Erratum to: Theor Appl Climatol

DOI 10.1007/s00704-015-1546-3

The original version of this article unfortunately contained mistakes. Four of the Appendix equations were incorrect. The corrected equations are given below.

Old

$$ {d}_t{\overrightarrow{y}}_j^s+A{\overrightarrow{y}}^s(t)={\displaystyle \sum_{j=1}^P{\overrightarrow{N}}_j(t)} $$
(A1)

New

$$ {d}_t{\overrightarrow{y}}^s(t)-A{\overrightarrow{y}}^s(t)=\sum_{j=1}^p{\overrightarrow{N}}_j(t) $$
(A1)

Old

$$ {\overrightarrow{y}}^s\left(t+\varDelta t\right)={\overrightarrow{y}}^s(t)+G\left(t+\varDelta t\right){\overrightarrow{y}}^s(t)+G\left(t+\varDelta t\right){\displaystyle {\int}_t^{t+\varDelta t}{G}^{-1}\left(\tau \right)}{\displaystyle \sum_j{N}_j\left(\tau \right)}d\tau $$
(A9)

New

$$ {\overrightarrow{y}}^s\left(t+\varDelta t\right)=G\left(\varDelta t\right){\overrightarrow{y}}^s(t)+G\left(t+\varDelta t\right){\int}_t^{t+\varDelta t}{G}^{-1}\left(\tau \right)\sum_{j=1}^p{\overrightarrow{N}}_j\left(\tau \right)d\tau $$
(A9)

Old

$$ {N}_j(t)={\displaystyle \sum_{d=1}^n{\overrightarrow{\psi}}_{jd}{\pi}_d{R}_d(t)} $$
(A12)

New

$$ {\overrightarrow{N}}_j(t)={\displaystyle \sum_{d=1}^n{\overrightarrow{\psi}}_{jd}{\pi}_d{R}_d(t)} $$
(A12)

Old

$$ {\overrightarrow{y}}^s\left(t+\varDelta t\right)={\overrightarrow{y}}^s(t)+G\left(t+\varDelta t\right){\overrightarrow{y}}^s(t)+G\left(t+\varDelta t\right){\displaystyle {\int}_t^{t+\varDelta t}{G}^{-1}}\left(\tau \right)\left({\displaystyle \sum_{j=1}^p{\displaystyle \sum_{d=1}^n{\overrightarrow{\psi}}_{jd}{\pi}_d{R}_d(t)d\tau }}\right) $$
(A.13)

New

$$ {\overrightarrow{y}}^s\left(t+\varDelta t\right)=G\left(\varDelta t\right){\overrightarrow{y}}^s(t)+G\left(t+\varDelta t\right){\displaystyle {\int}_t^{t+\varDelta t}{G}^{-1}}\left(\tau \right)\left({\displaystyle \sum_{j=1}^p{\displaystyle \sum_{d=1}^n{\overrightarrow{\psi}}_{jd}{\pi}_d{R}_d(t)d\tau }}\right) $$
(A.13)