Predicting long-term hydrological change caused by climate shifting in the 21st century in the headwater area of the Yellow River Basin

Abstract

The Qinghai-Tibetan Plateau (QTP) is one of the amplifiers of global climate change. The headwater area of the Yellow River Basin (HYRB) on the QTP is the dominant water source region for the whole Yellow River Basin. However, the sensitive responses of hydrological processes to the intensifying climate change are exerting high uncertainties to the water cycle in the HYRB. The aim of this study was to investigate the potential climate change under three Representative Concentration Pathways (RCP 2.6, 4.5, and 8.5) and their hydrological impacts in this region using the ensemble climate data from eight general circulation models (GCMs) and the Soil and Water Assessment Tool (SWAT). Compared to the baseline (1976–2015), the projected climate indicated a rise of 7.3–7.8% in annual precipitation, 1.3–1.9 °C in maximum air temperature, and 1.2–1.8 °C in minimum air temperature during the near future period (2020–2059), and an increment of 9.0–17.9%, 1.5–4.5 °C, and 1.3–4.5 °C in precipitation, maximum and minimum temperature, respectively, during the far future period (2060–2099). The well-simulated SWAT modeling results suggested that due to a wetter and warmer climate, annual average actual evapotranspiration (AET) would increase obviously in the future (31.9–35.3% during the near future and 33.5–54.3% during the far future), which might cause a slight decrease in soil water. Water yield would decrease by 16.5–20.1% during the near future period, implying a worsening water crisis in the future. Till the end of this century, driven by the increased precipitation, water yield would no longer continue to decrease, with a decline by 15–19.5%. Overall, this study can not only provide scientific understanding of the hydrological responses to the future climate in both semi-arid and alpine areas, but also contribute to the decision support for sustainable development of water resources and protection of eco-environment in the HYRB.

Appendices

Appendix 1: Model performance assessment

To measure the model performance, the Nash–Sutcliffe Efficiency (NSE) (Mandeville et al. 1970), the coefficient of determination (R²), and the percentage bias (PBIAS) were used in this study. These criteria were calculated as follows:

$$ NSE = 1 - \frac{{\mathop \sum \nolimits_{i = 1}^{n} \left( {Q_{m.i} - Q_{s,i} } \right)^{2} }}{{\mathop \sum \nolimits_{i = 1}^{n} \left( {Q_{m.i} - Q_{m,avg} } \right)^{2} }} $$

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$$ R^{2} = \frac{{\left[ {\mathop \sum \nolimits_{i = 1}^{n} \left( {Q_{m.i} - Q_{m,avg} } \right)\left( {Q_{s.i} - Q_{s,avg} } \right)} \right]^{2} }}{{\mathop \sum \nolimits_{i = 1}^{n} \left( {Q_{m.i} - Q_{m,avg} } \right)^{2} \mathop \sum \nolimits_{i = 1}^{n} \left( {Q_{s.i} - Q_{s,avg} } \right)^{2} }} $$

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$$ PBIAS = \frac{{\mathop \sum \nolimits_{i = 1}^{n} \left( {Q_{s.i} - Q_{m,i} } \right)}}{{\mathop \sum \nolimits_{i = 1}^{n} Q_{m.i} }} \times 100\% $$

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where $Q_{m.i}$ and $Q_{s,i}$ are measured and simulated streamflow at each time step $i$; $Q_{m,avg}$ and $Q_{s,avg}$ are the mean measured and simulated streamflow; and $n$ is the number of time steps.

The NSE describes the explained variance for the observed values over time that is accounted for by the model (Green and Griensven 2008). The PBIAS measures the average difference between observation and simulation. The closer NSE and R² are to 1, and PBIAS to 0, the better the SWAT model performs.

Appendix 2: Bilinear interpolation downscaling method

Bilinear interpolation, as an extension of linear interpolation, is used to interpolate functions of two variables (e.g., x and y) on a rectilinear 2D grid in mathematics (https://en.wikipedia.org/wiki/Bilinear_interpolation). The method is described as follows:

Suppose get the value of the unknown function $f$ at point $P = \left( {x, y} \right)$. It’s assumed that we know the value of the four points of the function $f$ at $Q_{11} = \left( {x_{1} , y_{1} } \right)$, $Q_{12} = \left( {x_{1} , y_{2} } \right)$, $Q_{21} = \left( {x_{2} , y_{1} } \right)$, $Q_{22} = \left( {x_{2} , y_{2} } \right)$ (Figure S2).

First, linear interpolation is performed in the $x$-direction:

$$ f(R_{1} ) \approx \frac{{x_{2} - x}}{{x_{2} - x_{1} }}f(Q_{11} ) + \frac{{x - x_{1} }}{{x_{2} - x_{1} }}f(Q_{21} ) $$

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where $R_{1} = \left( {x, y_{1} } \right)$,

$$ f(R_{2} ) \approx \frac{{x_{2} - x}}{{x_{2} - x_{1} }}f(Q_{12} ) + \frac{{x - x_{1} }}{{x_{2} - x_{1} }}f(Q_{22} ) $$

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where $R_{2} = \left( {x, y_{2} } \right)$.

Then, linear interpolation is performed in the $y$-direction:

$$ f\left( P \right) \approx \frac{{y_{2} - y}}{{y_{2} - y_{1} }}f(R_{1} ) + \frac{{y - y_{1} }}{{y_{2} - y_{1} }}f(R_{2} ) $$

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Finally, the desired estimate of $f\left( {x, y} \right)$:

$$ f\left( {x,y} \right) \approx \frac{{f(Q_{11} )}}{{\left( {x_{2} - x_{1} } \right)\left( {y_{2} - y_{1} } \right)}}\left( {x_{2} - x} \right)\left( {y_{2} - y} \right) + \frac{{f(Q_{21} )}}{{\left( {x_{2} - x_{1} } \right)\left( {y_{2} - y_{1} } \right)}}\left( {x - x_{1} } \right)\left( {y_{2} - y} \right) + \frac{{f(Q_{12} )}}{{\left( {x_{2} - x_{1} } \right)\left( {y_{2} - y_{1} } \right)}}\left( {x_{2} - x} \right)\left( {y - y_{1} } \right) + \frac{{f(Q_{22} )}}{{\left( {x_{2} - x_{1} } \right)\left( {y_{2} - y_{1} } \right)}}\left( {x - x_{1} } \right)\left( {y - y_{1} } \right) $$

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