The data were collected on an experimental site established in L’Acadie, Quebec, Canada [1] [8]. The turfgrass stands were composed of equal proportions of Kentucky bluegrass cultivars Baron, Argyle, Gnome, and Regent. Soils were a St-Blaise-Macdonald loamy soil (Haplaquent) and a normalized USGA sandy soil. Soil physical and chemical analyses, sampling procedure, and climatic conditions were reported in [1]. The soils were analyzed at the onset of the experiment for grain-size distribution by sedimentation, pH in water (1:1), Mehlich3-extractible nutrients [26] and Walkley-Black carbon content [1]. Soil pH was 6.17 ± 0.27 in the loam and 7.10 ± 0.16 in the sand. Mehlich-III extracts averaged 68 mg P kg^–1, 63 mg K kg^–1, 165 mg Mg kg^–1, 2587 mg Ca kg^–1 and 1131 mg Al kg^–1 in the loam, and 58 mg P kg^–1, 39 mg K kg^–1, 143 mg Mg kg^–1, 1925 mg Ca kg^–1 and 333 mg Al kg^–1 in the sand. Carbon content was 17.4 g C kg^–1 in the loam and 10.4 g C kg^–1 in the sand.

The stand was deemed uniform during the summer following the establishment one year earlier. The trial was a factorial combination of four rates of N (0 or 50, 100, 200, and 300 kg N ha⁻¹), three rates of P (0 or 21.8, 43.7 and 87.3 kg P ha⁻¹), and four rates of K (0 or 41.7, 83.3, 166.7, and 250 kg K ha⁻¹) applied at eight occasions during three consecutive years. The stands were irrigated to avoid drought stress and facilitate the incorporation of fertilizer granules into the soil. Foliage color was rated during eight consecutive periods, i.e., in summer and autumn of year 1, and in the spring, summer and autumn of year 2, and in the spring, summer and autumn of year 3. Color ratings were recorded weekly and summarized as the median value across weekly evaluations preceding and including each clipping harvest.

Clippings were collected at the same time as foliage color was rated, two days following fertilization to avoid collecting fertilizer granules in mower’s basket. Mowing height was 38 mm for clipping harvest on areas of 2.38 by 0.56 m, and 50 mm otherwise (2 - 3 times per week as a regular maintenance). Harvests started in April or May and ended in September or October. Clippings were weighed then dried at 70˚C. Total carbon was not quantified in the clipping biomass but may range between 360 and 395 g C kg⁻¹ [27] or 355 to 418 g C kg⁻¹ [28], averaging 380 g C kg⁻¹. Total N was determined by micro-Kjeldahl. Tissues were acid-digested [29]. The dissolved nutrients were quantified by plasma emission spectroscopy.

The foliage compositional simplex comprised eleven elements and a filling value as follows:

S D = { [ N , S , P , K , M g , C a , B , F e , M n , Z n , C u , F v ] ; [ N > 0 , S > 0 , P > 0 , K > 0 , M g > 0 , C a > 0 , B > 0 , F e > 0 , M n > 0 , Z n > 0 , C u > 0 , F v > 0 ] ; N + S + P + K + M g + C a + B + F e + M n + Z n + C u + F v = 1000   g ⋅ kg − 1 } (1)

where F_v is the filling value between measurement unit (here, 1000 g∙kg⁻¹) and the sum of the individual nutrient concentrations expressed in g∙kg⁻¹. The centered log ratios were computed as follows Equation (2) [16]:

c l r i = ln ( c i G ) (2)

where ln is the natural logarithm, c_i is i^th concentration, and G is the geometric mean across components of the whole including the filling value, computed as follows (3):

G = N × S × P × K × M g × C a × B × F e × M n × Z n × C u × F v 12 (3)

The geometric mean across components avoids over-optimistic assumptions on equal (Law of minimum) or optimum (Law of optimum) levels of other nutrients [30]. Equation (2) is a combination of pairwise ratios reflecting dual interactions, as follows for N Equation (4):

c l r i = ln N G = ln ( N 12 N × S × P × K × M g × C a × B × F e × M n × Z n × C u × F v ) 1 12 = ln ( N N × N S × N P × N K × N M g × N C a × N B × N F e × N M n × N Z n × N C u × N F v ) 1 12 = 1 12 ( ln N S + ln N P + ln N K + ln N M g + ln N C a + ln N B + ln N F e + ln N M n + ln N Z n + ln N C u + ln N F v ) (4)

The N/P ratio that relates protein production to internal energy [31] and the N/K ratio that highlights the role of K in regulating the N transfer from roots to shoot [19] should be properly balanced in turfgrass [32]. Other nutrient interactions and cross-talks are documented in [18] and [21].

Three relational models were tested as follows:

Y t = f ( X t ) , (5)

Y t = f ( X t − 1 ) , (6)

Y t = f ( X t − 2 ) , (7)

where Y t is foliage color rating at time t (the season), whereas X t , X t − 1 and X t − 2 are features collected at times t, t − 1 and t − 2, respectively. Equation (5) represents the current diagnosis where laboratory analyses are calibrated against plant performance at time t [8]. Equation (6) predicts future plant performance at time t from the results of laboratory analyses of tissues sampled at time t − 1. Equation (7) predicts future plant performance at time t from laboratory analyses of tissues sampled at time t − 2.

Features were periods, soil texture, NPK fertilization, tissue nutrients and clipping biomass. Soils were a loam and an USGA sand. Periods were spring, summer and autumn. Because there are D − 1 degrees of freedom in the D clr variables adding up exactly to zero [33], one redundant clr variable (here, c l r F v ) was removed from the ML model. The target variable was the category of turfgrass color (within or outside the range between 7.0 and 8.9) for high quality turfgrass. We used the Orange Data Mining software 3.32 to process the data (https://orangedatamining.com/download/#windows). The most accurate ML model was extreme gradient boosting (xgboost) using 40 trees, learning rate of 0.100 and a limiting depth to three individual trees. Data were partitioned in the confusion matrix as follows:

1) True negative (TN) specimens showing balanced mineral nutrition and high turfgrass quality.

2) False negative (FN) specimens showing balanced mineral nutrition but low turfgrass quality (Type II error).

3) True positive (TP) specimens showing imbalanced mineral nutrition but high turfgrass quality.

4) False positive (FP) specimens showing imbalanced mineral nutrition and low turfgrass quality (Type I error).

Model accuracy was measured as follows:

Accuracy ( % ) = 100 × VN + TP TN + TP + FN + FP (8)

The area under curve (AUC) is another criterion for model performance. It has been suggested that AUC of 0.5 has no diagnostic interest [34]. The model would be little informative in the AUC range of 0.5 to 0.7, moderately informative if 0.7 ≤ AUC < 0.9 and very informative if AUC ≥ 0.9.

Nutrient standards were computed as mean and standard deviation of the clr values of true negative (TN) specimens. The clr indices were computed to rank nutrients, as follows [16]:

c l r x i   i n d e x = c l r x i − c l r x i * S D x i *

where c l r x i is the clr value for component x i , and c l r x i * and S D x i * are the corresponding seasonal clr nutrient standards.

There were 3072 observations to run model 1. Model 2 processed 2688 observations because one of the eight periods must be sacrificed at both the loamy and the sandy sites to account for carryover effects. Model 3 processed 2304 observations. The most successful combination of features comprised soil texture, season, clipping biomass, nutrients and NPK fertilization (Table 1). The model was little affected after excluding clipping biomass. Soil texture was an important feature, particularly in models 2 and 3 (scenario no. 3 vs. scenario no. 2). The minimum dataset to predict color rating comprised soil texture, season and NPK fertilization provided by the field manager, as well as nutrient analyses from the preceding season supplied by the laboratory.

Table 1 shows that collecting tissue samples one or two periods in advance to predict color rating provided higher area under curve (AUC) compared to nutrient analysis and concomitant color rating at the time of tissue sampling. Models were moderately to very informative. The AUC and accuracy were comparable to other perennials [10] [11] [23] [24] [25].

Model 2 allows laboratory analyses to be available in time for the early correction of the fertilizer program. Nutrient standards for turfgrass, computed for

^§The highest AUC or accuracy value is 1.

every season using the feature combination no. 7 in model 2, were not stationary across seasons (Table 1). The means and standard deviations of the clr values for TN specimens are presented in Table 2. Between spring and autumn, tissue S tended to increase and tissue N and P to decrease by more than 0.2 clr unit. The quartile concentration ranges for tissue N, P and S did not overlap, indicating seasonal effects on plant nutrition that are attributable in part to differential nutrient mobility [35] or nutrient dilution in the growing plant [20].

^§Standard deviation; ^†Lower and higher quartiles, respectively.

Adams [32] reported optimum N/K ratio varying between 1.0 and 1.4 and optimum N/P ratio in the range of 5.7 to 9.0 for turfgrass. The N/K and N/P ratios of TN specimens used to run Model 2 averaged 1.06 ± 0.26 and 6.69 ± 1.34, respectively, across seasons. While a concept of optimum N:K:P:Ca:Mg proportions in plants stable during the exponential growth of woody perennials has been elaborated by [36], such diagnostic approach appeared to be illusionary for turfgrass due to seasonal variations attributable to large seasonal variation in clipping removal. The highest rate of removal occurred in summer (Table 3) where nutrient balances were most impacted compared to spring conditions (Table 2).

Nutrient standards averaged across seasons differed from those presented by [8] because the FP specimens were excluded by the confusion matrix to derive the clr standards. False positive specimens comprise cases of luxury consumption or suboptimal nutrient levels leading to high aesthetic turfgrass quality despite nutrient imbalance. The ML model can isolate the high-quality and nutritionally balanced TN specimens in the confusion matrix.

We propose following five steps from data collection to diagnosis:

1) Collect nutrient concentration data using the same measurement unit (g∙kg⁻¹) or scale (dry matter basis) to constitute a large and diversified dataset of turfgrass experimental and observational data as reference file.

2) In a separate file, organize data for the specimens under diagnosis using the same features and measurement units as those documented in the reference data set.

3) Run the ML model to classify the diagnosed specimens into the high- (color rating between 7.0 and 8.9) or low-quality (outside range) categories.

4) If turfgrass quality is declared low by the ML model, compare clr values to clr standards and rank the clr indices from the most negative (relative shortage) to the most positive (relative excess).

5) Draw a histogram of clr indices to illustrate the diagnosis.

^§Standard deviation.

Turfgrass clippings are collected on an USGA sand in the spring. The manager reports a fertilizer regime of 300 kg N ha⁻¹∙yr⁻¹, 100 kg P₂O₅ ha⁻¹∙yr⁻¹, and 300 kg K₂O ha⁻¹∙yr⁻¹. Soil properties were comparable to those of the one used in the above experiment. The manager asks whether the fertilization could be reduced to prevent grass degradation, the eutrophication of surrounding ponds, and, overall, the apparently imbalanced or excessive fertilization and nutrient waste.

The Orange 3.32 Machine Learning Software processed the data using object-oriented algorithms (Figure 1). The software can be easily operated by field managers and crop advisers. The reference dataset is first retrieved. Variables are selected (select columns) as features or target to run the model. Several learners are available in Orange 3.32. After sampling 100% of the data, run the ML model using stratified cross-validation, setting the number of folds at 10. Use 40 trees to run xgboost. Note that data can also be divided into calibration and validation data sets to assess model accuracy. Data are partitioned in a confusion matrix (Figure 2).

The mineral analysis of clippings is presented in Table 4. Data to be diagnosed are saved in a separate file. The diagnosed specimen is classified by the ML model as high- or low-quality specimen, and nutrients are ranked in an order of limitation. The xgboost model predicted a higher probability to reach high than low aesthetic quality at the time of sampling the grass in the spring. Using Excel, the clr indices in Table 4 can be presented in a histogram to illustrate relative nutrient imbalance even if the specimens appeared to be well rated (Figure 3). False positive specimens could be rebalanced.

The nitrogen appeared to be well balanced (clr value near zero), yet at relatively higher level under spring conditions compared to summer and autumn (Table 2). However, N fertilization should still sustain turfgrass aesthetic quality by fertilization due to high removal rate of the clippings at high N application rate. Tissue N tended to decrease in the summer (Table 2) due in part to higher rate of clipping removal that reduced N storage (Table 3). Because turfgrass response to added N is nor-linear, achieving a color rating of 7.0 in an USGA sandy soil was found to be ≥245 kg N ha⁻¹ [1], a potential gain of 55 kg N ha⁻¹ compared to current N management. The P and K fertilization could also be reduced substantially without quality loss because turfgrass was little or not responsive to P and K additions at those levels of soil test [1].

The apparent S excess indicated that potassium sulfate could be replaced by the less expensive potassium sources. Less potassium could also have a positive impact on Mg and Ca acquisition by the plant by alleviating antagonisms [18]. Excess sulfur may also impact the transfer of metals from the roots to the shoot through cross-talks, depending on the plant [21]. The Zn appeared to be in relative excess and could be skipped from the fertilization program.