Understanding the impacts of climate change and human activities on streamflow: a case study of the Soan River basin, Pakistan

Abstract

Climate change and land use change are the two main factors that can alter the catchment hydrological process. The objective of this study is to evaluate the relative contribution of climate change and land use change to runoff change of the Soan River basin. The Mann-Kendal and the Pettit tests are used to find out the trends and change point in hydroclimatic variables during the period 1983–2012. Two different approaches including the abcd hydrological model and the Budyko framework are then used to quantify the impact of climate change and land use change on streamflow. The results from both methods are consistent and show that annual runoff has significantly decreased with a change point around 1997. The decrease in precipitation and increases in potential evapotranspiration contribute 68% of the detected change while the rest of the detected change is due to land use change. The land use change acquired from Landsat shows that during post-change period, the agriculture has increased in the Soan basin, which is in line with the positive contribution of land use change to runoff decrease. This study concludes that aforementioned methods performed well in quantifying the relative contribution of land use change and climate change to runoff change.

Appendices

Appendix

Mann-Kendall trend test

The MK test statistic S is expressed as

$$ S=\sum_{k=1}^{n-1}\sum_{j=k+1}^n\mathit{\operatorname{sgn}}\left({X}_j-{X}_k\right) $$

(15)

where n represents total number of data values in the time series, X _k represents the sequential datasets, i.e., {X _k , K = 1, 2, 3,  ⋯ , n} and $\operatorname{sgn}\left(\theta \right)=\left\{\begin{array}{l}1\\ {}0\\ {}-1\end{array}\kern0.5em \begin{array}{l} if\theta >0\\ {} if\theta =0\\ {} if\theta <0\end{array}\right.$.

The statistic S is documented to approximately follow normal distribution with the mean and variance as follows:

$$ E(S)=0,\kern0.5em Var(S)=\frac{n\left(n-1\right)\left(2n+5\right)\hbox{-} \sum_{i=1}^n{t}_ii\left(i-1\right)\left(2i+5\right)}{18} $$

(16)

where t represents the total number of ties of extent i, and the test statistic Z can be expressed as $Z=\frac{S-\mathit{\operatorname{sgn}}(s)}{\sqrt{VAR(S)}}\cdot$.

The p value of test statistic Z, ${p}_{\mathrm{value}}=\frac{1}{2}\hbox{-} \frac{1}{2}{\int}_0^{\left|z\right|}{e}^{-{t}^2/2} dt$, indicates the presence of statistically significant trend in the series at predefined significant level α. If the computed p value is less than significant level α, i.e., (p _value < α), the null hypothesis of no trend is rejected

1.1 Pettit change point test

In a series X _i , the Mann-Whitney statistic U _t,N checks the times that an element of the 1st sample exceed than that of 2nd where both samples are separated by xi and can be written as

$$ {U}_{t,N}={U}_{t-1,N}+{\sum}_{j=1}^N\operatorname{sgn}\left({x}_t-{x}_j\right)\kern0.5em t=2,\cdots, N $$

(17)

According to the null hypothesis of Pettit test that the series has no change point, the test statistics and its associated probability can be expressed as

$$ k(t)={\mathrm{max}}_{1\le t\le N}\left|{U}_{t,N}\right|,p\cong 2\exp \left[-6k{(t)}^2/\left({N}^3+{N}^2\right)\right] $$

(18)

A change point exists in the data series if the calculated value of p is smaller than the assigned significance level. The data series can be divided into two sub-series as per change point.