Simulation of the contribution of minerogenic particles to particulate phosphorus concentration in Cayuga Lake, New York

Transcription

1 Simulation of the contribution of minerogenic particles to particulate phosphorus concentration in Cayuga Lake, New York Rakesh K. Gelda 1, Steven W. Effler 1, Anthony R. Prestigiacomo 1,*, Feng Peng 1, Martin T. Auer 2, and Anika Kuczynski 2 1 Upstate Freshwater Institute, P.O. Box 506, Syracuse, New York, U.S.A., Michigan Technological University, Department of Civil and Environmental Engineering, Houghton, Michigan, U.S.A., *Corresponding author. Tel.: ; Fax: Address: tonyp@upstatefreshwater.org 1

2 Abstract Phosphorus (P) associated with minerogenic particles delivered from the watershed interferes with the use of total P (TP) concentration as a trophic state metric in lacustrine systems because of its limited bioavailability. A mass balance model for the unavailable minerogenic component of the concentration of particulate P (PP m/u ) is developed and tested for Cayuga Lake, New York. This is supported by: (1) long-term monitoring of the lake and its primary tributaries for sediment concentrations, fractions of P, and chlorophyll-a, and characterizations of the minerogenic particle populations, that include their projected area per unit volume of water (PAV m ), (2) results of bioavailability bioassays conducted on particulate P (PP) from the tributaries, (3) tributary loading estimates of PP m/u and its relationship with PAV m loading, and (4) previously tested submodels for lake transport and PAV m. The central roles of major runoff events and localized tributary loading at one end of the lake in driving patterns of PP m/u in time and space are well simulated, including: (1) the higher PP m/u concentrations in a shallow area ( shelf ) adjoining the inputs, relative to pelagic waters, following runoff events, and (2) the positive dependence of the shelf increases on the magnitude of the event. Predicted temporal patterns of the ratio PP m/u :PAV m in the lake reflect the strong dynamics in this ratio of the tributary inputs. The model also performs positively in predicting independently measured increases in deposition rates of PP on the shelf following major runoff events. The PP m/u component was largely responsible for the higher summer average TP on the shelf versus pelagic waters, and the exceedance of a TP water quality limit on the shelf. Keywords: minerogenic particles; phosphorus; trophic state; bioavailability; modeling 2

3 1. Introduction Cultural eutrophication and the concentration of phosphorus (P), the limiting nutrient for algal growth in the vast majority of fresh waters, remain primary contemporary water quality issues for lacustrine systems (Cooke et al., 2005). Of the three common metrics of trophic state, the concentrations of total P (TP) and chlorophyll-a (Chl-a) and Secchi depth (SD), TP is the most widely applied in the United States in setting water quality goals or limits to protect against excessive cultural eutrophication (Chapra, 1997; Cooke et al., 2005; Prestigiacomo et al., 2015). Phosphorus exists in a wide array of chemical forms (Dodds, 2003; Reynolds, 2006), that can differ substantially in their availability to support primary production (Reynolds and Davies, 2001; Prestigiacomo et al., 2015). Particulate forms of P dominate TP in the upper waters of most lacustrine systems (Wetzel, 2001). Minerogenic forms of particulate P (PP m ), associated with various minerals (Effler et al., 2014), are important because of their generally low levels of bioavailability, but often dominant contribution to TP concentration and the associated external load of TP received during major runoff events (e.g., DePinto et al., 1981; Young et al., 1985; Auer et al., 1998; Effler et al., 2002, Prestigiacomo et al., 2015). Lake TP is compromised as a trophic state and related regulatory metric where and when PP m makes noteworthy contributions (Effler et al., 2014). A modeling capability for the unavailable component of PP m (PP m/u ) is desired where such circumstances occur. Development of such a capability faces two primary challenges, effective representation of: (1) the delivery, transport, and fate of the minerogenic particle population, and (2) the P associated with these particles and its bioavailability. Common gravimetric water quality monitoring data sets for external lotic sources provide strong evidence for the dominance of minerogenic particle components of sediment (e.g., as the inorganic (ISPM) fraction of suspended particulate material (SPM); ISPM:SPM; Longabucco 3

4 and Rafferty, 1998; Prestigiacomo et al., 2007) and particulate P (PP) entering many systems (e.g., Peng and Effler, 2015). Large fractions of annual ISPM and PP loads are often delivered over relatively brief intervals during major runoff events (Longabucco and Rafferty, 1998); (Prestigiacomo et al., 2007; 2015). However, use of the same gravimetric measures in receiving lacustrine waters has failed to support the development of a representative model that simulates minerogenic particle patterns and associated PP m/u. Specifically, ISPM has a number of limitations for representing the minerogenic particle populations within lacustrine systems: (1) poor precision of analyses for the dilute conditions common to many lakes (Effler et al., 2014), (2) the pore size of the most commonly used filter (1.5 µm; Clesceri et al., 1998) fails to capture smaller particles with noteworthy optical (Peng and Effler, 2007;2012) and PP m/u pool (Effler et al., 2014) impacts, (3) undefined and variable inclusion of non-minerogenic particle contributions (e.g., diatom frustules) in the measurement, (4) it fails to resolve the contributions of different particle size classes, and (5) gravimetric results are inferior to determinations of particle surface area for representing adsorption-desorption potential for P (Effler et al., 2014). In particular, the behavior of natural polydispersed (i.e., multiple size classes) minerogenic particle populations (Peng et al., 2009a; Effler and Peng, 2014), commonly manifested as wide distributions of dependent bulk characteristics in time and space in receiving lakes and reservoirs (Gelda et al., 2009; 2013; Peng and Effler, 2015), cannot be simulated based on a single state variable (i.e., single settling velocity) such as ISPM. Recently, an individual particle analysis (IPA) technique, scanning electron microscopy interfaced with automated image and x-ray analyses (SAX), has been successfully applied to lacustrine as well as lotic waters to provide robust characterizations of minerogenic particle populations (Peng et al., 2009a; Peng and Effler, 2012; 2015). Direct measurement of particle 4

5 number concentration, particle size distribution (PSD), and elemental composition of the particles of these populations with SAX eliminates all the disadvantages identified above in attempting characterization through gravimetric analyses instead (Peng and Effler, 2015; Gelda et al., 2015b). The total projected area of minerogenic particles per unit volume of sample (PAV m ; m -1 ) has been established as a particularly valuable bulk summary metric from SAX characterizations, that is linearly related to multiple measures of the water quality impacts of these particles (Peng et al., 2009b; Peng and Effler, 2010; 2015), including PP m/u (Effler et al., 2014). Clay minerals, of inherently terrigenous origins, have been found to dominate the minerogenic particle populations of most lacustrine systems, with dynamics positively linked to the timing of major runoff events when large quantities are received (Effler and Peng, 2014; Peng and Effler, 2015). The development and testing of the first mechanistic multiple size class PAV m model has been reported for Cayuga Lake, New York, that was supported by detailed SAX monitoring of that lake and its primary tributaries, and focused on the effects runoff events (Gelda et al., 2015a). The lake PP m/u model requires the development of relationships between PAV m and associated PP m in the tributaries and external loads for both, and representation of the unavailable fraction in each input and thereby the associated PP m/u load. Two types of associations of P with minerals can be identified (Reddy et al., 1999): (1) P contained within the internal mineral structure or tightly bound to the surfaces, and (2) P associated with mineral particle surfaces that is subject to desorption. The P of the first case essentially has limited potential function in P cycling related to primary production, being essentially unavailable (Reynolds and Davies, 2001). The second case, including for clay minerals, can have a role in the P cycle of lakes, influenced by the adsorption/desorption process, that is driven by 5

6 differences in ambient concentrations of dissolved reactive P (SRP; Froelich, 1988; Reddy et al., 1999). Given that tributaries are generally enriched in SRP relative to lake surface waters (Wetzel, 2001), some desorption from clay minerals is expected to be common upon entry of PP m into a lake (Reddy et al., 1999). This desorption corresponds to a level of bioavailability of the PP m, that can be quantified in bioassay experiments (Auer et al., 1998; Prestigiacomo et al., 2015), and thereby support estimates of PP m/u concentrations and loads. The overarching goals of this paper are to develop and test the first PP m/u lake model, that adopts a multiple size class PAV m submodel (Gelda et al., 2015a), and is supported by detailed external loading estimates of PP m/u and PAV m from its watershed. The model is demonstrated for Cayuga Lake, New York, for which the initiative is supported by: (1) monitoring of the lake for fractions of P, Chl-a and multiple size classes of PAV m, (2) monitoring of its primary tributaries for fractions of P, SPM and ISPM, and the size classes of PAV m, (3) results of bioavailability bioassays conducted on particulate P (PP) from primary tributaries (Prestigiacomo et al., 2015), (4) previously tested submodels for lake transport (Gelda et al., 2015b) and the four sizes classes of PAV m (Gelda et al., 2015a), and (5) loading estimates of PAV m, and PP m/u from the lake s tributaries. The central role of major runoff events in driving increases, and patterns in time and space, of PP m/u in the lake s water column, as well as its local deposition, are resolved. The utility of model predictions of PP m/u in supporting management deliberations for P and cultural eutrophication, and in applying numeric standards for TP, is considered. 2. Methods 2.1 Study system Cayuga Lake ( N; W) is the fourth easternmost of the New York Finger Lakes, positioned approximately centrally in the state (Fig. 1). It has the second largest 6

7 volume (9.4 x 10 9 m 3 ) and surface area (172 km 2 ) of this group of lakes, with maximum and mean depths of 133 and 55 m, respectively. This long and narrow lake is positioned along a prominent wind direction (Gelda et al., 2015b). Cayuga Lake has a warm monomictic stratification regime, stratifying strongly in summer through mid-fall (Oglesby, 1978). The lake s shape and the wind conditions promote extensive mixing, including seiche activity (Effler et al., 2010; Gelda et al., 2015b). The average residence time of tributary inputs within the lake is 5.5 y (Gelda et al., 2015b). Algae growth in this mesotrophic lake (Effler et al., 2010) is P limited (Oglesby, 1978). The shallow ( 6 m) southernmost 2 km of the lake, designated the shelf (Fig. 1), has generally been considered degraded relative to the lake s pelagic waters (Oglesby, 1978; Effler et al., 2010). Water quality concerns for the shelf identified by government regulators include high concentrations of sediment and TP, which are qualitatively consistent with elevated loads of these constituents received during runoff events from local streams (Gelda et al., 2015a; Prestigiacomo et al., 2015). Irregular exceedance of New York State s regulatory TP limit of a summer (June-September) average concentration of 20 µg/l on the shelf (Effler et al., 2014) was the basis of establishing high TP as a water quality management issue for that area (Effler et al., 2014). Nearly 40% of the total tributary inflow enters the shelf, with agriculture representing from ~ 20 to 50% of the landuse in those local contributing tributaries (Table 1). Dreissenid bivalve mussels invaded the lake in the mid-1990s, quagga mussels are presently dominant (Watkins et al., 2012). The average areal density of mussel tissue in the epilimnion in 2013 in pelagic areas was ~ 85 g dry weight (DW)/m 2, but was much lower on the shelf (~ 9 gdw/m 2 ) (J. Watkins, unpublished data). These non-selective filter feeding benthic 7

8 organisms represent a loss pathway for PP m/u, as they remove particle sizes ( 1 µm; Reeders and Bij de Vaate, 1992) that are important contributors to PAV m (Peng and Effler, 2010; 2015). 2.2 Lake and tributary monitoring support Sampling Sampling conducted over the April-October interval of 2013 played a prominent role in testing of the PP m/u model as well as the transport (Gelda et al., 2015b) and multiple size class PAV m (Gelda et al., 2015a) submodels. Stream samples were collected near the mouths of four tributaries (Fig. 1; Table 1) that together represent ~ 50% of the lake s watershed. The numerous other tributaries are each small by comparison (Prestigiacomo et al., 2015). Stream sampling had two components: (1) bi-weekly (fixed frequency) manual collections, and (2) runoff event collections with automated equipment, with a goal of providing a robust representation of their effects (Prestigiacomo et al., 2015). Two of these tributaries enter via the same 2 km long channel (depth ~ 2 m, designated Inlet; Fig. 1) that modifies the dynamics of the particulate loads reaching the lake. Similar sampling of this channel was conducted to accommodate its modifying effects on local loading to the shelf. Lake near-surface water samples (~0.5 m) were collected at four sites along its primary axis in 2013, including two shelf sites (Sites 1 and 2) and two pelagic locations (Sites 3 and 5; Fig. 1). Sites 1, 2 and 3 were monitored twice per week over the June-September interval, and bi-weekly in April, May and October. Site 5 was monitored bi-weekly over the entire study interval of An earlier bi-weekly lake monitoring program ( ) at Sites 3 and 2, and five additional shelf sites (samples the average of 0, 2 and 4 m collections), supported additional testing of the PP m/u model Measurements 8

9 Paired analyses for the concentrations of SPM and ISPM (tributaries only), total dissolved P (TDP), TP, and Chl-a ( lake only), and characterizations of the minerogenic particle population through SAX, were conducted. Concentrations of SPM, ISPM, TDP and TP were measured accordingly to standard methods (Clesceri et al., 1998). Particulate P (PP) was calculated as the residual of TP and TDP (PP=TP-TDP; available for and 2013, TP only for ). Chl-a, the most commonly used proxy of phytoplankton biomass, was measured according to Parsons et al. (1984). Protocols for IPA by SAX have been described in detail, including PAV m measurements, previously (Peng and Effler, 2007; Peng et al., 2009b), and specifically in support of the PAV m submodel for the lake (Gelda et al., 2015a). Example PSDs for clay mineral particles are presented in the common density function format (F(d); Peng and Effler, 2007) for one of the primary streams during a runoff event and in pelagic lake waters (Fig. 2a), that establish the minerogenic particle populations are polydispersed (i.e., representing a broad size range), over wide concentration ranges (y-axis) in both tributaries and the lake. The general curvature of the PSD and particle size with the peak concentration have been recurring features of the PSDs for minerogenic particle populations for fresh waters (e.g. Peng et al., 2009; Peng and Effler, 2012; 2015). An important feature of the PSDs is the broad size dependencies of PAV m (Fig. 2b), and thereby the associated impacts on water quality (Effler et al., 2014; Peng and Effler, 2015). The PAV m for tributaries is associated mostly with sizes between 1 and 30 µm; this is shifted lower in the lake (e.g., 1 to 11 µm), because of the greater settling rates of the larger sizes (Gelda et al., 2015a; Peng and Effler, 2015). Demarcations for the four size classes adopted for modeling PAV m (< 2, 2-5.6, , and > 11µm) in Cayuga Lake (Gelda et al., 2015a) have been added to the example PSDs and size distributions of PAV m (Fig. 2) for reference. X-ray characterizations 9

10 from SAX have established that clay minerals (i.e., watershed inputs) dominate external inputs and levels of minerogenic particle populations in Cayuga Lake (Effler and Peng, 2015; Peng and Effler, 2015). 2.3 Bioavailability of PP Algal bioassays (Auer et al., 1998; Prestigiacomo et al., 2015) were conducted on three runoff event samples for each of the largest tributaries (Table 1) to quantify the bioavailable fraction (f BAP ) of PP, as well as for two components of dissolved P, SRP and soluble unreactive P (SUP=TDP-SRP). A single bioassay was conducted on a shelf PP sample after an early July 2013 runoff event. Bioassays on the particulate phase were conducted with a two-chamber device, separated by a semi-permeable membrane, in which P mobilized from the particles diffuses across the membrane and is taken up by P-starved algae (DePinto et al., 1981; Auer et al., 1998; Prestigiacomo et al., 2015). P taken up by the algae was monitored at approximately 3 d intervals over 20 d incubations to describe the time course of mobilization and the fraction of the initial PP that was bioavailable (Prestigiacomo et al., 2015). Dissolved components of tributary P were observed to be much more bioavailable than particulates. SRP was essentially completely available, SUP was mostly available (60 to 80%; Prestigiacomo et al., 2015). Tributary PP was substantially less bioavailable, with average f BAP for the four tributaries ranging from ~ 6 to 21%, but tributaries entering the shelf area were in the lower part of the range (Table 1; Prestigiacomo et al., 2015). The most bioavailable source (Salmon Creek; Table 1) is located substantially north of the shelf (Fig. 1). The higher tributary SRP concentrations (Table 1) relative to the epilimnion (0.5 to 2 µg/l), were consistent with the occurrence of desorption from clay particles delivered to the lake, as manifested in the bioavailable fraction results from the bioassays (Table 1). The temporal progression of the 10

11 exertion of tributary particle bioavailability, represented by cumulative f BAP during the bioassays normalized by its final value (Fig. 3), shows most of the mobilization/algal uptake occurred early in the experiments, in some cases potentially earlier than resolved by the timing of the measurements. This character, together with the even lower f BAP value (1.7%) of the shelf sample soon after a runoff event, supports the position that the bioavailability of the delivered tributary PP is small and short-term. 2.4 Partitioning minerogenic and bioseston particle contributions to PP and related lake observation patterns The contributions of the unavailable P associated with minerogenic particles (PP m/u ) vs. organic particles (PP o ) to PP in epilimnetic waters have been described by a two-component summation (Effler et al., 2014) PP = PP m/u + PP o (1) The available component of PP m has been established to be minor in its tributary origins (Prestigiacomo et al., 2015). PP o is dominated by bioseston, that includes primarily phytoplankton biomass and secondarily the associated retinue of organic particles (e.g., bacteria, phytoplankton detritus, protozoans; Reynolds, 2006). Terrigenous PP o makes only minor contributions adjoining tributary inputs, and only immediately following runoff events (Effler et al., 2014). Though substantial delay may be involved in the cycling details, PP o, in contrast to PP m/u, is considered to be bioavailable (Reynolds and Davies, 2001). The predicted partitioning of PP presented here is based on model predictions of PP m/u and estimates of PP o based on Chl-a observations. The PP o estimates adopt a stoichiometric relationship empirically developed and tested independently for the lake (Effler et al., 2014), PP o = (PP o :Chl-a) Chl-a (2) 11

12 where the stoichiometric ratio, PP o : Chl-a, equals Temporal patterns of PP and metrics of its two components, Chl-a and PAV m, are compared for the upper waters of the shelf and pelagic Site 3 for the 2013 study interval, in the context of parallel stream hydrology, as indicated by the time series of daily Q in Fall Creek (Fig. 4a; Effler et al., 1989; Prestigiacomo et al., 2015). PP concentrations were similar on the shelf and in pelagic waters, and < 12 µg/l most of interval, except immediately following runoff events when shelf levels became greater (Fig. 4a and b). PAV m patterns were similar to those of PP, with major shelf vs. pelagic differences also linked to runoff events; e.g., levels on the shelf were ~50 fold higher for brief intervals following the early July and early August events (Fig. 4c). Chl-a levels were much more spatially uniform, without clear coupling to the runoff events, though substantial temporal variations occurred (Fig. 4d). The distributions of the PP:TP ratio (Fig. 4e) based on the entire records for these sites establish particulate forms (e.g., vs. dissolved fractions) dominate overall TP in the upper waters of this lake; median values of PP:TP have been 64%, occasionally PP accounts for > 90%. The PP:Chl-a ratio is widely considered in the context of the stoichiometry of phytoplankton composition (Hecky at al., 1993; Chapra, 1997). The distribution of PP:Chl-a for the shelf has been shifted significantly higher (Fig. 4f; Mann-Whitney U test; p < ) than for pelagic waters, a clear indicator of the greater contribution of non-bioseston on the shelf, and conceptually consistent with higher PAV m (Fig. 4c) and PP m/u (eq. (1)) levels in that area. The differences between the PP observations for these two lake areas were similar for 2013 and the longer-term record (Fig. 5a), establishing the recurrence of the high concentration events on the shelf; with much lower variability in pelagic waters. PP o (estimated by eq. (2)) has dominated 12

13 the pelagic pool of PP (Fig. 5b). The PP o contribution is subject to much wider variations on the shelf, including irregular low values, from runoff event-driven inputs of PP m/u (Fig. 5b). 2.5 Sediment trap assessments of deposition The dynamics of deposition of PP and its relationship with ISPM deposition on the shelf were resolved through analyses of collections by a single sediment trap deployed at Site 2. Trap design was consistent with widely accepted features (e.g., cylindrical tubes, aspect ratio of six; Rosa et al., 1991; Bloesch, 1996). Traps were deployed at a depth of ~ 6 m, approximately 1 m above the bottom, continuously over the April-October interval, with collections usually made weekly. Metalimnetic deployments (i.e., deeper) are commonly adopted in studies that target the interplay of lake-wide metabolism with deposition of various constituents (Rosa et al., 1991; Effler and Matthews, 2004). Our focus on local deposition effects of tributary inputs to the shelf following runoff events dictated the epilimnetic deployment instead. Such epilimnetic deployments have been successfully adopted in a number of studies (Dillon et al., 1990; James and Barko, 1993; Weyhenmeyer et al., 1995; Effler and Matthews, 2004). Trap collection observations are considered in the context of runoff events, as indicated again by the daily flow measurements from Fall Creek (Fig. 6a). Substantial increases in the downward flux of PP (DF pp (g/m 2 /d), Fig. 6b) coincided with the largest flow events of the study, indicative of major contributions from local tributaries. Downward fluxes during dry weather intervals are expected to instead represent lake-wide conditions (Bloesch, 2003). The relationship between PP and ISPM deposition on the shelf changed over the study, as represented by the value of the cumulative PP:ISPM ratio for these downward fluxes over the interval of trap deployment (Fig. 6c). The most conspicuous change was the abrupt decrease that accompanied 13

14 the largest (early August) runoff event. These signatures represent model testing opportunities to describe the relative role of tributary PP m/u inputs in influencing the timing of PP deposition losses and changes in PP:ISPM. The lack of noteworthy deposition flux events outside of the runoff events (Fig. 6b), despite intervals of high wind and upwelling on the shelf (Gelda et al., 2015b), supports the position that resuspension is not an important source of PP m/u (Effler and Matthews, 2004)to the water column on the shelf Empirical estimates of PP m/u and the ratio PP m/u PAV m The empirical stoichiometry-based model that was developed and tested independently for PP for the lake (Effler et al., 2014) is described by PP = (PP o :Chl-a) Chl-a + (PP m/u :PAV m ) PAV m (3) where PP o :Chl-a and PP m/u :PAV m are the stoichiometric ratios used to estimate the bioseston and unavailable minerogenic components of PP, respectively. Single values were developed for each of the ratios; PP o :Chl-a = 1.53, as identified above, and PP m/u :PAV m = 7.1 mg/m 2. Predictions of PP m/u and the PP m/u :PAV m ratio with this empirical model represent valuable tests of performance of the mechanistic dynamic PP m/u model developed here. The empirical model was based on a nonlinear optimization protocol that took advantage of the robust variations in Chl-a, PAV m and PP documented at Sites 2 and 3 over the period (Effler et al., 2014). 3. Model Description 3.1 Transport submodel The transport submodel, W2/T, is a two-dimensional laterally averaged framework that serves elsewhere as the transport submodel of the CE-QUAL-W2 water quality model (Cole and Wells, 2013). This dynamic model is based on the finite difference solution in the vertical and longitudinal dimensions of laterally- and layer-averaged mass, momentum, and heat conservation 14

15 (Cole and Wells, 2013). Cayuga Lake is represented by 48 longitudinal segments (Fig. 1) and 132 vertical layers (1 m thick) (Gelda et al., 2015b). The average segment length at the southern end of the lake (includes shelf) is 275 m (10 segments), increasing to 1,355 m for its remainder. This two-dimensional framework is appropriate to represent the primary spatial signature and management concern for PP m/u along the lake axis, differences between the shelf and pelagic areas following runoff events (Effler et al., 2010; 2014). The model s heat budget includes terms for short- and long-wave radiation, evaporative heat loss, convection, conduction, and back radiation (Cole and Wells, 2013). Meteorological drivers for the model include wind speed and direction, air temperature (T), dew point T, and incident solar radiation. The transport submodel was tested separately (Gelda et al., 2015b) from the PAV m submodel (Gelda et al., 2015a), and this PP m/u modeling initiative, based on an array of monitoring elements for physical lake attributes in time and space and the meteorological drivers. The model has six coefficients that may be adjusted in the calibration process (Cole and Wells, 2013), though these coefficients have been found to be relatively uniform for different systems (Gelda and Effler, 2007; Gelda et al., 2009; 2012; 2013). W2/T performs well for Cayuga Lake in the simulation of: (1) long-term (seasonal and multiple years) dynamics of the stratification regime, (2) short-term oscillations of stratified layers associated with seiche activity, and (3) the timing and magnitude of upwelling events on the shelf (Gelda et al., 2015b). Excellent temporal stability was demonstrated for the Cayuga Lake W2/T model; it performed well in uninterrupted simulations over a 15 y period. For example, the average root-meansquared-error for 10 y of simulated pelagic vertical T profiles was 1.18 C (Gelda et al., 2015b). 3.2 PAV m submodel 15

16 The state variables for the PAV m submodel are the four size classes (PAV m/1, PAV m/2, PAV m/3, and PAV m/4 ; see Fig. 2); their summation is PAV m. The single source of these terrigenous particles is external loading from tributaries (Gelda et al., 2015a). Three in-lake loss processes are represented (Gelda et al., 2015a): (1) size-dependent settling, (2) particle aggregation (coagulation; Weilenmann et al., 1989), and (3) filter feeding by dreissenid mussels (Reeders and Bij de Vaate, 1992). Settling is quantified according to Stokes Law, with sizes specified as the geometric means of the sizes included in the four size classes. The density of the particles is specified as 2.6 kg/m 3, corresponding to that of kaolinite (Babin et al., 2003), a dominant clay mineral (Peng and Effler, 2012). Aggregation is interactive with settling as these combinations of particles generally settle more rapidly than individual particles. Increased particle concentrations, such as prevail after major runoff events, promote aggregation by increasing particle collisions (Weilenmann et al., 1989). Direct evidence of the operation of the process in Cayuga Lake was presented in SAX micrographs that depicted increased occurrence of aggregates during intervals of high concentrations that followed a major runoff event compared to dry weather conditions (Peng and Effler, 2015). A parsimonious representation of the process has been adopted to limit the number of coefficients that must be specified to quantify the process. In this submodel the three smallest size classes are subject to aggregation through conversion to the largest, most rapidly settling, size class (PAV m/4, >11µm). The aggregation rate constants are represented in a Michaelis-Menten format, that acts to effectively decrease the operation of the process when particle concentrations are low (Gelda et al., 2013; 2015a). The benthic areal filtering rate of the mussels is specified based on: (1) the detailed 2013 lake-wide survey of biomass (Gelda et al., 2015a; J. Watkins, unpublished data), and (2) 16

17 literature tissue biomass-specific filtering rates and their temperature dependency (Baldwin et al., 2002; Vanderploeg et al., 2010). Ambient hydrodynamic conditions (e.g., formation of boundary layers) can limit the effect of this filtering potential in lakes, and has been well represented by W2/T for other systems (Boegman et al., 2008; Zhang et al., 2008). The development of tributary loading estimates for the four size classes of PAV m was supported by application of the FLUX32 software (FLUX32, 2013), which is widely used for the case of available continuous daily flow (Q) records combined with more temporally limited constituent observations. Strong positive dependencies of ISPM (Fig. 7a), PAV m (Fig. 7b), and PAV m/n on Q prevail for the Cayuga Lake tributaries (Peng and Effler, 2015). These have been quantified in a power law (i.e., log-transformed) format (Peng and Effler, 2015), widely adopted to support loading estimates for an array of constituents (Vogel et al., 2003; Prestigiacomo et al., 2015). Loads for 2013 were based on observations for days of tributary monitoring, and on estimates supported by the power law PAV m/n -Q relationships for unmonitored days (Method 6 of FLUX32). Flows and PAV m/n load estimates for unmonitored tributaries were prorated from the monitored tributary estimates according to watershed areas (Prestigiacomo et al., 2015), protocols supported by the success of earlier lake-wide modeling of chloride that adopted the same approach (Effler et al., 1989) and the well-defined land uses for the entire system (Haith et al., 2012). PAV m/n load estimates for earlier years ( ) are based solely on the power law PAV m/n -Q dependencies. The linkage between runoff events and tributary loading of PAV m (summation from four size classes) to the lake is illustrated by the combined temporal features of the Fall Creek hydrograph (Fig. 7c) and the cumulative estimated total PAV m load (Fig. 7d) for the 2013 study interval. The largest runoff event of the study in early August (recurrence interval of 3.5 y) made the dominant contribution in delivering minerogenic particles to the lake. 17

18 3.3 Modeling PP m/u This mechanistic lake PP m/u model targets the epilimnion and accepts the fundamental linkage of this P with minerogenic particles, as represented by PAV m (Effler et al., 2014), and the watershed origins of this material (Peng and Effler, 2015). The mechanistic support for a relationship between particle surface area and the associated P (Effler et al., 2014) justifies partitioning PP m/u into the same four size classes according to their contributions to overall PAV m (i.e., PAV m/n :PAV m ). The PP m/u modeling initiative has two key components, quantification of: (1) the amount and bioavailability of the P associated with the minerogenic particles delivered to the lake by tributaries, and (2) the transport and fate of these minerogenic particles in the lake, as represented by the PAV m submodel (Gelda et al., 2015a). There are no noteworthy hypolimnetic sources of PAV m, PP m/u, or SRP, that would contribute to PP m or PP m/u in the epilimnion. Strong positive dependencies of PP on Q have been documented for the monitored tributaries (Peng and Effler, 2015; Prestigiacomo et al., 2015), as illustrated here for Fall Creek (Fig. 7e). Moreover, PP becomes an increasingly dominant fraction of TP in these tributaries (Table 1) as Q increases (Fig. 7e, y-axis on right). The concentrations of PP associated with minerogenic particles (PP m ) were estimated for the monitored tributaries from the paired PP, ISPM, and SPM measurements, based on the parsimonious assumption that the PP content per unit mass of the dominant inorganic and minor organic SPM fractions were equal, according to PP m = PP (ISPM:SPM) (4) This is qualitatively consistent with the lower P content of terrigenous vs. limnetic particulate organic material (Hecky et al., 1993). 18

19 The amount of P associated with the minerogenic particles, represented by the ratio PP m :PAV m, did not remain temporally uniform. This ratio was generally negatively dependent on Q (Fig. 7f), decreasing particularly for the major runoff events, as illustrated for Fall Creek (Fig. 7g, left and right y-axes). These dynamics and the Q dependency reflect differences in the origins of P and minerogenic sediment in the watersheds of these tributaries. The primary sources of this sediment (i.e., PAV m ) delivered to the lake, and particularly the shelf, are eroding streamside glaciolacustrine deposits (Nagle et al., 2007). This contrasts the likely wider spatial origins of P from these watersheds (Haith et al., 2012) that can become associated with these particles before delivery to the lake. Estimates of daily loads of PP m (PP m/load ) were made, using the same FLUX32 software that supported the PAV m submodel, by multiplying the daily PAV m load estimates (Gelda et al., 2015a) by the daily PP m :PAV m ratio values for each of the tributaries PP m/load = PAV m load (PP m :PAV m ) (5) The loads of PP m/u (PP m/u/load ) were estimated from PP m loads and tributary-specific bioavailability of PP (Table 1) according to PP m/u/load = (1-f BAP ) PP m/load (6) This assumes an immediate transition to completely unavailable P upon entry of the lake, that is qualitatively consistent with the: (1) known rapid kinetics of desorption from mineral particles (Reddy et al., 1999), (2) the bioassays observations (Fig. 3), and (3) low f BAP values for both the local tributaries and the shelf (Table 1). These PP m/u/load estimates were apportioned to the four size classes of PAV m/n according to each of their contributions to overall PAV m in each tributary. The PP m/u/load estimates for unmonitored tributaries were prorated according to watershed areas, again as conducted successfully for the chloride model (Effler et al., 1989), and for other forms 19

20 of P (Prestigiacomo et al., 2015) and PAV m/n (Gelda et al., 2015a) for this lake. The assumption of the model of no further changes in PP m/u per unit PAV m within the lake is supported by the low epilimnetic SRP concentrations (usually 1µg P/L) compared to levels in the tributary sources (Table 1; Prestigiacomo et al., 2015). Strong temporal signatures in the external loading drivers of the model occurred over the monitored interval of 2013 (Fig. 7h and i). The major runoff events of early July and August caused dramatic abrupt increases in the cumulative particulate load of PP m/u (Fig. 7h) associated with those events, because of the positive dependencies of PP on Q (Fig. 7e). The corresponding estimated PP m loading for Fall Creek is included (Fig. 7h) to illustrate the minor effect of the level of bioavailability observed for these tributaries. The temporal character of the cumulative loads for PAV m (Fig. 7d) and PP m/u (Fig. 7h) had similar features, but the relative increase in PP m/u loading for the August event was substantially less. These differences for PAV m and PP m/u loading dynamics are represented as the PP m/u :PAV m ratio of the cumulative loads for the interval, for the overall loads, as well as for Fall Creek and the Inlet (Fig. 7i). Abrupt reductions in the ratio occurred after both events for Fall Creek, and after the second event for the Inlet, and overall, that reflect the differences in the origins of PAV m vs. associated P within the contributing watersheds. The decreases in early August were coincident with that observed for PP:ISPM in the sediment trap (Fig. 6c). The flow weighted ratio values, based on the total loads of PAV m and PP m/u for the 2013 study interval for the various tributaries, ranged from ~ 4.3 to 7.4 (mg/m 2 ; Table 1). 4. Model Results and Analyses 4.1 Performance 20

21 Evaluation of the performance of this mechanistic PP m/u model targeted three attributes, including the extent of consistency: (1) with predictions of the independently tested empirical PP model for lake (Effler et al., 2014), that partitions the contributions of PP m/u and PP o (eq. s (1) and (3)), (2) of PP m/u predictions with historic TP and PP observations, and (3) of predicted PP m/u deposition on the shelf from local runoff event inputs with sediment trap observations. The mechanistic model predictions of the dynamics of the PP m/u :PAV m ratio in 2013 for the shelf (average for Sites 1 and 2) and pelagic Site 3 are presented (Fig. 8b) in the context of the timing of the runoff events (Fall Creek daily average Q; Fig. 8a). Similar degrees of temporal variability were predicted for the shelf and pelagic waters (coefficient of variation, cv = 0.22, for each). These were substantially lower than estimated for the tributaries (e.g., cv = 0.46 for Fall Creek; Fig. 7g). Decreases in the in-lake ratio were predicted following the runoff events, but particularly after the major early July and August events (Fig. 8b), consistent with the dynamics in the tributaries (e.g., Fig. 7g). The average predicted ratio values for the 2013 study interval for both the shelf (8.0 mg/m 2 ) and pelagic waters (7.4 mg/m 2 ) closed well with the single value of 7.1 (mg/m 2 ) developed for the previously tested empirical model (Effler et al., 2014). The predicted average for the shelf was consistent with local tributary conditions, being between the estimated temporal and volume-weighted averages for the local tributaries (Table 1). The temporal uniformity of the empirical model value is a requirement that attends the simplicity of its structure (eq. (3)). The simulation of dynamics in the ratio instead is a conceptual advantage of the mechanistic framework, more consistent with the character of tributary observations (Fig. 7, Table 1). This difference between the models contributes to the differences in the predicted time series of PP m/u for the two models for the shelf (Fig. 8c) and pelagic waters (Fig. 8d). The predicted increases on the shelf from the runoff events closed reasonably well for the two models 21

22 (r 2 = 0.43 overall, average percent difference of 22%). The extent of closure with respect to temporal structure is diminished for pelagic waters because of the attenuation of the runoff event signatures (average percent difference of 29%). The average values of the ratio of PP m/u predictions for the mechanistic and empirical models were ~ 0.7 and 0.9 for the shelf and pelagic sites, respectively. The predicted distributions of the contributions of PP m/u, and PP o (accepting the same bioseston estimation approach of the empirical model; Effler et al., 2014) for the shelf and pelagic waters for the entire populations of lake PP, compare favorably for the two models (Fig. 5b and c). Both models simulated the: (1) generally higher PP m/u values on the shelf compared to pelagic waters, and (2) greater variability on the shelf (e.g., separation of mean and median values). Central metrics of these predicted populations from the two models closed reasonably well; e.g., median values of the PP m/u contributions for the shelf are 20 and 16% for the mechanistic and empirical models, respectively and 11 and 8% for pelagic waters. Though the timing of monitoring on the shelf has not targeted resolution of the effects of runoff events, a number of event opportunities emerged because of the long tenure of the program (Table 2). The mechanistic model s predictions of PP m/u performed reasonably well in explaining the TP (Fig. 9a) and PP (Fig. 9b) differences resolved for these historic events. A reasonable approach to closure for PP on the shelf, over the range of these events, resulted (Fig. 9c) from addition of PP o estimates (that accommodated differences in Chl-a; eq. (2)), with only modest improvement in explaining the observed differences from this addition. The nonhomogenous distribution of sediment, as observed in aerial photographs (Fig. 9d; Effler et al., 2010; Gelda et al., 2015) and manifested as substantial cv values for post-event shelf PP observations (Table 2), associated with the turbidity plume character of the tributary inputs, 22

23 contributes to imperfect performance of this two-dimensional model. The plume trajectories have been observed to be variable, but short-lived overall from ambient mixing effects (Gelda et al., 2015b). The mechanistic model predictions of PP m/u, combined with PP o estimates to yield PP predictions, also demonstrated a reasonable degree of closure with shelf and pelagic observations, when considered on an annual average basis over the record (Fig. 9e, mostly for shelf, r 2 = 0.24, p = 0.03; average ratio of observations and predictions of 1.03). This feature of performance provides indirect support for the representations of the PP o estimates at that annual time scale. The plume trajectories early in the post-runoff event interval (Fig. 8d), and their variations event-to-event (Effler et al., 2010; Gelda et al., 2015a), limit the extent to which fixed sediment trap position data (Fig. 6b) can be portrayed as a quantitative representation of deposition conditions across the entire shelf. Despite this limitation (e.g., semi-quantitative test) the PP m/u predictions of deposition are generally supportive of the model, depicting the enhanced operation of this loss process locally on the shelf from the input of large quantities of PAV m, and the attendant PP m/u, received from local tributaries during runoff events. Predictions of increased PP m/u deposition for the three largest events (early July through early August) coincided with trap observations of increased values of downward flux of PP. The PAV m submodel supported similarly positive predictions of the dynamics of the downward flux of ISPM, that were also driven primarily by the timing of the runoff events (Gelda et al., 2015a). The predicted PP m/u :ISPM stoichiometry of depositing minerogenic sediment received from the tributaries, presented in a cumulative format, differed substantially from the PP:ISPM of the trap observations in May and June (Fig. 6c) when tributaries flows were lower, reflecting the importance of lake-wide processes in that interval. However, the signature of the predicted 23

24 deposition from the larger local sediment inputs received from the tributaries for the major runoff events converged well with the trap observations (Fig. 6c), depicting their important role relative to this feature of the shelf deposits. 4.2 Analyses The positive dependence of post-event shelf PP m/u on the magnitude of the runoff events is described in simple terms through the predicted peak PP m/u vs. the peak Fall Creek Q for the historic events considered (Fig. 9f). Multiple factors contribute to the variance in the relationship, including the limitation of peak Q for this single tributary in specifying total local Q and PAV m (Gelda et al., 2015a) and PP m/u loading, and the effects of variations in ambient mixing (Gelda et al., 2015b). Earlier analyses with the transport (Gelda et al., 2015b) and PAV m (Gelda et al., 2015a) submodels established features that translate to importance in the overall simulations of PP m/u. These included the effective representation of: (1) the depths of entry of the tributaries, including below the epilimnion for negatively buoyant (e.g., colder) inflows, and (2) uncertainties in PAV m predictions associated with the description of the three loss processes and the estimates of the external loads of PAV m (Gelda et al., 2015a). The largest source of uncertainty was the loading estimates, associated primarily with the variance in PAV m -Q relationships (e.g., Fig. 7b). Analyses of the model predictions support depiction of the magnitudes and relative roles of the three PP m/u (and PAV m ) in-lake loss processes for the shelf (model segments 2-7) vs. pelagic waters (segments 8-33, Fig. 1). The cumulative loss format shows (Fig. 10a and b) the dominant role of runoff event-driven external loading events (Fig. 7d and h). The predicted local losses on the relatively small shelf area (Fig. 10a) were somewhat greater, and shorter-term, than those for the much larger pelagic areas (Fig. 10b). The mussel sink was not important on the 24

25 shelf, but was predicted to be more noteworthy in pelagic waters. The dominant loss pathway for PP m/u (i.e., also PAV m ; Gelda et al., 2015a) was deposition, as driven by particle size based settling, and augmented following runoff events by minerogenic particle aggregation. The additional sources of uncertainty for the PP m/u model, beyond those of the submodels, are associated with the loading estimates, and include: (1) potential variations in f BAP (Prestigiacomo et al., 2015), and (2) the dependence of the estimates on the PP-Q relationships (e.g., Fig. 7e). The second of these is more important (specified at ± 50% limits) in this case, that causes noteworthy effects on the summed internal losses, depicted for the early August event (Fig. 10c). Expanding monitoring of PP and PAV m in these tributaries could reduce this uncertainty (e.g., stronger PP-Q and PAV m -Q relationships). The summer average TP concentration was higher on the shelf than in pelagic waters in each of the monitored years (Fig. 11). The PP m/u predictions demonstrate the important role played by variations in the contribution of this form (e.g., runoff events) in driving year-to-year differences in the TP metric. Predicted PP m/u was lower at the pelagic site in each year. Interannual differences in PP m/u between the sites explained much of the year-to-year differences in TP between these sites (45%, p = 0.07), as well as much of the year-to-year variations in TP at both sites (47%, p < 0.004), according to linear least-squares regression. The positive dependence of occurrences of high PP m/u on streamflow is described by day counts for multiple concentration thresholds (5 to 50 µg/l) predicted for the shelf for the June- September interval for the years of the period (Fig. 12b-e). High flow is represented here by the number of days Fall Creek Q was in the upper 10% of its record in these summers (Fig. 12a). At high flow, strong interannual differences in PP m/u from the were predicted; e.g., greater than 30 d with PP m/u > 5 µg/l in 2004 and 2006, but essentially no days in the dry

26 2010 interval (Fig. 12b). Extreme cases of high PP m/u (>50 µg/l) were predicted for 2006 (8d) and 2011 (12d, Fig. 12e), that included a few days > 100 µg/l in both years. Clearly the relative effects of PP m/u on summer TP levels is subject to major interannual differences, driven by variations in occurrences and streamflow. 5. Discussion 5.1 Applicability of findings The approaches and general findings of our development and testing of the first mechanistic PP m/u lake model, presented here for Cayuga Lake, have broad applicability associated with: (1) improved usage of TP as a trophic state measure, (2) the similarities of the settings and issues of many other lacustrine systems to this lake, and (3) advancement of water quality management models in representation of the limited bioavailability of minerogenic particle-based P delivered from watersheds. The presence of high concentrations of minerogenic particles (Fig. 4c) and the associated PP m/u (Fig. 8c) compromises the TP measurement as a metric of trophic state. Such a problem for certain systems has been qualitatively recognized for decades (Carlson, 1977; Hecky et al., 1993; Carlson and Havens, 2005). Predictions of PP m/u represent a distinct and quantitative advancement, as the TP minus PP m/u residual more closely approaches a nearly completely available P pool, that drives trophic state in most lacustrine waters (Reynolds and Davies, 2001). A credible independent chemical analysis of the PP m/u fraction needs to be established (e.g., Penn and Auer, 1997; Auer et al., 1998; Effler et al., 2002; Baker et al., 2014) to support more robust characterizations and model validation. This short-coming in TP as a trophic state metric should not be considered fatal relative to the alternate use of one or both of the other two common metrics of SD and Chl-a. These parameters have their own limitations. The short-comings in SD are generally concurrent and 26

27 conceptually consistent with those for TP as the same minerogenic particle populations act to diminish this clarity measurement, mediated through coupled increases in the regulating light scattering process (Davies-Colley et al., 2003; Peng and Effler, 2015). This coincidence of short-comings of TP and SD to differentiate trophic state conditions between the shelf and pelagic waters was identified in an earlier empirical analysis of long-term monitoring data for the lake (Effler et al., 2010). While Chl-a is the most widely used proxy of phytoplankton biomass, the relationship is often weak because of the dependency of cellular pigment content on species composition and ambient conditions (Reynolds, 2006). Moreover, appropriate quantification and apportioning of the forms that contribute to the TP pool is central to supporting the development and testing of mechanistic eutrophication/water quality models (Chapra, 1997; Robson, 2014). The population of PAV m observations for Cayuga Lake (Fig. 4c) with respect to magnitude and variability is typical, based on the growing number of characterizations being conducted for lacustrine systems in the mid-west and northeast of the United States (Effler et al., 2015; Peng and Effler, 2015). This supports the position that noteworthy concentrations of PP m/u occur widely in lacustrine waters associated with inputs of minerogenic (mostly clay minerals) particles delivered by their watersheds (Peng and Effler, 2012; Gelda et al., 2015a). Disproportionately large fractions of these inputs are received during runoff events (Fig. 7h, Table 1; Longabucco and Rafferty, 1998; Prestigiacomo et al., 2007;2015), that in this region can be expected to be manifested as substantial year-to-year differences in timing and magnitude (Fig. 12) because of the generally stochastic character of the meteorological drivers (Effler, 1996). Interannual variations in both the long-term predictions of PP m/u (Fig. 12) and observations of TP and PP for Cayuga Lake (Fig. 11) are supportive of this position. However, longer time scale increasing trends in PP m/u, and degradation of other water quality metrics 27

28 driven by PAV m (Peng and Effler, 2015), are reasonable expectations for this lake and others in the northeastern portion of the United States, given the predicted increases in occurrences and severity of runoff events from climate change (National Oceanic and Atmospheric Administration, 2013). The extent and character of variations and systematic differences in the stoichiometry of the PP m/u -PAV m relationship (i.e., PP m/u :PAV m ) of watershed inputs (e.g., Fig. 7g; Table 1) need further investigation to support representative predictions of PP m/u in other lacustrine waters. These efforts should prioritize monitoring during runoff events and evaluation of bioavailability. The spatial differences predicted for PP m/u (Figs. 5c and 11) and observed in measured forms of P (Figs. 5a and 11) are a result of the localization of external tributary loading (e.g., 40% of the hydrologic and PP m/u loads), delivered mostly during runoff events (Fig 7h), that directly enters the shelf. Such spatial structure in PP m/u doubtless occurs widely in other lacustrine waters after runoff events, as localization of loading at one end of a basin is a common case, particularly for reservoirs (Wetzel, 2001). Localized deposition of much of the load also occurs widely (Effler and Matthews, 2004). Analyses of the model predictions indicate the higher shelf PP m/u concentrations and their interannual variations are primarily responsible (Fig. 11) for the: (1) higher TP (e.g., summer average) concentrations on the shelf versus pelagic waters, (2) interannual variations in the differences between the sites, and (3) the irregular exceedances of the regulatory TP limit of 20 µg/l on the shelf. Accordingly, TP should not be applied as an equivalent metric of trophic state spatially in this lake, and many others with similar lake-tributary configurations. In particular, it is problematic for the application of a single TP guidance value throughout Cayuga Lake (Effler et al., 2010; 2014; Peng and Effler, 2015; Prestigiacomo et al., 2015). The predicted PP m/u should be subtracted from TP 28

29 observations made on the shelf following runoff events, if regulatory use of the guidance value were to continue. 5.2 Modeling issues and advancements Mechanistic mass balance-type P-eutrophication models play an important role in guiding water quality management deliberations related to the cultural eutrophication issue (Chapra, 1997; Robson, 2014). Despite the rather long history of findings that a major fraction of external loads of P are not bioavailable (DePinto et al., 1981; Young et al., 1982; 1985; 1988; Auer et al., 1998; Ekholm and Krogerus, 2003; Ellison and Brett, 2006; Prestigiacomo et al., 2015), this effect has only rarely been represented in such models. Heretofore these models have generally considered only the external load of TP as the P driver, or loads of the various analytical (e.g., Clesceri et al., 1998) fractions, without bioavailability adjustments (Arhonditsis and Brett, 2004; Robson, 2014). Accordingly, these critical model inputs are false high relative to the potential for primary production and algae growth, a situation that inevitably leads to compensating misrepresentation of in-lake sink and/or source processes for P as part of model testing (Chapra, 1997). The importance of the bioavailability of P loads relative to lake management has recently been dramatically depicted in analysis of the re-eutrophication of Lake Erie. This reeutrophication occurred despite the lack of an increase in TP loading, because of a shift to more bio-available forms in the delivered P (Baker et al., 2014). Only ~ 20% of the TP load received by Cayuga Lake is bioavailable, with the non-bioavailable fraction dominated by PP (i.e., PP m/u ), conditions that likely prevail widely. This first lake PP m/u model represents a valuable advancement to accommodate the effects of the bioavailability of P loads and the contributions of PP m/u to TP concentrations in epilimnia. The generally good performance of the model was supported by multiple attributes, 29

30 that included: (1) reasonable closure of the predicted seasonal average shelf vs. pelagic waters PP m/u and PP m/u :PAV m levels with those predicted with an independent empirical model (Fig. 8bd; Effler et al., 2014), (2) consistency with certain features of the sediment trap measurements (Fig. 6b and c), (3) consistency of the predicted in-lake patterns of PP m/u :PAV m in time and space with the documented dynamics of this ratio in the tributaries (Fig. e.g., 7g), and (4) a partitioning of the PP pool (eq. (1)) that was consistent with the stoichiometry of phytoplankton (PP o :Chl-a; Figs. 5b and, 9c). This advancement is, however, accompanied by the added complexities of: (1) assigning PP m/u to minerogenic particle population (PAV m ) size classes in tributaries, (2) development of estimates of loading rates of these particles, and (3) simulation of their transport and fate within the lake. Isolation of this model from the complexities of the overall P cycle (Reynolds and Davies, 2001; Wetzel, 2001) here has served to support resolution of patterns and testing of model performance for this form of P. This isolation is justified by the assumed lack of reactions with other forms of P within the epilimnion, that is consistent with the prevalence of epilimnetic SRP concentrations that are low relative to the tributaries (Table 1; Froelich, 1988). Thus, this PP m/u model can be considered as potentially additive to larger P-based eutrophication models; an invaluable addition in those cases where PP m/u represents a substantial, or even noteworthy, fraction of TP. Instead of the simplifying assumption adopted here of essentially immediate release of the small bioavailable fraction of PP m (i.e., conversion to PP m/u ), a kinetic representation alternative to describe the timing of this process (Auer et al., 1998; see Fig. 3) could be implemented within the larger model. Broader implementation of PP m/u modeling, including within the context of larger P-eutrophication models, is limited by the availability of data sets such as used here to support this model, despite recent expansions in PAV m data sets for 30

31 both tributaries and lakes (Peng and Effler, 2012; Peng and Effler, 2015)and assessments of bioavailability of externally loaded PP elsewhere (Prestigiacomo et al., 2015). Given the broad importance of the much lower bioavailable P loading relative to TP loading and noteworthy-to-substantial contributions of PP m/u to lake TP concentrations, secondary (e.g., partially compromised and interim) alternative approaches should be considered where data sets such as used here are not available. These initiatives would rely on recurring features established for the minerogenic particle populations (Fig. 2) based on SAX characterizations of other systems (Peng and Effler, 2015). These secondary cases would require at least comprehensive PP, TP, SPM and ISPM tributary data. Realistic bounds of f BAP could be specified from the literature (Auer et al., 1998; Effler et al., 2002; Prestigiacomo et al., 2015). The gravimetric closure demonstrated between paired PAV m (and an associated particle volume metric) and ISPM (Peng and Effler, 2012, 2015) observations, and the recurring characteristics of the minerogenic particle populations (Fig. 2), would support first estimates of the required external loads of multiple size classes of PAV m and the associated PP m/u. The in-lake framework developed here for PAV m and PP m/u could then be used to support simulations of patterns for other lakes. The inclusion and representation of losses to biological communities (Effler et al., 2015) would of course need to be consistent with system-specific conditions. Acknowledgements Funding for portions of this study was provided by Cornell University. Staff of the Upstate Freshwater Institute provided critical support through sampling and laboratory analyses. This is contribution number 333 of the Upstate Freshwater Institute. 31

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35 Longabucco, P. and M. R. Rafferty, Analysis of Material Loading to Cannonsville Reservoir: Advantages of Event-Based Sampling. Lake and Reservoir Management 14: Nagle, G. N., T. J. Fahey, J. C. Ritchie, and P. B. Woodbury, Variations in Sediment Sources and Yields in the Finger Lakes and Catskills Regions of New York. Hydrological Processes 21: NOAA (National Oceanic and Atmospheric Administration), Regional Climate Trends and Scenarios for the U.S. National Climate Assessment. Part 1. Climate of the Northeast U.S. NOAA Technical Report NESDIS U.S. Department of Commerce, Washington, DC. Oglesby, R. T., The Limnology of Cayuga Lake. In: Lakes of New York State, Volume I, Ecology of Finger Lakes, J. A. Bloomfield (Editor). Academic Press, New York, pp Parsons, T. R., Y. Maita, and C. M. Lalli, A Manual of Chemical and Biological Methods for Seawater Analysis. Pergamon Press, New York, NY. Peng, F. and S. W. Effler, Suspended Minerogenic Particles in a Reservoir: Light Scattering Features From Individual Particle Analysis. Limnology and Oceanography 52: Peng, F. and S. W. Effler Characterizations of individual suspended mineral particles in western Lake Erie: Implications for light scattering and water clarity. Journal of Great Lakes Research 36(4): Peng, F. and S. W. Effler, Mass-Specific Scattering Coefficient for Natural Minerogenic Particle Populations: Particle Size Distribution Effect and Closure Analyses. Applied Optics 51: Peng, F. and S. W. Effler, Quantifications and Water Quality Implications of Minerogenic Particles in Cayuga Lake and Its Tributaries. Journal of the American Water Resources Association Peng, F., S. W. Effler, D. M. O'Donnell, A. D. Weidemann, and M. T. Auer, 2009a. Characterization of Minerogenic Particles in Support of Modeling Light Scattering in Lake Superior Through a Two-Component Approach. Limnology and Oceanography 54: Peng, F., S. W. Effler, D. Pierson, and D. G. Smith, 2009b. Light-Scattering Features of Turbidity-Causing Particles in Interconnected Reservoir Basins and an Intervening Stream. Water Research 43: Penn, M. R. and M. T. Auer, The Seasonal Variability in Phosphorus Speciation and Deposition in a Calcareous Eutrophic Lake. Journal of Marine Geology 139:

36 Prestigiacomo, A. R., S. W. Effler, D. A. Matthews, M. T. Auer, B. E. Downer, A. Kuczynski, and M. T. Walter, Apportionment of Bioavailable Phosphorus Loads Entering Cayuga Lake, New York. Journal of the American Water Resources Association (in internal review). Prestigiacomo, A. R., S. W. Effler, D. M. O'Donnell, J. M. Hassett, E. M. Michelanko, Z. Lee, and A. D. Weidemann, Turbidity and Suspended Solids Levels and Loads in a Sediment Enriched Stream: Implications for Impacted Lotic and Lentic Ecosystems. Lake and Reservoir Management 23: Reddy, K. R., R. H. Kadlec, E. Flaig, and P. M. Gale, Phosphorus Retention in Streams and Wetlands: A Review. Critical Reviews in Environmental Science and Technology 29: Reeders, H. H. and A. bij de Vaate, Bioprocessing of Polluted Suspended Matter From the Water Column by Zebra Mussel (Dreissena Polymorpha Pallas). Hydrobiologia 239: Reynolds, C., The Ecology of Phytoplankton. Cambridge University Press, Cambridge, MA. 436 p. Reynolds, C. S. and P. S. Davies, Sources and Bioavailability of Phosphorus Fractions in Freshwaters: a British Perspective. Biological reviews of the Cambridge Philosophical Society 76: Robson, B. J., State of the Art in Modelling of Phosphorus in Aquatic Systems: Review, Criticisms and Commentary. Environmental Modelling & Software (in press): Rosa, F., J. Bloesch, and D. E. Rathke, Sampling the Settling and Suspended Particulate Matter (SPM). In: Handbook of Techniques of Aquatic Sediment Sampling, A. Mudroch and S. C. Macknight (Editors). CRC Press, Ann Arbor, MI, pp Vanderploeg, H. A., J. R. Liebig, T. F. Nalepa, G. L. Fahnenstiel, and S. A. Pothoven, Dreissena and the Disappearance of the Spring Phytoplankton Bloom in Lake Michigan. Journal of Great Lakes Research 36: Vogel, R. M., J. R. Stedinger, and R. P. Hooper, Discharge Indices for Water Quality Loads. Water Resources Research 39:1273. Weilenmann, U., C. R. O'Melia, and W. Stumm, Particle Transport in Lakes: Models and Measurements. Limnology and Oceanography 34:1-18. Wetzel, R. G., Limnology: Lake and Reservoir Ecosystems. Academic Press, New York. Weyhenmeyer, G. A., M. Meili, and D. C. Pierson, A Simple Method to Quantify Sources of Settling Particles in Lakes: Resuspension Versus New Sedimentation of Material From Planktonic Production. Marine and Freshwater Research 46:

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38 Table 1 Cayuga Lake tributaries, selected support information. ISPM b ISPM c : d f BAP PP Tributary Watershed Landuse a % Load SPM PP Load e f PP m/u :PAV m SRP g (%) A F/BR U % % % % (mg/m 2 ) µg/l Fall Cr (12) 8 Inlet (10) 10 Cayuga Inlet Cr (11) 3 Six Mile Cr (10) 8 Salmon Cr (19) 26 Unmonitored h h - - a A agriculture; F/BR forest/brush, other rural, U urban (Haith et al., 2009) b fraction of ISPM load received during high runoff intervals c fraction of SPM as ISPM during high runoff intervals d fraction of PP bioavailable, average of three bioassays (Prestigiacomo et al., 2015) e fraction of PP load received during high runoff intervals f flow-weighted value of the ratio, PP m/u :PAV m, temporal average parenthetically g SRP concentration at high flows h estimated, based on monitored portion 38

39 Table 2 Features of selected Fall Creek runoff events and subsequent PAV m and PP monitoring observations for the shelf of Cayuga Lake, NY for the period. Peak Q a t b PAV m PP d Event No. Sampling Date (m 3 /s) (hr) (m -1 ) (NTU) 1 15-Jun (0.4) (0.4) 2 28-Jun (0.6) (0.2) 3 18-Apr (0.2) (0.2) 4 16-May (1) (0.2) 5 5-Jun (0.2) (0.3) 6 6-May (0.1) (0.5) 7 14-Apr (12) (0.3) 8 29-Jun (1) (0.2) 9 1-May (<0.1) c 10.6 e (0.2) Apr (<0.1) c 8.6 e (0.1) Apr (0.1) c 20.5 e (0.1) Apr (0.1) c 27.9 e (0.2) 13 3-Jul (<0.1) (-) 14 9-Aug (3.5) (-) Aug (3.5) (-) a event peak return, in years, parenthetically b time from event peak in Fall Creek to shelf sample collection c estimated from T n samples d Site 2 PP with coefficients of variation of multiple shelf observations, parenthetically e estimates from TP 39

40 Figure Captions Fig. 1. Cayuga Lake map with monitoring sites for tributaries and lake, longitudinal segmentation for transport submodel, expanded view of shelf, and position within the Finger Lake region of New York. Fig. 2. Example minerogenic particle population characteristics for the system, based on measurements of sample collected from Fall Creek (July 1) and a pelagic lake site (July 9): (a) particle size distributions (PSDs represented by F(d), the density function), and (b) cumulative contributions of particle sizes to PAV m, with boundaries for the four size classes adopted for the model. Fig. 3. Temporal progression of the bioavailability measurements for PP for samples from Cayuga Lake tributaries, collected during runoff events. This is represented by the ratio of cumulative fraction of the PP that was bioavailable at the time of bioassay measurements (f BAP,t ) divided by the final f BAP. Fig. 4. Time series and stoichiometric distributions related to PP in Cayuga Lake, with comparisons of conditions for the shelf vs. pelagic waters: (a) time series of daily average flow (Q) in Fall Creek for 2013, (b) time series of PP in the upper waters for 2013, (c) time series of PAV m in the upper waters for 2013, (d) time series of Chl-a in the upper waters for 2013, (e) distributions of the PP:TP ratio for the monitored record, and (f) distributions of the PP:Chl-a ratio for the monitored record. Fig. 5. Comparisons of distributions of PP and its components, PP o and PP m/u, in Cayuga Lake, in a Box-Whisker format, comparing shelf (Sites 1 and 2) and pelagic waters (Site 3): (a) PP concentrations in 2013 and in the period, (b) % contributions of PP o and PP m/u to PP 40

41 according to empirical model, (c) % contributions of PP o and mechanistic model predictions of PP m/u to PP. Empirical model documentation in Effler et al. (2014). Fig. 6. Temporal patterns for the May-August interval of 2013 for the Cayuga Lake system: (a) daily average flow (Q) in Fall Creek, (b) the downward flux of PP at Site 2, from analysis of sediment trap collections, and model predicted PP m/u deposition rate, and (c) the cumulative PP:ISPM ratio from analysis of sediment trap collections, and model predicted cumulative PP m/u :ISPM ratio for depositing PP m/u. Fig. 7. Example Cayuga Lake tributary metric-q relationships and dynamics of input conditions, including external loads, for 2013: (a) ISPM-Q (left y-axis) and ISPM:SPM-Q (right y-axis) relationships for Fall Creek, (b) PAV-Q relationship for Fall Creek, (c) time series of daily average Q in Fall Creek, (d) cumulative PAV m loading for two inflows, Fall Creek (FC) and the Inlet, (e) PP-Q (left y-axis) and PP:TP-Q (right y-axis) relationships for Fall Creek, (f) PP:PAV- Q relationship for Fall Creek, (g) time series of the ratio PP m/u :PAV m (left y-axis) and Q (right y- axis) for Fall Creek, (h) cumulative PP m/u loading for two inflows, Fall Creek (FC) and the Inlet, and for PP m loading for Fall Creek, and (i) cumulative PP m/u :PAV m ratio for overall load, Fall Creek (FC) and Inlet. Fig. 8. Temporal patterns for the April-October interval of 2013 for the Cayuga Lake system: (a) daily average Q in Fall Creek, (b) predictions of PP m/u :PAV m patterns for the shelf and pelagic waters from this mechanistic model, with single fixed value from empirical model included, (c) comparison of model performance for PP m/u predictions for the shelf, this mechanistic model vs. the empirical model, and (d) comparison of model performance for PP m/u predictions for pelagic waters, this mechanistic model vs. the empirical model. 41

42 Fig. 9. Performance of mechanistic PP m/u model based on evaluation of relationships: (a) TP observations vs. PP m/u predictions on the shelf for 15 runoff events (numbered in Table 2), (b) PP observations vs. PP m/u predictions on the shelf for 15 runoff events, (c) PP observations vs. the summation of predicted PP m/u and estimated PP o on the shelf for 15 runoff events, (d) aerial photograph of southern end shelf of Cayuga Lake following a runoff event in October 1999, (e) PP observations vs. PP predictions on the shelf and in pelagic waters on a seasonal average basis, and (f) dependency of PP m/u levels on the shelf, as predicted maxima, on the severity of the same historic runoff events, as Fall Creek peak Q for the events. Fig. 10. Model analyses of PP m/u losses according to three processes for the July-August interval of 2013 and sensitivity analyses for source uncertainty for the August runoff event: (a) temporal progression of partitioning of the loss processes for the shelf, (b) temporal progression of partitioning of the loss processes for pelagic waters, and (c) sensitivity analysis results for the predicted summer losses for the early August event, at ± 50% of PP m/u load estimates. Fig. 11. Predictions with the PP m/u model in the context of the TP metric for management of trophic state, through comparisons of summer average concentrations in Cayuga Lake for 8 years of observed TP, TDP and PP for 2 sites (s-shelf, and p-pelagic), with predictions of PP m/u (and estimates of PP o ). Fig. 12. Predictions of days of high PP m/u on the shelf associated with runoff events for the summer intervals of the period: (a) number of days of Q in the upper 10 percentile for Fall Creek, (b) number of days PP m/u 5 µg/l, (c) number of days PP m/u 10 µg/l, (d) number of days PP m/u 20 µg/l, (e) number of days PP m/u 50 µg/l. 42

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