Comment on acp-2020-1262

Jones et al. present an inverse modeling study on methane emissions from the city of Indianapolis. While a number of studies have been published to address the same problem, the study is unique and novel by using data from five portable solar-tracking Fourier transform infrared (FTIR) spectrometers and an inversion method devised to comprehensively account for uncertainties, especially those uncertainties that are not often adequately addressed in the literature, namely, uncertainties of the background methane concentration, and uncertainties in the spatial pattern of the prior inventory. As such, this study is positioned to complement previous efforts in painting a fuller picture on the issue and to help point to future directions of research. The paper is well written, including key information regarding the inversion method and a concise presentation of the key results in figures and tables. I recommend publication of the paper, and provide the following questions and comments for the authors to consider. I realize addressing the comments below might require some additional model experiments. I encourage the authors to do what they deem as appropriate with available resources and time, as I believe a better understanding and discussion of these issues would further strengthen the paper.

years of ceilometer data from 138 continental sites in the Great Plains of the USA ( Figure R1, this figure is also provided as Figure A2 in the Appendix of the paper). These ceilometer data are derived from Automated Surface Observation System (ASOS). The data source is https://mesonet.agron.iastate.edu/request/download.phtml (last access: May 2021), which is maintained by Iowa Environmental Mesonet of Iowa State University. The data period used in this 55 study is taken from 2017 to 2020 because during this period, the ceilometers provide better time resolution of cloud base measurements. The ASOS uses a laser beam ceilometer with a time interval of 5-30 minutes, with a vertical 60 resolution of ~30 m, and a vertical detection range of ~3700 m. In order to ensure the data quality of the ASOS ceilometer observations, we only use ceilometer data with CBH less than 3000 m and limit the number of valid cloud observations to no less than 2 during 1 hour.
Then, based on the CBH retrieval algorithm developed from the cloud observations over ocean, we conducted the same experiment on land to test the applicability of our algorithm. Since the cloud 65 base is not as homogeneous over land as over ocean, we consider using the cloud information below the first peak nearest to the surface in the cloud fraction profile of 1° scene as a proxy for all cloud base information in this scene (which we defined as the first local peak above surface). In this way, we avoid missing the newly developed clouds with small size. Therefore instead of using Hmin at 10 % quantile of all clouds as the initial CBH over ocean, we tested the CBH at different quartiles of the 70 first local peak as the initial CBH for the scene. Table R1 shows the corresponding statistical results (this table is also provided as Table B1 in the Appendix of the paper), which can be seen there is a minimum RMSE when the initial CALIPSO CBH is at the 40% quantile of the first local peak which closest to surface. This has also been verified in the results of other years (2007-2016, not shown).
Thus on land the CALIPSO-retrieved initial CBH is 40% quantile of first local peak, while over the 75 ocean it is Hmin at 10 % quantile. Then, based on the CBH data obtained from the above processing, we further tested the effects of Fmulti, Elidar and Flidar_full over land following the same process as over ocean, as showed in Figure R2 80 (this figure is also provided as Figure A3 in the Appendix of the manuscript). From the results it can be seen that the optimal thresholds for Elidar>50%, and Flidar_full>50% over land are consistent with those over ocean, which also shows that the CBH retrieval algorithm we developed based on cloud observations from the ocean is applicable on land. The parameters Fmulti<40% has little meaning over land due to the scarcity of the cases that fulfil that condition. It is kept over land for consistency with 85 the ocean criteria. As mentioned before due to the complexity of topography and land surface situation, the cloud bases height varies at larger spatial scales. The 150 km distance between the shortest distance from the 95 CALIPSO ground track to the ceilometer site cannot be used for over land validation. We have to shrink the distance to minimize the spatial variability due to the changes over land. We tested the effect of distance (that is the shortest distance from the CALIPSO ground track to the ceilometer site) and observation time on the retrieval results ( Figure R3, which is also provided as Figure A4 in the Appendix of the manuscript). The results ( Figure R3b) show that the absolute error between the 100 CALIPSO CBH and the ceilometer CBH becomes smaller as the distance decreases, stabilizing at distances less than 50 km. It is therefore preferable to limit the distance to 50 km for studies on land to better meet the assumptions of a homogeneous CBH within 1° scenes. It can also be seen that the cloud base heights are more evenly distributed during the day-time ( Figure R3a, 300-1800 m) than at night, while at night CBHs are mainly concentrated below about 700 m and are most frequent very 105 near the surface, where validation becomes unreliable. In addition to the distance limitation, the cloud base homogeneity further constrained by comparing the lifted condensation level (HLCL) to ceilometer cloud base height. To satisfy the cloud base homogeneity assumption (Efraim et al., 2020), cases are selected when the absolute difference between the HLCL(calculated from ASOSobserved air temperature and dew point temperature) and ceilometer CBH is less than 200 m. In 110 summary, the ceilometer measurements need to satisfy the following conditions for validating CALIPSO CBH retrieval: 1) The ceilometer is within 50 km radius to the center of CALIPSO ground track; 2) the ceilometer measured CBH should have an absolute difference less than 200 m against HLCL as calculated from surface measured air temperature and dew point.  . The statistical analysis of these matching cases ( Figure R4a) shows that, the CALIPSOretrieved CBH has a good consistency with the CBH observed by the ceilometers at these continental sites. The R is 0.92, the RMSE is 217.2 m and the standard deviation is 217.1 m. The cumulative distribution of the CBH difference between CALIPSO and ceilometer in Figure R4b indicates that  Figure R4e it can be seen that the CBH at night is mainly concentrated below 800 m. This may be due to the effect of low-level clouds and fog patches, which possibly contaminate the ceilometer data. Therefore, it is unreasonable to validate the CALIPSO retrieval against the night-time ceilometer 135 measurements and day-time data are more suitable for validation. The above analysis has been added to the Section 4 (Evaluation of CALIPSO-retrieved CBH) as a new section as follow:

Over land
To validate the applicability over land of the CBH retrieval algorithm, we conducted additional validation experiments using 4 years of continental ceilometer data from 138 sites in the southern Great Plains of the USA (as showed in Figure A2). The data period is taken from 2017 to 2020 because during this period, the ceilometers provide better time resolution of cloud base 150 measurements. Since the cloud base is not as homogeneous over land as over ocean, we consider using the cloud information below the first peak nearest to the surface in the cloud fraction profile of 1° scenes as a proxy for all cloud base information in this scene (which we defined as the first local peak above surface). In this way, we avoid missing the newly developed clouds with small size. Therefore instead of using Hmin at 10 % quantile of all clouds as the initial CBH over ocean, we 155 tested the CBH at different quartiles of the first local peak as the initial CBH for the scene (detailed information is provided in Table B1 in the Appendix). The results show that there is a shallow minimum RMSE when the initial CALIPSO CBH is at the 40 % quantile of the first local peak which closest to surface. Thus on land the CALIPSO-retrieved initial CBH is 40 % quantile of the first local peak, while over the ocean it is Hmin at 10 % quantile. Then, based on the CBH data obtained from 160 the above processing, we further tested the effects of Fmulti, Elidar and Flidar_full over land following the same process as over ocean, as showed in Figure A3 in the Appendix. From the results it can be seen that the optimal thresholds for these parameters (Fmulti<40 %, Elidar>50 %, and Flidar_full>50 %) on land are consistent with those over ocean, which also shows that the CBH retrieval algorithm we developed based on cloud observations from the ocean is applicable on land. These final criteria for 165 CALIPSO CBH retrieval used over ocean and land is also summarized is Table B2.
As mentioned before due to the complexity of topography and land surface situation, the cloud bases height varies at larger spatial scales. The 150 km distance between the shortest distance from the CALIPSO ground track to the ceilometer site cannot be used for over land validation. We have to shrink the distance to minimize the spatial variability due to the changes over land. We tested the 170 effect of distance (that is the shortest distance from the CALIPSO ground track to the ceilometer site) and observation time on the retrieval results ( Figure A4 in the Appendix). The results ( Figure A4b) show that the absolute error between the CALIPSO CBH and the ceilometer CBH becomes smaller as the distance decreases and stabilizes at distances less than 50 km. It is therefore preferable to limit the distance to 50 km for studies on land to better meet the assumptions of a homogeneous CBH 175 within the scene. It can also be seen that the cloud base heights are more evenly distributed during the day-time (Figure A4a, 300-1800 m) than at night, while at night CBHs are mainly concentrated below about 700 m. In addition to the distance limitation, the cloud base homogeneity is further constrained by comparing the lifted condensation level (HLCL) to the ceilometer cloud base height.
To satisfy the cloud base homogeneity assumption (Efraim et al., 2020), cases are selected when the 180 absolute difference between the HLCL (calculated from ASOS-observed air temperature and dew point temperature) and ceilometer CBH is less than 200. In summary, the ceilometer measurements over land need to satisfy the following conditions for validating CALIPSO CBH retrieval: 1) The ceilometer is within 50 km radius to the centre of CALIPSO ground track; 2) the ceilometermeasured CBH should have an absolute difference less than 200 m against HLCL as calculated from 185 the surface measured air temperature and dew point.
Ceilometer data that passed these conditions were used for validating the CALIPSO retrieved cloud base height. Figure 8 shows  Figure 8e it can be observed that the CBH at night is mainly concentrated below 800 m. This might be due to the effect of low-level clouds and fog patches, which possibly contaminate the ceilometer data. Therefore, it is unreasonable to validate the CALIPSO retrieval against the night-time ceilometer measurements and day-time data are more suitable for validation.

Question 2:
How do you consider the clouds with multiple layers? Particularly, there are considerable amount of multiple layer clouds on the globe. How do you consider the time representation error and sample representation errors when you do the statistics for only partial clouds that you can retrieve?

RE:
We exclude the situations where elevated obscure cloud bases. For each CALIPSO 1° scene, 205 approximately 345 CALIPSO lidar profiles exist and we extracted the cloud base height using only the profiles containing single-layer clouds. In addition, we also considered the effect of the fraction of multi-layered clouds in each scene; when the fraction of multi-layered clouds was greater than 40%, the CALIPSO-retrieved CBH for that scene was considered invalid. That is, we qualify that the cloud base heights only for the conditions satisfying the multiple-layer cloud selection criteria.

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Moreover, given there are considerable amount of multi-layered clouds on the globe, we have actually been more lenient in our restrictions on multilayered clouds, rejecting only a small number of data with unusually large multilayered cloud fractions (greater than 40%) on a global scale. Figure  R5 shows the ratio of scenes were rejected based on which criterion (this figure is also provided as Figure A6 in the Appendix of the manuscript). It can be seen that only a small number of data (~0.5%) 215 were rejected by the multilayer cloud criteria ( Figure R5b). The results also show a global average rejection ratio of ~29.5%, which is mainly influenced from penetration efficiency (penetration efficiency of 333-m resolution cloud: 28.4%; penetration efficiency of all resolution cloud: 29.5%).
Since the CBH is homogeneous over a certain range (over ocean: 100 km; over land: 50 km), as pointed out in Figure R3, it is reasonable to use a permeable cloud base as a proxy for the entire 220 cloud base of the scene.
We have also added these information to the manuscript:

Paragraph 4 in Section 5.1:
We also counted the ratio of scenes were rejected based on each criterion (as shown in Figure A6 in the Appendix). The results show a global average rejection ratio of ~29.5 %, which is mainly 225 influenced from penetration efficiency (penetration efficiency of 333-m resolution cloud: 28.4 %; penetration efficiency of all resolution cloud: 29.5 %), with less influence from multilayer clouds. In addition, the results in Figure A6a show that a higher rejection ratio is at high latitudes than at middle and low latitudes, particularly in the Southern Ocean region.  4. Line 50, why? For radar-based cloud retrieval, I do not think CTH is crucial unless the retrieval method is based on MWR LWP (to adjust). RE: Thank you for your comment. This sentence about CTH at Paragraph 2 in Introduction has been removed. 5. Line 59-60, how about the satellite radar observations, such as CloudSat? 265 RE: For CloudSat radar observations, we have added the following to the paper.

Paragraph 3 in Introduction:
CloudSat is an essential active cloud radar observation satellite. However, CloudSat has difficulties to retrieve CBH of low-level clouds for the following reasons: a) The ground clutter prevents detection of very low base. b) Rain from precipitating clouds produces radar returns 270 below cloud base. c) Due to the dependence of radar reflectivity on the 6 th power of cloud droplet diameter, the reflectivity of clouds with small droplets can be below the CloudSat minimum detectable signal, especially near cloud base where cloud droplets are smallest. 6. Line 82-84, it is not always this case, depending on the amount of aerosols. This case is particularly significant over East Asia, South Asia and desert regions.

Section 2.2:
The temporal resolution of the ceilometer at Barbados site is 10 seconds, and the vertical resolution is 15 m.

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At the ENA site, the ceilometer has a temporal resolution of 16 seconds, a vertical resolution of 30 m and a maximum detection range of 7700 m. The ASOS uses a laser beam ceilometer with a time interval of 5-30 minutes, with a vertical resolution of ~30 m, and a vertical detection range of ~3700 m. In order to ensure the data quality of the ASOS ceilometer observations, we only use ceilometer data with cloud base heights less 295 than 3000 m. 8. Line 109-110. This sentence is too redundant. You can simply use "The retrieval algorithm is validated using the ground-based ceilometer observations." RE: Thank you for your suggestion. The sentence has been revised as "The retrieval algorithm is developed and validated using the ground-based ceilometer observations." at Paragraph 1 in 300 Section 2.2. 9. Line 110-111, do you have any reference or support that much of the low-level cloud occurs over the ocean, while it might be true? RE: The description here have been revised as following: Section 2.2: 305 The retrieval algorithm is developed and validated using the ground-based ceilometer observations. To represent the different types of low-level clouds around the world, we used ceilometer sites located at different latitudes over ocean and land (two marine sites and 138 continental sites) respectively to validate the CALIPSO-retrieved CBH. 10. Section 2, in addition to the ground-site observation based evaluation, why do not the authors We have perform a sensitivity study to the size of the domain as shown in above Figure R3. Over land, when the distance is less than 50 km, the deviation between CALIPSO-retrieved CBH and ceilometer CBH has little to do with the distance. (Please see the reply to Question 1 of 320 General comments for detailed responses.) Over ocean this distance can be extended to 150 km (Section 4.1 in the manuscript). 12. Line 125-126. Sine this assumption is a key basis of this study, the authors need approve its reliability based on further in-detail analysis using observations, such as what I mentioned above. RE: Please see the reply to Question 11 of Detailed comments.

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13. Line 135-139. The question is that clouds can form via various mechanisms, the mixing of cold and warm air masses, the surface heating, the fronts, the radiative cooling, and so on. Based on the point mentioned here, could all cloud bases be determined? If yes, may you please explain more? If not, how many clouds (in fraction) globally could be determined with this method? RE: Please see the reply to Question 2 of General comments for detailed responses.

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15. Figure 4 and corresponding analysis. As I know, there are long-term observations of clouds over the Azores site, why do not the authors use long-term observations to evaluate the performance of the retrieval algorithm? Anyway, the sample number seems too small to me in current Figure  4.

RE:
The results in Figure 4 are all available valid data for the year 2017 at the two marine sites.

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These data were used to develop our CBH retrieval method. To validate the applicability of the retrieval algorithm in this study and to increase the number of coincident satellite-and groundbased observations for validation, we conducted additional validation experiments using 4 years of ceilometer data from 138 terrestrial sites in the southern Great Plains of the USA. Please see the reply to Question 1 of General comments for detailed responses.

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16. Section 3.4.1 Are you sure with the method, all multi-layer clouds can be excluded.

RE:
The CBH information for this algorithm is extracted from the CALIPSO single layer cloud profile only. For the treatment of multi-layer clouds, please refer to the response to Question 2 of General comments. 17. Lines 260-270, with these limitations, I wonder how many cloud samples have been removed and 350 how many cloud samples are kept. In addition, the CALIPSO not continuously observe the clouds at a fixed location (coarse time resolution). How could these sample limitation, time limitation affect the statistical results obtained in later analysis (Section 5). RE: The remaining cases are those which boundary layer clouds are not obscured by higher layers and do not form a solid thick cloud deck. These are the conditions that allow us to sample the 355 cloud base heights. Moreover, we also have provided the geographic distribution of rejection ratio by each selection criterion in Figure R5. Please see the reply to Question 2 of General comments for detailed responses. In addition we address the sample and time limitations of CALIPSO by assuming that the cloud base height is homogeneous over a certain range (over ocean: ~100 km; over land: ~50 km), 360 which is consistent with the study of Mülmenstä dt et al. (2018). We also provide a detailed analysis of the effect of distance. Please see the reply to Question 1 of General comments for detailed responses. 18. Line 291, "indicates" -> "indicate" RE: This "indicates" has been revised as "indicate" at Paragraph 1 in Section 5.1.

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19. Line 294, do you have a reference to support this claim that there are more scenes with lots of optical thicker clouds and multilayer clouds over land. RE: According to the geographic distribution of rejection ratio by each selection criterion in Figure R5 (the reply to Question 2 of General comments), the description here has been revised as "…because there are more scenes with cloud bases above 3 km or more cloud free scenes (e.g.

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Sahara, Australia)" at Paragraph 1 in Section 5.1. 20. Line 297-300, personally, I think the CTHs are particularly large over the Tibetan Plateau region, which is worthy to mention. Also, you may compare your statistical findings (actually only partial of clouds existing) with those from MODIS (polar-orbiting satellite) and Himawari (such as Yang et al. 2020, doi: 10.1016/j.atmosres.2020.104927).

RE:
Thank you for your suggestion. We have added the following at Paragraph 2 in Section 5.1. In particular, there is a peak area of CTH in the Tibetan Plateau region, essentially greater than 2800 m, which is consistent with the conclusions obtained by Yang et al. (2020) based on high spatial resolution Himawari imager data.