6. A framework for comparative evaluation of TPR and gauge errors
6.6. Conditional stochastic simulation for error determination over entire TPR obser-
6.8.2. Comparison of Error Components
The sampling and retrieval error components are comparable for the observed gauge time-series. Observed sampling error (medianσerror = 1.1 mm hr-1) exceeds values reported in the literature
(e.g. <0.8 mm hr-1Nesbitt and Anders, 2009). However, sampling error is assessed for the TPR native resolution against ground-based observations at the point-scale, whereas previous studies assessed the sampling error at larger spatial scales (Fisher, 2007; Nesbitt and Anders, 2009; Iida et al., 2010; Indu and Nagesh Kumar, 2014), against other remote sensing products, e.g. TRMM 3B42 (Nesbitt and Anders, 2009), or against the TPR itself using a bootstrap method (Iida et al., 2010; Indu and Nagesh Kumar, 2014). In this study, the sampling error statistics are also found to reduce notably when simulated over the entire TRMM period, whereas the retrieval error statistics show an increase. While the reduction in sampling error is expected, the magnitude of reduction as well as the increase in retrieval error are likely to be affected by limitations of the stochastic generator as discussed previously. Compared to the retrieval error, which is
evaluated against gauge observations, the algorithm error, which is based only on the 2A25 algorithm estimates, is approximately one order of magnitude smaller, both for the observed gauge periods and the simulations. On the one hand, this suggests the 2A25 algorithm may be markedly under-estimating the true error associated with TPR near-surface rainfall estimates, in particular due to its limitations in accurately classifying rainfall type (Duan et al., 2015; Kirstetter et al., 2014) and appropriately converting reflectivity to rainfall rate as a result of the rainfall type classification (Rasmussen et al., 2013). On the other hand, evaluation of the gauge errors shows that gauge measurements are affected by considerable spatial, temporal and local random errors. Major contributions to the TPR retrieval error may therefore stem from comparison of the instantaneous rainfall rate averaged over a 5 km grid as observed by the TPR with point-based, 10-min accumulations of rainfall reported by the gauges. In fact, superposition of the (theoretically independent) spatial gauge error (point-area difference) and the temporal accumulation error exceeds the TPR retrieval error.
However, both the point-area difference and the temporal accumulation error are computed for only a subset of the available gauges and these results may therefore not be accurate quan- tifications of these error components for the entire gauge dataset. In addition, the gauge density in this study was much lower compared to that by Ciach and Krajewski (1999) (72.9 km2 per gauge compared to 28.8 km2). Hence, the same assumption, i.e. that the small-scale rainfall
correlation structure is dominated by the immediate correlation jump (i.e. the nugget term), is adopted in this study too. This is supported by the explorative analysis into the correlation- distance relationship (fig. 6.2). However, an accurate quantification of the difference between point-scale rainfall observations and 5 km spatial mean rainfall rates would require a much higher gauge density. The temporal accumulation error calculations are also affected by the short duration (maximum 1.5 years) of the available 1-min observations, which may not capture the full rainfall distribution and the relationship between 1-min and 10-min rainfall statistics. Lastly, the local random gauge errors are determined for the entire set of 78 10-min gauges but are based on parameter estimates from the empirical results obtained by Ciach (2003) in a different hydro-climatic setting. Of course, the differing rainfall regimes and dynamics in tropical mountain environments compared to mid-latitude sites limit parameter transferability, but comparable implementations in a tropical mountain rainfall regime that would allow for validation of parameter values have not been reported in the literature.
6.9. Conclusions
The satellite-gauge error and its contributing components are assessed for the TPR using a high-frequency rain gauge dataset distributed across the northern tropical Andes. The analysis of satellite-gauge error components reveals major error contributions from both satellite and gauge error sources. While satellite errors are in excess of gauge errors, the latter are substantial and should not be discounted in a high-resolution satellite-gauge evaluation. However, quantifi-
cations of both satellite and gauge errors are subject to some uncertainty due to limitations in the spatial and temporal resolutions of the available gauge datasets. The estimates of satellite sampling and retrieval errors need to be considered with caution and should be used as qualita- tive indicators as opposed to accurate quantifications. In addition, while satellite errors reported in this study are in excess of those reported in the literature, previous studies have focused on larger spatial scales. Due to limited gauge observations, conditional stochastic simulations were performed to estimate the distribution of 10-min rainfall across the entire TRMM observational period. These confirm the expected decrease in sampling error over the entire TRMM period, but also estimate an increase in the satellite retrieval error. However, this may be attributed to the limited predictive ability of the stochastic simulations and should therefore be considered with caution. Furthermore, it should be noted that the first and second statistical moment only give an accurate description of the satellite-gauge error, if it is, in fact, normally distributed. Ultimately, a better understanding of the individual gauge and satellite (TPR) error compo- nents requires higher density gauge networks within regions of homogeneous tropical rainfall regimes (i.e. high Andes, lowland Amazon, coastal regions). This is a prerequisite for obtaining robust statistical models to estimate satellite error components, especially the sampling error, in ungauged locations, on the basis of readily available TPR variables (statistical moments, sampling frequency, occurrence frequency, algorithm error estimate, etc.). Power-law models to describe this relationship, such as those proposed by Steiner et al. (2003); Gebremichael et al. (2006), do not yield robust fits based on the current TPR sampling error estimates for the tropical Andes (results not shown).