Review of "Understanding variations in downwelling longwave radiation using Brutsaert's equation" by Tian et al.

A simple empirical model of surface downwelling longwave radiation (Rld) is evaluated against state of the art simulations and used to understand the driving factors influencing this important surface flux quantity. Others have applied or proposed empirical models of Rld which would be useful to refer to and discuss briefly e.g. Prata (1996) QJRMS doi:10.1002/qj.49712253306, Dilly & O'Brien (1998) QJRMS doi:10.1002/qj.49712454903 while there are also comparisons against reanalyses, more for clear-sky simulations e.g. Allan et al. (2004) JGR doi:10.1029/2004JD004816. Missing terms include well mixed greenhouse gas concentrations and large aerosol particles which can influence the Rld in drier atmospheres though may not contribute much for spatial/seasonal/diurnal variation discussed in the present study. Cloud base is also clearly important in determining the cloud radiative effect on Rld and the correlation between cloud and humidity could be implicitly included in the calibration of the equation. Analysing the importance of the different drivers on changes in Rld from year to year may lead to differing conclusions to spatial/seasonal variation yet may be more relevant to long term climate change though were not assessed. So some discussion of these issues along with limitations of the data sources would strengthen the manuscript in my opinion.  There are a number of further specific points that can be considered.

1) L20 - it should be stated if this is the spatial correlation which is much less stringent than for variability since there is a large amount of spatial autocorrelation yet large spatial ranges in driving terms 

2) L23 - presumably cloud is correlated to humidity so is the contribution from cloud also implicitly including a contribution from humidity via the calibration of the empirical formula?

3) L24 - It should be stated that this refers to spatial variation in aridity from one region to another rather than changes over time. This is an important distinction to make since the conclusion may differ depending on whether changes are spatial or for the same location over time (either seasonally or interannual also may differ in character)

4) L33 - Although Rld is the dominant term, since it is strongly correlated with surface emitted longwave due to coupling of surface and near surface tempertaure, the net longwave flux is quite small e.g. Wild (2020) Clim Dyn, doi:10.1007/s00382-020-05282-7 and yet more strongly influenced by emissivity changes

5) eq(4) - when cloud fraction is 100%, an emissivity of 1 is implied yet high altitude cloud will not emit much longwave to the surface. The authors should comment on the deficiencies in the empirical formulation

6) L62 - what is deemed "very good" agreement?

7) L67 Effects of cloud on surface longwave flux can also be estimated from cloudy minus clear-sky flux calculations e.g. Allan (2011) Met Apps doi:10.1002/met.285

8) L68 - in humid regions, since much of the longwave spectrum is saturated, much of the downward emission will be determined by the near surface temperature which may or may not reflect the heat content of the atmosphere and can also differ from the surface skin temperarture quite markedly leading to a large sensitivity to how this emitting temperature is defined e.g. Raisenen (1996) Tellus doi:10.1034/j.1600-0870.1996.t01-2-00004.x; Allan (2000) J. Clim doi:10.1175/1520-0442(2000)013<1951:EOSCSL>2.0.CO;2

9) L80 - full attribution would involve radiative transfer calculations which are more accurate than an empirical formula

10) L83 - since near surface temperature is more physically related to Rld than atmospheric heat storage, the referal to heat storage is not needed and not useful in my opinion

11) Section 2 can be improved by stating limitations and accuracies of the data and whether the analysis is restricted to monthly or hourly data. How is missing FLUXNET data accounted for, particularly in relation to sampling of the diurnal and seasonal cycle? Did the authors consider BSRN data which provide well calibrated Rld estimates from a number of sites or GEBA which provides more sites with a lower level of quality control e.g. Wild et al. (2017) ESSD doi:10.5194/essd-9-601-2017 or are these included in FLUXNET?

12) Figure 2 - is this monthly gridpoint data, or climatological mean or also higher resolution daily/hourly data. This information along with the time period considered seem necessary

13) Figure 4 - is this multiannual average and if so for what years? It would also be useful to show the actual dTa and dε. Were spatial maps of the maximum minus minimum considered like in Figure 5?

14) L158 - a map of FLUXNET coverage at the beginning would be useful (perhaps as dots on Figure 1 or an extra panel)

15) Figure 5 - I am used to seeing blue/red color scale to denote positive and negative values so a single color scale may be more appropriate. A total dRld map would also be useful and perhaps a residual in case the terms do not add up to the total or alternatively a map showing the dominant term in each region (T, fc, εcs)

16) L164 - it is not surprising that areas with very large seasonal temperature changes produce large changes in Rld and the changes are themselves determined by the very large downward solar changes. Over monsoon regions I expect that there is some compensation as it moves from hot/dry/clear to cool/moist/cloudy. Again, the mean dTa and dε would be useful to show. Cloud and humidity are correlated so I wonder if this effect accentuates the apparent influence of cloud?

17) L174 - I did not completely understand this sentence

18) Figure 6 - the caption needs more explanation. Are the map values the dRld compared to global (land) mean? I did not find the lower plots compelling since it is obvious the temperature effect relates to latitude (strength of the sun) and has no simple bearing on aridity so inferring relationships between temperature effect on aridity seem misleading (error bars are very large compared to the variation across AI). Contours of Aridity Index may be useful for interpretation

19) L209/L230 - "very well" and "very useful" are quite qualitative descriptions - how good is good enough? How does it compare to observational accuracy? 

20) Summary - a missing component of the work is to look at interannual changes over time and how tempertaure and humidity determine year to year changes in Rld. This may be quite different to seasonal and spatial changes which are strongly determined by solar forcing and yet be more relevant to longer term climate change.

This is a clear manuscript that cleanly demonstrates the utility of Brutsaert’s equation for calculating DLR from two easily observable state variables (two meter air temperature and vapor pressure).  I had never heard of Brutsaert’s empirical equation before reading this paper, and the manuscript gave some nice physical insights on DLR variations across time and space. One major question I have is, how does Brutsaert’s equation compare to radiative kernels, which have been used by a few recent studies (e.g. Shakespeare & Roderick 2022 and Vargas Zeppetello et al. 2019) to attribute changes in DLR to changes in near surface state variables? This might help give Brustaert’s equation a more interpretable physical intuition, because the kernels are calculated via climate models and their radiative transfer schemes. Other than that, I have a few minor comments, listed below.

Comments:

Figs 1 and 5: This is totally a personal preference, but I don’t like diverging colorbars when all the values are positive. I would use a sequential color bar for these figures to contrast them with the bias/difference maps in the rest of the paper.

Line 33: Check if it’s the dominant term (isn’t surface OLR bigger?)

Line 44: This is a nice description of the development of Brutsaert’s Equation, but I’d love for a bit more physical intuition of why we should expect the 1/T_a dependence of the emissivity on temperature. 

Lines 50-51: I understand this equation is empirical, so the units don’t have to make sense, but I think you should name the correct units for this equation in your description so readers who want to use this formula immediately know how to apply it. I also assume e_a corresponds to the 2m vapor pressure, but it’s not stated explicitly.

Line 62: Can you be specific about what “this” estimate refers to. Is it Eq. 4, or 5?

Lines 105-107: Is the cloud cover fraction from CERES used for all the calculations? If so, what’s the relationship between cloud cover calculated from CERES and the very specific way it is defined in Eq. 3?

Lines 127-131: Similar to my question about line 44, there’s not much physical explanation for these biases, the authors merely note that Brutsaert also discussed how the equation was biased for places with big temperature departures away from the global mean. I’m also not sure why the fact that the biases are less than the seasonal cycle is relevant.

Lines 132-135: Could the consistent positive bias in the all sky calculation be driven by the cloud fraction definition related to my comment on lines 105-107? I think the definition of cloud fraction in these equations is pretty important to potential biases.

Fig 3: Can you also show the biases from the AMERIFLUX dataset? Do those biases line up with the expectations from the global datasets?

Line 147: Is it small compared to delta R_ea or just small compared to delta R T from the Stephan Boltzman law? Are the water vapor and temperature components from the the emissivity equation of the same order of magnitude? If so, I think both temperature terms should be included.

Lines 166-169: The monsoonal regions really stick out as having a sizable water vapor control on DLR. Even though the cloud cover causes the changes in seasonal cycle strength, the ultimate cause is changing water vapor or monsoonal circulation patterns, and I think this should be noted.

Lines 183-187: I’m confused about what’s being plotted in Fig. 6a-d. Are these departures from the global mean that includes the ocean or just the terrestrial global mean?

Line 195: 20W/m2 across the entire aridity index spectrum.