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  • View in gallery

    The locations of GEBA stations after (a) level-1 and (b) level-2 quality control. The 277 level-1 stations are randomly split into training/test sets (252 stations) for MTE model training and a validation set (25 stations) for model performance evaluation. There are 255 stations in level 2.

  • View in gallery

    (a) The satellite product with the least RMSE compared to GEBA. For each product, the percentage (%) of stations recording best performance is listed in parentheses. (b) Training and validation sets for the SA, INV, and BMA approaches, with colors indicating the number of valid monthly records.

  • View in gallery

    Relative bias (RBIAS; %) in mean monthly Rsd between GEBA and satellite datasets (a) SRB, (b) ISCCP, and (c) UMD. Monthly Rsd are extracted at the grid cells of GEBA locations. RMSE (W m−2) between GEBA mean monthly Rsd and satellite datasets (d) SRB, (e) ISCCP, and (f) UMD.

  • View in gallery

    (a) RBIAS in mean seasonal Rsd between satellite datasets and GEBA. Each box indicates the interquartile range (top: the third quartile; bottom: the first quartile), with a horizontal gray solid line indicating the median and a black dot referring to the mean. (b) Probability distribution functions of monthly Rsd from GEBA, SRB, ISCCP, and UMD at all GEBA stations.

  • View in gallery

    (a)–(e) Fivefold cross validation: boxplots of GEBA, MTE, SRB, ISCCP, UMD for each subgroup. (f) Accumulated scatterplot of the fivefold cross validation of MTE prediction vs GEBA across five test sets; MAPE represents the mean absolute percentage error, and R2 represents the goodness-of-fit measure. (g) Scatterplot of the MTE prediction vs GEBA at the 25 validation set stations (3527 records).

  • View in gallery

    (a) RBIAS in station average monthly Rsd between CMA and SRB, ISCCP, UMD, and MTE datasets for all CMA locations. (b) RBIAS between ground measurements and SRB, ISCCP, UMD, and MTE datasets at the six FLUXNET2015 sites.

  • View in gallery

    The performance of satellite-derived and weighted averaged products. (a) Bias and (b) RMSE of the monthly Rsd from SRB, ISCCP, UMD, SA, INV, and BMA over the training stations. (c) The validation of monthly Rsd from SRB, ISCCP, UMD, and BMA over the unused stations.

  • View in gallery

    (a) Spatial pattern of mean annual MTE Rsd. (b) The zonal average of Rsd of the four datasets. (c) Time series of annual Rsd for the 1984–2006 period. The orange line and area show the median and spread of the 25 best model trees ensemble members, respectively.

  • View in gallery

    (a) Map of Asia subregions. Boxplots of the monthly (b) latent heat, (c) runoff, (d) Rsd, (e) sensible heat, and (f) snow water equivalent for the entire Asia and subregions, from the Noah-UMD and Noah-MTE simulations.

  • View in gallery

    Elasticity of sensible heat, latent heat, ground heat, runoff, surface layer soil moisture (0–10 cm), and snow water equivalent to Rsd.

  • View in gallery

    Monthly elasticities of key surface fluxes and hydrological variables to Rsd in Asia and each subregion.

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Reducing Solar Radiation Forcing Uncertainty and Its Impact on Surface Energy and Water Fluxes

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  • 1 Department of Civil and Environmental Engineering, Princeton University, Princeton, New Jersey
  • | 2 Food Program, World Resources Institute, Washington, D.C.
  • | 3 Guangdong Province Key Laboratory for Climate Change and Natural Disaster Studies, School of Atmospheric Sciences, Sun Yat-Sen University, Guangzhou, China
  • | 4 Southern Marine Science and Engineering Guangdong Laboratory (Zhuhai), Zhuhai, China
  • | 5 School of Environmental Science and Engineering, Southern University of Science and Technology, Shenzhen, China
  • | 6 School of Geography and Environmental Science, University of Southampton, Southampton, United Kingdom
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Abstract

Downward shortwave radiation Rsd determines the surface energy balance, alters evapotranspiration and hydrological conditions, and feeds back to the regional and global climate. Large-scale Rsd estimates are usually retrieved from satellite-based top-of-atmosphere radiation and cloud parameters. These estimates are subject to biases and temporal inhomogeneity due to errors in atmospheric parameters, algorithms, and sensor changes. We found that three satellite products overestimate Rsd by 8%–10% over Asia for 1984–2006, particularly in high latitudes. We used the model tree ensemble (MTE) machine-learning algorithm and commonly used ensemble averaging methods to integrate ground observations and satellite products. Validations based on test stations and independent networks showed that the MTE approach reduces the median relative biases from 8%–10% to 2%, which is more effective than the ensemble averaging methods. We further evaluated the impacts of uncertainty in radiation forcing on surface energy and water balances using the land surface model Noah-MP. The uncertainty of radiation data affects the prediction of sensible heat the most, and also largely affects latent heat prediction in humid regions. Holding the other variables constant, a 10% positive bias in Rsd can lead to a 20%–60% positive bias in the monthly median sensible heat. The simulated hydrological responses to changing radiation forcing are nonlinear as a result of the interactions among evapotranspiration, snowpack, and soil moisture. Our analysis concludes that reducing uncertainty of radiation data is beneficial for predicting regional energy and water balances, which requires more high-quality ground observations and improved satellite retrieval algorithms.

© 2021 American Meteorological Society. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

Corresponding author: Liqing Peng, pengliqing51@gmail.com

Abstract

Downward shortwave radiation Rsd determines the surface energy balance, alters evapotranspiration and hydrological conditions, and feeds back to the regional and global climate. Large-scale Rsd estimates are usually retrieved from satellite-based top-of-atmosphere radiation and cloud parameters. These estimates are subject to biases and temporal inhomogeneity due to errors in atmospheric parameters, algorithms, and sensor changes. We found that three satellite products overestimate Rsd by 8%–10% over Asia for 1984–2006, particularly in high latitudes. We used the model tree ensemble (MTE) machine-learning algorithm and commonly used ensemble averaging methods to integrate ground observations and satellite products. Validations based on test stations and independent networks showed that the MTE approach reduces the median relative biases from 8%–10% to 2%, which is more effective than the ensemble averaging methods. We further evaluated the impacts of uncertainty in radiation forcing on surface energy and water balances using the land surface model Noah-MP. The uncertainty of radiation data affects the prediction of sensible heat the most, and also largely affects latent heat prediction in humid regions. Holding the other variables constant, a 10% positive bias in Rsd can lead to a 20%–60% positive bias in the monthly median sensible heat. The simulated hydrological responses to changing radiation forcing are nonlinear as a result of the interactions among evapotranspiration, snowpack, and soil moisture. Our analysis concludes that reducing uncertainty of radiation data is beneficial for predicting regional energy and water balances, which requires more high-quality ground observations and improved satellite retrieval algorithms.

© 2021 American Meteorological Society. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

Corresponding author: Liqing Peng, pengliqing51@gmail.com

1. Introduction

Downward shortwave radiation Rsd is the most fundamental input forcing for different kinds of land surface and hydrological models (Ek et al. 2003; Liang et al. 1994; Vinukollu et al. 2011), as well as climate and Earth system models (Kay et al. 2015). Since the 1980s, satellite retrievals have provided estimates of surface fluxes regionally and globally (Pinker and Laszlo 1992; Breon et al. 1994; Charlock et al. 1996; Möser and Raschke 1984; Lu et al. 2010). However, large uncertainties such as biases and spurious abrupt changes exist in the satellite-derived Rsd estimates (Wang et al. 2012). These errors are mainly caused by the spatiotemporal inhomogeneity of the cloud and aerosol input data (Skeie et al. 2011; Regayre et al. 2014; Tang et al. 2016), sensor changes, data processing algorithms (Wang and Dickinson 2013), and complex surface properties (Wang et al. 2015).

Providing accurate Rsd estimates at a large scale remains a key challenge for Earth system science (Pinker 2005; Wang and Dickinson 2013; Wild 2005; Mercado et al. 2009; Sanchez-Lorenzo et al. 2017; Pedruzo-Bagazgoitia et al. 2017). The discrepancies in Rsd estimates derived from satellites can strongly influence the simulations of the global terrestrial carbon cycle (Ito and Sasai 2006). Prediction of drought events and trends requires long-term accurate Rsd data as solar radiation determines the surface energy balance and the associated evapotranspiration (ET) process. Many studies have considered the role of Rsd on potential ET estimates (e.g., Gao et al. 2006; Peng et al. 2018), and some studies found that radiation data uncertainty results in different long-term means, trends, and interannual variability of ET estimates (Badgley et al. 2015; Vinukollu et al. 2011).

Despite the direct effect of ET on soil moisture and runoff, fewer studies have evaluated the effect of radiation data uncertainty on these hydrological variables. For offline land surface model (LSM) simulations, uncertainties induced by hydrological parameterizations received substantially larger attention than that by input forcing data other than precipitation (e.g., Rutter et al. 2009; Lapo et al. 2017). However, recent studies suggested that the data quality in Rsd obtained from reanalysis and satellite products has significant influences on simulated runoff (Hinkelman et al. 2015) and ET (Badgley et al. 2015; Fisher et al. 2017; J. Zhang et al. 2020) and can strongly control the speed of snow melting (Lapo et al. 2015). Oliveira et al. (2011) investigated the impacts of using reanalysis radiation as input for hydrological simulations and concluded a nonnegligible effect of radiation on simulated runoff. Ménard et al. (2015) conducted a sensitivity analysis using the Joint U.K. Land Environment Simulator (JULES) LSM and found that the model performance is mainly limited by the accuracy of the input meteorological datasets, including Rsd. Hence, understanding the impact of satellite-derived radiation data uncertainty on hydrological modeling is useful for assessing the confidence of freshwater availability predictions using satellite products.

At a local scale, Rsd can be accurately measured by ground stations (Augustine et al. 2000; Wang and Liang 2009; Inamdar and Guillevic 2015). The monitoring networks, such as the Baseline Surface Radiation Network (BSRN; Ohmura et al. 1998; Driemel et al. 2018) and the Global Energy Balance Archive (GEBA; Gilgen and Ohmura 1999; Wild et al. 2017), provide daily to monthly radiative fluxes. However, compared to the precipitation and temperature gauges, high-quality stations that monitor these radiative fluxes are much scarcer over the globe, particularly in the less densely populated areas (Driemel et al. 2018). Although the ground-based records are useful for local evaluation of surface energy balance and long-term analysis, it is difficult to estimate large-scale Rsd directly from these records because the traditional interpolation techniques for upscaling point observations are not appropriate for the sparsely distributed radiation network over a large domain.

Machine-learning is a powerful tool to draw information from both ground observations and satellite products of surface radiation (Mellit et al. 2010; Wang et al. 2012; Yang et al. 2018; Wei et al. 2019). The model tree ensemble (MTE) technique (Jung et al. 2010) is one of the machine-learning approaches that can enhance the predictive capacity of target variable, especially in regions that are not covered by training data (Jung et al. 2009). In the field of machine-learning, the model tree is a binary decision tree hierarchy that fits several subsets of the training data such that they can perform adaptive and nonlinear data fitting. Another approach that has the potential to reduce errors and improve spatial correlations is ensemble averaging of multiple datasets. For example, combining data from polar-orbiting and geostationary satellites can enhance the temporal resolution of cloud properties. Huang et al. (2011) and Tang et al. (2016) obtained high-resolution Rsd by combining the Moderate Resolution Imaging Spectroradiometer (MODIS) and Multifunctional Transport Satellite (MTSAT) data.

Asia, including the Tibetan Plateau, exhibits large biases in satellite-derived or reanalysis-based Rsd (e.g., Huang et al. 2019; Yang et al. 2006; Jia et al. 2013). Assimilating multisource products to improve estimates of solar energy have important implications for climate and energy sectors. The goal of this study is to evaluate and reduce the uncertainty of satellite-derived Rsd in this region and to explore how such uncertainties affect the simulation of land surface processes. First, we evaluated Rsd estimates derived from satellite datasets using GEBA. Second, we estimated Rsd over Asia for 1984–2006 using a machine-learning approach and compared its performance with ensemble averaging techniques. Finally, we used a land surface model to investigate the sensitivity of surface energy and water balances to the uncertainty of radiation forcing.

2. Materials and methods

a. Satellite datasets

In this study, we used three different satellite products, including the International Satellite Cloud Climatology Project (ISCCP), the Surface Radiation Budget (SRB), and the University of Maryland Radiation Dataset (UMD). The details and inputs of these products are introduced in Table 1.

Table 1.

Summary of retrieval algorithms and main inputs of the satellite products.

Table 1.

1) International Satellite Cloud Climatology Project

The ISCCP provides monthly mean daytime total cloud amount values on a 280-km equal-area global grid (Rossow and Dueñas 2004; Zhang et al. 2004). Additionally, the ISCCP Flux Dataset (FD, https://isccp.giss.nasa.gov/pub/data/FC/) includes shortwave and longwave radiation fluxes at the top of the atmosphere (TOA) and the surface (SRF) for all-sky and clear-sky conditions. These fluxes were calculated by feeding the National Aeronautics and Space Administration (NASA) Goddard Institute for Space Studies (GISS) radiative transfer model with cloud properties retrieved from the ISCCP-D1 dataset, the Television Infrared Observation Satellite (TIROS) Operational Vertical Sounder (TOVS) temperature and humidity profile, and other ancillary data.

2) Surface radiation budget

The NASA/GEWEX SRB Rel3.0 and 3.1 provide global surface and TOA monthly shortwave and longwave radiation at 1.0°, respectively (Stackhouse et al. 2011; https://eosweb.larc.nasa.gov/project/srb/srb_table). The shortwave fluxes were calculated with the Pinker and Laszlo radiative transfer algorithm (Pinker and Laszlo 1992) by using the cloud and surface properties derived from the ISCCP DX dataset and meteorological inputs from the NASA Global Modeling and Assimilation Office (GMAO) GEOS-4 reanalysis. Note that both ISCCP and SRB projects use a mean aerosol climatology and are therefore not able to incorporate regional atmospheric variability from volcanoes or biomass burning (Raschke et al. 2006).

3) University of Maryland radiation dataset

The UMD is a relatively new global dataset that provides global surface and TOA monthly shortwave and longwave radiation at 0.5° for the period of 1984–2009 (Pinker 2005; Ma and Pinker 2012). This dataset developed at the University of Maryland uses the updated Ma and Pinker (2012) radiative transfer algorithm and utilizes the latest ancillary data to reduce the uncertainty.

b. Ground observations

1) Global Energy Balance Archive

The GEBA provides in situ measurements of long-term monthly mean values of surface downward solar radiation Rsd around the globe (Gilgen and Ohmura 1999). This dataset has been widely used in evaluating the trends in Rsd fluxes, including increases (“brightening”) and more recent decreases (“dimming”) (Wild 2005). GEBA observations have been compiled from various sources, such as the World Radiation Data Center (WRDC), Baseline Surface Radiation Network (BSRN), the Atmospheric Radiation Measurement Program (ARM), the Surface Radiation (SURFRAD) network, different periodicals, publications, data reports, and individual weather services (Wild et al. 2017). Over Asia, 354 GEBA stations are unevenly spatially distributed, with the densest GEBA network in East Asia and the sparsest in North Asia.

The original GEBA observations contain some errors because of instrument changes and technical failures in this region (Shi et al. 2008). We used the quality-controlled GEBA dataset (https://geba.ethz.ch/data-quality/procedure.html) and conducted two levels of additional quality-control to filter out suspicious stations or records. Under level-1 quality control, we selected the station years with at least 1 month and discarded the stations with less than 2 years of temporal coverage during 1984–2006. We used level-1 data (277 stations) for machine-learning because the discontinuities or gaps in the records will not affect the model training; the model sees no difference in the time step and location of a data record. Using level-1 data also gives us an advantage of including more stations with missing data and increase the diversity of the samples for model training. Under level-2 quality control, we only selected the station years with at least 10 months and discarded the stations with less than 2 years of temporal coverage. When evaluating the satellite data with the GEBA stations, we used level-2 data (255 stations) to ensure the comparability of annual values and climatology. Figure 1 shows the spatial distribution of the level-1 and level-2 stations.

Fig. 1.
Fig. 1.

The locations of GEBA stations after (a) level-1 and (b) level-2 quality control. The 277 level-1 stations are randomly split into training/test sets (252 stations) for MTE model training and a validation set (25 stations) for model performance evaluation. There are 255 stations in level 2.

Citation: Journal of Hydrometeorology 22, 4; 10.1175/JHM-D-20-0052.1

2) CMA quality-controlled measurements

The China Meteorological Administration (CMA) Meteorological Information Center provides daily data for temperature, relative humidity, and other meteorological variables since 1961. The CMA has 122 stations that have global solar radiation measurements using the DFY-4 and TBQ-2 total radiation meter (X.-X. Zhang et al. 2020). Tang et al. (2010) implemented a set of quality control procedures for the CMA solar radiation measurements, which removed obvious operational and more insidious errors due to systematic or unexpected factors. These procedures produced 96 widely distributed stations with high data quality (worst-case errors < 5%). We used these CMA stations as our primary source of validation data.

3) FLUXNET2015

FLUXNET is a global network of micrometeorological eddy flux tower sites providing half-hour measurements of surface energy and moisture fluxes. The FLUXNET2015 FULLSET dataset (http://fluxnet.fluxdata.org/data/fluxnet2015-dataset/) is a standardized and gap-filled synthesis database (Vuichard and Papale 2015). We processed the FLUXNET2015 into NetCDF files with the FluxnetLSM R package (Ukkola et al. 2017) and only near-complete records were selected. There are six sites in total from FLUXNET2015 that have incoming solar radiation measurements and encompass the same period and spatial domain. We used these records to perform additional validation analysis.

c. Model tree ensemble

We used a machine-learning approach, the MTE technique (Jung et al. 2010), to upscale the GEBA station radiation with the satellite observations in the ungauged areas, where the error structures between satellite prediction and real values are usually unknown. Model tree ensembles can enhance the predictability in regions without training data (Jung et al. 2009; Zeng et al. 2014). A model tree is a binary decision tree hierarchy to fit the target variable with many piece-wise linear approximations. First, an ordinary large decision tree is grown based on recursive classification conditioned on the explanatory variables. Second, this tree replaces subtrees with linear regression functions wherever this reaches a specific criterion (Frank et al. 1998). The model tree is then applied to any region to predict the target variable given the explanatory variables (Jung et al. 2010).

The MTE method consists of the model tree induction algorithm (TRIAL) and the evolving trees with random growth (ERROR) algorithm (Jung et al. 2010, 2009). The final nodes of the trees are multiple linear regressions based on the stepwise forward selection of significant explanatory variables. TRIAL can deal with different kinds of explanatory variables: split variables (for decisions), regression variables (for multiple regressions in the leaves), or both. The search strategy to split a given node is based on minimizing the sum of squared errors of the multiple regressions in the two subnodes. ERROR allows for random splits without searching for the best split, which avoids local optimization and potentially increases the global performance. Finally, a subset of model trees that exhibit best performances and are independent of each other is selected for the ensembles. For details and global applications such as predicting global surface fluxes from FLUXNET eddy covariance sites, please refer to Jung et al. (2009, 2010).

In the present study, the target variable is Rsd, and the explanatory variables for in situ Rsd values are the satellite-derived Rsd from SRB, ISCCP, and UMD, along with other meteorological variables, including surface air temperature, cloud cover, and precipitation. To find the relationship between the target variable and the explanatory variables from the training data, the output Y of the desired model is given by monthly GEBA data, and the inputs include satellite radiation, monthly air temperature and precipitation from the Climatic Research Unit (CRU), and cloud cover from ISCCP.

For the level-1 stations, we split the GEBA observations into three pools, the training set, test set, and validation set. The validation set is built by a collection of “untouched” stations. We first filtered out the station years with less than 6 valid monthly records and then randomly selected 25 stations (~10% of the total number of stations) as the validation set (Fig. 1a). This way the records are spatially randomly distributed. The purpose of this is to ensure that the spatiotemporal representation of the validation set is diverse. For the monthly records in the remaining 252 stations, 45 176 records in total, we conducted a fivefold cross validation by randomly splitting the records into five groups of training and test sets. The training set consists of data records for model fitting, whereas the test set presents the error statistics for model selection. For each group, we trained the model tree ensembles using the training set (~36 141 records) and compared the predictions with observations in the test set (~9033 records).

A preliminary evaluation based on the fivefold cross validation shows that the combination of SRB, ISCCP, UMD, and CRU-Tair provides the most accurate results with high efficiency, while adding cloud cover and precipitation causes sharp spatial discontinuities in areas such as the Arabian Peninsula. Consequently, we selected the MTE model with SRB, ISCCP, UMD, and CRU-Tair covariates to predict Rsd. For each ensemble, we generated 1000 different model trees, selected 25 best trees, and calculated the median of the 25 model trees as the final prediction. The MTE approach is carried out in MATLAB.

d. Noah-MP land surface model

Noah-MP is an LSM with multiple parameterization options for key land–atmosphere processes (Niu et al. 2011) built upon the classic Noah model (Chen et al. 1996). Multiple options are available for various processes such as radiative transfer in the canopy, stomatal conductance, water infiltration and runoff generation, and snow and soil parameterizations. It is used as the land scheme coupled to the atmospheric Weather Research and Forecasting (WRF) Model, also known as WRF-Hydro (Skamarock et al. 2008), and has been evaluated intensively over the United States (Cai et al. 2014; Barlage et al. 2015).

In this study, we implemented version 1.6 of Noah-MP within the WRF-Hydro framework using the offline forcing mode (Gochis et al. 2015). This mode feeds external meteorological forcing to the model, which allows us to examine the impact of shortwave radiation forcing uncertainty on hydrological processes. We spun up the Noah-MP model for 30 years using meteorological forcing of year 1984 and ran two experiments for the 1984–2006 period. The first experiment used UMD 3-hourly Rsd flux and provides a baseline to be compared with, hereafter called Noah-UMD. Then we adjusted the original UMD 3-hourly Rsd to match the monthly values of the MTE prediction. The second experiment used this adjusted UMD 3-hourly Rsd, hereafter called Noah-MTE.

The parameterization options of Noah-MP in this study are given in Table 2 and explained in Niu et al. (2011). We used the Jarvis scheme because it directly considers the effect of radiation on stomatal conductance (Jarvis 1976). We turned off dynamic vegetation, surface, subsurface, and channel routing schemes included in WRF-Hydro, so that relating sensitivities to process parameters became clearer (Cuntz et al. 2016).

Table 2.

Noah-MP parameterization options.

Table 2.

The sensitivity of surface fluxes and hydrological variables to the adjustment of radiation forcing was quantified by the elasticity ϵX,Rsd:
ϵX,Rsd=ΔX|X|ΔRsdRsd=XMTEXUMD|XUMD|RsdMTERsdUMDRsdUMD,
where ΔRsd/Rsd is the relative change of MTE Rsd compared to UMD Rsd, and ΔX/|X| is the relative change in X after the adjustment of Rsd, also written as (XMTEXUMD)/|XUMD|. The term X can be fluxes such as latent heat (LE), sensible heat (H), ground heat (G), and hydrological variables such as runoff (Q), radiative temperature (Tr), snow water equivalent (SWE), or soil moisture (SM). For example, given elasticity ϵH,Rsd = 2 and a 10% increase in solar radiation, while holding the other variables constant, there will be a 20% increase in sensible heat. For each grid, we aggregated the hourly model outputs to monthly averages or totals, and then calculated monthly values of ϵ for the 1984–2006 period.

e. Other multisource data merging approaches

When we first evaluated the errors in the satellite products with GEBA, we found that the performance of three satellite products is complementary in space because the best product with the smallest root-mean-square error (RMSE) varies spatially (Fig. 2a). Given the highly complementary nature of the three products in different locations and seasons, we also tested three widely used weighted ensemble averaging methods by obtaining weights at the stations for four seasons [March–May (MAM), June–August (JJA), September–November (SON), December–February (DJF)]. To ensure that the training data has a larger number of valid records for each season, we selected the 1994–2000 period when the seasonal missing ratios were the smallest. There are 214 qualifying stations (>50% valid records) for 1994–2000, and the remaining 63 stations are used for validation (Fig. 2b).

Fig. 2.
Fig. 2.

(a) The satellite product with the least RMSE compared to GEBA. For each product, the percentage (%) of stations recording best performance is listed in parentheses. (b) Training and validation sets for the SA, INV, and BMA approaches, with colors indicating the number of valid monthly records.

Citation: Journal of Hydrometeorology 22, 4; 10.1175/JHM-D-20-0052.1

1) Simple averaging

Simple averaging (SA) produces an arithmetic mean of ensemble members at each time step. It is an effective approach in weather and hydrological forecasting to reduce the forecast error variance and avoid systematic biases compared to a single-run deterministic forecast (Ebert 2001). SA assigns an equal weight for each satellite product:
wk=1K,
where wk is the weight for individual product k, and k = 1, …, K.

2) Inverse variance averaging

Instead of equal weighting, inverse variance averaging (INV) determines the optimal weights that minimize the total error variance of all ensemble members (Lobell and Field 2008). This approach considers the errors between each product and station observations and provides an averaging estimate with minimum possible total error variance. Given that the errors of Rsd vary with season, we estimated the weight for each product k and each season s. The weight wks is proportional to the inverse of the variance:
wks=1σks2(k=1K1σks2)1,
where σks2 is the error variance between the satellite product k and the station observations for the season s.

3) Bayesian model averaging

Bayesian model averaging (BMA) is a statistical method for combining multiple model ensembles using weights conditioned on the posterior probabilities of different ensemble members (Raftery et al. 2005). The BMA predictive probability distribution is given by
p(y)=k=1KwkGk(y|fk),
where y is the variable of interest to be simulated and fk is a bias-corrected model simulation or forecast. Here, y represents true Rsd values, and f1, f2, and f3 represent SRB, ISCCP, and UMD satellite observations, respectively. The weight wk is the posterior probability of forecast k, P(fk|yt), being the best forecast given the station observation at time t, yt. This posterior probability is based on the errors between fk and the GEBA observations in the training period, which reflects how well fk fits the observational data. Parameter Gk(y|fk) is the conditional probability distribution function (PDF) based on fk alone, given that fk is the best forecast in the ensemble. It is typically assumed that Gk(y|fk) is a normal distribution centered at a linear function of fk.
To solve the posterior probability, namely, the weights wk, we can maximize the likelihood function, which is the probability of observing the training data given the parameters wk to be estimated. For a specific season, assuming independence of forecast errors in time, the log-likelihood function for the predictive probability [Eq. (5)] given GEBA data (yt) can be written as
l(w1,,wk,σ2)=tTlog[k=1KwkGk(yt|fkt)].
This log-likelihood function can be maximized using the expectation–maximization (EM) algorithm (Raftery et al. 2005). The EM algorithm is iterative and alternates between the expectation step and the maximization step, which are then iterated to convergence within some specified small tolerances.

4) Regionalization

After obtaining the individual weight wk for SRB, ISCCP, and UMD at the 214 training stations (Fig. 2b) for each season (MAM, JJA, SON, DJF), we used the Universal Kriging with External Drift approach (UKED; Hudson and Wackernagel 1994) to spatially interpolate the weights to each grid. The errors between satellite and observation are possibly related to the magnitude of Rsd and the local climate, therefore we added other high-resolution climatology covariates (e.g., temperature, precipitation, and solar radiation climatology from WorldClim2, http://worldclim.org/version2). Given that the gridded interpolated weights may not add up to one, it is necessary to normalize each individual weight by the sum of all weights.

3. Results

a. Evaluation of satellite datasets

We first examined the differences between GEBA and satellite observations at the GEBA stations with level-2 quality control (Fig. 1b, station number = 255). UMD has the highest mean monthly Rsd over all station years (173.14 W m−2), followed by ISCCP (170.99 W m−2), SRB (170.54 W m−2), and GEBA (161.02 W m−2). The median standard deviation of mean annual Rsd at all stations in SRB (6.22 W m−2), ISCCP (5.59 W m−2), and UMD (6.09 W m−2) are smaller than GEBA (8.99 W m−2). Figures 3a–c display the spatial patterns of relative biases (RBIAS) in mean monthly Rsd between satellite and GEBA measurements. We found positive RBIAS up to 40% at the stations in southwest China, northern China, the Korean Peninsula, the Arabian Peninsula, and Pakistan. Similarly, the stations in these regions show higher RMSE (Figs. 3d–f). On average, SRB has fewer stations with positive RBIAS and large RMSE than ISCCP and UMD.

Fig. 3.
Fig. 3.

Relative bias (RBIAS; %) in mean monthly Rsd between GEBA and satellite datasets (a) SRB, (b) ISCCP, and (c) UMD. Monthly Rsd are extracted at the grid cells of GEBA locations. RMSE (W m−2) between GEBA mean monthly Rsd and satellite datasets (d) SRB, (e) ISCCP, and (f) UMD.

Citation: Journal of Hydrometeorology 22, 4; 10.1175/JHM-D-20-0052.1

Figure 4 further shows the seasonal RBIAS between satellite datasets and GEBA. All SRB, ISCCP, and UMD consistently overestimate monthly Rsd by about 8%–15% regarding the median RBIAS (Fig. 4a), which confirms the spatial patterns of RBIAS in Figs. 3a–c. SRB’s median RBIAS is slightly lower than UMD and ISCCP. The range of satellite–GEBA errors in winter (DJF) season (from −25% to 50%) is much larger than other seasons because Rsd is lower in magnitude (<100 W m−2) during winter. The probability density functions (PDF) of the satellite products are compared to that of the GEBA observations in Fig. 4b. All three satellite datasets show a bimodal structure with strong peaks at 100 and 200 W m−2. The positive RBIAS of satellite products in Fig. 4a is associated with higher probability density between 200 and 300 W m−2 and lower probability density between 50 and 200 W m−2. SRB and UMD have very similar PDF structures, which suggests the special treatments of aerosol, land use, water and ice clouds in UMD (Ma and Pinker 2012) have marginal effects on the overall PDF in this region. The PDF of ISCCP is closer to that of GEBA between 40 and 100 W m−2 relative to other products, resulting in a lower RBIAS in DJF.

Fig. 4.
Fig. 4.

(a) RBIAS in mean seasonal Rsd between satellite datasets and GEBA. Each box indicates the interquartile range (top: the third quartile; bottom: the first quartile), with a horizontal gray solid line indicating the median and a black dot referring to the mean. (b) Probability distribution functions of monthly Rsd from GEBA, SRB, ISCCP, and UMD at all GEBA stations.

Citation: Journal of Hydrometeorology 22, 4; 10.1175/JHM-D-20-0052.1

b. Performance and validation of the MTE method

The scatterplot of MTE and GEBA for the fivefold cross validation (Fig. 5f) shows that MTE can reproduce Rsd across the five test sets [mean RMSE = 21.19 W m−2, mean mean absolute percentage error (MAPE) = 10.57%, mean R2 = 0.89]. The statistics of individual cross validation with 9033 records in each test set (Figs. 5a–e, KF1 to 5) show that MTE predicts the GEBA mean and median correctly, and significantly reduces RBIAS from 8%–10% to 2%, and RMSE from 25 to 21 W m−2. The MTE model also predicts Rsd well in the validation set (Fig. 5g, 25 stations, 3527 records) with a high R2 = 0.92. The RMSE (18.34 W m−2) and mean RBIAS (1.46%) of MTE prediction in the validation set are even lower than those in the test set. We further evaluated the accuracy of the MTE approach with two additional datasets. We first compared the satellite datasets and our MTE prediction with the quality-controlled CMA stations. We aggregated the daily CMA measurements to monthly values and calculated RBIAS in the mean monthly Rsd between gridded data and CMA (Fig. 6a). MTE successfully reduced the median RBIAS of satellite datasets to a range from around −2% to 5%, especially in the winter. We also used an independent dataset from FLUXNET. We calculated monthly Rsd from half-hourly estimates and then compared them against monthly estimates from the satellite gridded products and MTE prediction. Figure 6b compares the RBIAS between gridded datasets and FLUXNET. Although MTE shows about 10% negative biases in CN-Cha, CN-Dan, CN-Ha2, and CN-HaM where satellite products underestimate Rsd, MTE is able to reduce the positive bias in CN-Din (20%–30%) and CN-Qia (15%–20%) to below 10%.

Fig. 5.
Fig. 5.

(a)–(e) Fivefold cross validation: boxplots of GEBA, MTE, SRB, ISCCP, UMD for each subgroup. (f) Accumulated scatterplot of the fivefold cross validation of MTE prediction vs GEBA across five test sets; MAPE represents the mean absolute percentage error, and R2 represents the goodness-of-fit measure. (g) Scatterplot of the MTE prediction vs GEBA at the 25 validation set stations (3527 records).

Citation: Journal of Hydrometeorology 22, 4; 10.1175/JHM-D-20-0052.1

Fig. 6.
Fig. 6.

(a) RBIAS in station average monthly Rsd between CMA and SRB, ISCCP, UMD, and MTE datasets for all CMA locations. (b) RBIAS between ground measurements and SRB, ISCCP, UMD, and MTE datasets at the six FLUXNET2015 sites.

Citation: Journal of Hydrometeorology 22, 4; 10.1175/JHM-D-20-0052.1

c. Other ensemble averaging approaches

A comparison between satellite products and weighted averaged datasets (SA, INV, BMA) shows that the weighted averaging methods mostly limited the range of biases from within −20 to 40 W m−2 (Fig. 7a) and slightly reduced RMSE by about 2–4 W m−2 (Fig. 7b) at the training stations. BMA provides the best estimates of Rsd, with the smallest range of bias and RMSEs. As a test of the transferability of these weights to the ungauged areas, we compared the best dataset BMA as well as the original satellite estimates with the GEBA observations (Fig. 7c). The satellite datasets estimated double the values of GEBA observations between 50 and 200 W m−2 (e.g., 250 versus 100 W m−2), shown by the considerable scatters above the 1: 1 line (Fig. 7c). These positive biases almost always occur at high latitudes (>50°N, mostly in Russia) during the winter period (December–March, mainly in February). BMA is not able to reduce the RMSE at the 63 validation stations as it has a slightly greater RMSE (37.12 W m−2) than SRB (36.10 W m−2). The RBIAS of BMA (16.34%) over these validation stations is also even higher than that of SRB (13.41%) and ISCCP (15.10%), probably a result of the biases from UMD.

Fig. 7.
Fig. 7.

The performance of satellite-derived and weighted averaged products. (a) Bias and (b) RMSE of the monthly Rsd from SRB, ISCCP, UMD, SA, INV, and BMA over the training stations. (c) The validation of monthly Rsd from SRB, ISCCP, UMD, and BMA over the unused stations.

Citation: Journal of Hydrometeorology 22, 4; 10.1175/JHM-D-20-0052.1

d. The MTE reconstruction of surface downward radiation

We reconstructed the monthly Rsd during 1984–2006 by applying the final MTE model (trained in the 252 stations) to the entire domain. The spatial pattern of mean annual Rsd reconstructed by MTE is shown in Fig. 8a. The Rsd increases from 180 to 240 W m−2 with latitude ranging from 0° to 20°N, and then gradually decreases from 240 to 60 W m−2 with a further increase of latitude. The maximum Rsd occurs in the deserts of the Arabian Peninsula where cloud cover is minimal, and in the Tibetan Plateau due to the low extinction rate of air mass, water vapor, and aerosol (Yang et al. 2010). The zonally averaged MTE Rsd is generally lower than the satellite datasets, particularly in latitudes between 0° and 40°N (Fig. 8b). Compared to MTE, the ISCCP Rsd has greater values in South China and Southeast Asia, with a maximum difference of 25 W m−2 between 0° and 10°N (Fig. 8b). UMD has larger Rsd values in the Middle East (25%) and South China (20%), but lower values in high latitudes above 70°N as well as in the Tibetan Plateau. The relative differences between MTE and SRB are generally smaller (<8%), which suggests that SRB has the best performance in terms of long-term climatology relative to MTE compared to the other satellite datasets.

Fig. 8.
Fig. 8.

(a) Spatial pattern of mean annual MTE Rsd. (b) The zonal average of Rsd of the four datasets. (c) Time series of annual Rsd for the 1984–2006 period. The orange line and area show the median and spread of the 25 best model trees ensemble members, respectively.

Citation: Journal of Hydrometeorology 22, 4; 10.1175/JHM-D-20-0052.1

Figure 8c shows the annual mean time series averaged over the entire domain. There are clear negative linear trends in UMD (−0.33 W m−2 yr−1) and ISCCP (−0.17 W m−2 yr−1), while the negative trend in SRB is marginally significant (p = 0.057). MTE produces similar interannual variability to UMD, as both datasets show concurrently high Rsd values in 1993, 1998, and 2001, and it has a clear negative trend similar to UMD (−0.26 W m−2 yr−1). These negative trends are consistent with the results for 1983–2001 shown by Pinker (2005) in latitude belts between 60° and 90°N (−0.25 W m−2 yr−1) and over global land (−0.05 W m−2 yr−1). Pinker (2005) found contrasting trends of Rsd on the land and ocean, where the land shows solar dimming and the ocean shows solar brightening.

e. Noah-MP simulations

The 8%–15% positive relative biases (Figs. 3 and 4) might propagate to model simulations of ET, runoff, and associated land surface processes (Schwingshackl et al. 2018). We ran the Noah-MP land surface model to investigate how the radiation forcing uncertainty propagates into the simulation of surface energy and water balances. Noah-MP is run at a 3-hourly time step for the 1984–2006 period with two different radiation inputs, the original UMD Rsd and the bias-corrected UMD Rsd using MTE monthly values, hereafter referred to as Noah-UMD and Noah-MTE, respectively.

A comparison of the distribution of the key surface fluxes (LE, H) and hydrological variables (Q, SWE) between Noah-UMD and Noah-MTE provides an initial understanding of the impact of Rsd forcing uncertainty on the energy and water balances (Fig. 9). The differences in the UMD and MTE Rsd in six subregions are summarized in Fig. 9d. Large differences (20–30 W m−2) are found in the Middle East and South Asia. Figure 9e highlights a strong reduction of H in Noah-MTE as a result of lower MTE Rsd, especially in the Middle East, where the mean H is reduced from 60 to 40 W m−2. The regional differences of mean LE between Noah-UMD and Noah-MTE are smaller than 2 W m−2 (Fig. 9b), much less than that of H. There are almost no significant changes of LE in the Middle East and Central Asia as ET is limited by water availability rather than evaporative demand over these regions, which results in higher partitioning of available energy to H than LE. The changes of median Q and SWE caused by the change of Rsd are very small (Figs. 9c,f) in the regional averages. However, they exhibit interesting spatiotemporal patterns, as discussed below in Figs. 10 and 11.

Fig. 9.
Fig. 9.

(a) Map of Asia subregions. Boxplots of the monthly (b) latent heat, (c) runoff, (d) Rsd, (e) sensible heat, and (f) snow water equivalent for the entire Asia and subregions, from the Noah-UMD and Noah-MTE simulations.

Citation: Journal of Hydrometeorology 22, 4; 10.1175/JHM-D-20-0052.1

Fig. 10.
Fig. 10.

Elasticity of sensible heat, latent heat, ground heat, runoff, surface layer soil moisture (0–10 cm), and snow water equivalent to Rsd.

Citation: Journal of Hydrometeorology 22, 4; 10.1175/JHM-D-20-0052.1

Fig. 11.
Fig. 11.

Monthly elasticities of key surface fluxes and hydrological variables to Rsd in Asia and each subregion.

Citation: Journal of Hydrometeorology 22, 4; 10.1175/JHM-D-20-0052.1

The sensitivity of fluxes and water budgets to the change of radiation forcing is further analyzed by calculating the elasticity ϵX,Rsd. The monthly averages of elasticity of the main variables to Rsd in May and November are shown in Fig. 10. In May, the positive Rsd response of H to Rsd is spatially uniform with ϵH,Rsd above 2 over the entire domain. Large ϵLE,Rsd (>2.5) occurs in high latitudes (>65°N), whereas close-to-zero and negative responses occur in Central Asia, North China, and Mongolia. Although no significant change in the overall distribution of Q is found (Fig. 9c), there is a strong negative response of Q to Rsd (<−2) between 20° and 50°N (Fig. 10d). Surface soil moisture (SM) and SWE show overall negative responses to changes in Rsd (Figs. 10e,f). Regions with the largest ϵSWE,Rsd (<−2) overlap with regions that have the climatologically highest SWE values. Shifting from late-spring/early summer to wintertime (November), H and LE show stronger positive responses to Rsd compared to May (Figs. 10g–l), while all variables exhibit much weaker sensitivities at the high latitudes (−1 < ϵ <1).

Figure 11 summarizes the monthly elasticities of four main variables (H, LE, Q, SWE) to Rsd in each subregion. Overall, the responses of water and energy fluxes to the change in radiation forcing are the strongest in East Asia (Fig. 11d) and the weakest in Southeast Asia (Fig. 11g). Sensible heat H has very high elasticities (median = 2–6), which always exceed the elasticity of LE by at least 2–3 times. When analyzing the seasonal cycle of elasticity, we found that H has much larger elasticity magnitude and spread in the cold season (Figs. 11b,d–g). The relative changes in LE, Q, and SWE are typically smaller than the relative change in radiation forcing (ϵ ≤ 1). Runoff Q has strong negative elasticities (close to −1) for all 12 months in East Asia, while showing weak elasticities (close to 0) in the Middle East, South Asia, and Southeast Asia. The peaks of SWE elasticity are usually one or two months ahead of the peaks of Q elasticity in Central and East Asia (Figs. 11b,c).

4. Discussion

a. Uncertainty in satellite datasets

Our results show that the satellite datasets tend to overestimate Rsd in Asia, especially in southwestern China. Zhang et al. (2015) evaluated these datasets with GEBA stations and additional Chinese observation sites. They found that satellite overestimation was more dominant than underestimation. However, we noticed that this on-average overestimation may be a biased conclusion due to the sparse ground observational network in high altitudes. A previous study showed 10%–30% underestimations of solar radiation in Tibet because these satellite algorithms do not take the elevation effect on Rayleigh scatter into account (Yang et al. 2006).

Zhang et al. (2015) associated the overestimation in this region with the inappropriate representation of aerosols and clouds due to the rapid economic development and heavy pollution (Qian et al. 2007; Wu and Fu 2011). Gupta et al. (1999) attributed the positive biases at high latitudes to the underestimation of cloud amounts. The overestimations of Rsd may be due to a lack of adequate representation of cloud depth and absorbing aerosols, particularly from biomass burning and desert dust prevailing in lower latitudes (Wild 1999). A recent assessment of SRB, ISCCP, and Clouds and the Earth’s Radiant Energy System (CERES) satellite-derived Rsd in the Arctic confirmed the systematic biases in the satellite estimates, and attributed these errors to the spatial heterogeneity of the surface, the influence of the cloud, the accuracy of input inversion parameters, and the low spatial resolution of the radiation products (Sun et al. 2018). Current satellite products remain uncertain due to algorithms and parameters such as elevation, cloud cover, and aerosol loading. Quantitative analysis to identify the sources of uncertainty for these products are out of scope of this study, but warrants further research. Readers can refer to a recent review by Huang et al. (2019) for a detailed discussion on the challenges of satellite estimates of solar radiation.

Although substantial efforts have been made to calibrate and homogenize ISCCP cloud products, there are several temporal discontinuities when the orbiters and satellite were replaced. For example, the National Oceanic and Atmospheric Administration’s NOAA-11 satellite was replaced by NOAA-14 in 1995, and then by NOAA-16 in 2001. These temporally inconsistent cloud input and other ancillary data (https://gewex-srb.larc.nasa.gov/common/php/SRB_known_issues.php) might affect the detection and interpretation of the long-term analysis in these satellite products (Raschke et al. 2006).

b. Uncertainty in ground observations

The discrepancies between GEBA and satellite datasets are also subject to measurement errors in the GEBA database. The data quality varies significantly across different archives, stations, and years, caused by using different instrumentation, calibration, and data processing strategies. It is known that the original GEBA data quality in this region is relatively low as a result of instrument replacement (Shi et al. 2008; Tang et al. 2010; Wang 2014). Therefore, readers should treat the magnitudes of the discrepancies with caution as they may not be accurate. We recommend future researchers conduct sufficient quality control before using this data.

Meanwhile, the unevenly distributed network undermines the accuracy of data fusion in the data-scarce areas. Another caveat is the relatively coarse temporal scale of GEBA. We aggregated the half-hourly and daily data in the validation datasets into monthly data for comparison. We advocate additional efforts to correct errors, provide long-term accurate ground observations, and conduct finer-scale (e.g., daily) evaluation.

c. Performance of the merging methods

We first applied the weighted ensemble averaging approaches and found that they improve the satellite datasets to a very limited extent. We present these results to the readers because it facilitates a comparison of multiple approaches and so that future researchers can learn from this unsuccessful experiment to avoid redundant efforts. For the three weighted ensemble averaging approaches, the most complicated method, BMA, has a relatively smaller bias and RMSE than the SA and INV methods in the training stations (Figs. 7a,b). When extrapolating the weights of satellite datasets to the validation stations, however, BMA is not able to further improve the error outcomes (Fig. 7c). Besides, the error patterns for SA are almost identical to those for INV, for example, in winter (DJF). The little difference between SA and INV suggests that, even without knowing the error structures in different datasets, ensemble averaging is a simple, yet effective way to reduce data uncertainty.

The weighted ensemble averaging approaches are less effective than the MTE approach in the untrained or ungauged domains. This is primarily because all the three products overestimate the observed Rsd, while the weight for each product is restricted between 0 and 1. Therefore, positive biases still exist after averaging these products with positive weights. Second, the three products are not independent because they are based on either the same satellite-derived cloud data (ISCCP clouds) or a similar radiative transfer algorithm (Ma and Pinker 2012). This is a violation of the assumption of independence in optimal ensemble averaging, which requires uncorrelated errors between different datasets (Lobell and Field 2008; Bishop and Abramowitz 2013).

On the other hand, the machine-learning MTE approach removes the widespread positive satellite biases (Fig. 4) from 8%–10% to 2% (Fig. 5). The MTE approach can adjust these overestimated satellite-derived values with regression coefficients to match the station observations. It has been shown to improve performance in situations of extrapolation (Jung et al. 2009). Therefore, it offers an advantage over regionalization of the weights in ungauged areas, where the error structures between satellite prediction and real values are usually unknown. We also found that MTE tends to constrain the satellite data to the mean of ground observations. Even though GEBA has some errors, the MTE prediction is much less sensitive to data gaps, sharp discontinuities, and random errors in GEBA.

Although the MTE method compares more favorably than the methods of individual trees, it is unclear how well this method performs if the trained data has systematic biases, or if there is a sample selection bias. As mentioned above, the ground stations are clustered in the highly populated, easily accessed region. The data collected from the underrepresented area such as high altitudes and latitudes are diluted by the large sample size from those areas. The model trained with a biased sample is closer to the sample world (Phillips et al. 2009) rather than the real world, where the complex terrain and a variety of climate conditions may not have been factored in. The choice of sample data is as important as the choice of machine-learning method (Phillips et al. 2009), and the choice of sample data is not just simply increasing sample size but also requires attention on how data are used (Perry and Dickson 2018). Future studies may further address this problem by discarding data collected in oversampled regions, generating synthetic data in underrepresented regions, or including more physically related predictor variables.

A second issue worth consideration is how well MTE can capture the temporal variations in ground observations. When training the model trees with the GEBA observations, we used all valid records (level 1) for the entire 23-yr period. If the relationships between GEBA and satellite Rsd are stationary, then the model tree application to the entire period may hold. However, it is unlikely that such relationships are independent of time given the temporally inconsistent ancillary data feeding into the satellite products. Thus, it is uncertain how well MTE trained on data from a certain time will predict in another period. We found that MTE does not show significant differences in representing long-term variations compared to the satellite products. In other words, our MTE approach may not be able to capture the temporal variations of GEBA, which are also subject to data uncertainty (see section 4b). Therefore, the trend analysis of MTE Rsd and the original ground and satellite datasets should be treated with caution. In addition, we used almost the same explanatory variables as the weighted ensemble averaging approaches to facilitate the evaluation of these approaches, so future work is needed to extend to other explanatory variables such as cloud and atmospheric input data. Nevertheless, we should note that the long-term temporal variation is of a relatively smaller magnitude (a 5 W m−2 decrease for 20 years), compared to the substantial systematic annual biases in the satellite datasets (~10 W m−2).

Another caveat of current MTE approach is the consistency of spatial pattern. Although MTE can largely constrain the prediction close to the mean values, it generates sharp discontinuities in some regions after adding the explanatory variables that have weaker relations with Rsd (e.g., cloud and precipitation). On the other hand, adding covariates that have strong controls on Rsd (e.g., solar angle and latitude) generates spatial patterns that have smooth gradients and therefore loses local details. We encourage future studies to explore various machine-learning algorithms and to identify the physical factors that reduce uncertainty in radiation data.

d. Impacts of radiation forcing uncertainty on land surface model simulations

Uncertainty in radiation forcing can propagate to the estimates of surface fluxes and hydrological variables, similar to the other climate forcings like temperature and precipitation (Liu et al. 2015; Douville 1998). Sensible heat shows positive responses to changes in Rsd across Asia and latent heat shows positive responses in most places (Figs. 10a,b,g,h). Runoff shows a strong negative response of runoff to Rsd between 20° and 50°N, especially in East Asia (Figs. 10d,j,11). Surface soil moisture and snow water equivalent show overall negative responses to changes in Rsd (Figs. 10e,f,k,l). We found that all variables exhibit lower sensitivities at the high latitudes in the wintertime. This is mainly because there is too little Rsd to drive hydrologic responses. This dampened wintertime sensitivity at the high latitudes is in line with previous studies focusing on snow (Lin et al. 2016; Xu and Dirmeyer 2011), suggesting that the hydrological sensitivity to changing input forcings follows the seasonal cycle of solar radiation.

The positive elasticity of sensible heat to Rsd is expected because decreased solar radiation directly reduces surface temperature and sensible heat. In fact, we found that sensible heat has large positive elasticity (median = 2–6), which exceeds the elasticity of latent heat by 2–3 times (Fig. 11), similar to the findings of Oliveira et al. (2011). Such high elasticity might be caused by several factors. First, the available energy induced by solar radiation is partitioned between sensible heat and latent heat. When latent heat is limited by the water supply, the relative change of latent heat is smaller than the relative change of radiation, and the remaining solar radiation will be partitioned to sensible heat. Second, in this offline sensitivity analysis, air temperature has not been adjusted along with the change in radiation forcing, which may induce physical inconsistency and generate unrealistic sensible heat (Oliveira et al. 2011). Third, the larger elasticity magnitude and spread in the cold season (Fig. 11) are primarily due to a small change in radiation accompanied with a relatively large change in sensible heat. Lower solar radiation during the freezing season may maintain a larger snow cover extent in the early warm season. This lagged effect produces higher albedo and results in stronger upward shortwave radiation, which modifies net radiation and amplifies the influence of radiation forcing change on available energy.

The relative changes in latent heat, runoff, and snow water equivalent are smaller than the relative change in radiation forcing. Apparently, latent heat is not only limited by incoming energy, but also constrained by water availability (precipitation, soil moisture, vapor deficit) and vegetation growth. Therefore, latent heat is less sensitive to radiation changes compared to sensible heat in water-limited regions. The runoff response to radiation is mainly contributed by subsurface runoff, which is reasonable because surface runoff is arguably more directly controlled by precipitation while subsurface runoff can be more directly related to slower processes like ET (Zheng et al. 2019).

We found that the response of latent heat and runoff vary by latitude and climate (Fig. 10) and we tried to understand the underlying mechanisms. As for low latitudes (<30°N) in East Asia and Southeast Asia, cooler temperature induced by lower solar radiation loads may result in decreased ET (positive ϵLE,Rsd), leading to increased soil moisture and runoff (negative ϵSM,Rsd and ϵQ,Rsd, Rsd↓ → Ts↓ → ET↓ → SM, Q↑). In hot subtropical/tropical regions such as India, lower radiation may lead to less stomatal stress and enhance transpiration and latent heat (negative ϵLE,Rsd in Figs. 10b,h). For arid regions, such as the Middle East, latent heat is much less sensitive to radiation forcing than sensible heat due to limited water availability.

In high latitudes (>60°N), lower radiation may reduce snowmelt and increase snow water equivalent (negative ϵSWE,Rsd), and hence less soil moisture and runoff (positive ϵSM,Rsd and ϵQ,Rsd, Rsd↓ → Ts↓ → SWE↑ → SM, Q↓). On the other hand, no increase of SWE was found in midlatitudes (30°–60°N), and more water becomes available for soil moisture and runoff, and hence more ET (Rsd↓ → SM, Q↑ → ET↑). The low elasticity during November in high latitudes (Figs. 10g–l) is because winter shortwave radiation is close to zero, as discussed earlier.

We also noticed that the peaks of snow water equivalent elasticity are ahead of the peaks of runoff elasticity in Central and East Asia (Figs. 11b,c). Snow cover changes can trigger other hydrological processes but tend to have a lagged effect (Xu and Dirmeyer 2011, 2013). For example, snowmelt can moisten shallow and deep soil, and generate subsurface runoff that contributes to the total runoff at a slower rate compared to surface runoff. In addition, snow in East and Central Asia may have impacts on runoff in large basins lying in other subregions, such as Southeast Asia, South Asia, and the Middle East. Future studies can account for such a cross-region effect by extending the elasticity analysis from grid scale to basin scale.

Overall, it is interesting to observe that the simulated hydrological responses to changing radiation forcing are not monotonic linear responses, but rather a result of the complex interaction among ET, snowpack, and soil moisture which depend on the climate and location (Oliveira et al. 2011). These complex temporal interplays are similarly discussed in a recent study focusing on hydrological simulation sensitivity to multiple physical parameterizations (Zheng et al. 2019). They imply that the memory terms of hydrological cycle can propagate the simulated runoff response to different seasons. Hence, the importance of accurate Rsd input data is highlighted as they can have prolonged influences on hydrological simulations. However, running an offline LSM has the disadvantage of ignoring the interaction between incoming radiation and the other forcings such as air and surface temperature. In reality, a reduction in the incoming solar radiation will also be accompanied by changes in other meteorological variables. The goal of our sensitivity experiments is to examine how much of the LSM outputs error is caused by given amount of solar radiation error, instead of the response of LSM to the change of input. The latter requires running a coupled land–atmosphere simulation to assess the relationship between the amount of solar radiation and land surface processes.

5. Conclusions

The uncertainty of radiation forcing derived from satellite data is large and has direct consequences on the model estimates of surface energy and water balances. We found spatially systematic positive biases in the satellite datasets (with a median 8%–10%), which are on average (~10 W m−2) larger than the effect of long-term change over the entire 23-yr period (~5 W m−2). The model tree ensemble algorithm combines ground observations and satellite data and effectively reduces the positive biases in satellite products over ungauged areas. The commonly used ensemble averaging methods do not show improved performance, mainly because of the universal positive biases in satellite-derived products due to the similar input data and algorithms. The sensitivity analysis in the Noah-MP model shows that sensible heat is extremely sensitive to the biases in the radiation forcing data, and that latent heat is sensitive only when there is sufficient water supply. The simulated hydrological responses to changing radiation forcing are not monotonic linear responses, but a result of the interactions among ET, snowpack, and soil moisture. More efforts are needed to correct the biases and spurious changes by updating the algorithm and merging more ground observations. The improved forcing data could substantially enhance ET estimation, hydrological prediction, and long-term assessment of ecosystem productivity.

Acknowledgments

This research was sponsored by NASA under Grant NNX14AB36A. The Institute for Climate and Atmospheric Sciences at ETH Zurich provides the Global Energy Balance Archive records (https://geba.ethz.ch/data-retrieval/data-formats.html). The following institutions and projects provide free access to the satellite datasets: the NASA Goddard Institute for Space Studies (https://isccp.giss.nasa.gov/), the NASA Langley Research Center Atmospheric Sciences Data Center (https://eosweb.larc.nasa.gov/project/srb/srb_table), Rachel Pinker from the University of Maryland. The FLUXNET community processes and provides the FLUXNET2015 dataset (https://fluxnet.fluxdata.org/data/fluxnet2015-dataset/). We especially thank Dr. Wenjun Tang from the National Tibetan Plateau Data Center in China for providing the quality-controlled CMA radiation measurements. We thank Xiaogang He at National University of Singapore for his help on interpolation schemes. We thank Christopher Monroe and Philip Lu for proofreading. Finally, we deeply thank the three anonymous reviewers for their constructive criticisms that improved the work substantially.

Data availability statement

The data generated in our study are in this public repository: https://doi.org/10.6084/m9.figshare.11845557.v1.

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