Characterization of precipitation product errors across the United States using multiplicative triple collocation

Abstract

Abstract. Validation of precipitation estimates from various products is a challenging problem, since the true precipitation is unknown. However, with the increased availability of precipitation estimates from a wide range of instruments (satellite, ground-based radar, and gauge), it is now possible to apply the triple collocation (TC) technique to characterize the uncertainties in each of the products. Classical TC takes advantage of three collocated data products of the same variable and estimates the mean squared error of each, without requiring knowledge of the truth. In this study, triplets among NEXRAD-IV, TRMM 3B42RT, GPCP 1DD, and GPI products are used to quantify the associated spatial error characteristics across a central part of the continental US. Data are aggregated to biweekly accumulations from January 2002 through April 2014 across a 2° × 2° spatial grid. This is the first study of its kind to explore precipitation estimation errors using TC across the US. A multiplicative (logarithmic) error model is incorporated in the original TC formulation to relate the precipitation estimates to the unknown truth. For precipitation application, this is more realistic than the additive error model used in the original TC derivations, which is generally appropriate for existing applications such as in the case of wind vector components and soil moisture comparisons. This study provides error estimates of the precipitation products that can be incorporated into hydrological and meteorological models, especially those used in data assimilation. Physical interpretations of the error fields (related to topography, climate, etc.) are explored. The methodology presented in this study could be used to quantify the uncertainties associated with precipitation estimates from each of the constellations of GPM satellites. Such quantification is prerequisite to optimally merging these estimates.

Water, Energy, and Carbon with Artificial Neural Networks (WECANN): a statistically based estimate of global surface turbulent fluxes and gross primary productivity using solar-induced fluorescence

“…TC is a method to estimate the RMSE (and, if desired, correlation coefficients) of three spatially and temporally collocated measurements by assuming a linear error model between the measurements (McColl et al, 2014;Stoffelen, 1998). This methodology has been widely used in error estimation of land and ocean parameters, such as wind speed, sea surface temperature, soil moisture, evaporation, precipitation, f APAR, and in the rescaling of measurement systems to reference system for data assimilation purposes (Alemohammad et al, 2015;D'Odorico et al, 2014;Gruber et al, 2016;Hain et al, 2011;Lei et al, 2015;Miralles et al, 2010Miralles et al, , 2011bParinussa et al, 2011), as well as in validating categorical variables such as the soil freeze-thaw state (McColl et al, 2016). The relationship between each measurement and the true value is assumed to follow a linear model:…”

An assessment of the performance of global rainfall estimates without ground-based observations

“…Based on this assumption, Alemohammad et al (2015) proposed the application of TC to the rainfall by introducing a multiplicative error model:…”

“…(2)- (6), can be applied to the -potentially more relevant -case of multiplicative rainfall accumulation errors. The resulting log RMSE can then be back-transformed into linear rainfall accumulation errors by exploiting a Taylor series expansion of the logarithm operator (see Alemohammad et al, 2015 for further details).…”

“…An alternative approach for assessing the quality of satellite rainfall products was proposed by Roebeling et al (2012) and Alemohammad et al (2015) based on the triple collocation (TC) method (Stoffelen, 1998). The first applications of TC concerned geophysical variables such as ocean wind speed and wave height (Stoffelen, 1998).…”

“…Alemohammad et al (2015) applied TC to 14-day cumulated rainfall estimates derived from satellite, gauges, radars and models in order to retrieve the error and the correlation of each data set in the United States. They also proposed the use of a logarithmic (i.e.…”