2003 readings, we employed a viewer box to minimize uncertainty on visual measurements due to sea-surface reflected light during the vertical sighting measurements, following Smith (2001). In some cases, errors for Z_D could have been caused by non-zero sighting angle and by light reflection from the bottom at very shallow locations. Both errors yield lower Z_D readings. Horizontal sighting range was measured ~0.3 m below the water surface with a horizontal sighting viewer assembled at CICESE. The basic design was similar to that of Davies-Colley (1988) and Steel and Neuhausser (2002). We used both black (HS_B) and white (HS_W) spheres as targets. The viewer was placed at a 90° angle with respect to the sun. To avoid sun glitter during HS measurements, a diving mask was attached to the observer's window. Distilled water was used between HS measurements to clean the windows. Special care was paid to eliminate floating seagrass leaves attached to visual targets and radiometric sensors.

Measurements were performed at different locations throughout the lagoon on 11 March and 15 July 1999, and 1 October 2003 (fig. 1). Sampling coincided with spring tides and covered shoals and main channel. Light measurements and visual water clarity readings were performed between 10:00 and 14:00 h by one observer, at high tide. In order to characterize the K_par-Z_SD empirical relationship under different tidal conditions (flood and ebb flow), measurements were performed every 30 min at three fixed locations in the main channel on 13 July 1999 (the mouth), and on 29 (western arm) and 30 (eastern arm) September 2003 (fig. 1). The bottom of the channel was free of vegetation. During the 1999 studies, only radiometric and Secchi depth measurements were performed, but during the 2003 studies, readings for Z_BD and HS were also performed to determine the K_PAR-Z_SD, K_par-HS_W and K_par-HS_B relationships.

Visually estimated cloud fraction and wave height were recorded during all observations. Wind speed and direction were measured with a manual anemometer 2 m above the sea surface.

The K_PAR-Z_SD, K_PAR-Z_BD,K_PAR-HS_W and K_PAR-HS_B relationships were evaluated with regression analysis (Sokal and Rohlf, 1995). Linear regression on log-transformed variables was applied to data from the 1999 and 2003 samplings to obtain power equations such as:

where m and n are the regression parameters. Regression parameters of Kpar-HS and K_PAR-Z_D relationships for different regions of the lagoon (eastern and western arms) and for different tidal conditions (ebb and flood flow) were compared. For each regression coefficient, the null hypothesis µ = 0 was tested (Student's t-test), where µ is the estimated regression parameter (m or n). To avoid errors due to bottom reflectance, Z_SD > 0.5 Z_B values were excluded from the fitted curves, following Tyler (1968). To explore the possibility of a common set of regression parameters for northwestern Baja California coastal lagoons, for each Kpar empirical relationship additional comparisons of m and n for San Quintín Bay and Punta Banda Estuary (data from Montes-Hugo et al., 2003) were carried out. Also, in the particular case of the Kpar-Zsd relationship, comparisons of the m and n parameters for northwestern Baja California and southern California (data from Holmes, 1970) coastal waters were done (Student's t-test).

Results

Sampling for this work was done during very dry non-El Niño years. There were no significant differences between values of the regression parameters m and n for the K_PAR-Z_SD model when comparing different tidal conditions or regions in the lagoon (P >> 0.05, P range was 0.76-0.95, Student's t-test). Measurements used to derive these K_PAR-Z_SD relationships were taken in 1999 and 2003, and in summer and winter, with no significant time-dependent effects on the regression parameters. This suggests that there was no systematic effect of different environmental conditions (i.e., cloudiness, waves, winds, flood flow, ebb flow, etc.) on m and n. Therefore, 1999 and 2003 data sets were pooled into a single empirical relation (fig. 2a). Parameter n, estimated from this model, was not significantly different from one (P > 0.05, Student's t-test). Minimum and maximum Z_SD values were 1.15 m for the western arm and 5 m for the eastern arm, respectively. In general, the western arm had a wider range of ZSD values than the eastern arm. Consistently lower ZSD readings in the western arm coincided with stronger winds (up to 9 m s^-1) having a dominant NW direction (not illustrated).

Similar to Secchi depth, there were no significant differences between values of the regression parameters for the K_PAR-Z_BD and K_PAR-HS models when comparing ebb- and flood-flow conditions, or when comparing the two arms of the lagoon (P >> 0.05, p range was 0.72-0.85, Student's t-test). Thus, the whole 2003 data set was used to develop general K_PAR models. Contrary to the case for the K_PAR-Z_SD relationship, the K_PAR-Z_BD relationship had an exponent n significantly different from one (fig. 2b) (P < 0.05, Student's t-test), and a parameter m not significantly different from one (p > 0.05, Student's t-test). The opposite resulted for the KPAR-HS relations (fig. 2c, d). Although HSB values were always smaller than HS_W values, the scattering of data (which resulted in large standard errors for the parameters m and n) and the small range for KPAR produced power models for the KPAR-HS relationships that are not statistically different from each other (fig. 2c, d). Horizontal sighting range data could not be obtained when highest KPAR values were produced because during the spatial survey there was intense wave activity and precise HS measurements from the boat were not possible.

A 1:1 linear covariation between vertical and horizontal sighting range was found when the black target was used (Z_BD= 1.11 (0.36) HS_B - 0.32 (0.82), where numbers within parentheses are one standard error, r² = 0.61, n = 8) (not illustrated).

Since the regression parameters of the K_PAR-Z_D and K_PAR-HS_B models for San Quintín Bay were not statistically different from those reported by Montes-Hugo et al. (2003) for Punta Banda Estuary, the two sets of data were pooled together (fig. 3a-(b)c). Likewise, parameters of the K_PAR-Z_SD relationship for these two lagoons were not significantly different from those estimated for Goleta Bay, near Santa Barbara, California, with data from Holmes (1970). Thus, a single model was derived for the K_PAR-Z_SD relationship for San Quintín Bay, Punta Banda Estuary and Goleta Bay (fig. 3d). Note that Punta Banda Estuary is characterized by a broader range of K_PAR values than those of San Quintín Bay and Goleta Bay (fig. 3).

Discussion

The product K_PAR-Z_SD for San Quintín Bay (this work), Punta Banda Estuary (Montes-Hugo et al., 2003) and Goleta Bay (Holmes, 1970) varied from 0.76 to 1.95, from 0.64 to 2.05, and from 1.12 to 2.31, respectively. Since the product KPAR-ZSD is influenced by water reflectance, these results suggest that southern California coastal waters have a water reflectance range similar to that of coastal lagoons of northwestern Baja California.

Holmes' (1970), Montes-Hugo et al.'s (2003), and our results show that there is a large scattering of the K_PAR-Z_SD data, which indicates a relatively large water reflectance range in these lagoons. Nevertheless, our K_PAR-Z_SD regression model may be an appropriate tool to estimate K_PAR if, as mentioned above, average Z_SD from several readings are used instead of single instantaneous local measurements (the larger the number of readings the smaller the standard error). Furthermore, to attain a high precision for a local instantaneous optical measurement may not be relevant for coastal lagoons. Cabello-Pasini et al. (2002) reported that light attenuation in Punta Banda Estuary and adjacent coastal waters increased six-fold as a result of sediment resuspension caused by storms in the area. There is a large variability of water properties in coastal lagoons due to patchiness and tidal currents, and gravity waves cause patchiness and temporal variation in sediment concentration (Millán-Núñez et al., 1982). Such variability invalidates the usefulness of instantaneous local measurements and leaves us representative averages as an acceptable alternative. Montes-Hugo and Álvarez-Borrego (2003) proposed representative averages of optical properties and chlorophyll concentration for large areas of Punta Banda Estuary and for large periods (i.e., seasons) for the purpose of monitoring phy-toplankton production. Averages of optical properties and other variables over large areas and periods minimize errors. Our algorithms may provide very precise representative averages of K_PAR for large areas within San Quintín Bay when a high number of readings are performed. Furthermore, the generality of the K_PAR-Z_SD relationship for coastal waters of northwestern Baja California and southern California may provide a means to convert historical Secchi disk data into more useful estimates of K_PAR. This could be useful for determining historical patterns and long-term trends in light transparency.

A sensitivity analysis was performed to test the ability to predict depths at the middle and bottom of the euphotic zone (10% and 1% light levels) given the uncertainties in the parameters m and n. For example, for a K_PAR = 0.5 m^-1, local instantaneous visual clarity readings would yield estimates of these two depths with errors of ±1.3 and 2.7 m with the Secchi depth, 3.1 and 6.1 m with the black disk (Z_BD), 1.5 and 3.1 m with the white sphere (HS_W), and 1.2 and 2.4 with the black sphere (HSB). But, with several readings the uncertainties of the averages would decrease with the number of readings. With the exception of the black disk, even the errors of single instantaneous measurements are acceptable given the fact that plants attached to the bottom suffer changes of water column depth of up to >2 m with the tides, and phytoplankton have large vertical excursions due to turbulence. In coastal lagoons, bottom depth is often smaller than the 10% light depth.

Unlike HS_B, parameters m and n of the K_PAR-HS_W relationship for San Quintín Bay were significantly different from those for Punta Banda Estuary. Possibly, different sediment type in the two lagoons could explain these differences. As a whole, Punta Banda Estuary has finer sediments (up to 6.7 phi) than San Quintín Bay (up to 1.5 phi) (Gorsline and Stewart, 1962). Silt and clay particles (<63 µm) scatter light more strongly than sand particles (>63 µm) producing smaller contrast (Davies-Colley et al., 1993), and this could cause lower HSW values for Punta Banda Estuary than for San Quintín Bay for the same K_PAR values. We could expect that changes of sediment type would also have a significant effect on the KPAR-ZSD relationship; however, we were not able to detect such sediment influence possibly because the contribution of finer sediments was more important at very shallow depths where ZSD data could not be generated.

Empirical K_PAR algorithms were developed in this work for non-El Niño years. Higher fresh-water input during El Niño years would increase PAR attenuation in these coastal lagoons mainly because of a higher input of humic substances and suspended particles, but possibly the same parameters m and n could apply. Given that we can use general K_PAR-Z_SD, K_PAR-Z_BD, and K_PAR-HS_B empirical curves to estimate KPAR for San Quintín Bay and Punta Banda Estuary from visibility readings, we propose extending the validity of these algorithms to other shallow water bodies of the Pacific coast of the Baja California peninsula since climatic and hydrologic characteristics are very comparable. Since the K_PAR-Z_SD relationship obtained in this work may also apply to southern California coastal bodies, the K_PAR-Z_BD and K_PAR-HS_B empirical models obtained for Baja California lagoons may also be valid for southern California coastal systems; however, more data are needed to test this possibility.

Acknowledgements

We thank Violeta Loya-Núñez for her collaboration during the field work. Silvia Ibarra (CICESE) kindly facilitated the LiCor PAR irradiometer. Aquaculture specialists Vicente Guerrero and Alfonso Aguirre supported the logistics of boat and pier surveys. We are very grateful to three anonymous reviewers for their positive criticisms that helped to improve the manuscript significantly.

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