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Sci Rep
Sci Rep
Scientific Reports
2045-2322
Nature Publishing Group UK London

39266590
72183
10.1038/s41598-024-72183-8
Article
Spatiotemporal evolution of dry and wet and quantitative analysis of the influence of meteorological factors based on MI and the FAO P–M model
Ma Yali
Niu Zuirong niuzr@gsau.edu.cn

Sun Dongyuan
Wang Xingfan
https://ror.org/05ym42410 grid.411734.4 0000 0004 1798 5176 College of Water Conservancy and Hydropower Engineering, Gansu Agricultural University, Lanzhou, 730070 China
12 9 2024
12 9 2024
2024
14 2134330 4 2024
4 9 2024
© The Author(s) 2024
2024
https://creativecommons.org/licenses/by-nc-nd/4.0/ Open Access This article is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License, which permits any non-commercial use, sharing, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if you modified the licensed material. You do not have permission under this licence to share adapted material derived from this article or parts of it. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by-nc-nd/4.0/.
The frequent occurrence of extreme climate events disrupts the regional water budget balance and leads to changes in the dry and wet conditions of the surface, making the water surplus and deficit more complex and variable. To explore the quantitative relationship between the spatiotemporal evolution of dry and wet conditions and meteorological factors in the Hexi Corridor under changing environmental conditions, the relative moisture index (MI) and FAO Penman–Monteith (FAO P–M) model were combined to construct a partial differential quantitative attribution model for dry and wet variations affected by climate factors in the Hexi Corridor. The results show that: (1) MI in the Hexi Corridor increased significantly (Z = 2.341) during 1960–2019, showing a wet-trend change, and the degree of drought increased from southeast to northwest in the Hexi Corridor. (2) The order of drought degree in four seasons is as follows: winter (− 0.95), spring (− 0.93), autumn (− 0.89) and summer (− 0.83). (3) The frequency of extreme drought, severe drought, moderate drought, and mild drought within 60 years of 21 meteorological stations accounted for 28.38%, 50.48%, 8.85%, and 7.38%, respectively, and the frequency above severe drought was the highest. (4) The sensitivity of meteorological factors gradually increased from northwest to southeast, and MI was the most sensitive to the change of precipitation (P), followed by net radiation (Rn), wind speed (u2), mean temperature (Tmean), relative humidity (RH) and maximum temperature (Tmax). MI was the least sensitive to the change of minimum temperature (Tmin). P is the most important meteorological variable that contributes to the increase of MI, followed by u2, Tmean, and Tmin. Rn, Tmax, and RH have the least influence, and the total contribution of the seven meteorological factors is 85.59%. Compared with the reference evapotranspiration, P is the main factor affecting the dry and wet variations in Hexi Corridor.

Keywords

Dry and wet variations
MI
FAO P–M model
Meteorological factors
Quantitative attribution
Hexi Corridor
Subject terms

Climate sciences
Hydrology
the National Natural Science Foundation of China42261003 the Key R&D Plan of Gansu Province21YF5FA094 22YF7GA107 the Discipline Team Construction Project of GAUGAU-XKTD-2022-08 issue-copyright-statement© Springer Nature Limited 2024
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pmcIntroduction

In recent decades, the frequency and intensity of extreme climate events such as drought and flood have been increasing. According to the IPCC report, evaporation from inland lands on a global scale is leading to an increase in atmospheric evaporative demand and drought events. Droughts are likely to become more frequent under the combined effects of global warming and human activities1,2. Studies have shown that the extremely warm and cold events in China have shown a significant increase and decline respectively, and the extreme precipitation events have increased significantly3,4, destroying the regional water budget balance and leading to changes in the dry and wet conditions of the surface5. Compared with the general climate state, extreme climate events have a more serious impact on natural ecosystems and human society6,7, making the law of water surplus and deficit more complex and changeable. Water deficit induces drought, and water surplus leads to flood disasters. Since the 1970s, droughts and floods in China have been characterised by the vulnerability to drought in the north and concurrent droughts and floods in the south, and most of them are multi-seasonal or multi-year droughts8. Precipitation and potential evapotranspiration, as two important components of the atmospheric water budget, are the two main aspects affecting the dry and wet conditions of climate5. Internationally, drought is usually classified into four categories: meteorological drought, hydrological drought, agricultural drought, and socio-economic drought9. Drought is usually assessed quantitatively using a drought index, which varies for different types of drought. In fact, the indicators used for drought monitoring and assessment have been developed into more than 150 indicators10. The Standardised Precipitation Index (SPI) and Standardised Precipitation Evapotranspiration Index (SPEI) are standardised indices that describe meteorological drought. The calculation of standardised indices relies on the calculation of probability distributions under consistency conditions, and the distribution parameters vary when the length of the selected time series is different, which will lead to bias in the calculated index11. At the same time, in the context of climate change, the time series will no longer satisfy the consistency assumption and traditional standardised indices will no longer be applicable. Palmer Drought Severity Index (PDSI) is a meteorological drought index. The fact that many of the parameters involved are obtained through experiments and the calculation process is cumbersome leads to its limited use and non-universal applicability12. Crop Moisture Index (CMI) is often used as an evaluation of agricultural drought, taking into account the state of the vegetation cover and involving soil water status. The index is very intuitive and directly reflects the degree of crop drought, which is suitable for reflecting field-scale drought and unsuitable for long time series and large area drought studies13. The MI selected in this paper, which is a meteorological drought index, reflects the water shortage situation caused by the imbalance between precipitation and evaporation. The MI and FAO P–M model were combined to construct a partial differential quantitative attribution model. Using the constructed partial differential quantitative attribution model, the contribution of each meteorological factor to dry and wet changes is quantitatively distinguished, which is not possible with standardised indices such as SPI and SPEI.

The temporal and spatial variations in regional dry and wet conditions caused by climate change have attracted the attention of scholars from various disciplines and relevant studies have been carried out. By analysing the global drought situation, Dai1 found that drought is mainly caused by climate change. With decreasing precipitation and increasing evaporation, severe and widespread droughts will occur in many land areas in the next 30–90 years. Based on observations and climate modelling assessments, Gudmundsson et al.14 has revealed that anthropogenic climate change increases the risk of drought in southern Europe. Smirnov et al.15 found that climate change plays a major role in predicting the magnitude of extreme drought impacts in the future and is the main cause of increased drought risk in 129 countries. Over the next century, warming will increase the risk and severity of drought in most subtropical and mid-latitude regions of both hemispheres as a result of reduced regional precipitation and widespread warming16. Ayugi et al.17 found that complex interactions of dynamic and thermodynamic factors contribute to the occurrence of extreme drought events on the African continent. The accuracy of meteorological drought simulations can be improved by combining atmospheric circulation indices and meteorological variables, which indicates that climatic factors are closely related to meteorological drought18. Zhu19 found that the warm and humid change of climate in the Hexi Corridor was the main reason for the reduction of sand and dust storms, which promoted the potential reverse process of desertification in the Hexi Corridor during the same period. In the previous studies, most of the relevant studies on dry and wet conditions focused on the spatiotemporal characteristics of dry and wet variations based on drought indicators, qualitative attribution analysis, and possible environmental impacts. However, the quantitative interactions between various climatic factors and dry and wet variations were not clearly revealed. The warming and humidifying changes in the climate on a local or a large scale worldwide reflect the influence of climatic factors. Under the background of changes in multiple climate factors, it is difficult to divide the differential impacts of various climatic factors. This is the starting point of this study.

In the northwest arid region of China, as the trend of precipitation increase weakens, the temperature continues to rise and the evaporation increases, which increases the risk of ecological drought20,21, aggravates the regional water shortage, promotes the development of land desertification, seriously threatens the stability of the terrestrial ecosystem, and disrupts the normal agricultural production22. The pattern of climate change in Hexi Corridor is complex and meteorological disasters occur frequently. Drought is one of the main meteorological disasters in this region23,24. Under the changing environmental conditions, the dry and wet conditions of Hexi Corridor will change, which will have a series of impacts on social and economic development, agricultural production, and ecological environment in the region, and seriously threaten the development of the regional agricultural economy23. Therefore, the Hexi Corridor was selected as the research area, and based on daily meteorological data from 1960 to 2019, the relative moisture index (MI) and FAO Penman–Monteith (FAO P–M) model were combined to construct a partial differential quantitative attribution model for dry and wet variations affected by climate factors in the Hexi Corridor. The effects of climate change on dry and wet variations were quantitatively calculated, and the relative contribution of each climate factor to dry and wet variations in Hexi Corridor was revealed. Exploring the quantitative relationship between the spatial–temporal evolution of regional dry and wet conditions and meteorological factors is of great significance for reducing the impact of natural disasters on agricultural production, rational utilization of water resources, and scientific planning of industrial layout.

The research has three purposes: (1) To analyze the variation trend and mutation characteristics of MI and the meteorological variables in the region and to determine the spatial distribution of MI and the meteorological variables. (2) To construct a partial differential quantitative attribution model for dry and wet variations affected by climate factors. (3) To quantify the impact of climate change on dry and wet variations, and to reveal the relative contribution of each climate factor to dry and wet variations in the Hexi Corridor.

Materials and methods

Study area

The Hexi Corridor is located in the northwest of China, with a latitude coordinate of 37°15′–42°69′ and a longitude coordinate of 92°27′–104°20′. It starts from Wushao Mountain in the east and ends at Yumenguan in the west, bordering the Qilian Mountains in the south and the Beishan Mountain system in the north. The Hexi Corridor is about 1000 km long from east to west, 100–200 km wide from north to south, and covers an area of 2.26 × 105 km2, accounting for about 60% of the total area of Gansu Province. It is an important grain and oil production center in Gansu Province. The climate of Hexi Corridor is a temperate continental dry climate, with annual precipitation below 200 mm and strong temperature variations. Moreover, the wind is strong, with an average wind speed of 3.01 m/s at 10 m above the ground in the Hexi Corridor and a maximum wind speed of 5.60 m/s at the Wushaoling station in the region. Meteorological disasters such as sandstorms (maximum frequency of 21.7 d/a) and droughts (maximum drought frequency of 36.8%) occur frequently in the Hexi Corridor. Except for the only oases on the alluvial plain along the river, most areas are Gobi desert dominated by wind and dry denudation. The oasis area gradually decreases from east to west, and there are many desert areas in the west, accounting for about 46.6% of the total area of the region, with a bare surface, strong evapotranspiration, and extremely fragile ecological environment19,25.

Data source

The daily meteorological data of 21 meteorological stations in the Hexi Corridor and its surrounding areas from 1960 to 2019 are derived from China Meteorological Data Network (http://data.cma.cn), including precipitation, temperature, relative humidity, wind speed, sunshine duration, altitude, latitude, and longitude, etc. Regional characteristics of meteorological data in Hexi Corridor from 1960 to 2019 are shown in Table 1. It is the daily dataset from national ground-based meteorological stations in China (V3.0), with the observation data produced by the National Meteorological Information Center after strict quality control. They are widely used in scientific research26–28. The geographical location and distribution of meteorological stations in Hexi Corridor are shown in Fig. 1.Table 1 Regional characteristics of meteorological data in Hexi Corridor from 1960 to 2019.

Regional characteristics	Tmean (°C)	Tmax (°C)	Tmin (°C)	RH (%)	u10 (m/s)	P (mm)	ET0 (mm)	n (h)	
Average value	6.98	14.93	− 0.02	43.48	3.01	98.27	1186.30	3177.93	
Maximum value	8.27	16.35	1.65	47.67	3.77	157.36	1270.23	3305.68	
Year of maximum value	2016	2013	2016	1964	1970	1979	1974	2013	
Minimum value	5.48	13.30	− 1.48	39.21	2.59	60.44	1088.09	3041.11	
Year of minimum value	1967	1967	1967	2014	2003	1962	1993	1998	
Variation coefficient Cv	0.10	0.05	 − 34.54	0.05	0.11	0.20	0.03	0.02	
Change trend	↑	↑	↑	↓	↓	↑	↑	↑	
M–K statistic Z	6.00	5.21	6.61	 − 0.76	 − 3.76	2.88	0.66	0.49	
Significance level	**	**	**		**	**			
Tmean, Tmax, Tmin, RH, u10, P, ET0, n represent mean temperature, maximum temperature, minimum temperature, relative humidity, wind speed at 10 m, precipitation, reference evapotranspiration, and sunshine duration, respectively. ↑ and ↓ represent upward trend and downward trend. ** represent a significance level of 0.05.

Fig. 1 Geographical location and distribution of meteorological stations in the Hexi Corridor.

Methods

Calculation of relative moisture index (MI)

Relative moisture index (MI) is the difference between precipitation in a certain period and reference evapotranspiration in the same period and then divided by the reference evapotranspiration in the same period. The smaller the value, the more severe the drought. It is used to evaluate and monitor the drought situation of crop growth, and the calculation formula is as follows29,30:1 MI=P-ET0ET0

where P is the precipitation (mm) for a given period; ET0 is the reference evapotranspiration (mm) for the same period. ET0 was calculated using the Penman–Monteith formula31 recommended by the Food and Agriculture Organization of the United Nations (FAO). The FAO P–M equation can be expressed as follows Eqs. (2)–(4):2 ET0=0.408ΔRn-G+γ900T+273u2es-eaΔ+γ1+0.34u2

where ET0 is the daily reference evapotranspiration (mm·d−1); Δ is the slope of saturation vapor pressure curve (kPa·°C−1); Rn is the net solar radiation (MJ·m−2·d−1); G is the soil heat flux (MJ·m−2·d−1), which is ignored on the daily scale and assumed to be zero31; γ is the psychrometric constant (kPa·°C−1); u2 is the wind speed at a height of 2 m (m·s−1); T is the mean daily air temperature (°C); (es − ea) is the saturation vapor pressure deficit (kPa).

The measured wind speed at a height of 10 m is converted to a wind speed at a height of 2 m required by the FAO P–M formula32, and the conversion formula of wind speed at different altitudes is shown in Eq. (3):3 u2=uz4.87log(67.8z-5.42)

where u2 is the wind at a height of 2 m (m·s−1); uz is the wind at the height of z m (m·s−1); z is the height above the ground, and z is 10 m in this paper.

The expression (4) of solar net radiation Rn is as follows:4 Rn=Rns-RnlRns=1-αas+bsnNRa

where Rns is the net shortwave radiation (MJ·m−2·d−1); Rnl is the net longwave radiation (MJ·m−2·d−1); Ra is the extraterrestrial radiation (MJ·m−2·d−1); The albedo α is 0.23; According to Zhu Changhan33, the values of as and bs in Northwest region are 0.281 and 0.441 respectively; n is the actual duration of sunshine (h); N is the daylight hours (h).

The meteorological drought classification method based on relative moisture index was adopted, which is proposed in the National Meteorological Drought Classification34, with the month as the unit. The drought classification and types are shown in Table 2.Table 2 Classification and types of meteorological drought based on relative moisture index.

Meteorological drought classification	1	2	3	4	5	
Meteorological drought type	No drought	Mild drought	Moderate drought	Severe drought	Extreme drought	
Relative moisture index	− 0.40 < MI	− 0.65 < MI ≤ − 0.40	− 0.80 < MI ≤ − 0.65	− 0.95 < MI ≤ − 0.80	MI ≤ − 0.95	

Drought characteristic index

Drought characteristics of drought events were identified by analyzing drought intensity, drought frequency, and drought station ratio. Drought intensity is used to evaluate the severity of drought, and drought intensity can generally be reflected by the value of the relative moisture index. The average annual relative moisture index of each station represents the average drought intensity of the station. The smaller the relative moisture index value, the more severe the drought.5 MIi=1M∑j=1MMIij

where MIi is the average annual drought intensity of i station; i represents different weather stations; j represents different years, and M is the total year number. Drought frequency is the frequency of drought, which refers to the percentage of years or seasons that have drought in the total number of years or seasons35.6 Fi=mM×100%

where i is a meteorological station; m is the number of years in which drought of a certain grade occurs in a station; M is the total year number. The classification criteria of drought frequency are as follows: seldom (0–20%), rarely (20–40%), often (40–60%), frequently (60–80%), and very frequently (80–100%)36. The drought station ratio is used to evaluate the scope and severity of drought, that is, the percentage of drought occurrence stations of each grade in all stations in a certain period.7 Pj=nN×100%

where j is the year; n is the number of stations where drought of a certain grade occurs; N indicates the total number of meteorological stations in the region.

Partial differential quantitative attribution model

Since the FAO P–M model can be expressed as ET0 = f (Rn,u2, Tmean, Tmax, Tmin, RH), MI = f (P, ET0) = f (P, Rn, u2, Tmean, Tmax, Tmin, RH), with P, Rn, u2, Tmean, Tmax, Tmin, and RH being the independent variables. The full differentiation of MI32 is:8 dMI≈∂MI∂PdP+∂MI∂RndRn+∂MI∂u2du2+∂MI∂TmeandTmean+∂MI∂TmaxdTmax+∂MI∂TmindTmin+∂MI∂RHdRH

According to Schaake’s37 definition of the elasticity coefficient, the elasticity coefficient of the relative moisture index to changes in meteorological factors can be expressed as the ratio of the change rate of the relative moisture index to the change rate of the meteorological factor. The expression can be shown as:9 εx=limΔxΔxxx→0ΔMIΔMIMIMIΔxΔxxx=∂MI∂x·xMI

where εx is the elasticity coefficient of meteorological factor x, and ∂ET0/∂x is obtained by partial differentiation37. The elasticity coefficients of each meteorological factor are expressed as follows:10 εP=∂MI∂PPMI,εRn=∂MI∂RnRnMI,εu2=∂MI∂u2u2MI,εTmean=∂MI∂TmeanTmeanMI,εTmax=∂MI∂TmaxTmaxMI,εTmin=∂MI∂TminTminMI,εRH=∂MI∂RHRHMI

Substitute Eq. (10) into Eq. (8) to derive Eq. (11)32:11 dMIMI≈εPdPP+εRndRnRn+εu2du2u2+εTmeandTmeanTmean+εTmaxdTmaxTmax+εTmindTminTmin+εRHdRHRH

MI is affected by variations in multiple meteorological factors, and according to the concept of full differentiation of MI, the amount of variation in MI can be considered as the sum of the variations in MI caused by each meteorological factor32.12 ΔMI=ΔMIP+ΔMIRn+ΔMIu2+ΔMITmean+ΔMITmax+ΔMITmin+ΔMIRH

13 ΔMI=εPMIPΔP+εRnMIRnΔRn+εu2MIu2Δu2+εTmeanMITmeanΔTmean+εTmaxMITmaxΔTmax+εTminMITminΔTmin+εRHMIRHΔRH

The contribution of meteorological factor x to the variation in MI32 is expressed in Eq. (14):14 δMIx=ΔMIxΔMI×100%

where δMIx is the contribution rate of meteorological factor x to the variation in MI (%); ∆MIx is the contribution of meteorological factor x to the variation in MI; ∆MI is the variation in MI.

Trend and mutation analysis

The linear regression method was used to analyze the change trend of the time series of MI and meteorological factors, and the significance level of the change was determined by the Mann–Kendall non-parametric test38,39, and the confidence interval of the statistical change trend was defined. A variety of mutation testing methods were comprehensively applied, including Mann–Kendall, Moving-t test40, and Pettitt Test41, to analyze the mutation characteristics of MI time series. Meanwhile, referring to the mutation characteristics of Hexi Corridor in previous studies42,43, the change points of MI time series in Hexi Corridor during 1960–2019 were determined, and the base period and change period were divided.

Results and analysis

Spatial and temporal distribution of MI

Dry and wet intensity variation

MI in Hexi Corridor showed a significant increase over the years, with a linear change rate of 0.0003/a. M–K statistic Z was 2.341, reaching the significance level of 0.05. The annual mean value of MI from 1960 to 2019 was − 0.907, the minimum value was − 0.943 in 1962a, and the maximum value was − 0.855 in 1979a. The results are shown in Fig. 2a. Mutation tests of M–K, Moving-t test, and Pettitt test showed that MI mutated in 1989a, which was consistent with the conclusion of Tian et al.43 that “in the recent 50 years, there was an obvious trend of dry to wet in the Hexi region, especially after 1990”. According to the results of wavelet analysis and drought index, Gao et al.42 divided the study period into two periods before and after 1990. The annual mean values of MI during 1960–1989a and 1990–1919a were − 0.911 and − 0.903, respectively. Compared with 1960–1989a, the degree of drought decreased during 1990–2019a, showing a wetness change, and the UF value was mostly positive (UF > 0), which verified that MI showed an upward trend and a humidification trend during 1960–2019a, as shown in Fig. 2b,c.Fig. 2 Interannual variation and spatial distribution of MI in the Hexi Corridor from 1960 to 2019.

Based on the annual mean MI of 29 meteorological stations in the Hexi Corridor from 1960 to 2019, Kriging spatial interpolation was carried out. The annual mean MI of the 29 meteorological stations in the Hexi Corridor from 1960 to 2019 was between − 0.96 and − 0.67, while the MI of the whole region in the Hexi Corridor was less than − 0.65, and the dry and wet grade was above moderate drought. The medium drought (− 0.80 < MI ≤ − 0.67) is located in the southeastern part of the Hexi Corridor, accounting for 15.49% of the total area; the severe drought (− 0.95 < MI ≤ − 0.80) is located in the central and western part of the region, accounting for 64.97%; the extreme drought (MI ≤ − 0.95) is located in the western part of the region, accounting for 19.54%. The degree of drought in the Hexi Corridor increased from southeast to northwest, and the area proportion above severe drought was as high as 84.51%, which was distributed in the central and western parts of the Hexi Corridor, as shown in Fig. 2d. The Hexi Corridor showed a humidification trend from 1960 to 2019, with the linear change rate of MI in most regions positive, and the MI at 76.19% of stations showed a significant increase (P < 0.1). The range of humidification change was larger in the southeast and smaller in the west, as shown in Fig. 2e.

The spatial distribution of MI in four seasons in Hexi Corridor is shown in Fig. 3. The annual mean MI in spring ranged from − 0.97 to − 0.81, and the weighted value of the region was − 0.93. The dry and wet grades were extreme drought and severe drought in spring. Extreme drought is distributed in the western part of Hexi Corridor, accounting for 52.68% of the area, and severe drought is distributed in the central and eastern parts of Hexi Corridor. The area above severe drought accounted for 100%. The annual mean MI in summer ranged from − 0.94 to − 0.54, and the weighted value of the region was − 0.83. The dry and wet grades included severe drought, moderate drought, and mild drought in summer. The severe drought was distributed in the western part of the Hexi Corridor, accounting for 69.16% of the total area, while moderate drought and mild drought were distributed in the middle and eastern parts of the Hexi Corridor respectively. The annual mean MI in autumn ranged from − 0.98 to − 0.56, and the weighted value of the region was − 0.89. The dry and wet grades included extreme drought, severe drought, moderate drought, and mild drought in autumn. Extreme drought distributed in the west end of Hexi Corridor, accounting for 41.71% of the total area, severe drought distributed in the middle of the corridor, accounting for 39.68%, and the area above severe drought accounted for 81.39%. Moderate drought and mild drought are distributed in the middle and eastern parts of the Hexi Corridor. The annual mean MI in winter ranges from − 0.99 to − 0.90, and the weighted value of the region is − 0.95. The dry and wet grades include extreme drought and severe drought in winter. Extreme drought is distributed in the west of Hexi Corridor, accounting for 64.63% of the total area, while severe drought is distributed in the central and eastern parts of Hexi Corridor, the total area above severe drought accounting for 100%. The area proportion of each dry and wet grade and the weighted value of MI of the basin are shown in Table 3. Therefore, the order of drought degree in four seasons is winter (− 0.95) > spring (− 0.93) > autumn (− 0.89) > summer (− 0.83). In the Hexi Corridor, there are two dry and wet grades in spring and winter including extreme drought and severe drought, four dry and wet grades in autumn including extreme drought, severe drought, moderate drought, and mild drought, and three dry and wet grades in summer including severe drought, moderate drought and mild drought in summer.Fig. 3 Spatial distribution of annual mean values of MI in the Hexi Corridor in four seasons.

Table 3 Statistics on the area ratio and spatial distribution of dry and wet grades in the four seasons.

Seasons	Dry and wet grades	MI	Area (km2)	Area proportion (%)	Weighted value of the region of MI	Geographical distribution	
Spring	Extreme drought	− 0.97 to  − 0.95	1.07 × 105	47.32	− 0.93	West	
Severe drought	− 0.95 to  − 0.81	1.19 × 105	52.68	Central and eastern part	
Summer	Severe drought	− 0.94 to  − 0.80	1.56 × 105	69.16	− 0.83	West	
Moderate drought	− 0.80 to  − 0.65	5.31 × 104	23.51	Central and eastern part	
Mild drought	− 0.65 to  − 0.54	1.65 × 104	7.33	South	
Autumn	Extreme drought	− 0.98 to  − 0.95	9.42 × 104	41.71	− 0.89	West	
Severe drought	− 0.95 to  − 0.80	8.96 × 104	39.68	Central and eastern part	
Moderate drought	− 0.80 to  − 0.65	3.37 × 104	14.93	South	
Mild drought	− 0.65 to  − 0.56	8.30 × 103	3.68	South end	
Winter	Extreme drought	− 0.99 to  − 0.95	1.46 × 105	64.63	− 0.95	West	
Severe drought	− 0.95 to  − 0.90	7.98 × 104	35.37	Central and eastern part	

Dry and wet station ratio of each grade

In the Hexi Corridor, the total number of extreme droughts that occurred at 21 meteorological stations in 60 years was 354, accounting for 28.38%. In 1965a, extreme droughts occurred at 11 stations, and the degree of drought was the most serious. The total number of severe droughts that occurred from 1960 to 2019 was 626, accounting for 50.48%. Among them, there were the least sites in 2018a (4 stations) that had severe droughts, and 15 stations in 1981a and 2016a respectively. The proportion of moderate drought and mild drought was 8.85% and 7.38%, respectively, as shown in Figs. 4a and 5a.Fig. 4 Annual and seasonal frequency boxplots for dry and wet grade at 21 sites from 1960 to 2019.

Fig. 5 Area proportion of frequency of each dry and wet grade at 21 sites from 1960 to 2019.

The statistical results of the frequency of dry and wet grades at 21 stations of Hexi Corridor during the four seasons from 1960 to 2019 are shown in Figs. 4 and 5 ((a) Year; (b) Spring; (c) Summer; (d) Autumn; (e) Winter). The total number of extreme droughts that occurred in spring was 639, accounting for 51.51%. In 1995, 18 sites had severe drought, and in 2007 and 2016, 2 sites had extreme drought. The total number of severe droughts was 451, accounting for 36.52%. In 2007 and 2016, severe droughts occurred at 16 stations, followed by moderate and mild droughts accounting for 6.83% and 4.04%, respectively. The total number of occurrences of extreme drought in summer was 246, accounting for 19.67%. In 2001, 11 sites had severe drought. The total number of severe droughts was 597, accounting for 48.17%. In 1971 and 1975, severe droughts occurred at 16 stations, followed by moderate droughts and mild droughts accounting for 14.98% and 6.32%, respectively. The total number of extreme droughts in autumn was 491, accounting for 39.76%. In 1972, the number of stations that experienced extreme drought was the highest (16 stations), and the degree of drought was serious. The total number of severe droughts was 407, accounting for 33.02%. In 1990, severe drought occurred at 14 stations, followed by moderate drought and mild drought accounted for 13.99% and 7.37%, respectively. The total number of extreme droughts in winter was 732, accounting for 59.74%. In 1964, 20 sites had severe drought. The total number of severe droughts was 461, accounting for 38.01%. In 1988, severe droughts occurred at 18 stations, followed by moderate droughts accounting for 2.25%. Therefore, the order of extreme drought is winter, spring, autumn, and summer, while the order of severe drought is summer, winter, spring, and autumn. In spring, summer, autumn, and winter, the frequency above severe drought was 88.02%, 67.84%, 72.78%, and 97.75%, respectively. The drought was the most serious in winter, followed by spring and autumn, and the lightest in summer.

Dry and wet frequency distribution at each station

The spatial distribution of dry and wet grades in Hexi Corridor during 1960–2019 is shown in Fig. 6. Mild drought occurred in the northwest and the southeast of Zhangye City and the south of Wuwei City in the Hexi Corridor, with the highest frequency of 89.91%. Moderate drought was distributed in Jinchang City in the eastern part of Hexi Corridor, and the highest frequency was 46.64%. Severe drought occurred mainly in the central and eastern parts of the Hexi Corridor, including Zhangye City and Wuwei City, with a frequency between 60 and 98.31%, which was a frequent or extremely frequent area. Extreme drought occurred frequently or extremely frequently in the west of Hexi Corridor, located in the west of Jiuquan City, with a frequency of 60–93.30%. Therefore, during 1960–2019, extreme drought occurred in Jiuquan City in the west of the Hexi Corridor, severe drought occurred in Zhangye City and Wuwei City in the middle and east of the Hexi Corridor, moderate drought occurred in Jinchang City in the east of the Hexi Corridor, and mild drought occurred in the northwest and southeast of Zhangye City and the south of Wuwei City in the Hexi Corridor.Fig. 6 Spatial distribution of dry and wet grades in Hexi Corridor from 1960 to 2019.

Spatiotemporal variation of meteorological factors

Based on MI = f (P, ET0) = f (P, Rn, u2, Tmean, Tmax, Tmin, RH), the meteorological factors such as P, Rn, u2, Tmean, Tmax, Tmin, RH were chosen to analyze the spatiotemporal variation of meteorological factors from 1960 to 2019, as shown in Figs. 7 and 8. The mean value of P from 1960 to 2019 was 98.27 mm, which showed a significant increase over the years, reaching the significance level of 0.05 (Z = 2.88), and the linear change rate was 4.2 mm/10a. The mean value of Rn was 2929.48 MJ·m−2·d−1, which showed no significant decrease over the years, and the linear rate of change was − 3.3 MJ·m−2·d−1/10a. The annual mean value of u2 was 2.25 m/s, which decreased significantly and reached the significance level of 0.05 (Z = − 3.76), and the linear change rate was − 0.07 mm·s−1/10a. The annual mean values of Tmean, Tmax, Tmin were 6.98 °C, 14.93 °C and − 0.02 °C, respectively, and the annual mean values increased significantly, reaching the significance level of 0.05 (Z = 6.0, 5.21, 6.61), and the linear change rates were 0.30 °C/10a, 0.26 °C/10a and 0.37 °C/10a, respectively. The annual mean value of RH was 43.48%, which showed no significant decrease over the years, and the linear rate of change was − 0.16%/10a. Therefore, the annual mean values of P, Tmean, Tmax, and Tmin from 1960 to 2019 were 98.27 mm, 6.98 °C, 14.93 °C, and − 0.02 °C, respectively, showing a significant increase over the years. The annual mean values of Rn, u2 and RH were 2929.48 MJ·m−2·d−1, 2.25 m/s, 43.48%, and showed a decrease over the years.Fig. 7 Interannual variation of meteorological factors in the Hexi Corridor from 1960 to 2019.

Fig. 8 Spatial distribution of annual mean values of meteorological factors in Hexi Corridor.

The spatial distribution of the annual mean values of meteorological factors from 1960 to 2019 in Hexi Corridor is shown in Fig. 8. Precipitation increased from northwest to southeast, and the annual mean value of precipitation ranged from 35.9 to 314.2 mm, with a weighted value of 98.27 mm in the Hexi corridor. The net radiation gradually increased from north to south. The annual mean net radiation ranged from 2795.5 to 3072.4 MJ·m−2·d−1, and the weighted value in Hexi Corridor was 2929.48 MJ·m−2·d−1. The maximum wind speed at the height of 2 m was 3.71 m/s in the northwest, while the wind speed was smaller than that in the central and eastern parts of Hexi Corridor. The annual mean wind speed ranged from 1.32 to 3.71 m/s, and the weighted value in Hexi Corridor was 2.25 m/s. The spatial distribution of daily mean temperature, daily maximum temperature, and daily minimum temperature was similar, and the high values were located in the central and eastern parts of Jiuquan City, the north of Zhangye City, and the north of Wuwei City. The variation ranges of daily mean temperature, daily maximum temperature, and daily minimum temperature were − 0.52 to 9.84 °C, 6.01 to 18.28 °C, − 8.60 to 3.09 °C, and the weighted values in Hexi Corridor were 6.98 °C, 14.93 °C, and − 0.02 °C, respectively. The relative humidity decreased from southeast to northwest, which was consistent with the distribution of precipitation, and the value was larger in the eastern part of Hexi Corridor. The relative humidity ranged from 30.5 to 58.4%, and the weighted value in Hexi Corridor was 43.48%.

Sensitivity analysis of MI to changes in meteorological factors

The annual mean sensitivity coefficients of MI to changes in the meteorological factors at 21 meteorological stations in Hexi Corridor were used to obtain the spatial distribution of the sensitivity coefficients of S_P, S_Rn, S_u2, S_Tmean, S_RH, S_Tmax, and S_Tmin, as shown in Fig. 9. The sensitivity coefficients of all meteorological factors gradually increased from northwest to southeast in general, with the high values in the east of the Hexi Corridor and the low values in the west. The variation range of sensitivity coefficient S_P was between 0.06 and 2.59, and P played a positive role in promoting MI change. If P increased by 10%, MI increased by 0.6% to 25.9%. The sensitivity coefficient S_Rn ranged from − 2.58 to − 0.06, and Rn had a reverse effect on MI change. If Rn increased by 10%, MI decreased by 0.6% to 25.8%. The sensitivity coefficient S_u2 ranged from 0.01 to 1.06, and u2 had a positive effect on MI change. If u2 increased by 10%, MI increased by 0.1% to 10.6%. The sensitivity coefficient S_Tmean ranged from − 0.13 to − 0.01, and Tmean had a reverse effect on MI change. If the Tmean increased by 10%, MI decreased by 0.1–1.3%. The sensitivity coefficient S_RH varied from 0.12 × 10−3 to 13.0 × 10−3, and RH had a positive effect on MI change. If RH increased by 10%, MI increased by 0.0012% to 0.13%. The sensitivity coefficient S_Tmax ranged from − 2.60 × 10−3 to − 0.14 × 10−3, and Tmax had a reverse effect on MI change. If Tmax increased by 10%, MI decreased by 0.0014% to 0.026%. The sensitivity coefficient S_Tmin ranged from − 9.49 × 10−4 to − 0.03 × 10−4, and Tmin had a reverse effect on MI change. If Tmin increased by 10%, MI decreased by 0.00003% to 0.00949%. Therefore, there are differences in the sensitivity distribution of MI to changes in various meteorological factors in the Hexi Corridor. MI is the most sensitive to changes in P, followed by Rn, u2, Tmean, RH, and Tmax, and MI is the least sensitive to changes in Tmin. P, u2, and RH have positive effects on changes in MI, while Rn, Tmean, Tmax, and Tmin have negative effects.Fig. 9 Spatial distribution of sensitivity coefficients of various meteorological factors.

Quantitative effects of meteorological factors on MI

According to the results of the change point analysis of MI time series in section “Dry and wet intensity variation”, with 1960–1989a as the base period and 1990–2019a as the change period, the contribution rate of meteorological variables to MI variation is shown in Table 4. The annual mean sensitivity coefficients of various meteorological factors at 21 stations in Hexi Corridor from 1960 to 2019 were used to obtain the annual mean value of the basin using Thiessen polygon weighting method. The maximum value of S_P was 0.278, followed by that of S_Rn and S_u2, 0.277 and 0.074, and S_RH and S_Tmin were the smallest. P is the most sensitive meteorological variable affecting MI, followed by Rn and u2. MI increased by 0.007 per year in the change period (1990–2019) compared with the base period (1960–1989). As MI = f (P, Rn, u2, Tmean, Tmax, Tmin, RH), the contribution rates of each meteorological variable of P, Tmean, Rn, Tmin, u2, Tmax, RH to MI variation are 331.80%, − 88.72%, 1.42%, − 30.90%, − 127.62%, − 0.36% and − 0.03%, respectively. P is the most important meteorological variable that contributes to the increase of MI, followed by u2, Tmean, and Tmin. Rn, Tmax, and RH have the least influence, and the total contribution of the 7 meteorological factors is 85.59%.Table 4 Contribution of meteorological factors to MI variation during the change period 1990–2019.

Meteorological factors	Elasticity coefficient	Average annual value	Average annual change	Contribution rate (%)	
P	0.2778	98.27 mm	9.323 mm	331.80	85.59	
Rn	− 0.2770	2929.48 MJ × m−2 × d−1	− 1.194 MJ × m−2 × d−1	1.42	
Tmax	− 0.0005	14.93 °C	0.950 °C	− 0.36	
Tmin	− 0.0001	0.02 °C	1.184 °C	− 30.90	
u2	0.0739	2.25 m/s	− 0.309 m/s	− 127.62	
RH	0.0008	43.48%	− 0.115%	− 0.03	
Tmean	− 0.0481	6.98 °C	1.022 °C	− 88.72	
MI	–	0.91	0.007	–	–	

Discussion

From 1960 to 2019, the MI in the Hexi Corridor increased significantly and showed a humidifying change, which is consistent with the findings of Liu et al.44 “Northwest China showed a trend of wetting from 1961 to 2016”. Gao et al.42 and Qin et al.45 found that the Hexi Corridor presents a humidifying change in the context of global warming, which is consistent with the conclusions of this paper. With the rise of temperature and precipitation in Northwest China, the so-called “warm and wet” trend does appear in the inland river basin in an arid region46,47, which verifies the conclusion of warming and humidifying changes in the Hexi Corridor. This “warm and wet” is an improvement of moisture in an arid region. The degree of drought in the Hexi Corridor shows a decreasing trend, which is consistent with the conclusion of Fu et al.48 that “the degree of drought is decreasing in the Hexi Corridor”. The drought was the most serious in winter, followed by spring and autumn, and the lightest in summer. As the influence of geographical environment and atmospheric circulation, the temporal and spatial distribution of precipitation changes in the Hexi Corridor. The distribution of precipitation in the Hexi Corridor is correlated and opposite to the degree of drought, with precipitation increasing from northwest to southeast and the degree of drought increasing from southeast to northwest. There was a significant increase in precipitation from 1960 to 2019 in the Hexi Corridor, which played a key role in the occurrence of droughts. This is consistent with the findings of Chen et al.49 that “increased precipitation contributes the most to wetting in northern China”. It may be due to the enhanced water circulation in the region50, and the increase of actual evapotranspiration to atmospheric water vapor51, which increases the precipitation conversion rate. Some studies have shown that the precipitation increase in the arid region of Northwest China is caused by the inner cycle formed by the accelerated melting of ice and snow in the surrounding mountains52. MI is the most sensitive to changes in P and P is the most important meteorological variable that contributes to the increase of MI. This is consistent with the conclusion of Chen et al.49 that “the changes in wetting in northern China mainly result from the increase of precipitation”. Li et al.53,54 combined the possibility of external water vapor transport and local circulation and believed that precipitation recirculation and precipitation conversion rate played an important role in arid areas.

The change of warmth and humidity in the Hexi Corridor will not cause changes in the basic climate state and pattern, and the basic characteristics of the future climate in this region will still be a warm, cool, and arid climate environment, and it is unlikely to change into a warm and humid climate within a predictable time45. The positive feedback effect of warming and humidifying change in the Hexi Corridor is an environmental problem that deserves special attention and needs to be systematically, scientifically, and deeply understood and studied.

Conclusions

The change trend and spatial distribution of MI were analysed using multivariate statistical methods and spatial interpolation method. The influence of climatic factors on dry and wet variations in the Hexi Corridor was quantitatively determined using the partial differential quantitative attribution model, which combined the MI formula and FAO P–M model. The main research results are as follows: (1) From 1960 to 2019, MI increased significantly (Z = 2.341), showing a humidifying change, with a large increase in the southeast of the Hexi Corridor and a small increase in the west. The degree of drought in the Hexi Corridor increased from southeast to northwest. The drought was the most serious in winter, followed by spring and autumn, and the lightest in summer. (2) MI is the most sensitive to changes in P, followed by Rn, u2, Tmean, RH, and Tmax, and MI is the least sensitive to changes in Tmin. P, u2, and RH have positive effects on changes in MI, while Rn, Tmean, Tmax, and Tmin have negative effects. (3) P is the most important meteorological variable that contributes to the increase of MI, followed by u2, Tmean, and Tmin. Rn, Tmax, and RH have the least influence, and the total contribution of the 7 meteorological factors is 85.59%.

Acknowledgements

The authors would like to thank all funds and lab facilities. We also gratefully acknowledge the anonymous reviewers for their constructive comments.

Author contributions

Data curation, Y.M., and X.W.; formal analysis, Y.M.; funding acquisition, D.S., and Z.N.; supervision, Y.M., and Z.N.; writing—original draft preparation, Y.M.; writing—review and editing, Y.M., D.S., and X.W. All authors have read and agreed to the published version of the manuscript.

Funding

This research was funded by the National Natural Science Foundation of China (NSFC) (42261003), the Water Conservancy Technical Service Guarantee Centre Proiect of Gansu Water Resources Department (GSAU-JSFW-2024-49), the Key R&D Plan of Gansu Province (21YF5FA094; 22YF7GA107), and the Discipline Team Construction Project of GAU (GAU-XKTD-2022-08).

Data availability

The datasets used during the current study available from the corresponding author on reasonable request.

Competing interests

The authors declare no competing interests.

Publisher's note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
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