The moisture distribution in wall-to-floor thermal bridges and its influence on mould growth

Reply to reviewers’ comments

The moisture distribution in wall-to-floor thermal bridges and its influence on mould growth

by Yucong Xue, Yifan Fan, Jian Ge, submitted to UCL Open: Environment

We thank the editor and reviewers for the detailed and thoughtful suggestions. Replies to these comments are presented below.

Reply to Reviewer 1

General comments: This document needs proofreading

Reply: Thank you for your considerable effort in improving the quality of our paper. Your comments were very helpful and are addressed individually below.

Specific comments:

Comment 1: There are a number of sentences where more information is needed  (e.g., line number 16, where was moisture distribution modelled?

Reply: Thank you for your comment. A sentence was added to clarify where the moisture distribution was modelled.

“in a humid and hot summer cold winter region of China (Hangzhou City)” on lines 15-16.

Sentences on lines 145-146 (The indoor environment data and meteorological data last for a year in Hangzhou, a typical city in the HSCW climate zone, are adopted as the ambient conditions) also indicate that the meteorological data for the boundary conditions of the numerical simulation are taken from a weather station in Hangzhou. Whereas the indoor background condition referred to the hygrothermal record of a typical residential building located in that city.

Comment 2: In line 42, the author referred to condensation for the germination and development of mould, however, mould only develop under high levels of humidity and not condensation.

Reply: Thanks for the excellent suggestion. There are some studies implying that condensation may result in mould growth.

“Especially during Canadian winters, this humid air will condense within the walls and thus becomes an ideal location for fungal growth” in Reference [7].

“Moisture condensation …, which also can aggravate the growth and reproduction of fungi.” in Reference [8].

“Mould growth … can easily geminate and expand …, mainly through condensation within a building form.” in Reference [9].

According to the above literature, high levels of humidity are bound to induce mould growth and condensation. However, the authors believe that whether condensation is a cause of mould development or it is adverse to mould growth needs to be further studied and discussed.

Comment 3: Also, in line 42, the authors indicate that mould could grow inside building envelopes. Please provide a few examples of where inside the envelope, mould could grow.

Reply: Thank you for the reminder. There are considerable studies indicating that mould could grow inside the building envelopes.

“Moisture through breaks in the building envelope … creates a condition for mould growth when, inevitably, spores are also drawn into the building” in Reference [7].

“Especially during Canadian winters, this humid air will condense within the walls and thus becomes an ideal location for fungal growth” in Reference [7].

“Mould growth … can easily geminate and expand inside building envelopes” in Reference [9].

“Case studies of housing in cooler climate zones investigating interstitial mould within the building envelope …” in Reference [10].

“When the relative humidity of wall inside … reaches the critical condition, there will be a great mould risk.” in Reference [11].

According to the above literature, it can be found that mould could grow at the interface between two elements of building envelopes (e.g., the interface of the beam and the wall), as well as the breaks in building envelopes, i.e., mould may grow in any area of building envelopes, as long as there is a break. Consequently, the mould risk predicted in this paper is only intended to provide a rough assessment of mould growth, not to imply mould must germinate.

Comment 4: It is not clear why the software COMSOL was used.

Reply: A sentence was added to clarify why COMSOL was used.

“Because the proposed partial differential equations in the developed models are fully coupled and highly nonlinear…” on lines 104-105.

This commercial software has been widely used to obtain the fields of temperature and relative humidity in the building envelope, as References [2-4, 11] show.

Comment 5: More details should be provided regarding the weather climate used in the modelling presented in Figure 2. You refer to a climate zone in China.

Reply: The weather climate used in the modelling presented in Fig. 2 has been introduced in Section 2.3.2 in detail. The hot summer and cold winter zone of China is a typical hot-humid climatic region, which has over 40% of the total population of China and shares 48% of China’s gross domestic product. The target building was located in Hangzhou, a typical city in the HSCW climate zone.

Comment 6: Fig 2a should be uninsulated, while 2b insulated. Please amend.

Reply: Thank you for the kind reminder. The relative sentences were amended (lines 132-133).

Comment 7: You also refer in section 2. 3.1 to an existing Atlas; what exactly is this?

Reply: Thanks for the reminder. Some references were supplemented (lines 130 and 468-475) as follows:

Reference [19],   China Institute of Building Standard Design & Research, Structure of Autoclaved Aerated Concrete (AAC) Blocks and Slabs (GJCT-016/06CG01), Beijing, 2007.

Reference [20],   China Institute of Building Standard Design & Research, Building Construction of Autoclaved Aerated Concrete (AAC) Blocks and Slabs (GJCT-009/06CJ05), Beijing, 2007.

Reference [21], Chongqing Construction Technology Development Center, Atlas of Architectural Structure of Self-insulation Wall with Autoclaved Aerated Concrete (DJBT-039/08J07), Chongqing, 2008.

Comment 8: In section 2.3.2 please provide more information on how data was collected from a residential building in Hangzhou.

Reply: Thank you for the suggestion. The collection method of indoor background conditions was introduced on lines 148-150:

“The temperature and relative humidity of indoor air at 1.1 m above the ground were real-time recorded by automatic RHT recorders [JTR08ZI, JANTYTECH Co., Ltd., Beijing, the P.R.C.].”

Comment 9: In figure 3, please use lines to express temperature and relative humidity. The use of dots makes it extremely difficult to read and understand the environmental conditions in both graphs.

Reply: Thanks for the suggestion. Figs. 3(a) and (b) were revised, in which the dots of indoor and outdoor temperature have been changed to the lines, whereas the dots of relative humidity are reserved. Since the relative humidity usually fluctuates violently, it is extremely difficult to distinguish if this parameter is drawn in the form of lines, as the followings show.

Comment 10: Correct the text in lines 181 and 182; it should read Figure 4a and 4b.

Reply: Thanks for the reminder. The sentence was revised (lines 191).

Comment 11: Explain what each of the values in Table 3 refers to. But also how they were used to assess the risk of mould growth. Did you consider time in the evaluation?  

Reply: The values in Table 3 are the coefficients of the two-term exponential ( ), which is the mathematical expression of the isopleth system for computational calculation purposes. That means that these values have no physical meaning.

The isopleth system gives the time required for spore germination and the growth rate of mycelia under different conditions, which are closely related to the time. It is, therefore, can be said that time was considered in the evaluation.

Comment 12: Please explain the concepts used in the analysis, moisture sink and moisture shadow. This is very unclear in the document.

Reply: Agree. For ease of understanding, the above-mentioned concepts were changed in expression, i.e., the moisture sink and the moisture shadow are now called the high moisture area (HMA) and the low moisture area (LMA) (lines 203-205).

Comment 13: Please add some explanation in Fig 5, so what do the colours represent; red=cold and blue=warm?

Reply: Thanks for the suggestion. A legend was supplemented in Fig. 5. The red and blue refer to high and low relative humidity, respectively.

Comment 14: Are you presenting in Fig 5 the results for the uninsulated or insulated detail?

Reply: Thanks for your insights. As an example, Fig. 5 is only used to illustrate and explain what the moisture sink and moisture shadow (i.e., HMA and LMA, respectively) are, so whether the WFTB is insulated or not does not have to be mentioned. The title of the figure was revised, which points out that the WFTB was insulated (lines 209-210).

Comment 15: Why is it important to calculate the area for each moisture sink and moisture shadow? Please explain, in more detail, how they were generated and how they can be used.

Reply: Thank you for your reminder. The explanation for the calculation of moisture sink and moisture shadow (i.e., HMA and LMA, respectively) and their potential value in the practical application is supplemented on lines 219-224:

“Calculating the A has a potential value in the practical application because it can provide guidance on the arrangement of the moisture insulation. For example, HMA confined to the range of the WFTB means that the moisture-proof measures for the WFTB alone are sufficient. Otherwise, the moisture-proof measures may need to be extended to the main part of the wall, as Fig. 5 shows. Similarly, the appearance of LMA means that there is less prone to mould growth and condensation than other adjacent areas.”

Comment 16: Please enlarge Fig 6. The moisture shadows and most of the information you are trying to describe in the text is unreadable.

Reply: Thanks for your reminder. The figure was redrawn (line 255).

Comment 17: In line 242, you refer to the germination of mould spores inside the building envelope; are you referring to the space between the insulation and concrete?

Reply: According to the following literature, it can be inferred that mould could grow at the interface between two elements of building envelopes (e.g., the interface of the beam and the wall), as well as the breaks in building envelopes.

“Moisture through breaks in the building envelope … creates a condition for mould growth when, inevitably, spores are also drawn into the building … especially during Canadian winters, this humid air will condense within the walls and thus becomes an ideal location for fungal growth” in Reference [7].

“Mould growth … can easily geminate and expand inside … a building form.” in Reference [9].

Comment 18: Regarding mould assessment, did you use the info in the isopleth to define transient conditions? The isopleths were created based on steady-state conditions.

Reply: Due to its convenience, the isopleth system was employed in our study to evaluate mould growth under transient boundary conditions. Dr. Klaus Sedlbauer, who proposed the isopleth system, indicates that such the isopleths can also be adopted under transient boundary conditions, though it was created based on steady-state conditions.

“To be in a position to compare the biological growth conditions with the calculated hygrothermal conditions, one has to compare, on basis of the isopleth model, the calculated transient courses of temperature and relative humidity in the building component surface with the spore germination time and mycelium growth data in the respective isopleth systems … The growth conditions characterized by the time courses of temperature and relative humidity, serve as input parameters. These microclimatic boundary conditions are entered into the isopleth systems as hourly values. The computer allows to carry out the evaluations on basis of the isopleth model automatically” in Reference [25].

However, it should also be admitted that the isopleth system is deficient when it is used in the transient case. That is, more frequent germination of spores than the actual situation will be predicted because an interim drying out of the fungi spores cannot be taken into account (lines 196-199).

Comment 19: Please better explain figure 7; it is unclear what exactly you are showing and where in the diagram and wall detail you have assessed mould growth. Also still very unclear how the risk of mould growth was calculated. What do the red arrows and red area represent?

Reply: Thanks for your reminder. The figure was revised (lines 293-300). We believe that the illustration in each subgraph can make it clear where we have assessed mould growth.

Following Sedlbauer [25], the calculation method was introduced on lines 200-204: “the calculated microclimatic boundary conditions, including both temperature and relative humidity, are entered into the isopleth systems as hourly values. If the growth conditions are above the respective LIM curve for a certain duration, mould activity may take place, which is automatically evaluated by the computer.”

As said on lines 303-305: “the moisture transfers from outside to inside in general, which results in the mould at the exterior surface growing earlier and faster than that inside the building envelopes.” Therefore, the red arrows in Fig. 7 are used to display the growth trend from outside to inside. Whereas the red boxes show a phenomenon that does not conform to the above-mentioned growth trend, i.e., the mould grows only inside the building envelope and the surface part has less risk of mould growth. This phenomenon can be attributed to the existence of HMA, which abnormally increased the relative humidity inside the building envelope and thus created an appropriate microclimate for mould growth.

Comment 20: Mould need time to germinate and grow. So, the conditions of RH and Temperature presented in the isopleths (Fig.4) need to be constantly occurring for the time there indicated for mould to germinate and grow. Under transient conditions, mould will take much longer or don't react to those conditions. Please explain and discuss.

Reply: Agree. Different hygrothermal environments change the development rate of spore and mycelia. Therefore, various isolines were proposed to evaluate different development rates under different conditions. The areas between the isolines are interpolated. The above method was detailed introduced in Reference [25] and is widely recognized and thus adopted in our study.

However, it was also admitted in Reference [25] that the method does not consider the conditions when mould will take much longer or do not react, which makes “(that) will therefore predict the germination of spores more often …”

In view of this defect, we explained it on lines 196-199:

“However, it should be mentioned that the isopleth system is deficient when it is used in the transient case. That is, more frequent germination of spores than the actual situation will be predicted because an interim drying out of the fungi spores cannot be taken into account”

and discussed on lines 326-332:

“However, when the microclimate in building envelopes frequently switches between appropriate and inappropriate, mould may take a much longer time to develop or even do not react to such conditions, which is not considered in the isopleth system. Therefore, the predicted mould risk is generally higher than the real situation because of the neglect of the interim drying out of the fungi spores. In future studies, another prediction model for mould growth, such as the VTT model or biohygrothermal model should be employed to further evaluate the mould risk.”

Comment 21: Regarding your discussion, please expand the discussion on the urban heat island effect and how the phenomenon found could be affected in winter.

Reply: Thanks for the suggestion. The process of moisture accumulation (i.e., HMA) was discussed in detail on lines 333-346:

“Enhancing our understanding of the causes of the HMA helps to take measures to mitigate moisture accumulation. Therefore, the year-average profiles of the partial pressure of water vapour (p_v) in the insulated WFTB (x=0-150 mm, y=800 mm) are displayed in Fig. 8 The three types of lines refer to period 1 (8:00-16:00), period 2 (16:00-20:00), and period 3 (20:00-8:00 the next day), respectively.

As Fig. 8 shows, the process of moisture accumulation can be concluded as follows: 1) in the daytime (8:00-16:00), the heat caused by the intense solar radiation is blocked in area A by the insulation layer, which results in a high temperature and low relative humidity here. Then, according to Darcy’s law, moisture transfers from the surrounding area to area A and increases the p_v; 2) When the sun sets, the sharp decrease of temperature in area A raise the relative humidity. Consequently, a part of moisture follows Fick’s law and then transfers inward (as the arrows in Fig. 8 show), leading to the increment of p_v in area B; 3) As the night wore on (20:00-8:00), the building-envelope temperature further decreases, increasing relative humidity, and spreading the moisture in building envelopes to the ambient, which causes the p_v to decrease”

and the discussion on the urban heat island (UHI) was expanded on lines 357-361:

“If the UHI is more intense in period 1 (8:00-16:00) than in periods 2 and 3 (16:00-20:00 and 20:00-8:00), the HMA will become more apparent because the first step mentioned above will be enhanced and subsequently cause the building envelope to absorb much more moisture. Conversely, the HMA could be less obvious when the UHI in the last two periods is more intense.”

Comment 22: Explain further the role of solar radiation and wind-driven rain and their impact on the results obtained. This was not at all assessed in the paper. You need to consider that in practice, external wall insulation won't be just insulation on the external pane of the wall. Other materials will be installed and

Reply: Agree. The role of solar radiation and wind-driven rain and their impacts have critical effects on the obtained results. Therefore, we will specifically discuss the environmental factors in future studies, as written on lines 350-355:

“According to the above steps, the phenomenon of HMA will become more obvious when the heat flow and moisture flow increase, which means the distribution of moisture is closely related to the orientation because of the different intensity of solar radiation and moisture load caused by wind-driven rain. It is, therefore, necessary to analyse the moisture distribution in building envelopes that face different orientations in future studies. The mould risk shall also be apparently different when the orientation changes.”

The study objects were selected from the existing atlas (Reference [20-22]), in which other materials, such as finishing materials, are not demonstrated. Following the atlas, the ideal building envelopes were thus employed to display the moisture distribution as well as the transfer process of heat and moisture in such a category of building envelope.

Comment 23: Explain in more detail the white dew and cold dew concepts

Reply: Thanks for your reminder. Detailed explanations of the 15^th solar term (White Dew) and the 17^th solar term (Cold Dew) were supplemented on lines 283-292:

“White Dew, the 15th solar term of the year, indicates the real beginning of cool autumn. At the night during this period, the temperature declines gradually and the vapour in the air often condenses into dew, which looks like white, on the foliage of plants or the exterior surface of buildings. Different from White Dew, which means the weather transitions from hot to cool, Cold Dew, as the 17th solar term in late autumn, indicates that the weather transitions from cool to cold. At this time, the air temperature is much low than during White Dew in most areas of China, and the dew is becoming frost. Therefore, the water vapour in the air condenses easily between these two solar terms due to the considerable diurnal temperature variation, which promotes spore germination and mycelial growth.”

Reply to Reviewer 2

General comments: Very interesting article. However, the information and messages the authors want to convey are unclear on several occasions. Proofreading might help to communicate the messages more effectively.

Reply: Thank you for your thoughtful comments and suggestions. Your detailed comments are replied to below. We would like to express our gratitude for your affirmation. Your constructive comments are very useful to us, which can help us improve the quality of our paper. We shall now address each of your specific comments.

Comment 1: 45-47 Could you please rephrase / Also not entirely true (Can provide a few references but it might be a little impolite

(Ilomets, S., Kalamees, T. Evaluation of the criticality of thermal bridges. J Build Rehabil 1, 11 (2016). https://doi.org/10.1007/s41024-016-0005-6

Sedlbauer, K. (2001) Prediction of Mould Fungus Formation on the Surface of and inside Building Components. Ph.D. Dissertation, Stuttgart University, Stuttgart)

Reply: Thank you for your excellent suggestion. Both the two literature provides great support and reference for our study. The former (Reference [12] in the paper) could be used as evidence to explain that the risks of mould and condensation in the area of thermal bridges differ from the other areas. Whereas the latter (Reference [25] in the paper) established the isopleth system, which was employed as the evaluation model of mould growth in this study, and further proposed the method of using the isopleth system under transient conditions.

Consequently, the sentences were revised to lines 45-49:

“Whereas the above issues could be apparently magnified by thermal bridges because the transfer process of heat and moisture in the thermal bridge area differs from that in other areas. In order to eliminate the negative effects of thermal bridges, a long-term evaluation of the moisture distribution in the building envelope is urgently required.”

Comment 2: 50-51 occupies the largest area?

Reply: Thanks for your reminder. The sentence was rewritten:

“The wall-to-floor thermal bridge (WFTB) takes the most considerable fraction of the building envelope and has the largest heat flux.”

That means the WFTB has the largest proportion among all kinds of thermal bridges and therefore most worthy of investigation.

Comment 3: 246 Figure 7 The y-axis of this figure is a bit unclear. Could you please explain a little bit more what information does this figure wants to convey?

Reply: Thanks for your reminder. The figure was revised (lines 293-300). The illustrations in each subgraph of Fig. 7 can make it clear where we have assessed mould growth. And the sentences (lines 273-278) explain the information conveyed by the figure:

“Fig. 7 gives the rate of mycelial growth (RMG) along different cross-sections (see Fig. 2 and the illustrations in Fig. 7) in the year. The uninsulated and insulated WFTBs are represented by cross-sections uB and iB, respectively. While both cross-section uA and cross-section iA represent the main part of the wall as this area has beyond the influence range of WFTBs. Further, different chromas of the colour in Fig. 7 represent different growth rates of mycelia, i.e., the darker the higher the growth rate, whereas the lighter the lower the growth rate.”

Comment 4: 246-256 I believe it is very difficult for fungi to grow inside such a construction even if the temperature and relative humidity conditions are favourable for growth. Two major reasons for this are 1st) there are no air-gaps between the elements of the construction so it is very unlikely that fungal spores could have been stored and would be able to flourish inside the material and  2nd) the materials used are concrete, expanded polystyrene and  autoclaved aerated concrete and cement mortar so the availability of nutrients is debatable.

Reply: Agree. The influence of air on mould growth was neglected in our study, which should be taken into consideration in future studies. But even so, the evaluation results can still indicate which areas and periods are favourable to mould growth, and the influence of the building envelope structure (e.g., insulated or not) on mould growth can also be qualitatively analysed. Besides, when there are tiny cracks or breaks appear on the wall surface, all conditions for spore germination are then met, which could finally lead to mould growth inside the wall, as the literature indicates:

“Moisture through breaks in the building envelope … creates a condition for mould growth when, inevitably, spores are also drawn into the building … especially during Canadian winters, this humid air will condense within the walls and thus becomes an ideal location for fungal growth” in Reference [7].

In order to account for the influence of the substrate, i.e., the building material itself and its possible soiling, on the formation of mould fungi, isopleth systems for four substrate categories are suggested that could be derived from experimental examinations. The materials used in the study (including cement mortar, concrete, expanded polystyrene, and autoclaved aerated concrete) are renderings or mineral building materials, which belong to Substrate category II, i.e., building materials with porous structure such as renderings, mineral building materials, certain wood species as well as insulation material not covered by Substrate category I. Therefore, the isopleth system Substrate category II was employed in our study.

(K. Sedlbauer, Prediction of Mould Growth by Hygrothermal Calculation, Journal of Thermal Env. & Bldg. Sci., Vol. 25, No. 4, DOI: 10.1106/109719602024093)

Comment 5: 260-268 These statements might be true for the case examined in the context of this study but they cannot be generalized. The direction of the moisture transfer relies on the internal and external conditions and in different climatic conditions the opposite direction might be the norm.

Reply: Thank you for your reminder. These statements were restricted:

“Under the selected indoor and outdoor boundary conditions” on lines 302-303.

Comment 6: 263-264 Could you please explain this a little more

Reply: Thank you for the reminder. The explanation was expanded on lines 305-310:

“Whereas the red boxes in Fig. 7 show a phenomenon that does not conform to the above-mentioned growth trend, i.e., the mould grows only inside the building envelope and the surface part has less risk of mould growth. This phenomenon can be attributed to the existence of HMA (see Fig. 6-a), which abnormally increased the relative humidity inside the building envelope and thus created an appropriate microclimate for mould growth.”

Comment 7: 309-310 These conclusions can be drawn only for the cases examined in the context of this paper. Please avoid generalizing these conclusions.

Reply: Thanks for the kind reminder. A sentence (lines 403-406) was added to limit the scope of application of the conclusions drawn in our study:

“However, it should be noted that the above conclusions were drawn for the specific case located in the HSCW climate zone and serviced by the air-conditioning system that operated in an intermittent mode, whether the conclusion could be generalized to other cases should be further discussed.”

Comment 8: 321-322 The 4 and 5 conclusions are debatable. As mentioned earlier it is very unlikely that mould could grow inside the building construction. Therefore, the seasonal effect on the temperature and RH conditions within the construction cannot be used to assess whether the conditions become favourable for mould growth during different seasons.

Reply: Thank you for your suggestion. Conclusions 4 and 5 were revised on lines 392-395 (“Due to the dependence on background temperature and relative humidity, mould growth shows a significant seasonality. The distribution of moisture on the surface or inside the building envelope could also influence spore germination and mycelial growth.”) to avoid excessive generalization.

Language comments:

37-39 Could you please rephrase this sentence?

41 This part could be changed: Further, Mould/ indoor surface

41-43 Could you please rephrase this sentence?

44 negative effects … is (are)more apparent

51-52 This a little unclear could you please rephrase?

80-81 Could you please rephrase

82-83 bring out the moisture flow, Eq (7) are used… could you please rephrase

248-252 Could you please rephrase?

260 The moisture affects the fungal growth. Seasons have an effect on fungal growth because of the changes in temperature and RH.

280-282 Please rephrase

294 Please rephrase

329-330 Please rephrase.

Reply: Thank you for your suggestions. These issues were carefully resolved.

Reply to reviewers’ comments

The moisture distribution in wall-to-floor thermal bridges and its influence on mould growth

by Yucong Xue, Yifan Fan, Jian Ge, submitted to UCL Open: Environment

We thank the editor and reviewers for the detailed and thoughtful suggestions. Replies to these comments are presented below.

Reply to Reviewer 1

General comments: This document needs proofreading

Reply: Thank you for your considerable effort in improving the quality of our paper. Your comments were very helpful and are addressed individually below.

Specific comments:

Comment 1: There are a number of sentences where more information is needed  (e.g., line number 16, where was moisture distribution modelled?

Reply: Thank you for your comment. A sentence was added to clarify where the moisture distribution was modelled.

“in a humid and hot summer cold winter region of China (Hangzhou City)” on lines 15-16.

Sentences on lines 145-146 (The indoor environment data and meteorological data last for a year in Hangzhou, a typical city in the HSCW climate zone, are adopted as the ambient conditions) also indicate that the meteorological data for the boundary conditions of the numerical simulation are taken from a weather station in Hangzhou. Whereas the indoor background condition referred to the hygrothermal record of a typical residential building located in that city.

Comment 2: In line 42, the author referred to condensation for the germination and development of mould, however, mould only develop under high levels of humidity and not condensation.

Reply: Thanks for the excellent suggestion. There are some studies implying that condensation may result in mould growth.

“Especially during Canadian winters, this humid air will condense within the walls and thus becomes an ideal location for fungal growth” in Reference [7].

“Moisture condensation …, which also can aggravate the growth and reproduction of fungi.” in Reference [8].

“Mould growth … can easily geminate and expand …, mainly through condensation within a building form.” in Reference [9].

According to the above literature, high levels of humidity are bound to induce mould growth and condensation. However, the authors believe that whether condensation is a cause of mould development or it is adverse to mould growth needs to be further studied and discussed.

Comment 3: Also, in line 42, the authors indicate that mould could grow inside building envelopes. Please provide a few examples of where inside the envelope, mould could grow.

Reply: Thank you for the reminder. There are considerable studies indicating that mould could grow inside the building envelopes.

“Moisture through breaks in the building envelope … creates a condition for mould growth when, inevitably, spores are also drawn into the building” in Reference [7].

“Especially during Canadian winters, this humid air will condense within the walls and thus becomes an ideal location for fungal growth” in Reference [7].

“Mould growth … can easily geminate and expand inside building envelopes” in Reference [9].

“Case studies of housing in cooler climate zones investigating interstitial mould within the building envelope …” in Reference [10].

“When the relative humidity of wall inside … reaches the critical condition, there will be a great mould risk.” in Reference [11].

According to the above literature, it can be found that mould could grow at the interface between two elements of building envelopes (e.g., the interface of the beam and the wall), as well as the breaks in building envelopes, i.e., mould may grow in any area of building envelopes, as long as there is a break. Consequently, the mould risk predicted in this paper is only intended to provide a rough assessment of mould growth, not to imply mould must germinate.

Comment 4: It is not clear why the software COMSOL was used.

Reply: A sentence was added to clarify why COMSOL was used.

“Because the proposed partial differential equations in the developed models are fully coupled and highly nonlinear…” on lines 104-105.

This commercial software has been widely used to obtain the fields of temperature and relative humidity in the building envelope, as References [2-4, 11] show.

Comment 5: More details should be provided regarding the weather climate used in the modelling presented in Figure 2. You refer to a climate zone in China.

Reply: The weather climate used in the modelling presented in Fig. 2 has been introduced in Section 2.3.2 in detail. The hot summer and cold winter zone of China is a typical hot-humid climatic region, which has over 40% of the total population of China and shares 48% of China’s gross domestic product. The target building was located in Hangzhou, a typical city in the HSCW climate zone.

Comment 6: Fig 2a should be uninsulated, while 2b insulated. Please amend.

Reply: Thank you for the kind reminder. The relative sentences were amended (lines 132-133).

Comment 7: You also refer in section 2. 3.1 to an existing Atlas; what exactly is this?

Reply: Thanks for the reminder. Some references were supplemented (lines 130 and 468-475) as follows:

Reference [19],   China Institute of Building Standard Design & Research, Structure of Autoclaved Aerated Concrete (AAC) Blocks and Slabs (GJCT-016/06CG01), Beijing, 2007.

Reference [20],   China Institute of Building Standard Design & Research, Building Construction of Autoclaved Aerated Concrete (AAC) Blocks and Slabs (GJCT-009/06CJ05), Beijing, 2007.

Reference [21], Chongqing Construction Technology Development Center, Atlas of Architectural Structure of Self-insulation Wall with Autoclaved Aerated Concrete (DJBT-039/08J07), Chongqing, 2008.

Comment 8: In section 2.3.2 please provide more information on how data was collected from a residential building in Hangzhou.

Reply: Thank you for the suggestion. The collection method of indoor background conditions was introduced on lines 148-150:

“The temperature and relative humidity of indoor air at 1.1 m above the ground were real-time recorded by automatic RHT recorders [JTR08ZI, JANTYTECH Co., Ltd., Beijing, the P.R.C.].”

Comment 9: In figure 3, please use lines to express temperature and relative humidity. The use of dots makes it extremely difficult to read and understand the environmental conditions in both graphs.

Reply: Thanks for the suggestion. Figs. 3(a) and (b) were revised, in which the dots of indoor and outdoor temperature have been changed to the lines, whereas the dots of relative humidity are reserved. Since the relative humidity usually fluctuates violently, it is extremely difficult to distinguish if this parameter is drawn in the form of lines, as the followings show.

Comment 10: Correct the text in lines 181 and 182; it should read Figure 4a and 4b.

Reply: Thanks for the reminder. The sentence was revised (lines 191).

Comment 11: Explain what each of the values in Table 3 refers to. But also how they were used to assess the risk of mould growth. Did you consider time in the evaluation?  

Reply: The values in Table 3 are the coefficients of the two-term exponential ( ), which is the mathematical expression of the isopleth system for computational calculation purposes. That means that these values have no physical meaning.

The isopleth system gives the time required for spore germination and the growth rate of mycelia under different conditions, which are closely related to the time. It is, therefore, can be said that time was considered in the evaluation.

Comment 12: Please explain the concepts used in the analysis, moisture sink and moisture shadow. This is very unclear in the document.

Reply: Agree. For ease of understanding, the above-mentioned concepts were changed in expression, i.e., the moisture sink and the moisture shadow are now called the high moisture area (HMA) and the low moisture area (LMA) (lines 203-205).

Comment 13: Please add some explanation in Fig 5, so what do the colours represent; red=cold and blue=warm?

Reply: Thanks for the suggestion. A legend was supplemented in Fig. 5. The red and blue refer to high and low relative humidity, respectively.

Comment 14: Are you presenting in Fig 5 the results for the uninsulated or insulated detail?

Reply: Thanks for your insights. As an example, Fig. 5 is only used to illustrate and explain what the moisture sink and moisture shadow (i.e., HMA and LMA, respectively) are, so whether the WFTB is insulated or not does not have to be mentioned. The title of the figure was revised, which points out that the WFTB was insulated (lines 209-210).

Comment 15: Why is it important to calculate the area for each moisture sink and moisture shadow? Please explain, in more detail, how they were generated and how they can be used.

Reply: Thank you for your reminder. The explanation for the calculation of moisture sink and moisture shadow (i.e., HMA and LMA, respectively) and their potential value in the practical application is supplemented on lines 219-224:

“Calculating the A has a potential value in the practical application because it can provide guidance on the arrangement of the moisture insulation. For example, HMA confined to the range of the WFTB means that the moisture-proof measures for the WFTB alone are sufficient. Otherwise, the moisture-proof measures may need to be extended to the main part of the wall, as Fig. 5 shows. Similarly, the appearance of LMA means that there is less prone to mould growth and condensation than other adjacent areas.”

Comment 16: Please enlarge Fig 6. The moisture shadows and most of the information you are trying to describe in the text is unreadable.

Reply: Thanks for your reminder. The figure was redrawn (line 255).

Comment 17: In line 242, you refer to the germination of mould spores inside the building envelope; are you referring to the space between the insulation and concrete?

Reply: According to the following literature, it can be inferred that mould could grow at the interface between two elements of building envelopes (e.g., the interface of the beam and the wall), as well as the breaks in building envelopes.

“Moisture through breaks in the building envelope … creates a condition for mould growth when, inevitably, spores are also drawn into the building … especially during Canadian winters, this humid air will condense within the walls and thus becomes an ideal location for fungal growth” in Reference [7].

“Mould growth … can easily geminate and expand inside … a building form.” in Reference [9].

Comment 18: Regarding mould assessment, did you use the info in the isopleth to define transient conditions? The isopleths were created based on steady-state conditions.

Reply: Due to its convenience, the isopleth system was employed in our study to evaluate mould growth under transient boundary conditions. Dr. Klaus Sedlbauer, who proposed the isopleth system, indicates that such the isopleths can also be adopted under transient boundary conditions, though it was created based on steady-state conditions.

“To be in a position to compare the biological growth conditions with the calculated hygrothermal conditions, one has to compare, on basis of the isopleth model, the calculated transient courses of temperature and relative humidity in the building component surface with the spore germination time and mycelium growth data in the respective isopleth systems … The growth conditions characterized by the time courses of temperature and relative humidity, serve as input parameters. These microclimatic boundary conditions are entered into the isopleth systems as hourly values. The computer allows to carry out the evaluations on basis of the isopleth model automatically” in Reference [25].

However, it should also be admitted that the isopleth system is deficient when it is used in the transient case. That is, more frequent germination of spores than the actual situation will be predicted because an interim drying out of the fungi spores cannot be taken into account (lines 196-199).

Comment 19: Please better explain figure 7; it is unclear what exactly you are showing and where in the diagram and wall detail you have assessed mould growth. Also still very unclear how the risk of mould growth was calculated. What do the red arrows and red area represent?

Reply: Thanks for your reminder. The figure was revised (lines 293-300). We believe that the illustration in each subgraph can make it clear where we have assessed mould growth.

Following Sedlbauer [25], the calculation method was introduced on lines 200-204: “the calculated microclimatic boundary conditions, including both temperature and relative humidity, are entered into the isopleth systems as hourly values. If the growth conditions are above the respective LIM curve for a certain duration, mould activity may take place, which is automatically evaluated by the computer.”

As said on lines 303-305: “the moisture transfers from outside to inside in general, which results in the mould at the exterior surface growing earlier and faster than that inside the building envelopes.” Therefore, the red arrows in Fig. 7 are used to display the growth trend from outside to inside. Whereas the red boxes show a phenomenon that does not conform to the above-mentioned growth trend, i.e., the mould grows only inside the building envelope and the surface part has less risk of mould growth. This phenomenon can be attributed to the existence of HMA, which abnormally increased the relative humidity inside the building envelope and thus created an appropriate microclimate for mould growth.

Comment 20: Mould need time to germinate and grow. So, the conditions of RH and Temperature presented in the isopleths (Fig.4) need to be constantly occurring for the time there indicated for mould to germinate and grow. Under transient conditions, mould will take much longer or don't react to those conditions. Please explain and discuss.

Reply: Agree. Different hygrothermal environments change the development rate of spore and mycelia. Therefore, various isolines were proposed to evaluate different development rates under different conditions. The areas between the isolines are interpolated. The above method was detailed introduced in Reference [25] and is widely recognized and thus adopted in our study.

However, it was also admitted in Reference [25] that the method does not consider the conditions when mould will take much longer or do not react, which makes “(that) will therefore predict the germination of spores more often …”

In view of this defect, we explained it on lines 196-199:

“However, it should be mentioned that the isopleth system is deficient when it is used in the transient case. That is, more frequent germination of spores than the actual situation will be predicted because an interim drying out of the fungi spores cannot be taken into account”

and discussed on lines 326-332:

“However, when the microclimate in building envelopes frequently switches between appropriate and inappropriate, mould may take a much longer time to develop or even do not react to such conditions, which is not considered in the isopleth system. Therefore, the predicted mould risk is generally higher than the real situation because of the neglect of the interim drying out of the fungi spores. In future studies, another prediction model for mould growth, such as the VTT model or biohygrothermal model should be employed to further evaluate the mould risk.”

Comment 21: Regarding your discussion, please expand the discussion on the urban heat island effect and how the phenomenon found could be affected in winter.

Reply: Thanks for the suggestion. The process of moisture accumulation (i.e., HMA) was discussed in detail on lines 333-346:

“Enhancing our understanding of the causes of the HMA helps to take measures to mitigate moisture accumulation. Therefore, the year-average profiles of the partial pressure of water vapour (p_v) in the insulated WFTB (x=0-150 mm, y=800 mm) are displayed in Fig. 8 The three types of lines refer to period 1 (8:00-16:00), period 2 (16:00-20:00), and period 3 (20:00-8:00 the next day), respectively.

As Fig. 8 shows, the process of moisture accumulation can be concluded as follows: 1) in the daytime (8:00-16:00), the heat caused by the intense solar radiation is blocked in area A by the insulation layer, which results in a high temperature and low relative humidity here. Then, according to Darcy’s law, moisture transfers from the surrounding area to area A and increases the p_v; 2) When the sun sets, the sharp decrease of temperature in area A raise the relative humidity. Consequently, a part of moisture follows Fick’s law and then transfers inward (as the arrows in Fig. 8 show), leading to the increment of p_v in area B; 3) As the night wore on (20:00-8:00), the building-envelope temperature further decreases, increasing relative humidity, and spreading the moisture in building envelopes to the ambient, which causes the p_v to decrease”

and the discussion on the urban heat island (UHI) was expanded on lines 357-361:

“If the UHI is more intense in period 1 (8:00-16:00) than in periods 2 and 3 (16:00-20:00 and 20:00-8:00), the HMA will become more apparent because the first step mentioned above will be enhanced and subsequently cause the building envelope to absorb much more moisture. Conversely, the HMA could be less obvious when the UHI in the last two periods is more intense.”

Comment 22: Explain further the role of solar radiation and wind-driven rain and their impact on the results obtained. This was not at all assessed in the paper. You need to consider that in practice, external wall insulation won't be just insulation on the external pane of the wall. Other materials will be installed and

Reply: Agree. The role of solar radiation and wind-driven rain and their impacts have critical effects on the obtained results. Therefore, we will specifically discuss the environmental factors in future studies, as written on lines 350-355:

“According to the above steps, the phenomenon of HMA will become more obvious when the heat flow and moisture flow increase, which means the distribution of moisture is closely related to the orientation because of the different intensity of solar radiation and moisture load caused by wind-driven rain. It is, therefore, necessary to analyse the moisture distribution in building envelopes that face different orientations in future studies. The mould risk shall also be apparently different when the orientation changes.”

The study objects were selected from the existing atlas (Reference [20-22]), in which other materials, such as finishing materials, are not demonstrated. Following the atlas, the ideal building envelopes were thus employed to display the moisture distribution as well as the transfer process of heat and moisture in such a category of building envelope.

Comment 23: Explain in more detail the white dew and cold dew concepts

Reply: Thanks for your reminder. Detailed explanations of the 15^th solar term (White Dew) and the 17^th solar term (Cold Dew) were supplemented on lines 283-292:

“White Dew, the 15th solar term of the year, indicates the real beginning of cool autumn. At the night during this period, the temperature declines gradually and the vapour in the air often condenses into dew, which looks like white, on the foliage of plants or the exterior surface of buildings. Different from White Dew, which means the weather transitions from hot to cool, Cold Dew, as the 17th solar term in late autumn, indicates that the weather transitions from cool to cold. At this time, the air temperature is much low than during White Dew in most areas of China, and the dew is becoming frost. Therefore, the water vapour in the air condenses easily between these two solar terms due to the considerable diurnal temperature variation, which promotes spore germination and mycelial growth.”

Reply to Reviewer 2

General comments: Very interesting article. However, the information and messages the authors want to convey are unclear on several occasions. Proofreading might help to communicate the messages more effectively.

Reply: Thank you for your thoughtful comments and suggestions. Your detailed comments are replied to below. We would like to express our gratitude for your affirmation. Your constructive comments are very useful to us, which can help us improve the quality of our paper. We shall now address each of your specific comments.

Comment 1: 45-47 Could you please rephrase / Also not entirely true (Can provide a few references but it might be a little impolite

(Ilomets, S., Kalamees, T. Evaluation of the criticality of thermal bridges. J Build Rehabil 1, 11 (2016). https://doi.org/10.1007/s41024-016-0005-6

Sedlbauer, K. (2001) Prediction of Mould Fungus Formation on the Surface of and inside Building Components. Ph.D. Dissertation, Stuttgart University, Stuttgart)

Reply: Thank you for your excellent suggestion. Both the two literature provides great support and reference for our study. The former (Reference [12] in the paper) could be used as evidence to explain that the risks of mould and condensation in the area of thermal bridges differ from the other areas. Whereas the latter (Reference [25] in the paper) established the isopleth system, which was employed as the evaluation model of mould growth in this study, and further proposed the method of using the isopleth system under transient conditions.

Consequently, the sentences were revised to lines 45-49:

“Whereas the above issues could be apparently magnified by thermal bridges because the transfer process of heat and moisture in the thermal bridge area differs from that in other areas. In order to eliminate the negative effects of thermal bridges, a long-term evaluation of the moisture distribution in the building envelope is urgently required.”

Comment 2: 50-51 occupies the largest area?

Reply: Thanks for your reminder. The sentence was rewritten:

“The wall-to-floor thermal bridge (WFTB) takes the most considerable fraction of the building envelope and has the largest heat flux.”

That means the WFTB has the largest proportion among all kinds of thermal bridges and therefore most worthy of investigation.

Comment 3: 246 Figure 7 The y-axis of this figure is a bit unclear. Could you please explain a little bit more what information does this figure wants to convey?

Reply: Thanks for your reminder. The figure was revised (lines 293-300). The illustrations in each subgraph of Fig. 7 can make it clear where we have assessed mould growth. And the sentences (lines 273-278) explain the information conveyed by the figure:

“Fig. 7 gives the rate of mycelial growth (RMG) along different cross-sections (see Fig. 2 and the illustrations in Fig. 7) in the year. The uninsulated and insulated WFTBs are represented by cross-sections uB and iB, respectively. While both cross-section uA and cross-section iA represent the main part of the wall as this area has beyond the influence range of WFTBs. Further, different chromas of the colour in Fig. 7 represent different growth rates of mycelia, i.e., the darker the higher the growth rate, whereas the lighter the lower the growth rate.”

Comment 4: 246-256 I believe it is very difficult for fungi to grow inside such a construction even if the temperature and relative humidity conditions are favourable for growth. Two major reasons for this are 1st) there are no air-gaps between the elements of the construction so it is very unlikely that fungal spores could have been stored and would be able to flourish inside the material and  2nd) the materials used are concrete, expanded polystyrene and  autoclaved aerated concrete and cement mortar so the availability of nutrients is debatable.

Reply: Agree. The influence of air on mould growth was neglected in our study, which should be taken into consideration in future studies. But even so, the evaluation results can still indicate which areas and periods are favourable to mould growth, and the influence of the building envelope structure (e.g., insulated or not) on mould growth can also be qualitatively analysed. Besides, when there are tiny cracks or breaks appear on the wall surface, all conditions for spore germination are then met, which could finally lead to mould growth inside the wall, as the literature indicates:

“Moisture through breaks in the building envelope … creates a condition for mould growth when, inevitably, spores are also drawn into the building … especially during Canadian winters, this humid air will condense within the walls and thus becomes an ideal location for fungal growth” in Reference [7].

In order to account for the influence of the substrate, i.e., the building material itself and its possible soiling, on the formation of mould fungi, isopleth systems for four substrate categories are suggested that could be derived from experimental examinations. The materials used in the study (including cement mortar, concrete, expanded polystyrene, and autoclaved aerated concrete) are renderings or mineral building materials, which belong to Substrate category II, i.e., building materials with porous structure such as renderings, mineral building materials, certain wood species as well as insulation material not covered by Substrate category I. Therefore, the isopleth system Substrate category II was employed in our study.

(K. Sedlbauer, Prediction of Mould Growth by Hygrothermal Calculation, Journal of Thermal Env. & Bldg. Sci., Vol. 25, No. 4, DOI: 10.1106/109719602024093)

Comment 5: 260-268 These statements might be true for the case examined in the context of this study but they cannot be generalized. The direction of the moisture transfer relies on the internal and external conditions and in different climatic conditions the opposite direction might be the norm.

Reply: Thank you for your reminder. These statements were restricted:

“Under the selected indoor and outdoor boundary conditions” on lines 302-303.

Comment 6: 263-264 Could you please explain this a little more

Reply: Thank you for the reminder. The explanation was expanded on lines 305-310:

“Whereas the red boxes in Fig. 7 show a phenomenon that does not conform to the above-mentioned growth trend, i.e., the mould grows only inside the building envelope and the surface part has less risk of mould growth. This phenomenon can be attributed to the existence of HMA (see Fig. 6-a), which abnormally increased the relative humidity inside the building envelope and thus created an appropriate microclimate for mould growth.”

Comment 7: 309-310 These conclusions can be drawn only for the cases examined in the context of this paper. Please avoid generalizing these conclusions.

Reply: Thanks for the kind reminder. A sentence (lines 403-406) was added to limit the scope of application of the conclusions drawn in our study:

“However, it should be noted that the above conclusions were drawn for the specific case located in the HSCW climate zone and serviced by the air-conditioning system that operated in an intermittent mode, whether the conclusion could be generalized to other cases should be further discussed.”

Comment 8: 321-322 The 4 and 5 conclusions are debatable. As mentioned earlier it is very unlikely that mould could grow inside the building construction. Therefore, the seasonal effect on the temperature and RH conditions within the construction cannot be used to assess whether the conditions become favourable for mould growth during different seasons.

Reply: Thank you for your suggestion. Conclusions 4 and 5 were revised on lines 392-395 (“Due to the dependence on background temperature and relative humidity, mould growth shows a significant seasonality. The distribution of moisture on the surface or inside the building envelope could also influence spore germination and mycelial growth.”) to avoid excessive generalization.

Language comments:

37-39 Could you please rephrase this sentence?

41 This part could be changed: Further, Mould/ indoor surface

41-43 Could you please rephrase this sentence?

44 negative effects … is (are)more apparent

51-52 This a little unclear could you please rephrase?

80-81 Could you please rephrase

82-83 bring out the moisture flow, Eq (7) are used… could you please rephrase

248-252 Could you please rephrase?

260 The moisture affects the fungal growth. Seasons have an effect on fungal growth because of the changes in temperature and RH.

280-282 Please rephrase

294 Please rephrase

329-330 Please rephrase.

Reply: Thank you for your suggestions. These issues were carefully resolved.

Moisture in the building envelopes increase the energy consumption of buildings and induce mould growth, which may be amplified within the area of thermal bridges due to their different hygrothermal properties and complex structures. In this study, we aimed to (1) reveal the moisture distribution in the typical thermal bridge (i.e., wall-to-floor thermal bridge, WFTB) and its surrounding area, and (2) investigate the mould growth in the building envelope that includes both WFTB and the main part of the wall, in a humid and hot summer cold winter region of China (Hangzhou City). The transient numerical simulations that lasted for five years were performed to model the moisture distribution. Simulated results indicate that the moisture distribution presents significant seasonal and spatial differences due to the WFTB. The areas where moisture accumulates have a higher risk of mould growth. The thermal insulation layer laid on the exterior surface of WFTB can reduce the overall humidity while uneven moisture distribution, which may promote mould growth and water vapour condensation.