Jökull - 01.01.2013, Page 77

Sensitivity of Icelandic river basins to recent climate variations
years and the sensitivity to precipitation variations by
comparing wet and dry years, in a similar way as was
done by Krasovskaia and Gottschalk (1992). The two-
sided non-parametric Mann–Whitney test was used
to assess the significance of a shift in the median of
these variables, between warm and cold years and be-
tween wet and dry years, except the flood occurrence
rate (FOR) which was examined with a test based
on the Poisson distribution described below. The
Mann–Whitney test has been used in a similar con-
text by Whitfield (2001) to examine temperature, pre-
cipitation and discharge variations in Canada. For the
Mann–Whitney test, pre-whitening was undertaken to
remove serial correlation, as recommended by Yue
and Wang (2002):
Yt = Xt − r1Xt−1 (2)
where r1 is the serial correlation coefficient for a time
lag of 1 year, Xt is the original time series and Yt
the pre-whitened series. After pre-whitening, the se-
ries is expected to be uncorrelated, i.e. a white noise.
The pre-whitened series were only used for the Mann–
Whitney test whereas results regarding the sign and
magnitude of changes between subsets were calcu-
lated from the original series without pre-whitening.
The change in flood occurrence rate between
warm and cold years and then between wet and dry
years was evaluated by comparing their ratio, θ, as-
suming that the flood process can be described by a
Poisson distribution. This comparison was performed
by testing the null hypothesis H0 : θ = 1 against
H1 : θ 6= 1. The R-package rateratio.test (Fay, 2009)
was used. The test is based on conditioning the sum
of two independent Poisson random variables X and
Y as follows:
Y |X + Y = Z ∼ Binomial(Z, p(θ)) (3)
where X ∼Poisson(nxλx), Y ∼Poisson(nyλy), λx
is the average flood occurrence rate per year of X ,
λy is the average flood occurrence rate per year of
Y , nx and ny the number of years in each sample,
θ = λy/λx, and
p(θ) =
nyλy
nyλy + nxλx
=
nyθ
nyθ + nx
(4)
The 100(1-α)% confidence interval for θ is then de-
rived from the 100(1-α)% confidence interval for
p(θ).
RESULTS
The hydrological response to temperature and precip-
itation variations was examined by calculating differ-
ences in the hydrological variables between warm and
cold years and wet and dry years respectively. Ta-
ble 3 presents the temperature, precipitation and dis-
charge statistics for each subset within the 1971–2006
period and Tables 4 and 5 present the derived differ-
ences. The change in the median timing is given in
days, whereas the change in the median of all vari-
ables describing a magnitude is given in % of the me-
dian in cold and dry years, respectively. Only changes
for which the p-value < 0.1 were considered signifi-
cant. Maps showing the results of the statistical tests
are presented in Figures 3–4.
Annual temperature and precipitation differences
Depending on catchment, the median annual temper-
ature in warm years was 1.1–1.4 ◦C warmer than in
cold years. This difference was significant at the
5% level for all catchments. The corresponding me-
dian annual precipitation was not significantly dif-
ferent between warm and cold years, except for the
southern basins VHM-64 (p < 0.1) and VHM-96 (p <
0.05) where warm years were slightly wetter than cold
years, and for the basin VHM-144 (p < 0.05) north
of Hofsjökull glacier, for which warm years brought
slightly less precipitation than cold years. The median
annual precipitation in wet years was 40–58% larger
than in dry years and this difference was significant
at the 5% level for all catchments. The corresponding
median annual temperature was not significantly dif-
ferent between wet and dry years except in the south,
at catchment VHM-96 (p < 0.1), where wet years were
warmer than dry years, and in the northeast, at catch-
ment VHM-26 (p < 0.1), where wet years were colder
than dry years.
Hydrological response to temperature variations
The hydrological response to temperature variations
was examined by testing the significance of differ-
ences in the median or mean of each annual hydrolog-
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