Actual daily evapotranspiration and crop coefficients for an alpine meadow in the Qilian Mountains, northwest China

The majority of inland rivers in China, including the Heihe River, the Shiyang River, and the Shule River, originate from the Qilian Mountains, northwestern China, a huge mountain range on the northeastern Qinghai–Tibet Plateau (Dong et al. 2015). As a main water source conservation zone of northwest China (Sun & Liu 2013), the Qilian Mountains play a critical role in regional sustainable development, especially for the oasis belt in the arid Hexi Corridor (Dong et al. 2015). Under the influence of global warming, the rate of warming in high mountain regions is amplified with elevation (Mountain Research Initiative EDW Working Group 2015), and the temperature on the north slope of Qilian Mountains has increased by 0.29 °C/10a in the past 50 years (Li et al. 2012). As in other cold high mountain regions, warming has caused a series of changes in hydrological processes in the Qilian Mountains, including changes in glacier melt (Wu et al. 2015), seasonal snow cover (Bourque & Mir 2012), alpine permafrost distribution (Zhao et al. 2012), and runoff (Li et al. 2012), which have influenced the water resources of the mountains and the middle and downstreams area of inland rivers. However, evapotranspiration (ET), an integral part of the water cycle under cold high mountain conditions (Herrnegger et al. 2012), is still incompletely understood in the Qilian Mountains because of sparse observations and a lack of measured data (Kang et al. 2008).

In fact, measuring ET in cold high mountain regions poses a number of challenges. The low temperatures test the endurance of fieldworkers and their instruments, and the distance of these areas from large urban centers raises the cost of logistics and reduces the availability of measured data (Woo 2008). The Bowen ratio–energy balance and eddy correlation methods are widely used to obtain actual evapotranspiration (ET_a) in a diversity of sites, but in cold alpine meadow regions, they are both time- and apparatus-consuming and applicable only when a number of requirements are fulfilled, and their assumption of spatial homogeneity is also frequently violated (Pauwels & Samson 2006). Micro-lysimeters offer a relatively cheap, robust and practical alternative for measuring ET_a, particularly for the high mountains (Zhang et al. 2003; Yang et al. 2013), where it is too expensive and difficult to build the large-scale weighing lysimeters. Although there are some limitations to the use of micro-lysimeters to estimate ET_a, such as the influence on ET_a of lysimeter length and surface soil moisture content, they have long been used for this purpose, and their reliability and modifications have been discussed by Lascano & van Bavel (1986) and Zhang et al. (2003). In sum, their low cost and ease of application renders micro-lysimeters appropriate for measuring ET_a on alpine meadows.

Owing to the difficulties of direct ET measurement in cold high mountain conditions, estimated methods provide an acceptable way of obtaining ET. As an analytical approach, the FAO-56 publication on crop ET_a (Allen et al. 1998) is the most widely used method worldwide (e.g., Sumner & Jacobs 2005; Pauwels & Samson 2006; Ngongondo et al. 2013; Reddy 2015). Ma et al. (2015b) proposed a complementary relationship method to simulate the ET in high-altitude regions. The FAO-56 method is commonly called the two-step approach, because it calculates the reference evapotranspiration (ET₀) first, and is then empirically adjusted using the crop coefficients (K_c) (Allen et al. 1998). Although the FAO-56 method has attracted criticism, it is a convenient way to estimate ET_a (Lhomme et al. 2015; Ma et al. 2015c). However, as an important adjustment ratio, K_c depends on the type and varieties of crops, crop height, leaf characteristics, soil properties, climate conditions, irrigation methods, and so on (Reddy 2015). Due to data limitations and for calculation simplification, Allen et al. (1998) suggest that K_c can be assumed to be a constant for a given vegetation growth stage, involving initial, crop development, mid-season and late season. Following the guidelines for computing ET_a (Allen et al. 1998), K_c can be simply estimated as a function of the green-leaf area index (LAI) (Sumner & Jacobs 2005), a regression function of air temperature (T_a), soil water content, relative humidity (RH), and RN (Zhou & Zhou 2009; Yang & Zhou 2011), or a polynomial function of sowing day (Reddy 2015). However, unlike the low altitude regions, because of a lack of ET_a measurements, there are few reports and/or discussions on K_c in high altitude mountainous regions.

The aims of this paper were to: (1) measure actual daily ET_a by micro-lysimeters, compare it with daily ET₀ from the FAO-56 Penman–Monteith (FPM) approach method; (2) investigate the factors influencing ET_a and K_c; and (3) develop a K_c and daily ET_a model on the basis of FPM ET₀ estimates for the application on an alpine meadow in the Qilian Mountains, northwest China.

Two lysimeters (labeled A and B) used in this study, of metal material, filled with a block of natural soil of the same size and shape as the drum, were installed by setting a cylindrical container into the soil at the level of the natural surface. Drawing from the useful research in similar localities (Zhang et al. 2003; Yang et al. 2013), the two lysimeters chosen for this work were both 40 cm in depth and 31.5 cm in diameter, to accommodate the depth of the majority of vegetation roots. The lysimeters were installed in the standard meteorological observation field, which was located in a flat pasture with representative vegetation and soil. Each was weighed daily at 20:00 (China Standard Time), with a balance of 2 g in precision, which corresponds to 0.026 mm. There are some limitations of micro-lysimeters in obtaining ET_a in an alpine environment. The lysimeter container could block the deep drainage, and the lysimeter material could influence the soil heat transfer. In this study, the designed length of the lysimeters was long enough to reduce the influences from deep soil water flow, and the metal material could transfer the heat well between soils in and out of the lysimeters. There have been some successful field experiments with similar lysimeters in an alpine environment (Yang et al. 2013), so it was reasonable and acceptable to use the designed lysimeters to obtain ET_a at the research site. The micro-lysimeters were installed on 25 June 2009, with measurements taken from 1 July 2009 to 30 June 2011, to obtain the daily ET_a readings for the two consecutive years. Owing to the fact that soil freezes during the cold seasons in high-altitude mountainous regions, the measurement period was divided into unfrozen and frozen periods based on the measured soil surface temperature (T_s). Days on which T_s fell below 0 °C constituted the frozen period, and all other days were the unfrozen period.

The principal meteorological parameters affecting ET_a are radiation, T_a, RH, and WS (Allen et al. 1998). Water in the near surface soil is the source of ET_a. T_s was used to distinguish the frozen and unfrozen periods in this paper. Therefore, the influential meteorological factors discussed to control ET_a in this paper were RN (W m⁻²), T_a (°C), T_s (°C), RH (%), WS (m s⁻¹), and SWC (%).

The Pearson correlation coefficients between ET_a and the meteorological factors were computed at daily scale (Table 1), with T_s, T_a, and RN found to be the most important factors in controlling ET_a throughout the whole measurement period, followed by SWC and RH. As most of the precipitation took place in the warm season on the research site, the SWC was close to saturation most of the time during the summer months (minimum of 22.5% and maximum of 35.5%, Figure 2). The land surface was wet or nearly wet in the unfrozen period, and the strong relationship between ET_a and RN indicated that the dominant factor affecting ET_a in this period was radiation, followed by T_s and T_a (Table 1). In the frozen period, in contrast, the plants grew very slowly and the frozen soil had very little liquid water content, roughly about 6% (Figure 2). The Pearson coefficients between ET_a and the meteorological parameters showed that ET_a was dominated by T_s and T_a in the frozen period, with RN and SWC exerting a similarly sized effect on ET_a. RH influenced ET_a over the entire measurement period, but its separate effects in the frozen and unfrozen periods could not be distinguished. WS was not a major control factor on ET_a in either period at the research sites.

The controlling factors that affect ET_a over different underlying surfaces in different climate regions are different; climate background, plant and soil type, and human interference can all be dominant factors. Over wet temperate grassland in Japan, RN, the atmospheric vapor pressure deficit, canopy surface conductance, and LAI all had an appreciable effect on ET_a measured via the eddy covariance technique (Li et al. 2005). Ryu et al. (2008) measured ET_a directly with the eddy covariance technique on a grassland in the Mediterranean climate zone of California, and found that monthly ET_a scaled negatively with solar radiation and was restrained by precipitation in the water-limited period; in the energy-limited period, on the other hand, the majority of ET_a scaled positively with solar radiation. In the temperate desert steppe in Inner Mongolia, China, ET_a measured via the eddy covariance method during the growing season showed SWC to be the dominant influential factor (Yang & Zhou 2011). In a study carried out in seven cropping zones in the Indus Basin in Pakistan, monthly ET_a estimated by the surface energy balance system was significantly controlled by mean T_a and rainfall, among several other climatological variables (e.g., RN, sunshine hours, and WS) (Liaqat et al. 2015).

The three models were tested using ET_a data collected during the measurement period. The slope of regression line (0.87) between the estimated (Equation (10)) and measured ET was close to 1, with R² of 0.89, RMSE of 0.49 mm day⁻¹, and MAD of 0.32 mm day⁻¹ in the calibration period, whereas the slope was 1.08, with R² of 0.83, RMSE of 0.79 mm day⁻¹, and MAD of 0.46 mm day⁻¹ in the validation period. Equation (11) based on T_s, RH, and SWC achieved better performance, with the slope of the regression line of 0.94, R² of 0.88, RMSE of 0.55 mm day⁻¹, and MAD of 0.36 mm day⁻¹ over the entire validation period. A possible reason for this result was that T_s, rather than T_a, was the key indicator parameter of the energy process on soil surface, and exerted a strong influence on both K_c and ET. Based on the relationship between K_c and DOY, Equation (12), although it displayed poorer performance than the two other models over the entire validation period, with a slope of 1.17, R² of 0.80, RMSE of 1.28 mm day⁻¹, and MAD of 0.96 mm day⁻¹, could be used when data were limited because of its minimal input needs.

On an alpine meadow site located in the high Qilian Mountains, the total ET_a measured from micro-lysimeters, from 1 July 2009 to 30 June 2011, was 887.8 mm, 1.2 mm per day. The total ET_a was 451.5 mm in the first year (from 1 July 2009 to 30 June 2010), and 436.3 mm in the second. The ratio of ET to precipitation in the measurement period showed that ET was the main cause of water loss at the research site. Seasonal variations were found in the measured ET_a in the high-mountain regions, with the mean daily ET_a in the unfrozen and frozen periods measuring 2.0 and 0.2 per day, respectively. The dominant factor affecting ET_a in the unfrozen period was RN, whereas it was T_s and T_a in the frozen period.

The crop coefficient (K_c) for the alpine meadow in the high mountains showed obvious daily and seasonal variations, with daily K_c ranging from 0.07 to 2.47 in the unfrozen period, with a mean value of 0.82, and from 0.01 to 0.79 in the frozen period, with a mean value of 0.19. T_a, T_s, RH, and SWC, but not RN, were the major factors of influence for K_c over the whole measurement period and during the unfrozen period, but there were no clear correlative relationships between K_c and these meteorological factors in the frozen period.

Three daily K_c models were constructed. The first one was a function of T_a, RH, and SWC, while the second one was a function of T_s, RH, and SWC. The third K_c model was a polynomial function of DOY. Then, three empirical daily ET_a models derived from the FPM method were developed on the basis of those K_c models. The results indicated that the ET_a model based on T_s, RH, and SWC offered the best performance, with the slope of the regression line of 0.94, R² of 0.88, RMSE of 0.55 mm day⁻¹, and MAD of 0.36 mm day⁻¹ for the whole validation period, and slope, R², RMSE, and MAD was 0.85, 0.81, 0.72, mm day⁻¹ and 0.55 mm day⁻¹, respectively for the unfrozen validation period; and 0.55, 0.25, 0.17 mm day⁻¹, and 0.13 mm day⁻¹, respectively, for the frozen validation period. The three empirical daily ET_a models performed well in calculating ET_a at the research site during the unfrozen period, but were not suitable for the frozen period. The probable reason was that K_c and ET₀ from the FPM method provided inappropriate assumption for the actual plant growing and meteorological conditions in the high-altitude mountainous regions during the frozen period.

It is difficult to achieve a true understanding of ET in high mountain areas, because direct measurements of ET_a in those regions are not easily obtained. The results from this study will advance the understanding of actual daily ET_a and the difference in control factors between frozen and unfrozen periods. The three empirical daily ET_a models provided in this paper can be used for accurate quantitative estimates of the sensitivity of alpine meadow to climate change in high-altitude mountainous regions.

This work was carried out with financial support from the National Basic Research Program of China (2013CBA01806) and the National Natural Sciences Foundation of China (41401041). We thank the four reviewers and the editor for their constructive comments that led to improvements in the manuscript.