Methods


Upper Klamath Lake Field Sites


Upper Klamath Lake has a surface area of about 230 km², but a mean depth of only about 2.4 m (fig. 1). The lake trends generally from northwest to southeast. The northern end of the lake is dominated by the marshes that surround Agency Straits, the lake’s connection to adjoining Agency Lake, and by the delta of the Williamson River, the largest tributary to the lake. At the southern end, the lake ends at the Link River Dam and the city of Klamath Falls, Oregon. Although most of the lake is relatively shallow, a 15-km-long trench with depths as great as about 15 m runs along the western side of the lake between Bare Island and Eagle Ridge to the north and Sesti Tgawaals Point to the south.


In response to water quality concerns, the U.S. Geological Survey (USGS) established a water-quality monitoring network in Upper Klamath Lake in 2002 (Wood and others, 2006). As part of ongoing research by the USGS, ADCP measurements of water velocity profiles were collected annually starting in 2003. Those ADCP measurements (Gartner and others, 2007) in conjunction with use of a numerical hydrodynamic model (Wood and others, 2008) provide understanding of horizontal water circulation in Upper Klamath Lake.


Locations of the (upward oriented) ADCP moorings in the lake were selected based on needs for calibration and validation of the numerical model used to describe wind driven circulation patterns present in the lake. During 2005 and 2006, most of the ADCPs were deployed in generally shallow regions of the lake; however, one ADCP was moored in the channel on the western side of the lake at a depth of about 12–14 m during 2005 and 2006 (fig. 1). ADCP data from 2005 include measurements from five locations; this dataset constitutes the most complete simultaneous spatial coverage of velocity measurements in Upper Klamath Lake. The deployment periods for the ADCPs were June 21–September 12, 2005, and May 24–September 25, 2006.


The use of measurements of RB and vertical velocity was not an objective of the deployment of these instruments in 2005, nor was it anticipated. Therefore, water quality sample collection to support estimation of SSC from RB was not performed until the latter part of the 2006 field season at the two ADCP sites that were established in that year. Twenty water quality samples were collected in 2006 and analyzed for suspended solids using a gravimetric technique (SSC analytical method ASTM 3977-97) (American Society for Testing and Materials, 2000) and for percentage of organic material using a technique to determine the loss on ignition of volatile suspended solids (Fishman and Friedman, 1989). Results were used to convert backscatter measurements from the two ADCPs deployed that year to profiles of computed SSC. The water samples were taken at near-surface, mid‑depth, and near-bottom locations in the water column at a deep site (ADCP1) and a shallow site (ADCP9); ADCP9 was located about 1.5 km south and east of the location of ADCP3 in 2005 (fig. 1). 


Air temperature was recorded at a site located on the shoreline of the lake near the mouth of the Williamson River (WMR-MET). Wind speed and direction were measured from rafts at two sites on the lake [midnorth (MDN) and midlake (MDL)] and from one site on the shoreline of Howard Bay (HDB-MET). Water temperature and dissolved oxygen were measured using YSI 600XLM, 6920, or 6600 continuous water quality monitors located at Eagle Point (EPT), midtrench (MDT), and in the northern part of the lake (MDN, fig. 1). Water depths at the start of the study period were 12.5 m at site EPT, 14.8 m at site MDT, and 4.5 m at site MDN. Two water temperature monitors were deployed at each of these sites, one at 1 m from the lake bottom, and one at 1 m from the lake surface. Chlorophyll a, as a surrogate for algal biomass, was determined from weekly water samples that were collected, preserved, and later analyzed by a commercial laboratory (Hoilman and others, 2008).


ADCP Measurements


The velocity profilers used in this study were 1,200 and 600 kHz Broadband and Workhorse ADCPs manufactured by TeledyneRD Instruments. The location of the center of the lowest measurement (bin) for each ADCP profile depended on the mooring platform design and ADCP setup. The 600 kHz ADCP (deep station, ADCP1) was programmed with a 50 cm bin size, thus the center of the first bin was located at about 125 cm above bottom and subsequent measurements in the profile were at 50 cm intervals. The center of the first bin in the 1,200 kHz datasets ranged from about 90 to155 cm above bottom depending on instrument and mooring design; subsequent measurements in the profile were at 25 cm intervals. The ADCPs recorded water velocity measurements every 30 minutes. Sufficient individual acoustic pulses (300 pings taking about 40–50 seconds) were averaged to decrease the theoretical standard deviation of the recorded horizontal velocities to be less than 0.7 cm/s for each measurement. Standard deviations for vertical velocities were approximately 0.3 cm/s.


ADCPs calculate water velocity from the Doppler frequency shift or phase difference of sound backscattered from particles in the water, under the assumption that the particles travel with the velocity of the water. However, vertical particle velocity and the vertical component of water velocity may differ greatly. Thus, the ADCP has the potential to quantitatively measure the vertical motion of inorganic particles or of biological populations that actively migrate within the water column. Although the theoretical standard deviation of vertical velocity measurements in Upper Klamath Lake were the same order of magnitude as the actual measured vertical velocities for each ensemble (of averaged single acoustic pings), additional averaging served to decrease the standard deviation of the measurement. However, suspended material in an ADCP measurement bin may consist of a mixture of organic and inorganic material that may be actively rising, sinking, or passively moving with the water mass. It is only possible, therefore, to state that the average for the particles was rising, sinking, or stationary based on the computed vertical velocity.


A drawdown of just more than 1 cm/d throughout the summer meant that water depths at each ADCP site were approximately 1 m shallower at the end of the measurement period than they were at the start. Thus, there were 2-4 more good measurement bins at the start of the deployment than there were at the end of the deployment. Therefore, in order to identify near-surface characteristics, “near-surface” time series of measurements were created from appropriate bin data from sequentially lower bins as the deployment progressed and the water depth became gradually shallower. Lake water depths at the start of the 2005 deployments were as follows: ADCP1, 14.2 m; ADCP3, 4.3 m; ADCP5, 5.6 m; ADCP6, 4.4 m; and ADCP7, 5.1 m. 


Time Series Analyses


Seasonally averaged diel cycles in wind speed, differences in water temperature between near-surface and near-bottom (ΔT°), RB, vertical velocity, horizontal current speed, and SSC were determined by averaging all valid measurements of the variable of interest collected during the (June–September) deployment at each sample time of day (for example, 00:00 h, 00:30 h, etc. for a 30-minute sampling interval). For variables measured by the ADCPs, seasonally averaged diel cycles were determined for each vertical measurement bin. Averaging over the deployment season exposed daily patterns that otherwise would be lost in large variability. The phase shift between diel cycles in RB and diel cycles in wind speed, ΔT°, and horizontal current speed were found by determining the lead or lag that maximized the linear correlation between the 24-hour time series.


Correlations between RB or vertical velocity and horizontal currents and water temperatures at subseasonal timescales were investigated by first filtering the time series in each bin with a series of Lanczos filters to remove high and low frequency variations to discern characteristics varying over time scales equivalent to weather patterns (Emery and Thompson, 2001). The first filter passed frequencies greater than 0.0667 cycles day^-1 (15-day period), and then a second filter passed frequencies less than 0.833 cycles day^-1 (1.2‑day period). Pearson correlation coefficients were computed between the filtered RB or vertical velocity and horizontal current speed in each bin. 


Correlations between filtered RB in each vertical bin and air temperature were examined by processing the air temperature time series with the same set of Lanczos filters. The vertical velocity or SSC in the top one-half of the water column (top one-third in the case of ADCP1) was first averaged, then passed through the series of Lanczos filters, and then correlated with filtered horizontal currents, also averaged over the top one-half of the water column, and filtered air temperature. For the purposes of determining significance of the correlations, the degrees of freedom in the filtered time series was estimated to be N = 63, which was the number of frequencies that still contained at least 1 percent of the total variance in the periodogram of the filtered time series. Using that number of degrees of freedom, rejection of the null hypothesis of no correlation would occur with 95 percent certainty at a correlation coefficient of 0.25.


Converting ADCP Backscatter to Relative Backscatter and Suspended Solids Concentrations


The theoretical technique presented here to convert acoustic backscatter to RB and ultimately to SSC is described in terms of the logarithmic form of the sonar equation, which is the typical method used for applications using ADCPs. It is well suited because commercially available ADCPs typically provide the conversion factor from raw backscatter counts to decibels, which facilitates accounting for transmission losses and empirical calibration of backscatter to SSC. The logarithmic form of the sonar equations can be inverted to obtain an expression for calculated SSC: SSC_computed = 
10 ^{(A + B × RB)}. The exponent contains the term for the RB, the sum of the echo level measured at the transducer plus the two‑way transmission losses (Thevenot and others, 1992), that is, RB = RL + 2TL, where RL is the reverberation level and 2TL is the two-way transmission loss.


In its simplified form, the sonar equation (Urick, 1975) can be written as RL = SL – 2TL + TS, where SL is the source level, which is the intensity of emitted signal that is known or measurable, and TS is the target strength, which is dependent on the ratio of wavelength to particle diameter. All variables are measured in decibels. In terms of ADCP parameters, RL = K_c (E– E_r), where E is ADCP echo intensity recorded in counts, E_ris ADCP received signal strength indicator (RSSI) reference level (the echo baseline when no signal is present), in counts, and K_c is the RSSI scale factor used to convert counts to decibels. K_c varies among instruments and transducers and has a value of 0.35–0.55 (Deines, 1999). The two-way transmission loss is defined as 2TL = 2(α_w + α_s)R + 20log₁₀ (R), where R is the range to the ensonified volume, in meters; α_w is an absorption coefficient for water; α_s is an attenuation coefficient accounting for viscous and scattering losses due to suspended particles, both in decibels per meter; 2 (α_w + α_s) R is the combined transmission loss due to water absorption and sediment attenuation; and 20log₁₀ (R)is the loss due to spreading. The absorption coefficient for water is a function of acoustic frequency, salinity, water temperature, and pressure (Schulkin and Marsh, 1962). Because of non‑spherical spreading in the transducer near field, the spreading loss is different in near and far transducer fields. The transition between near and far transducer fields is called the critical range, R_crit. R_crit = πα_tλ where α_t is the transducer radius, in centimeters, and λ is the acoustic wavelength. The near-field correction for spreading loss can be easily calculated as described in Downing and others (1995).


Gartner (2004) describes a practical approach to compute a time series of SSC from a time series of ADCP acoustic backscatter. First, the RB is determined, and the log₁₀ of the SSC measurements, SSC_measured, are calculated. The needed calibration coefficients consisting of slope, B, and intercept, A, for a regression between log₁₀(SSC_measured) and RB is determined such that log₁₀(SSC_measured) = A + B × RB. The theoretical value for slope, B, is 0.1 and the intercept is a function of particle and instrument characteristics; values are appropriate for a concentration of uniform particles of the same mass and other properties (Thevenot and others, 1992). After values of A and B are determined for the distribution of particles in the field, new time series of profiles of SSC can be computed from ADCP RB profiles utilizing the exponential form of the equation, SSC_computed = 10^(A+B×RB ). An alternative to using regression to determine A and B is to use the theoretical value of slope, B, equal to 0.1, and to calculate the intercept based on the log₁₀ of the measured SSC and the RB from A = log₁₀(SSC) – 0.1 × RB. 


To determine appropriate calibration coefficients for data from Upper Klamath Lake, water quality samples were analyzed for mass concentration and percentage of organic material. Mass concentration of the 20 water quality samples collected in 2006 ranged from about 4 to 43 mg/L, but results from replicate pairs ranged from 0 to 100 percent (Gartner and others, 2007). SSC comprises both organic and inorganic fractions in Upper Klamath Lake. Because calibration coefficients depend on size and other characteristics of the suspended particles, temporal or spatial (including vertical) variations in the ratio of organic to inorganic material is of interest. The organic fraction dominates in Upper Klamath Lake; the average organic fraction for all 20 water samples was about 77 percent (standard deviation about 11 percent). 


Coefficients for use in converting RB measured in 2006 to estimates of profiles of SSC were calculated several ways, including determining an average slope and average intercept, using a theoretical slope (0.1) and single average intercept, and using a theoretical slope (0.1) and intercepts calculated from near-surface, mid-depth, and near-bottom samples for the shallow and for the deep sites. Standard deviations of the differences between measured and estimated SSC for the three techniques were about 10.2, 22.8, and 9.9 mg/L, respectively. The organic fraction was generally somewhat lower near‑bottom than it was near-surface but still predominated. Although some spatial and temporal variations existed in SSC and the percentage of organic material, variations were small and the samples insufficient to calculate reliable trends. Thus, the theoretical slope (0.1) and different average intercepts for the deep and shallow sites were used but the intercepts were not varied with vertical position in the water column when estimating new profiles of SSC. For the four shallowest sites in 2005, SSC was computed from ADCP backscatter measured in 2005 using the theoretical slope (0.1) and the average intercept determined for the single shallow station in 2006 (-7.08). For the deep site in 2005, the theoretical slope (0.1) and the average of the intercept determined for the deep station at the same location in 2006 was used (-6.92). (When this technique was applied to the 2006 datasets, the standard deviation was 19.1 mg/L.) 1,200 kHz ADCPs were used at all shallow stations and a 600 kHz ADCP was used at the deep station. 


No compensation was made for potential variations in ADCP transmit power (Deines, 1999; Wall and others, 2006) from changes in internal battery voltage during the deployment. The average of the backscatter from all four ADCP acoustic beams was used in calculations as the beams have different source levels and sensitivities. Averaging also helps to overcome the impact of patchiness of the suspended material. In addition, transmission losses from particle attenuation were not accounted for in computing SSC.


First posted March 16, 2011