Trophic State Evolution of 45 Yellowstone Lakes over Two Decades: Field Data and a Longitudinal Study

Abstract

From 1998 to 2024, we collected field samples at 45 selected lakes in Yellowstone National Park during the months of April through October. We estimated inflows, outflows, and Secchi depths for most lakes. We analyzed the samples for total phosphorous and chlorophyll-a. We used these data to classify the lake trophic states using the Carlson TSI (CTSI), Vollenweider (VW), and Larsen–Mercier (LM) models to assess how trophic states evolved over this 26-year period. This longitudinal dataset is unique because of its extensive 26-year time span gathered from difficult-to-access locations. We found that the data depended on lake size, lake elevation, and the month when data were collected. Most of the lakes exhibit mesotrophic conditions, with variations depending on the trophic state model used. The CTSI distribution shows median values typically between 40 and 55, while the VW and LM index distributions present a somewhat similar pattern but with fewer lakes categorized due to data requirements. We visualized temporal patterns using heatmaps and analyzed trends using the Mann–Kendall test to identify trends and if they were statistically significant. We found only four lakes with statistically significantly increasing trends and two with decreasing trends. Because of the difference in the months when data were collected, the increasing trends in three of the lakes are less certain. We found that, except for four lakes, the trophic states of Yellowstone lakes were maintained or improved over this ~20-year period. Only the trophic state of Nymph Lake clearly deteriorated. The remaining lakes had stable trophic states, with three having weak evidence of worsening conditions. This long-term dataset, which we publish for others’ use, provides an opportunity to better understand eutrophication processes and water quality dynamics in Yellowstone, providing critical information for park management and conservation efforts.

1. Introduction

Freshwater lakes play a critical role in global ecosystems and the hydrologic cycle. They support a diverse range of flora, fauna, and microorganisms, while also serving as essential sources of freshwater. However, these systems are particularly vulnerable to the impacts of anthropogenic activity [1,2]. Long-term monitoring efforts have primarily relied on Landsat imagery, which offers a record spanning over four decades [3,4,5,6,7], and other remote sensing methods [8], though some use in situ data [9]. The freshwater lakes within Yellowstone National Park are a complex and dynamic ecological network that has potentially been affected by anthropogenic activities. As a result, there is interest in assessing the ecological condition of these lakes. However, there is a scarcity of long-term datasets capable of providing comprehensive longitudinal insights into their health and ecological change [10].

Established in 1872, Yellowstone was the world’s first national park. Since its founding, Yellowstone National Park has experienced a notable increase in visitation, welcoming over 4.5 million visitors in 2023 [11]. Yellowstone’s numerous water features, including over 220 lakes and 2650 miles of streams, which constitute 5% of the park’s 2.25 million acres [12], represent ecosystems that are sensitive to natural and anthropogenic changes. Evaluating how the lakes change over time provides a unique opportunity to assess and understand the impacts of changes in the park.

Over time, freshwater lakes undergo eutrophication. This process can be exacerbated by environmental or anthropogenic changes. Eutrophication is caused by excess nutrients, particularly nitrogen and phosphorus, which cause enhanced growth of primary producers, leading to oxygen depletion and other detrimental ecological effects [13,14,15]. While human activities, such as agricultural runoff, wastewater discharge, and urban development, are significant contributors to this phenomenon, eutrophication also occurs naturally in response to nutrient loading from natural sources like decaying organic matter and sediment erosion [16]. Eutrophication can diminish the ability of a lake to support biodiversity [17] and can contribute to numerous other detrimental outcomes [18,19,20]. Trophic state analysis is often used to study and manage freshwater lake ecosystems [21].

Increased tourism at Yellowstone National Park has the potential to accelerate lake eutrophication. As visitor numbers rise, the likelihood of increased nutrient loads from human activities—such as littering and increased soil erosion due to foot traffic—increases and can introduce excess nitrogen and phosphorus, which can be primary drivers of eutrophication [22].

Trophic state analysis is a common method for evaluating water quality and eutrophication. Lake trophic states are used worldwide to help assess water quality and guide resource allocation and management decisions often related to nutrient loads [2,21,23,24]. Trophic state assessments have been used to identify the need to control excess nutrients [25], investigate pollution sources and geochemical characteristics for lakes [26], develop sustainable management and conservation policies [26], and review the effects of anthropogenic activities on water quality [27] and the health of aquatic life [28].

Trophic state models are essential tools in limnology for assessing the productivity and health of aquatic ecosystems. Trophic state models assign a eutrophication state or classification based on various parameters. Three widely used indexes for assessing trophic states are: the Carlson Trophic State Index (CTSI), the Vollenweider (VW) model, and the Larsen–Mercier (LM) model. The CTSI, developed by Robert Carlson in 1977, uses three variables—chlorophyll-a (chl-a) concentration, in-lake total phosphorus (TP) concentration, and Secchi depth (SD)—to estimate algal biomass and classify lakes into different trophic states [29]. The CTSI is particularly useful because it provides a numerical value that can be easily interpreted and compared across different water bodies. The VW model, developed by Richard Vollenweider in the 1970s, considers the inflowing TP concentration and hydraulic residence time (HRT), which is the average time water remains in a lake, to compute a trophic state [30]. The LM model uses the phosphorus retention coefficient (PRC), which is the fraction of incoming phosphorus retained within the lake, and inflowing phosphorus load to assign a trophic state [31].

We present data from 1998 to 2024 from 45 Yellowstone lakes collected from April to October because of weather limitations. We collected water samples and either measured or estimated the Secchi depth along with estimating the inflow and outflow to each lake and found the lake area and elevation. We analyzed the water samples for TP and chl-a using a certified laboratory.

We perform a basic statistical analysis on this dataset and apply the three trophic state models described above to each lake and provide graphical representations of the trophic states. We use statistical methods to quantify the trends and trophic state temporal behavior and to help quantify our findings.

This dataset and accompanying analysis are unique because of the long period which it covers and the inaccessibility of many of the lakes sampled for this study. Because of the time span covered by our data, they support a longitudinal analysis to evaluate if the trophic state of the lakes has changed over time in Yellowstone National Park. We provide the dataset to support other researchers.

2. Methods

2.1. Study Area

We collected data for 45 lakes in Yellowstone National Park from 1998 to 2024. We were not able to sample every lake every year and typically only sampled a lake once or at most a few times in any given year. Therefore, each lake has a varying amount of data. In general, the more accessible lakes have more data, while the less accessible and smaller lakes have less data.

Figure 1 provides a map showing the locations of these lakes. Lake elevations range from 1866 to 2588 m (6121 to 8492 feet) above mean sea level. The largest, Yellowstone Lake, is about 352 square kilometers (136 square miles) and the smallest, Isa Lake, is just 0.004 square kilometers (1 acre).

2.2. Data

2.2.1. Field Data Collection

We collected samples using a rubber raft, wading into the lake, or taking a sample near the shore using a fallen tree or rock to reach as far as possible into the lake. For each sample, we collected about 1.8 L of water, from which we used about 30 mL for TP analysis and the remainder to analyze for chl-a. For the samples destined for TP analysis, we put about 30 mL of the water into a bottle with nitric acid to fix the sample, then placed the bottle in a cooler on ice for transport. We also stored the 2 L bottle with the remainder of the water in the cooler for chl-a analysis. Acid prevents microbial growth and any alterations in the phosphorous content in the sample that could be caused by metal precipitation. We measured transparency using a Secchi disk, which was lowered into the lake until it was no longer visible. That length is reported as the Secchi depth. When the samples were collected near shore, we estimated the Secchi depth visually without using a Secchi disk.

We delivered the 30 mL samples to the state-certified Chemtech-Ford Laboratory in Sandy, Utah, where they analyzed the samples for TP using Standard Methods 4500-P B5 F. We prepared samples for chl-a analysis by pumping about 1000 mL of water through a glass 47 mm microfiber filter. We placed the filter in a film case for storage and placed the case in a freezer for preservation. We shipped the frozen samples in dry ice to the Bureau of Reclamation PN Regional Laboratory in Boise, Idaho, for chl-a analysis where they used method number SM10200 H: Spectrophotometric Determination of Chlorophyll from Standard Methods for the Examination of Water and Wastewater. Initially, we also analyzed the samples for nitrogen levels, but the nitrogen concentration was almost always below the detection level, so we stopped nitrogen analysis after the second year.

2.2.2. Physical Parameters

We used Google Earth to obtain the longitude, latitude, and elevation data at approximately the center point of each lake. We estimated lake areas and assigned them to a size range defined in

Table 1. Lake size classification scheme.

Size (ha)	Classification
Area < 2	Extra small
2 ≤ Area < 10	Small
10 ≤ Area < 30	Medium
30 ≤ Area < 3000	Large
Area ≥ 3000	Extra large

. The majority of these lakes and associated inflows are too small to have published or archived data on volume or stream flow.

Table 2. Parameters for Yellowstone lakes analyzed: coordinates, elevation, lake area, size category, number of in-lake samples, and number of inlet samples.

Lake	Latitude	Longitude	Elevation (meters)	Est. Lake Area (ha)	Size Category	In-Lake Samples (Number)	Inlet Samples (Number)
Beaver Lake	−110.73	44.82	2243	0.63	Extra small	10	8
Clear Lake	−110.48	44.71	2380	1.62		24	2
Eleanor Lake	−110.14	44.47	2588	1.70		13	5
Hazle Lake	−110.72	44.75	2282	1.92		16	12
Isa Lake	−110.72	44.44	2515	0.51		7	NI *
Lily Pad Lake	−111.01	44.17	2385	1.33		24	NI
Shrimp Lake	−110.13	44.91	2161	0.90		6	NI
Terrace Spring	−110.85	44.65	2098	0.58		8	NI
Blacktail Pond	−110.60	44.96	2014	5.67	Small	15	1
Buck Lake	−110.13	44.90	2130	2.79		35	34
Druid Lake	−110.17	44.87	2038	3.85		10	0
Feather Lake	−110.84	44.54	2191	7.46		8	0
Floating Island	−110.45	44.94	2013	2.10		4	NI
Harlequin Lake	−110.89	44.64	2096	7.41		17	NI
Hot Lake	−110.79	44.54	2239	2.94		5	1
Lost Lake	−110.10	43.78	2086	5.26		38	16
Lower Basin Lake	−110.82	44.54	2201	4.14		12	NI
North Twin Lake	−110.74	44.78	2293	5.22		24	23
Nymph Lake	−110.73	44.75	2280	5.00		20	18
Ribbon Lake	−110.45	44.72	2381	3.86		4	0
Scaup Lake	−110.77	44.43	2404	2.26		8	NI
South Twin Lake	−110.73	44.77	2290	8.12		29	21
Trout Lake	−110.13	44.90	2124	6.36		37	34
Trumpeter Pond	−110.37	44.92	2066	4.68		4	NI
Cascade Lake	−110.52	44.75	2437	13.90	Medium	14	11
Duck Lake	−110.58	44.42	2368	17.80		22	NI
Goose Lake	−110.84	44.54	2195	15.80		14	13
Hot Beach Pond	−110.30	44.55	2361	15.60		10	NI
Ice Lake	−110.63	44.72	2407	29.70		17	4
Indian Pond	−110.32	44.56	2366	12.00		48	23
Lake of the woods	−110.71	44.80	2356	11.20		2	1
Mallard Lake	−110.78	44.48	2443	13.00		1	1
Swan Lake	−110.74	44.92	2211	20.90		27	NI
Sylvan Lake	−110.16	44.48	2568	16.00		26	21
Tanager Lake	−110.69	44.14	2133	13.20		10	NI
Wolf Lake	−110.59	44.75	2442	20.20		5	3
Grebe Lake	−110.56	44.75	2450	62.80	Large	5	3
Grizzly Lake	−110.77	44.81	2290	73.30		2	0
Heart Lake	−110.49	44.27	2282	993.00		4	2
Lewis Lake	−110.63	44.30	2374	1252.00		16	5
Riddle Lake	−110.55	44.36	2414	137.00		2	1
Shoshone Lake	−110.70	44.37	2380	2946.00		6	4
Turbid Lake	−110.27	44.56	2392	68.00		3	3
Yellowstone Lake (YSL@Bridge Bay)	−110.44	44.53	2357	3,5143.00	Extra large	8	0
Yellowstone Lake (YSL@WestThumb)	−110.55	44.39	2357	3,5143.00		7	0

Note: * NI = No Inlet.

provides lake details including coordinates, elevation, estimated lake area, size category, and the number of samples taken from both the lake (in-lake sample) and the number of samples taken at the inlet. Some lakes do not have inlets but are fed by groundwater.

The VW model requires values for HRT and the LM model requires values for PRC. HRT uses values for lake volumes and outflow rates. As we did not have measured values, we estimated lake volume using lake area and an estimated depth. We estimated lake outflow by observing either the inflow or outflow and making simple measurements such as stream width and depth.

We computed the HRT in units of years using:

$$\mathrm{HRT}=\left({\displaystyle \frac{\mathrm{Lake}\mathrm{Volume}}{\mathrm{Outflow}\mathrm{Rate}}}\right)$$

(1)

We computed PRC as:

$$\mathrm{PRC}={\displaystyle \frac{\left(\mathrm{Inflow}\mathrm{TP}-\mathrm{Outflow}\mathrm{TP}\right)}{\mathrm{Inflow}\mathrm{TP}}}$$

(2)

We assumed the lake outflow TP concentration was the same as the in-lake TP concentration. In cases where the outflow or in-lake TP was greater than the inflow TP, we set the coefficient at 0 because the LM trophic state analysis model does not allow for negative values.

2.3. Trophic State Models

2.3.1. Trophic State Model Overview

We used the CTSI, VW, and LM models to classify the trophic state of the lakes. These models classify lakes as: oligotrophic (low productivity), mesotrophic (moderate productivity), eutrophic (high productivity), and hyper-eutrophic (very high productivity). The CTSI model computes a eutrophication index that ranges from 1 to 100 that is used to define the trophic state. The other two models, VW and LM, do not compute a numerical value but are only used to assign a trophic classification. To support trend analysis, we assigned a numerical value for these models based on the CTSI classification and numerical value.

2.3.2. CTSI Model

The CTSI model classifies lakes into trophic states based on chl-a, in-lake TP, and SD measurements [29]. The CTSI model calculates a trophic state index (TSI) value which commonly ranges from 20 to 80 but can range from 0 to 100. Higher values indicate more eutrophic conditions, reflecting higher biological productivity and nutrient levels.

The TSI is computed by [32]:

$${\mathrm{TSI}}_{\mathrm{TP}}=14.42\mathit{ln}\left(\mathrm{T}\mathrm{P}\left[{\displaystyle \frac{\mathsf{\mu }\mathrm{g}}{\mathrm{L}}}\right]\right)+4.15$$

(3)

$${\mathrm{TSI}}_{\mathrm{chl}\text{-}\mathrm{a}}=9.81\mathit{ln}\left(\mathrm{chl}\text{-}\mathrm{a}\left[{\displaystyle \frac{\mathsf{\mu }\mathrm{g}}{\mathrm{L}}}\right]\right)+30.6$$

(4)

$${\mathrm{TSI}}_{\mathrm{SD}}=60-14.1\mathit{ln}\left(\mathrm{S}\mathrm{D}\left[\mathrm{m}\right]\right)$$

(5)

$$TSI={\displaystyle \frac{{TSI}_{TP}+{TSI}_{chl\text{-}a}+{TSI}_{SD}}{3}}$$

(6)

Figure 2 graphically presents the numerical TSI values along with the component values for TSI_TP, TSI_chl-a, and TSI_SD.

The CTSI model uses the natural logarithm of the measured values, which means that small changes in low concentrations or SD values have a larger impact on the TSI than changes in higher concentrations. For example, a change from 0.01 to 0.1 µg/L (ppb) of chl-a results in the same numerical change to the TSI values as a change from 10 to 100 µg/L. This is because natural eutrophication processes are more sensitive to changes when the nutrient or condition is limiting. Once values are higher than the limiting value, further changes have less impact on trophic state.

Table 3. Classification of trophic state based on CTSI model’s TSI value [13].

Classification	Sub-Classification	Scale
Oligotrophic	Strongly oligotrophic	TSI < 26
	Oligotrophic	26 ≤ TSI < 33
	Slightly oligotrophic	33 ≤ TSI < 38
Mesotrophic	Slightly mesotrophic	38 ≤ TSI < 43
	Mesotrophic	43 ≤ TSI < 49
	Strongly mesotrophic	49 ≤ TSI < 54
Eutrophic	Slightly eutrophic	54 ≤ TSI < 58
	Eutrophic	58 ≤ TSI < 62
	Strongly eutrophic	62 ≤ TSI < 65
Hyper-Eutrophic	Slightly hyper-eutrophic	65 ≤ TSI < 70
	Hyper-eutrophic	70 ≤ TSI

shows the different trophic states associated with TSI value ranges. The CTIS model includes both the four main states, oligotrophic, mesotrophic, eutrophic, and hyper-eutrophic, and sub-classifications. Traditionally, values for a waterbody are plotted on this graph, showing both the overall trophic state, and the trophic state based on each of the sub-categories of the model. We used Equation (6) and Table 3 to classify each of the lakes.

2.3.3. VW Model

The VW model uses inflow TP concentration along with the HRT to classify the lake trophic state. We only applied VW classification to the lakes with inflow and inlet data, which was only 26 of 45 lakes in this study (Table 2). To classify a waterbody using the VW model, values for HRT and inflow TP concentration are plotted on Figure 3. The graph is divided into sections related to the trophic state. Depending on where the point plots, a trophic state is assigned.

For this analysis, we needed to assign a numerical value in addition to a trophic state. To assign a trophic state classification with the VW model, we visually interpolated between the lines to provide a sub-classification, like those used by the CTSI. We then assigned a trophic index value using the ranges for the CTSI model listed in Table 3. We assigned this numerical classification so we could analyze long-term trends and compare results among the models.

2.3.4. LM Model

The LM model uses the PRC with the inflow TP concentration to classify a water body. As with the VW model, we only applied the LM model where we had inlet data. The values are plotted on Figure 4 to obtain the trophic states. As with the VW model, we used the classification and values from Table 3 to assign a numerical value to the trophic state.

2.4. Trend Analysis

We used the Mann–Kendall test to evaluate trends [34]. The Mann–Kendall test is a nonparametric test, which means that it does not assume a distribution for the data and works well for data that are not normally distributed. It is widely used in hydrology and recommended by the Environmental Protection Agency (EPA) to evaluate trends in environmental data [35]. The Mann–Kendall test evaluates the signs of changes in values over time to detect the presence of any monotonic trend in the data along with the uncertainty associated with the trend [34]. We applied the Mann–Kendall test individually to each lake to identify increasing or decreasing trends in CTSI values over the study period.

2.5. Statistical Grouping

We used regression analysis to examine how the classifications from different models compared to each other and changed over time. For this analysis, we used several standard statistical metrics [36,37], such as:

(1)

Pearson’s correlation coefficient (r):

$$r={\displaystyle \frac{\sum \left(x_i-\overline{x}\right)\left(y_i-\overline{y}\right)}{\sqrt{\sum {\left(x_i-\overline{x}\right)}^2\sum {\left(y_i-\overline{y}\right)}^2}}}$$

(7)

where r ranges from −1 to +1, indicating the strength and direction of linear relationships between variables, and where ±1 represents perfect correlation and 0 indicates no correlation.

(2)

Coefficient of determination (R²):

$$R^2=1-{\displaystyle \frac{RSS}{TSS}}$$

(8)

where R² represents the proportion of variance in the dependent variable explained by the independent variable, ranging from 0 to 1, and where 1 indicates perfect prediction.

(3)

p-values: which show the probability of obtaining test results at least as extreme as the observed results under the null hypothesis (no relationship between variables). A p-value < 0.05 indicates statistical significance or a 5% chance the result is because of variance in the dataset, rather than an actual difference.

3. Results and Discussion

3.1. Data Analysis

3.1.1. Data Statistical Distributions

We collected 635, 620, and 916 measurements for SD, chl-a, and TP, respectively, in the 45 lakes over the study period. As noted, some SD values were estimated rather than measured. We estimated lake areas, volumes, and flows and used these data to compute HRT and PRC. This section provides a quantitative description of the data we collected, how they are distributed, and how the data are associated with factors such as time of year (month), lake size, elevation, and change over the period of the study.

Figure 5 presents a summary of the data we collected for: (A) SD (m), (B) chl-a (mg/m³), and (C) TP (mg/L). The box-and-whisker plots illustrate the distribution of data. The box represents the 25th to 75th quantiles, with the median (50th quantile) indicated by a line. The diamond marks the mean value, with its ends showing the associated uncertainty. The whiskers extend to 1.5 times the interquartile range (IQR), and dots indicate individual measurements outside this range. Each panel’s shadowgram shows the data distribution. A shadowgram overlays a smooth curve on histogram bars, making it easier to grasp the data distribution without focusing too much on bin sizes.

Table 4. Summary statistics for the measured data, Secchi depth, chl-a concentration, and TP concentration.

Statistic	Secchi Depth (m)	Chl-a (mg/m3)	TP (mg/L)
N	635	620	916
Mean	2.904	4.923	0.081
Std Dev	1.287	8.103	0.125
Std Err Mean	0.051	0.325	0.004
Upper 95% Mean	3.005	5.562	0.089
Lower 95% Mean	2.804	4.284	0.073
Skewness	1.311	5.148	2.914
Interquartile Range	1.500	3.575	0.060

and

Table 5. Quantiles for the measured data, Secchi depth, chl-a concentration, and TP concentration.

Quantile	Name	Secchi Depth (m)	Chl-a (mg/m3)	TP (mg/L)
100.0%	maximum	8.000	87.100	0.680
99.5%		7.500	61.095	0.610
97.5%		7.000	27.480	0.530
90.0%		4.500	11.460	0.190
75.0%	quartile	3.500	4.775	0.080
50.0%	median	2.500	2.400	0.030
25.0%	quartile	2.000	1.200	0.020
10.0%		1.500	0.700	0.010
2.5%		1.000	0.500	0.010
0.5%		0.536	0.000	0.009
0.0%	minimum	0.150	0.000	0.008

provide summary statistics for the data we collected. We measured or estimated SD in the lakes during each sampling event (n = 635). We gathered chl-a data from the lakes for almost all sampling events (n = 620). We gathered TP data during each sampling event which included both in-lake samples and inflow samples at lakes where there were inlets. Hence the larger number of TP samples (n = 916). We estimated inflows for most of the lakes during selected sampling events (n = 257). The SD data are approximately normally distributed with a skewness value of 1.3 (Table 4). Both the chl-a and TP data are right skewed, with larger skewness values. This is reflected in the quantile data shown in Table 5.

SD ranges from 0.15 to 8 m, with mean and median values of 2.9 and 2.5 m, respectively (Table 4 and Table 5). Chl-a varies widely, ranging from 0 to 87 mg/m³, with mean and median values of 4.9 and 2.4 mg/m³, respectively, indicating significant skewness (Table 5). Chl-a exhibits several outliers, or values larger than the 1.5 IQR. Figure 5 shows that the chl-a data below about 20 mg/m³ have an approximate normal shape, with a long tail for higher values, causing high skewness.

TP data also show a right-skewed distribution, similar to chl-a, with most values below 0.2. mg/L. The mean TP concentration is 0.08 mg/L, and the median concentration is 0.03 mg/L. TP ranges from 0.008 to 0.68 mg/L. Figure 5 illustrates a much smaller second TP distribution peak around 0.52 mg/L. Generally, TP values are low, with occasional higher values associated with this second peak. There are fewer data points between 0.3 and 0.5 mg/L.

3.1.2. Data by Month, Lake Size, Elevation, and Year

To better understand how various environmental conditions and processes affected our data, we analyzed how the data changed with the month in which the samples were collected, the size of the lake, the elevation of the lake, and how the data changed over the course of the study. We expected time of year and elevation to influence both SD and chl-a directly, as temperature affects algae growth and turbidity.

Figure 6 shows the distribution of SD, chl-a, and TP by month (the y-axis was selection to only show values within 1.5 IQR). The median SD values remain relatively constant throughout the months, with a slight decrease in the fall. The 25th percentile and the lower 1.5 IQR of the SD values have a notable change from May to June with the smallest depth observed in August. The decreasing value of the 1.5 IQR may be caused by algal growth, which can be observed in the second panel.

The second panel shows that chl-a concentrations increase throughout the year. The maximum values peak in September, shown by the five-number summary, but the 1.5 IQR values peak in October. This shows that while some outliers are larger in the late summer, the distribution increases through October. There is less variation in the median, though it also increases, while the 75th percentile and the upper 1.5 IQR show significant increases and changes as temperature rises over the year.

TP quartiles and median values are relatively constant throughout the year; however, the upper 1.5 IQR increases from early spring to later in the year. The five-number summary shows that there is little variation in the maximum values from June through October, with values ranging from 0.57 to 0.68 mg/L.

Figure 7 shows the distribution of SD, chl-a, and TP by lake size category without outliers. The first panel shows that the median SD values remain relatively constant for the small and medium lake sizes, though the larger lakes have larger median values. Chl-a concentrations are highest in the small lakes, though the extra-small and medium lakes have similar distributions. The larger lakes have lower chl-a values. TP is highest in the smaller lakes, up to the medium category. Large lakes have lower TP concentrations. The maximum values show that the medium lakes do have a few higher values, with the maximum of 0.68 mg/L, these values are outside the y-axis range for the box plots.

Figure 8 shows the distribution of SD, chl-a, and TP by elevation category without outliers. Generally, SD increases with elevation, while chl-a is relatively constant with elevation. TP is highest in the mid-elevation category, with lower values and less spread in the lower and higher elevations. The five-number summaries indicate that the maximum values for any of the variables are similar, except for TP, which has a lower maximum value for the high elevation lakes.

Figure 9 shows the yearly changes in SD, chl-a, and TP distribution. Outliers are included for SD and TP but not for chl-a because chl-a values can reach up to 80 mg/m³, which compresses the boxes making trends hard to see. Outliers are defined as values beyond the 1.5 IQR and can be seen in Figure 5. The median SD, chl-a and TP values show slight variations but generally remain relatively constant throughout the years. Early data (1998–2003) are sparse, making trends less clear. In general, these measures of water quality are slightly trending toward more eutrophic conditions. We will analyze these trends in Section 3.3.

3.2. Trophic Model State and Comparison

Figure 10 and Figure A1 show the CTSI and VW classifications for the sampled lakes, respectively. The background shading indicates the four trophic classifications’ ranges: oligotrophic (20–38), mesotrophic (38–58), eutrophic (58–65), and hyper-eutrophic (65–80). The boxplots display the median, quartiles, 1.5 IQR, and outliers for lake-computed TSI or estimated TSI over the study period. As noted, the CTSI model computes a TSI; for the VW model, we estimated a TSI based on the trophic state and values from the CTSI classification ranges.

The CTSI distribution (Figure 10) shows that most lakes fall within the mesotrophic range, with median TSI values typically between 40 and 55. Notable exceptions include Hot Beach Pond and Trumpeter Pond, which exhibit hyper-eutrophic conditions with median values exceeding 65. Several lakes, including Grizzly, Eleanor, Duck, Heart, Lewis, and Shoshone Lakes, demonstrate consistently oligotrophic conditions with median values below 38.

The VW classification distribution (Figure A1) presents a similar pattern but contains fewer lakes than the CTSI analysis. This difference in the number of lakes classified arises because the VW index requires additional parameters such as hydraulic residence time and inlet phosphorus measurements, which were not available for all lakes. Among the lakes with sufficient data for VW calculation, North Twin Lake and Indian Pond show notably high VW values, consistently falling in the eutrophic to hyper-eutrophic range. In contrast, Heart Lake and Hot Lake maintain oligotrophic conditions according to the VW classification. While both indices generally agree in their trophic state classifications for lakes, the VW measurements tend to show greater variability within individual lakes, as evidenced by the larger interquartile ranges in Figure A1 compared to Figure 10.

We assigned each lake’s overall trophic state classification based on the median value over the study period for each of the three models.

Table 6. Median trophic state over the study period for the CTSI, VW, and LM models. Lakes are listed alphabetically. Some of the lakes do not have VW and LM values due to not having inlets.

Site Location	CTSI	VW	LM
Beaver Lake	Mesotrophic	Slightly eutrophic	Slightly eutrophic
Blacktail Pond	Mesotrophic	Strongly mesotrophic	Slightly eutrophic
Buck Lake	Mesotrophic	Slightly hyper-eutrophic	Slightly eutrophic
Cascade Lake	Mesotrophic	Slightly eutrophic	Slightly eutrophic
Clear Lake	Mesotrophic	Slightly hyper-eutrophic	Eutrophic
Druid Lake	Mesotrophic
Duck Lake	Slightly oligotrophic
Eleanor Lake	Slightly oligotrophic	Mesotrophic	Mesotrophic
Feather Lake	Eutrophic
Floating Island	Strongly eutrophic
Goose Lake	Slightly mesotrophic	Mesotrophic	Strongly mesotrophic
Grebe Lake	Mesotrophic	Slightly mesotrophic	Strongly mesotrophic
Grizzly Lake	Slightly oligotrophic
Harlequin Lake	Mesotrophic
Hazle Lake	Mesotrophic	Eutrophic	Slightly eutrophic
Heart Lake	Slightly oligotrophic	Slightly oligotrophic	Slightly oligotrophic
Hot Beach Pond	Strongly eutrophic
Hot Lake	Slightly mesotrophic	Slightly oligotrophic	Slightly mesotrophic
Ice Lake	Slightly mesotrophic	Slightly mesotrophic	Slightly eutrophic
Indian Pond	Strongly eutrophic	Slightly hyper-eutrophic	Slightly hyper-eutrophic
Isa Lake	Mesotrophic
Lake of the woods	Slightly eutrophic	Eutrophic
Lewis Lake	Slightly oligotrophic	Slightly mesotrophic	Slightly mesotrophic
Lily Pad Lake	Mesotrophic
Lost Lake	Mesotrophic	Slightly eutrophic	Slightly eutrophic
Lower Basin Lake	Eutrophic
Mallard Lake	Slightly mesotrophic	Mesotrophic
North Twin Lake	Mesotrophic	Slightly hyper-eutrophic	Slightly eutrophic
Nymph Lake	Eutrophic	Eutrophic	Slightly hyper-eutrophic
Ribbon Lake	Strongly mesotrophic
Riddle Lake	Mesotrophic	Strongly eutrophic
Scaup Lake	Strongly mesotrophic
Shoshone Lake	Slightly mesotrophic	Slightly mesotrophic	Mesotrophic
Shrimp Lake	Strongly mesotrophic
South Twin Lake	Mesotrophic	Mesotrophic	Slightly eutrophic
Swan Lake	Mesotrophic
Sylvan Lake	Slightly mesotrophic	Slightly mesotrophic	Slightly mesotrophic
Tanager Lake	Slightly mesotrophic
Terrace Springs	Mesotrophic
Trout Lake	Mesotrophic	Slightly hyper-eutrophic	Eutrophic
Trumpeter Pond	Hyper-eutrophic
Turbid Lake	Strongly eutrophic	Eutrophic
Wolf Lake	Mesotrophic	Mesotrophic	Strongly mesotrophic
YSL [Bridge Bay]	Slightly mesotrophic
YSL [West Thumb]	Slightly oligotrophic

compares the trophic states of Yellowstone lakes under the CTSI, VW, and LM classifications. Each lake’s trophic state is presented according to all three models, highlighting areas of agreement and divergence among the classification systems.

We show visual comparisons between the different median model classifications. Figure 11 and Figure 12 show the VW and LM model classifications, respectively, compared to the CTSI classifications. Figure A2 compares the VW and LM model median classifications. Neither the VW or LM models assign quantitative values. We assigned numerical trophic state values to these model classifications as described in Section 2, using the classification boundary values from the CTSI model.

Each lake is labeled in the plots. In these figures, the colored boxes along the 1:1 line represent the main trophic state categories, oligotrophic, mesotrophic, and eutrophic, and sub-categories with the box size based on the bounds for each model (Section 2). If a lake median classification falls within these boxes, on the 1:1 slope line, the median classifications for the two models match. Points above or below the line indicate one model classifying a lake higher or lower relative to the other model. For lakes above the 1:1 line (Figure 11 and Figure 12), the VW or LM models classify the lake as more eutrophic than the CTSI model with the converse for points below the line. In addition, we fit a linear regression line to show the general relationship between the classification values of each of the model pairs.

In Figure 11, the regression line reflects a strong positive correlation between CTSI and VW values, with the VW model generally assigning higher classifications (points above the 1:1 line). This tendency is evident in the oligotrophic and mesotrophic regions, where VW categorizes more lakes as slightly mesotrophic or eutrophic relative to CTSI. This is reflected in the linear fit (red dashed line), which is consistently higher than the 1:1 line, indicating that the VW model generally results in a higher median trophic state classification for these lakes.

In Figure 12, we observed that the trophic state values from the CTSI model and LM model showed a positive correlation with $R^2=0.68$. This indicates that the two models generally agree in their median trophic classifications. The regression line is nearly parallel to the 1:1 line and an upward offset, which indicates that the LM model gives higher trophic state values compared to the CTSI model, but that the offset is roughly the same for measurements at both ends of the scale.

In Figure A2, the regression line shows a weaker linear relationship between VW and LM values. The data suggest that LM frequently classifies lakes as having higher values than VW in the low-trophic states (points above the 1:1 line), but in the higher trophic states, the VW model has a higher classification (points below the 1:1 line). This is reflected in the linear fit, where the LM classifications are higher until the mesotrophic category, then lower after that. The data distribution spans oligotrophic to eutrophic states, with stronger divergence near the upper end of the trophic scale.

The comparative analysis of the CTSI, VW, and LM classification results highlights important distinctions in their behavior. While the models generally align in identifying mesotrophic lakes, discrepancies become more pronounced in higher trophic states. LM consistently assigns higher trophic classifications, often exceeding those of CTSI and VW, whereas classifications based on the VW model tend to be more conservative at high values but still exceed the CTSI classifications. This finding emphasizes the need to understand and carefully select a trophic state classification model, as different approaches may lead to varying conclusions about a lake’s trophic state, particularly in more nutrient-rich, higher trophic-state conditions.

The classification model selected for a water quality study should match the study’s objectives and context. Each trophic state classification model has strengths and biases that can affect assessments, resulting in assigning different trophic states. Understanding these differences helps researchers and managers make accurate evaluations and informed decisions. By recognizing each model’s tendencies, stakeholders can tailor their approach to better meet the analysis goals.

3.3. Time Series Analysis

3.3.1. Changes over Time

We visualized the temporal variations in the annual trophic states using heatmaps. The results are shown in Figure 13 and Figure 14, representing the CTSI and VW values, respectively. We did not generate a plot for the LM model, as it is similar to the VW model. The color scheme indicates four trophic classifications: oligotrophic (light blue), mesotrophic (light green), eutrophic (orange), and hyper-eutrophic (red), with white spaces indicating missing data. These simple plots show the average annual trophic state, though most lakes only had one sampling event in a year, and how the assigned trophic state changed over the 24-year study period. We did not include sub-categories in these plots.

The CTSI data (Figure 13) span from 1998 to 2023, with the most comprehensive data coverage collected between 2008 and 2016. Most of the lakes only exhibit two different trophic states. However, a few lakes, e.g., Duck Lake or South Twin Lake, exhibit three different states. These lakes generally have more data. Several lakes demonstrate notable temporal patterns: Buck Lake and Cascade Lake show frequent fluctuations between mesotrophic and eutrophic states, while Duck Lake maintained predominantly oligotrophic conditions throughout the monitoring period. Hot Beach Pond and Indian Pond exhibit recurring hyper-eutrophic conditions, particularly during the latter part of the study period. Visually, these lakes generally exhibit higher trophic state classifications in the middle of the study period with no general trend, though individual lakes appear to have slight trends which we will analyze in Section 3.3.2.

The VW data (Figure 14) cover a shorter time span and fewer lakes due to the requirement for inflow data in VW calculations. Two of the lakes have a single VW value, Hot Lake and Blacktail Pond, while Heart Lake has two values. Despite the reduced coverage, some distinct temporal patterns emerge: Buck Lake and North Twin Lake consistently show elevated trophic states, predominantly in the eutrophic to hyper-eutrophic range. Conversely, Sylvan Lake demonstrates more variable conditions, transitioning between oligotrophic and mesotrophic states.

The temporal classification data from both the CTSI and VW trophic state models show that the Yellowstone lakes exhibit different temporal patterns. Some lakes maintain relatively stable trophic states, while others exhibit considerable temporal variability, suggesting complex interactions between environmental factors and lake ecosystem dynamics.

3.3.2. Mann–Kendall Results

To quantitatively analyze trends, or lack of trends, in the data, we applied the Mann–Kendall trend at the 95% confidence level (p = 0.05). We computed both the trends and statistical significance to each parameter in the study for both measured data (chl-a and TP) and computed values based on estimates (PRC) and trophic model classifications (CTSI, VW). We did not include flow and Secchi depth as they were mostly estimated. We separated data collected or computed from in-lake values, and inlet values (

Table 7. Mann–Kendall test results showing lakes and variables with statistically significant trends.

Lake	CTSI	Chl-a (In-Lake)	TP (In-Lake)	VW (Inlet)	TP (Inlet)	PRC (Inlet)
Blacktail Pond			Increasing
Cascade Lake				Increasing	Increasing	Increasing
Buck Lake			Decreasing
Feather Lake	Decreasing	Decreasing	Decreasing
Harlequin Lake	Increasing		Increasing
Hazel Lake				Increasing	Increasing	Increasing
Lewis Lake		Decreasing
Lost Lake	Decreasing
North Twin Lake			Increasing
Nymph Lake	Increasing			Increasing	Increasing	Increasing
Scaup Lake	Increasing

). The in-lake parameters included CTSI model results, TP (in-lake), and chl-a (in-lake). The inlet values included VW model results, TP (inlet), and PRC (computed).

Of the 45 lakes, only 11 exhibited any statistically significant trend at the 95% confidence level (p = 0.05). Most of the lakes had no statistically significant trend for parameters or trophic states. Nine lakes had one or more parameters with statistically significant trends based on in-lake data or models, while three lakes had statically significant trends based on inlet data or models (Table 7). Only one lake, Nymph Lake, had statistically significant trends in both in-lake and inlet data.

Both Scaup Lake and Lost Lake had increasing trends in CTSI, but the TP or chl-a concentration trends were not statistically significant. We attribute this to how the CTSI is calculated; it increases values non-linearly with changes in TP, chl-a, or SD so changes in small concentrations can generate trends in the classification data. None of the lakes that exhibited statistically significant trends based on the VW model had statistically significant trends in the in-lake data that are used for the CTSI model. The lakes with statistically significant trends in VW values also had statistically significant trends in both inlet TP and PRC values.

Figure 15 shows the CTSI values plotted over time and a general trendline for the five lakes with a statistically significant trend in the CTSI. Figure 16 shows the three lakes with statistically significant trends in VW values. We included a linear regression line with a 95% confidence boundary in the plots for visualization. The Mann–Kendall test does not use linear regression for trend analysis; therefore, these features do not indicate the trends evaluated by the test.

Figure 15 shows the values for the five lakes with statistically significant trends in lake trophic state as classified by the CTSI model. Of these lakes, three, Harlequin Lake, Nymph Lake, and Scaup Lake, showed statistically significant increasing trends. Two lakes, Feather Lake and Lost Lake, showed statistically significant decreasing trends.

While the trends for these lakes are all statistically significant, Figure 15 shows that the data for Harlequin Lake and Scaup Lake have minimal trends. Without the initial low values for Harlequin Lake, the trend would not be significant. These lower classifications were taken early in the year. The plot shows that there were three measurements in that year, two relatively low and one more toward the median value. Those early measurements create the statistically significant trend. The plot for Harlequin Lake shows a clear initial trend in trophic state. However, the last classification results in a large decrease in trophic state. Unfortunately, from 2013 to 2023 there are no data, so it is not clear if Harlequin Lake is getting worse, or if the statistically significant trend is the result of missing data. Scaup Lake has only eight classifications over the study period. While the trend appears to be real, it could be the result of limited data.

For the two lakes that show decreasing trends in trophic state based on the CTSI model, Feather Lake and Lost Lake, both graphs visually support these findings.

Figure 16 shows the data for the three lakes with statistically significant increasing trends in the VW trophic state classifications. The trends for both Nymph Lake and Hazle Lake are visually apparent in the plots. While the plot for Cascade Lake also shows an increasing trend, this is driven by the four measurements in 2001, with several early in the spring when the trophic states were lower. Without the multiple measurements in this year, the trend would likely not be statistically significant.

While we used the Mann–Kendall test to analyze the data for trends and determine if any trends were statistically significant, the fact that data were not all collected in the same month complicates the analysis. Figure 6 shows that the month in which data are collected has a large influence on the data distribution mean and range. As the trophic state models depend on these data, classification based on data from the early spring will most likely be different from classifications based on data from the late summer or early fall. Because of the difficulty accessing these lakes, and the limited data available for trend analysis, we recommend caution in evaluating these trend data. The same caution holds true for the temporal plots in Figure 13 and Figure 14. In these plots, the boxes are colored by the mean value for the year, which could be misleading depending on when the data were collected.

For similar reasons, readers should use caution when comparing any of these values over time, as the trophic classification could change based on the time of year in which the data were collected. This is true for any study relying on a trophic state classification model. While TP concentration may show less annual variability, chl-a values are dependent on the time of year in which they are collected (Figure 6).

4. Conclusions

In this study, we collected and analyzed water quality data from 45 lakes in Yellowstone National Park over a period spanning from 1998 to 2024. We used three trophic state models: the Carlson Trophic State Index (CTSI), the Vollenweider (VW) model, and the Larsen–Mercier (LM) model along with these data to classify the trophic state of each lake on the day the data were collected. Yellowstone National Park, located primarily in Wyoming but also extending into Montana and Idaho, is renowned for its rich biodiversity and numerous geothermal features. The park includes a variety of lakes, each with unique ecological characteristics and environmental conditions. These lakes serve as critical habitats for native flora and fauna, and we hope this study offers insights into the impacts of natural and anthropogenic changes on aquatic ecosystems over time.

We collected chl-a and TP data and estimated most SD measurements. The samples included both in-lake samples and inlet samples. This is a unique dataset because of the difficulty in accessing many of the lakes in this study and the long-term nature of the study, over 20 years. This dataset allowed us to analyze lake health in Yellowstone and start to provide insight into how various parameters varied with lake size, elevation, and seasonal changes.

We found that, in general, larger lakes tended to exhibit lower TP concentrations, but smaller lakes tended to exhibit higher chl-a values. Elevation also showed correlations with the data, with higher elevation lakes showing reduced TP levels, possibly due to lower nutrient inputs from surrounding catchments. Chl-a levels were about the same for all elevations. The month in which the data were collected had a considerable impact on the distributions of these variables. Early spring measurements typically indicated lower trophic states compared to late summer or early fall measurements, underscoring the importance of timing in trophic state assessments. This was mostly driven by chl-a values, as we expect higher chl-a in warmer parts of the year.

The analysis revealed that most Yellowstone lakes exhibited mesotrophic conditions, with TSI values predominantly between 38 and 54, indicating moderate productivity levels. Comparisons among the CTSI, VW, and LM models showed that the CTSI model provided more stable measurements across various trophic states. The VW and LM models exhibited greater variability, with them consistently assigning higher trophic classifications than the CTSI model. This variability underscores the importance of using multiple classification methods to capture the full range of possible trophic conditions. The differences in model outputs suggest that no single model can comprehensively characterize lake trophic states, and a multi-faceted approach offers a more robust assessment.

We used the Mann–Kendall test to evaluate trends in lake trophic states and identified significant trends in only a few lakes. Specifically, for trophic state, five lakes showed significant trends based on the CSTI model, while three lakes showed significant trends using the VW model. Only one lake exhibited trends in trophic state for both the CTIS and VW models. These results indicate that eutrophication is not a widespread issue in Yellowstone National Park’s lakes, though specific lakes exhibit notable changes. The trend analysis was complicated by the fact that data were not collected consistently across the same months each year. Our study highlighted that the trophic state models’ reliance on seasonal data can lead to misleading classifications if the temporal variability is not accounted for.

In conclusion, our findings emphasize the necessity of using multiple classification models for a complete and accurate assessment of lake trophic states. The study also highlights the need for consistent and frequent data collection across different times of the year to better understand and manage the trophic dynamics of these lakes. Future research should focus on the impacts of climate change and tourism on lake trophic states to inform effective park management strategies.