## Abstract

Reference Evapotranspiration (ET_{0}) is an essential factor in irrigation scheduling, climate change studies, and drought assessment. The study's main objective was to identify the influences of detrending input climatic parameters (CPs) on ET_{0} using linear and nonlinear approaches throughout 1980–2015 in Gangtok, East Sikkim, India. The benchmark values of ET_{0} were calculated using the global standard FAO56 Penman–Montieth equation. The ET_{0}-related CPs included for the analysis are maximum temperature (*T*_{max}), minimum temperature (*T*_{min}), maximum relative humidity (RH_{max}), minimum relative humidity (RH_{min}), and sunshine duration (SSH). The linear and nonlinear trends in various CPs affect ET_{0} change. Linearly detrended series was obtained by linear regression method whereas, nonlinearly detrended series was obtained using the Complete Ensemble Empirical Mode Decomposition with Adaptive Noise method. Twenty-three scenarios, including the original scenario, 11 scenarios in Group 1 (CPs de-trended linearly), and 11 scenarios in Group 2 (CPs de-trended nonlinearly) were generated. Influences of *T*_{max} and SSH were more substantial than the influences of other CPs for both Group 1 and Group 2. The SSH masked the weak influence of other CPs. The effects of the trends in CPs, especially of SSH and *T*_{max}, were clearly shown. The ET_{0} values decreased significantly during 1980–2015; however, no significant decreasing trend was observed in the case of SSH, during the same period. The nonlinear detrending gave closer results to the benchmark values as compared to linear detrending because of non-monotone variations of the ET_{0} and CPs. Therefore, the results from nonlinear detrending were more plausible as compared to linear detrending. The diminishing trend of ET_{0} prompted an overall alleviation of the dry spell, hence there would be a somewhat lower risk of water use in the study region.

## HIGHLIGHTS

Sunshine hour (SSH) and maximum temperature (

*T*_{max}) independently were the most important variables affecting reference evapotranspiration (ET_{0}).Detrending of minimum temperature and relative humidity insignificantly affects the ET

_{0}process.Effect of detrending sunshine hour (SSH) masked the increasing trend effects of other climatic parameters on ET

_{0}.ET

_{0}estimated by nonlinear detrending of climatic parameters (CPs) was satisfactory and convincing compared to linear detrending.

## INTRODUCTION

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 (ET_{0}) 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 ET_{0} 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 ET_{0} 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 ET_{0} 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 ET_{0} 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 ET_{0} (Li *et al.* 2017).

The analysis of impacts of CPs on ET_{0} is useful to know the climatic change impacts on ET_{0} (Xu *et al.* 2006; McVicar *et al.* 2012). There are two conventional approaches to quantify the influence of CPs on ET_{0}. 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 ET_{0} 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 ET_{0}, not the simultaneous effects of different factors on ET_{0}. 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 ET_{0}. Studies mentioned above have not recognized the influence of different temperature factors (*T*_{min} and *T*_{max}) on ET_{0}. 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 ET_{0} 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 (ET_{0}) Gangtok, Sikkim.

## METHODS

### Description of the study area and data sets

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 km^{2} 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 ET_{0} and different meteorological parameters are depicted in Table 1.

Time scale . | Statistics . | T_{max}
. | T_{min}
. | RH_{max}
. | RH_{min}
. | SSH . | ET_{0}
. |
---|---|---|---|---|---|---|---|

Annual | Average | 22.97 | 13.72 | 86.28 | 55.72 | 3.76 | 2.85 |

Max | 33.50 | 20.60 | 94.60 | 83.50 | 9.90 | 5.51 | |

Min | 11.80 | 3.30 | 67.60 | 24.90 | 0.00 | 1.53 | |

Std | 3.97 | 4.70 | 4.61 | 11.40 | 1.48 | 0.66 | |

CV | 0.17 | 0.34 | 0.05 | 0.20 | 0.39 | 0.23 | |

Monsoon | Average | 26.40 | 18.84 | 90.14 | 68.54 | 2.59 | 3.20 |

Max | 33.45 | 20.60 | 94.20 | 83.50 | 5.60 | 5.65 | |

Min | 21.70 | 14.40 | 75.50 | 51.70 | 1.00 | 2.62 | |

Std | 1.47 | 1.36 | 2.42 | 5.60 | 0.89 | 0.55 | |

CV | 0.06 | 0.07 | 0.03 | 0.08 | 0.34 | 0.17 | |

Post monsoon | Average | 19.56 | 9.64 | 84.37 | 48.86 | 4.13 | 2.24 |

Max | 26.70 | 17.20 | 94.40 | 69.00 | 7.90 | 3.28 | |

Min | 11.80 | 3.30 | 71.70 | 24.90 | 1.00 | 1.55 | |

Std | 3.51 | 3.25 | 3.71 | 7.35 | 1.46 | 0.38 | |

CV | 0.18 | 0.34 | 0.04 | 0.15 | 0.35 | 0.17 | |

Pre monsoon | Average | 24.09 | 13.68 | 84.30 | 50.12 | 4.64 | 3.50 |

Max | 28.10 | 18.30 | 94.60 | 68.30 | 7.30 | 5.39 | |

Min | 17.20 | 6.70 | 67.60 | 29.60 | 2.10 | 2.82 | |

Std | 2.33 | 2.56 | 4.90 | 7.77 | 0.95 | 0.42 | |

CV | 0.10 | 0.19 | 0.06 | 0.15 | 0.21 | 0.12 |

Time scale . | Statistics . | T_{max}
. | T_{min}
. | RH_{max}
. | RH_{min}
. | SSH . | ET_{0}
. |
---|---|---|---|---|---|---|---|

Annual | Average | 22.97 | 13.72 | 86.28 | 55.72 | 3.76 | 2.85 |

Max | 33.50 | 20.60 | 94.60 | 83.50 | 9.90 | 5.51 | |

Min | 11.80 | 3.30 | 67.60 | 24.90 | 0.00 | 1.53 | |

Std | 3.97 | 4.70 | 4.61 | 11.40 | 1.48 | 0.66 | |

CV | 0.17 | 0.34 | 0.05 | 0.20 | 0.39 | 0.23 | |

Monsoon | Average | 26.40 | 18.84 | 90.14 | 68.54 | 2.59 | 3.20 |

Max | 33.45 | 20.60 | 94.20 | 83.50 | 5.60 | 5.65 | |

Min | 21.70 | 14.40 | 75.50 | 51.70 | 1.00 | 2.62 | |

Std | 1.47 | 1.36 | 2.42 | 5.60 | 0.89 | 0.55 | |

CV | 0.06 | 0.07 | 0.03 | 0.08 | 0.34 | 0.17 | |

Post monsoon | Average | 19.56 | 9.64 | 84.37 | 48.86 | 4.13 | 2.24 |

Max | 26.70 | 17.20 | 94.40 | 69.00 | 7.90 | 3.28 | |

Min | 11.80 | 3.30 | 71.70 | 24.90 | 1.00 | 1.55 | |

Std | 3.51 | 3.25 | 3.71 | 7.35 | 1.46 | 0.38 | |

CV | 0.18 | 0.34 | 0.04 | 0.15 | 0.35 | 0.17 | |

Pre monsoon | Average | 24.09 | 13.68 | 84.30 | 50.12 | 4.64 | 3.50 |

Max | 28.10 | 18.30 | 94.60 | 68.30 | 7.30 | 5.39 | |

Min | 17.20 | 6.70 | 67.60 | 29.60 | 2.10 | 2.82 | |

Std | 2.33 | 2.56 | 4.90 | 7.77 | 0.95 | 0.42 | |

CV | 0.10 | 0.19 | 0.06 | 0.15 | 0.21 | 0.12 |

*Note*: *T*_{max}: maximum temperature, °C; *T*_{min}: minimum temperature, °C; RH_{max}: maximum relative humidity, %; RH_{min}: minimum relative humidity, % ; SSH: sunshine duration, (hours); ET_{0}: reference evapotranspiration, mm d^{−1.}

### Modeling of reference evapotranspiration (ET_{0})

*et al.*1998) equation is used as the standard method for the computation of ET

_{0}from meteorological data. The mathematical equation of the FAO56-P-M, ET

_{0}can be written as:where is reference evapotranspiration (mm d

^{−1}), is net radiation (MJ m

^{−2}d

^{−1}), is difference between the saturation vapor pressure (kPa) and the actual vapor pressure (kPa), is the slope of the saturation vapor pressure–temperature curve (kPa °C

^{−1}), is the psychometric constant (kPa °C

^{−1}), is the wind speed at 2 m height (m s

^{−1}), is the average air temperature (°C), and

*G*

_{hf}is the monthly soil heat flux density (M J m

^{−2}d

^{−1}). The detailed procedure for estimating different secondary parameters of FAO-56-P-M can be found elsewhere (Allen

*et al.*1998).

### Data management for analysis

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 ET_{0} was estimated using the FAO56-P-M equation. The baseline values were fixed as mean values of monthly, seasonal ET_{0}, and CPs.

### Trend and change point (*T*_{AC}) analysis

*T*

_{max}(°C),

*T*

_{min}(°C), RH

_{max}(%), RH

_{min}(%), SSH (h), and ET

_{0}(mm d

^{−1}), were used for trend and abrupt change year (

*T*

_{AC}). The modified nonparametric Mann–Kendall (MM-K) (Yue & Wang 2004) was used for trend analysis. The MM-K statistics (

*Z*

_{c}) can be estimated using the Mann–Kendall method (Mann 1945; Kendall 1975) by eliminating the influence of serial autocorrelation in

*x*(

_{i}*i*= 1, 2, 3 …..

*n*, where

*n*is the total number of years). The correction in MM-K statistics

*Z*'s variance was performed, as in Hameed & Rao (1998) and Sonali & Nagesh Kumar (2013).where

*n*is the number of data points,

*n** is the effective sample size, and

*n*/

*n** is the correction factor for serial correlation in sample data,

*V*(

*Z*) is the variance of

*Z*of MK (Mann–Kendall) statistic for the time series, estimated using the following relationship:

*n*/

*n** in Equation (2) can be estimated as:where

*r*is the lag-l serial correlation coefficient of rank

_{l}^{R}*R*

_{X}_{t}of the sample data

*X*

_{t}. Salas

*et al.*'s (1980) equation given below is used for estimating values

*r*by substituting the sample data

_{k}^{R}*X*

_{t}by their ranks

*R*

_{X}_{t}.where

*r*

_{l}is the serial correlation coefficient at lag1 of the sample (

*X*), and

_{s}*E*(

*X*) is the mean of the sample.

_{s}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).

*et al.*2008; Sonali & Nagesh Kumar 2013; Sayemuzzaman & Jha 2014; Jones

*et al.*2015). The SQM-K is a sequential progressive

*S*(

_{q}*t*) and backward

*S*′ (

_{q}*t*) analysis of the MK test. In this case, sequential progressive

*S*(

_{q}*t*) and backward

*S*′ (

_{q}*t*) series intersect or diverge from each other for an extended period. The beginning of the year of divergence exhibits the

*T*

_{AC}. In

*S*(

_{q}*t*) analysis, the number of cases

*X*(

_{j}*j*= 1,2,3 …

*n*) >

*X*(

_{k}*k*= 1, 2 …

*j*− 1), denoted by

*n*

_{t}_{,}is counted at each comparison. In

*S*(

_{q}*t*) estimation, the number of times,

*N*for which

_{t}*X*>

_{j}*X*was counted. The sequential test statistics

_{k}*S*are calculated by:

_{t}The *S _{q}*′ (

*t*) was determined, estimated similarly, with

*x*'s termination point being the beginning.

_{i}### Detrending of CPs

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 (

*m*_{1}) between both upper and lower envelopes. - 5.
The first component is calculated as

*h*_{1}(*t*) =*x*(*t*) −*m*_{1}(*t*).

*h*

_{1}(

*t*) as the next input signal. This procedure is repeated for

*k*times until it fulfills the IMF conditions i.e.,

*h*

_{1k}(

*t*) =

*h*

_{(1-k)}(

*t*) −

*m*

_{1k}(

*t*), then

*c*

_{1}(

*t*) =

*h*

_{1k}(

*t*) is considered as the first IMF. Then residue is determined by subtracting the first IMF from

*x*(

*t*) (i.e.,

*r*

_{1}(

*t*) =

*x*(

*t*) −

*c*

_{1}(

*t*)). Continue this procedure for until series (t) becomes a monotonic function such that the extraction of further IMF is not possible. Therefore, signal

*x*(

*t*) can be illustrated as:

*t*) =

*x*(

*t*) + (

*t*), where (

*t*) are the white realization and then decomposing it via the EMD method. Procured from the first series (

*t*), one can compute the first series component

*x*(

*t*) as

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.

### Scenarios of ET_{0} estimated using the detrended CPs

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 ET_{0} using various sets, as shown in Table 2 of the observed and detrended CPs.

Climatic parameters . | Scenarios/ Combinations . | |||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|

CP1 . | CP2 . | CP3 . | CP4 . | CP5 . | CP6 . | CP7 . | CP8 . | CP9 . | CP10 . | CP11 . | CP12 . | |

T_{max} (°C) | * | * | * | |||||||||

T_{min} (°C) | * | * | * | |||||||||

RH_{max} (%) | * | * | * | * | * | |||||||

RH_{min} (%) | * | * | * | * | * | |||||||

SSH (h) | * | * | * | * | * |

Climatic parameters . | Scenarios/ Combinations . | |||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|

CP1 . | CP2 . | CP3 . | CP4 . | CP5 . | CP6 . | CP7 . | CP8 . | CP9 . | CP10 . | CP11 . | CP12 . | |

T_{max} (°C) | * | * | * | |||||||||

T_{min} (°C) | * | * | * | |||||||||

RH_{max} (%) | * | * | * | * | * | |||||||

RH_{min} (%) | * | * | * | * | * | |||||||

SSH (h) | * | * | * | * | * |

*Climatic parameter de-trended in the scenario and used for re-estimating ET_{0}.

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).

## RESULTS

### Trend analysis and comparison between Sen's slope (*b*) and regression slope

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).

CPs . | Z_{C}
. | b
. | Regression slope . | T_{AC}
. |
---|---|---|---|---|

T_{max} (°C) | 1.24 | 0.006 (°C per year) | 0.0044 (°C per year) | 1985 |

T_{min} (°C) | 3.93** | 0.095 (°C per year) | 0.0978 (°C per year) | – |

RH_{max} (%) | 0.34 | 0.031 (% per year) | 0.0214 (% per year) | 1983 |

RH_{min} (%) | 0.4 | 0.013 (% per year) | 0.021 (% per year) | 1982 |

SSH (h) | −5.65** | −0.049 (h per year) | −0.052 (h per year) | – |

ET_{0} (mm d^{−1}) | −4.57** | −0.0078 (mm d^{−1} per year) | −0.0078 (mm d^{−1} per year) | – |

CPs . | Z_{C}
. | b
. | Regression slope . | T_{AC}
. |
---|---|---|---|---|

T_{max} (°C) | 1.24 | 0.006 (°C per year) | 0.0044 (°C per year) | 1985 |

T_{min} (°C) | 3.93** | 0.095 (°C per year) | 0.0978 (°C per year) | – |

RH_{max} (%) | 0.34 | 0.031 (% per year) | 0.0214 (% per year) | 1983 |

RH_{min} (%) | 0.4 | 0.013 (% per year) | 0.021 (% per year) | 1982 |

SSH (h) | −5.65** | −0.049 (h per year) | −0.052 (h per year) | – |

ET_{0} (mm d^{−1}) | −4.57** | −0.0078 (mm d^{−1} per year) | −0.0078 (mm d^{−1} per year) | – |

*Z*_{C}, MMK statistic; *b*, Sen's slope; *T*_{AC}, abrupt change year, **significant trend at 5% significance level.

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 ET_{0}, *T*_{AC} was not observed as the two series, *S _{q}* (

*t*) and

*S*′ (t) did not cross each other. The Sen's slope

_{q}*b*for ET

_{0}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 ET

_{0}. 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 of CPs and ET_{0} and their trends

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 ET_{0}. These major or minor differences in linear and nonlinear trends in basic input parameters for ET_{0} estimation create a difference in recalculated ET_{0} after linear and nonlinear detrending.

The distinct variations of the five principal CPs resulted in a difference of ET_{0.} The ET_{0} variation (Figure 2(f)) and its linear and nonlinear trend represented a decreased trend. The significant difference between the linear and nonlinear trends in ET_{0} contributes to the difference in regenerated ET_{0} between Group 1 and 2.

### Impact of removing linear trends from annual CPs on ET_{0}

In this analysis, the ET_{0} 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 ET_{0} with the original calculated ET_{0} under Scenario 1 (CP1).

For CP2, as depicted in Figure 3(a), the recalculated ET_{0} 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 ET_{0} value decreased. For CP3, the recalculated ET_{0} values obtained after detrending the *T*_{min} are higher during 1980–1983, 1986–1988; from 1993 to 2010, the detrended ET_{0} is slightly lower than the CP1 ET_{0} (Figure 3(b)), and from 2011 to 2015, the detrended ET_{0} 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 ET_{0} values. Comparing CP4 and CP1 (Figure 3(c)) shows the decreasing values of ET_{0}. The recalculated ET_{0} values are higher during 1981–1982 and in 1997. Overall, the detrended ET_{0} is lower than the CP1 ET_{0}.

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 ET_{0} value. Thus, it may be concluded that detrending of *T*_{max} and *T*_{min} has a negative effect on ET_{0}. Thus, for temperature parameters, except for scenario CP3 (*T*_{min} de-trended), the recalculated ET_{0} was below the ET_{0} curve of CP1, which concludes that detrending T factors (CP2, CP3, CP4) result in decreasing ET_{0}.

Detrending RH parameters (CP5 to CP7), as depicted in (Figure 3(d)–(f)), showed a slight increase in ET_{0} 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 ET_{0} 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 ET_{0} values is much stronger than an insignificant increase in RH factors (Figure 3(h)–(j)).

Variation in ET_{0} 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 ET_{0} is much stronger than an insignificant increase in *T*_{max} and a significant increase in *T*_{min}.

### Impact of removing nonlinear trends from annual CPs on ET_{0}

For nonlinear detrending, CP2 insignificantly affects the variation in ET_{0} during the study period (Figure 4(a)). Analysis of Figure 4(a) revealed that the original ET_{0} and the values of recalculated ET_{0} of CP3 show decreasing values of ET_{0} for both the scenarios. The estimates of recalculated ET_{0} 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 ET_{0}. 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 ET_{0}. The increasing trend of RH_{max} and RH_{min} has an insignificant effect on ET_{0} 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 ET_{0}. However, the impact of decreasing sunshine duration CP8 (Figure 4(g)) on reducing ET_{0} is much more substantial than an insignificant increase in RH factors, which is similar to linear detrending. The ET_{0} 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 ET_{0} in the region. Hence, we can conclude that the detrending sunshine hour surpasses the detrending of other selected CPs.

### Impact of detrending all the CPs on ET_{0}

The original ET_{0} (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 ET_{0} and nonlinearly detrended ET_{0} for scenario CP12, whereas, trend and intercept for linearly detrended ET_{0} 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 ET_{0} 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).

S No . | Scenarios . | Slope of linear regression trend line . | Intercept of linear regression . |
---|---|---|---|

1 | CP1 (original ET_{0}) | −0.0078 | 18.989 |

2 | CP12 (linear de-trended) | −0.0003 | 4.018 |

3 | CP12 (nonlinear de-trended) | −0.0074 | 18.213 |

S No . | Scenarios . | Slope of linear regression trend line . | Intercept of linear regression . |
---|---|---|---|

1 | CP1 (original ET_{0}) | −0.0078 | 18.989 |

2 | CP12 (linear de-trended) | −0.0003 | 4.018 |

3 | CP12 (nonlinear de-trended) | −0.0074 | 18.213 |

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 ET_{0} 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 ET_{0} 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 ET_{0}.

### ΔET_{0} variations under different scenarios

ΔET_{0} is the difference in the original ET_{0} and the recalculated ET_{0} 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 ΔET_{0}, in which values of ET_{0} were re-computed using linearly and nonlinearly detrended *T*_{max} (CP2). The total absolute ΔET_{0} 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 ΔET_{0} 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 ET_{0}, 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 ΔET_{0} 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 ET_{0} on detrending; these will increase the value of ET_{0} significantly for both the groups. In contrast, in the case of CP5, the average estimates of ΔET_{0} move near to zero. Hence detrending RH_{max} has the least influence on ET_{0}. For the ΔET_{0} variations of Group 1 and Group 2 for scenarios CP8 to CP11, the pattern of detrending is the same, i.e., the ΔET_{0} values for scenario CP8 and CP9, and CP10 and CP11 showed the same pattern, and similar to ΔET_{0} 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}).

Scenarios . | Group 1 . | Group 2 . | ||||||
---|---|---|---|---|---|---|---|---|

Maximum (mm d^{−1})
. | Minimum (mm d^{−1})
. | Abs. Sum (mm d^{−1})
. | Mean (mm d^{−1})
. | Maximum (mm d^{−1})
. | Minimum (mm d^{−1})
. | Abs. Sum (mm d^{−1})
. | Mean (mm d^{−1})
. | |

CP2 | 0.21 | −0.05 | 3.19 | 0.09 | 0.06 | −0.07 | 0.60 | 0.02 |

CP3 | 0.06 | −0.14 | 1.07 | 0.03 | 0.03 | −0.04 | 0.34 | 0.01 |

CP4 | 0.25 | −0.07 | 3.37 | 0.09 | 0.07 | −0.09 | 0.73 | 0.02 |

CP5 | 0.08 | −0.06 | 0.77 | 0.02 | 0.04 | −0.03 | 0.41 | 0.01 |

CP6 | 0.15 | −0.24 | 2.88 | 0.08 | 0.07 | −0.09 | 1.09 | 0.03 |

CP7 | 0.37 | −0.18 | 3.47 | 0.10 | 0.06 | −0.08 | 0.99 | 0.03 |

CP8 | 0.26 | −0.32 | 4.62 | 0.13 | 0.10 | −0.08 | 1.45 | 0.04 |

CP9 | 0.32 | −0.33 | 4.80 | 0.13 | 0.13 | −0.08 | 1.55 | 0.04 |

CP10 | 0.31 | −0.30 | 4.85 | 0.13 | 0.13 | −0.11 | 1.58 | 0.04 |

CP11 | 0.29 | −0.32 | 4.90 | 0.14 | 0.12 | −0.09 | 1.60 | 0.04 |

CP12 | 0.37 | −0.24 | 4.12 | 0.11 | 0.18 | −0.08 | 1.77 | 0.05 |

Scenarios . | Group 1 . | Group 2 . | ||||||
---|---|---|---|---|---|---|---|---|

Maximum (mm d^{−1})
. | Minimum (mm d^{−1})
. | Abs. Sum (mm d^{−1})
. | Mean (mm d^{−1})
. | Maximum (mm d^{−1})
. | Minimum (mm d^{−1})
. | Abs. Sum (mm d^{−1})
. | Mean (mm d^{−1})
. | |

CP2 | 0.21 | −0.05 | 3.19 | 0.09 | 0.06 | −0.07 | 0.60 | 0.02 |

CP3 | 0.06 | −0.14 | 1.07 | 0.03 | 0.03 | −0.04 | 0.34 | 0.01 |

CP4 | 0.25 | −0.07 | 3.37 | 0.09 | 0.07 | −0.09 | 0.73 | 0.02 |

CP5 | 0.08 | −0.06 | 0.77 | 0.02 | 0.04 | −0.03 | 0.41 | 0.01 |

CP6 | 0.15 | −0.24 | 2.88 | 0.08 | 0.07 | −0.09 | 1.09 | 0.03 |

CP7 | 0.37 | −0.18 | 3.47 | 0.10 | 0.06 | −0.08 | 0.99 | 0.03 |

CP8 | 0.26 | −0.32 | 4.62 | 0.13 | 0.10 | −0.08 | 1.45 | 0.04 |

CP9 | 0.32 | −0.33 | 4.80 | 0.13 | 0.13 | −0.08 | 1.55 | 0.04 |

CP10 | 0.31 | −0.30 | 4.85 | 0.13 | 0.13 | −0.11 | 1.58 | 0.04 |

CP11 | 0.29 | −0.32 | 4.90 | 0.14 | 0.12 | −0.09 | 1.60 | 0.04 |

CP12 | 0.37 | −0.24 | 4.12 | 0.11 | 0.18 | −0.08 | 1.77 | 0.05 |

The value for absolute ΔET_{0} 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).

### ΔET_{0} variations of Group 1 and Group 2 for scenario CP12

In both the linear and nonlinear detrending, the detrending pattern is the same for scenario CP12 (Figure 7). The maximum and minimum value of ΔET_{0} 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 ΔET_{0} 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 ΔET_{0} like maximum, minimum, and average ΔET_{0} are represented in Figure 8. The ΔET_{0} statistic for Group 1 is significantly higher than Group 2, which may be because meteorological data follow a nonlinear pattern. Hence, nonlinear detrended ET_{0} is closer to actual ET_{0,} which resulted in the lowest ΔET_{0} values. Therefore, it may be proposed that nonlinear detrending gives closer results to the benchmark ET_{0} values than linear detrending. In all the ΔET_{0} analyses, it is concluded that a significant difference was observed in all the CPs scenarios. For linear detrending, ΔET_{0} values in all the cases are on the higher side. The similar values of ΔET_{0} were found on the lower side in the case of nonlinear detrending.

## DISCUSSION

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 ET_{0} 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 ET_{0} were the biggest when contrasted with the effects of detrending of single parameters. Furthermore, the effects of detrending SSH on decreasing ET_{0} 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 ET_{0} in the eastern Himalayan region.

The decreasing trend in ET_{0} 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 ET_{0} 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 ET_{0}. 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 ET_{0} over northeast India. Patle *et al.* (2019), using sensitivity analysis for Gangtok, East Sikkim, concluded that ET_{0} changes positively related to SSH and T factors. According to Li *et al.* (2014), one of the main reasons behind the decreasing trend of ET_{0} 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 ET_{0} 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 ET_{0} in Sikkim, dissimilarities were found for the recalculated ET_{0} between Group 1 and Group 2 scenarios. Due to the seasonal periodicity in the CPs, including ET_{0}, the results from Group 2 were even more conclusive for assessing the impacts of global warming and climate change on ET_{0}.

The decrease of ET_{0} results in reduced crop water/ irrigation requirements for crops and plants in the region. Diminished ET_{0} 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.

## CONCLUSIONS

This study aims to identify the impacts of eliminating trends (linear and nonlinear) from the meteorological parameters (CPs) that drive ET_{0} processes. Accordingly, 23 scenarios, including the non-de-trended ET_{0} (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 ET_{0} for the period 1980–2015 in Gangtok, East Sikkim. To study the influence of trend, the ET_{0} was re-estimated after detrending the respective CPs and then compared with non-de-trended ET_{0} (CP1). The main conclusions derived are as follows:

- 1.
The difference between ET

_{0}and the detrended ET_{0}(ΔET_{0}) was significantly higher for linear detrending (Group 1) as compared to nonlinear detrending (Group 2). For linear detrending, the maximum difference ΔET_{0}was observed as 0.37 mm d^{−1}for 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 ΔET

_{0}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 ET_{0}. 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 ET

_{0}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 ET_{0}, which neutralized increased*T*_{min}and RH on ET_{0}. - 4.
The declines of

*T*_{max}and increment of RH likewise added to the low abatement of ET_{0}. Overall, the combined impacts of all CPs caused the general decline of ET_{0}. - 5.
Additionally, the comparison of removing trends nonlinearly from single or multiple CPs may be useful to understand the changing pattern of ET

_{0}under global warming conditions.

## AUTHOR'S CONTRIBUTION STATEMENT

**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.

## CONFLICT OF INTEREST

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.

## DATA AVAILABILITY STATEMENT

Data cannot be made publicly available; readers should contact the corresponding author for details.

## REFERENCES

*,*