Aims: This study focused on the applicability of back-propagation (BP) neural networks in simulating sap flow (SF) using meteorological factors and a phenological index (PI) for Liquidambar formosana, a deciduous broad-leaf tree species in subtropical China, and thus providing a useful and promising alternative to traditional methods for transpiration prediction.

Methods: Three-layered BP models with an architecture 4-10-1 (four neurons in the input layer, ten neurons in the hidden layer and one neuron in the output layer) were trained and tested using the Levenberg-Marquardt (LM) algorithm based on in situ observations of SF and concurrent microclimate at the Qianyanzhou Ecological Station, Jiangxi Province, Southeast China. The model performance was verified with testing data not used in model development.

Results: The BP models with eight input combinations proved a satisfactory fit: the determination coefficients (R²) and fitting accuracies (Acc) (about 0.8 and 70%) were significantly higher than those of the multivariate linear regression (MLR) (about 0.5 and 50%), indicating their advantage in solving complex nonlinear problems involved in transpiration. In addition, the BP models showed a bit better performance by adding PI to the input family. The best BP model was achieved taking air temperature (T_a), relative humidity (RH), average net radiation (ANR) and PI as the input and sap flux density (v_s) as the output, with maximum R² and Acc as high as 0.95 and 90%, respectively.

Conclusions: The BP models with input combination of T_a, RH, ANR and PI mirrored very well measured daily variations in v_s. The results could be used to fine-tune sap flow estimation by Liquidambar formosana, and thus shed light on the eco-hydrological process related to transpiration for deciduous broad-leaf trees.

This research was conducted in Qianyanzhou Ecological Station (115°04′13″E, 26°44′48″N; 102 m a.s.l.), affiliated with the Institute of Geographic Sciences and Natural Resources Research, Chinese Academy of Science, located in Taihe County of Jiangxi Province, Southeast China. It is characteristic of a typical subtropical monsoon climate with high temperatures and abundant precipitation. The annual accumulative sunshine hours is 1360 h with gross radiation intensity reaching 4349 MJ·m^-2. The annual average temperature is 17.8 ^oC with the maximum monthly average temperature being 28.8 ^oC in July and the minimum of 6.4 ^oC in January, respectively. Sample plot investigation was conducted on a mixed broadleaf-conifer forest (Liquidambar formosana, Cunninghamia lanceolate, Pinus massoniana, Schima superba) in 2015. The stand density was 2280 stems·ha^-1 with the average DBH and height of Liquidambar formosana being 20.5 cm and 15.7 m, respectively. The canopy cover is as high as 0.9 in the sample plots, with a few shrubs of Symplocos sumunti and herbs of Dalbergia hupeana sparsely distributed in the understorey. 

Sap flux density (v_s, cm³·cm^-2·s^-1) was continuously measured on nine sample trees (three in each plot) using the thermal dissipation probes (TDP-30, Dynamax Inc., Houston, TX, USA) from April 2014 to December 2014. The DBH of sample trees ranged between 20.6 cm and 21.8 cm, averaging around 21.2 cm. The data were recorded at 60 second intervals and stored as 30 minute averages on a data logger (DT-50, Thermo Fisher Scientific Inc., Waltham, USA). Sap flux density (v_s) was calculated based on the empirical relationship established by Grainer (1987). Air temperature (T_a), relative humidity (RH), wind velocity (W_s) and average net radiation (ANR) were synchronously monitored by the routine meteorological instruments (Moldel HMP 45C, Vaisala Inc., Finland) at 15 m on the flux tower, where was about 200 m away from the study plot. Besides, soil moisture (θ) at depth of 10 cm was also obtained by soil moisture sensor (Model CS616，Campbell Scientific Inc., USA). All data were collected by a datalogger (Model CR1000, Campbell Scientific Inc., USA), calculated and stored at 30 min intervals. Cross-correlation analyses were used to estimate the time-lag between SF and meteorological factors (Phillips et al. 1997).

        A three-layer feed-forward back-propagation (BP) neural network was presented to simulate sap flux density(v_s) using a commercial software package (MATLAB, The MathWorks Inc., Natwick, MA, 2014). Data pre-processing should be conducted before training, including input variables selection, outlier exclusion, data division and normalization. A single-variable analysis was performed on related driving factors affecting sap flow (i.e. T_a, RH, W_s, ANR and θ) to determine the input vaiables. The phenological index (PI), a kind of time factor with a specific value assigned for any sampling time, was also added to the input family. Following the method suggested by Li et al. (2006), we obtained a total of 10800 groups of data set. The data set were randomly split into two groups with the coin flipping method: about 50% for model training and the remaining for model testing. The values of input variables were standarized to ensure that all variables were equally treated and to improve the precision of the model simulation. The normalization function hyperbolic tangent was adopted, and thus all the original data were transformed into the range of [0,1]. Various meteorological parameters and the phenological index (PI) were selected as the input variables, and sap flow velocity as the output. We used a trial and error method, starting from an initial minimum of 5 and increasing the number of neurons in the hidden layer repeatedly until the desired accuracy was achieved. The training process repeated until a minimum acceptable error (0.0001) was achieved between the measured and target output values. After about 2000 iterations, the optimum BP architecture 4-10-1 (four neurons in the input layer, ten neurons in the hidden layer and one neuron in the output layer) was identified though comparisons of different network structures by cross-validation and adjusting the network parameters. The coefficients of determination (R²) and fitting accuracy (Acc) were used to assess the performance of BP neural network and MLR.