Modeling and comparison of hourly photosynthetically active radiation in different ecosystems

Renewable and Sustainable Energy Reviews 56 (2016) 436–453

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Renewable and Sustainable Energy Reviews journal homepage: www.elsevier.com/locate/rser

Modeling and comparison of hourly photosynthetically active radiation in different ecosystems Lunche Wang a,b,n, Ozgur Kisi c, Mohammad Zounemat-Kermani d, Bo Hu e, Wei Gong f,g a

Department of Geography, School of Earth Sciences, China University of Geosciences, Wuhan 430074, China State Key Laboratory of Biogeology and Environmental Geology, China University of Geosciences, Wuhan 430074, China c Canik Basari University, Faculty of Architecture and Engineering, Civil Engineering Department, Samsun, Turkey d Department of Water Engineering, Shahid Bahonar University of Kerman, Kerman, Iran e State Key Laboratory of Atmospheric Boundary Layer Physics and Atmospheric Chemistry (LAPC), Institute of Atmospheric Physics, Chinese Academy of Sciences, Beijing 100029, China f State Key Laboratory of Information Engineering in Surveying, Mapping and Remote Sensingó, Wuhan University, Wuhan, Hubei Province 430079, China g Collaborative Innovation Center for Geospatial Technology, Wuhan 430079, China b

art ic l e i nf o

a b s t r a c t

Article history: Received 29 August 2015 Received in revised form 15 November 2015 Accepted 22 November 2015 Available online 12 December 2015

Long-term hourly observations of photosynthetically active radiation (PAR), global solar radiation (Eg) and meteorological variables [air temperature (TA), relative humidity (RH), dew point (TD), water vapor pressure (VW), air pressure (PA)] observed at different types of ecosystems (agricultural farmland, wetland, forest, bay, grassland, desert and lake) in China are reported for developing and validating PAR estimating models. Three improved Artificial Neural Network (ANN) methods, Multilayer Perceptron (MLP), Generalized Regression Neural Network (GRNN), and Radial Basis Neural Network (RBNN) are proposed in this study for predicting the hourly PAR using the combinations of above meteorological variables as model inputs. The ANN models have been compared with an efficient all-sky PAR model (ALSKY) through statistical indicies root mean square errors (RMSE) and mean absolute errors (MAE) at each station. The effects of meteorological variables on the hourly PAR predictions are further analyzed for investigating the main influencing factors for each model. The results indicate that there are large differences in model accuracy for each model at each ecosystem, for example, the MLP and RBNN models whose inputs are the Eg and TA (RMSE, MAE and R2 are 7.12, 5.24 and 98.90, respectively) perform better than the GRNN and ALSYK models at the agricultural farmland AKA station, while the GRNN model (RMSE and MAE are 12.47 and 8.98, respectively) performs better than other methods at DHL station. The model inputs also play different roles in different ecosystems for each ANN model, for example, TA and PA generally have more effects than the RH, TD and VW variables in the farmland stations, while RH is more important for hourly PAR prediction than the other variables in the bay stations. Finally, the overall rank of the model accuracy is obtained, MLP and RBNN models are more accurate for estimating hourly PAR at various ecosystems in China. & 2015 Elsevier Ltd. All rights reserved.

Keywords: Photosynthetically active radiation Ecosystems Artificial Neural Networks Model accuracy Comparison Meteorological variables China

Contents 1. 2.

3.

n

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 437 Materials and methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 438 2.1. Sites and data acquisition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 438 2.2. Hourly PAR models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 440 2.2.1. Multi-Layer Perceptron . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 440 2.2.2. Radial Basis Neural Network . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 442 2.2.3. Generalized Regression Neural Networks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 442 2.2.4. All-sky PAR model (ALSKY) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 443 Model applications and results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 444

Corresponding author at: Department of Geography, School of Earth Sciences, China University of Geosciences, Wuhan 430074, China. Tel.: þ86 13349889828. E-mail address: [email protected] (L. Wang).

http://dx.doi.org/10.1016/j.rser.2015.11.068 1364-0321/& 2015 Elsevier Ltd. All rights reserved.

L. Wang et al. / Renewable and Sustainable Energy Reviews 56 (2016) 436–453

3.1. Comparison statistics. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2. Modeling hourly PAR in different ecosystems in China . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4. Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5. Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

1. Introduction Photosynthetically active radiation (PAR), defined as solar radiation between 400 and 700 nm [1,2], is an important component of global solar radiation (Eg) reaching the surface because it is one of the key factors driving the process of photosynthesis and therefore the production and storage of organic carbon [3]. Photosynthesis is a basic process involved in plant growth and contributes to the primary productivity of natural ecosystems and crop production [4]. Accurate estimation of PAR is understandably crucial for investigating the exchange of CO2, water and energy in the planetary soil–plant–atmosphere system [5], which play improtant roles in understanding the impacts of changing climate, atmospheric chemistry and land use on regional to global scale biogeochemical cycling [6]. PAR is therefore a key determinant of global water and carbon balance and the regional and global climate change [7,8]. Besides their importance to numerous ecophysiological and climate models, accurate determination and clear understanding of the PAR solar components are also required in many solar energy applications (e.g. renewable energy development and management) due to the increasing global energy demands [9,10]. Despite its importance, there are relatively few places around the world where PAR is routinely measured due to the great difficulties in conducting accurate observations (maintaining the sensors and quality control) and high cost, unlike other meteorological variables such as air temperature, precipitation and sunshine hours [11–13]. Thus, PAR has to be estimated through semiempirical methods, radiative transfer models or satellite-based observations from a prescribed atmospheric state [14]; for

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444 444 448 450 452 452

example, Mizoguchi et al. [13] estimate the PAR values in a temperate humid area using atmospheric pressure, air temperature and relative humidity; Tan and Ismail [15] compare different PAR models in equatorial Singapore using direct observations; Janjai and Wattan [16] developed a model for estimating PAR from geostationary satellite in a tropical environment (Thailand); Li et al. [17] develop a method for estimating PAR in China by combining geostationary and polar-orbiting satellite data. It is known that PAR solar irradiance is reduced while passing through the atmosphere because part of it is absorbed and scattered by molecules and substances, including water vapor, dust particles and various gases, and in particular the presence of cloud which varies temporally and spatially, so the model results are greatly affected by local climatic and geographic conditions up till now (e.g. optical properties of the atmosphere) [18,19]. These methods should be further recalibrated to account for local characteristics like cloudiness, water vapor and aerosol loadings [20,21]. Despite Wang et al. [22] developed an all-sky PAR model by investigating its dependence on clearness index (Kt) and cosine of solar zenith angle (μ) based on observations from Chinese Ecosystem Research Network (CERN) during the 2006–2012 period. This method has not been compared with other PAR models, and the model accuracies also differ greatly from different observation stations. It is still essential to set up as many PAR observation networks as possible and develop and compare different models for improving the accuracy of PAR estimations [23,24]. PAR related studies in the literature are mainly focused on daily or monthly scales because the direct instantaneous measurements of the PAR component are very scarce worldwide [25–27]. There

Fig. 1. Spatial distribution of the PAR observation stations at different ecosystems in China.

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L. Wang et al. / Renewable and Sustainable Energy Reviews 56 (2016) 436–453

are very few studies analyzing the PAR evolutions at hourly scales, which is of vital importance to accurately describe and predict the plant biochemical processes in photosynthesis (at the micro-level) [23,28,29]. Unfortunately, although there are few studies conducted on PAR characteristics at sites of China (Beijing, Wuhan, Northwest, Northeast) [12,19,27,30], there have been almost no studies focusing on analyzing and comparing the variation patterns and related causes at different ecosystems (e.g. Farmland, wetland, forest, bay, grassland, desert and lake stations); not to mention developing efficient PAR models for investigating PAR variability at hourly basis in different climate conditions. Nevertheless, the solar radiation components have been approximated using different Artificial Neural Network (ANN) methods in recent decades which constitute a widely accepted technique offering an alternative way to synthesize complex problems associated with

Table 1 The geographical locations of PAR observation stations. Station AKA FQA LSA YCA ALF CBF DHL THL FKD SPD NMG HBG JZB SYB SJM

Longitude 0

89°49 E 114°240 E 91°200 E 116°220 E 101°010 E 128°280 E 114°230 E 120°130 E 87°550 E 104°570 E 116°420 E 101°190 E 119°560 E 109°280 E 133°310 E

Latitude 0

40°37 N 35°000 N 29°400 N 36°400 N 24°320 N 42°240 N 30°330 N 31°240 N 44°170 N 37°270 N 43°380 N 37°370 N 35°430 N 18°130 N 47°350 N

Altitude (m)

Ecosystem type

1028 67.5 3688 22 2478 738.1 21 10 460 1350 1267 3280 21 3 55

Farmland Farmland Farmland Farmland Forest Forest Lake Lake Desert Desert Grassland Grassland Bay Bay Wetland

solar energy [31–33]. In the literature there exist numerous articles for modeling global solar radiation, direct solar radiation and diffuse radiation by means of neural network techniques [34,35]; for example, Jacovides et al. [10] estimated the daily solar global UV and broadband radiant fluxes using ANN methods in an eastern Mediterranean site. This layed the foundation for modeling hourly PAR using different ANN methods and comparing with the semi-emprical models. Bearing the above in mind, there is an increasing demand for accurate and reliable PAR data for climate change research and solar energy applications. The purpose of this research is to propose different ANN-models, Multi layer Perceptron (MLP), Generalized Regression Neural Network (GRNN), and Radial Basis Neural Network (RBNN) for predicting hourly PAR at different ecosystems (classified as farmland, wetland, forest, bay, grassland, desert and lake stations) using a limited number of widely available input meteorological variables (global solar radiation, air temperature, relative humidity, dew point, water vapor pressure, air pressure) at 15 stations. The dependences of ANN models on hourly meteorological parameters will be examined for investigating the major factors influencing the model accuracy. The ANNmethods will be also validated and compared with an efficient semi-empirical all-sky PAR model at each typical station using stastical indices [root mean square errors (RMSE), mean absolute errors (MAE) and determination coefficient (R2)]. This will constitue the first report on the assessment of various PAR models at different ecosystems in China.

2. Materials and methods 2.1. Sites and data acquisition The hourly observations of radiation and meteorological parameters at 15 stations (Fig. 1) in China are provided by the Chinese

Fig. 2. Schematic diagram of (a) Multi-layer Perceptron; (b) radial basis, and (c) generalized regression neural network architectures.

Fig. 3. The dependence of hourly PAR on Kt and cosine of solar zenith angle μ.

L. Wang et al. / Renewable and Sustainable Energy Reviews 56 (2016) 436–453

Ecosystem Research Network (CERN), which is the first standard network established to investigate the radiation budget/climate change and its spatial and temporal variations in China [26]. The geographical locations and their ecosystem types are given by Table 1: AKA, FQA, LSA and YCA belong to the agricultural farmland stations; ALF and CBF stations are in the forests; DHL and THL are sites around the lakes; FKD and SPD stations are in the desert; HBG and NMG sites are locating in the grasslands; JZB and SYB are near the bay; SJM station is at wetland in northeast China. The detailed natural/ecological conditions about above stations have been clearly described in earlier studies Hu et al. [26] and Wang et al. [22]. A series of instruments have been installed at the above stations since October 2004; for example, Eg is measured using a CM11 radiometer (Kipp & Zonen, Delft, The Netherlands) with an

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uncertainty of 2–3%, whereas the PAR measurements are obtained using LICOR quantum sensors (LI-190SZ) with a relative error less than 5%; The HMP45D apparatus (Vaisala, Finland) has been used to measure the relative humidity (RH) and air temperature (TA) with an uncertainty of 3% and 0.1 °C, respectively; the air pressure is measured using a DPA501 device with an accuracy of 0.2 hPa [20,22,26]. All the radiation and meteorological parameters are recorded at 1-min intervals, and the hourly values were derived from the 1min values through integrations. Data collection, calibration and quality control are conducted at the atmosphere subcenter of CERN in Beijing, where annual calibration of above instruments is undertaken. The calibration process and data quality control procedures have been described in earlier studies Hu et al. [26] and Wang et al. [22]; for example, the calibration of the LI-190SA

Table 2 Comparison of ANN and empirical ALSKY models in modeling PAR for farmland stations. Model

Input

Validation RMSE

LSA station MLP

GRNN

RBNN

ALSKY YCA Station MLP

GRNN

RBNN

ALSKY

Test MAE

2

R

RMSE

MAE

R2

Eg Eg and PA Eg and TA Eg and TD Eg and RH Eg and VW Eg, TA and RH Eg, TA, RH, PA, TD and VW Eg Eg and PA Eg and TA Eg and TD Eg and RH Eg and VW Eg, TA and RH Eg, TA, RH, PA, TD and VW Eg Eg and PA Eg and TA Eg and TD Eg and RH Eg and VW Eg, TA and RH Eg, TA, RH, PA, TD and VW KT , μ

8.32 8.32 8.03 6.54 7.13 6.54 6.54 6.55 7.73 7.73 7.43 6.24 6.84 6.24 6.54 6.85 8.32 8.03 7.73 6.54 7.13 6.54 6.54 6.85 7.15

6.24 6.24 5.95 5.05 5.35 5.05 5.35 5.06 6.24 6.24 5.95 5.05 5.35 5.05 5.35 5.36 6.24 6.24 5.95 5.05 5.35 5.05 5.05 5.36 5.66

99.13 99.11 99.36 99.52 99.32 99.54 99.57 99.60 99.05 99.05 99.27 99.44 99.26 99.48 99.50 99.30 99.18 99.18 99.36 99.56 99.33 99.55 99.59 99.50 99.50

18.82 18.49 18.49 17.52 17.52 17.52 17.52 17.52 17.52 17.19 17.84 16.55 16.87 16.87 17.19 16.87 18.82 17.84 18.49 17.52 17.52 17.52 17.84 17.52 16.55

13.95 13.95 13.95 13.63 13.63 13.63 13.95 13.95 13.95 13.63 13.95 13.30 13.30 13.30 13.63 13.63 13.95 13.63 13.95 13.63 13.63 13.63 13.95 13.95 13.63

97.08 97.25 97.45 98.23 97.95 98.23 98.18 98.20 96.98 97.48 97.49 98.28 97.86 98.20 98.12 98.10 97.10 97.49 97.47 98.27 97.97 98.27 98.17 98.20 97.80

Eg Eg and PA Eg and TA Eg and TD Eg and RH Eg and VW Eg, TA and RH Eg, TA, RH, PA, TD and VW Eg Eg and PA Eg and TA Eg and TD Eg and RH Eg and VW Eg, TA and RH Eg, TA, RH, PA, TD and VW Eg Eg and PA Eg and TA Eg and TD Eg and RH Eg and VW Eg, TA and RH Eg, TA, RH, PA, TD and VW KT , μ

12.73 12.89 11.09 11.62 12.78 11.71 11.29 11.32 11.96 10.62 10.40 10.85 12.17 10.89 10.73 10.78 12.70 11.36 11.12 11.56 12.60 11.65 11.17 11.18 11.60

9.10 8.53 8.21 8.52 9.40 8.56 8.28 8.56 9.22 8.17 7.93 8.41 9.38 8.46 8.21 8.24 9.14 8.30 8.17 8.45 9.35 8.52 8.29 8.30 8.63

98.49 98.78 98.80 98.68 98.42 98.67 98.72 98.72 98.27 98.63 98.61 98.52 98.29 98.47 98.57 98.44 98.52 98.82 98.81 98.73 98.48 98.69 98.82 98.71 98.78

10.30 10.20 11.10 10.99 10.55 10.96 11.11 11.11 10.23 10.33 11.34 10.88 10.56 11.00 11.36 11.73 10.19 10.06 11.42 10.82 10.47 10.84 11.05 11.49 10.16

7.20 7.31 7.93 7.89 7.51 7.81 8.00 7.94 7.67 7.76 8.64 8.27 7.87 8.43 8.54 8.83 7.06 7.14 8.18 7.73 7.54 7.76 8.05 8.48 7.40

98.22 98.24 97.96 97.97 98.11 98.01 97.90 97.95 98.03 97.97 97.59 97.76 97.92 97.70 97.63 97.42 98.27 98.29 97.87 98.05 98.11 98.04 97.99 97.77 98.37

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Table 2 (continued ) Model

AKA station MLP

GRNN

RBNN

ALSKY FQA station MLP

GRNN

RBNN

ALSKY

Input

Validation

Test

RMSE

MAE

R2

Eg Eg and PA Eg and TA Eg and TD Eg and RH Eg and VW Eg, TA and RH Eg, TA, RH, PA, TD and VW Eg Eg and PA Eg and TA Eg and TD Eg and RH Eg and VW Eg, TA and RH Eg, TA, RH, PA, TD and VW Eg Eg and PA Eg and TA Eg and TD Eg and RH Eg and VW Eg, TA and RH Eg, TA, RH, PA, TD and VW KT, μ

12.65 11.62 10.60 10.94 12.99 10.94 10.60 10.59 12.99 12.30 10.94 11.62 13.33 11.62 10.94 11.62 12.30 11.62 10.25 11.28 12.99 11.28 10.60 10.94 11.62

9.23 8.89 7.86 7.86 9.57 7.86 7.52 7.86 10.3 9.57 8.20 8.54 10.3 8.54 7.86 8.20 9.23 8.89 7.86 8.20 9.57 7.86 7.52 7.86 8.89

96.69 97.21 97.84 97.32 96.36 97.20 97.52 97.40 96.77 97.08 97.67 96.98 96.42 96.95 97.46 97.10 96.75 97.21 97.80 97.07 96.37 97.16 97.40 97.30 97.20

8.62 7.87 7.12 8.24 8.62 8.62 7.87 7.87 8.99 7.87 7.49 8.24 8.99 8.62 7.49 8.24 8.62 7.49 7.12 8.62 8.99 8.24 8.24 7.87 7.49

6.37 5.62 5.24 6.37 6.74 6.37 5.99 6.37 7.12 5.99 5.62 6.37 7.12 6.37 5.99 6.74 6.37 5.62 5.24 6.37 6.74 6.37 5.99 5.99 5.62

98.38 98.65 98.92 98.54 98.26 98.53 98.75 98.80 98.39 98.61 98.82 98.52 98.29 98.47 98.79 98.60 98.40 98.67 98.90 98.53 98.24 98.58 98.74 98.80 98.70

Eg Eg and PA Eg and TA Eg and TD Egg and RH Eg and VW Eg, TA and RH Eg, TA, RH, PA, TD and VW Eg Eg and PA Eg and TA Eg and TD Eg and RH Eg and VW Eg, TA and RH Eg, TA, RH, PA, TD and VW Eg Eg and PA Eg and TA Eg and TD Eg and RH Eg and VW Eg, TA and RH Eg, TA, RH, PA, TD and VW KT, μ

9.74 8.85 8.85 8.85 9.30 8.85 9.30 8.90 10.3 9.74 9.74 9.30 10.6 9.30 10.2 10.6 9.74 8.85 8.85 8.85 9.30 8.85 8.85 8.90 8.48

7.08 6.64 6.20 6.20 6.64 6.20 6.64 6.36 7.53 7.08 7.08 6.64 7.97 6.64 7.53 7.63 7.08 6.20 6.20 6.20 6.64 6.20 6.20 6.36 5.93

98.24 98.44 98.43 98.55 98.38 98.54 98.40 98.30 98.22 98.34 98.28 98.38 98.01 98.38 97.97 97.60 98.29 98.45 98.47 98.53 98.35 98.53 98.44 98.30 98.50

12.96 11.57 11.57 12.03 12.96 12.03 11.57 11.57 13.42 12.03 11.57 12.50 13.89 12.03 12.03 12.49 12.96 11.57 11.57 12.03 12.96 12.03 11.57 12.03 12.03

9.26 8.33 8.33 8.33 9.26 8.33 8.33 8.33 9.26 8.33 8.33 8.79 9.72 8.79 8.79 8.79 8.79 8.33 8.33 8.33 9.26 8.33 8.33 8.33 8.33

97.21 97.80 97.83 97.66 97.25 97.68 97.84 97.80 97.20 97.76 97.92 97.65 97.06 97.69 97.75 97.50 97.23 97.80 97.80 97.66 97.23 97.67 97.77 97.70 97.70

sensor has been conducted with a standard light source in standard spectral irradiance that can be traced to the National Bureau of Standards lamp, and the pyranometers are calibrated using the “alternate method” [11,19]. Daily checks have been conducted to ensure that the instruments are positioned horizontally and free of dirt. The quality assessment for PAR is mainly based on two principles: the observed hourly PAR should be less than the extraterrestrial PAR flux values at the same geographical coordinates, and PAR/Eg index should be in the range of 1.3–2.8, otherwise it is considered as questionable observation [20,23]. Finally, the data measured in situ from 2005 to 2012 are used for analyzing the PAR properties and developing different models. After examination, approximately 5% of the measured data were eliminated from the dataset, ensuring the reliability of the analyzing results in this study.

RMSE

MAE

R2

2.2. Hourly PAR models Artificial neural networks (ANNs) are flexible nonlinear models that can discover patterns and dynamical procedures adaptively from the observations and data. ANNs have the ability to learn from measurements, data and experiences and do the estimation/ prediction process with reasonable accuracy. Although several types of neural network models have been proposed, in this study, the most three popular supervised ones for time series prediction are presented and described continuously. 2.2.1. Multi-Layer Perceptron The Multi-layer Perceptron (MLP) neural network, the most common types of ANNs, has been proved to function well in modeling complex and nonlinear phenomena [36]. A typical feed

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Fig. 4. The PAR estimates of the optimal models for the FQA station in farmland ecosystem.

Table 3 Comparison of ANN and empirical ALSKY models in modeling PAR for wetland stations. Model

SJM station MLP

GRNN

RBNN

ALSKY

Input

Eg Eg and PA Eg and TA Eg and TD Eg and RH Eg and VW Eg, TA and RH Eg, TA, RH, PA, TD and VW Eg Eg and PA Eg and TA Eg and TD Eg and RH Eg and VW Eg, TA and RH Eg, TA, RH, PA, TD and VW Eg Eg and PA Eg and TA Eg and TD Eg and RH Eg and VW Eg, TA and RH Eg, TA, RH, PA, TD and VW KT , μ

Validation

Test

RMSE

MAE

R2

RMSE

MAE

R2

11.6 11.1 10.2 10.2 11.6 9.78 10.2 10.7 11.6 10.7 9.78 9.33 11.6 9.78 9.78 10.2 11.6 11.1 9.78 9.78 11.6 9.78 9.78 10.2 9.33

8.45 7.56 6.67 6.67 8.00 6.67 6.67 7.11 8.45 7.56 6.67 6.22 8.45 6.67 6.67 6.67 8.45 7.56 6.67 6.22 8.00 6.67 6.67 6.67 6.22

97.5 97.8 98.0 98.1 97.7 98.1 98.2 97.7 97.4 97.7 98.1 98.2 97.5 98.1 98.1 98.1 97.5 97.8 98.1 98.3 97.6 98.2 98.2 98.1 98.4

18.18 18.67 18.67 18.67 18.67 18.67 18.67 18.18 17.69 17.69 17.69 18.18 17.69 18.18 18.18 18.18 18.18 18.67 18.67 18.18 18.67 18.67 18.67 18.18 18.18

12.78 12.28 12.28 12.28 12.28 12.28 12.28 12.78 12.78 12.28 12.28 12.28 12.28 12.28 12.28 12.29 12.78 12.28 12.78 12.28 12.28 12.28 11.79 11.79 12.29

96.05 95.95 96.00 95.99 96.05 95.93 95.97 95.40 95.90 95.75 95.71 95.87 95.96 95.87 95.75 95.90 96.04 95.91 95.97 95.97 96.06 95.96 95.94 96.00 96.10

forward MLP network consists of an input layer, one or more hidden layer(s) and an output layer (Fig. 2a). The hidden and output layers contain a certain number of artificial neurons (processors). Each single neuron receives a set of input signals (x) from the external inputs or the layer preceding it. The connections between the neural network's layers contain weights (w) are determined through the training process of the system [37,38]. Neurons calculate weighted averages (z) of input signals (x),

weights (w) and biases (b) using the summation function and then use a nonlinear transfer (activation) function (f) to produce an output as below:

yðxÞ ¼ f ðzÞ ¼ f

n X i¼1

! ðx i w i þ b Þ

ð1Þ

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Fig. 5. The PAR estimates of the optimal models for the SJM station in wetland ecosystem.

Sigmoid function is known as a common transfer function which varies from 0 to 1 for a range of inputs where: f ðzÞ ¼

1 1þez

ð2Þ

In supervised ANNs, training (a process of weight adjustment) is used to minimize the error between the network output and the target. Back-propagation algorithm is known as the most common training algorithm in the ANN models. The back-propagation algorithm minimizes the least square error function to determine the optimal weights and biases which would produce an output vector as close as possible to the specific target values with a predetermined accuracy. The total least square error (E) can be computed as: X X E¼ ðt k  zk Þ2 ¼ v2k ð3Þ k

k

where tk and zk are the target and predicted/simulated values, vk stands for the error of output unit k. In this study, in order to modify the network weights and biases, the conjugate gradient algorithm is used. In this algorithm, a search is performed along conjugate directions, so that the results are in faster convergence than the basic steepest descent algorithm [36,39]. 2.2.2. Radial Basis Neural Network The Radial Basis Function Neural Network (RBNN) is a feedforward type of ANN which is very similar with the supervised MLP network in architecture. Fig. 2b shows a schematic diagram of a general RBNN model having input layer, output layer and one hidden layer [40]. The network consists of Gaussian basis functions in the hidden layer and linear activation functions in the output layer. The input data (e.g. n input nodes) are transferred to the hidden layer using a radial basis activation function (Eq. (4)). In this study, the activation function of jth hidden node is the Gaussian function which can be expressed as: ! jj x  cj jj 2 zj ðxÞ ¼ exp  ð4Þ 2σ 2j

where zj ðxÞ is hidden node output, x stands for the input set; cj is the center value of the radial basis function for the hidden node j; σ j is variance and j j x  cj j j represents the Euclidean distance between the center of the radial basis function and input. In the third layer (which is the output layer with k nodes) the output of the network is calculated considering the sum of the linear weighted zj ðxÞ yk ¼ w0 þ

J X

wkj zj ðxÞ

ð5Þ

j¼0

where yk is the kth component of the output layer; wlj is the weight coefficient between the jth node of hidden layer and the kth node of output layer and w0 is the bias. During the training process, the variance and center of each function are adopted and determined [41]. 2.2.3. Generalized Regression Neural Networks The generalized regression neural network (GRNN) can be viewed as the normalized RBNN network in which there is a unit centered at every training process. But unlike the MLP and RBNN model, GRNN does not require the iterative training process (as used in the back-propagation method). In other words, in a GRNN network, an arbitrary function can be approximated directly from the training data [42,43]. As shown in Fig. 2c, GRNNs consist four layers: input layer, pattern layer, summation layer and output layer. The number of input nodes in input layer depends on the total number of the observation parameters. The first layer with the number of input nodes is connected to the pattern layer. The second layer which is the pattern layer, each neuron presents a training pattern and its output. In connection to the pattern layer, the third layer (summation layer) is placed. Each unit in the pattern layer is connected to the summation neurons. Finally the output layer covers the output units of the network. It divides the output of each summation neuron, which yields to the simulated/predicted value _ y i to

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Table 4 Comparison of ANN and empirical ALSKY models in modeling PAR for forest stations. Model

Input

ALF station MLP

GRNN

RBNN

ALSKY CBF station MLP

GRNN

RBNN

ALSKY

Test

RMSE

MAE

R2

RMSE

MAE

R2

Eg Eg and PA Eg and TA Eg and TD Eg and RH Eg and VW Eg, TA and RH Eg, TA, RH, PA, TD and VW Eg Eg and PA Eg and TA Eg and TD Eg and RH Eg and VW Eg, TA and RH Eg, TA, RH, PA, TD and VW Eg Eg and PA Eg and TA Eg and TD Eg and RH Eg and VW Eg, TA and RH Eg, TA, RH, PA, TD and VW KT , μ

8.82 8.82 8.40 8.40 8.82 8.82 8.40 8.40 9.66 9.66 9.66 9.66 10.1 9.66 9.66 10.9 8.40 8.40 7.98 8.40 8.82 8.40 8.40 8.82 8.82

5.88 5.88 5.88 5.88 5.88 6.30 5.88 5.88 7.14 7.14 6.72 7.14 7.14 7.14 7.14 7.98 5.88 5.88 5.88 5.88 5.88 5.88 5.88 6.30 6.30

99.00 99.07 99.11 99.06 99.02 98.99 99.07 99.00 98.98 98.99 98.99 98.96 98.92 98.95 98.88 98.50 99.07 99.08 99.10 99.02 99.04 99.01 99.01 99.00 99.10

17.51 18.01 17.51 17.51 17.51 18.01 18.01 18.01 17.01 16.51 17.01 17.01 17.01 17.01 17.51 17.51 17.51 17.51 18.01 18.01 17.51 18.01 18.01 17.51 18.01

12.01 12.51 12.51 12.51 12.51 13.01 12.51 13.01 12.01 12.01 12.51 12.51 12.51 12.51 13.01 13.01 12.01 12.01 12.51 12.51 12.01 12.51 12.51 12.51 12.51

97.32 97.40 97.46 97.37 97.34 97.33 97.38 97.30 98.28 97.37 97.34 97.27 97.23 97.26 97.25 97.10 97.38 97.43 97.44 97.34 97.34 97.34 97.39 97.50 97.30

Eg Eg and PA Eg and TA Eg and TD Eg and RH Eg and VW Eg, TA and RH Eg, TA, RH, PA, TD and VW Eg Eg and PA Eg and TA Eg and TD Eg and RH Eg and VW Eg, TA and RH Eg, TA, RH, PA, TD and VW Eg Eg and PA Eg and TA Eg and TD Eg and RH Eg and VW Eg, TA and RH Eg, TA, RH, PA, TD and VW KT , μ

8.09 7.64 6.29 6.29 7.19 6.29 6.29 6.29 8.09 7.64 6.29 6.29 7.64 6.29 6.74 7.64 8.09 7.64 6.29 6.29 7.19 6.29 6.29 6.29 6.29

5.39 4.94 4.49 4.49 4.94 4.49 4.49 4.49 5.84 5.39 4.49 4.49 5.39 4.49 4.94 5.84 5.39 4.94 4.49 4.49 4.94 4.04 4.04 4.49 4.49

98.74 98.89 99.23 99.28 99.02 99.26 99.23 99.30 98.70 98.84 99.15 99.17 98.89 99.19 99.03 98.80 98.77 98.90 99.24 99.26 99.03 99.29 99.28 99.20 99.20

9.96 9.53 8.23 8.23 9.10 8.23 8.23 8.23 10.4 9.53 8.66 8.66 9.53 8.66 8.66 9.53 9.96 9.53 8.23 8.23 9.10 8.23 8.23 8.23 8.23

7.36 6.50 5.63 5.63 6.50 5.63 6.06 5.63 7.80 6.93 6.06 6.06 6.93 6.06 6.50 6.93 6.93 6.50 5.63 5.63 6.06 5.63 5.63 5.63 5.63

97.98 98.27 98.65 98.67 98.36 98.63 98.61 98.70 97.97 98.22 98.61 98.57 98.22 98.58 98.55 98.30 98.04 98.28 98.66 98.66 98.37 98.67 98.69 98.70 98.70

an unknown input vector x as below: Pn _ i ¼ 1 yi :exp½  Dðx; xi Þ yi ¼ P n i ¼ 1 exp½  Dðx; xi Þ Dðx; xi Þ ¼

Validation

 m  X xi  xik 2 σk k¼1

ð6Þ

ð7Þ

where x stands for the input vector, xi is the ith element and xik is the kth data value in the input vector. yi is the weight connection between the pattern and summation layer, D is the radial basis (Gaussian) function, n and m are the number of the training patterns and input vector elements respectively, σ k is the smoothing factor (spread parameter) for the kth variable, whose optimal value is determined experimentally. During the training process,

the above calculation runs several times with different smoothing factors until reaching the desired threshold RMSE criterion [42,44]. 2.2.4. All-sky PAR model (ALSKY) Another efficient all-sky semi-empirical PAR model is also used in this study, the main thoughts can be described as investigating the dependence of hourly PAR on Kt and cosine of solar zenith angle μ. Here we take LSA station as an example to illustrate the main process of this ALSKY model. Half of the radiation data are used for model development, and the remaining data for model validation. As shown in Fig. 3, the hourly PAR generally increases exponentially with μ for a giving Kt interval, which is suggested to be described with power law equation [21–24,30,45]: PAR ¼

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Fig. 6. The PAR estimates of the optimal models for the ALF Station in forest ecosystem.

PARm  μb, where PARm is the maximum PAR per μ and b decides how PAR changes with μ. The relationship between PARm and Kt is explored by first binning Kt in 0.02 increments beginning at 0.03, power law equation is used to fit the data in each bin to obtain the hourly maximum PAR at one unit μ. Then, the parameters of ALSKY model can be finally calculated through analyzing the relationship between hourly PAR and μ [22,45].

3. Model applications and results 3.1. Comparison statistics The comparison statistics (in percentage) used in the present study includes root mean square errors (RMSE), mean absolute errors (MAE) and determination coefficient (R2). The comparison statistics can be expressed as vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi u N u1 X ðXmi  Xoi Þ2 RMSE ¼ t ð8Þ Ni¼1 MAE ¼

n 1X jXmi  Xoi j Ni¼1

 Pn R2 ¼ P

  2 Xmi  Xm Xoi  Xo  2 Pn  2 Xmi  Xm i ¼ 1 Xoi  Xo

ð9Þ

i¼1

n i¼1



ð10Þ

where N and bar respectively indicate the number of data and mean of the variable, Xm and Xo are the modeled and observed hourly PAR. 3.2. Modeling hourly PAR in different ecosystems in China In this study, three different ANN methods, MLP, GRNN and RBNN were used for modeling hourly PAR in different ecosystems (classified by Farmland, Wetlands, Forest, Grassland, Bay, Desert and Lake) in China using global solar radiation (Eg), air

temperature (TA), relative humidity (RH), dew point (TD), water vapor pressure (VW), air pressure (PA) as inputs to the models. Before applying MLP, GRNN and RBNN methods to the data, the input and output values were normalized using the following equation b1

xi  xmin þ b2 xmax  xmin

ð11Þ

where xmin and xmax indicate the minimum and maximum values of the dataset, respectively; xi is the observed value of the variable at time i. Scaling factors a1 and a2 can take different values. In this study, 0.8 and 0.2 were assigned for the b1 and b2, respectively, thus, training data were scaled in the range [0.2, 0.8]. Considering the correlations between each input and PAR, the following input combinations were selected and tried as: i) Eg; ii) Eg and PA; iii) Eg and TA; iv) Eg and TD; v) Eg and RH; vi) Eg and VW; vii) Eg, TA and RH; viii) Eg, TA, RH, PA, TD and VW. Different hidden node numbers are tried for the MLP and RBNN models and the optimal ones that gave the lowest RMSE values are selected for each input combination. For the RBNN and GRNN models, different spread constants have been tried and the optimal values are obtained for each model. The optimal ANN models are compared with the semi-empirical ALSKY model in Table 2 for the farmland stations (LSA, YCA, AKA and FQA). For the LSA station, the RMSE values of the MLP, GRNN and RBNN model range 17.52–18.82, 16.55–17.84 and 17.52–18.82, respectively; the MAE values range 13.63–13.95, 13.30–13.95, 13.63–13.95, respectively. The GRNN and ALSKY models have almost same accuracy and they perform better than the other models. The GRNN model has slightly better accuracy than the ALSYK from the MAE and R2 viewpoints (MAE and R2 are 13.30 and 98.28, respectively for Eg and TD inputs). For the YCA station, the RMSE values of the MLP, GRNN and RBNN model range 10.20–11.11, 10.23–11.73 and 10.06–11.49, respectively; MAE values for MLP, GRNN and RBNN model range 7.2–8.0, 7.67–8.83 and 7.06– 8.48, respectively. The RBNN with Eg and PA inputs seem to be slightly better than the other models (RMSE, MAE and R2 are 10.06, 7.14 and 98.29, respectively). For the AKA station, the RMSE values of the MLP, GRNN and RBNN range 7.12–8.62, 7.49–8.99 and 7.12–

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Table 5 Comparison of ANN and empirical ALSKY models in modeling PAR for bay stations. Model

Input

Validation RMSE

JZB station MLP

GRNN

RBNN

ALSKY SYB station MLP

GRNN

RBNN

ALSKY

Test MAE

R2

RMSE

MAE

R2

Eg Eg and PA Eg and TA Eg and TD Eg and RH Eg and VW Eg, TA and RH Eg, TA, RH, PA, TD and VW Eg Eg and PA Eg and TA Eg and TD Eg and RH Eg and VW Eg, TA and RH Eg, TA, RH, PA, TD and VW Eg Eg and PA Eg and TA Eg and TD Eg and RH Eg and VW Eg, TA and RH Eg, TA, RH, PA, TD and VW KT , μ

8.63 8.13 8.13 7.62 8.13 7.62 8.13 8.13 8.63 8.63 8.63 8.63 8.63 8.63 9.14 10.2 8.63 8.13 7.62 7.62 8.13 7.62 8.13 8.13 7.11

6.10 6.10 5.59 5.59 6.10 5.59 5.59 5.59 6.60 6.60 6.10 6.10 6.60 6.10 6.60 7.11 6.10 6.10 5.59 5.59 6.10 5.59 5.59 6.09 5.08

98.72 98.89 98.95 98.97 98.81 98.98 98.94 98.90 98.67 98.78 98.86 98.87 98.71 98.86 98.79 98.50 98.73 98.92 98.97 98.99 98.80 99.00 98.96 98.90 99.10

13.37 11.07 11.53 10.61 11.99 11.07 11.53 11.53 14.30 11.99 12.45 11.53 13.37 11.53 12.91 13.38 13.37 11.07 11.53 10.61 12.45 10.61 11.53 11.99 11.07

10.2 8.30 8.30 7.84 8.76 7.84 8.30 8.30 10.6 8.76 9.22 8.76 10.2 8.76 9.68 9.69 10.2 7.84 8.30 7.84 9.22 7.84 8.30 8.76 8.30

97.29 98.36 98.07 98.34 97.84 98.30 98.13 98.30 97.22 98.31 98.08 98.29 97.54 98.26 97.90 97.90 97.31 98.37 98.10 98.35 97.74 98.37 98.15 98.10 98.30

Eg Eg and PA Eg and TA Eg and TD Eg and RH Eg and VW Eg, TA and RH Eg, TA, RH, PA, TD and VW Eg Eg and PA Eg and TA Eg and TD Eg and RH Eg and VW Eg, TA and RH Eg, TA, RH, PA, TD and VW Eg Eg and PA Eg and TA Eg and TD Eg and RH Eg and VW Eg, TA and RH Eg, TA, RH, PA, TD and VW KT , μ

12.71 13.08 13.44 14.17 14.17 14.17 14.17 14.53 12.71 12.71 13.08 13.80 12.71 13.80 13.44 13.44 12.71 12.71 13.08 13.80 13.80 13.44 13.80 13.80 13.08

9.08 9.08 9.44 10.2 10.2 10.2 10.2 10.5 9.44 9.44 9.81 10.5 9.81 10.9 10.2 10.5 9.08 9.08 9.08 9.81 9.81 9.44 10.2 10.2 9.44

97.94 98.02 98.01 98.03 97.91 98.03 97.94 98.00 97.83 97.83 97.96 97.74 97.57 97.73 97.67 97.70 98.00 98.00 98.08 97.99 97.79 97.87 97.97 97.60 98.00

16.61 17.36 17.36 17.74 17.74 17.74 17.74 17.74 16.23 16.61 16.98 16.61 15.85 16.61 16.98 16.98 16.98 17.36 17.36 17.74 17.36 17.74 17.74 18.11 17.36

13.59 14.34 14.34 14.34 14.34 14.72 14.72 14.34 13.96 14.34 14.34 14.72 13.96 14.72 14.72 14.72 13.96 13.96 13.96 14.34 14.34 14.34 14.34 14.72 14.34

99.47 99.45 99.37 99.43 99.46 99.39 99.40 99.30 99.25 99.20 99.24 99.03 98.92 98.98 98.79 98.60 99.55 99.48 99.47 99.38 99.41 99.38 99.36 99.10 99.50

8.99, respectively; MAE values for MLP, GRNN and RBNN model range 5.23–6.74, 5.62–7.12 and 5.24–6.74, respectively. The MLP and RBNN models whose inputs are the Eg and TA (RMSE, MAE and R2 are 7.12, 5.24 and 98.90, respectively) perform better than the GRNN and ALSYK models. For the FQA station, the RMSE values of the MLP, GRNN and RBNN range 11.57–12.96, 11.57–13.89 and 11.57–12.96, respectively; the MAE values for MLP, GRNN and RBNN model range 8.33–9.26, 8.33–9.26 and 8.33–9.26, respectively. It is clear from Table 2 that all the models show the same performance in modeling hourly PAR for this station. It should be noted that the TA and PA variables generally have more effects on hourly PAR than the RH, TD and VW variables in the farmland stations. The estimates of the MLP, GRNN and RBNN models comprising Eg and TD inputs are compared with the semi-empirical ALSYK model in Fig. 4 in the form of

scatterplot for the FQA station. The difference between the ANN and ALSKY model is not clearly seen for the high PAR values (41 mol m  2 h  1). The ANN models give overestimations for the low PAR values (o1 mol m  2 h  1) while the ALSKY model provides underestimations. Table 3 gives the comparisons of optimal ANN models and semi-empirical ALSKY model for the wetland SJM station. The RMSE values of the MLP, GRNN and RBNN range 18.18–18.67, 17.69–18.18 and 18.18–18.67, respectively; MAE values range 12.28–12.78, 12.28–12.78 and 11.79–12.78, respectively. The MLP, RBNN and ALSKY models gave almost the same estimates and their accuracy inferior to GRNN model comprising Eg input. Similar to the farmland FQA station, the estimates of the optimal ANN and ALSYK models are shown in Fig. 5. The ANN models overestimate

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Fig. 7. The PAR estimates of the optimal models for the SYB station in bay ecosystem.

lower PAR values while the semi-empirical ALSKY model gives underestimations. The optimal ANN models are compared with ALSKY model in Table 4 for the forest stations (ALF and CBF). For the ALF station, the RMSE values of the MLP, GRNN and RBNN range 17.51–18.01, 16.51–17.51 and 17.51–18.01, respectively; MAE values for MLP, GRNN and RBNN models range 12.01–13.01, 12.01–13.01 and 12.01–12.51, respectively. All three ANN methods seem to be better than the ALSKY model which the RMSE, MAE and R2 values are 18.01, 12.51 and 97.30, respectively. Among the ANN methods, the GRNN has the lowest RMSE (16.51) and MAE (12.01) for Eg and PA inputs. For the CBF station, the RMSE values of the MLP, GRNN and RBNN range 8.23–9.96, 6.06–6.93 and 5.63–6.93, respectively; MAE values range 5.63–7.36, 6.06–7.80 and 5.63–6.93, respectively. The MLP, RBNN and ALSKY models have almost same accuracy which perform better than the GRNN models in estimating hourly PAR. As an example, the estimates of the MLP, GRNN and RBNN models comprising Eg and TA inputs are compared with ALSYK model in Fig. 6 for the ALF station. It is clear that the ANN models have less scattered estimates for the high PAR values ( 4 1 mol m  2 h  1) than the semi-empirical ALSKY model while the ALSKY model gives closer estimates to the low values. The comparisons of the optimal ANN and ALSKY models are made in Table 5 for the bay stations (JZB and SYB). For the JZB station, the RMSE values of the MLP, GRNN and RBNN range 10.61–13.37, 11.53–14.30 and 10.61–13.37, respectively; MAE values for MLP, GRNN and RBNN models range 7.84–10.2, 8.76– 10.6 and 7.84–10.2, respectively. It is clear from the table that the ANN models provide better estimates than the ALSKY model. Among the ANN methods, the MLP and RBNN have the lowest RMSE (10.61) and MAE (7.84) for Eg and TD inputs. For the SYB station, the RMSE values of the MLP, GRNN and RBNN models range 16.61–17.74, 15.85–16.98 and 16.98–18.11, respectively; MAE values range 13.59–14.72, 13.96–14.72 and 13.96–14.34, respectively. Here three ANN methods also provide better accuracy than the semi-empirical ALSKY model. The

GRNN model with Eg and RH inputs (RMSE, MAE and R2 are 15.85, 13.96 and 98.92, respectively) performs better than the MLP and RBNN models in estimating hourly PAR. It clear from Table 5 that the RH variable generally has more effect on hourly PAR than the TA, PA, TD and VW variables in the bay stations; for example, the estimates of the optimal MLP, GRNN, RBNN and ALSYK models are illustrated in Fig. 7 for the SYB station. Similar to the previous applications, the MLP and GRNN models significantly overestimate low PAR values while the RBNN and ALSKY slightly overestimates and underestimates, respectively. The ALSKY model have more scattered estimates than the ANN models for the medium values. Table 6 indicates the validation and test accuracies of the optimal ANN and ALSKY models for the grassland stations (NMG and HBG). For the NMG station, the RMSE values of the MLP, GRNN and RBNN range 11.18–15.87, 15.14–16.59 and 12.62– 15.14, respectively; MAE for MLP, GRNN and RBNN models range 8.65–9.74, 9.38–10.8 and 8.29–10.5, respectively. Table 6 clearly indicates that the MLP model with Eg, TA, RH, PA, TD and VW inputs and ALSKY model (RMSE, MAE and R2 are 11.18, 8.29 and 98.50, respectively) produce almost the same accuracy and they perform better than the GRNN and RBNN in hourly PAR prediction. For the HBG station, the RMSE values of the MLP, GRNN and RBNN range 13.67–15.57, 13.29–15.57 and 14.05–15.95, respectively; MAE values all range from 9.49 to 11.4 for each ANN model. All three ANN methods perform better than the ALSKY model (RMSE, MAE and R2 are 15.19, 11.0 and 96.3, respectively). Among the ANN methods, the GRNN model with Eg input provides better accuracy than the MLP and RBNN models in estimating hourly PAR. It is apparent from Table 6 that adding TA, RH, PA, TD and VW into the input combinations do not increase the model accuracies. As an example, the estimates of the optimal MLP, GRNN, RBNN and ALSYK models are illustrated in Fig. 8 for the HBG station. All three ANN models provide better (less scattered) estimates than the ALSKY model in hourly PAR estimation. However, the MLP and GRNN models give some overestimations for the low PAR values.

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Table 6 Comparison of ANN and empirical ALSKY models in modeling PAR for grassland stations. Model

NMG station MLP

GRNN

RBNN

ALSKY HBG station MLP

GRNN

RBNN

ALSKY

Input

Validation

Test

RMSE

MAE

R2

RMSE

MAE

R2

Eg Eg and PA Eg and TA Eg and TD Eg and RH Eg and VW Eg, TA and RH Eg, TA, RH, PA, TD and VW Eg Eg and PA Eg and TA Eg and TD Eg and RH Eg and VW Eg, TA and RH Eg, TA, RH, PA, TD and VW Eg Eg and PA Eg and TA Eg and TD Eg and RH Eg and VW Eg, TA and RH Eg, TA, RH, PA, TD and VW KT, μ

14.00 12.52 13.26 13.63 13.63 13.63 13.26 9.210 14.73 14.37 14.73 14.00 14.37 14.00 14.37 14.73 11.05 12.89 12.16 12.16 12.16 12.16 11.79 11.79 9.940

8.10 8.10 8.10 8.47 8.10 7.74 8.47 7.00 8.84 8.84 8.84 8.47 8.84 8.47 9.21 9.58 8.84 8.10 7.74 8.10 8.10 7.74 7.74 8.10 7.73

95.71 96.59 96.22 96.25 95.98 96.13 96.35 98.50 95.69 95.70 95.95 96.05 95.91 96.22 96.05 95.80 97.64 96.49 97.16 96.99 96.82 97.01 97.15 97.20 98.80

15.87 14.78 15.14 15.51 15.51 15.14 15.14 11.18 16.23 16.23 15.51 15.14 16.23 15.14 15.87 16.59 12.98 15.14 13.70 13.70 14.42 14.06 12.62 14.06 11.18

9.74 9.74 9.01 9.74 9.74 8.65 9.74 8.65 10.1 10.1 9.74 9.38 10.1 9.38 10.1 10.8 10.5 9.74 9.01 9.01 9.38 9.01 8.29 9.38 8.29

95.15 95.91 95.64 95.70 95.34 95.64 95.76 98.10 95.25 95.16 95.75 95.87 95.30 95.95 95.66 95.20 97.28 95.61 96.63 96.57 96.12 96.45 96.97 96.60 98.50

Eg Eg and PA Eg and TA Eg and TD Eg and RH Eg and VW Eg, TA and RH Eg, TA, RH, PA, TD and VW Eg Eg and PA Eg and TA Eg and TD Eg and RH Eg and VW Eg, TA and RH Eg, TA, RH, PA, TD and VW Eg Eg and PA Eg and TA Eg and TD Eg and RH Eg and VW Eg, TA and RH Eg, TA, RH, PA, TD and VW KT, μ

9.19 9.19 8.48 8.48 8.84 8.48 8.48 8.13 9.19 9.19 8.84 8.48 9.19 8.48 8.48 8.84 9.19 9.19 8.48 8.48 8.84 8.48 8.13 8.48 8.48

6.36 6.01 5.30 5.30 6.01 5.30 4.95 4.95 6.72 6.36 5.66 5.66 6.36 5.66 5.30 5.66 6.36 6.01 5.30 4.95 6.01 4.95 4.95 5.30 5.30

98.16 98.21 98.39 98.50 98.27 98.50 98.51 98.50 98.11 98.15 98.31 98.41 98.18 98.44 98.42 98.30 98.20 98.24 98.41 98.51 98.31 98.52 98.56 98.50 98.50

13.67 14.05 15.19 15.57 14.05 15.57 15.57 15.57 13.29 13.67 14.81 15.19 13.67 15.19 15.19 15.57 14.05 14.43 15.19 15.57 14.43 15.95 15.57 15.95 15.19

9.49 9.87 10.6 11.4 9.87 11.4 11.0 11.4 9.49 9.87 11.0 11.0 9.87 11.4 11.4 11.4 9.49 9.11 10.6 11.4 9.87 11.4 11.0 11.4 11.0

97.02 96.81 96.30 95.96 96.82 95.92 96.05 96.00 96.97 96.71 96.16 96.05 96.80 95.80 95.96 95.80 96.94 96.77 96.26 95.95 96.69 95.88 96.00 95.90 96.30

The optimal ANN models are compared with empirical ALSKY model in Table 7 for the desert stations (FKD and SPD). For the FKD station, the RMSE values of the MLP, GRNN and RBNN models range 6.06–9.63, 6.42–7.14 and 6.42–7.14, respectively; MAE values range 4.28–6.78, 4.64–5.35 and 4.28–4.99, respectively. It is obviously seen from the table that the MLP model with Eg, TA, RH, PA, TD and VW inputs (RMSE, MAE and R2 are 6.06, 4.28 and 99.1, respectively) performs better than the GRNN, RBNN and ALSKY models which have almost same accuracy in hourly PAR estimation. For the SPD station, the RMSE values of the MLP, GRNN and RBNN range 7.19–9.96, 7.19–11.1 and 7.19–9.96, respectively; MAE values range 4.92–7.38, 5.30–8.12 and 4.92–7.38, respectively. The ANN methods show better performances than the ALSKY model. It clear from Table 7 that the TD variable generally has more effect on

hourly PAR than the TA, RH, PA and VW in the desert stations. As an example, the estimates of the optimal MLP, GRNN, RBNN and ALSYK models are illustrated in Fig. 9 for the SPD station. Similar to the SYB (bay ecosystem) and HBG (grassland ecosystem) stations, the RBNN model does not provide significantly overestimations for the low PAR values when compared to the MLP and GRNN models. Table 8 reports the comparisons of ANN models with ALSKY model for the lake stations (DHL and THL). For the DHL station, the RMSE values of the MLP, GRNN and RBNN range 12.97–13.47, 12.47–13.47 and 12.97–13.47, respectively; MAE values all range from 8.98 to 9.48 for each model. From the table, it is clear that the GRNN model (RMSE and MAE are 12.47 and 8.98, respectively) performs better than the MLP, RBNN and ALSKY models

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Fig. 8. The PAR estimates of the optimal models for the HBG station in grassland ecosystem.

which have almost same accuracy. For the THL station, the RMSE values of the MLP, GRNN and RBNN range 6.95–8.49, 7.72–9.26 and 9.26–11.58, respectively; MAE values range 6.95–8.49, 7.72– 9.26 and 6.95–8.49, respectively. The superior accuracy of the ANN models are clearly seen from the table, the VW seems to have more effect on hourly PAR than the other variables in the lake stations. As an example, the estimates of the optimal MLP, GRNN, RBNN and ALSYK models are illustrated in Fig. 10 for the THL station. Similar to the farmland FQA station, here also the difference between the ANN and semi-empirical ALSKY model is not clearly seen for the high PAR values ( 4 1 mol m  2 h  1). The ANN models give overestimations for the low values ( o 1 mol m  2 h  1) while the ALSKY provides slightly underestimations. It is clear from the Figs. 4–10 that the ANN models generally underestimate low hourly PAR values, which may due to the fact that these models are trained (calibrated) using the RMSE criterion. This leads the ANN models significantly underestimate low hourly PAR values.

4. Discussion It can be seen from above analysis that there are relative lower statistical indices (RMSE and MAE) at AKA station and higher deviations at LSA and FQA stations (for the agricultural farmland stations). The Eg and TA inputs bring the most accurate hourly PAR estimations for AKA station. For the wetland SJM station, the GRNN model produces slightly lower RMSE values, especially with Eg and TA (or PA) inputs. For the forest sites, the RMSE and MAE values at CBF station are lower than those at ALF station. Adding the RH parameter into the ANN models would not increase the model accuracies, which indicates that RH is not a key variable influencing the hourly PAR variations at CBF station. The statistical indices (RMSE and MAE) at JZB station for all ANN models are generally lower than those at SYB station, and Eg and TD inputs produce more accurate estimations at JZB stations. Similarly, ANN models bring lower values of RMSE and MAE at

FKD station, and the TD, TA and VW are the important factors influencing the hourly variations of PAR. For the lake stations, PA and TA are the main variables determining the model accuracy at DHL station, while TD, VW and RH are more important parameters in hourly PAR evolutions at THL station. It is clear from above analysis, different meteorological parameters play different roles in different ecosystems (and stations) and there are also some differences in model accuracies at each type of station for the ANN models. The accuracy ranks of the ANN and ALSKY models are further given in Table 9. It is clear from the table that the overall rank of the methods’ accuracies are: MLP, RBNN, GRNN and ALSKY. The overall results obtained from above 15 stations in different ecosystems indicated that all the ANN models generally performed better than the semi-empirical ALSKY model. The main advantage of ANN model is its flexibility and capability to model nonlinear relationships. Mathematically, an ANN model can be accepted as a universal approximation [46]. This method has already become a promising research area owing to the ease of application and simple formulation [46,47]. All the ANN models significantly overestimated the low PAR values at all stations. The reason should be the fact that the ANN models are obtained according to the RMSE criterion which implies that the high PAR values are much more effective on model accuracy than the low values. Among the ANN methods, the MLP and RBNN models were found to have better accuracy than the GRNN in predicting hourly PAR. This result is compatible with the relevant literature [48–50]; for example, Kisi [48] investigated the accuracy of MLP, RBNN and GRNN models in estimating daily suspended sediment concentration and the results indicated that the MLP and RBNN methods provided better test results than the GRNN model [48]. The potential of different ANN techniques is also examined in modeling reference evapotranspiration by Kisi [49]. GRNN model gave inferior results when compared with MLP and RBNN models, for example, Seckin et al. [50] compared the accuracy of three different ANN methods in predicting flood

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Table 7 Comparison of ANN and empirical ALSKY models in modeling PAR for desert stations. Model

Input

Validation RMSE

FKD station MLP

GRNN

RBNN

ALSKY SPD station MLP

GRNN

RBNN

ALSKY

Test R2

MAE

RMSE

MAE

R2

Eg Eg and PA Eg and TA Eg and TD Eg and RH Eg and VW Eg, TA and RH Eg, TA, RH, PA, TD and VW Eg Eg and PA Eg and TA Eg and TD Eg and RH Eg and VW Eg, TA and RH Eg, TA, RH, PA, TD and VW Eg Eg and PA Eg and TA Eg and TD Eg and RH Eg and VW Eg, TA and RH Eg, TA, RH, PA, TD and VW KT , μ

7.23 6.87 6.87 6.87 6.87 6.87 5.06 6.58 7.60 7.23 7.23 7.23 7.60 7.23 7.23 8.04 7.23 6.87 6.87 6.87 6.87 6.87 6.51 6.58 5.85

5.43 4.70 4.70 4.70 5.06 4.70 3.98 4.75 5.43 5.06 5.06 5.06 5.43 5.06 5.06 5.48 5.06 4.70 4.70 4.70 5.06 4.70 4.34 4.39 4.02

98.76 98.99 98.99 98.99 98.89 98.99 99.35 99.00 98.78 98.93 98.92 98.89 98.80 98.93 98.90 98.70 98.84 98.99 99.01 98.99 98.89 98.99 99.05 99.10 99.20

7.14 6.78 6.42 6.42 6.78 6.42 9.63 6.06 7.14 6.78 6.42 6.42 7.14 6.42 6.42 7.14 7.14 6.78 6.42 6.42 6.78 6.42 6.42 6.42 6.42

4.99 4.64 4.28 4.28 4.99 4.28 6.78 4.28 4.99 4.99 4.64 4.64 5.35 4.64 4.64 4.99 4.99 4.64 4.64 4.28 4.99 4.28 4.28 4.28 4.64

98.73 98.93 99.02 98.99 98.81 99.02 98.27 99.10 98.74 98.90 98.99 98.92 98.74 98.97 98.97 98.80 98.78 98.93 98.99 99.01 98.81 99.01 99.00 99.00 99.10

Eg Eg and PA Eg and TA Eg and TD Eg and RH Eg and VW Eg, TA and RH Eg, TA, RH, PA, TD and VW Eg Eg and PA Eg and TA Eg and TD Eg and RH Eg and VW Eg, TA and RH Eg, TA, RH, PA, TD and VW Eg Eg and PA Eg and TA Eg and TD Eg and RH Eg and VW Eg, TA and RH Eg, TA, RH, PA, TD and VW KT , μ

12.55 12.18 11.07 10.33 11.81 12.18 10.33 7.190 12.92 12.92 11.44 11.44 12.55 12.92 11.07 7.190 12.18 11.81 11.07 10.33 11.81 10.33 10.33 7.190 6.810

9.96 9.60 8.12 7.38 9.23 9.60 7.38 4.92 10.3 10.3 8.86 8.86 10.3 10.3 8.12 5.30 9.60 9.23 8.12 7.38 9.23 7.38 7.38 4.92 4.92

97.74 97.87 98.34 98.51 97.85 97.91 98.49 98.90 97.76 97.77 98.26 98.36 97.79 97.79 98.36 98.90 97.81 97.97 98.36 98.54 97.87 98.54 98.55 98.90 99.00

8.33 7.95 7.19 7.19 8.33 7.95 7.19 9.96 8.33 8.33 7.57 7.19 8.33 8.33 7.19 11.1 8.33 7.95 7.19 7.19 8.33 7.19 7.19 9.96 10.3

6.05 5.68 4.92 4.92 6.05 6.05 4.92 7.38 6.43 6.43 5.30 5.30 6.43 6.43 5.30 8.12 6.05 5.68 4.92 5.30 6.05 4.92 4.92 7.38 8.12

98.52 98.64 98.88 98.88 98.59 98.62 98.86 98.50 98.52 98.53 98.79 98.93 98.57 98.54 98.87 98.40 98.54 98.74 98.88 98.88 98.59 98.93 98.95 98.60 98.60

peaks of various return periods at ungauged sites and the MLP and RBNN models performed better than the GRNN method; Pinar et al. [51] investigated the accuracy of MLP, RBNN and GRNN models in estimating backwater through arched bridge constrictions with normal and skewed crossings and it is found that the MLP and RBNN models produced more accurate predictions. The main advantages of MLP model are: 1) MLP makes global approximations, while RBNN approximates locally nonlinear input–output relationships; 2) MLP may need less number of parameters than the RBNN model for reaching the same accuracy [52]. Even though its inferior results, the GRNN model may be preferred instead of MLP because of the following advantages: 1) The MLP accuracy is very sensitive to

randomly assigned initial weight values [53]; 2) The GRNN does not need an iterative training process [54,55]; 3) there is not the local minima problem for GRNN model. At the same time, the major factors influencing the hourly variations of PAR may differ greatly from each ecosystem (and station); for example, the LSA station is located in the Qinghai– Tibet Plateau (the detailed climatic characteristics can be seen at Cheng and Wang [56]), where the air is dry and thin in the atmosphere, so the hourly PAR is more sensitive to the changes of water vapor (T D , V W and R H), so the model accuracy (using T D as input) is slightly higher than other parameters (Table 2). YCA, FQA and AKA station belong to the zone of temperate climate (enough sunlight), the diurnal variations of P A and T A

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Fig. 9. The PAR estimates of the optimal models for the SPD station in desert ecosystem.

are relatively larger than those at the subtropical zone (for example, the ALF and DHL station), so the input combinations of P A and T A may determine the hourly PAR variations for agricultural farmland stations to a certain extent. The climate of ALF station is mild and humid, the annul mean T A and rainfall amount are about 11.3 °C and 1931 mm, respectively, while the annual mean T A is the range of  7 to 3 °C (the monthly mean T A in July is also lower than 10 °C ) at CBF station; the annual rainfall amount is below 1400 mm, so it is reasonable to say that the T A (and T D ) is more important for estimating hourly PAR at CBF stations. Meanwhile, both SPD and FKD stations are in the arid desert region, the determining factor for the variations of solar radiation should be the T A and V W; the altitude for HBG station is about 3280 m, so the meteorological parameter PA may largely influences the hourly PAR variations when compared with above desert stations. Moreover, the DHL and THL stations are in the monsoon climate region (subtropical monsoon climate), it is cold and dry in winter for the intrusions of northwest cold air, hot and humid in summer due to the effects of subtropical high pressure (tropical storms and typhoons), so VW may also play important roles in regulating the PAR evolutions at lake stations in this study. In general, one important reason for the different model results at different ecosystems is related to the local climatic and geographical conditions at each station.

5. Conclusion Three ANN-models (Multi layer Perceptron, Generalized Regression Neural Network, and Radial Basis Neural Network) are proposed for predicting hourly PAR using radiation and meteorological observations from the year 2005 to 2012 at 15 stations in different ecosystems. The ANN-models have been tested and validated at each station and the model results are further compared with a semi-emperical ALSKY model using statistical indices RMSE and MAE. Both models can bring out satisfied

hourly PAR estimations, but there are some differences in model accuracies for each type of ecosystem (and each station); the meteorological variables play different roles in different ecosystems for each ANN-model. The main results can be summarized as: For the agricultural farmland stations (LSA, YCA, AKA and FQA), the ANN-models perform better at AKA station with lower values of RMSE and MAE, and MLP and RBNN models whose inputs are the Eg and TA (RMSE, MAE and R2 are 7.12, 5.24 and 98.90, respectively) perform better than the GRNN and ALSYK models. Generally, the combinations of TA and PA variables have more effects on hourly PAR than the RH, TD and VW variables. The ANN models overestimates the low PAR values (o1 mol m  2 h  1) while the ALSKY model provides underestimations in the farmland stations. For the forest stations, the GRNN model produces the lowest RMSE (16.51) and MAE (12.01) for Eg and PA inputs at ALF station, while MLP, RBNN and ALSKY models perform better than the GRNN model. The ALSKY model gives closer estimates to the low PAR values, and the ANN models have less scattered estimates for the high PAR values ( 4 1 mol m  2 h  1). It is also indicated that RH is not a key variable influencing the hourly PAR variations. For the bay stations, the ANN models generally provide better estimates than the ALSKY model. The MLP and RBNN models have the lowest RMSE (10.61) and MAE (7.84) for Eg and TD inputs at JZB station while GRNN model with Eg and RH inputs performs better than the MLP and RBNN models at SYB station. MLP and GRNN models significantly overestimate low PAR values while the RBNN and the ALSKY model slightly overestimates and underestimates, respectively. For the grassland stations, the MLP and ALSKY model (RMSE, MAE and R2 are 11.18, 8.29 and 98.50, respectively) bring more accurate hourly PAR estimations than the GRNN and RBNN models at NMG station, while GRNN model with Eg input provides the lowest statistical indices at HBG station. For the wetland SJM station, the GRNN model comprising Eg input produces slightly lower RMSE values.

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Table 8 Comparison of ANN and empirical ALSKY models in modeling PAR for lake stations. Model

DHL station MLP

GRNN

RBNN

ALSKY THL station MLP

GRNN

RBNN

ALSKY

Input

Validation

Test

RMSE

MAE

R2

RMSE

MAE

R2

Eg Eg and PA Eg and TA Eg and TD Eg and RH Eg and VW Eg, TA and RH Eg, TA, RH, PA, TD and VW Eg Eg and PA Eg and TA Eg and TD Eg and RH Eg and VW Eg, TA and RH Eg, TA, RH, PA, TD and VW Eg Eg and PA Eg and TA Eg and TD Eg and RH Eg and VW Eg, TA and RH Eg, TA, RH, PA, TD and VW KT, μ

8.29 6.90 6.90 6.44 7.36 6.44 6.44 6.45 8.75 7.83 7.83 7.36 8.75 7.36 8.29 9.21 7.83 6.90 6.90 6.44 7.36 5.98 6.44 6.45 6.45

5.98 5.52 5.06 5.06 5.52 4.60 5.06 5.06 6.44 5.98 5.98 5.52 6.44 5.52 6.44 6.91 5.98 5.52 5.06 4.60 5.52 4.60 5.06 5.06 5.06

98.97 99.30 99.32 99.35 99.13 99.34 99.35 99.40 98.94 99.21 99.22 99.29 98.91 99.30 99.13 98.80 99.01 99.31 99.34 99.38 99.13 99.40 99.32 99.30 99.40

12.97 12.97 12.97 13.47 13.47 13.47 13.47 13.47 12.47 12.47 12.47 12.97 12.47 12.97 12.97 13.47 12.97 12.97 12.97 13.47 12.97 13.47 13.47 13.47 12.97

9.48 9.48 9.48 9.48 9.48 9.48 9.48 9.48 9.48 8.98 8.98 9.48 8.98 9.48 9.48 9.48 8.98 8.98 8.98 9.48 9.48 9.48 9.48 9.48 9.48

98.23 98.25 98.36 98.21 98.20 98.20 98.27 98.20 98.26 98.18 98.27 98.16 98.21 98.16 98.15 98.00 98.32 98.27 98.37 98.25 98.22 98.24 98.26 98.20 98.30

Eg Eg and PA Eg and TA Eg and TD Eg and RH Eg and VW Eg, TA and RH Eg, TA, RH, PA, TD and VW Eg Eg and PA Eg and TA Eg and TD Eg and RH Eg and VW Eg, TA and RH Eg, TA, RH, PA, TD and VW Eg Eg and PA Eg and TA Eg and TD Eg and RH Eg and VW Eg, TA and RH Eg, TA, RH, PA, TD and VW KT, μ

12.45 11.32 10.94 10.19 10.56 9.810 9.810 9.810 13.20 12.07 11.70 11.32 12.45 11.32 12.07 12.07 12.07 11.32 10.94 9.810 10.94 9.810 9.810 10.18 10.94

9.43 8.68 8.30 7.55 7.92 7.55 7.55 7.54 9.81 9.43 9.05 8.68 9.81 8.68 9.05 9.43 9.05 8.68 8.30 7.55 7.92 7.17 7.55 7.54 8.30

98.64 99.24 99.35 99.42 98.98 99.41 99.39 99.4 98.61 99.20 99.28 99.34 98.77 99.33 99.17 99.00 98.67 99.25 99.32 99.36 99.01 99.27 99.42 99.40 99.30

11.58 10.42 10.04 9.650 10.42 9.260 9.260 9.260 12.35 11.19 10.81 10.42 11.97 10.42 10.81 11.19 11.58 10.42 10.04 9.260 10.42 9.260 9.260 9.650 10.42

8.49 7.72 7.33 7.33 7.72 6.95 6.95 6.95 9.26 8.49 8.11 7.72 8.88 7.72 8.11 8.49 8.49 7.72 7.33 6.95 7.72 6.95 6.95 6.95 7.33

98.28 98.94 99.18 99.26 98.76 99.27 99.22 99.30 98.26 98.92 99.14 99.20 98.56 99.21 99.11 99.00 98.33 98.94 99.15 99.22 98.82 99.18 99.25 99.20 99.00

For the desert stations, the MLP model (RMSE, MAE and R2 are 6.06, 4.28 and 99.1, respectively) performs better than the GRNN, RBNN and ALSKY models at FKD station, and the TD variable generally has more effect on hourly PAR predictions than the TA, RH, PA and VW in the desert stations. For the lake stations, the GRNN model (RMSE and MAE are 12.47 and 8.98, respectively) performs better than other methods at DHL station, and the VW is the most important parameter influencing the hourly PAR variations in the lake stations. From above, it can be concluded that the MLP and RBNN models are more accurate in estimating hourly PAR at different ecosystems in China, which will be of vital importance for terrestrial photosynthesis modeling and surface energy budget. There

are different meteorological parameters determining the PAR variation patterns at different ecosystems, which suggested that more attention should be focused on the key influencing factors in estimating hourly PAR. The present study proposes to estimate hourly PAR using routine meteorological variables in different climatic regions, which will lay the foundation for accurately monitoring and mapping instantaneous PAR values at regional and global scales. Meanwhile, more effects dealing with the radiative transfer process and surface observations should be made to further improve the model applications. We will also validate and compare the model accuracy with satellite observations in our next work.

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Fig. 10. The PAR estimates of the optimal models for the THL station in lake ecosystem. Table 9 Accuracy rank of the MLP, GRNN, RBNN, ALSKY models in estimating hourly PAR. Station

MLP

GRNN

RBNN

ALSKY

LSA YCA AKA FQA SJM ALF CBF JZB SYB NMG HBG FKD SPD DHL THL Total

2 3 1 1 1 2 1 1 2 1 1 1 1 2 1 21

1 4 2 1 1 1 2 3 1 3 2 2 1 1 2 27

2 1 1 1 1 2 1 1 3 2 1 2 1 2 1 22

1 2 2 2 1 3 1 2 4 1 3 2 2 2 2 30

Acknowledgments This work was financially supported by National Basic Research Program (Grant no. 2011CB707106), National Natural Science Foundation of China (NSFC) (Program no. 41127901) and the Special Fund for Basic Scientific Research of Central Colleges, China University of Geosciences, Wuhan (No. CUG150631). We would like to thank the observation team of Chinese Ecosystem Research Network (CERN) for their hard work in collecting data.

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