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Journal of Arid Land  2023, Vol. 15 Issue (4): 477-490    DOI: 10.1007/s40333-023-0051-2
Research article     
Responses of vegetation yield to precipitation and reference evapotranspiration in a desert steppe in Inner Mongolia, China
LI Hongfang1,2, WANG Jian1,2,*(), LIU Hu1,2, MIAO Henglu1,2, LIU Jianfeng3
1Yinshanbeilu Grassland Eco-hydrology National Observation and Research Station, China Institute of Water Resources and Hydropower Research, Beijing 100038, China
2Institute of Water Resources for Pastoral Area, Ministry of Water Resources, Hohhot 010020, China
3Inner Mongolia Hydraulic Research Institute, Hohhot 010020, China
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Drought, which restricts the sustainable development of agriculture, ecological health, and social economy, is affected by a variety of factors. It is widely accepted that a single variable cannot fully reflect the characteristics of drought events. Studying precipitation, reference evapotranspiration (ET0), and vegetation yield can derive information to help conserve water resources in grassland ecosystems in arid and semi-arid regions. In this study, the interactions of precipitation, ET0, and vegetation yield in Darhan Muminggan Joint Banner (DMJB), a desert steppe in Inner Mongolia Autonomous Region, China were explored using two-dimensional (2D) and three-dimensional (3D) joint distribution models. Three types of Copula functions were applied to quantitatively analyze the joint distribution probability of different combinations of precipitation, ET0, and vegetation yield. For the precipitation-ET0 dry-wet type, the 2D joint distribution probability with precipitation≤245.69 mm/a or ET0≥959.20 mm/a in DMJB was approximately 0.60, while the joint distribution probability with precipitation≤245.69 mm/a and ET0≥959.20 mm/a was approximately 0.20. Correspondingly, the joint return period that at least one of the two events (precipitation was dry or ET0 was wet) occurred was 2 a, and the co-occurrence return period that both events (precipitation was dry and ET0 was wet) occurred was 5 a. Under this condition, the interval between dry and wet events would be short, the water supply and demand were unbalanced, and the water demand of vegetation would not be met. In addition, when precipitation remained stable and ET0 increased, the 3D joint distribution probability that vegetation yield would decrease due to water shortage in the precipitation-ET0 dry-wet years could reach up to 0.60-0.70. In future work, irrigation activities and water allocation criteria need to be implemented to increase vegetation yield and the safety of water resources in the desert steppe of Inner Mongolia.

Key wordsprecipitation      reference evapotranspiration      vegetation yield      Copula functions      desert steppe      dry and wet events      Inner Mongolia     
Received: 13 June 2022      Published: 30 April 2023
Corresponding Authors: *WANG Jian (E-mail:
Cite this article:

LI Hongfang, WANG Jian, LIU Hu, MIAO Henglu, LIU Jianfeng. Responses of vegetation yield to precipitation and reference evapotranspiration in a desert steppe in Inner Mongolia, China. Journal of Arid Land, 2023, 15(4): 477-490.

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Fig. 1 Overview of land use/land cover in the study area (Darhan Muminggan Joint Banner; a), and photos showing Artemisia frigida (b) and Stipa krylovii (c)
Type Factor Unit Period
Meteorological data Solar radiation kJ/(m2•d) 2002-2020
Minimum temperature °C 2002-2020
Maximum temperature °C 2002-2020
Relative humidity % 2002-2020
Water vapor pressure kPa 2002-2020
Average wind speed m/s 2002-2020
Precipitation mm/a 2002-2020
Sunshine hours h/d 2000-2019
Yield data Annual dry weight of yield per unit area g/(m2•a) 2002-2020
Table 1 Description of the data used in this study
Copula function Function expression Condition
Clayton $H(u,v)=\mathop{\left( \mathop{u}^{-\theta }+\mathop{v}^{-\theta }-1 \right)}^{-\text{ }\frac{1}{\theta }}$ θ≥0
Gumbel-Hougaard $H(u,v)=\exp \left\{ -\mathop{\left[ \mathop{(-\ln u)}^{\theta }+\mathop{(-\ln v)}^{\theta } \right]}^{-\text{ }\frac{1}{\theta }} \right\}$ θ≥1
Frank $H(u,v)=-\frac{1}{\theta }\ln \left[ 1+\frac{\left( \mathop{\text{e}}^{-\theta u}-1 \right)\left( \mathop{\text{e}}^{-\theta v}-1 \right)}{\mathop{\text{e}}^{-\theta }-1} \right]$ θ≠0
Table 2 Description of the two-dimensional (2D) Copula functions
Copula function Function expression Condition
Clayton $H({{u}_{1}},{{u}_{2}},{{u}_{3}})={{\left( {{u}_{1}}^{-\theta }+{{u}_{2}}^{-\theta }+{{u}_{3}}^{-\theta }-2 \right)}^{-\text{ }\frac{1}{\theta }}}$ θ≥0
Gumbel-Hougaard $H({{u}_{1}},{{u}_{2}},{{u}_{3}})=\exp \left\{ -\left[ {{(-\ln {{u}_{1}})}^{\theta }}+{{(-\ln {{u}_{2}})}^{\theta }}+{{(-\ln {{u}_{3}})}^{\theta }} \right] \right.\left. ^{-\text{ }\frac{1}{\theta }} \right\}$ θ≥1
Frank $H({{u}_{1}},{{u}_{2}},{{u}_{3}})=-\frac{1}{\theta }\ln \left[ 1+\frac{\left( {{\text{e}}^{-\theta {{u}_{1}}}}-1 \right)\left( {{\text{e}}^{-\theta {{u}_{2}}}}-1 \right)\left( {{\text{e}}^{-\theta {{u}_{3}}}}-1 \right)}{{{\left( {{\text{e}}^{-\theta }}-1 \right)}^{2}}} \right]$ θ>0
Table 3 Description of the three-dimensional (3D) Copula functions
Situation Frequency
Precipitation-ET0 wet-wet type ${{p}_{1}}=p(X\ge {{x}_{pf}},\text{ }Y\ge {{y}_{pf}})$
Precipitation-ET0 wet-normal type ${{p}_{2}}=p(X\ge {{x}_{pf}},\text{ }{{y}_{pf}}<Y<{{y}_{pf}})$
Precipitation-ET0 wet-dry type ${{p}_{3}}=p(X\ge {{x}_{pf}},\text{ }Y\le {{y}_{pk}})$
Precipitation-ET0 normal-wet type ${{p}_{4}}=p({{x}_{pk}}<X<{{x}_{pf}},\text{ }Y\ge {{y}_{pf}})$
Precipitation-ET0 normal-normal type ${{p}_{5}}=p({{x}_{pk}}<X<{{x}_{pf}},\text{ }{{y}_{pk}}<Y<{{y}_{pf}})$
Precipitation-ET0 normal-dry type ${{p}_{6}}=p({{x}_{pk}}<X<{{x}_{pf}},\text{ }Y\le {{y}_{pk}})$
Precipitation-ET0 dry-wet type ${{p}_{7}}=p(X\le {{x}_{pk}},\text{ }Y\ge {{y}_{pf}})$
Precipitation-ET0 dry-normal type ${{p}_{8}}=p(X\le {{x}_{pk}},\text{ }{{y}_{pk}}<Y\le {{y}_{pf}})$
Precipitation-ET0 dry-dry type ${{p}_{9}}=p(X\le {{x}_{pk}},\text{ }Y\le {{y}_{pk}})$
Table 4 Division of occurrences of wet, normal, and dry situations for precipitation-ET0
Fig. 2 Relationships between precipitation and reference evapotranspiration (ET0; a), precipitation and yield (vegetation yield; b), and ET0 and yield (c) from 2002 to 2020
Characteristic variable Marginal distribution function Parameter K-S test
Shape Scale Statistic P
Precipitation WEI 3.45 304.7600 0.20 0.38
GAMMA 13.18 0.0500 0.16 0.68
EXP - 0.0036 0.45 0.04×10-2
ET0 WEI 19.99 967.4000 0.13 0.85
GAMMA 288.14 0.3100 0.11 0.95
EXP - 0.0011 0.59 8.59×10-7
Yield WEI 1.92 83.0500 0.19 0.45
GAMMA 4.11 0.0600 0.17 0.55
EXP - 0.0100 0.36 0.01
Table 5 Parameters of the univariate marginal distributions
Wet (frequency of 37.50%) Dry (frequency of 62.50%)
Precipitation (mm/a) ET0 (mm/a) Precipitation (mm/a) ET0 (mm/a)
Division value 293.38 959.20 245.69 923.84
Table 6 Division values for dividing precipitation and ET0 into wet and dry
Relationship of variables Copula function θ AIC RMSE
Precipitation-ET0 Frank -2.71 -82.85 0.11
Precipitation-yield Frank 4.13 -62.95 0.18
Clayton 1.03 -90.30 0.09
Gumbel-Hougaard 1.84 -97.22 0.07
ET0-yield Frank -1.11 -115.79 0.05
Precipitation-ET0-yield Frank 0.09 -75.53 0.13
Clayton 0.24 -72.85 0.14
Gumbel-Hougaard 1.24 -69.86 0.15
Table 7 Parameter values and goodness-of-fit tests of the Copula functions
Fig. 3 Empirical frequency and theoretical frequency of joint distributions of precipitation-ET0-yield (a), precipitation-ET0 (b), precipitation-yield (c), and ET0-yield (d)
Fig. 4 Two dimensional (2D) joint distribution contours of precipitation-ET0 (a), precipitation-yield (b), and ET0-yield (c) in DMJB
Fig. 5 2D joint distribution probability contours of precipitation-ET0 with at least one of the two events (precipitation was dry or ET0 was wet) occurred (a) and with both events (precipitation was dry and ET0 was wet) occurred (b)
Fig. 6 Three dimensional (3D) joint distribution probability of precipitation, ET0, and yield in DMJB
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