Crop coefficient determination and evapotranspiration estimation of watermelon under water deficit in a cold and arid environment

To investigate the evapotranspiration and crop coefficient of oasis watermelon under water deficit (WD), mild (60%–70% field capacity, FC)and moderate (50%–60% FC) WD levels were set up at the various growth stages of watermelon, including seedling stage (SS), vine stage (VS), flowering and fruiting stage (FS), expansion stage (ES), and maturity stage (MS), with adequate water supply (70%–80% FC) during the growing season as a control. A two-year (2020-2021) field trial was carried out in the Hexi oasis area of China to explore the effect of WD on watermelon evapotranspiration characteristics and crop coefficient under sub-membrane drip irrigation. The results indicated that the daily reference crop evapotranspiration showed a sawtooth fluctuation which was extremely significantly and positively correlated with temperature, sunshine hours, and wind speed. The water consumption during the entire growing season of watermelon varied from 281–323 mm (2020) and 290–334 mm (2021), among which the phasic evapotranspiration valued the maximum during ES, accounting for 37.85% (2020) and 38.94% (2021) in total, followed in the order of VS, SS, MS, and FS. The evapotranspiration intensity of watermelon increased rapidly from SS to VS, reaching the maximum with 5.82 mm·d-1 at ES, after which it gradually decreased. The crop coefficient at SS, VS, FS, ES, and MS varied from 0.400 to 0.477, from 0.550 to 0.771, from 0.824 to 1.168, from 0.910 to 1.247, and from 0.541 to 0.803, respectively. Any period of WD reduced the crop coefficient and evapotranspiration intensity of watermelon at that stage. And then the relationship between LAI and crop coefficient can be characterized better by an exponential regression, thereby establishing a model for estimating the evapotranspiration of watermelon with a Nash efficiency coefficient of 0.9 or more. Hence, the water demand characteristics of oasis watermelon differ significantly during different growth stages, and reasonable irrigation and water control management measures need to be conducted in conjunction with the water requirements features of each growth stage. Also, this work aims to provide a theoretical basis for the irrigation management of watermelon under sub-membrane drip irrigation in desert oases of cold and arid environments.


Introduction
Desert oases are an essential barrier to guaranteeing regional food and ecological security. In the interior of northwest China, the oasis agricultural region of Hexi features a temperate continental desert climate with little to no annual rainfall and a severe water resource constraint (Deng et al., 2017). As is well known, oasis agriculture is dominated by irrigated agriculture, so without irrigation, there would be no agriculture (Li et al., 2016). The proportion of agricultural water use in the total water resources of the Hexi area is the largest, at 88.40% (Wang et al., 2019). At present, agricultural cultivation in most areas of the Hexi Oasis region still uses the traditional check-field flood irrigation, with its backward and unreasonable irrigation techniques and low water use efficiency (WUE) (Wang et al., 2020a). Moreover, together with the long years of machine well extraction, this has led to the overexploitation of local groundwater resources, aggravating the degree of arable desert and deteriorating the ecological environment (Chai et al., 2014). Although, the area has long sunshine hours, a short frost-free period, abundant light and heat resources, and a 15-20°C temperature difference between day and night, all of which make it an ideal base for melon cultivation (Yang et al., 2018;Li et al., 2022a). A shortage of water resources and water waste in the region (Huang et al., 2017;Zhou et al., 2022), along with the recent blind expansion of watermelon and other specialty cash crops, has severely hampered the development of the local watermelon industry. T hu s, studies on water c onsumption and evapotranspiration of oasis watermelon under water deficit conditions are of vital practical value for water resources deployment and to ensure stable and high watermelon yields.
The production of special melons in the oasis is a highly advantageous enterprise. But the watermelon's growth can be significantly affected by changes in water availability because of its high water requirements and sensitivity to soil moisture (Leskovar et al., 2007;Zhang et al., 2009). During certain growth periods maintaining an appropriate water deficit (WD) not only enhances the conversion of photosynthetic products to fruits but also suppresses excessive nutrient growth in the above-ground parts and promotes root growth, thereby improving yield and quality (Rahmati et al., 2018;Zuniga et al., 2018). The results of a study using daily evaporation from the water surface of the evaporation dish as the water control criterion showed that the overall benefits for watermelon were best when the evaporation coefficients were determined at 0.75, 0.75, 1.25, and 1.00 for the seedling (SS), flowering and fruiting (FS), expansion (ES) and maturity (MS) stages in that order (Lin et al., 2010). As for the study that used drip irrigation frequency as a water control criterion, the recommended drip irrigation system for greenhouse watermelon in the arid zone was one drip every four days at both SS and ES, while one drip every two days at FS and one drip every six days at MS . In addition, the results of the experiment by Wu and Wang (2008) showed that soil water content (SWC) in watermelon fields was controlled at 70.92%-81.24% while leaf area index (LAI) was between 1.44-1.32, which both enhanced leaf photosynthetic efficiency and promoted the accumulation of assimilates. Kuscu et al. (2015) achieved an optimum balance between water productivity, quantity, and quality in watermelon fruits under semi-humid conditions with 100% crop evapotranspiration (ET c ) before maturity and 50% ET c recovery afterward. Accordingly, by scientifically managing the water demand pattern during the watermelon's growing season in the oasis, high-quality and efficient ecological watermelon cultivation may be achieved.
Evapotranspiration (ET) is a critical component of farmland water balance during the hydrologic cycle, which has a significant effect on crop development and yield (Cui et al., 2008b). The water in farmland under sub-membrane drip irrigation is mainly consumed by ET c (Skaggs et al., 2010;Feng et al., 2018). Thus, accurate estimation of ET c is crucial to reducing water consumption during the crop reproductive period, improving WUE, and developing water-saving agriculture (Liu et al., 2002;He et al., 2013). There are two main methods for calculating ET c : one is a direct calculation approach, and the other uses the reference crop evapotranspiration (ET 0 ) and the crop coefficient (K c ). Since most of the direct calculation methods are empirical formulas with strong geographical limitations, the prevailing method is based on ET 0 . Related studies have indicated that the ET 0 calculated using the Penman-Monteith (P-M) is the closest to the measured values in both humid and arid regions, so it is a preferred calculation method that is widely used (Allen et al., 1989;Allen et al., 2011).
The LAI is an essential growth indicator that reflects the quality of crop population and is strongly linked to photosynthesis, transpiration, and water productivity (Zhao et al., 2018;Wang et al., 2021). A study has shown that variation in plant leaf area has a substantially greater effect on evapotranspiration than that of variation in the climate and that climatic factors have a stronger influence on evapotranspiration indirectly through plant cover (Yang et al., 2022). As well known, K c is relevant to LAI dynamics, intercepted solar radiation, and crop phenological stage (Netzer et al., 2009). Meanwhile, crop stage water requirement is equal to the product of stage ET 0 and K c (Meng, 2011).
For apple trees under irrigated conditions, Du et al. (2017) discovered a positive correlation between transpiration and LAI, while Juhasz and Hrotko (2014) reached the same conclusion for the Hungarian sweet cherry. Munitz et al. (2019) reported a significant linear relationship between LAI and K c for irrigated vineyards, i.e., K c could be estimated by measuring the LAI of the vineyard and combining it with meteorological data from neighboring weather stations to calculate ET 0 , and then ET c is obtained. As can be seen, it is feasible to establish a regression model of LAI against K c . However, K c is greatly influenced by environmental conditions such as climate, soil, and degree of WD in different areas (Wang et al., 2020b). Therefore, investigating the relationship between LAI and K c under WD conditions is critically valuable for accurately predicting oasis watermelon ET in the Hexi region.
In conclusion, a model can be established to estimate the ET of oasis watermelon in the Hexi region using LAI and meteorological factors, thereby letting the model to master the dynamic water consumption law of local watermelon during various growth periods, which has excellent practical significance for enhancing the level of watermelon precision management, formulating a reasonable water dynamic management plan, and maintaining the stability of fruit yield. However, there exists a seriously limited knowledge in the Hexi region about the water consumption characteristics of watermelon under mulched drip irrigation, and studies on the determination of K c and ET estimation models for oasis watermelon have not been reported. Therefore, the aims of this study were: (1) to analyze the stages evapotranspiration characteristics of oasis watermelon under WD and its change law; (2) to accurately calculate ET 0 during the reproductive period of watermelon based on the PM equation and then invert K c of oasis watermelon; and (3) to establish an estimation model of oasis watermelon evapotranspiration, thereby achieving precise irrigation at various growth phases of oasis watermelon and effectively improving the water productivity in the Hexi region.

Description of the study site
The experiment was conducted from May to August 2020 and 2021 at the Yimin Irrigation Experiment Station (100°43′ E, 38°39′ N, altitude: 1,970 m, total area: 20 mu), which is a joint scientific research and training base of Gansu Agricultural University. The test site is in a typical desert oasis of China's northwestern arid region, where the annual average temperature is 6°C, the frost-free period is 165 days, the annual precipitation mostly ranges between 183-285 mm, the annual average evaporation is 2,000 mm, the annual average sunshine hours is 3,000 h, and the climate is temperate continental grassland. The soil texture of the test site is a light loam with a soil bulk density of 1.4 g·cm -3 and a pH of 7.2. The field capacity (FC) of tilled soil is 24.0% (mass water content), and the wilting point is 8.2%. The salinization hazard is negligible due to the large depth of groundwater burial.

Experimental design and agronomic management
The watermelon variety tested was the "Xinong 8," a local main planting. The main growth period of oasis watermelon was divided into five stages: seedling stage (SS), vine stage (VS), flowering and fruiting stage (FS), expansion stage (ES), and maturity stage (MS). Deep plowing, weeding, fertilizer application, drip irrigation, and mulching were carried out before sowing so that the initial conditions of water and nutrients in each plot were similar. Planting was done manually by breaking the film in a northsouth direction, with two rows at 30 cm × 210 cm spacing in each plot. The irrigation method was sub-membrane drip irrigation, with one pipe controlling one row of crops and the length of the pipe equaling the length of the plot. Specific agronomic management measures are presented in Table 1.
The experiment was a one-way completely randomized design. WD treatments were applied mainly at the watermelon SS, VS, ES, and MS. The amount of irrigation was calculated as the average SWC as a percentage of the FC in the planned wet layer (0-60 cm), and irrigation was applied immediately to the upper limit when the measured SWC was below (or close to) the design lower limit of the treatment. A total of nine treatments were set up, with three replications of each treatment, in which suitable irrigation was performed throughout the reproductive period and served as the control treatment. The specific experimental design scheme is illustrated in Table 2.

Meteorological information
Meteorological data was achieved from a fully automatic weather station located at the experimental site. Meteorological factors such as precipitation (P), air temperature (T), relative humidity (RH), sunshine hours (n), wind speed (u), wind direction, and air pressure were automatically measured in the test area.

Soil water content (SWC)
The SWC of the planned wet layer (sampled every 20 cm) was determined layer by layer using the dry method every 7-10 days after the start of the treatment, with the sampling points randomly selected in the middle of two watermelon plants and the average value taken to determine the amount and timing of irrigation, with additional measurements before and after irrigation.

Leaf area index (LAI)
The non-linear regression equation for single leaf area (LA) against leaf width (w) was established according to the reference (Zheng, 2009): LA = exp -0.096 w 1.758 , where the determination coefficient R 2 = 0.912 (p< 0.01). The LAI was gained by calculating the total LA of all plants per unit of land and then comparing it to the land area.

Crop evapotranspiration
Crop evapotranspiration (ET c ) was calculated by using the water balance equation (Cui et al., 2008a).
where P r is the effective precipitation in each period (mm); U is the groundwater recharge (mm), the test site is in an inland arid area, the groundwater burial depth is below 20 m, so the groundwater recharge can be neglected, i.e., U=0. I is the amount of irrigation water during the period (mm); D is the amount of deep seepage (mm), because the soil moisture design is lower than the field capacity, and the design flow rate of under-film drip irrigation is 2 L·h -1 , there is no deep seepage problem, so the amount of deep seepage is negligible, i.e., D=0; S is the surface runoff (mm), the test field is in flat mulching, there is no surface runoff, i.e., S=0; DW is the change of soil water storage in the 0-100 cm-layer during the period (mm).
ET c ¼ P r + I + DW (2) DW and I in Eq.
where q i2 and q i1 are the volumetric SWC of i-layer at the end and beginning of the calculation period, respectively (%); H i is the thickness of i-layer (mm); I is the volume of single irrigation (mm); r is the soil bulk density (g·cm -3 ); H is the depth of the plan wetted layer (cm); p is the design wetting ratio, 0.65 is taken for this test; q max is the design upper limit of SWC (%); q t is the SWC before irrigation (%); h is the irrigation water utilization ratio, taken as 0.95 in this experiment.
The stage evapotranspiration intensity and water consumption modulus can be found in Wei et al. (2017).
where ET 0 is the reference crop evapotranspiration (mm); R n is the net radiation (MJ·m -2 ·d -1 ); G is the soil heat flux (MJ·m -2 ·d -1 ); D is the slope of the saturation water vapor pressure against temperature curve (kPa·°C -1 ); g is the hygrometer constant (kPa·°C -1 ); T is the mean air temperature (°C); u 2 is the wind speed at a height of 2 m above ground (m·s -1 ); e s is the saturation water vapor pressure of air (kPa); e a is the actual water vapor pressure of air (kPa).

Crop coefficient
The crop coefficient (K c ) under no WD conditions is determined by the ratio of evapotranspiration under adequate water supply conditions to the ET 0 . This is calculated by Eq. (6).
where K c0 is the K c without water stress; ET c is the evapotranspiration under adequate water supply (mm); ET 0 is the reference crop evapotranspiration (mm).
When soil moisture is insufficient, the K c is not only affected by meteorological factors and the crop's characteristics but also by the SWC. Therefore, the moisture stress coefficient is introduced into the calculation of the K c . The moisture stress coefficient is derived from the evapotranspiration measured under WD conditions, the ET 0 , and the K c0 (Allen et al., 1998) and is calculated as follows.
where K s is the water stress coefficient; ET WD is the evapotranspiration under water stress conditions (mm); ET 0 is the reference crop evapotranspiration (mm).
The K c is calculated as follows.

Methodology for testing of ET c estimation model
The correlation coefficient (r), Nash efficiency coefficient (NSE), and total equilibrium coefficient (R) were considered as statistical coefficients to evaluate the merits of the ET estimation model (Wang et al., 2014). The error analysis was performed quantitatively using average relative error (ARE) and mean absolute percentage errors (MAPE).

Data processing
The average and standard deviation (± SD) of the data were calculated in Microsoft Excel 2010 (Microsoft Corp., Raymond, Washington, USA). The software Origin 2020 (Origin Lab, Corp., Hampton, Massachusetts, USA) was used for graphing and regression analysis. Significance analysis with Duncan's multiple range test was performed at a 5% level using SPSS 19.0 (IBM, Inc., New York, USA).

Distribution characteristics of ET 0
The daily ET 0 variation and effective rainfall distribution for oasis watermelon during two consecutive growing seasons from 2020-2021 are indicated in Figures 1A, B. We can see from Figure 1, the daily ET 0 fluctuated in a sawtooth pattern with sharp fluctuations, especially in late July and early August, but the overall trend was relatively stable, with the peak occurring from late July to early August. Moreover, the higher ET 0 was concentrated after the fruit set, among which the frequency of daily variation was higher in 2020 and reached a peak of 6.40 mm on 28 July, while the frequency of daily variation was relatively low in 2021 and reached a maximum of 6.66 mm on 1 August. This is mainly related to the climatic characteristics (temperature) of the trial site. Besides, the distribution of rainfall also showed that the greater the daily rainfall on a rainy day, the smaller the corresponding daily ET 0 , with a negative correlation between them.
As seen in Figure 1, the effective rainfall during the watermelon reproductive period in 2020 was 68 mm, and the rainfall during the SS, VS, FS, ES, and MS was 28.50 mm, 29.90 mm, 0.00 mm, 0.00 mm, and 9.60 mm, respectively, with the highest rainfall of 28.5 mm on 21 June. Similarly, it can be seen that the effective rainfall in 2021 for different growth stages and the whole reproductive period was 28.70 mm, 16.90 mm, 0.00 mm, 6.50 mm, 9.30 mm, and 61.40 mm, respectively. The largest amount of rainfall was 9.7 mm on 23 June. It can be concluded that irrigation should be controlled during the SS in watermelon cultivation to avoid excessive irrigation consuming the less water-demanding reproductive period, and on the contrary, timely irrigation is required during the melon ES to replenish soil water to avoid WD. It is also clear from Figure 1 that the ET 0 of stage cumulative was highest at the VS (128.32 mm in 2020 and 117.17 mm in 2021), while the ET 0 of the FS was relatively lowest because of its shortest duration (19.30 mm in 2020 and 23.27 mm in 2021). The mean of daily ET 0 results was highest at SS and lowest at FS in 2020, highest at ES and lowest at VS in 2021.
ET 0 and its composition for different growing periods of oasis watermelon in the Hexi region are illustrated in Table 3. The ET 0 calculated by the P-M equation is derived from the sum of the solar radiation term (ET rp ) and the aerodynamic term (ET op ), both of which constitute the effect on the ET 0 (Glasbey and Allcroft, 2008). As can be seen in Table 3, the proportion of ET rp in each stage of oasis watermelon (in 2020, for example) was 71.48%, 76.67%, 80.09%, 78.14%, and 75.97%, in that order. The proportion of ET rp in ET 0 showed a single-peak trend of increasing and then decreasing as the growth period progressed and increased to the largest proportion at FS and ES. Meanwhile, the weight of ET rp influencing ET 0 was greater than 70%, much higher than ET op , while the total ET rp share was 75.60% throughout the growing season. This is mainly because the respective ratios of ET rp and ET op are affected by the regional geography and climatic environment and change over time. The Hexi Oasis lies in the interior, where there is an enormous amount of ET rp rather than ET op in ET 0 due to the region's arid environment, lack of precipitation, high evaporation intensity, and long daylight hours.

Effects of meteorological factors on ET 0
The results of the ET 0 calculation are directly influenced by the meteorological factors needed in the P-M equation. Due to the unique climatic conditions of the Hexi Oasis region, it is imperative to examine the correlations between the following meteorological variables: daily maximum temperature (T max ), daily minimum temperature (T min ), daily mean temperature (T mean ), sunshine hours (n), atmospheric pressure (P), relative air humidity (RH), water vapor pressure (e a ), wind speed (u 2 ) and ET 0 , as well as the correlation between ET 0 and meteorological data under the interaction of multiple factors. The meteorological data for 2021 was used as an example in the study that was done above. Figure 2 presents the bivariate correlation analysis between meteorological factors and ET 0 during the watermelon growing season. The Pearson correlation analysis shows that ET 0 had a highly significant positive correlation with T max , T mean , n, and u 2 whose coefficients were 0.721, 0.644, 0.870, and 0.392, respectively; a significant positive correlation with T min whose coefficient was 0.234; and a negative correlation with P, RH, and e a whose coefficients were -0.439, -0.761, and -0.195, which were negatively correlated. Figures 3A-H shows the functional correlation between a particular meteorological factor and ET 0 during the watermelon growing season. From Figure 3, we can see that T max , T mean , n, and RH were highly correlated with ET 0 with an R 2 > 0.4 (p< 0.05); and P was somewhat negatively correlated with ET 0 , but the R 2 was only 0.1933. While T min , e a , and u 2 did not demonstrate a functional relationship for the effect of ET 0 . With an R 2 of 0.757, both T and n were significantly and positively correlated with ET 0 , indicating that temperature, sunshine duration, and wind speeds had a significant promoting effect on ET 0 .
The r and significance analysis was subsequently computed for each step to conduct a thorough investigation into the relationship between ET 0 and various climatic parameters within each growth stage. The results are displayed in Figure 4. The correlations between meteorological factors and total ET 0 during the entire growing season were consistent with the results of the above analysis. The correlations between ET 0 and each meteorological factor within different growth stages had co-factor influences, although there was some variability. Both the r of n at FS and P at MS with ET 0 were 0.823 and 0.509, but neither was statistically significant. This was mostly because the growing time was not significantly affected by the relatively small sample size. T min peaked at the SS and became extremely significant, but they were unimportant at all other growth stages and had negative correlations at the VS and MS. While u 2 demonstrated a highly significant positive correlation at both the VS and ES with no significant influence at any other stage, e a displayed a highly significant negative correlation at both the SS and the ES. To further explore the role of multiple factors in driving the dependent variable, a multiple linear regression equation was constructed between ET 0 and the meteorological parameters subsumed in its calculation for the watermelon growing season and each period. Table 4 displays the specific results, and the R 2 was all above 0.9 (p< 0.01), which was a better fit. Tables 5-9 show the ET, K c , ET intensity, and water consumption modulus of oasis watermelon under various water treatments during various growing period. The ET of watermelon during the whole growing season was 323 mm and 334 mm in 2020 and 2021, respectively, with adequate water supply. Compared with CK, the ET of WD treatments decreased to different degrees, and the most significant was the WD treatment at the ES, while the water consumption of watermelon showed a bimodal trend during the growing season. Table 5 shows that for mild (WD1) and moderate (WD2) WD, respectively, the ET was considerably reduced in 2020 and 2021 compared with CK by 6.45%-6.65% and 12.79%-12.84%, respectively (p< 0.05), whereas the other treatments did not significantly differ from CK (p > 0.05). The ET intensities of WD1 and WD2 were 1.85-1.93 mm·d -1 and 1.74-1.79 mm·d -1 , respectively, and both were significantly lower than CK. The moderate treatment saw a higher decline, whereas the other treatments did not differ significantly from CK. The water consumption modulus of the treatments ranged from 15.08%-20.03% in both years due to short, slow-growing watermelon plants and relatively low temperatures during the SS.

Effect of WD at the vine stage (VS)
As can be seen from Table 6, ET was highest in 2020 with 87.30 mm for CK, and 89.79 mm for treatment WD8 in 2021, which was only 2.85% higher than that of CK, but the difference was not significant, while ET was lowest in 2a moderate WD treatment WD4 with a decrease of 16.08%-19.15%, while mild WD treatment WD3 decreased by 10.09%-12.26%, and the rehydration treatment WD1 was at the same level as CK. The ET intensity was highest in CK, with 2a at 2.91 mm·d -1 and 3.01 mm·d -1 respectively, followed by the rehydration treatment WD1. The ET intensity of treatment WD4 was significantly reduced by 18.85%-19.15% compared to CK, and the reduction in treatment WD3 was 12.26%-13.07%. When watermelon entered the VS, the root crown developed rapidly, the temperature rose gradually and the water consumption modulus increased, which ranged from 24.95% to 30.75%. Correlation analysis of ET 0 and meteorological elements during the watermelon growing period in 2021. Correlations between the two indicators were significant at *p< 0.05 and **p< 0.01. T max , daily maximum temperature; T min , daily minimum temperature; T mean , daily mean temperature; n, sunshine hours; P, atmospheric pressure; RH, relative air humidity; e a , water vapor pressure; u 2 , wind speed.  Table 7 indicates that the water consumption of the various water treatments was the same as that of the preceding stage, with a relatively small water consumption modulus of 6.48%-8.03%. This was caused by the stage's brief duration as well as the stage's higher ET intensity of approximately 4.30 mm·d -1 , which occurred as the plants were in a crucial stage of transition from nutritional to reproductive growth.

Effect of WD at the expansion stage (ES)
As can be seen from Table 8, ET was highest for CK in 2020 and 2021, with treatments WD1 and WD3 not significantly different from CK, while ET for the mild (WD5) and moderate (WD6) WD treatments decreased significantly by 18.90% and 26.95%, respectively, compared to CK, while WD treatments WD3 and WD4 were still smaller than CK during the VS, and the differences were significant. The ET intensity was highest in CK, reaching 5.23 mm·d -1 and 5.82 mm·d -1 , but the effect of WD on watermelon water consumption was greater at this stage, with treatments WD5 decreasing by 18.93%-19.24%, while treatment WD6 had the least ET intensity, decreasing by 25.60%-26.96%. Since the ES was the critical period of water demand for watermelon, to ensure the rapid expansion of the flesh cells, water demand was at its maximum, with a water consumption modulus of 32.71%-41.18%.

Effect of WD at the maturity stage (MS)
As can be seen from Table 9, in 2020 and 2021, evapotranspiration was highest in CK, while treatment WD6 Correlation analysis of ET 0 and meteorological elements during the watermelon growth period. * and ** represent significance at the p<0.05 and 0.01 levels , respectively. Relationships between meteorological elements and ET 0 during the growing season in 2021. (A-H) describes the relationship between daily maximum temperature (T max ), daily minimum temperature (T min ), daily mean temperature (T mean ), sunshine hours (n), atmospheric pressure (P), relative air humidity (RH), water vapour pressure (e a ), wind speed (u 2 ) and reference crop evapotranspiration (ET 0 ), respectively.
remained the lowest at 24.63 mm and 26.32 mm, significantly lower than CK by 23.72% and 21.29%, respectively, while treatments WD2 and WD3 were not significantly different from CK, while mild (WD7) and moderate (WD8) WD treatments were significantly lower than CK by 5.53%-5.67% and 13.13%-13.25%, respectively. The evapotranspiration intensity of CK was still the highest, with treatments WD1-WD3 at the same level as CK, but WD8 demonstrated a significant decrease of 13.26%-18.45% compared with CK, and WD7 indicated a decrease of 5.67%-2.73%. Moreover, at watermelon MS, the growth rate also slowed down and the water consumption modulus dropped to 8.78%-10.66%. In summary, (1) the ET results revealed that the ET of the SS in 2020 was similar to that of the SS in 2021, and the remaining treatments except for the WD at this stage were not significantly different from CK. The ET at the VS and ES decreased with increasing WD levels, with a significant decrease compared with CK, and the ET at the ES in 2021 was higher than that in 2020. The ET of CK was the highest at the MS. (2) The ET intensity showed that it was lowest at the SS (about 1.94 mm·d -1 ), higher at the VS and MS (about 2.81 and 2.59 mm·d -1 ), and highest at the FS (about 4.36 and 5.14 mm·d -1 ). The ET intensity of oasis watermelon ranged from 1.74 to 5.82 m·d -1 under different water treatments throughout the entire reproductive period.
(3) The water consumption modulus showed a relatively similar distribution pattern for watermelon during the two-year reproductive period, i.e., 32.71%-40.52% at the ES, 24.95%-30.75% at the VS, 15.24%-20.03% at the SS and 8.78%-10.66% at the MS. This is mainly since many factors influence the water consumption modulus, such as ET intensity, total evapotranspiration during the growing season, environmental factors, and the duration of the growth stage, which cannot be directly related to the magnitude of the WD. The values shown are the mean ± SD, n = 3. Different lowercase letters on a line indicate significant differences at p< 0.05.
The K c is related to the crop type, variety, reproductive period, and LAI, reflecting the physiological characteristics of the crop itself. As can be seen from Tables 5-9, K c generally showed a single-peaked curve fluctuation of increasing and then decreasing, reaching peaks of 1.246 and 1.237 at the ES, followed by 1.154 and 1.006 at the FS, and a minimum of 0.459 and 0.473 at the SS. Irrigation had a large effect on K c , with any stage of WD reducing the K c for that stage, and the greater the stress the smaller the corresponding K c . K c for both years was smallest at 0.400 and 0.412 for the moderate WD treatment at SS (WD2), largest in 2020 (1.247), and largest in 2021 (1.237) for the moderate WD treatment at ES (WD8), while the average values of K c were 0.803 and 0.784 for the whole reproductive period. Figure 5 shows the variation curves of watermelon LAI with time under different water treatments. The trend of the LAI of oasis watermelon under different water treatments is generally similar, with the LAI gradually increasing from the beginning of the growing season, and the LAI increasing rapidly during the VG, which is a critical stage for the growth of watermelon vine leaves and other nutrient organs, reaching a peak in the early ES. The late ES to the MS, the plant's nutritional growth stalled, most of the vine-leaves nutrients were absorbed by the fruit, the crop metabolism tended to slow down, the base leaves gradually withered and fell off, and the LAI showed a slow decrease trend.

Effects of different WD treatments on LAI
For reasons of length, only 2020 data was analyzed. Compared with CK, WD treatments WD1 and WD2 at SS reduced LAI by 6.35% and 16.90%, respectively, with significant differences (p< 0.05). At VS, WD1 grew faster and higher than CK by 4.42% after rehydration, but the difference was not significant (p > 0.05), while WD2 still decreased by 2.58%, and the LAI of WD treatments WD3 and WD4 decreased significantly by 5.80% and 13.25%, respectively, compared with CK. The results of all treatments at FS were the same as that of VS. Upon entering the ES, the LAI of treatment WD1 was the largest, while the leaf growth of treatments WD2 and WD3 accelerated after rehydration and were still lower than that of CK but not significantly different, and the WD treatments WD5 and WD6 were both lower than that of CK during this period, with a significant difference for treatment WD6. By the end of MS, the LAI of all treatments decreased, among which all treatments were lower than CK except for the mild WD treatment at the SS, with a decrease of 0.11%-7.53%, while treatment WD4 (moderate WD at the VS) was significantly different from CK. The LAI was affected differently by different WD treatments at different growth stages. SS to the beginning of FS was the rapid formation stage of watermelon stems and leaves and other nutrient organs, WD at this stage had a significant effect on the LAI, but it is not significantly different from CK due to the compensation result of light stress after rehydration. The values shown are the mean ± SD, n = 3. Different lowercase letters on a line indicate significant differences at p< 0.05.

Relationship between K c and LAI
K c has a dynamic process of change during the reproductive period, and it is generally accepted that there is a correlation between K c and LAI. In this paper, the regression equation between K c and mean LAI under different water treatments was established based on the actual data measured in two consecutive growing seasons of oasis watermelon in the Hexi region, as shown in Figure 6.
The LAI and K c were first analyzed for correlation, with r = 0.759 (p< 0.01), indicating a highly significant positive correlation between the LAI and K c of oasis watermelon. The regression analysis in Figure 6 shows that there was a good exponential relationship between K c and LAI for oasis watermelon, with the fitted relationship equation K c = 0:463e 0:686LAI and R 2 = 0.5811 (p< 0.01), indicating that it is possible to estimate the K c by measuring the LAI of watermelon using this relationship equation, thereby providing a practical reference for watermelon irrigation.

ET estimation model and error analysis
The quantitative relationship between the LAI and K c and the integrated P-M equation enabled the modeling of the actual ET of oasis watermelon in the Hexi region with the LAI and meteorological factors.
To evaluate the reliability of the model established under different water treatment conditions, the experimental data from 2020 and 2021 were employed to validate the established ET estimation model. The quantitative evaluation analysis was conducted by comparing the actual evapotranspiration values (ET s ) obtained from the water balance equation with the modeled values (ET m ). The evaluation results are shown in Figure 6. Figure 6 shows the results of the statistical coefficients comparing ET s with ET m for the assessment phase of the model equation. The r for the actual values obtained from the water balance method and the estimated model modeling values in 2020 and 2021 were 0.965 and 0.973 respectively (p< 0.01), i.e., the correlation between both was good; the NSE was 0.917 and 0.919 respectively, i.e., the NSH of the model constructed was close to 1, indicating that the model had better fitting accuracy and high reliability; the R was 1.023 and 1.032 respectively, i.e., the totals were similar, which showed that the model has a better performance in the evaluation phase. In addition, ARE values for two-year were small and the MAPE values were 16.831% and 16.199%, indicating that the errors in the modeling results were relatively small. It can be shown that the model constructed in this study can better estimate the watermelon ET under the conditions of sub-membrane drip irrigation in the Hexi Oasis by using LAI and meteorological factors. The values shown are the mean ± SD, n = 3. Different lowercase letters on a line indicate significant differences at p< 0.05. The values shown are the mean ± SD, n = 3. Different lowercase letters on a line indicate significant differences at p< 0.05. ET 0 is a critical parameter for calculating crop water requirements and irrigation management (Ahmad et al., 2017;Kadam et al., 2021), and the ET 0 calculated based on the P-M equation is directly affected by the local climate (Neto et al., 2015;Borges and Pinheiro, 2019). In this study, the average ET 0 values during the watermelon growing season were found to be 4.15 mm (2020) and 4.33 mm (2021), with the relatively smallest ET 0 at MS. Simple correlation analysis between meteorological factors and ET 0 during the growing period showed that ET 0 was positively correlated with T, n, and u 2 , while it was negatively correlated with P, RH, and e a . Similar findings were obtained by Zeng (2018), which were mainly related to the evaporative properties of water. To further clarify the influence of meteorological factors on ET 0 , a multiple linear regression model was established between ET 0 and the meteorological factors involved in the calculation for the whole reproductive period and stage, and the fitting results were high. Wang et al. (2014) achieved similar results for the ET 0 estimation in the Hetao areas.

The ET pattern of oasis watermelon
ET 0 is determined by soil, irrigation, crop varieties, and meteorology, but WD can effectively reduce ET of melon crops (Leite et al., 2015;Qin and Leskovar, 2020), especially at the fruit growth and development stage, which has a more significant effect (Yavuz et al., 2021). According to the water consumption of the twoyear, WD at the VS and ES had a greater impact on the stage ET of watermelon, thereby leading to a significant reduction in total ET. Compared with CK, stage ET was significantly reduced by 10.09%-1.32% for mild WD at VS (WD3), and by 16.08%-19.15% for moderate WD treatment (WD4), and the difference between WD3 and WD4 was significant. During the ES, stage water consumption was highest in CK at 125.61 mm in 2020 and 133.76 mm in 2021, and was significantly reduced by 18.90%-19.16% and 25.50%-26.95% in the mild (WD5) and moderate (WD6) WD treatments, respectively, during this period. The difference between them was also significant. This is consistent with the findings of Zhang et al. (2021), where stage WD resulted in a linear decrease in the average daily ET of watermelon, with the greatest decrease occurring during the ES.
Studies (Ji et al., 2015) have shown that water regulation effectively reduced the stage water consumption modulus and ET intensity of crops. The results of two consecutive growing seasons indicated that ET showed an increasing and then decreasing law, with the highest water consumption modulus (about 40%) at the ES, followed by the second highest (29%) at the VS, the smallest (about 7%) at the FS, and about 19% and 10% at the SS and MS. The ET intensity is the smallest at the SS (about 1.9 mm·d -1 ), relatively large at the VS and MS (about 2.8 mm·d -1 ), and the largest at the FS (4-5 mm·d -1 ). This is because crop water requirements are mainly influenced by growth characteristics, meteorology, and agronomic management practices, but also follow the The values shown are the mean ± SD, n = 3. Different lowercase letters on a line indicate significant differences at p< 0.05.

FIGURE 5
LAI curve with time for different water treatments.

FIGURE 6
Relationship between K c and LAI for oasis watermelon. Zhang et al. 10.3389/fpls.2023.1153835 Frontiers in Plant Science frontiersin.org corresponding habitual and quantitative patterns. Furthermore, WD at various growth stages caused a decrease in both water consumption modulus and ET intensity of watermelon, and the more the corresponding stage ET, the more significant the effect of WDinduced decrease in water consumption. This is similar to the results of Wang et al. (2018b) and Huang et al. (2021) on the water requirements patterns of WD peppers.

Relationship between LAI and K c
K c can be employed to describe the effect of crop biological features, water productivity, and soil tillage conditions on crop water requirements as an indirect parameter for determining ET 0 (Wright, 1982;Pereira et al., 1999). Related studies (Yun et al., 2015;Li et al., 2022b) revealed that between crop LAI and K c existed a more favorable exponential relationship, which was consistent with the results of this work but differed from the findings of Hu et al. (2012) and He and Wu (2018), who discovered a quadratic curve relationship between K c and LAI of drip irrigated jujube trees. This might be related to crop varieties and cultivation areas. In addition, this paper established an ET estimation model for watermelon with under-mulched drip irrigation in the Hexi region based on the above-mentioned exponential regression relationship, and after evaluation and validation, the NSE reached more than 0.9, which was higher than the NSE of ET models established in different approaches by Wang et al. (2018a), thereby filling a research gap in the estimation of K c and ET for oasis watermelon.

Conclusion
(1) Water deficit at various growth stages led to a decrease in the evapotranspiration intensity of watermelon. Evapotranspiration was relatively highest at the ES, which is a critical water requirement period for oasis watermelon, ranging from 91.75 to 133.76 mm with an average evapotranspiration intensity of 5.06 mm·d -1 .
(2) There was a promotion of ET 0 by temperature, hours of sunlight, and wind speed, and the potential impact of hightemperature variation on watermelon growth was greater than other climatic factors. The crop coefficients for field watermelon at the SS, VS, FS, ES, and MS were in the order of 0.400-0.477, 0.550-0.771, 0.824-1.168, 0.910-1.237, and 0.552-0.803, under water deficit conditions in Hexi region.
(3) The leaf area index varied more significantly among the different water treatments and increased with increasing irrigation. Moreover, there was a strongly significant correlation between crop coefficient and leaf area index, showing a well-exponential relationship. Based on this relationship, a model for estimating the evapotranspiration of oasis watermelons concerning the leaf area index was also established, and the modeling results of the proposed model were empirically analyzed to be in good agreement with the actual values.
The model in this work is based on the results of two consecutive growing seasons trials of water deficit watermelon, and only single crop coefficient method were used to calculate and establish the estimation model, which might have some bias. In future studies, we will combine years of actual measurement data to build an evapotranspiration estimation model according to the dual-crop coefficient method to further improve the accuracy and practical application of the model.

Data availability statement
The original contributions presented in the study are included in the article/Supplementary Material. Further inquiries can be directed to the corresponding author.