Challenges in the closure of the surface energy budget at the continental scale

By: Bo Dong

Since satellite observations began in the late 1970s, our knowledge of energy flows in and out of the Earth’s climate system has been greatly advanced. Taking advantage of state-of-the-art Earth Observation (EO) programmes such as the Clouds and the Earth’s Radiant Energy System (CERES), energy exchanges at the top of the atmosphere (TOA) can be estimated with satisfying accuracy. EO based energy and water budgets at the surface, however, have not yet come to a consensus, largely because they cannot be directly measured from space but have to be inferred using additional physical or empirical models. As such, with large uncertainties, various combinations of surface energy and turbulent flux datasets can yield an imbalance of more than 20 Wm-2 on global annual mean basis, and even more at regional scales where transports of energy and water further complicate the surface state.

 Bringing necessary expertise from different disciplines together, a variational “Earth system inverse” modelling is one of the best methodologies for achieving a closure of the surface energy budget by optimising each balance flux component. With balance constraints at continental and global scales, the NASA Energy and Water Cycle Study (NEWS) of L’Ecuyer et al. (2015) and Rodell et al. (2015) were among the first to use inverse modelling approach to adjust multiple satellite data products for air-sea-land vertical fluxes of heat and freshwater within their uncertainty ranges, yielding balanced budgets. Although this approach has the advantage of reintroducing energy and water cycle closure information lost in the development of independent flux datasets, one caveat we note is that results are sensitive to the choices of input datasets and the associated uncertainty estimates (Thomas et al. 2019).

 One example is the mean seasonal cycle of the surface energy budget over North America (Figs. 1 and 2) that we optimised using a collocation of newer EO radiative energy flux products and machine-learning mapped in-situ land turbulent heat fluxes. At the land surface, energy budget closure requires

 DLR + DSR –ULW – USW –SH –LE = NSF (1),

 where terms from left to right are downward longwave radiation, downward solar radiation, upward longwave radiation, upward shortwave radiation, sensible heat flux, latent heat flux and net surface flux respectively.


Figure 1: 2001-2010 mean seasonal cycle of NSF over North America based on original flux datasets (dashed lines) and optimised solutions from the inverse model output (solid lines). 

While both NEWS and our (UoR) optimised energy budgets satisfy the zero annual mean NSF constraint (solid blue and red lines in Fig. 1), the resolved seasonal cycle contrasts notably with one another, in both timing and amplitude. Also, neither of the results compare closely with the DEEP-C NSF (Liu et al. 2015) which is derived using satellite measured TOA radiative fluxes and atmospheric reanalysis convergences. Because we do not have good prior knowledge of constraints on monthly time scales, the seasonal cycle of NSF is determined largely by the input budget components and their uncertainties, whereas annual constraints mostly adjust the seasonal time series up or down as a whole.


Figure 2: Optimised surface energy budget for NEWS (dashed lines) and UoR (solid lines) datasets. Positive (negative) values denote downward (upward) fluxes.

 To investigate which balance component accounts for the NSF discrepancy between NEWS and UoR, in Fig. 2 we dissected 6 budget terms on the left-hand side of the closure equation. It shows that discrepancies between NEWS (dashed lines) and UoR (solid lines) exist in all budget components, and none of the single budget terms are capable of explaining the NSF difference. Furthermore, we note that the difference in spring season USW between NEWS and UoR is ~35 Wm-2, one order of magnitude larger than the uncertainty given along with the data. This suggests that the uncertainty in USW might be considerably underestimated so that it restricts the inverse model from tuning the budget towards a more realistic state.

 Ongoing challenges remain for closing the surface energy budget at the continental scale, even though our estimates on global mean energy budget start to converge with increasing availability of observations. Unlike global annual mean budget, there are fewer prior hard constraints at regional and seasonal scales, such that the closure relies heavily on the accuracy of the observations of not only one but all budget terms. As most field measurements – which tends to be the data we “trust” the most – have failed to show closure of the surface energy budget, improving the quality of regional energy and water flux data is truly a long-term community effort. Equally important is the adequate representation of uncertainties in the observations, and there’s still plenty of room for improvement. For instance, structural biases in existing EO data products are likely underestimated and without realistic representation of seasonal variation. Nonetheless, with the current data we have, improvements in the variational modeling approach have been shown useful for producing a more realistic regional budget solution (Thomas et al. 2019), such as explicitly permitting spatially correlated errors in the original EO flux datasets, and incorporating inter-flux error covariance given that some retrievals share the same space-born instrument.


 L’Ecuyer et al., 2015: The Observed State of the Energy Budget in the Early Twenty-First Century. J. Clim. 28(21), 8319–8346, 10.1175/JCLI-D-14-00556.1

 Liu et al., 2015: Combining satellite observations and reanalysis energy transports to estimate global net surface energy fluxes 1985-2012. J. Geophys. Res. Atmos., 120 (18), 9374–9389,

 Rodell et al., 2015: The Observed State of the Water Cycle in the Early Twenty-First Century. J. Clim. 28(21), 8289–8318,  10.1175/JCLI-D-14-00555.1

 Thomas, C., B. Dong, and K. Haines 2019: Global and regional energy and water cycle fluxes from Earth observation data. J. Clim. Under review.


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