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Article

An Improved Sap Flow Prediction Model Based on CNN-GRU-BiLSTM and Factor Analysis of Historical Environmental Variables

by
Yane Li
1,2,3,†,
Lijun Guo
1,2,3,†,
Jiyang Wang
1,
Yiwei Wang
1,
Dayu Xu
1 and
Jun Wen
4,*
1
College of Mathematics and Computer Science, Zhejiang A&F University, Hangzhou 311300, China
2
Key Laboratory of Forestry Intelligent Monitoring and Information Technology of Zhejiang Province, Hangzhou 311300, China
3
China Key Laboratory of State Forestry and Grassland Administration on Forestry Sensing Technology and Intelligent Equipment, Hangzhou 311300, China
4
Department of Biomedical Informatics, Harvard Medical School, Boston, MA 02114, USA
*
Author to whom correspondence should be addressed.
†
These authors contributed equally to this work.
Forests 2023, 14(7), 1310; https://doi.org/10.3390/f14071310
Submission received: 11 April 2023 / Revised: 5 June 2023 / Accepted: 23 June 2023 / Published: 26 June 2023
(This article belongs to the Section Forest Inventory, Modeling and Remote Sensing)
Browse Figures
Review Reports Versions Notes

Abstract

:
Sap flow is widely used to estimate the transpiration and water consumption of canopies and to manage water resources. In this paper, an improved time series prediction model was proposed by integrating three basic networks—CNN, GRU and BiLSTM—to assess sap flow with historical environment variables. A dataset with 17,569 records of each, including 9 environment variables and 1 sap flow, was applied from a public database of SAPFLUXNET. After normalization, the environment variables were analyzed and composed with the factor analysis method. After the CNN-GRU-BiLSTM structure was designed, N records of three main factors were computed from environment variables, which were measured at N previous moments, and the sap flow was measured at the current moment, and they were applied for each training, validation, and testing cycle. To improve and compare the CNN-GRU-BiLSTM-based model, nine other models, using the methods of multiple linear regression, support vector regression, random forest, LSTM, GRU, BiLSTM, CNN-GRU, CNN-BiLSTM, and CNN-GRU-LSTM, were constructed in this study, respectively. Results show that the performance of the CNN-GRU-BiLSTM-based model has more accuracy than the other nine models we built in this paper, with the mean absolute error, mean squared error, mean absolute percentage error, and coefficient of determination (R2) being 0.0410, 0.0029, 0.2708 and 0.9329, respectively. Furthermore, for a comparison of the descending dimension method of factor analysis, principal component analysis (PCA) and singular value decomposition (SVD) methods were applied and compared, respectively. Results show that the performance of the factor analysis-based model is better than the PCA- or SVD-based model, with the R2 results of the factor analysis-based model being higher than the PCA- and SVD-based models by 5.06% and 10.63%, respectively. This study indicates that the CNN-GRU-BiLSTM-based sap flow prediction model established with a factor analysis of historical environmental variables has optimistic applications for analyzing the transpiration of trees and evaluating water consumption.

1. Introduction

Transpiration is an important part of the terrestrial water circulation system [1]. The accurate estimation of transpiration is a prerequisite for understanding its dynamics and relationships with various environmental variables, which has important practical implications for water resource management, urban forest construction and its intelligent management, as well as various other ecological functions or services [2,3]. Sap flow is formed when water is transported upward along the xylem ducts of the vegetation under the effect of leaf transpiration and water potential. More than 90% of the water absorbed by plant roots is consumed in this process. Therefore, the accurate prediction of the sap flow is important, to provide a basis for the accurate assessment of tree transpiration [4,5]. To measure sap flow, many popular techniques based on thermodynamics, electrodynamics, and magneto-dynamics have been proposed. Among the existing sap flow measurement methods, thermodynamics-based approaches are the major commonly used methods [6,7,8,9]. The advantages of these heat-based sap flow measurement methods are that they are easier to use than other methods. However, these methods also have disadvantages, including the wounding of trees and mechanical damage [10,11,12,13]; misalignment of probes, which may lead to substantial uncertainty in measurements [11,14,15,16,17]; and overestimation [18] or underestimation of sap flow [19]. Among the techniques available for the measurement of sap flow, nuclear magnetic resonance (NMR) is an appropriate non-invasive method [7,20]. However, the currently available NMR equipment is limited by bulkiness [21,22], operational complexity, poor instrument portability [23,24], and complex procedures and data processing techniques, and it is expensive [7,22,25]. Therefore, it is hard to use measurement tools to assess sap flow to satisfy the demands of the automatic prediction of tree transpiration.
Many studies have shown that sap flow is significantly related to environment factors. Stone et al. used the method of generalized additive modelling to predict the influence of individual climate parameters on sap flow, and the results show a 60% relative humidity (RH) critical threshold of predicted sap flow and the indirect effect that wind speeds have on sap flow under protected cropping systems [26]. Su et al. used principal component analysis (PCA) to understand the response of sap flow to water stress and microclimatic variables, and the results showed that there was a positive correlation between vapor pressure deficit and daytime sap flow [27]. Liu et al. clarified the characteristics and influencing factors of sap flow in Populus tomentosa Carr. and Salix babylonica L, and results shown that under typical cloudy and sunny conditions, the sap flow velocity of P. tomentosa and S. babylonica were highly significantly correlated with meteorological factors under typical cloudy and sunny conditions, and negatively correlated with the soil water content of 10–20 cm [5]. Liu et al. investigated the transpiration and the water sources of T. ramosissima by using heat balance and oxygen isotopic analysis and found that daily sap flow was positively correlated with air temperature (Ta), photosynthetically active radiation (PAR), and the vapor pressure deficit (VPD) [28]. Bouamama-Gzara et al. used the xylem sap flow of five Tunisian grapevine cultivars to investigate the xylem morphological dynamics, and the results showed that Hencha and Khamri were sensitive to environmental constraints, while the other three cultivars presented higher tolerance [29]. Ouyang et al. investigated the impact of urbanization on sap flow of common evergreen tree species, and results show that the impact of pollutant discharge on average sap flux density was greater than that of climatic factors [30]. Gowdy et al. used a non-parametric regression method to estimate the bulk stomatal conductance in grape canopies, and results show that transpiration flux and VPD were the most important variables for calculating the bulk stomatal conductance [31]. Shiferaw et al. have compared the water abstraction of P. juliflora and S. senegal trees, and the results showed that soil heat, latent heat, and soil moisture status influenced the sap flow rate of the two species of tree [32]. Shalini et al. investigated the relationship between environmental variables and sap flow velocity for balsam fir and black spruce tree species in humid boreal regions, and the results showed that the sap flow of these two species was closely related to VPD and solar radiation (RAD) [33]. Liu et al. compared sap flow patterns and their relationships with environmental factors, and results show that the sap flow density was significantly correlated with Ta, VPD, and PAR [34]. Blécourt et al. investigated the responses of global radiation, VPD and soil water availability to water consumption, indicating that soil water availability and global radiation are important factors influencing the water consumption of S. mellifera [35]. Hayat et al. studied the nighttime sap flow dynamics by changing biophysical variables of Salix psammophila, and results show that temperature and soil water content (SWC) were important factors influencing night sap flow [36]. Wei et al. explored the water consumption processes and responses of driving factors, and results show that the PAR had a great influence on sap flow [37]. In addition, the sap flow variation depended on the growing season, and on hourly and daily timescales. Lyu et al. investigated the sap flow characteristics in the growing season and non-growing seasons for three tree species, and results show that the sap flow was related to tree species, growing season, and stem diameter [38]. Chen et al. investigated the influence of photosynthetic stems on sap flow, indicating that the stem cortex may have an impact on the nighttime sap flow [39]. Korakaki et al. investigated the influence of climatic factors on sap flow by thorough evaluation at different time scales, and results show that VPD and SWC were related to sap flow [40]. Petrík et al. analyzed the effects of environmental conditions and seasonality on the allocation of transpiration and evapotranspiration in pure European beech forest ecosystems, showing that air temperature is the main environmental factor affecting the dynamics of daily and monthly transpiration and evapotranspiration [41]. In addition, the results of this study show that the response of mature European beech transpiration to soil water content is non-significant and that the response to VPD is linear. [41]. Dukat et al. investigated the effects of drought on forest function by analyzing ecosystem evaporation under normal and dry conditions and identified key drivers of these processes in Pinus sylvestris [42]. As a result, we can conclude that sap flow is correlated with environmental factors, such as Ta [28,36], RH [26], wind speed [26], SWC [37], VPD [28,32,34,41], RAD [34] and PAR [28]. Therefore, it is possible to predict sap flow using various meteorological factors.
Evapotranspiration can be described as a process consisting of a pair of adiabatic cooling and diabatic heating which leads to the energy state of the ambient air to chage in easily quantifiable ways. The Penman–Monteith equation is used as a standard method for modeling evapotranspiration by the United Nations Food and Agriculture Organization (FAO) [43], which can estimate the rates of heat and vapor transfers from less-than-saturated surfaces [44]. The Penman–Monteith equation requires daily mean temperature, wind speed, relative humidity, and solar radiation to predict net evapotranspiration [43]. Zerihun et al. derivated the Penman–Monteith equation with the thermodynamic approach, which shows two steps of evapotranspiration, including evaporation from a wet source/sink surface into quiescent ambient air and the dynamic influence of the wind–surface interaction and canopy system on evaporation [45]. Jiří et al. presented an improved approach for directly parameterizing the Penman–Monteith equation for calculating the diurnal variation process of stand canopy conductance (gc). This method was used to calculate gc and establish a sap flow model, which can describe canopy conductance and stand sap flow, with sub-hourly resolution under both day and night conditions [46]. In our study, an improved sap flow prediction model was established with environmental factors for further evaluating the transpiration instead of full evapotranspiration.
The prevalent sap flow prediction models are usually established with the back propagation (BP) of artificial neural networks, multiple linear regression (MLR), autoregressive moving average, and other methods. Tu et al. established a BP-based sap flow prediction model and compared its performance with that of an MLR-based model. Results show that the coefficients of determination (R2) and fitting accuracies achieved 0.9 and 89.7%, respectively, which were higher than the MLR-based model, which achieved 0.78 and 69% [2]. Salazar et al. established a cost-effective model for the prediction of sap flow using multiple microclimatic variables of cacao trees. Results show that the R2 and root mean squared error (RMSE) achieved 0.98 and 0.01, respectively [3]. Efrosinin et al. applied a Fourier series-based method to establish a sap flow density flux model, which showed that R2 and RMSE reached 0.9295 and 2.1235, respectively [47]. Zhao et al. used a hybrid model of Sarimax and Garch to estimate the time lags between sap flow and micro-meteorological factors [48].
In recent years, many researchers have used integrated methods based on deep learning to predict time series data. For example, in our previous study, a sap flow prediction model was developed by combining a convolutional neural network (CNN) and a gated recurrent unit (GRU) neural network [49]. Zhao et al. established a CNN-bidirectional long-short-term memory (CNN-BiLSTM) combined model to predict the multi-step interval of ultra-short-term wind power [50]. Yang et al. built an integrated prediction model based on an CNN-BiLSTM attention mechanism (AM) network to predict dissolved oxygen concentration in aquaculture, which had excellent performance compared with other comparative models [51]. Peng et al. established an integrated prediction model using CNN-GRU-AM to predict bicycle demand, which showed better performance than other models established in this paper [52]. LSTM is a kind of recurrent neural network (RNN), which can better capture long-distance dependency by controlling information flow [53]. BiLSTM can better capture bidirectional semantic dependencies [54]. CNN is a feedforward neural network with strong feature expression capacity [55]. The GRU neural network is a variant of an RNN, which has strong memory ability and can capture dependencies on different time scales [56]. Although the method based on comprehensive deep learning has better prediction performance than single methods for time series data, few integrated models of deep learning have been applied to the prediction of sap flow. In this study, a CNN-GRU-BiLSTM network was designed, and a hybrid integrated deep learning model was established to predict sap flow.

2. Materials and Methods

2.1. Dataset and Data Processing

2.1.1. Dataset

The dataset applied in this study was drawn from a public database of SAPFLUXNET, the first global database of sap flow measurements based on individual community-contributed datasets. The SAPFLUXNET database contains sap flow data and environmental variables and was developed by the Centre for Research on Ecology and Forestry Applications and others, in coordination with Rafael Poyatos [57]. The dataset we used in this paper was uploaded by researchers at the University of Auckland [58], which contains 35,137 observation records measured from midnight on 1 January 2012 to midnight on 31 December 2012, with interval of 15 min [59]. One observation record consists of one sap flow measured from one tree and nine environmental variables: deep soil water content (SWC-Deep, cm3·cm−3), the shallow soil water content (SWC-Shallow, cm3·cm−3), vapor pressure deficit (VPD) (kPa), air temperature (Ta) (°C), wind speed (WS) (ms−1), relative humidity (RH, %), shortwave incoming radiation (SW, W·m−2), photosynthetic photon flux density (PPFD) (μmol·m−2s−1) and net radiation (Rad, W·m−2), which were measured synchronously. Among them, the sample tree species of the sample tree is the kauri, Agathis australis (D. Don) Lindl. The sample tree site is in the University of Auckland Scientific Reserve. There is approximately 15 ha of forest at Huapai in the northern region of the Waitakere Ranges, west of Auckland in New Zealand [60]. The sap flows of six trees were measured from 6 July 2011 to 29 September 2015. We selected the largest one of the six trees, with a diameter at breast height of 176 cm, a height of approximately 35 m, a bark thickness of 10 cm, a sapwood area of 3676 cm2 (excluding bark), a sapwood depth of 17.8 cm (measured by the dye injection method [61]), an age of 520 years and a growth condition of unmanaged naturally regenerated [60]. Granier-type sap flow probes [62] with slight modifications were applied. After removing the bark, a 2.45 cm diameter drill-bit was used to drill paired holes with a vertical spacing of 10 cm at a height of 1.5 m [60]. The temperature difference between the two probes was converted from differential voltage measurements of the thermocouple leads and recorded every 15 min as an average of one-minute measurements [60]. The Granier equation reported by James et al. [63] was used to calculate the sap flux density (g m−2 s−1), as shown in Equation (1).
F d = 119 ( ( Δ T m − Δ T ) / Δ T ) 1.231
where ΔTm is the temperature difference when sap flux density is zero.
In this dataset, values of Fd are relative values which measured with sensors uncalibrated for kauri. Steppe et al. found that the thermal dissipation method underestimated Fd by about 60% [19]. In this study, we assume that an underestimation of Fd is consistent for different seasons and detection depths [60]. Because of the large amount of data, it is not ideal to visualize all the data directly, so we show values of nine environmental variables and sap flow resampled at daily intervals, as shown in Figure 1.

2.1.2. Data Processing

For these 35,137 records, we first performed interval sampling to obtain 17,569 records, which were used to establish the sap flow prediction model in this study. Due to sap flow and environmental variables having different measurement units, magnitudes and value ranges, normalization was carried out to avoid overtraining and improve the fitting speed, degree of convergence and performance of the model. In this study, the minimum-maximum normalization method was applied to the original data according to Formula (2).
v ’ = v − v min v max − v min

2.2. Methods

2.2.1. Deep Learning Method

CNN. CNN is one of the representative algorithms of deep learning technology. It is a kind of feedforward neural network with a deep structure of convolutional computation. Compared with a BP neural network, the most important characteristics of CNN are the local perception and the parameter sharing mechanism. Since AlexNet was proposed in 2012 [64], CNN has won in the ImageNet Large Scale Visual Recognition Challenge many times [65,66]. So far, CNN has become one of the hot spots in many scientific fields. The basic operations of CNN include convolution, nonlinear processing, subsampling and classification. The main purpose of convolution is to extract features from the input dataset. Nonlinear processing is mainly handled by activation functions, such as ReLu, Tanh and Sigmoid functions. Pooling, also known as subsampling or downsampling, reduces the dimension of each feature map and maintains the most important information. Common pooling operations include maximizing, averaging, adding and so on. The pooling layer can control the dimension and overfitting of features, which can reduce parameters and computation in the network, which enhances the robustness of the network model. The output of the convolution and pooling layer represents the high-level features of the input dataset that are used to classify the input dataset based on the training data of the full connection layer.
LSTM. Long-short-term memory is a kind of RNN, which can process long-term-related sequence data more efficiently. For LSTM networks, the input and output of each moment are delivered to the next time step and stored in the cell state. The LSTM network consists of three gates: input gate, forget gate and output gate. These gates control whether information flows into or out of the cell state, partly solving the problem of gradient disappearing or explosion. Specifically, the input gate determines what information needs to be updated in the cell state, the forget gate decides what information needs to be deleted from the cell state, and the output gate controls what information needs to be newly computed. These three gates perform calculations based on input from the current moment and memory from the previous moment. With the storage and computation mechanisms of cell states, LSTM can deal with the dependencies at long interval dependencies.
GRU. A gate recurrent unit is a kind of RNN. Like LSTM, GRU also proposes to solve problems of long-term memory and gradient in back propagation. Different from LSTM, there are two gates in the GRU network: the reset gate and update gate. In addition, in the GRU network, the cell unit is removed, and the second-order nonlinear function in the output is eliminated. The reset gate operates on the previously hidden state, which determines how much previous information needs to be forgotten. The update gate in a GRU can be taken as the combination of the forgotten gate and the input gate in LSTM. The operating object for the update gate is the hidden unit of the current moment and the previous moment, which decides how much useful information needs to be passed from the previous moment to the current moment. Compared with LSTM, the GRU can capture important features with fewer parameters.
BiLSTM. Bidirectional long-short-term memory is combination of forward LSTM and backward LSTM, used to capture bidirectional semantic dependencies. In a one-directional RNN, the model only uses only the above text information, but does not consider the following text information. In a real-world scenario, the prediction might require the entire input sequence of the text information above and below. BiLSTM combines information from the input sequence in both forward and backward directions. At a given time t, the output of the forward LSTM layer has information from before and at time t of the input sequence. The output of the backward LSTM layer has information from after and at time t about the input sequence. Then, the output vector of BiLSTM can be obtained by adding, averaging or joining the output of the forward LSTM layer and output of the backward LSTM layer.

2.2.2. CNN-GRU-BiLSTM-Based Sap Flow Prediction Model

In this study, an integrated network of CNN-GRU-BiLSTM was designed, including four functional sub-models of data preprocessing, CNN network, GRU network and BiLSTM network, as shown in Figure 2. The CNN sub-model is mainly used to extract local features from the input sequence data. GRU and BiLSTM sub-models are mainly applied to capture long-term dependencies of sequence data. Among them, GRU can effectively solve the problem of the gradient disappearance of RNN. BiLSTM combines both forward and backward propagation of information to better capture contextual information.
Data preprocessing sub-model. After normalization, three main hidden factors were computed from nine environment variables with the factor analysis method. The length of the slide window is set to N. According to the ratio of 8:2, the number of (14,055 − N) × 0.8 (14,055 − N) is multiplied by 0.2, and (3514 − N) bins are applied to model training, validation and testing. Each bin has N records, including three main hidden factors and one sap flow value. Among them, the three main hidden factors are computed from environment variables, which are measured at the previous N moments. The sap flow value is measured at the current moment. As shown in Figure 2, the input and output dimension of the data preprocessing sub-model are (L − N, N, 5) and (L − N, 1), respectively, where L is the total amount of data and N is the length the slide window.
CNN sub-model. Two one-dimensional convolution layers were used to establish the convolutional layer, and the number of convolutional kernels was set to 16 and 64, respectively. In order to adjust the output size and prevent the discarding of individual data, padding operation was applied in the window. The input parameters are the time step and the number of features, set to N and 4, respectively. The convolution kernel size was set as 3 and the activation function was set to LeakyReLU. The reason for selecting LeakyReLU as the activation function is that the LeakyReLU activation function can calculate the gradient if the input is less than zero in the process of back propagation, avoiding the zigzag problem in the gradient direction. In the pooling layer, the maximum pooling window size is set to 5, which plays roles of sampling, reduction of dimension and prevention of overfitting. Finally, a forgetting layer with a probability of 0.01 is added to prevent overfitting. The parameter settings of the CNN in this study are shown in Table 1.
GRU sub-model. In the GRU sub-model, two layers of GRUs are set with the convolution kernel number of 16 and 64, respectively. The activation function of the GRU is set to the Tanh function to ensure that there will be no gradient explosion due to the use of the activation function. The output of the GRU layer is the full result of the hidden state instead of the final state. Two dropout layers are interspersed in the GRU layers. After the GRU layer, a forgetting layer with a probability of 0.01 was set to prevent overfitting. The structure of the GRU sub-model is shown in Figure 3. The parameter settings for the GRU in this study are shown in Table 2.
BiLSTM sub-model. In the BiLSTM sub-model, two bidirectional LSTM layers are created. For each BiLSTM, the forward LSTM and backward LSTM are combined with neurons, and the number of neurons was set to 16 and 64, respectively. These two LSTM layers are trained from two directions. The output of the first LSTM layer is concatenated in series to produce a sequence containing all time steps. The output of the second LSTM layer contains only the last moment step. A dropout layer is inserted between each LSTM layer. Compared with LSTM, both forward and backward have hidden states, and the number of parameters is larger than unidirectional LSTM, enabling it to capture more data features. At the same time, since it is easier to learn noise from the data or specific patterns in the training set, a forgetting layer with a probability of 0.01 is inserted into each BiLSTM layer. The structure of the BiLSTM sub-model is shown in Figure 4. The parameter settings of BiLSTM in this study are shown in Table 3.
Output sub-model. Finally, two fully connected layers were established with 4 and 1 neurons, respectively. The weights are initialized to a uniform distribution, and the activation function was set to the LeakyReLU function.

2.2.3. Performance Evaluation Measures

In this study, the mean absolute error (MAE), mean square error (MSE), mean absolute percentage error (MAPE) and coefficient of determination (R2) are used to evaluate model performance. The calculation formulas of each index are shown in Equations (3)–(6), respectively.
M A E = 1 n ∑ i = 1 n | y i - y ∧ i |
M S E = 1 n ∑ i = 1 n ( y i - y ∧ i ) 2
M A P E = 1 n ∑ i = 1 n | y i - y ∧ i y i |
R 2 = 1 − ∑ i ( y i - y ∧ i ) 2 ∑ i ( y i - y ¯ ) 2
In Equations (3)–(6), the yi is the measured value of the ith sap flow, the y ∧ i is the ith predicted sap flow value, y ¯ is the average value of all the measured values of sap flow, and n is the total number of predicted values.

3. Results and Analysis

3.1. Experimental Environment and Parameter Settings

In this study, the sap flow prediction model was established in the Windows 64-bit system environment, in which the Anaconda software (version 3) was used with an environment of Pytorch 1.7, Python 3.9.9 and CUDA 11.1 to establish the sap flow prediction model. The operating system model was AMD Ryzen 7 6800H with Radeon Graphics at 3.20 GHz, RAM 16.0 GB (Lenovo xiaoxin Pro 16, Peking, China). Relevant model parameters are shown in Table 4.

3.2. Dimensionality Reduction Method Based on Factory Analysis

After the original data were processed by normalization, nine environment variables were analyzed and composed by the method of factor analysis, a statistical technique to extract common factors from variables. In the case of no loss or as little loss of the original data information as possible, nine environment factors are aggregated into a few independent common factors, which can reflect the main information of the original nine environmental factors. While reducing the number of variables, this also reflects the internal relationship between variables. The prerequisite for using the factor analysis method is to satisfy the Kaiser–Meyer–Olkin (KMO) test, which is an index to compare simple and partial correlation between variables. KMO values range from 0 to 1. When the sum of squares of correlation coefficients among environmental variables is larger than the sum of squares of partial correlation coefficients, the larger the KMO value is. The larger this value, the stronger the correlation between variables is, and the more suitable the original variables are for factor analysis. In this study, the KMO value is 0.6896, greater than 0.6, indicating that there is multi-collinearity between environment factors, such as air temperature, relative humidity and vapor pressure deficit. As a result, it is reasonable to adopt the method of factor analysis for these nine environment factors. Multiple variables with strong collinearity are classified as potential factors. In addition, some environment factors such as Ta, RH and VPD are all important to sap flow, so factor analysis is adopted to eliminate the collinearity of each variable by variance rotation technology to construct potential factors and improve the explanatory ability of factors. The logical block diagram of applying factor analysis to environment variables is shown in Figure 5.
Specifically, first, the KMO test was used to these nine environmental factors. Then, the eigenroots and eigenvectors were computed for the correlation matrices of nine environment variables. The eigenroots of the scree plot are shown in Figure 6.
The first three common factors were selected to establish the sap flow prediction model. The complex relationship between nine environment variables were analyzed. By factor analysis, the environment variables with the same essence were condensed into one factor, so that the dispersed and complex environmental variables tended to be integrated and simplified. The contribution of the nine environment variables to each of the three factors is shown in Figure 7.
From Figure 7, we can see that the nine environment variables with complex relationships are decomposed into common factors shared by these environment variables. The main environment variables of the first factor are vapor pressure deficit (VPD), relative humidity (RH) and air temperature (Ta). In fact, VPD represents the degree of water vapor saturation in actual air distance, which is calculated by Ta and RH. Studies have shown that VPD can affect the degree of stomatal opening and closing of plants, and thus influence the intensity of plant transpiration. When VPD is small, the stomatal conductance increases with the increase in VPD, and when the transpiration intensity increases, the rate of sap flow also increases. However, when VPD increased to a certain extent, stomata would decrease rapidly, and the rate of sap flow would decrease. If VPD continues to rise, plants are forced to close their stomata to prevent excessive water loss and physiological damage. Therefore, within a suitable range, the variation trend of VPD is significantly related to the rate of sap flow [28,31,33,40].
The main environment variables for the second factor are photosynthetic photon flux density (PPFD), shortwave incoming radiation (SW) and net radiation (RAD). PPFD, SW and RAD are all closely related to solar radiation, which can provide a healthy growing environment for plants. When the light intensity is too low, plants will suffer from stunted growth, yellowing and shedding of leaves, and even death. However, when the light intensity is too strong, plants will suffer from thin branches, light leaf color and fragile leaf quality. As a result, PPFD, SW and RAD are essential for plant growth and development, and are correlated with sap flow [28,33,34,37].
The main environment variables for the third factor are the shallow soil water content (SWC_shallow) and deep soil water content (SWC_deep), both of which reflect soil water content. Sap flow is largely limited by the soil water content. Under the condition of sufficient soil water content, the increase in SWC will lead to an increase in the water absorbed by root system, and the sap flow will also be accelerated. When the SWC is higher or lower than a certain threshold, the water application efficiency of the leaves is significantly reduced [67]. When the soil water content is too low, the available water for trees decreases, resulting in water or leaf loss, an increase in mesophyll cell space, and decreased or stopped stomatal conductance. Following this, the sap flow decreases or even stops [68]. The soil water content, including the deep soil water and the shallow soil water, is crucial to sap flow [28,35,36,37].

3.3. Comparison of Performance between Models Established with Different Methods

After major factor selection, each new record of all 17,569 records includes 1 sap flow value and 3 factor values, which are computed from the nine environment variables. These 17,569 records were divided into two groups for training and testing according to a ratio of 8:2, including 14,055 and 3514 records, respectively. Then, the training dataset of 14,055 records was divided into 2 groups for model training and validation, with a ratio of 8:2, which were used to update model parameters. In this study, the N records are used to predict one sap flow value measured at the current moment. Among them, each record of N records includes three main factors computed from nine environment variables, which were measured at previous N moments of one sap flow. A sliding window of length N was used to train, validate and test the prediction model. As a result, there are (14,055 − N) × 0.8, (14,055 − N) × 0.2, and (3514 − N) bins for model training, validation and testing, respectively. We conducted one training and one validation, and then determined whether the loss function values of them were overfitted. We repeated the training and validation process until the loss functions converged. Then, the test dataset was applied to adjust the hyperparameters of learning rate, optimization algorithm and length of the time window.
An improved sap flow prediction model was established by combining CNN, GRU and BiLSTM to produce the CNN-GRU-BiLSTM-based network we designed. In order to compare and prove the performance of the sap prediction model, another nine sap flow prediction models were established with the algorithms of multiple linear regression, support vector regression, random forest, LSTM, BiLSTM, GRU, a combination of CNN and BiLSTM (CNN-BiLSTM), a combination of CNN and GRU (CNN-GRU), and a combination of CNN-GRU-LSTM, respectively. Due to the existence of some randomness, the performance of each test is slightly different. The results reported in this paper are the best performances selected by random five-cycle tests. Figure 8 shows trends of sap flow values predicted by the CNN-GRU-BiLSTM-based prediction model and measured values. A comparison of the performance between different sap flow prediction models established with different methods is shown in Table 5.
A comparative analysis of Table 5 reveals the following results.
First, the performance of models established with deep learning-based networks such as LSTM, GRU and BiLSTM is better than the models built with traditional machine learning methods such as multiple linear regression, support vector regression and random forest. Specifically, the MAE and MAPE of multiple linear regression, support vector regression and random forest-based models all larger than those of the LSTM-, GRU- and BiLSTM-based models. The MSE of multiple linear regression- and support vector regression-based models is larger than that of LSTM-, GRU- and BiLSTM-based models. The MSE of the random forest-based model is less than that of the LSTM-, GRU- and BiLSTM-based models and larger than that of the integrated networks-based models. The R2 of multiple linear regression, support vector regression and random forest-based models is smaller than that of the LSTM-, GRU- and BiLSTM-based models. These compared results indicate that the prediction models established by deep learning-based networks such as LSTM, GRU and BiLSTM have better performance than the models established by traditional machine learning methods such as multiple linear regression and support vector regression.
Second, the performance of models established by combining two or three different networks, such as CNN-GRU, CNN-BiLSTM, CNN-GRU-LSMT and CNN-GRU-BiLSTM, is better than that of the models constructed with a single network such as LSTM, BiLSTM and GRU. Specifically, the MAE, MSE and MAPE of LSTM-, GRU- and BiLSTM-based single network models are all larger than those of CNN-GRU-, CNN-BiLSTM-, CNN-GRU-LSMT- and CNN-GRU-BiLSTM-based integrated networks models. The R2 of LSTM-, GRU- and BiLSTM-based single network models is smaller than that of CNN-BiLSTM-, CNN-GRU-, CNN-GRU-LSMT- and CNN-GRU-BiLSTM-based integrated networks models. These compared results indicate that prediction models established by integrating multiple networks have a better ability to extract features from data and provide a more accurate description of data. The possible reason is that different single networks describe data from a slightly different angle, obtaining some of the truthful information. Integrating these networks can describe data from multiple angles, acquiring more truthful information, which is a more realistic description for the data.
Third, by comparing the performance of BiLSTM-, GRU- and LSTM-based models, we found that BiLSTM-based model is better than the GRU-based model. Specifically, the MAE, MSE and MAPE of the BiLSTM-based model is smaller than that of GRU-based model, and the R2 of the BiLSTM-based model is higher by 4.72% than that of the GRU-based model. In addition, performance of the LSTM-based prediction model is better than that of the GRU-based model and slightly worse than that of the BiLSTM-based model. The R2 of the LSTM-based model is higher by 3.67% than the GRU-based model and smaller by 1.05% than the BiLSTM-based model. The possible reason is that the BiLSTM-based model can learn bidirectional information, while LSTM and the GRU can only learn one-directional information from data.
Fourth, by comparing performance of two integrating prediction models of CNN-BiLSTM and CNN-GRU, we found that the performance of the CNN-BiLSTM-based model is comparable with that of the CNN-GRU-based model. The MAE and MAPE of the CNN-BiLSTM-based model are slightly higher than those of the CNN-GRU-based model. The MSE of the CNN-BiLSTM-based model is slightly lower than that of the CNN-GRU-based model. In addition, the R2 of CNN-BiLSTM is comparable with that of CNN-GRU, which is only slightly higher, by 0.5%.
Fifth, by comparing the performance of CNN-GRU/CNN-BiLSTM- and CNN-GRU-LSTM/CNN-GRU-BiLSTM-based models, we found that the model established with three basic networks of CNN-GRU-LSTM/CNN-GRU-BiLSTM is better than two basic networks of CNN-GRU/CNN-BiLSTM. Specifically, the MAE, MSE, and MAPE of the CNN-GRU-LSTM- or CNN-GRU-BiLSTM-based model are all smaller than those of the CNN-GRU- or CNN-BiLSTM-based model. The R2 of CNN-GRU-LSTM is higher by 1.74% and 1.24% than the CNN-GRU- and CNN-BiLSTM-based model, respectively. The R2 of CNN-GRU-BiLSTM is higher by 2.69% and 2.19% than that of the CNN-GRU- and CNN-BiLSTM-based model, respectively. The possible reason is that by integrating three basic networks, we could obtain more useful information than integrating two basic networks.
Sixth, by comparing the performance of CNN-GRU-LSTM- and CNN-GRU-BiLSTM-based models, we found that performance of the model established with CNN-GRU-BiLSTM is better than the CNN-GRU-LSTM-based model. Specifically, the MAE, MSE, and MAPE of the CNN-GRU-BiLSTM-based model are all smaller than those of the CNN-GRU-LSTM-based model. The R2 of CNN-GRU-BiLSTM is higher by 0.95% than that of the CNN-GRU-LSTM-based model. The possible reason is that the BiLSTM-based model can learn bidirectional information, while LSTM can only learn one-directional information from data. As a result, by integrating CNN, GRU and BiLSTM, we can describe more useful information than by using CNN-, GRU- and LSTM-based models.

3.4. Comparison of Performance between Different Feature Selection Methods of CNN-GRU-BiLSTM-Based Models

In this study, to compare the effects of different variable selection methods on the performance of the CNN-GRU-BiLSTM integrated prediction model, factor analysis, principal component analysis (PCA) and singular value decomposition (SVD) methods were used, respectively. After the main factors or components were computed and selected, CNN-GRU-BiLSTM-based models were established. A comparison of performance between different feature selection methods of CNN-GRU-BiLSTM-based models is shown in Table 6.
As shown in Table 6, the performance of the CNN-GRU-BiLSTM sap prediction model based on factor analysis is superior to PCA-, SVD- and all environment variables-based CNN-GRU-BiLSTM prediction models. Specifically, the MAE, MSE and MAPE of the factor analysis-based CNN-GRU-BiLSTM model are all smaller than those of PCA- and SVD-based CNN-GRU-BiLSTM models. The R2 of the factor analysis-based CNN-GRU-BiLSTM model is higher by 5.06% and 10.63% than those of the PCA- and SVD-based CNN-GRU-BiLSTM models, respectively. By comparing the performance of models established with main factors computed by the factor analysis method and models constructed with all environment variables, we found that there is no significant difference in performance between these two models. The MAE and MSE of the factor analysis-based CNN-GRU-BiLSTM prediction model are slightly lower than those of all environment variables-based CNN-GRU-BiLSTM models. The R2 of the factor analysis-based CNN-GRU-BiLSTM prediction model is slightly higher by 0.2% than that of all environment variables-based CNN-GRU-BiLSTM models. However, as the data volume of the three main factors computed by factor analysis was smaller than that of the nine environment variables, the calculation amount and spending time are lower for the factor analysis-based CNN-GRU-BiLSTM prediction model.

3.5. Comparison of Performance between Different Lengths of Slide Window of CNN-GRU-BiLSTM-Based Model

In this study, to compare the influence of slide window length on the performance of the CNN-GRU-BiLSTM model, different CNN-GRU-BiLSTM models were established with different lengths of slide windows, respectively. Specifically, the slide window length was set to N, where the value of N ranges from 1 to 35, respectively. Then, N bins of three main factors were computed from nine environment variables, which were measured in previous N moments and used to predict one sap flow value measured in the current moment. A comparison of the performance between different CNN-GRU-BiLSTM models with different slide window lengths is shown in Figure 9.
From Figure 6, we can see that when the length of the slide window was set to 16, which means the 16 bins of environment variables measured in the 16 previous moments to the current moment were used to predict 1 sap flow measured at current moment, the MAE, MSE, MAPE as well as R2 curves begin to converge and stabilize. As a result, the parameter slide window length is set to 16 in this study.

4. Discussion

Sap flow technology has been widely applied for the estimation of tree transpiration, analysis of soil water content level, management of water resources and analysis of tree health status. The main external factors affecting the sap flow rate of trees are environmental factors, such as saturated vapor pressure deficit [28], air relative humidity [69], air temperature [70], wind speed [26], soil moisture content [65], and soil temperature [71]. In this paper, an improved sap flow prediction model was built with environmental factors by factor analysis and the CNN-GRU-BiLSTM network we designed. In this study, the following points were found.
First, the performance of models established with deep learning-based networks of LSTM, GRU and BiLSTM is better than that of models built with traditional machine learning methods of multiple linear regression and support vector regression. The reason could be that models established with deep learning-based networks have a better ability to capture data information than those built by traditional machine learning methods.
Second, the performance of models established by integrating two basic networks such as CNN-GRU or CNN-BiLSTM is better than that of models established with single networks such as LSTM, BiLSTM or GRU. In addition, the performance of models established by integrating three basic networks such as CNN-GRU-LSTM or CNN-GRU-BiLSTM is better than models established by integrating two basic networks, such as CNN-GRU or CNN-BiLSTM. The reason may be that the multi-network integration strategy can describe data from multiple perspectives and has a better ability to capture data information. As a result, models established by integrating multiple networks can describe data more accurately.
Third, the performance of models established by adding or using BiLSTM basic network is better than that of models constructed by combining or adopting LSTM or GRU basic networks. For single network-based models, the performance of the BiLSTM-based model is better than that of the GRU- or LSTM-based model— the R2 of the BiLSTM-based model is higher by 4.72% than that of the GRU-based model. For a model built by integrating two basic networks-based models, the performance of the CNN-BiLSTM-based model is slightly better than that of the CNN-GRU-based model. For the model established by integrating three basic networks-based models, the performance of the CNN-GRU-BiLSTM-based model is better than that of the CNN-GRU-LSTM-based model. The possible reason is that BiLSTM is combination of forward LSTM and backward LSTM, which can learn bidirectional information from time series data. However, LSTM or GRU can only capture semantic dependencies from one direction. As a result, models established by adding or using the BiLSTM basic network can learn bidirectional semantic dependencies and have better performance.
Fourth, in order to establish models with faster efficiency and higher accuracy, nine environment variables were first reduced in dimension. To find better dimensionality reduction methods suitable for this model, factor analysis, principal component analysis (PCA) and singular value decomposition (SVD) methods were used to reduce the dimension of environmental variables, respectively. Then, CNN-GRU-BiLSTM-based sap flow prediction models were established with main factors or components, respectively, using CNN-GRU-BiLSTM integrated networks. Results show that performance of the factor analysis-based model is better than that of the PCA- or SVD-based model, and the R2 of the factor analysis-based model is higher by 5.06% and 10.63% than that of the PCA- and SVD-based model, respectively. The basic principle of factor analysis is used to extract a few common factors that play an explanatory role in variables from data by analyzing the intrinsic dependence of the original variable correlation matrix. The basic principle of PCA is to convert multiple indexes into several unrelated principal components on the premise of losing little information. Because of the intricate relationship between environmental factors, the factor analysis method is more suitable for this study.
Fifth, nine environment variables were analyzed using the factor analysis method, and the main environment variables for the first to the third main hidden factors are (VPD, RH, Ta), (PPFD, SW, RAD) and (SWC_shallow, SWC_deep), respectively. For the first main hidden factor, the environment variables of VPD, RH and Ta are directionally dependent, and VPD can be computed from Ta and RH. In addition, many studies have shown that VPD, RH and Ta are related to sap flow [28,32,34,41]. For the second main hidden factor, the environment variables of PPFD, SW and RAD are all closely related to solar radiation. At the same time, PPFD, SW and RAD correlate with sap flow [28,34,35,38]. For the third main hidden factor, the environment variables of SWC_shallow and SWC_deep both reflect the soil water content. In addition, there is a significant correlation between the soil water content and the sap flow [28,35,36,37,67,68]. Results show that the main hidden factors used to establish the prediction model correlate with sap flow, which can drive the model to predict sap flow more accurately and efficiently.
In summary, this paper proposed an improved sap flow prediction model by integrating three basic networks of CNN-GRU-BiLSTM, which have better performance than CNN-GRU-LSTM-, CNN-GRU-, CNN-BiLSTM- and CNN-LSTM-based models. In addition, the factor analysis method was used to reduce the dimension of environmental variables, which is more suitable than the methods of PCA and SVD for environment variables. Although promising results and new observations were demonstrated in this study, there are some limitations. First, the performance of model needs to be further validated on a dataset measured over a longer period of time, over more environmental variables, over more trees and species, as well as on new dataset collected in recent years. Second, further studies needed to be performed by adding characteristics of trees, such as leaf shape and size, branch angles canopy structure, etc., which will lead to the difference in boundary layer conductance, thus affecting the sap flow rate [72]. Therefore, the sap flow prediction model established in this study needs to be validated and tested more with larger and newer datasets in further studies.

5. Conclusions

In this paper, a novel sap flow prediction model was proposed by integrating three basic networks of CNN-GRU-BiLSTM with a whole year of data. In addition, the factor analysis method was used to reduce the dimension of environmental variables. Results indicate that the CNN-GRU-BiLSTM-based sap flow prediction model has optimistic applications for analyzing tree transpiration and evaluating water consumption. This model is trained by using the environmental factors of trees under the condition that species, age, stand structure and other important parameters affecting sap flow are fixed. The idea of this study can be used as a reference to construct sap flow prediction models for trees of different species, ages, and geographical locations. In addition, the universality of the model we established in this paper still needs to be further studied. In order to produce a more efficient sap flow prediction model, extensive research is still necessary in future studies.

Author Contributions

Conceptualization, Y.L.; Formal Analysis, J.W. (Jun Wen); Investigation, L.G. and Y.L.; Data curation, L.G.; Funding acquisition, Y.L., D.X., J.W. (Jiyang Wang) and Y.W.; Methodology, Y.L. and L.G.; Writing—original draft, Y.L. and J.W. (Jun Wen); Writing—Review, Y.L. and J.W. (Jun Wen); Visualization, L.G. All authors have read and agreed to the published version of the manuscript.

Funding

This research was supported by grant (LQ21H180001) from the Natural Science Foundation of Zhejiang Province, grant (2019RF065) from the Research Development Foundation of Zhejiang A&F University, grant (20YJC630173) from the Ministry of Education of Humanities and Social Science Project, and grant (72001190) from the National Natural Science Foundation of China, grant (2021KX0145, S202210341166) from the Innovation Training Program of Zhejiang A&F University.

Data Availability Statement

The original datasets available in the SAPFLUXNET database (https://sapfluxnet.creaf.cat, accessed on 8 June 2021), the procedure code used in this study are available on request from the corresponding author.

Conflicts of Interest

The authors declare no conflict of interest.

Abbreviations

List of abbreviations and full names used in this paper.
AMAttention mechanism
BiLSTMBidirectional long short-term memory
CNNConvolutional neural network
FAOFood and Agriculture Organization
GRUGate recurrent unit
KMOKaiser–Meyer–Olkin
LSTMLong short-term memory
MAEMean absolute error
MAPEMean absolute percentage error
MLRMultiple linear regression
MSEMean square error
NMRNuclear magnetic resonance
PARPhotosynthetically active radiation
PCAPrincipal component analysis
PPFDPhotosynthetic photon flux density
R2Coefficient of determination
RADRadiation
RHRelative humidity
RMSERoot mean squared error
RNNRecurrent neural network
SVDSingular value decomposition
SWShortwave incoming radiation
SWCSoil water content
SWC_deepDeep soil water content
SWC_shallowShallow soil water content
TaTemperature
VPDVapor pressure deficit
WSWind speed

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Figure 1. Values of nine environmental variables and sap flow resampled at daily intervals. Ta is air temperature, VPD is vapor pressure deficit, RAD is net radiation, PPFD is photosynthetic photon flux density, SWC-Shallow is the shallow soil water content, SWC-Deep is the deep soil water content, WS is wind speed, SW is shortwave incoming radiation, Rh is relative humidity.
Figure 1. Values of nine environmental variables and sap flow resampled at daily intervals. Ta is air temperature, VPD is vapor pressure deficit, RAD is net radiation, PPFD is photosynthetic photon flux density, SWC-Shallow is the shallow soil water content, SWC-Deep is the deep soil water content, WS is wind speed, SW is shortwave incoming radiation, Rh is relative humidity.
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Figure 2. Network structure of CNN-GRU-BiLSTM proposed in this study.
Figure 2. Network structure of CNN-GRU-BiLSTM proposed in this study.
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Figure 3. GRU structure.
Figure 3. GRU structure.
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Figure 4. BiLSTM structure.
Figure 4. BiLSTM structure.
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Figure 5. The logical block diagram of factor analysis in this study.
Figure 5. The logical block diagram of factor analysis in this study.
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Figure 6. Scree plot for nine eigenroots of environment variables.
Figure 6. Scree plot for nine eigenroots of environment variables.
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Figure 7. Color map of the contribution to nine environment variables for each main factor. Note: SWC_Deep: deep soil water content, SWC_Shallow: the shallow soil water content, VPD: vapor pressure deficit, Ta: air temperature, WS: wind speed, RH: relative humidity, SW: shortwave incoming radiation, PPFD: photosynthetic photon flux density; Rad: net radiation.
Figure 7. Color map of the contribution to nine environment variables for each main factor. Note: SWC_Deep: deep soil water content, SWC_Shallow: the shallow soil water content, VPD: vapor pressure deficit, Ta: air temperature, WS: wind speed, RH: relative humidity, SW: shortwave incoming radiation, PPFD: photosynthetic photon flux density; Rad: net radiation.
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Figure 8. Trends of sap flow values predicted by CNN-GRU-BiLSTM-based prediction model and measured values.
Figure 8. Trends of sap flow values predicted by CNN-GRU-BiLSTM-based prediction model and measured values.
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Figure 9. Performance of CNN-GRU-BiLSTM-based models with different length of slide window.
Figure 9. Performance of CNN-GRU-BiLSTM-based models with different length of slide window.
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Table
Table 1. Parameter settings of CNN.
Table 1. Parameter settings of CNN.
Model ParametersMethod and Values
Activation functionLeakyReLU
Number of convolutional layer neurons16, 64
Convolution layer kernel size3
Pooling size5
Dropout rate0.01
Paddingsame
Table
Table 2. Parameter settings of GRU.
Table 2. Parameter settings of GRU.
Model ParametersMethod and Values
Number of GRU neurons16, 64
Activation functionTanh
Dropout rate0.01
Return_sequencesTrue
Input size16, 4
Table
Table 3. Parameter settings of BiLSTM.
Table 3. Parameter settings of BiLSTM.
Model ParametersMethod and Values
Number of BiLSTM. neurons16, 64
Dropout rate0.01
Input size16, 4
Return_sequencesFalse
Activation functiontanh
Table
Table 4. Experimental model parameter.
Table 4. Experimental model parameter.
Training ParameterParameter Value
Input picture size16
Batch size128
Epochs150
OptimizerRMSprop
Learning rate0.001
Learning decay rate0.9
Momentum0.9
Loss functionMSE
Table
Table 5. Performance of different sap flow prediction models established with different methods.
Table 5. Performance of different sap flow prediction models established with different methods.
ModelMAEMSEMAPER2
Multiple linear regression0.08960.01351.15190.6936
Support vector regression0.08850.01441.19710.6722
Random forest0.05060.00431.56240.9032
LSTM0.04950.00490.32970.8882
GRU0.06290.00650.53030.8515
BiLSTM0.05130.00450.33450.8987
CNN-GRU0.04810.00410.26810.9060
CNN-BiLSTM0.04820.00390.29560.9110
CNN-GRU-LSTM0.04410.00340.27860.9234
CNN-GRU-BiLSTM0.04100.00290.27080.9329
Table
Table 6. Performance of CNN-GRU-BiLSTM-based models with different feature selection methods.
Table 6. Performance of CNN-GRU-BiLSTM-based models with different feature selection methods.
Feature Selection MethodsMAEMSEMAPER2
All environment variables0.04220.00310.25570.9307
PCA0.05490.00520.32730.8823
SVD0.06240.00760.36350.8266
Factor Analysis0.04100.00290.27080.9329
Note: PCA means method of Principal Component Analysis; SVD stands for method of Singular Value Decomposition.
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Li, Y.; Guo, L.; Wang, J.; Wang, Y.; Xu, D.; Wen, J. An Improved Sap Flow Prediction Model Based on CNN-GRU-BiLSTM and Factor Analysis of Historical Environmental Variables. Forests 2023, 14, 1310. https://doi.org/10.3390/f14071310

AMA Style

Li Y, Guo L, Wang J, Wang Y, Xu D, Wen J. An Improved Sap Flow Prediction Model Based on CNN-GRU-BiLSTM and Factor Analysis of Historical Environmental Variables. Forests. 2023; 14(7):1310. https://doi.org/10.3390/f14071310

Chicago/Turabian Style

Li, Yane, Lijun Guo, Jiyang Wang, Yiwei Wang, Dayu Xu, and Jun Wen. 2023. "An Improved Sap Flow Prediction Model Based on CNN-GRU-BiLSTM and Factor Analysis of Historical Environmental Variables" Forests 14, no. 7: 1310. https://doi.org/10.3390/f14071310

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