Improving the mean and uncertainty of ultraviolet multi-filter rotating shadowband radiometer in situ calibration factors: utilizing Gaussian process regression with a new method to estimate dynamic input uncertainty

To recover the actual responsivity for the Ultraviolet Multi-Filter Rotating Shadowband Radiometer (UV-MFRSR), the complex (e.g., unstable, noisy, and with gaps) time series of its in situ calibration factors (V-0) need to be smoothed. Many smoothing techniques require accurate input uncertainty of the time series. A new method is proposed to estimate the dynamic input uncertainty by examining overall variation and subgroup means within a moving time window. Using this calculated dynamic input uncertainty within Gaussian process (GP) regression provides the mean and uncertainty functions of the time series. This proposed GP solution was first applied to a synthetic signal and showed significantly smaller RMSEs than a Gaussian process regression performed with constant values of input uncertainty and the mean function. GP was then applied to three UV-MFRSR V-0 time series at three ground sites. The method appropriately accounted for variation in slopes, noises, and gaps at all sites. The validation results at the three test sites (i.e., HI02 at Mauna Loa, Hawaii; IL02 at Bondville, Illinois; and OK02 at Billings, Oklahoma) demonstrated that the agreement among aerosol optical depths (AODs) at the 368 nm channel calculated using V-0 determined by the GP mean function and the equivalent AERONET AODs were consistently better than those calculated using V-0 from standard techniques (e.g., moving average). For example, the average AOD biases of the GP method (0.0036 and 0.0032) are much lower than those of the moving average method (0.0119 and 0.0119) at IL02 and OK02, respectively. The GP method's absolute differences between UV-MFRSR and AERONET AOD values are approximately 4.5%, 21.6%, and 16.0% lower than those of the moving average method at HI02, IL02, and OK02, respectively. The improved accuracy of in situ UVMRP V-0 values suggests the GP solution is a robust technique for accurate analysis of complex time series and may be applicable to other fields.