Response to climate change of runoff at different time scales in the Baiyangdian Lake Basin based on the Budyko model

doi:10.13745/j.esf.sf.2024.7.50

Abstract

Abstract:

Climate change significantly impacts the formation of water resources and the transformation of hydrological elements within basins. Accurately quantifying river runoff responses to climate change is crucial for the sustainable development and efficient utilization of water resources. However, research on hydrological climate elasticity under non-stationary conditions remains relatively limited. This study focuses on eight sub-basins in the mountainous region of the Baiyangdian Lake Basin, employing a newly developed non-stationary runoff elasticity coefficient analysis method based on the Budyko model to examine the annual runoff response to climate change. The proposed method is validated in a Chinese basin, broadening its applicability, and is compared with results obtained using the Budyko model-based elasticity method under multi-year stationary conditions. The results reveal the following: on an annual scale, the annual evapotranspiration ratio and water storage change ratio exhibit a strong linear correlation with the annual aridity index; runoff is more sensitive to changes in precipitation at both annual and multi-year time scales; the annual runoff elasticity coefficient is smaller than the coefficient calculated under multi-year stationary conditions, highlighting the significant regulatory role of basin water storage in runoff responses to climate change. Furthermore, the annual elasticity coefficient is strongly correlated with basin area. This study validates the effectiveness of the newly proposed non-stationary runoff elasticity coefficient method based on the Budyko model and extends its applicability from humid regions to semi-humid and semi-arid areas. These findings provide valuable guidance for the sustainable management of water resources in the Baiyangdian Lake Basin and the Xiong’an New Area.

Key words: Budyko framework, climate change, elasticity coefficient, Baiyangdian Lake Basin

CLC Number:

YU Tao, HAN Pengfei, WANG Xusheng, JIANG Xiaowei, ZHANG Zhiyuan, WAN Li. Response to climate change of runoff at different time scales in the Baiyangdian Lake Basin based on the Budyko model[J]. Earth Science Frontiers, 2025, 32(1): 449-458.

Figures/Tables 10

Fig.1 Overview map of the study area

Table 1 Overview of data collection

数据	时间	分辨率	数据来源
降水量、蒸发皿蒸发量	1982—2010	逐日	中国地面气候资料日值数据集(V3.0)
实际蒸散量	2000—2010	逐年;500 m	MOD16A3数据集
实际蒸散量	1982—2010	逐月;1 km	Synthesized ET数据集^[33]
径流量	1982—2010	逐月	海河流域水文年鉴
耕地面积	1986—2010	逐年;30 m	CACD数据集^[34]

Table 2 Basic information of the eight sub-basins

流域编号	水文站	流域面积/km²	年均降水量/mm	年均潜在蒸散量/mm	年均径流深/mm	干旱指数	耕地占比
#1	城头会	1 613	435.5	966.7	35.7	2.22	28.7%
#2	倒马关	2 746	458.4	960.9	52.3	2.10	17.8%
#3	阜平	2 190	526.9	958.2	53.8	1.82	0.6%
#4	王快水库	3 758	528.1	958.7	94.9	1.82	1.3%
#5	西大洋水库	4 414	476.2	955.3	59.6	2.01	15.6%
#6	张坊	4 937	486.4	928.3	67.1	1.91	5.5%
#7	紫荆关	1 769	489.9	937.1	39.4	1.91	12.7%
#8	中唐梅	3 450	468.6	957.6	53.5	2.04	15.1%

Fig.2 Distribution of annual evapotranspiration ratio and aridity index in Budyko space

Fig.3 Distribution of annual storage change ratio and aridity index in Budyko space

Table 3 Interannual elasticity coefficients calculated for eight sub-basins

流域编号	水文站	$ε Q P i$	$ε Q E 0 i$	ε_QP	$ε Q E 0$
#1	城头会	0.04~0.72	0.28~0.96	0.50	0.50
#2	倒马关	1.12~1.60	-0.60~-0.12	1.39	-0.39
#3	阜平	1.09~1.38	-0.38~-0.09	1.21	-0.21
#4	王快水库	1.26~4.33	-3.33~-0.26	2.61	-1.61
#5	西大洋水库	1.30~3.72	-2.72~-0.30	2.16	-1.16
#6	张坊	1.16~2.12	-1.12~-0.16	1.67	-0.67
#7	紫荆关	1.17~2.01	-1.01~-0.17	1.55	-0.55
#8	中唐梅	1.28~4.09	-3.09~-0.28	2.41	-1.41
平均值				1.69	-0.69
变异系数				0.38	-0.94

Table 3 Interannual elasticity coefficients calculated for eight sub-basins

流域编号	水文站	$ε Q P i$	$ε Q E 0 i$	ε_QP	$ε Q E 0$
#1	城头会	0.04~0.72	0.28~0.96	0.50	0.50
#2	倒马关	1.12~1.60	-0.60~-0.12	1.39	-0.39
#3	阜平	1.09~1.38	-0.38~-0.09	1.21	-0.21
#4	王快水库	1.26~4.33	-3.33~-0.26	2.61	-1.61
#5	西大洋水库	1.30~3.72	-2.72~-0.30	2.16	-1.16
#6	张坊	1.16~2.12	-1.12~-0.16	1.67	-0.67
#7	紫荆关	1.17~2.01	-1.01~-0.17	1.55	-0.55
#8	中唐梅	1.28~4.09	-3.09~-0.28	2.41	-1.41
平均值				1.69	-0.69
变异系数				0.38	-0.94

Fig.4 Distribution of multi-year average evapotranspiration ratio and aridity index for eight sub-basins in Budyko space. ω represents the underlying surface parameter in Fu Baopu’s formula[37].

Table 4 Runoff elasticity coefficients for eight sub-basins at a multi-year average scale

流域编号	水文站	参数ω	$ε ¯ Q P$	$ε ¯ Q E 0$
#1	城头会	2.80	2.72	-1.72
#2	倒马关	2.59	2.49	-1.49
#3	阜平	2.92	2.78	-1.78
#4	王快水库	2.34	2.20	-1.20
#5	西大洋水库	2.56	2.45	-1.45
#6	张坊	2.53	2.41	-1.41
#7	紫荆关	3.08	2.96	-1.96
#8	中唐梅	2.62	2.52	-1.52
平均值			2.56	-1.56
变异系数			0.09	-0.14

Table 4 Runoff elasticity coefficients for eight sub-basins at a multi-year average scale

流域编号	水文站	参数ω	$ε ¯ Q P$	$ε ¯ Q E 0$
#1	城头会	2.80	2.72	-1.72
#2	倒马关	2.59	2.49	-1.49
#3	阜平	2.92	2.78	-1.78
#4	王快水库	2.34	2.20	-1.20
#5	西大洋水库	2.56	2.45	-1.45
#6	张坊	2.53	2.41	-1.41
#7	紫荆关	3.08	2.96	-1.96
#8	中唐梅	2.62	2.52	-1.52
平均值			2.56	-1.56
变异系数			0.09	-0.14

Fig.5 Scatter plots of annual runoff elasticity coefficient and watershed area (a, b), aridity index (E0/P) (c, d) and proportion of cultivated land (e, f)

Fig.6 Scatter plots of correlation curve slope and watershed area (a,d,g), aridity index (E0/P) (b,e,h) and proportion of cultivated land (c,f,i)

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