the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
SIMO v1.0: Simplified model of the vertical temperature profile in a small warm monomictic lake
- Department of Geophysics, Faculty of Science, University of Zagreb, Zagreb, 10000, Croatia
- Department of Geophysics, Faculty of Science, University of Zagreb, Zagreb, 10000, Croatia
Abstract. A simple 1-D energy budget model (SIMO) for the prediction of the vertical temperature profiles in small, monomictic lakes forced by a reduced number of input meteorological variables is proposed. The model estimates the net heat flux and thermal diffusion using only routinely measured hourly mean meteorological variables (namely, the air temperature, relative humidity, atmospheric pressure, wind speed, and precipitation), hourly mean ultraviolet B radiation (UVB), and climatological monthly mean cloudiness data. Except for the initial vertical temperature profile, the model does not use any lake-specific variables. The model performance was evaluated against lake temperatures measured continuously during an observational campaign in two lakes belonging to the Plitvice Lakes, Croatia (Lake 1 and Lake 12). Temperatures were measured at 15 and 16 depths ranging from 0.2 to 27 in Lake 1 (maximum depth of 37.4 m) and 0.2 to 43 m in Lake 12 (maximum depth of 46 m). A sensitivity analysis of the simulation length was performed for simulation lengths from 1 to 30 days. The model performed reasonably well and it was able to satisfactorily reproduce the vertical temperature profile at the hourly scale, the deepening of the thermocline with time, and the annual variation in the vertical temperature profile. A yearlong simulation initiated with an approximately constant vertical profile of the lake temperature (≈ 4 °C) was able to reproduce the onset of stratification and convective overturn. However, the thermocline depth was underestimated while the epilimnion temperatures were overestimated. Nevertheless, the values of the model performance measures obtained for a yearlong simulation were comparable with those reported for other more complex models. Thus, the presented model can be used for the assessment of the onset and duration of lake stratification periods when water temperature data are unavailable, which can be useful for various lake studies performed in other scientific fields, such as biology, geochemistry, and sedimentology.
Kristina Šarović and Zvjezdana Klaić
Status: final response (author comments only)
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RC1: 'Comment on gmd-2021-118', Anonymous Referee #1, 08 Sep 2021
General comments
This manuscript describes a new, comparably simple model for the 1D-simulation of the vertical temperature profiles in a lake. The paper is clearly structured and easy to read, and I appreciate the detailed and self-critical analysis of the model results. However, I have some general concerns about the scientific novelty and approach as well as the scientific rigour of the work.
First, the scientific focus and novelty of the paper remains unclear. It includes two different topics that are, from the scientific point of view, largely independent. And for both of these topics, a different approach would have been more appropriate for a thorough scientific investigation.
The first topic deals with estimating the heat fluxes at the lake surface in the absence of direct measurements of shortwave and longwave radiation. Such parameterizations of the surface heat fluxes have been previously described in numerous publications. If there is any novelty in the approach that the authors use here for this purpose, it is not made clear to the reader. The only thing that I haven’t seen in the context of lake modelling is the suggestion to derive the daily dynamics of solar radiation from UV-B measurements. However, this seems to be mainly a workaround for this specific case than a generally applicable approach, as in general, observations of global radiation are much more frequently available than observations of UV-B radiation. Furthermore, the approach used in the study does not allow to check whether the applied heat flux parameterization works well. In fact, the results seem to indicate that it doesn’t, given that simulated lake surface temperatures significantly and consistently overestimate observations even in very short model runs of a few days.
The second topic is the temperature model for the given lakes. Again, it is not clearly pointed out what is new about the modelling approach. The model seems to be mostly taken from the paper of Sun et al. (2007) with the addition of a turbulent term. And also here, the approach of the study doesn’t really allow to assess how well the model works. This would probably be done best by comparing the simulations with those of other models forced with the same surface heat fluxes, which might then allow to assess to what extent the relatively large discrepancies between simulations and observations are caused by the surface heat flux parameterization and by the actual lake model.
Second, the model description and the equations contain several errors that are described in the following detailed comments. I did not check all equations in detail, but some things are clearly wrong. Some of the errors are probably only typos in the text or errors when creating the figures, but others might also be wrong in the model formulation.
For these reasons, I cannot recommend to accept publishing this paper in Geoscientific Model Development in its present form.
Specific comments
Line 15: I don’t think that it is clear for the reader here what is meant with “a sensitivity analysis of the simulation length”
Study area: it would be easier for the reader to have the lake properties in a table rather than in the text.
Figure 3: is there any specific reason for using J/m2/h rather than the standard W/m2 for UV radiation?
Line 149: check the usage of phi, there is capital phi in the text and small phi in the equation. Small phi is also used for latitude and capital phi later for the surface heat flux. Please use consistent and unique symbols.
Equation (2): I don’t know the source of that equation, as Sun et al (2007) don’t give a reference for it, but for high temperatures, the density calculated with this equation seems to be quite far from other standard equations that are usually applied in lake and ocean models (e.g., Chen and Millero or IES-80).
Equation (3): I think there is a factor z missing in the equation.
Line 169: I don’t think it makes sense to neglect turbulent transport even in lakes shallower than 10 m. This is usually one of the main drivers determining the surface mixed layer depth (e.g. Monismith and MacIntyre, 2009, https://doi.org/10.1016/B978-012370626-3.00078-8 )
Chapter 3.1.1: It is not clear from the text how exactly the chosen approach accounts for the effect of cloudiness on surface downward solar radiation.
Equation (12): I think this should be 6.11 not 0.611 if the unit of the vapor pressure is hPa (=mbar). It is correctly implemented in the code, although the wrong unit is given there (Pa instead of hPa).
Line 227: difference in day length between what and what?
Equation (22): the function of light transmission as a function of depth was somehow derived by Wu et al. based on a relationship between Secchi depth and lake depth of a range of Swedish lakes by Hakanson (1995). That means, the information of surface clarity (Secchi depth) as a function of total lake depth for a range of lakes is transferred to a function of lake clarity within a specific lake as a function of depth. In my opinion, this does not make sense. If no Secchi depth measurements or other clarity information is available for the studied lakes, I think it is preferable to use a constant default value for clarity.
Equations (23) and (26): I think the first epsilon is redundant in both these equations. Furthermore, reflection of the longwave radiation at the lake surface of about 3% of longwave radiation is neglected (e.g. Henderson-Sellers, 1986, https://doi.org/10.1029/RG024i003p00625). Randomly, these two things (neglecting 3% removal and adding an epsilon factor of 0.96) more or less cancel each other.
Lines 260 ff: In Crawford and Duchon (1999), f was defined as 1 minus the ratio of observed radiation to clear-sky radiation. This never reaches zero because even at 100% cloudiness, significant radiation remains. Does this have any implications for how the model is applied here?
Chapter 3.1.4: I don’t think this approach is correct. Assume Tprec is equal to the lake surface temperature. Then the precipitation does not change the lake surface temperature. But in the model it does increase the temperature. Tprec should probably be replaced by (Tprec-Ts) in the equation?
Line 320: The implicit Euler method is unconditionally stable, but it can still lead to significant errors if the time step is too large. A time step of one hour seems comparably long for this model, where the forcing data can change quite strongly from hour to hour. Did you check whether the solution would be significantly different with a shorter time step?
Figure 5: There is something wrong here. The theoretical upper limit of the shortwave heat flux is the solar constant of 1368 W/m2, the typical upper limit of observed surface solar radiation is about 1000 W/m2. The July peak in the figure is 20’000 W/m2.
Line 396: Add some quantitative information about the error in the onset of stratification. That is difficult to read from the figures.
Figures 9 and 10: for which period are these measures averaged? This should be mentioned in the caption of the figures. Also, the fact that the temperature bias at the lake surface is consistently positive even in simulations of very short duration (1 day), seems to clearly indicate that there is something wrong with the surface heat flux parameterization (see main comment above).
Line 474: Again, some quantitative information on the error of the simulated onset and termination of stratification as well as the thermocline depth would be useful.
Table 2: There are numerous lake modelling studies reporting quantitative errors compared to observed data. Below, some other studies that could be considered here, but there are many more:
- LakeMIP publications: Goyette et al. (2013), https://doi.org/10.5194/gmd-6-1337-2013 and Perroud et al. (2009), https://doi.org/10.4319/lo.2009.54.5.1574
- Read et al. (2017), https://doi.org/10.1016/j.ecolmodel.2014.07.029
- Gaudard et al. (2019), https://doi.org/10.5194/gmd-12-3955-2019
- Moore et al. (2021), https://www.sciencedirect.com/science/article/pii/S1364815221001444
I understand it would exceed the scope of this manuscript to completely review this literature, but at least the formulation that there are only few studies reporting such information should be reconsidered.
Line 521: I find it surprising that the turbulent term has no effect. This would imply that for the present lakes, vertical mixing is practically exclusively driven by convection, which seems unlikely. Maybe the turbulent term is underestimated and this is the reason why the simulated thermocline position is too shallow as suggested on line 430? What are the vertical turbulent diffusivities resulting from the model?
Line 542: I disagree that the position of the thermocline and its deepening were well captured. The position of the thermocline seems to be 5 to 10 m off for most of the year in Figure 13 (but see request above to provide some quantitative measures for this).
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AC1: 'Reply on RC1', Kristina Šarović, 13 Dec 2021
Please find the answer in the supplemented pdf file.
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RC2: 'Reply on AC1', Anonymous Referee #2, 14 Mar 2022
The authors presented a detailed response to the comments suggesting the study would have been deeply revised. In particular, a comparison with other lake models is to be added, which would certainly add a value to the manuscript and would provide the reader with necessary information on the model performance and usability. The numerous changes described in the response imply the results differ significantly from what was presented in the original version, and the discussion assumed to be focused on the model performance compared to other lake models. After reworked in such a form, the study might provide a significant contribution to GMD and would find an appropriate readership among modelers. One remaining general question on my side is whether the proposed model has sufficient novelty compared to that of Sun et al. (2007). Below are also remarks on the Authors’ responses to the first round of comments:
[11] The shortwave radiation model of Henderson-Sellers appears to be too complex for the case when no data on the light extinction properties of the lakes are available. A one-band exponential Beer Law or the two-band Jerlov’s model would provide more robust alternatives, where the value(s) of the extinction coefficient(s) might be carefully adjusted based on the comparison of the model results against observations. It is an important issue, since shortwave radiation absorption will strongly affect the final modeling results in terms of the vertical stratification as well as surface temperatures.
[12] Longwave radiation balance on the lake surface: note that r=\epsilon only in thermodynamic equilibrium, which is generally not the case for the lake surface. Better use more careful formulations here.
- AC2: 'Reply on RC2', Kristina Šarović, 18 Mar 2022
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RC2: 'Reply on AC1', Anonymous Referee #2, 14 Mar 2022
Kristina Šarović and Zvjezdana Klaić
Model code and software
SIMO v1.0: Simplified model of the vertical temperature profile in a small warm monomictic lake Šarović, Kristina; Klaić, Zvjezdana https://doi.org/10.5281/zenodo.4679796
Kristina Šarović and Zvjezdana Klaić
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