Understanding variations in downwelling longwave radiation using Brutsaert's equation
Abstract. A dominant term in the surface energy balance and central to global warming is downwelling longwave radiation (Rld). It is influenced by radiative properties of the atmospheric column, in particular by greenhouse gases, water vapour, clouds and differences in atmospheric heat storage. We use the semi-empirical equation derived by Brutsaert (1975) to identify the leading terms responsible for the spatio-temporal climatological variations in Rld. This equation requires only near-surface observations of air temperature and humidity. We first evaluated this equation and its extension by Crawford and Duchon (1999) with observations from FLUXNET, the NASA-CERES dataset , and the ERA5 reanalysis. We found a strong agreement with r2 ranging from 0.87 to 0.99 across the datasets for clear-sky and all-sky conditions. We then used the equations to show that diurnal and seasonal variations in Rld are predominantly controlled by changes in atmospheric heat storage. Variations in the emissivity of the atmosphere form a secondary contribution to the variation in Rld, and are mainly controlled by anomalies in cloud cover. We also found that as aridity increases, the contributions from changes in emissivity and atmospheric heat storage tend to offset each other (−40 W m−2 and 20−30 W m−2, respectively), explaining the relatively small decrease in Rld with aridity (−(10−20) W/m−2). These equations thus provide a solid physical basis for understanding the spatio-temporal variability of surface downwelling longwave radiation. This should help to better understand and interpret climatological changes, such as those associated with extreme events and global warming.
Yinglin Tian et al.
Status: open (until 13 Jul 2023)
- CC1: 'Comment on egusphere-2023-451', Lucas Vargas Zeppetello, 07 Jun 2023 reply
Yinglin Tian et al.
Yinglin Tian et al.
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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.
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 or just small compared to 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.