A simple metric for predicting the timing of river phytoplankton blooms

Abstract

In rivers, phytoplankton populations are continuously exported by unidirectional, advective flow. Both transport and growth conditions determine periods of excess phytoplankton growth, or blooms, in a given reach. Phytoplankton abundance, however, has mainly been compared to the state of either growth or transport conditions alone rather than in tandem. Previous studies have not yielded consistent driver–response relationships, limiting our ability to predict the timing of riverine phytoplankton blooms based on environmental factors. Here, we derive a simple joint metric that combines the state of growth and transport conditions, specifically the ratio of temperature and discharge ($$$ T/Q $$$). We then compare the metric to biomass abundance data (daily, sensor-based chlorophyll a [chl a] data) from a mid-sized Great Plains river (the Kansas). $$$ T/Q $$$ was an excellent predictor of low to high biomass, outperforming either variable alone. However, it could not differentiate between very high biomass values, values well above the biomass threshold designating bloom conditions. Our findings of reduced performance at the highest values of T/Q indicated that $$$ T/Q $$$ could predict the occurrence (timing) but not magnitude of phytoplankton blooms, and we used T/Q to correctly predict 71% of days when bloom conditions occurred. Analyzing chl a abundance with $$$ T/Q $$$ also revealed likely switching from transport and temperature to nutrient control. $$$ T/Q $$$ offers a simple tool for (1) predicting the timing of river phytoplankton blooms, (2) forecasting how river ecosystems will respond to surrounding environmental changes, and (3) determining which environmental factors shape phytoplankton blooms at specific locations along a river.

INTRODUCTION

Phytoplankton blooms are pervasive and create management challenges because the excess biomass negatively impacts the smell, taste, and appearance of freshwater resources (Whitehead & Hornberger, 1984). Phytoplankton blooms in rivers can also produce toxins just like in lake and marine settings (Graham et al., 2020). Water resource managers can take proactive steps to reduce the damage using predictive information on the timing of blooms (Hipsey et al., 2015). Predicting bloom timing is therefore an active area of research, but most work has occurred in lakes and reservoirs. River phytoplankton blooms are less studied, yet also more complex as they are shaped by not just growth conditions but also transport conditions (Lucas et al., 2009).

Of the rare studies on true river phytoplankton (sensu Reynolds & Descy, 1996), most compare phytoplankton biomass to growth (e.g., nutrients, light, and temperature) or transport conditions in isolation (Basu & Pick, 1996; Bowes et al., 2016; Bukaveckas et al., 2011; Dolph et al., 2017; Graham et al., 2018; Soballe & Kimmel, 1987). The resulting relationships are weak and inconsistent (Lucas et al., 2009), and thus few studies have successfully used environmental factors to predict the timing of river phytoplankton blooms.

In this paper, we ask the following question: can bloom timing be explained by the relative balance of growth rate and transport loss? We propose and evaluate a simple joint metric of growth and transport conditions, based on the ratio of temperature and discharge ($$$ T/Q $$$). First, we provide a process-based derivation of $$$ T/Q $$$. Then, we compare $$$ T/Q $$$ to chlorophyll a (chl a, shown at our site to be a reliable proxy for phytoplankton biomass) in an 8-year, daily water quality record from a mid-sized Great Plains river (Kansas River, mean Q = 222 m³/s, drinking water source for >800,000) to evaluate its values as a predictive metric of the potential for river phytoplankton blooms.

T/Q DERIVATION

We derive the $$$ T/Q $$$ metric using a minimal, process-based model for river blooms, following the “fast-and-frugal” modeling approach for ecosystems (Carpenter, 2003). Assume the chl a concentration measured at a site ($$$ {B}_{\mathrm{sensor}} $$$) results from the exponential growth of some fixed initial phytoplankton population ($$$ {B}_{\mathrm{initial}} $$$) as it travels from some fixed location ($$$ {C}_{\mathrm{length}} $$$ river kilometer [rkm] away) downstream to the site. Also follow a common assumption that in rivers, nutrients are replete and nonlimiting, and thus growth is limited by light and temperature (Bukaveckas et al., 2011). Temperature has direct and well-quantified effects on phytoplankton growth rates (Grimaud et al., 2017). Light is rarely measured, but we assume that for wide rivers that are unaffected by riparian tree shading, changes in water temperature not only directly affect growth rates but also approximate seasonal dynamics in surface light dose. Altogether, we can write the following simple model describing exponential phytoplankton growth in river-transported water parcels as they travel toward a sensor location from a fixed upstream location:[Image Omitted. See PDF] [Image Omitted. See PDF]where r is a temperature-dependent, per-capita growth rate. Because growth time is the transport time between the sites, we can rewrite time as a function of velocity using the distance $$$ {C}_{\mathrm{length}} $$$ to the fixed upstream location, explicitly:[Image Omitted. See PDF]

Substitution then yields:[Image Omitted. See PDF]

Dropping constants (including fixed initial population, $$$ {B}_{\mathrm{initial}} $$$) produces the relation:[Image Omitted. See PDF]

Finally, we arrive at $$$ T/Q $$$ by (1) assuming discharge approximates velocity and (2) the relationship between temperature and growth rate is constant and linear.[Image Omitted. See PDF]

The assumed linear relationship between temperature and growth rate will not hold at locations and times when growth is limited by nutrients or light, or when temperature and light are decoupled. While we use discharge as a proxy for velocity, temperature/velocity could also be broadly assessed because stage-velocity rating curves can be developed at many flow gages.

SITE AND DATA

We assessed the performance of $$$ T/Q $$$ for predicting the timing of river phytoplankton blooms using an 8-year, near-continuous water quality record maintained by the USGS on the Kansas River. The Kansas River is a seventh-order channel flowing 276 km across northern Kansas until it joins the Missouri River at Kansas City. As a prairie river system, it is characterized by mobile, sandy substrate, large width:depth ratios (width ~150 m), and an annual hydrograph dominated by summer thunderstorms (Dodds et al., 2006).

The USGS has deployed multiparameter sensor units on several channel-spanning bridges down the Kansas mainstem. We focus our analysis on a single site (Kansas River at De Soto, id: 06892350) that has 8 years of 15-min water quality and quantity measurements, including chl a, nitrate (SUNA), turbidity, temperature, and discharge. The USGS maintains sensor calibration and has published post-correction, analysis-ready data. Published sensor chl a measurements are field measurements of florescence corrected to lab-measured chl a (Graham et al., 2018). Because chl a sensors have daily-scale artifacts (see Carberry et al., 2019 for discussion of the general problem, termed nonphotochemical quenching), we aggregated all fields to daily median measurements. For a secondary analysis, we used an additional site 158 rkm upstream (Kansas River at Wamego, id: 06887500), with a similar record but no nitrate.

Suspended chl a can reflect both phytoplankton biomass and material scoured from benthic algal mats. The USGS directly assessed the source of chl a in the data we used. The results found that, at both sites, chl a approximates phytoplankton biomass and not material scoured from benthic algal mats. Total phytoplankton biomass was directly measured and found to have a strong and direct correlation with chl a at both sites through the entire year ($$$ {R}^2>0.85 $$$, p < 0.01 at both sites). Further, taxonomic analysis found similar community compositions at both sites that were dominated by true phytoplankton species (Graham et al., 2018). We therefore assumed that at both of our study sites, chl a was a reliable proxy for phytoplankton biomass. Finally, we defined periods when chl a exceeded 30 μg/L as bloom events, following the Kansas USGS and other state agencies that define rivers with chl a above 30 μg/L as eutrophic (Graham et al., 2018; following Dodds et al., 1998).

RESULTS

The chl a record (Figure 1) showed repeated bloom events where chl a concentrations surpassed and remained above the 30 μg/L threshold for tens of days. The frequency and duration of these bloom events varied, ranging from one bloom during 2019 to three blooms during 2016 and 2017. The duration of individual bloom events ranged from 12 days (2019) to 8 months (2018). When aggregating across all bloom events, chl a exceeded the 30 μg/L threshold for 33% of the record.

FIGURE 1. Daily USGS water quality record at gage 06892350, Kansas River at De Soto. The horizontal line in the chlorophyll a (chl a) panel indicates bloom threshold, 30 μg/L.

The onset and offset of the bloom events always occurred with a change in either temperature or discharge. Spring bloom events (March, April, and May) began when discharge was low and when water temperature increased. Spring blooms ended with the commencement of a high discharge event (summer thunderstorm season). In the summer (June, July, and August), when water temperatures were consistently elevated, bloom events occurred in between high discharge events, that is, when discharge decreased in the summer, a bloom occurred. In general, during the summer (June, July, and August), blooms were separated by periods of high discharge (i.e., when the discharge dropped, bloom events occurred). In autumn (September, October, and November), bloom events began when discharge fell and ended when water temperature decreased. The year with consistently low discharge (2018) had a single bloom that lasted 8 months.

During different seasons, the chl a time series clearly followed either discharge or temperature (Figure 1). $$$ T/Q $$$ however, combining the state of each, followed the chl a dynamics during the entire year. We tested the correspondence by fitting linear regressions of log(chl a) to $$$ T/Q $$$ and its two components alone, temperature and discharge⁻¹. $$$ T/Q $$$ had a strong and significant positive relationship with log(chl a), and model fits on $$$ T/Q $$$ were substantially better than model fits with discharge⁻¹ or temperature ($$$ {R}^2 $$$ of 0.44, 0.24, and 0.063 respectively, see Figure 2).

FIGURE 2. T/Q$$ T/Q $$ serves as a better linear predictor of log(chl a) (R2=0.44$$ {R}^2=0.44 $$) than either discharge (R2=0.24$$ {R}^2=0.24 $$) or temperature (R2=0.063$$ {R}^2=0.063 $$) alone. chl a, chlorophyll a.

The relationship between $$$ T/Q $$$ and chl a was not uniform across the range of $$$ T/Q $$$. Nonparametric, local regression produced a saturating relationship between $$$ T/Q $$$ and log(chl a) (Figure 3, left), where a critical $$$ T/Q $$$ value (approximately when $$$ T/Q $$$ > 0.35) demarcated two ranges of T/Q that had different relationships with chl a. In the upper range of $$$ T/Q $$$ above 0.35, occurring during 21% of the record, chl a was almost always high, well above the 30 μg/L threshold, indicating bloom conditions (mean daily chl a: 45 μg/L with an interquartile range (IQR) of 32–55 μg/L). However, $$$ T/Q $$$ could not explain the variation between these high values of chl a (R² = 0.002 for linear model fit on days when $$$ T/Q>0.35 $$$). In contrast, within the lower range of $$$ T/Q $$$ (0–0.35), representing 79% of the record, chl a was lower (mean daily chl a: 20 μg/L with an IQR of 5–24 μg/L), and $$$ T/Q $$$ could directly explain variation between these lower chl a values ($$$ {R}^2=0.5 $$$ for linear model fit on days when $$$ T/Q<0.35 $$$). Finally, the linear model fit between $$$ T/Q $$$ and chl a in the lower range predicted that $$$ T/Q=0.35 $$$ corresponded to chl a of 64 μg/L. In summary, $$$ T/Q $$$ explained variation in chl a for low to high chl a values (0–64 μg/L), a range that contains the threshold chl a indicating bloom conditions (30 μg/L). It did not explain variation in the highest values of chl a beyond 64 μg/L. Therefore, $$$ T/Q $$$ could predict when chl a crossed 30 μg/L and thus bloom timing, but $$$ T/Q $$$ could not predict peak biomass and thus could not predict bloom magnitude.

FIGURE 3. Elevated chlorophyll a (chl a) always corresponded with low nitrate, suggesting that high chl a draws down nitrate to limiting concentrations. It therefore appears that nitrate limitation and total nitrate loading set the upper limit of phytoplankton bloom magnitude.

The upper range of $$$ T/Q $$$ values also consistently co-occurred with low measured nitrate. Similarly, when chl a was elevated (and $$$ T/Q $$$ was high), nitrate was always low (Figure 3, right). The two pieces of evidence together suggest that at high values of $$$ T/Q $$$ (above $$$ 0.35 $$$), the dominant controls on chl a at the study site shift from temperature and transport to nutrient availability. Therefore, the upper boundary on the magnitude of river phytoplankton blooms (maximum chl a concentration) may be controlled by antecedent nutrient conditions, that is, total nutrient loading.

Finally, we directly assessed the capacity of $$$ T/Q $$$ to predict the occurrence of blooms. We used the state-mandated threshold of 30 μg/L to define “bloom status” and used a linear fit of $$$ T/Q $$$ and chl a to find the $$$ T/Q $$$ value that corresponded to 30 μg/L ($$$ T/Q $$$ of 0.24, model fit on days when $$$ T/Q<0.35 $$$). This $$$ T/Q $$$ threshold of 0.24 correctly predicted the bloom status of 81% of all days in the record. Seventy one percent of days with bloom conditions were correctly predicted (516 true positives of 727 bloom days), and only 13% of nonbloom days were mischaracterized as bloom days (1321 true negatives of 1626 nonbloom days). To assess the sensitivity of our analysis on our specific $$$ T/Q $$$ threshold of 0.24, we also performed an exceedance analysis (Figure 4). We computed the relative probability of exceeding the USGS eutrophic-river threshold (30 μg/L) when conditions equaled or exceeded $$$ T/Q $$$ thresholds. To ensure sufficient data at all thresholds, we set the maximum threshold as the 95th percentile of $$$ T/Q $$$ values in the record (0.61). The exceedance analysis showed a positive, saturating relationship, where increases in the $$$ T/Q $$$ threshold corresponded with a diminishing increase in the probability of achieving bloom conditions. The relationship achieved its horizontal asymptote at similar values to the local regression in Figure 3, around 0.35.

FIGURE 4. Probability of chlorophyll a (chl a) exceeding 30 μg/L when conditions equal or exceed T/Q$$ T/Q $$ threshold values. Maximum threshold (0.61) is the 95th percentile of T/Q$$ T/Q $$.

DISCUSSION

Rivers continuously export their phytoplankton populations downstream. Phytoplankton blooms in rivers are therefore controlled by both export rates (transport conditions) and growth conditions. Most previous attempts to predict river phytoplankton blooms use growth or transit conditions alone (e.g., Basu & Pick, 1996; Bukaveckas et al., 2011; Bowes et al., 2016; Dolph et al., 2017; Graham et al., 2018; Soballe & Kimmel, 1987; however, see Lucas et al., 2009 for a unifying conceptual model). Here, we demonstrate how $$$ T/Q $$$, which instead combines the state of transport and growth conditions, outperforms either of its components when predicting river phytoplankton blooms. A joint metric is particularly important in the Kansas because its hydrograph is dominated by summer thunderstorms, which means the highest light and temperature co-occur with the highest variation in discharge. It is likely that in rivers where T and Q are more tightly correlated, for instance, systems with consistent low summer flows, prediction with $$$ T/Q $$$ will show reduced improvement over prediction with T or Q individually.

Our use of $$$ T/Q $$$ to predict bloom timing resembles a rating curve approach, where individual sites have a site-specific, informative $$$ T/Q $$$ to chl a relationship. While we compared $$$ T/Q $$$ to an unusually dense chl a record (8 years of daily measurements), the relationship can be constructed using sparser chl a records as long as they cover the range of $$$ T/Q $$$ values. Most current and historic river chl a data have coincident temperature and discharge measurements. Therefore $$$ T/Q $$$ to chl a relationships can be constructed and tested for generality on many rivers (see Ross et al., 2019 for assessment of the chl a historic record), although chl a does not always approximate phytoplankton biomass like it does on the Kansas (Graham et al., 2018). If $$$ T/Q $$$ indeed predicts bloom timing on many rivers, it can be widely used by water managers as a river-bloom forecasting tool, informing management actions for phytoplankton control like release policies from impoundments. Further, because $$$ T/Q $$$ has a clear process derivation incorporating temperature and flow conditions, it can also be used for predicting river ecosystem response to changes in climate and water management.

We have so far focused on the use of $$$ T/Q $$$ for predicting the timing of a phytoplankton bloom, but it likely has additional use for understanding dynamic controls on bloom magnitude. Specifically, $$$ T/Q $$$ had two distinct ranges. In its lower range, the colder, faster 79% of the record when $$$ T/Q<0.35 $$$, the ratio was a robust linear predictor of chl a. In its upper range, the slowest, hottest 21% of the record when $$$ T/Q>0.35 $$$, chl a was high but $$$ T/Q $$$ could not explain differences between the high chl a values. In the upper range of $$$ T/Q $$$, nitrate was also consistently low, suggesting that nutrients likely became limiting. In other words, at the highest $$$ T/Q $$$ values, vigorous growth of phytoplankton upstream appeared to consume the entire pool of available nitrate, yielding a maximum abundance downstream set by nutrient loading (and therefore not sensitive to small changes in velocity or temperature.) Basin-level nutrient control, therefore, likely plays an important role at this site by setting the upper boundary of phytoplankton bloom magnitude (Hilton et al., 2006).

Finally, the process derivation of $$$ T/Q $$$ creates predictions of how the site-specific relationship between $$$ T/Q $$$ and phytoplankton biomass should vary with location along a river. Specifically, the derivation assumes that chl a spatial patterns result from the growth-in-motion of phytoplankton populations within moving water parcels. Therefore, under fixed growth and transport conditions, downstream sites see “older water” that has experienced more total growth time than upstream sites. Downstream sites should thus have more chl a than upstream sites at fixed values of $$$ T/Q $$$ and a higher likelihood of reaching the peak chl a set by nutrient loading. These predictions matched results from repeating the local regression between $$$ T/Q $$$ and log(chl a) at an additional, upstream site where chl a was also shown to approximate phytoplankton biomass (Wamego, 158 km upstream from our focal site, see Appendix S1: Figure S2 for full record): the upstream site had lower chl a at specific values of $$$ T/Q $$$, and the relationship between T/Q and chl a remained strictly positive and linear, not showing a saturating relationship like at the downstream site (Figure 5; exceedance analysis repeated at these same two sites shows a similar pattern, see Appendix S1: Figure S1). The mechanistic, site-specific variation in the $$$ T/Q $$$, chl a relationship has implications for both river management and river ecology. For managers, the result implies that $$$ T/Q $$$ can be used to determine both when and where nutrient management will impact phytoplankton bloom magnitude. Our analysis indicates that nutrient management will likely impact bloom magnitude at the downstream but not upstream site, and only within a distinct upper range of $$$ T/Q $$$ values (sufficiently slow, warm conditions). For river scientists and ecologists in general, the spatial variation in the $$$ T/Q $$$, chl a relationship implies that mechanistic, Lagrangian (particle following, sensu Doyle & Ensign, 2009) models of phytoplankton population dynamics within water parcels will likely reveal more insight into how spatial patterns of chl a respond to changes in relevant environmental conditions (Ensign et al., 2017).

FIGURE 5. Local regression between T/Q$$ T/Q $$ and  chlorophyll a (chl a) at two sites on the Kansas River, separated by 158 river kilometers.

ACKNOWLEDGMENTS

We thank John Gardner, Emily Bernhardt, Phillip Savoy, Robert Shriver, and several anonymous reviewers for their rich feedback on drafts. We also thank Alex Brooks and John Mallard for the vigorous conversation during initial data analysis. This work was supported under US Fish and Wildlife grant: F18AC00114.

CONFLICT OF INTEREST

The authors declare no conflict of interest.

DATA AVAILABILITY STATEMENT

Data (Bruns, 2022a) were generated from public USGS data and are available from Figshare: https://figshare.com/articles/dataset/Kansas_River_continuous_WQ_data_RData/21498588/2. A sub-portion of that public dataset was published in Graham et al. (2018). The scripts used to prepare data and generate manuscript figures (Bruns, 2022b) are available from Figshare: https://doi.org/10.6084/m9.figshare.21498582.v1.