# Evaluation of the Methods for Estimating Leaf Chlorophyll Content with SPAD Chlorophyll Meters

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## Abstract

**:**

^{−2}to 86.34 μg cm

^{−2}in the field datasets, and it ranges from 5 μg cm

^{−2}to 80 μg cm

^{−2}in the synthetic dataset. The relationships between LCC and SPAD readings were examined using linear, polynomial, exponential, and homographic functions for the field and synthetic datasets. For the field datasets, the assessments of these approaches were conducted for (i) all three datasets together, (ii) individual datasets, and (iii) individual vegetation species. For the synthetic dataset, leaves with different leaf structures (which mimic different vegetation species) were grouped for the evaluation of the approaches. The results demonstrate that the linear function is the most accurate one for the simulated dataset, in which leaf structure is relatively simple due to the turbid medium assumption of the PROSPECT-5 model. The assumption of leaves in the PROSPECT-5 model complies with the assumption made in the designed algorithm of the SPAD meter. As a result, the linear relationship between LCC and SPAD values was found for the modeled dataset in which the leaf structure is simple. For the field dataset, the functions do not perform well for all datasets together, while they improve significantly for individual datasets or species. The overall performance of the linear ($\mathrm{LCC}=a\ast \mathrm{SPAD}+b$), polynomial ($\mathrm{LCC}=a\ast {\mathrm{SPAD}}^{2}+b\ast \mathrm{SPAD}+c$), and exponential functions ($\mathrm{LCC}=0.0893\ast \left({10}^{{\mathrm{SPAD}}^{\alpha}}\right))$ is promising for various datasets and species with the R

^{2}> 0.8 and RMSE <10 μg cm

^{−2}. However, the accuracy of the homographic functions ($\mathrm{LCC}=a\ast \mathrm{SPAD}/\left(b-\mathrm{SPAD}\right)$) changes significantly among different datasets and species with R

^{2}from 0.02 of wheat to 0.92 of linseed (RMSE from 642.50 μg cm

^{−2}to 5.74 μg cm

^{−2}). Other than species- and dataset-dependence, the homographic functions are more likely to produce a numerical singularity due to the characteristics of the function per se. Compared with the linear and exponential functions, the polynomial functions have a higher degree of freedom due to one extra fitting parameter. For a smaller size of data, the linear and exponential functions are more suitable than the polynomial functions due to the less fitting parameters. This study compares different approaches and addresses the uncertainty in the conversion from SPAD readings into absolute LCC, which facilitates more accurate measurements of absolute LCC in the field.

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Datasets

#### 2.1.1. Field Datasets

^{−2}, with a minimum of 9.40 μg cm

^{−2}and a maximum of 46.79 μg cm

^{−2}, and the LCC of sugar beet ranged between 15.12 μg cm

^{−2}and 35.48 μg cm

^{−2}with a mean value of 28.74 μg cm

^{−2}. In comparison, the LCC of barley and corn had more substantial variation relative to wheat and sugar beet. The LCC of barley ranged from 23.10 μg cm

^{−2}to 54.88 μg cm

^{−2}with an average of 35.46 μg cm

^{−2}, and that of corn varied from 15.00 μg cm

^{−2}to 43.57 μg cm

^{−2}with a mean value of 32.27 μg cm

^{−2}. The four crops generally exhibited low-to-moderate LCC.

^{−2}to 47.44 μg cm

^{−2}with a mean value of 21.29 μg cm

^{−2}and C.V. of 65.66%. In contrast, the LCC of vine presented the smallest variation among these species, with a mean value of 18.40 μg cm

^{−2}, a minimum of 9.77 μg cm

^{−2}, and a maximum of 28.84 μg cm

^{−2}. Similar to Delegido’s dataset, the LCC of the nine species ranged from low to medium.

^{−2}to 86.34 μg cm

^{−2}, with a mean value of 50.82 μg cm

^{−2}and C.V. of 37.23%. The variation of LCC in Houborg’s dataset was between Delegido’s and Vuolo’s datasets. Moreover, Delegido’s, Vuolo’s, and Houborg’s datasets all possess the LCC of corn, whereas the variation of these three corn data is not fully identical. The LCC of corn in Vuolo’s dataset retained the most substantial variation, while that of Delegido’s dataset delivered the least variation among the three data. In addition, the LCC of corn in Delegido’s and Vuolo’s datasets ranged from low to moderate, while that in Houborg’s dataset exhibited a widely distributed LCC from low to high.

#### 2.1.2. Simulated Dataset with the PROSPECT Model

^{2}) of 0.998 across commonly used SPAD chlorophyll meters [38].

#### 2.2. Mathematical Functions for Relationships between SPAD Readings and LCC

#### 2.3. Accuracy Assessment

^{2}) and root-mean-square error (RMSE) were registered as indicators of the strength of assessing each function. The R

^{2}is a measure of the degree of fitting between the independent and dependent variables, and the RMSE accounts for the difference between the estimated and observed values. The two metrics were used to comprehensively evaluate the accuracy of the functional relationships between LCC and SPAD values. The R

^{2}and RMSE can be calculated as follows:

^{2}, the better the model fit, and the lower the RMSE, the closer the estimated value is to the observed value and the lower the estimated error.

## 3. Results

#### 3.1. All the Field Datasets Together

^{2}as high as ~0.5, while the exponential 1 (i.e., $\mathrm{LCC}=a\ast {e}^{b\ast \mathrm{SPAD}}$) function performed slightly deficiently with an R

^{2}of 0.38, and the homographic function was the poorest with an R

^{2}of 0.02. The quadratic coefficient of the polynomial function was approximately zero, making it level off to the linear function. Therefore, regardless of the differences in the datasets and species, the linear, polynomial, and exponential functions were suited for estimating the LCC, whereas the homographic function was less suitable for the LCC estimation.

#### 3.2. For Each Field Dataset

^{2}of ~0.78, and their errors were small with an RMSE of ~3.82 μg cm

^{−2}(i.e., mean RMSE of the five functions). However, the homographic function was inferior to the other four functions for the nine species in Vuolo’s dataset with an R

^{2}of ~0.00 and RMSE of ~138.72 μg cm

^{−2}. Especially at high SPAD values, similar to the results in Section 3.1, the homographic fitting curve shifted from monotonically increasing to sharply decreasing, even making the estimated LCC negative. Similar to Delegido’s dataset, the five SPAD–LCC functional relationships were comparable for the corn crop in Houborg’s dataset with an R

^{2}of ~0.95 and RMSE of ~4.47 μg cm

^{−2}, whereas they generally excelled those expressed in Delegido’s dataset. In general, the linear, polynomial, and exponential functions could reasonably express associations between LCC and SPAD readings without considering differences in species, and the polynomial function could be approximated by the linear function because its quadratic coefficient was as small as zero. However, the exponential 1 function changed slightly, and the homographic function had significant variability across various vegetation species.

#### 3.3. For Each Species

^{2}of not less than ~0.8 and RMSE less than 10 μg cm

^{−2}) (Figure 3). In comparison, the linear and polynomial functions were slightly better than the exponential functions. However, the performance of the homographic function exhibited substantial variation. In wheat and grass, it performed poorly with the R

^{2}of 0.02 and 0.04 and RMSE of up to 642.50 μg cm

^{−2}and 45.49 μg cm

^{−2}, respectively. However, in other species, the homographic function had similar performance to the linear, polynomial, and exponential functions. Similar to the results in Section 3.2, linear, polynomial, and exponential 2 functions performed similarly promisingly. In contrast, the performance of the exponential 1 function varied little, and the homographic function changed significantly.

^{2}and RMSE for the five functions in Figure 4. Similar to the results in Section 3.2 and Section 3.3, there was slight variability in the exponential 1 function, and the performance of the homographic function exhibited considerable variation and more caution was required when using this type of function for an unknown species. In comparison, the linear, polynomial, and exponential 2 functions were sufficiently accurate for most cases. Taking into account the fact that even though the variation range of α in the exponential 2 function is smaller than coefficients from other functions, small changes of α can lead to very large differences in LCC, such as corn in Figure 3b, and polynomial functions have quadratic coefficients close to zero according to the above results. Therefore, we recommended using a linear function to estimate LCC and listed the fitting coefficients of linear functions for specific vegetation species in Table 4 for future usage.

#### 3.4. For the Simulated Dataset from the PROSPECT Model

^{2}of ~0.99 over different leaf structural parameters (Figure 5), while the estimation error of the exponential 2 function had a large variation from RMSE = 10.44 μg cm

^{−2}for N = 1 to RMSE = 2.46 μg cm

^{−2}for N = 3. In comparison, the exponential 1 function showed a slight change, and the homographic function varied significantly. The secondary coefficient of the polynomial function was approximately zero, making it close to the linear function, implying that when the leaf structure was determined, the SPAD reading had a significantly linear relationship with the LCC. Moreover, the performance of the linear, polynomial, and homographic functions decreased with increasing leaf structural parameters, whereas the behavior of the two exponential functions was reversed.

^{2}value achieved was as high as 1.00 (Figure 6a), providing some improvement over the SPAD meter (R

^{2}= 0.90 for ${\mathrm{log}}_{10}\left({T}_{940}/{T}_{650}\right)$). Similar to ${\mathrm{log}}_{10}\left({T}_{\lambda 1}/{T}_{\lambda 2}\right)$, the transmittance-based index ${T}_{\lambda 1}/{T}_{\lambda 2}$ had the highest R

^{2}at ${\lambda}_{1}=677\text{}\mathrm{nm}$ and ${\lambda}_{2}=679\text{}\mathrm{nm}$ (R

^{2}= 1.00) (Figure 6b), improving estimates of LCC over the SPAD meter. However, it had a generally lower relationship with LCC compared with ${\mathrm{log}}_{10}\left({T}_{\lambda 1}/{T}_{\lambda 2}\right)$, which was in line with the logarithmic algorithm of the transmittance ratio designed by the SPAD meter. For the wavelengths used in the SPAD meter, the R

^{2}of the logarithm of the transmittance ratio (R

^{2}= 0.90 for ${\mathrm{log}}_{10}\left({T}_{940}/{T}_{650}\right)$) was significantly higher than the simple transmittance ratio (R

^{2}= 0.50 for ${T}_{940}/{T}_{650}$).

## 4. Discussion

#### 4.1. Relationship between LCC and SPAD Readings

#### 4.2. Comparison of Different Functions

#### 4.3. Limitations

^{2}of >0.80 [32], and the exponential function $\mathrm{LCC}=a\ast {e}^{b\ast \mathrm{SPAD}}$ showed promising results for the LCC estimation of six Amazonian tree species with an R

^{2}of 0.79 overall [50]. However, whether the exponential function $\mathrm{LCC}=0.0893\ast \left({10}^{{\mathrm{SPAD}}^{\alpha}}\right)$ is applicable to forest leaves and the variation of leaves in different woody types remains to be further investigated.

## 5. Conclusions

^{2}of >0.8 and RMSE of <10 μg cm

^{−2}overall in the field datasets. In contrast, the homographic function has considerable dependence on datasets and species and is prone to numerical singularities due to the idiosyncrasies of the function per se. Therefore, more caution is needed when using this functional relationship to estimate LCC for an unknown species. The polynomial functions provide more freedom since one more fitting parameter is included, and they are approximated by linear models due to quadratic coefficients approaching zero. The study recommends the use of linear and exponential functions when calibration data for the conversion of SPAD readings into absolute LCC values are insufficient, and a polynomial function when the amount of calibration data is sufficient. The evaluation presented in this study is expected to assist in more accurately estimating absolute LCC using SPAD meters in the field.

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

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**Figure 1.**The assessment of five functions (i.e., linear, polynomial, exponential 1, exponential 2, and homographic models) for the estimation of the LCC using all three field datasets together. Blue squares, pale-yellow dots, and red triangles represent Delegido’s, Vuolo’s, and Houborg’s datasets, respectively. Exponential 1 is the exponential function $\mathrm{LCC}=a\ast {e}^{b\ast \mathrm{SPAD}}$, and Exponential 2 is the exponential function $\mathrm{LCC}=0.0893\ast \left({10}^{{\mathrm{SPAD}}^{\alpha}}\right)$. Note that the part of the homographic fitting curve is not shown because its value goes from incremental to negative infinity as the denominator of the function progressively approaches zero.

**Figure 2.**The assessments of five functions for the estimation of the LCC of all species in Delegido’s (

**a**), Vuolo’s (

**b**), and Houborg’s dataset (

**c**). The right panel corresponds to the statistics of the five function evaluations for each dataset in the left panel.

**Figure 3.**The assessments of five functions for the estimation of the LCC of each species across all field datasets with the R

^{2}(

**a**) and RMSE (

**b**). Exponential 1 is the exponential function $\mathrm{LCC}=a\ast {e}^{b\ast \mathrm{SPAD}}$, and Exponential 2 is the exponential function $\mathrm{LCC}=0.0893\ast \left({10}^{{\mathrm{SPAD}}^{\alpha}}\right)$. Central lines represent the medians, boxes represent 50% of the data, squares represent mean values, whiskers represent minimum and maximum values, and symbols outside the whiskers represent outliers.

**Figure 4.**Boxplots for the coefficients of determination of five functions for the relationships between LCC and SPAD readings based on the model assessments of field datasets from three aspects: (i) all datasets together, (ii) individual datasets from three different data sources, and (iii) individual vegetation species. Central lines represent the medians, boxes represent 50% of the data, squares represent mean values, and whiskers represent minimum and maximum values.

**Figure 5.**The evaluations of five functions for estimating the LCC based on the simulated dataset from the PROSPECT-5 model. The left, middle, and right panels represent model evaluations for N = 1, N = 2, and N = 3, respectively. Exponential 1 is the exponential function $\mathrm{LCC}=a\ast {e}^{b\ast \mathrm{SPAD}}$, and Exponential 2 is the exponential function $\mathrm{LCC}=0.0893\ast \left({10}^{{\mathrm{SPAD}}^{\alpha}}\right)$. N is the leaf structure parameter.

**Figure 6.**Variation in R

^{2}of relationships between the transmittance-based index and LCC, as a function of incorporated wavelengths, for ${\mathrm{log}}_{10}\left({T}_{\lambda 1}/{T}_{\lambda 2}\right)$ (

**a**), and ${T}_{\lambda 1}/{T}_{\lambda 2}$ (

**b**).

**Table 1.**Statistics of leaf chlorophyll content in Delegido’s, Vuolo’s, and Houborg’s datasets. S.D. is the standard deviation, C.V. is the coefficient of variation, and n represents the number of observations.

Data Sources | Species | n | Minimum (μg cm^{−2}) | Maximum (μg cm ^{−2}) | Mean (μg cm ^{−2}) | S.D. (μg cm ^{−2}) | C.V. (%) |
---|---|---|---|---|---|---|---|

Delegido et al. (2011) | Wheat | 20 | 9.40 | 46.79 | 38.17 | 7.38 | 19.33 |

Sugar beet | 29 | 15.12 | 35.48 | 28.74 | 4.63 | 16.11 | |

Barley | 20 | 23.10 | 54.88 | 35.46 | 9.05 | 25.53 | |

Corn | 36 | 15.00 | 43.57 | 32.27 | 8.02 | 24.85 | |

Vuolo et al. (2012) | Bean | 32 | 1.86 | 43.26 | 25.54 | 11.68 | 46.00 |

Grass | 23 | 2.38 | 37.62 | 16.69 | 9.25 | 55.43 | |

Wheat | 30 | 1.40 | 47.44 | 21.29 | 13.98 | 65.66 | |

Linseed | 28 | 2.79 | 58.14 | 29.09 | 16.77 | 57.64 | |

Corn | 28 | 3.26 | 34.42 | 16.73 | 10.36 | 61.94 | |

Oat | 30 | 3.26 | 55.35 | 28.67 | 15.05 | 52.48 | |

Olive | 26 | 9.30 | 58.14 | 30.25 | 11.95 | 39.49 | |

Orange | 24 | 4.19 | 28.84 | 14.52 | 6.76 | 46.59 | |

Vine | 25 | 9.77 | 28.84 | 18.40 | 6.07 | 32.96 | |

Houborg et al. (2009) | Corn | 48 | 12.20 | 86.34 | 50.82 | 18.92 | 37.23 |

Parameter | Interpretation | Unit | Input Values |
---|---|---|---|

N | Leaf structure parameter | — | 1.0, 2.0 or 3.0 |

${C}_{ab}$ | Chlorophyll a + b content | μg cm^{−2} | 5, 10, 20, 30, 40, 50, 60, 70 or 80 |

${C}_{cx}$ | Carotenoid content | μg cm^{−2} | 10, 20 or 30 |

${C}_{bp}$ | Brown pigments content | — | 0.0, 0.5 or 1.0 |

${C}_{w}$ | Equivalent water thickness | cm | 0.02, 0.04, 0.08 or 0.10 |

${C}_{m}$ | Dry matter content | g cm^{−2} | 0.005, 0.010 or 0.020 |

**Table 3.**The commonly used functions for estimating leaf chlorophyll content (LCC in the unit of μg cm

^{−2}) from SPAD readings.

Model Forms | Equations | References |
---|---|---|

Linear | $\mathrm{LCC}=a\ast \mathrm{SPAD}+b$ | Schaper and Chacko (1991) |

Polynomial | $\mathrm{LCC}=a{\ast \mathrm{SPAD}}^{2}+b\ast \mathrm{SPAD}+c$ | Monje and Bugbee (1992) |

Exponential 1 | $\mathrm{LCC}=a\ast {e}^{b\ast \mathrm{SPAD}}$ | Uddling et al. (2007) |

Exponential 2 | $\mathrm{LCC}=0.0893\ast \left({10}^{{\mathrm{SPAD}}^{\alpha}}\right)$ | Markwell et al. (1995) |

Homographic | $\mathrm{LCC}=\frac{a\ast \mathrm{SPAD}}{b-\mathrm{SPAD}}$ | Coste et al. (2010); Cerovic et al., (2012) |

**Table 4.**Assessments of the linear function based on all datasets together, individual datasets, and each species per dataset in terms of three field datasets.

Data Sources | Species | a | b | R^{2} | RMSE (μg cm ^{−2}) |
---|---|---|---|---|---|

All | All | 0.709 | −1.576 | 0.52 | 11.11 |

Delegido et al. (2011) | Wheat | 0.788 | −1.053 | 0.88 | 2.56 |

Sugar beet | 0.486 | 8.664 | 0.53 | 3.16 | |

Barley | 1.174 | −22.248 | 0.79 | 4.13 | |

Corn | 0.879 | −8.602 | 0.84 | 3.17 | |

All | 0.840 | −5.783 | 0.78 | 3.83 | |

Vuolo et al. (2012) | Bean | 0.770 | −6.765 | 0.85 | 4.48 |

Grass | 0.797 | −7.232 | 0.79 | 4.22 | |

Wheat | 0.879 | −9.350 | 0.94 | 3.28 | |

Linseed | 0.776 | −7.157 | 0.90 | 5.20 | |

Maize | 0.664 | −1.761 | 0.88 | 3.62 | |

Oat | 0.828 | −1.520 | 0.85 | 5.78 | |

Olive | 0.875 | −27.494 | 0.87 | 4.36 | |

Orange | 0.388 | −5.950 | 0.84 | 2.73 | |

Vine | 0.495 | 4.376 | 0.32 | 5.00 | |

All | 0.550 | 0.443 | 0.61 | 8.33 | |

Houborg et al. (2009) | Corn/All | 1.639 | −26.955 | 0.94 | 4.60 |

Models | Deficiencies |
---|---|

$\mathrm{LCC}=a\ast \mathrm{SPAD}+b$ | Relatively lower accuracy compared to a polynomial model |

$\mathrm{LCC}=a{\ast \mathrm{SPAD}}^{2}+b\ast \mathrm{SPAD}+c$ | Unsuitable for limited data |

$\mathrm{LCC}=a\ast {e}^{b\ast \mathrm{SPAD}}$ | Moderate dependence on dataset and species Slightly lower accuracy than the linear and polynomial models |

$\mathrm{LCC}=0.0893\ast \left({10}^{{\mathrm{SPAD}}^{\alpha}}\right)$ | Slightly lower accuracy than the linear and polynomial models |

$\mathrm{LCC}=\frac{a\ast \mathrm{SPAD}}{b-\mathrm{SPAD}}$ | Strong dependence on dataset and species Significant variability Numerical singularity |

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## Share and Cite

**MDPI and ACS Style**

Zhang, R.; Yang, P.; Liu, S.; Wang, C.; Liu, J.
Evaluation of the Methods for Estimating Leaf Chlorophyll Content with SPAD Chlorophyll Meters. *Remote Sens.* **2022**, *14*, 5144.
https://doi.org/10.3390/rs14205144

**AMA Style**

Zhang R, Yang P, Liu S, Wang C, Liu J.
Evaluation of the Methods for Estimating Leaf Chlorophyll Content with SPAD Chlorophyll Meters. *Remote Sensing*. 2022; 14(20):5144.
https://doi.org/10.3390/rs14205144

**Chicago/Turabian Style**

Zhang, Runfei, Peiqi Yang, Shouyang Liu, Caihong Wang, and Jing Liu.
2022. "Evaluation of the Methods for Estimating Leaf Chlorophyll Content with SPAD Chlorophyll Meters" *Remote Sensing* 14, no. 20: 5144.
https://doi.org/10.3390/rs14205144