Abstract. 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 (V0) 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 V0 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 V0 determined by
the GP mean function and the equivalent AERONET AODs were consistently better
than those calculated using V0 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
V0 values suggests the GP solution is a robust technique for accurate
analysis of complex time series and may be applicable to other fields.