Spatio-temporal variability of temperature and potential evapotranspiration over India

Accurate hydro-climatological change detection study is essential, and has been considered as an emerging research field for the past couple of decades (Chattopadhyay & Hulme 1997; Hobbins et al. 2004; Espadafor et al. 2011; Fu et al. 2013). Long term spatio-temporal hydro-climatological change patterns provide valuable information for modeling various processes in hydrology, climatology, forestry and agriculture.

Evapotranspiration, which is one of the most significant components of the hydrological cycle, is influenced by meteorological conditions directly or indirectly. It is the union of evaporation and transpiration. Changes in meteorological variables due to climate change will affect evapotranspiration, which affects the crop water requirement, and subsequently water allocation for agriculture and food production (Zhang et al. 2011). Evapotranspiration is affected differently in different regions due to global warming. Determining the evaporation rate is essential for efficient management of water resources in a country like India. Long-term changes in potential evapotranspiration (PET) can have profound implications on hydrological processes as well as on agricultural crop performance (Hobbins et al. 2004). Liang et al. (2010) manifested the usefulness of study based on the temporal variation of PET in hydrological modeling, irrigation planning and water resources management.

As per Doorenbos & Pruitt's (1977) definition, ‘the PET is the one that takes place when the ground is completely covered by actively growing uniform green grass of eight to fifteen centimeters tall in abundance of soil moisture’. Factors affecting PET are climatological data, crop factor and moisture level in the soil. Climatological data consist of surface air temperature, percentage of sunshine hours, wind speed, humidity, etc.

The fifth Intergovernmental Panel on Climate Change (IPCC) assessment report states that almost all regions of the world have experienced a heating process over the past half century (IPCC 2013). The fourth IPCC assessment report states that the surface air temperature has increased by 0.74 ± 0.18°C during 1906 to 2005, and is also likely to increase during the 21st century (IPCC 2007). This could cause changes in the hydrological cycle (Bates et al. 2008). PET may be going to rise in most parts of the world in future because the water holding capacity of the atmosphere increases with higher temperature, i.e. about 7% per 1°C warming (Trenberth 2011), but relative humidity is not projected to change markedly. Consequently, the evaporation rate is likely to go up due to water vapor deficit. Thus historical PET analysis is of significant importance in the hydro-climatological perspective.

Extensive research has been carried out in different parts of the world (such as Australia, China, Gulf of Mexico, Northern Eurasia and Beijing) to assess the likely impact of climate change on PET (Helfer et al. 2012; Huo et al. 2013; Liu et al. 2013, 2014; Haijun et al. 2014). These studies reported that in the recent past the evapotranspiration change rate has increased considerably. Espadafor et al. (2011) found a significant increment in PET in southern Spain and inferred that the changes are mainly due to an increase in air temperature, solar radiation and a decrease in relative humidity. Tabari et al. (2011) ascertained the presence of a significant positive trend in annual evapotranspiration in the western half of Iran. They concluded that trend magnitudes are more intense in winter and summer compared to other seasons, and these variations are primarily because of significant increase in temperature. Zhang et al. (2013) inferred that the main causes for the decrease in reference evapotranspiration during 1960–1992 in China were the decrease in solar radiation in humid regions and decrease in wind speed in arid and semi-arid regions. Few studies ascertained that the effects of intensified temperature on evapotranspiration can be offset by the impact of other climatic variables (Chattopadhyay & Hulme 1997; Hobbins et al. 2004; Ramírez et al. 2005).

Roderick et al. (2007) mentioned that PET is an important indicator of global climate and environmental change owing to its close connection with key physical factors such as temperature, wind speed, solar radiation and humidity. A significant declining trend of surface solar radiation was observed over India during 1981–2004 (Kumari et al. 2007). Similarly, several studies focused on variations of solar radiation over different parts of the world and determined a decline of solar radiation (Wild 2009). Chattopadhyay & Hulme (1997) reported decreasing trends both in pan evaporation and PET in India from 1960 to 2000 in spite of an increment in temperature in the second half of the 20th century. But they also indicated that PET is going to rise unevenly in different seasons and regions of India in the future. Generally, an increasing trend is expected with increase in surface temperature. Despite the temperature increases, a large number of studies indicated a declining trend in PET (Jiang et al. 2011; Fu et al. 2013). This is known as the ‘pan evaporation paradox’ (Brutsaert & Parlange 1998; Hobbins et al. 2004). From literature, it can be inferred that the increase in relative humidity and decrease in radiation might be the main sources for this declining trend in PET over a few regions, whereas warming might cause a significant increasing PET trend in future.

Goyal (2004) detected that over the arid zone of Rajasthan in India, change in PET was highly sensitive to surface temperature followed by radiation, wind speed and vapor pressure during the last three decades of the 20th century. Nandagiri & Kovoor (2006) evaluated the performance of several approaches for reference evapotranspiration estimation both at daily and monthly timescales over different ranges of Indian climate. Their results were closer to the estimation by the Food and Agriculture Organization-56 Penman–Monteith approach. They reported that temperature based approaches have performed better than others, and the temperature-related variables appeared to be the most crucial inputs for evapotranspiration estimation across all Indian climates.

Bandyopadhyay et al. (2009) attributed the declining trend in wind speed to tall construction works. Decrease in reference evapotranspiration at annual and seasonal scales is observed in the north-east region of India (Jhajharia et al. 2012). A recent study by Jain (2012) on India's water balance and evapotranspiration suggested that the estimated evapotranspiration in India was much lower than anticipated with respect to changes in climate and land use, which may have major implications for India's water resources management.

The evaporative demand, a central process of the climate system, is expected to be altered along with the change in climate. In order to efficiently manage water resources, the amount of water used for irrigation needs to be properly organized. For this purpose, actual evapotranspiration (AET) assessment is needed. Although a lysimeter can be used for accurate measurement of evapotranspiration it is quite costly, which limits its usage. PET scores higher than AET in analyzing future changes as it can be obtained using a meteorological dataset. Evapotranspiration may vary perceptibly year to year with changing climate. Investigation on spatial and temporal variations of historical PET is useful in guiding present and future water management.

A few studies such as Khaliq et al. (2009) and Sonali & Nagesh Kumar (2013) have extensively reviewed various approaches for trend detection, and summarized the strengths and weaknesses of each of those approaches separately. Parametric, non-parametric, Bayesian and non-parametric with resampling approaches are generally used for performing trend analysis of time series data. Proper interpretation of data and relevant test assumptions are essential for conducting any statistical test. Parametric trend detection approaches require both independent and a particular (normal) distribution in the data, while non-parametric approaches only require the data to be independent. Hence non-parametric approaches have been widely used in trend detection analysis during the last couple of decades. But not all non-parametric approaches satisfy the independence assumption, and the presence of serial correlation enhances the type-I error. An improper assumption of independent observations could result in erroneous conclusions. So the effect of serial correlation should be considered in the case of hydrologic and climatic variables, which generally are serially correlated. Analysis by Khaliq et al. (2009) and Sonali & Nagesh Kumar (2013) strongly support the consideration of the effect of serial correlation in usual trend detection practice which is missing in most of the literature concerning India. But here a trend detection method, which considers the effect of serial correlation, is employed to deflect from spurious conclusions.

In spite of changing climate conditions, it is noticed that only a few studies are focusing on spatio-temporal change detection of PET over the whole of India compared to other parts of the world. Usually the influence of meteorological variables on PET change rate is region-specific. Moreover, in recent decades there has been a considerable increase in night time T_min compared to day time T_max. A consistent increasing trend was detected in T_min for most of the regions over India during the last three decades (Sonali & Nagesh Kumar 2013). Sonali & Nagesh Kumar (2016) found that most of the changes in T_min lie above the bounds of natural internal climate variability. This significant trend in T_min during recent decades could be considered as a signature of climate change over the whole of India (Sonali et al. 2016). T_max and T_min are among the six most commonly used variables for climate change impact assessment studies (IPCC 2001). Hence all these studies were motivated to analyze PET along with T_max and T_min. The present study mainly focused on long term spatio-temporal change detection. Short length data may lead to spurious conclusions in trend analysis. Based on the above discussion and availability of data (of different meteorological variables), the PET response to the changing climate from 1950 through 2005 (the second half of the 20th century) using T_max and T_min is studied.

Correlation assessments of PET with T_max and T_min are demonstrated. A spatio-temporal change detection study is performed separately for T_max, T_min and PET during each of the seasons. This study could provide useful information for improving the simulation of regional hydrometeorology. It could also be helpful for the policy-maker in the layout, development, utilization, management and protection of water resources in a sustainable and reasonable way.

The whole of India is taken as the subject for the present study. Due to the non-availability of a historical dataset from the India Meteorological Department (IMD) (Srivastava et al. 2009), for the considered time period (i.e. 1950–2005), gridded historical monthly time series of T_max, T_min and PET from the latest version of the CRU3.21 dataset (developed by the Climatic Research Unit, which is a component of the university of East Anglia) has been used in this study (http://badc.nerc.ac.uk/browse/badc/cru/data/cru_ts/cru_ts_3.21, Harris et al. 2014). Data of these variables are available at 0.5 × 0.5° resolution.

The CRU3.21 data were interpolated to IMD grid points (which are available at 1 × 1° resolution), and absolute gridded average differences were obtained at annual, seasonal and monthly scales for both T_max and T_min. One of the most common spatial interpolation techniques, inverse distance weighting, is used here (Raju et al. 2016; Sonali et al. 2016; Sonali & Nagesh Kumar 2016). This is a standard deterministic interpolation approach in geographic information science, with easy and fast computation. The division into seasons considered here is based on conventional meteorological seasons defined by IMD (http://www.imdpune.gov.in/weather_forecasting/glossary.pdf), i.e. January–February (winter), March–May (pre monsoon), June–September (monsoon), October–December (post monsoon). Using these re-gridded datasets, the correlations and absolute gridded average differences were computed between the CRU3.21 and IMD datasets. This exercise was also repeated for all the months and all the seasons for both T_max and T_min. Consistently better correlation and lesser absolute gridded average differences are ascertained at all the grid points except a few (>30° North and >88° East), both at monthly and the seasonal timescale (Sonali et al. 2016). The same pattern has been observed for all seasons and months. The threshold of difference for excluding grids is more than 5 Kelvin (Sonali et al. 2016). Due to the significant differences, those grids were not considered further. In this analysis all the grid points, excluding the grid points beyond 30° North and 88° East, are considered. Most of the excluded grid points are located in the Western Himalaya region and partially in the north-east temperature homogenous region of India. Hence, in this study, the observed T_max and T_min dataset obtained from the CRU3.21 is used as a proxy to the IMD dataset.

None of the observed datasets are freely available for the validation of the gridded CRU3.21 PET dataset over the whole of India. But the CRU3.21 T_max and T_min dataset has ascertained better correlation with the IMD dataset (as explained above). Both T_max and T_min are among the most important parameters used in PET estimation. Hence the CRU3.21 PET dataset is used for the present analysis. The CRU3.21 PET dataset has been derived from a variant of the Penman–Monteith method (Allen et al. 1994). Gridded monthly averaged daily maximum, minimum and mean temperatures, vapor pressure and cloud cover datasets have been used for the estimation of the CRU3.21 PET dataset (Ekström et al. 2007).

Initially the variations of PET climatology with respect to different months are obtained. Then Spearman rank correlation is used to assess the correlation of PET with T_max and T_min. Finally grid wise trend detection study is conducted to locate any significant changes in different considered variables. Depending on the availability and importance of the variable (as explained in the introduction section), spatio-temporal change detection of PET along with T_max and T_min have been analyzed for whole of India. PET is also sensitive to climatic variables such as solar radiation, relative humidity and wind speed along with temperature. Hence these different contributory sources to PET changes can be identified and studied in detail at different months and seasons in the future over the whole of India upon availability of data.

The most preferred statistical approaches from literature (in the presence of serial correlation) viz. Trend Free Pre-Whitening Mann Kendall (referred to as TFPW-MK), Modified Mann Kendall by Hamed & Rao (1998) (referred to as MMK-CF1) and Modified Mann Kendall by Yue & Wang (2004) (referred to as MMK-CF2) are employed for the present analysis. In both MMK-CF1 and MMK-CF2, the variance of the MK test statistic is multiplied by a correction factor, and hence they are known as variance correction approaches. All the trend detection approaches are evaluated at 5% significance level (α). Brief descriptions of the employed approaches are provided below.

The non-parametric rank based MK approach has been employed mostly to detect monotonic (linear/non-linear) trends in hydro-climatological time series (Mann 1945; Kendall 1975).

Yue et al. (2002) found that pre-whitening alters the true slope present in the time series, and suggested TFPW to take care of the serial correlation effect in trend detection approaches. Hamed & Rao (1998) reported that the presence of serial correlation in a time series does not falsify either the asymptotic normality or mean of the MK test statistic S_mk, but the variance changes. Hence correction factors are proposed to correct the variance of S_mk using only those samples which are uncorrelated.

The TFPW-MK approach was suggested by Yue et al. (2002). This approach works with the assumption of the AR(1) process. In this approach, the slope (linear trend) of the time series using SS is calculated initially. Then the linear slope from the time series is de-trended. If the lag-1 correlation coefficient of the de-trended time series is significant at a defined level, then the MK test is applied to the de-trended pre-whitened series recombined with the estimated slope (using the SS approach), else the MK test is directly applied to the original series.

Results and discussion are explained in three parts.

In the second step, the study analyzes the correlation of PET with T_max and T_min to assess their linkages and to observe the patterns in different seasons and regions over the whole of India. Correlation is determined individually for T_max and T_min with PET by considering all months together and also for the considered four seasons. The non-parametric Spearman rank correlation is used to conduct the correlation analysis. This is less sensitive to outliers (as it considers rank instead of magnitude) compared to the Pearson correlation. It measures the monotonic relationship (either linear or non-linear). It takes care of duplicate values existing in the time series.

Analysis of PET trends and its driving climatic factors can provide scientific insights for improving water management, especially under predicted climate change. Assessment of T_max, T_min and PET spatio-temporal variabilities is useful in terms of hydro-climatological perspective. Here in the third step, trends in PET, T_max and T_min are investigated through TFPW-MK and MMK approaches. Using the Kolmogorov–Smirnov test, it is observed that none of the time series (over all the grid points) are following a normal distribution. Hence there is no scope of parametric approaches for this trend detection analysis. Trend detection analysis was conducted individually for the three considered parameters, viz. T_max, T_min and PET, for the same time period (1950–2005). This exercise is repeated for four different seasons separately. As mentioned earlier, 5% significance level is considered for all trend detection approaches.

Analysis is repeated using each of the three considered trend detection approaches. Good agreement is found between all the implemented approaches. In all the correction approaches, i.e. MMK-CF1, MMK-CF2 and TFPW-MK, proper care has been taken to locate both positive and negative correlations. As discussed, pre-whitening has a problem in maintaining the important feature of a statistical test, the nominal significance level. It also affects the magnitude of true slope of a time series (Khaliq et al. 2009). Hence TFPW-MK, an improved version of pre-whitening developed for serial correlated data, is employed in this study.

There are more grid points with significant upward trend for T_min compared to T_max and PET in all the seasons except post monsoon. In post monsoon, the number of grid points with significant upward trend is greater compared to the other seasons for both T_max and PET.

The total number of grid points with significant upward trend is fewer in winter for T_min compared to other seasons. Significant upward trends in T_max, T_min and PET are observed over most of the grid points covering the interior peninsular region of India during all four seasons, except PET in the monsoon and pre monsoon seasons. Grid points with significant downward trend are fewer for T_min than for PET in all four seasons. In pre monsoon and monsoon, the number of grid points with significant upward trend is very high for T_min. Temperature is one of the significant factors in explaining changes in PET. In spite of the high seasonal correlation between PET and T_max, the spatio-temporal variability patterns do not entirely match. T_max varies greatly during post monsoon, but no proportional change is observed in PET.

Significant upward trends in T_min establish a signature of climate change that has already been verified by the previous studies by Kothawale & Rupa Kumar (2005) and Sonali & Nagesh Kumar (2013). Even though there is a significant rise in both T_max and T_min, PET has declined over some of the grids. This tendency may be because of a decrease in wind speed, net radiation and to some extent due to the saturation vapor pressure deficit, which has already been reported in many former studies for different parts of the world along with India (Chattopadhyay & Hulme 1997; Zhang et al. 2013). In future, wind speed, net radiation and saturation vapor pressure can also be considered for a detailed assessment of change in PET over India. Currently, due to unavailability of these datasets, spatio-temporal change in PET is studied with respect to only T_max and T_min.

Change in climate is likely to have a profound effect on different components of the hydrological cycle. Evapotranspiration is one among them. Evapotranspiration is likely to be affected by global warming because of its dependence on surface temperature. As explained, PET is the amount of evapotranspiration in an abundance of water supply. Changes in PET over space and time provide a clearer picture about the movement of the water cycle (Bates et al. 2008). Evaluation of the spatio-temporal variability of PET, T_max and T_min was the primary focus of this study. Long-term gridded datasets of PET along with T_max and T_min from CRU were used to perform the spatio-temporal change detection analysis over all India, except most parts of the Western Himalaya and the north-east region.

Monthly climatology patterns for PET were obtained. The results confirmed a higher PET rate during the months of March, April, May and June. A high correlation of PET with T_max was observed both at monthly as well as seasonal scales. Hence, temperature is one of the significant factors in explaining changes in PET. The change in PET, T_max and T_min from 1950 to 2005 in India was analyzed for all four seasons (winter, pre monsoon, monsoon and post monsoon) using MMK and TFPW-MK approaches. A significant trend was observed in T_min when compared with T_max and PET. The present assessment, in line with previous studies, concluded that even though there is a significant increase in both T_max and T_min (T_min being greater), grid points with significant upward trend are fewer in number in the case of PET. Major changes in various components of the hydrological cycle are expected in response to global warming (Huntington 2006). But the effect of temperature is offset by other significant parameters that influence PET. Significant positive trends in T_max, T_min and PET were observed over most of the grid points in the interior peninsular region. Overall, the trend in PET showed substantial spatial and temporal heterogeneities over all India during the second half of the 20th century. This study provides a broad vision of water resources planning and management by analyzing the change in PET along with temperature. These historical correlation assessment results might hold good in the future, and can be used further for future projections with respect to different scenarios. Also, findings from this analysis could be utilized further in hydro-climatological study, and can also provide extra inputs for optimized estimation of crop water requirement at a broad scale during different seasons.