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Biogeosciences, 13, 2511-2535, 2016 
ing S st rat(0 to Eq. (2), and subsequently the daily MLD of 
the region is defined as the median of these 16 daily values. 
The annual MLD for each region was then determined as the 
median of this daily time series. Finally, the annual maxi 
mum MLD among all four regions is used to determine the 
reference depth D re f, which is defined as the bottom depth of 
the layer directly below this maximum MLD. 
The values for these O2 -related quantities were calculated 
for individual years relative to D re f and temporally integrated 
over the period from 1 April to 30 September (hereafter 
“summer”). Consequently, the average values over the entire 
period 2000-2012 are calculated and presented in Table 1, 
additionally including the average O2 concentrations at the 
beginning and end of the summer period as well as the aver 
age duration of stratification. 
2.4.2 Development of a spatially resolved index for 
North Sea O2 deficiency 
In order to obtain a North Sea wide indicator for O2 defi 
ciency under stratified conditions, it is necessary to extend 
the regionally confined characteristic described in the previ 
ous section. For this purpose, we extract the key factors af 
fecting O2 from this regional information and combine them 
into a single index - the oxygen deficiency index (ODI). The 
ODI aims to represent the main spatial and temporal pat 
terns of O2 deficiency in the North Sea under stratified con 
ditions, while being as simple as possible and incorporating 
only a very limited number of parameters. 
Stratification period, organic matter export and sub- 
thermocline volume are considered as the key parameters 
controlling the bottom O2 dynamics. Surface primary pro 
duction can be used as a proxy for organic matter export as 
suming that most of the exported organic matter is produced 
locally. Bottom depth can be used as an indicator for the sub- 
MLD volume assuming only minor fluctuations of the MLD 
during the summer stratified period. In addition, the bottom 
depth directly influences the amount of organic matter reach 
ing the bottom layer relative to the amount being produced 
near the surface, due to the exposure of sinking matter to 
pelagic remineralisation. Thus, the following key factors are 
used for the calculation of this index: (longest continuous) 
stratification period (i stra t; in days), summer surface primary 
production (PPmid; in g Cm -2 ; 1 April to 30 September), and 
bottom depth (A, 0 t; in m). 
First, individual dimensionless indices are calculated for 
each of these quantities. The individual indices range be 
tween 0 and 1, indicating conditions counteracting and sup 
porting O2 deficiency, respectively. The calculation of the 
stratification and production indices, 7 strat and 7 pp , is based 
on the work by Druon et al. (2004) and reads as 
Qi( x > y) — Ô/,min\\ 
Qi,max Qi,min ) ) 
with Qi = f strat , Q 2 = 7 pp . (3) 
iQi ( x ’ y) 
— min M, max K 
/q / ( v. y) represents the index corresponding to the actual 
value of the quantity Qi(x,y) with its defined upper and 
lower thresholds, g/, max and g/, min . For f strat , g/, max and 
Qi min are set to 50 and 150 days, respectively. Stratification 
periods of less than 50 days are considered to be too short to 
facilitate the evolution of O2 deficiency, while periods longer 
than 150 days are considered seasonally well-stratified. The 
lower threshold for PP m id was set to 120gCm -2 as PP m id 
does not reach lower values in most parts of the North Sea. 
The upper threshold was set to 200 g C m -2 as such high val 
ues and even higher are simulated in the southeastern North 
Sea. 
For the depth index, 7d, a different definition was chosen 
as lowest O2 concentrations occur in areas of intermediate 
depth, where seasonal stratification can develop and the O2 
inventory is limited due to a small volume below the thermo- 
cline. Therefore, we defined Id as follows: 
7d(v,v) 
maX (°’ ) Dbot ’ y) < ö peak 
1 - min ( 1, gb ° t(x '^~ gpeak ) otherwise 
\ •L'max ¿-»peak J 
Dbot represents the actual bottom depth at location (x, y). 
D p eak — 40 m is the bottom depth we found to be most 
favourable for O2 deficiency in the North Sea. The lower 
threshold /) nlm = 25 m corresponds to the maximum MLD 
we found for the shallower southern North Sea. The up 
per threshold 7) max = 90 m was chosen to exclude the areas 
where the initial O2 inventory is sufficient to prevent O2 de 
ficiency due to the large volume below the thermocline. 
Finally, the ODI combines the three individual indices ac 
cording to the following equation: 
2 
ODI(x, y) = 7 d (x, y) • w Qi lQi( x ,y), 
i — 1 
with wq 1 — 1/4, wq 2 — 3/4. 
(5) 
Here, Iq î and wq î represent the index for a quantity and the 
related weight, respectively. The values for f stra t are referred 
to by Q\ and those for PP m id by Q 2 - The equation for ODI 
implies that it is zero in areas where Id — 0. The stronger 
weighting of PP m id implies that variations in the ODI be 
tween different years are more strongly affected by variations 
in summer surface productivity than by the duration of strat 
ification. 
The ODI ranges between 0 (low risk of O2 deficiency) and 
1 (high risk) and is calculated for each water column (x, y ) 
within the model domain. By this we obtain a spatially re 
solved indicator for O2 deficiency in the North Sea, which 
helps régionalisé the North Sea in terms of O2 conditions. 
2.5 Quantification of driving processes: spatial and 
temporal variability, and data interpretation 
In order to quantify the processes driving the O2 dynamics in 
different regions, we calculated O2 mass balances for three