Determination of Soil Thermal Properties Across Seasons in Alkaline–Nonalkaline Soils of Igdır, Türkiye

R1-1

Self-plagiarism was detected in the submitted manuscript.

This refers to the publication of the same results in multiple articles.

To maintain academic integrity and originality, each new contribution to the scientific literature must be unique.

We urge you to review your manuscript and remove content that duplicates previously published work. 

Response

Unlike our previous articles, two different soils were discussed in this study.

In addition, although only one summer season temperature values ​​were used in the previous study, thermal properties were calculated using 365-day (4 seasons) data in this article.

We did not know that it was forbidden to use and refer to methods we developed ourselves.

(Similar style is used in many publications, e.g. DOI https://doi.org/10.21203/rs.3.rs-1457633/v2 ,

https://doi.org/10.1002/2017JD027290 ,  https://doi.org/10.3390/land11111960 ,

https://doi.org/10.3390/app9224799,       https://doi.org/10.3390/su13147796     and et al).

We reviewed our study and contents that repeated our previous publications were added to the end of the article as additional material, taking into account the referee's recommendations and recommendations.

 R1-2a

Page 2-Line 83: Mistake at start paragraph,  “he objectives of this study were…”

Response

ORRecTed> The referee is right. The objectives of this study were

R1-2b

The current introduction is excessively long.

The standard for most journals, including MDPI's Land, is a concise introduction that provides necessary background, states the research gap, and outlines the paper's objectives. A typical introduction is 1-3 pages.

Detailed mathematical formulation should be included in a separate section, usually in the "Methods" or "Theoretical Framework" section, not in the introduction.

This should present only the main idea of the model or formulation, not its complete derivation.

Response

The introduction part of the study has been reduced and theoretical issues have also been transferred to the Method part.

The most important part of the article is the behavior of the heat conduction model in the semi-finite soil layer, which has not been included in any literature sources or publications so far.

The study does not include mathematical proofs and explanations of theoretical information.

Only results are given here

R1-2c

Dear authors, such a lengthy introduction, dominated by complex equations, will likely overwhelm the reader and obscure the article's main message.

An introduction is intended to capture the reader's attention and lay the groundwork for research, not to be a detailed technical manual.

Response

Since the mathematical proof of this topic could cover tens of pages, we sometimes had to refer to our previous publications where the proofs were given.

It is important to explain in detail the boundary value problems of the Soil Heat Conduction model that accurately reflect the environment and their analytical solutions.

Since there are no such explanations, different values ​​are found in determining the thermal diffusion parameter in most studies.

Therefore, we would like to point out that the explanations in our article are important.

2d

At the end of your manuscript (before the acknowledgements and references), add a heading like "Supplementary Materials."

You can also create a separate file and submit it as supplementary material during the submission process

We are satisfied with this idea.

Additions have been made as 'Additional Materials' at the end of the article.

R1-2e

Page 13-Line 458:

Comparison of Methods, Models assessment Section.

Please, dear authors, this section should not be here.

When you mention it in the materials and methods section, please do not include the formulas in this manuscript.

You could create another supplementary information file.

Response

This suggestion of the referee was taken into consideration, another 'Supplementary Material' was created and the necessary criteria were added at the end of the article as "Supplementary Materials-C Model Selection Criteria".

The criteria used in many publications are used in full detail.

For example, in the RMSE and AICc criteria: n-number of data n≤30 or n/p ≥ 40 is ignored.

In this respect, we deemed it appropriate to provide more detailed information.

R1-3a

Page 15-Figure 1: The legend “toprak yüzeyi” must be in English.

Please, dear authors, clarify the correct placement of the sensors in Figure 1, because there is a symbol at depth of 60 cm and there is no symbol at depth of 15 cm, but in the same page 15 line specify different depths (0, 5, 10, 15, 20, 40 cm).

.

Response

For Figure-1, the deficiencies have been completed and corrected again

R1-3b

Page 14-Line 498: Please, dear authors, provide the exact latitude and longitude of the experimental site. This is a standard requirement for field studies, allowing other researchers to locate the site precisely. Include the elevation of the site.

This is important for understanding the climate and microclimatic conditions that influence soil properties

The experimental site is located at 39°55'44.9"N 44°05'36.4"E.

R1-3c

Page 16-Line 532: authors, please clarify the methodology used to determine ESP. This is mainly derived from experimental determinations of cation exchange capacity and exchangeable sodium, for which experimental tests are mandatory and should be mentioned; it is not a simple calculation

response

 Where; ESP is Exchangeable Sodium Percentage, CEC is Cation Exchange Capacity. CEC means the sum of exchangeable cations.

Saline and alkaline soils are formed by the accumulation of exchangeable cations on the soil surface or in layers near the surface. Determination of cation exchange capacity is important in determining the salinity and alkalinity of soils. Especially by determining the amount of exchangeable sodium in soils, it can be determined whether the soils are saline or alkaline.

R1-4a

Page 26-27Table 7 and 8 : Why are some cells in the table highlighted?

Response

The highlights in Tables 7 and 8 have been removed.

R1-4b

Dear authors, Why is the reason that shows the Pearson’s Correlation Coefficient (r)

Response

It is known that the coefficient of determination (R²) found from a sample in the case of linear  pairwise (paired) correlation is equal to the square of the linear correlation coefficient (r), i.o. R²=r^2.

When the relationship between the measured (T_mes) and predicted temperature values ​​(T_cal) was examined using a linear regression equation, namely,

                     Tmes (zi,tj) = a + bTcal,

the Pearson correlation coefficient (r) was used in this study because the values ​​of the correlation and determination coefficients were the same.

To use a linear regression model in practice, its quality must first be assessed.

For this purpose, a number of metrics have been proposed, each designed for use in different situations and with its own application characteristics (linear and nonlinear, robust to anomalies, absolute and relative, etc.).

It includes the following measures:

Standard deviation (MSE). The root of the root mean square error (RMSE), The standard deviation in percent (MSPE), Average absolute error (MAE), Average absolute percentage error (MAPE), Symmetric mean Absolute percentage error (SMAPE), Average Absolute Scaled Error (MASE), Average relative error (MRE), Root-mean-square logarithmic error (RMSLE), The coefficient of determination is squared R², Adjusted coefficient of determination R²_adj.

R1-4c

Dear authors, Why is the reason that shows the Root mean squared error (RMSE) in the information of Tables 7 and 8.

Response

The expression of the RMSE and R2adj criteria contains the number of model parameters.

Since the R² and R²_adj criteria are almost identical for a linear regression model, it is appropriate to use the RMSE, which in our case is:

R1-4d

Please dear authors, a better way to demonstrate the goodness of fit of a regression model is to show the coefficient of determination R2, it provides more information than a linear correlation, please place this statistical parameter (R2) in this table.

Response

An explanation has been made about this above.

At the suggestion of the reviewer, the newly calculated values of the Coefficient of Determination (R²) were added in Tables 7 and 8 instead of the Correlation Coefficient (r).

R1-4e

Page 17-Line 576: Comparison of Methods Section, in the introduction section (Page 13-Line 458), mentioned the criteria for method selection

Response

Corrected

R1-4f

Page 15- Table 1. Some physical and chemical soil properties: 

Self-plagiarism with Table 1.

Some physical and chemical soil properties in the work: Mikail, R., Hazar, E., Shein, E., & Mikailsoy, F. (2024). Determination of Thermophysical Parameters of the Soil According to Dynamic Data on Its Temperature. Eurasian Soil Science, 57(2), 233-244

Response

Our previously published article (2024) covers only the non-alkaline soil data and results for the summer of 2024.

Therefore, some parts of our previously published article were included in this study and also cited.

For this reason, parts of our previously published article are included in this study and are also referenced.

R1-4g

Figure 2-Summer 01.06.2020-31.08.2020. Self-plagiarism with the figure 1 in the work: Mikail, R., Hazar, E., Shein, E., & Mikailsoy, F. (2024). Determination of Thermophysical Parameters of the Soil According to Dynamic Data on its Temperature. Eurasian Soil Science, 57(2), 233-244.

Response

This study was conducted in non-alkaline and alkaline soils, as well as in 4 seasons, from 01-12-2019 to 30-11-2020

R1-4h

Table 2- Parameters of the nonalkaline soilssurfaces and model performance for all seasons: Self-plagiarism with the Table 3. Parameters (T0, Ti, and εi) of the soil surface in the work:

Mikail, R., Hazar, E., Shein, E., & Mikailsoy, F. (2024). Determination of Thermophysical Parameters of the Soil According to Dynamic Data on its Temperature. Eurasian Soil Science, 57(2), 233-244.

Response

The trial area where this study was conducted, the soil properties and temperature data used also include the data and results in the article previously published by us only for non-alkaline soils.

Therefore, it also includes the data and results in the article previously published only for non-alkaline soils.

Furthermore, without losing generality, we deemed it appropriate to present all the values ​​in the graphs and tables together.

If the judge finds our explanations insufficient on this matter, we may remove the repetitions.

R2-1

The title is informative but too long; it needs to be trimmed retaining key words (thermal properties – alkaline soils – seasonal variation) for better visibility and indexing.

Response

Determination of soil thermal properties with various models across seasons in alkaline-nonalkaline soils of Igdır, Türkiye

Or Determination of soil thermal properties across seasons in alkaline-nonalkaline soils of Igdır, Türkiye

R2-2

The abstract is comprehensive but duplicates words (e.g., thermal conductivity being repeated in a sentence).

A concise and polished one would facilitate easier reading.

Response

In accordance with the referee's suggestion, we can write it this way:

Climate, which has important effects on pedogenesis, affects soils and its structure and mass transport through temperature and precipitation. Soil salinity or alkalinity, which is caused by the effect of climate, parent material, topography and anthropogenic factors, is one of the important problems of arid and semi-arid regions and has negative effects on soil quality and need specific attention due to the limited little researched. In this study, thermal properties were calculated using various classical and improved models in winter, spring, summer and fall in alkaline and non-alkaline soil.
For this purpose, temperature sensors were placed at different depths (0, 5, 10, 15, 20, 40 cm) on non-alkaline and alkaline lands, and temperature data were collected from the sensors for 365 days. The study showed that (i) the thermal properties of both soils vary depending on the seasons of the year, and (ii) the thermal properties (thermal conductivity, thermal conductivity coefficient, thermal conductivity, attenuation depth, thermal conductivity coefficient, speed and length of the heat wave) were lower in alkaline soil. The result coul be usedmfor consideration of climate change mitigationin in similar semi-arid zone

R2-3

The objectives are clearly stated but could be accorded more precision, with every objective being stated in a definitive, straightforward sentence.

The objectives of this study were: (i) to calculate thermal diffusivity (κ) using both classical methods and the new "point" method developed by our team, and to identify the most accurate method for the study area; (ii) to determine key thermal properties of the soil—namely volumetric heat capacity, thermal diffusivity, thermal conductivity, damping depth, thermal effusivity, heat wave velocity, heat wavelength, and heat flow—across different seasons; and (iii) to investigate the effect of soil alkalinity on these thermal properties.

R2-4

The theory section (derivations and equations) is thorough but overly wordy. Lay readers may find it discouraging. Having some of the derivations in an appendix would make for better readability.

Response

Many parts of the theoretical section have been included in the appendix at the referee's recommendation.

R2-5

References to some sources are cited in ranges (e.g., [9–10]) without making distinctions explicit.

More precise referencing would establish credibility

Response

The referee's recommendation has been taken into consideration:

In works  [9-10] it was also found that increasing the amount of added salts at a given humidity reduces the thermal conductivity.

R2-6

Although multiple models are employed, their performances are not well compared through tables or figures. Adding comparative charts would make model performance more transparent.

Response

Information about the models is provided in more detail at the end of the article and in the appendix.

R2-7

Discussion is far too numerical with little mention of agricultural or environmental implications (e.g., how reduced conductivity in alkaline soils affects plant growth). Expanding this section would add applied value.

Response

The referee is right.

Since our current work is primarily theoretical in nature, we will provide more detailed information on its applications in agriculture in our subsequent studies.

R2-8

The methods section clearly describes the study site, but climatic data range from 1941–2021 with no explanation of how these longer records were added to a year of sensor data. This needs clarification.

Response

The data in question represent the region's long-term temperature values and are not from the year in which the data were collected. It is provided for the purpose of providing preliminary information about the region. The data is from the Turkish State Meteorological Service.

R2-9

Convoluted, long sentences (sometimes 4–5 lines) are difficult to follow.

Briefer, unadorned sentences would be more clear.

Response

We will definitely take the referee's advice into consideration in the future.

R2-10

Minor linguistic errors (e.g., "the result coul be usedmfor consideration") suggest the value of strict English proofreading before submission.

Response

Edited

R3-1

Line 336-413. Consider adding a table/flow diagrams, or conceptual figures to illustrate how each method (M1-M8) differs in assumptions and required inputs

Response

We agree with the comments of the respected reviewer.

Based on the recommendation of the referee, methods M1-M8 were arranged in a separate Table and added to the article as Appendix C

R3-2a

Some references are outdated; consider adding more recent studies on soil thermal modeling to strengthen the context and novelty.

Response

We agree with the comments of the respected reviewer.

The work is mainly devoted to determining the diffusion parameter with classical and proposed methods, as well as comparing their values and choosing a computational algorithm.

There are many works on classical methods from the 1900s to the present day.

We have mainly referred to the authors who developed the classical mathematical formulas and to recent works on the application of these works.

Regarding the proposed methods, since these studies began in 2009, we believe that the necessary references to them are provided in the article

R3-2b

Additionally, the novelty of incorporating soil depth L (in M7, M8) could be contrasted more with earlier works.

Response

The main novelties of the work, in contrast to the earlier works, are as follows,

1 The paper presents analytical solutions to the problem of heat transfer in soil of finite and semi-infinite thickness under boundary conditions of the first kind with infinite harmonics on the soil surface. As well as boundary conditions of the 2nd kind at depth, i.e., ∂T(L,t) / ∂z = 0 and ∂T(z→∞, t)/∂z=0.

2. Based on these solutions, methods have been developed for determining the thermal conductivity coefficient from a point value of soil temperature of a given power based on the results of an analysis of temperature dynamics at one depth based on eight daily observations with an interval of 3 hours

Methods have been developed for determining the thermal diffusivity coefficient based on the point value of soil temperature of a given thickness, based on the results of an analysis of temperature dynamics at one depth based on eight daily observations at 3-hour intervals.

When using this method, the temperature distribution in the soil layer [0, L] is used for eight time points in the calculated time interval t0 for each depth.

The proposed methods are based on the solution (with two harmonics on the soil surface) of inverse problems of the heat transfer equation.

.3. The introduction of the second harmonic in the boundary conditions at the soil surface (z=0) makes it possible to determine with high accuracy the parameters of the temperature distribution on the soil surface and especially the thermal conductivity parameter using the proposed point method M8.

4. The proposed methods, in addition to the amplitude of fluctuations (Ta) of the soil surface temperature, also take into account the depth of the soil profile (L).

These methods make it possible to evaluate the thermal diffusivity in the soil under natural conditions, which should increase the adequacy and expand the boundaries of using mathematical models of the thermal regime of soils.

R3-3

For the methodological explanation, since the article contains a lot of equations, the mathematical derivations are extensive.

For better readability, consider adding a table to summarize all the terms(e.g., Ta, ε, κ, d) to their physical interpretation.

Response

The suggestion has been taken into consideration and added to the end of the article.

Supplementary Materials :List of symbols and abbreviations

R3-4

It clearly shows M8’s superiority, but the discussion lacks depth in explaining why alkaline vs. non-alkaline soils behave differently (beyond amplitude and Cv). (i.e., from a soil chemistry and structure perspective).

Consider discussing limitations more explicitly—e.g., the reliance on one field site, specific climate (Bsh semi-arid ), and whether M8 generalizes to other soils.

Response

The esteemed judge raised a very relevant issue.

We believe it would be appropriate for this issue to be examined using mathematical modeling, despite the fact that some research has already been conducted on this topic.

In our future research, we plan to conduct more detailed studies of the effect of salinity on heat transfer (including the parameter of the coefficient of thermal  diffusivity), using the mathematical theory of heat transfer

Symbol

Definition

AIC

Akaike Information Criterion

C_v

Volumetric heat capacity (J m^{-3  °}C^-1)

c_s

The specific heat capacity (J kg^-1 °C^-1)

C_m,_s

Volumetric heat capacity of the soil solid phase (J kg °C^-1)

C_v,w

Volumetric heat capacity of soil moisture equals to 4186.6 (kJ m^{-3  °}C^-1)

C_m,org

The specific heat capacities of organic components of the soil solid phase (J kg^-1 °C^-1)

C_m,min

The specific heat capacities of mineral components of the soil solid phase (J kg^-1 °C^-1)

C_va

Volumetric heat capacity of air phase

D

Willmott’s index of agreement

e

Thermal effusion (W s^0.5 m^-2 °C^-1)

d

Damping depth, (cm)

J

The soil heat flux (Wm⁻²);

j

Index of the harmonic in the series

L

Soil depth (m) starting from which T(z, t) = const or ∂T(L, t)/∂z = 0

m_org

The mass of soil organic matter, kg;

m_org/m

The organic matter content in the soil, %.

m

The mass soil mass

N

Sample number

n

The number of the used data

p

The number of variable coefficients of model

R

Earth's radiation balance-Radiation (heat balance)

R²

Coefficient of determination

R²_adj

Adjusted R-square

RMSE

Root mean squared error

T

Temperature, ^°C

T₀

Average (daily, annual) temperature of the active soil surface (^oC or K);

T_i

 Amplitude of the wave at the surface level for the j^th harmonic (^oC or K);

T_mes

Measured temperature

T_cal

Calculated temperature

t

Time (hour, day, year);

UI

Theil's forecast accuracy coefficient 

q_1,2

Heat flux from the soil surface.

y

Dimensionless depth

z

Vertical depth (m)

Greek Symbol

F_i (b,y_i)

The amplitude of the temperature fluctuations at the dimensionless depth yi (^°C)

α_j (b,y_i)

Phase angle of the wave at the surface level for the j^th harmonic  (radians)

e_j

Phase angle of the wave at the surface level for the j^th harmonic (radians).

j(t)

Function of the soil surface temperature

k

Thermal diffusivity of the soil, m² s^-1

l

Thermal) conductivity of the soil, Wm^-1 °C^-1

Λ

heat wave length (m)

υ

heat wave velocity (m s^-1)

q

The volumetric water content (m³ m^-3)

r_b

soil bulk density (kg m^-3)

s_T/t

Standard deviation of mean

t

Dimensionless time

t₀

Temperature wave period (days or years), for τ₀=24 hours: ω = 7,27∙10^-5 (rad/s)

w

Angular daily (or annual) frequency of periodic temperature fluctuation,