^{1}

^{*}

^{2}

A clear understanding of plant transpiration is a crucial step for water cycle and climate modeling, especially for arid ecosystems in which water is one of the major constraints. Traditional field measurements of leaf scale transpiration are always time-consuming and often unfeasible in the context of large spatial and temporal scales. This study focused on a dominant native plant in the arid land of central Asia, ^{2 }= 0.78, RMSE = 1.62 µmol g^{-1} s^{-1}). The accuracy is also relatively stable even at a spectral resolution of 10 nm, which is very close to the bandwidths of several running satellite-borne hyperspectral sensors such as Hyperion. The results also proved that the first-order derivative spectra within the shortwave infrared (SWIR) domain, especially at 2435, 2440, 2445, and 2470 nm, were critical for PLSR models to predict leaf transpiration. These findings highlight a promising strategy for developing remote sensing methods to potentially characterize transpiration at broad scales.

Plant transpiration, defined as the process of water movement through a plant and its evaporation from aerial parts, is a basic process regulated over short time periods by stomatal conductance (_{s} -

Field measurements of leaf scale transpiration are always based on the measurement of vapor added by transpiration into the air inside a chamber enclosing the leaf or a leaf surface (

Such challenge calls for the development of new approaches to determine absolute transpiration rates of plant leaves. Recently, the transpiration rate sensor with a multi-channel hygrometer using near infrared (NIR) tunable diode laser absorption spectroscopy (TDLAS) at 1.37 µm was developed (

With the development of hyperspectral remote sensing and imaging spectrometry, many empirical approaches have been proposed for spectroscopic analysis, such as vegetation indexes, single regression, stepwise multiple linear regression, partial least squares regression (PLSR), artificial neural networks, and others (

Reflected data collected by spectrometers hold thousands of generally collated bands within the visible to near-infrared domains. PLSR deals efficiently with such data sets including many highly correlated bands by avoiding the potential overfitting typically associated with multiple linear regression (_{cmax}) and regeneration (_{max}), can be effectively captured by reflectance using PLSR models even across species (

On the other hand, former studies exploring plant traits from reflectance suggested that a number of other modes or transformed formats of spectra, such as transmittance and derivative spectra, were helpful for data mining (

The main objective of the present study is to examine data taken simultaneously on both leaf transpiration and reflected spectra, from which the PLSR model was built up, to estimate leaf transpiration based on hyperspectral reflectance. The final target was the development of a methodology that can trace leaf transpiration promptly and accurately. This study focused on a dominant native plant in deserts,

Field measurement was carried out in 2013 at the Integrated Remote Sensing Experimental Site, 20 km north of the Fukang Station of Desert Ecology, Xinjiang Institute of Ecology and Geography, Chinese Academy of Sciences, located at 44° 17′ N, 87° 56′ E, with an elevation of 475 m a.s.l.

This region has a continental arid temperate climate and drought is quite prevalent. The extreme minimum temperature can reach -40 °C in winter, while the maximum temperature can be 40 °C in summer in the growing season. It is so far from the sea that the annual mean precipitation is as low as 80-160 mm, while pan evaporation can reach about 2000 mm in summer due to the high temperature (

The leaf-scale transpiration rate (Tr) was measured using a portable gas exchange system (HCM-1000, Walz, Germany). Diurnal variation measurements were made once per month at the key growth stages in the growing season from June to August. In each diurnal course measurement, two groups of leaves from the upper and lower layers of the sampling canopy were selected and inserted into the leaf chamber of the HCM-1000 for leaf transpiration measurement once per hour from 8:00 to 18:00 local time. As the system measures the change of H_{2}O pressure, and the transpiration rate (Tr, µmol g^{-1} s^{-1}) is calculated from the pre-set weight, the leaves placed in the chamber were clipped for fresh weight measurement. The real transpiration rate values were then converted from the values recorded by the HCM-1000.

Leaf hyperspectral spectra data (350 to 2500 nm, 1 nm step) were recorded with a field spectroradiometer (ASD FR Inc., Boulder, CO, USA) equipped with a leaf clip which can illuminate the leaves with a constant inner light source. To obtain spectra, five measurements were taken each time and the average value was used for further analysis. As the transpiration measurements took about 10 minutes each, the leaf spectra measurement was conducted on the leaves next to those whose transpiration was being measured in the meantime.

Based on the original reflectance data, the first-order derivative spectra of leaf reflectance were calculated using the following formula (

where _{λ} is the first-order derivative of reflectance at the wavelength of band _{λ+1} and _{λ} are the reflectance at the wavelengths

Selection of wavelengths is critical for the predictive ability of the PLSR model (

With numerous X-variables, there is a substantial risk of “over-fitting” in any empirical modeling procedure. To this purpose, it is necessary to test the predictive significance of each PLSR uncorrelated principal components (PCs) generated from selected spectral wavelengths, and to stop when components start to be non-significant (

Cross-validation is a model validation technique for assessing how the results of a statistical analysis will generalize to an independent data set. Cross-validation was used to determine the number of principal components of the PLSR models by minimizing the predicted residual sums of squares (PRESS -

To calculate the spectral loadings (or regression coefficients) of bands, a standard PLSR approach was applied, using the relevant spectral wavelengths selected by the stepwise regression, and the number of components determined by cross-validation. PLSR is a basically linear way to estimate relevant parameters in a model by reducing the large number of measured collinear spectral variables to a few uncorrelated principal components (PCs), which represent the relevant structural information contained in the measures of reflectance (

The coefficient of determination (R^{2}) and the root mean square error (RMSE) between measured and estimated transpiration values were then calculated and used to quantify the performance of the PLSR model. Of course, an effective model for assessing the transpiration should have a high R^{2} and small RMSE.

Diurnal variation in leaf transpiration was evident throughout the daytime, with a double-peak trend. Leaf transpiration rate rises in the morning, reaches the first peak around 11:00 local time, and then drops to low levels until about 17:00, due to the high temperature and the intensive light. Later, the transpiration rate rises again reaching a second peak, and then drops to the trough as the temperature falls, at the end of the daytime. Based on our field measurements taken from June to August, seasonal changes in leaf transpiration rate were not fully evident, but transpiration rates appeared to be higher in June than in July/August.

To generate the PLSR model for the estimation of leaf transpiration, both original reflectance and the first-order derivative spectra were examined. Generally, the leaves have the highest reflectance in August, though this trend was partially confounded by the diurnal variation in reflectance. Although monotonic variations in the reflectance and in the first-order derivative spectra cannot be identified over the whole range (350-2500 nm), consistent changes at some particular wavelengths were detected based on their high correlation coefficients with the transpiration rate.

The first-order derivative spectra clearly captured leaf transpiration more effectively, with higher correlation coefficients at many featured wavelengths (

Stepwise regression analysis based on the original reflectance data and transpiration rate was carried out first. Ten different wavelengths (465, 1545, 375, 1860, 440, 1400, 1800, 1795, 370, and 1885 nm) were finally selected for the PLSR analysis based on the results of the stepwise regression analysis.

The results of the cross-validation carried out to determine the number of components for PLSR analysis are reported in

^{2}) for transpiration estimation was 0.43, with an RMSE of 2.6 µmol g^{-1} s^{-1} (

Stepwise regression analysis, cross-validation, and PLSR analysis were carried out as described above on the first-order derivative spectra of leaf reflectance, obtaining much better performances in model predictions (

Unlike the original spectra data, wavelengths of the first-order derivative spectra selected by stepwise regression analysis (9) were mainly distributed within the SWIR domain, and were namely 2435, 2355, 1190, 2180, 2445, 2470, 2275, 2440, and 675 nm. Cross-validation results showed that the optimal number of components for the PLSR analysis was seven. The PRESS values obtained for the training set and the validation set were 1.61 and 1.66, respectively.

The PLSR model was finally run based on the above nine wavelengths of the first-order derivative spectra of leaf reflectance. Their coefficients obtained from the model are listed in ^{2}) for the transpiration estimate reached 0.78, and the RMSE between the observed and predicted values was 1.62 µmol g^{-1} s^{-1} (

In the scientific literature, reflectance has rarely been related to plant ecophysiological variables as compared with plant biochemical parameters, whose relationships with reflected wavelengths have been widely analyzed (_{max} and _{cmax} (_{900}/_{970}) is well correlated with the whole plant transpiration (^{2 }= 0.668 -

In this study, the observed high collinearity throughout the full spectrum and poor knowledge of the feature wavelengths for transpiration led to the difficult task of selecting the relevant information to be included in the PLSR model. Stepwise regression analysis was performed to select the wavelengths to be considered in themodel, instead of using the entire spectrum (350-2500 nm).

To assess the reliability of the band-selection approach described above, we checked the performance of PLSR analysis using the entire spectrum (350-2500 nm) of first-order derivative data rather than the selected bands only. The generated PLSR model showed poor predictive performances in the estimation of leaf transpiration (^{2 }= 0.21, RMSE = 3.07 µmol g^{-1} s^{-1}). The low effectiveness of this model is reasonably due to large noise derived from the inclusion in the model of a large amount of irrelevant information from the full spectrum.

High linear correlations between leaf transpiration and the original reflectance were frequently noted within the wavelengths of 400-800 nm and around 1400 or 1900 nm (_{s}. Indeed, wavebands such as 430-445 nm are known to be related to carotenoids, bands 531-570 nm to xanthophylls, and 550-680 nm and the “red-edge” position to chlorophyll (

More accurate predictions of leaf transpiration were obtained when first-order derivative spectra of the leaf reflectance were included in the PLSR model.

The importance of the different wavebands selected can be identified from the loading weights on principal components extracted by the PLSR model. High numerical values indicate high importance of the reflected wavelength in the PLSR analysis (^{-4}, 3.60 × 10^{-4}, and 3.28 × 10^{-4}, respectively. In addition, the wavelength of 2440 nm showed high loading weights on the fourth and fifth PCs. Therefore, we concluded that the first-order derivative spectra at 2435, 2440, 2445, and 2470 nm were critical to predict leaf transpiration using PLSR models.

PLSR analysis based on first-order derivative spectra yielded much more accurate estimations of leaf transpiration. Similarly, more accurate indexes of canopy transpiration could be identified based on derivative spectra in a former study (Jin & Wang, unpublished). This confirms that the derived spectra can improve the efficiency of transpiration predictions using PLSR models.

As already mentioned, the high accuracy of transpiration estimation based on derivative spectra may be primarily due to a better signal-to-noise ratio, according to

To further illustrate such relationship, we carried out a correlation analysis of leaf transpiration with each wavelength selected for the PLSR models based on both original reflectance and derivative spectra (

Two important criteria should be taken into account for extending

In this context, an additional PLSR analysis based on the first-order derivative spectra was carried out excluding all the above-mentioned noise bands by retaining every tenth wavelength in the spectrum 350-2500 nm. Such procedure finally resulted in 191 out of 2150 wavelengths being involved in the analysis. Eight wavelengths of 1450, 1960, 2000, 1070, 1980, 970, 920, and 2060 nm were then selected by stepwise regression analysis and included in the PLSR model. Six components were determined through cross-validation analysis (^{2}) was 0.76, with an RMSE of 1.69 μmol g^{-1} s^{-1} (

To verify straightforward statistical relationships between leaf transpiration and reflectance and its derivative spectra, we applied PLSR analysis based on transpiration measures and canopy reflectance spectra (as well as its first derivatives) taken simultaneously. This was carried out on a dominant native plant

This study was partly supported by the JSPS Grants-in-Aid for Scientific Research (Grant No. 25302001) to Q. Wang. The members of Quantitative Remote Sensing Group of XIEG, CAS are highly acknowledged for their support in field measurements.

Correlation between reflectance/first-order derivative spectra and leaf transpiration.

Cross-validation results for the original reflectance data set: relationships between the numbers of components and the predicted residual sums of squares (PRESS).

The observed

Cross-validation results for first-order derivative spectra mode: the relationships between the numbers of components and the predicted residual sums of squares (PRESS).

The observed

Cross-validation results for the first-order derivative spectra with removal of known noise regions for canopy data: the relationships between the numbers of components and the predicted residual sums of squares (PRESS).

The observed

The coefficients of the ten wavelengths from the original reflectance data set that were included in the PLSR model. (Int): intercept.

Int | Wavelength (nm) | |||||||||
---|---|---|---|---|---|---|---|---|---|---|

370 | 375 | 440 | 465 | 1400 | 1545 | 1795 | 1800 | 1860 | 1885 | |

2.96 | -488.15 | 900.42 | -716.20 | 216.04 | -750.42 | 1672.63 | -395.58 | -623.18 | 465.25 | -297.06 |

The coefficients of the nine selected wavelengths of the first-order derivative spectra included in the PLSR model.

Intercept | Wavelength (nm) | ||||||||
---|---|---|---|---|---|---|---|---|---|

675 | 1190 | 2180 | 2275 | 2355 | 2435 | 2440 | 2445 | 2470 | |

3.06 | 23001.37 | 87810.41 | 23790.46 | -50988.63 | -51988.05 | 20650.22 | 18325.10 | 16480.77 | 7987.47 |

The number of wavebands selected for transpiration estimation PLSR modeling within the visible (VIS), near-infrared (NIR), short-wave 1 (SWIR1), and short-wave 2 (SWIR2) spectral regions.

Origin | PLSRcomponents | Number of wavebands | ||||
---|---|---|---|---|---|---|

350-2500 nm | VIS(350-700nm) | NIR(700-1300nm) | SWIR1(1300-1900nm) | SWIR2(1900-2500nm) | ||

Original reflectance | 7 | 10 | 4 | 0 | 6 | 0 |

Derivative spectra | 7 | 9 | 1 | 1 | 0 | 7 |

Loading weights (LW, × 10^{-4}) of each waveband for the PLSR model based on the first-order derivative spectra of reflectance for the estimation of leaf transpiration. (a): high absolute numerical values indicate a high loading weight of the waveband to the given principal component (PC).

Axis | Wavelength (nm) | ||||||||
---|---|---|---|---|---|---|---|---|---|

675 | 1190 | 2180 | 2275 | 2355 | 2435 | 2440 | 2445 | 2470 | |

PC1 | -0.28 | 0.51 | -0.41 | 0.59 | 0.38 | 3.68^{ a} |
-0.20 | 3.60^{ a} |
3.28^{ a} |

PC2 | -0.25 | -0.08 | 0.41 | -0.93 | -0.71 | 2.42^{ a} |
-0.72 | 0.18 | -6.72^{ a} |

PC3 | -0.20 | -0.83 | 1.06 | -1.45 | -1.55 | -0.78 | 0.29 | -1.21 | 2.91^{ a} |

PC4 | 0.64 | 0.79 | -0.66 | 1.24 | -0.05 | -0.49 | 2.99^{ a} |
0.99 | -0.71 |

PC5 | 0.73 | 0.65 | -0.44 | -0.25 | -0.68 | -0.53 | -2.56^{ a} |
0.29 | 0.14 |

PC6 | 0.10 | 0.84 | -0.07 | -0.02 | 1.12 | 1.66 | 0.84 | -2.17^{ a} |
0.32 |

PC7 | -0.78 | 0.09 | 0.49 | -1.06 | 0.51 | -1.03 | 0.04 | 1.34 | -0.19 |

Correlation matrix between leaf transpiration (Tr) and the original reflectance of wavelengths involved in the PLSR model.

- | Tr | Wavelength (nm) | |||||||||
---|---|---|---|---|---|---|---|---|---|---|---|

370 | 375 | 440 | 465 | 1400 | 1545 | 1795 | 1800 | 1860 | 1885 | ||

Tr | 1.00 | - | - | - | - | - | - | - | - | - | - |

370 | -0.05 | 1.00 | - | - | - | - | - | - | - | - | - |

375 | -0.04 | 0.99 | 1.00 | - | - | - | - | - | - | - | - |

440 | -0.18 | 0.77 | 0.80 | 1.00 | - | - | - | - | - | - | - |

465 | -0.18 | 0.71 | 0.75 | 0.99 | 1.00 | - | - | - | - | - | - |

1400 | -0.06 | 0.53 | 0.57 | 0.90 | 0.92 | 1.00 | - | - | - | - | - |

1545 | -0.02 | 0.51 | 0.55 | 0.88 | 0.90 | 0.99 | 1.00 | - | - | - | - |

1795 | -0.01 | 0.48 | 0.53 | 0.86 | 0.88 | 0.99 | 1.00 | 1.00 | - | - | - |

1800 | -0.01 | 0.48 | 0.53 | 0.86 | 0.88 | 0.99 | 1.00 | 1.00 | 1.00 | - | - |

1860 | -0.04 | 0.50 | 0.54 | 0.87 | 0.90 | 0.99 | 0.99 | 0.99 | 0.99 | 1.00 | - |

1885 | -0.08 | 0.58 | 0.63 | 0.91 | 0.92 | 0.98 | 0.97 | 0.96 | 0.96 | 0.97 | 1.00 |

Correlation matrix between leaf transpiration (Tr) and the first derivative spectra of reflectance of wavelengths involved in the PLSR model.

- | Tr | Wavelength (nm) | ||||||||
---|---|---|---|---|---|---|---|---|---|---|

675 | 1190 | 2180 | 2275 | 2355 | 2435 | 2440 | 2445 | 2470 | ||

Tr | 1.00 | - | - | - | - | - | - | - | - | - |

675 | -0.03 | 1.00 | - | - | - | - | - | - | - | - |

1190 | 0.27 | 0.08 | 1.00 | - | - | - | - | - | - | - |

2180 | 0.07 | -0.19 | -0.70 | 1.00 | - | - | - | - | - | - |

2275 | -0.12 | 0.14 | 0.59 | -0.71 | 1.00 | - | - | - | - | - |

2355 | -0.25 | 0.16 | 0.39 | -0.33 | 0.32 | 1.00 | - | - | - | - |

2435 | 0.49 | -0.12 | 0.34 | -0.16 | 0.13 | 0.22 | 1.00 | - | - | - |

2440 | 0.01 | 0.05 | 0.15 | -0.12 | 0.39 | 0.27 | -0.07 | 1.00 | - | - |

2445 | 0.40 | -0.08 | 0.24 | -0.32 | 0.26 | 0.12 | 0.39 | -0.04 | 1.00 | - |

2470 | 0.13 | 0.00 | -0.03 | -0.05 | 0.15 | 0.09 | -0.14 | 0.08 | 0.14 | 1.00 |