Wavelet transform analysis of reference crop evapotranspiration during the growing season in three typical regions of Inner Mongolia, China

The reference crop evapotranspiration (ET₀) is one of the most important hydrological variables, which affects the water and energy exchanges at the land surface/atmosphere interface (Liu et al. 2013; Xie et al. 2014). To estimate ET₀ requires a good understanding of the hydrological cycle. Accurate estimates of ET₀ are critical for scheduling irrigation activities and are also required for a variety of hydro-meteorological applications, e.g. certain hydrological and water-balance models and in calculating the potential/actual evapotranspiration of a region and/or a basin (Blaney & Criddle 1950; Dyck 1983; Hobbins et al. 2001a, 2001b; Xu & Li 2003; Xu & Singh 2005; Gong et al. 2006). The major factors that affect ET₀ are elevation, latitude and longitude, meteorological conditions, land use (land cover) and changing climatic conditions at different spatio-temporal scales (Jhajharia et al. 2006, 2009a, 2009b).

Many studies have analysed the methods of estimating ET₀ and their validity in different parts of the world (Jhajharia et al. 2004a, 2004b, 2006, 2009a, 2009b). Further, ET₀ has been evaluated in the context of its spatial and temporal variations. For instance, Thomas (2000) analysed the spatial and temporal characteristics of the ET₀ trends across China. Jhajharia et al. (2012) found that the reduction in ET₀ in the humid region of northeast India was mainly due to the net radiation and wind speed. In assessing a monthly reference evapotranspiration model, Buttafuoco et al. (2010) found that there was spatial uncertainty in the results, which were caused by the uncertainties in the inputs, particularly the temperature, on a regional scale. Using the parametric t-test and the non-parametric Mann–Kendall test, Xu et al. (2006) analysed the temporal trend of ET₀ and compared it with the pan evaporation (E_pan) trend in the Chang Jiang river basin. They found that for both the ET₀ and E_pan between 1961 and 2000, there were significant decreasing trends. Mo et al. (2004) analysed the seasonal and annual variations of ET₀ between 1984 and 1997 for a mountainous region in the Lu Shi basin, China. Tong et al. (2007) analysed the temporal variations of ET₀ from spring wheat in the last 50 years (1955–2005) in northwest China and tested the ET₀ trend using the Mann–Kendall test and linear regression analysis. In a study in Iran, Dinpashoh et al. (2011) found that the wind speed was the most dominant factor affecting ET₀ throughout the year except for the winter months. Using the data from 34 meteorological stations between 1957 and 2007 in the Hai He river basin of China, Wang et al. (2011) analysed ET₀ spatial and temporal patterns and trends. Liang et al. (2010) analysed the ET₀ temporal variations between 1961 and 2005 in the Taoer River basin in northeast China.

In recent years, wavelet transform analysis has been widely used in the field of water resources and meteorological sciences. For instance, wavelet transform analysis was used to investigate the multi-timescale features of ET₀ at the Chang Ping station in China (Ren et al. 2009). The complexity associated with ET₀ was solved based on wavelet de-noising and symbolic dynamics by Chen et al. (2012). The decomposed inter-decadal and inter-annual components of the rainfall data during the rainy seasons in north China have been analysed using wavelet transformation (Lu 2002). Kişi (2010) investigated the accuracy of a wavelet regression approach for modelling ET₀. A synthetic model of wavelets was used to downscale and forecast ET₀ with support vector machines (Kaheil et al. 2008). Wavelet transform analysis in conjunction with power laws was used to perform wet-spell and dry-spell analyses of precipitation from the global climate models (Ashok et al. 2011).

In earlier studies, using the Penman–Monteith equation, as recommended by Food and Agriculture Organization of the United Nations (FAO), and meteorological data from the weather stations, ET₀ and its spatial and temporal variations were investigated (Song et al. 2013). However, ET₀ is affected by both aerodynamic and radiometric variables, as these two variables reflect the combined effects of topography, soil, vegetation and climate. The Inner Mongolia Autonomous Region (IMAR) is predominantly an agricultural region in China, where irrigation activities are highly dependent on the available water resources. Due to variations in the natural geographical and climatic conditions in the IMAR, there is no consistency in the ET₀ trend. Therefore, an analysis of ET₀ and its components (ET_r and ET_a) for different sub-regions are needed in order to understand the ET₀ variation over one whole year. In view of the uncertainties in ET₀, the wavelet transform method has been used in this study to investigate the variations in ET₀ in the western, central and eastern regions of the IMAR during a growing season.

The main objectives of this study are: (1) to use the wavelet transform method (a data-driven approach) to examine the spatial and temporal patterns of ET₀, (2) to investigate the spatial differences of relevant hydrological variables and (3) to improve the understanding of ET₀ for agricultural water management.

Due to the large variations in the climatic and physical conditions, the ET₀-distribution in the IMAR is complex. However, from the 135 weather stations within the IMAR (Figure 1), there are three that are representative of the ET₀ variations. Hence, the data from these three stations have been used for analysis. The selected stations are in: (1) an extreme arid area in Ejina County, (2) a semiarid area in Hohhot and (3) a relative humid area in Erguna Zuo County. They are situated within the western, central and eastern areas of the IMAR, respectively, as shown in Figure 1.

To reduce the interface effect in the wavelet analysis, the most commonly used method is to extend the time-series in both the forward and backward directions. After the wavelet transform, the part of the series being extended can then be abandoned.

Using the Penman–Monteith model and the daily meteorological recorded data between April and September, 2007, ET₀, ET_a and ET_r were calculated for the three selected stations. The ET₀, ET_a and ET_r time-series were extended in both the forward and backward directions, according to Equations (12) and (13). Using the Mexican hat function (MHF), the ET₀, ET_a and ET_r time-series were then analysed at multiple time scales, according to Equations (8) and (9).

The results of the wavelet analysis and their implications for the three sub-regions of the IMAR (Ejina County in the western area, Hohhot City in the central area and Erguna Zuo County in the eastern area) are discussed in this section. The differences among the three sub-regions are highlighted below.

As shown in Figures 2(c), 3(c) and 4(c) respectively, the largest variance is on Day 45 (i.e. end of June) for ET₀, on Day 40 (i.e. early June) for ET_a and on Day 50 (i.e. mid-July or end of June for ET_r. However, at the smaller scale, the fluctuations are more complicated and less certain. Figures 2(c), 3(c) and 4(c) also show that during the growing season, the wave period is approximately 45 days for ET₀, 40 days for ET_a and 50 days for ET_r. These results indicate that the changes are dependent on several parameters, such as the roughness of surface and the leaf area index. Hence, to assess these parameters accurately they need to be rescaled in the timeline. Further, the time lag can be attributed to the windy climatic condition in the western area of the IMAR, which has affected ET_a after April. Hence, the ET_a fluctuations are 1 month earlier than those of ET₀ and ET_r. The ET_a results obtained in this study are closely related to ET₀, which is consistent with the findings by Huo et al. (2004). They found that ET_a is dominant in the more arid area of the IMAR (Huo et al. 2004).

The periods and dates corresponding to the largest variations in ET₀ and ET_r are similar to those in Ejina County. Figures 5(c), 6(c) and 7(c) show that during the growing season, the wave periods are approximately 10 days and 45 days for ET₀, 10 days, 30 days for ET_a and 50 days for ET_r. These wave periods are an indication that solar radiation has an effect on the ET₀ in the Hohhot area, which is consistent with the findings by Huo et al. (2004), showing that ET_r is beginning to affect ET₀ in the semi-arid area of the IMAR (Huo et al. 2004).

The timing of the largest variations in ET₀ and ET_r in the eastern area is 1 month earlier than those in the western and central areas. From Figures 8(b), 9(b) and 10(b), it can be seen that there are two large fluctuations in ET_a (i.e. a 30-day period in early June and a 10-day period in mid-August). Figures 8(c) and 9(c) show that for both ET₀ and ET_r, there is a fluctuation period of approximately 50 days, and Figure 10(c) shows that for ET_a, there is a fluctuation period of 25 days during the growing season.

As shown in Figures 8–10, it can be seen that ET_r is largest in June and July. These results are consistent with the global trend of radiation. This can be attributed to the large area of the IMAR, with widely varying topography and climatic conditions. It should be noted that the results of ET₀, ET_r and ET_a as presented in this study are for a typical dry year with normal precipitation, in which the relationships among the hydro-meteorological parameters are generally close.

A comprehensive evaluation of the daily reference crop evapotranspiration (ET₀), aerodynamic (ET_a) and radiometric (ET_r) in the IMAR has been carried out in this study. The variability of the ET₀, ET_a and ET_r was investigated in three regions of the IMAR during a typical growing season (April–September, 2007). The wavelet transform method (a data-driven approach) was used to analyse the meteorological data from the three selected stations. Such analyses are important to understand the regional differences in ET₀, ET_a and ET_r, information which is useful for irrigation water management.

The results of this study show significant periodicities in the estimated daily ET₀, ET_a and ET_r over the entire growing season. Further, the results show that there are close relationships of ET₀ with ET_a and ET_r. The timing of the largest ET_a is 1 month earlier than those of the ET₀ and ET_r. In the eastern area, the wave period is 40 days, which is 10 days shorter than that in the western area. The characteristics of the ET_r wave are closer to those of the ET₀ wave than those of the ET_a wave. This is an indication that there is a strong influence of ET_r on ET₀. This may be attributed to the relatively intense solar radiation in the western area during early April. However, the ET_a wave is strongly affected by wind. In the central area, the wave period of ET_a is 20 days shorter than those of ET₀ and ET_r. Further, for both ET₀ and ET_a within a 10-day period, there are some sporadic small-scale fluctuations, which can be attributed to the short duration rainfall events. For both the western and the central areas, there are two abrupt changes, two transitions and the wave periods for ET₀, ET_a and ET_r are all approximately 50 days. However, for the ET₀ and ET_r in the eastern area, there are three abrupt changes and three transitions. For the ET_a in the eastern area, the wave period is approximately 25 days.

The findings from this study can be used to improve the ET₀-estimation at both regional and local scales. They can also be used as a technical support for irrigation water management decisions and scheduling. This study has shown that using the wavelet transformation method to analyse ET₀ enables a more rational understanding of the regional differences in ET₀, ET_a and ET_r.

While this study has used the wavelet transform method to carry out a comprehensive evaluation of ET₀, ET_a and ET_r so as to rationally understand the evapotranspiration characteristics and its variation, there are limitations. First, the modelled results are only based on one meteorological station in each sub-region. Second, only data of a typical year (2007) have been used. Moreover, the results may be limited due to the fundamental assumptions and approaches used in the model. These shortcomings can be overcome by comparing the results of this study with those from other meteorological stations in other regions with similar soil, vegetation, topography, meteorology and climate conditions. Therefore, while further exploration of this approach is needed, this study has provided useful experience and knowledge for the investigation of crop evapotranspiration.

We would like to thank the National Natural Science Foundation of China (51369018), 13th Five-Year National Key Development Program (2016YFC0400205-1), the State Key Program of National Natural Science of China (51539005), and the Scientific Research Foundation for the Returned Overseas Chinese Scholars, State Education Ministry ([2013]693), China.