Solar radiation is the main cause for diurnal variations on land. Looking at this slightly differently than how it is normally done helps to better understand observations and evaluate models of the land surface

My former postdoc, Maik Renner, just got his paper published in the Journal of Hydrometeorology, in which he evaluated the performance of common land surface models at the diurnal time scale using FluxNet observations. The evaluation was based on a simple concept that we developed in my group: that solar radiation is the main driver of the diurnal variation of variables that characterize the land-atmosphere system. This sounds trivial. Of course solar radiation is the dominant driver, so what novel insights can be gained from this view?

The diurnal variation shown as (left) a function of time and (right) a function of the main forcing, absorbed solar radiation at the surface. Figure is taken from Panwar et al. (2019).

Typically, the diurnal cycle is plotted against time – a straightforward way to plot observations, as shown conceptually in the Figure on the left. One can easily distinguish night (solar radiation (orange line) is zero) from day (solar radiation is much greater than zero), but one cannot easily see the response of variables, such as surface or air temperature, to the main driver. Given that solar radiation is the main driver, why not plot variables against solar radiation instead? This yields quite a different picture (right panel of Figure). In doing so, one can focus on the relationship of variables during the day, and one can easily see if a variable responds directly to solar radiation (such as the turbulent heat fluxes), or whether there is a storage effect that results in a lagged response and a phase shift of the variable (like air temperature, shown in the Figure). We found this picture very useful, and already utilized it in previous work, e.g. to understand biases in evaporation parameterizations (Renner et al., 2019), the linear increase of air temperature with solar radiation in the morning (which we refer to as warming rate, see Panwar et al., 2019, and here), or when using the maximum power limit to infer surface energy balance partitioning at the diurnal scale (Kleidon and Renner, 2018; Conte et al., 2019).

What Maik did in the paper was to use this concept and analyzed various land surface models. Observations from 20 FluxNet sites were used, they were classified into forested and non-forested sites, and phase lags in observed and modeled energy balance partitioning were analyzed. There were, naturally, quite a few model-specific biases, but one general bias emerged: that most models generally tended to overestimate the soil heat flux, particularly at forested sites. The bias was quite significant, with a diurnal range in the soil heat flux at forested sites being somewhere between 100 and 200 Watt per square meter, while observations are close to zero. As the soil heat flux is associated with heat storage change below the surface, this then led to a bias in the turbulent fluxes, including phase shifts.

What this implies is that land surface models appear to buffer too much of the solar variation during the day below the surface. I found this to be an interesting insight, consistent with what I often hear from colleagues. My perception is that most colleagues would think that the diurnal variation at the land surface is buffered mostly by heat storage changes below the surface in the soil. But this is not the case. Actually, most of the buffering takes place above the surface in the lower atmosphere, as represented by the diurnal growth of the convective boundary layer. Radiosonde observations, which we evaluated in Kleidon and Renner (2018), show that the diurnal heat storage variations in the lower atmosphere are much larger than in the soil. This results in a very well known observation: That air temperatures lag behind solar radiation, with the maximum temperatures being reached sometime in the afternoon (this can also be seen in the Figure). This phase shift is a sign of a storage effect, but one that takes place in the atmosphere, and not in the soil. Maik’s previous paper (Renner et al. 2019) showed this phase lag to be more than two hours, much larger than that for surface temperature (less than an hour).

Representing these storage effects during the day have important consequences. When air temperature is used to estimate potential evaporation, for instance with the Penman-Monteith approach, this introduces an artificial phase lag (the lag from air temperature) that is not supported by observations. And this buffering in the lower atmosphere over land plays a key role in understanding the difference in climate sensitivity between land and ocean (Kleidon and Renner, 2017). While open water surfaces buffer the diurnal variation below their surface (with the main reason being that water is transparent, and not, as is often described, due to the greater heat capacity), over land it is buffered above the surface (because the soil or the canopy is opaque). This, in turn, results in a different diurnal variation of turbulent heat fluxes, with none over water and a strong variation over land. This, on land, then results in a different sensitivity of nighttime and daytime temperatures to radiative change.

Hence, representing the diurnal cycle and its associated storage changes right goes far beyond just the immediately affected variables. It leaves imprints on evaporation estimates and temperature sensitivities that are at the core of climate change research.


Conte, L., Renner, M., Brando, P., Santos, C. O. d., Silvério, D., Kolle, O., Trumbore, S. E., and Kleidon, A. (2019). Effects of tropical deforestation on surface energy balance partitioning in southeastern Amazonia estimated from maximum convective power. Geophysical Research Letters, 46(8), 4396-4403. doi:10.1029/2018GL081625.

Kleidon, A., and Renner, M. (2017). An explanation for the different climate sensitivities of land and ocean surfaces based on the diurnal cycle. Earth System Dynamics, 8(3), 849-864. doi:10.5194/esd-8-849-2017.

Kleidon, A., and Renner, M. (2018). Diurnal land surface energy balance partitioning estimated from the thermodynamic limit of a cold heat engine. Earth System Dynamics, 9(3), 1127-1140. doi:10.5194/esd-9-1127-2018.

Panwar, A., Kleidon, A., and Renner, M. (2019). Do surface and air temperatures contain similar imprints of evaporative conditions? Geophysical Research Letters, 46(7), 3802-3809. doi:10.1029/2019GL082248.

Panwar, Annu, Renner, Maik, and Kleidon, Axel (in press) Imprints of evaporation and vegetation type in diurnal temperature variations, Hydrol. Earth Syst. Sci. Discuss., 2020.

Renner, M., Brenner, C., Mallick, K., Wizemann, H.-D., Conte, L., Trebs, I., Wei, J., Wulfmeyer, V., Schulz, K., and Kleidon, A. (2019). Using phase lags to evaluate model biases in simulating the diurnal cycle of evapotranspiration. Hydrology and Earth System Sciences, 23(1), 515-535. doi:10.5194/hess-23-515-2019.

Renner, Maik, Kleidon, Axel, Clark, Martyn, Nijssen, Bart, Heidkamp, Marvin, Best, Martin, and Abramowitz, Gab (2020) How well can land-surface models represent the diurnal cycle of turbulent heat fluxes? Journal of Hydrometeorology, published online, doi: 10.1175/JHM-D-20-0034.1


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