A Simple Theoretical Model for Lags and Asymmetries of Surface Temperature

Round 1

Reviewer 1 Report

The concept of the manuscript is really interest due to their target, simplification. From the regression until chaos theory, most of theoretical model have inevitable complexities to imitate natural phenomenons including nonlinearity, shock, and delayed response. However, the manuscript focused on the simplification of climate phenomenons and it would be a good alternative in the perspective of climatic modeling. It shows good logical development, of course, it also have the important issues that have to have solved before publication, "convey the meaning" and "uncertainty". 

I'm suggest to authors just two thing before publications. 

1. Totally revise the manuscript to better convey the meaning of author's research.
2. All of simplifications have same problem, how much of uncertainty are included in the simple form. There are no discuss about uncertainty. Plz, discuss about "the uncertainty of simple models of three climatic phenomenon"  

Author Response

We have extensively rewritten the article. We have included some quantitative analysis for the climatic phenomena in a new section 6, and we have estimated the average error of the simulated solutions with respect to the real ones. We attach an accompanying email for all the referees.

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We thank the reviewer for their comments/questions and the editor for the patience.

  We have reconsidered the whole manuscript, some minor changes are in red, some sentences have been reformulated for better clarity without indications. There are a few major observations we made:   - we have included the year 2020 in the time series, we also adjusted the averages. In the previous manuscript we were averaging samples with the same time, but older dataseries often had a different time discretization. This caused an unnatural sawtooth behaviour in the averages. The new averaging considers equal all data that fall within the same 1hour interval (recent time series have between 10000 and 15000 measures per year). The real averaged time series have now a much more reasonable aspect.   - simulated humidity was not quite acceptable in the previous manuscript (we did observe it in the conclusions). We have found out that a change in the evaporation coefficients outside of the expected range (in particular for evaporation from the water component of the model) makes the simulated humidities almost identical to the measured one. In particular for Kufra (an extremely dry climate) we have managed to obtain an extremely reasonable simulated humidity time-evolution decreasing the evaporation of a factor 10 below the minimum we were accepting. The reason is probably that we were using a model for evaporation that is fine for water in swimming pools and artificial lakes, but it is most likely not acceptable for type of bodies we consider. (See for example Orvos, M., Szabo, V., and Poos, T. (2016). Rate of evaporation from the free surface of a heated liquid, Journal of Applied Mechanics and Technical Physics, 57:1108–1117.)   - we have computed both lags (seasonal and diurnal) for both time evolutions (real and simulated). For the seasonal lag the simulated and the real lags are in reasonable accordance, we argument this fact in a new section.   - We have introduced in the model the elliptic shape of the Earth. This changes the results very little.   We conclude observing that our model, although very simple, allows to make some observations that we hope we made clear in the article:  1. the lags are due to the existence of two thermodinamic bodies, and the asymmetric shape of daily temperatures is strongly influenced by air humidity; 2. the fact that the simulated evolution of temperature and humidity can be made so symilar to the recorded one indicates that the overally interactions are correct, and possibly give indications on the magnitude of some coefficients that many applied scientist discuss in publications (evaporation from water bodies, to say one). 3. A lot about climatic evolution and interaction of basic thermodynamic parameters can be understood from simple models.   We include the revised manuscript. We can provide one without the coloring of the changed sentences.   Best Regards, Gabriele Di Bona and Andrea Giacobbe. 

Reviewer 2 Report

This paper introduces a theoretical model that considers astronomical theories and parameters, atmospheric radiation and atmospheric thermodynamic processes. The authors claim that the model could reproduce the seasonal lag, diurnal lag and asymmetry of daily temperature variation. Overall, this is a very interesting work, especially because of its simplicity and potential application for exoplanet climate research. However, the information in the paper is insufficient for reproducing the results, and the validity of model is not systematically evaluated. For the above reason, I think the current manuscript is not ready for publishing on Climate.

 

Major comments

1. Choices of parameters: The authors mentioned that the parameters of the introduced model are mostly given by experimental evidence, but they did not clearly mention how these parameters were collected. I am a bit confused about how the authors determine the choices of different parameters (e.g. albedo, thermal capacity) in section 4? The choices of parameters, which greatly determine the model results (e.g. that in section 4), are important to readers who intend to use the model. The authors should state clearly how these parameters were taken/estimated/collected.
2. Evaluation of model results: The authors claimed that the introduced model could reproduce the properties of the seasonal lag, diurnal lag and asymmetry of daily temperature variation. Although their results (Fig. 4-8) support the above statements to some extent, there are obviously errors existing in the model outputs. For example, the simulated temperature peak hour of the diurnal cycle is apparently behind (ahead) the observed one in Catania (Kufra). While errors are acceptable in theoretical models, it is necessary to perform a systematic evaluation so as to state out the pros and cons of the model. If the mentioned 3 fundamental climate properties are the main study target of this research, I suggest the authors respectively verify (in statistical ways) the model’s ability in reproducing these properties in different regions (or climate zones).

 

Minor comments

1. The manuscript title is too general for me. I suggest the authors give a more specific title, such as “A simple theoretical model for the seasonal and daily asymmetry of surface temperature”.
2. Figure 4: missing description of the blue line of the top right panel.
3. Typo: an extra bracket in Eq. 18
4. A missing reference in line 397?

Author Response

In section 3 we discuss the choice of fixed parameters. They are extracted from the cited literature. Some other parameters have some variability, and have been fitted with a minimising technique. We have included some quantitative analysis for the climatic phenomena in a new section 6, and we have estimated the average error of the simulated solutions with respect to the real ones. We also attach below an accompanying email for all the referees.

%%%%%%%%%%%%%%%%%%%%%%%

We thank the reviewer for their comments/questions and the editor for the patience.

  We have reconsidered the whole manuscript, some minor changes are in red, some sentences have been reformulated for better clarity without indications. There are a few major observations we made:   - we have included the year 2020 in the time series, we also adjusted the averages. In the previous manuscript we were averaging samples with the same time, but older dataseries often had a different time discretization. This caused an unnatural sawtooth behaviour in the averages. The new averaging considers equal all data that fall within the same 1hour interval (recent time series have between 10000 and 15000 measures per year). The real averaged time series have now a much more reasonable aspect.   - simulated humidity was not quite acceptable in the previous manuscript (we did observe it in the conclusions). We have found out that a change in the evaporation coefficients outside of the expected range (in particular for evaporation from the water component of the model) makes the simulated humidities almost identical to the measured one. In particular for Kufra (an extremely dry climate) we have managed to obtain an extremely reasonable simulated humidity time-evolution decreasing the evaporation of a factor 10 below the minimum we were accepting. The reason is probably that we were using a model for evaporation that is fine for water in swimming pools and artificial lakes, but it is most likely not acceptable for type of bodies we consider. (See for example Orvos, M., Szabo, V., and Poos, T. (2016). Rate of evaporation from the free surface of a heated liquid, Journal of Applied Mechanics and Technical Physics, 57:1108–1117.)   - we have computed both lags (seasonal and diurnal) for both time evolutions (real and simulated). For the seasonal lag the simulated and the real lags are in reasonable accordance, we argument this fact in a new section.   - We have introduced in the model the elliptic shape of the Earth. This changes the results very little.   We conclude observing that our model, although very simple, allows to make some observations that we hope we made clear in the article:  1. the lags are due to the existence of two thermodinamic bodies, and the asymmetric shape of daily temperatures is strongly influenced by air humidity; 2. the fact that the simulated evolution of temperature and humidity can be made so symilar to the recorded one indicates that the overally interactions are correct, and possibly give indications on the magnitude of some coefficients that many applied scientist discuss in publications (evaporation from water bodies, to say one). 3. A lot about climatic evolution and interaction of basic thermodynamic parameters can be understood from simple models.   We include the revised manuscript. We can provide one without the coloring of the changed sentences.   Best Regards, Gabriele Di Bona and Andrea Giacobbe. 

Reviewer 3 Report

In this manuscript, the authors wrote several non-linear ODE (ordinary differential equations) that solves energy balance, particularly for temperature and humidity. And the authors concluded that the ODE solutions have implications on the study of exoplanets’ environments.  This manuscript is heavily theoretical and very interesting. It fits the scope of the journal climate. I recommend for publication with a few minor revisions.

#1. L16-17 I suggest authors mention important similarities/differences.

#2 L21 This sentence is vague (I think).

#3 L37-41 Long sentence. Could be broken into multiple simple sentences

#4 L470 Explain the implication in detail.

 

Author Response

We thank the referee for indicating the mistakes. We attach below an accompanying email for all the referees.

%%%%%%%%%%%%%%%%%%%%%%%

We thank the reviewer for their comments/questions and the editor for the patience.

  We have reconsidered the whole manuscript, some minor changes are in red, some sentences have been reformulated for better clarity without indications. There are a few major observations we made:   - we have included the year 2020 in the time series, we also adjusted the averages. In the previous manuscript we were averaging samples with the same time, but older dataseries often had a different time discretization. This caused an unnatural sawtooth behaviour in the averages. The new averaging considers equal all data that fall within the same 1hour interval (recent time series have between 10000 and 15000 measures per year). The real averaged time series have now a much more reasonable aspect.   - simulated humidity was not quite acceptable in the previous manuscript (we did observe it in the conclusions). We have found out that a change in the evaporation coefficients outside of the expected range (in particular for evaporation from the water component of the model) makes the simulated humidities almost identical to the measured one. In particular for Kufra (an extremely dry climate) we have managed to obtain an extremely reasonable simulated humidity time-evolution decreasing the evaporation of a factor 10 below the minimum we were accepting. The reason is probably that we were using a model for evaporation that is fine for water in swimming pools and artificial lakes, but it is most likely not acceptable for type of bodies we consider. (See for example Orvos, M., Szabo, V., and Poos, T. (2016). Rate of evaporation from the free surface of a heated liquid, Journal of Applied Mechanics and Technical Physics, 57:1108–1117.)   - we have computed both lags (seasonal and diurnal) for both time evolutions (real and simulated). For the seasonal lag the simulated and the real lags are in reasonable accordance, we argument this fact in a new section.   - We have introduced in the model the elliptic shape of the Earth. This changes the results very little.   We conclude observing that our model, although very simple, allows to make some observations that we hope we made clear in the article:  1. the lags are due to the existence of two thermodinamic bodies, and the asymmetric shape of daily temperatures is strongly influenced by air humidity; 2. the fact that the simulated evolution of temperature and humidity can be made so symilar to the recorded one indicates that the overally interactions are correct, and possibly give indications on the magnitude of some coefficients that many applied scientist discuss in publications (evaporation from water bodies, to say one). 3. A lot about climatic evolution and interaction of basic thermodynamic parameters can be understood from simple models.   We include the revised manuscript. We can provide one without the coloring of the changed sentences.   Best Regards, Gabriele Di Bona and Andrea Giacobbe. 

Round 2

Reviewer 2 Report

The authors have well addressed the problems I raised in the previous review. Although some minor mistakes are spotted, I think the manuscript could be accepted after minor revision.

1. Line 413 and 414: What do f(i) and g(i) stand for?
2. Missing units: e.g. line 421, 429, 441, 452, 460, 473 etc.

Author Response

Dear referee,

you are right. We have added the units, and we have explained better that f(I) are the average temperatures at the sampled times and g(i) are the temperatures predicted at the same time by our model.

Thanks again, best regards.