# Uncertainty in Satellite-Derived Surface Irradiances and Challenges in Producing Surface Radiation Budget Climate Data Record

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## Abstract

**:**

^{−2}, 6.7 Wm

^{−2}, and 9.7 Wm

^{−2}. In addition, the uncertainty in surface downward irradiance monthly anomalies and their trends are estimated based on the difference derived from EBAF surface irradiances and observations. The uncertainty in the decadal trend suggests that when differences of decadal global mean downward shortwave and longwave irradiances are, respectively, greater than 0.45 Wm

^{−2}and 0.52 Wm

^{−2}, the difference is larger than 1σ uncertainties. However, surface irradiance observation sites are located predominately over tropical oceans and the northern hemisphere mid-latitude. As a consequence, the effect of a discontinuity introduced by using multiple geostationary satellites in deriving cloud properties is likely to be excluded from these trend and decadal change uncertainty estimates. Nevertheless, the monthly anomaly timeseries of radiative cooling in the atmosphere (multiplied by −1) agrees reasonably well with the anomaly time series of diabatic heating derived from global mean precipitation and sensible heat flux with a correlation coefficient of 0.46.

## 1. Introduction

## 2. Uncertainty Estimate

#### 2.1. Uncertainty in the Net Surface and Atmospheric Irradiances

^{−2}for shortwave and 2 Wm

^{−2}for longwave when monthly mean irradiances are averaged over 46 ocean and 36 land sites [6] (uncertainties shown under global annual in Table 1). These are within the reported uncertainty of observed surface irradiances of ~5 Wm

^{−2}[11,12,13,14,15,16]. However, the world infrared standard group calibration that is used to calibrate BSRN pyrgeometers is biased low up to 5 Wm

^{−2}depending on column water vapor amount (i.e., revising the calibration increases longwave irradiances up to 5 Wm

^{−2}) [16]. Although the correction of archived longwave irradiance is not straightforward, the work is in progress [16].

_{net}is the correlation coefficient between net shortwave and net longwave irradiance adjustments. Resulting uncertainties are listed in Table 1. The regional uncertainty of monthly surface net shortwave and longwave irradiances are, respectively, 5 Wm

^{−2}and 13 Wm

^{−2}over ocean and 20 Wm

^{−2}and 21 Wm

^{−2}over land. These uncertainties combined with correlation coefficients between shortwave and longwave net irradiance adjustments lead to the uncertainty of monthly mean regional net total surface irradiance of 13 Wm

^{−2}over ocean and 30 Wm

^{−2}over land. When global annual mean irradiances combined with correlation coefficients are used in a similar way, the uncertainty in the annual global net total irradiance is 10 Wm

^{−2}(Table 1).

^{−2}. The irradiance conversion error is 1 Wm

^{−2}[3] and instrument calibration uncertainty is 1% (1σ) or 1 Wm

^{−2}. When these uncertainties are used, the uncertainty in regional TOA shortwave irradiance is approximately 2.5 Wm

^{−2}[2]. Similar to the shortwave, the uncertainty in regional TOA longwave irradiance is also 2.5 Wm

^{−2}. If shortwave and longwave errors are independent and the uncertainty in insolation is ignored, the uncertainty in the regional net TOA irradiance is 3.5 Wm

^{−2}.

^{2}+ 3.5

^{2})

^{1/2}= 13.5 Wm

^{−2}. While this gives mean uncertainty in regional monthly net atmospheric irradiance, uncertainty in the surface and TOA irradiance highly depends on region. Because most buoys and land sites used for validation of EBAF-surface irradiances are, respectively, in the tropics and mid-latitudes (Figure 1), the uncertainty over ocean likely represents tropical ocean and the uncertainty over land likely represents midlatitude land.

#### 2.2. Uncertainty in Surface Irradiance Trend and in Observing Decadal Surface Irradiance Change

_{g}. The second through fourth steps are, therefore,

_{i}, ${\sigma}_{x}\left({y}_{j}\right)=\sqrt{\frac{1}{{n}_{j}}{\displaystyle \sum}_{i=1}^{{n}_{j}}{\left[\Delta {F}_{x}\left({t}_{i},{y}_{j}\right)\right]}^{2}}$ and $\widehat{\sigma}=\sqrt{\frac{1}{n}{\displaystyle \sum}_{i=1}^{n}{\left[\Delta {\widehat{F}}_{x}\left({t}_{i}\right)\right]}^{2}}$. The anomaly time series from the EBAF-surface product is also derived in the same way by matching geolocations and time periods of surface observations.

_{i},

_{x,anom}is the monthly anomaly of irradiance x, t is the number of months counted from the beginning of the time series, ${\widehat{F}}_{x,amon}\left({t}_{i}\right)={a}_{x,y}+{b}_{x,y}{t}_{i}$ and a is the intercept of the linear regression line and subscript y is either EBAF or obs. Slopes derived from EBAF and observed surface deseasonalized anomalies as well as 95% confidence interval (2σ) of the slopes are shown in Table 2. In Equation (5), in addition to the difference of slopes estimated from EBAF and observations (first term on the right side of Equation (5)), the measure of goodness of fit to EBAF (second term on the right side of Equation (5)) and observed (third term on the right side of Equation (5)) anomalies defined by Equation (6) are added based on the confidence interval. Equation (6) states that if the record length n is sufficiently long (e.g., 20 years or longer), then the uncertainty of the slope of the linear regression is proportional to the standard deviation of irradiance deseasonalized anomalies and inversely proportional to ${\left(\frac{{n}^{3}}{12}+\frac{{n}^{2}}{4}+\frac{n}{6}\right)}^{1/2}\approx \frac{{n}^{3/2}}{\sqrt{12}}.$ Therefore, the second and third terms on the right side of Equation (5) become small compared to the first term as the time series gets longer.

^{−2}per decade. If we assume that the uncertainties in anomalies for both decades are the same and the error in the first decade is not correlated with the error in the second decade, the uncertainty (1σ) in detecting the change with two decadal mean irradiances is $\sqrt{2}$ times the uncertainty of the slope, i.e., $U\left(\Delta {\overline{F}}_{x,EBAF}\right)=\sqrt{2}U\left({b}_{x,EBAF}\right)$. Therefore, if differences of decadal global mean downward shortwave and longwave irradiances are, respectively, greater than 0.45 Wm

^{−2}and 0.52 Wm

^{−2}, then the difference is significant.

## 3. Impact of New Generation Geostationary Satellites on Compute Surface Irradiances

## 4. Consistency Check Using Energy Balance

^{−2}, 0.16 Wm

^{−2}, and 0.51 Wm

^{−2}. The net annual energy input to the atmosphere is very close to 0 when fluxes are averaged over the entire globe. The balance is achieved by diabatic heating by precipitation, sensible heat flux at the surface, and radiative cooling. However, when satellite derived data products are used, the residual of the atmospheric energy balance averaged over 10 years (from July 2005 through June 2015) is −14 Wm

^{−2}, where the means of net atmospheric irradiance, diabatic heating by precipitation, and sensible heat flux are, respectively, −109 Wm

^{−2}, 78 Wm

^{−2}, and 17 Wm

^{−2}. Even though the global annual mean atmospheric energy budget derived from these products has the residual, the anomaly time series derived from GPCP+ERA5 and EBAF data products are reasonably consistent with a correlation coefficient of 0.46. Given that precipitation and radiation are derived independently from different instruments, this agreement is encouraging. As longer time series become available and more energy flux components are observed by many different instruments, the energy balance can be a useful tool to assess the quality of data products or derive missing flux components.

## 5. Discussion and Conclusions

^{−2}, which balances by a 1.7% to 2% precipitation change [28]. Although recent CERES observations indicate that the TOA net irradiance is increasing with time, if we assume that the TOA net irradiance does not change, net surface irradiance needs to decrease 2 Wm

^{−2}per 1 K surface temperature increase. A study by Ramaswamy et al. [29] indicates that global mean net surface irradiance change is predominately due to the net longwave irradiance change. For the surface temperature of 290 K, the upward longwave irradiance increases by 5.5 Wm

^{−2}, which suggests that the downward longwave irradiance increases by 3.5 Wm

^{−2}per 1 K increase of surface temperature. The surface temperature increases with a rate of 0.2 K per decade under the Representative Concentration Pathway (RCP) 6.0 scenario [30], which gives a rate of increase of 0.7 Wm

^{−2}global mean downward longwave irradiance per decade. The uncertainty in estimating decadal change of downward longwave irradiance derived in Section 2.2 is smaller than the predicted decadal change of global mean downward longwave irradiance change. We must, however, mitigate the discontinuity caused by changing instruments.

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## Appendix A

**Figure A1.**Temporal correlation coefficients of (

**top left**) shortwave downward and upward irradiance perturbations, (

**top right**) longwave downward and upward irradiance perturbations, and (

**bottom left**) shortwave and longwave net perturbations in 1° × 1° grids. Sixteen years of data from March 2000 through February 2016 are used.

## Appendix B

**Figure A2.**Histogram of (

**top**row) correlation coefficients, (

**middle**row) root-mean-square (RMS) differences, and (

**bottom**row) slope differences derived from ground-based observations and EBAF at individual sites for downward shortwave irradiance anomalies.

**Figure A3.**Same as Figure A2 but for downward longwave irradiance anomalies.

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**Figure 1.**Geolocations of 43 buoys (blue diamond) and 30 land-surface sites (white diamond) where downward irradiances used in validation were taken (after Rutan et al. [5]).

**Figure 2.**(

**a**) Deseasonalized monthly surface downward shortwave anomalies computed with observed irradiances shown at 43 buoys and 30 land sites. Black and red lines are observed and energy balanced and filled (EBAF)-computed irradiance anomalies. Linear regression lines are also shown with the same color. A 95% confidence interval of the observed trend is shown by shade. “Corr” and “Reg(ional)” indicate correlation coefficient and standard deviation. The slope of the linear regression line shown on bottom right is Wm

^{−2}decade

^{−1}. (

**b**,

**c**) plots show anomaly time series for, respectively, 43 buoys and 30 land sites separately.

**Figure 4.**Regional anomalies of longwave surface downward irradiance in Wm

^{−2}for July 2018. Anomalies are computed as the difference between July 2018 regional downward longwave irradiance minus regional July downward longwave irradiance climatology (average from July 2005 through June 2015). Himawar-8 covers 60°N–60°S 90°E–180°E and GOES-16 covers 60°N–60°S 35°W–105°W.

**Figure 5.**Global monthly deseasonalized anomaly time series of surface downward (

**top**) shortwave and (

**bottom**) longwave irradiances. Two numbers shown at the top of each plot are the standard deviation of anomalies (σ) and slope regression line (dashed line).

**Figure 6.**Deseasonalized anomaly time series of surface downward (

**a**) longwave and (

**b**) shortwave irradiances from buoys and a land site within the region covered by Himawari-8. Included surface sites are, in the Pacific Ocean 8-TAO buoys, in the Indian Ocean 5-RAMA buoys, in the N Pacific the Kuroshio Current Buoy (KEO) and a ground site at Alice Springs, AU. Anomalies at individual sites are normalized by the standard deviation (see text for the detail). Black and red lines are observed and EBAF irradiance anomalies. Linear regression lines are also shown with the same color. A 95% confidence interval of the observed trend is shown by shade. Himawari-8 replaced MTSAT2 on 6 July 2015.

**Figure 7.**Global monthly deseasonalized anomaly time series of (blue) the sum of diabatic heating due to precipitation and sensible heat flux and (red) −1 time radiative cooling in the atmosphere. Anomalies are averaged with a 12-month moving window.

**Table 1.**Uncertainty in regional (1° × 1°) monthly and global annual downward, upward, and net shortwave, longwave, and total surface irradiances.

Mean Irradiance Downward [Upward] (Wm ^{−2}) | Uncertainty | Correlation Coefficient | Net Irradiance Uncertainty (Wm^{−2}) | ||
---|---|---|---|---|---|

Downward (Wm^{−2}) | Upward (Wm^{−2}) | ||||

Regional monthly | |||||

Ocean | |||||

Shortwave (SW) | 191 (12) | 11 | 11 | 0.88 | 5.4 |

Longwave (LW) | 364 (402) | 5 | 13 | 0.20 | 13.0 |

SW + LW (Total) | 555 (414) | −0.21 | 13.0 | ||

Land | |||||

Shortwave (SW) | 195 (53) | 12 | 12 | −0.36 | 19.8 |

Longwave (LW) | 333 (394) | 10 | 19 | 0.06 | 20.9 |

SW + LW (Total) | 528 (447) | 0.07 | 29.8 | ||

Global annual | |||||

Shortwave (SW) | 187 (23) | 4 | 3 | −0.29 | 5.7 |

Longwave (LW) | 345 (398) | 5 | 3 | −0.36 | 6.7 |

SW + LW (Total) | 532 (421) | 0.26 | 9.8 |

**Table 2.**Surface downward shortwave and longwave anomaly root-mean-square (RMS) differences, trends and their 95% confidence intervals.

Downward Irradiances | Standard Deviation of Anomalies ^{1} (Wm^{−2}) | RMS Difference (Wm^{−2}) | Correlation Coefficient | Observation | EBAF | ||||
---|---|---|---|---|---|---|---|---|---|

Trend (Wm ^{−2} decade^{−1}) | Upper (Wm ^{−2} decade^{−1}) | Lower (Wm ^{−2} decade^{−1}) | Trend (Wm ^{−2} decade^{−1}) | Upper (Wm ^{−2} decade^{−1}) | Lower (Wm ^{−2} decade^{−1}) | ||||

Land + ocean | |||||||||

Longwave | 1.015 | 0.478 | 0.889 | 0.66 | 0.89 | 0.44 | 0.33 | 0.57 | 0.09 |

Shortwave | 0.773 | 0.464 | 0.820 | −0.19 | −0.00 | −0.37 | 0.10 | 0.28 | −0.09 |

Ocean | |||||||||

Longwave | 0.996 | 0.590 | 0.825 | 0.10 | 0.34 | −0.14 | 0.06 | 0.30 | −0.18 |

Shortwave | 0.991 | 0.668 | 0.773 | −0.50 | −0.28 | −0.73 | 0.04 | 0.28 | −0.19 |

Land | |||||||||

Longwave | 1.572 | 0.801 | 0.870 | 1.14 | 1.48 | 0.79 | 0.59 | 0.95 | 0.22 |

Shortwave | 1.333 | 0.655 | 0.879 | 0.35 | 0.67 | 0.04 | 0.20 | 0.52 | −0.12 |

^{1}σ

_{g}in Equation (4).

Downward Irradiances | ${\mathit{b}}_{\mathit{x},\mathit{E}\mathit{B}\mathit{A}\mathit{F}}-{\mathit{b}}_{\mathit{x},\mathit{o}\mathit{b}\mathit{s}}$ | ${\mathit{\sigma}}_{\mathit{x},\mathit{E}\mathit{B}\mathit{A}\mathit{F}}$ | ${\mathit{\sigma}}_{\mathit{x},\mathit{o}\mathit{b}\mathit{s}}$ | $\mathit{U}\left({\mathit{b}}_{\mathit{x},\mathit{E}\mathit{B}\mathit{A}\mathit{F}}\right)={\left[{({\mathit{b}}_{\mathit{x},\mathit{E}\mathit{B}\mathit{A}\mathit{F}}-{\mathit{b}}_{\mathit{x},\mathit{o}\mathit{b}\mathit{s}})}^{\mathbf{2}}+{\mathit{\sigma}}_{{\mathit{b}}_{\mathit{x},\mathit{E}\mathit{B}\mathit{A}\mathit{F}}}^{\mathbf{2}}+{\mathit{\sigma}}_{{\mathit{b}}_{\mathit{x},\mathit{o}\mathit{b}\mathit{s}}}^{\mathbf{2}}\right]}^{\mathbf{1}/\mathbf{2}}$ | $\sqrt{\mathbf{2}}\mathit{U}\left({\mathit{b}}_{\mathit{x},\mathit{E}\mathit{B}\mathit{A}\mathit{F}}\right)$ |
---|---|---|---|---|---|

Land + ocean | |||||

Longwave | −0.33 | 0.12 | 0.11 | 0.37 | 0.52 |

Shortwave | 0.29 | 0.09 | 0.09 | 0.32 | 0.45 |

Ocean | |||||

Longwave | −0.03 | 0.12 | 0.12 | 0.17 | 0.24 |

Shortwave | −0.55 | 0.12 | 0.11 | 0.57 | 0.81 |

Land | |||||

Longwave | −0.55 | 0.18 | 0.17 | 0.60 | 0.85 |

Shortwave | −0.15 | 0.16 | 0.16 | 0.27 | 0.38 |

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## Share and Cite

**MDPI and ACS Style**

Kato, S.; Rutan, D.A.; Rose, F.G.; Caldwell, T.E.; Ham, S.-H.; Radkevich, A.; Thorsen, T.J.; Viudez-Mora, A.; Fillmore, D.; Huang, X.
Uncertainty in Satellite-Derived Surface Irradiances and Challenges in Producing Surface Radiation Budget Climate Data Record. *Remote Sens.* **2020**, *12*, 1950.
https://doi.org/10.3390/rs12121950

**AMA Style**

Kato S, Rutan DA, Rose FG, Caldwell TE, Ham S-H, Radkevich A, Thorsen TJ, Viudez-Mora A, Fillmore D, Huang X.
Uncertainty in Satellite-Derived Surface Irradiances and Challenges in Producing Surface Radiation Budget Climate Data Record. *Remote Sensing*. 2020; 12(12):1950.
https://doi.org/10.3390/rs12121950

**Chicago/Turabian Style**

Kato, Seiji, David A. Rutan, Fred G. Rose, Thomas E. Caldwell, Seung-Hee Ham, Alexander Radkevich, Tyler J. Thorsen, Antonio Viudez-Mora, David Fillmore, and Xianglei Huang.
2020. "Uncertainty in Satellite-Derived Surface Irradiances and Challenges in Producing Surface Radiation Budget Climate Data Record" *Remote Sensing* 12, no. 12: 1950.
https://doi.org/10.3390/rs12121950