Long-term temperature trend analysis associated with agriculture crops

Abstract

Temperature is one of the most significant elements in climate and weather forecasting. There was an increase in the earth’s surface (land and ocean) temperature by 0.6 ± 0.2 °C during 1901–2000 (NOAA, Global Climate Report 2017). In evaluating the effects of climate change, the spatiotemporal variability of temperature was examined in the Chhattisgarh State, India, using monthly data at 16 stations over the period 1901–2016 with a length of 116 years. The standard normal homogeneity test was used to evaluate the homogeneity of temperature data. Linear regression analysis and four altered versions of the Mann-Kendall (MK) method were utilized to analyze the existence of trends in temperature series. These four versions of the MK tests include the conventional Mann-Kendall method (MK1), the removed influence of noteworthy lag-1 autocorrelation (MK2), the removed influence of all noteworthy autocorrelation coefficients (MK3) and the considered Hurst coefficient (MK4). The results of both parametric and non-parametric tests indicated an increase in the annual and seasonal temperature in the Chhattisgarh State over the period 1901–2016. The most likely change year in the state was 1950. There was a decreasing trend at some stations during the period 1901–1950, which reversed in the following period 1951–2016. Overall, annual and seasonal temperature time series showed increasing trends in all stations over the course of the long-term period. Our results confirmed a fact that the agriculture crop production has been decreased due to climate change.

Appendix

1.1 Trend analysis using MK (MK1/MK2/MK3/MK4) tests

1.1.1 Trend analysis based on MK1 test

The following procedure was followed to identify trend in the time series temperature: in the expectation that the time series will be autonomous, the Mann-Kendall value $\mathcal{S}$ will be described as

$$ \mathcal{S}=\sum \limits_{i=1}^{m-1}\sum \limits_{j=i+1}^m\operatorname{sign}\left({y}_j-{y}_i\right) $$

(4)

where ${y}_i,{y}_j$and $m$ are i^th and j^th terms sequential data and sample size respectively and

$$ \operatorname{sign}\left({y}_j-{y}_i\right)=\left\{\begin{array}{c}-1,\mathrm{if}\kern0.5em {y}_j-{y}_i<1\\ {}\kern0.5em 0,\mathrm{if}\kern0.75em {y}_j-{y}_i=0\kern1em \\ {}1,\mathrm{if}\ {y}_j-{y}_i>1\end{array}\right. $$

(5)

The statistic $\mathcal{S}$ is generally Gaussian when $m=18$ with the variance $\mathrm{Var}\left(\mathcal{S}\right)$ and mean $\mathcal{E}\left(\mathcal{S}\right)$ of the statistic $\mathcal{S}$ expressed as

$$ \mathcal{E}\left(\mathcal{S}\right)=0, Var\left(\mathcal{S}\right)=\frac{\left(m-1\right)m\left(2m+5\right)}{18} $$

(6)

However, if there are ties in the data set, the adjusted articulation for Var($\mathcal{S}$) will be

$$ \mathrm{Var}\left(\mathcal{S}\right)=\frac{\left\{\left(m-1\right)m\left(2m+5\right)-\sum \limits_{p=1}^q\left({t}_p-1\right){t}_p\left(2{t}_p+5\right)\ \right\}}{18} $$

(7)

The variables q and ${t}_p$in Eq. (7) denote the number of tied groups and data values in the p-th group, individually. The institutionalized statistic $\left(\mathcal{Z}\right)$for one- followed trial of the statistic $\mathcal{S}$ is

$$ {\mathcal{Z}}_{mk}=\left\{\begin{array}{c}\frac{S+1}{\sqrt{\mathrm{Var}(S)}},\mathrm{if}\ \mathcal{S}<0\\ {}0,\mathrm{if}\ \mathcal{S}=0\\ {}\frac{\mathcal{S}-1}{\sqrt{\mathrm{Var}\left(\mathcal{S}\right)}},\mathrm{if}\ \mathcal{S}>0\end{array}\right. $$

(8)

The trend is increasing for a positive value of ${\mathcal{Z}}_{mk}$ and decreasing for a negative value of it.

1.1.2 Trend analysis based on MK2 test

The effect of serial correlation on the MK test was removed by eliminating from the temperature time sequence the lag-1 serial correlation section before using the MK test for trend analysis. This is called the trend free pre-whitening (TFPW) treatment. Afterwards, trends were identified using the MK test in the remaining (or pre-whitened) sequence. Steps 1 through 4 used the MK2 to analyze trends:

• 1. The new time series suggested by Kumar et al. (2009) was acquired as

$$ {y}_i^{\prime }={y}_i-\left(\beta \times i\right) $$

(9)

where, β = magnitude of slope.

• 2. After calculating the ${r}_1$for ${y}_i^{\prime }$ time data set, the residual series was determined as

$$ {x}_i^{\prime }={y}_i^{\prime }-{r}_1\times {y}_{i-1}^{\prime } $$

(10)

• 3. The estimation of $\left(\beta \times i\right)$ was added again to the remaining data set as taken after

$$ {x}_i={x}_i^{\prime }+\left(\beta \times i\right) $$

(11)

• 4. MK1 was used for trend analysis of ${x}_i$ series.

1.1.3 Trend analysis based on MK3 test

In this technique, an improved variance of $\mathcal{S}$, assigned as Var($\mathcal{S}$)*, was utilized to remove the impact of every critical coefficients of autocorrelation from a data set as follows (Hamed and Rao 1998):

$$ \mathrm{Var}{\left(\mathcal{S}\right)}^{\ast }=\frac{m}{m^{\ast }}V\left(\mathcal{S}\right) $$

(12)

where ${m}^{\ast }=$ effective sample size. Hamed and Rao (1998) proposed the accompanying condition to directly calculate the $\frac{m}{m^{\ast }}$ ratio:

$$ \frac{m}{m^{\ast }}=1+\frac{2}{m\left(m-1\right)\left(m-2\right)}\sum \limits_{i=1}^{m-1}\left(m-i\right)\left(m-i-1\right)\left(m-i-2\right){r}_i $$

(13)

where $m=$ actual number of perceptions and ${r}_i=\mathrm{lag}-i$ significant coefficient of autocorrelation of rank i of time series. After computing Var($\mathcal{S}$)* from Eq. (13), it is substituted for Var($\mathcal{S}$) in Eq. (12). Ultimately, the Mann-Kendall 풵 was tried for significance of trend contrasting it with limit levels 1.645 for 10%, 1.96 for 5% and 2.33 for 1% level of significance.

1.1.4 Trend analysis based on MK4 test

Kumar et al. (2009) explained the Mann-Kendall method’s fourth version, which considers the Hurst coefficient (ℌ) of a series for long-term persistence. In order to apply the MK4, the calculation of the Hurst coefficient (ℌ) was carried out. The standard deviation and mean of (ℌ) are the function of $m$  and can be calculated using the method described by Dinpashoh et al. 2014 (Hamed 2008). As suggested by Kumar et al. (2009), improved variance for the $\mathcal{S}$ static was calculated for significant (ℌ) values.