Useful Hints
The forthcoming text
presents a couple of hints that should help users to avoid the application of
FLake beyond the limits of applicability of the model. Since FLake is a
onedimensional twolayer model, caution should be exercised in "extreme" cases,
e.g. when FLake is applied to very shallow or very deep lakes. Some caution is
also required when interpreting the model results.
(i) Lake depth. In case a
basinmean temperature structure is a major concern, experience suggests that
the best results (first of all, with respect to the lake surface temperature and
to the ice cover) are obtained when a mean depth of a lake/reservoir in question
is used, not its maximum depth or a depth at a particular location. This is
actually consistent with a singlecolumn nature of the
model.
(ii) Bottom sediment module. Thermal
interaction between the water column and the bottom sediments is an issue for
shallow lakes only. A seasonal cycle in shallow lakes may be noticeably affected
by the accumulation of heat in the bottom sediments during spring and summer and
the release of heat from the sediments during autumn and, in particular, winter.
Apart from shallow lakes, the bottom heat flux can be set to zero. To do so,
just set a logical switch lflk_botsed_use to .FALSE.
in MODULE flake_configure (see the Synopsis of FLake
Routines). Experience suggests that for lakes deeper than about 5 m the heat
flux through the bottom can safely be neglected. In case the interaction between
the water column and the bottom sediments is to be accounted for, prior
empirical information is required to estimate the depth of the thermally active
layer of bottom sediments, FLake variable depth_bs_lk,
and the climatologicalmean temperature at that depth,
T_bs_lk. Unfortunately, such information is rarely available. As a rule
of the thumb, an estimate in the range from about 4 m to about 10 m may be used
for depth_bs_lk, and T_bs_lk
may be set to a longterm (annual, decadal) mean of the water temperature near
the lake bottom.
(iii) Modelling deep lakes. Strictly
speaking, FLake is not suitable for deep lakes, where a twolayer representation
of the temperaturedepth curve with the lake thermocline extending from the
outer edge of the upper mixed layer down to the lake bottom becomes
inapplicable. For deep lakes, it is suggested to run FLake with a "false
bottom". That is, an artificial lake bottom is set at a depth of about 50
m (perhaps 60 m), and the bottomsediment module is switched off. The reasoning
behind this trick is pretty simple. The deep abyssal zone of a temperate deep
lake is usually filled with the water at the temperature close the temperature
of maximum density, FLake variable tpl_T_r, and
seasonal variations of abyssal temperature are usually small. Setting bottom
heat flux to zero and using tpl_T_r as the initial
condition for the water temperature at the bottom, one can expect FLake to
reproduce this behaviour. Notice, however, that equatorial lakes may have their
abyssal temperature well above tpl_T_r and they may
never mix down to the bottom. In such a case, it is better to initiate FLake
with the "climatological mean" temperature profile. Such profile can be obtained
with FLake by computing a perpetual year solution.
(iv) Optical
characteristics of lake water. Using the
exponential approximation of the decay law for the flux of solar radiation, the
optical characteristics of the lake water are given by the number
of wavelength bands, the fractions
of the total radiation flux for different wavelength
bands, and the attenuation coefficients
γ
for different bands. The optical characteristics are lakespecific and
should be estimated in every particular case. If
empirical data are lacking, default values of the optical characteristics
offered by FLake can be used (see the FLake source code for details). The
simplest option is the oneband approximation with
γ=3
m^{1}
that leads to the absorption of 95% of the incoming solar radiation within the
uppermost 1 m of the lake water. For the lake ice, the recommended choice is the
"opaque ice" oneband approximation with a very large value of
γ=10^{7}
m^{1}
leading to the absorption of solar radiation at the ice surface.
(v) Snow over lake ice. Although
provision is made to model the evolution of snow cover above the lake ice, the
snow module of FLake has not been sufficiently tested so far. Any contribution
along this line is very welcome! A recommended choice at the moment is to
account for the effect of snow implicitly (parametrically) through the
dependence of the ice surface albedo with respect to solar radiation on the
surface temperature. To implement this choice, one only has to set the rate of
snow accumulation to zero (see the Synopsis of FLake Routines for details). Make
sure to specify the ice surface albedo in a rational way as e.g. in SUBROUTINE
flake_interface.
(vi) FLake initialisation. The
initialisation of FLake is straightforward if the integration is started when
the lake considered is mixed down to the bottom and the ice is absent. Then, the
model is initialised as follows (see SUBROUTINE
flake_interface, variables
h_snow_in, h_ice_in, T_snow_in, T_ice_in, C_T_in, T_mnw_in,
T_wML_in, T_bot_in, T_B1_in, h_ML_in and
H_B1_in). The snow
thickness and the ice thickness are set to zero, the surface temperatures of
snow and of ice are (formally) set to the freshwater freezing point, the shape factor with respect to the temperature profile in the thermocline is (formally) set to its minimum value of 0.5, and the mean temperature of the water column, the mixedlayer
temperature and the bottom temperature are all set equal to the observed water
temperature. If the bottom sediment module is switched
off, the choice of initial values of the thickness of the upper layer of bottom
sediments penetrated by thermal wave and of the temperature at that depth is
irrelevant. In case the bottom sediment module is
switched on, the observed values of the above two variables should be used. If
no observational data are available, the thickness of the upper layer of bottom
sediments is set to depth_bs_lk and
the temperature at that depth is set to
T_bs_lk, see (ii) above.
In the event that the lake considered is initially stratified, some caution is
required when setting FLake variables that specify the water temperature
profile. That is, T_mnw, T_wML, T_bot, h_ML and
C_T cannot be set completely independently as they are
functionally related through the selfsimilar parameterisaton of the evolving
temperature profile (see Eq. (23) in Mironov 2008). It is recommended to set the
mean temperature of the water column, T_mnw, as close
to its observed value as possible (this is important as T_mnw
represents the heat content of a lake) and to adjust the other variables as
needed so that Eq. (23) is satisfied. In the event of FLake initialisation
during the period of ice cover, the initial values of ice thickness an of ice
surface temperature should be set according to the observation. If the snow above the lake ice is not considered explicitly (a recommended choice),
h_snow is set equal to zero and
T_snow is (formally) set equal to T_ice.
(vii) Perpetual year solution. A perpetual year solution represents the annual cycle of temperature and mixing in a given lake that corresponds to a given annual cycle of input meteorological quantities (temperature, humidity and wind speed in the surface air layer, downward radiation fluxes) that are used to force the lake model. Starting with arbitrary initial conditions, the yearlong simulation is repeated, using one and the same annual cycle of forcing. The initial conditions for the next yearlong run are specified using the values of the lakemodel prognostic variables at the end of the previous yearlong run. After a few model years, a periodic "perpetual year" solution is obtained. That is, running the model for one more year will not change the annual cycle of the lakemodel variables. To obtain a perpetual year solution, FLake usually requires less than ten iterations (yearlong runs) if a "reasonable" initial state is used that can be set on the basis of common sense. A perpetual year solution obtained with FLake is useful in many respects. For example, it may give an idea of the state of the lake in question if no data from measurements in the lake are available (but the atmospheric forcing can be specified in a rational way).
