183in the monimolimnion than in the lower part of the mixolim-
nion due to salt gradients. Moreover, the standard deviation
of Kz is higher in the hypolimnion than at the thermocline or
at the chemocline. This standard deviation can reach 3–4
orders of magnitude in weak stratified parts of the water
body, whereas it is closer to 2 orders of magnitude at the
thermocline and at the chemocline.
In May, values of Kz between 30 and 50 m depth are in
average equal to 5 × 10-7 m^2 /s whereas in July and November,
Kz can reach values of 5 × 10−6 m^2 /s. Simultaneously an
increase in the standard deviation is observed indicating that
increase of mean Kz and intermittency are related.
Moreover, trends are observed on the evolution of vertical
diffusivity along year 2006. In fact, stabilization is increased
below 50 m depth and destabilized in the hypolimnion. The
stabilization just above the chemocline comes from the dif-
fusion of the saline interface between mixoliminion and
monimolimnion. The destabilization above 50 m is certainly
caused by a more active turbulence weather in the second
part of year 2006.
Kz in 2007 are in average one order of magnitude higher
in the hypolimnion than in the second part of year 2006 (data
not shown). This is in agreement with the decrease of the
static stability (N^2 ) of the order of one order of magnitude
too.
10.2.7 Consequences of Kz Intermittency
on the Estimate of Solute Transport
The estimate of Kz is very important to predict the vertical
diffusion of solutes and finally the reactions between chemi-
cal compounds in the lake. In previous studies, Kz was evalu-
ated from tracer experiments and only the mean value of Kz
throughout the year was considered (Aeschbach-Hertig et al.
2002 ). But this average value is unable to reproduce the
impact of the real small fluctuations of Kz value that cause
the transport in the water column of Lake Pavin.
Lake physical models usually link Kz fluctuations to wind
forcing fluctuations (mettre ref, par exemple l’article sur le
modèle thermique du lac du Bourget, Hydrobiologia 2014).
This kind of approach is usually effective to simulate Kz
close to the lake surface but lacks precision to simulate Kz in
the deep part of the lake, close to the chemocline.
Therefore, a direct observation of the variability of Kz in
depth is useful and it can be used as an input data in a model
in order to evaluate the influence on tracer concentrations in
the monimolimnion and in the mixolimnion of Lake Pavin.
Therefore, the impact of using Kz from SCAMP measure-
ments on the prediction of solute concentrations was com-
pared with using rough and averaged estimates of Kz, as used
in previous studies.
To achieve this goal, the Aquasim model (Reichert 1994 )
is used. Aquasim model is a one-dimensional vertical numer-
ical model based on the advection–diffusion equation. The
base equation is the following :∂
∂+∂()
∂=∂
∂C
tCw
zKC
zz2
2 (10.3)with C the solute concentration, w the vertical speed and Kz
the vertical turbulent dispersion coefficient.
The AQUASIM configuration adapted to Lake Pavin is
described in Lopez et al. ( 2011 ). Surface processes linked to
daily meteorological conditions are neglected as the study
focuses on in-depth processes. The model simulates O 2 , Fe
particle concentration and NO 3 between two field surveys of
July 2007 and August 2007. In this configuration, O 2 concen-
tration conditions the whole reaction chain. The initial con-
ditions are based on CTD measurements and in situ chemical
analysis (Fe particle concentration, dissolved O 2 concentra-
tion, NO 3 concentration). Validation is done on measured O 2
and NO 3 concentration in August 2007 because no data for
Fe particle concentration were available at the end of simula-
tion period. The Kz variability is investigated by creating five
sets of different Kz values. From the variability of Kz
observed during the July survey where Kz was calculated
from different SCAMP profiles performed at the same loca-
tion in the lake (see Sect. 11.3.2), Kz values are allocated at
random every 10 min using the values available at each depth
in the data set. Therefore, 1 month long time-series of Kz are
generated and used as input for the Aquasim model between
July and August 2007. Three independent random draws of
Kz are then compared with constant values of Kz for the
month: arithmetic and logarithmic average of measured Kz
from SCAMP profiles and constant formulation of Kz from
CTD measurements during the whole duration of the simula-
tion (Bonhomme et al. 2011a, b). In fact, CTD measurements
can give a rough evaluation of Kz by calculating the buoy-
ancy frequency and simply finding a proportional relation-
ship between the inverse of the buyoancy frequency and Kz.
The outputs of the model are evaluated by calculating the
cumulative error for O 2 and NO 3 concentrations at different
depths in August 2007.
Cumulative error is defined as:ECC
m CAugustmodelAugustobserved
Augustobser=−
∑
50 ,, 5356 , 59,,
, vved^(10.4)With C, the concentration of the chemical concentration of
the followed species.
With randomly Kz values calculated from SCAMP mea-
surements, the concentration of O 2 is predicted with a cumu-
lative error of 0.32 whereas the NO 3 concentration is even
better with a cumulative error of 0.048. With rough estimates
of Kz from CTD measurements, the cumulative error
becomes worse, about 10 times higher for both compounds:
it becomes 3.41 for O 2 and 0.43 for NO 3 concentrations.10 Lake Pavin Mixing: New Insights from High Resolution Continuous Measurements