The field experiment was conducted at the Mizhi Experimental Station of Northwest A& F University in the Chinese Loess Plateau (38° 11'N, 109° 28'E; 1049 m a.s.l.). The study area is characterized by a semi-arid temperate climate with mean annual precipitation of 451.6 mm and annual mean temperature of 8.4° C. It should be noted that most of the annual total precipitation occurs in the rainy season spanning from July to September. The annual sunshine duration and total radiation are 2761 h and 580.5 kJ/cm², respectively. Soil texture in the study area is loessial soil with mean soil bulk density (1.0-m depth) of 1.29 g/cm³, field capacity of 23%, and gravimetric water content of 5.16%. Groundwater table in the study area is more than 50 m.

2.2.1 Experimental design

The experiment site was in a rain-fed jujube orchard with tree spacing of 2 m× 3 m and total area of 4× 10³ m². Three 5-year jujube trees that grew uniformly (average height of 2 (± 0.12) m) near the center of the orchard were selected as the objectives of dew measurements. It should be stated that the dielectric leaf wetness sensor developed by Decagon Devices Inc. was found to be suitable for on-site dew measurement (Sentelhas et al., 2004). Thus, the dielectric leaf wetness sensor was used in this study for dew measurements. We established a micro-climate system including the dielectric leaf wetness sensors, VP-3 Relative Humidity/Temperature Sensor, High Resolution Rain Gauge and Davis Cup Anemometer near the center of the orchard to conduct field measurements.

2.2.2 Measurements

Field measurements were conducted from 26 July to 23 October, 2012 and from 24 June to 17 October, 2013. Specifically, three dielectric leaf wetness sensors (Decagon Devices Inc., USA) were respectively set up at the canopy top of the three selected jujube trees to monitor dew intensity and dew duration (precisions of 0.01 mm and 1 min, respectively). Furthermore, relative humidity and temperature, rainfall, and wind speed were measured using an automatic weather station (Decagon Devices Inc., USA) installed 2.0 m above the ground surface. Relative humidity and temperature were measured using a VP-3 Relative Humidity/Temperature Sensor (precisions of 1% and 0.1° C, respectively), rainfall was measured using a High Resolution Rain Gauge (precision of 0.2 mm), and wind speed was measured using a Davis Cup Anemometer (precision of 0.1 m/s). All these sensors were connected to a single Em50 data logger and the data were automatically recorded at 15-min intervals. The leaf area index (LAI) of trees was measured every 10 days using the Winscanopy analysis equipment (Regent Instruments Inc., Canada).

Based on field measurements, we established logistic functions of LAI with time in 2012 and 2013 using the Winscanopy 2005 software (Fig. 1).

Fig. 1

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	Fig. 1 Leaf area index (LAI) in 2012 and 2013. DOY, day of year.

In this study, the daily dew amount was defined as the maximum dew amount calculated from the highest dew intensity measured within a day (Zangvil, 1996). Dew amount at the i^th interval of time (W_di) was calculated as follows (Kabela et al., 2009; Xu et al., 2012):

$$W_{di}=I_i\times (2\times LAI_i), \ \ (1)$$

where, W_di is the dew amount at the i^th interval of time (mm); I_i is the dew intensity measured using the dielectric leaf wetness sensors at the i^th interval of time (mm); 2 represents the coefficient related to the upper and lower sides of the leaf; and LAI_i is the leaf area index measured at the i^th interval of time (m²/m²).

It is commonly accepted that leaf can acts as a reservoir because free water could accumulate on leaf surfaces through condensation. The capacity of leaf reservoir (W_max) was calculated by the following formula (Wilson et al., 1999):

$$W_{max}=2\times W_{leaf}\times LAI, \ \ (2)$$

where, W_leaf is the maximum potential capacity of leaf reservoir storing free water per unit leaf area (mm; W_leaf≤ 0.15 mm).

Daily dew duration refers to the cumulative duration of all dew events (free water from the air condenses and stays on the leaf surfaces) within one day. It can be calculated as follows:

$$DD=\sum^n_{i=1}T_i\ \ (3)$$

where, DD is the measured daily dew duration (h); T_i is the measured duration of the i^th dew event (h); and n is the total number of dew events per day.

2.4.1 Model description

We used the empirical models to estimate daily dew duration in this study and the following two empirical models were selected for daily dew duration estimation.

(1) Relative humidity model (RH model; Monteith, 1956): this model can conveniently estimate daily dew duration because relative humidity is the only parameter for estimation. Specifically, daily dew duration is equal to the number of hours with relative humidity greater than or equal to a specific threshold within a day.

(2) Dew point depression model (DPD model; Lawrence, 2005): in this model, dew point depression is the difference between air temperature and atmospheric dew point temperature (° C), which can be calculated using the Magnus-Tetens approximation method.

$$T_d=\frac{B_1(ln\frac{RH}{100}+\frac{A_1\times T}{B_1+T})}{A_1-(ln\frac{RH}{100}+\frac{A_1\times T}{B_1+T})}, \ \ (4)$$

where, T_d is the atmospheric dew point temperature (° C); RH is the relative humidity (%); T is the air temperature (° C); and B₁ and A₁ are constants, with the values of 243.04° C and 17.62, respectively.

The length of time that dew point depression remains between two critical temperatures of T₁ and T₂ (T₁< T₂) is regarded as the daily dew duration, where T₁ and T₂ are the threshold temperatures of wetness onset and dry-off (Gillespie et al., 1993).

2.4.2 Model calibration

The RH model and DPD model were calibrated through the following steps. First, the atmospheric dew point temperature was calculated using Equation 4. Second, the measured air temperature, relative humidity and dew duration combined with the calculated dew point depression (difference between air temperature and atmospheric dew point temperature) were employed to set up a database. Third, the initial thresholds of parameters in the RH model and DPD model were selected from previous studies (Rao et al., 1998; Kruit et al., 2004; Wang and Zhang, 2011) (Table 1). Fourth, each of the models was run at the step sizes of 1% in relative humidity and 0.1° C in dew point depression to estimate daily dew duration. Fifth, the relationship between estimated daily dew durations and measured daily dew durations was established by calculating the coefficient of determination (R²) using Equation 5. Sixth, steps (4) and (5) were repeated by changing the thresholds of parameters for the two models until the optimal thresholds appeared (corresponding to the highest R²). The final optimal thresholds of parameters for the two models are shown in Table 1. Then, daily dew duration could be estimated using the two models with the final optimal thresholds. More detailed information about the model calibration can be found in Li et al. (2010).

(5)

where, E_i is the estimated daily dew duration at the i^th day (h); \(\overline{E}\) is the average of estimated daily dew durations (h); O_i is the measured daily dew duration at the i^th day (h); \(\overline{O}\) is the average of measured daily dew durations (h); and n is the measurement days (n=55 d).

Table 1

Table 1

Table 1 Thresholds of parameters in the RH model and DPD model Model Parameter Threshold Initial Final RH model Relative humidity (%) 80 78 DPD model Dew point depression (° C) Wet leaf 1.8 1.0 Dry leaf 2.2 5.0 Note: RH model, relative humidity model; DPD model, dew point depression model. The initial thresholds were selected from the previous studies (Rao et al., 1998; Kruit et al., 2004; Wang and Zhang, 2011), while the final thresholds were determined from this study.

Table 1 Thresholds of parameters in the RH model and DPD model

2.4.3 Model verification

The performances of the two empirical models (RH model and DPD model) were verified using the following indices: coefficient of determination (R²), Willmott agreement index (W), confidence index (C), mean bias error (MBE) and mean absolute error (MAE) (Gao, 2004; Sentelhas et al., 2007).

(6)

(7)

(8)

(9)

where, E_i is the estimated daily dew duration at the i^th day (h); O_i is the measured daily dew duration at the i^th day (h); \(\overline{E_i}\) is the mean deviation of estimated daily dew durations (h); \(\overline{O_i}\) is the mean deviation of measured daily dew durations (h); and n is the measurement days (n=82 d).

In this study, all statistical analyses were performed using PASW Statistics 18.0 (SPSS Inc., Chicago, Illinois, USA). Significant differences of dew amounts versus the different meteorological factors at 15-min intervals were analyzed by Duncan’ s multiple comparison test at the 0.05 level. Furthermore, models were calibrated using R software (version 2.15.1), and all figures were plotted using Origin (version 2016).

In this study, we analyzed correlations between frequency of dew occurrence and main meteorological factors (including relative humidity, dew point depression, and wind speed) and between dew amount and main meteorological factors. It can be seen from Figure 2 that at 15-min intervals, dew formed (frequency of dew occurrence=5%) when relative humidity was in the range of 72%-78% and the cumulative frequency of dew occurrence reached up to 95% when the values of relative humidity were > 78% (Fig. 2a). For dew amount, it differed significantly among different levels of relative humidity (Ρ < 0.05; Fig. 2d). The average dew amount was 0.31 mm when relative humidity was > 90%, and was 0.11 mm when relative humidity was in the range of 72%-78%. These results demonstrated that relative humidity of 78% is an optimal threshold of relative humidity for dew formation, and dew will form more easily beyond the threshold.

Fig. 2

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Fig. 2 Frequency of dew occurrence (a, b, c) and dew amount (d, e, f) under different meteorological factors at 15-min intervals from 26 July to 23 October, 2012 and from 24 June to 17 October, 2013. “ ○” represents the average daily dew amount” ; “ × ” represents the minimum daily dew amount; “ +” represents the maximum daily dew amount; bars represent the standard errors. Different lowercase letters indicate significant difference at the P< 0.05 level (Duncan’ s multiple range test).

Figure 2b shows that the cumulative frequency of dew occurrence at 15-min intervals was 96% when dew point depression was in the range of 1° C-4° C and was 50% when dew point depression was in the range of 2° C-3° C. For dew amount, no significant difference was observed between the dew point depressions of 1° C-2° C and 2° C-3° C (average dew amounts of 0.64 and 0.58 mm, respectively; Ρ > 0.05), while significant difference was observed between the dew point depressions of 3° C-4° C and 4° C-5° C (average dew amounts of 0.29 and 0.23 mm, respectively; Ρ > 0.05; Fig. 2e). Dew amount decreased with increasing dew point depression, especially after dew point depression reaching 3° C. The lowest value of dew amount at dew point depression of 3° C-5° C was 0.23 mm, which was lower than the minimum average dew amount (0.35 mm) at dew point depression of 1° C-3° C. These results demonstrated that dew point depression of 1° C-3° C was favourable for dew formation. Furthermore, frequency of dew occurrence was high (82%) when wind speed was < 0.5 m/s (Fig. 2c), and there was no significant difference of dew amount among different wind speeds (Ρ > 0.05; Fig. 2f).

The daily dew amount, rainfall and relative dew frequency during the experimental periods (i.e., 26 July-23 October, 2012 and 24 June-17 October, 2013) are shown in Figure 3. The total dew amount was 83.03 mm during the whole experimental period, which was much lower than the total rainfall (638.2 mm). The daily dew amount differed without any regular patterns. There were a total of 108 days with dew fall, accounting for 52.43% of the total experimental days; and there were a total of 69 days with rainfall, accounting for 33.49% of the total experimental days (Fig. 3a). Although the total daily dew amount was much lower than the total rainfall, dew occurred more frequently than rainfall did. Moreover, the coefficient of variation of rainfall (150.2%) was higher than that of dew (70.3%), indicating that daily dew amount varied less than rainfall did. The daily dew amount ranged between 0.11 and 2.30 mm in the all dew-falling days (totally 108 days), with a daily average of 0.75 mm (Fig. 3a). Moreover, the days with daily dew amount > 0.2 mm accounted for 85.18% of the 108 dew-falling days (Fig. 3b), and 73.15% of the 108 dew-falling days had dew fall that exceeded the capacity of leaf reservoir storing free water.

Fig. 3

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	Fig. 3 (a) Daily dew amount and rainfall and (b) relationship between daily daw amount and relative dew frequency during the experimental periods (26 July-23 October, 2012 and 24 June-17 October, 2013)

In this study, the RH model and DPD model were used to estimate daily dew duration during the experimental periods. It should be noted that we run the model calibration firstly by determining the final optimal thresholds of parameters for the two models (relatively humidity for RH model and dew point depression for DPD model). The estimated daily dew durations were compared with the measured daily dew durations (Fig. 4). For the two models, the regression lines between estimated and measured daily dew durations were not significantly different from the 1:1 line, indicating that the estimated daily dew durations were as good as the measured durations. Furthermore, the performances of the two models are shown in Table 2, with R² values of 0.86 and 0.83 for RH model and DPD model, respectively. These results demonstrated that the final thresholds of relatively humidity (78%) and dew point depression (1.0° C for wet leaf and 5.0° C for dry leaf) determined in this study are acceptable to be respectively applied in RH model and DPD model for accurately estimating daily dew durations.

Fig. 4

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	Fig. 4 Correlation of measured and estimated daily dew durations using RH model (a) and DPD model (b). RH model, relative humidity model; DPD model, dew point depression model.

Table 2

Table 2

Table 2 Indices of verifying the performances of RH model and DPD model Model R2 W C MAE(h) MBE(h) RH model 0.86 0.96 0.89 1.29 -0.27 DPD model 0.83 0.95 0.86 1.60 0.73 Note: R2, coefficient of determination; W, Willmott agreement index; C, confidence index; MAE, mean absolute error; MBE, mean bias error.

Table 2 Indices of verifying the performances of RH model and DPD model