J. Meteor. Res.  2016, Vol. 30 Issue (6): 1019-1032   PDF    
http://dx.doi.org/10.1007/s13351-016-6031-0
The Chinese Meteorological Society
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Article Information

PIYOOSH Atul Kant, GHOSH SanjayKumar . 2016.
A Comparative Assessment of Temperature Data from Different Sources for Dehradun, Uttarakhand, India. 2016.
J. Meteor. Res., 30(6): 1019-1032
http://dx.doi.org/10.1007/s13351-016-6031-0

Article History

Received March 10, 2016
in final form August 1, 2016
A Comparative Assessment of Temperature Data from Different Sources for Dehradun, Uttarakhand, India
PIYOOSH Atul Kant, GHOSH SanjayKumar     
. (Department of Civil Engineering, Indian Institute of Technology Roorkee, Roorkee 247667, Uttarakhand, India);
ABSTRACT: A comparative study of extreme temperature parameters from different sources is carried out by examining standardized anomalies, trends, correlation, and equivalence of datasets. Maximum temperature (Tmax) and minimum temperature (Tmin) for Dehradun, from two different sources such as computed and gridded data from Climatic Research Unit (CRU) and observed data from India Meteorological Department (IMD) are used for 1901-2012. The CRU data are compared initially with IMD, by graphical assessment of standardized anomalies. Subsequently, change points are identified by using Cumulative Sum (CUSUM)-chart technique for trend analysis. The magnitude and significance of trends are determined by applying Sen's slope test, and on the basis of these, trends are compared. Further, correlation analysis is carried out and datasets are tested for equivalence by using Wilcoxon-Mann-Whitney test. The result shows that annual standardized anomalies of CRU data follow the pattern of annual standardized anomalies of IMD data. The CRU data exhibit similar trends and are well correlated with IMD dataset. Moreover, CRU anomaly data are identical with IMD anomaly data in the recent decades. High resolution gridded CRU data have open access and may be more useful due to its spatio-temporal continuity for land areas of the world.
Key words: cumulative sum     Sen's slope     temperature trend     temperature anomaly     correlation     Wilcoxon-Mann-Whitney test    
1Introduction

Long-term analysis of trends for temperature data is required for study of climate change and its impacts. Most of the observational and meteorological station data lack in spatio-temporal continuity in an area of interest for longer period (van Wart et al., 2015). Moreover, there is often limited and restricted access to such directly measured datasets (Hughes et al., 2009). Western Himalayan region has logistic difficulties and observational data availability are poor at high elevations (Yadav et al., 2004). Due to this, Himalayan region is not adequately studied (Bhutiyani et al., 2007) and climate of the region is not well known (Yadav et al., 2004). Time series of gridded data for temperature are freely available from various open sources for longer periods and are being widely used. These datasets are spatio-temporally continuous and may useful for regions lacking in observational datasets. One of the most referred data products is from Hadley Centre and Climatic Research Unit (CRU; Cowtan and Way, 2014).

High resolution CRU datasets are freely available from 1901 and onwards as monthly time series for various climatological variables including temperature parameters Tmax and Tmin. This dataset is computed on the basis of compiled station data from many sources and provides data in usable format for entire land surface except Antarctic region (Harris et al., 2014). Rao et al. (2014) gave preference to this data in comparison to data from National Data Centre (NDC), India and India Meteorological Department (IMD) due to its finer resolution. Robertson et al. (2013) compared CRU and IMD data for a specific grid box near 26.5°N, 80.5°E in northern India for winter seasons from 1982 to 2005. On the basis of graphical comparison, they found a good degree of closeness between the time series of two data. This has opened great possibility for researchers to use CRU data for their purpose. However, to strengthen observation of Robertson et al. (2013), more in-depth and detailed comparative study on the basis of statistical analysis is required.

Many researchers have compared data from different sources for their studies. To compare SST data of three gridded products and time series from in-situ measurements, Hughes et al. (2009) calculated annual mean anomalies and carried out correlation analysis. Variable degree of correlation was found with different SST products and they show greater variation (higher amplitude) in comparison to the in-situ data.

Tang et al. (2010) compared five Chinese mean temperature series, including CRU TS3.10 and four others, on the basis of annual mean temperature anomalies, correlation and magnitude of temperature trend. The anomalies differ widely before 1950; however, after 1951 they have shown close agreement with each other. The correlation coefficients found between any two of the five series range from 0.73 to 0.97. The magnitude of rising trends for different data ranges from 0.34 to 1.20℃ (100 yr)-1. Wen et al. (2011) compared three global mean temperature data series of HadCRUT3, NCDC, and GISS. They used 10-yr av eraged temperature anomalies and 100-yr warming trend of these datasets for inter-comparison and found that three series yielded similar trends of warming.

Cheema et al. (2011) carried out a comparative study for identifying trend of minimum temperature using meteorological and projected model data. The analysis of trend and statistical based applications, such as scatter-plot and correlation are used to compare station data for 44 locations in Pakistan and projected temperature data from statistical downscale model (SDM) for the period of 1991-2010. The strong correlation has suggested that model data may be used for other purposes. A graphical comparison of CRU TS3.10 temperature data constructed by Harris et al. (2014) and other dataset developed by University of Delaware (UDEL) is carried out on subcontinental scale using temperature anomalies (Harris et al., 2014). Further, these datasets are also compared on the basis of magnitude of long-term trends and correlation between the two datasets. The dataset compares well; however, in the regions and time periods with thinly distributed observed data major deviations are also found.

In the present study, a comparative assessment of Tmax and Tmin of computed and gridded CRU data with observed IMD data is carried out. This study evaluates CRU data for its possible usefulness, for larger areas lacking in observational records in Dehradun region of Uttarakhand, India. Objectives of this study are initially to compare the time series of annual standardized anomalies for Tmax and Tmin of CRU data with IMD data. Subsequently, identification of change points in the time series of CRU and IMD datasets and splitting time series in the sub-series for trend analysis. Further, to compare the sub-series of two datasets by magnitude of trend and correlation analysis on monthly, seasonal, and annual timescales. Finally, anomalies in the sub-series of two datasets were tested for equality on monthly, seasonal, and annual timescales.

2Study area and data

Dehradun city is chosen for study, which is the state capital of Uttarakhand, India (Fig. 1). It is located at 30°1901.200N, 78°01058.800E. New state of Uttarakhand was formed by separating northern portion of Uttar Pradesh in the year 2000. After designation as state capital, Dehradun has observed sudden and phenomenal changes in population and climate. Dehradun district has great variation in its topography and includes Himalayan Mountains, Shivalik Hills, Plains, Dun Valley, and two major rivers, e.g., Ganges on the east side while Yamuna River on the western side of Dehradun.

Figure 1 The study area.

Table 1 shows list of temperature data used in this study. CRU TS3.21 data of monthly Tmax and Tmin (Jones and Harris, 2013) are used in this study. It is high resolution gridded dataset of grid size 0.5° × 0.5°. These data are downloaded from Centre for Environmental Data Archival (CEDA) of British Atmospheric Data Centre (BADC), UK. Temperature data for Tmax and Tmin of IMD are downloaded for Dehradun city from web site of the organization (IMD data, 1901-2000) and it is updated from ENVIS (Environmental Information System) Centre, Uttarakhand, India (IMD data 2000-2012).

Table 1 Data description
3Methodology

Methodology adopted for the present study is shown in Fig. 2. A brief description of different steps involved and techniques used is given in the following sub-sections.

Figure 2 Flow chart of methodology.
3.1Data interpolation

Out of two datasets used, CRU data are gridded dataset at 0.5° × 0.5° grid size and require interpolation for the location of Dehradun. CRU data are interpolated from four nearest grids using inverse distance squared weighting, also called as power-2 inverse distance weighting (Nalder and Wein, 1998; Shen et al., 2001) technique.

3.2Anomaly and standardized anomaly

An anomaly is the deviation from mean of the given time series (Jain and Kumar, 2012). It provides better understanding of trends in the data series (Singh et al., 2013). In case of temperature, a positive anomaly indicates warming and negative anomaly indicates cooling with respect to the reference value. An anomaly (x'i) at ith time period in the data series can be computed by the difference of average value (x) from data value (xi) as follows (Wilks, 2011),

(1)

For comparing two datasets, data normalization is required and standardized anomaly (SA) (z) is computed by dividing anomaly by its corresponding standard deviation Sx (Wilks, 2011),

(2)

The SA removes the influences of location and spread from a data sample. Division by the standard deviation puts excursions from the mean in different batches of data on equal footings (Wilks, 2011).

3.3Magnitude and significance of trends 3.3.1CUSUM-chart for change points detection

CUSUM-chart technique is a statistical procedure introduced and studied by Page (1954, 1961) and may be used to detect sequential changes and climatic fluctuations. For detection of change points, CUSUMchart technique is used. If the samples of size n > 1 are collected, and xj is average of jth sample, then cumulative sum chart is constructed by plotting the value Ci against the sample i as follows (Montgomery, 2007):

(3)

where Ci is called cumulative sum up to and including ith sample, and µ0 is a constant representing target value for the process mean. The target value may be taken as the mean of the distribution. Cumulative charts combine information from several samples and they are effective for detecting small process shift. They are particularly effective for n=1, where rationale subgroups are of size equal to one.

The tubular CUSUM works on cumulative deviations above and below target value and is represented by C+ and C-, respectively. The statistics C+ and C- are called one-sided upper and lower CUSUM, respectively. Upper and lower CUSUM depend upon a value K, which is known as allowance. It is generally selected in such a way that it is halfway between target µ0 and out of control value of the mean µ1, which needs to be detected through CUSUM analysis.

The process is said to be out of control, if either of Ci+ and Ci- exceeds the decision interval H for a two-sided CUSUM chart. If H and K are defined as H= and K=, where σ is standard deviation of sample variable used for constructing CUSUM; usually h=4 or 5 and k=0.5 (Montgomery, 2007). In this study, allowance and decision interval remain as K=±0.5σ and H=±2σ, respectively.

3.3.2Sen’s slope estimator for magnitude and significance of trends

Sen’s slope (Sen, 1968) is a non parametric method for estimating slope of the trend in a given sample of N pairs of data. If the linear trend is present in time series, then the true slope of the trend which is change per unit time is expressed as below (Gocic and Trajkovic, 2013; Liu et al., 2013):

(4)

where xj and xk represent values in the time series data for time j and k, respectively (j > k).

If there exists a single datum for each observation tion time, the value N=(n(n -1))/2, where n is the number of observation time. If there exist multiple observation values in one or more observation time, then the value N < (n(n -1))/2, where n is total number of points of time for which observations have been taken. The N numbers of values for Qi are arranged in ascending order. Then the computation for median of slope or Sen’s slope estimator may be carried out as follows:

(5)

The trend of data is reflected by the sign of Qmed and its magnitude gives the steepness of the trend.

For n number of data points, variance Var (S) is defined as follows:

(6)

For determining, slope is statistically different from zero or not, the confidence interval of median slope at a particular probability may be computed as follows:

(7)

where Var (S) is obtained from Eq. (6) and for Z1-α/2, the standard normal distribution table may be referred. Computation for confidence interval has been done at a significance 5% level (α=0.05) for this study.

Thereafter, the values of and are calculated. The lower limit (Qmin) and upper limit (Qmax) of the confidence interval are the M1th largest and the (M2 + 1) th largest of the N ordered slope estimates. Interpolation is done for fractional values of M1 and (M2 + 1) (Gilbert, 1987). The slope Qmed is said to be statistically different from zero, if the two limits ofQmin and Qmax have similar sign (Gocic and Trajkovic, 2013; Liu et al., 2013).

3.4Correlation analysis

The correlation is a statistical method used for finding the relationship between two variables. Correlation has been studied by using scatter plot, correlation coefficient, coefficient of determination, and probability (p) in this study. To make proper judgement about significance of correlation between variables, p is calculated assuming that null hypothesis, which states that correlation between variables is not significantly different from zero, is true. Null hypothesis is rejected if p is sufficiently small (Devore and Berk, 2007). For this study, a significance level of 5% has been considered. Null hypothesis is rejected if p 6 0.05 and alternative hypothesis of significant correlation is accepted.

3.5Mann-Whitney test

The Mann-Whitney test is a non-parametric rank based test and it is used for testing equality of two samples coming from two different populations with respect to their median or mean. This test was first introduced by Wilcoxon (1945) for samples of same dimension. Mann and Whitney (1947) were the first to consider the samples of different dimensions. In this test, it is not necessary that the samples are normally distributed and also the test is not sensitive to the non-homogeneity of the sample data. The null hypothesis H0 for the test is that the two populations from which samples (one from each population) have been drawn, have equal median or mean. The alternative hypothesis is that the populations do not have equal median or mean. Pinto et al. (2006) have used this test to compare two datasets from automated weather station and conventional weather station. They performed this test on the original data and standardized anomalies of data.

Suppose there are two samples (X1, X2, ···, Xm) and (Y1, Y2, ···, Yn) of dimensions m and n and from two different populations 1 and 2, respectively. The two samples are combined and total numbers of observations in the combined sample are N=m + n. These observations in the combined sample are ranked in ascending order. The Mann-Whitney test statistic U is given as follows (Yue and Wang, 2002),

(8)
(9a)
(9b)

with U1 + U2=m·n, where U1 is total number Xi preceding Yi and U2 is total number of Yi preceding Xi and R1, and R2 are rank sums of the samples 1 and 2, respectively. When the null hypothesis H0 is true and both m and n > 8, the test statistic U is approximately normally distributed with mean E(U)=m·n/2 and variance V (U)=m·n(N +1)/12. The random standardized variable u is given as below (Toutenburg, 2002),

(10)

If |u| > u1-α/2, the hypothesis H0 is rejected at α% significance level for a two-tailed test. In the present study, 5% significance level is considered.

4Results

Results of comparative analysis of interpolated CRU data from four nearest grids and IMD data for Dehradun are presented and discussed in subsequent sections for Tmax and Tmin. For each parameter, comparative analysis is based on annual SA time series, trends in the time series, correlation between time series and Wilcoxon-Mann-Whitney test performed on the anomaly time series of the data sets.

4.1Standardized anomaly (SA)

Annual SA for CRU and IMD data for Tmax and Tmin are shown in Figs. 3a and 3b, respectively. A similar graphical pattern is visualized for two datasets of Tmax and Tmin. For Tmax, difference in the SA is found large for 1990-1995, while CRU SAs are closer to IMD SAs for the rest period (Fig. 3a). However, mean absolute error (MAE) for 1901-2012 is found to be 0.80, which is less than the standard deviation (1.0) of IMD SA series. This shows that MAE of CRU data is within the natural variability of observed IMD data. The difference in SAs of Tmin is observed large for 1961-1965 and 1982-1986, while for the rest period, SAs of two datasets are closer to each other. MAE of CRU for Tmin is 0.62, which is also less than standard deviation (1.0) of IMD Tmin SA series. Thus, MAE of CRU Tmin data is also within natural variability of observed IMD data.

Figure 3 Annual standardized anomalies (SAs) of CRU and IMD data for (a) Tmax and (b) Tmin.

Figure 4 shows histogram of annual Tmax and Tmin SA of CRU and IMD data. Frequencies of annual SAs are shown for common 95-yr data availability in both the datasets from 1901 to 2012. The histogram provides a comparison of frequencies in different ranges of SAs. It is observed that frequencies of CRU have a similar pattern with frequencies of IMD data for Tmax (Fig. 4a) and Tmin (Fig. 4b).

Figure 4 Histograms of SA of CRU and IMD for (a) Tmax and (b) Tmin.
4.2Change points

The whole study period is analyzed in three sub-periods. The sub-periods are based on annual change points, obtained from CUSUM-chart analysis. CUSUM charts for Tmax and Tmin are shown in Fig. 5. Major change points for Tmax are found in 1974 and 1997 (Fig. 5a). Analysis for Tmax is carried out for the three periods 1901-1974, 1974-1997, and 1997-2012. Similarly, major change points for Tmin are identified in 1959 and 1986 (Fig. 5b). Tmin is analyzed for three periods 1901-1959, 1959-1986, and 1986-2012.

Figure 5 CUSUM charts of of CRU and IMD Data for (a) Tmax and (b) Tmin.
4.3Trend analysis

The results obtained from trend analysis of CRU and IMD data for Tmax and Tmin using Sen’s slope are shown in Table 2. A comparison of CRU and IMD data for Tmax and Tmin is carried out on the basis of magnitude of trends. The trends are analyzed at monthly, seasonal, and annual scales in this study. Four seasons winter (December-January-February), pre-monsoon (March-April-May), monsoon (June-July-August-September), and post-monsoon (October-November) are considered throughout the year. For Tmax, on a monthly scale, except for the months of July and August during 1901-1974, March and May during 1974-1997, and January, February, and August during 1997-2012, all other months have shown similar trends. Significant trends are observed in individual datasets for few months, but none of the months in common are found having significant trends. Most of the months are having rising, falling, and rising trend for the periods 1901-1974, 1974-1997, and 1997-2012, respectively. On the seasonal scale, all seasons show similar trends except winter during 1974-1997 and 1997-2012. General trend of all seasons for 1901-1974 and 1997-2012 is rising, while for 1974-1997, seasons have both rising and falling trends. On the annual scale, both the datasets have shown a rising trend during 1901-1974, falling trend during 1974-1997, and rising trend during 1997-2012. Annual trend is significant in both datasets for 1901-1974 at the 5% significance level, while it is significant for CRU data during 1974-1997 and is significant for IMD data during 1997-2012 (Table 2).

Table 2 Magnitude of trend (℃ yr-1) in CRU and IMD data

On a monthly scale for Tmin, all the months except January for 1901-1959 have exhibited similar trends in three sub-periods (Table 2). General trend of all the months is rising, falling, and rising trend for 1901-1959, 1959-1986, and 1986-2012, respectively. The seasonal and annual Tmin also exhibit rising, falling, and rising trend respectively in the three sub-periods. On the annual scale, both datasets have shown significant trends at the 5% significance level in three sub-periods.

4.4Correlation analysis

Table 3 shows correlation coefficients of two data sets for Tmax and Tmin, where bold values show a significant correlation at the 5% significance level. For Tmax, monthly, seasonal, and annual correlation coefficients of CRU and IMD data are positive and significant for the periods of 1901-1974 and 1974-1997. For period 1997-2012, months of January, May, August, and September are positively correlated but not significant, while there is a positive and significant correlation for other months. When the temperature cor relations are examined for this period on the seasonal and annual scales, both the datasets have positive and significant correlation. For three sub-periods, correlations are moderate to very strong on the seasonal scale, while strong on the annual scale (Table 3). Figure 6 shows scatter plots on the seasonal and annual scales for Tmax SA data series in three sub-periods. Figures 6a-c show scatter plots for CRU and IMD data for three periods 1901-1974, 1974-1997, and 1997-2012. It is observed from scatter plots that both datasets show a positive correlation for each time period.

Table 3 Correlation analysis of CRU and IMD data
Figure 6 Tmax std anomaly for (a) 1901-1974, (b) 1974-1997, and (c) 1997-2012.

For Tmin, on the monthly, seasonal, and annual scales, all correlation coefficients of CRU and IMD data are positive and significant at the 5% level in the periods 1901-1959, 1959-1986, and 1986-2012. On the seasonal scale, correlation is moderate to very strong, while it is strong to very strong on the annual scale (Table 2). Scatter plots of Tmin SA series of two data are shown in Figs. 7a-c for 1901-1959, 1959-1986, and 1986-2012, respectively. A positive correlation is reflected in the three sub-periods.

Figure 7 Tmin std anomaly for (a) 1901-1959, (b) 1959-1986, and (c) 1986-2012.
4.5Wilcoxon-Mann-Whitney test

The outcomes of Wilcoxon-Mann-Whitney test performed on SAs of Tmax and Tmin data of CRU and IMD are shown in Table 4. Test shows that for Tmax, all months in three sub-periods except August and September during 1901-1974, and August during 1974-1997, are having identical anomalies. On the seasonal and annual scales, Tmax anomalies are found identical for 1901-1974 and 1997-2012 except monsoon during 1901-1974. During 1974-1997, winter and pre-monsoon anomalies are identical, while monsoon, post-monsoon, and annual anomalies are not found identical. Anomalies of Tmin in two datasets, for all months except August (1959-1986), are found identical. All seasonal and annual Tmin anomalies except winter (1959-1986) are identical for three sub-periods. 5. Discussion Temperature anomalies are able to describe climate variability more accurately than absolute temperature in mountainous regions where data are sparsely available. Computation of anomalies normalizes the time series of temperature data effectively. Moreover, normalized or SAs are re-expression of absolute time series in to normalized time series. For comparing two datasets, these need to be transformed on same scale by using SAs. In the present study, com-parison of CRU and IMD data is based on SAs and absolute data. Annual SAs are graphically compared and these are used for equivalence test and correlation analysis on the monthly, seasonal, and annual scales to show closeness in two datasets. However, absolute data are used for CUSUM chart and trend analysis. The SAs are computed on the basis of long-term av erage for whole study period and they have mean and standard deviation equal to 0 and 1, respectively (Wilks, 2011). However, mean and standard deviation of SAs may be near 0 and 1, respectively, when computed SAs are considered for different sub-periods.

Table 4 Wilcoxon-Mann-Whitney test and MAE for CRU and IMD standardized anomalies

Graphical comparison of annual SAs of CRU and IMD data shows a similar pattern in the two datasets. CUSUM chart analysis provides change points for Tmin and Tmax. Trend analysis using Sen’s slope method has exhibited similar trends for CRU and IMD data on the annual and seasonal scales except winter for Tmax, while similar trends on the annual and seasonal scales for Tmin. The trends on the monthly scale are similar for all months except 2-3 months in each sub-period for Tmax, while similar for all months except only one month in first sub-period for Tmin. The trends found in this study are in accordance with the studies conducted for NW Himalayan region in India by Yadav et al. (2004) and Bhutiyani et al. (2007).

Correlation of CRU and IMD data is strong to very strong on the annual scale, while moderate to very strong on the seasonal scale for Tmax and Tmin in different sub-periods. All the correlation coefficients on the annual and seasonal scales are significant at the 5% level. On the monthly scale, correlation is significant at the 5% level for all months in the first and second sub-periods for Tmax, while for all months in all the three sub-periods for Tmin. Some of the months do not have significant correlation in the third subperiod for Tmax. Similarly, for winter season during 1982-2005, Robertson et al. (2013) have also found that Tmin exhibits more closeness than Tmax for CRU and IMD datasets at a grid box near 26.5°N, 80.5°E.

Comparison of Tmax and Tmin of CRU and IMD datasets is carried out by multiple parameters, based on graphical and statistical techniques. Moreover, MAE is also computed on the annual scale for SAs for whole period and also on the monthly, seasonal, and annual scales for three sub-periods. It is checked that whether MAE remains within one standard deviation of observed IMD data. One standard deviation shows the natural variability of the dataset (Hansen et al., 2011).

MAEs of annual SAs of both Tmax and Tmin are found within natural variability of observed IMD SAs for the whole period and three different sub-periods (Table 4). On the seasonal scale, MAE is within natural variability of IMD for first and third sub-periods. However, for second sub-period, MAE during all seasons, except monsoon for Tmax and except winter for Tmin is within natural variability of IMD. For monsoon (Tmax) and winter (Tmin) in the second sub-period, MAE is comparable with one standard deviation of IMD SAs. MAE is slightly exceeding the standard deviation of IMD anomalies, in the months of August and November for Tmax and in the months of July and August for Tmin during some of the sub-periods. All the rest months have MAE of SAs within natural variability of observed SAs (Table 4).

This study presents a comparison of computed and gridded CRU data with observed IMD data in Dehradun, Uttarakhand, India. Such studies are rare in India for temperature parameters. However, Gulati et al. (2009) have found correlation coefficients of CRU and IMD monthly rainfall data greater than 0.90 for 1901-1950 at district level in Orissa, India. In China, Tang et al. (2010) have found that correlation coefficient of CRU temperature series with other five Chinese temperature series varies between 0.73 and 0.88 for period 1906-2005. Further, increasing trends of temperature are similar and strongest for CRU in comparison to other Chinese series.

6Conclusions

Extreme temperature parameters of Tmax and Tmin are analyzed for CRU and IMD data for different periods. Analysis of standardized anomalies, trends, correlation and Wilcoxon-Mann-Whitney test have resulted in close agreement of CRU data with IMD data. IMD station data has certain limitations in terms of spatio-temporal continuity and IMD gridded data has coarser resolution (1° × 1°). High resolution (0.5° × 0.5°) CRU data has spatio-temporal continuity and it is an open access dataset. Tmax and Tmin of CRU data has been found reliable for study of temperature trends in Dehradun. Following conclusions may be drawn from the present study:

(1) Annual standardized anomalies of Tmax and Tmin show similar patterns for CRU and IMD data sets.

(2) Nature of annual trends in CRU and IMD datasets are found to be similar for Tmax and Tmin in all three sub-periods. The trends of Tmax are similar for all seasons except winter, while trends of Tmin are similar throughout all the seasons. Monthly trends have a better degree of similarity for Tmin than Tmax in two datasets.

(3) CRU and IMD data of Tmax are well correlated on the annual and seasonal scales in all the three sub-periods, while on the monthly scale, these are well correlated in first and second sub-periods. For Tmin, two datasets are well correlated on the annual, seasonal, and monthly scales for all three sub-periods.

(4) Annual, seasonal, and monthly standardized anomalies of Tmax and Tmin for CRU and IMD data are either identical or their MAEs are within natural variability of IMD, except for the month of August and monsoon season for Tmax and winter for Tmin, in the second sub-period. However, MAEs of above mentioned exceptions are found to be comparable with one standard deviation of IMD.

Acknowledgments: Authors acknowledge the editor and anonymous reviewers for devoting their valuable time and putting their efforts for evaluating the manuscript and providing helpful suggestions to improve it.
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