Impact of Climatic and Land Use Changes on River Flows in the Southern Alps

Abstract

River flow time series are far from being stationary and always experienced changes in the past, also dramatic in long time horizons. In recent years it seems that both climatic and anthropogenic factors are accelerating the variability of hydrological processes. It is not clear, however, whether climatic or anthropic factors represent the major forcing to the hydrological cycle. Long-term statistics, lasting over 150 years, of annual runoff for the five major Italian rivers in the Central Alps are presented and compared with precipitation, temperature and land use changes. A homogeneous decreasing trend of annual runoff is observed, and the significance of such a trend at the local and regional scale is tested with Mann-Kendall, Sen-Theil and Sen-Adichie statistical tests. It is shown that for some rivers, the increased agricultural water demand and land use changes are a likely major source of non-stationarity, possibly more relevant than meteorological ones. A natural feedback which is being observed also at the global scale is discussed on the basis of land use in the Adige river basin by comparing cadastral maps of the mid-nineteenth century with recent aerial photographs in four sample areas. Results are consistent with the reduced speed of deforestation observed at the global scale and the natural afforestation observed in Europe occurring over the last decades. This process can play a major role in regulating the hydrological cycle and mitigating flood and drought extremes, but also enhancing evapotranspiration losses and thus reducing runoff volumes.

Appendices

Appendices

1.1 Appendix A: Estimation of the Regression Line

According to Theil-Sen estimator (Theil 1950a, b, c; Sen 1968; Hollander et al. 2014), trend slope can be computed as

$$ \widehat{\beta}= median\left({S}_{ij},1\le i<j\le n\right), $$

(A.1)

where S _ij denote the N = n(n-1) individual slopes between values Y _i and Y _j of the series, corresponding to time positions x _i and x _j :

$$ {S}_{ij}=\frac{Y_j-{Y}_i}{x_j-{x}_i}. $$

(A.2)

To calculate (A.1) the sample slopes S _ij are ranked in ascending order S ⁽¹⁾ ≤ … ≤ S ^(N); then

$$ \widehat{\beta}={S}^{\left(k+1\right)},\kern1em N\ \mathrm{odd}\kern1em \left(N=2k+1\right) $$

(A.3)

$$ \widehat{\beta}=\frac{S^{(k)}+{S}^{\left(k+1\right)}}{2},\kern1em N\ \mathrm{even}\kern1em \left(N=2k\right). $$

(A.4)

Accordingly, the intercept of the regression line can be estimated as (Hollander et al. 2014)

$$ \widehat{\alpha}= median\;\left({A}_1,\dots, {A}_n\right),\kern1em {A}_i={Y}_i-\widehat{\beta}{x}_i. $$

(A.5)

In this way, if A ⁽¹⁾ ≤ … ≤ A ⁽ⁿ⁾ denote the ordered A _i values,

$$ \widehat{\alpha}={A}^{\left(k+1\right)},\kern1em n\ \mathrm{odd}\kern1em \left(n=2k+1\right) $$

(A.6)

$$ \widehat{\alpha}=\frac{A^{(k)}+{A}^{\left(k+1\right)}}{2},\kern1em n\ \mathrm{even}\kern1em \left(n=2k\right). $$

(A.7)

1.2 Appendix B: Confidence Interval for the Trend Slope

A symmetric two-sided confidence interval for the trend slope can be obtained in terms of the upper (α/2)th percentile k _α/2 of the null distribution of the Kendall statistic (Hollander et al. 2014):

$$ C={\displaystyle \sum_{i=1}^{n-1}{\displaystyle \sum_{j=1+1}^n sign}}\left({D}_j-{D}_i\right),\kern1em {D}_s={Y}_s-\widehat{\beta}{x}_s. $$

(B.1)

Setting C_α = k _α/2–2 and

$$ M=\frac{N-{C}_{\alpha }}{2},\kern1em Q=\frac{N+{C}_{\alpha }}{2}=M+{C}_{\alpha}\kern1em \mathrm{with}\kern0.5em N=\frac{n\left(n-1\right)}{2} $$

(B.2)

the (1–α) confidence interval (β _L , β _U ) is given by

$$ {\beta}_L={S}^{(M)},\kern1em {\beta}_U={S}^{\left(Q+1\right)} $$

(B.3)

according to the notation of Appendix A.

For large n, the following approximation can be used:

$$ {C}_{\alpha}\approx {z}_{\alpha /2}{\left[\frac{n\left(n-1\right)\left(2n+5\right)}{18}\right]}^{1/2}, $$

(B.4)

where z _α/2 denotes the upper (α/2)th percentile of the standard normal distribution. In general, Eq. (B.4) provides a noninteger value; in this case the integer part of the right-hand side can be used.

1.3 Appendix C: Test for the Parallelism of Several Regression Lines

The null hypothesis H ₀ is that k regression lines have a common, but unspecified slope β:

$$ {H}_0:\kern1em \left[{\beta}_1=\dots ={\beta}_k=\beta, \kern1em \mathrm{with}\ \beta\ \mathrm{unspecified}\right]. $$

(C.1)

The first step is to obtain an estimate of the common slope β under the null hypothesis (C.1); to this purpose, the following pooled least squares estimator is used:

$$ \overline{\beta}=\frac{{\displaystyle \sum_{i=1}^k{\displaystyle \sum_{j=1}^{n_i}\left({x}_{ij}-{\overline{x}}_i\right)}}{Y}_{ij}}{{\displaystyle \sum_{i=1}^k{\displaystyle \sum_{j=1}^{n_i}{\left({x}_{ij}-{\overline{x}}_i\right)}^2}}},\kern1em {\overline{x}}_i=\frac{1}{n_i}{\displaystyle \sum_{j=1}^{n_i}{x}_{ij}}, $$

(C.2)

where Y _ij is the value of the i-th response variable Y _i corresponding to the value x _ij and the ith independent variable x _i (for i = 1,…, k).

Then for each of the k regression lines, the aligned observations can be computed as

$$ {Y}_{ij}^{*}={Y}_{ij}-\overline{\beta}{x}_{ij}\kern1em i=1,\dots, k;\kern1em j=1,\dots, {n}_i, $$

(C.3)

whose rank in the ith regression sample is denoted by r ^* _ij .

Setting

$$ {T}_i^{*}=\frac{{\displaystyle \sum_{j=1}^{n_i}\left({x}_{ij}-{\overline{x}}_i\right)}{r}_{ij}^{*}}{n_i+1};\kern1em i=1,\dots, k $$

(C.4)

and

$$ {C}_i^2={\displaystyle \sum_{j=1}^{n_i}{\left({x}_{ij}-{\overline{x}}_i\right)}^2};\kern1em i=1,\dots, k, $$

(C.5)

the Sen-Adichie statistic V is given by

$$ V=12{{\displaystyle \sum_{i=1}^k\left[\frac{T_i^{*}}{C_i}\right]}}^2. $$

(C.6)

Under the null hypothesis (C.1), V is asymptotically distributed as a chi-square with k–1 Degrees of freedom (Sen 1969). This implies that hypothesis (C.1) versus the alternative

$$ {H}_1:\kern1em \left[{\beta}_1,\dots, {\beta}_k\kern0.75em not\ all\ equal\right] $$

(C.7)

has to be rejected at the level of significance α if

$$ V\ge {\chi}_{k-1,\kern0.1em \alpha}^2 $$

(C.8)

where χ² _k-1,α is the upper αth percentile of a chi-square distribution with k–1 degrees of freedom (Adichie 1976, 1984; Hollander et al. 2014).