Study site

The present study was carried out during three consecutive winter seasons (2012 to 2014) at the ‘C’ Block Farm of Bidhan Chandra Krishi Viswavidyalaya, Kalyani (22^o59'13’’ N, 88^o27'20’’ E, altitude 10.8 m), West Bengal, India. The study area belongs to the IGP of Eastern India and is characterized by tropical sub-humid climate with hot and humid summer seasons. During monsoon seasons, the south-west monsoon circulation system accommodates necessary energy and water vapour from the Bay of Bengal and carries the moist air to the inland of the continent which provides around 73% of the total annual rainfall (1443.5 mm) of the region (Samanta et al., 2012). However, winter season receives 40.5 mm rainfall which is only 2.83% of mean total annual rainfall. They also reported that in recent past, onset of monsoon (normal date is 8th June for the region) has been delayed by one week to 10 days. Long term (1960–2015) data analysis shows that May is the hottest month of the year (36.0 ^oC average). January is the coolest month throughout the year as the mean monthly temperature remains close to 11.0 ^oC. During winter months, the mean monthly maximum temperature ranges from 25.5 to 29.1 ^oC and the mean monthly minimum temperature ranges from 11.0 to 15.0 ^oC. The mean monthly average BSS always ranges between 7.1 and 8.1 hr d^-1. During winter, fog is observed only at early morning hours. The soil of the study area is mainly alluvial in nature (Entisol) and silty clay in texture. The percentage of the silt, clay and sand are 72.2, 21.7 and 6.1% respectively. The soil is slightly basic (7.45) in nature and also well-drained.

Field experiments and cultivation management

Field experiment was laid out in a split-plot design to assess the performances of potato cultivars under actual weather condition with irrigation supply i.e., with no water stress to constantly monitor their canopy structure and light interception. In lower Gangetic West Bengal, the potato planting window generally starts from post monsoon period i.e., mid-November and continues up to December. Following local farmers’ practice, potato cultivars were planted on three days starting in 15th Nov with 14 days interval (D1= 15^th Nov; D2= 29^th Nov; D3=13^th Dec). The net plot size was 22.5 m² (5 m × 4.5 m) with three replications and pre-sprouted seed tubers were planted at a spacing of 50 cm (row to row) × 15 cm (plant to plant). Main plots and sub-plots were divided by a 1.25 m irrigation channel and 0.75 m bund respectively acting as a buffer.

We selected three Indian potato varieties, ˈKufri Suryaˈ (KS), ˈKufri Chandramukhiˈ (KC) and ˈKufri Jyotiˈ (KJ). KC is known to be heat-susceptible and the other two heat-tolerant varieties (Minhas et al., 2006). In the f irst year, we started our experiment with two varieties (KS and KJ) and the third one, KC, was included in the second year. The recommended dose of fertilizer (N:P:K=200:150:150) was applied through urea (46% N), single superphosphate (16% P₂O₅) and muriate of potash (60% K₂O). The full dose of P and K were applied as basal dose, but urea was applied in three splits. Half of the urea was applied during soil preparation and the rest was equally divided and applied as top dressing during earthing up [at 20 days after planting (DAP)] and during second irrigation (at 30 DAP). Every year, data collection was started at 30 DAP and continued up to maturity with 15 days interval. During sampling, proper care was taken to avoid edge effect.

 Meteorological observation and weather data collection

Daily maximum and minimum temperature, sunshine hour, relative humidity, rainfall, wind speed, rainy day, pan evaporation and cloud cover were recorded for the study period at Kalyani Meteorological Observatory, situated at AICRP on Agrometeorology, Bidhan Chandra Krishi Viswavidyalaya. The GSR values (W m^-2 sec^-1) with a wavelength of 0.3–3.0 µm on a horizontal surface were recorded from Aug 2013 to Dec 2015 using a Pyranometer sensor (Kipp & Zones CMP6 model) mounted at 1.5 m height. During the crop growth period, diurnal variation of incident and transmitted PAR (TPAR) were measured at weekly interval starting from 8 am to 4 pm with a gap of one hour. A line quantum sensor (Model No.: Q-301, APOGEE, Logan UT, UK) was used manually to capture the radiation in and above the canopy. To maintain parity with GSR, PAR data were also conver-ted into its energy flux (W m^-2 sec^-1) using the constant conversion factor of 1.08.

NASA POWER website also provides SR data along with other meteorological parameters for 1^o × 1^o (i.e., ~110 km × ~110 km) resolution across the world. For the study period, the daily global solar irradiance and GSR values were collected from the NASA POWER website (NASA POWER, 2016) and compared with the observed GSR data. The comparison was done to find out the possibility of using the NASA POWER in the study region.

Calculation of GSR from Angstrom equation

The facility to measure GSR using Pyranometer sen-sors is scanty in developing countries like India. Hence, GSR is calculated from different empirical equations using temperature, BSS, rainfall, cloud cover etc. Nowa-days satellite imageries are also widely used. But among the existing correlations, the following relation is the wi-dely accepted modification of Angstrom-type regression equation, relating the clear sky GSR to BSS duration. Angstrom (1924), one of the pioneers, first proposed the equation, which was later modified by Prescott (1940) and Page (1961) to its present form which is popularly known as Angstrom-Prescott (A-P) correlation and presented as:

where H=incoming daily GSR (MJ m^-2 d^-1); H0=daily extra-terrestrial radiation (MJ m^-2 d^-1); a and b=empirical constants; n=bright sunshine hours per day (hr); N=as-tronomical day length (hr). N was calculated by the following formula:

where Φ=latitude in radian; δ=solar declination angle in radian.

H0 was calculated using the equation defined by Mar-tinez-Lozano et al. (1984):

where k=Julian day and ω=sunset hour angle in radians; δ and ω can be calculated from the following expressions:

Calculation of K and RUE

 Based on the measured values of LAI and PAR data (inci-dent PAR above the canopy and incident PAR transmitted through the canopy) amount of K of the crop was deter-mined using the Beer-Lambert equation, which is an ex-ponential form of the equation (Sarmadnia & Koocheki, 1994; Goudriaan & van Laar, 1994; Whisler et al., 1986; Thornley & France, 2007):

 where I_t=transmitted PAR (TPAR), I₀=incident PAR and K=light extinction coefficient. From this equation, we can calculate IPAR as:

RUE was calculated from the slope of the linear re-gression of cumulative IPAR on cumulative dry biomass obtained from the sequential samplings (Kiniry et al., 2001).

In the present study, LAI was measured during each biomass sampling through gravimetric technique. A cir-cular cutter of known diameter (2.5 cm) was used to cut randomly chosen ten green leaves. After that the cut pie-ces were dried in a hot air oven. By using the area-weight relationships, leaf area of leaf samples from 1-m2 were calculated. Then the LAI was obtained using standard formulas (Watson, 1947; Gardner et al., 1985):

Testing the performance of Angstrom equation

Performance of the Angstrom equation for this region was tested by using some statistical indicators. Besides correlation coefficient (r), and coefficient of determination (R²):

‒Mean bias error (MBE) is simply the average of the predicted value minus the average observed value:

where P_i is the calculated GSR, O_i is the observed GSR and N is the number of observations.

‒Mean absolute error (MAE) is the average of the absolute difference between predicted and observed value:

‒Standard error (SE) was calculated comparing the actual value and the model output value. The equation of standard error of the predicted value is:

‒Root mean squared error (RMSE) is simply the root of the MSE value. It is usually better to report the RMSE than the MSE, because the RMSE is measured in the same units as the data, rather than in squared units.

‒Mean percentage error (MPE) can be defined as the percentage deviation of the monthly average daily radiation values estimated by the model used from the measured values:

‒Mean absolute percentage error (MAPE):

‒ Nash Sutcliffe efficiency (NSE):

These parameters are most commonly used to compare the model output value with the observed value (Tadros, 2000; Sabziparvar & Shetaee, 2007; Banerjee et al., 2016). All these statistical tests, including ANOVA test for biological parameters, were done using MS-Excel. R2 denotes the multiple coefficient of determination, which is a measure of how well the regression equation fits the sample data whereas RMSE conveys information on the short term performance of different equations since it ena-bles a term-by-term comparison of the actual variations between the estimated and measured value. For more accurate estimation, lower values of RMSE should be obtained (Akpabio & Etuk, 2003). The values of MBE represent the systematic error or bias. The closer the MBE, RMSE and MPE are to zero, the better the model is. Positive values represent overestimation and negative values represent underestimation. If the value of R is clo-se to unity, the model is said to be better. MPE is a test of long term performance of the examined regression equa-tion and its positive and negative value represents similar trends like MBE. For a better model performance, a low value of MPE is desirable and the percentage error between -10% and +10% is considered acceptable (Menges et al., 2006). NSE is a simple measure to determine the model precision by plotting observed values against simulated data in a 1:1 line. Generally, NSE ranges between -∞ and 1.0 and the model is more efficient when NSE is closer to 1.

DiscussionTop

Comparison of measured and estimated GSR

From the obtained results of empirical coefficients, it can be assessed that they are well within the range derived by previous researchers. For example, Angstrom (1924) recommended values of 0.25 and 0.75, respectively for the constants a and b based on the data from Stockholm. Martinez-Lozano et al. (1984), after reviewing the literature for 101 locations around the world, reported that the values of a may vary between 0.06 and 0.4 and b between 0.19 and 0.87. Thus, it is evident that the analysed values of a and b for the present study are also within the range described by different researchers. Irrespective of experimental year and month, Angstrom equation under-estimated GSR very slightly. The low negative MPE value also indicated the underestimation of calculated GSR compared with measured value. The value of MPE was within acceptable range (-10% to +10%), so the Angstrom equation can be used in the study region for the estimation of GSR. High correlation (88%) and coefficient of determination (77%) values along with low RMSE and SE values indicated that the Angstrom equation can be used safely. NSE values confirm that measured GSR is plotted very well against the estimated data (Fig. 1). Calculation of GSR for different locations across the globe through Angstrom equation provides high accuracy as observed in the present study (El-Sebalii & Trabea, 2005; Bakirci, 2009; Muzathik et al., 2011; Khorasanizadeh & Mohammadi, 2013). Acceptable MPE and less RMSE indicated that performance of Angstrom equation is viable for both short and long term. Values of MBE, MPE and NSE re-vealed that A-P correlation fits better compared to NASA POWER (Table 1). The reason may be due to the error occurred during the process of downscaling of SR data.

Table 2. Phenological stage wise radiation use efficiency (RUE), light extinction coefficient (K) and maximum leaf area index (LAI) value achieved by the three potato varieties under different days of planting (DOP) along with statistical analysis. Total sample size=27; number of replications=3.

Relationship between transmitted and intercepted PAR

The change of values of TPAR and IPAR were well fitted with crop age through second order polynomial equation. The equations for the three varieties were ob-served significant at 1% level and confirmed that the pa-ttern of PAR components change over time. Irrespective of variety, the pattern of IPAR and TPAR variation over time followed similar pattern. The intercepted portion increased with growth of crop and increase of LAI. On the other hand, the transmitted portion decreased with growing period due to increase in crop canopy structure. The phenomena can be explained as at the initial stage of crop growth, when the LAI was low, most of the incident PAR was transmitted through crop canopy. Up to 33 DAP, the TPAR was higher than IPAR. With crop growth the IPAR value gradually increased with time up to 80 DAP for var. KS (Fig. 2). Afterwards, due to gradual drying of leaves, the IPAR decreased slowly, but never became lower than TPAR value as observed during initial phase. For the other two varieties, IPAR gradually increased up to 70 days. Irrespective of the dates of planting (DOP) and of the variety, cumulative IPAR from emergence to harvest ranged 246-429 MJ m^-2. In Philippines, Demagante et al. (1996) reported 740, 900 and 945 MJ m^-2 radiation interception (RI) for early, medium and late maturing potato cultivars respectively. Whereas, in Netherlands, RI varied from 1180 to 1435 MJ m^-2 for different varieties in different seasons (Haverkort et al., 1991).

Derivation of light extinction coefficient (K)

It was observed that LAI values sharply increased after 30 days. It might be due to the application of urea prior to that time. The decreasing trend after 75 days might be due to senescence of older leaves or leaf damage and leaf drop. Thus it is expected that these differences in LAI values throughout the growing period would lead to wide variations in the amount of radiation intercepted and consequently would be reflected in the accrued total dry weight. Beadle (1993) documented that maximum LAI varied between 6 to 8 for deciduous forest and 2 to 4 for annual crops. But, in general, values of LAI have been reported to vary between 3.5 and 6.0 depending on the cultivar (Wright & Stark, 1990; Battilani & Mannini, 1993). Praharaj et al. (2007) observed highest LAI value (4.8) under var. ˈKufri Pukhrajˈ followed by ˈKufri Ashokaˈ (2.82). Thus the LAI values measured throughout the growing period of potato were relatively close to the reported values in the literature. The difference in K value of all three cultivars was probably due to differences in canopy morphology. Vijaya Kumar et al. (1993) worked out the K values for non-horizontal orientation of leaves (< 1.0) and for horizontal leaves (> 1.0). In case of var. KC, more upright leaves were observed and K value was the lowest among the three varieties.