Effect of de-trending climatic parameters on temporal changes of reference evapotranspiration in the eastern Himalayan region of Sikkim, India

Climate-related risks to food security, agriculture, livelihoods, and water supply are anticipated to increment with global warming of 1.5 °C above temperatures in the pre-industrial period and increment further with 2 °C by 2100 (Intergovernmental Panel on Climate Change (IPCC 2019)). In the context of global warming and climate change, accurate estimation and prediction of evapotranspiration is of vital importance in the studies related to hydrological modeling, climate change prediction, water resources planning and management, irrigation scheduling, and determining crop water requirement. The reference evapotranspiration (ET₀) can be used as an index to assess agricultural water demand. The FAO had identified the FAO56 Penman–Montieth (FAO-56-P-M) model as a benchmark for the precise estimation of ET₀ following an extensive comparison with lysimetric measured data globally (Allen et al. 1998).

A literature survey confirms that studies worldwide reported that the trend of ET₀ was found to have increased or decreased in various areas of the world. Studies reported both increasing and decreasing trends in Iran (Dinpashoh et al. 2011), China (Mo et al. 2017; Liu et al. 2020), and India (Sonali & Nagesh Kumar 2016). Significant increasing trends of ET₀ were reported in the Korean Peninsula (Ghafouri-Azar et al. 2018), in Iran (Azizzadeh & Javan 2015), in central Europe (Zaninović & Gajić-Čapka 2000), and China (Niu et al. 2019). The strong decreasing trend in ET₀ was observed in Canada (Burn & Hesch 2007), in the United States (Golubev et al. 2001), in Australia (Donohue et al. 2010), in India (Verma et al. 2008; Jhajharia et al. 2012; Yadav et al. 2016; Goroshi et al. 2017), and in China (Niu et al. 2019).

The reference evapotranspiration is a multivariate parameter and function of climatic parameters (CPs), namely temperature (T), relative humidity (RH), solar radiation (Rs), and wind Speed (Ws). The temporal variability of CPs is mainly responsible for the upward and downward trend in ET₀ (Li et al. 2017).

The analysis of impacts of CPs on ET₀ is useful to know the climatic change impacts on ET₀ (Xu et al. 2006; McVicar et al. 2012). There are two conventional approaches to quantify the influence of CPs on ET₀. The first approach is based on sensitivity analysis (Mckenney & Rosenberg 1993; Tabari & Hosseinzadeh Talaee 2014; Zhao et al. 2014; Patle & Singh 2015), while the second method re-calculates ET₀ by using detrended CPs (Huo et al. 2013; Zhao et al. 2014; Li et al. 2017). However, these studies analyzed only the impacts of the single climatic parameter on ET₀, not the simultaneous effects of different factors on ET₀. Since CPs change simultaneously, a single CP such as a different temperature (maximum T(max) and minimum T(min)) may vary in a different pattern. It is not sufficient to know only the influences of a single CP on ET₀. Studies mentioned above have not recognized the influence of different temperature factors (T_min and T_max) on ET₀. Additionally, eliminating linear trends from CPs is sufficient, yet eliminating the nonlinear trend in CPs is vital because most CPs change nonlinearly with time.

Statistical trend analysis can be further carried out under parametric and nonparametric analysis. The difference between the two is the way of using collected data. In the parametric analysis, actual parameters are used to determine the trend, considering data are normally distributed and independent. However, the nonparametric test does not necessarily require data to be normally distributed. The most often utilized nonparametric test for identifying the pattern in data is the Mann–Kendall test (Kahya & Kalayci 2004; Jayawardene et al. 2005; Burn & Hesch 2007; Li et al. 2007; Thepprasit et al. 2009; Aksu et al. 2010; Espadafor et al. 2011; Tabari & Marofi 2011; Jhajharia et al. 2012; Karmeshu 2012; Kousari & Ahani 2012; Shadmani et al. 2012; Gocic & Trajkovic 2014) to detect the trend in climatic time series.

Before implementing any parametric or nonparametric tests, the data's independence should be checked using the lag-1 autocorrelation test. The trend-free pre-whitening with Mann–Kendall is one common approach, which shows the relation between a linear trend and a lag-one autocorrelation (Yue et al. 2002, 2003; Dinpashoh et al. 2011). The elimination of trend components before pre-whitening removes the serial correlation from the time series. The elimination of positive serial correlation components through pre-whitening causes the magnitude of the prevailing trend to reduce. In their variance correction approach, Hameed & Rao (1998) reported that the existence of positive or negative serial correlation results in an increase or decrease in the variance of Mann–Kendall test statistic (S). Therefore, to prevent the effect of the problem, the variance correction approach was recommended.

Detrending is a mathematical or statistical operation of removing trends from a climatic time series. The detrending technique is a combined methodology that considers both the sensitivity coefficient and the rate of climatic factors. The empirical mode decomposition (EMD) is a versatile technique developed to examine non-stationary and nonlinear signals. It comprises a nearby and completely information-driven detachment of a signal in rapid and moderate oscillations. The decomposition is produced from the traditional assumption that any data consist of oscillation's various basic intrinsic modes.

Every mode might be linear and may have a similar number of extrema and zero intersections. However, EMD encounters a few issues, such as oscillation of unique amplitude in a mode of the existence of fundamentally the same oscillations in various modes, called ‘mode mixing.’ Torres et al. (2011) suggested an ensemble empirical mode decomposition (EEMD) with the addition to Gaussian white noise over EMD. The addition of Gaussian white noise eliminates the problem of mode mixing (Guo et al. 2016). Sang et al. (2014) in a comparison of the Mann–Kendall and EMD method of trend analysis reported that EMD can be an effective alternative for trend identification of hydrological time series. Even though EEMD by then was proven to help investigate geophysical data, it additionally has a few disadvantages. The main disadvantage is that the signal reproduced by EEMD has a residual noise, and the problem of mode mixing still exists in outermost applications to real data. Antico et al. (2014) developed the CEEMDAN (complete ensemble empirical mode decomposition with adaptive noise) method. The CEEMDAN gives an accurate reconstruction of the original signal and an apparent spectral detachment of modes, thus eliminating the mode mixing problem (Antico et al. 2014; Marusiak & Pekar 2014). Antico et al. (2014) successfully applied CEEMDAN on river discharge data to determine the time-scale components of hydrological time series and concluded that it is the powerful method for extracting physically meaningful information from hydroclimatic data. Therefore, CEEMDAN is a powerful means for separating physically relevant data from hydroclimatic time series, particularly when the previously mentioned issues are experienced.

The authors did not find the same or at least similar earlier conducted studies which analyzed the influence of removing both (linear and nonlinear) trends from various CPs on ET₀ in India. In this case study, we performed a trend analysis of different CPs. In the next step, CPs are detrended both linearly and nonlinearly to study the effect of detrending the CPs on temporal variations of annual reference evapotranspiration (ET₀) Gangtok, Sikkim.

The study area is situated in the eastern Himalayas, according to the agro-climate zone of India (Government of India 1989). The investigation was conducted in east Sikkim, which has a latitude range between 27°9′ and 27°25′ N and longitude from 88°27′ and 88°56′ E, and covers about 900 km² area. Geographically, East Sikkim occupies the southeast corner of the state (Figure 1). Almost the entire east Sikkim is hilly, with an elevation range of 811–1,650 m. The average annual sum of the precipitation during the observed period at Gangtok is about 3,090 mm. The average annual temperatures (T_max and T_min) during the observed period were 22.97 and 13.72 °C, respectively (Table 1). The district's average index of wetness is more than one, and the number of rainy days ranges from 128 to 205 days. The study region gets a significant part of precipitation from the south-west monsoon. For most periods in the course of a year, the climate is cold and humid as precipitation occurs each month. Pre-monsoon rain occurs in April–May, and monsoon (south-west) operates normally from May and continues up to early October. The descriptive statistics of ET₀ and different meteorological parameters are depicted in Table 1.

The daily meteorological data from 1980 to 2015 for various CPs namely T_max (°C), T_min (°C), RH_max (%), RH_min (%) and SSH (h) to apply FAO56-P-M were collected from the Indian Meteorological Department, Tadong, Sikkim. The mean monthly and seasonal ET₀ was estimated using the FAO56-P-M equation. The baseline values were fixed as mean values of monthly, seasonal ET₀, and CPs.

The increasing or decreasing trend in x_i is identified based on Z_c's calculated values at a 5% significance level (greater than 0 and −1.96 ≥ Z_c ≥ 1.96) on r_l (lag-l autocorrelation). The magnitude of the trend was identified using Sen's (Sen 1968) method (Adarsh & Janga Reddy 2015).

The S_q′ (t) was determined, estimated similarly, with x_i's termination point being the beginning.

The linear detrended data series is obtained by eliminating the original data series linear trend each year. The original data series value is added to the detrended data series to maintain a close variation range to the original data.

In the present study, the nonlinear detrending of the various CPs was performed using the CEEMDAN technique (Antico et al. 2014). The CEEMDAN technique of signal processing decomposes the input data to intrinsic mode functions (IMFs) with varying phase and amplitude and residuals (trend). An IMF is a continuous map, which fulfills the following condition (Huang et al. 1998): (a) the number of zero intersections and the extrema must be equivalent or have a difference limited to one, (b) the mean estimation of the upper envelope framed by local maxima and lower envelope shaped by lower minima must be equivalent to zero at any point. Within this condition of IMF, the decomposition procedure of CEEMDAN is given below:

• 1.

  Show the input signal, x(t).

• 2.

  Identify the local maxima and minima of time series.

• 3.

  Calculate both upper and lower envelopes by joining all local maxima using any suitable signal decomposition method, such as cubic splines.

• 4.

  Calculate the local average value (m₁) between both upper and lower envelopes.

• 5.

  The first component is calculated as h₁(t) = x(t) − m₁(t).

Moreover, then, c⁻¹ (t) is calculated as the average of the individual series of the implementation of (t) series along with the first component of EMD white noise decomposition (t).

The CEEMDAN was preferred for obtaining the nonlinearly detrended data series using the ‘Rlibeemd’ package (Luukko et al. 2016) of R software in the present study. The original data of various CPs (T_max, T_min, RH_max, RH_min, SSH) are imported into the software. With the help of the Rlibeemd package, CEEMDAN decomposes the input data to IMFs and a residual series.

In the present study, the main objective is to compare the effects of linear and nonlinear detrending (i) between different temperature factors (T_max, T_m, T_min) and (ii) non-temperature factors (i.e., RH_max, RH_min, and SSH) on changing ET_0. The number of total combinations created was 23, including the original scenario CP1. The original scenario CP1 is estimated from the observed CPs, and two other groups (i.e., linear and nonlinear) are created. Both the scenarios contain 11 different combinations of recalculated ET₀ using various sets, as shown in Table 2 of the observed and detrended CPs.

Single or multi CPs were detrended from Group 1, consisting of a linear trend, and Group 2 of nonlinear trends. The detrended CPs with other observed CPs were utilized for the re-estimation of ET_0. A total of 23 combinations of ET_0, including the original set CP1, CP2 to CP11 in Group 1, and CP2 to CP11 in Group 2, are applied. In the combination CP2 to CP4, the influences of detrending one or more temperature factors are contrasted gradually, i.e., in CP2, T_max is detrended, CP3 T_min is detrended, CP4 both T_max and T_min are detrended. At the same time, in CP5 to CP11, the influences of detrending one or more non-temperature factors CP5 to CP10 are non-temperature factors, i.e., in CP5 RH_max is detrended, CP6 RH_min is detrended, CP7 both RH_max and RH_min are detrended, CP8 SSH is detrended, CP9 SSH and RH_max are detrended, CP10 SSH and RH_min are detrended, in CP11 SSH, RH_max and RH_min are detrended. In CP12, all the observed CPs are detrended. The effect level between temperature and non-temperature parameters could be shown by comparing scenarios (CP2 to CP4) with scenarios (CP5 to CP11) (Table 2).

In the Mann–Kendall test, parameters like modified Mann–Kendall Statistics (Z_c) and Sen's slope (b) were assigned to distinguish the increasing or decreasing trends in the climatic time series parameters. From Table 3, it is clear that at a 5% level of significance, the estimated Z_c value predicts a significant increasing trend for T_min. In contrast, a significant decreasing trend was observed for sunshine duration and evapotranspiration. The remaining CPs show an insignificant increasing trend at a 5% level of significance (Table 3).

The results obtained for abrupt change year (T_AC) are also presented in Table 3. The T_AC for T_max, RH_max, and RH_min was observed in 1985, 1983 and 1982, respectively. However, for T_min, SSH, and ET₀, T_AC was not observed as the two series, S_q (t) and S_q′ (t) did not cross each other. The Sen's slope b for ET₀ and 5 CPs vary to a small degree. The magnitude of positive Sen's slope follows a sequence of T_min > RH_min > RH_max > T_max that the mean rate of increase of T_min per year is maximum for the studied parameters. In contrast, the rate of increase of T_max is the lowest of the studied parameters. However, for sunshine duration and evapotranspiration, the value of the Sen slope (b) is negative. Total sunshine duration decreases at a rate of 0.049 h per year, and evapotranspiration decreases at a rate of 0.078 mm d⁻¹ per year. This helps to determine the most critical parameter responsible for negative trends in ET₀. The same table also depicts that the magnitude of Sen slope (b) and the regression slope (RS) of related CPs are close. Although Sen slope (b) detector is nonparametric and the RS technique is a parametric technique, both the techniques are linear. Therefore, a minor difference in the b and RS values gives very similar results for analyzing the detrending impacts on reference evapotranspiration and verified the correctness of using RS values for detrending.

Temporal changes in annual CPs and their linear trends and nonlinear trends during the study period 1980–2015 are shown in Figure 2(a)–(f). Figure 2(a) shows that the linear and nonlinear trend lines are separate until the nonlinear line decreases and meets the linear range. The linear trend line of T_max is similar to the nonlinear trend from 1996 onwards until 2015. Before 1996, nonlinear trends are on a higher side than the linear trend. The significant increasing linear trend of T_min (Figure 2(b)) is different from the significant increasing nonlinear trends except in 1986–1988 and 2006–2008. The fluctuation patterns of RH_max (Figure 2(c)) and RH_min (Figure 2(d)) were generally similar. However, the magnitude of fluctuation in RH_min was more than the RH_max. In RH_max and RH_min trends, there was a weak increase from 1980–2015. For RH_max, both linear and nonlinear trends differed insignificantly (the linear trend is minuet differing from the nonlinear trend) except in 1986–1991 and 2010–2012. For RH_min, the linear trend was generally different from the nonlinear trend except in 1987 and 2001, where the nonlinear trend increased and decreased back, respectively. For the SSH (Figure 2(e)), both the linear and nonlinear trends sharply decreased from 1980–2015. The linear trend was generally different from nonlinear trends throughout the study period except in 1988 and 2004–2005. From the nonlinear trends, SSH seems to decrease, and the nonlinear variation of SSH adds to the nonlinear change of ET₀. These major or minor differences in linear and nonlinear trends in basic input parameters for ET₀ estimation create a difference in recalculated ET₀ after linear and nonlinear detrending.

The distinct variations of the five principal CPs resulted in a difference of ET_0. The ET₀ variation (Figure 2(f)) and its linear and nonlinear trend represented a decreased trend. The significant difference between the linear and nonlinear trends in ET₀ contributes to the difference in regenerated ET₀ between Group 1 and 2.

In this analysis, the ET₀ was recalculated using the linearly detrended CPs (Table 2) from Group 1 (linearly detrended) throughout the study period, i.e., from 1980 to 2015, and compared the recalculated ET₀ with the original calculated ET₀ under Scenario 1 (CP1).

For CP2, as depicted in Figure 3(a), the recalculated ET₀ values obtained after detrending the T_max are lower throughout the study years except in 1997, where the recalculated value is higher than the CP1 value. The results of the study showed that although the T_max is insignificantly increasing during the study period, the ET₀ value decreased. For CP3, the recalculated ET₀ values obtained after detrending the T_min are higher during 1980–1983, 1986–1988; from 1993 to 2010, the detrended ET₀ is slightly lower than the CP1 ET₀ (Figure 3(b)), and from 2011 to 2015, the detrended ET₀ is the same as CP1 ET_0. However, T_min is significantly increased during the study period but detrending of T_min did not affect the ET₀ values. Comparing CP4 and CP1 (Figure 3(c)) shows the decreasing values of ET₀. The recalculated ET₀ values are higher during 1981–1982 and in 1997. Overall, the detrended ET₀ is lower than the CP1 ET₀.

The findings of the study showed that although T_max and T_min have been increased during the study period, however, detrending both T_max and T_min resulted in a decrease in the ET₀ value. Thus, it may be concluded that detrending of T_max and T_min has a negative effect on ET₀. Thus, for temperature parameters, except for scenario CP3 (T_min de-trended), the recalculated ET₀ was below the ET₀ curve of CP1, which concludes that detrending T factors (CP2, CP3, CP4) result in decreasing ET₀.

Detrending RH parameters (CP5 to CP7), as depicted in (Figure 3(d)–(f)), showed a slight increase in ET₀ in all three cases. Hence, an insignificant increase in both RH_max and RH_min did not affect the decreasing trend of ET_0. Overall, the significant decreasing trend of sunshine duration (CP8) explains the decreasing trend of evapotranspiration (Figure 3(g)). After 2002, the recalculated ET₀ is higher than that estimated in scenario CP1. Detrending of sunshine duration counters the detrending effect of humidity factors CP9, CP10, and CP11, or we can conclude that the effect of the significantly decreasing sunshine duration decreasing ET₀ values is much stronger than an insignificant increase in RH factors (Figure 3(h)–(j)).

Variation in ET₀ for CP1 and CP12 (detrending all the CPs) is similar to that obtained by detrending sunshine duration and RH (CP11) (Figure 3(k)). The result shows that with the decreasing trend in sunshine duration the decreasing trend in ET₀ is much stronger than an insignificant increase in T_max and a significant increase in T_min.

For nonlinear detrending, CP2 insignificantly affects the variation in ET₀ during the study period (Figure 4(a)). Analysis of Figure 4(a) revealed that the original ET₀ and the values of recalculated ET₀ of CP3 show decreasing values of ET₀ for both the scenarios. The estimates of recalculated ET₀ for CP3 (Figure 4(b)) are the same as the CP1 from 1985 onwards except for 1981–1982 and 1983. The results show that although the T_min is significantly increased during the study period, detrending the T_min did not affect ET₀. A similar insignificant impact was observed for CP4 (Figure 4(c)). The detrending of both the T_max and T_min has a negligible effect on ET₀. The increasing trend of RH_max and RH_min has an insignificant effect on ET₀ after nonlinear detrending CP5, CP6, and CP7 (Figure 4(d)–(f)). The findings of the study revealed that the detrending of RH_max and RH_min has an insignificant effect on ET₀. However, the impact of decreasing sunshine duration CP8 (Figure 4(g)) on reducing ET₀ is much more substantial than an insignificant increase in RH factors, which is similar to linear detrending. The ET₀ curve of CP12 (Figure 4(k)) increased as CP8, CP9, and CP10 (Figure 4(g)–(i)) when compared with CP1. Thus, in the annual series, for both the linear and nonlinear detrending, sunshine duration is the dominant climatic parameter to explain the decreasing trend of ET₀ in the region. Hence, we can conclude that the detrending sunshine hour surpasses the detrending of other selected CPs.

The original ET₀ (CP1) was compared with scenario CP12 of both Group 1 and Group 2 to know the effect of detrending if all the CPs were detrended. Thus obtained, the results are presented in Table 4 and Figure 5 (for both Group 1 and Group 2). From Table 4, it is clear that the trend and intercept obtained by linear regression were similar for both original ET₀ and nonlinearly detrended ET₀ for scenario CP12, whereas, trend and intercept for linearly detrended ET₀ was not identical to the other two scenarios. However, the nature of the trend was decreasing in all the scenarios (Figure 5). Findings support that the linear detrending of CPs significantly influences ET₀ compared to nonlinear detrending. However, the results obtained by nonlinear detrending are more convincing than linear detrending based on the analysis of trend and intercept (Table 4).

Except for scenario CP12, there is no other scenario that combines the temperature and non-temperature factors because the results from the present study show that (i) the impact of detrending two temperature factors on declining ET₀ is most significant when compared with the effect of detrending single temperature factors. Furthermore, the effect of detrending T_max and SSH as a single parameter was more significant than detrending RH factors and T_min, which accentuate the critical roles of T_max and SSH on the varying ET₀ as an individual factor_.

Therefore, it is not required to add more scenarios to illustrate the impacts of the detrending of combined RH_max, RH_min, and T_min because their impacts will be small. Therefore, CP12, which contains CPs of temperature and non-temperature factors, would thoroughly illustrate the effects of detrending CPs on ET₀.

ΔET₀ is the difference in the original ET₀ and the recalculated ET₀ in which one or multiple CPs (different scenarios) have been de-trended linearly or nonlinearly. The difference is estimated for Group 1 (linearly detrended) and Group 2 (nonlinearly detrended). Figure 6(a) represents the variations of ΔET₀, in which values of ET₀ were re-computed using linearly and nonlinearly detrended T_max (CP2). The total absolute ΔET₀ for CP2 is 3.19 mm d⁻¹, and that for nonlinear detrending is 0.6 mm d⁻¹ (Table 5). Similarly, Figure 6(b,c) represents both sets of detrending considering CP3 (T_min) and CP4 (T_max and T_min) scenarios. Linear detrending ΔET₀ values of temperature factors are more substantial than those of nonlinear detrending ΔET_0, as shown in Table 5. In both the detrending methods, detrending T_min has the least influence on ET₀, followed by T_max's detrending and combining the two temperature factors. Similarly, the linear and nonlinear detrending for scenarios (CP5–CP7) showed similar trends, i.e., the ΔET₀ values in both the cases are higher for scenarios CP6 and CP7 compared to scenario CP5 (Figure 6(d)–(f)). For linear detrending, the total absolute linear detrending differencing decreased from CP7 (3.47 mm d⁻¹) > CP6 (2.88 mm d⁻¹) > CP5 (0.77 mm d⁻¹) and for nonlinear detrending, total absolute linear detrending differencing decreased from CP6 (1.09 mm d⁻¹) > CP7 (0.99 mm d⁻¹) > CP5 (0.41 mm d⁻¹). The analysis also concludes that scenarios CP6 and CP7 have a similar influence on ET₀ on detrending; these will increase the value of ET₀ significantly for both the groups. In contrast, in the case of CP5, the average estimates of ΔET₀ move near to zero. Hence detrending RH_max has the least influence on ET₀. For the ΔET₀ variations of Group 1 and Group 2 for scenarios CP8 to CP11, the pattern of detrending is the same, i.e., the ΔET₀ values for scenario CP8 and CP9, and CP10 and CP11 showed the same pattern, and similar to ΔET₀ values (Figure 6(g)–(j)). For linear detrending, total absolute linear detrending differencing decreased from CP11 (4.9 mm d⁻¹) > CP10 (4.85 mm d⁻¹) > CP9 (4.8 mm d⁻¹) > CP8 (4.62 mm d⁻¹). The same pattern was observed for nonlinear detrending, where total absolute differencing decreased from CP11 (1.6 mm d⁻¹) > CP10 (1.58 mm d⁻¹) > CP9 (1.55 mm d⁻¹) > CP8 (1.45 mm d⁻¹).

The value for absolute ΔET₀ is significantly higher for linear detrending than nonlinear detrending in all the cases. Hence, the influence of linear detrending is more significant than that of nonlinear detrending. From the analysis, it may be concluded that T_min (CP3) and RH_max (CP5) have the least influence on ET_0, whereas the most influencing independent climatic parameter was Sunshine duration (CP8).

In both the linear and nonlinear detrending, the detrending pattern is the same for scenario CP12 (Figure 7). The maximum and minimum value of ΔET₀ for linear detrending was observed as 0.37 and −0.24 mm d⁻¹ in 1988 and 2011. In nonlinear detrending, 0.18 mm d⁻¹ was the maximum ΔET₀ in 1999, and −0.08 mm d⁻¹ was the minimum value observed in the years 2004 and 2011. Total absolute linear detrending differencing for both linear and nonlinear detrending is 4.12 and 1.77 mm d⁻¹, respectively (Table 5).

Different statistical properties of ΔET₀ like maximum, minimum, and average ΔET₀ are represented in Figure 8. The ΔET₀ statistic for Group 1 is significantly higher than Group 2, which may be because meteorological data follow a nonlinear pattern. Hence, nonlinear detrended ET₀ is closer to actual ET_0, which resulted in the lowest ΔET₀ values. Therefore, it may be proposed that nonlinear detrending gives closer results to the benchmark ET₀ values than linear detrending. In all the ΔET₀ analyses, it is concluded that a significant difference was observed in all the CPs scenarios. For linear detrending, ΔET₀ values in all the cases are on the higher side. The similar values of ΔET₀ were found on the lower side in the case of nonlinear detrending.

Most CPs are stochastic and generally have non-normal distribution. Therefore, the application of linear detrending may be unable to capture trends correctly. Table 3 depicts the comparison between the linear RS (S) and Sen's slope (b) values of all the selected CPs, which helps to understand the similarity or differences between linear and nonlinear trending.

The results showed that the deviation between S and b values for CPs was small. Even though Sen's slope method is nonparametric and the linear RS method a parametric technique, the two approaches are linear. In this way, the slight dissimilarities between S and b estimates would prompt a very close outcome for examining detrending impacts on ET₀ and affirmed the appropriateness of utilizing S values to detrend CPs.

The scenario 12 (CP12) is the only case that combines both temperature and non-temperature parameters mainly because simultaneously detrending the temperature parameters (T_max and T_min) on declining ET₀ were the biggest when contrasted with the effects of detrending of single parameters. Furthermore, the effects of detrending SSH on decreasing ET₀ were much more significant than the detrending of temperature, RH parameters in all three cases (i.e., RH_max and RH_min), which highlighted that sunshine duration (SSH) plays the most vital role in decreasing ET₀ in the eastern Himalayan region.

The decreasing trend in ET₀ identified in this study is concurrent with many studies in India and worldwide. Pandey et al. (2016) concluded that SSH is the main factor driving the ET₀ process in Northeast India. Poddar et al. (2018), in a study on the humid environment in the western Himalayan region of India, reported that solar radiation and temperature are the crucial factors to control ET₀. Jhajharia & Singh (2011) stated that the decrease in SSH has a positive relationship with the diurnal temperature range (DTR) and evaporation, leading to a reduction in evapotranspiration in Northeast India. Goroshi et al. (2017), in a study of evapotranspiration over India, also reported a decreasing trend in ET₀ over northeast India. Patle et al. (2019), using sensitivity analysis for Gangtok, East Sikkim, concluded that ET₀ changes positively related to SSH and T factors. According to Li et al. (2014), one of the main reasons behind the decreasing trend of ET₀ in northwestern China is a decrease in DTR. All these studies generally agree that the SSH is the most influential parameter in modeling the evapotranspiration process, especially in the humid climate. The conclusion of our study of the original and re-estimated ET₀ found in both cases (linear and nonlinear detrended) CPs also similar to the studies mentioned above.

By relating the influence of eliminating trends (linear and nonlinear) from the CPs on ET₀ in Sikkim, dissimilarities were found for the recalculated ET₀ between Group 1 and Group 2 scenarios. Due to the seasonal periodicity in the CPs, including ET₀, the results from Group 2 were even more conclusive for assessing the impacts of global warming and climate change on ET₀.

The decrease of ET₀ results in reduced crop water/ irrigation requirements for crops and plants in the region. Diminished ET₀ would bring about increased overland flow. Accordingly, it may increase the flood risk due to accelerated snowmelt on the alpine zone in the summer season, resulted from increased temperature. Therefore, the region's wetter conditions under the present global warming scenarios and drier are subsequently detrending the CPs and re-evaluating dry spell conditions.

This study aims to identify the impacts of eliminating trends (linear and nonlinear) from the meteorological parameters (CPs) that drive ET₀ processes. Accordingly, 23 scenarios, including the non-de-trended ET₀ (CP1), and Group 1 (by eliminating linear trend from CPs) and Group 2 (by eliminating nonlinear pattern from CPs), were set to know how the CPs influenced ET₀ for the period 1980–2015 in Gangtok, East Sikkim. To study the influence of trend, the ET₀ was re-estimated after detrending the respective CPs and then compared with non-de-trended ET₀ (CP1). The main conclusions derived are as follows:

• 1.

  The difference between ET₀ and the detrended ET₀ (ΔET₀) was significantly higher for linear detrending (Group 1) as compared to nonlinear detrending (Group 2). For linear detrending, the maximum difference ΔET₀ was observed as 0.37 mm d⁻¹for CP 7 and CP 12 scenario, and the minimum difference was observed as −0.05 mm d⁻¹ for CP 2.

• 2.

  In both the groups, the consistent mean difference of ΔET₀ was observed for CP 8 to CP 12 when sunshine duration and RH parameters were detrended. However, results from Group 2 were reasonable and conclusive as the Group 2 results were closer to those of the ET₀. The nonlinear detrending gives closer results to the original as compared to linear detrending.

• 3.

  The SSH was the most crucial parameter affected because there was the highest increase in ET₀ when SSH was detrended either in Group 1 linearly or nonlinearly in Group 2. A decline in SSH and T_max caused a general reduction of ET₀, which neutralized increased T_min and RH on ET₀.

• 4.

  The declines of T_max and increment of RH likewise added to the low abatement of ET₀. Overall, the combined impacts of all CPs caused the general decline of ET₀.

• 5.

  Additionally, the comparison of removing trends nonlinearly from single or multiple CPs may be useful to understand the changing pattern of ET₀ under global warming conditions.

Vanita Pandey studied the conception and design, acquisition of data and drafted the manuscript. Indira Taloh analysed and interpreted the data. P. K. Pandey edited and made critical revisions. All authors of this paper have directly participated in the writing, editing, planning, execution, and analysis of this study.

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

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